Answer:
The volume of cube is increasing at a rate 7.5 cubic meter per hour.
Step-by-step explanation:
We are given the following in the question:
Surface area of cube = 24 square meters.
Let l be the edge of cube.
Surface area of cube =
[tex]6l^2 = 24\\l^2 = 4\\l = 2[/tex]
Thus, at that instant the edge of cube is 2 meters.
[tex]\dfrac{dS}{dt} = 15\text{ square meters per hour}\\\\\dfrac{d(6l^2)}{dt} = 15\\\\12l\dfrac{dl}{dt} = 15\\\\\dfrac{dl}{dt} = \dfrac{15}{12\times 2} = \dfrac{15}{24}[/tex]
We have to find the rate of change in volume.
Volume of cube =
[tex]l^3[/tex]
Rate of change of volume =
[tex]\dfrac{dV}{dt} = \dfrac{d(l^3)}{dt} = 3l^2\dfrac{dl}{dt}\\\\\dfrac{dV}{dt} = 3(2)^2\times \dfrac{15}{24} \\\\\dfrac{dV}{dt} = 7.5\text{ cubic meter per hour}[/tex]
Thus, the volume of cube is increasing at a rate 7.5 cubic meter per hour.
The rate of change of the volume of the cube at the given instant is; dV/dt = 7.5 m³/h
Surface area is increasing at a rate of 15 m²/h
Thus, dS/dt = 15 m²/h
Now, at a certain instant the surface area of the cube is 24 m².
Formula for cube surface area is; S = 6l²
Thus;
6l² = 24
l² = 24/6
l² = 4
l = √4
l = 2 m
From S = 6l², differentiating both sides with respect to t gives;
dS/dt = 12l(dl/dt)
We know that dS/dt = 15
Thus;
12l(dl/dt) = 15
dl/dt = 15/(12l)
putting 2 for l gives;
dl/dt = 15/(12 * 2)
dl/dt = 0.625 m/h
Now formula for volume of a cube is; V = l³
Differentiating both sides with respect to t gives;
dV/dt = 3l²(dl/dt)
plugging in then relevant values gives;
dV/dt = 3 × 2² × (0.625)
dV/dt = 7.5 m³/h
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Scientific research on popular beverages consisted of 70 studies that were fully sponsored by the food industry, and 30 studies that were conducted with no corporate ties. Of those that were fully sponsored by the food industry, 15 % of the participants found the products unfavorable, 23 % were neutral, and 62 % found the products favorable. Of those that had no industry funding, 38 % found the products unfavorable, 16 % were neutral, and 46 % found the products favorable.a. What is the probability that a participant selected at random found the products favorable?
b. If a randomly selected participant found the product favorable, what is the probability that the study was sponsored by the food industry?
c. If a randomly selected participant found the product unfavorable, what is the probability that the study had no industry funding?
Answer:
a. 0.26
b. 0.7
c. 0.38
Step-by-step explanation:
For a)
For sponsored studies: 62 % found the products favorable. The percentage is 0.62.
For non-sponsored studies 46% found the products favorable. The percentage is 0.46
Total probability = P(A) × P (B)
= 0.46 × 0.62
= 0.2604
For b)
Probability for the food industry = 0.7
For c) 1 - ( 0.62) = 0.38
The overall probability that a participant finds the product favorable is 57.2%. If the product was found favorable, the probability the study was industry-sponsored is 75.8%. If the product was found unfavorable, the probability the study was not industry-funded is 71.7%.
Explanation:The first step to answer the given question is understand that this is a problem of conditional probability, related to the concept of favorability or unfavorability towards products based on industry-sponsored studies and non-sponsored studies.
To find the overall probability of a participant finding the product favorable, we add the probabilities of a product being favorable under both industry funding and no industry funding, weighted by their respective chances of occurrence.
Begin by finding probability that industry sponsored and product was favorable: ((70/100) * (62/100) = 0.434)Then find probability that no industry funding and product was favorable: ((30/100) * (46/100) = 0.138)Add these two probabilities together, which gives 0.434 + 0.138 = 0.572, or 57.2%To work out the conditional probabilities:
For an industry sponsored study given that the product was favorable, the probability is ((70/100) * (62/100)) divided by 0.572 = 0.758, or 75.8%For the study having no industry funding given that the product was unfavorable, the probability is ((30/100) * (38/100)) divided by ((70/100)*(15/100) + (30/100)*(38/100)) = 0.717, or 71.7%Learn more about Probability here:https://brainly.com/question/22962752
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A jar contains 11 green marbles, 6 red marbles, and 9 blue marbles. A marble is selected at random, not replaced, and then a second marble is selected. What is the probability of selecting a red marble followed by a green marble?
Write In a fraction.
The probability of selecting a red marble and then a green marble, without replacement, is 33/325.
Explanation:The probability in this case is being calculated as the outcome of two independent events - selecting a red marble first and then selecting a green marble. The total number of marbles in the jar is the sum of green, red, and blue marbles which is 11+6+9 = 26.
First, let's calculate the probability of drawing a red marble. There are 6 red marbles out of a total 26 marbles, so the probability is 6/26 (which reduces to 3/13).
Next, the jar now has 25 marbles left, and 11 of them are green. So, our probability of drawing a green marble after a red one is 11/25.
For both events to happen one after the other, we multiply the individual probabilities together. Hence, the combined probability of these two events would be (3/13) * (11/25), which equals 33/325.
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The probability of first selecting a red marble and then a green marble from a jar containing 11 green, 6 red, and 9 blue marbles is 33/325.
Explanation:The subject of this question is probability, which is a branch of mathematics. The problem involves calculating the probably of two events occurring in sequence: selecting a red marble and then a green one from a jar of colored marbles. In total there are 26 marbles: 11 green, 6 red, and 9 blue.
The probability of selecting a red marble first is 6/26 as there are 6 red marbles and 26 total marbles in the jar. Once you've chosen a red marble, it's removed from the jar. So for the second event, there are now 25 marbles in the jar, with 11 of them being green. So, the probability of selecting a green marble is 11/25.
The probability of both events (Choosing a red marble then a green one) happening one after the other is the product of the individual probabilities. So, the probability is (6/26) × (11/25) which simplifies to 33/325.
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a circle is centered at (-8, -13) and has a radius of 13. what is the equation of the circle? enter the equation in the box using lower case variables x and y.
Answer:
(x+8)² + (y+13)² = 169
Step-by-step explanation:
Equation of circle:
(x-h)² + (y-k)² = r²
(h,k) is the centre, r is the radius
(x-(-8))² + (y-(-13))² = 13²
(x+8)² + (y+13)² = 169
Answer: the equation of the circle is
(x + 8)² + (y + 13)² = 169
Step-by-step explanation:
A circle is the set of all points in a plane equidistant from a fixed point called the origin or center.
The center of the circle is (-8, -13)
The formula for determining the equation of a circle us expressed as
(x - h)² + (y - k)² = r²
Where
r represents the radius of the circle
h and k represents the x and y coordinates of the center of the circle. Comparing with the given points,
h = - 8 and k = - 13
Radius, r = 13
Substituting into the formula, it becomes
(x - h)² + (y - k)² = r²
(x - - 8)² + (y - - 13)² = 13²
(x + 8)² + (y + 13)² = 169
Peter is Distributing pamphlets about dog care and samples of dog biscuits. The dog biscuits come in packages of 12 in the pamphlets are in packages of 20 how many packages of dog biscuits and pamphlets will Peter need
Answer:
3 packeges of Pamphlets and 5 packages of dog biscuits.
Step-by-step explanation:
Peter have to distribute a pamphlet with one dog buscuit to each person they need equal amount of pamphlets and biscuitsby taking LCM of both 12 and 20 theanswer is 60. Peter needs 60 pamphlets and 60 dog biscuits. So he require 3packages of pamphlets and 5packages of dog biscuits.
Several companies have chosen to start factories in Georgia to manufacture automobiles or heavy construction equipment. The efficient road transportation system in the state allows these bulky products to be shipped fairly inexpensively. This is one example of how the road transportation system A. Helps Georgians avoid traffic jams. B. Provides jobs for many Georgians. C. Keeps taxes lower for Georgians. D. Allows Georgians to travel to work.
Answer: C. Keeps taxes lower for Georgians
Step-by-step explanation:
Since the road system allows the bulky products to be shipped inexpensively this must apply that the taxes are lower for georgians otherwise this might not have been the case.
Answer:
B
Step-by-step explanation:
i just did it
The frequency f of vibration of a violin string is inversely proportional to its length L. The constant of proportionality k is positive and depends on the tension and density of the string.
(A) write an equation that represents this variation.
(B) what effect does doubling the length on the string have on the frequency of its vibration?
Answer:
(A) [tex]f=\frac{k}{L}[/tex]
(B) Frequency becomes half.
Step-by-step explanation:
We have been given that the frequency f of vibration of a violin string is inversely proportional to its length L. The constant of proportionality k is positive and depends on the tension and density of the string.
(A) We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of proportionality.
Upon substituting our given values, we will get:
[tex]f=\frac{k}{L}[/tex]
Therefore, our required equation would be [tex]f=\frac{k}{L}[/tex].
(B) For part, we have been given that length is twice, so our new frequency will be [tex]f_n[/tex] and new length [tex]L_n[/tex] is [tex]2L[/tex].
Upon substituting [tex]2L[/tex] in our equation as:
[tex]f_n=\frac{k}{L_n}[/tex]
[tex]f_n=\frac{k}{2L}[/tex]
[tex]f_n=\frac{1}{2}\cdot \frac{k}{L}[/tex]
[tex]f_n=\frac{1}{2}\cdot f[/tex]
Upon comparing [tex]f_n[/tex] with [tex]f[/tex], we can see that [tex]f_n[/tex] is half the value of [tex]f[/tex].
Therefore, the frequency of vibration of violin gets half, when we double the length of the string.
The frequency f of a vibrating string is represented by the equation f = k/L, where k is a constant and L is the string's length. If the length of the string is doubled, the frequency of the string's vibration is halved due to the inverse relationship.
Explanation:Answer:(A) Considering the problem describes the frequency f of a vibrating string being inversely proportional to its length L, we can represent this information mathematically with the equation f = k/L, where k is a constant of proportionality. This constant is positive and depends on the tension and density of the string.
(B) Because frequency and length are inversely proportional, if you double the length of the string (L), the frequency (f) will halve. This is due to the inverse relationship, with the longer string taking more time to complete each vibration and thus reducing the frequency of vibration.
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A ball is launched from 8 yards off the ground and travels in parabolic motion, landing in a net 80 yards away and also 8 yards off the ground. A wall lies 75% of the way down the path, which the ball cleared by 13 yards.
If the ball’s maximum height during its flight was 80 yards, how many yards tall is the wall?
Answer:
The answer to this question is the wall is 45.95 yards tall
Step-by-step explanation:
To solve this, we list out the given variables and the unknowns thus
Height of ball at launch = 8 yards
Distance of net from the ball = 80 yards
Distance of the wall down the path = 75%
Maximum height of the ball= 80 yards
equation of Motion of the ball = parabolic motion =
v² = u² - 2gS
S = 80 - 8 = 72 yards
at maximum height v = 0 thus u² = 2×9.81×72 =1412.64
u = 37.59 m/s
also v = u - gt and again at max height v = 0
Therefore 37.59 = 9.81×t or t = 3.83 s
If the motion of the ball is free of obstruction then time of flight before the ball just reaches the 8 yards off the ground = 3.83×2 = 7.66 seconds
Taking the initial velocity as zero at maximum height and from the equation
S = ut + 0.5×gt² we get, where S is the heigt of the ball from touching the actual field ground which is 80 yards we have
80 = 0.5×9.81×t²
so that t² = 2×80÷9.81 = 16.31 or t = 4.04s
Therefore the total time of flight = 4.04 + 3.83 = 7.87 seconds
if the ball is considered as having a constant horizontal velocity, therefore
at 75% of the way the time it took will be 0.75×7.87 = 5.9 seconds
However time it took the ball to reach maximum height and then starts descent = 3.83s, and the time at which the ball is directly over the wall = 2.07 seconds on the second half just after reaching mximum height
Thus at 2.07 seconds the distance trvelled from the maximum height is
S = ut +0.5gt² as before where u = 0
hence S = 0.5×9.81×2.07² = 21.05 yards or (80 -21.05) yards off the ground = 58.95 yards
As stated in the question, the ball cleared the wall by 13 yards therefore the height of the wall is 58.95 - 13 = 45.95 yards
Joe uses a ladder to reach a window 10 feet above ground. If the ladder is 3 feet away from the wall, show whether a 12 foot ladder is long enough to reach the window.
Answer:
Step-by-step explanation:
Answer: the ladder would be long enough.
Step-by-step explanation:
The ladder forms a right angle triangle with the wall of the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the window to the base of the building represents the opposite side of the right angle triangle.
The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.
To determine if a 12 foot ladder is long enough to reach the window, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Let h represent the height that the ladder would get to. Therefore
12² = h² + 3²
144 = h² + 9
h² = 144 - 9 = 135
h = √135 = 11.62 feet
Since the height of the window is 10 feet above the ground, the ladder would be long enough.
Answer:
c.square root of 28
Step-by-step explanation:
Start with x2 + 4x = 12 and complete the square, what is the equivalent equation? A) (x + 2)2 = 16 B) (x + 2)2 = 14 C) (x + 4)2 = 16 D) (x + 4)2 = 28
Answer: The answer is A
Step-by-step explanation: Add the coefficient of x to the both sides.
X²+4x=12
X²+4x+4=12+4
X²+4x+4=16
X²+2x+2x+4=16
X(x+2)+2(x+2)=16
(X+2)(x+2)=16
(X+2)²=16
The equivalent equation is (x+2)²=16
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: The expression x²+4x-12=0
Thus simplifying the equation we get
x²+2.2x+4-12-4=0
(x+2)²-4²=0
(x+6) (x-2)=0
x=-6,2
or the equation can also be rewritten as (x+2)²=16
Thus the equivalent equation is (x+2)²=16
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a. Can you draw a decision tree having 100% accuracy on this training set? If you answer is yes, draw the decision tree in the space provided below. If your answer is no, explain why? b. Which attribute among A, B and C has the highest information gain? Explain your answer.
Answer:
Day Weather Temperature Humidity Wind Play?
1 Sunny Hot High Weak No
2 Cloudy Hot High Weak Yes
3 Sunny Mild Normal Strong Yes
4 Cloudy Mild High Strong Yes
5 Rainy Mild High Strong No
6 Rainy Cool Normal Strong No
7 Rainy Mild High Weak Yes
8 Sunny Hot High Strong No
9 Cloudy Hot Normal Weak Yes
10 Rainy Mild High Strong No
Step-by-step explanation:
Kylie and Amelia go to the movie theater and purchase refreshments for their friends. Kylie spends a total of $125.50 on 12 bags of popcorn and 7 drinks. Amelia spends a total of $87.50 on 6 bags of popcorn and 8 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.
Answer: a drink costs $5.5
Step-by-step explanation:
Let x represent the cost of one bag of popcorn.
Let y represent the cost of one drink.
Kylie spends a total of $125.50 on 12 bags of popcorn and 7 drinks. This means that
12x + 7y = 125.50 - - - - - - - - - - 1
Amelia spends a total of $87.50 on 6 bags of popcorn and 8 drinks. This means that
6x + 8y = 87.50 - - - - - - - - - -- - - 2
Multiplying equation 1 by 1 and equation 2 by 2, it becomes
12x + 7y = 125.50
12x + 16y = 175
Subtracting, it becomes
- 9y = - 49.5
y = - 49.5/ - 9
y = 5.5
Substituting y = 5.5 into equation 2, it becomes
6x + 8 × 5.5 = 87.50
6x + 44 = 87.5
6x = 87.5 - 44 = 43.5
x = 43.5/6 = 7.25
Maggie's mom agrees to let Maggie buy small gifts for some friends. Each gift costs $4. Maggie's mom gave her a budget of $19. When Maggie went online to order gifts, she discovered there was a $7 shipping fee no matter how many gifts she bought.
Answer:
If you`re trying to figure out how many gifts Maggie can get without the fee going over the budget, then I would say that she can buy 3 gifts. 4 times 3 is 12, and when you add 7 it equals 19. Of course, if 3 is pushing it, Maggie can also buy 1 or 2 gifts, and she`d be fine. Hope this helps!
Step-by-step explanation:
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 110 miles per week to commute to work. With gas prices currently at $2.65 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision. The old car Manny owns currently gets 16 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $740 per year (as long as nothing serious goes wrong). The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $6,500 over a three-year loan process. This car gets 28 miles per gallon and would only require an average of $10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
In this exercise we have to use the knowledge of finance to identify the best cost benefit is to buy a new car or a used car, thus we find that:
The new car costs more, that can be prove if;
Old car: [tex]\$5062.125[/tex] New car: [tex]\$7161.357[/tex]
Manny drives an average of 110 miles per week with his old car. The old car gets 16 miles per gallon. The cost per gallon is [tex]\$2.65[/tex] repair and maintainance costs an average of [tex]\$740[/tex] per year. For the old car, to find the amount spent on the car we have:
[tex](110/16) * (2.65) = \$18.21875 / week[/tex]
There are 52 weeks in a year. We have:
[tex](10.21875)*(52) = \$ 947.375\\947.375 + 740 = \$1687.375\\(1687.357) * (3) = \$5062.125[/tex]
The new car cost [tex]\$6500[/tex] over a three year loan process. The car gets 28 miles per gallon. It requires a maintenance of [tex]\$10[/tex] per month. For the new car to find the amount, we have:
[tex](110)*(28) * (2.65) *(52) = \$541.357\\541.357 + 10*(12) + 6500 = \$ 7161.357[/tex]
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This year , Lara paid 2,024 for season tickets to her favorite baseball team , which is 10% more expensive than last year . What was the price of season tickets last year?
Answer:
The price of season ticket last year was 1,840.
Step-by-step explanation:
Given:
Price of season tickets this year = 2024
Also given:
The Price of season tickets this year is 10% more than amount paid last year.
We need to find the Price of season tickets last year.
Solution:
Let the Price of season tickets last year be 'x'.
Now we know that;
The Price of season tickets this year is 10% more than amount paid last year.
so equation can be framed as;
[tex]x+ \frac{10}{100}x=2024\\\\x+\frac{x}{10}=2024\\\\x+0.1x=2024\\\\1.1x=2024[/tex]
Now dividing both side by 1.1 we get;
[tex]\frac{1.1x}{1.1}=\frac{2024}{1.1}\\\\x= 1840[/tex]
Hence The price of season ticket last year was 1,840.
The intensity of the sound of a subway train was measured at 108 dB. Find the intensity in W/m2. (Give your answer in scientific notation, correct to one decimal place.)
Answer:
I = 0.0631 W/m²
Step-by-step explanation:
Value in Decibel = 10 Log [tex]\frac{I}{10^{-12} }[/tex]
108 / 10 = Log [tex]\frac{I}{10^{-12} }[/tex]
10.8 = Log [tex]\frac{I}{10^{-12} }[/tex]
[tex]\frac{I}{10^{-12} }[/tex] = [tex]10^{10.8}[/tex]
I = [tex]10^{10.8}[/tex] x [tex]10^{-12}[/tex]
I = 0.0631 W/m²
The amount of money in Tara's account with respect to the day of the month was recorded for 31 days. The correlation coefficient was calculated to be r = −0.9870. Interpret the meaning of the correlation coefficient in terms of the scenario.
There is a weak, negative correlation between the amount of money in Tara's account and the day of the month.
There is a strong, positive correlation between the day of the month and the amount of money in Tara's account.
There is a strong, negative correlation between the amount of money in Tara's account and the day of the month.
There is a weak, positive correlation between the day of the month and the amount of money in Tara's account.
There is no correlation between the amount of money in Tara's account and the day of the month.
Answer:
There is a strong, negative correlation between the amount of money in Tara's account and the day of the month.
Step-by-step explanation:
r is between -1 and +1. r values close to -1 are strongly negative. r values close to +1 are strongly positive. r values close to 0 are weak.
r = -0.9870 is strongly negative. So there is a strong, negative correlation between the amount of money in Tara's account and the day of the month.
Final answer:
The correlation coefficient r = -0.9870 shows a strong, negative correlation between the day of the month and the amount of money in Tara's account, meaning as the days pass, her account balance generally decreases. So, the correct statement is 'There is a strong, negative correlation between the amount of money in Tara's account and the day of the month.'
Explanation:
The correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between two variables. Given that the correlation coefficient in the scenario is r = −0.9870, this indicates a strong, negative correlation between the amount of money in Tara's account and the day of the month. This means that as the days of the month increase, the amount of money in Tara's account tends to decrease, and this pattern is quite consistent, considering the high absolute value of the coefficient, which is close to -1.
A factory produces toy dolls at the rate of 400 per hour and has to recycle 3% of them because the clothes are torn. Express the recycle percent as a rate per 100
Answer:
The recycle percent as a rate per 100 is 0.03 per hour.
And 12 dolls are recycled each hour during production.
Step-by-step explanation:
The question is incomplete so below is the complete question:
A factory produces toy dolls at a rate of 400 per hour and has to recycle 3% of them because the clothes are torn. Express the recycle percent as a rate per 100. How many dolls are recycled each hour during production?
Now, to express the recycle percent as a rate per 100, And to find the number of dolls are recycled each hour during production.
Number of dolls factory produces at rate per hour = 400.
Percent of recycle = 3%.
So, to express the recycle percent as a rate per 100:
[tex]3\%\ per\ 100[/tex]
[tex]=\frac{3}{100} \ per\ hour[/tex]
[tex]=0.03\ per\ hour.[/tex]
So, to get the number of dolls are recycled each hour during production:
3% of number of dolls factory produces at rate per hour.
[tex]=\frac{3}{100} \times 400[/tex]
[tex]=0.03\times 400[/tex]
[tex]=12.[/tex]
The dolls are recycled each hour = 12.
Therefore, the recycle percent as a rate per 100 is 0.03 per hour.
And 12 dolls are recycled each hour during production.
Jaclyn plays singles for the varsity tennis team where she won the sudden death tie breaker point with a cross-court passing shot. The 57.5 g ball hit her racket with a northward velocity of 26.7 m/s. Upon impact with her 331g racket, the ball rebounded in the exact opposite direction with a speed of 29.5 m/s
Answer:
Incomplete question
Complete question: Jaclyn plays singles for South's varsity tennis team. During the match against North, Jaclyn won the sudden death tiebreaker point with a cross-court passing shot. The 57.5-gram ball hit her racket with a northward velocity of 26.7 m/s. Upon impact with her 331-gram racket, the ball rebounded in the exact opposite direction (and along the same general trajectory) with a speed of 29.5 m/s.
a. Determine the pre-collision momentum of the ball.
b. Determine the post-collision momentum of the ball.
c. Determine the momentum change of the ball.
Answer:
A. 1.5353kgm/s
B. 1.6963kgm/s
C. 0.161kgm/s
Step-by-step explanation:
A. The pre-collision momentum of the ball = mass of ball × velocity of ball
Mass of ball = 57.5g = 0.0575kg
Velocity of ball = 26.7m/s
Pre-collision momentum of ball = 0.0575×26.7
= 1.5353kgm/s
B. Post collision momentum of the ball = mass of ball × velocity of ball after impact
Velocity of ball after impact = 29.5m/s
Post collision momentum of ball after impact = 0.0575×29.5
= 1.6963kgm/s
C. Momentum change of ball = momentum after impact - momentum before imlact
= 1.6963kgm/s - 1.5353kgm/s
= 0.161kgm/s
Dan reads 12 books over winter break. Over summer break, Dan reads 8 times the number of books he read over winter break. How many books did Dan read over summer break? Books
Answer:
96 books
Step-by-step explanation:
Given:
Dan reads 12 books over winter break.
Dan reads 8 times the number of books he read over winter break.
Question asked:
How many books did Dan read over summer break ?
Solution:
By doing multiplication:
Dan reads number of books over winter break = 12
Dan reads number of books over summer break = 8 times of winter break
[tex]= 8\times12\\\\= 96[/tex]
Therefore, 96 books is read by Dan over summer break.
Final answer:
Dan read 96 books over summer break by multiplying the 12 books he read during winter break by 8.
Explanation:
The question asks us to calculate how many books Dan reads over summer break given that he reads 8 times the number of books he read over winter break. To find the answer, we need to multiply the number of books Dan read in winter break by 8. Dan read 12 books during winter break, so for summer break, we will calculate:
12 books × 8 = 96 books
Therefore, Dan read 96 books over summer break.
In Mozambique a currency crisis led the government to mandate that citizens from Mozambique could only spend up to $13,600 on their credit or debit cards when shopping abroad. This is an example of a(n)__________.
Answer:
In Mozambique a currency crisis led the government to mandate that citizens from Mozambique could only spend up to $13,600 on their credit or debit cards when shopping abroad. This is an example of a(n) ______________.
A. import tariff
B. quota
C. self-reference criterion
D. embargo
E. exchange control
The correct answer is E. exchange control
Step-by-step explanation:
Exchange controls are government imposed controls on the selling, buying or transfer of foreign currencies by residents of the country and on the selling and buying of the country's local currency by nonresidents, as well as control of cross border currency transfer.
Exchange contrl is meant for in-country economic management to prevent exchange rate volatility and is common in countries with developing economies.
Generally types of exchange controls are as follows:
1. Allowing foreign exchange transaction through only government approved channels
2. Placing a ban on the possession of foreign currency
3. Placing a ban on the use of foreign currency within the country
4. setting fixed exchange rates
5. Placing a restriction on the amount of currency flow across border
Rectangle ABCD is shown with diagonal AC drawn. Point F is on AC and point E on DC such that FE is perpendicular to DC. Prove triangle ABC is similar to triangle CEF
Triangle ABC is similar to triangle CEF.
Explanation:
Diagram is inserted for the reference.
ABCD is a rectangle.
ABC is a right angled triangle because all the angles of the rectangle are 90◦ - (a)
CEF is a right angled triangle because FE is perpendicular to DC – (b)
In triangles ABC and CEF,
1. Angle ABC = Angle CEF = 90◦ (Both are right angles from a and b)
2. Angle BCA = Angle EFC (Alternate angles on parallel lines are equal on intersection)
Hence using Similarity property of AA (Angle, Angle), Triangle ABC and CEF are similar.
ΔABC and ΔCEF are similar triangles by the AA similarity theorem.
What is the AA Similarity Theorem?The angle-angle similarity theorem (AA) states that when two triangles have two pairs of corresponding congruent angles, both triangles are similar triangles.
In ΔABC and ΔCEF, we have the following:
Two pairs of corresponding congruent angles - ∠FEC ≅ ∠ABC (right angles) and ∠FCE ≅ ∠BAC
Therefore, ΔABC and ΔCEF are similar triangles by the AA similarity theorem.
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Translate the given statement into a linear equation in the form ax + by = c using the indicated variable names. Do not try to solve the resulting equation. HINT [See Example 7 and the end of section FAQ.] The number of new clients (x) is 154% of the number of old clients (y).
The statement 'the number of new clients (x) is 154% of the number of old clients (y)' can be translated into a linear equation in the standard form 'ax + by = c' as '-1.54y + x = 0' or '-154y + 100x = 0' where a, b, and c are constants.
Explanation:To translate the given statement into a linear equation, we need to interpret the percentages as a ratio. When we say 'the number of new clients (x) is 154% of the number of old clients (y)', it means 'x is equivalent to 1.54 times y'. So, we can write that as a linear equation:
x = 1.54y
However, that's not in the form 'ax + by = c'. To get it into that form, we can write it as:
-1.54y + x = 0
Or alternately you might prefer, if you wish to avoid decimals:
-154y + 100x = 0
Where a = -154, b = 100 and c = 0.
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What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x? 1. The distributive property: 4x – 12 + 4 < 10 + 6x 2. Combine like terms: 4x – 8 < 10 + 6x 3. The addition property of inequality: 4x < 18 + 6x 4. The subtraction property of inequality: –2x < 18 5. The division property of inequality: ________ x < –9 x > –9 x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction. X > –x is greater than or equal to negative StartFraction 1 Over 9 EndFraction.
Answer:
X>-9
X is greater than -9
Step-by-step explanation:
4(X-3)+4<10+6X
By clearing up the bracket :
4X-12+4<10+6X
Collecting like terms:
4X-6X<10+12-4
-2X<18
Dividing both sides by -2:
-2X/-2>18/-2
Therefore, X>-9
The mission step is in combining like terms which is 4X-8<10+6X instead of 4X-6X<10+8.
The missing step in solving the given inequality 4(x – 3) + 4 < 10 + 6x is; x > -9
How to solve Inequalities?We are given the inequality as:
4(x – 3) + 4 < 10 + 6x
The steps are given as:
The distributive property: 4x – 12 + 4 < 10 + 6xCombine like terms: 4x – 8 < 10 + 6xThe addition property of inequality: 4x < 18 + 6xThe subtraction property of inequality: –2x < 18The next step in solving the inequality is to apply the division property of inequality by dividing both sides by -2.
This gives; x > -9
Thus, the missing step in the inequality is x > -9
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What percent of 7.5 is 0.9
Answer:
12%
Step-by-step explanation:
0.9/7.5 *100
= 12%
Carrie earned $3673 from a summer job and put it in a savings account that earns 10% interest compounded annually. When Carrie started college, she had $7614 in the account which she used to pay her tuition. How long was the money in the account?
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
A = 7614
r = 10% = 10/100 = 0.1
n = 1 because it was compounded once in a year.
P = 3673
Therefore,
7614 = 3673(1+0.1/1)^1 × t
7614/3673 = 1.01^t
2.073 = 1.01^t
Taking log of both sides, it becomes
Log 2.073 = log 1.01^t
0.3166 = t × 0.0043
t = 0.3166/0.0043
t = 73.3
At the end of January of last year, stock A was selling at A dollars a share, and stock B was selling a B dollars a share, where A > B. Between January and June, stock A rose x%, and stock B rose y%, where y > x. Suppose a certain investor owned N shares of A, but at the end of January last year, sold those shares and used all of that money to buy shares of B, and held those shares through the end of June. These are the only stocks in this portfolio. Do not mark more than one answer in each column.
Answer: a) yNA/100
b) NA(y-x)/100
c) (NA)/B
Step-by-step explanation:
a) The total amount of dollars owned by the shares' owner = N number of shares × A dollars per share = NA dollars
This total is then transferred to buy B shares which then appreciates by y%.
The amount of increase in portfolio from January to June = y% of total dollars invested = y% of NA dollars = yNA/100
b) If the shares were left with A, the increase in portfolio from January to June would be x% and = x% of the total Dollar amount = x% of NA dollars = xNA/100
How much more money made in that time would be the difference in interest, between taking the dollars to invest in share B or keeping the dollars on investment A
That is, (yNA/100) - (xNA/100) = NA(y-x)/100
c) Total dollars available after sale of the A stock = NA
Number of B stock this dollar can buy = Total dollars available/amount of B stock per share
That is, (NA)/B
QED!
Rs 144 is distributed among 2 boys and 3 girls in such a way that each girl gets three times as much as each boy gets. Find how much each boy should get.
Answer:
Each boy gets approximately Rs 13.09
Step-by-step explanation:
We are given the following in the question:
Total money = Rs 144
Let x be the amount each girl gets and y be the amount each boy gets.
The money is distributed among 2 boys and 3 girls. Thus, we can write:
[tex]3x + 2y = 144[/tex]
Also, each girl gets three times as much as each boy gets.
Thus, we can write:
[tex]x = 3y[/tex]
Substituting these values, we get,
[tex]3(3y) + 2y = 144\\11y = 144\\\\y =\dfrac{144}{11} \approx 13.09\\\\x = 3(\dfrac{144}{11}) \approx 39.27[/tex]
Thus, each boy gets approximately Rs 13.09
Answer: each boy should get $39.27
Step-by-step explanation:
Let x represent the amount that each boy should get.
Let y represent the amount that each girl should get.
The total amount of money that would be distributed among the 2 boys and 3 girls is 144 Rs. This is expressed as
2x + 3y = 144 - - - - - - - - - - - -1
The money is shared in such a way that each girl gets three times as much as each boy gets. This is expressed as
y = 3x
Substituting y = 3x into equation 1, it becomes
2x + 3 × 3x = 144
2x + 9x = 144
11x = 144
x = 144/11 = 13.09
y = 3x = 3 × 13.09
y = $39.27
Ill help you if you help me WILL MARK BRAINLIEST!You can create special effects in an image using a camera or a photo-editing tool. Compare special effects created using only a camera and lens versus special effects achieved in a photo-editing tool. What do you prefer? Justify your choice.
Answer:
Special Lenses For Special Effects. ... These specialty lenses may be designed with movable focal planes for amazing depth of field, or built to focus extremely close to tiny subjects for macro enlargements, or even to produce a specific type of soft focus that's flattering for portraits
The meaning of photo editing is the act of altering an image, simply put. But that’s oversimplifying a subject which is quite complex.
For example, some photo editing techniques are done manually, while others are conducted through automated software. Some photo editing is even done offline, on actual photographs, posters or other printed collateral.
Other terms for photo editing:
Image editing
Post-processing
Image/photo manipulation
Photoshopping
Image/photo enhancement
Explanation:
so they both are alike because they can both be used to edit photos and both are great to use
Step-by-step explanation:
They both are alike because they can both be used to edit photos and both are great to use.
What is photo editing?The procedure used to change a picture, including digital photography, analog photography, and graphics is referred to as image editing.
Special Lenses For Special Effects. These specialty lenses may be designed with movable focal planes for amazing depth of field, built to focus extremely close to tiny subjects for macro enlargements, or even to produce a specific type of soft focus that's flattering for portraits.
The meaning of photo editing is the act of altering an image, simply put. But that’s oversimplifying a subject that is quite complex.
For example, some photo editing techniques are done manually, while others are conducted through automated software. Some photo editing is even done offline, on actual photographs, posters, or other printed collateral.
Other terms for photo editing:
Image editing
Post-processing
Image/photo manipulation
Photoshopping
Image/photo enhancement
Therefore, both are alike because they can both be used to edit photos and both are great to use.
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: Let x represent any number in the set of odd integers less than 5. Which inequality is true for all values of x? A x<0 B x>0 C x<5 D x>5
Answer:
(C) X<5
Step-by-step explanation:
Set of all old integers less than 5=(1,3)
X will represent this in inequality :
X<5.
Therefore, the answer is C.
Before beginning to balance an equation, you should check each formula for correctness and NEVER change the formulas once they are correct. TRUE FALSE
Answer: False
Step-by-step explanation:
Answer:
False
Step-by-step explanation: