Answer: The initial number of shoes in the store is 300.
Step-by-step explanation:
Given : Kelly is a salesperson at a shoe store, where she must sell a pre-set number of pairs of shoes each month.
At the end of each work day the number of pairs of shoes that she has left to sell that month is given by the equation
[tex]S=300-15x[/tex] , where S = Number of pair of shoes Kelly still needs to sell.
x = Number of days she has worked that month.
When x= 0 , we get S= 300
i.e. When she started working in that month , she has 300 pairs of shoes to sell.
Therefore , Number 300 means that the initial number of shoes in the store is 300
what is 5/6 y - 8 = 2
a. 12
b. 8 1/3
c. -7 1/5
d. 13
Answer:
[tex]a.\ 12[/tex]
Step-by-step explanation:
[tex]\frac{5}{6}y-8=2\\\\Add\ 8\ both\ sides\\\\\frac{5}{6}y-8+=2+8\\\\\frac{5}{6}y=10\\\\Multiply\ by\ 6\ both\ the\ sides\\\\\frac{5}{6}y\times 6=10\times 6\\\\5y=60\\\\divide\ by\ 5\ both\ the\ sides\\\\\frac{5y}{5}=\frac{60}{5}\\\\y=12[/tex]
I need help with this practice problem
Answer:
a. see below
b. Rita: 300; John: 900; Rodell: 925
c. Rita: L; John: 3L; Rodell: 3L+25
d. L +3L +(3L+25) = 2125
e. Rita: $600; John: $1800; Rodell: $1850
Step-by-step explanation:
Since John's number of laps is expressed in terms of Rita's number of laps, it makes a certain amount of sense to use Rita's laps as a unit of measure. We don't yet know what that unit of measure is, but we can use it to describe both John's laps and Rodell's laps. Rodell will have 25 additional laps added to the 3 units that match John's laps.
Altogether, these 7 units +25 laps will match the total of 2100 +25 laps. It is pretty clear that 1 unit will be 2100/7 = 300 laps. This is shown in the attachment.
__
a) The attachment matches the above description.
__
b) 1 unit of 300 laps is the number of laps Rita swam. Then John's 3 units correspond to 3×300 = 900 laps, and Rodell's laps will be 25 more than John's, so 925.
__
c) In this part, we define 1 unit as L, so the three contributors are ...
Rita: LJohn: 3LRodell: 3L+25__
d) The equation shows that the sum of the parts is equal to the whole:
L + 3L + (3L+25) = 2125
__
e) The numbers of part (b) get multiplied by $2, so are ...
Rita: $600John: $1800Rodell: $1850The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
Answer:
Step-by-step explanation:
x+x+(x+12)=180
3x=180-12=168
x=56
third angle=56+12=68
so angles are 56°,56°,68°
The larger angle is x + 12 i.e. 56 + 12 = 68⁰.
What is Triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.
Let the first angle be x.
then second angle is equal to first i.e. x
and third angle = x + 12
we know that,
Sum of all angles of a triangle is 180⁰.
Now,
x + x + x + 12 = 180
3x = 180 -12
3x = 168
x = 168/3
x = 56
Thus, the larger angle is x + 12 i.e. 56 + 12 = 68⁰.
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The sum of two numbers is 29
and their product is 180.
Find the numbers.
Final answer:
To find the two numbers with a sum of 29 and product of 180, we set up a system of equations, solve for one variable in terms of the other, and then factor a quadratic equation to find that the two numbers are 20 and 9.
Explanation:
The student's question is about finding two numbers based on their sum and product. To solve this, we can set up two equations based on the given information: let's call our numbers x and y. The first equation based on their sum is x + y = 29, and the second equation based on their product is xy = 180.
We can find one number in terms of the other using the first equation: y = 29 - x. We then substitute this into the second equation to get x(29-x) = 180. Simplifying, we have x² - 29x + 180 = 0. Factoring the quadratic equation, we get (x - 20)(x - 9) = 0, which gives us two possible values for x: 20 or 9. Thus, the two numbers are 20 and 9.
2. An 82 kg man on a diving board drops from rest 3.0 m above the surface of the water
and he comes to rest 0.55 s after reaching the water. What is the average net force on
the diver as he is brought to rest? Remember to first find the velocity of the man after he
falls 3.0 m off of the diving board.
The average net force on the man as he is brought to rest is: F = -1143.9N
The man on the diving board has a potential energy, P.E = mghWhen the man dives, he has a kinetic energy, K.E = (1/2)mv²Therefore, P.E = K.E
mgh = (1/2)mv²82 × 9.8 × 3 = (1/2)× 82 × v²v² = 58.8V = 7.67 m/sWhen the man comes to rest, the final velocity becomes, 0.
As, such, acceleration which is the rate of change of velocity becomes;
a = (0 - 7.67)/0.55a = -13.95 m/s².The force on the man; F = mass × acceleration.
F = 82 × -13.95F = -1143.9NRead more:
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The average net force on the diver as he is brought to rest is approximately 689.56 N.
First, we can find the velocity of the man just before he reaches the water using the kinematic equation:
d = vt + 1/2at²
Now, let's calculate the velocity of the man just before he reaches the water using the equation:
vf=0+(−9.8m/s2)×0.782s≈−7.664m/s
Since the velocity is negative, it means the man is moving downward.
After entering the water, the man comes to rest in 0.55 seconds. During this time, he decelerates due to the force of gravity, but this time in the opposite direction to his motion. We can use the equation:
Finally, we can determine the average net force using Newton's second law:
Given that the mass m of the man is 82 kg, we find:
F net = 82 kg × 14.025 m/s 2 ≈ 1147.35 N
Therefore, the average net force on the diver as he is brought to rest is approximately 1147.35 N.
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A very bright student is described as having an IQ that is three standard deviations above the mean. If this student's IQ is reported as a z-score, what would the z-score be?
a. z = m + 3
b. z = m + 3s
c. z = 3
d. cannot be determined from the information given
Answer:
Option C) z = 3
Step-by-step explanation:
We are given the following in the question:
IQ scores are normally distributed.
An IQ score is three standard deviations above the mean. Let x be the IQ score. Then, we can write,
[tex]x = \mu + 3\sigma[/tex]
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]z = \dfrac{\mu + 3\sigma-\mu}{\sigma} = \dfrac{3\sigma}{\sigma} = 3[/tex]
Thus, the z-score is 3.
Thus, the correct answer is
Option C) z = 3
The z-score for a student with an IQ three standard deviations above the mean would be z = 3.
Explanation:If a very bright student is described as having an IQ that is three standard deviations above the mean, and if this student's IQ is reported as a z-score, the z-score would be z = 3. This is because a z-score is a measure of how many standard deviations an observation is above or below the mean. When we say an observation is three standard deviations above the mean, we are describing a z-score of 3. Thus, the correct answer is c. z = 3.
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Write a numerical expression for the phase The quotient of 36 and the sum of -4 and -8 a numerical expression for this phrase is ? Simplified this is ?
The sum of -4 and -8 is -12, so the numerical expression for the given phrase is 36 / (-12) and the simplified expression is -3.
Explanation:To write a numerical expression for the phrase 'The quotient of 36 and the sum of -4 and -8,' we need to divide 36 by the sum of -4 and -8. The sum of -4 and -8 is -12, so the numerical expression is 36 / (-12).
Simplifying this expression, we get -3. Therefore, the simplified expression is -3.
The equation R= -0.028t +20.8 can be used to predict the world record in the 200 meter dash, where R stands for the record in seconds and t for the number of years since 1920. In what year did the record become 19.68 seconds?
Final answer:
To find the year when the record became 19.68 seconds, substitute the value of R into the equation. Solve for t and add 1920 to get the year.
Explanation:
To find the year when the record became 19.68 seconds, we need to substitute the value of R into the equation:
R = -0.028t + 20.8
19.68 = -0.028t + 20.8
Solving for t:
Subtract 20.8 from both sides: -0.028t = -1.12
Divide both sides by -0.028: t = 40
Since t represents the number of years since 1920, we add 1920 to the result to get the year:
t + 1920 = 40 + 1920 = 1960
Therefore, the record became 19.68 seconds in the year 1960.
Create at least 3 subtraction problems that have a common denominator of 20 using the fractions one sixth two fifths four sevenths three fourths three eights one half
Answer:
1. 1/2-2/5
2. 3/4-2/5
3. 1/2-3/4
Step-by-step explanation:
For you to be able to create such fractions you must make sure that the numerator is divisible by 20.
Clearly the number 2,4 and 5 can divide 20.so therefore any fraction formed with them will give the denominator 20
x and y vary inversely, and y =7 when x = 4. What is the constant of variation?
Answer:
Y doesn't vary directly with x
Answer:28
Step-by-step explanation:
X varies inversely as y
X©1/y
X=k/y
4=k/7
Cross product
We get 4×7=k×1
28=k
Therefore constant (k)=28
Demont used 4 gallons of gasoline in three days driving to work .Each day he used the same amount of gasoline. How many gallons of gasoline did he use each day?
Answer:
1 1/3 gallons per day
Step-by-step explanation:
To find gallons per day, divide gallons by days. ("per" means "divided by")
(4 gal)/(3 day) = (4/3) gal/day
Demont used 4/3 = 1 1/3 gallon each day.
To find out how many gallons of gasoline Demonte used each day, divide the total amount used (4 gallons) by the number of days (3), yielding approximately 1.33 gallons per day.
Demonte used 4 gallons of gasoline in three days driving to work and used the same amount of gasoline each day. To calculate the amount of gasoline he used each day, you divide the total gallons of gasoline by the number of days. This can be represented by the following equation:
Gallons per day = Total gallons used ÷ Number of days
Gallons per day = 4 gallons ÷ 3 days
Gallons per day = 1.33 gallons per day (approximately)
Therefore, Demonte used approximately 1.33 gallons of gasoline each day.
Please help!
Two models are used to predict monthly revenue for a new sports drink. In each model, x is the number of $1-price increases from the original $2 per bottle price. Answer parts a and b below.
a. Identify the price you would set for each model to maximize monthly revenue.
Using Model A, the price should be $____ to maximize monthly revenue because the _-intercept occurs at x=_?
Model A
f(x)=-12.5x^2+75x+200
Model B
Model A's optimal price is $5, with a $3 increase, and Model B's optimal price is $6, with a $4 increase.
Let's walk through the step-by-step calculations for both Model A and Model B.
Model A:
Given Function:
f(x) = -12.5x^2 + 75x + 200
Completing the Square to Find Vertex:
f(x) = -12.5(x^2 - 6x - 16)
f(x)/(-12.5) = (x^2 - 6x - 16)
f(x)/(-12.5) + 16 + 9 = (x-3)^2
f(x)/(-12.5) + 25 = (x-3)^2 - 25
f(x) = (-12.5)[(x-3)^2 + 312.5]
Vertex Form:
f(x) = (-12.5)(x-3)^2 + 312.5
The vertex is at (3, 312.5).
Optimal Price Calculation:
The x-coordinate of the vertex indicates the optimal increase, which is $3. So, the optimal price is 3 + 2 = $5.
Y-intercept:
f(x) = -12.5(9) + 312.5 = 200
The y-intercept is $200.
X-intercepts:
Factorizing the original equation, we get x = 8 and x = -2.
Model B:
Symmetry Axis Calculation:
Midpoint between x-intercepts x = (-2 + 10)/2 = 4.
Optimal Price Calculation:
The optimal increase is $4, resulting in a price of 4 + 2 = $6.
Y-intercept:
The y-intercept is graphically determined to be between $180 and $210.
In summary, Model A's optimal price is $5, achieved with a $3 increase, while Model B's optimal price is $6, attained with a $4 increase.
What is the perimeter of a square whose diagonal is 3 square root 2? Show all work on how you got your answer
Answer:
12
Step-by-step explanation:
Given: Diagonal of square= [tex]3\sqrt{2}[/tex]
To find the perimeter of square, we need to find the length of sides of square.
∴ Using the formula of diagonal to find side of square.
Formula; [tex]Diagonal= s\sqrt{2}[/tex]
Where, s is side of square.
⇒ [tex]3\sqrt{2} = s\sqrt{2}[/tex]
Dividing both side by √2
⇒[tex]s= \frac{3\sqrt{2} }{\sqrt{2} }[/tex]
∴[tex]s= 3[/tex]
Hence, Length of side of square is 3.
Now, finding the perimeter of square.
Formula; [tex]Perimeter= 4s[/tex]
⇒[tex]Perimeter= 4\times 3[/tex]
∴ [tex]Perimeter= 12[/tex]
Hence, Perimeter of square is 12.
The perimeter of a square with a diagonal of 3 square root 2 units is 12 units.
Explanation:To find the perimeter of a square with a diagonal of 3√2, we can use the fact that the diagonal of a square divides it into two congruent right triangles. The length of each leg of the triangle is equal to one side of the square. We can use the Pythagorean theorem to find the length of the side of the square. Let's assume that the length of the side of the square is s.
Using the Pythagorean theorem, we have s2 + s2 = (3√2)2. Simplifying, we get 2s2 = 18. Dividing by 2, we have s2 = 9. Taking the square root of both sides, we get s = 3.
The perimeter of the square is equal to 4 times the length of one side, so the perimeter is 4 * s = 4 * 3 = 12 units.
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It usually took josh 2/5 of an hour to ride his bike to work. But on Monday, his bike was broken, so he took the bus to work which took 5/8 of an hour. How much longer was it to take the bus to work?
Final answer:
To find the difference in time, subtract the bike time from the bus time by finding a common denominator and subtracting the fractions.
Explanation:
To compare the time it took Josh to bike to work with the time it took him to take the bus, we need to subtract the bike time from the bus time.
The time it took Josh to bike to work is given as 2/5 of an hour. We can represent this as a fraction, 2/5.
The time it took Josh to take the bus is given as 5/8 of an hour. This can also be represented as a fraction, 5/8.
To find the difference, we subtract the bike time from the bus time: 5/8 - 2/5. To do this, we need a common denominator, which in this case is 40.
Multiplying the numerator and denominator of 5/8 by 5, we get 25/40. Multiplying the numerator and denominator of 2/5 by 8, we get 16/40.
Now we can subtract the fractions: 25/40 - 16/40 = 9/40.
Therefore, it took the bus 9/40 of an hour longer than it took Josh to bike to work.
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A jar contains 5 green, 3 black, and 2 red marbles. Brandi draws a marble from the jar and then puts it back. She then draws
another marble. What is the probability that Brandi draws
a. 2 greens
b. 2 reds
c. 1 black and 1 green
d. 1 green and 1 red
Step-by-step explanation:
a. 5/10 x 5/10 = 25%
b. 2/10 x 2/10 = 4%
c. 3/10 x 5/10 = 15% (Probability for getting black then green)
5/10 x 3/10 = 15% (Probability of getting green then black)
Thus, probability of getting green and black in any order is 30%
d. SIimilarly,
5/10 x 2/10 = 10% (Green then red)
2/10 x 5/10 = 10% (Red then green)
Green and red in any order 20%
Answer:
Depending on the remaining of the question. C is the answer
Step-by-step explanation:
5/10 x 5/10 = 25%
2/10 x 2/10 = 4%
3/10 x 5/10 = 15% Probability for getting black then green
5/10 x 3/10 = 15% Probability of getting green then black
green and black in any order is 30% the changes are higher in this case.
5/10 x 2/10 = 10% (Green then red)
2/10 x 5/10 = 10% (Red then green)
Green and red in any order 20%
Ena's income is $1900 a month, and she plans to budget 29 of her income for entertainment and 15 of her income for groceries. Step 1 of 2 : What fraction of her income does she plan to spend each month on these two items together? Express your answer in lowest terms.
Answer:
2/10 of her income will go to these items
Step-by-step explanation:
29 +15 = 41
41/1900 equal 2/10
Final answer:
Ena plans to spend 29% of her income on entertainment and 15% on groceries, which is a total of [tex]\(\frac{44}{100}\)[/tex]of her income. Simplifying this to its lowest terms gives us [tex]\(\frac{11}{25}\)[/tex] of her income spent on these two items together.
Explanation:
To find the fraction of Ena's income that is spent on entertainment and groceries together, we need to sum the fractions of income allocated to each category. Ena plans to spend 29% of her income on entertainment and 15% on groceries. In fractional terms, 29% is the same as 29/100 and 15% is equivalent to 15/100. Adding these fractions together:
[tex]\(\frac{29}{100} + \frac{15}{100} = \frac{44}{100}\)[/tex]
Now, we simplify the fraction to its lowest terms:
[tex]\(\frac{44}{100} = \frac{44 \div 4}{100 \div 4} = \frac{11}{25}\)[/tex]
Thus, Ena plans to spend [tex]\(\frac{11}{25}\)[/tex]of her income on entertainment and groceries together.
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of car: economy or luxury. The charge E (in dollars) to rent an economy car is given by the function E -0.70M+14.95, where M is the number of miles driven. The charge L (in dollars) to rent a luxury car is given by the function L 1.05M+18.20 Let C be how much more it costs to rent a luxury car than an economy car (in dollars). Write an equation relating C to M. Simplify your answer as much as possible. Clear Undo Help Next > Explain
Answer:
C = 1.75M + 3.25
Step-by-step explanation:
Let E represent Economy
Let L represent Luxury
Let M be the number of miles driven
Let C be how much it cost to rent a luxury car than economy
E = -0.70M + 14.95
L = 1.05M + 18.20
C = L - M
C =(1.05M + 18.20) - (-0.70M + 14.95)
C = 1.05M + 18.20 + 0.70M - 14.95
collect like terms
C = 1.05M + 0.70M + 18.20 - 14.95
C = 1.75M + 3.25
The equation representing how much more it costs to rent a luxury car than an economy car, given the number of miles driven, is C = 1.75M + 3.25. This is derived by subtracting the equation for economy car costs from the equation for luxury car costs and simplifying.
Explanation:The value of C, which is the cost difference between renting a luxury and an economy car, can be found by finding the difference between the charge equations for the two types of cars. To find C in terms of M, subtract the equation for the economy car (E) from the equation for the luxury car (L).
So, C = L - E
Substitute the given equations for L and E into the equation for C:
C = (1.05M + 18.20) - (-0.70M + 14.95)
Simplify the equation by distributing the negative sign on the right side of the equation:
C = 1.05M + 18.20 + 0.70M - 14.95
Combine like terms:
C = 1.75M + 3.25
This equation represents how much more it costs to rent a luxury car than an economy car based on the number of miles driven.
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Lines a and b are parallel.
what is the measure of angle b
enter in the box
B=
Answer:
Ans _ angle b = 79
Hope it helps
∠B4 = ∠A2
b° = 79°
hope this helps :)
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y = x^2 +2x -5
Answer:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y -intercept(s): ( − 1 + √ 6 , 0 ) , ( − 1 − √ 6 , 0 ) y-intercept(s): ( 0 , − 5 )
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠K.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠K = °
Answer:
Step-by-step explanation:
[tex]tan K=\frac{2}{3} \\m \angle K=tan^{-1} (\frac{2}{3} ) \approx 33.7 ^\circ[/tex]
In which of the following cases is productive efficiency not satisfied? Assume we start at a point on the PPF between two products. Select the correct answer below: The economy switches to producing less of one product without increasing the production of the other product. The economy switches to producing at the point of intersection of the PPF and the vertical axis. The economy switches to producing more of one product and less of the other product but remains on the PPF. The economy switches to producing at the point of intersection of the PPF and the horizontal axis.
Answer:
A. The economy switches to producing less of one product without increasing the production of the other product
Step-by-step explanation:
PPC is the graphical representation of product combinations that an economy can produce, given resources & technology. It is downward sloping because given resources & technology, production of a good can be increased by decreasing production of other good.
It is based on assumption that resources are efficiently utilised. Points on PPC show resources efficient utilisation, Points under PPC show under utilisation, Points outside PPC are beyond country's productive capacity.
If country produces less of a good without increasing production of other goods, implying wasted resources & production below PPC. This case doesn't satisfy productive efficiency
Other cases : Producing more of a good & less of other is just re allocative movement on the PPC itself. Production point at PPF intersection with either axis implies economy is producing only the good on that axis.
In all the cases except A. satisfy the 'productive efficiency'
Estimate the value of the function at x = 4 given the following graph.
Yo sup??
The only way to solve this problem is by observing the graph closely and making some approximations.
We have to compare the value of x with the corresponding y value.
at x=4 you will find that the value of y is around 3.8-3.9
Therefore the answer is 3.8
Hope this helps.
Answer:
[tex]f(4) \approx 3.73[/tex]
Step-by-step explanation:
We can see that this function looks like a square root function but only shifted to the right by 1 and up by 2.
A square root function is:
[tex]f(x) = \sqrt{x}[/tex]
Shifting a function up means adding that value to the f(x):
[tex]f(x) = \sqrt{x}+2[/tex]
Shifting a function to the right means replacing a value x with the value (x-the value of shifting a function to the right):
[tex]f(x) = \sqrt{x-1}+2[/tex]
We can check that this really is a graph of a function [tex]f(x) = \sqrt{x-1}+2\\[/tex]:
[tex]f(1) = \sqrt{1-1}+2 = 0+2=2[/tex]
We can see on the graph that this really is the case : f(1)=2
Also,
[tex]f(2) = \sqrt{2-1}+2 = 1+2=3[/tex]
This is also the case if we check the graph.
So, now we have to estimate f(x) at x=4:
[tex]f(4) = \sqrt{4-1}+2 = \sqrt{3}+2[/tex]
where [tex]\sqrt{3} \approx 1.73[/tex] , hence:
[tex]f(4) \approx 1.73+2 = 3.73[/tex]
-5=x-3y
11=-3x+7y
This will be elimination
Answer:
Step-by-step explanation:
The given system of simultaneous equations is expressed as
-5=x-3y
11=-3x+7y
Rearranging both equations, it becomes
x - 3y = - 5- - - - - - - - - - 1
- 3x + 7y = 11 - - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by1, it becomes
3x - 9y = - 15 - - - - - - - - - - -3
- 3x + 7y = 11 - - - - - - - - - - - 4
Adding equation 3 to equation 4, it becomes
- 2y = - 4
Dividing the left hand side and the right hand side of the equation by
- 2, it becomes
- 2y/ - 2 = - 4y/- 2
y = 2
Substituting y = 2 into equation 1, it becomes
x - 3 × 2= - 5
x - 6 = - 5
Adding 6 to left hand side and the right hand side of the equation, it becomes
x - 6 + 6= - 5 + 6
x = 1
A square purple rug has a green square in the center. The side length of the green square is x inches. The width of the purple band that surrounds the green square is 2 in. What is the area of the purple band?
BLANK in^2
The area of the purple band is [tex]A = 4 - x^2[/tex]
The calculation is:Since both the shape contains the square so here the area square should be applied,
A = Total purple area - Total green area
[tex]A = (2)^2 - (x)^2\\\\A = 4 - x^2[/tex]
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Final answer:
The area of the purple band around the green square is calculated by finding the difference between the area of the larger purple square and the green square. It is determined by subtracting the green square's area (x²) from the total area of the larger square ((x + 4)²), resulting in an area of 8x + 16 square inches for the purple band.
Explanation:
To calculate the area of the purple band on the rug, we must first determine the dimensions of both the inner green square and the larger purple square that includes the band. The side length of the green square is given as x inches, and we know the width of the purple band surrounding it is 2 inches. To find the side length of the larger purple square, we add twice the width of the purple band (2 inches on each side) to the side length of the green square, giving us x + 2 + 2 or x + 4 inches.
The area of the larger purple square is therefore (x + 4)² square inches. The area of the inner green square is x² square inches. To find the area of just the purple band, we subtract the area of the green square from the area of the larger purple square.
So, the area of the purple band is (x + 4)² - x² square inches. Expanding this expression, we get x² + 8x + 16 - x² which simplifies to 8x + 16 square inches. Therefore, the area of the purple band around the green square is 8x + 16 in²
Maria ordered a pizza. She ate 2/9 of it and gave the remaining pizza to her 3 brothers. What fraction of the whole pizza will each of Maria's brothers receive if they share the remaining pizza equally?
A. 7/9
B. 3/7
C. 1/3
D. 7/27
E. 2/27
Answer:
D 7/27
Step-by-step explanation:
If Maria ate 2/9 of the pizza, that means she DIDN'T eat 7/9 of the pizza. So far so good? Ok, then you just need to find out what is 1/3 of 7/9, because the three brothers are dividing the leftover pizza equally, right? Hint - "of" usually means multiply. And remember multiplying fractions is lovely - you simply multiply the numerators together, then multiply the denominators together (no common denominator mumbo jumbo). So...
1/3 * 7/9 = 7/27.
Maria's brothers will each receive option D. 7/27 of the pizza.
To determine the fraction of the whole pizza each of Maria's brothers will receive, if they share the remaining pizza equally, follow these steps:
Maria ate 2/9 of the pizza, so the remaining fraction of the pizza is 1 - 2/9 = 7/9.The remaining pizza (7/9) is shared equally among her 3 brothers.To find the fraction each brother gets, divide 7/9 by 3. This can be done by multiplying 7/9 by the reciprocal of 3 (which is 1/3): (7/9) * (1/3) = 7/27Therefore, each of Maria's brothers will receive option D. 7/27 of the whole pizza.
Three numbers, of which the third is equal to 12, form a geometric progression. If 12 is replaced with 9, then the three numbers form an arithmetic progression. Find these three numbers.
Final answer:
To find the three numbers, we determine 'a' and 'r' using a system of equations derived from the conditions that they form a geometric progression with 12 and an arithmetic progression with 9. By solving these equations, we obtain the three numbers in sequence.
Explanation:
The question requires us to find three numbers that form a geometric progression with the third being 12, and when the third number is changed to 9, the numbers form an arithmetic progression.
Let's denote the first number as 'a' and the common ratio of the geometric progression as 'r'. The three numbers in the geometric progression can be represented as 'a', 'ar', and 'ar^2'. Given that the third number is equal to 12, we have 'ar^2 = 12'.
When 12 is replaced with 9 to form an arithmetic progression, the common difference 'd' can be found by subtracting the first term from the second term. The three numbers in this sequence are 'a', 'a + d', and 'a + 2d'. Given that the third number is now 9, we have 'a + 2d = 9'.
To find 'a' and 'r', we can set up a system of equations using the fact that the second number in both progressions is the same. So 'ar = a + d'. We have the following system:
ar^2 = 12 (1)
a + 2d = 9 (2)
ar = a + d (3)
From equation (3), we can solve for 'd' in terms of 'a' and 'r': 'd = ar - a = a(r - 1)'. Substituting 'd' in equation (2), we get 'a + 2(a(r - 1)) = 9', which simplifies to 'a(2r + 1) = 9'.
Using this new equation along with equation (1), we solve for 'a' and 'r' to find the three numbers:
a(2r + 1) = 9 (4)
ar^2 = 12 (1)
From equation (1), 'a = 12/r^2'. Substituting this into equation (4) gives us a single equation: '12/r^2(2r + 1) = 9', which we can solve to find 'r', and subsequently, 'a'. After solving these, we find the three numbers that form both the geometric and arithmetic progressions.
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Find m∠E.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠E = °
Answer:
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle,
DE represents the hypotenuse of the right angle triangle.
With m∠E as the reference angle,
EF represents the adjacent side of the right angle triangle.
DF represents the opposite side of the right angle triangle.
To determine m∠E, we would apply
the Tangent trigonometric ratio.
Tan θ = opposite side/adjacent side. Therefore,
Tan E = 8/5 = 1.6
E = Tan^-1(1.6)
W = 58.0° to the nearest tenth.
Write a system of equations (3 points) for the problem below and then solve it The candy shack has 20 lb. Of mixed white and dark chocolate worth $7.50 per pound. White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. How many pounds of each are in the mixture?
Answer: the mixture contained 15 pounds of white chocolate and 5 pounds of dark chocolate.
Step-by-step explanation:
Let x represent the number of pounds of white chocolate in the candy shack mixture.
Let y represent the number of pounds of dark chocolate in the candy shack mixture.
The candy shack has 20 lb of mixed white and dark chocolate. This means that
x + y = 20
The 20lb mixture is worth $7.50 per pound. This means that the total cost of the mixture is
20 × 7.50 = $150
White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. This means that
8x + 6y = 150 - - - - - - - - - - - - - -1
Substituting x = 20 - y into equation 1, it becomes
8(20 - y) + 6y = 150
160 - 8y + 6y = 150
- 8y + 6y = 150 - 160
- 2y = - 10
y = - 10/ - 2
y = 5
x = 20 - y = 20 - 5
x = 15
Barry runs at an average rate of 8 mi/hr. He walks at an average rate of 3 mi/hr. If x represents the time spent running and y represents the time spent walking, write a linear equation that relates the time he could spend running and walking if he travels a total distance of 16 miles
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Work Shown:
x = number of hours spent running
8x = distance he runs (since he runs at 8 mph)
y = number of hours spent walking
3y = distance he walks (he walks at a speed of 3 mph)
8x+3y = total distance = 16 miles
8x+3y = 16
This equation is in standard form Ax+By = C
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Extra Info
Solving for y will get
8x+3y = 16
3y = -8x+16
y = (-8x+16)/3
y = (-8x)/3+16/3
y = (-8/3)x+16/3
This is in slope intercept form y = mx+b
m = -8/3 is the slope
b = 16/3 is the y intercept
A researcher records the levels of attraction for various fashion models among college students. He finds that mean levels of attraction are much higher than the median and the mode for these data. a. What is the shape of the distribution for the data in this study? b. What measure of central tendency is most appropriate for describing these data? Why?
Answer:
a) Positively skewed
b) Median
Step-by-step explanation:
We are given the following in the question:
For a particular data, mean levels of attraction are much higher than the median and the mode for these data.
[tex]\text{Mean} > \text{Median}\\\text{Mean} > \text{Mode}[/tex]
a) Shape of data
Since the mean of data is greater than the median and mode of the data, thus, is a skewed data.
For a positively skewed data:
[tex]\text{Mean} > \text{Median} > \text{Mode}[/tex]
Thus, the given data is positively skewed data.
b) Measure of central tendency
Since it is a positively skewed data, median is a better measurement of central of tendency.
Advantage of median:
The median is less affected by outliers and skewed data than the mean.Final answer:
The data likely has a right-skewed distribution, making the median the most suitable measure of central tendency due to the impact of outliers.
Explanation:
a. What is the shape of the distribution for the data in this study?
The data distribution is likely skewed to the right, as the mean is much higher than the median and mode, indicating a long tail to the right.
b. What measure of central tendency is most appropriate for describing these data? Why?
In this case, the median is the most appropriate measure of central tendency because it is less affected by extreme values compared to the mean. Since the mean is much higher than the median and mode, it suggests outliers are pulling the mean upwards.