Answers
Answer:
View Image
Step-by-step explanation:
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Related Questions
What is the probability of rolling a die twice, and having it land on a number greater than 1 both times?
Answers
Answer: 25/36
Step-by-step explanation:
A die has six faces, therefore its sample space S is 6
Since we are rolling a die twice(at different times), the probability of one turning up the first time is 1/6(i.e expected outcome/total outcome)
Similarly, if we throw the die the second time, the probability of one turning up the second time is also 1/6
The probability of having number greater than 1 land at each time will be (1- 1/6) which is 5/6.
Therefore the probability of having number greater than 1 land at "both times" will be 5/6×5/6 = 25/36
Newton’s law of cooling states that for a cooling substance with initial temperature T0 , the temperature T(t) after t minutes can be modeled by the equation T(t)=Ts+(T0−Ts)e−kt , where Ts is the surrounding temperature and k is the substance’s cooling rate.A liquid substance is heated to 80°C . Upon being removed from the heat, it cools to 60°C in 12 min.What is the substance’s cooling rate when the surrounding air temperature is 50°C ?The substances cooling rate when the surrounding air temperature is 50C is 0.0916.0.06870.07320.08130.0916
Answers
Answer:
k = 0.0916
Step-by-step explanation:
T(t) = [tex]T_{s} + ( T_{o} - T_{s} )e^{-kt}[/tex]
from question; t = 12 mins , [tex]T_{s}[/tex] = 50 C , [tex]T_{o}[/tex] = 80 C , T = 60 C
60 = 50 + (80 - 50) [tex]e^{-12k}[/tex]
60-50 = 30 [tex]e^{-12k}[/tex]
10/30 = [tex]e^{-12k}[/tex] (Taking natural Log of both sides)
In(0.3333) = In [tex]e^{-12k}[/tex]
-1.0986 = -12k
k = 0.0916
If a player rolls 2 dice and gets a sum of 2 or 12, he wins $30. If the person gets a 7, he wins $10. Otherwise he wins nothing. If the cost to play the game is $3, what does a player expect to get out of this game every time he/she plays?
Answers
If they were to win $30 they would expect to get $27 in profit.
If they were to win $10 they would expect $7.
If they were to win $0 they would expect $-3 in profit, so technically if they win nothing they lose money.
Hope I could help! :D
If player expect to get out of this game every time he/she plays then they would loose money.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
If a player rolls 2 dice and gets a sum of 2 or 12, he wins $30.
and, If they were to win $30, they would anticipate making a profit of $27.
Also, if they would anticipate $7 if they were to win $10.
So, if they were to win nothing, they would lose money because they would expect to make $-3 in profit.
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to find the probability of flipping heads at least once if you flip a coin two times. The possible outcomes (we don't care about the order) are (each equally likely) TT, TH, HT, HH. Three out of four have an H in them, so the probability is 34. Is this correct? Is there a better and efficient way (especially when dealing with a higher number of flips? Please use only very basic terminology and concepts from probability because I've never taken a class.
Answers
Answer:
The probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
The probability of an event, say E, is the ratio of the favorable outcomes to the total number of outcomes, i.e.
[tex]P (E) = \frac{Favorable\ outcomes}{Total\ outcomes}[/tex]
The sample space of flipping two coins is:
S = {HH, HT, TH and TH}
Total number of outcomes = 4
Compute the probability of flipping Heads at least once as follows:
Let X = heads.
P (X ≥ 1) = P (X = 1) + P (X = 2)
[tex]=\frac{2}{4}+\frac{1}{4} \\=\frac{3}{4}[/tex]
Thus, the probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].
The experiment of flipping a coin is a binomial experiment.
Since there are only two outcomes of the experiment, either a Heads or a Tails.
So if X is defined as the number of heads in n flips of a coin then the random variable X follows a binomial distribution with probability p = 0.5 of success.
Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day how long do they need to ride on the third day to make their goal of biking a total of 20 hours in the park
Answers
Answer:
Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.
Step-by-step explanation:
Given:
Goal of Total number of hours of biking in park =20 hours.
Number of hours rode on first day = [tex]5\frac34 \ hrs.[/tex]
So we will convert mixed fraction into Improper fraction.
Now we can say that;
To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.
[tex]5\frac34 \ hrs.[/tex] can be Rewritten as [tex]\frac{23}{4}\ hrs[/tex]
Number of hours rode on first day = [tex]\frac{23}{4}\ hrs[/tex]
Also Given:
Number of hours rode on second day = [tex]6\frac45 \ hrs[/tex]
[tex]6\frac45 \ hrs[/tex] can be Rewritten as [tex]\frac{34}{5}\ hrs.[/tex]
Number of hours rode on second day = [tex]\frac{34}{5}\ hrs.[/tex]
We need to find Number of hours she need to ride on third day in order to achieve the goal.
Solution:
Now we can say that;
Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.
framing in equation form we get;
Number of hours she need to ride on third day = [tex]20-\frac{23}{4}-\frac{34}{5}[/tex]
Now we will use LCM to make the denominators common we get;
Number of hours she need to ride on third day = [tex]\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}[/tex]
Now denominators are common so we will solve the numerator we get;
Number of hours she need to ride on third day =[tex]\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.[/tex]
Hence Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.
Final answer:
Rebecca and Dan need to ride for 7 9/20 hours on the third day to reach their goal of biking a total of 20 hours in the national park, having already biked 5 3/4 hours on the first day and 6 4/5 hours on the second day.
Explanation:
Rebecca and Dan are biking in a national park and want to achieve a goal of biking a total of 20 hours over three days. They biked 5 3/4 hours on the first day and 6 4/5 hours on the second day. To find the time they need to bike on the third day, we first convert the hours they biked into improper fractions:
First day: 5 3/4 hours = (5×4 + 3)/4 = 23/4 hoursSecond day: 6 4/5 hours = (6×5 + 4)/5 = 34/5 hoursNext, we add these two amounts together:
(23/4) + (34/5) = (23×5 + 34×4) / (4×5) = (115 + 136) / 20 = 251/20 hours.
Now we convert 251/20 hours to a mixed number:
251/20 = 12 11/20 hours
They have biked a total of 12 11/20 hours over the first two days. Their total goal is 20 hours, so we need to subtract the time already biked from the total goal:
20 hours - 12 11/20 hours = (20×20 - 12×20 - 11)/20 = (400 - 240 - 11)/20 = 149/20 hours.
Finally, we convert 149/20 hours back to a mixed number to find out how long they need to ride on the third day:
149/20 hours = 7 9/20 hours.
So, Rebecca and Dan need to ride for 7 9/20 hours on the third day to meet their goal of biking a total of 20 hours in the park.
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
Answers
To figure this out, use the acronym SOHCAHTOA to determine which trigonometric function to use.
8 is opposite to <R and 3 is adjacent to <R so we use tangent.
Set up the following equation: tan(x)=8/3
Find the inverse (aka. tan^-1): x=69.44
So your answer is <R=69.4 degrees
Hope this helped!
It takes painter A 3 hours to paint a certain area of a house. It takes painter B 5 hours to do the same job. How long would it take them, working together, to do the painting job?
Answers
Answer:
Step-by-step explanation:
First step is to read the question thoroughly and make sure you understand it alright. Second step is to get paper and a pencil and write down the question. Third step is to grab a calculator if you don't have one then try to use addition. Fourth step is to write down the problem which is 3 + 5 = 8 so that equals 8 as u can see. Fifth step is to write the answer and there is your answer hopefully i helped out thank you for having patients Have a Great EveningIt would take them 8 hours to complete the painting task if they worked together.
What is the addition operation?The addition operation in mathematics adds values on each side of the operator.
For example 4 + 2 = 6
If painter A can paint the area in 3 hours, and painter B can paint the same area in 5 hours, then it would take them a total of 3+5=8 hours to paint the area together.
It's worth noting that this assumes that both painters are able to work at their full capacity while working together and that they are able to divide the work between them in an efficient manner. If either of these conditions is not met, it could take them longer than 8 hours to complete the job.
Hence, working together, it would take them 8 hours to complete the painting job.
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Since f(x, y) = 1 + y2 and "∂f/∂y" = 2y are continuous everywhere, the region r in theorem 1.2.1 can be taken to be the entire xy-plane. use the family of solutions in part (a) to find an explicit solution of the first-order initial-value problem y' = 1 + y2, y(0) = 0.
Answers
Answer:
The solution to the differential equation
y' = 1 + y²
is
y = tan x
Step-by-step explanation:
Given the differential equation
y' = 1 + y²
This can be written as
dy/dx = 1 + y²
Separate the variables
dy/(1 + y²) = dx
Integrate both sides
tan^(-1)y = x + c
y = tan(x+c)
Using the initial condition
y(0) = 0
0 = tan(0 + c)
tan c = 0
c = tan^(-1) 0 = 0
y = tan x
In this exercise we have to use our knowledge of differential equations to calculate the value of the first solution, so we have to:
[tex]y = tan x[/tex]
Then say the differential equation as:
[tex]y' = 1 + y^2[/tex]
then rewriting as:
[tex]dy/dx = 1 + y^2\\dy/(1 + y^2) = dx[/tex]
Integrate both sides, we have that:
[tex]tan^{(-1)}y = x + c\\y = tan(x+c)[/tex]
So we already have a preview of the solution, so we will have to apply the initial conditions and this results in:
[tex]y(0) = 0\\0 = tan(0 + c)\\tan c = 0\\c = tan^{(-1)} 0 = 0\\y = tan x[/tex]
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If you run around the house randomly and then end up back where you started moving a total of 44 meters what is distance and what is change in position
Answers
Answer:
Distance = 44 m
Change in position = 0 m
Step-by-step explanation:
Given:
Running around the house covering a total length of 44 m and reaching the same position where you started.
So, initial position is same as final position.
Change in position is given as:
Change = Final position - Initial position
Now, since, final position = Initial position.
So, Change in position = 0 m
Now, distance is the total length of the path covered. So, you started from your initial position and ran around the house covering a path length of 44 m before reaching the same starting position.
Therefore, the distance is equal to the path length and hence is equal to 44 meters
INPUT SU,0 IF OFF OUTPUT M,0 OUTPUT T,0 OUTPUT W,0 OUTPUT TH,0 OUTPUT F,0 ELSE ON OUTPUT M,0 OUTPUT T,0 OUTPUT W,0 OUTPUT TH,0 OUTPUT F,0 ENDIF INPUT M,0 INPUT T,0 INPUT W,0 INPUT TH,0 INPUT F,0 OR OR OR OR INPUT SA,0 INPUT SU,0 AND NOT OR ON OUTPUT SU,0 OFF OUTPUT SU,0 END
Answers
Solve the equation and check the solution . X-13.8=-20.4 the solution set is ?
Answers
Answer:
The answer is x = -6.6
Step-by-step explanation:
Answer:
X= -6.6
Step-by-step explanation:
Just do 13.8 - 20.4. It will equal -6.6.
find the equation of the line that is perpendicular to y=3x and passes through the point (4,-2)
Answers
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
y = 3x
Comparing with the slope intercept form, slope = 3
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.
Therefore, the slope of the line passing through (4,-2) is - 1/3
To determine the intercept, we would substitute m = - 1/3, x = 4 and
y = -2 into y = mx + c. It becomes
- 2 = - 1/3 × 4 + c = 4/3 + c
c = - 2 + 4/3 = - 2/3
The equation becomes
y = - x/3 - 2/3
Start of Questions
Write sinπ/5cosπ/8+cosπ/5sinπ/8 as a trigonometric function of one number. Keep π in your answer. Be sure to PREVIEW your answer before submitting!
Answers
Answer:
sin(13π/40)
Step-by-step explanation:
The given expression matches the pattern ...
sin(a)cos(b) +cos(a)sin(b) = sin(a+b)
Then ...
sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)
= sin(13π/40)
_____
π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)
The trigonometric expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 can be simplified to sin(13π/40) by using the sine addition formula.
Explanation:The expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 resembles the formula for the sine of a sum, sin(a+b) = sin(a)cos(b) + cos(a)sin(b). By applying this trigonometric identity, we can rewrite the expression as the sine of a single angle. Therefore, sinπ/5 cosπ/8 + cosπ/5 sinπ/8 is equivalent to sin(π/5 + π/8). To simplify it further, we must find a common denominator for the two angles, π/5 and π/8, which is 40. Thus, we get sin((8π + 5π)/40), which simplifies to sin(13π/40).
PLEASE HE LPPP!!! QUESTION AND ANSWERS IN PICTURE !!2
Answers
Answer:
Line ED
Explanation:
Opposite side is EF (because its opposite to the angle)
Hypotenuse side id FD (opposite of right angle)
Adjacent is the line leftover
Answer:
B
Step-by-step explanation:
Adjacent is the one with 90° and the angle, theta
ED in this case
Depending on the product, there may be a person who act as__________ a(n) in the buyer center, often by providing specifications for the product being purchased or the vendor being considered.
Answers
Answer:
Influencer
Step-by-step explanation:
An influencer is a person who has the power affect purchase decisions of others because of his ability such as knowledge, position with audience.
Final answer:
A person acting as a specifier in the buying center provides product specifications and may influence the purchase decision by setting requirements, interacting with both customer and seller but not making final purchasing decisions.
Explanation:
Depending on the product, there may be a person who acts as specifier in the buying center, often by providing specifications for the product being purchased or the vendor being considered.
A specifier plays a crucial role in the procurement process, ensuring that the product or service meets the organization's needs and standards. In a buying center, this individual might not have the authority to make final purchase decisions but is influential by setting the requirements that the potential products or suppliers must meet.
A specifier may interact closely with both the customer and seller to ensure that the right features, quality, and functionalities are captured in the procurement specifications.
This person may also assess the long-term reliability of supplier relationships, such as through exclusive dealer agreements, to safeguard the company's interests. The role of the specifier is analogous to that of a product consultant, providing insights without directly engaging in sales or price negotiations.
Solve the inequality 1 2p + 7 ) 1 39
Answers
Answer: p=11
Step-by-step explanation:
12p+7)139
-7 -7
12p)132
÷12 ÷12
P)11
Answer:
p= 11
Step-by-step explanation:
1 2p + 7 > 1 39
collection of like term
12p > 139 - 7
12p > 132
Divide both side by the coefficient of p
12p/12 > 132/12
p = 11
30 POINTS AND RAINLIEST! URGENT DUE IN 30 MINS!
Koji is installing a rectangular window in an office building. The window is 823 feet wide and 534 feet high.
The formula for the area of a rectangle is A=bh.
I NEED A FRACTION!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the area of the window?
Enter your answer as a mixed number in simplest form in the box.
$$
Answers
Answer:
We have: b = 823 foot
h = 534 Ft ,
Substitute their values,
A = 823 * 534
A = 439482 Ft² briefly, Your Answer would be: 439482 Ft²
~
For a fraction;
49 and 10/12
multiply 8 and 2/3 by 5 and 3/4!
Determine the point of discontinuity if it exists
v(x)=x^2-25/2x^2+13x+15
Answers
Answer:
x=-5 and x=-1.5
Step-by-step explanation:
The given function is
[tex]v(x) = \frac{{x}^{2} - 25}{2 {x}^{2} + 13x + 15} [/tex]
The points of discontinuity occurs at where the denominator is zero.
[tex]2 {x}^{2} + 13x + 15= 0[/tex]
We solve by factoring.
We first split the middle term:
[tex]2 {x}^{2} + 3x + 10x + 15= 0[/tex]
We factor by grouping:
[tex]x(2x + 3) + 5(2x + 3)= 0[/tex]
[tex](x + 5)(2x + 3) = 0[/tex]
The points of discontinuity occur at x=-5, and x=-1.5
Final answer:
The function v(x) has discontinuities at x = -3 and x = -5/2.
Explanation:
A point of discontinuity in a mathematical function refers to a location where the function fails to be continuous. In other words, it's a point at which the function exhibits a break or abrupt change in its behavior.
The point of discontinuity for the function [tex]v(x) = (x^2-25)/(2x^2+13x+15)[/tex] can be found by setting the denominator equal to zero and solving for x. In this case, the denominator factors to (x+3)(2x+5), indicating discontinuities at x = -3 and x = -5/2. These are the points where the function is not defined.
Points of discontinuity are essential to understanding the behavior and properties of functions, particularly in areas like calculus and real analysis. They are critical in identifying where a function fails to meet the criteria for continuity and in analyzing the behavior of functions in various contexts.
a wise man once said, “ 400 reduced by 3 times my age is 163”. what is his age?
Answers
400-3x=163
-3x=-400+163
-3x=-237
/-3
x=79
age is 79 years
Answer:
79 years old
Step-by-step explanation:
Let his age be x
400-3x=163
400-163=3x
237=3x
Divide both side by 3
237/3 =3x/3
79=x
The man's age (x) =79 years old
8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?
Answers
The probability of selecting the 8 tallest players randomly from a list of 27 is found by dividing the single way to choose the tallest players by the number of ways to choose any 8 players from 27, calculated using the combination formula C(n, k).
To determine the probability that the 8 tallest players will be selected from a list of 27 players, we need to consider the combinatorial aspect of the selection process. Since the selection is random, any group of 8 players can be chosen. The total number of ways to select 8 players out of 27 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of players (27), and k is the number of players to be selected (8).
Firstly, the number of ways to choose the 8 tallest players is 1, since there is only one group of the 8 tallest players. Secondly, we calculate the total number of ways to choose any 8 players from the 27, which is C(27, 8). We can then find the probability by dividing the number of ways to choose the tallest players by the total number of ways to choose any group of 8 players.
Using the combination formula, C(27, 8) is calculated as:
27! / (8! * (27-8)!)
= 27! / (8! * 19!)
Factor out the common terms from the numerator and denominator
The remaining terms give us the total number of combinations
The probability is therefore: 1 / C(27, 8).
Red apples cost $1.20 per pound green apple cost 1.50$ per pound what is the total cost if you buy 3 pounds of red apples and 2 pounds of green apples
Answers
6.60 would be the total cost for both 3 pounds and two pounds :D
Answer:
$6.60
Step-by-step explanation:
multiply 1.20 (red apples) by 3 (lbs) = 3.6
and 1.50 (green apples) times 2 (lbs) = 3
then add the two totals = $6.60
Since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year. Predict the number of cases that will be reported in 2020 and the trend continues
Answers
Answer:
20,158 cases
Step-by-step explanation:
Let [tex]t=0[/tex] represent year 2010.
We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.
Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.
We can represent this information in an exponential decay function as:
[tex]F(t)=102,390(1-0.15)^t[/tex]
[tex]F(t)=102,390(0.85)^t[/tex]
To find number of cases in 2020, we will substitute [tex]t=10[/tex] in our decay function as:
[tex]F(10)=102,390(0.85)^{10}[/tex]
[tex]F(10)=102,390(0.1968744043407227)[/tex]
[tex]F(10)=20,157.970260446597\approx 20,158[/tex]
Therefore, 20,158 cases will be reported in 2020.
Refer to the following breakdown of responses to a survey of room service in a hotel: Response - Frequency Not satisfied - 20 Satisfied - 40 Highly satisfied - 60 What percentage of the responses indicated that customers were satisfied?A. 40%B. 33%C. 50%D. 100%
Answers
Answer: B. 33%
Step-by-step explanation:
Given : Response - Frequency
Not satisfied - 20
Satisfied - 40
Highly satisfied - 60
Total customers = (Number of customers Not satisfied) + (Number of customers satisfied) + ( (Number of customers Highly satisfied) )
= 20+40+60=120
Now , the percentage of the responses indicated that customers were satisfied = [tex]\dfrac{\text{Number of customers are satisfied}}{\text{Total customers}}\times100[/tex]
[tex]=\dfrac{40}{120}\times100=33.33\%\approx33\%[/tex]
Hence, the percentage of the responses indicated that customers were satisfied = 33%
Thus , the correct answer is B. 33%
To find the percentage of customers who were satisfied, add up all responses, calculate the fraction of satisfied responses, then convert that to a percentage. The answer is 33%.
Explanation:To find out what percentage of the responses indicated that customers were satisfied, we first need to add up all the responses. This would include those who were Not satisfied, Satisfied, and Highly satisfied. The total number of responses will be 20 (Not satisfied) + 40 (Satisfied) + 60 (Highly satisfied) = 120 responses in total.
Next, we find the fraction of responses that were satisfied. For this, we divide the number of Satisfied responses (40) by the total number of responses (120). That gives us 40/120 = 0.333 or one-third.
To convert this fraction to a percentage, we simply multiply by 100. So, 0.333 x 100 = 33.3%, which rounds down to 33%. Thus, the answer to the question is 33%, option - B.
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The function f(x) = Negative Startroot x EndRoot is shown on the graph.
On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the left through (4, negative 2).
Which statement is correct?
The domain of the function is all real numbers less than or equal to −1.
The range of the function is all real numbers greater than or equal to 0.
The range of the function is all real numbers less than or equal to 0.
The domain of the function is all real numbers less than or equal to 0.
Answers
Answer:
the answer is c
Step-by-step explanation:
i took the test and got a 100
The range of the function is all real numbers less than or equal to 0.
A function is an expression that shows the relationship between two or more variables or numbers.
The domain of a function is the set of input values while the range is the set of output values.
From the graph, The range of the function is all real numbers less than or equal to 0.
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1. Determine whether the lines given by the equations 2x + 3y = and y=3/2x+4
are perpendicular.
2. Two lines having the same -intercept are perpendicular. If the equation of one of
these lines is y= −4/5x+6, what is the equation of the second line?
Answers
Answer:
1. Yes, the lines are perpendicular.
2. [tex]y=\frac{5}{4}x+6[/tex]
Step-by-step explanation:
The first equation of Exercise 1 is incomplete. Let's assume that it is:
[tex]2x + 3y =n[/tex]
Where "n" is a number.
First, it is important to remember that the equation of a line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
By definition, the slopes of perpendicular lines are negative reciprocals.
1 . If you solve for "y" from the first equation, you get:
[tex]2x + 3y =n\\\\3y=-2x+n\\\\y=-\frac{2}{3}x+\frac{n}{3}[/tex]
You can identify that the slope is:
[tex]m=-\frac{2}{3}[/tex]
The second equation of the line is:
[tex]y=\frac{3}{2}x+4[/tex]
And its slope is:
[tex]m=\frac{3}{2}[/tex]
Since the slopes are negative reciprocals, the lines are perpendicular.
2. Given the first equation of the line:
[tex]y= -\frac{4}{5}x+6[/tex]
You can identify that:
[tex]m=-\frac{4}{5}\\\\b=6[/tex]
Since the first line and the second one are perpendicular, you know that the slope of the other line is:
[tex]m=\frac{5}{4}[/tex]
According to the information given in the exercise, both lines have the same y-intercept; therefore, the equation of the second line is:
[tex]y=\frac{5}{4}x+6[/tex]
A 72.5-foot rope from the top of a circus tent pole is anchored to the ground 44.4 feet from the bottom of the pole. What angle does the rope make with the pole? (Assume the pole is perpendicular to the ground.
Answers
sinx = 43.2/72.5
=> x = 36.57 degrees
Ella finished a bike race in 37.6 minutes. Miranda finished the race 9 1/10minutes sooner than Ella finished it. How many minutes did it take Miranda to finish the race
Answers
Answer:
x = 28.5 minutes
Step-by-step explanation:
Let x be the time taken for finishing the bike race.
Given:
Ella finished a bike race = 37.6 minutes
Miranda finished the race sooner than Ella = [tex]9\frac{1}{10} = \frac{91}{10} = 9.1\ minutes[/tex]
We need to find the minutes did it take Miranda to finish the race.
Solution:
From the statement, Miranda finished the race 9.1 minutes sooner than Ella finished it while Ella finished the same bike race in 37.6 minutes.
So, time taken by Miranda to finish the race:
[tex]Mirianda\ finshed\ a\ bike\ race = (Ella\ finshed\ a\ bike\ race) - 9.1[/tex]
[tex]x=37.6-9.1[/tex]
x = 28.5 minutes
Therefore, Miranda finished the bike race in 28.5 minutes.
The graph shows the distance y, in centimeters, a pendulum moves to the right (positive displacement) and to the left (negative displacement), for a given number of seconds x.
How many seconds are required for the pendulum to swing from its position furthest to the right to its position furthest to the left?
Answers
It's 1.25 seconds, I just took the test and got 100% Good Luck!!! :)
A 63 liter mixture contains milk and water in a ratio of 4:5. then x liters of milk and y liters of water are added to the mixture, resulting in a milk to water ratio of 7:5. finally , 60 liters of the mixture are drained and replaced with 60 liters of water, resulting in a milk to water ratio of 7:8. what is the value of x+y ?
Answers
Answer:
X+y=237Litres
Step-by-step explanation:
Let a be mixture of milk and water.
Let x =milk
Let y= water
z = x+y
Final volume of mixture =63litres + z
5/12(3+z))+60=8/15(63-z)
z =x+y= 237litres
The value of [tex]x+y[/tex] is 237 liters.
Given information:
A 63 liter mixture contains milk and water in a ratio of 4:5.
Let the initial amount of water be a. So, the amount of milk will be [tex]63-a[/tex].
The initial mixture can be written as,
[tex]\dfrac{63-a}{a}=\dfrac{4}{5}[/tex]
The initial amount of water and milk will be,
[tex]\dfrac{63-a}{a}=\dfrac{4}{5}\\315-5a=4a\\9a=315\\a=35\\63-a=28[/tex]
x liters of milk and y liters of water are added to the mixture, resulting in a milk to water ratio of 7:5.
The mixture, now, can be written as,
[tex]\dfrac{28+x}{35+y}=\dfrac{7}{5}\\140+5x=245+7y[/tex]
60 liters of the mixture are drained and replaced with 60 liters of water, resulting in a milk to water ratio of 7:8.
Draining will release the amount of water and milk in the ratio 7:5 which is its concentration. So, 35 liters of milk and 25 liters of water will be drained.
The final mixture can be written as,
[tex]\dfrac{28+x-35}{35+y-25+60}=\dfrac{7}{8}\\\dfrac{x-7}{y+70}=\dfrac{7}{8}\\8x-56=7y+490[/tex]
Solve for x and y as,
[tex]140+5x=245+7y\\8x-56=7y+490\\3x-196=245\\x=147\\y=90[/tex]
So, the value of [tex]x+y[/tex] will be,
[tex]x+y=147+90\\=237[/tex]
Therefore, the value of [tex]x+y[/tex] is 237 liters.
For more details, refer to the link:
https://brainly.com/question/11897796
Students who attend Washington Middle School are either in seventh or eighth grade. At the end of the first semester 25% of the students at Washington Middle School were on the honor roll. Seventh graders represented 60% 60 % of the students on the honor roll. If 124 124 students on the honor roll were in eighth grade, how many students attend Washington Middle School? There are students who attend Washington Middle School.
Answers
Answer:
There are 1240 students who attended Washington Middle School.
Step-by-step explanation:
Given:
Students who attend Washington Middle School are either in seventh or eighth grade.
At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.
Seventh graders represented 60% of the students on the honor roll.
If 124 students on the honor roll were in eighth grade.
Now, to find the students attend Washington Middle School.
Let the total number of students be [tex]x.[/tex]
So, the students at Washington Middle School were on the honor roll:
25% of [tex]x[/tex]
[tex]=\frac{25}{100} \times x[/tex]
[tex]=\frac{25x}{100}[/tex]
[tex]=\frac{x}{4}[/tex]
As, given seventh graders represented 60% of the students.
So, the students on the honor roll represented as seventh graders:
[tex]60\%\ of\ \frac{x}{4}[/tex]
[tex]=\frac{60}{100} \times \frac{x}{4}[/tex]
[tex]=0.6\times \frac{x}{4}[/tex]
[tex]=\frac{0.6x}{4}[/tex]
As, 124 students on the honor roll were in eighth graders.
Thus,
According to question:
[tex]\frac{x}{4} -\frac{0.6x}{4} =124[/tex]
[tex]\frac{x-0.6x}{4} =124[/tex]
[tex]\frac{0.4x}{4} =124[/tex]
Multiplying both sides by 4 we get:
[tex]0.4x=496[/tex]
Dividing both sides by 0.4 we get:
[tex]x=1240.[/tex]
Therefore, there are 1240 students who attended Washington Middle School.