When a stone is dropped from a height, the time taken to fall, t, is proportional to the square root of the distance fallen, d.

Write down a formula, using k, connecting the time taken to fall and the distance traveled.

To reflect the triangle AGH across the x-axis, we need to keep the x-coordinates the same but negate the y-coordinates. So, the new coordinates of G' (the image of G) would be (-2, -3), the new coordinates of H' would be (-1, -2), and the new coordinates of A' would be (-3, -1). Now, to find the coordinates of W, we need to determine the intersection of the lines GH' and A'G'. To do this, we need to first find the equations of these lines.

The equation of a line can be found using the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula:
m = (y2 - y1) / (x2 - x1) For line GH', the two points are G(-2, 3) and H'(-1, -2). So, the slope of GH' is: mGH' = (-2 - 3) / (-1 - (-2)) = -5 / 1 = -5

Since the slope is 0, the line is horizontal and its equation is simply y = -1 (which is also the y-coordinate of A').
Now, to find the intersection of GH' and A'G', we can set their equations equal to each other and solve for x:
the y-coordinate of W, we can plug x = -6/5 into either equation:
y = -5(-6/5) - 7 = 1
the coordinates of W are (-6/5, 1).

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The outcome of a simulation experiment is a probability distribution for one or more output measures.

Simulation experiments involve using computer models to imitate real-world processes and study their behavior. The output measures are the results generated by the simulation, and their probability distribution is a statistical representation of the likelihood of obtaining a particular result. This information is useful in decision-making, as it allows analysts to assess the potential impact of different scenarios and identify the most favorable outcome. To determine the probability distribution, the simulation is run multiple times with varying input values, and the resulting outputs are analyzed and plotted. The shape of the distribution indicates the degree of uncertainty associated with the outcome.

The probability distribution obtained from a simulation experiment provides valuable information about the likelihood of different outcomes and helps decision-makers make informed choices.

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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The group of participants who are not exposed to the independent variables are the known as the control group.

Good luck! :)

120 will be the shape of the sampling distribution.

Quantitative data's distribution shape may be characterized as having a logical order to the numbers and allowing for the identification of the "low" and "high" end values on the histogram's x-axis. Since qualitative data are not numerical, the distribution shape cannot be specified.

Given that,

Sample size of A, n = 200

Sample size of B, n = 100

Proportion of adults in district A = 60%

Proportion of adults in district B = 45%

In the sample size of 200, the number of adults that support a new ballot measure is:

= (60%) × 200

= 120

Those that oppose is:

= 200 -120

= 80

If 45% supports a new ballot measure in district B, then 55% do not support. The difference between those that support and do not support is:

(55% - 45%) × 100

= 10

Hence, the sampling distribution of p(A) and p(B) is approximately normal, because the number of success in district A is 120.

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Answer:

680

Step-by-step explanation:

x = total number

.6x  = bus riders = 408              (.6 is decimal for 60%)

.6x = 408

x = 408/.6 = 680

Answer:

b= -9

Step-by-step explanation:

Plug in -9 for b.

3= -9+12

Solve.

3=3

Since both sides are equal, the answer is -9

I hope this helped you ;)

Answer:

0.6

Step-by-step explanation:

first you well have a 3 and then dived it by 5 and after you dived them to you well get the answer 0.6

The calculated area of the cross-section is 14 square inches

from the question, we have the following parameters that can be used in our computation:

The prism (see attachment 1)

When a vertical plane intersects the vertex and the shorter edge of the base, the shape formed is a triangle with the following dimensions

Base = 7 inches

Height = 4 inches

See attachment 2

So, we have

Area = 1/2 * 7 * 4

Evaluate

Area = 14

Hence, the area of the cross-section is 14 square inches

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Answer:

uhhhhhhh nice

Step-by-step explanation:

Answer:

Just why

Step-by-step explanation:

Answer:

Problem 1: 120

Problem 2: 145%

Problem 3: 6

Problem 4: 17 %

Problem 5: 122.4

Problem 6: When the school raised $6750 the goal was 5400.

Problem 7: There is a 5% sales tax.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

Problem 1:
120

Problem 2:
145%

Problem 3:
6

Problem 4:
17 %

Problem 5:
122.4

Problem 6:

When the school raised $6750 the goal was 5400.

Problem 7:
There is a 5% sales tax.

Step-by-step explanation:

Have a great rest of your day
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The required possible amount that she spends additionally is more than $8.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

Elsa will spend more than $25 on gifts. So far, she has spent $17.

Let the possible additional amounts she will spend be x,
According to the quesiton,
x + 17 > 25
x > 25 - 17
x > 8

Thus, the required possible amount that she spends additionally is more than $8, as of the given condition.

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Student 1 made measurements with the least variability after performing the natural logarithm transformation on each measurement taken by the four students.

To determine which student made measurements with the least variability, we need to calculate the standard deviation for each student's set of measurements.

First, we calculate the natural logarithm of each measurement for all three students and compute their means

Student 1: ln(6.8), ln(6.3), ln(5.8), ln(5.8), ln(6.8)

Mean = 1.906

Student 2: ln(7.4), ln(3.6), ln(5.8), ln(5.3), ln(7.3)

Mean = 2.924

Student 3: ln(7.4), ln(3.6), ln(5.8), ln(5.3), ln(7.3)

Mean = 2.924

Then, we calculate the sample standard deviation for each student's set of measurements

Student 1: s = 0.367

Student 2: s = 1.592

Student 3: s = 1.592

Therefore, student 1 made measurements with the least variability, as their set of measurements has the smallest standard deviation.

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Answer: -2.4 gallons per hour

Step-by-step explanation:

Think of this as a linear equation where the rate of change is m.

m = (Y₂ - Y₁) / (X₂ - X₁)

Assume the points are: (2, 15) (7, 3)

m = (3 - 15) / (7 - 2)

= (-12) / 5

= - 2.4 gallons per hour

Gas is reducing by 2.4 gallons per hour.

To make a boxplot of the six measurements, first arrange them in order from smallest to largest: 1.303, 1.308, 1.310, 1.311, 1.316, 1.321. Then, draw a number line and plot a box that spans the range from the first quartile (Q1) to the third quartile (Q3), with a line inside the box representing the median.

The whiskers should extend to the smallest and largest observations that fall within 1.5 times the interquartile range (IQR) from the box. Any observations that fall outside of this range are considered outliers and should be plotted as individual points.

In this case, Q1 is 1.308, Q3 is 1.316, the median is 1.311, and there are no outliers. Therefore, the boxplot would show a box from 1.308 to 1.316, with a line at 1.311 in the middle.

As for whether the t distribution should be used to find a 99% confidence interval for the thickness, it depends on whether we know the population standard deviation or not. If we know it, we could use a z-score instead of a t-score to calculate the confidence interval. However, if we do not know the population standard deviation, we would need to use the t distribution to account for the extra uncertainty in our sample estimate of the standard deviation. In either case, a 99% confidence interval would be wider than a 95% confidence interval, since we are more certain that the true population mean falls within the wider range.

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Answer:

11

Step-by-step explanation:

Let's call the number of games of Balloon Bouncer that Amy played as "x".

Amy started with 35 tokens and used 2 for Roll-and-Score, so she had 35 - 2 = 33 tokens left.

Each game of Balloon Bouncer costs 3 tokens, so the total number of tokens used for Balloon Bouncer games is 3x.

Therefore, the equation to find the number of games Amy played is:

33 = 3x

Solving for x, we get:

x = 11

So Amy played 11 games of Balloon Bouncer.

Answer: 3g + 3 = 35

Step-by-step explanation:

Answer:

$180

Step-by-step explanation:

\(P\times{(1-0.20)}=144\)

\(P\times{0.80}=144\)

\(P=\frac{144}{0.80}\)

\(P=180\)

Answer:

D. linear; y = –3x – 6

B. quadratic; y = –x2

Step-by-step explanation:

Let

A (0,-2) B (1,-3) C (2,-4) D ( 3,-5) E (4,-6)

using a graph tool

see the attached figure N 1

case a) exponential

see the attached figure N 2

case b) quadratic

see the attached figure N 3

case c) linear

see the attached figure N 4

case d) linear

see the attached figure N 5

therefore

the answer is

the case c) linear

...............................................................................................................................................

Answer:

For the first part

What type of function best models the data in the graph?

✔ quadratic

y = 0.433x2 for the second part.

...............................................................................................................................................

Answer:    

Option (2).

Step-by-step explanation:

From the figure attached,

Since there is a common difference in each successive term and previous term of y,

          = -3

          = -3

Therefore, this data represents a linear equation.

Now we choose two points from the table given.

Let the points are (0, -6) and (1, -9)

Slope of this line 'm' =  

m =  = -3

Y-intercept 'b' = -6

Equation of the line will be,

y = -3x - 6

Option (2) will be the answer.

Using it's concept, it is found that the probability that three randomly chosen students will all stay after school for extracurricular activities today is of \(\frac{1}{216}\).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, for each student, one out of six rolls represent staying after school, hence there is a \(\frac{1}{6}\) probability they stay after school. For the three students, the probability is given by:

\(p = \left(\frac{1}{6}\right)^3 = \frac{1}{216}\)

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Answer:

d

Step-by-step explanation:

in c greatest common factor is 8

But in D

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 20 = 1, 2, 4, 5, 10, 20

Look only 4 is GCF

Applying the expression for get the slope of a line, the slope was found to be 2/3Slope and InterceptsGiven Datax1 = 4y1 = 8x2 = 1y2 = 6Applying the expression for finding slope we haveSlope of line = (y2-y1)/(x2-x1)Substituting our data we haveSlope of line = (6-8)/(1-4)Slope of line = (-2)/(-3)Slope of line =2/3

Answer: part a is 5 x 12 = 60 , then 40 divided by ten which is 4 and I’m too stupid for part b lol

Answer:

greater than

Step-by-step explanation:

positive is higher than negative

Answer:

Width = 15 ft

Length = 25ft

Step-by-step explanation:

Given that:

Total area = 375 ft²

Length = 10 + width

Let ;

Width = x

Length = x + 10

Area of a rectangle = Length * Width

Area of rectangle = 375 ft²

375 = x * (x + 10)

375 = X² + 10x

x² + 10x - 375 = 0

X² + 25x - 15x - 375 =. 0

x(x + 25) - 15(x + 25) = 0

x +. 25 = 0

x - 15 = 0

Hence,

x = - 25 or x = 15

X cannot be negative

Hence, x = 15

Width = 15 ft

Length = x + 10 = 15 + 10 = 25 ft

The new data values after the increment by 20% are 14.4, 10.8, 20.4, 18 and 12

From the question, we have the following parameters that can be used in our computation:

Data values: 12,9,17,15,10

Increment: by 20%

This means that

new data values = old data values * (1 + Increment)

when the above equation is applied to the individual data values, we have

New 12 = 12 * (1 + 20%) = 14.4

New 9 = 9 * (1 + 20%) = 10.8

New 17 = 17 * (1 + 20%) = 20.4

New 15 = 15 * (1 + 20%) = 18

New 10 = 10 * (1 + 20%) = 12

So, the new values are 14.4, 10.8, 20.4, 18 and 12

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Answer:

False;18 ≥ 20

Step-by-step explanation:

Add  11  and 7

The left side  18  is less than the right side  20 , which means that the given statement is false.

The probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

Assuming that each die is fair and that the outcome of rolling one die does not affect the outcome of rolling the others, the probability of rolling a 6 with the red die is 1/6, the probability of rolling a 5 with the green die is also 1/6, and the probability of rolling a 4 with the blue die is 1/6.

Since the three events of rolling each die are independent of each other, we can multiply their probabilities to get the probability of all three events happening at the same time, i.e., rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die:

Probability of rolling 6 with the red die = 1/6

Probability of rolling 5 with the green die = 1/6

Probability of rolling 4 with the blue die = 1/6

Probability of rolling 6 (R), 5 (G), 4 (B) at the same time = Probability of rolling R and G and B together = Probability of R × Probability of G × Probability of B

= 1/6 × 1/6 × 1/6 = 1/216

Therefore, the probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

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You have three dice: one red (R), one green (G), and one blue (B). When all three dice are rolled at the same time, calculate the probability of the following outcome: 6 (R), 5 (G), 4 (B)?

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Answer: 185.7 miles

Step-by-step explanation:

To find the total distance, add the smaller distances together.

47.8 + 72 + 65.9 = 185.7