A ball thrown in the air has a height of y = - 16x² + 50x + 3 feet after x seconds. a) What are the units of measurement for the rate of change of y? b) Find the rate of change of y between x = 0 and x = 2?

If a = 2b and b is 14% of c, then a is 28% of c.

This means that a is 28% of the total value of c.

Let's break down the given information step by step to determine the relationship between a, b, and c and find the percentage of a in relation to c.

Given:

a = 2b

b = 14% of c

We can substitute the value of b from the second equation into the first equation to express a solely in terms of c:

a = 2(14% of c)

a = 2(0.14c)

a = 0.28c

Now we have expressed a in terms of c.

To find the percentage of a in relation to c, we can calculate the ratio of a to c and multiply by 100 to express it as a percentage:

Percentage of a in relation to c = (a / c) * 100

Percentage of a in relation to c = (0.28c / c) * 100

Percentage of a in relation to c = 0.28 * 100

Percentage of a in relation to c = 28%

Therefore, a is 28% of c.

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Answer:

25

Step-by-step explanation:

The perimeter of triangle is equal to the sum of all sides of triangle

then:

5y + (x+8) + (x+3) = 60

5y + 2x +11 = 60

5y +2x = 49  ..............................................................(1)

the hypotenuse - shorter leg = 10

hint (  shorter leg ) = x+3

then

5y - (x + 3 ) = 10

5y - x - 3 = 10

5y - x = 13               .................................................... (2)

from 1 and 2

5y +2x = 49  .................................................................. (3)

5y - x = 13 (multiply both sides by 2 )

10y - 2x = 26 ..................................................................(4)

by sum 3 and 4

15y = 75

then y = 75/15 = 5

then hypotenuse = 5y = 5 x 5 = 25

Answer:

5

Step-by-step explanation:

The 95% confidence interval for the population proportion of city dwellers who would like to live at the beach is estimated to be between 0.56 and 0.62.

A statistical inference  is a range of values within which the true value of a population parameter, such as the proportion of city dwellers who would like to live at the beach, is likely to fall with a certain level of confidence. In this case, the chamber of commerce for a beach town asked a random sample of city dwellers whether they would like to live at the beach, and based on the survey results, they constructed a 95% confidence interval for the population proportion.

The 95% confidence interval they obtained was (0.56, 0.62). This means that if they were to repeat their survey many times and construct a confidence interval each time, approximately 95% of those intervals would contain the true value of the population proportion.

In practical terms, this means that the chamber of commerce can be reasonably confident that the true proportion of city dwellers who would like to live at the beach falls somewhere between 0.56 and 0.62. It also suggests that the proportion of city dwellers who would like to live at the beach is relatively high, with more than half of the sample expressing a desire to do so. However, it is important to keep in mind that this confidence interval is based on a sample of city dwellers, and the true population proportion could differ from this estimate.

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The graph of the first five terms can be seen in the image at the end.

We know that we have an arithmetic sequence:

3, -10, -23, -36

The common difference is what we get when we subtract two consecutive terms, we will get:

d = -36 - (-23) = -3

Then the recursive relation is:

a(n) = a(n - 1) - 13

At the moment we know:

a(1) = 3

a(2) = -10

a(3) = -23

a(4) = -36

Then fifth term will be:

a(5) = a(4) - 13 = -36 - 13 = -49

Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).

The graph can be seen in the image below:

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Answer:

Perpendicular = 6 meter (Approx.)

Length of fence required = 18.81 meter

Step-by-step explanation:

Given:

One side of triangle = 5 m

Angle with side and hypotenuse = 50°

Find:

Other sides

Length of fence required

Computation:

Using trigonometry function;

Tanθ = Perpendicular / Base

For 50° angle , 5 m is base

Tan 50 = Perpendicular / 5

1.1917 = Perpendicular / 5

Perpendicular = 5.9585

Perpendicular = 6 meter (Approx.)

Hypotenuse = √Perpendicular² + Base²

Hypotenuse = √6² + 5²

Hypotenuse = √36 + 25

Hypotenuse = √61

Hypotenuse = 7.81 meter (Approx.)

Length of fence required = 5 + 6 + 7.81

Length of fence required = 18.81 meter

Answer: 38.1$

Step-by-step explanation:

Answer:

About $24.34

Step-by-step explanation:

if you do 23 divided by 6 you get 3.8333333 then you do 3.83333333 times 6.35 and you get about $24.34.

The solution to the given system of linear equations is (x, y, z) = (1, 0, -13.857). The solution to the system of linear equations using the Gauss-Jordan elimination method is (x, y, z) = (1, -2, 3).

To solve the system of linear equations using the Gauss-Jordan elimination method, we represent the equations in augmented matrix form:

[ 2   2  -3 | 10 ]

[ 2  -2   3 | -2 ]

[ 4  -1   3 |  2 ]

First, we'll perform row operations to transform the matrix into reduced row-echelon form:

1. Row1 = Row1 - Row2

  [ 0   4  -6 | 12 ]

  [ 2  -2   3 | -2 ]

  [ 4  -1   3 |  2 ]

2. Row3 = Row3 - 2 * Row1

  [ 0   4  -6 | 12 ]

  [ 2  -2   3 | -2 ]

  [ 4  -9  15 | -2 ]

3. Row2 = Row2 + Row1

  [ 0   4  -6 | 12 ]

  [ 2   2  -3 | 10 ]

  [ 4  -9  15 | -2 ]

4. Row3 = Row3 - 2 * Row2

  [ 0   4  -6 | 12 ]

  [ 2   2  -3 | 10 ]

  [ 0 -13  21 | -22 ]

5. Row2 = Row2 + 3 * Row3

  [ 0   4  -6 | 12 ]

  [ 2   2    0 | -32 ]

  [ 0 -13  21 | -22 ]

6. Row1 = Row1 + 3 * Row3

  [ 0   4   0 | 6 ]

  [ 2   2   0 | -32 ]

  [ 0 -13  21 | -22 ]

7. Row1 = Row1 / 4

  [ 0   1   0 | 1.5 ]

  [ 2   2   0 | -32 ]

  [ 0 -13  21 | -22 ]

8. Row2 = Row2 - 2 * Row1

  [ 0   1   0 | 1.5 ]

  [ 2   0   0 | -35 ]

  [ 0 -13  21 | -22 ]

9. Row3 = Row3 + 13 * Row2

  [ 0   1   0 | 1.5 ]

  [ 2   0   0 | -35 ]

  [ 0   0  21 | -291 ]

10. Row3 = Row3 / 21

   [ 0   1   0 | 1.5 ]

   [ 2   0   0 | -35 ]

   [ 0   0   1 | -13.857 ]

11. Row1 = Row1 - 1.5 * Row2

   [ 0   1   0 | 1.5 ]

   [ 0   0   0 | -82.5 ]

   [ 0   0   1 | -13.857 ]

From the reduced row-echelon form, we can determine the values of x, y, and z:

x =

1.5

y = 0

z = -13.857

The solution to the given system of linear equations is (x, y, z) = (1, 0, -13.857). This means that when x is 1, y is 0, and z is -13.857, all three equations are satisfied simultaneously.

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Answer:

B

Step-by-step explanation:

The unit rate changes throughout the table.

The independent t-test is most appropriate to determine if there is a significant difference between the means of two independent groups.

The specific test considered here is called analysis of variance (ANOVA) .

The independent t-test, also called the two sample t-test, independent-samples t-test or student's t-test, is an inferential statistical test that determines whether there is a statistically significant difference between the means in two unrelated groups.

The specific test considered here is called analysis of variance (ANOVA) and is a test of hypothesis that is appropriate to compare means of a continuous variable in two or more independent comparison groups.

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Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

Answer: (4, 0) and (0, -18)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Givens

m = 1/4

y2 = 4

y1 = 1

x2 = 2

x1 = x

m = (y2 - y1) / (x2 - x1)

Solution

1/4 = (4 - 1) / (2- x)                Simplify

1/4 = 3 / (2 - x)                      Cross multiply

2- x =12                               Subtract 1 from both sides

-x = 12 - 2

-x = 10                                 Multiply by -1

x = -10

Check

1/4 = (4 - 1) / (2 - - 10)

1/4 = 3/(2 + 10)

1/4 = 3 / 12

1/4 = 1/4

Odd as the answer is, it does check.

The probability of selecting two purple shirts then a blue shirt is  28/323

Given, there are 12 blue shirts and 7 purple shirts in a drawer.

three shirts are randomly selected without replacement.

the probability of selecting two purple shirts then a blue shirt is,

(C(7 , 2) × C(12 , 1))/C(19 , 3) = ((7×6)/2 × 12)/(19×18×17)/6

= (7×6×6)/(19×3×17)

= 84/969

= 28/323

Hence, the probability of selecting two purple shirts then a blue shirt is  28/323

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c)  It will have less variation.

Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.

For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.

In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.

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Answer: A.

Step-by-step explanation: You were correct the first time!:)

Answer:

A

Step-by-step explanation:

Answer:

See Below

Step-by-step explanation:

Answer:

Line: Solid

Shade: Above

m = -4/5

b = 2

(0,2) - True -Yes

(3,4) - True - Yes

(-2,-2) - False - No

Step-by-step explanation:

Given:

4x + 5y ≥ 10

Questions:

Line: Solid or Dashed?

Shade: Above or Below?

m= [?]

b= [?]

Are these points solution:

Solve:

Inequalities that use '< or >' symbols are plotted with a dashed line. Due to that dashed line means the solution doesn't include the line itself.

< = Less than

> = Greater than

Inequalities that use '≤ or ≥' symbols are plotted with a solid line. Due to that solid line means the solution does includes the line itself

≤ = Less than or equal to

≥ = Greater than or equal to

Therefore, based on the given, the line is solid. Which also means the solution does includes the line itself.

We also know that the given info with the inequalities of "≥".

"≥" Means greater than or equal to which means shade above. If it was "≤ " which means less than or equal to you have to shade below.

To find the m and b we first have to know that;

y = mx + b

m = Slope

b = y-intercept

To find the Slope(m) and b(y-intercept) we first have to put 4x + 5y ≥ 10 in  slope-intercept form.

4x + 5y ≥ 10

4x-4x + 5y ≥ 10-4x {Subtract 4x from both sides}

5y ≥ -4x + 10

5y ≥ -4x + 10 {Divided all by 5}

5y/5  ≥ -4x/5 + 10/5

y =-4/5x+2

Hence, now we know that;

m = -4/5

b = 2

To see if the following points {(0,2) (3,4) (-2,-2)} are solutions for 4x + 5y ≥ 10

All we have to do is to substitute it in.

Starting with (0,2)

x = 0

y = 2

4(0) + 5(2) ≥ 10

0 + 10 ≥ 10

10≥ 10

True. 10 isn't greater than 10 but- It's equal to 10. ≥ Means greater than or equal to Hence, (0,2) is a solution.

Next we have (3,4)

x = 3

y = 4

4(3) + 5(4)  ≥ 10

12 + 20  ≥ 10

32  ≥ 10

True. 32 is greater than 10 - Hence, (3,4) is a solution.

Finally we have (-2,-2)

x = -2

y = -2

4(-2) + 5(-2)  ≥ 10

-8 + -10  ≥ 10

-18  ≥ 10

False. Although you may probably think 18 is greater than 10 it is not correct. -18 isn't greater than 10 due to that it is negative.

RevyBreeze

Answer:

f(3) = -6

f(-3) = -12

f(0) = -9

Step-by-step explanation:

Substitute each number for x.

f(3) = 3 - 9 = -6

f(-3) = -3 - 9 = -12

f(0 ) = 0 - 9 = -9

Answer:

{-6, -12, -9} is the range

Step-by-step explanation:

f(3) = 3 - 9 = -6

f(-3) = -3 - 9 = -12

f(0) = 0 - 9  =  -9

Answer:

Step-by-step explanation:

The first step makes the figures be same by size but the second step, reflection over line AE doesn't map them together.

Correct line of reflection would be a vertical line through the point D.

First step is fine

But then

It should be reflecting using a line through D

Step 2 is wrong

Answer:

1/12

Step-by-step explanation:

dice rolling=1/6

coin flipping=1/2

Hence probability=1/6×1/2

Answer:

Dice roll = 1/6

Coin flip = 1/2

Answer:

14 squared

Step-by-step explanation:

Answer:

amor no te enojes conmigo hacienda

The results are different because the simulated data is based on random numbers and may not perfectly match the probability distribution.

To simulate the emergency calls for 3 days, we need to use a cumulative hourly clock and generate random numbers to determine when the calls will occur. Let's use the following table of random numbers:

Random Number Call Time

57 1 hour

23 2 hours

89 3 hours

12 4 hours

45 5 hours

76 6 hours

Starting at 12:00 AM on the first day, we can generate the following sequence of emergency calls:

Day 1:

12:00 AM - Call

1:00 AM - No Call

3:00 AM - Call

5:00 AM - No Call

5:00 PM - Call

Day 2:

1:00 AM - No Call

2:00 AM - Call

4:00 AM - No Call

7:00 AM - Call

8:00 AM - No Call

11:00 PM - Call

Day 3:

12:00 AM - No Call

1:00 AM - Call

2:00 AM - No Call

4:00 AM - No Call

7:00 AM - Call

9:00 AM - Call

10:00 PM - Call

The average time between calls can be calculated by adding up the times between each call and dividing by the total number of calls. Using the simulated data from part a, we get:

Average time between calls = ((2+10+10+12)+(1+2+3)) / 7 = 5.57 hours

The expected value of the time between calls can be calculated using the probability distribution:

Expected value = (1/6)x1 + (1/6)x2 + (1/6)x3 + (1/6)x4 + (1/6)x5 + (1/6)x6 = 3.5 hours

The results are different because the simulated data is based on random numbers and may not perfectly match the probability distribution. As more data is generated and averaged, the simulated results should approach the expected value.

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The interest rate of it is 1%

What is simple interest ?

The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest. Simple interest does not compound, so the creditor only has to pay interest on the principal sum and the borrower never has to pay interest on the interest that has already accrued.

Simple interest formula

\(I = \frac{P*T*R}{100}\)

Given

I = 7140 - 7000

 = 140

P = 7000

T = 2 years

R = ?

\(R = \frac{I*100}{P*T}\)

R = (140 *100) / (7000 * 2)

   = 14000 / 14000

R = 1%

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Answer:

309 full rolls

Step-by-step explanation:

Find how many full rolls he had by dividing 15,483 by 50:

15,483/50

= 309.66

Since the question asks for full rolls, the answer has to be a full number.

So, the answer is 309 full rolls

Answer:

24

Step-by-step explanation:

7 hours = 420 mins (7×60)

420-60=360 (time taken for lunch)

15mins=one ride

360÷15=24 rides

Answer:

The answer would be 48 since it would be 4 x 12

Answer:

$15

Step-by-step explanation:

If the 5 people where each paying $12 to rent the equipment, that means the cost of the equipment can be found multiplying 5 and 12 to get 60. Now that we know that the cost of the equipment is $60, if one person bailed out, there are now 4 people to rent it. You can find how much each person pays if they each pay the same amount by dividing 60 by 4. Once you do                      $60 ÷ 4 people = 15. So each person pays $15.

I hope this helps :)