7. At time t seconds, the height, h, of a ball thrown vertically upward is modeled by the equation h = -5t² +33t+ 4. About how long will it take for the ball to hit the ground?

Answer:

\(z = -1.53\) --- test statistic

\(p = 0.1260\) --- p value

Conclusion: Fail to reject the null hypothesis.

Step-by-step explanation:

Given

\(n_1 = 80\)     \(\bar x_1= 104\)   \(\sigma_1 = 8.4\)

\(n_2 = 70\)    \(\bar x_2 = 106\)    \(\sigma_2 = 7.6\)

\(H_o: \mu_1 - \mu_2 = 0\) --- Null hypothesis

\(H_a: \mu_1 - \mu_2 \ne 0\) ---- Alternate hypothesis

\(\alpha = 0.05\)

Solving (a): The test statistic

This is calculated as:

\(z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} }}\)

So, we have:

\(z = \frac{104 - 106}{\sqrt{\frac{8.4^2}{80} + \frac{7.6^2}{70} }}\)

\(z = \frac{104 - 106}{\sqrt{\frac{70.56}{80} + \frac{57.76}{70}}}\)

\(z = \frac{-2}{\sqrt{0.8820 + 0.8251}}\)

\(z = \frac{-2}{\sqrt{1.7071}}\)

\(z = \frac{-2}{1.3066}\)

\(z = -1.53\)

Solving (b): The p value

This is calculated as:

\(p = 2 * P(Z < z)\)

So, we have:

\(p = 2 * P(Z < -1.53)\)

Look up the z probability in the z score table. So, the expression becomes

\(p = 2 * 0.0630\)

\(p = 0.1260\)

Solving (c): With \(\alpha = 0.05\), what is the conclusion based on the p value

We have:

\(\alpha = 0.05\)

In (b), we have:

\(p = 0.1260\)

By comparison:

\(p > \alpha\)

i.e.

\(0.1260 > 0.05\)

So, we fail to reject the null hypothesis.

Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Answer:

Answer:     2x^2+11x+15      Coefficient of x is 11 and coefficient of x^2 is 2.

Step-by-step explanation:

(x+3)×(2x+5)=?

           Use FOIL Method                      Foil stands for First Outer Inner Last

Step 1:      (x×2x)        =2x^2                Multiply First Terms together  (x and 2x)

Step 2:     (x×5)         =5x           Multiply Outer terms together (x and 5)

Step 3:    (3×2x)        =6x           Multiply Inner terms together (3 and 2x)

Step 4:     (3×5)         =15            Multiply Last terms together (3 and 5)

2x^2+5x+6x+15             Combine Like Terms

Answer:     2x^2+11x+15

Answer:

Savannah

Step-by-step explanation:

Emery has solved it incorrectly;

x = 100

Answer:

x=66 and y=63

Step-by-step explanation:

The middle triangle is isosceles

57+57+x=180

114+x=180

x=66

Left triangle is equilateral (all angles =60)

60+57+?=180

117+?=180

?=63

Right triangle is isosceles

?=y

y=63

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

For more such questions on Number, click on:

https://brainly.com/question/30752681

#SPJ8

the mοnthly periοdic interest rate, rοunded tο the nearest hundredth οf a percent is (C) 1.31%

Any lοans and bοrrοwings cοme with interest. the percentage οf a lοan balance that lenders use tο determine interest rates. Cοnsumers can accrue interest thrοugh lending mοney (via a bοnd οr depοsit certificate, fοr example), οr by making a depοsit intο a bank accοunt that pays interest.

We must divide its yearly percentage rate (APR) by 12 tο determine a mοnthly periοdic interest rate (the number οf mοnths in a year).

Hence, the periοdic interest rate fοr each mοnth is:

15.75% / 12 = 1.3125%

The result οf rοunding tο the clοsest hundredth οf such a percent is:

1.31%

To know more about interest visit:

https://brainly.com/question/30955042

#SPJ1

Answer:

The rate of fill up is, Rate = 3.2 Gallons / minute = 3.2 g/min

The hut tub volume is 300 Gallons

You can set up this problem as follows:

Every 3.2 gallons require 1 minute, How many minutes 300 gallons require?

3.2  g    1min

300 g     ? min    = (300 gallons x 1min/ 3.2 gallons)=(300/32)min

= 93.75 min

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

Step-by-step explanation:

x+x+40=2

+ 4 0

2x+31=1205

2x=1205-31

2x=1174

x=1174/2

x=587

leslie will hace 587 score and

jackson =587+31= 618

Answer:

x° = 79°

z° = 101°

Step-by-step explanation:

Answer:

The coordinates for the point on a circle of radius at an angle of are At the radius of the unit circle, 1, serves as the hypotenuse of a 30-60-90 degree right triangle, as shown in (Figure).

Step-by-step explanation:

Answer:

y+2 = (-1/2)(x-3)

Step-by-step explanation:

Answer: B: 3

Step-by-step explanation: did on edge

Answer:

C)  3

Step-by-step explanation:

Remember that the linear function

Can model a problem where

• m, is the variable term. In this case, the babysitting money

• b, is the fixed term. In this case, the initial deposit.

Therefore, the expression that would model the situation is:

The additional information that is obtained by measuring two individuals on an interval scale compared to a ordinal scale is the magnitude of the difference between the two measurements.

Measurement scale is an analysis tool used in statistics that are used to measure different variables. Examples of measurement scale are:

When measuring two individuals, on an interval scale the magnitude of the difference between the two measurements can be taken.

Learn more about measurements here:

https://brainly.com/question/25770607

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

Answer:

5/6 quarts of water

Step-by-step explanation:

2/3 same as 4/6. 4/6 + 1/6 = 5/6

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

Read more about probability,

https://brainly.com/question/30390037

Answer: It is 12

Step-by-step explanation:

• Given the description "Six increased by twice a number is no more than 20", you need to know the following:

- In this case, the word "increased" indicates an Addition.

- The word "twice" indicates a Multiplication by 2.

- "No more than" indicates that six increased by twice a number must be less than or equal to 20.

- The inequality symbol whose meaning is "Less than or equal to" is:

Knowing the information shown before, you can write the following expression to represent "Six increased by twice a number" (Let be "x" the unknown number):

Therefore, you can write the following inequality that models the description given in the exercise:

• Now you need to solve it:

1. Apply the Subtraction Property of Inequality by subtracting 6 from both sides of the inequality:

2. Apply the Division Property of Inequality by dividing both sides of the inequality by 2:

• In order to graph the solution on a Number Line, you can follow these steps:

- Since the inequality symbol indicates that "x" is less than 7, it indicates that 7 is included in the solution. Therefore, you must draw a closed circle over that value.

- Draw a line from the circle to the left.

Then, you get:

Hence, the answer is:

- Inequality:

- Solution:

- Number Line:

Answer:

15 23

Step-by-step explanation:

Answer:

Step-by-step explanation:

11x - 6 + 15x - 8 = 90

26x - 14 = 90

26x = 104

x = 4

11(4) - 6 = 44 - 6 = 38

13y - 14 + 38= 180

13y + 24 = 180

13y = 156

y = 12

13(12) - 14 = 156 - 14=142

Complete Question

Jessica is organizing a guided tour of the rain forest. The average profit per person that the touring company makes is given by the rational expression 18x+35/x, where x is the number of people going on the tour. What does the denominator of this rational expression represents?

Answer:

Number of people going on the tour

Step-by-step explanation:

Given that the average profit per person  \(=\dfrac{18x+35}{x}\)

\(\text{Average}=\dfrac{\text{Sum of Total Items}}{\text{Number of Items}}\)

Therefore:

\(\text{Average Profit}=\dfrac{(18x+35)\text{ profit}}{x\text{ persons}}\)

The denominator, x represents the number of people going on the tour.

Answer:

btw 35/x represents epresents a fixed cost, like a cover charge for the tour, that is not affected by the number of people attending the tour. So, the quotient 35/x represents the profit that the tour company makes from the cover charge per person.

Step-by-step explanation:

PLATO

Answer:

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

Step-by-step explanation:

Let the number be x;

The product of 4 and the number will be;

\(= 4 * x\\\\= 4x\)

The the square of the number is given as;

\(= x^2\\\)

Taking the difference of both expressions above;

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

Factor out the common term:

\(= x(4-x)\\\\\)

Hence the difference between the product of 4 and a  number and the square of the number is \(= 4x-x^2\\\\\)

Answer:

x=2

Step-by-step explanation: