Identify the value of the TEST STATISTIC used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. -0.218
b. -1.645
c. -1.946
d. -1.667

Answer:

The value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.

Step-by-step explanation:

We are given with the following polynomial function below;

[tex]\text{P}(x) = 2x^{5} +9x^{4} +9x^{3} +3x^{2}+7x-6[/tex]

Now, we have to calculate the value of P(x) at x = 1 and x = -2.

For this, we will substitute the value of x in the given polynomial and find it's value.

At x = 1;

[tex]\text{P}(1) = 2(1)^{5} +9(1)^{4} +9(1)^{3} +3(1)^{2}+7(1)-6[/tex]

[tex]\text{P}(1) = (2\times 1) +(9\times 1)+(9 \times 1)+(3\times 1)+(7\times 1)-6[/tex]

[tex]\text{P}(1) = 2 +9+9+3+7-6[/tex]

P(1) = 30 - 6

P(1) = 24

At x = -2;

[tex]\text{P}(-2) = 2(-2)^{5} +9(-2)^{4} +9(-2)^{3} +3(-2)^{2}+7(-2)-6[/tex]

[tex]\text{P}(-2) = (2\times -32) +(9\times 16)+(9 \times -8)+(3\times 4)+(7\times -2)-6[/tex]

[tex]\text{P}(-2) = -64 +144-72+12-14-6[/tex]

P(-2) = 156 - 156

P(-2) = 0

Hence, the value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.

Answer:

The Total of employees

=216 employees

Step-by-step explanation:

Ratio of men to women is 7 to 5

Meaning

Men/women= 7/5

If their are 90 women

Let men= x

X/women= 7/5

X= women *7/5

X= 90*7/5

X= 18*7

X= 126

There are a total of 126 men

The Total of employees=men + women

The Total of employees=126+90

The Total of employees

=216 employees

Answer:

97 m

Step-by-step explanation:

Perimeter = 2 * (length + width); perimeter = 344, width = 75 (solving for length)

344 = 2(length + 75)

172 = length + 75

length = 97

Answer:

6<y<∞

Step-by-step explanation:

Logarithmic curves can never go left to 0 and go on forever to the right.

x=6 would make the function 0, so 6 is the lower limit and infinity would be the upper limit.

Answer:

Step-by-step explanation:

Let, present age of son be 'x'

present age of father be 'y'

y = 4x→ equation ( i )

After five years,

Son's age = x + 5

father's age = y + 5

According to Question,

[tex]y + 5 = 3(x + 5)[/tex]

Put the value of y from equation ( i )

[tex]4x + 5 = 3(x + 5)[/tex]

Distribute 3 through the parentheses

[tex]4x + 5 = 3x + 15[/tex]

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S. and change its sign

[tex]4x - 3x = 15 - 5[/tex]

Collect like terms

[tex]x = 15 - 5[/tex]

Calculate the difference

[tex]x = 10[/tex]

Now, put the value of X in equation ( i ) in order to find the present age of father

[tex]y = 4x[/tex]

plug the value of X

[tex] = 4 \times 10[/tex]

Calculate the product

[tex] = 40[/tex]

Therefore,

Present age of son = 10

present age of father = 40

Hope this helps..

Best regards!!

Answer:

the linear system has two valid solution.

Answer:one solution

Step-by-step explanation:

Answer:

[tex] A = 50.7 [/tex] (to nearest tenth)

Step-by-step explanation:

Use the Law of Cosines to find the value of angle A as follows:

[tex] cos(A) = \frac{b^2 + c^2 - a^2}{2*b*c} [/tex]

Where,

a = 7 in

b = 5 in

c = 9 in

Plug in the values into the formula

[tex] cos(A) = \frac{5^2 + 9^2 - 7^2}{2*5*9} [/tex]

[tex] cos(A) = \frac{57}{90} [/tex]

[tex] cos(A) = 0.6333 [/tex]

[tex] A = cos^{-1}(0.6333) [/tex]

[tex] A = 50.7 [/tex] (to nearest tenth)

Answer:

[tex]Probability = \frac{1}{8}[/tex]

Step-by-step explanation:

Given

Box of Cards -- 1 -- 2 -- 3 -- 4 -- 5 -- Total

Black --------------1 ---1 ----1 ----1 ---1 ----5

Red ---------------- 1 ---1 ----1 ----0--- 0--- 3

Total --------------- 2 ---2 --2-----1 -----1 ---8

Required

Determine the probability of a card being black and being card 1

To solve this, we the the number of card 1 that is black

This is shown below

Box of Cards -- 1

Black --------------1

This implies that, 1 card is black and also card 1

Represent this with [tex]n(Black\ and\ 1)[/tex]

[tex]n(Black\ and\ 1) = 1[/tex]

Next, is to get the total number of cards

From the given parameters;

[tex]Total = 8[/tex]

The probability is calculated as follows

[tex]Probability = \frac{n(Black\ and\ 1)}{Total}[/tex]

[tex]Probability = \frac{1}{8}[/tex]

Answer:

Step-by-step explanation:

The surface area of a cone is:

● Sa = Pi*r^2 +Pi*r*l

r is the radius and l is the slant heigth

The diameter of this cone is 12 inches so the radius is 6 (12/2=6).

●Sa = Pi*36 +Pi*6*10

●Sa = 301.59 in^2

Answer:

pi (6) * 10+ pi ( 6)^2

Step-by-step explanation:

The surface area of a cone is given by

SA =  pi rl +pi r^2  where r is the radius and l is the slant height

We know the diameter is 12 so the radius is 12/2 = 6

SA =  pi (6) * 10+ pi ( 6)^2

Answer:

Step-by-step explanation:

Given,

Perpendicular ( p ) = 9x

Base ( b ) = 10

Hypotenuse ( h ) = x + 10

Now, let's find the value of x

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plug the values

[tex] {(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2} [/tex]

Using [tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex] , expand the expression

[tex] {x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2} [/tex]

To raise a product to a power , raise each factor to that power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2} [/tex]

Evaluate the power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + 100[/tex]

Cancel equal terms on both sides of the equation

[tex] {x}^{2} + 20x = 81 {x}^{2} [/tex]

Move x² to R.H.S and change its sign

[tex]20x = 81 {x}^{2} - {x}^{2} [/tex]

Calculate

[tex]20x = 80 {x}^{2} [/tex]

Swap both sides of the equation and cancel both on both sides

[tex]80x = 20[/tex]

Divide both sides of the equation by 80

[tex] \frac{80x}{80} = \frac{20}{80} [/tex]

Calculate

[tex]x = \frac{20}{80} [/tex]

Reduce the numbers with 20

[tex]x = \frac{1}{4} [/tex]

The value of X is [tex] \frac{1}{4} [/tex]

Now, let's replace the value of x to find the approximate value of hypotenuse

Hypotenuse = [tex] \frac{1}{4} + 10[/tex]

Write all numerators above the common denominator

[tex] \frac{1 + 40}{4} [/tex]

Add the numbers

[tex] \frac{41}{4} [/tex]

[tex] = 10.25[/tex] inches

Hope this helps..

best regards!!

Answer:

10.25

Step-by-step explanation:

because I said so ya skoozie

Answer: options 2,3and 6

Answer:

option

2-Twelve students answered Mr. Chiu’s question.

3-Three people studied for two hours.

6-Four people studied for four or more hours.

Step-by-step explanation:

hope this helps:)

Answer:

the answer is A) h=3V/(Pi*r^2)

Step-by-step explanation:

This question is asking to solve for h, the equation is allready solved for V.

to solve for h means to get h by itself on one side of the equation.

1) V=(1/3)*pi*r^2*h. Divide 1/3*pi*r^2 to the other side of the equation

2) V/(1/3)*pi*r^2=h. 1/3 on the bottom denominator means we can multiply the reciprocal to the bottom and the top and get an equivalent answer. In short, move the 3 from the 1/3 onto the top.

3) (3*V)/(pi*r^2)=h. Simplify.

4) 3V/(Pi*r^2)=h.

The price that guarantees the maximum revenue is $40.

The maximum revenue possible in this situation is $8000.

Given that the company can sell 225 items at a price of $35, and for every dollar increase in price, the number of items sold decreases by 5, we can set up a relationship between price and quantity sold.

Let's denote the price as "P" and the quantity sold as "Q". We can express this relationship as follows:

Q = 225 - 5(P - 35)

This equation represents the decrease in quantity sold as the price increases.

To find the price that guarantees the maximum revenue, we need to find the price at which the quantity sold multiplied by the price is maximized. This is equivalent to finding the maximum value of the revenue function.

Revenue (R) is calculated as:

R = P × Q

To find the price that guarantees the maximum revenue, we need to maximize the revenue function R(P).

Let's substitute the expression for Q into the revenue function:

R(P) = P × (225 - 5(P - 35))

Now, simplify and expand the equation:

R(P) = P × (225 - 5P + 175)

= P × (400 - 5P)

To find the maximum revenue, we need to find the value of P that maximizes R(P). This can be done by finding the critical points of the function, which are the values of P where the derivative of R(P) equals zero.

Let's take the derivative of R(P) with respect to P:

dR(P)/dP = 400 - 10P

Setting the derivative equal to zero and solving for P:

400 - 10P = 0

10P = 400

P = 40

Therefore, the price that guarantees the maximum revenue is $40.

To find the maximum revenue, substitute P = 40 into the revenue function:

R(40) = 40 × (225 - 5(40 - 35))

= 40 × (225 - 5(5))

= 40 × (225 - 25)

= 40 × 200

= 8000

Hence, the maximum revenue possible in this situation is $8000.

To learn more about the derivative;

https://brainly.com/question/24898810

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Answer:

k ≥ 24

Step-by-step explanation:

ᵏ⁄₄ ≥ 6

Multiply each side by 4

ᵏ⁄₄ *4 ≥ 6*4

k ≥ 24

Answer:

k≥24

Step-by-step explanation:

k/4≥6

Use the multiplication property of equality by multiplying both sides by 4 to get

k≥24

If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem

Thank you

Answer:

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Step-by-step explanation:

The rate is -1 4/5 lbs  per hour

The time is 3 1/2 hours

Multiply to find the weight change

-1 4/5 * 3 1/2

Change to improper fractions

- ( 5*1 +4) /5 * ( 2* 3+1)/2

- 9/5 * 7/2

-63/10

Changing back to a mixed number

-6  3/10

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Answer:

-6 3/10 pounds

Step-by-step explanation:

The weight of ice sculpture changes -1 4/5 pounds every 1 hour.

In 3 1/2 hours, multiply the time with the weight.

-1 4/5 × 3 1/2

Multiply.

-9/5 × 7/2

-63/10 = -6 3/10

Answer:

38.68 cm

Step-by-step explanation:

Perimeter of an equilateral triangle : P = 3a

Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]

a = side length

The area is given, solve for a.

[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]

[tex]a = 12.894839[/tex]

The side length is 12.894839 centimeters.

Find the perimeter.

P = 3a

P = 3(12.894839)

P = 38.684517 ≈ 38.68

The perimeter is 38.68 centimeters.

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.

Answer:

There are 2 * 32 = 64 possible ways for choosing three course meal.

Step-by-step explanation:

1-If we choose an appetizer, main course and a soup then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be an appetizer, main course and a soup in the meal.

2-If we choose a soup, main course and a dessert then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be a soup, main course and a dessert in the meal.

There are 2 possible ways to choose either an appetizer or dessert in a 3 course meal. There will be 64 ways in total for the three course meal.

Answer:

a) Mean = 4.55

   Median = 4.7

   Mode = 1.9

b) S =  2.3952

   CV = 52.64 %

   Range = 6.3

c) Yes, since the average and median values are both over "acceptable" ranges.

Step-by-step explanation:

Explanation is provided in the attached document.

Hey there! I'm happy to help!

Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.

10x+50y=1080

x+y=28

We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.

x+y=28

Subtract x from both sides.

y=28-x

Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.

10x+50(28-x)=1080

We use distributive property to undo the parentheses.

10x+1400-50x=1080

We combine like terms.

-40x+1400=1080

We subtract 1400 from both sides.

-40x=-320

We divide both sides by -40.

x=8

Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.

Have a wonderful day! :D

Answer:

3057.6 cm³

Step-by-step explanation:

You have a cylinder and a rectangular prism.  Solve for the area of each separately.

Cylinder

The formula for volume of a cylinder is V = πr²h.  The radius is 7, and the height is 7.

V = πr²h

V = π(7)²(7)

V = π(49)(7)

V = 343π

V = 1077.57 cm³

Rectangular Prism

The formula for volume of a rectangular prism is V = lwh.  The length is 20, the width is 11, and the height is 9.

V = lwh

V = (20)(11)(9)

V = (220)(9)

V = 1980 cm³

Add the areas of the two shapes.

1077.57 cm³ + 1980 cm³ = 3057.57 cm³

Round to the nearest tenth.

3057.57 cm³ ≈ 3057.6 cm³

Answer:

Step-by-step explanation:

Can you please include a image?

Thanks!!!

Answer:

c

Step-by-step explanation:

Answer:

3¾

Step-by-step explanation:

Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.

Formula for geometric sequence:

[tex] a^n = a ( n-1 ) * r [/tex]

Given:

First term, a1 = 30

ratio, r = ½

Required:

Find the fourth term

Where, the first term, a¹ = 30

Second term: a² = 30 * ½ = 15

Third term: a³ = 15 * ½ = 7.5

Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾

Therfore the fourth term of the geometric sequence is 3¾

Answer:

1/30

Step-by-step explanation:

The probability of getting ”E” is 1/6.

There is only 1 “E” out of 6 letters.

There is no replacement.

There are now 5 letters without “E”.

”A”, “B”, “C”, “D”, “F”

The probability of getting ”B” is 1/5.

There is only 1 “B” out of 5 letters.

⇒ 1/6 × 1/5

⇒ 1/30

Answer:

78 pork sliders

Step-by-step explanation:

The food concession owner sold 120 beef, vegetable and pork sliders.

20% were beef.

15% were vegetable.

The percentage of pork sliders sold is:

100 - (20 + 15) = 100 - 35 = 65%

The number of pork sliders sold is therefore:

65/100 * 120 = 78

78 pork sliders were sold.

Answer:

The standard Deviation would increase

Step-by-step explanation:

Is this advantages?

Answer:

x1= -4, x2 = 7

Step-by-step explanation:

Move expression to the left-hand side:

1/4x-3/4-7/x=0

Write all the numerators above a common denominator:

x^2 - 3x - 28 /4x =0

When the quotient of expressions equal 0, the numerator has to be 0

x^2 + 4x - 7x - 28 = 0

x(x+4) - 7(x+4) =0

(x+4) × (x-7) =0

Separate into possible cases:

x+4=0

x-7=0

Answer: -9

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

14(z + 3) = 14z + 21

Expand brackets.

14z + 42 = 14z + 21

Subtract 14z on both sides.

42 = 21

There are no solutions.

Answer:

No solution

Step-by-step explanation:

First, We have to simplify the right side.

Distribute 14, 14z+42.

Now the equation stands as 14z+42=14z+21

Subtract 14z from both sides,

this makes it 42=21.

We know when the solution is #=#, our answer is no solution.

Answer:

C. μ = 3.60

Step-by-step explanation:

Two tables have been attached to this response.

One of the tables contains the given data and distribution with two columns: Houses Sold and Probability

The other table contains the analysis of the data with additional columns: Frequency and Fx

=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,

When the number of houses sold = 0

F = P(0) x Total number of houses sold

F = 0.24 x 28 = 6.72

When the number of houses sold = 1

F = P(1) x Total number of houses sold

F = 0.01 x 28 = 0.28

=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,

When the number of houses sold = 0

Fx = F * x

F = 6.72 x 0 = 0

Now to get the mean, μ we use the relation;

μ = ∑Fx / ∑F

Where;

∑Fx = summation of the items in the Fx column = 100.8

∑F = summation of the items in the Frequency column = 28

μ = 100.8 / 28

μ = 3.60

Therefore, the mean of the given probability distribution is 3.60

The mean of the discrete probability distribution is given by:

C. μ = 3.60

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:

[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]

Hence option C is correct.

More can be learned about the mean of discrete distributions at https://brainly.com/question/24855677