Researchers for a company that manufactures batteries want to test the hypothesis that the mean battery life of their new battery is greater than the known mean battery life of their older version. The researchers selected random samples of 32 of the new batteries, subjected the batteries to continuous use, and determined the mean and standard deviation of the battery lives in the sample.
Which of the following is an appropriate test for the researchers’ hypothesis?
a. A one-sample z-test for a population mean
b. A one-sample t-test for a population mean
c. A one-sample z-test for a population proportion
d. A matched-pairs t-test for a mean difference
e. A two-sample t-test for a difference between means

a. The hypothesis test is right-tailed.

b. The P-value is 0.2525.

c. Using a significance level of a = 0.01, we fail to reject the null hypothesis .

a) The hypothesis test is right-tailed because the alternative hypothesis is p > 0.4.

b) To find the P-value, we need to use a standard normal distribution table or a calculator. Since the test statistic is positive, we look for the area to the right of z = 0.67. Using a standard normal distribution table or a calculator, we find that the area to the right of z = 0.67 is 0.2525. This is the P-value.

c) Using a significance level of a = 0.01, we compare the P-value to the significance level. The P-value is greater than the significance level, so we fail to reject the null hypothesis . There is not enough evidence to support the claim that p > 0.4 at the 1% significance level.

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The given question is incomplete, the complete question is :

The test statistic of z = 0.67 is obtained when testing the claim that p>0.4. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of a = 0.01, should we reject null hypothesis or should we fail to reject null hypothesis?

Answer:

The equation 4x - 3y > 12 can be graphed by finding two points that satisfy the inequality. For example, you could use the points (0, 4) and (3, 0). Then, you can plot the points on a graph and draw the line that passes through them. This line is the graph of the inequality. You can also put the equation into slope-intercept form by rearranging the equation to y = (4/3)x - (4/3). The graph of y = (4/3)x - (4/3) is the same as the graph of the original inequality.

Answer:

i do to and i need help but its not helpingggg

Step-by-step explanation:

The  converted value from Celsius to Fahrenheit is given by 39 Celsius is equal to 102.2 Fahrenheit.

Units represents the measure of the temperature in standard form Celsius and Fahrenheit .

Formula relates the Celsius and Fahrenheit are equal to

(°C × 9/5) + 32 =°F

Now, Substitute the value 39 Celsius which required to convert  into Fahrenheit we have,

(39°C × 9/5) + 32

= ( 351 / 5 ) + 32

= ( 70.2 ) + 32

= 102.2°F

Therefore, the converted value from Celsius to Fahrenheit for the given 39 Celsius is given by 102.2 Fahrenheit.

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The above question is incomplete, the complete question is:

What is the conversion of 39 degrees Celsius to °F ?

90 kilograms(kg) are about equivalent to 198.416 lbs (pounds).

To convert 90 kilograms to pounds, you may use the conversion factor of 2.20462 pounds per kilogram. 90 divided by 2.20462 results in:

90 kg x 2.20462 pounds per kilogram = 198.416 pounds (rounded to three decimal places)

= 198.416 lbs

Kilogram (kg) and pound (lbs) are units of mass or weight. The kilogram is the base unit of mass in the International System of Units (SI), while the pound is a commonly used unit of mass or weight in the imperial system of measurement.

One kilograms is equivalent to 2.20462 pounds. Conversely, one pound is approximately equal to 0.453592 kilograms. To convert from kilograms to pounds, you can multiply the number of kilograms by 2.20462, and to convert from pounds to kilograms, you can divide the number of pounds by 2.20462.

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Answer: 11.3 or 11 if you are to round to nearest whole number.

Step-by-step explanation:

Take the problem step by step.

You know she has the monthly fee and a fee for each gigabyte of data she stores in her house.

Take how much she paid and Subtract the monthly fee from it since it has been a month.

$60.95 - $14.95 = $36

Now take that answer and divide it by the cost of each gigabyte to see how many she used that month.

$65 / $5.75 = 11.30434743, which rounds to 11.3 or 11 if you are to round to nearest whole number.

Answer:

a) Algebraic expression for new area =  (x + 5)(x - 5 )

b) New area will be 25 square meters less than old area

Step-by-step explanation:

Lena' s square garden with side x has area x times x or x² square meters

If one side is lengthened by 5 meters that side becomes x + 5 meters

If the other side is shortened by 5 meters that side becomes x - 5 meters

New area = (x + 5)(x - 5 )

Using the identity(a + b)(a - b) = a² - b² we get

(x + 5)(x - 5 ) =x² - 5²

= x² - 25

Area difference square - rectangle =
x² - (x² - 25) = x² - x² + 25

= 25

So the area will decrease  by 25 square meters

Answer:

15 = 9 + j

Step-by-step explanation:

"15 is 9 more than j"

"15 is"  may be written as "15 ="

"9 more than j" may be written as "9+j"

Put these two expression together:

15 = 9 + j

The link represented by function g multiplies the dependent variable by 9 for every increase of 2 units in the independent variable. The equation that represents g is [tex]g(x)= 2 \times3^x[/tex],and the function has a value of 2 at 0

Let x be the independent variable, and let g(x) be the dependent variable.

According to the problem, for every 2 units the independent variable increases, the dependent variable is multiplied by 9. This suggests an exponential relationship of the form:

 [tex]g(x)= a \times b^x[/tex]

where a is the initial value of the dependent variable (when x=0), and b is the growth factor (how much the dependent variable changes for every unit increase in x).

We are given that g(0) = 2, so we can plug in these values and solve for a:

 [tex]g(0)= a \times b^0[/tex]

a = 2

So now we have:

[tex]g(x)= 2 \times b^x[/tex]

We still need to find the growth factor b. We are told that the dependent variable is multiplied by 9 for every 2 units the independent variable increases. In other words:

[tex]g(x+2) = 9 \times g(x)[/tex]

Using our equation for g(x), we can substitute in and simplify:

  [tex]2 \times b(x+2) = 9 \times 2\times b^x[/tex]

Simplifying, we get:

[tex]b^2[/tex] = 9

Taking the square root of both sides (we take the positive square root since b must be positive in order for g to be an increasing function), we get:

b = 3

So the final equation for g(x) is:

[tex]g(x) = 2 \times 3^x[/tex]

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The number of years will take for his money to double is 10.87 years

Let's assume the amount of money Latrell needs to buy the car "P". Since Latrell only has half of that amount, we can say that he has 0.5P. We want to find out how long it will take for Latrell's money to double, so we want to solve for the time "t" in years.

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = final amount of money (in this case, 2P, since we want to find out how long it takes for Latrell's money to double)

P = initial amount of money (0.5P, since that's what Latrell has now)

r = annual interest rate (6.3%)

n = number of times the interest is compounded per year (4, since it's compounded quarterly)

t = time (in years)

Substituting in the values we know, we get:

2P = 0.5P(1 + 0.063/4)^(4t)

Simplifying, we can divide both sides by 0.5P:

4 = (1 + 0.063/4)^(4t)

Taking the natural logarithm of both sides, we get:

ln(4) = 4t ln(1 + 0.063/4)

Dividing both sides by 4 ln(1 + 0.063/4), we get:

t = ln(4) / (4 ln(1 + 0.063/4))

t ≈ 10.87 years

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Answer:

100[tex]\pi[/tex]

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex]

The diameter is 20,.  The radius is 1/2 of the diameter.

A = [tex]\pi 10^{2}[/tex]

A = [tex]\pi 100[/tex]

Answer:

Step-by-step explanation: That is actually the hidden number that is on the other side of the circle so it says how or what numbers is on the hidden circle so good luck finding the number

The number of participants in this year's parade are 141 which is 27 more than last year's parade.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

According to the question, Last year's local parade had 114 participants, which is 27 less than this year's parade.

Let number of participants in this year's parade = x

Number of participants in last year = 114

So, according to the question:

x - 27 = 114

x = 114 + 27

x = 141

So, the number of participants in this year's parade = 141

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Answer:

Earned Income

Step-by-step explanation:

I get this money from chores I do around the house and my side job of selling sandwiches to my classmates (this is just an example you can personalize it)

Answer:

The roots of the equation
[tex]x^{3}-10x^{2}+31 x-30 = 0[/tex]

correspond to the x-intercepts of the function graph

Step-by-step explanation:

The roots of the equation
[tex]x^{3}-10x^{2}+31 x-30 = 0[/tex]

are x = 2, x = 3, x = 5

which are located at points (2, 0), (3, 0), (5,0)

These points are the x-intercepts of the graph of the equation
So the x-intercepts of the equation are the roots of the equation

I have graphed this using Geogebra which I am familiar with. You should probably use Desmos as per the instructions

The remaining angles of the parallelogram are 60°, 120°, and 120°.

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. This means that:

- Angle A = Angle C
- Angle B = Angle D
- Angle A + Angle B = 180°
- Angle C + Angle D = 180°

Given that angle A = 60°, we can use the above properties to find the remaining angles:

- Angle C = Angle A = 60°
- Angle B + Angle A = 180° => Angle B + 60° = 180° => Angle B = 180° - 60° = 120°
- Angle D = Angle B = 120°

Therefore, the remaining angles of the parallelogram are 60°, 120°, and 120°.

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A null space calculator finds the null space of a matrix used in linear algebra.

An invalid space mini-computer is a web-based instrument used to track down the invalid space, otherwise called the portion, of a framework. The invalid space of a framework is the arrangement of all vectors that fulfill the condition Ax= 0, where An is the lattice and x is the vector of questions. The invalid space can be utilized to decide if an arrangement of straight conditions is steady or not, and to find the reason for the arrangement space. An internet based invalid space number cruncher permits clients to enter a network and get the invalid space, as well as different properties like the position, determinant, and eigenvalues of the framework. This can be helpful for understudies and experts in fields like science, physical science, and designing who need to address frameworks of straight conditions and dissect the properties of networks.

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Liam has 19 chairs.

Let x be the number of chairs Liam has.

According to the problem, x = 4a + 3 and x = 2b + 19 for some integers a and b.

Equating these two expressions, we get:

4a + 3 = 2b + 19

4a - 2b = 16

2a - b = 8

Therefore, b = 2a - 8.

Substituting this expression for b into x = 2b + 19, we get:

x = 4a + 35

Now, since x = 4a + 3, we have:

4a + 3 = 4a + 35 - 32

Therefore, x = 4a + 35 = 2(2a + 4) + 3 = 2b + 19, where a = 4 and b = 11.

Thus, Liam has x = 4a + 3 = 4(4) + 3 = 19 chairs.

The solution to this problem involves the use of two key mathematical concepts: algebraic equations and systems of equations.

We are given two equations in terms of the same variable x, each representing a different way of arranging chairs. By setting these two equations equal to each other, we obtain an equation in terms of x that allows us to find a value of x that satisfies both of the original equations simultaneously. This process of setting two equations equal to each other is an example of solving a system of equations.

To solve the resulting equation, we use algebraic manipulation to isolate the variable x on one side of the equation. This involves a combination of simplification, substitution, and rearrangement of terms. Ultimately, we arrive at a specific value of x that satisfies both equations, which is the answer to the problem.

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Answer: x = 136.4 minutes

Step-by-step explanation:

x = (100/22)(30) minutes = 136.4 minutes

The given function is solved using the power rule. The nth derivative of the given function f(x)=xⁿ is  [tex]f^{(n)}(x) = n!x^{n-n }= n![/tex].

The power rule instructs how to differentiate xⁿ. It is used to determine the slope of polynomial functions as well as any other function with a real number exponent.

The given function is considered a power function. This is because the x is raised to the power (n). This n is considered a real number. So the derivative of this function is derived using the power rule.

First, differentiating the given function as follows,

[tex]\begin{aligned}f'(x)&=nx^{n-1}\\f''(x)&=n(n-1)x^{n-2}\\f'''(x)&=n(n-1)(n-2)x^{n-3}\end{aligned}[/tex]

So observing the pattern, the nth derivative is found as follows, [tex]f^{(n)}(x) = n!x^{n-n }= n![/tex]

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The complete question is -

Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

f(x)=xⁿ

(a) Here's a tree diagram for the sample space of all dinner combinations:

               Fish

          /      |      \

        /        |        \

    Salmon    Trout    Halibut

    / | \      / | \      / | \

 Fries Carrots Coleslaw  Fries Carrots Coleslaw

(b) To determine the total number of dinner combinations, we can multiply the number of fish options by the number of side dish options:

3 fish options * 3 side dish options = 9 dinner combinations

Therefore, Javier has 9 choices for dinner combinations.

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For dinner, Javier will choose one of three fish options and one of three side dishes. His choices for fish are salmon, trout, and halibut. His choices for side dishes are fries, cooked carrots, or coleslaw.

(a)Draw a tree diagram for the sample space of all dinner combinations.

(b)How many choices for dinner combinations does Javier have?

Answer:

Answer: C

Step-by-step explanation:

the value of a remains the same

To convert 2 pm in the 12-hour clock format to military time, we add 12 to the hour to get 14, and the minutes remain the same, resulting in a military time of 14:00pm.

In military time, the day is divided into 24 hours, starting from midnight (00:00 hours) and ending at 23:59 hours. Each hour is numbered from 0 to 23, instead of repeating the numbers from 1 to 12 twice in a day.

Military time uses a four-digit number to represent the time, where the first two digits represent the hour and the last two digits represent the minutes.

To convert 2 pm in the 12-hour clock format to military time, we need to add 12 to the hour since 2 pm is in the afternoon and military time does not use the "am" or "pm" designations.

So, 2 pm in military time would be 14:00 hours, where 14 represents 2 pm in the 24-hour clock format.

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Answer:

Part A: The most appropriate design for this investigation would be an experiment. An experiment is the best choice because it allows the teacher to compare the two erasers under the same conditions, which will make it easier to determine if the new eraser reduces paper tears.

Part B: To implement the design, the teacher can set up an experiment by dividing a group of students into two groups. Each group should use the same type and amount of paper, and be given instructions to erase the same number of mistakes. One group should then use the current popular brand of eraser, while the other group should use the new eraser. After the test is completed, the teacher can count the number of paper tears in each group and compare the results.

Part C: One benefit of this design is that the results are more likely to be objective and reliable. By having a controlled experiment, the teacher can be sure that any differences observed are due to the erasers, and not any other factors.

Answer:

y=3x^2-6x-5

Step-by-step explanation:

Answer:

a. 651

Step-by-step explanation:

To solve the problem, you can start by finding out how many students bike or walk to school by multiplying the total number of students by the percentage that bike or walk:

1860 x 0.45 = 837

Next, you can subtract the number of students who drive to school to find out how many students travel by bus:

1860 - 837 - 372 = 651

Therefore, the answer is 651, so the option (a) is correct.

Answer:

a. 651

Step-by-step explanation:

We first need to find the number of students that bike or walk.

We can do this by plugging the numbers into this equation:

[tex]\frac{is}{of} = \frac{percent}{100}[/tex]

We know that the percent is 45, and we know the total amount of students, 1860, so we are solving for is.

[tex]\frac{x}{1860} = \frac{45}{100}[/tex]  where x = is.

To solve this, we cross multiply:

1860(45) = 100x

83,700 = 100x

837 = x

Now we know that 837 students bike or walk, and 372 drive.

We can calculate how many students travel by bus by subtracting these numbers from the total number of students, 1860.

1860 - 837 - 372 = 651

Therefore, 651 students travel to school by bus.

The half of the time that Arnold skied without falling is 712 as 2 x 356=712>223 .

Inequality is a mathematical statement that illustrates the connection between two expressions by using the inequality symbol. The phrases on both sides of an inequality sign are distinct. It indicates that the left expression should be larger or smaller than the right expression, or vice versa. When the link between two algebraic expressions is expressed using inequality symbols, literal inequalities arise.

The discrepancy represents the incident in which Kelvin skied for more than twice as long as anybody else in his family:

2f < 223

Here 223 is the time for Kelvin.

Check for Lori as follows:

2f < 223

2 x 55=110 < 223

Kelvin skied without falling more than twice as long as Lori.

Check for Vanessa as follows:

2f < 223

2 x 265=530>223

Check for Arnold as follows:

2f < 223

2 x 356=712>223

Kelvin skied without falling less than twice as long as Arnold.

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Complete question:

Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.

Lori 55

Vanessa 265

Devon 172

Celia 112

Arnold 356

The average rate of change of the total cost as his shirt production increases from 10 to 20 is 150.

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing.

Given that, the total cost to produce by James shirts is represented by a function, f(x) = 5x²+6.

We are to find the average rate of change of the total cost as his shirt production increases from 10 to 20.

The average rate of change is given by =

f(b) - f(a) / b-a, where a and b are given intervals,

Here, we have, a = 10 and b = 20

f(b) = 5(20)²+6 = 2006

f(a) = 5(10)²+6 = 506

The rate of change =

2006 - 506 / 20-10

= 1500 / 10

= 150

Hence, the average rate of change of the total cost as his shirt production increases from 10 to 20 is 150.

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Answer:

-3, 1, 5, 9

Step-by-step explanation:

Read the y-coordinate of each point.

The x-intercepts of the function f(x) are (-3,0), (5/4,0), and (1,0).

A relation is a function if it has only One y-value for each x-value.

To find the x-intercepts of the function f(x) = -(x+3)(4x-5)(x-1), we need to set f(x) equal to zero and solve for x:

f(x) = -(x+3)(4x-5)(x-1) = 0

Since the product of three factors is zero if and only if one or more of the factors is zero, we can set each factor equal to zero and solve for x:

x+3 = 0 => x = -3

4x-5 = 0 => x = 5/4

x-1 = 0 => x = 1

Therefore, the x-intercepts of the function f(x) are (-3,0), (5/4,0), and (1,0).

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