You wish to test the following claim (Ha) at a significance level of a = 0.02. Hp =0.32 Hp0.32 You obtain a sample of size n = 655 in which there are 226 successful observations Determine the test statistic formula for this test What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic= What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that.. O There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.32

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

For more questions on adjacent sides, click on:

https://brainly.com/question/28394984

#SPJ8

The scale used to make the model is approximately 1:669.7 (or 1 cm on the model represents 669.7 cm or 6.697 m in the actual building).

We need to first convert the units to either feet or meters to make sure they are consistent. Let's convert the height of the original building from meters to feet:

\($110 \text{ m} \times \frac{3.28 \text{ ft}}{1 \text{ m}} = 360.88 \text{ ft}$\)

So, the original building is 360.88 feet tall.

Now, we can use the scale model to find the scale:

\($\frac{\text{height of scale model}}{\text{height of original building}} = \frac{5.4 \text{ ft}}{360.88 \text{ ft}}$\)

Simplifying the fraction gives:

\($\frac{27}{18044}$\)

So, the scale used to make the model is approximately 1:669.7 (or 1 cm on the model represents 669.7 cm or 6.697 m in the actual building).

Learn more about scale here

https://brainly.com/question/29967135

#SPJ11

After simplification, the value of the expression is,

⇒ 2f + 54

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 6 ( f + 5 ) - 4 ( f - 6 )

Now, Simplify the expression as;

⇒ 6 ( f + 5 ) - 4 ( f - 6 )

⇒ 6f + 30 - 4f + 24

⇒ 2f + 54

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Hey there! I'm happy to help!

When building equations, the word "is" means "equals".

First, we have the sum of a number and six. You can use any letter to represent the number. I will use n.

(n+6)

We see that this is multiplied by 5. We can just put the 5 next to the parentheses. This shows multiplication.

5(n+6)

Is 48

5(n+6)=48

Have a wonderful day! :D

#1

6pints=6(2)=12cups

1-D

#2.

16pints=

#3

8fluid ounces=1gallon.

3(C)

Answer: #1

1pint=2cups

6pints=6(2)=12cups

1-D

#2.

16pints=

16(2)=32cups=8quarts

#3

8fluid ounces=1gallon.

3(C)

Answer:

Option G

Step-by-step explanation:

We know that both triangles are similar in proportion. We see that the base of 8 is similar to 6, and therefore the side length of x should be similar to 5.

x/5 = 8/6

Cross multiply.

6x = 40

x = 40/6

x = 6 + 2/3

x = 6.67

Answer:

2.3 : 0.83

Step-by-step explanation:

Simplify

Answer:

130

Step-by-step explanation:

674 - 284 = 390

3 partners

390/3 = 130

Answer:

Nick can bake 16 cupcakes at most

Step-by-step explanation:

If you divide 200 by 16, you get 16.667. Because .667 is not a full cupcake, you cannot round up to get 17 cupcakes.

If you have any questions, feel free to ask in the comments. If you find my answer helpful, please consider marking brainliest. Hope this helps!

Given the functions:

Solve the equations means finding the values of x provided that f(x) = g(x)

so,

Make the square root alone on the right-side

Square both sides to eliminate the square root:

Simplifying the equation:

Solve the last equation to find the values of x

We can use the calculator to find the values of x

So,

Rounding to the nearest tenth

So, the answer will be x = {-1.7, 4.1 }

Harrison will spend $26,366.97 on Option A, which includes a $2900 down payment and 2.1% APR financing over 36 months for a car priced at $29,089.

For Option A with 2.1% APR financing over 36 months and a $2900 down payment, Harrison will spend a total of $26,266.97 on the car.

To calculate the total amount Harrison will spend on the car for Option A, we need to consider the financing terms, down payment, and the car price.

The car price is $29,089, and Harrison has saved $2900 for the down payment. Therefore, the loan amount will be $29,089 - $2900 = $26,189.

Now, let's calculate the total amount including interest for the financing. Using the formula for the monthly payment on a loan:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

The monthly interest rate is (2.1% / 100) / 12 = 0.00175, and the number of months is 36.

Plugging in the values, we can calculate the monthly payment:

Monthly Payment = ($26,189 * 0.00175) / (1 - (1 + 0.00175)^(-36)) = $732.36

To find the total amount spent, we multiply the monthly payment by the number of months:

Total Amount = Monthly Payment * Number of Months = $732.36 * 36 = $26,366.97

Therefore, the total amount Harrison will spend on the car for Option A is $26,366.97.

Learn more about financing terms here: brainly.com/question/30225504

#SPJ11

Answer:

            \(\bold{a\,=\,\dfrac{8(g+m)}r}\)

Step-by-step explanation:

\(\bold{g = -m+\frac18ra}\\^{+m}\qquad^{+m}\\\bold{g+m=\frac18ra}\\{}\quad^{\times8} \qquad^{\times8}\\\bold{8(g+m)=ra}\\{}\qquad^{\div r}\qquad^{\div r}\\\bold{\dfrac{8(g+m)}r=a}\)

Answer: The integral of the function y = cos(x) from x = k to x = π/2 represents the area under the curve of the function between those limits. We can evaluate this integral as follows:

∫[k, π/2] cos(x) dx = sin(k) - sin(π/2) = sin(k) - 1

We are given that this area is 0.1, so we can write:

0.1 = sin(k) - 1

Adding 1 to both sides gives:

1.1 = sin(k)

To solve for k, we take the inverse sine (or arcsine) of both sides, keeping in mind that k is between 0 and π/2:

k = arcsin(1.1)

However, arcsin(1.1) is not a real number since the sine function is only defined between -1 and 1. Therefore, there is no value of k that satisfies the given conditions.

Answer:

The distance between point A(-3,6) and another point is 10.

=> That point belongs to the circle with center A and radius 10.

=> The coordinate (x, y) of that point satisfies the equation of circle:

(x - -3)^2 + (y - 6)^2 = 10^2

or

(x + 3)^2 + (y - 6)^2 = 100

Hope this helps!

Answer:

The function that describes the height of the ball in time is  \(h(t) = 32\cdot t -16.087\cdot t^{2}\).

Step-by-step explanation:

Let suppose that ball experiments a free fall motion, which means that the ball is accelerated because of gravity and gravitational acceleration can be considered constant since height reached by the object is too small in comparison with the radius of the Earth. Therefore, we can assume that ball is accelerated uniformly.

Hence, the kinematic formula for the height of the ball (\(h(t)\)), in feet, is described below:

\(h(t) = s + v\cdot t + \frac{1}{2}\cdot g \cdot t^{2}\) (1)

Where:

\(s\) - Initial height with respect to the ground, in feet.

\(v\) - Initial velocity, in feet per second.

\(t\) - Time, in seconds.

\(g\) - Gravitational acceleration, in feet per square second.

If we know that \(s = 0\,ft\), \(v = 32\,\frac{ft}{s^{2}}\) and \(g = -32.174\,\frac{ft}{s^{2}}\), then the function that describes the height of the ball in time is:

\(h(t) = 32\cdot t -16.087\cdot t^{2}\) (2)

Answer:

12.8

Step-by-step explanation:

tan(theta) = opposite/adjacent

in this question, theta should be 59 deg, opposite is EF which is x, and adjacent is DE which is 7.7

So plug in these data

tan(59deg) = x/7.7 ==> x = 7.7 * tan(59deg) ~~12.8

Answer:

in edg is B

Step-by-step explanation:

Answer:

It's B

Step-by-step explanation:

The sculptor must remove approximately 1.57 cubic feet of stone. Rounded to the nearest hundredth, this is 1.57 cubic feet.

To solve this problem, we need to use the formula for the volume of a cylinder and the volume of a cone. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.

In this case, we are given that the height of the cylindrical block is 3 feet and the diameter of the base is 2 feet. Since the diameter is 2 feet, the radius is 1 foot. Therefore, the volume of the cylindrical block is V = π(1)^2(3) = 3π cubic feet.

To create a cone from the cylindrical block, the sculptor needs to remove some stone. The diameter of the base of the cone is also 2 feet, so the radius is 1 foot.

We are not given the height of the cone, but we know that it must be less than 3 feet in order for the cone to fit inside the cylindrical block. Let's call the height of the cone h.

Using the formula for the volume of a cone, we can write the volume of the removed stone as V = (1/3)π(1)^2h = (1/3)πh. To find the height of the cone, we can use similar triangles.

The height of the cone is to the height of the cylinder as the radius of the cone is to the radius of the cylinder. Therefore, h/3 = 1/2, or h = 3/2 feet.

Plugging in the value of h, we get V = (1/3)π(1)^2(3/2) = π/2 cubic feet. Therefore, the sculptor must remove approximately 1.57 cubic feet of stone. Rounded to the nearest hundredth, this is 1.57 cubic feet.

To know more about value click here

brainly.com/question/30760879

#SPJ11

The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

Learn more about the area of the trapezoidal here:

https://brainly.com/question/1463152

#SPJ4

The volume of an ice cube produced by this machine is of:

Volume ice cube = 1 inch³

  A volume is the physical space that an object occupies in space, although it is also defined as the capacity of space that a hollow object may have.

If this machine produces ice that has a cube shape with a side of 1 inch, then to know the value of the volume of these cubes we will use the following equation:

Volume cube = side x side x side

Volume cube = side³

side = 1 inch

Volume ice cube = 1 inch³

As the side is 1 the volume and area will be 1 but with corresponding unit

Learn more about volume at:

https://brainly.com/question/12410983

#SPJ4

The quotient of the division x - 3 | 4x^2 + 3x + 2 is 4x + 15

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

x - 3 | 4x^2 + 3x + 2

Using the long division method of quotient, we have

x - 3 | 4x^2 + 3x + 2

The division steps are as follows

          4x + 15

x - 3 | 4x^2 + 3x + 2

          4x^2 - 12x

------------------------------------------------

              15x + 2

              15x - 45

------------------------------------------------

                        47

Hence, the quotient is 4x + 15

Read more about long division at

brainly.com/question/25289437

#SPJ1

-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ1

Answer:

a metal brush to simulate wear and tear from wind, rain, and other environmental factors. The shingle is then exposed to extreme temperatures and humidity levelsthat it may encounter during its lifetime, and the overall effect of these tests is used to estimate the shingle's durability over time.

The manufacturer uses statistical analysis to determine the expected failure rate of its shingles based on the results of the accelerated-life

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

Learn more about Fourier transform

brainly.com/question/29063535

#SPJ11

Answer:

-1/3x

Step-by-step explanation:

the slope formula is y divided by x. it goes down 1 unit and right 3 units. so

-1 divided by 3 is -\(\frac{1}{3}\)

Answer: f (-4). -1

Step-by-step explanation:

Answer:

768 students are expected to enroll

Step-by-step explanation:

24 : 1

? : 32

24 times 32 = 768

From the question, given:

Let f(x) = -53x + 4

We are asked to evaluate f(-1) without using calculator.

f(x) = -53x + 4

f(-1) = -53(-1) + 4 (replace the value of x with -1)

= 53(1) + 4 (negative signs cancelling out)

= 53 + 4

= 57

Therefore, the answer is 57.

Answer: 3500

Step-by-step explanation:

7 x 10 to the 5th power = 700000

2 x 10 squared = 200

700000/200 = 3500

Answer:

4201750

Step-by-step explanation:

7*10^5/2*10^2

7*10=70

2*10=20

70^5/20^2

70^5 =1680700000

20^2=400

1680700000/400=4201750

The measure of angles ∠1 and ∠2 is 72 and 54.

Option C is the correct answer.

We have,

The total angle of a polygon can be found using the formula:

total angle = (n - 2) x 180 degrees

So,

The given polygon is a pentagon (5 sides).

n = 5

Now,

Total angle.

= (5 -2) x 180

= 3 x 180

= 540

Now,

There are 5 angles that make 540.

So,

1 angle = 540/5 = 108

And,

One angle is split into two where one is ∠2.

So,

∠2 = 108/2

∠2 = 54

Now,

We can see that ∠2 and ∠1 form a triangle.

Where the other angle is equal to ∠2.

So,

∠2 + ∠2 + ∠1 = 180

∠1 = 180 - (54 + 54)

∠1 = 180 - 108

∠1 = 72

Thus,

The measure of angles ∠1 and ∠2 is 72 and 54.

Learn more about the Pentagon here:

https://brainly.com/question/30182047

#SPJ1