A group of consumers were asked whether they prefermed Brand A or Brand B

Using the Central Limit Theorem, it is found that the sampling distribution of the sample proportion of the 50 questions on which you get the correct is approximately normal, with mean of 0.7 and standard error of 0.0648.

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1 - p)}{n}}\), as long as \(np \geq 10\) and \(n(1 - p) \geq 10\).

In this problem, we have that p = 0.7, n = 50, hence the mean and the standard deviation are given as follows:

\(\mu = p = 0.7\)

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{50}} = 0.0648\)

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Answer

Given the 2 equations

x = y + 4 → (1)

2x - 3y = - 2 → (2)

Substitute x = y + 4 into (2)

2(y + 4) - 3y = - 2 ← distribute and simplify left side

2y + 8 - 3y = - 2

- y + 8 = - 2 ( subtract 8 from both sides )

- y = - 10 ( multiply both sides by - 1 )

y = 10

Substitute y = 10 into (1) for corresponding value of x

x = 10 + 4 = 14

Solution is (14, 10 ) → D

Step-by-step explanation:

Answer:

x=3

x=3y=1

I hope this helps!

Step-by-step explanation:

x+y=4

2x-3y=3

y = 4-x

2x-3(4-x) = 3

2x-12+3x = 3

5x = 15

x = 3

y = 4-x

4-3 = 1

y = 1

Answer:

\(A = 89.1327\)

Step-by-step explanation:

1. Approach

To solve this problem, one must divide the figure up into two smaller figures. Calculate the areas of these smaller figures, and then finally, add up the result. The given figure can be divided into a square and a semi-circle. One can solve for the area of the square using the formula (\(length*width=area\)). One can solve for the area of the semicircle by solving for the area of the circle, and then dividing it by (2).

2. Solve for the area of the square

This is the easier part, all one has to do is multiply the length of the square by the width;

\(length * width = area\\\\8 * 8 = area\\\\64 = area\)

3. Solve for the area of the semi-circle

The formula for the area of a circle is;

\((pi)r^2=A\)

Where coefficient (\(pi\)) represent the values (\(3.1415...\)), parameter (\(r\)) represent the radius of the circle, and (\(A\)) represents the area.

In the problem, one is given the diameter of the semicircle. The diameter is the largest cord (a line that is drawn in a circle) in the circle, this cord will pass through the center of the circle. The radius is the distance from the center of the circle to the outer edge of the circle. The radius, by its definition will always be half of the diameter. It is given that the diameter of the given circle is (\(8\)), therefore the radius is (\(4\)), because (\(8\)÷\(2=4\)).

Substitute in the values and solve;

\((pi)(4)^2 = A\\\\3.1415*(16)=A\\\\50.2655=A\)

Don't forget to divide this in half, because the given figure is a semi-circle, not a circle;

\(25.1327\)

4. Putting it together

Now add the value for the area of the semi-circle, with the value for the area of the square;

\(square + semi-circle = Total\ area\\\\64 + 25.1327 = Total\ area\\\\89.1327 = Total\ area\)

Answer:

1/6

Step-by-step explanation:

He has 2/3 of a pie, and half of that is gonna be 1/3. If he gives away 1/3, 2/3-1/3=1/6 left because its not a fraction of his original piece that the question is asking for, but the whole pie

Answer:

7n + 16

Step-by-step explanation:

Answer:

12 apples is the answer because 1/2 divided by 6 is 12

Step-by-step explanation:

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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An example of a continuous random variable is a Normal random variable.

What is a normal random variable?

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable can be either discrete (having definite values) or continuous (any value in a continuous range).

Here, we have

We have to determine the example of a continuous random variable.

We concluded that the example of a continuous random variable is a normal random variable.

Hence, an example of a continuous random variable is a Normal random variable.

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Answer:

YES

Step-by-step explanation:

(-9, - 1) is a solution to the given system of linear equations.

x = - 9

x + 3y = - 9 + 3(-1) = - 9 - 3 = - 12

Answer:

o=3

Step-by-step explanation:

3+0+3=6

16/100 = 0.16

Hope it helps

Answer:

860

--------

100

86

-----

10

43

----

5

8.6 is answer

Answer:

Health insurance protects you from unexpected, high medical costs. You pay less for covered in-network health care, even before you meet your deductible. You get free preventive care, like vaccines, screenings, and some check-ups, even before you meet your deductible.

Step-by-step explanation:

:)

Answer:

(0, 2)

Step-by-step explanation:

Answer:

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

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Solution

For this case the triangle COP and ERP are similar then we can set up the following proportional rule:

Solving for PR we got:

320 PR = 25800 +215PR

105PR = 25800

PR= 1720/7 =245.71 ft

Rounded the answer would be:

246 ft

Solution

- The figure STUV and its image S'T'U'V' can be plotted on a graph together as follows:

(The above image was plotted using a graphing calculator)

- Thus, all we just need to do is to count the number of units V has moved to V' or S to S' or any of the other points.

- Using V to V', this can be illustrated as follows:

- Thus, we can see that the image was formed by moving the original 4 units down and 4 units to the right.

Final Answer

The answer is OPTION D

Step-by-step explanation:

If x and y vary inversely, we can write the equation:

xy = k

where k is a constant of proportionality. To solve for k, we can use the values x = -3 and y = 4:

(-3)(4) = k

-12 = k

So the equation relating x and y is:

xy = -12

To find y when x = 6, we can plug in these values and solve for y:

(6)y = -12

y = -2

So when x = 6, y = -2.

Answer:

A)5

D) Z

I dunno

D) X

number 68 I dunno sorry

Answer:

66) A) 5

67) D) Z

68) D) T

69) D) X

Answer and Step-by-step explanation:

Given Asin(wt + phi), we know that sin (A + B) = sinAcosB + sinBcosA. This means:

Asin(wt + phi) = Asin(wt)cos(phi) + Asin(phi)cos(wt).

Let Acos(phi) = c2 and Asin(phi) = c1 we have:

Asin(wt + phi) = c2sin(wt) + c1cos(wt)

Answer:

Step-by-step explanation:

In order to prove that Asin(ω⁢t+ϕ) equals c2sin ω⁢t+ c1cos ω⁢t we need use the sin (A+B) sum identity.

The sin sum identity is sin(A+B)= sinA × cosB + cosB × sinA

Now lets plug in our info.

Asin(ω⁢t+ϕ)= (sin wt × cosϕ) + (cos wt × sinϕ)

We know that Asin= c1 and Acos= c2.

Once we input c1 and c2 and solve, our end result becomes c2sin(wt)+c1cos(wt)​

Answer:

If its x^2 + 3x - 1 it is not a factor.

Step-by-step explanation:

x^2+3x - 1  is a factor of x^3+2x^2-5x-6​?

Try dividing:

x^2+3x - 1 ) x^3 + 2x^2 - 5x - 6​( x - 1

                  x^3 + 3x^2 - x

                          - x^2  -4x - 6

                          -x^2 - 3x + 1

                                   - x - 7  <------- remainder.

Answer:

Dialation Point OA(6 , 9)Dialation Point OB(12 , 15)

Step-by-step explanation:

Answer:

∠ MON = 51°

Step-by-step explanation:

∠ LON is composed of the 2 angles LOM and MON , that is

∠ LOM + ∠ MON = ∠ LON

42° + ∠ MON = 93° ( subtract 42° from both sides )

∠ MON = 51°

Answer:

<MON= 51°

Step-by-step explanation:

Look at the diagram and locate LON. You can see that LON is the angle of the complete line. Now LOM is given which is the angle of a part of the lines. So that means that to find MON we can minus LON with LOM.

<MON= <LON - <LOM

= 93-42

<MON= 51°

Feel free to ask any doubt you have!

Answer:

  about 1.1%

Step-by-step explanation:

Given a moon has a diameter of 22% of the diameter its planet, you want the volume of the moon as a percent of the planet's volume.

The ratio of moon diameter to planet diameter is given as 22%. The ratio of moon volume to planet volume will be the cube of this scale factor:

  moon volume / planet volume = (0.22)³ ≈ 0.0106 = 1.06%

The volume of the moon is about 1.1% of the volume of the planet.

<95141404393>

Answer:a

Step-by-step explanation:

The solution is, O A. Are paid to the government, the phrase best completes the list. Types of Expenses.

Here, we have,

Explanation:

Utilities are expenses on essential and vital services common to households and businesses. They include water and sewage bills, electricity bills, and garbage disposal expenses. A firm offering such services generate utility bills. The cost covers a regular period, say mostly monthly.

Heating and internet or data costs are also being considered as utility expenses. They are common and essential for domestic and business use.

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9514 1404 393

Answer:

  5/10

Step-by-step explanation:

0.5 is five tenths is 5/10

Answer:

It is:475.19.

HOPE THIS HELPED

Answer:

475.19.

Step-by-step explanation:

The hundredths place is two places to the right of the decimal, or (0.01).

In the number given, the number to the right of the hundredths place is larger than 5, meaning we will round up giving us:

475.189 --> 475.19.