In order to estimate the average electric usage per month, a sample of 121 houses was selected and the electric usage was determined. Assume a population standard deviation of 370 kilowatt-hours. The standard error is 33.64. Find the size of the margin of error at 95% confidence.
a. 1.64
b. 1.96
c. 55.33
d. 65.93

Answer:

Rational

Step-by-step explanation:

Improper fractions are always rational.

The values of θ for different conditions were calculated with the help of trigonometric functions.

Given that;

The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function,

f (θ) = 2 sin θ + √ 2

Hence, We can simplify as;

A) Function is,

f (θ) = 2 sin θ + √ 2

f (θ) = 2 sin θ + √ 2 = 0

2 sin θ + √ 2 = 0

2 sin θ = -  √ 2

sin θ = - 1/√2

θ = nπ ± π/4

Where, n = 1, 3, 5, 7, ...

So, At θ = nπ ± π/4 pogo stick's spring will be equal to its non compressed length.

2) If the angle was doubled, the function will look like this,

f (θ) = 2 sin 2θ + √ 2

f (θ) = 2 sin 2θ + √ 2 = 0

2 sin 2θ + √ 2 = 0

2 sin 2θ = -  √ 2

sin 2θ = - 1/√2

θ = nπ/2 + π/8

Where, n = 1, 3, 5, 7, ...

n = 1;

θ = π/2 + π/8

θ = 5π/8

n = 2;

θ = π + π//8

θ = 9π/8

Hence, Solutions are, 5π/8, 9π/8, ...

3) g (θ) = 1 - cos²θ + √2

g (θ) = sin²θ + √2

sin²θ + √2 = 2 sinθ + √2

sin²θ - 2 sinθ= 0

sinθ (sinθ - 2) = 0

sinθ = 0

θ = nπ

Where, n = 1, 3, 5, 7, ..

So, θ = nπ , the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.

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Answer:

x = 8

Step-by-step explanation:

[tex]5|x-8|+2=2 \\ −5∣x−8∣=0 \\ ∣x−8∣=0 \\ x = 8[/tex]

First, you need to cancel out the 2 by subtracting 2 from both sides. Then, we divide both sides by -5. And finally, we remove the absolute value.

To find when the two equations 65x + 20 = y and 730 + 35x = y will meet on the graph, we need to solve for the value of x that satisfies both equations.

We can begin by setting the right-hand sides of the two equations equal to each other:

65x + 20 = 730 + 35x

Subtracting 35x from both sides, we get:

30x + 20 = 730

Subtracting 20 from both sides, we get:

30x = 710

Dividing both sides by 30, we get:

x = 23.67

Now that we have found the value of x that satisfies both equations, we can substitute it into either equation to find the corresponding value of y. Let's use the first equation:

y = 65x + 20

y = 65(23.67) + 20

y = 1539.55

Therefore, the two equations will meet on the graph at the point (23.67, 1539.55).

Answer:

[tex]6x + 5y = - 30[/tex]

[tex]5y = - 6x - 30[/tex]

[tex]y = - \frac{6}{5} x - 6[/tex]

Since the slope of this line is -6/5, the slope of a perpendicular line is 5/6. The slopes of perpendicular lines are negative reciprocals.

Answer: graphed and attached

Step-by-step explanation:

to graph a y intercept and slope, first find the y intercept on the graph and place your point. here the y intercept is 3, so (0, 3) because x=0 at a y intercept.

next use slope to find your next point. slope of -2 is the same as -2/1 or down -2 and right +1. so from your y intercept of 3, go down -2 and right 1 and place your point (1, 1). do this again for a 3rd point at (2, -1).

graph is attached.

The half life of the decaying material is found to be 13.9 days to the nearest 10th of a day.

Using the radioactivity formula given to find out the concertation and the half life of the material. In this case, we are given the function A(t) = 600e^(-0.05t), which represents the quantity of the material at time t.

Let A(0) be the initial amount of the material, then we have,

[tex]A(0) = 600e^{-0.05(0)} = 600[/tex]

To find the half-life, we need to solve for t when A(t) = A(0)/2:

A(t) = A(0)/2

[tex]600(e^{-0.05t}) =\frac{600}{2}[/tex]

Taking natural logarithm,

[tex]ln(e^{-0.05t}) = ln(\frac{1}{2})[/tex]

-0.05t = ln(1/2)

t = -ln(1/2)/0.05

t ≈ 13.9

Hence, the half life is found to be about 13.9 to the nearest tenth of the day.

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The formula for T in terms of m and p is: [tex]T = 15m + 40p[/tex]

We are given that number of marbles in each small bag is 15, and Rosanna sells m small bags, so the total number of marbles in the small bags is: [tex]15m[/tex]

Also given that number of marbles in each large bag is 40, and Rosanna sells p large bags, so the total number of marbles in the large bags is:[tex]40p[/tex]

So, total number of marbles that Rosanna sells is the sum of the marbles in the small bags and in the large bags will be addition of both values which will give us: [tex]T = 15m + 40p[/tex].

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The solution is,  2.5 miles per hour was her walking rate in miles per hour.

We know that,

Speed is measured as distance moved over time.

The formula for speed is speed = distance ÷ time.

To work out what the units are for speed, you need to know the units for distance and time.

In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

Here, given that,

Bao walked 15 miles in 6 hours.

so, we get,

in 6 hours = 15 miles

so, in 1 hour = 15 / 6 miles

                    =2.5 miles

Hence, The solution is,  2.5 miles per hour was her walking rate in miles per hour.

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The large jar has better value for money than the smaller one.

To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.

For the first jar we have:

q = £4.10/540 = 0.0075

For the second jar we have:

q' = £2.81/360 = 0.0078

Then we can see that the large jar has the best value for money.

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Answer :

Step-by-step explanation :

It's given that :

The volume of a cylinder is 180π cubic meters. The height of the cylinder is 11.25 meters.

Formula of volume of cylinder = πr²h

where,

By substituting the values of values of height and volume in the above formula we'll get the required value of the radius.

[tex]:\implies [/tex] 180π = πr² 11.25

[tex]:\implies [/tex] 180π = r² × 11.25 π

[tex]:\implies [/tex] 180π/11.25 π = r²

[tex]:\implies [/tex] 16 = r²

[tex]:\implies [/tex] r² = √16

[tex]:\implies [/tex] r = 4

Hence, Radius of the cylinder is 4 meters.

The length of the indicated segments are determined as:

17. VX = 6      18. SU = 15

Based on the side-splitter theorem, the sides that are intercepted are divided proportionally. Using this theorem, we will find the length of the indicated segments below:

17. 8/20 = VX/15

Cross multiply:

VX * 20 = 8 * 15

VX * 20 = 120

VX = 120/20

VX = 6

18. SU/10 = 12/8

Cross multiply:

SU = 120/8

SU = 15

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A graph of this function d = 45t is shown in the image below.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

d = kt

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 45/1 = 90/45

Constant of proportionality, k = 45.

Therefore, the required linear equation or function is given by;

d = kt

d = 45t

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Step-by-step explanation:

( 11 * x ) + 2     where 'x' is a number

To install the gas riser in 10 days, a total number of 11 plumbers would be needed.

We can use the formula:

(number of workers) × (time) = (constant amount of work)

Let's let x be the number of plumbers needed to install the gas riser in 10 days. We can set up the equation:

(7 workers) × (15 days) = (x workers) × (10 days)

Simplifying the left side, we get:

105 worker-days = (x workers) × (10 days)

Dividing both sides by 10 days, we get:

10.5 workers = x

Since we can't have a fraction of a worker, we need to round up to the nearest whole number.

Therefore, we would need 11 plumbers to install the gas riser in 10 days.

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Results:

The equivalent pairs are:

A. 5.80; 5+0.08,

C. 6.050; six and five thousandths, and

E. nine and nine-tenths; 9.9

A. 5.80; 5+0.08

The two are equivalent expressions because they both represent the same decimal number. 5.80 can be interpreted as 5 units and 0.80 units, which is the same as 5 units and 0.08 units. So 5.80 is equal to 5+0.08.

C. 6.050; six and five thousandths

The two expressions describe the same decimal number. 6.050 means 6 whole units, 5 hundredths, and 0.005 thousandths, while "six and five thousandths" means the same thing - 6 whole units, 5 hundredths, and 0.005 thousandths.

E. nine and nine tenths; 9.9

They are also equivalent. Nine and nine-tenths mean 9 whole units and 9 tenths, while 9.9 means the same thing - 9 whole units and 9 tenths.

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To determine the range you need to evaluate and find a maximum/minimum if you can.

For a function f(x) = y, we define the range as the set of the possible outputs of the function.

So, to find the range of any function, we need to evaluate it and try to find the minimum and maximum values of the function. To do so it is useful to understand the behavior of different types of functions.

For example linear ones have a range of all the real numbers.

Quadratic ones have a range that depends on its vertex, and so on.

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The total area of all six sides that will be painted on the wooden cube is 96 square centimeters.

First, we need to understand that each cube has six faces or sides, which are all squares of the same size. When we paint the cube, we will be painting all six sides of it. Therefore, we need to find the total area of all six sides that will be painted.

To calculate the area of each side, we need to know the length of the side. You mentioned that the wooden blocks are cubes, so each side will have the same length. Let's say the length of each side is 4 cm.

Now, we can calculate the area of one side of the cube by squaring the length of the side. In this case, the area of one side will be:

Area of one side = (length of side)²

= (4 cm)²

= 16 cm²

Since there are six sides to each cube, we can find the total area of all six sides by multiplying the area of one side by six:

Total painted area = 6 x Area of one side

= 6 x 16 cm²

= 96 cm²

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From the given value of z = 3(cos pi/2 + isin pi/2),  the exact value of z⁷ is -2187i.

Given z = 3(cos pi/2 + isin pi/2)

which can be represented as 3sin(pi/2) in polar form.

Now, by applying De-Moivre's theorem,

z⁷  = (3cis(pi/2))⁷

      =   3⁷cis(7pi/2)

      = 3⁷cis(3pi/2)                   [7pi/2 --- 3pi/2 ]

To write it in complex form,

z⁷  = 3⁷(cos(3pi/2) + isin(3pi/2))

z⁷  = 3⁷(0-i)                                    [cos(3pi/2) = 0 and sin(3pi/2) = -1]

z⁷  = 3⁷(-i)

z⁷  = -2187i

From the above explanation, we can conclude that the value of  z⁷ is -2187i.

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The two triangles are congruent since they have equal angles and equal sides.

Congruent triangles are two triangles that have exactly the same size and shape.

In other words we can say that they have the same angles and the same side lengths.

So when two triangles are congruent, all of their corresponding parts including the angles and sides are equal.

For the given triangles

The missing value of angle C = 180 - (18 + 110) = 52⁰

The missing value of angle F = 180 - (18 + 52) = 110⁰

So it is obvious that the two triangles are congruent since they have equal angles and equal sides.

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The cost of one small box of fruit and the cost of one large box of fruit is $11.5 and $14.5 respectively.

Let

cost of one small box of fruit = x

cost of one large box of fruit = y

15x + 15y = 390

20x + 25y = 592.50

From (1)

x + y = 26

x = 26 - y

Substitute x = 26 - y into (2)

20x + 25y = 592.50

20(26 - y) + 25y = 592.50

520 - 20y + 25y = 592.50

- 20y + 25y = 592.50 - 520

5y = 72.50

divide both sides by 5

y = 72.50/5

y = 14.5

Substitute y = 14.5 into

15x + 15y = 390

15x + 15(14.5) = 390

15x + 217.5 = 390

15x = 390 - 217.5

15x = 172.5

divide both sides by 15

x = 172.5/15

x = 11.5

Therefore, small box cost $11.5 and large box cost $14.5

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The correct answer is,

C. 60(x - 3) = 45x.

This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.

Since,  Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.

Now, To solve this equation, we must use algebra and solve for x.

First, we multiply both sides of the equation by 4/5. This gives us:

48x + 36 = 45x

-36 = 3x

Finally, we divide left side of the equation by 3, giving us the final solution:

x = -12

Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.

that is, 60 (x - 3) = 45x

This equation shows the correct relationship between the two types of wood that the contractor purchased.

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The area of the region in this problem is given as follows:

A = 1 square unit.

The curve represented in this problem is given as follows:

y = sin(x).

The bounds of the region are given as follows:

Hence the area of the region is represented by the definite integral presented as follows:

[tex]\int_{0}^{\frac{\pi}{2}} \sin{x} dx[/tex]

The integral of the sine is the negative cosine, hence the area is:

A = -cos(x), from x = 0 to x = π/2.

Applying the Fundamental Theorem of Calculus, we have that the area is given as follows:

A = -cos(π/2) + cos(0)

A = -0 + 1

A = 1 square unit.

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Answer:

( x - 3 ) 3 .

Step-by-step explanation:

Since f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) ) = x , then f−1(x)=3√x+3 f - 1 ( x ) = x 3 + 3 is the inverse of f(x)=(x−3)3 f ( x ) = ( x - 3 ) 3 .

Answer:

Step-by-step explanation:

To solve this problem, we can use the multiplication principle of counting, which states that if there are k choices for one task and m choices for a second task, then there are k x m choices for both tasks combined.

In this case, we can apply this principle to each shelf of books, as there are different numbers of books on each shelf. For the first shelf, there are 12 choices, for the second shelf there are 18 choices, for the third shelf there are 25 choices, and for the fourth shelf there are 30 choices.

To choose one book from each shelf, we need to multiply the number of choices for each shelf together, which gives us:

12 x 18 x 25 x 30 = 16,200,000

Therefore, there are 16,200,000 ways to choose three books, one from each shelf, in the library.

The total number of ways of choosing three books , one from each shelf is given by A = 162,000 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

There are 12 ways to choose a book from the first shelf, 18 ways to choose a book from the second shelf, 25 ways to choose a book from the third shelf, and 30 ways to choose a book from the fourth shelf

So , the total number of ways = 12 x 18 x 25 x 30

A = 162,000 ways

Hence , the combination is solved and there are 162,000 ways

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The solution to the system of linear equation is:

x = 10 2/3, y = 5

The correct option is the last option   10 2/3, 5

From the question, we are to solve the given system of linear equation.

The given system of linear equations is

1/2x + 1/3y = 7

1/4x + 2/3y = 6

Multiply the first equation by 2

1/2x + 1/3y = 7      × 2

x + 2/3y = 14

Subtract the second equation from the resulting equation

     x + 2/3y = 14

- 1/4x + 2/3y = 6

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

3/4x = 8

Multiply both sides of the equation by 4/3

4/3 × 3/4x = 8 × 4/3

x = 32/3

x = 10 2/3

Substitute the value of x into

x + 2/3y = 14

To determine y

(10 2/3) + 2/3y = 14

32/3 + 2/3y = 14

Multiply through by 3

32 + 2y = 42

Subtract 32 from both sides

32 - 32 + 2y = 42 - 32

2y = 10

Divide both sides by 2

2y / 2 = 10 / 2

y = 5

Hence, the solution is:

x = 10 2/3, y = 5

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The value of the product of the rational expressions is,

⇒ (4x - 32) (x² - 36)

We have to given that;

The rational expressions is,

⇒ 4x/(x+6) times (x-8) / (x-6)

Now, We can multiply as;

⇒ 4x/(x+6) times (x-8) / (x-6)

⇒ 4x/(x+6) × (x-8) / (x-6)

⇒ 4 (x - 8) / (x + 6) (x - 6)

⇒ (4x -32) / (x² - 6²)

⇒ (4x - 32) (x² - 36)

Thus, The value of the product of the rational expressions is,

⇒ (4x - 32) (x² - 36)

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Answer:

Step-by-step explanation:

1. $4,076.92

2. Assets = Liabilities + Equity

3. They can be used to make online purchases.

4. by using an emergency fund for this unplanned expense

5. a fund with a minimum investment that tracks the value of cash (This question)

6. 1930s

7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.

8. their vacation cabin

9. You should shop around for the best overall deal.

10. If you use a credit card, it is easy to run up huge debts.

11. They are tied directly to your bank account.

12. preventative care

13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage

14. how long the coverage lasts, how much the premium costs, and the cash value

15. 1-year renewable group term life

16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.

17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.

18. 2 year in state community college degree

19. tuition assistance

20. -a sundae, -movie tickets

Explanation: All of these answers are correct!

Personal Finance Semester Exam

5/11/2023