For a confidence level of 90% with a sample size of 19, find the critical t value. Check Answer

Answer:8,800

Step-by-step explanation:

1760 times 5 = 8,800

At the point on the curve r(t) where the tangent line is parallel to the plane V3z + y = 1, the x-component of the vector must be equal to zero, so 2cos(t)= 0.  This means that t = π/2. To find the coordinates of the point, we can plug this value into the equation of the curve.  This gives us the point (0, 2, e^t), where t = π/2.

By definition, the tangent line to the curve at a given point is the line that passes through the point and has the same slope as the curve at the point. In this case, the tangent line must have the same slope as the plane V3z + y = 1.

To find the equation of the tangent line, we can use the equation of the curve and the point we found. This gives us the equation of the tangent line, y = e^(π/2).

The point at which the tangent line to the curve r(t) is parallel to the plane V3z + y = 1 is (0,2,e^(π/2)). The equation of the tangent line is y = e^(π/2).

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Trader Bubba Industries should recommend buying the solar truck as it has a higher NPV than the electric-powered truck.

a) After-tax cost of the loans

The cost of the loan is given as $50 million borrowed at 3%. The tax rate is 40%.

Formula to calculate the after-tax cost of debt: After-tax cost of debt = cost of debt * (1 - tax rate)

After-tax cost of the loan = 3% * (1 - 0.4) = 1.8%

b) After-tax cost of the bonds

The cost of the bonds is given as $200 million, paying 4% coupon with semi-annual payments, and maturity of 10 years. Trader Bubba sold its $1,000 par-value bonds for $1020 and had to incur $20 flotation cost per bond. The tax rate is 40%.

Formula to calculate the after-tax cost of debt: After-tax cost of debt = cost of debt * (1 - tax rate) * (1 - flotation cost) / (1 - tax rate)

After-tax cost of bonds = 4% * (1 - 0.4) * (1 - 0.02) / (1 - 0.4) = 2.424%

c) After-tax cost of the preferred stocks

The cost of preferred stocks is given as $100 million, paying $15 dividends per share. Trader Bubba sold its preferred shares for $220 and had to incur $20 per share flotation cost. The tax rate is 40%.

Formula to calculate the after-tax cost of preferred stocks: After-tax cost of preferred stocks = cost of preferred stocks * (1 - flotation cost / market price) / (1 - tax rate)

After-tax cost of preferred stocks = $15 * (1 - 20 / 220) / (1 - 0.4) = 9.75%

d) After-tax cost of the common stocks

The beta of common stocks is given as 2, the risk-free rate is 2%, and the market rate is 6%. The tax rate is 40%.

Formula to calculate the after-tax cost of common stocks: After-tax cost of common stocks = risk-free rate + beta * (market rate - risk-free rate) * (1 - tax rate)

After-tax cost of common stocks = 2% + 2 * (6% - 2%) * (1 - 0.4) = 5.2%

e) Weighted average cost of capital (WACC)

WACC = w1r1 + w2r2 + w3r3 + w4r4

Where w = weight,

r = cost of capital.

W1 = $50 million / $400 million = 0.125 or 12.5% (weight of loans)

W2 = $200 million / $400 million = 0.5 or 50% (weight of bonds)

W3 = $100 million / $400 million = 0.25 or 25% (weight of preferred stocks)

W4 = $50 million / $400 million = 0.125 or 12.5% (weight of common stocks)

WACC = 0.125 * 1.8% + 0.5 * 2.424% + 0.25 * 9.75% + 0.125 * 5.2% = 3.874%

f) Net Present Value (NPV) and Internal Rate of Return (IRR) for both types of trucks

Formula to calculate NPV: NPV = -Initial Investment + ∑(Net Cash Flows / (1 + r)t)

Where Initial Investment is the cost of the truck,

Net Cash Flows are the cash flows of each year,

r is the discount rate, and

t is the year.

For the solar truck,Initial investment = $30,000

Net Cash Flows per year = $8,000

Discount rate = WACC

NPV = -$30,000 + $8,000 / (1 + 3.874%) + $8,000 / (1 + 3.874%)2 + ... + $8,000 / (1 + 3.874%)8 = $28,845.80IRR = 12.23%

For the electric-powered truck,Initial investment = $20,000

Net Cash Flows per year = $5,000

Discount rate = WACC

NPV = -$20,000 + $5,000 / (1 + 3.874%) + $5,000 / (1 + 3.874%)2 + ... + $5,000 / (1 + 3.874%)8 = $17,716.80IRR = 13.15%

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Answer:

- Yes, They agree

Step-by-step explanation:

Do Rachel and Dylan argree?

- Yes, They agree

Prove your answer using the values of the ratio.

100 of your friends listen to it

- Total Number = 100

Rachel said the ratio of the number of the people who liked the playlist to the number of people who did not like the playlist is 75:25.

The ratio can be simplifies further by diving all through by 25;

75/25  : 25/25

3 : 1

Dylan said that for every three people who liked the playlist, one person did not.

This simplifies to 3 : 1.

Same thing with what rachel said, so they both agree

Answer:

Step-by-step explanation:

The answer is B or  "8 x 10 to the 12th power"

I took the test and I got it right for 2 points.

Also, multiplying exponents was covered in the 1.06 lesson if you read the material carefully and followed the examples in the lesson.

Good Luck and have a great day.

The product in scientific notation is 8*10^2

Here we want to find the product between 4*10^6 and 2*10^6, and write that in scientific notation.

First, we can solve the direct product:

(4*10^6)*(2*10^6) = (4*2)*(10^6*10^6)

Here we used the fact that we can multiply in any order we want.

Now we will use the property:

a^n*a^n = a^{n + m}

(4*2)*(10^6*10^6) = 8*10^{6 + 6} = 8*10^12

The correct option is the second one, counting from the top.

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A decimal number with a digit or group of digits that repeats forever is called a repeating decimal.

Answer: 6.5

Step-by-step explanation:

2x-4=9

2x=13

x=6.5

The difference of 7.2 and 2.5 simply means we should subtract 2.5 from 7.2. The solution is express below

To find the median winning bid, we need to first arrange the bids in order from lowest to highest:

$2.00 $2.00 $3.00 $3.00 $3.00 $5.00 $6.00

There are seven bids in total, which means that the median is the fourth value when the bids are arranged in order. In this case, the fourth value is $3.00.

Therefore, the median winning bid is $3.00.

The cost of the film for the whole area of the figure is $73.6.

Given that,

Chris is covering a window with a decorative adhesive film to filter light.

The figure is a window in the shape of a parallelogram.

We have to find the area of the figure.

Area of parallelogram = Base × Height

Area = 8 × 4 = 32 feet²

Cost for the film per square foot = $2.3

Cost of the film for 32 square foot = 32 × $2.3 = $73.6

Hence the cost of the film is $73.6.

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To find the cooling rate of the car, we need to determine the temperature decrease per unit of time.

Given that the car overheats at 280°F and can be driven again at 230°F, we can calculate the temperature difference:

Temperature difference = overheating temperature - driving temperature
Temperature difference = 280°F - 230°F
Temperature difference = 50°F

Since the cooling rate of the car is not explicitly given, we cannot directly determine it. However, we can make some assumptions based on the information provided.

Assuming that the cooling rate is linear, we can calculate the temperature decrease per degree Fahrenheit.

Temperature decrease per degree Fahrenheit = temperature difference / (overheating temperature - outside temperature)
Temperature decrease per degree Fahrenheit = 50°F / (280°F - 80°F)
Temperature decrease per degree Fahrenheit = 50°F / 200°F
Temperature decrease per degree Fahrenheit = 0.25°F

Therefore, the cooling rate of the car would be 0.25°F per degree Fahrenheit.

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Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

42 un^2

Step-by-step explanation:

You can split the hexagon into 2 triangles and a rectangle. For this, I will use the triangle that goes from (-5, 2) to (2, 2) to (-1, 4), the triangle that goes from (-5, -2) to (2, -2) to (-2, -4), and the rectangle that goes from (-5, 2) to (-5, -2) to (2, -2) to (2, 2). The top triangle is 7 units by 2 units, so using triangle formula, you get 7*2/2 = 7. The rectangle is 4 by 7, so you get 4*7=28, and the bottom triangle is 7 units by 2 units (identical to top triangle) so you get 7. 28+7+7=42 units^2

Step-by-step explanation:

1. find P of semicircle

perimeter of a semicircle = pi×r+d

=3.14×5+10

=25.7

2.find P of rectangle

P=10×4=40cm

3. add P of semicircle and P of rectangle

25.7+40=65.7cm

Using the subtraction between two amounts, it is found that:

The difference between the longest and shortest measurement is of 33 cm.

The measurements are given as follows:

To find the difference between difference between the longest and shortest measurement, we have to subtracted the longest measurement by the shortest measures.

From the measurements given, we have that:

Hence, the subtraction is given as follows:

41 cm - 8 cm = 33 cm.

The difference between the longest and shortest measurement is of 33 cm.

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The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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Answer:

- 10.35°C

Step-by-step explanation:

Given that :

Temperature at 6 AM for four consecutive days :

X : -12.1°C, -7.8°C, -14.3°C, and -7.2°C

The average temperature :

ΣX / n

n = sample size = number of days = 4

[(-12.1) + (-7.8) + (-14.3) + (-7.2)] / 4

= - 41.4 / 4

= - 10.35°C

Hence, the average 6 AM temperature for the four days is - 10.35°C

The slope of the line that passes through the given points (2 12) and (6 11) is  -1/4.

Two points are given: (2, 12), (6, 11).

A line's "steepness" is quantified by a quantity called the slope, which is typically represented by the letter m. It is the adjustment of y for a unit adjustment of x.

We are aware that the formula for the slope of a line using two points is

m= y2 - y1 /x2 - x1

In this instance, x1 = 2, Y1 = 12, X2 = 6, Y2 = 11.

m = 11 - 12 / 6 - 2

m = -1/4

The slope is therefore -1/4.

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The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Sample size for proportions of kidney transplant patients under age, can be calculated using the formula n = (Z^2 * p * (1-p)) / E^2.

To determine the sample size needed for the sample proportion of kidney transplant patients under a certain age to be approximately normally distributed, we need to consider the formula for calculating the sample size for proportions.

The formula is given as:
n = (Z^2 * p * (1-p)) / E^2

In this case, we are looking for the sample size, denoted by "n". "Z" represents the desired level of confidence (typically 1.96 for a 95% confidence level), "p" represents the expected proportion of kidney transplant patients under the age of (which is not provided in the question), and "E" represents the desired margin of error (which is also not provided in the question).

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Carlos needs 636 square feet of insulation to properly insulate the room he just finished framing in his home.

First, we need to calculate the square footage of the walls by multiplying the perimeter of the room by the height of the walls. The perimeter of the room is calculated by adding up the length of all four walls. In this case, the perimeter is 2(16 ft.) + 2(12 ft.) = 56 ft. Therefore, the total square footage of the walls is 56 ft. x 9 ft. = 504 ft².

Next, we need to calculate the square footage of the ceiling. The ceiling measures 16 ft. by 12 ft., so the total square footage is 16 ft. x 12 ft. = 192 ft².

Finally, we need to account for the windows in the room. The total square footage of the windows is 2(5 ft. x 6 ft.) = 60 ft².

To determine the total square footage of insulation needed, we add the square footage of the walls and ceiling and subtract the square footage of the windows. Therefore, the total square footage of insulation needed is (504 ft² + 192 ft²) - 60 ft² = 636 ft².

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Answer:

The right analytical model for the profits of the company for any given year n, (pₙ) is that of a geometric series and it is given as

pₙ = 3000 (3ⁿ⁻¹)

Step-by-step explanation:

Concluding part of the question

In year one, a company earned $3,000 in profits; in year two they earned $9,000 in profits. In year 3 they earned $27,000 in profits and in year 4 they earned $81,000. Which analytical model illustrates this profit pattern?

Solution

From the pattern of the profits, it is evident that the profits follow a geometric series' pattern with the first term equal to the profits in the first year, $3000, the profit in the second year is the second term and so on.

First term = a = Profits in the first year = 3000

Second term = a₂ = Profits in the second year = 9000

Third term = a₃ = Profits in the third year = 27000

Fourth term = a₄ = Profits in the fourth year = 81000

The general formula for any term of a geometric series is

aₙ = arⁿ⁻¹

a = first term

r = common ratio

But for a geometric series, common ratio is given as the next term divided by the very previous term.

r = (aₙ/aₙ₋₁)

For this question,

r = (9000/3000) = (27000/9000) = (81000/27000) = 3

So, the right model for the profits for any given year n is

pₙ = 3000 × 3ⁿ⁻¹

pₙ = 3000 (3ⁿ⁻¹)

Hope this Helps!!!

The factored form of the equation 2x² + x - 3 should be written as follows;

(x - 1)(2x + 3)

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

c represents the constant term.

By using the sum-product pattern, we have the following:

2x² + 3x - 2x - 3

By writing the common factor from the two pairs, we have the following:

(2x² + 3x) + (-2x - 3)

x(2x + 3) - 1(2x + 3)

By rewriting in factored form, we have the following:

(x - 1)(2x + 3)

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Answer:

you can do the normal operation

or use a calculator

Answer:

x < 3

(*￣3￣)╭

Answer:

The answer is x < 3.

Step-by-step explanation:

1) Simplify 3x - 3 - 6 to 3x - 9.

\(0 > 3x - 9\)

2) Add 9 to both sides.

\(9 > 3x\)

3) Divide both sides by 3.

\( \frac{9}{3} > x\)

4) Simplify 9/3 to 3.

\(3 > x\)

5) Switch sides .

\(x < 3\)

Therefor, the answer is x < 3.

The probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².

Given data;

Five games are played. Each play has a probability of winning, P(W), of 0.4, and a probability of losing, P(L), of 0.6. The results of the plays are probabilistically independent.

To get the probability of the sequence W, W, L, L, W.

Now,

As the results are probabilistically independent,

The probability of the sequence is;

→ [(P(W)]³ + [(P(L)]²

→ (0.4)³ + (0.6)²

Hence, the probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².

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Answer:

912 cm^2

Step-by-step explanation:

The total surface area of a 3-dimensional object is the sum of the areas of the faces or surfaces of a 3-dimensional object

Lateral area of a prism = 4 x height x sides

624 = 4 x 13 x s

s = 12

Surface area = 2 x 12^2 + 624

(2 x 144) + 624  = 912 cm^2

The experimental probability that at least two heads would be gotten is 11 / 25.

The theoretical probability that at least two heads would be gotten is 1/2.

Probability calculates the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Experimental probability is based on the result of an experiment that has been carried out multiples times.

Experimental probability = number of times at least two heads would be gotten / total number of tosses

( 5 + 6 + 6 + 5)/50 = 22/50 = 11 / 25

Theoretical probability = number of times at least two heads would be gotten / total number of possible outcomes

4 / 8 = 1/2

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Through the given information we can conclude that the volume of the solid figure is 114 cubic feet.

The overall number of cube units that the cube totally occupies is the definition of a cube's volume. Volume is simply the total amount of space an object takes up. The cube's volume can be calculated using the formula a3 where an is the cube's edge.

To find the volume of the solid figure, we need to add the volumes of the two rectangular prisms together.

The volume of the top prism is:

V1 = 8 ft x 4 ft x 3 ft = 96 cubic feet

The volume of the bottom prism is:

V2 = 1 ft x 6 ft x 3 ft = 18 cubic feet

Therefore, the total volume of the solid figure is:

V = V1 + V2 = 96 cubic feet + 18 cubic feet = 114 cubic feet

So, the volume of the solid figure is 114 cubic feet.

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