a tower that is 124 feet tall casts a shadow 138feet long. find the angle of elevation of the sun to the nearest degree.

Answer:

D. f=S+22 /3

Step-by-step explanation:

S= 3fs-22

3f/3=S+22/3

f= S+22/3

Answer:

yes

Step-by-step explanation:

you just need too

Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

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Answer:

1/3

Step-by-step explanation:

3*3*3=27

1/3*1/3*1/3=1/27

The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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The value of y = 12.

Given,

m ∠ABC = 40° and BD is the angle bisector of ∠ABC.

To find the value of y=?

Now, According to the figure,

For value x, (Adjacent angles)

3x - 1 = 34 - 2x

3x + 2x = 34 +1

5x = 35

x = 7

And, For value of y ,

A and C are altitude

3y +6 =  5y - 18

3y - 5y = -18 - 6

-2y = -24

y = 12

Hence, The value of y = 12.

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Volume of a Triangular Prism = base area x height

Area of a Triangle = 1/2 x length x width

First, we'll find the area of the base triangle. This is quite easy to do because we are given the length and width.

Length = 8

Width = 6

A = 1/2 x 8 x 6

A = 1/2 x 48

A = 24

Next, we'll plug the base area and the height into our formula.

Base area = 24

Height = 8

V = 24 x 8

V = 192

Answer: 192 m^3

Hope this helps!

In a linear equation, the value of Y when X is 0 is called the y-intercept, not the slope.

In order to determine whether the differences between group means are statistically significant, ANOVA examines the differences between groups.

ANOVA, which stands for Analysis of Variance, is a statistical method used to compare the means of two or more groups.

It analyzes the variability between group means and within group variability to assess whether there are significant differences among the groups.

The main idea behind ANOVA is to compare the variation between groups with the variation within groups.

If the variation between groups is significantly larger than the variation within groups, it suggests that there are meaningful differences among the groups.

This implies that the differences between group means are statistically significant, indicating that the groups are not just randomly different.

ANOVA achieves this by calculating an F-statistic, which is the ratio of the variability between groups to the variability within groups.

If the F-statistic is large enough to exceed a critical value based on the chosen significance level, it indicates that the group means are significantly different.

Regarding the statement about a linear equation, it is incorrect.

In a linear equation, the value of Y when X is 0 is called the y-intercept, not the slope.

The slope refers to the rate of change of Y with respect to changes in X.

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Answer:

Technically, it already works because you have $16.15

Step-by-step explanation:

The statement is true - Independent variables are beyond the experimenter's control.

The statement is true. Independent variables are those factors that cannot be manipulated by the experimenter. They are the variables that are naturally occurring and cannot be changed. For example, age, gender, or genetics are independent variables that are beyond the experimenter's control. In contrast, dependent variables are those variables that can be manipulated by the experimenter, such as the amount of light, the temperature, or the dosage of a drug. Understanding the difference between independent and dependent variables is crucial in designing and conducting experiments.

Independent variables are those variables that are beyond the control of the experimenter. They are naturally occurring factors that cannot be manipulated, whereas dependent variables are those that can be manipulated.

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By the end of week 52, Westway Company deducted $8,857.60 for Social Security and $2,426.48 for Medicare from Suzle Chan's earnings.

To calculate the deductions made by Westway Company, we'll need to consider the Social Security and Medicare taxes.

Social Security tax:

The Social Security tax rate is 6.2% on income up to $142,800.

Since Suzle Chan earns $3,220 per week, their annual income is $3,220 * 52 = $167,440.

However, the maximum taxable income for Social Security is $142,800.

Therefore, the Social Security tax deduction is $142,800 * 0.062 = $8,857.60.

Medicare tax:

The Medicare tax rate is 1.45% on all income.

The Medicare tax deduction is $167,440 * 0.0145 = $2,426.48.

By the end of week 52, Westway Company would have deducted a total of $8,857.60 for Social Security and $2,426.48 for Medicare from Suzle Chan's earnings.

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(a) The sampling error is 0.03. (b) The probability that a sample of size 100 would have a sample proportion of 0.33 or less, given a population proportion of 0.30, is approximately 0.008.

(a) The sampling error measures the difference between the sample proportion and the population proportion. It is calculated as:

Sampling error = Sample proportion - Population proportion

Given that the sample proportion is 0.33 and the population proportion is 0.36, we have:

Sampling error = 0.33 - 0.36 = -0.03

Therefore, the sampling error is -0.03.

Note: The sampling error can be positive or negative, indicating whether the sample proportion is overestimating or underestimating the population proportion.

(b) To find the probability that a sample of size 100 would have a sample proportion of 0.33 or less, given a population proportion of 0.30, we can use the normal distribution approximation.

The sample proportion follows an approximately normal distribution with mean equal to the population proportion (0.30 in this case) and standard deviation given by the formula:

Standard deviation = sqrt((population proportion * (1 - population proportion)) / sample size)

Substituting the given values:

Standard deviation = sqrt((0.30 * (1 - 0.30)) / 100) ≈ 0.048

To calculate the probability, we need to standardize the sample proportion using the z-score formula:

z = (sample proportion - population proportion) / standard deviation

z = (0.33 - 0.30) / 0.048 ≈ 0.625

Using a standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of 0.625, which is approximately 0.734. This probability represents the area under the curve to the left of 0.625.

However, since we are interested in the probability of obtaining a sample proportion of 0.33 or less, we need to subtract this probability from 1:

Probability = 1 - 0.734 ≈ 0.266

Therefore, the probability that a sample of size 100 would have a sample proportion of 0.33 or less, given a population proportion of 0.30, is approximately 0.266.



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Answer:

3.24 kg

Step-by-step explanation:

internal Vol = (30-0.5)(16-1)(17-1) = 7080 cm^3 = 7.08ltrs

external Vol= 30* 16* 17 = 8160cm^3 = 8.16ltrs

Vol of thickness = 8160 - 7080 = 1080cm^3

Mass of the tank= density * volume = 3*1080 = 3,240g = 3.24 kg

Answer:

Step-by-step explanation:

Its number line 2.

The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

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Step-by-step explanation:

a) 3×2×t=6t

b)500 years

The length of the square base that minimizes the surface area is \((10\sqrt[3]{10})\)cm.

To find (f'(2)), we need to differentiate both sides of the given equation with respect to (x) using the chain rule and product rule. We get:

\(x f'(x) + f(x) + 3[f(x)]^2 f'(x) &= 0 \\\\\Rightarrow f'(x) (x + 3[f(x)]^2) &= -f(x) \\\\\Rightarrow f'(x) &= -\frac{f(x)}{x + 3[f(x)]^2}\)

Now, we can substitute the given value of (f(2) = 1) into this equation to get:

\(f'(2) &= -\frac{f(2)}{2 + 3[f(2)]^2} \&= -\frac{1}{2 + 3(1)^2} \&= -\frac{1}{11}\end{align*}\)

Therefore, the answer is (-1/11).

Let the side length of the square base be (x) and the height of the box be (h). Then, the volume of the box is given by (V = x^2h = 500) cm(^3). Solving for (h), we get \((h = \frac{500}{x^2})\). The surface area of the box is given by (A = x^2 + 4xh). Substituting (h), we get:

\(A &= x^2 + 4xh \&= x^2 + 4x \left(\frac{500}{x^2}\right) \&= x^2 + \frac{2000}{x}\end{align*}\)

To minimize (A), we differentiate it with respect to (x) and set the derivative equal to zero:

\(\frac{dA}{dx} &= 2x - \frac{2000}{x^2} \\\\Rightarrow 2x &= \frac{2000}{x^2} \\Rightarrow x^3 &= 1000 \\\\Rightarrow x &= \sqrt[3]{1000} \&= 10\sqrt[3]{10}\end{align*}\)

Therefore, the length of the square base that minimizes the surface area is\((10\sqrt[3]{10})\) cm.

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The area of the remaining rectangular plot of land is 4680m²

Area of rectangle:

Area of rectangle means the area covered by the rectangle.

The formula for area of rectangle is

A = l x b

where,

l is the length of the rectangle

b is the breadth or width of the rectangle

Given,

A rectangular plot of land measures 40.0 m by 120.0 m, with a parcel 10.0 m by 12.0 m out of one corner for an electrical transformer.

Here we need to find the remaining area of the rectangular plot land.

For that first, we have to find the area of each separately,

Like,

The area of the rectangular plot is,

A₁ = 40.0 x 120.0 m²

A₁ = 4800m²

Similarly, the area of the electric transformer is,

A₂ = 10.0 x 12.0 m²

A₂ = 120m²

Now the remining area is,

A = A₁ - A₂

A = 4800 - 120 m²

A = 4680m²

Therefore, the area of the remaining rectangular plot is 4680m².

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Player A scored 27 points, Player B scored 22 points, Player C scored 20 points, Player D scored 13 points, and Player E scored 13 points.

To determine the number of points each player scored, we can analyze the relevant quotes from the players and use the information provided. Since the final score was 95-94, the total points scored by the team must be 95.

From the quotes, we gather that Player A scored the most points, with 27. Player B mentions that Player A scored five more points than him, indicating that Player B scored 22 points.

Player C states that he scored three points less than Player B, so Player C's score is 20 points.

Player D and Player E both mention that they each scored the same number of points, and their combined total is 26 (95 - 69 = 26). Therefore, both Player D and Player E scored 13 points.

In summary, Player A scored 27 points, Player B scored 22 points, Player C scored 20 points, Player D scored 13 points, and Player E also scored 13 points, resulting in a total of 95 points for the team.

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Answer:

about 12

Step-by-step explanation:

Answer: A

Given:

First, distribute the negative sign:

Then, combine like terms:

Then factor out 3x:

With this, we know that:

The answer would then be A.

Answer:

16.6

Step-by-step explanation:

In 3.5 hours, a total of 1950 gallons of water will be filled in swimming pool.

The general form of a linear function is given as follows -

y = kx

or

y = kx + c

Given is a swimming pool that holds 10,000 gallons of water is being filled at a rate of 600 gallons per hour. The function h(x)=600x represents the amount of water in the pool after [x] hours.

The linear function that represents the amount of water in the pool after [x] hours is given by -

h[x] = 600x

Now, for x = 3.5, the amount of water in the pool will be -

h[3.25] = 600 x 3.25 = 1950 gallons of water.

Therefore, in 3.5 hours, a total of 1950 gallons of water will be filled in swimming pool.

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1. The break-even point in unit sales and in dollar sales is 4,500 units and $324,000 respectively.

2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher break-even point.

3. Income statements before and after changes are implement net income of $36,000 and $(28,000) respectively.

4. The company has to sell 5,401 units to achieve the target profit of $35,000 per month.

1. The break-even point in unit sales and dollar sales is computed as follows:

Break-Even Point in Unit Sales = Fixed Costs / Contribution Margin per Unit = $108,000 / ($50 - $32) = 4,500 units

Break-Even Point in Dollar Sales = Fixed Costs / Contribution Margin Ratio = $108,000 / ($50 / $18) = $324,000

2. If variable expenses per stove increase as a percentage of selling price, it will result in a higher break-even point. Since variable expenses would have a higher percentage of revenue, contribution margin would be lower, making it more challenging to cover fixed costs.

3. Present Income Statement

Sales (8,000*$50) $400,000

Less variable expenses (8,000*$32) (256,000)

Contribution Margin $144,000

Less fixed expenses 108,000

Net Income $36,000

Income Statement if Changes are Implemented

Sales (8,000*$45) $360,000

Less variable expenses (8,000*$35) (280,000)

Contribution Margin $80,000

Less fixed expenses 108,000

Net Loss $(28,000)

4. The contribution margin ratio is 36% ($18/$50). So, the sales revenue required to achieve the target profit is:

$35,000 / 0.36 = $97,222

The number of units required to be sold is:

$97,222 / $18 = 5,401 units

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Answer:

\(-\frac{1}{5}\)

Step-by-step explanation:

Notice that the equation y = 5x - 16 is in slope-intercept form, or \(y = mx + b\) format. Whenever an equation is in slope-intercept form, the number in place of the \(m\), or the coefficient of the x-term, represents the slope of that line. So, the slope of the given line is 5.

Slopes that are perpendicular to each other are opposite reciprocals. So, we need to find the opposite reciprocal of 5. To do that, write it as a fraction, making it \(\frac{5}{1}\). Then, switch the sign and flip the numerator and denominator. This means that the opposite reciprocal of 5 is \(-\frac{1}{5}\), so \(-\frac{1}{5}\) is the perpendicular slope.

The area of the piece of cake that Marty eats is: 64π square inches * (1/8) = 8π square inches. the area of the piece of cake that Marty eats is 8π square inches.

To find the area of the piece of cake that Marty eats, we first need to calculate the area of the entire round cookie cake.

The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.

Given that the diameter of the cake is 16 inches, the radius (r) is half the diameter, which is 16/2 = 8 inches.

So, the area of the entire round cookie cake is:

A = π(8)^2 = 64π square inches.

Since the cake is divided into 8 equal pieces, each piece represents 1/8th of the total area.

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So to find the sale price of any item with a regular price of $45, you would multiply $45 by 0.8889 to get $40.

Proportion refers to the relationship between two ratios or two fractions. It indicates that two ratios or fractions are equal to each other. Proportions are commonly used in mathematics and everyday life to compare different quantities or to solve problems related to ratios and fractions.

Here,

To find the sale price, you multiply the regular price by a constant of proportionality. The constant of proportionality is equal to the ratio of the sale price to the regular price.

For example, if the regular price is $10 and the sale price is $8, then the constant of proportionality is:

$8/$10 = 0.8

So to find the sale price of any item with a regular price of $10, you would multiply $10 by 0.8 to get $8.

Looking at the table provided, we can see that the sale price is always less than the regular price. We can calculate the constant of proportionality for any pair of regular and sale prices. For example, for the first pair (regular price $25, sale price $24), the constant of proportionality is:

$24/$25 = 0.96

So to find the sale price of any item with a regular price of $25, you would multiply $25 by 0.96 to get $24.

Similarly, for the second pair (regular price $45, sale price $40), the constant of proportionality is:

$40/$45 = 0.8889 (rounded to four decimal places)

So to find the sale price of any item with a regular price of $45, you would multiply $45 by 0.8889 to get $40.

We can repeat this process for each pair of regular and sale prices to find the constant of proportionality for each pair.

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Answer:

7.5 < 10 <1 2

Step-by-step explanation:

The order of this shows them from least to greatest using the inequality symbols.

.........................

The equivalent exponential decay function is given as \(m(t)=18000(0.81)^t\)

An exponential function is in the form

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let m(t) represent the value of the car after t years, hence the exponential decay is given by:

\(m(t) = 18000(0.9)^{2t}\\\\m(t)= 18000(0.9)^{2(t)}\\\\m(t)=18000(0.81)^t\)

The equivalent exponential decay function is given as \(m(t)=18000(0.81)^t\)

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When the probability is 0.77 for the sample mean to be greater than certain value, tis value is solved to be 4.3

The problem will be solved with t-scores as the number of sample is less than 30

number of sample, n = 25

degree of freedom, df

= n - 1

= 25 - 1 = 24

Assuming a confidence level of 95%, probability of 0.77, with a df of 24 the t-score is 2.064

the question is asking for greater than = 1 - 2.064 = -1.064

Using the formula for t scores

t = (X - μ) / σ

Definition of variables

mean, μ  = 4.70

standard deviation, σ = 0.40

-1.064 = (X - 4.7)/0.4

-1.064 * 0.4 = X - 4.7

-0.4256 = X - 4.7

-0.4256 + 4.7 = X

X = 4.2744 approximately 4.3

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