See Picture:
Given :
Prove :​

Answer:

3071.6 ft

Step-by-step explanation:

In this situation,

We can use sine law,

in which Sin angle = opposite side/ hypotenuse

Similarly

In triangle ABC

SIn A=BC/AC

Sin 19°=1000/AC

Doing criss cross multiplication:

AC= 1000/(Sin 19°)

AC=3071.55 ft

Therefore, the distance I ski down the mountain is 3071.6 ft

The diagram is below.

==============================================

Work Shown:

sin(angle) = opposite/hypotenuse

sin(19) = 1000/x

xsin(19) = 1000

x = 1000/sin(19)

x = 3071.553487

x = 3071.6

Refer to the diagram below.

Note that the angle of depression ACD is equal to the angle of elevation BAC because of the alternate interior angles theorem.

The diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm (option e).

Given that the diameter of the engine cylinder needs to be 5 cm wide with a tolerance of ± 0.005 cm.

To determine the permissible range of the diameter, we need to consider both the upper and lower limits.

Upper limit: Add the tolerance to the desired diameter.

  Upper limit = 5 cm + 0.005 cm = 5.005 cm.

Lower limit: Subtract the tolerance from the desired diameter.

  Lower limit = 5 cm - 0.005 cm = 4.995 cm.

Therefore, the permissible range for the diameter of the engine cylinder is between 4.995 cm and 5.005 cm.

Hence, the final answer is that the diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm.

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The correct answer is A- A model with 12 squares labeled exact value and 3 squares labeled error.

To determine which model represents a percent error of 25%, we need to compare the number of squares labeled "exact value" and "error" in each model and calculate the ratio between them.

Let's calculate the ratio for each model:

Model A: 3 squares labeled error / 12 squares labeled exact value = 0.25 or 25%.

Model B: 5 squares labeled error / 10 squares labeled exact value = 0.5 or 50%.

Model C: 3 squares labeled error / 9 squares labeled exact value ≈ 0.3333 or 33.33%.

Model D: 4 squares labeled error / 8 squares labeled exact value = 0.5 or 50%.

From the calculations, we can see that only Model A represents a percent error of 25%. The other models have ratios of 50% and 33.33%, which do not match the desired 25% error.

Consequently, the appropriate response is A- A model with 12 squares labeled exact value and 3 squares labeled error.

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Answer:

Step-by-step explanation:

12 14 33 35========1,234,000,124,581.

The height, h, of the cylinder is approximately 1.27 centimeters when the volume is 100 cm^3 and the radius is 5 cm, rounded to the nearest tenth.

To find the height, h, of the cylinder, we can rearrange the formula for the volume of a cylinder:

V = πr^2h

Given that the volume, V, is 100 cm^3 and the radius, r, is 5 cm, we can substitute these values into the formula:

100 = π(5^2)h

Simplifying further:

100 = 25πh

To solve for h, divide both sides of the equation by 25π:

100 / (25π) = h

To calculate the value, we'll use an approximation for π as 3.14:

100 / (25 * 3.14) ≈ h

Simplifying:

100 / 78.5 ≈ h

h ≈ 1.27 cm

Therefore, when the volume is 100 cm3 and the radius is 5 cm, the cylinder's height, h, is about 1.27 centimetres, rounded to the closest tenth.

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a. The distribution of X is a normal distribution.

b. The median giraffe height is also 19 feet.

c. The Z-score for a giraffe that is 22 foot tall is 3.

d. The probability that a randomly selected giraffe will be shorter than 18.9 feet tall is less than -0.1.

f. The 80th percentile represents the value below which 80% of the data falls.

a. The distribution of X is a normal distribution (or Gaussian distribution) with a mean of 19 feet and a standard deviation of 1 foot. This can be denoted as X ~ N(19, 1).

b. The median of a normal distribution is equal to its mean.

c. To find the Z-score for a giraffe that is 22 feet tall, we can use the formula: Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (22 - 19) / 1 = 3.

d. To find the probability that a randomly selected giraffe will be shorter than 18.9 feet tall, we need to calculate the area under the normal curve to the left of 18.9. This can be done using the Z-score and a standard normal distribution table or a calculator.

Alternatively, we can use the Z-score formula from the previous question. The Z-score for 18.9 feet can be calculated as Z = (18.9 - 19) / 1 = -0.1. We can then look up the corresponding probability in the standard normal distribution table or use a calculator to find the probability that Z is less than -0.1.

e. To find the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall, we need to calculate the area under the normal curve between these two values.

Again, we can use the Z-score formula to standardize the values and then find the corresponding probabilities using a standard normal distribution table or a calculator.

f. To find the height at the 80th percentile, we can use the standard normal distribution table or a calculator to find the Z-score that corresponds to the 80th percentile.

Once we have the Z-score, we can use the formula Z = (X - μ) / σ to solve for X. Rearranging the formula, we have X = Z * σ + μ. Plugging in the values for Z (obtained from the percentile) and μ (mean) and σ (standard deviation), we can calculate the height at the 80th percentile.

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The expression equivalent to -x--xy is 4x(3 + y).

To simplify the expression -x--xy, we can apply the rules of combining like terms and distribute the negative sign.

-x - (-xy)

Removing the double negative:

-x + xy

Factoring out the common factor of x:

x(-1 + y)

Now, let's compare the simplified expression with the given options:

Option 1: 2x - xy

This expression is not equivalent to -x - (-xy) as it includes an additional term of 2x.

Option 2: x(3 - y)

This expression is equivalent to the simplified expression x(-1 + y), as it represents the distribution of x over the terms inside the parentheses.

Option 3: 4x(3 - y)

This expression is not equivalent to -x - (-xy) as it includes the constant term 4.

Option 4: x(3 + y)

This expression is not equivalent to -x - (-xy) as it includes the positive sign before the y term.

Option 5: 4x(3 + y)

This expression is not equivalent to -x - (-xy) as it includes the constant term 4 and the positive sign before the y term.

From the given options, the expression that is equivalent to -x - (-xy) is:

Option 2: x(3 - y).

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Answer:

16

Step-by-step explanation:

(|7 − 3 x 5| ÷ 4)³ + √64

(|7 − 3 x 5| ÷ 4)³ + √64

(|7 − 15| ÷ 4)³ + √64

(|7 − 15| ÷ 4)³ + √64

(8 ÷ 4)³ + √64

(8 ÷ 4)³ + √64

2³ + √64

8 + 8

16

Answer:

16

Step-by-step explanation:

To solve, use PEMDAS as it applies to the expression.

First, you must carry out what is in the parenthesis.

Multiply (3*5 = 15), then subtract (7 - 15 = -8). The two little vertical lines surrounding (7 - 3 x 5) mean absolute value. This means that you will write -8 as +8.

Continuing on in the parenthesis, carry out (8 ÷ 4 = 2).

Next, we must do exponents.

We see that everything in the parenthesis is being raised to the power of three (cubed). Since we've solved what was in the parenthesis, we simply need to carry out ([tex]2^{3}[/tex] = 8).

Now, we need to quickly carry out [tex]\sqrt{64}[/tex]. Square roots are just whatever number can be multiplied by itself to get, in this case, 64.

[tex]\sqrt{64} = 8[/tex].

Finally, we must add what remains.

8 + 8 = 16.

So, (|7 - 3 x 5) | ÷ [tex]4)^{3}[/tex] + [tex]\sqrt{64}[/tex] = 16.

The correct answer is an option (d): Impossible.

Both the geometric mean and harmonic mean require positive values. However, in the given set of values, we have negative values (-11 and -14), which makes it impossible to calculate the geometric mean and harmonic mean. Therefore, the correct answer is that it is impossible to calculate the geometric mean and harmonic mean for the given values.

Step-by-step explanation:

1. Answer is 2

2. Answer is -3

3. Answer is 4

Answer:

i) -5x + 3/2

ii) x = 11

iii) x + 9/2

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Answer:

Step-by-step explanation:

First, we multiply 2×2 then the answer we obtain we add to it 6 which in total gives us 10

The person's expenditure is $1,755. (30 words)

To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.

Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)

In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.  

Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.

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The length of the arc in terms of π and the actual length is as follows;

8.17π m²

25.68 m²

Let's find the length of the arc of the circle as follows:

Therefore,

length of an arc = ∅ / 360 × 2πr

where

Hence,

∅ = 180 - 88 = 92 degrees

r = 16 m

length of an arc MA = 92 / 360 × 2 × π × 16

length of an arc MA = 2944π / 360

length of an arc MA = 8.17π

Therefore,

length of an arc MA = 25.68 m²

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The strength of the correlation as shown in the scatter plot can be concluded to be: b) no correlation.

To estimate the strength of the correlation in a scatter plot, visually assess the clustering and linearity of the data points. If the points cluster tightly around a linear trend, it indicates a strong correlation, whereas dispersed and non-linear points suggest a weak correlation.

However, if the points on a scatter plot do not exhibit a discernible pattern (as shown in the image given above), it can be concluded that there is no correlation between the variables being plotted.

Therefore, the answer is: b. no correlation.

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Step-by-step explanation:

The formula to calculate the circumference (C) of a circle is C = 2πr, where r represents the radius of the circle.

In this case, the given circumference is 68 cm. Plugging this value into the formula, we can solve for the radius (r):

68 = 2πr

To find the radius, we can divide both sides of the equation by 2π:

r = 68 / (2π)

Using an approximate value of π ≈ 3.14159, we can calculate the radius:

r ≈ 68 / (2 × 3.14159) ≈ 10.8419 cm

Therefore, the radius of the circle, which has a circumference of 68 cm, is approximately 10.8419 cm.

Therefore, The Radius of the Circle is 10.8 cm.

Answer:

the solution would be X=3 as 3.1 represents 3×1.

Answer:

f(0) = 1

f(1) = 21.1

Step-by-step explanation:

Do as the problem says:

[tex]f(0)=4^{2.2(0)}=4^0=1\\f(1)=4^{2.2(1)}=4^{2.2}\approx21.1[/tex]

(a) The average cost in 2011 is  $2247.64.

(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.

(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.6Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2011 - 2006) + 6

x = 5 + 6

x = 11 years.

Next, we would substitute 11 for x in the function:

g(11) = -1736.7 + 1661.6In(11)

g(11) = $2247.64

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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Juan could have a maximum of 3 quarters.

1. Let's assume Juan has x quarters.

2. The value of x quarters in dollars would be 0.25x.

3. We are given that Juan has 18 dimes, which have a value of 0.10 * 18 = $1.80.

4. The combined value of Juan's dimes and quarters should be less than or equal to $2.75.

5. We can write the equation: 0.25x + 1.80 ≤ 2.75.

6. Subtracting 1.80 from both sides of the equation, we have: 0.25x ≤ 2.75 - 1.80.

7. Simplifying, we get: 0.25x ≤ 0.95.

8. Dividing both sides of the inequality by 0.25, we have: x ≤ 0.95 / 0.25.

9. Evaluating the expression, we find: x ≤ 3.8.

10. Since Juan cannot have a fraction of a quarter, the maximum number of quarters he could have is 3.

11. However, we need to check if the combined value of the dimes and quarters is at least $0.20.

12. If Juan has 3 quarters (0.25 * 3 = $0.75) and 18 dimes ($1.80), the combined value is $0.75 + $1.80 = $2.55.

13. Since $2.55 is less than $2.75, Juan can have 3 quarters.

14. Therefore, the maximum number of quarters Juan could have is 3.

Note: There are no possible solutions where Juan has more than 3 quarters and still satisfies the conditions.

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The graph that displays the line of best fit for the data is the one where the line with the best fit goes through the points.

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Answer:

it 10:579

Step-by-step explanation:

it is the anser

Step-by-step explanation:

a. 4/64= 1/16 for red marble

b. 40/64= 5/8 black marbles

c. 20/64= 5/16 blue marble

d. highest: black marble

e. lowest: red marble

The line that intersects two of the planes is : Line X

The line that intersects one of the planes is : Line Z

The line that that has points on three of the planes shown is Line Y

From this figure you can see that there are 3 different levels and 3 different lines. One line intersects two planes (line X), another line intersects only one plane (line Z). Line Y, on the other hand, has points in all three planes.

A line y has points A and B in all three planes.

A plane is simply a plane that can be intersected by a straight line connecting any two points on the plane.

Therefore, we can conclude from the figure

A line that intersects two planes is: line x

A line that intersects one of the planes is: line Z

A line with points on the three planes shown is Line Y. 

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The correct statement regarding the relative extremas of F(x) is given as follows:

F(x) has a relative maximum at x = -1 and a relative minimum at x = -0.8.

Hence the extremas for this problem are given as follows:

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The probability that all four cards are clubs is approximately 0.0026. Option A.

To understand why, let's break down the calculation. In a well-shuffled deck, there are 13 clubs out of 52 cards.

When dealing the first card, there are 13 clubs out of the total 52 cards, so the probability of getting a club on the first draw is 13/52.

For the second card, after the first club has been removed from the deck, there are now 12 clubs left out of the remaining 51 cards. Therefore, the probability of getting a club on the second draw is 12/51.

Similarly, for the third card, after two clubs have been removed, there are 11 clubs left out of the remaining 50 cards. The probability of drawing a club on the third draw is 11/50.

Finally, for the fourth card, after three clubs have been removed, there are 10 clubs left out of the remaining 49 cards. The probability of drawing a club on the fourth draw is 10/49.

To find the probability of all four cards being clubs, we multiply the probabilities of each individual draw:

(13/52) * (12/51) * (11/50) * (10/49) ≈ 0.0026.

This calculation takes into account the fact that the deck is being dealt without replacement, meaning that the number of available clubs decreases with each draw.

The third option, 1/4, is incorrect because it assumes that each card dealt is independent and has an equal probability of being a club. However, as cards are drawn without replacement, the probability changes with each draw. So Option A is correct.

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Note the complete question is

A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.

What is the probability that all four cards are clubs?

A.) 13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026

B.) 13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023

C.) 1/4 because 1/4 of the cards are clubs

Answer:

Step-by-step explanation:

We must simplify and rearrange the variables to divide x in order to determine the comparable inequality to the supplied inequality, -4(x + 7) 3(x - 2).

Below are the steps to solve the problem:

-4(x + 7) < 3(x - 2)

Expanding the equation:

-4x-28<3x-6

Gather the variable term on one side and constants on the other:

Adding -4x and 28 on both sides:

-4x + 4x - 28 + 28 < 3x + 4x - 6 + 28

=>0 < 7x + 22

To make the coefficient of x positive, we divide the entire inequality by 7:

0/7 < (7x + 22)/7

=> 0 < x + 22/7

Answer:

[tex]f(x) = - 3 {x}^{2} - 6x - 1[/tex]