Yak Travel Agency arranges trips for climbing Mount Everest. For each trip, they charge an initial fee in addition to $0.15 for each vertical meter climbed. For instance, the price for climbing all the way to the summit, which is 3500 meters above the base of the mountain, is $645.



Let y represent the fee (in dollars) of a trip where they climbed x vertical meters.


Complete the equation for the relationship between the fee and vertical distance.


y=

The expected value of the insurance policy is $46,738.831. This means that, on average, the insurance company can expect to pay out approximately $46,738.831 for each policy sold. To calculate the expected value of the insurance policy, we need to consider both the cost of the policy and the probability of an event occurring.

In this case, the event is the man living through the year. The expected value is calculated by multiplying each possible outcome by its corresponding probability and summing them up. In this scenario, there are two possible outcomes: the man living or dying.

If the man lives through the year, the insurance company does not have to pay out the coverage amount, so the outcome is $0. However, if the man dies, the insurance company will have to pay out the coverage amount of $159,667.

The probability of the man living through the year is given as 0.707, while the probability of him dying is 1 - 0.707 = 0.293.

Now we can calculate the expected value:

Expected Value = (Probability of Living * Outcome if Living) + (Probability of Dying * Outcome if Dying)

             = (0.707 * $0) + (0.293 * $159,667)

             = $0 + $46,738.831

             = $46,738.831

Therefore, the expected value of the insurance policy is $46,738.831. This means that, on average, the insurance company can expect to pay out approximately $46,738.831 for each policy sold.

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Answer:

Step-by-step explanation:

twelve triangles make 2 hexagons, which means there are 12 groups of in 2

The SUV's speed before the collision would be greater than 40 m/s

Let's assume the initial speed of the SUV is denoted by V (the value we're trying to find). The momentum of the car before the collision can be calculated as the product of the car's mass (m₁) and its speed (40 m/s), which is given as 40m1. Similarly, the momentum of the SUV before the collision is given by the product of its mass (m₂) and its speed (V), which is Vm₂.

Since the two vehicles come to a halt, the total momentum after the collision is zero. Therefore, the sum of the momenta of the car and the SUV before the collision must also be zero:

40m₁ + Vm₂ = 0

Since the car's mass (m₁) and the SUV's mass (m₂) are not given, we cannot solve for the actual values. However, we can still determine the relationship between the speeds of the car and the SUV before the collision. By rearranging the equation, we can solve for V:

V = -40m₁/m₂

From the equation, we can see that the speed of the SUV before the collision (V) is directly proportional to the speed of the car (40 m/s) and inversely proportional to the mass ratio of the car (m₁) to the SUV (m₂). The negative sign indicates that the SUV was traveling in the opposite direction to the car.

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Answer:

D

Step-by-step explanation:

Answer:

Statement (b) is equivalent to statement (c), but neither is equivalent to statement (a).

Step-by-step explanation:

Let \(F\) denote that "Fido is our fish's name" and let \(R\) denote that "Rex is our dog's name". The statements listed in this question would then become:

Apply de Morgan's Law \(\lnot (P \land Q) \iff (\lnot P) \lor (\lnot Q)\) to rewrite statement (b). Let \(P = (\lnot F)\) and \(Q = (\lnot R)\). By de Morgan's Law:

\(\begin{aligned} & \lnot ((\lnot F) \land (\lnot R)) \\ \iff \; & \lnot (P \land Q)\\ \iff \; & (\lnot P) \lor (\lnot Q) && (\text{by de Morgan's Law}) \\ \iff \; & (\lnot (\lnot F)) \lor (\lnot (\lnot R)) \\ \iff \; & F \lor R\end{aligned}\).

In other words, statement (b) \(\lnot ((\lnot F) \land (\lnot R))\) is equivalent to statement (c) \(F \lor R\).

Statement (a) \(F \implies R\) isn't equivalent to \(F \lor R\).

For example, when \(F = \texttt{True}\) and \(R = \texttt{False}\), \(F \implies R\) would be false since \(\texttt{True}\) does not imply \(\texttt{False}\). However, for the same \(F\) and \(R\), \(F \lor R\) would be true since \(F = \texttt{True}\!\).

Answer:

f(y - 3) = y - 2

Step-by-step explanation:

to find f(y - 3) , substitute x = y - 3 into f(x) , that is

f(y - 3) = y - 3 + 1 = y - 2

The wideness of the actual balcony would be = 5.2 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

The actual size = scale factor × blueprint

where actual length = 9 inches

blueprint = 11.7 = 140.4 inches

scale factor = actual size/blue print

= 140.4/9 = 15.6

If the blue print width size = 4

the actual size = 4× 15.6 = 62.4 inches = 5.2 feet

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Answer:

0.5 pounds of butter.

Explanation

X pounds for 0.25 gallons.

0.5 gallon of cream - 1 pound of butter

0.25 gallons of cream - X pounds of butter

Applying cross multiplication:

0.5X = 0.25

X = 0.25 over 0.5 or 0.25/0.5

X = 0.5

Therefor, you could make 0.5 pounds of butter with 0.25 gallons of cream.

By the 0.25 gallons of cream, we can make 0.5 pounds of butter.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

It takes 0.5 gallons of cream to make 1 pound of butter.

So,

0.5 gallons of cream ⇒  1 pound of butter

Divide both sides by 2

0.5/2 gallons of cream ⇒  1/2 pound of butter

0.25 gallons of cream ⇒ 0.5 pounds of butter

Hence "By the 0.25 gallons of cream, we can make 0.5 pounds of butter".

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Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.

Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n

Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))

To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)

As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0

Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.

Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.

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Answer:

it is infinite solutions

Step-by-step explanation:

because 20+5t=20+5t even if you put any number as the variable

To set up the equation for the length of each supporting cable (d) as a function of the angle θ, we can use trigonometry.

The supporting cables form right triangles with the ground, where the tower serves as the height (h) of the triangle, and the length of the supporting cable (d) is the hypotenuse. The angle θ is the angle between the supporting cable and the ground.

Step-by-step process to set up the equation:

Step 1: Identify the Relevant Trigonometric Function

Since we know the height (h) of the triangle and the angle θ, we can use the trigonometric function "cosine" (cos) to relate the angle θ to the length of the supporting cable (d).

Step 2: Write the Equation

The cosine function relates the adjacent side (h) and the hypotenuse (d) of the right triangle:

cos(θ) = h / d

Step 3: Isolate the Variable (d)

To find the length of the supporting cable (d), we need to isolate the variable (d) on one side of the equation:

d = h / cos(θ)

Now, we have the equation that gives us the length of each supporting cable (d) as a function of the angle θ.

b. To find d when θ = 60° and when θ = 50°:

Step 4: Substitute the Values of h and θ into the Equation

In the given problem, the height (h) is given as 100 ft above the ground. We'll use this value to find d for θ = 60° and θ = 50°.

For θ = 60°:

h = 100 ft

θ = 60°

d = h / cos(θ)

d = 100 ft / cos(60°)

Using the value of cosine for 60° (cos(60°) = 0.5√3), we get:

d = 100 ft / (0.5√3) ≈ 115.47 ft (rounded to two decimal places)

For θ = 50°:

h = 100 ft

θ = 50°

d = h / cos(θ)

d = 100 ft / cos(50°)

Using the value of cosine for 50° (cos(50°) ≈ 0.64279), we get:

d = 100 ft / 0.64279 ≈ 155.67 ft (rounded to two decimal places)

So, when θ = 60°, the length of each supporting cable (d) is approximately 115.47 ft, and when θ = 50°, the length of each supporting cable (d) is approximately 155.67 ft.

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To model the length (d) of each supporting cable as a function of the angle (θ) that it makes with the ground, we can use trigonometry.

As mentioned before, the supporting cables form right triangles with the ground, where the tower serves as the height (h) of the triangle, and the length of the supporting cable (d) is the hypotenuse. The angle θ is the angle between the supporting cable and the ground.

Step-by-step process to derive the model:

Step 1: Identify the Relevant Trigonometric Function

Since we know the height (h) of the triangle and the angle θ, we can use the trigonometric function "cosine" (cos) to relate the angle θ to the length of the supporting cable (d).

Step 2: Write the Equation

The cosine function relates the adjacent side (h) and the hypotenuse (d) of the right triangle:

cos(θ) = h / d

Step 3: Isolate the Variable (d)

To find the length of the supporting cable (d), we need to isolate the variable (d) on one side of the equation:

d = h / cos(θ)

Now we have the equation that gives us the length of each supporting cable (d) as a function of the angle θ.

Step-by-step process to find d when θ = 60° and θ = 50°:

Given: h = 100 ft (height above the ground)

For θ = 60°:

θ = 60°

d = h / cos(θ)

d = 100 ft / cos(60°)

Step 4.1: Calculate the value of cos(60°):

cos(60°) = 0.5

Step 4.2: Substitute the value of cos(60°) into the equation:

d = 100 ft / 0.5

d = 200 ft

So, when θ = 60°, the length of each supporting cable (d) is 200 ft.

For θ = 50°:

θ = 50°

d = h / cos(θ)

d = 100 ft / cos(50°)

Step 4.3: Calculate the value of cos(50°):

cos(50°) ≈ 0.64279

Step 4.4: Substitute the value of cos(50°) into the equation:

d = 100 ft / 0.64279

d ≈ 155.67 ft (rounded to two decimal places)

So, when θ = 50°, the length of each supporting cable (d) is approximately 155.67 ft.

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9514 1404 393

Answer:

  $92,400

Step-by-step explanation:

The amount in the account after t years is ...

  A = P(1+rt)

where P is the principal invested, r is the annual interest rate, and t is the number of years.

Here, the number of years is (240 months)/(12 months/year) = 20 years, so the formula tells you the amount is ...

  A = $28,000(1+0.115*20) = $28000(3.3) = $92400

The total amount in the account after 240 months is $92,400.

hope this pic helps. enjoy

To determine the optimal order quantity for Rocky Mountain Tire Center, you must consider ordering costs, storage costs, and the purchase price of the tires. The order quantity should minimize the total cost including both ordering cost and storage cost.

The EOQ formula is given by: EOQ = √((2DS) / H)

Where: D = Annual demand (7,000 go-cart tires)

S = Ordering cost per order ($40) H = Holding cost - percentage of the purchase price (40% of the purchase price)

we need to determine the purchase price per tire based on the quantity ordered.

EOQ = √((2 * 7,000 * 40) / (0.4 * 15))

=118 tires

they should order approximately 118 tires.

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The rectangle is symmetrical about the y-axis. Then both the figures are rectangles and all the rectangles are similar. Then the correct option is B.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

The rectangle EFGH is dilated of the rectangle ABCD with a center of the dilation at the origin.

From the figure, it is clear that the rectangle is symmetrical about the y-axis. Then both the figures are rectangles and all the rectangles are similar.

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Answer:

x-7

Step-by-step explanation:

Answer and explanation:

Given: Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:  

Number of years 1 2 3

Option 1 (amount in dollars) 1100 1200 1300

Option 2 (amount in dollars) 1100 1210 1331  

To find:

Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2?  

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.  

Part C: Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1?

Solution:

Part A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years using option 1 and option 2, respectively.  

Part B: (n=n+100) and (n=n+100x) are the functions for each option to describe the value of the investment f(n), in dollars, after n years.  

Part C: Yes, there will be a significant difference of 1900 in the value of Belinda's investment after 20 years if she uses option 2 over option 1.

Part A:

In the case of option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This is because, in option one, the amount increases by a fixed amount every year.

In the case of option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. This is because, in option 2, the amount increase is higher than last year.

Part B:

For option 1, the function is

For option 2, the function is

Here, x is the increase in amount every consecutive year.

Part C:

After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference between 1900.

Therefore,

Part A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years using option 1 and option 2, respectively.  

Part B: (n=n+100) and (n=n+100x) are the functions for each option to describe the value of the investment f(n), in dollars, after n years.  

Part C: Yes, there will be a significant difference of 1900 in the value of Belinda's investment after 20 years if she uses option 2 over option 1.

Hope this helps

The total area of the garden when the rectangle with given vertices is added is 55 square feet.

Both length and breadth are metrics that are used to define an object's size. Although width is the measurement of an object's shorter dimension, length is the measurement of an object's longest dimension. The longer side of two-dimensional objects like rectangles is often referred to as the length, and the shorter side as the width. The length, width, and height, however, can refer to any one of the three dimensions in three-dimensional objects like boxes, depending on how the item is orientated.

The vertices of the new rectangle are (−21, 7), (−23, 7), (−21, 12), and (−23, 12).

The length of the rectangle is: 12 - 7 = 5

The width of the rectangular piece is: 23 - 21 = 2

The area of the rectangular piece is:

A = 5 × 2 = 10 square feet

The total area is:

Total area = 45 + 10 = 55 square feet

Hence, the total area of the garden when the rectangle with given vertices is added is 55 square feet.

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Answer: B.55 ft2

Step-by-step explanation:

The small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.

Similar triangles are triangles that have the same shape but can have different sizes. In this case, the shadow of the boy, the boy himself, and the light post form similar triangles.

Let h be the height of the light post, x be the distance between the boy and the light post, and s be the length of the shadow, we can use the following ratios -

(boy's height) / (boy's shadow) = (light post height) / (light post shadow)

i.e. (4 feet 6 inches) / (3 feet 4 inches) = (h) / (x)

Now, we can find the height of the light post by using the above equation and the given values of the boy's height and the shadow.

The small boy can measure the distance between him and the light post, and he can use this value in the above equation to determine the height of the light post. The equation is h/x = (4.5)/(3.33)

This is the ratio of the height of the light post and the distance between the boy and the light post, so h = (4.5 * x) / (3.33)

In this way, the small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.

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\(7x + 12 = 9x - 6\)

\(7x + 12 - 7x = 9x - 6 - 7x\)

\(12 = 2x - 6\)

\(12 - 6 = 2x -6 - 6\)

\(6 = 2x - 12\)

\(6 + 12 = 2x\)

\(18 = 2x\)

\(18 \div 2 = x\)

\(9 = \bold{ x}\)

In pythagoras, c is the hypotenuse. That is AC. Where a is AB and b is BC.

\( {c}^{2} = {a}^{2} + {b}^{2} \)

\( {(6 x + 5)}^{2} = {(7x + 12)}^{2} + {BC}^{2} \)

\( {((6 \times 9) + 5)}^{2} = {((7 \times 9)}^{2} + 12)^{2} +{BC}^{2} \)

\( {(54 + 5)}^{2} = {(63 + 12)}^{2} + {BC}^{2} \)

\( {59}^{2} = {75}^{2} + {BC}^{2} \)

\(3481 = 5625 + {BC}^{2} \)

\(3481 - 5625 = {BC}^{2} \)

\( - 2144 = {BC}^{2} \)

\( \sqrt{ - 2144} = BC\)

Answer:

its 10 bro calm down ok chill

Answer:

10

Step-by-step explanation:u have 5 and add 5 more

Answer:

B. 4

Step-by-step explanation:

there are 12 in. in one foot and since there are 2 ft there would be 24 in.

24 divided by 6 is 4 hope it helped :)

There are 4 pieces would be possible to cut 6 in. long board from 2 ft. long board.

The dimension of a physical quantity is defined as the power to which the fundamental quantities are raised to express the physical quantity

Here, Total board size = 2 ft

         We know that, 1 ft. = 12 in.

                  so, 2 ft. = 24 in.

We have to cut board into 6 in. board

Total number of boards = Bigger Board Size / Small size

                                         = 24 / 6

                                         = 4 pieces

Thus, there are 4 pieces would be possible to cut 6 in. long board from 2 ft. long board.

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Answer: Find the perimeter of the yard ( the distance around the yard).

A rectangle has two sides of each dimension.

The perimeter is 20 + 20 + 45 + 45 = 130 feet.

Now multiply the total feet by the cost per foot:

130 feet x 25 per foot = $3,250 total.

Step-by-step explanation:

Answer:

$225

Step-by-step explanation:

The area to be fenced in is 20 ft by 45 ft, or 900 ft^2.  But "25 per foot based on the area" is illogical.  Please ensure that you have copied this problem down accurately, and be sure to provide units of measurement:  did you mean $25 per square foot, or per foot, or what?

The fencing cost is usually dependent on the unit cost and the length of the yard perimeter.  The perimeter is P = 2L + 2W, which here is P = 2(45 ft) + 2(20 ft), or 130 ft.  If the fencing is 25 cents per foot, $130 ft of fencing would come to $32.50.

Answer:

B. -h

Step-by-step explanation:

Additive inverses are two numbers that add to 0.

h + (-h) = 0

-h is the additive inverse of h since h and -h add to 0.

Answer: B. -h

Answer:

-h

Step-by-step explanation:

The additive inverse of a number simply means that same number, but with an opposite sign. For example:

Additive inverse of 9 = -9

Additive inverse of -2 = 2

Additive inverse of -(-6) = -6

Additive inverse of -(+4) = 4

The required expression for the Junior started saving money and y represents the total money he has saved is y =2x.

Given that,
Junior is saving money in his piggy bank. He starts with and adds two pennies each day.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

Let the number of days, junior saved money be x and the total amount of money he saved be y.
He starts with and adds two pennies each day. which implies,

On day 1 he saved 2 pennies, the next day i.e. day 2 is saved 4 pence and so on and on day x he saved a total of 2x pennies in his piggy bank. Results,
y = 2x

Thus, the required expression for the Junior started saving money and y represents the total money he has saved is y =2x.

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Answer: the placement/ digest are the same but because on is positive and the other is negative, the answer will be different

Step-by-step explanation:

Answer:

different y-intercepts; same slopes
Step-by-step explanation:

if x=0, then y=7,-7

Answer:

1 3/15

1 5/15

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

3:12 is the amount of shaded circles to all circles, 8:2 is basically the same thing as 3:12 and 9:3 is the amount of shaded circles to the amount of non-shaded circles.  1:3 wouldn't work because it is not the right ratio.

The highest frequency of any score in the histogram would be 5/20 = 0.25.

The score that has the highest frequency is 8. This is determined by counting the number of bars corresponding to each score. In this histogram, there are 5 bars corresponding to the score 8, which is the highest number compared to any other score.

Formulaically, we can calculate the frequency for each score by dividing the number of observations for that score by the total number of observations. For the score 8, this would be 5/20 = 0.25. This is the highest frequency of any score in the histogram.

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