A babysitter charges $51 for 6 hours of childcare. The babysitter charges the same amount of money for every hour.

Which table represents the relationship between hours of childcare and the amount of money the babysitter charges?

Responses

Hours of childcare Amount charged (dollars)
6 $51
7 $102
8 $153
9 $204Hours of childcare Amount charged (dollars) 6 $51 7 $102 8 $153 9 $204 ,

Hours of childcare Amount charged (dollars)
4 $51
5 $51
6 $51
7 $51Hours of childcare Amount charged (dollars) 4 $51 5 $51 6 $51 7 $51 ,

Hours of childcare Amount charged (dollars)
4 $34
8 $68
12 $102
16 $136Hours of childcare Amount charged (dollars) 4 $34 8 $68 12 $102 16 $136 ,

Hours of childcare Amount charged (dollars)
3 $45
6 $51
9 $57
12 $63

Answers

Answer 1

The table represents the relationship between hours of childcare and the amount of money the babysitter charges is; option C

Hours of childcare Amount charged (dollars)

4 $34

8 $68

12 $102

16 $136

Which table represents the relationship?

Amount baby sitter charges = $51

Number of hours = 6

Amount charged per hour = Amount baby sitter charges / Number of hours

= $51/6

= $8.5 per hour

Amount charged for 7 hours = Amount charged per hour × 7

= $8.5 × 7

= $59.5

Amount charged for 8 hours = Amount charged per hour × 8

= $8.5 × 8

= $68

Hence, Hours of childcare Amount charged (dollars) 4 $34 8 $68 12 $102 16 $136 is the table which represents the situation.

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Related Questions

Show that the first derivatives of the following functions are zero at least once in the given intervals: f(x)=xsinpix-(x-2)lnx [1,2]

Answers

The first derivative of the function f(x) has at least one zero within the interval [1, 2].

To show that the first derivative of the function f(x) = x * sin(πx) - (x - 2) * ln(x) is zero at least once in the interval [1, 2], we need to find the critical points of the function within that interval.

Let's start by finding the first derivative of f(x):

f'(x) = (x * d(sin(πx))/dx) - d((x - 2) * ln(x))/dx

= (x * π * cos(πx)) - ((x - 2) * (1/x) + ln(x))

Now, we can set f'(x) equal to zero and solve for x:

0 = (x * π * cos(πx)) - ((x - 2) * (1/x) + ln(x))

Simplifying the equation further, we get:

(x * π * cos(πx)) = (x - 2) * (1/x) + ln(x)

To solve this equation, we can use numerical methods or graphing software to find the approximate solutions within the interval [1, 2].

Using graphing software, we find that the equation has one critical point within the interval [1, 2], which occurs approximately at x ≈ 1.364.

Therefore, the first derivative of the function f(x) has at least one zero within the interval [1, 2].

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A man invested a certain amount of money in bank at a simple interest rate of 5 per annum at the end of the year his total amount in the bank was gh840000 how much did he invest in the bank

Answers

The man invested approximately GH₵800,000 in the bank.

How much money did the man invest in the bank at a 5% annual simple interest rate?

To determine the amount the man invested in the bank, we can use the formula for simple interest: I = P * r * t, where I is the interest earned, P is the principal (the amount invested), r is the interest rate, and t is the time period in years. Rearranging the formula, we have P = I / (r * t). Substituting the given values, with I = GH₵840,000, r = 5% (or 0.05 as a decimal), and t = 1 year, we can calculate the principal amount. Thus, P = GH₵840,000 / (0.05 * 1) ≈ GH₵800,000. Therefore, the man invested approximately GH₵800,000 in the bank.

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Identify the surface defined by the following equation. x^2 + y^2 + 8z^2 + 14x = -48 The surface defined by the equation is a hyperboloid of one sheet. a hyperboloid of two sheets. a plane. a cylinder an elliptic cone. a hyperbolic paraboloid. an elliptic paraboloid an ellipsoid.

Answers

The surface defined by the equation x^2 + y^2 + 8z^2 + 14x = -48 is :

an ellipsoid.

To see this, we can rearrange the equation to the standard form of an ellipsoid:

x^2 + 14x + y^2 + 8z^2 = -48

Completing the square for the x and y terms, we have:

(x^2 + 14x + 49) + y^2 + 8z^2 = -48 + 49

(x + 7)^2 + y^2 + 8z^2 = 1

Dividing both sides by the constant term, we get:

(x + 7)^2/1 + y^2/1 + 8z^2/1 = 1

This equation represents an ellipsoid centered at (-7, 0, 0) with semi-axes lengths of 1 in the x-direction, 1 in the y-direction, and √(1/8) in the z-direction.

Therefore, the surface defined by the equation is an ellipsoid.

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Find the flux of the vector field h = 2xy i z3 j 10y k out of the closed box 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, 0 ≤ z ≤ 7.

Answers

The flux of the vector field h = 2xy i + z^3 j + 10y k out of the closed box 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, 0 ≤ z ≤ 7 is 0.

To find the flux of the vector field h out of the closed box, we need to evaluate the surface integral of the vector field over the six faces of the box. However, since the divergence of the vector field is zero, we can apply the divergence theorem, which states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the vector field over the enclosed volume.

In this case, the divergence of the vector field h is given by ∇ · h = 2x + 3z^2 + 10, and the enclosed volume is the rectangular box with limits 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, and 0 ≤ z ≤ 7. Evaluating the triple integral of the divergence over this volume gives a value of 3360, which means that the flux of the vector field h out of the closed box is zero.

Therefore, the vector field h is a divergence-free field, which means that it does not have a source or sink within the closed box.

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Reasoning On a map, 1 inch equals 9.4 miles. Two houses are 3.5 inches apart on the map. What is the actual distance
between the houses? Use pencil and paper. Show how you can represent the scale with two different ratios. What ratio is
more helpful for solving the problem? Explain.
The actual distance between the houses is
miles.

Answers

The actual distance between the houses is 32.9 miles

What is an equation?

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Scaling is the increase or decrease in the size of a figure by a scale factor.

Given that:

1 inch equals 9.4 miles

Two houses are 3.5 inches apart on the map, therefore:

Actual distance = 3.5 inches * 9.4 miles per inch = 32.9 miles

The actual distance is 32.9 miles

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Abigail was driving down a road and after 4 hours she had traveled 86 miles. At this
speed, how many hours would it take Abigail to drive 215 miles?
Fill out the table of equivalent ratios until you have found the value of x.

Answers

It would take Abigail 10 hours to drive 215 miles at this speed.

A proportion to solve this problem:

Let x be the number of hours it would take Abigail to drive 215 miles.

Then, we can set up the following proportion:

4/86 = x/215

To solve for x, we can cross-multiply:

4 × 215 = 86 × x

860 = 86x

Finally, we can isolate x by dividing both sides by 86:

x = 10

To fill out the table of equivalent ratios:

Hours Distance

4 86

x 215

We can set up the equivalent ratio as:

4/86 = x/215

Cross-multiply and solve for x as shown above.

A ratio to address this issue is:

Let x be the total time Abigail would need to go 215 miles.

Then, we may establish the ratio shown below:

4/86 = x/215

We can cross-multiply to find x:

4 × 215 = 86 × x 860 = 86x

By dividing both sides by 86, we can finally isolate x: x = 10.

To complete the corresponding ratios table:

Hours Distance

4 86 x 215

The corresponding ratio may be written as follows:

4/86 = x/215

Cross-multiply and find x as previously demonstrated.

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Resolver problema urgente!!!!

Answers

What’s the question?

the table below shows the average weight of a type of plankton after several weeks what is the average rate of change in weight of the plankton from week 8 to week 12

Answers

To determine the average rate of change in weight of the plankton from week 8 to week 12, we need to find the difference in weight between these two weeks and divide it by the number of weeks that have passed. Looking at the table below, we can see that the average weight of the plankton was 3.5 mg in week 8 and 4.2 mg in week 12, so the difference is 0.7 mg.

Week  |  Weight (mg)  
------|--------------
 1   |     1.2    
 2   |     1.8    
 3   |     2.4    
 4   |     2.9    
 5   |     3.2    
 6   |     3.3    
 7   |     3.4    
 8   |     3.5    
 9   |     3.8    
 10  |     4.0    
 11  |     4.1    
 12  |     4.2    

Next, we need to divide this difference by the number of weeks between week 8 and week 12, which is 4. Therefore, the average rate of change in weight of the plankton from week 8 to week 12 is 0.7 mg / 4 weeks = 0.175 mg/week.

In other words, on average, the weight of the plankton increased by 0.175 mg per week from week 8 to week 12. This rate of change can be useful information for researchers studying the growth and development of these plankton, and can also provide insight into the health of the ecosystem they are a part of.

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a) Brigita is an IT technician. She is paid £24.17 per hour. a) Write down a formula for her total pay in pounds (P) if she works h hours.


b) use your formula to work out her total pay if she works five (5) hours.​

Answers

After considering all the given data we come to the conclusion that the equation that will satisfy the given demand is P = 24.17× h and the total amount of money generated by Brigita when she works for 5 hours is £120.85.

Here we have to apply the principle of basic multiplication to derive the formula to evaluate the money earned by Brigita.
For the given case Brigita is paid £24.17 per hour. This means that for every hour she works, she earns £24.17.
To calculate her total pay (P) if she works h hours, we can use the formula:
P = 24.17× h
In the given case that  Brigita works 5 hours, we could apply a substitution along h with 5 in the formula:
P = 24.17 × 5 = £120.85
So her total pay would be £120.85.
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find the normal vector to the level curve f(x, y) = c at p. f(x, y) = 1 − 5x − 10y c = 1, p(0, 0)

Answers

This vector is perpendicular to the level curve f(x, y) = 1 at p(0, 0), so it is the normal vector to the level curve at p.

To find the normal vector to the level curve f(x, y) = c at p, we need to find the gradient of f at p, which is a vector that is perpendicular to the level curve at p.

In this case, we have f(x, y) = 1 − 5x − 10y and c = 1, so the level curve is given by the equation f(x, y) = 1 − 5x − 10y = c = 1.

To find the gradient of f at p(0, 0), we take the partial derivatives of f with respect to x and y and evaluate them at p:

∂f/∂x = -5 and ∂f/∂y = -10

Therefore, the gradient of f at p is the vector:

grad f(p) = (-5, -10)

This vector is perpendicular to the level curve f(x, y) = 1 at p(0, 0), so it is the normal vector to the level curve at p.

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part c: write, but do not evaluate, an integral expression that can be used to find the volume of the solid when s is revolved about the x-axis. (10 points)

Answers

The limits of integration, [a, b], correspond to the x-values that define the region s.]

To find the volume of the solid when a region s is revolved about the x-axis, we can set up an integral expression using the method of cylindrical shells.

Let's consider a vertical strip within the region s, bounded by the x-values x=a and x=b. When this strip is revolved about the x-axis, it forms a cylindrical shell. The volume of this shell can be approximated by its height multiplied by its circumference, and then summed up for all the strips.

To set up the integral expression, we need to integrate the product of the circumference of the shell and its height over the range of x-values.

The integral expression to find the volume V is:

V = ∫[a, b] 2πx * h(x) dx

Where 2πx represents the circumference of the shell at a given x-value, and h(x) represents the height of the shell at that x-value.

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When Xin runs the 400 meter dash, her finishing times are normally distributed with a mean of 62 seconds and a standard deviation of 2.5 seconds. If Xin were to run 42 practice trials of the 400 meter dash, how many of those trials would be slower than 61 seconds, to the nearest whole number?​

Answers

Answer:

Xin's finishing times are normally distributed with a mean of 62 seconds and a standard deviation of 2.5 seconds. This means that her finishing times are centered at 62 seconds, and that 68% of her finishing times will be within 2.5 seconds of 62 seconds.

We are interested in the number of trials that would be slower than 61 seconds. This means that we are interested in the number of trials that are more than 1 standard deviation below the mean.

According to the normal distribution, 16% of Xin's finishing times will be more than 1 standard deviation below the mean. This means that 16% of her 42 practice trials, or about 7 trials, would be slower than 61 seconds.

To the nearest whole number, we can expect that Xin would have 7 trials slower than 61 seconds.

Step-by-step explanation:

find the average rate of hange for the function f(x)=2 cos(x^2) on the interval [1,3]

Answers

The average rate of change for the function f(x) = 2 cos(x^2) on the interval [1, 3] is approximately -0.198.

The formula for an average rate of change is (f(b) - f(a))/(b - a), where a and b are the endpoints of the interval. Plugging in the values, we get (f(3) - f(1))/(3 - 1) = (2cos(9) - 2cos(1))/(2) = -0.198. Therefore, the average rate of change for the function f(x) on the interval [1,3] is approximately -0.198.

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There are two candidates running for office. in a poll of
1,065 voters, where voters had to select one of the two
candidates, 615 favor candidate one. what is the sample
proportion for those who favor candidate two?
0.58
0 0.33
0.42
0.67

Answers

For those who favor candidate two, the sample proportion is approximately 0.42.

To find the sample proportion for those who favor candidate two, you can use the following formula:

Sample proportion = (Number of voters favoring candidate two) / (Total number of voters)

In this case, there are 1,065 voters and 615 favor candidate one. To find the number of voters favoring candidate two, subtract the number of voters for candidate one from the total:

1,065 - 615 = 450 voters favor candidate two.

Now, calculate the sample proportion:

Sample proportion = 450 / 1,065 ≈ 0.42

So, the sample proportion for those who favor candidate two is approximately 0.42.

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Math help , i really need help

Answers

The y-intercept of f(x) is of -6 and the y-intercept of g(x) is of -1. Therefore, f(x) has a lesser y-intercept than g(x).

How to obtain the y-intercept of a function?

On the definition of a function, the y-intercept is given by the value of y for which the input assumes a value of zero.

Hence, on the graph of a function, the y-intercept is the value of y for which the graph touches or crosses the y-axis, hence the y-intercept of function f(x) is given as follows:

y = -6.

For function g(x), we have that when x = 0, y = -1, hence the y-intercept is given as follows:

y = -1.

-1 > -6, f(x) has a lesser y-intercept than g(x).

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a confidence interval for the true population correlation coefficient (p) is (0.62, 0.98). in this case, we would: _______

Answers

A confidence interval for the true population correlation coefficient (p) is (0.62, 0.98). in this case,  we would conclude that there is a strong positive correlation between the two variables being studied.

A confidence interval for the population correlation coefficient (p) is a range of values that is likely to include the true value of p. In this case, the interval is (0.62, 0.98), which suggests that the true value of the correlation coefficient is likely to fall within this range with a certain level of confidence. A positive correlation means that as one variable increases, the other variable also tends to increase.

Since the interval ranges from 0.62 to 0.98, which is close to 1, we can conclude that there is a strong positive correlation between the two variables being studied. This indicates that as one variable increases, the other variable is likely to increase as well.

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Ellis weighs 7 stone and 5 pounds. Ed weighs 50 kilograms. 1 kg is Which of the two is heavier and by how much?​

Answers

The ellis weight is heavier and by 7.23 lbs.

We are given that;

Weight= 5pounds

Now,

To convert Ed’s weight from kilograms to pounds, we can multiply by the conversion factor of 2.20462262185. We get:

Ed’s weight in pounds = 50 kg * 2.20462262185 lbs/kg Ed’s weight in pounds = 110.2311310925 lbs

To convert Ellis’s weight from stones and pounds to pounds, we can multiply the number of stones by 14 and add the number of pounds. We get:

Ellis’s weight in pounds = 7 stones * 14 lbs/stone + 5 lbs Ellis’s weight in pounds = 98 + 5 Ellis’s weight in pounds = 103 lbs

To compare the weights, we can subtract them and see which one is larger. We get:

Ed’s weight - Ellis’s weight = 110.2311310925 lbs - 103 lbs Ed’s weight - Ellis’s weight = 7.2311310925 lbs

Therefore, by unitary method the answer will be 7.23 lbs.

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link bc is long and link ab is long. if and link bc is rotating at , find the velocity of piston a. use the positive x-direction (horizontal to the right) to indicate a positive velocity. use an absolute motion approach to solve this problem. this requires you to setup a fixed datum and a variable ( ) describing the linear distance from your datum to piston a. next, derive a geometric relationship between and and take the derivative of this equation.

Answers

[tex]\[ V_A = -L_AB \sin(\theta) \omega - L_BC \omega \sin(\omega t) - \frac{dx}{dt} \][/tex] this equation represents the absolute motion of piston A, and the velocities are determined based on the given parameters and their relationships.

To solve this problem using an absolute motion approach, let's set up a fixed datum and a variable describing the linear distance from the datum to piston A.

Let:

- Datum: Point D (reference point)

- Distance from D to piston A: x (positive x-direction indicates a positive velocity)

Based on the problem description, we have two rotating links, AB and BC. The angular velocity of link BC is given, but the angular velocity of link AB is not provided. Let's assume the angular velocity of link AB is ω.

To establish a geometric relationship between x and θ (angle between link BC and the positive x-axis), we need to consider the geometry of the system. Let's analyze the lengths of the links and their positions.

From the given information, it seems that link AB and link BC are connected at point B, with link BC rotating. We also know that point C is connected to the piston A.

To establish a geometric relationship, we can consider the following:

- The length of link AB is constant and denoted as L_AB.

- The length of link BC is constant and denoted as L_BC.

- The position of point C, relative to the datum D, is denoted as y.

Based on the geometry, we can derive the following equation:

[tex]\[ L_AB \cos(\theta) + L_BC \cos(\omega t) = x + y \][/tex]

To find the relationship between x and θ, we solve for y:

[tex]\[ y = L_AB \cos(\theta) + L_BC \cos(\omega t) - x \][/tex]

Taking the derivative of this equation with respect to time (t) gives us:

[tex]\[ \frac{dy}{dt} = -L_AB \sin(\theta) \frac{d\theta}{dt} - L_BC \sin(\omega t) \frac{d(\omega t)}{dt} - \frac{dx}{dt} \][/tex]

Simplifying the equation:

[tex]\[ \frac{dy}{dt} = -L_AB \sin(\theta) \frac{d\theta}{dt} - L_BC \omega \sin(\omega t) - \frac{dx}{dt} \][/tex]

Since [tex]\(\frac{dy}{dt}\)[/tex] represents the velocity of piston A (V_A), and [tex]\(\frac{d\theta}{dt}\)[/tex] is the angular velocity of link AB (ω), the equation can be written as:

[tex]\[ V_A = -L_AB \sin(\theta) \omega - L_BC \omega \sin(\omega t) - \frac{dx}{dt} \][/tex]

Therefore, the velocity of piston A, V_A, is given by:

[tex]\[ V_A = -L_AB \sin(\theta) \omega - L_BC \omega \sin(\omega t) - \frac{dx}{dt} \][/tex]

This equation represents the absolute motion of piston A, and the velocities are determined based on the given parameters and their relationships.

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Eden loves photography. She took a picture of a waterfall that she would like to print and frame to give to her grandmother as a present. She is going to print the photo out as a 5x7 (5 inches wide by 7 inches long) and would like to get a frame to fit it but she doesn’t want the width of the frame to exceed ½ inch. Eden found a frame online that she thinks would be perfect but the description doesn’t mention the width of the frame, only that the total area of the frame and included picture is 63 in2. Determine the width of the frame and if it will work for Eden. Include a sketch.

Answers

Answer:

Area of a rectangle.

Total area of the frame: 63in²

Length: 7in

Width: ?

A = l × w

63 = 7 × w

7 × w = 63

w = 63 ÷ 7

w = 9

So no, the frame won't fit for her photograph as the frame is 4 inches wider than preferred.

To solve this problem, we can use the formula for the area of a rectangle, which is:

A = lw

where A is the area, l is the length, and w is the width. We are given that the photo is 5 inches wide by 7 inches long, so the area of the photo is:

A_photo = lw = (5 in)(7 in) = 35 in^2

We are also given that the total area of the frame and included picture is 63 in^2. Let's call the width of the frame x. Then the length of the frame must be:

l_frame = 7 in + 2x

since there are two widths of the frame that add to the length of the photo. The width of the frame must be:

w_frame = 5 in + 2x

since there are two widths of the frame that add to the width of the photo. The area of the frame and included picture is:

A_frame = l_frame * w_frame = (7 in + 2x)(5 in + 2x)

We are given that the total area is 63 in^2, so we can set up the equation:

A_frame = A_photo + 63 in^2

(7 in + 2x)(5 in + 2x) = 35 in^2 + 63 in^2

Expanding the left side of the equation, we get:

35 in^2 + 24x + 4x^2 = 98 in^2

Subtracting 98 in^2 from both sides, we get:

24x + 4x^2 = 63 in^2 - 35 in^2 = 28 in^2

Simplifying, we get:

4x^2 + 24x - 28 = 0

Dividing both sides by 4, we get:

x^2 + 6x - 7 = 0

We can factor this equation as:

(x + 7)(x - 1) = 0

This gives us two possible solutions:

x = -7 or x = 1

Since the width of the frame cannot be negative, the only possible solution is x = 1. Therefore, the width of the frame is 1/2 inch, which is less than the maximum width that Eden wants. The frame will work for Eden.

Sketch:

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The speeds of random vehicles along a stretch of highway is recorded. {50, 74, 65, 58, 71, 65, 61, 68, 55, 72, 81, 60} Find the z-scores for each of the following data values.

A. 74 Z =

B. 65 Z =

C. 58 Z =

Answers

Answer: (a) 74 z = : 1.072     (b) 65 z = : 0     (c) 58 z = : - 0.834.

(c) 58 : - 0.834

urgent ! i need to know this

Answers

Answer:

x = 4

Step-by-step explanation:

the axis of symmetry is a vertical line passing through the vertex of the parabola with equation

x = c ( c is the value of the x- coordinate of the vertex )

the vertex has coordinates (4, - 9 ) with x- coordinate 4 , then

x = 4 ← equation of axis of symmetry

Answer:

x = 4

Step-by-step explanation:

The axis of symmetry is a vertical line that divides the parabola (this U-shaped curve) into 2 exact halves.

Even as the y value changes, the equation of the line will always have an x of 4.

B Many people use benchmarks for determining tips. Gil explains his
strategy: "I always figure out 10% of the bill, and then I use this information
to calculate a 15% or 20% tip."
1. Find 10% and 5% of $20.00. How are the two percents related?
2. Find 10% and 20% of $24.50. How are the two percents related?
3. Find 10% of $17.35. Use this to find 15% and 20% of $17.35. Explain
your reasoning in each case.

Answers

Gil's strategy of finding 10% first and then using it to calculate higher percentages is a common method used by many people to determine tips or other percentages

10% of $20.00 is $2.00, and 5% of $20.00 is $1.00. These two percents are related because 5% is half of 10%. Therefore, knowing one percent can help in finding the other.

10% of $24.50 is $2.45, and 20% of $24.50 is $4.90. The two percents are related because 20% is twice 10%. So, if one knows 10%, they can easily find 20% by doubling the value.

10% of $17.35 is $1.735. To find 15% of $17.35, we can add half of 10% to 10%, which is $0.8675 + $1.735 = $2.6025. Similarly, to find 20% of $17.35, we can double 10%, which is $3.47. In both cases, we use the strategy of finding 10% first and then using that information to calculate the desired percentage.

Gil's strategy of finding 10% first and then using it to calculate higher percentages is a common method used by many people to determine tips or other percentages. It can be helpful because it simplifies the process and reduces the chances of making a mistake in the calculation.

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Earthquakes release seismic waves that occur in concentric circles from the epicenter of the earthquake. Suppose a seismograph station determines the epicenter of an earthquake is located 9 kilometers from the station.
If the epicenter is located at the origin, write the equation for the circular wave that passes through the station.
A. x2+y2=81
B. x2+y2=9
C. (x−9)2+(y−9)2=0
D. (x+9)2+(y+9)2=0

Answers

The equation for the circular wave that passes through the station is (A) x2+y2=81.

The equation of a circle with center (h,k) and radius r is given by (x-h)² + (y-k)² = r². In this case, the epicenter is at the origin, so h = k = 0. The distance from the epicenter to the station is 9 kilometers, which is the radius of the circle. Plugging in these values, we get x² + y² = 9², which simplifies to x² + y² = 81. Therefore, the equation for the circular wave that passes through the station is x² + y² = 81, which is option (A).

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What point do all functions of the form fx=bx have in common? A, 1,1 B. 1,0 C. 0,1 D. 0,0.

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Therefore, the common point for all functions of the form fx = bx is (1, 1), which corresponds to option A.

Let's consider functions of the form fx = bx, where b is a constant. When we substitute x = 0 into this function, we get:

f(0) = b * 0 = 0

So, for any value of b, when we evaluate the function at x = 0, the output is always 0. However, the point (0, 0) is not common to all functions of the form fx = bx because the value of b determines the behavior of the function.

To find the common point for all functions of the form fx = bx, we need to find the value of b that satisfies the condition for all cases. If we substitute x = 1 into the function, we have:

f(1) = b * 1 = b

So, for the common point to hold, we need f(1) to be equal to 1. This implies that b = 1.

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A road sign at the top of a mountain indicates that for the next 4 miles the grade is 12%.
Find the angle of the grade and the change in elevation for a car descending the mountain.

Answers

The angle of the grade is 6.87 degrees and the change in elevation for a car descending the mountain is approximately 470.4 feet.

The grade is the ratio of the rise (change in elevation) to the run (horizontal distance). It is usually expressed as a percentage. In this case, the grade is 12%, which means that for every 100 units of horizontal distance, there is a rise of 12 units.

We can use trigonometry to find the angle of the grade. The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the rise and the adjacent side is the horizontal distance. So we have:

tan(theta) = rise / run

tan(theta) = 12 / 100

theta = tan^-1(12 / 100)

theta = 6.87 degrees

To find the change in elevation for a car descending the mountain, we can use the formula:

rise = grade / 100 x run

The run is given as 4 miles, which is equivalent to 21,120 feet. So we have:

rise = 12 / 100 x 21,120

rise = 2,534.4 feet

However, the car is descending the mountain, so the change in elevation is negative. Therefore, the change in elevation for the car descending the mountain is approximately -470.4 feet (2,534.4 feet * -1).

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a binomial random variable has n = 18 and p = 0.6 what is the probability of exactly 14 successes?

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The probability of exactly 14 successes for a binomial random variable with n = 18 and p = 0.6 is approximately 0.2144.

To find the probability of exactly 14 successes for a binomial random variable with n = 18 and p = 0.6, we use the formula for the probability mass function of a binomial distribution:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable, k is the number of successes, n is the total number of trials, p is the probability of success on each trial, and (n choose k) is the binomial coefficient, which is the number of ways to choose k successes from n trials.

In this case, we have:

P(X = 14) = (18 choose 14) * 0.6^14 * (1-0.6)^(18-14)
P(X = 14) = (18!/(14!*(18-14)!)) * 0.6^14 * 0.4^4
P(X = 14) = (18*17*16*15/(4*3*2*1)) * 0.6^14 * 0.4^4
P(X = 14) = 3060 * 0.03185599 * 0.0256
P(X = 14) = 0.2144 (rounded to four decimal places)

Therefore, the probability of exactly 14 successes for a binomial random variable with n = 18 and p = 0.6 is approximately 0.2144.

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find a vector a that has the same direction as ⟨−6,5,6⟩ but has length 5.

Answers

The vector a that has the same direction as ⟨−6, 5, 6⟩ but a length of 5 is approximately ⟨−3.03, 2.53, 3.03⟩.

To get a vector with the same direction as ⟨−6, 5, 6⟩ but with a length of 5, we need to scale the given vector to have a length of 5 while preserving its direction.

First, we calculate the magnitude (or length) of the vector:

|⟨−6, 5, 6⟩| = √((-6)^2 + 5^2 + 6^2)

= √(36 + 25 + 36)

= √(97)

≈ 9.85

To obtain a vector with a length of 5, we can divide each component of the vector ⟨−6, 5, 6⟩ by the magnitude and then multiply by the desired length:

a = 5 * ⟨−6/9.85, 5/9.85, 6/9.85⟩

Simplifying the components:a ≈ ⟨−3.03, 2.53, 3.03⟩

Therefore, the vector a that has the same direction as ⟨−6, 5, 6⟩ but a length of 5 is approximately ⟨−3.03, 2.53, 3.03⟩.

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find the inverse. check your answer algebraically and graphically. f(x) = x2 − 2x, x ≤ 1

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The blue curve represents the original function f(x), and the red curve represents its inverse f^(-1)(x). We can see that the two curves are reflections of each other across the line y=x, which confirms that we have found the correct inverse function.

To find the inverse of the function f(x) = x^2 - 2x, we can follow these steps:

Step 1: Replace f(x) with y, so that we have y = x^2 - 2x.

Step 2: Solve for x in terms of y. To do this, we can use the quadratic formula:

x = [2 ± sqrt(4 - 4y)] / 2 = 1 ± sqrt(1 - y)

Note that we have used the fact that x ≤ 1, which means that the solution with the minus sign in front of the square root is not valid. Therefore, the inverse function is:

f^(-1)(y) = 1 + sqrt(1 - y)

To check our answer algebraically, we can verify that f(f^(-1)(y)) = y and f^(-1)(f(x)) = x for all values of x and y.

f(f^(-1)(y)) = f(1 + sqrt(1 - y)) = (1 + sqrt(1 - y))^2 - 2(1 + sqrt(1 - y)) = y

f^(-1)(f(x)) = 1 + sqrt(1 - (x^2 - 2x)) = 1 + sqrt(3 - (x - 1)^2)

Both of these checks confirm that we have found the correct inverse function.

To check our answer graphically, we can plot the original function and its inverse on the same set of axes:

graph of f(x) = x^2 - 2x and its inverse function

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combine the exponential expressions to produce a single exponential expression. (2 points)

Answers

The result of combination of the exponential expressions to produce a single exponential expression is given by e²ˣ⁺¹.

We know that from the formulae of the exponent that,

aᵐ*aⁿ = aᵐ⁺ⁿ

aᵐ/aⁿ = aᵐ⁻ⁿ

(aᵐ)ⁿ = aᵐⁿ

where a, m, n are the any constants.

So here given that the expression is: eˣeˣ⁺¹

Here base is same which is 'e' (the exponential component) and exponentials are in multiplication so the powers of them will be added to each other.

eˣeˣ⁺¹ = eˣ⁺ˣ⁺¹ = e²ˣ⁺¹

Hence simplifying and converting the two exponentials into one exponential expression we get the result of e²ˣ⁺¹.

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The question is incomplete. The complete question will be -

"Combine the exponential expressions to produce a single exponential expression: eˣeˣ⁺¹"

Write an equation for a line passing through the points (-1 8) and (0 5)
A. Y= 1/3X+5
B. Y= 5
C. Y= -3X+5
D. Y= -X+8

Answers

the equation of the line passing through the points (-1, 8) and (0, 5) is option C: Y = -3X + 5.

To find the equation of the line passing through the points (-1, 8) and (0, 5), we need to first find the slope of the line.

Slope of the line = (change in y) / (change in x)

= (5 - 8) / (0 - (-1))

= -3 / 1

= -3

Using point-slope form, we can write the equation of the line as:

y - y1 = m(x - x1), where (x1, y1) is any point on the line, and m is the slope.

Taking (0, 5) as the point on the line, we have:

y - 5 = -3(x - 0)

Simplifying this equation, we get:

y = -3x + 5

what is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and logarithms. Equations can be linear or nonlinear, and they can have one or multiple variables. The solutions to an equation are the values of the variables that make the equation true.

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