You babysat your neighbor's children, and they paid you $45 for 6 hours.

What is the rate?

What is the unit rate?

Write a function rule to represent this situation.

Alexander stacked  16 unit cubes required to build the rectangular prism.

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Here we need to find the number of cubes required to build the rectangular prism.

Here first we need to find how many cubes stack in the base layer

Number of unit cubes in the base layer = Number of cubes along the length * Number of cubes along the width

The number of unit cubes in the base layer = 2 * 4 = 8 cubes.

Total number of unit cubes in prism =Number of unit cubes in the base layer *Number of layers = 8 * 2 = 16 unit cubes

So, there are 16 unit cubes are required to build the rectangular prism.

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Complete question :

Alexander stacked unit cubes to build the rectangular prism below. Use the rectangular prism to answer​ the question.

How many cubes are required to build the rectangular prism?

There is a vertical asymptote at x = 0.

A vertical asymptote is a vertical line that the graph of a function approaches but never touches or crosses. In the case of a rational function such as f(x) = x^3/(x^2-4), vertical asymptotes occur where the denominator of the function is equal to zero.

In this case, the denominator is x^2 - 4, which is equal to zero when x = ±2. However, we need to check whether these values are in the domain of the function. Since the interval of interest is (–18, 19), we see that only x = 2 is in the domain of the function.Therefore, the only vertical asymptote of the function f(x) = x^3/(x^2-4) on the interval (–18, 19) is at x = 0, which is the value of x where the denominator is closest to zero.

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Where the above figures are given, The right triangles are: B and C.

Using the phythagoren theorem, we can determind the options that represent a right ttriangle.


A 5,8, and 9:

5^2 + 8^2 = 25 + 64 = 89

9^2 = 81

Not a right triangle.

B 20, 21, and 29:

20^2 + 21^2 = 400 + 441 = 841

29^2 = 841

It is a right triangle.

C 9, 12, and 15:

9^2 + 12^2 = 81 + 144 = 225

15^2 = 225

It is a right triangle.

D 5, 6, and 11:

5^2 + 6^2 = 25 + 36 = 61

11^2 = 121

Not a right triangle.

The right triangles are: B and C.

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The monthly payment for the loan is $328.05. So we can determine that the family can afford the monthly payment.

Money spend =  $400

Time = 120 months

Loan amount = $30,000

Interest rate = 6.5%.

The formula is given P = [tex]PV*(i / (1 - (1+i)^{-n}))[/tex]

The interest should be calculated at the monthly rate. So, we can divide the interest rate by 12.

i = 0.065/12 = 0.00541667  

Substituting the values into the formula,

P = [tex]30000 * 0.00541667 / (1 - (1+0.00541667)^{-120})[/tex]

P = $328.05

Therefore, we can conclude that the monthly payment for the loan is $328.05.

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Substituting these values into the expression for f(θ), we get:
f(θ) = -sin(θ) - cos(θ) + 5θ + 4

To find f, we need to integrate f''(θ) twice.

First, we integrate sin(θ) + cos(θ) with respect to θ to get f'(θ):

f'(θ) = -cos(θ) + sin(θ) + C1
where C1 is the constant of integration.
Next, we integrate f'(θ) with respect to θ to get f(θ):

f(θ) = -sin(θ) - cos(θ) + C1θ + C2

where C2 is the constant of integration.

Using the initial conditions given, we can solve for C1 and C2:
[tex]f(0) = -1 - 1 + C2 = 2[/tex]
C2 = 4
f'(0) = -1 + 0 + C1 = 4

C1 = 5

Substituting these values into the expression for f(θ), we get:
f(θ) = -sin(θ) - cos(θ) + 5θ + 4

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The equation of the line passing through the given points is y = 3x-1.

Given that is a line passing through two points (0, 2) and (-1, -1) we need to find the equation of the line using them,

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (0, 2) and (-1, -1),

Therefore, the required equation is =

y+1 = -1-2/-1 (x-0)

y+1 = 3x

y = 3x-1

Hence, the equation of the line passing through the given points is y = 3x-1.

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Answer:

b

Step-by-step explanation:

The expression √x+3 means the square root of x+3. We can rewrite this as (x+3)^(1/2), using the exponent rule that says taking the square root is the same as raising to the power of 1/2.

So the options become:

a. 3x^(1/2)

b. (x+3)^(1/2)

c. x^(1/2) + 3

d. (3x)^(1/2)

None of the other options match the given expression. So the correct answer is (b) (x+3)^(1/2).

To find the volume of a cone, we use the formula:

[tex]V = (1/3)\pi r^2h[/tex]

where V is the volume, r is the radius of the circular base, h is the height of the cone, and [tex]\pi[/tex] is approximately 3.14159.

In this problem, the height of the cone is given as 10 ft and the radius of the circular base is given as 6 ft.

First, we need to find the slant height of the cone. We can use the Pythagorean theorem:

[tex]l = \sqrt{(r^2 + h^2)[/tex]

[tex]l = \sqrt{(6^2 + 10^2)[/tex]

[tex]l = \sqrt{\\(36 + 100)[/tex]

[tex]l = \sqrt{136[/tex]

[tex]l = 11.66 ft[/tex]

Now we can substitute the values into the formula for the volume:

[tex]V = (1/3)\pi r^2h[/tex]

[tex]V = (1/3)\pi (6^2)(10)[/tex]

[tex]V = 120\pi /3[/tex]

[tex]V = 40\pi[/tex]

[tex]V= 125.6 cubic feet[/tex]

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The mean decreases, and the median remains the same from plot 1 to plot 2.

In the first box-and-whisker plot, the hourly wages earned by 20 employees are displayed, with a range from $8.70 per hour to $11.50 per hour. The median, which is the value that separates the higher half of the data from the lower half, is $10 per hour. The mean, which is the average of all the wages, is calculated by adding up all the wages and dividing the total by 20.

When one employee earning $15 per hour quits and is replaced by a new employee earning $8 per hour, the second box-and-whisker plot is created. The range of wages extends from $8 per hour to $15 per hour, with a median of $9.50 per hour. Since the new employee is earning a lower wage, the mean hourly wage decreases.

Therefore, the correct answer to the question is that the mean decreases, and the median remains the same. It is important to note that while the median does not change in this case, it is not always the case in other situations where data is added or removed from a set. It is also important to note that box-and-whisker plots are helpful in visualizing the spread of data and identifying any outliers.

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Sam can give pencils and pens to 14 classmates, with each classmate receiving 3 pencils and 4 pens (since 42 divided by 14 is 3, and 56 divided by 14 is 4).

Sam has 42 pencils and 56 pens, and he wants to distribute them equally among his classmates. To find the greatest number of classmates, we need to find the greatest common divisor (GCD) of 42 and 56.

The GCD of 42 and 56 is 14. Therefore, the greatest number of classmates Sam can give pencils and pens to is 14.

Each classmate will receive:
- 42 pencils / 14 classmates = 3 pencils per classmate
- 56 pens / 14 classmates = 4 pens per classmate

So, each of the 14 classmates will receive 3 pencils and 4 pens.

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The percent increase in the interstate highway system from 1960 to now is 381%.

option A.

The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.

percent increase =  100% x (new value - old value) / old value

percent increase = 100% x  (77,000 - 16,000) / 16,000

percent increase = 100% x 61,000 / 16,000

percent increase = 381.25%

Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.

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If Susan stands 300 m away from the lighthouse and looks up at it with an angle of elevation of 5 degrees, the height of the lighthouse is approximately 26 meters. This calculation is important for navigation and other purposes.

To determine the height of the lighthouse, we can use trigonometry. We know that the angle of elevation, which is the angle between Susan's line of sight and the ground, is 5'. We also know the distance between Susan and the lighthouse, which is 300 m.

We can use the tangent function to find the height of the lighthouse:

tan(5') = height/300

To solve for height, we can cross-multiply and simplify:

height = 300 x tan(5')

Using a calculator, we get that the height of the lighthouse is approximately 26.2 m.

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Answer:

Step-by-step explanation:

You want various angle and arc measures in the given figure.

The relevant angle relationships are ...

These answer the given questions as follows:

  LP is a ray.

  The angle at M is 90°.

  The angle at P is 90°.

 The angle at L is 360° -90° -90° -154° = 26°

  Arc MP has the same measure as angle MOP, 154°

  Arc MNP completes the circle, so is 360° -154° = 206°

The salesman's actual profit earnings after suffering a 5% loss due to damages when assembling the computer is $14,820.

Let's first calculate the original cost price of the computer to the salesman. We know that the salesman sold the computer for $15,600 and made a profit of 25%, which means that the selling price is 125% of the cost price.

Let the cost price of the computer be x.

Selling price = 125% of cost price

$15,600 = 1.25x

Solving for x, we get:

x = $12,480

So, the salesman's cost price of the computer was $12,480.

Now, the salesman suffered a loss of 5% due to damages when assembling the computer.

Loss = 5% of cost price

Loss = 5% of $12,480

Loss = $624

So, the actual earnings of the salesman after the loss is: $15,600 - $624 = $14,820.

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The surface area of the triangular prism is 4800 square yard.

The surface area of a triangular prism is sum of the areas of the faces that make the prism.

The surface area of a triangular prism is given by:

SA = (a + b + c)L + bc

Where a and b are the bases of the rectangular faces, c is the height of the triangle and h is the total length of the prism

In this case:

L = 40, a = 34, b = 32 and c = 30

SA = (34 + 32 + 30)40 + (32 * 30)

SA = 3840 + 960

SA = 4800 square yard

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dx/dy = -sin(t)/cos(t) when x = sin^3(t) and y = cos^3(t).

To find dx/dy, we first need to find dx/dt and dy/dt, and then we can use the chain rule.

Given x = sin^3(t) and y = cos^3(t),

dx/dt = d(sin^3(t))/dt = 3sin^2(t) * cos(t) (using the chain rule)
dy/dt = d(cos^3(t))/dt = -3cos^2(t) * sin(t) (using the chain rule)

Now, we can find dx/dy by dividing dx/dt by dy/dt:

dx/dy = (dx/dt) / (dy/dt) = (3sin^2(t) * cos(t)) / (-3cos^2(t) * sin(t))

Simplify the expression:

dx/dy = -sin(t)/cos(t)

So, dx/dy = -sin(t)/cos(t) when x = sin^3(t) and y = cos^3(t).

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The differential equation that models the problem is: dN/dt = 0.2*N(t) - 3.04174E+07.

Let's denote the current number of fish in the pond by N(t), where t is time in years.

The rate of change of N(t) is given by the difference between the number of births and deaths, minus the number of fish harvested from the pond:

dN/dt = (0.6N(t)) - (0.4N(t)) - (3.04174E+07)

The first term represents the number of births, which is 60% of the current population N(t). The second term represents the number of deaths, which is 40% of the current population N(t). The third term represents the number of fish harvested from the pond each year.

Therefore, the differential equation that models the problem is:

dN/dt = 0.2*N(t) - 3.04174E+07

Note that we have simplified the expression (0.6-0.4)N(t) to 0.2*N(t) for simplicity.

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The number of adult male whales in Antarctic feeding grounds, w(x), depends on the number of million squid available, x(t). At a surface temperature of 32°F, x(32) = 710 million squid, and w(710) = 6000 whales. The population of squid is increasing by 3 million per degree, and the population of whales is increasing by 4 whales per million squid.

The following expressions when the surface temperature of the ocean is 32°F is

(a) To evaluate x(t) when t=32°F, we use the given information that "there are an estimated 710 million deep-water squid in the feeding grounds, with the number of squid increasing by approximately 3 million squid per degree." Thus, at 32°F, we have:

x(32) = 710 + 3(32-32) = 710 million squid

Interpretation: When the water temperature is near 32°F, there are approximately 710 million deep-water squid in the feeding grounds.

(b) To evaluate w(x) when x=710 million squid, we use the given information that "there are 6,000 adult male whales in the Antarctic feeding grounds, with the number of male whales increasing by 4 whales per million squid." Thus, at 710 million squid, we have:

w(710) = 6,000 + 4(710-710) = 6,000 adult male whales

Interpretation: When there are approximately 710 million deep-water squid in the feeding grounds, there are approximately 6,000 adult male whales in the Antarctic feeding grounds.

(c) To evaluate dx/dt when t=32°F, we use the given information that "the number of available squid is x(t) when the water is t°F, with the number of squid increasing by approximately 3 million squid per degree." Thus, at 32°F, we have:

dx/dt = 3 million squid per degree

Interpretation: When the water temperature is near 32°F, the population of deep-water squid in the feeding grounds is increasing by approximately 3 million squid per degree.

(d) To evaluate dw/dx when x=710 million squid, we use the given information that "the number of male whales increases by 4 whales per million squid." Thus, at 710 million squid, we have:

dw/dx = 4 whales per million squid

Interpretation: For every additional 1 million deep-water squid that are present in the feeding grounds, the number of adult male whales in the Antarctic feeding grounds increases by approximately 4 whales.

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The value of x that will make a parallel to b is 30. We solved the equation 4x + 2x = 180 and obtained x = 30.

According to the definition of interior consecutive angles, when a transversal intersects two parallel lines, the sum of the measures of the two interior consecutive angles formed on the same side of the transversal is always 180°.

In this case, we are given that lines A and B are parallel, and line q intersects these lines at two distinct points, forming two interior consecutive angles with measures 4x and 2x, respectively.

Since the two angles are consecutive and on the same side of the transversal, their sum is equal to 180°. Therefore, we can set up the following equation

4x + 2x = 180

Simplifying the equation, we get

6x = 180

Dividing both sides by 6, we get

x = 30

Therefore, the value of x that will make a parallel to b is 30.

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--The given question is incomplete, the complete question is given

" Find the value of x that will make a parallel to b.

Lines A and B are parallel lines and a transverse line is intersecting these lines at two distinct points, making the angle 4x and 2x

x= "--

The probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.

The total wait time over 60 days will have a mean of 360 minutes (6 minutes per day x 60 days) and a variance of 720 minutes (12 minutes per day x 60 days). Since the wait times are uniformly distributed, the total wait time over 60 days will follow a normal distribution.

To find the probability that the total wait time over 60 days is less than 5.5 hours, we need to standardize the value using the z-score formula:

z = (x - μ) / σ

where x is the total wait time in minutes, μ is the mean total wait time in minutes, and σ is the standard deviation of the total wait time in minutes.

Substituting the values, we get:

z = (330 - 360) / sqrt(720) = -1.4434

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.4434 is 0.0746.

Therefore, the probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.

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Answer:

< 3 = 3x + 105°

Step-by-step explanation:

There is remot angle theory which is the exterior angle is congrent to the other non adjecent angle in triangle.

so <1 + <EDF = <3

(3x + 15 ) ° + 90° = <3

3x°+ 105° = <3

< 3 = 3x + 105° .... so the measur of angle 3 interms of x is 3x + 105°

A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.

To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.

= 2 1/5% / 100

= (2 + (1/5)) / 100

= 0.022

A value that is less than 0.022 from the given data is 0. 0215.

Therefore, a value less than 2 1/5% is 0. 0215.

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The spring constant is 180 N/m.

To solve for the spring constant, we can use the equation: k = (m * g) / x
where k is the spring constant, m is the mass of the box, g is the acceleration due to gravity (9.8 m/s^2), and x is the compression distance of the spring.
First, let's get the final velocity of the box when it hits the spring. We can use the equation:
v^2 = u^2 + 2as
where v is the final velocity (0 m/s), u is the initial speed (3.0 m/s), a is the acceleration (which is constant and equal to -k/m since the force from the spring is in the opposite direction of the box's motion), and s is the compression distance of the spring (0.30 m).
Rearranging the equation, we get:
k/m = (u^2 - v^2) / (2s)
k/4.0 = (3.0^2 - 0^2) / (2 * 0.30)
k/4.0 = 45
k = 180 N/m
Therefore, the spring constant is 180 N/m.

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Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.

Let's assume that x is the number of bottles of cherry soda sold and y is the number of bottles of grape soda sold. We can set up a system of equations to represent the given information:

x + y = 210 (equation 1: the total number of bottles sold is 210)

1.15x + 0.99y = 230.30 (equation 2: the total cost of the sodas is $230.30)

We can use the first equation to solve for y in terms of x:

y = 210 - x

Substituting this expression for y into the second equation, we get:

1.15x + 0.99(210 - x) = 230.30

Simplifying and solving for x, we get:

1.15x + 207.9 - 0.99x = 230.30

0.16x = 22.4

x = 140

So Bill sold 140 bottles of cherry soda. Substituting this value into equation 1, we get:

140 + y = 210

y = 70

Therefore, Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.

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The image of point (-3, 8) after a rotation of 180 counterclockwise about the origin is (3, -8)

Transformation is the movement of a point in the coordinate plane from one location to another. Transformation can either be reflection, rotation, translation and dilation.

Rotation is the flipping of a figure about a point in the coordinate plane; this point of rotation is usually origin.

(x, y) → (-x, -y) represents a rotation 180° counterclockwise.

The image of point (-3, 8) after a rotation of 180 counterclockwise about the origin is (3, -8)

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Your answer is D. 1/18  is the probability that she will choose a chocolate bar and then a piece of gum

First, let's determine the total number of snacks in the bag:
4 bags of chips + 5 fruit snacks + 6 chocolate bars + 3 pieces of bubble gum = 18 snacks

Next, let's find the probability of choosing a chocolate bar:
There are 6 chocolate bars and 18 snacks total, so the probability is 6/18, which simplifies to 1/3.

Since she puts the chocolate bar back, the total number of snacks remains the same. Now, let's find the probability of choosing a piece of gum:
There are 3 pieces of gum and 18 snacks total, so the probability is 3/18, which simplifies to 1/6.

Finally, to find the probability of both events happening, multiply the probabilities together:
(1/3) * (1/6) = 1/18

So, the probability that Debra will choose a chocolate bar and then a piece of gum is 1/18. Your answer is D. 1/18.

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The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.

The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.

Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]

Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for  [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]

Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]

So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

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if you meant simplification

[tex]4^3\sqrt{-88}\implies 64\sqrt{-88}\implies 64\sqrt{(-1)(2^2)(2)(11)}\implies 64(2)\sqrt{(-1)(2)(11)} \\\\\\ 128\sqrt{(2)(11)}\cdot \sqrt{-1}\implies 128\sqrt{22}~i[/tex]

The ∠BAE ≅ ∠DCF by SAS congruence of triangles. The solution has been obtained by using the congruence of triangles.

What is congruence of triangles?

If all three corresponding sides and all three corresponding angles of two triangles have the same size, the triangles are said to be congruent. These triangles can be moved, flipped, twisted, and turned to achieve the same result. They are parallel to one another when moved.

We are given the following:

AB ≅ CD

AD || BC

BG ≅ HD

∠CGE ≅ ∠AHF

AE ≅ FC

Now,

EF ≅ EF as it is the common side

Since, AD || BC so,

∠BCA ≅ ∠CAD as they are alternate interior angles

From this we get that triangle BAC ≅ triangle ACD.

So, the ∠BAE ≅ ∠DCF.

Hence, the ∠BAE ≅ ∠DCF by SAS congruence of triangles.

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