Calculus problem. Can anybody solve this? Thank you.

The new coordinates of the vertices of the translated triangle are A′(−3, 6), B′(0, 10), and C′(−3, 3). (option 2)

A triangle is a three-sided polygon with three vertices. In this problem, we are given a triangle ABC with vertices A(−3, 3), B(0, 7), and C(−3, 0). The coordinates of the vertices represent the location of each vertex in the coordinate plane.

Using this method, we can determine the new coordinates of the vertices of the translated triangle. The options given for the new coordinates of the vertices are:

A′(−3, 0), B′(0, 4), C′(−3, −3)

A′(−3, 6), B′(0, 10), C′(−3, 3)

A′(−6, 3), B′(−3, 7), C′(0, 0)

A′(0, 3), B′(3, 5), C′(0, 0)

We can check each option by adding 3 to the y-coordinate of each vertex in the original triangle.

In the first option, the new coordinates of vertex A are (−3, 3+3) = (−3, 6), which matches the coordinates given in option 2.

Therefore, the correct answer is option 2.

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The equation of a line for the given graph is y=2x+5.

From the given graph, the coordinate points are (0, 5) and (1, 7)

Part A:

Slope = (7-5)/(1-0)

= 2

Part B:

The slope mean for the relationship between the number of races and the number of track meets 2 races per track

Part C:

Substitute m=2 and (x, y)=(0, 5) in y=mx+c, we get

5=2(0)+c

c=5

Part D:

Substitute m=2 and c=5 in y=mx+c, we get

y=2x+5

Therefore, the equation of a line for the given graph is y=2x+5.

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Answer:

Shandin should use the median to describe the prices since it is a more robust measure of center that is not affected by extreme values. In this case, the median is $80, which represents the middle value when the prices are arranged in ascending order: $65, $79, $80, $95, and $175. The mean and range can be affected by the extreme value of $175, and the MAD is a measure of dispersion rather than center.

Answer:

D

Step-by-step explanation:

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}[/tex]

Not all intersecting lines are perpendicular.

Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.

Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.

As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.

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Answer:

2 and 4

Step-by-step explanation:

Answer: 4,2

Step-by-step explanation:

Mode: Number that repeats itself more

If there are 2 or more numbers that repeat themself the same amount you put both.

4,2,4,2,3,0,1,2,4,1,3,4,2

4: 4 times

2: 4 times

3: 2 times

0: 1 time

1: 2 times

Jasica should invest $878.84 per month in a sinking fund with 3% interest compounded monthly to accumulate $83,000 in 7 years.

To determine how much Jasica should make in a sinking fund, we can use the formula for the future value of an annuity due:

FV = PMT x [tex](((1 + r/n)^nt[/tex] - 1) / (r/n))

Where:

FV = future value

PMT = monthly payment

r = interest rate (as a decimal)

n = number of compounding periods per year

t = number of years

In this issue, we are solving for PMT.

Given:

FV = $83,000,

r = 0.03 (3% expressed as a decimal),

n = 12 (monthly compounding),

t = 7 years.

Plugging in the values, we have:

$83,000 = PMT x [tex](((1 + 0.03/12)^(12*7)[/tex] - 1) / (0.03/12))

Simplifying:

$83,000 = PMT x (94.4523)

PMT = $83,000 / 94.4523

PMT = $878.84 (rounded to the nearest cent)

Therefore, Jasica should invest $878.84 per month in a sinking fund with 3% interest compounded monthly.

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The volume of the rectangular prism is 97.5 cubic yards. (option b).

In this case, the rectangular prism has dimensions of 3 yards by 5 yards by 6 and one-half yard. To find its volume, we need to multiply these three dimensions together.

First, we need to convert the height of the prism to yards, as the other two dimensions are already given in yards. We know that 1 yard is equal to 3 feet, so 6 and one-half yards is equal to (6 x 3) + (1/2 x 3) = 18 + 1.5 = 19.5 feet. We then convert this to yards by dividing by 3, which gives us 6.5 yards.

Now, we can find the volume of the rectangular prism by multiplying the three dimensions together:

Volume = length x width x height

Volume = 3 yards x 5 yards x 6.5 yards

Volume = 97.5 cubic yards

Hence the correct option is (b).

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Answer:

Many buildings and structures around us involve transformed shapes in their design. For example, a skyscraper may have a rectangular base that is transformed into a triangular shape as it reaches higher levels. This transformation is achieved by using a technique called tapering, where the building's width gradually decreases as it goes up, resulting in a triangular shape at the top.

Another common transformation is the use of rotation, which is seen in the design of many cylindrical structures like water towers or chimneys. The cylinder is rotated around its axis to create a three-dimensional shape.

These transformed shapes contribute to the design of the object in many ways. For instance, the triangular shape of a skyscraper's top helps to reduce wind resistance and improve stability. Tapering also allows more sunlight to reach street level and reduces the impact of shadows on the surrounding area. In the case of cylindrical structures, rotation can provide structural stability while minimizing the amount of material used in the construction.

Overall, the use of transformed shapes in building and structure design helps to achieve specific aesthetic and functional goals, from stability to energy efficiency.

Step-by-step explanation:

Answer:

The Empire State Building is a skyscraper in Midtown Manhattan, New York City, on Fifth Avenue between West 33rd and 34th Streets. It has a roof height of 1,250 feet (381 m), and with its antenna spire included, it stands a total of 1,454 feet (443.2 m) high. Its name is derived from the nickname for New York, the Empire State.

The Empire State Building is an example of a transformed shape. The original shape is a square, but the architects transformed it into a triangle by adding a spire to the top. The spire adds height and visual interest to the building. It also helps to make the building more stable.

The use of transformed shapes in the design of the Empire State Building contributes to its overall aesthetic appeal. The building is both visually striking and structurally sound. It is a testament to the skill and ingenuity of the architects who designed it.

Here are some other examples of transformed shapes in buildings and structures:

* The Parthenon in Athens, Greece, is a rectangular building with a triangular pediment at each end. The pediments are decorated with sculptures that depict scenes from Greek mythology.

* The Eiffel Tower in Paris, France, is a wrought iron lattice tower that was built for the 1889 World's Fair. The tower is a transformed shape of a regular hexagon.

* The Gateway Arch in St. Louis, Missouri, is a stainless steel arch that spans the Mississippi River. The arch is a transformed shape of a catenary curve.

These are just a few examples of the many ways that transformed shapes are used in the design of buildings and structures. Transformed shapes can be used to add visual interest, create a sense of movement, or simply to make a building more structurally sound.

Step-by-step explanation:

The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1

Total numbers on wheel = total possible outcomes

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Grey colored portion = {3}

White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}

X = Event that wheel stops on a white slice

P(X) = number of white slices ÷ total number of slices

P(X) = 9 / 10 = 0.9

P(not X) = 1 - P(X)

P(not X) = 1 - 0.9 = 0.1

Therefore, the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1

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There are 6 different ways can the flags be arranged in a row.

We have,

Total number of flags = 6

So, to find the number of ways to arranged n object = n!

Then, the number of ways to arrange the flag

= 6!

= 6 x 5 x 4 x 3 x 2 x 1

=120 x 6

= 720 ways

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We can see that the dot plot is seen below.

We can see here that An example of a graphical representation of data is a dot plot. It is a number line with dots above each value to indicate the frequency or count of that value.

Depending on the type of data being shown, the dots are often arranged either horizontally or vertically.

Dot plots are known to be useful for showing the distribution of data, particularly for small data sets.

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a) The range of chest measurements contains 68% which falls closest to the mean is between 38 inches and 42 inches

b) The chest measurements for the 2.5% of the men with the smallest chest measurements in the population to be approximately 36 inches

Given data ,

The Empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline that describes the approximate distribution of data in a normal distribution.

Approximately 68% of the data falls within one standard deviation (σ) of the mean (μ)

Approximately 95% of the data falls within two standard deviations of the mean (μ ± 2σ)

Approximately 99.7% of the data falls within three standard deviations of the mean (μ ± 3σ)

It would be within one standard deviation of the mean for the range of chest measures that accounts for 68% of the data and is closest to the mean. Since the standard deviation is 2 inches and the mean chest measurement is 40 inches, we can get the range as follows:

Mean - 1 standard deviation = 40 - 2 = 38 inches

Mean + 1 standard deviation = 40 + 2 = 42 inches

b)

We may look at the bottom end of the distribution to obtain the chest dimensions for the 2.5% of males with the smallest chest measurements in the population. The empirical rule states that 2.5% or less of the data goes outside of two standard deviations of the mean. So, using the following formula, we can get the chest size of the 2.5% of men:

Mean - 2 standard deviations = 40 - 2(2) = 36 inches

Hence , the standard deviations are solved

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well, first of all, you don't want to go into the oven, is too hot and you'll get burned, so you may not want to do that.

now, if we start to bake something at 3:40pm and it requires 35 minutes, it'll be done by 3:40 + 35, or 3pm and 40 + 35 minutes, or 3pm plus 75 minutes or 3pm plus 60 + 15 minutes, but since 60 minutes is 1hr, that'd be 3pm plus 1hr plus 15 minutes, 4:15pm.

The coordinates of the vertices for the image is A′(−3, 6), B′(0, 10), C′(−3, 3).

The vertices of the preimage triangle ABC are given as A(-3,3), B(0,7), and C(-3,0). To translate the preimage 3 units up, we need to add 3 to the y-coordinate of each vertex. Therefore, the vertices of the image triangle A'B'C' will be A'(-3,6), B'(0,10), and C'(-3,3). Thus, option B, A′(−3, 6), B′(0, 10), C′(−3, 3), is the correct answer.

To check the answer, we can plot the points on a coordinate plane and observe that the image triangle is obtained by moving the preimage triangle 3 units up. Translation is a type of transformation in which the position of a figure is changed without changing its shape or orientation.

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The distribution that is positively skewed is Option C.

A positive skew is a statistical pattern, in which the majority of the data points are concentrated at one end within the range and wherein the tail is longer on the right side of the graph.

This phenomenon is also identified as a "right-skewed distribution," oppositely to its counterpart: the negative skew or "left-skewed distribution."

In conclusion, the distribution that is positively skewed is the third distribution or Option C.

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Barrington pays 24 for 0 gallons of water and Barrington pays 55.9 for 11 gallons of water

Given that we have

P = 24 + 2.9w

When they used 0 gallons, we have

P = 24 + 2.9(0)

P = 24

When they used 11 gallons, we have

P = 24 + 2.9(11)

P = 55.9

Hence, the amount paid for 11 gallons is 55.9

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Answer:

.................D

Step-by-step explanation:

I took the test

The inverse of the given function include the following: A. G⁻¹(x) = (x + 2)/5

In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

g(x) = y = 5x - 2

x = 5y - 2

5y = x + 2

By dividing all through by 5, we have;

G⁻¹(x) = y⁻¹ = (x + 2)/5

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The graph of the equation above include the following: D. graph D.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first graph of a quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function y= 1/2x² + 2x -6 is positive 1/2, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -8.

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The equations to represent the total cost C, for m miles on the hike for each guide are C(m) = 50 + 15m, C(m) = 200 and C(m) = 20m

From the question, we have the following parameters that can be used in our computation:

Larry

Initial fee = 50

Rate = 15 per mile

Connie

Initial fee = 200

Teo

Rate = 20 per mile

Represent the number of miles with m

So, we have

Larry

Initial fee = 50

Rate = 15 per mile

C(m) = 50 + 15m

Connie

Initial fee = 200

C(m) = 200

Teo

Rate = 20 per mile

C(m) = 20m

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The solution to the simultaneous equation is x = 6 and y = 3.

To solve this system of equations, we can use the method of elimination. First, we want to eliminate one of the variables, either x or y. In this case, it is easiest to eliminate y. To do so, we can multiply the second equation by 3, which gives us:

6x + 3y = 45

6x - 6y = 18

Now, we can subtract the second equation from the first:

6x + 3y - (6x - 6y) = 45 - 18

Simplifying this expression, we get:

9y = 27

Dividing both sides by 9, we get:

y = 3

Now that we know the value of y, we can substitute it into either equation to find the value of x. Let's use the first equation:

6x + 3y = 45

6x + 3(3) = 45

6x + 9 = 45

Subtracting 9 from both sides, we get:

6x = 36

Dividing both sides by 6, we get:

x = 6

Correct Question :

Solve the following simultaneous equation using algebra

6x+3y=45

2x-2y=6

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The total cost to install new wood floor in a room is $164.64.

Given that, Khalil's dining room is 3 meters wide and 7 meters long.

We know that, area of a rectangle is Area = Length×Width

Area of a room = 7×3

= 21 square meters

Total cost = Total area × Cost of per square meter

= 21×7.84

= $164.64

Therefore, the total cost to install new wood floor in a room is $164.64.

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After filling up the gravy dish, Bernice will have 410 ml of gravy left in the pot.

We have,

Determine the amount of gravy needed to cover the turkey:

We know that Bernice made 950 ml of gravy to go with a 5 kg turkey.

There are different ways to estimate how much gravy is needed to cover a turkey, but a common rule of thumb is to allow for about 1/2 cup (or 120 ml) of gravy per serving.

Assuming that the turkey will be served to about 8 people, we can estimate that Bernice will need:

We can write it as an expression:

= 120 ml/serving x 8 servings

= 960 ml of gravy

This means that Bernice made just enough gravy to cover the turkey and have a little bit left over.

Calculate how much gravy will be left in the pot:

We know that the capacity of the gravy dish is 540 ml.

If Bernice fills up the gravy dish with gravy, she will have.

= 950 ml - 540 ml

= 410 ml of gravy left in the pot.

Therefore,

After filling up the gravy dish, Bernice will have 410 ml of gravy left in the pot.

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The surface area of the prism including rectangles and triangles is equal to 13920 square units.

Prism has,

Two rectangles with side length 20 and 120.

Area of rectangle = length × width

                             = 20 × 120

                             = 2400

2400 × 2 = 4800

Two rectangles with side length 20 and 30.

Area of rectangle = length × width

                             = 20 × 30

                             = 600

600 × 2 = 1200

Two rectangles with side length 17 and 120.

Area of rectangle = length × width

                             = 17 × 120

                             = 2040

2040 × 2 = 4080

One rectangle with side length 120 and 30

Area of rectangle = length × width

                             = 30 × 120

                             = 3600

Two triangles with base 30 and height 8.

area of triangle = ( 1/2) × 30 × 8

                          = 120

120 × 2 = 240

Surface area of the prism

= Area of all rectangles + Area of two triangles.

= 4800 + 1200 + 4080 + 3600 + 240

= 13920

Therefore, the surface area of the prism is equal to 13920 square units.

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Answer:

c

Step-by-step explanation:

That's all because it makes more sense and uses a explanation

The 10th term of the sequence is 1024/729

From the question, we have the following parameters that can be used in our computation:

a2 = 36

a7 = 128/27

The nth term of a geometric sequence is

an = a1 * r^(n -1)

So, we have

a2 = a1 * r = 36

a7 = a1 * r^6 = 128/27

Divide the equations

r^5 = (128)/(27 * 36)

This gives

r = [(128)/(972)]^1/5

So, we have

r = [(32)/(243)]^1/5

r = 2/5

Also, we have

a1 = 128/(27r^6)

The 10th term of the sequence is

a10 = a1 * r^9

So, we have

a10 = 128/(27r^6) * r^9

This gives

a10 = 128/(27) * r^3

This gives

a10 = 128/(27) * [2/3]^3

Evaluate

a10 = 128/27 * 8/27

This gives

a10 = 1024/729

Hence, the 10th term is 1024/729

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Answer:

The mathematical equation for calculating the monthly interest is

I = P * (r / n)

where:

I is the monthly interest

P is the loan amount minus the down payment (i.e., $245,000 - $44,000 = $201,000 in this case)

r is the annual interest rate (i.e., 3.5%)

n is the number of payments per year (i.e., 12 for monthly payments)

then I = $201,000 * (0.035 / 12) = $711.06

The length of segment EC is 24 in the given triangle

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

3x=2(x+4)

Apply distributive property on RHS

3x=2x+8

Subtract 2x from both sides

x=8

The segment EC =3x

=3(8)

=24

Hence, the length of EC is 24 in the given triangle

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