Triangle ABC with vertices at A(-3, -3), B(3, 3), C(0, 3) is dilated to create triangle A'B'C' with vertices at A'(-12, -12), B'(12, 12), C'(0, 12). Determine the scale factor
used

John will be able to fill 8 glasses with iced tea.

To convert quarts to cups, we need to multiply the number of quarts by 4, since 1 quart is equal to 4 cups. So, 3 quarts of iced tea is equivalent to 3 x 4 = 12 cups of iced tea.

Since each glass holds 1½ cups of iced tea, John will need to divide the total cups of iced tea by the capacity of each glass: 12 cups / 1.5 cups/glass = 8 glasses.

Therefore, John will fill 8 glasses with iced tea.

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The correct answer is false. A reduced echelon matrix [tex]T(x) = 0[/tex] with a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], where[tex]b \neq 0[/tex], is not considered one-to-one.

Let's first define what it means for a matrix to be one-to-one.

A matrix is said to be one-to-one if each column of the matrix is linearly independent.

This means that for any given input, there is only one possible output.
Now, let's consider the reduced echelon matrix T(x) = 0. If this matrix has a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], b ≠ 0, it means that one of the variables in the system of equations represented by the matrix is a free variable.

This free v[tex]T(x) = 0.[/tex]ariable can take on any value, and the other variables will adjust accordingly.
If the reduced echelon matrix is [tex][1 0 | 2; 0 0 | 0],[/tex] the system of equations would be [tex]x = 2[/tex] and y can be any value.

This means that the matrix is not one-to-one, because there are multiple outputs for the same input.
the correct answer is false.

A reduced echelon matrix[tex]T(x) = 0[/tex] with a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], where [tex]b \neq 0[/tex], is not considered one-to-one.

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On average, the number of cars on the busy road increases by 25 cars per hour from midnight to 12:00pm

The average rate of change of a function from x=a to x=b is given by the formula:

average rate of change = (f(b) - f(a)) / (b - a)

Using this formula, we can calculate the average rate of change of the function f(x) from x=0 to x=12 as follows:

average rate of change = (f(12) - f(0)) / (12 - 0)

Where

f(0) = 0 and f(12) = 300 -- from the graph

So, we have

Rate = (300 - 0) / 12

Rate = 25

Therefore, the approximate average rate of change of the function from x=0 to x=12 is 25 cars per hour.

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The expression for the number of slices Harris ate is [tex](n/44) - 11.[/tex]

Let s be the number of slices each friend received.

Then the total number of slices on the pizza is n and we have: 44s = n because pizza was evenly divided among the 44 friends). Harris ate 11 fewer slices than he received, so he ate s - 11 slices.

The no of slices he  received is s and we have:

s = (s - 11) + Harris's slices eaten

Substituting 44s = n, we will solve for s:

44s = n

s = n/44

So, the expression for the number of slices Harris ate is [tex](n/44) - 11.[/tex]

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Answer:

5.25 or 5 1/4

Step-by-step explanation:

-8(0.5x-3)=3

first, just multiply -8 by 0.5x and -8 by -3 and you'll get:

-4x+24=3

next, subtract 24 on both sides, meaning subtract 24 by 24 on the left side and subtract 24 by 3 on the ride side:

-4x=-21

the final thing you have to do is divide -4 on both sides to get the x by itself:

x=5.25 or 5 1/4

The radius of the pool is changing at a rate of 3 / (20π) cm/min when the radius is 10 cm.

To solve this problem, we'll use the given information and the area formula for a circle.
Write the formula for the area of a circle:

[tex]A = \pi r^2[/tex],

where A is the area and r is the radius.
Differentiate both sides of the equation with respect to time (t): [tex]dA/dt = d(\pi r^2)/dt.[/tex]
Apply the chain rule on the right side: [tex]dA/dt = 2\pi r(dr/dt),[/tex]

where dr/dt is the rate of change of the radius.
Plug in the given values:

dA/dt = 3 cm²/min (given) and r = 10 cm (given at the moment of interest).
Solve for dr/dt:
3 = 2π(10)(dr/dt).

Isolate dr/dt:
dr/dt = 3 / (20π)
Simplify:
dr/dt = 1 / (20π/3) = 3 / (20π).

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Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years.

To determine the rate Hannah needs to earn to reach $1,000,000 in 25 years, we can use the future value formula for an annuity:

[tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex]

where:

FV = future value (in this case, $1,000,000)

Pmt = periodic payment (in this case, Hannah's annual contribution)

r = annual interest rate

n = number of periods (in this case, 25 years)

Hannah will deposit $3,000 this year and increase her deposits by $750 each following year. So her annual contributions will be:

Year 1: $3,000

Year 2: $3,750

Year 3: $4,500

...

Year 25: $21,750

To simplify the calculation, we can use the average annual contribution over the 25-year period, which is:

[tex][(3,000 + 21,750) / 2] = $12,375[/tex]

Now we can plug in the values into the formula and solve for r:

[tex]1,000,000 = 12,375 * [(1 + r)^25 - 1] / r[/tex]

Multiplying both sides by r and dividing both sides by 12,375, we get:

[tex]r x (1 + r)^25 = 120.75[/tex]

We can solve for r using trial and error, or using a financial calculator or spreadsheet. Using trial and error, we can try different interest rates until we find the one that makes the equation true. One possible method is to start with a reasonable guess, such as 6%, and adjust up or down until we get close to 120.75. After a few iterations, we find that:

r = 5.88%

Therefore, Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years, assuming she deposits $3,000 this year and increases those deposits by $750 each following year.

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The total number of cards drawn is 16 and As a result, we have the following:

6 face cards, Aces 1, 9 numbered cards

Because there are 12 face cards, half of them are 6 face cards.

There are 4 aces, so we draw 1.

There are 36 numbered cards in total, therefore one-fourth of them are 9 numbered cards.

We draw a total of 6 + 1 + 9 = 16 cards.

We may use the information provided in the problem to determine how many of each card type we have. We chose:

6 face cards make up half of the deck.

1 ace: 1 ace

9 numbered cards are one-fourth of the numbered cards.

As a result, we have:

6 face cards

Aces: 1

9 numbered cards

We can also ensure that the total number of cards drawn (16) corresponds to the number of cards in a regular deck by subtracting the cards we drew from the total number of cards: a deck of playing cards (52)

There are 52 - 16 = 36 cards left.

This means that there are 36 - 6 - 1 - 9 = 20 undrawn cards in the deck.

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Answer:

  15.0 in

Step-by-step explanation:

You want the height of a cone with radius 8 in and slant height 17 in.

The right triangle shown in the figure has height h, base x = 8 in, and slant height y = 17 in. The Pythagorean theorem tells you the relationship between these side lengths:

  x² +h² = y²

  8² +h² = 17²

  h² = 17² -8² = 289 -64 = 225

  h = √225 = 15.0

The height of the cone is 15.0 inches.

__

Additional comment

A triple of 3 integers that form the sides of a right triangle is called a "Pythagorean triple." The triple in this problem is one of those: {8, 15, 17}. Other Pythagorean triples you will often see in algebra, trig, and geometry problems are {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {9, 40, 41}. You will also see multiples of these, for example 3×{3, 4, 5} = {9, 12, 15}.

It can be worthwhile to remember some of these. For this problem, recognizing 8 and 17 as part of the triple {8, 15, 17} means you can write down the answer with no further work.

The hypothesis statement h: μ < 60 is an example of an alternative hypothesis in a one-tail test is true

A hypothesis is a proposed explanation or prediction for an observation or phenomenon that is based on limited evidence or data. It is a tentative statement or idea that can be tested through further observation, experimentation, or data analysis. Hypotheses are often used in scientific research as a starting point to investigate a research question or problem.

The hypothesis statement "μ < 60" is an example of an alternative hypothesis in a one-tailed test.

In a one-tailed test, the alternative hypothesis is directional and states that the population parameter is either greater than or less than the null hypothesis value.

In this case, the alternative hypothesis states that the population mean is less than 60.

The null hypothesis, in contrast, is typically a statement of "no effect" or "no difference" and is often denoted by H0.

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The picture below shows the graph of the inequality of x² ≤ 4

Option B is correct.

In mathematics, an inequality is described as a relation which makes a non-equal comparison between two numbers or other mathematical expressions which is used most often to compare two numbers on the number line by their size.

A graph of inequality denotes that the variables is the set of points that represents all solutions to the inequality.

A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

Therefore, the correct option is B. x² ≤ 4

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Nathan needs 24 cups of water to make his lemonade recipe.

Let's call the amount of lemon juice Nathan uses "x".

We know that Nathan uses 3 cups of lemon juice, so we can substitute x = 3 into the problem.

According to the recipe, the amount of sugar Nathan needs is twice the amount of lemon juice, so he needs 2x cups of sugar.

Substituting x = 3, we get that Nathan needs 2(3) = 6 cups of sugar.

The amount of water Nathan needs is four times the amount of sugar he needs, so he needs 4 times 6 cups of water, which is equal to 24 cups of water.

Therefore, Nathan needs 24 cups of water to make his lemonade recipe.

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Answer:

B

Step-by-step explanation:

the equation y=3/2x-3 has a slope of 3/2 and a y intercept of -3

So, first find the graph(s) that have the y intercept of -3.  The only options would be B and C.

Next, from the y-intercept of -3, go UP 3, and to the RIGHT 2 to find your next point.  This eliminates option C for the slope.  The slope of option C is 2/3, not 3/2.

So, option B is correct.  Hope this helps ;)

Answer:

B

Step-by-step explanation:

y = mx + b

y = mx (slope) + b (y-intercept)

The y-intercept of y = 3/2x - 3 is -3, so the graph needs to have a point at (0, -3). The slope is 3/2, if you go up 3 times and to the right twice from the point (0, -3), it will point (2, 0).

Answer:

(i) Calculation:

1 GB = 1000 MB

Number of videos that could be stored = (1 GB / 100 MB) = 10

Therefore, William can store 10 videos on his computer if each video is 100MB in size.

(ii) Algorithm using pseudocode:

Ask the user to input the file size in megabytes.

Multiply the file size by 1,000,000 to convert it to bytes.

Print the result in a user-friendly format by dividing the bytes by 1,048,576 and rounding to two decimal places, and adding "MB" and "bytes" to the output.

Pseudocode:

Input file_size_in_mb

Set bytes = file_size_in_mb * 1000000

Set result = round((bytes / 1048576), 2)

Output "There are " + result + " MB " + bytes + " bytes".

The slope and derivative of a vertical tangent are both undefined due to the vertical nature of the tangent line.

The slope/derivative of a vertical tangent.
A vertical tangent occurs when a curve has a point where its tangent line is vertical.

In terms of the slope and derivative, the following is true about the vertical tangent:
Slope:

The slope of a vertical tangent is undefined because the vertical line has no run (change in x). Slope is calculated as the rise (change in y) divided by the run (change in x), and division by zero is not possible.
Derivative:

The derivative of a function at a point represents the slope of the tangent line to the curve at that point.

When the tangent is vertical, the derivative is also undefined because the slope is undefined.

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Quadrilateral ABCD can be dilated by a scale factor 1.25 to create a smaller image and by a scale factor 1.5 to create a bigger image.

To calculate the scale factor of a given shape for its dilation or reduction, the formula that should be used is given as follows:

Scale factor = bigger dimension/smaller dimension.

To create a smaller image;

bigger dimension length AB = 22in

smaller dimension length AB = 17.6in

Scale factor = 22/17.6 = 1.25

To create a bigger image:

Bigger dimension length = 33in

Smaller dimension length = 22in

scale factor = 33/22 = 1.5

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The missing lengths of a geometric system are listed below: AC = 114, BC = 96, BE = 3

In this problem we find a geometric system formed by two similar triangles. Two triangles are similar if every pair of corresponding sides have the same proportion. Then, the system is described by this proportion formula:

AB / AC = AE / AD = BE / CD

18 / AC = 15 / 95 = BE / 19

Then,

18 / AC = 15 / 95

AC = 18 × (95 / 15)

AC = 114

15 / 95 = BE / 19

BE = 19 × (15 / 95)

BE = 3

Now, we determine the length of side BC:

BC = AC - AB

BC = 114 - 18

BC = 96

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Answer:

240 tickets sold

Step-by-step explanation:

first, you would set up the proportion by writing [tex]\frac{228}{95} =\frac{x}{100}[/tex]

with "x" being the number of seats that needs to be sold

then, you would cross multiply

and you get

[tex]95x=228*100[/tex]    next, you simplify to get the inequality [tex]95x=22800[/tex]

then divide both sides by 95

[tex]x=240[/tex]

so 240 tickets to fill all the seats

hope this helps ;)

Step-by-step explanation:

We can use trigonometry to solve this problem. The grade of the road is given as an angle of 9.5°. This means that for every 1 unit of horizontal distance traveled, the elevation changes by the tangent of 9.5°.

We want to find the change in elevation for a car descending the 4-mile stretch. To do this, we can multiply the length of the road by the tangent of the grade angle:

Change in elevation = 4 miles x tan(9.5°)

Using a calculator, we can find that tan(9.5°) = 0.1664. Substituting this value into the equation, we get:

Change in elevation = 4 miles x 0.1664 ≈ 0.67 milesTo convert this to feet, we can multiply by the number of feet in a mile:

Change in elevation = 0.67 miles x 5,280 feet/mile ≈ 3,539 feetTherefore, the change in elevation for a car descending the 4-mile stretch is approximately 3,539 feet.

The like radicals are 3x√x²y and x√yx², and the answer is:

3x√x²y, -2x√xy³², x√yx²,  2√xy

An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. It does not have an equal sign and can be simplified or evaluated by applying the appropriate rules of arithmetic.

According to the given information:

The like radicals have the same radicand (expression under the radical sign) and the same index (the number outside the radical sign). Checking each expression:

Therefore, the like radicals are 3x√x²y and x√yx², and the answer is:

3x√x²y, -2x√xy³², x√yx²,  2√xy

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The surface area of the rectangular pyramid is 75 m².

Surface area is the sum of all the surfaces on each side of a three-dimensional shape.

To calculate the surface area of the rectangular pyramid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equaation 1

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Answer: Work done= F.d

= 15000 J

Step-by-step explanation:

Work done= Force*distance

where

Force= mass*acceleration

mass=30kg,  acceleration= 10 m/s^2, distance

=30*10

=300 N

then by formula of work done

Work done= F.d

= 300*50

=15000J

option B is correct: [tex](x+2)^2+(y+7)^2=36[/tex]

The general equation of the circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]              

where,

(h, k) is the center of the circle and r is the radius of the circle.

As per the statement:

The center of a circle is at (−2, −7) and its radius is 6.

[tex]\implies (h, k) = (-2, -7)[/tex] and [tex]r = 6[/tex] units

Substitute these we have:

[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]

[tex]\implies(x+2)^2+(y+7)^2=36[/tex]

Therefore, the equation of circle is, [tex]\bold{(x+2)^2+(y+7)^2=36}[/tex]

The total surface area of the prism is  177.2 m².

The total surface area of the prism is calculated by applying the formula for total surface area of prism.

S.A = bh + (s₁ + s₂ + s₃)L

where;

The surface area of the prism is calculated as;

S.A = 4 m (3 m) + (3.8 m + 4 m + 4 m) x 14 m

S.A = 177.2 m²

Thus, the surface area of the prism is calculated using the formula for surface of right prism.

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The two quantities needed to determine the total amount of money Monte paid his employees this month are:

A. the hourly salary of each employee

C. the number of hours each employee worked this month.

With four employees at the Monte Bakery, who earn a different hourly wages, to work out the total salary for the month, Monte needs to multiply the hourly wage of each employee by the total number of hours each worked.

Thus, in this mathematical operation, we first use multiplication and then add each individual employee's total salary to sum the total salary for the month.

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A four members of the Harrison family save  $896 on airfare by vacationing in Vancouver.

Here, the airplane tickets to Fairbanks Alaska will cost $958 each.

⇒ c₁ = $958

where c₁ represents the airfare to Fairbanks Alaska

and the airplane tickets to Vancouver Canada will cost $734.

⇒ c₂ = $734

Let us assume that s represents the amount of savings per ticket.

⇒ s = c₁ - c₂

⇒ s = 958 - 734

⇒ s = $224

Since there are four members in the family.

So using unitary method the total savings would be,

⇒ t = 4 × s

⇒ t = 4 × 224

⇒ t = $896

Therefore, the total savings =  $896

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The complete question is:

Airplane tickets to Fairbanks Alaska will cost $958 each. Airplane tickets to Vancouver Canada will cost $734. How much can the four members of a Harrison family save on airfare by vacationing in Vancouver?

in this case since it's a cylinder always have to do is multiply the two given measurements dancing that she gets all you need to do is run it off to the nearest two decimal places when you say to the nearest two decimal places while trying to say they are two numbers after the coma

The lateral surface area of the rectangular prism is 308 units² and the total surface area is 398 units²

The formula of lateral surface area of the rectangular prism is given as;

LSA = 2(l +b)h

substituting the values into the formula;

LSA = 2(5 + 9) * 11

LSA = 308 units²

The total surface area is given by

TSA = 2(lb + bh + lh)

TSA = 2[(5*9) + (9*11) + (11*5)

TSA = 398 units²

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The volume of the figure is approximately 50101mm^3 and the surface area is approximately 8253mm^2.

The figure consists of a sphere and a cylinder. We can find the volume and surface area of the figure by calculating the volume and surface area of each component separately and adding them together.

The height of the cylinder is given as 76mm, which means the remaining height of the figure must be occupied by the sphere. Thus, the radius of the sphere can be calculated as half the difference between the total height of the figure and the height of the cylinder:

Radius of sphere = (102mm - 76mm)/2 = 13mm

Now we can calculate the volume and surface area of each component:

Volume of cylinder = πr^2h = π(13mm)^2(76mm) ≈ 40899mm^3

Surface area of cylinder = 2πrh + 2πr^2 = 2π(13mm)(76mm) + 2π(13mm)^2 ≈ 6128mm^2

Volume of sphere = (4/3)πr^3 = (4/3)π(13mm)^3 ≈ 9202mm^3

Surface area of sphere = 4πr^2 = 4π(13mm)^2 ≈ 2125mm^2

Finally, we can find the total volume and surface area of the figure by adding the values for the cylinder and sphere:

Total volume = Volume of cylinder + Volume of sphere ≈ 50101mm^3

Total surface area = Surface area of cylinder + Surface area of sphere ≈ 8253mm^2

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