A superhero action figure has volume 1700 cubic centimeters. The figure is dilated to create a store display.
The volume of the dilated figure is 25,500 cubic centimeters
What was the approximate scale factor of the dilation? (Round your answer to the nearest tenth, one decimal place ex. 4.2)

The required graph of the given line y = -(2/3)x + 1 is shown in the attached figure.

The equation of the line is given in the question as:

y = -(2/3)x + 1

First, we have to find the intercepts of the equation y = -(2/3)x + 1

The y-intercept is the value of y when the value of x is appropriately zero.

For x = 0

y = -2/3(0)+1

y = 1

The y-intercept is the point where (0.1)

Determine the x-intercept.

The x-intercept is the value of x when the value of y equals zero.

For y = 0

0 = (-2/3)x + 1

-1 = (-2/3)x

x = 3/2 or 1.5

The y-intercept is the point (1.5,0).

To graph, the line, draw the intercepts and connect the dots as indicated in the image.

As a result, the graph for the line y = -(2/3)x + 1 is provided below.

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Answer:

T can be equal to 1 1/10 or 1.1 or 11/10

Step-by-step explanation:

10t=11

So divide by 10 on both sides.

t=11/10 which can be simplified to t=1 1/10 or t=1.1

:)

Answer:

(a) \(x=\frac{19}{4}=4.75\)

(b) \(x=-\frac{1+\sqrt{193}}{6}\approx-2.4821, x=-\frac{1-\sqrt{193}}{6}\approx2.1487\)

Step-by-step explanation:

The detailed explanation is shown in the attached documents below.

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Based on the fact that in the simple random variable, 5 is the sample mean, then it is a d. point estimate.

A point estimate refers to a specific value in a random group of variables that tell us more about the variables.

The mean is therefore a point estimate as it tells us the average value amounts the random sample of 31 observations.

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Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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Answer:A

Step-by-step explanation:

Answer:

Step-by-step explanation:

1). f(x) = 2x

   f(-3) = 2(-3) = -6

   f(1) = 2(1) = 2

   f(4) = 2(4) = 8

   Ordered pairs → (-3, -6), (1, 2), (4, 8)

2). f(x) = 2x + 1

    f(-3) = 2(-3) + 1 = -5

    f(1) = 2(1) + 1 = 3

    f(4) = 2(4) + 1 = 9

   Ordered pairs → (-3, -5), (1, 3) and (4, 9)

     x       -3        1        4      

    f(x)     -5       3        9

3). f(x) = -3x

    f(-3) = -3(-3) = 9

    f(1) = -3(1) = -3

    f(4) = -3(4) = -12

    Ordered pairs → (-3, 9), (1, -3), (4, -12)

       x       -3       1        4

     f(x)       9      -3     -12

1 - In order to solve this problem we have to solve the following equation

20 = 25t - 5t²

2 - In order to solve that equation we have to options

1 - Use the quadratic equation

2 - Factor the expression

For this probem we will facor the expression. The first thing that we will do is divide everything by 5, so we get

20/5 = ( 25/5 ) t - (5 / 5 ) t²

which would give us

4 = 5t - t²

Now we subtract 4 and we get

t² - 5t +4 = 0

then

t² - 5t +4 = (t - 4 ) (t - 1 ) = 0

Therefore there are two answers

t = 4

t = 1

Notice that the answer is correct because

h = 25(1) - 5*(1)² = 20

Answer: See explanation

Step-by-step explanation:

Your question isn't complete as you didn't give the sales tax percent. In order to solve the question, let's assume that the sales tax is 6%.

(a) What is the amount of sales tax that Mr. Speer has to pay?

This will be:

= Sales tax percent × Amount charged

= 6% × $300

= 6/100 × $300

= 0.06 × $300

= $18

The sale tax is $18

(b) What is the total amount Mr. Speer has to pay?.

The total amount will be the addition of the amount charged and the sales tax. This will be:

= $300 + $18

= $318

Based on the boxplot, approximately 50% percent of the people who entered the amusement park met the height requirement for the attraction.

Box-Plot is a summary of the sample distribution presented graphically which can describe the shape of data distribution (skewness), a measure of central tendency and a measure of dispersion (diversity) of observational data. There are 5 statistical measures that we can read from the boxplot, namely:

In addition, the boxplot can also show whether there are outlier values and extreme values from the observed data.

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Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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Complete question :

Leah is creating satin bows for a wedding. From a 15-meter-long ribbon, she first cuts a piece 3 4/9 meters long. Then she cuts a piece 6 5/9 meters long from the remaining ribbon. How much ribbon does Leah have left?

Answer:

5 m

Step-by-step explanation:

Total ribbon cut :

3 4/9 + 6 5/9 =

31/9 + 59/9

= 90 /9

= 10 meters

Total Length of ribbon = 15 m

Ribbon left :

15 - 10 = 5 m

Answer:

3/9  3/8  3/7

Step-by-step explanation:

The higher the denominator, the higher number of times  a number will be divided which means, the number will become smaller.

The collection of sample averages, known as the sampling distribution, would have an average that is equal to the average height of the entire population.

When measuring the height of each team and calculating their average, we are essentially taking samples from the population of all teams. The sampling distribution is created by repeating this process multiple times and calculating the average for each sample. According to the central limit theorem, as the sample size increases, the sampling distribution approaches a normal distribution regardless of the shape of the population distribution.

Therefore, the average of the sampling distribution, which represents the average height of all teams, would be equal to the average height of the entire population. The sampling distribution allows us to make inferences about the population based on the collected samples and provides a measure of the variability of the sample averages.

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The simplified expression of 6 - (3x - 2i)² is -9x² + 12xi + 10.

To simplify the expression 6 - (3x - 2i)², we need to expand the square and perform the necessary calculations. Let's go through the steps:

Step 1: Square the binomial (3x - 2i)²:

(3x - 2i)² = (3x - 2i)(3x - 2i)

Step 2: Expand using the FOIL method:

(3x - 2i)(3x - 2i) = 9x² - 6xi - 6xi + 4i²

Step 3: Simplify the expression by combining like terms and using the fact that i^2 = -1:

9x² - 6xi - 6xi + 4i² = 9x² - 12xi - 4

Step 4: Combine the simplified expression with the initial expression:

6 - (3x - 2i)² = 6 - (9x² - 12xi - 4)

Step 5: Distribute the negative sign to each term inside the parentheses:

6 - (9x² - 12xi - 4) = 6 - 9x² + 12xi + 4

Step 6: Combine like terms:

6 - 9x² + 12xi + 4 = -9x² + 12xi + 10

Therefore, The simplified expression of 6 - (3x - 2i)² is -9x² + 12xi + 10. Therefore, the answer is option 1) -9x² + 12xi + 10.

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Answer:

(x-4,y+8)

Step-by-step explanation:

Given

\(Point = (x,y)\)

Required

Translate

8 units up

The general rule for up translation is;

\(f'(x,y) = f(x,y+h)\)

Where h is the unit translated up

In this case:

\(h = 8\)

So, we have:

\(f'(x,y) = f(x,y+8)\)

4 units left

The general rule for up translation is;

\(f'(x,y) = f(x-b,y)\)

Where b is the unit translated left

In this case:

\(b = 4\)

So, we have:

\(f"(x,y) = f(x -4,y+8)\)

Hence, the rule of translation is: (x-4,y+8)

Answer:

translation is

x-4,y+8

Step-by-step explanation:

Required correct options B, C, D, A, C, A are solution of questions 3,4,5,6,7,8 respectively.

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. It usually contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are often used to describe relationships between different quantities or variables and are an essential tool for solving mathematical problems. For example, a simple equation could be:

2x + 3 = 7

Question #3:

If x = 4, then x + 12 = 4 + 12 = 16. Therefore, the answer is B) 16.

Question #4:

If r = 8, then 9r = 9(8) = 72, 8,r is not a valid expression, 7r = 7(8) = 56, and 6,r is not a valid expression. Therefore, the answer is C) 7r.

Question #5:

Using the order of operations, we first solve the parentheses: 8-4 = 4, and then we solve the exponent: 4² = 16. Then, we divide 16 by 2 to get 8, and finally add 10 to get 18. Therefore, the answer is D) 18.

Question #6:

If b = 5, then 8 - b = 8 - 5 = 3, 12 - b = 12 - 5 = 7, b + 4 = 5 + 4 = 9, and b + 6 = 5 + 6 = 11. Therefore, the answer is A) 8 - b = 13.

Question #7:

If everybody on the team scores 6 points, and the team has a total of 42 points, then the number of people on the team can be represented by the equation 6p = 42, where p is the number of people. Solving for p, we get p = 7. Therefore, the answer is C) 7p = 42.

Question #8:

If x = 4, then y = 8 - 4 = 4 for the first function, y = 4 + 8 = 12 for the second function, y = 16 - 4 = 12 for the third function, and y = 3(4) = 12 for the fourth function. Therefore, the answer is option A.

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Answer:

I put the answers in the picture below!

Step-by-step explanation:

The area to which Zippy's Pizza makes delivery is 16·π square miles

The responses are;

Reasons:

The radius of the area that Zippy delivers pizza = 4 miles

Direction in which Empire Street runs = East to west

Direction of the route 26 route = North to south

Location of Zippy's Pizza parlor = 3 miles south of Empire street

-First Part:

The equation that represents the radius of delivery for Zippy's Pizza is given by the equation of a circle as follows;

(x - h)²+ (y - k) = r²

Where:

(h, k) = The center of the circle which is the location of Zippy's Pizza

r = The radius of the circle

Zippy's Pizza is at the center of the circular area with coordinates (h, k) = (0, 0)

r = 4 miles

-Which gives;

(x - 0)² + (y - 0)² = 4²

The equation that represent the radius is; x² + y² = 4²

-Second part:

The locations of addresses on Empire street, relative to Zippy's Pizza are given by the equation;

y = 3

Therefore, we have;

The furthest distances east and west on Empire street that can receive Zippy's Pizza delivery are given by the equation;

x² + 3² = 4²

x = √(4² - 3²) = ±√5

The furthest distances that can receive Zippy's Pizza delivery are ±√5 miles (east and west) from route 26

-Third Part:

Location of Little Cubs = 2 miles west and 4 miles north of Zippy's

The distance from Little Cubs Field to Zippy's = √((2² + 4²) = 2·√5

The distance from Little Cubs Field to Zippy's = 2·√5 miles

-Fourth Part:

The distance between Little Cubs Field from Zippy's radius of delivery, d, is found as follows;

d = 2·√5 - 4 = 2·(√5 - 2)

Therefore, d = 2·(√5 - 2) miles

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(a) The given vectors form a lattice known as a primitive cubic lattice. In a Cartesian coordinate system, a primitive cubic lattice consists of points arranged at the corners of a cube.

b) The volume of the primitive cell is V_primitive = 0.

c) Since the volume of the primitive cell is zero, there is no conventional unit cell for this lattice.

d) The separation between adjacent planes is d = 2π / (4a²) = π / (2a²).

e) The volume of the primitive cell with the new set of primitive vectors is V_primitive' = 0, which remains the same as the previous case.

a) The lattice vectors can be represented as a₁ = (2a, 0, 0), a₂ = (0, 2a, 0), and a₃ = (0, 0, 2a), where 'a' is the lattice parameter.

(b) To evaluate the volume of the primitive cell, we can find the scalar triple product of the lattice vectors:

V_primitive = |a₁ · (a₂ x a₃)|

The cross product of a₂ and a₃ is:

a₂ x a₃ = (2a, 0, 0) x (0, 0, 2a) = (0, 4a², 0)

Taking the dot product with a₁:

a₁ · (a₂ x a₃) = (2a, 0, 0) · (0, 4a², 0) = 0

(c) The lattice cannot be represented by a repeating unit cell with non-zero volume.

(d) The vectors a₁ and a₂ define a plane in the lattice. To find the separation between adjacent planes, we can use the formula:

d = 2π / |a₁ x a₂|,

where |a₁ x a₂| represents the magnitude of the cross product of a₁ and a₂. Since a₁ and a₂ are in the x and y directions, respectively, their cross product is in the z direction.

a₁ x a₂ = (2a, 0, 0) x (0, 2a, 0) = (0, 0, 4a²)

The magnitude of a₁ x a₂ is |a₁ x a₂| = 4a².

(e) Another possible choice of primitive lattice vectors could be:

b₁ = (a, 0, 0)

b₂ = (0, a, 0)

b₃ = (0, 0, a)

To evaluate the volume of the primitive cell using these vectors, we can calculate the scalar triple product:

V_primitive' = |b₁ · (b₂ x b₃)|

The cross product of b₂ and b₃ is:

b₂ x b₃ = (0, a, 0) x (0, 0, a) = (0, 0, a²)

Taking the dot product with b₁:

b₁ · (b₂ x b₃) = (a, 0, 0) · (0, 0, a²) = 0

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Answer:

x = 3

y = 14

z= 7

\(\huge{\underline{\underline{\mathcal{\bf\pink{AnSwer}}}}}\)

8.) ∆MRP

9.) SSS

they both are congruent by SSS

Answer:

Marie should rent the trombone

Step-by-step explanation:

If Marie rents it for 12 months it'll be 12x34= $408.

If Marie buys a trombone it'll cost her 495 which is more expensive.

The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.

From the information,

We are told to convert 2 litres into ml.

This will be:

= 1000 × 2

= 2000ml

The number of eggs that will be bought to make 500 muffins will be:

= 500 × 2

= 1000 eggs.

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The complete question is:

The grade 10 class is going to bake muffins. The recipe that they are going to use requires the following ingredients: RECIPE ✓2 Egga ✔125ml Cooking oll ✓375ml brown sugar (300g) ✓800ml Milk ✓300g Whole wheat flour ✓ 375ml cake flour (210g) ✓5ml Salt ✓ 5ml Vanilla Essence ✓ 10ml Bicarbonate of soda ✓ 250ml Raisins (150g) 2.1 The volume of 150g of Whole wheat is 250ml. Calculate the volume of the Whole wheat flour in the recipe 2.2 When they are all mixed together, all the above ingredients make up 2 litres of mixture (because some parts dissolve into other parts). 2.2.1 Convert 2 litres into ml 2.2.2 How many muffins can the above recipe make if 60ml is required for each muffin? 2.2.3 Using your answer to question 2.2.2, how many eggs will the girls need to buy to make 500 muffins? 2.3 The students need to make 500 muffins, using muffin trays that hold 6 muffins par tray. They plan to put 4 trays at a time into the ovens. Each oven takes 30 minutes to bake. How long will they take to make 500 muffins if they will be using 4 ovens?​

Carly needs to perform 33 additional sales to earn 100 this week.

Firstly forming the expression as per the weekly earning and individual payment on extra sale. Writing the expression -

Amount earned = 35 + 2×number of sales

Keep the value of amount earned in mentioned formula to find the number of sales.

100 = 35 + 2×number of sales

2×Number of sales = 100 - 35

Performing subtraction on Right Hand Side of the equation

2×Number of sales = 65

Shifting 2 to Right Hand Side of the equation

Number of sales = 65/2

Performing division on Right Hand Side of the equation

Number of sales = 32.5

Round off the number

Number of sales = 33

Therefore, she needs to make 33 additional sales.

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Answer:

The cost of each cotton candy bag is $4.

Step-by-step explanation:

Consider the provided information.

Let, the vendor has \(x\) dollar at the starting of each day.

Let, the cost of each cotton candy bag is \(y\).

Now when she sells a total of 12 bags, she has $128.

\(x+12y=128\)  .....(1)

After she sells a total of 20 bags, she has $160.

\(x+20y=160\)  ....(2)

Subtract equation 1 from equation 2.

\((x+20y)-(x+12y)=160-128\)

\(8y=32\)

\(y=4\)

Hence, the cost of each cotton candy bag is $4.