AABC DEF. What sequence of transformations will move AABC onto ADEF?

A. A dilation by a scale factor of 2, centered at the origin, followed by
a 90° clockwise rotation about the origin

B. A dilation by a scale factor of centered at the origin, followed by
the translation (x, y) - (x+4, y-2)

C. A dilation by a scale factor of, centered at the origin, followed by
a 180° clockwise rotation about the origin

D. A dilation by a scale factor of 2, centered at the origin, followed by
a reflection over the y-axis

Answer:

58 nickels; 234 dimes; 20 quarters

Step-by-step explanation:

number of dimes = d

number of nickels = n

number of quarters = q

n + d + q = 312

d = 3(n + q)

0.05n + 0.1d + 0.25q = 31.3

n + d + q = 312

d = 3n + 3q

5n + 10d + 25q = 3130

n + 3n + 3q + q = 312

5n + 30n + 30q + 25q = 3130

4n + 4q = 312

35n + 55q = 3130

n + q = 78

7n + 11q = 626

n = 78 - q

7(78 - q) + 11q = 626

546 - 7q + 11q = 626

4q = 80

q = 20

n = 78 - 20 = 58

d = 3(58 + 20) = 3(78) = 234

Answer: 58 nickels; 234 dimes; 20 quarters

There are 10 bundles and 1 sticks in the Popsicle sticks

Given that  Sasha has 47 Popsicle sticks (4 bundles of 10 and 7 sticks)

4B+7S=47

Jose has 62 (6 bundles of 10 and 2 sticks).

6B+2S=62

We have to find B and S values

12B+21S=141

12B+4S=124

Subtract both the equations

21S-4S=141-124

17S=17

Divide both sides by 17

S=1

Now let us plug in the value of S

4B+7=47

4B=40

B=10

Hence, there are 10 bundles and 1 sticks in the Popsicle sticks

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The logarithmic equation is equivalent to this exponential equation is x = log (8/25) (option c).

In this case, we are asked to find the logarithmic equation that is equivalent to the given exponential equation:

2,400 = 7,500(10)⁻ˣ

To solve for x, we need to isolate it on one side of the equation. We can start by dividing both sides by 7,500:

2,400/7,500 = (10)⁻ˣ

The choice of base for the logarithm doesn't matter, as long as we use the same base for both sides. Let's use base 10:

log(2,400/7,500) = log(10⁻ˣ)

Using the properties of logarithms, we can simplify the right-hand side:

log(2,400/7,500) = -x*log(10)

We know that log(10) = 1, so we can simplify further:

log(2,400/7,500) = -x

x = log(8/25) = log(8) - log(25) = 0.9031 - 1.3979 = -0.4948

So the only answer choice that gives us the same equation as the original exponential equation is (C) x = log (8/25).

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Complete Question:

Which logarithmic equation is equivalent to this exponential equation?

2,400 = 7,500(10)^(-x)

A. x= -log (25/8)

B. x = log(-25/8)

C. x = log (8/25)

D. x = -log (8/25)

The volume of air of a sphere with diameter 9 centimeters is 381.51 cubic centimeters

The formula for the volume of a sphere is:

V = (4/3)πr³

where r is the radius of the sphere.

The diameter of the sphere is 9 cm, which means the radius is half of that:

r = 9/2 = 4.5 cm

Substituting this value into the formula, we get:

Volume = (4/3)π(4.5)³

Volume = (4/3)×3.14 × 91.125

Volume = 381.51 cubic centimeters

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Answer: 638

Step-by-step explanation:1

2

3

4

5

7

6

7

8

9

3/8 x ?/? > 1

3/8 x ?/? = 1

Answer:

the answer is C!

Answer:

7 schools have fewer than 50 classrooms.

Step-by-step explanation:

'Find the product...'   just means multiply the two numbers together:

(use your calculator)    5602 x 17 =   95,234

Product means multiply them together. Please see image showing multiplication. You could also break this up into (5602 x 7) + (5602 x 10), which is basically what I did vertically.

Using Pythagorean trigonometric identity, the value of cosθ is √2/2

To find the value of cosθ, we can use Pythagorean identity to do this. However, we are also told that θ terminates in the the first quadrant.

sinθ = √2/2

sin²θ + cos²θ = 1

Substituting the value of sin θ into the formula above

cos²θ + (√2/2)² = 1

cos²θ + 1/2 = 1

collect like terms

cos²θ = 1 - 1/2

cos²θ = 1/2

cosθ = √(1/2)

cosθ = √2/2

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The equation of the new line will be y = -9x + 4. Then the correct option is B.

Given that:

Linear equation, y = x + 2

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The y-value of the y-intercept will be raised by 2 units, and the slope will be multiplied by -9.

Then the slope of the equation will be given as,

m = -9 x 1

m = - 9

The y-intercept of the equation is given as,

c = 2 + 2

c = 4

The equation of the new line will be y = -9x + 4. Then the correct option is B.

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In the function y = x + 2, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function

An equation to represent A, the area in square feet, as a function of w, the width in feet will be; A = 120W -2W²

Here, the perimeter of the rectangle will give:

120 = L + 2W

Area = LW

We know that the area of a rectangle is l × w

When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000

When w = 20, length = 120 - 40 = 80,  area =  80 x 20  = 1600

When w = 40, length = 120 - 80 = 40.  area = 40 x 40 = 1600.

So, the completed table will be

Width            Length          Area

10                    100              1000

20                    80              1600

40                    40              1600  

w                  120 - 2w        (120 - 2w) w

To maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60

On substituting, we have,

A = LW = (120 - 2W) W

L = 120 - 2W,

On simplification, we have

A = 120W -2W²

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Answer:

66 inches

Step-by-step explanation:

Every foot is twelve inches

Answer: 66 inch is in 5 1/2 feet

Step-by-step explanation: there is 12 inches in 1 foot so you do 12 x 5= 60 then there is 6 inches in a half of a foot so you add 60 and 6 and you get 66 inches

The mean and standard deviation is x ~ N(76,3).

Given that a population has a mean = 76 and a standard deviation o = 24

We need to find the standard deviation of a sampling distribution of sample means with sample, n = 64.

The mean of the sampling distribution of sample means is =

x = μ

x = 76

Now,

SD = σ/√n

= 24/√64

= 24/8

= 3

Hence, x ~ N(76,3).

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The exact value of sin θ, given that cosθ = 1/2 and θ terminates in Quadrant IV, is -√(3)/2.

The Pythagorean Identity states that sin²θ + cos²θ = 1. This identity can be used to find the value of sinθ, given the value of cosθ, and vice versa.

In Quadrant IV, the cosine function is positive, and the sine function is negative. This is because in Quadrant IV, the x-coordinate is positive, and the y-coordinate is negative.

Given that cosθ=1/2, we can use the Pythagorean Identity to find the value of sin²θ.

sin²θ + cos²θ = 1

sin²θ + (1/2)² = 1

sin²θ + 1/4 = 1

sin²θ = 1 - 1/4

sin²θ = 3/4

To find the value of sinθ, we take the square root of both sides of the equation:

sinθ = ±√(3/4)

However, since θ terminates in Quadrant IV, sinθ is negative. Therefore, we take the negative square root of 3/4:

sinθ = -√(3/4)

We can simplify this expression by writing 3/4 as a fraction in terms of its square roots:

sinθ = -√(3/4)

sinθ = -√(3)/√(4)

sinθ = -√(3)/2

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The statement "Each additional serving will require 1 additional can of beans" is not correct.

It should be noted that to make more than 3 servings, Robert will need to increase the amount of both beans and ground turkey used in the recipe.

Assuming that the recipe calls for one 18-ounce can of beans for 3 servings, Robert will need to use 6 cans of beans for 12 servings.

This is because each serving requires 6 ounces of beans (18 ounces ÷ 3 servings), and 12 servings would require a total of 72 ounces of beans (12 servings × 6 ounces per serving).

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The expressions that shows a correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is (-4-6) / (-7 - 3) (option c).

To find the slope of a line that passes through two points, we can use the slope formula, which is:

slope = (change in y) / (change in x)

This formula tells us how much the y-coordinate changes (rise) for every one unit of change in the x-coordinate (run).

Now let's use the given points (3,6) and (-7,-4) to set up the slope formula. We'll call the first point (x₁, y₁) and the second point (x₂, y₂). Then we can plug these values into the slope formula:

slope = (y₂ - y₁) / (x₂ - x₁)

Plugging in the coordinates of the two given points, we get:

slope = (-4 - 6) / (-7 - 3)

We simplify this expression to get:

slope = (-10) / (-10)

Which simplifies further to:

slope = 1

So the correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is:

slope = (y₂ - y₁) / (x₂ - x₁)

= (-4 - 6) / (-7 - 3)

= 1

Therefore, the slope of the line passing through these two points is 1.

Hence the correct option is (c).

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Step-by-step explanation:

At least twice means it could be   2  3  4  5  6  7  or  8 heads

 there is 8 chances of having only one TAIL

there are   2^8 outcomes = 256 outcomes possible

     take away the EIGHT with one tail

                  248 out of 256 have at least 2 heads

248/256 = 31/32

( Let me know if this is incorrect and I will re-evaluate !)

Answer:

[tex]\frac{247}{256}[/tex]

Pre-requisite Knowledge:

Permutations and Combinations

Elementary Probability

Step-by-step explanation:

Total number of outcomes (Cardinality of the sample space) = [tex]2^{8}[/tex]  

P(at least 2 heads show up) = 1 - [ P(no Head) + P(exactly 1 Head) ]

[tex]= 1-\frac{C(8,0)+C(8,1)}{2^8}\\\\=1-\frac{1+8}{256}\\\\ =1-\frac{9}{256}\\\\= \frac{247}{256}[/tex]

g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.

Option C is the correct answer.

We have,

To find the transformation that maps f(x) to g(x), we need to determine how the points of g(x) relate to the points of f(x).

First, we can see that the two functions have the same x-coordinates (1 and 4). This means that the transformation only affects the y-coordinates of the points.

At x = 1,

f(x) has a y-value of 4, and g(x) has a y-value of 2.

This means that g(x) is f(x) after vertical compression by a factor of 1/2.

At x = 4, f(x) has a y-value of 8, and g(x) has a y-value of 4.

This means that g(x) is f(x) after vertical compression by a factor of 1/2.

Therefore,

g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.

i.e

g(x) = (1/2) f(x)

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The hypothesis are

Null Hypothesis: The proportion of time the penny lands on heads 0.5

Alternative Hypothesis: The proportion of times the penny lands on heads in not 0.5.

We can denote the proportion of times the penny lands on heads as p.

If the null hypothesis is true, then p = 0.5. If the alternative hypothesis is true, then p is not equal to 0.5.

We can use a hypothesis test to determine if the sample data provides evidence to reject the null hypothesis in favor of the alternative hypothesis. One possible hypothesis test is the two-tailed z-test for proportions.

To perform this test, we would calculate the test statistic :

z = (p' - p) / √(p x (1-p) / n)

where p' is the sample proportion, p is the null hypothesis proportion (0.5), and n is the sample size.

In this case, we have a sample size of n = 50 and a sample proportion of p' = 30/50 = 0.6. We can calculate the test statistic:

z = (0.6 - 0.5) / √(0.5 x 0.5 / 50)

z ≈ 2.24

To determine if this test statistic is significant at the 5% level, we would compare it to the critical values from the standard normal distribution. For a two-tailed test at α = 0.05, the critical values are -1.96 and 1.96.

Since 2.24 falls outside of this range, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the proportion of times the penny lands on heads is not 0.5.

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The values with Charged Chip model are

9 + (-4) = 5.

9-(-4)=13

-9+4=-5

-9-(-4)=-5

To solve 9 + (-4), we start with 9 positive chips and take away 4 negative chips. We can represent this as:

[+][+][+][+][+][+][+][+][+]

[-][-][-][-]

When we combine the chips, we end up with 5 positive chips remaining:

[+][+][+][+][+]

Therefore, 9 + (-4) = 5.

To solve 9 - (-4), we start with 9 positive chips and add 4 negative chips. We can represent this as:

[+][+][+][+][+][+][+][+][+]

[-][-][-][-]

When we combine the chips, we end up with 13 positive chips remaining:

[+][+][+][+][+][+][+][+][+][+][+][+][+]

Therefore, 9 - (-4) = 13.

Similarly -9+4 value is -5

-9-(-4) value is -5

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Answer:

The answer is D

Step-by-step explanation:

8× the number

let the number be n

8×n=8n

Answer:

8n

Step-by-step explanation:

whenever a number is attached to a variable, that means multiplication. 8n is the correct answer.

have a great day and thx for your inquiry :)

Answer:

the absolute value of 6 is just 6

The rational numbers are solved and the incorrect number is A = 3/0

Given data ,

Let the rational number be represented as A

Now , the value of A is

A)

The division 0/3 will be a rational number because any number divided by 0 is undefined, but in this case, the division is defined and the result is 0, which is a rational number.

B)

The division 3/0 will not be a rational number because any number divided by 0 is undefined, and therefore, the division is not defined.

C)

The division -3/8 will be a rational number because it can be expressed as a ratio of two integers (-3 and 8) and can be written in the form of a fraction -3/8

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Answer:

∠x = 38°

Step-by-step explanation:

∠x + ∠y = 180°

∠x + 142° = 180°

∠x = 180° - 142

∠x = 38°

The total amount of paper required is 3π(3+√71)unit²

The equation for the surface area of a cone is given as follows:

A = πr²+πrs.

Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)

Substituting the values of r & h to determine s

s = √(8²+3²)

s = √71

Substituting the values to get Area,

A=π*3²+π*3*√71.

A=3π(3+√71)

Hence, the required paper will be A=3π(3+√71)unit²

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Answer:

Correct equation:

x + 22 + x + 22 + 10 = 48

The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

The class has a cat and a dog = 9

Has a dog and does not have a cat = 2

Does not have a dog and has a cat = 4

Does not have dog and cat = 5

The total strength of the class is 20

The probability that a student is chosen randomly from the class has a cat or a dog =  Number of favorable outcomes / total number of outcomes

P(E) = 15 /20

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Answer:

Step-by-step explanation:

its 11/28

Answer:

The answer is C) 2.

Step-by-step explanation:

Since g(x) is the inverse of f(x), we know that f(g(x)) = x for all x in the domain of g.

Therefore, f(g(2)) = 2.

The answer is C) 2.

The complete factorization of the original expression is:

4x² (x + 1)²

We have,

First, we can factor out 4x².

4x² (x² + 2x + 1)

Next, we can see that the expression inside the parentheses is a perfect square trinomial, which means it can be factored as:

4x² (x + 1)²

Thus,

The complete factorization of the original expression is:

4x² (x + 1)²

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