If the side that is 6 units long is the base of this parallelogram, what is its corresponding height.

The three basic types of rigid transformations are rotation, reflection and translation transformation

The correct options are;

Quadrilateral ABCD is reflected over the x-axis → (2, 4)

Quadrilateral ABCD translated 2 units right and 1 unit down → (4, -5)

Quadrilateral ABCD dilated about the origin by a scale factor of 3 → (6, -12)

Quadrilateral ABCD rotated 180° clockwise about the origin → (-2, 4)

The reasons the above matches are correct are as follows:

The given coordinates of the preimage are A(2, -4)

The image of (x, y) following a reflection over the x-axis is (x, -y)

Therefore

The image of (x, y) following a translation of 2 units right and 1 unit down → (x + 2, y - 1)

Therefore;

The image of (x, y) following a dilation about the origin by a scale factor of 3 is (3×x, 3×y)

Therefore;

The image of the point (x, y) rotated 180° clockwise about the origin is (-x, -y)

Therefore;

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Answer:

look at the pic for correct answer

or my explanation below

Step-by-step explanation:

1....(2.4)

2...(4.-5)

3...(6.-12)

4...(-2.4)

John's percentile rank is 60%.

The percentile rank is a measure used to indicate the percentage of scores that fall below a particular value in a given data set. To calculate John's percentile rank, we first need to determine how many students are below his rank.

In this case, John's rank is 120, which means that 119 students are ranked higher than him, and 300 - 119 = 181 students are ranked lower than him. To find John's percentile rank, we divide the number of students ranked below him by the total number of students and multiply by 100: (181/300) x 100 = 60%.

Therefore, John's percentile rank is 60%, indicating that he scored higher than 60% of the students in his class.

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No, we cannot find a unique price for an apple and an orange

Let the price of an apple be $x and that of orange be $y.

Condition 1.

They need $10 for 4 apples and 4 oranges.

Then, 4x + 4y = 10

or, 2x + 2y = 5 .....(1)

Condition 2.

They need $12 for 6 apples and 6 oranges.

Then, 6x + 6y = 12

or, 2x + 2y = 5 .....(2)

Two identical linear equations have been discovered.

They do, however, create a system of dependent linear equations that reduces to:

2x + 2y = 5

There are infinite possible solutions to this linear equation.

Thus, we get the conclusion that an apple and an orange cannot have different prices.

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Step-by-step explanation:

\(2x + 3y = 12 \\ 3y = - 2x + 12 \\ y = - \frac{2}{3} x + 4\)

slope is -2/3

y intercept is 4

Answer:

The slope is -2/3 and the y intercept is 4

Step-by-step explanation:

2x + 3y = 12

Slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

2x + 3y = 12

Subtract 2x from each side

2x-2x+3y = -2x+12

3y = -2x+12

Divide by 3

3y/3 = -2x/3 +12/3

y = -2/3 x +4

The slope is -2/3 and the y intercept is 4

Answer:

The value will be $1,411.20

Step-by-step explanation:

What we do here is to set up an exponential equation to calculate the value.

Mathematically it will look like this;

V = I(1-r)^n

where V is the future value

I is the initial amount = 24,600

r is rate of decrease = 13.75% = 13.75/100 = 0.1375

n is the number of years = 15 years

substituting these values, we have

V = 24,600(1-0.1375)^15

V = 24600(0.8625)^15

V = 1,411.165582454129

= $1,411.20

Answer:

La suma de las medidas de los ángulos interiores de un decágono (polígono de 10 lados) es 1,440.

By showing for every point x in V, there exists an open ball B(x, ε) that is contained entirely within V we proved V is open.

To prove that V is open, we need to show that for every point x in V, there exists an open ball B(x, ε) that is contained entirely within V.

So take any point x in V. Since s < ||x − a|| < r,

we know that x is at a distance greater than s from a, but less than r.

Say this distance d = ||x − a||.

Now, Consider the point y that is halfway between x and a.

That is, let y = (x + a)/2.

Notice that ||x − y|| = ||a − y|| = d/2.

Since 0 < s < d/2, we know that s + d/2 < d.

Therefore, we can choose ε = d/2 − s such that B(x, ε) is contained entirely within set V.

To see this, let z be any point in B(x, ε). Then ||x − z|| < ε = d/2 − s,

which means that ||x − z|| + s < d/2.

But ||z − a|| ≤ ||x − a|| + ||x − z||, so we have,

⇒ ||z − a|| > ||x − a|| − ||x − z|| > d − (d/2 − s) = d/2 + s > s.

Therefore, z is in V, and since z was arbitrary,

we've shown that B(x, ε) is contained entirely within V.

Thus, we've shown that for every point x in V,

We can find an open ball B(x, ε) that is contained entirely within V. Therefore, V is open.

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Step-by-step explanation:

7.5 cups of raisins, 10 cups of peanuts and 5 cups of chocolate chips.

Step-by-step explanation:

We are given that,

The amount of ingredients needed for the trail mix are,

Raisins = \frac{3}{4}

4

3

cup

Peanuts = 1 cup

Chocolate chips = \frac{1}{2}

2

1

cup

Since, Kiran needs to make 10 cups of the trail mix.

The amount of ingredients needed will be,

Raisins = \frac{3}{4}\times 10

4

3

×10 = \frac{30}{4}

4

30

= 7.5 cups

Peanuts = 1 × 10 = 10 cups

Chocolate chips = \frac{1}{2}\times 10

2

1

×10 = 5 cups

Hence, the ingredients needed are 7.5 cups of raisins, 10 cups of peanuts and 5 cups of chocolate chips.

4 1/4 not sure tho i got it from internet

If each box is numbered , so that they are distinguishable , then professor can distribute the journal in  40!/(10! )⁴   ways .

In the question ,

it is given that

the professor had 40 issues of mathematics journal;

number of boxes to be packed in = 4 boxes

number of issues per box = 10 issues

since the 4 boxes are numbered ,

So , in

Box 1 , the 10 issues out of 40  can be packed  in ⁴⁰C₁₀ ways .

and

for box 2 the number of issues remaining is 30

So , in Box 2 the 10 issues out of 30 can be packed in ³⁰C₁₀ ways .

for Box 3

the number of issues remaining is 20

so, in box 3 the 10 issues out of 20 can be filled in ²⁰C₁₀ ways .

for Box4

the umber of issues remaining is 10 ,

so , in box 4 the 10 issues out of 10 can be filled in ¹⁰C₁₀ ways .

The journals can be distributed in ⁴⁰C₁₀ × ³⁰C₁₀ × ²⁰C₁₀ × ¹⁰C₁₀ ways

= (40!)/(30! * 10! ) × (30!)/( 20! * 10!) × (20!)/(10! * 10!) × 1

On simplifying further , we get

= 40!/(10! )⁴ ways .

Therefore , If each box is numbered , so that they are distinguishable , then professor can distribute the journal in  40!/(10! )⁴   ways .

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The coefficient for household income growth is statistically significant at the 5% level.

To determine the statistical significance of the coefficient for household income growth, a significance level or alpha is needed. The significance level indicates the threshold below which the coefficient is considered statistically significant.

The given statement states that the coefficient is statistically significant at the 5% level. This means that the probability of observing such a large coefficient due to random chance is less than 5%. In other words, there is strong evidence to suggest that the coefficient is not zero and that there is a significant relationship between household income growth and the variable of interest.

It is important to note that the other options stating significance at the 1% level or 0.73% level would indicate even stronger evidence against the null hypothesis.

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Answer:

B

Step-by-step explanation:

a function doesn't have any repeating x values

To determine the number of ways to select five male and five female members for the organization's board of directors, we'll use the combination formula C(n, r) = n! / (r! * (n-r)!). So, there are 132,819,072 ways to select five male and five female members for the organization's board of directors.

C(20, 5) = 20! / (5! * (20-5)!)

C(20, 5) = 20! / (5! * 15!)

C(20, 5) = 15,504

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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

It is given to us that -

Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving

Company now advertises that its new small cars average more than 45 miles per gallon in highway driving

52 automobiles were tested

Sample average is 46.1 miles per gallon

Sample standard deviation is 5.3 miles per gallon

Significance level is 0.01

We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.

Let us assume that -

p = population of average gasoline of new small cars in highway driving

According to the given information,

Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -

\(H_{0}\) : \(p\leq 45\) miles per gallon

Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -

\(H_{A}\) : \(p > 45\) miles per gallon

For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.

According to one sample z test, the value of test statistic is given as -

\(T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }\) ------ (1)

where,

\(X_{avg}\) = Sample mean

p = hypothesized population mean

S = Sample standard deviation

n = Sample size

According to the given information, we have

\(X_{avg}\) = 46.1 miles per gallon

p = 45 miles per gallon

S = 5.3 miles per gallon

n = 52

Substituting the above values in equation (1), we have

\(T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }\\= > T = \frac{(46.1 -45)}{\frac{5.3}{\sqrt{52} } }\\= > T = \frac{1.1}{0.735}\\ = > T = 0.634\)

It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.

But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,

0.634 < 2.58

This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.

Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

It is given to us that -

Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving

Company now advertises that its new small cars average more than 45 miles per gallon in highway driving

52 automobiles were tested

Sample average is 46.1 miles per gallon

Sample standard deviation is 5.3 miles per gallon

Significance level is 0.01

We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.

Let us assume that -

p = population of average gasoline of new small cars in highway driving

According to the given information,

Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -

H0 = p<= 45 :  miles per gallon

Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -

HA : p > 45 :  miles per gallon

For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.

According to one sample z test, the value of test statistic is given as -

T = (X - p)/(SD/√n)

where,

X = Sample mean

p = hypothesized population mean

S = Sample standard deviation

n = Sample size

According to the given information, we have

X = 46.1 miles per gallon

p = 45 miles per gallon

S = 5.3 miles per gallon

n = 52

Substituting the above values in equation (1), we have

T = 46.1-45/(5.2/√52)

T = 1.1/0.735

T = 0.634

It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.

But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,

0.634 < 2.58

This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.

Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

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Answer:

-11

Step-by-step explanation:

Just add 7 to -18

-18 + 7 = -11

Hope this helped :)

(If you want to check, just do -11 - 7)

Answer:

7 inches

Step-by-step explanation:

6x7=

42

Notice:

2 is first term

2*4 = 8 is second term

8*4 = 32 is third term

and so on

Each term is multiplied by 4 to get the next term, so it’s geometric. The “common ratio” is whatever you’re multiplying by, which is 4.

1. To have 50, 4-ounce portions of green beans, we need to find how many pounds of fresh green beans should be bought.

Firstly, we'll need to find out how many ounces are needed to have a total of 50 portions of 4-ounces each.

50 portions of 4 ounces each = 50 × 4 = 200 ounces.

To find the total weight in ounces of the green beans that need to be purchased, we divide 200 by 0.85 (as 85% of fresh green beans are edible) as follows:

Total weight in ounces = 200/0.85 = 235.29 ounces.

1 pound is equal to 16 ounces, so to find the total weight in pounds of fresh green beans, we divide 235.29 by 16 as follows:

Total weight in pounds = 235.29/16 = 14.7 pounds.

Therefore, approximately 15 pounds of fresh green beans should be purchased.

2. We need to find out how much whole fish we need to buy to obtain 10 pounds of fish after it has been cleaned (with 40% yield).

We can solve for this using the formula: Yield% = (edible portion ÷ raw portion) × 100.

We can rearrange the formula as: Edible portion = (yield% ÷ 100) × raw portion

We need a 40% yield, so substituting the given values in the formula above, we get:

Edible portion = (40 ÷ 100) × Raw portion

Let's say Raw portion is R. We need 10 pounds of edible portion, so:

10 pounds = (40 ÷ 100) × R10 ÷ (40 ÷ 100) = R25 = R

Therefore, 25 pounds of whole fish should be purchased.

3. We are serving 60 people with half-pound strip sirloin, so we need to find how many pounds of sirloin should be brought in, assuming that 20% of it will be wasted after trimming.

Each serving requires a half-pound, so 60 people need a total of 60 × 0.5 = 30 pounds of sirloin.

To find out the total weight of sirloin that should be brought in, we can use the formula:

Total weight of sirloin = Required weight of sirloin ÷ (1 - Waste%)

Required weight of sirloin = 30 pounds

Waste% = 20% = 0.2

Substituting these values into the formula, we get:

Total weight of sirloin = 30 ÷ (1 - 0.2)= 30 ÷ 0.8= 37.5 pounds.

So, approximately 38 pounds of sirloin should be brought in.

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Analyzing the function f(x) = -2•x³ + 5•x² - 3•x + 1, using the criteria f(x) = f(-x) for even functions and f(x) = -f(-x) for odd functions, gives the correct option as the option

A. Neither even or odd

An even function satisfy the equation f(x) = f(-x)

An even function is one that is symmetrical about the y-axis

An odd function satisfy the equation f(x) = -f(-x)

The shape graph of an odd function is inverted as it crosses the y-axis.

Analyzing the function f(x) = -2•x³ + 5•x² - 3•x + 1 gives;

f(1) = -2•1³ + 5•1² - 3•1 + 1 = -1

f(-1) = -2•(-1)³ + 5•(-1)² - 3•(-1) + 1 = 11

f(1) ≠ f(-1)

-f(-1) = -2•(-1)³ + 5•(-1)² - 3•(-1) + 1 = 11

f(1) ≠ -f(-1)

The function is therefore;

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Answer:

B.

Step-by-step explanation:

Lets break this down piece by piece.

So first, add 500,000 and 30,000. that would be 530,000.

Next, add on 5,000, which is 535,000

After that, add 300. ( 535,300. )

Then add up 50 and 3 which is 53.

Lastly, your answer is 535,353.

Answer:

b

Step-by-step explanation:b

b

Answer:

HL

Step-by-step explanation:

It's a right triangle.

Answer: HL

Step-by-step explanation: because they are right triangles

The probability of the shop purchasing is 5/9.

Let X be the number of non-defective engines purchased by the auto shop out of the 4 engines bought. We want to find P(X >= 3), the probability of getting at least 3 non-defective engines.

Using the hypergeometric distribution formula, we have:

P(X >= 3) = P(X = 3) + P(X = 4)

where

P(X = k) = (C(7, k) * C(2, 4-k)) / C(9, 4)

So, we have:

P(X = 3) = (C(7, 3) * C(2, 1)) / C(9, 4) = (35 * 2) / 126 = 5/18

P(X = 4) = (C(7, 4) * C(2, 0)) / C(9, 4) = (35 * 1) / 126 = 5/18

Therefore,

P(X >= 3) = 5/18 + 5/18 = 10/18 = 5/9

So the probability of the shop purchasing at least 3 non-defective engines is 5/9.

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The shortest lifespan will last less than 2.5 years.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

First, we must utilize the conventional normal table to determine the value for z if 10% of the region (probability) to its left will be present. We can observe that about z = -1.282.

Now, we have to find the value of x, that corresponds to the value of z.

Since,

(x - μ) / σ = z

(x - 3.1) / 0.5 = -1.282

                 x = 2.459

Hence, the shortest lifespan will last less than 2.5 years.

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Answer:

Step-by-step explanation:

1)

∠1 = ∠2     {Angles opposite to equal angles are equal}

∠1 = ∠2 = x

x +x + 55 = 180  {angle sum property of triangle}

2x + 55 = 180

        2x = 180 - 55

        2x = 125

          x = 125/2

x = 62.5

∠1 = 62.5

2) ∠2 = 62.5

3) ∠3 = 55         {Vertically opposite angles are congruent}

4) ∠4 + 105 = 180        {linear pair}

∠4 = 180 - 105

∠4 = 75

5) ∠3 + ∠4 + ∠5 = 180 {Angle sum property of triangle}

    55 + 75 +∠5 = 180

            130 + ∠5 = 180

                     ∠5 = 180 - 130

∠5 = 50

Answer:

a1=1

d=3-1

=2

an=a1+(n-1)d

=1+ (n-1)2

=1+2n-2

2n-1

The “yearly tuition costs” as an independent variable which should be plotted on X-axis and “mid-career salary” as a dependent variable on Y-axis. The scatterplot is made of them.

Based on the table provided, it is possible to observe that there is not necessarily a clear relationship between the cost of tuition and mid-career salary.

While some of the colleges with higher tuition costs (such as MIT and Stanford) have high mid-career salaries, others (such as Harvey Mudd and Caltech) also have high mid-career salaries despite lower tuition costs. Additionally, some colleges with low or zero tuition costs (such as the US Naval Academy and West Point) also have high mid-career salaries.

Therefore, it is not safe to assume that a higher cost of tuition will necessarily translate into higher-paying jobs. The scatter plot of yearly tuition costs and mid-career salary is made.

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Answer:

Given Below.

Explanation:

(a)

\(x^2 - 12x = 45\)

\(x^2 - 12x -45 = 0\)

\(x^2 - 15x + 3x - 45 = 0\)

\(x ( x-15) + 3 ( x - 15) = 0\)

\((x+3)(x-15) = 0\)

\(x = -3 , 15\)

(b)

\(x^2 - 6x = 7\)

\(x^2 - 6x -7 = 0\)

\(x^2-7x + x -7 = 0\)

\(x(x-7)+1(x-7) = 0\)

\((x+1)(x-7) =0\)

\(x = -1, 7\)

1. )

\(x^{2} -12x=45\\x^{2} -12x-45 = 0\\(x-15)(x+3) = 0\\x = -3, 15\)

2. )

\(x^{2}-6x=7\\x^{2} -6x-7=0\\(x-7)(x+1) = 0\\x = -1, 7\)

Answer:

-19 and 3

Step-by-step explanation:

-19 x 3 = -57

-19 + 3 = -16

Answer:

Step-by-step explanation: To find the answer to "What two numbers have a product of 57 and a sum of 16?" we first state what we know. We are looking for x and y and we know that x • y = 57 and x + y = 16.

Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which This means that when we create one equation to solve the problem, we will have two answers.

To solve the problem, we take x + y = 16 and solve it for y to get y = 16 - x. Then, we replace y in x • y = 57 with 16 - x to get this:

x • (16 - x) = 57

Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of 57 and a sum of 16. The numbers are:

5.35425

10.64575

That's it! The two numbers that have a product of 57 and a sum of 16 are 5.35425 and 10.64575 as proven below:

5.35425 • 10.64575 = 57

5.35425 + 10.64575 = 16

HOPE THAT HELP YOU PLS MARK ME BRANLITS PLSSSS

Option B: \(10x^2 + 47.62x - 84.18.\) is correct

What is the quadratic equation?

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable being solved for.

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions.

If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other.

To simplify the expression, we need to use the distributive property of multiplication.

\((5x - 6.9)(2x + 12.2)\\= 5x(2x) + 5x(12.2) - 6.9(2x) - 6.9(12.2)\\= 10x^2 + 61x - 13.38x - 84.18\\= 10x^2 + 47.62x - 84.18\\\)

Hence, (5x - 6.9)(2x + 12.2) simplifies to \(10x^2 + 47.62x - 84.18\).

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Answer:

\(4km\)

Step-by-step explanation:

In order to find the answer to this question you must simply divide.

\(5m=8km\)

\(2.5m=4km\)

\(8\div2=4\)

\(5=2.5+2.5\)

\(=4km\)

Hope this helps