If P(-2, 1) is rotated 90°, its image is

Answer:

a) 3 standard deviations above 16

b) More than 2 standard deviations of the mean, so yes, 22 inches is faw away from the mean of 16 inches.

c) Less than 2 standard deviations, so not far away.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If Z < -2 or Z > 2, X is considered to be far away from the mean.

In this question, we have that:

[tex]\mu = 16[/tex]

​(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 22 inches from 16 ​inches?

This is Z when [tex]X = 22, \sigma = 2[/tex].

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 16}{2}[/tex]

[tex]Z = 3[/tex]

So 22 inches is 3 standard deviations fro 16 inches.

​(b) Is 22 inches far away from a mean of 16 ​inches?

3 standard deviations, more than two, so yes, 22 inches is far away from a mean of 16 inches.

(c) Suppose the standard deviation of the underlying data is 4 inches. Is 22 inches far away from a mean of 16 ​inches?

Now [tex]\sigma = 4[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 16}{4}[/tex]

[tex]Z = 1.5[/tex]

1.5 standard deviations from the mean, so 22 inches is not far away from the mean.

Answer:

The answer is 2.5 hours

Step-by-step explanation:

Answer:

10ft[tex]{3}[/tex]

Step-by-step explanation:

One face has 15 blocks of 1/3 ft. You can clearly see 2 sets of blocks.

15 x 2 = 30

30 ÷ 3 or 30 x 1/3

= 10 ft cubed

Answer:

22.7

Step-by-step explanation:

ok so, First we need to find new values:

       96( 1 + 0.25) =120

       85( 1+0.2)=  102

Boys last year        girls last year      total this year

   96                             85                        181

Boys this year        girls this year        total this year

  120                         102                           222

   Find the overall increase:

181( 1+r)= 1.226519

THEN U SUBTRACT 1

r=0.226519

Multiply by 100 and round to nearest 10th

22.7%

Final Answer: 22.7%

HOPED IT HELPED:)

Answer:

(E) $24,800.00

Step-by-step explanation:

[tex]ln(\hat{price})=3.748-0.1395ln(miles)[/tex]

If a used truck has been driven for 47,000 miles

Miles=47 (in thousands)

We therefore have:

[tex]ln(\hat{price})=3.748-0.1395ln(47)\\ln(\hat{price})=3.2109\\$Take the exponential of both sides\\e^{ln(\hat{price})}=e^{3.2109}\\Price=e^{3.2109}\\$Price=24.80 \\Since the price is in thousands of dollars\\Price=24.80 X \$1000\\Predicted Price=\$24800.00[/tex]

The correct option is E.

Answer:

A.

Step-by-step explanation:

Add 4:

-5x ≤ 10

Divide by -5:

x ≥ -2

Answer:48

Step-by-step explanation:

Given

Amar wants 12 tablespoons of sugar in water.

Amar has teaspoon whose four times is equivalent to 1 tablespoon

i.e. [tex]4\ \text{teaspoon}\equiv 1\ \text{tablespoon}[/tex]

therefore

[tex]12 tablespoon is 4\times 12[/tex]

[tex]\Rightarrow 4\times 12[/tex]

[tex]\Rightarrow 48\ \text{teaspoons}[/tex]

So, amar need to add [tex]48\ \text{teaspoons}[/tex] for lemonade

Answer:6328565394729

Step-by-step explanation:213

sorry

Answer: 28

Step-by-step explanation: Im taking the same class here is a photo of the work, divide 56/2 than you get 28

A) $400

B) $800

C) 400*X

D) revenue=400x

Answer:

The probability that the next mattress sold is either king or queen-size is P=0.8.

Step-by-step explanation:

We have 3 types of matress: queen size (Q), king size (K) and twin size (T).

We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.

We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:

[tex]P_Q=\dfrac{P_K+P_T}{4}\\\\\\4P_Q-P_K-P_T=0[/tex]

We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:

[tex]P_K=3P_T\\\\P_K-3P_T=0[/tex]

Finally, we know that the sum of probablities has to be 1, or 100%.

[tex]P_Q+P_K+P_T=1[/tex]

We can solve this by sustitution:

[tex]P_K=3P_T\\\\4P_Q=P_K+P_T=3P_T+P_T=4P_T\\\\P_Q=P_T\\\\\\P_Q+P_K+P_T=1\\\\P_T+3P_T+P_T=1\\\\5P_T=1\\\\P_T=0.2\\\\\\P_Q=P_T=0.2\\\\P_K=3P_T=3\cdot0.2=0.6[/tex]

Now we know the probabilities of each of the matress types.

The probability that the next matress sold is either king or queen-size is:

[tex]P_K+P_Q=0.6+0.2=0.8[/tex]

Answer:

[tex]58,464 \: \: miles[/tex]

Step-by-step explanation:

[tex]speed = \frac{distantce}{time} \\ [/tex]

[tex]distance = speed \times time \\ x = 72 \times 812 \\ x = 58,464 \: \: miles[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

  G(x) = x^2 -10x +25

Step-by-step explanation:

To translate F(x) 5 units to the right, replace x with (x-5).

  G(x) = F(x-5) = (x -5)^2

  G(x) = x^2 -10x +25

Answer:

123.7 meters

Step-by-step explanation:

If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 30. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.

30^2 + 120^2 = c^2

c=123.7

Answer:

DID IT oN EDGEN UITY

Step-by-step explanation:

The first graph correctly represents our piecewise function f(x) = - 1.5x + 3.5 for x < 2 and 4 + x for x ≥ 2.

A function that is piecewise-defined by numerous subfunctions, each of which has a separate domain interval for which it is applicable.

Piecewise definition is more of an expression of the function than it is a property of the function.

Given a piecewise function f(x) = - 1.5x + 3.5 for x < 2 and 4 + x for x ≥ 2.

Now, strictly less or greater than will be shown as an open circle in the graph and less than or greater than equal to will be shown by a closed circle on the graph.

If we observe the first graph when x = 0, y = 3.5, and the end is represented as an open circle which is < 2 and when x ≥ 2 it is 6 and represented with a closed circle.

learn more about piecewise function here :

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Completed Question

Outputs to be matched to the functions are:

Answer:

Step-by-step explanation:

Given the vector x: x <- c(2, 43, 27, 96, 18)

Sort

In R, the sort(x)  function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.

Therefore, the output that matches the sort function is:

sort(x): 2, 18, 27, 43, 96

Rank

The rank function returns a vector with the "rank" of each value.

x <- c(2, 43, 27, 96, 18)

Therefore, the output of rank(x)  is: 1, 4, 3, 5, 2

Order

When the function is sorted, the order function gives the previous location of each of the element of the vector.

Using the sort(x) function, we obtain: 2, 18, 27, 43, 96

In the vector: x <- c(2, 43, 27, 96, 18)

Therefore, the output of order(x) is: 1, 5, 3, 2, 4

Answer:

Step-by-step explanation:

A linear transformation must satisfy the following properties.

- T(0) = 0.

- For vector a,b then T(a+b) = T(a) + T(b).

- For a vector a and a scalar r, it must happen that T(ra) = rT(a)

In this case we have that T(a,b,c) = (a,0,c).

Note that T(0) = T(0,0,0) = (0,0,0) = 0. So, the first property holds.

Let [tex] a=(a_1,a_2,a_3), b=(b_1,b_2,b_3) [/tex]. Then

[tex]T(a+b) = T((a_1+b_1,a_2+b_2,a_3+b_3)) = (a_1+b_1,0,a_3+b_3) = (a_1,0,a_3)+(b_1,0,b_3) = T(a) + T(b)[/tex]

So the second property holds.

Finally, let r be a scalar and let [tex] a=(a_1,a_2,a_3)[/tex]. Then

[tex] T(ra) = T((ra_1,ra_2,ra_3)) = (ra_1,0,ra_3) = r(a_1,0,a_3)= rT(a)[/tex]

So, the three properties hold, and therefore, T is a linear transformation.

It is true that T represents a linear transformation

A linear transformation is such that have the following properties

For the first property, we have:

T(x1,x2,x3) = (x1,0,x3)

The above property becomes

T(0) = T(0,0,0)

T(0) = (0,0,0)

T(0)= 0.

So, we can conclude that the first property of the linear transformation is satisfied

For the second property, we make use of the following:

u = (u1, u2, u3) and b = (v1,v2,v3)

The above property becomes

T(u + v) = T(u1 + v1, u2 + v2, u3 + v3)

Expand

T(u + v) = T(u1 + v1, 0, u3 + v3)

Expand

T(u + v) = (u1,0,u3) + (v1, 0, v3)

Simplify

T(u + v) = T(u) + T(v)

The above means that the second property is also satisfied

Recall that:

u = (u1, u2, u3)

So, we have:

T(ru) = (ru1, ru2, ru3)

Where r is a scalar

Expand

T(ru) = (ru1, 0, ru3)

Further, expand

T(ru) = r(u1, 0, u3)

So, we have:

T(ru) = rT(u)

The above means that, the third property is also satisfied

Hence, T represents a linear transformation

Read more about linear transformation at:

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Answer:

(x, y) → (4/5 x, 4/5 y)

Question:

The answer choices to determine the rule that represent the dilation were not given. Let's consider the following question:

A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?

A) (x, y) → (0.5 − x, 0.5 − y)

B) (x, y) → (x − 7, y − 7)

C) (x, y) → ( 5/4 x, 5/4 y)

D) (x, y) → (4/5 x, 4/5 y)

Step-by-step explanation:

To determine the rule that could represent the dilation, we would multiply each coordinate by a dilation factor (a constant) to create a dilation. Since the dilation would be used to create a smaller polygon, the constant multiplied with the coordinates of x and y would be less than 1.

Let's check the options out.

In option (A), the coordinates is subtracted from the constant (0.5).

In option (B), the constant (7) is subtracted from the coordinates.

In option (C), the coordinates are multiplied by constant (5/4).

But 5/4 = 1.25. This is greater than 1.

In option (D), the coordinates are multiplied by constant (4/5).

4/5 = 0.8

The constant multiplied with the coordinates of x and y is less than 1 in option (D) = (x, y) → (4/5 x, 4/5 y)

4/5 = 0.8

0.8 is less than 1

Answer:

A.

Step-by-step explanation:

Volume of cone = 1/3πr²h

= (1/3)(3.14)(1.5)²(5)

= (1/3)(3.14)(2.25)(5)

= (1/3)(35.3)

= 11.78

≈ 11.8 cubic inches

Answer:

a) N(2617, 586)

b) 0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c) 0.4013 = 40.13% of the customers consume over 2764 calories

d) 3981 calories.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 2617, \sigma = 586[/tex]

a. What is the distribution of X?

Here we first place the mean, then the standard deviation.

N(2617, 586)

b. Find the probability that the customer consumes less than 2409 calories.

This is the pvalue of Z when X = 2409. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2409 - 2617}{586}[/tex]

[tex]Z = -0.355[/tex]

[tex]Z = -0.355[/tex] has a pvalue of 0.3613

0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c. What proportion of the customers consume over 2764 calories?

This is 1 subtracted by the pvalue of Z when X = 2764. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2764 - 2617}{586}[/tex]

[tex]Z = 0.25[/tex]

[tex]Z = 0.25[/tex] has a pvalue of 0.5987

1 - 0.5987 = 0.4013

0.4013 = 40.13% of the customers consume over 2764 calories

d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?

Top 1%, so the 100-1 = 99th percentile.

The 99th percentile is the value of X when Z has a pvalue of 0.99. So it is X when Z = 2.327. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.327 = \frac{X - 2617}{586}[/tex]

[tex]X - 2617 = 2.327*586[/tex]

[tex]X = 3980.6[/tex]

Rounding to the nearest calorie, 3981 calories.

Answer:

12.08

Step-by-step explanation:

For each sunflower, there are only two possible outcomes. Either it germinates, or it does not. The probability of a sunflower germinating is independent of other sunflowers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Seventy-six percent of sunflower seeds will germinate into a flower

This means that [tex]p = 0.76[/tex]

Samples of 800:

This means that [tex]n = 800[/tex]

The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.76*0.24} = 12.08[/tex]

Answer:

0.7125

Step-by-step explanation:

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes (with probability p) in a sequence of n independent events.

The probability of getting exactly x successes in n independent Bernoulli trials =  [tex]n_{C_{x}}(p)^x(1-p)^{n-x}[/tex]

Total number of watches in the shipment = 50

Number of defective watches = 6

Number of selected watches = 10

Let X denotes the number of defective digital watches such that the random variable X follows a binomial distribution with parameters n and p.

So,

Probability of defective watches = [tex]\frac{X}{n}=\frac{6}{50}=0.12[/tex]

Take n = 10 and p = 0.12

Probability that the shipment will be rejected = [tex]P(X\geq 1)=1-P(X=0)[/tex]

[tex]=1-n_{C_{x}}(p)^x(1-p)^{n-x}\\=1-10_{C_{0}}(0.12)^0(1-0.12)^{10-0}[/tex]

Use [tex]n_{C_{x}}=\frac{n!}{x!(n-x)!}[/tex]

So,

Probability that the shipment will be rejected = [tex]=1-\left ( \frac{10!}{0!(10-0)!} \right )(0.88)^{10}[/tex]

[tex]=1-(0.88)^{10}\\=1-0.2785\\=0.7125[/tex]

Answer:

x ≤ -4

Step-by-step explanation:

2(3 - x) ≥ 14

Divide by 2

2/2(3 - x) ≥ 14/2

(3 - x) ≥ 7

Subtract 3 from each side

3-x-3  ≥ 7-3

- x ≥ 4

Divide each side by -1, remembering to flip the inequality

x ≤ -4

Answer:

-4

Step-by-step explanation:

6-2x≥14 (/expand )

-2x≥14-6=-2x≥8

x≤8/-2=-4

Answer:

direction

shape

scatter plots

shape and outliers

Step-by-step explanation:

Correlation is defined as the degree of correspondence between two variables.

When the values increase together, correlation is positive and when one value decreases as the other increases, correlation is negative .

Calculating a correlation can help describe a relation between two quantitative variables' direction and shape. However, it is not sufficient to use a correlation coefficient to describe two variables.  The addition of scatter plots can provide other helpful details such as shape and outliers

Answer: choice B

Step-by-step explanation:

The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x-axis.

Answer: B

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

Point G is coplanar with points B, C, H.

Answer:

2nd option is the correct answer

Step-by-step explanation:

3 times a number decreased by 6 is - 2

Answer:

150 miles

Step-by-step explanation:

If the distance between Seattle and Boise is 400 miles and the image illustrates 4", then there must be a proportionate between the two values. Therefore, if the distance between Seattle and Portland is 1.5", then the real distance must be 150 miles.

Answer:

radius=7

diameter =2×radius

d=2×7

diameter=14

Answer:

Hello!

The answer is-

Radius: 7

Diameter: 14

Step-by-step explanation:

Diameter:

2*(radius)

d=2(7)

Diameter is 14

Answer:

Step-by-step explanation:

factor out the numerator and demoninator

(m-2)(m-1)/m(m-1)

= (m-2)/m