Dilate line f by a scale factor of 3 with the center of dilation at the origin to create line f'. Where are points A' and B' located after dilation, and how are lines f and f' related?

The locations of A' and B' are A' (0, 2) and B' (6, 0); lines f and f' intersect at point A.
The locations of A' and B' are A' (0, 6) and B' (2, 0); lines f and f' intersect at point B.
The locations of A' and B' are A' (0, 2) and B' (2, 0); lines f and f' are the same line.
The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

Answer:

Step-by-step explanation:

x = 4y+18

xy = -18

x = -18/y

-18/y = 4y+18

4y² + 18y + 18 = 0

2y² + 9y + 9 = 0

y = [-9 ±√(9²-4(2)(9))]/[2(2)] = [-9 ± 3]/4 = -1.5, -3

-1.5 is an extraneous solution, so y = -3

x = 6

Answer:

23

Step-by-step explanation:

We are given that

f(2)=13

[tex]f'(x)\geq 2[/tex]

[tex]2\leq x\leq 7[/tex]

We have to find the possible small value of f(7).

We know that

[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]

Using the formula

[tex]f'(x)=\frac{f(7)-f(2)}{7-2}[/tex]

[tex]f'(x)=\frac{f(7)-13}{5}[/tex]

We have

[tex]f'(x)\geq 2[/tex]

[tex]\frac{f(7)-13}{5}\geq 2[/tex]

[tex]f(7)-13\geq 2\times 5[/tex]

[tex]f(7)-13\geq 10[/tex]

[tex]f(7)\geq 10+13[/tex]

[tex]f(7)\geq 23[/tex]

The small value of f(7) can be 23.

Answer:

60/100

Step-by-step explanation:

Hope it helps you in your learning process

Answer:

123

Step-by-step explanation:

Yw

Answer:

0.0171

0.89158

Step-by-step explanation:

Given :

μ = 60

Standard deviation , σ = 17

The probability that a randomly chosen score is greater than 96;

P(Z > Zscore)

Zscore = (score, x - μ) / σ

Zscore = (96 - 60) / 17 = 2.118

P(Z > 2.118) = 1 - P(Z < 2.118) = 1 - 0.9829 = 0.0171

The probability that a randomly chosen score is less than 81;

P(Z < Zscore)

Zscore = (score, x - μ) / σ

Zscore = (81 - 60) / 17 = 1.235

P(Z < 1.235) = 0.89158

The probability that the player will get at least 7 hits in the game is approximately 0.192, or 19.2%.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

To solve this problem, we need to use the binomial distribution formula. The binomial distribution is used when we have a fixed number of independent trials (in this case, 9 at bats), where each trial has only two possible outcomes (hit or no hit), and the probability of success (getting a hit) is constant across all trials (0.305 in this case).

Let X be the number of hits the player gets in the game. Then X follows a binomial distribution with parameters n=9 (number of trials) and p=0.305 (probability of success).

The probability of getting at least 7 hits is equal to the sum of the probabilities of getting exactly 7, 8, or 9 hits:

P(X ≥ 7) = P(X=7) + P(X=8) + P(X=9)

Using the binomial probability formula:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

where C(n,k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

For k=7:

P(X=7) = C(9,7) * 0.305^7 * (1-0.305)^(9-7) = 0.154

For k=8:

P(X=8) = C(9,8) * 0.305^8 * (1-0.305)^(9-8) = 0.036

For k=9:

P(X=9) = C(9,9) * 0.305^9 * (1-0.305)^(9-9) = 0.002

Therefore:

P(X ≥ 7) = 0.154 + 0.036 + 0.002 = 0.192

Therefore,  the probability that the player will get at least 7 hits in the game is approximately 0.192, or 19.2%.

To learn more about Probability from given link.

https://brainly.com/question/30034780

#SPJ1

Answer & Step-by-step explanation:

Using the information given in the question we can form the following 3 equations (in the order of the first 3 sentences)

w = 2h (twice the price)

t = h - 4 ($4 less)

3w + 2h + 5t = 136 (total purchasing and cost)

We can solve all 3 equations for h first, by substituting the first two equations, into the third equations w and t

3(2h) + 2h + 5(h-4) = 136

Simplify

6h + 2h + 5h - 20 = 136

13h = 136 + 20

13h = 156

h = 156/13

h = $12

Using this information, we can solve for w and t

w = 2h

w = 2(12)

w = $24

And finally

t = h - 4

t = 12 - 4

t = $8

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Answer:

  (a) The set must have a constant additive rate of change

Step-by-step explanation:

If a linear function is suitable for representing the data, the data will demonstrate a constant slope. That is, for evenly spaced values of the independent variable, the differences of the values of the dependent variable will be constant. We can say ...

  The set must have a constant additive rate of change.

Answer:

the answer is option A population standard deviation

Answer:7

Step-by-step explanation:7

Answer:

The answer is "[tex]1.54 \times 10^{-6}[/tex]".

Step-by-step explanation:

Calculating the probability of the cards that hand from a 52-card deck.

The aces are high or low in poker.

There are 13 cards in the bridge hand.

A royal flush (5 suit top cards) in poker.

There are 5 various poker hands with [tex]\binom{52}{5}[/tex].

There are four royal flushes, one in each suit.

[tex]P (royal\ flush) =\frac{4}{\binom{52}{5}}\\\\[/tex]

                         [tex]=\frac{4}{2598960}\approx 1.54 \times 10^{-6}[/tex]

Answer:

I think the answer would be

y = 0.5x -8

tough this might be wrong?

Step-by-step explanation:

(2, 7) ( 4,6)

to find the gradient- mx

y2-y1/ x2 - x1

chose which would be 1/ 2

if I chose (2,7) as 1 then (4, 6) as 2

mx = 6- 7/ 4-2

= -0.5x

y = -0.5x + c

substitute

6 = -0.5(4) + c

6= -2+ c

c = -8

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Answer:

  they are not collinear

Step-by-step explanation:

A graph shows that a line through points A and C misses point B, so the points are not collinear.

__

If the points are collinear, then the slope of the segment between the first pair would be the same as the slope of the segment between the second pair.

  m = (y2 -y1)/(x2 -x1)

  m = (-18 -(-4))/(-3 -0) = -14/-3 = 14/3 . . . . slope of AB

__

  m = (6 -(-18))/(2 -(-3)) = 24/5 . . . . slope of BC ≠ slope of AB

The points are not collinear.

_____

Additional comment

With about the same amount of computational effort, you can find the area of the triangle bounded by the three points. If it is zero, then the points are collinear. Here, it is 1 square unit, so the points are not collinear.

Answer:

y-18=-3(x+2)

Step-by-step explanation:

The Slope-intercept form is -3x+12

Answer:

B

Step-by-step explanation:

$3 per gallon

that is the procedure above

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Answer:

  = 53(20 +4)  or  =24(50 +3)   or  =(20 +4)(50 +3)

Step-by-step explanation:

Either number can be rewritten as a sum. Typically, the sum will be based on place value: 53 = 50 + 3, for example, as opposed to something like 53 = 26 +27.

The usual method of multiplication taught in grade school makes use of this sort of rewriting.

53 × 24 = 53 × (4 +20) = 53×4 +53×20 = 212 +1060 = 1272

__

Additional comment

We find this easier to multiply as 53(20 +4) than as 24(50 +3) because doubling (multiplying by 2) and doubling again (multiplying by 4) is generally easier than multiplying by 3 or 5.

In grade school, we did this digit by digit, so ...

  53×24 = (3 +50)(4 +20) = 3(4 +20) +50(4 +20) = 3×4 +3×20 +50×4 +50×20

  = 12 +60 +200 +1000 = 1272

Answer:

The mean and median number of apples in a bag are 21.71 and 22 respectively.

Step-by-step explanation:

The mean is the arithmetic mean of a set of numbers. In other words, the mean is the average value of all my data.

The mean is calculated by adding all the values ​​and dividing the sum by the total number of values. In this case:

[tex]Mean=\frac{23+19+26+17+21+24+22}{7}[/tex]

[tex]Mean=\frac{152}{7}[/tex]

Mean= 21.71

The median of a set of numbers is the average number in the set, that is, it is the value that occupies the central place of all the values.

The median can be calculated by putting the numbers in ascending order and then:

In this case:

Putting the numbers in ascending order: 17, 19, 21, 22, 23, 24, 26

Since the quantity is odd numbers, the median is the number in the center of that distribution. So Median= 22

The mean and median number of apples in a bag are 21.71 and 22 respectively.

Answer:

x = 55

Step-by-step explanation:

In a rhombus, each diagonal bisects a pair of opposite angles.

For this parallelogram t be a rhombus, the angles with measures 2x - 40 and x + 15 must be congruent.

2x - 40 = x + 15

Subtract x from both sides.

x - 40 = 15

Add 40 to both sides.

x = 55

Answer:

Hello,

x=55

Step-by-step explanation:

The rhombus is formed of 2 isocele triangles

(since sides are equals)

The drawn diagonal  bissects the angle

x+15=2x-40

2x-x=15+40

x=55

Answer:

A. <BED and <DEA, <AEC and <BEC

Step-by-step explanation:

Supplementary angles add up to give 180°.

m<BED = 90°

m<DEA = 90°

m<BED + m<DEA = 180°

Therefore, <BED and <DEA are supplementary.

m<AEC = 90°

m<BEC = 90°

m<AEC + m<BEC = 180°

Therefore, <AEC and <BEC are supplementary.

Answer:

Step-by-step explanation:

(9-3)(2/5) = 6(2/5) = 12/5 = 2 2/5

9-32/5 = 2.6

Answer: 17 hours

Step-by-step explanation: Because he worked an hour over I added an hour. Then I subtracted his lunch break and and 2 breaks. I then took that number and subtracted it by 24.

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Answer:

  D. Logistic growth

Step-by-step explanation:

The logistic growth function models a situation where the rate of growth is jointly proportional to the population and to the difference between the population and the carrying capacity.

Attached is an example of such a function.

Answer:

The p-value of the test is 0.0088 < 0.05, which means that at the 0.05 significance level, we can conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Pernod 5:

23 out of 390, so:

[tex]p_P = \frac{23}{390} = 0.059[/tex]

[tex]s_P = \sqrt{\frac{0.059*0.941}{390}} = 0.0119[/tex]

Action:

46 out of 420, so:

[tex]p_A = \frac{46}{420} = 0.1095[/tex]

[tex]s_A = \sqrt{\frac{0.1095*0.8905}{420}} = 0.0152[/tex]

Test if there is a difference in proportions:

At the null hypothesis, we test if there is not a difference, that is, the subtraction of the proportions is 0. So

[tex]H_0: p_A - p_P = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0. So

[tex]H_1: p_A - p_P \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_A - p_P = 0.1095 - 0.059 = 0.0505[/tex]

[tex]s = \sqrt{s_A^2+s_P^2} = \sqrt{0.0119^2+0.0152^2} = 0.0193[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.0505 - 0}{0.0193}[/tex]

[tex]z = 2.62[/tex]

P-value of the test and decision:

The p-value of the test is the probability of a difference in proportions of at least 0.0505 to either side, which is P(|z| > 2.62), that is, 2 multiplied by the p-value of z = -2.62.

Looking at the z-table, z = -2.62 has a p-value of 0.0044.

2*0.0044 = 0.0088

The p-value of the test is 0.0088 < 0.05, which means that at the 0.05 significance level, we can conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Answer:

[tex]\begin{array}{cccccc}{x} & {V} & {W} & {X} & {Y} & {Z} & P(x) & {0.20} & {0.20} & {0.20} & {0.20} & {0.20} \ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]S = \{V,W,X,Y,Z\}[/tex]

[tex]n(S) = 5[/tex]

Required

The probability model

To do this, we simply calculate the probability of each container.

So, we have:

[tex]P(V) = \frac{n(V)}{n(S)} = \frac{1}{5} = 0.20[/tex]

[tex]P(W) = \frac{n(W)}{n(S)} = \frac{1}{5} = 0.20[/tex]

[tex]P(X) = \frac{n(X)}{n(S)} = \frac{1}{5} = 0.20[/tex]

[tex]P(Y) = \frac{n(Y)}{n(S)} = \frac{1}{5} = 0.20[/tex]

[tex]P(Z) = \frac{n(Z)}{n(S)} = \frac{1}{5} = 0.20[/tex]

So, the probability model is:

[tex]\begin{array}{cccccc}{x} & {V} & {W} & {X} & {Y} & {Z} & P(x) & {0.20} & {0.20} & {0.20} & {0.20} & {0.20} \ \end{array}[/tex]

Answer:

answer is V=.20, W=.20, X=.20, Y=.20, X=.20

Step-by-step explanation:

Answer:

  26 2/3

Step-by-step explanation:

Average speed is total distance divided by total time.

The time for the first trip was ...

  (90 mi)/(20 mi/h) = 4.5 h

The time for the return trip was ...

  (90 mi)/(40 mi/h) = 2.25 h

Then the average for the trip and return is ...

  total miles/total time = (90 +90)/(4.5 +2.25) = 26 2/3 . . . . mi/h

The average speed for the round trip was 26 2/3 miles per hour.

Answer:

Option B.

Step-by-step explanation:

Remember that the profit is defined as the difference between the revenue and the cost.

So, having a profit y = 0 means that the woodworker did not win nor lose anything.

Then the zeros of the function, the values of x such that the graph intersects the x-axis, are the prices such that she does not win nor loss anything.

In the graph we can see that the zeros are at:

x = 15 (the first one)

x = 70 (the second one)

so the zeros are at x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.

The correct option is B.

Answer:

x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.

Step-by-step explanation:

Answer:

x= 30 degrees

Step-by-step explanation:

This is an isosceles triangle as indicates by the lines on the sides.

Since the sides lengths are equal, the base angles are  equal

x= 30 degrees

Answer:

I think it is the last one.

Apply radical rule

= (10^1/2)3/4x

Apply exponent rule: (a^b)^c = a^bc

= 10^1/2 . 3/4x

Simplify: 1/2 . 3/4x:  3x/8

= 10^3x/8

Answer:

[tex]\frac{73,331}{75,516}\approx 97.11\%[/tex]

Step-by-step explanation:

The probability that she will find at least one student cheating is equal to the probability that she finds no students cheating subtracted from 1.

Each time she randomly chooses a student the probability she will catch a cheater is equal to the number of cheaters divided by the number of students.

Therefore, for the first student she chooses, there is a [tex]\frac{9}{35}[/tex] chance that the student chosen is a cheater and therefore a [tex]\frac{26}{35}[/tex] chance she does not catch a cheater. For the second student, there are only 34 students to choose from. If we stipulate that the first student chosen was not a cheater, then there is a [tex]\frac{9}{34}[/tex] chance she will catch a cheater and a [tex]\frac{25}{34}[/tex] chance she does not catch the cheater.

Therefore, the probability she does not catch a single cheater after randomly choosing ten students is equal to:

[tex]\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26}[/tex]

Subtract this from one to get the probability she finds at least one of the students cheating after randomly selecting nine students. Let event A occur when the professor finds at least one student cheating after randomly selecting ten students from a group of 35 students.

[tex]P(A)=1-\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26},\\\\P(A)=1-\frac{2,185}{75,516},\\\\P(A)=\boxed{\frac{73,331}{75,516}}\approx 0.97106573441\approx \boxed{97.11\%}[/tex]