Find the slope and y-intercept of the line represented by the table.
.
Please help me

(a) The coordinates after Rotation of 270° counterclockwise are W(5, -1), X(5, -7), Y(2, -7) and Z(2, -1).

(b) The coordinates after translation: (x, y) =(x-7, y + 3) are W(-6, 8), X(0, 8), Y(0, 5) and Z(-6, 5).

What is Rotation and Translation of coordinates ?

A rotation is any movement within a specific space that keeps at least one point. A rigid body's motion around a fixed point is one example of what it can be used to explain.

Every point in a figure, shape, or space is moved by the same amount and in the same direction by a translation, which is a geometric transformation.

Since the Rotation of Rectangle is 270° counterclockwise, it will shift the rectangle from 1st Quadrant to 4th Quadrant with transition from (x, y) to   (y, -x).

So, the coordinates after rotation of 270° counterclockwise are :

W(1, 5) ⇒ W(5, -1)

X(7, 5) ⇒X(5, -7)

Y(7, 2) ⇒Y(2, -7)

Z(1, 2) ⇒Z(2, -1)

Similarly, The coordinates after translation of (x, y) ⇒ (x-7, y+3 )

W(1, 5) ⇒ W(1-7, 5+3) = W(-6, 8)

X(7, 5) ⇒X(7-7, 5+3) = X(0, 8)

Y(7, 2) ⇒Y(7-7, 2+3) =Y(0, 5)

Z(1, 2) ⇒Z(1-7, 2+3) = Z(-6, 5)

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The submarine's depth relative to sea level after the first minute is 1.2 miles

To find the submarine's depth after the first minute, we first need to find the rate at which the submarine descends, r.

The rate at which the submarime descends is r = d/t where

Given that submarine descended at a constant rate to a depth of −3/4 mile relative to sea level in 5/8 minutes, we have that

So, substituting these into r, we have

r = d/t

= -3/4 mile ÷ 5/8 min

= -3/4 × 8/5

= -3 × 2/5

= -6/5

= -1.2 mile/min

So, the depth of the submarine after the first minute is given by D = rt where r = rate of descent =  -1.2 mile/min and t = time = 1 min

So, substituting these into D, we have

D = rt

=  -1.2 mile/min × 1 min

= -1.2 mile

So, the submarine's depth relative to sea level after the first minute is 1.2 miles

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This is an example of a comparative study that uses random sampling to ensure representation from different socioeconomic groups and educational backgrounds in the samples. The study aims to compare mathematics knowledge among 15-year-olds in the US and Japan by administering a mathematics achievement test to 1000 students from each country.
Hi! I'd be happy to help with your question. You would like to compare mathematics knowledge among 15-year-olds in the US and Japan by giving a mathematics achievement test to samples of 1000 15-year-olds in each of the two countries, with 200 students from low-income families, 400 students from middle-income families, and 400 students from high-income families in each country. This is an example of a stratified random sampling method.

In this case, the population is divided into different strata based on socioeconomic groups (low-income, middle-income, and high-income families), and then random samples are drawn from each stratum. This ensures that the samples include individuals from all different socioeconomic groups and educational backgrounds, which allows for a more accurate comparison between the two countries.

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Answer:

9

Step-by-step explanation:

Answer:

x = 45

Step-by-step explanation:

15 = \(\frac{1}{3}\) x ( multiply both sides by 3 to clear the fraction )

45 = x

Answer:

x = 45

Step-by-step explanation:

15 =  x

15(3)=x

45=x or x=45

Answer:

\( \frac{2b}{a} \)

Step-by-step explanation:

\( \frac{2}{a} \div \frac{1}{b} \)

\(\frac{2}{a} \: \times \:b\)

\( \frac{2b}{a} \)

The p-value of the test examining the hypotheses H0: μ = 350 vs Ha: μ < 350 with a sample size of n = 20 and a t-statistic of t = -1.68 is greater than 0.05 but less than 0.10.

In this one-sample t-test, you have a null hypothesis H0: μ = 350 and an alternative hypothesis Ha: μ < 350. You are given a sample size of n = 20 and a t-statistic of t = -1.68. To determine the p-value, you need to find the area to the left of the t-statistic in the t-distribution with n-1 (19) degrees of freedom.

Using a t-table or calculator, you can determine that the p-value is between 0.05 and 0.10. A p-value greater than 0.05 indicates that the result is not statistically significant at the 5% level, meaning you cannot reject the null hypothesis.

However, since the p-value is less than 0.10, you could consider the result as weak evidence against the null hypothesis at the 10% level.

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Answer:

4w4 + 10w5 - 5w3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply the amount by 0.46 and subtract from the amount.

The difference between amount  and 0.46 * amount is the answer.

Given:

Sample space be S = 1, 2 ,3 , 4, 5, 6.

The outcomes are equally likely.

To find:

The probability of the event E ="an even number".

Solution:

We have,

Sample space is S = 1, 2 ,3 , 4, 5, 6.

So, the total number of outcomes is 6.

E ="an even number".

E = {2,4,6}

So, the total number of favorable outcomes is 3.

The probability of the event E is

\(P(E)=\dfrac{Favorable outcomes}{Total outcomes}\)

\(P(E)=\dfrac{3}{6}\)

\(P(E)=\dfrac{1}{2}\)

\(P(E)=0.5\)

Therefore, the probability of the event E is 0.5.

A discrete random variable has a countable number of possible values. In this case I am pretty sure it is either none of the above or maybe the phone one.

Discrete random variables are simply countable, which should be a finite number and it should not change continuously. So, Time worked on a job is the discrete random variable among the four options.          

A random variable is said to be discrete if an experiment gives a finite number that is countable and should not change continuously.

Here, Time worked on a job has a fixed time for a job has to be done. So, it is a discrete random variable.

No. of girls in a family,

No. of outcomes of the head when two coins are flipped.

No. of defective street lights out of 100 bulbs in a certain area.

No. of the possible outcome of getting 4 when a dice is thrown twice.

The weight of a child changes as the child grows. So, it cannot be a discrete random variable.

The first digit of a phone number also changes for each and every person, whenever a person changes his /her number automatically will get a new number and it will have a different digit. So, it cannot be a discrete random variable.

The length of fish also varies according to the different sizes of fish. So, it cannot be a discrete random variable.

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According to the chi square test, yes and at alpha 0.05 there is a significant difference in music preferred by the three restaurants' customers.

The term chi square test refers a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large.

Here we have given that a researcher is interested in whether a significant trend exists regarding the popularity of certain music played at restaurants. a random sample of 50 customers from each of three restaurants is selected. the customers are asked to indicate which of three music types: country, jazz, and classical they preferred

And we need to find results deviate significantly from what would be expected due to chance.

While we reading the given question, we know that a researcher is interested in whether a significant trend exists regarding the popularity of certain music played at restaurants.

And the number of samples = 50

When we convert it into the percentage then we get,

=> 50/1000

=> 0.05

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Here, we want to write the decimal as a percent

We first re-write as a fraction then multiply by 100%

We have this as;

Answer:

n=15

Step-by-step explanation:

Answer:

\(y=\frac{3}{5} x-3\)

Step-by-step explanation:

Slope-intercept form: y = mx+ b

m = slope

b = y-intercept

Rearrange the equation:

\(-20y=-12x+60\)

Divide each side by -20:

\(\frac{-20y}{-20} =\frac{-12x}{-20} +\frac{60}{-20}\)

\(y=\frac{3}{5} x-3\)

\(y=\frac{3}{5} x-3\) is your simplified, slope-intercept form equation.

Step-by-step explanation:

The position of the median of an even data set is 1/2(8+1)=4.5

That is between two values, 4 and 5.

(5x-10+3x+30)/2=82

(8x+20)/2=82

(8x+20)=41

8x=41-20

8x=21

x=21/8

y > x - 3

y > x - 1

The above system of inequalities was given from the question

Firstly, we will need to graph the system of inequalities

y > x - 3

Change the inequality sign to equality sign

The equation becomes

y = x - 3

To find y, let x = 0

y = 0 - 3

y = -3

To find x, let y = 0

0 = x - 3

Make x the subject of the formula

0 + 3 = x

x = 3

For the system of inequality, y > x - 3

The points is (3, -3)

For the second system of inequality

y > x - 1

Change the inequality ss

Answer:

Bunnies= 13    Chickens=28

Step-by-step explanation:

Let's put

x = bunnies------4 legs

y = chickens-----2 legs

x + y = 41----------------x= 41-y

4x+ 2y = 108

replace in 2nd equation

4(41 - y) + 2y = 108

164 - 4y + 2y = 108

2y = 56

y = 56/2= 28

x = 41 - 28= 13

Answer:

13

Step-by-step explanation:

1. Go to desmos and pick the graphing calculator it. it's the first picture

2. Then type in the word (distance) and the points

3. the way to type it in is on 3 second screenshot

Answer:

Image result for Plot root 18 on the x-axis. Consider using the grid to help.

Step 1: Draw the graph of y=√x . Step 2: Move the graph of y=√x by 1 unit to the right to obtain the graph of y=√x−1 . Step 3: Move the graph of y=√x−1 by 2 units up to obtain the graph of y=√x−1+2 . The domain of the function y=√x−1+2 is x≥1 .

Answer:

The correct answer is letter D

Answer:

a) -4

Step-by-step explanation: you can either take two points on the graph and calculate the average or count from one point to the next. you'll count 1 to the right and 4 down.

Answer:

3.47 and 3.21

Step-by-step explanation:

Let us assume the nails length be X

\(X \sim N(3.34,0.07^2)\)

Value let separated the top 3% is T and for bottom it would be B

\(P(X < T)= 0.97\)

Now converting, we get

\(P(Z < \frac{T-3.34}{0.07})= 0.97\)

Based on the normal standard tables, we get

\(P(Z < 1.881)= 0.97\)

Now compare these two above equations

\(\frac{T-3.34}{0.07} = 1.881 \\\\ T = 1.881 \times 0.07 + 3.34 \\\\ = 3.47\)

So for top 3% it is 3.47

Now for bottom we applied the same method as shown above

\(P(Z < \frac{B-3.34}{0.07})= 0.03\)

Based on the normal standard tables, we get

\(P(Z < -1.881)= 0.03\)

Now compare these two above equations

\(\frac{B-3.34}{0.07} = -1.881\)

\(= -1.881 \times 0.07 + 3.34 \\\\ = 3.21\)

hence, for bottom it would be 3.21

Using differential equation the population of the mice is given by option e. None of the above and is equal to P = 6000 ( 3 + 7e^(-t/60) ).

Differential equation representing the population of mice is

(3000 /P) (dP/ dt) = 200 − P

⇒ 3000∫( 1 / P(200 - P) dP = ∫dt __(1)

Using partial differential we get,

( 1 / P(200 - P)  = ( A/ P) + B/ ( 200 -P)

⇒ A = -1/200 and B = 1/200

(1/200)[ ∫(1/P) dP - ∫dP/ (200 -P)

= (1/200)[ log P - log(200 -P)]

For P = 60

(1/200)[ log |P| - log|200 -P|]

= (1/200)[ log60 - log(200 -60)]

= (1/200) log(60/140)

= 1/200 log (3/7)

Substitute in (1) we get,

3000∫( 1 / P(200 - P) dP = ∫dt

= 3000 (1/200)[ log P - log(200 -P)] + c= t

t=0 , P(0) = 60

= 3000 [1/200 log (3/7)] + c = 0

⇒ c = - 60log(3/7)

Now,

60[log(P/200 -P) ] - 60log(3/7) = t

⇒60[ log(P /(200 -P)(3/7) ]= t

⇒P / (200 - P) = (3/7) e^(t/60)

⇒ P = 200(3/7) e^(t/60) - P((3/7) e^(t/60))

⇒P( 1 + (3/7) e^(t/60) ) =  200(3/7) e^(t/60)

⇒P = ( 6000)e^(t/60) / ( 7 + 3 e^(t/60) )

⇒P = 6000 ( 3 + 7e^(-t/60) )

Therefore, the function describes the population of the mouse using differential equation is equal to option e. none of the above and is equal to P = 6000 ( 3 + 7e^(-t/60) ).

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The above question is incomplete , the complete question is:

The population of mice on a farm is modeled by the differential equation (3000 /P) (dP/ dt) = 200 − P. If we know that today there are 60 mice on the farm, what function will describe how the mouse population will develop in the future?

(a) P = 200/1+ 7 3 e−t/15

(b) P = 200/1+ 7 3 e−200t

(c) P = 3000/1+49e−t/15

(d) P = 3000/1+49e−t/20

(e) None of the above

The test value for this hypothesis is 3.0.

The test value for this hypothesis can be calculated using the formula for a one-sample t-test:

test value = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Calculating the test value:

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Answer:

Perimeter in terms of the width,  W, is

P =  10W + 6

Step-by-step explanation:

Let variable L represent the length and W represent the width

Given length  is 3 more than  4 times the width, we can translate this word statement into a mathematical equation using L and W

The perimeter of a rectangle of length L and width W is:

2(L + W)

Substituting L = 4W + 3 into the perimeter equation gives us:
2(4W + 3 + W)

= 2(5W + 3)

= 10W + 6

Use the given function to find the \(y\)-coordinate of \(A\).

\(x=2 \implies y = 10+8\cdot2+2^2-2^3 = 22\)

Find the equation of the line through the origin and \(A\). This line has slope

\(\mathrm{slope} = \dfrac{22-0}{2-0} = 11\)

and passes through (0, 0), so its equation is

\(y - 0 = 11 (x-0) \implies y = 11x\)

Then the area of the shaded region is given by the definite integral

\(\displaystyle \int_0^2 (y - 11x) \, dx = \int_0^2 (10 + 7x + x^2 - x^3) \, dx \\\\ ~~~~~~~~ = \left(10x + \frac72 x^2 + \frac13 x^3 - \frac14 x^4\right)\bigg|_0^2 \\\\ ~~~~~~~~ = 10\cdot2+\frac72\cdot2^2+\frac13\cdot2^3-\frac14\cdot2^4 = \boxed{\frac{98}3}\)

The vector field vector f(vector r) = 4vector r in the xy-plane consists of vectors pointing towards the origin, and all the vectors are in the same direction. The lengths of the vectors increase as you move away from the origin, and they are not of length 1.

In the xy-plane, the vector field vector f(vector r) = 4vector r can be visualized as a collection of vectors emanating from the origin (0, 0) and extending outward.

Regarding the options:

- The lengths of the vectors decrease as you move away from the origin: False. The lengths of the vectors actually increase as you move away from the origin because they are scaled by a factor of 4.

- All the vectors point towards the origin: True. Since the vector field is defined as 4vector r, all the vectors point towards the origin.

- The length of each vector is 1: False. The length of each vector is determined by its magnitude, which in this case is 4 times the distance from the origin.

- All the vectors point in the same direction: True. All the vectors point radially inward towards the origin.

- All the vectors point away from the origin: False. The vectors in this vector field point towards the origin, not away from it.

Therefore, the correct statements are: All the vectors point towards the origin, and all the vectors point in the same direction.

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Answer:

A = 20

B = 12.5

C = 10.2

Step-by-step explanation:

A = (10 + 20 + 30)/3 = 20

B = (5 + 10 + 15 + 20) = 12.5

C = (1 + 5 + 10 + 15 + 20) = 10.2