Find the coordinates of the image under the transformation (x – 4, y + 6) for ∆XYZ at X(-6, 1), Y(4, 0), Z(1, 3)
A. X’(-10, 7) Y’(0, 6) Z’(-3, 9)
B. X’(10, -7) Y’(0, -6) Z’(3, -9)
C. X’(-8, 7) Y’(-2, 0) Z’(-5, 8)
D. X’(-3, 2) Y’(1, 3) Z’(-3, 5)

Answer:

2) y= -2/3x +4

Step-by-step explanation:

2x+3y=12 convert to y=mx+b form

move over the 2x to isolate y

3y= -2x+12

divide by 3 in order to completely isolate y

y= -2/3x +4

Using the functions f(x) and g(x) as F(x)=x²-16; g(x)=x+4, (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4. So, the correct answer is option D.

To find (f/g)(x), we need to divide f(x) by g(x). The notation (f/g)(x) is another way of representing the function f(x)/g(x).

So, we first need to find f(x)/g(x) by dividing f(x) by g(x):

f(x)/g(x) = (x^2 - 16)/(x + 4)

Now, we can plug in the values of x in each option and see which one gives us the correct function.

Option A: (f/g)(-4) = ((-4)^2 - 16)/(-4 + 4) = undefined

Option B: (f/g)(4) = (4^2 - 16)/(4 + 4) = -1

Option C: (f/g)(4 - 4) = (0^2 - 16)/(4 - 4) = undefined

Option D: (f/g)(-4 - 4) = ((-4)^2 - 16)/(-4 - 4) = 0

Therefore, the correct answer is option D: (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4.

Note that options A and C give undefined values because they have x + 4 in the denominator, which makes the function undefined at x = -4 and x = 4, respectively.

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The equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x

The expression is given as:

(8x)^-2/3 * (27x)^-1/3

Evaluate the exponent 8^-2/3

(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * (27x)^-1/3

Evaluate the exponent (27x)^-1/3

(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * 1/3(x)^-1/3

Multiply 1/4 and 1/3

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^-2/3 * (x)^-1/3

Evaluate the exponent

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-2/3 -1/3)

This gives

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-1)

So, we have

(8x)^-2/3 * (27x)^-1/3 = 1/12x

Hence, the equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x

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The slope of each line on the given graph is:

Figure 1: -1/4

Figure 2: 0

Figure 3: -4

Figure 4: 4

The slope (m) of a linear relationship is calculated as rise/run = change in y / change in x.

Figure 1:

Slope (m) = change in y / change in x = -1/4 (the line declines, so the slope will be negative).

Figure 2:

Slope (m) = 0 (this is because there is no rise but run), thus, the slope of any horizontal line is always 0.)

Figure 3:

Slope (m) = change in y / change in x = -4/1 = -4 (the line declines, so the slope will be negative).

Figure 4:

Slope (m) = change in y / change in x = 4/1 = 4 (the line rises, so the slope will be positive).

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To perform a "pooled variance t-test" in Excel, you should use the "t-Test: Two-Sample Assuming Equal Variances" data analysis tool.

Step-by-step explanation on how to use this tool:

1. Open Excel and ensure that the "Data Analysis ToolPak" add-in is installed. If it's not, go to File > Options > Add-Ins, select "Excel Add-ins" from the drop-down menu, click "Go", and then check the box for "Analysis ToolPak" and click "OK".

2. Organize your data into two columns, one for each sample group. Make sure there are no gaps or missing data points.

3. Click the "Data" tab at the top of the Excel window.

4. In the "Analysis" group, click "Data Analysis".

5. In the "Data Analysis" dialog box, scroll down and select "t-Test: Two-Sample Assuming Equal Variances" and click "OK".

6. In the "t-Test: Two-Sample Assuming Equal Variances" dialog box, enter the cell range for the first sample in the "Variable 1 Range" field and the cell range for the second sample in the "Variable 2 Range" field.

7. Choose the desired level of significance (commonly 0.05) in the "Alpha" field.

8. Select an output range or choose "New Worksheet Ply" to display the results.

9. Click "OK" to perform the pooled variance t-test.

The results will show the t-statistic, degrees of freedom, and p-value, which you can use to determine if there is a significant difference between the two sample groups.

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Answer: 4c+32

Step-by-step explanation:

The probability that a guesser does not pass the exam is approximately 0.3272 using the binomial distribution or 0.0228 using the normal approximation to the binomial distribution.

Since each question is True-False, the probability of guessing the correct answer is 0.5.

If a guesser answers each question randomly and independently, we can model the number of correct answers using a binomial distribution with n = 100 and p = 0.5.

The probability of passing the exam with a score of at least 60 is the probability of getting 60 or more correct answers, which can be calculated using the binomial distribution or by using the normal approximation to the binomial distribution.

However, we are interested in the probability of not passing the exam, which is the complement of the probability of passing.

Using the binomial distribution, we have:

P(not passing) = 1 - P(passing)

              = 1 - P(X ≥ 60)

              = 1 - Σ P(X = k), for k = 60 to 100

              = 1 - binomcdf(100, 0.5, 59)

              ≈ 0.3272

Using the normal approximation to the binomial distribution, we have:

μ = np = 100 × 0.5 = 50

σ = sqrt(np(1-p)) = sqrt(100 × 0.5 × 0.5) = 5

P(not passing) = P(X < 60)

              = P((X - μ)/σ < (60 - 50)/5)

              = P(Z < 2)

              ≈ 0.0228

Therefore, the probability that a guesser does not pass the exam is approximately 0.3272 using the binomial distribution or 0.0228 using the normal approximation to the binomial distribution.

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Hi!
Let's write this out.
Her limit is $900, and she's used $450. So, we subtract 450 from 900.
900-450 = 450.

So, she has $450 available credit left.
Hope this helps!
~~~PicklePoppers~~~

Answer: your credit utilization ratio on that card would be 50% but the answer is 450

Step-by-step explanation:

900-450 = 450

The required amount will be $3220.65 you would need to deposit now in order to have $5000 in the account after 15 years.

To determine the amount you would need to deposit in an account now in order to have $5000 in the account in 15 years, you can use the formula:

\(P = F / (1 + r)^t\)

Where P is the present value (the amount you need to deposit now), F is the future value (the amount you want in the account in 15 years), r is the interest rate (3% in this case), and t is the number of years (15 in this case).

Plugging in the given values, you get:

\(P = 5000 / (1 + 0.03)^{15}\\P = 5000 / 1.03^{15}\)

≈ $3220.65

Rounded to the nearest cent, the answer is $3220.65.

This is the amount you would need to deposit in the account now in order to have $5000 in the account in 15 years.

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Answer:

$8190

Step-by-step explanation:

So we know that were putting away $2 each month from  our allowance.

Jan-$2

Feb-$4

March-$8

April-$16

Ok so we already put away 4 months of our allowance from 12. So we need 8 more months to count how much.

So lets add: 2 + 4 + 8 + 16=30

Now we need to figure out how much in May and so on.

May- 16x2=32

June-32x2=64

July-64x2=128

August-128 x 2=256

September-256 x 2=512

October-512 x 2=1024

November-1024 x 2=2048

December-2048 x 2=4096

In total to add:

2 + 4 + 8 + 16 + 32 +64 + 128 + 256 + 512 + 1024 + 2048 + 4096 = 8190

Hope this helps :)

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

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

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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Answer:

1.2 x 10^8

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer : 5

Refer to the attachment

I hope this helps you...

The 95% confidence interval suggests if the nicotine patch is used for 2 months, there is a high likelihood that the proportion of individuals who will report no smoking incidents.

In the following year will fall between 17.4% and 24.8%. This means that the study results are statistically significant and reliable within this range, and it is likely that the nicotine patch can be effective in reducing smoking incidents for a significant proportion of users.
In the study of the nicotine patch, the appropriate interpretation of the 95% confidence interval (17.4%, 24.8%) is that we can be 95% confident that the true proportion of people who reported no smoking incidents in the following year after using the patch for 2 months lies between 17.4% and 24.8%.

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Answer:

In order of the questions asked, the answers are, C, D, A, C

Step-by-step explanation:

After three half-lives have elapsed, 12.5% of the original nuclide remains, so the answer is C.

if 17 % is daughter nuclide, then 83% is parent nuclide, so , the answer is D

the isotope for dating organic remains is A. carbon-14

for 25% of original, 2 half-lives must have passed, so we get (2)(5730) = 11460

so the answer is C

Answer:

2x° = 45°, 3x° = 67.5°

Step-by-step explanation:

Sum of angles in a triangle = 180°

2x+3x+3x=180°

8x=180°

x=22.5°

2x=22.5°x2=45°

3x=22.5°x3=67.5°

Answer:

A ≈ 1385.4 cm²

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

  = π × 21²

 = π × 441

 = 441π cm²

 ≈ 1385.4 cm² ( to 1 dec. place )

The shaded area is 239.4 ft²

3.1% To find the point estimate of the difference in the population proportion in Vermont and Hawaii, follow these steps:

1. Convert the percentages to proportions: Vermont had 65.3% who said yes, which is 0.653 as a proportion. Hawaii had 62.2% who said yes, which is 0.622 as a proportion.

2. Calculate the point estimate by finding the difference between the two proportions: 0.653 - 0.622 = 0.031.

The point estimate of the difference in the population proportion in Vermont and Hawaii is 0.031. This means that, based on the survey, the proportion of people who exercised more than 30 minutes a day for three days out of the week in Vermont was 3.1% higher than in Hawaii.

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The function f(x) is f(x) = (1/12) x⁴ - 2x² - 29.0278x + 126.1112

f(x) given that f'''(x) = 2x and satisfying the given conditions, we need to integrate the equation f'''(x) = 2x three times to find f(x).

Integration of f'''(x) = 2x gives: f''(x) = x² + C₁

Integration of f''(x) = x² + C₁ gives: f'(x) = (1/3) x³ + C₁x + C₂

Integration of f'(x) = (1/3) x³ + C₁x + C₂ gives: f(x) = (1/12) x⁴ + (1/2) C₁x² + C₂x + C₃

Now, we can use the given conditions to determine the values of the constants C₁, C₂, and C₃.

Using f(4) = 10:

(1/12)(4)⁴ + (1/2) C₁(4)² + C₂(4) + C₃ = 10

(1/12)(256) + (1/2) C₁(16) + 4C₂ + C₃ = 10

(64/12) + (8/2) C₁ + 4C₂ + C₃ = 10

(16/3) + 4C₁ + 4C₂ + C₃ = 10

4C₁ + 4C₂ + C₃ = 10 - (16/3)

4C₁ + 4C₂ + C₃ = 30/3 - 16/3

4C₁ + 4C₂ + C₃ = 14/3

Using f(7) = 25:

(1/12)(7)⁴ + (1/2) C₁(7)² + C₂(7) + C₃ = 25

(1/12)(2401) + (1/2) C₁(49) + 7C₂ + C₃ = 25

(200.0833) + (24.5) C₁ + 7C₂ + C₃ = 25

24.5C₁ + 7C₂ + C₃ = 25 - 200.0833

24.5C₁ + 7C₂ + C₃ = -175.0833

Using y'' = 0 at x = 2:

f''(2) = 2² + C₁ = 0

4 + C₁ = 0

C₁ = -4

Substituting C₁ = -4 in the previous equations

4(-4) + 4C₂ + C₃ = 14/3

-16 + 4C₂ + C₃ = 14/3

4C₂ + C₃ = 14/3 + 16/3

4C₂ + C₃ = 30/3

4C₂ + C₃ = 10

24.5C₁ + 7C₂ + C₃ = -175.0833

24.5(-4) + 7C₂ + C₃ = -175.0833

-98 + 7C₂ + C₃ = -175.0833

7C₂ + C₃ = -175.0833 + 98

7C₂ + C₃ = -77.0833

Solving the system of equations

4C₂ + C₃ = 10

7C₂ + C₃ = -77.0833

Subtracting the first equation from the second equation

(7C₂ + C₃) - (4C₂ + C₃) = -77.0833 - 10

3C₂ = -87.0833

C₂ = -87.0833/3

C₂ ≈ -29.0278

Substituting C₂ = -29.0278 in the first equation:

4C₂ + C₃ = 10 4(-29.0278) + C₃ = 10

-116.1112 + C₃ = 10

C₃ = 10 + 116.1112

C₃ ≈ 126.1112

Finally, we have the values of C₁, C₂, and C₃:

C₁ = -4

C₂ ≈ -29.0278

C₃ ≈ 126.1112

Therefore, the function f(x) is given by:

f(x) = (1/12) x⁴ - 2x² - 29.0278x + 126.1112

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1. The table of values showing the amount Kevin owes his friend after t weeks is as follows:

Week    Amount Owed

0               $90

 1               $85

2               $80

3               $75

4               $70

...

18              $0 ($5 - $5)

2. The equation representing the amount (L) Kelvin owes his friend after t weeks is L = 90 - 5t.

An equation is a mathematical statement showing that two mathematical expressions using the equation symbol (=) are equal or equivalent.

Equations establish the numerical relationship existing between two or more mathematical expressions, numbers, values, or variables.

Week    Amount Owed

0               $90

 1               $85 ($90 - $5)

2               $80 ($85 - $5)

3               $75 ($80 - $5)

4               $70 ($75 - $5)

The total amount borrowed = $90

The amount of repayment = $5

The repayment period = weekly

Let the balance after t weeks of payment = L

L = 90 - 5t

In eighteen weeks, Kevin will complete the repayment of the loan.

Check:

If t = 18

L = 90 - 5t

L = 90 - 5(18)

L = 90 - 90

L = 0

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Answer:

-5/2

Step-by-step explanation:

with slope always remember rise over run, vertically, the dots are 5 points away from each other so that is your rise. Horizontally they are only 2 away so that's your run. the answer is negative because the slope goes down to the right. If it went up to the right then the slope would be positive.

Answer:

Don't write the " ^ " that I'm typing, that's just showing its to the power of 2 (squared)

1. x^2 + y^2 = 100

2. (x+1)^2 + (y-8)^2 = 25

3. (x+5)^2 + (y+5)^2 =20

4. x^2 + y^2 = 85

5. x^2 + (y+2)^2 = 40

graph 6) middle of circle (dot) at origin (0,0), 5 out in every direction

graph 7) middle of circle (dot) at (-2, 1), 2 out in every direction

graph 8) middle of circle (dot) at (0, -3), 1 in every direction

graph 9) middle of circle (dot) at (1, 1), 4 in every direction

Step-by-step explanation:

Hope these are right, I just kind of banged them out real quick :)

Answer:

36

Step-by-step explanation:

Unit price: 9 / 5 = 1.8

20 box price: 1.8 * 20 = 36

Answer:

graph below

Step-by-step explanation:

Graphing lines in slope intercept form:

The equation of the line is in \(y=mx+b\) form, which makes this easy for us.

\(y=-\frac{1}{3}x-2\)

The y intercept of this equation is -2 because of click clack, which means we will start there.

The slope is negative, so when we are graphing we will go down 1 and 3 to the right while graphing.

Answer:

π is equivalent to 3.14

Circumfrance =  53

area = 227

Step-by-step explanation:

π is equal to 3.14

Circumfrance = 8.5*2*π

So 8.5 * 2 is 17 times π is 53.38

round to nearest whole number is 53

area is π * radius squared so

8.5 * 8.5 =72.25

* π is 226.865

round to the nearest whole number is 227

Answer:

40%

Step-by-step explanation:

20-12 = 8 difference

8/ 20  x100 = the percentage change  = 40%

Answer:

(0, 1 )

Step-by-step explanation:

Given the 2 equations

y = 2x + 1 → (1)

y = 5x + 1 → (2)

Substitute y = 5x + 1 into (1)

5x + 1 = 2x + 1 ( subtract 2x from both sides )

3x + 1 = 1 ( subtract 1 from both sides )

3x = 0 , then

x = 0

Substitute x = 0 into either of the 2 equations for corresponding value of y

Substituting into (1)

y = 0 + 1 = 1

solution is (0, 1 )