Function f is a linear function and function g is defined by g(x)=f(x)+k t . If the value of k is 7 , how does the graph of g compare with the graph of P?
The graph of g is the graph of f
Choose...
translated up 7 units translated left 7 units translated right 7 units translated down 7 units stretched vertically by a scale factor of 7 stretched horizontally by a scale factor of 7

Answer:

180

Step-by-step explanation:

The pattern is the previous number multiplied by 2, then subtracted by 4.

Proof: 15 x 2 = 30; 30 - 4 = 26

26 x 2 = 52 ; 52 - 4 = 48

So then, we do 92 x 2.

92 x 2 = 184

184 - 4 = 180

Answer: 40 years old.

Step-by-step explanation:

Let man's age = a

Let son's age = b

Since a man is 4 times as old as his son, therefore

a= 4b

In 5 years, he will only be 3 times as old as his son, therefore

a+5=3(b+5)

Apply substitution method :

4b+5=3b+15

b=10

a=40

a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.

b) To calculate the expected count for the bottom right cell, we can use the formula:

Expected count = (row total x column total) / grand total

The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:

Expected count = (100 x 100) / 300 = 33.33

The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.

c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.

Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.

The benefit of obtaining a personal loan is getting large amounts of money to use immediately.

Option D is the correct answer.

A personal loan is a type of loan that individuals can take out from a bank, credit union, or online lender to cover personal expenses such as home improvements, medical bills, or other unexpected expenses.

We have,

The benefit of obtaining a personal loan can vary depending on the specific terms and conditions of the loan, but typically it allows individuals to borrow a larger amount of money upfront with a fixed interest rate and set repayment schedule, which can be beneficial for large expenses such as home renovations, debt consolidation, or major purchases.

However, the interest rates and repayment terms can vary depending on the borrower's credit score, income, and other factors, so it's important to compare options and choose a loan that meets one's specific needs and budget.

Thus,

The benefit of obtaining a personal loan is getting large amounts of money to use immediately.

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a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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The value of x  from the solution is x > 6

Inequalities are defined as mathematical expression showing that both sides are not equivalent or equal to each other.

It is known for the comparison of  two values, showing that one is less than, greater than, or not equal to another value.

The symbols for inequality are ;

Given the inequality;

8x – 6 > 12 + 2x

collect like terms

8x - 2x > 12 + 6

add or subtract like terms

6x > 18

Make 'x' the subject of formula

x > 18/6

x > 6

Thus, the value of x  from the solution is x > 6

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Answer:

A line segment is 20 units long. The line segment is translated up 6 units and left 8 units. The length of the resulting line segment is 20 units because translations do not change the length.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

-------------

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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By definition of f(x),

f(k) = 1 - 2k + k = 1 - k

Then

f(f(k)) = f(1 - k) = 1 - 2 (1 - k) + k = 3k - 1 = 13

Solve for k :

3k - 1 = 13

3k = 14

k = 14/3

Find f(-1) :

f(-1) = 1 - 2 (-1) + 14/3 = 1 + 2 + 14/3 = 23/3

Answer:

Step-by-step explanation:

Answer:

12.8 so about 13

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

4/5 of his age = 16

1/5 of his age = 16/4=4

which means that 5/5 of his age = 16+4 = 20

Answer:

5x-9=26

Step-by-step explanation:

5x=35

5 5

x = 7

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Answer:

x = 7

Step-by-step explanation:

When five times a number is decreased by 9 ​, the result is 26 . What is the​ number?

5x - 9 = 26

add 9 to both sides:

5x - 9 + 9 = 26 + 9

5x =35

divide both sides by 5:

5x/5 =35/5

x = 7

The powers, (index) and coefficients of the polynomial indicates;

(A) The standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

(B) 4

(C) Positive zeroes; 2 or 0, negative zeroes; 0 or 2, complex zeroes; 0 or 2 or 4

(D) ±1/2, ±1, ±3/2, ±2, ±3, ±6

(E) Please find attached the graph of the polynomial created with MS Excel

(F) Four complex roots

A polynomial is a mathematical expression that consists of variables and coefficients joined together by addition, subtraction and multiplication, with the exponents of the variables consisting of positive integer values.

Part A) The polynomial in standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

Part B) The degree of the polynomial is 4, as the highest power of the polynomial is 4

Part C) The use of the Rule of Signs, to determine the options for the number of positive zeroes, negative zeroes and complex zeroes, can be presented as follows;

Positive zeroes options; The number of time the signs coefficients of the expression; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6, changes are two as follows;

+6 to -12, and from -12 to +9, therefore, the number of possible positive zeroes are 2 or 0, positive zeroes

The negative zeroes options; The negative zeroes options can be found by changing the sign of all the coefficients as follows; -2·x⁴ - 3·x³ - 9·x² + 12·x - 6, therefore, the number of times the sign of the coefficients change are again from -6 to +12, and from +12 to -9, which is 2 times, therefore;

The possible number of negative zeros are 2 or 0, negative zeroes

Whereby there are possibly 0 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 4

Whereby there are 2 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Whereby there are possibly 0 negative zeros and 2 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Part D) The rational roots theorem indicates that for a polynomial the rational roots are in the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.

The constant term is 6, and the leading coefficient is 2. The factors of 6 are ±1, ±2, ±3, and ±6 and the factors of 2 are; ±1, ±2 therefore;

p/q = ±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±2/2, ±3/2, ±6/2, which can be summarized as; ±1/2, ±1, ±3/2, ±2, ±3, ±6

Part E) Please find attached a screenshot of the graph of the polynomial created with MS Excel

Part F) The attached graph of the polynomial, created with MS Excel, indicates that there are no real zeros of the polynomial, therefore, there are four complex zeroes of the polynomial

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Answer:

e = 5h

$100

Step-by-step explanation:

Let e = earnings

e = 5h

For h = 20,

e = 5h = 5(20) = 100

Answer:

$ 100

Step-by-step explanation:

1 hour = $ 5

h (hours worked in a week) = 20 hrs

EXPRESSION: amount of money earned in a week = h × 5

EVALUATION: amount of money earned in a week = 20 × 5

amount of money earned in a week = $ 100 ... answer

hope that helps...

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Standard deviation will be √3.3516 .

To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².

After that , we have to calculate the Xbar by using

Xbar = ∑fiXi / N

for which we need the value of fi , Xi and N

N = 100

fiXi = 6478

we have calculated the values from the given data ,

Therefore ,

Xbar = 6478 / 100

= 64.78

Var(X) = αx² - ∑fiXi² / N - (Xbar²)

= 419980 / 100 - (64.78)²

= 4199.80 -4196.4484

=3.3516

Thus,

standard deviation ax = √var(X)

= √3.3516

Therefore , the standard deviation will be  √3.3516

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Answer:

No solutions

Step-by-step explanation:

3x^2=y

3(-2)^2=1

Follow P.E.M.D.A.S.

3(4)=1

12=1

Answer:

56,067

Step-by-step explanation:

there are 52 weeks in a year. and they work 40 hours a week.

\(26.96*40=1078\\1078*52=56,067\)

Answer:

The answer is C.

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The construction makes ray BF a bisector of angle ABC. That bisector divides ABC into the two congruent angles DBF and EBF. As a consequence, angle EBF will be half of ABC, not equal to ABC.

The measure of angle W in the kite WXYZ is 115°

A kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides.

Given that, In kite WXYZ, m ∠ x = 90° and m ∠ z =40°.

Please refer to figure attached,

We know that, in a kite, it has two opposite and equal angles.

According to figure, here,

m ∠ W = m ∠ Y

Let m ∠ W = m ∠ Y = x

Also, the sum of interior angles of quadrilateral = 360°

Therefore,

x + x + 90° + 40° = 360°

2x = 360° - 130°

2x = 230°

x = 115°

Thus, m ∠ W = m ∠ Y = 115°  

Hence, the measure of angle W in the kite WXYZ is 115°

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a) The minimum 75% of commuters in Boston has a commute time within 2 standard deviation of the mean.

b) The minimum 60.93% of commuters in Boston has a commute time within 1.6 standard deviation of the mean.

c) Commute times within 1.4 standard deviation are lie between 15.48 to 38.72.

Explanation:

Given that

To find

So, according to the question

We know that

                            = (1- \(\frac{1}{k^2}\) )×100

a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of the mean?

                            = (1- \(\frac{1}{2^2}\) )×100

                            = (1- \(\frac{1}{4}\) )×100

                            = ( \(\frac{4-1}{4}\) )×100

                            =  \(\frac{3}{4}\) ×100

                            = 3 × 25

                            = 75%

b) What minimum percentage of commuters in Boston has a commute time within 1.6 standard deviation of the mean?

                            = (1- \(\frac{1}{1.6^2}\) )×100

                            = (1- \(\frac{1}{2.56}\) )×100

                            = ( \(\frac{2.56-1}{2.56}\) )×100

                            =  \(\frac{1.56}{2.56}\) ×100

                            = 1.56 × 39.06

                           = 60.93%

c) What are the commute times within 1.4 standard deviation?

     commute times  = 27.1 ± (1.4×8.3)

                                 = 27.1 ± 11.62

      for + sign,

                                 = 27.1 + 11.62

                                 = 38.72

      for - sign,

                                 = 27.1 - 11.62

                                 = 15.48

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Answer:

Step-by-step explanation:

The milepost number of the rest area is 7 miles away from milepost 58, so it can be represented by the equation:

m = 58 + 7

This equation states that the milepost number of the rest area is equal to 58 plus 7, or 65. Therefore, the rest area can be located at milepost 65.

Answer:

$1,173.37 more with compound interest.

Step-by-step explanation:

Compound

3,000 * 1.04^20 = 6,573.37

Simple

3,000 * 1.80 = 5,400.00

Answer:

I think $490

Step-by-step explanation:

Don't quote me on that

Answer:

s+32 =187 is the equation for the total number of songs downloaded

s=155 is the number of songs initially downloaded in this situation,

Step-by-step explanation:

s+32 =187  

      s=187-32 solve for s

      s=155

Answer:

f(x) = sin(x)

Step-by-step explanation:

The graph above is the exact parent graph of f(x) = sin(x).

f(x) = cos(x) would have an y-intercept of 1, and would not be correct.

The negative functions would be incorrect as it would be flipped.