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4 years ago

Find the inverse function of f(x) = -1\3x+2

1 answer:

8 0

If f(x) = 2x – 5, find the inverse. This function passes the Horizontal Line Test which means it is a onetoone function that has aninverse. y = 2x – 5 Change f(x) to y. x = 2y – 5 Switch x and y. Solve for y by adding 5 to each side and then dividing each side by 2.

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The sum of two books and a pencil is $6.00. The difference of cost between 3 books and 2 pencils is $ 2.00. Find the cost of a b

Gala2k [10]

Answer:

The book costs $2 and the pencil also costs $2.

Step-by-step explanation:

It is easy to get the value of the book and the pencil if we use algebraic expressions.

Let x be the cost of the book and let y be the cost of the pencil.

The sum of 2 books and a pencil is $6.00

2x + y = $6.00

The difference of cost between 3 books and 2 pencils is $2.00.

3x - 2y = $2.00

Step 1: Let's get the value of y first.

2x + y = 6

y = 6 - 2x

Step 2: Let's substitute the value of y and look for the value of x.

3x - 2y = $2.00

3x - 2(6-2x) = 2

3x - 12 + 4x = 2

7x = 12 + 2

7x = 14

x = $\frac{14}{7}$

x = $2 (this is the cost of the book)

Step 3: Let's substitute the value of x and look for the value of y.

2x + y = 6

2 (2) + y = 6

4 + y = 6

y = 6 - 4

y = $2 (this is the cost of the pencil)

Let's check:

2x + y = $6

2(2) + 2 = 6

4 + 2 = 6

6 = 6 (CORRECT)

8 0

3 years ago

1. Let the test statistics Z have a standard normal distribution when H0 is true. Find the p-value for each of the following sit

Nonamiya [84]

Answer:

1 a $p -value = 0.030054$

1b $p -value = 0.0029798$

1c $p -value = 0.0039768$

2a $p-value = 0.00099966$

2b $p-value = 0.00999706$

2c $p-value = 0.0654412$

Step-by-step explanation:

Considering question a

The alternative hypothesis is H1:μ>μ0

The test statistics is z =1.88

Generally from the z-table the probability of z =1.88 for a right tailed test is

$p -value = P(Z > 1.88) = 0.030054$

Considering question b

The alternative hypothesis is H1:μ<μ0

The test statistics is z=−2.75

Generally from the z-table the probability of z=−2.75 for a left tailed test is

$p -value = P(Z < -2.75) = 0.0029798$

Considering question c

The alternative hypothesis is H1:μ≠μ0

The test statistics is z=2.88

Generally from the z-table the probability of z=2.88 for a right tailed test is

$p -value = P(Z >2.88) = 0.0019884$

Generally the p-value for the two-tailed test is

$p -value = 2 * P(Z >2.88) = 2 * 0.0019884$

=> $p -value = 0.0039768$

Considering question 2a

The alternative hypothesis is H1:μ>μ0

The sample size is n=16

The test statistic is t = 3.733

Generally the degree of freedom is mathematically represented as

$df = n - 1$

=> $df = 16 - 1$

=> $df = 15$

Generally from the t distribution table the probability of t = 3.733 at a degree of freedom of $df = 15$ for a right tailed test is

$p-value = t_{3.733 , 15} = 0.00099966$

Considering question 2b

The alternative hypothesis is H1:μ<μ0

The degree of freedom is df=23

The test statistic is ,t= −2.500

Generally from the t distribution table the probability of t= −2.500 at a degree of freedom of df=23 for a left tailed test is

$p-value = t_{-2.500 , 23} = 0.00999706$

Considering question 2c

The alternative hypothesis is H1:μ≠μ0

The sample size is n= 7

The test statistic is ,t= −2.2500

Generally the degree of freedom is mathematically represented as

$df = n - 1$

=> $df = 7 - 1$

=> $df = 6$

Generally from the t distribution table the probability of t= −2.2500 at a degree of freedom of $df = 6$ for a left tailed test is

$t_{-2.2500 , 6} = 0.03272060$

Generally the p-value for t= −2.2500 for a two tailed test is

$p-value = 2 * 0.03272060 = 0.0654412$

4 0

3 years ago

Gerri spends 9/22 of her money on pencils and 2 22 on paper. What fraction of her money does she spend? Write your answer in sim

NNADVOKAT [17]

Answer:

1/2

Step-by-step explanation:

To find out how much money Gerri spent, add up the two fractions.

(9/22) + (2/22) = (11/22)

(11/22) can then be simplified to (1/2).

7 0

4 years ago

What is the perimeter of this figure

fredd [130]

Answer:

perimeter is the sum of all sides

sum of all sides here is 5+5+11+7 = 28m

8 0

3 years ago

A rental car company charges $42.72 per day to rent a car and $0.10 for every mile driven. Zoey wants to rent a car, knowing tha

Colt1911 [192]

Answer:

7 Days

Step-by-step explanation:

Miles cost:

$0.10 * 200 = $20

Daily Cost

Her budget at this point is $330 because $350 - $20 (the miles)

$330 / 42.72 = Roughly 7.72

Therefore Zoey can drive for 7 days before her budget runs out.

6 0

3 years ago