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3 years ago

Tracy solved the system of equations by making a substitution for x in the second equation.

1 answer:

8 0

I: x = –2y – 2
II: 2x + 3y = –6

substitute I's x (x = –2y – 2) definition into II:
2*(-2y-2) + 3y = –6
-4y-4+3y=-6

which is the last option

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Drag each tile to the correct location on the image. Each tile can be used more than once, but not all images will be used.

OverLord2011 [107]

Answer:

Switch x and y, and solve for y

$f^{-1}(x) =\frac{(x -4)^3}{8}$

Step-by-step explanation:

Given

$f(x) = 3\sqrt{8x} + 4$

Required

Complete the steps to determine the inverse function

Solving (a): Complete the blanks

Switch x and y, and solve for y

Solving (b): Determine the inverse function

$f(x) = \sqrt[3]{8x} + 4$

Replace f(x) with y

$y = \sqrt[3]{8x} + 4$

Switch x and y

$x = \sqrt[3]{8y} + 4$

Now, we solve for y

Subtract 4 from both sides

$x -4= \sqrt[3]{8y} + 4-4$

$x -4= \sqrt[3]{8y}$

Take cube roots of both sides

$(x -4)^3= 8y$

Divide both sides by 8

$\frac{(x -4)^3}{8} = y$

So, we have:

$y =\frac{(x -4)^3}{8}$

Hence, the inverse function is:

$f^{-1}(x) =\frac{(x -4)^3}{8}$

7 0

3 years ago

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writin

Morgarella [4.7K]

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

Let $\mu$ = true average writing lifetime under controlled conditions

So, Null Hypothesis, $H_0$ : $\mu \geq$ 10 hr {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, $H_A$ : $\mu$ < 10 hr {means that the true average writing lifetime under controlled conditions is less than 10 hr}

The test statistics that is used here is one-sample t test statistics;

T.S. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean

s = sample standard deviation

n = sample size of pens = 18

n - 1 = degree of freedom = 18 -1 = 17

Now, the decision rule based on the critical value of t is given by;

If the value of test statistics is more than the critical value of t at 17 degree of freedom for left-tailed test, then we will not reject our null hypothesis as it will not fall in the rejection region.

If the value of test statistics is less than the critical value of t at 17 degree of freedom for left-tailed test, then we will reject our null hypothesis as it will fall in the rejection region.

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -1.74 < 0.57, so we fail to reject our null hypothesis.

8 0

2 years ago

Item 1

victus00 [196]

Step-by-step explanation:

the sign - "<" correctly compares this ( -35__-23).

hope this helps you.

3 0

2 years ago

Helpppp pls. Rotate traingle TUV 90 degrees clockwise around the origin

lutik1710 [3]

T -1,-1 ect ect hope helps

7 0

2 years ago

Liza needs a total of 22.23 square feet of cloth to make a bag and a towel the bag requires 5.13 square feet of cloth the height

Troyanec [42]

Answer:

5.7 feet

Step-by-step explanation:

Total cloth area recquired to make a bag and a towel is 22.23 square feet

Given the area of the cloth recquired to make the bag is 5.13 square feet.

The area of cloth recquired to make the towel is = 22.23-5.13=17.1 square feet

given the height of the towel = 3 feet

let the length of the towel be x

We know that $area = length\times height$

area=3x

$3x=17.1\\x=5.7$

therefore the length of the towel is 5.7 feet

6 0

2 years ago