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Write an expression that is equivalent to 3/5 (3y+15)<br> 3/5y +9, 3/5y+15, 9/5y+9, 9/5y + 15?

NISA [10]

Given the expression

$\frac{3}{5} (3y+15)$

The expression that is equivalent to the given expression is given by:

$\frac{3}{5} (3y+15)= \frac{9}{5} y+ \frac{3}{5} (15)= \frac{9}{5} y+9$

6 0

3 years ago

Find the inverse of the following matrix without using a calculator 1-1 2 -3 2 1 0 4 - 25

Artist 52 [7]

Answer:

18 -(17/3) (5/3)

25 (25/3) (7/3)

4 (4/3) (1/3)

Step-by-step explanation:

You can solve this problem by using the Gauss-Jordan method.

You have the original matrix and then the Identity matrix.

So:

Original Identity

1 -1 2 1 0 0

-3 2 1 0 1 0

0 4 -25 0 0 1

By the Gauss-Jordan method, in the original place you will have the identity and in the place that the identity currently is you will have the inverse matrix:

So, let's start by setting the first row element to 0 in the second and the third line.

The first row element of the third line is already at zero, so no changes there. In the second line, we need to do:

L2 = L2 + 3L1

So now we have the following matrixes.

1 -1 2 | 1 0 0

0 -1 7 | 3 1 0

0 4 -25 | 0 0 1

Now we need the element in the second line, second row to be 1. So we do:

L2 = -L2

1 -1 2 | 1 0 0

0 1 -7 | -3 -1 0

0 4 -25 | 0 0 1

Now, in the second row, we need to make the elements at the first and third line being zero. So, we have the following operations:

L1 = L1 + L2

L3 = L3 - 4L2

Now our matrixes are:

1 0 -5 | -2 -1 0

0 1 -7 | -3 -1 0

0 0 3 | 12 4 1

Now we need the element in the third line, third row being one. So we do:

L3 = -L3

1 0 -5 | -2 -1 0

0 1 -7 | -3 -1 0

0 0 1 | 4 (4/3) (1/3)

Now, in the third row, we need the elements in the first and second line being zero. So we do:

L1 = L1 + 5L3

L2 = L2 + 7L3

So we have:

1 0 0 | 18 -(17/3) (5/3)

0 1 0 | 25 (25/3) (7/3)

0 0 1 | 4 (4/3) (1/3)

So the inverse matrix is:

18 -(17/3) (5/3)

25 (25/3) (7/3)

4 (4/3) (1/3)

4 0

3 years ago

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per nig

Kitty [74]

Answer: No , at 0.05 level of significance , we have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.

Step-by-step explanation:

Let $\mu$ denotes the average hours of sleep per night.

As per given , we have

$H_0:\mu=7\\H_a:\mu$

, since $H_a$ is left-tailed and population standard deviation is unknown, so the test is a left-tailed t -test.

Also , it is given that ,

Sample size : n= 22

Sample mean : $\overline{x}=7.24$

Sample standard deviation : s= 1.93

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

i.e. $t=\dfrac{7.24-7}{\dfrac{1.93}{\sqrt{22}}}\approx0.58$

For significance level $\alpha=0.05$ and degree of freedom 21 (df=n-1),

Critical t-value for left-tailed test= $t_{\alpha, df}=t_{0.05,21}=- 1.7207$

Decision : Since the test statistic value (0.58) > critical value 1.7207, it means we are failed to reject the null hypothesis .

[Note : When $|t_{cal}|>|t_{cri}|$ , then we accept the null hypothesis.]

Conclusion: We have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.

6 0

3 years ago

I need help on this number sequence

MrRa [10]

You would square 3968 and subtract 1.

5 0

3 years ago

Read 2 more answers

Solve the inequality below<br> -8x + 4 > 20<br> Include x and number in answer

Genrish500 [490]

Answer:

x<-2

Step-by-step explanation:

You first subtract 4 from both sides. Then you divide both sides by -8 (note: when you multiply or divide by a negative the sign flips. Then you get your answer

7 0

3 years ago

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