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2 years ago

What is the determinant of the coefficient matrix of this system? 4x-3y=-8 8x-3y=12

Mathematics

1 answer:

gladu [14]2 years ago

8 0

The coefficient matrix is build with its rows representing each equation, and its columns representing each variable.

So, you may write the matrix as

$\left[\begin{array}{cc}\text{x-coefficient, 1st equation}&\text{y-coefficient, 1st equation}\\\text{x-coefficient, 2nd equation}&\text{y-coefficient, 2nd equation} \end{array}\right]$

which means

$\left[\begin{array}{cc}4&-3\\8&-3\end{array}\right]$

The determinant is computed subtracting diagonals:

$\left | \left[ \begin{array}{cc}a&b\\c&d\end{array}\right]\right | = ad-bc$

So, we have

$\left | \left[\begin{array}{cc}4&-3\\8&-3\end{array}\right] \right | = 4(-3) - 8(-3) = -4(-3) = 12$

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Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41 % of the viewing audience in the a

ZanzabumX [31]

Answer:

1) Null hypothesis: $p\geq 0.41$

Alternative hypothesis: $p < 0.41$

2) $\hat p=0.36$ estimated proportion of people indicated that they watch the late evening news on this local CBS station

3) $z_{crit}=-2.33$

And we can use the following excel code to find it: "=NORM.INV(0.01,0,1)"

4) $z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{1000}}}=-1.017$

5) $z_{crit}=-1.28$

And we can use the following excel code to find it: "=NORM.INV(0.1,0,1)"

6) We see that $|t_{calculated}|$ so then we have enough evidence to FAIL to reject the null hypothesis at 1% of significance.

7) Null hypothesis: $p\geq 0.41$

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

X represent the people indicated that they watch the late evening news on this local CBS station

$\hat p=0.36$ estimated proportion of people indicated that they watch the late evening news on this local CBS station

$p_o=0.41$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v{/tex} represent the p value (variable of interest) Part 1We need to conduct a hypothesis in order to test the claim that 11:00 PM newscast reaches 41 % of the viewing audience in the area: Null hypothesis:[tex]p\geq 0.41$

Alternative hypothesis: $p < 0.41$

Part 2

$\hat p=0.36$ estimated proportion of people indicated that they watch the late evening news on this local CBS station

Part 3

Since we have a left tailed test we need to see in the normal standard distribution a value that accumulates 0.01 of the area on the left and on this case this value is :

$z_{crit}=-2.33$

And we can use the following excel code to find it: "=NORM.INV(0.01,0,1)"

Part 4

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{1000}}}=-1.017$

Part 5

Since we have a left tailed test we need to see in the normal standard distribution a value that accumulates 0.1 of the area on the left and on this case this value is :

$z_{crit}=-1.28$

And we can use the following excel code to find it: "=NORM.INV(0.1,0,1)"

Part 6

We see that $|t_{calculated}|$ so then we have enough evidence to FAIL to reject the null hypothesis at 1% of significance.

Part 7

Null hypothesis: $p\geq 0.41$

4 0

2 years ago

A cake recipe says to bake the cake until the center is 180 degrees F, then let the cake cool to 110 degrees F. The table shows

jeka94

Answer:

Check the explanation

Step-by-step explanation:

a) The following exponential model would fit the given dataset : $\small y = 129.122 \times (0.9742)^x$

b) To cool down to 110 degrees, it would take approximately 7.3 minutes based on the above model.

4 0

2 years ago

The sets F and H are given below.

Vinil7 [7]

Answer:

F ∪ H = {c, d, e, f, g, h}

F ∩ H = { }

Step-by-step explanation:

The union is the list of elements that are in either of the two sets.

F ∪ H = {c, d, e, f, g, h}

The intersection is the list of only those elements that appear in both sets. (There are none.)

F ∩ H = { } . . . . the empty set

4 0

3 years ago

Find the value of X.

Kobotan [32]

Answer:

x = 18.46

Step-by-step explanation:

Find the last angle of the triangle.

180-90-72 = 18

The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

cos(b) = adj/hyp

CosB=a/c rewrite to get

6/CosB (72) = 19.41

Find the last side of the triangle using the Pythagorean theorem.

b=square root c^2 - a^2

b=square root 376.99 - 36

b= 18.46

3 0

2 years ago

Select the correct answer from each drop-down menu.

tester [92]

Answer:

April
She did not pack enough layers of centimeter cubes
240 cubic centimeters

Step-by-step explanation:

Dimensions of the prism is 5x8x6

April made a mistake, she packed 4 layers of unit cubes instead of 5 layers

<u>Correct volume of the prism is:</u>

5*8*6 = 240 cm³

<u>Correct answer choices:</u>

April
She did not pack enough layers of centimeter cubes
240 cubic centimeters

6 0

2 years ago