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3 years ago

19. Use Gauss-Jordan elimination to solve the following system of equations. 3x + 5y = 7 6x − y = −8

1 answer:

6 0

$\left[\begin{array}{cc}3&5\\6&-1\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}7\\-8\end{array}\right]\\\left[\begin{array}{cc|c}3&5 &7\\ 6& -1 & -8\end{array}\right] \rightarrow \left[\begin{array}{cc|c}3&5& 7\\0&-11 & -22\end{array}\right] \rightarrow \left[\begin{array}{cc|c}3&5& 7\\0&1 & 2\end{array}\right]\\3x +5y = 7\\\\y = 2\\\therefore x = -1$

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Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so

Makovka662 [10]

Answer: B. Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the old and the new dough players. The population proportions of customer complaints with the old and new dough would be p1 and p2

P1 - P2 = difference in the proportion of customer complaints with the old and new dough.

The null hypothesis is

H0 : p1 ≥ p2

pm - pw ≥ 0

The alternative hypothesis is

Ha : p1 < p2

p1 - p2 < 0

it is a left tailed test

Sample proportion = x/n

Where

x represents number of success(number of complaints)

n represents number of samples

For old dough

x1 = 6

n1 = 385

P1 = 6/385 = 0.016

For new dough,

x2 = 16

n2 = 340

P2 = 16/340 = 0.047

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (6 + 16)/(385 + 340) = 0.03

1 - pc = 1 - 0.03 = 0.97

z = (Pm - Pw)/√pc(1 - pc)(1/nm + 1/nw)

z = (0.016 - 0.047)/√(0.03)(0.97)(1/385 + 1/340) = - 0.031/√0.00553857907

z = - 0.42

Since it is a left tailed test, we would find the p value for the area to the left of the z score. From the normal distribution table,

p value = 0.337

For a 95% confidence level, the significant level, alpha is

1 - 0.95 = 0.05

Since 0.05 < 0.337, we would accept the null hypothesis

Therefore, Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

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3 years ago

Please help ASAP!! BRAINLIEST to best answer

Nina [5.8K]

Hello! I can help you! In general, the larger the size, the larger the cost. We will assume that $8 is the youth size and $12 is the adult size. x is the youth side and y is the adult side. The first part of the equation is 8x + 12y, BUT the key words in the problem are AT MOST, so out sign will be less than or equal to (≤), because the number can't be higher than 216, but it could be right at that number or less, so the equation is 8x + 12y ≤ 216. The answer is A.

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3 years ago

Help me please this test is very important !

Lilit [14]

Answer:

Step-by-step explanation:

5>2n+11

5-11>2n

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3 years ago

Sing acts are 5 min long and comedy acts are 3 min long. The show has 12 acts and last 50 min. How many singing acts and how man

ryzh [129]

Answer

so there are 7 singing acts and 5 comedy acts.

Step-by-step explanation:

Let x= number of singing acts.

Let y= number of comedy acts.

We will take x+y=12 as our first equation, as there are 12 shows in total. We will take 5x+3y=50 as our second equation as there are 50 total minutes, and singing acts are 5 mins and comedy acts are 3 mins.

We solve x+y=12

Y=-x+12

We know y=-x+12, so we will substitute that for the y in the second equation.

1. Substitute 5x+3(-x+12)=50

2. Distribute 5x-3x+36=50

3. Solve 2x+36=50

2x=14

X=7

Now that we have found x, we will find y by substitute the x in 5x+3y=50 with the value, 7, that we found for x.

5(7)+3y=50

35+3y=50

3y=15

Y=5

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3 years ago

state whether the lines represented by the equations y=1/2x-1 and y+4=-1/2(x-2) are paraller, perdendicular, or neither

Brrunno [24]

The easiest way to tell whether lines are parallel, perpendicular, or neither is when they are written in slope-intercept form or y = mx + b. We will begin by putting both of our equations into this format.

The first equation, $y = \frac{1}{2}x - 1$ is already in slope intercept form. The slope is 1/2 and the y-intercept is -1.

The second equation requires rearranging.
$y + 4 = -\frac{1}{2}(x - 2) \\ y + 4 = -\frac{1}{2}x + 1 \\ y = - \frac{1}{2} x- 3$
From this equation, we can see that the slope is -1/2 and the y-intercept is -3.

When lines are parallel, they have the same slope. This is not the case with these lines because one has slope of 1/2 and the other has slope of -1/2. Since these are not the same our lines are not parallel.

When lines are perpendicular, the slope of one is the negative reciprocal of the other. That is, if one had slope 2, the other would have slope -1/2. This also is not the case in this problem.

Thus, we conclude that the lines are neither parallel nor perpendicular.

8 0

4 years ago