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denis-greek [22]
3 years ago
6

What is the answer to w/2 +7=w/3+9?

Mathematics
2 answers:
Cerrena [4.2K]3 years ago
7 0
1. <span>Multiply both sides by </span>6<span> (the LCM of </span><span>2, 3,</span><span>)

3w + 42 = 2w + 54

</span>2. Subtract 42 from both sides

3w = 2w + 54 - 42

3. <span>Simplify 2w + 54 - 42 to 2w + 12

3w = 2w + 12

4. </span><span>Subtract 2w from both sides 

3w - 2w = 12

5. </span><span>Simplify 3w - 2w to w

w=12 

Your answer is 12</span>
Svetlanka [38]3 years ago
6 0
W/2 - w/3 = 9-7
3w - 2w = 9-7
W = 2
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fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed w
EastWind [94]

Answer:

The p-value obtained is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours

Step-by-step explanation:

Complete Question

fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed with a mean of 700 hours and a standard deviation of 45 hours. Test the hypothesis that mean is 700 hours against the alternative hypothesis that the mean is not equal to 700 hours, if a random sample of 30 bulbs has an average life of 688 hours. Use a P-value in your answer.

Solution

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the mean life of the fluorescent lights is 700 hours.

The alternative hypothesis will now be that the mean life of the fluorescent lights is significantly different from 700 hours.

Mathematically,

The null hypothesis is represented as

H₀: μ = 700

The alternative hypothesis is represented as

Hₐ: μ ≠ 700

To do this test, we will use the z-distribution because no information on the population standard deviation is known

So, we compute the z-test statistic

z = (x - μ₀)/σₓ

x = sample mean = 688 hours

μ₀ = 700 hours

σₓ = standard error = (σ/√n)

σ = standard deviation = 45 hours

n = Sample size = 30

σₓ = (45/√30) = 8.2158383626 = 8.216

z = (688 - 700) ÷ 8.216

z = 1.46

checking the tables for the p-value of this z-statistic

Significance level = 0.05 (This is used when significance level isn't given)

The hypothesis test uses a two-tailed condition because we're testing in two directions.

p-value (for z = 1.46, at 0.05 significance level, with a two tailed condition) = 0.14429

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.14429

0.14429 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours.

Hope this Helps!!

6 0
3 years ago
Simplify 14a over 15 Plus 2a + 36 over 5​
Yuliya22 [10]

Answer:

(20a+108)/15

Step-by-step explanation:

First find LCM of the denominators. U will find it to be 15

Then calculate the number like this.

[(14a)×1/15×1]+[(2a+36)×3/5]

[(14a/15)]+[(6a+108)/15

(14a+6a+108)/15

(20a+108)/15

5 0
3 years ago
Does anyone know what the slope equation is for this graph. PLz explain if you can. Ty!
yKpoI14uk [10]
<h3>Answer:   y = (-3/2)x+3</h3>

In decimal form, this is y = -1.5x+3

=========================================

Explanation:

Start at (0,3). Move three units down and two units to the right to get to (2,0)

slope = rise/run

slope = -3/2

rise = -3 = go 3 units down

run = 2 = go 2 units to the right

--------------------------

We could use the two points (0,3) and (2,0) in the slope formula below

m = (y2-y1)/(x2-x1)

m = (0-3)/(2-0)

m = -3/2

So this is another way to see the slope is -3/2

--------------------------

The y intercept is where the graph crosses the vertical y axis. In this case, it's at 3. So b = 3

Using m = -3/2 and b = 3, we go from y = mx+b to y = (-3/2)x+3 which is equivalent to y = -1.5x+3

5 0
3 years ago
Read 2 more answers
Show all work to factor x4 - 5x2 + 4 completely.
otez555 [7]
The answer is 2(2x-3)

Explanation: First you multiple 5 and 2 getting you ten
4x-10+4

Then you add -10 and 4 to get -6
4x-6

Finally you factor out the number to and divide both the 4 and -6
2(2x-3)
7 0
3 years ago
Can anyone help me solve these linear systems using substitution?
vivado [14]

The system of the linear systems of equation using substitution is;

  • x = 2, y = 2
  • x = -20, y = -1

<h3>Linear equation</h3>

3x-y=4

x+2y=6

from (2)

x = 6 - 2y

substitute into (1)

3x-y=4

3(6 - 2y) - y = 4

18 - 6y - y = 4

- 6y - y = 4 - 18

-7y = -14

y = 2

Substitute into

x+2y=6

x + 2(2) = 6

x + 4 = 6

x = 6 - 4

x = 2

2. 2x-y= -39

x+y= -21

From (2)

x = -21 - y

substitute into

2x-y= -39

2(-21 - y) - y = -39

-42 - 2y - y = -39

- 2y - y = -39 + 42

- 3y = 3

y = 3/-3

y = -1

substitute into

x+y= -21

x + (-1) = -21

x - 1 = -21

x = -21 + 1

x = -20

3. 2x+y =11

6x-5y =9

Learn more about linear equation:

brainly.com/question/4074386

#SPJ1

6 0
1 year ago
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