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valentina_108 [34]
3 years ago
11

Find the product. (4m^2 – 5)(4m^2 + 5)

Mathematics
1 answer:
aliya0001 [1]3 years ago
3 0

Answer: 16m^4−25


Step-by-step explanation:

(4m^2−5)(4m^2+5)

=(4m^2+−5)(4m^2+5)

=(4m^2)(4m^2)+(4m^2)(5)+(−5)(4m^2)+(−5)(5)

=16m^4+20m^2−20m^2−25

=16m^4−25

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A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 100 items, th
pochemuha

Answer:

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Step-by-step explanation:

A manufacturer considers his production process to be out of control when defects exceed 3%.

At the null hypothesis, we test if the production process is in control, that is, the defective proportion is of 3% or less. So

H_0: p \leq 0.03

At the alternate hypothesis, we test if the production process is out of control, that is, the defective proportion exceeds 3%. So

H_1: p > 0.03

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.03 is tested at the null hypothesis

This means that \mu = 0.03, \sigma = \sqrt{0.03*0.97}

In a random sample of 100 items, the defect rate is 4%.

This means that n = 100, X = 0.04

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.04 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{100}}}

z = 0.59

P-value of the test

The p-value of the test is the probability of finding a sample proportion above 0.04, which is 1 subtracted by the p-value of z = 0.59.

Looking at the z-table, z = 0.59 has a p-value of 0.7224

1 - 0.7224 = 0.2776

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

4 0
2 years ago
Please answer the question below and show working
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Answer:

i. Slope=-1/6

ii. Midpoint= (1,8.5)

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<em>iv.</em><em> </em><em> </em><em> </em><em> </em><em>Slope </em><em>of </em><em>t=</em><em>2</em>

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6 0
3 years ago
What is the value of x?<br><br> x-2/5=7
arsen [322]
X=37/5
or 7.4 in decimal form

3 0
3 years ago
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Paige made $1411.75 last year by investing a total of $15,250 in two accounts: one paying 8.5% annual interest and the other pay
Umnica [9.8K]
Lets x and y are 2 accounts Paige invested
x account invested with annual interest rate 8.5%
y account invested with annual interest rate 10%

x + y =<span>15,250 so x = 15,250 - y
0.085x + 0.1y = </span><span>1,411.75

substitute </span>x = 15,250 - y into 0.085x + 0.1y = 1,411.75

0.085x + 0.1y = 1411.75
0.085(15,250 - y) + 0.1y = 1,411.75
1,296.25 - 0.085y + 0.1y = 1,411.75
0.015y = 115.5
y = 7,700

x = 15,250 - y
x = x = 15,250 - 7,700
x = 7,550

answer

$7,550 invested on account with annual interest rate 8.5%
$7,700 invested on account with annual interest rate 10%
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Danny bought 6 ounces of sunflower seeds for $2.64. How much did 1 ounce of sunflower seeds cost?
vova2212 [387]
2.64 divided by 6 equals 0.44. one ounce costs 44 cents
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