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Amanda [17]
3 years ago
7

the area of a rectangle is 54x^9y^8 square yards if the length of the rectangle is 6x^3y^4 yards what expression represents the

width of the rectangle in yards

Mathematics
1 answer:
Vinvika [58]3 years ago
5 0
The area of a rectangle is given by:
 A = (w) * (l)
 Where,
 w: width
 l: long
 Substituting values we have:
 (54x ^ 9y ^ 8) = (w) * (6x ^ 3y ^ 4)
 Clearing w we have:
 w = (54x ^ 9y ^ 8) / (6x ^ 3y ^ 4)
 Rewriting:
 w = (9 * x ^ 6y ^ 4)
 Answer:
 
the length of the rectangle is:
 
w = (9 * x ^ 6y ^ 4)
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A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye
Katena32 [7]

Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

 \mu_{x}=n\mu

And the standard deviation of the distribution of the sum of values of X is given by,  

 \sigma_{x}=\sqrt{n}\sigma

The information provided is:

<em>μ</em> = $970

<em>σ</em> = $129

<em>n</em> = 102

Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

\sum X\sim N(\mu_{x}=98940,\ \sigma_{x}=1302.84)

Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:

P (\sum X \leq  100,000) =P(\frac{\sum X-\mu_{x}}{\sigma_{x}}

                              =P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

6 0
3 years ago
emergency Alejandro has gone to school 5 Over 7 of the last 35 days. Which expression can be used to determine the number of day
Yakvenalex [24]

Answer:

245 days.

Step-by-step explanation:

Hope this helps.

8 0
3 years ago
Read 2 more answers
The function f is defined by f(x)=2.1x−1.7. Use this formula to find the following values of f.
viktelen [127]

f(c + a) = 2.1 c + 2.1 a - 1.7

f(1/3 x - 2/3) = 0.7 x - 3.1

f(x + 2) = 2.1 x + 2.5

f(3c) = 6.3 c - 1.7

Step-by-step explanation:

The function is f(x) = 2.1 x - 1.7

We need to use this formula to find

  • f(c + a)
  • f(1/3x - 2/3)
  • f(x + 2)
  • f(3c)

To solve the problem substitute x by each value in the bracket

∵ f(x) = 2.1 x - 1.7

f(c + a) means substitute x by c + a

∵ x = c + a

∴ f(c + a) = 2.1(c + a) - 1.7

- Multiply the bracket by 2.1

∴ f(c + a) = 2.1 c + 2.1 a - 1.7

∵ f(x) = 2.1 x - 1.7

- f(1/3 x - 2/3) means substitute x by 1/3 x - 2/3

∵ x = 1/3 x - 2/3

∴ f(1/3 x - 2/3) = 2.1(1/3 x - 2/3) - 1.7

- Multiply the bracket by 2.1

∴ f(1/3 x - 2/3) = 0.7 x - 1.4 - 1.7

- Add the like terms

∴ f(1/3 x - 2/3) = 0.7 x - 3.1

∵ f(x) = 2.1 x - 1.7

- f(x + 2) means substitute x by x + 2

∵ x = x + 2

∴ f(x + 2) = 2.1(x + 2) - 1.7

- Multiply the bracket by 2.1

∴ f(x + 2) = 2.1 x + 4.2 - 1.7

- Add the like terms

∴ f(x + 2) = 2.1 x + 2.5

∵ f(x) = 2.1 x - 1.7

- f(3c) means substitute x by 3c

∵ x = 3c

∴ f(3c) = 2.1(3c) - 1.7

- Multiply 2.1 by 3c

∴ f(3c) = 6.3 c - 1.7

Learn more:

You can learn more about the functions in brainly.com/question/628130

#LearnwithBrainly

3 0
3 years ago
In 2008, data from the Center for Disease Control revealed that 28.5% of all male teenagers, aged 18-19 and attending U.S. colle
m_a_m_a [10]

Answer:

a) H0 : u = 28.5%

H1 : u < 28.5%

b) critical value = - 1.645

c) test statistic Z= - 1.41

d) Fail to reject H0

e) There is not enough evidence to support the professor's claim.

Step-by-step explanation:

Given:

P = 28.5% ≈ 0.285

X = 210

n = 800

p' = \frac{X}{n} = \frac{210}{800} = 0.2625

Level of significance = 0.05

a) The null and alternative hypotheses are:

H0 : u = 28.5%

H1 : u < 28.5%

b) Given a 0.05 significance level.

This is a left tailed test.

The critical value =

-Z_0.05 = -1.645

The critical value = -1.645

c) Calculating the test statistic, we have:

Z = \frac{p' - P}{\sqrt{\frac{P(1-P)}{n}}}

Z = \frac{0.2625 - 0.285}{\sqrt{\frac{28.5(1-28.5)}{800}}}

Z = -1.41

d) Decision:

We fail to reject null hypothesis H0, since Z = -1.41 is not in the rejection region, <1.645

e) There is not enough evidence to support the professor's claim that the proportion of obese male teenagers decreased.

5 0
3 years ago
Select the property NOT used in the following
Fudgin [204]

(2 + a) = (a + 2) it's commutative property

(a + 2) - 7 = a + (2 - 7) it's associative property

2 - 7 = -5 it's subtraction

Answer: distributive property { a(b + c) = ab + ac }

5 0
3 years ago
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