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yaroslaw [1]
3 years ago
5

The perimeter and area of each figure: a. A square with a side length of 3.5 inches.

Mathematics
1 answer:
Anna11 [10]3 years ago
5 0

3.5 \times 3.5 = 12.25 \: for \: are \\ 3.5 \times 4 = 14 \: for \: perimeter

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What is the remainder for the synthetic division problem below?
Luden [163]

7 |1 -8 10
X. 7. -7
1 -1 3

A remainder is 3
7 0
2 years ago
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
PLSSSSSSSSSSS HELPPP&gt;&gt; Show work solve the sysytem- y=1/2x^2+4x+4 y=-4x+12 1/2
Mrac [35]

Answer:

(1, 8.5 ) and ( - 17, 80.5 )

Step-by-step explanation:

Given the 2 equations

y = \frac{1}{2} x² + 4x + 4 → (1)

y = - 4x + 12 \frac{1}{2} → (2)

Substitute (1) into (2), that is

\frac{1}{2} x² + 4x + 4 = - 4x + 12 \frac{1}{2} ( multiply through by 2 to clear the fractions )

x² + 8x + 8 = - 8x + 25 ( add 8x to both sides )

x² + 16x + 8 = 25 ( subtract 25 from both sides )

x² + 16x - 17 = 0 ← in standard form

(x + 17)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 17 = 0 ⇒ x = - 17

x - 1 = 0 ⇒ x = 1

Substitute these values into either of the 2 equations and evaluate for y

Substituting into (2 )

x = 1 : y = - 4(1) + 12.5 = - 4 + 12.5 = 8.5 ⇒ (1, 8.5 )

x = - 17 : y = - 4(- 17) + 12.5 = 68 + 12.5 = 80.5 ⇒ (- 17, 80.5 )

5 0
3 years ago
Factor x³ + x² + x + 1 by grouping. What is the resulting expression?
vladimir1956 [14]
<h3>Answer:  (x² + 1)(x + 1)</h3>

Work Shown:

x³ + x² + x + 1

(x³ + x²) + (x + 1)

x²(x+1) + 1(x + 1)

(x² + 1)(x + 1)

The basic outline is to pair up the terms into two groups. We factor each group separately, and then factor out the overall GCF (x+1). You can use the FOIL rule to verify the answer.

4 0
2 years ago
Can someone help me with this: y=-5x+5
NikAS [45]

Answer:

I think it would be y=x

Step-by-step explanation:

I might be wrong

8 0
3 years ago
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