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3 years ago

A rectangle is removed from the middle of a larger rectangular shaped board. What is the area of the remaining board?

Mathematics

1 answer:

jeyben [28]3 years ago

8 0

Answer:

The area of the remaining board is [(L × B) - (l × b)].

Step-by-step explanation:

Suppose the bigger rectangle is labelled as ABCD and the smaller rectangle is labelled as PQRS.

Consider that the length and breadth of the bigger rectangle are L and B respectively. And the length and breadth of the bigger rectangle are l and b respectively.

The area of any rectangle is:

Area = Length × Breadth

The area of the bigger rectangle is:

Area of ABCD = L × B

The area of the smaller rectangle is:

Area of PQRS = l × b

Then the area of the remaining board will be:

Area of remaining board = Area of ABCD - Area of PQRS

= (L × B) - (l × b)

Thus, the area of the remaining board is [(L × B) - (l × b)].

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It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months an

Juli2301 [7.4K]

Answer:

340

Step-by-step explanation:

The first step is finding the percentage of those who fail within 19 months.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 18.2, \sigma = 1.7$

The proportion is the pvalue of Z when X = 19. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{19 - 18.2}{1.7}$

$Z = 0.47$

$Z = 0.47$ has a pvalue of 0.6808.

Jolt is expected to replace 0.6808 of the connectors sold. Out of 500, that is, on average, 0.6808*500 = 340.

Jolt expects to replace, on average, 340 of the connectors sold.

4 0

3 years ago

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE

EleoNora [17]

Answer:

0, 10

Step-by-step explanation:

The given function is:

$g(y) = \frac{y-5}{y^2-3y+15}$

According to the quotient rule:

$d(\frac{f(y)}{h(y)}) = \frac{f(y)*h'(y)-h(y)*f'(y)}{h^2(y)}$

Applying the quotient rule:

$g(y) = \frac{y-5}{y^2-3y+15}\\g'(y)=\frac{(y-5)*(2y-3)-(y^2-3y+15)*(1)}{(y^2-3y+15)^2}$

The values for which g'(y) are zero are the critical points:

$g'(y)=0=\frac{(y-5)*(2y-3)-(y^2-3y+15)*(1)}{(y^2-3y+15)^2}\\(y-5)*(2y-3)-(y^2-3y+15)=0\\2y^2-3y-10y+15-y^2+3y-15\\y^2-10y=0\\y=\frac{10\pm \sqrt 100}{2}\\y_1=\frac{10-10}{2}= 0\\y_2=\frac{10+10}{2}=10$

The critical values are y = 0 and y = 10.

5 0

3 years ago

What numbers are multiples of 7 and factors of 28

bija089 [108]

7 and 14 are both multiplies

4 0

4 years ago

Read 2 more answers

Nitella [24]

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

<h3>How to find the production level that'll maximize profit?</h3>

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

Read more on maximized profit here: brainly.com/question/13800671

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6 0

2 years ago

A clothing store offers a free T-shirt when a customer spends $75 or more. Lyndon has already spent $36.95. Which statement best

Brums [2.3K]

Answer:

34:05 more

Step-by-step explanation:

easy just add the toghter and you get 75

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3 years ago

Read 2 more answers