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3 years ago

Use the Distributive Property to determine which of the following statements is equivalent to 5(2a – 3b).

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

4 0

Answer:

Step-by-step explanation:

10a-15b

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Mark is 4 year older than 2 times his sister Helena's Age. Let h represent Helena's age and m represent Mark's age. Write an equ

andreyandreev [35.5K]

2h + 4 = m (twice the value of Helena's age plus 4 will equal Mark's age) 3j - 6 = g (three time John's age minus 6 will equal Glenn's age) 3.35s + .80b = 11.75

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3 years ago

Which table can be represented by a line? A) А B) B C С D D

wel

Step-by-step explanation:

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2 years ago

The miles-per-gallon rating of passenger cars is a normally distributed random variable with a mean of 33.8 mpg and a standard d

EleoNora [17]

Answer:

The probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.

Step-by-step explanation:

Let the random variable X represent the miles-per-gallon rating of passenger cars.

It is provided that $X\sim N(\mu=33.8,\ \sigma^{2}=3.5^{2})$ .

Compute the probability that a randomly selected passenger car gets more than 37.3 mpg as follows:

$P(X>37.3)=P(\frac{X-\mu}{\sigma}>\frac{37.3-33.8}{3.5})$

$=P(Z>1)\\\\=1-P(Z$

Thus, the probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.

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3 years ago

What is the ratio of the two values and what new value do they produce? $280 in 7m

3241004551 [841]

Answer:

The ratio between two values A and B is just the quotient between these two values:

ratio = A/B

a) $280 in 7m

Here the ratio is:

$280/7m = $40/m

This also can be read as:

$40 per meter.

b) 105 miles in 2 hours

Here the ratio is:

105mi/2h = 52.5 mi/h

This also can be read as:

52.5 miles per hour

c) $33 for 5lb

The ratio is:

$33/5lb = $6.6/lb

This can be read as:

$6.6 per pound.

d) 50 pages in 2 hours

the ratio is:

(50 pages)/2h = 25 pages/h

this can be read as:

25 pages per hour.

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3 years ago

Given: PRST is a square

xxTIMURxx [149]

Answer:

$(1-\sqrt{2})a^2$

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

$PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a$

Thus,

$MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a$

Consider isosceles triangle MSC. In this triangle

$MS=MC=(\sqrt{2}-1)a.$

The area of this triangle is

$A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}$

Consider right triangle PTS. The area of this triangle is

$A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}$

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

$A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2$

5 0

3 years ago