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sergij07 [2.7K]
3 years ago
5

If x= -8 and y=-4​, evaluate the expression.

title="\frac{3x-4}{y-3}" alt="\frac{3x-4}{y-3}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
bagirrra123 [75]3 years ago
6 0

Your answer would be 4.

If we substitute in x = -8 and y = -4 into the expression, we get:

\frac{3(-8) - 4}{-4 - 3}

This then becomes:

\frac{-24 - 4}{-7} = \frac{-28}{-7} = 4.

I hope this helps!

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Answer:

125 feet below sea level or -125

Step-by-step explanation:

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If the area of a triangular garden is 156 sq ft, and the base of this garden is 13 feet wide, what is the height?
Ilia_Sergeevich [38]

Answer:

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Step-by-step explanation:

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The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure
Ilia_Sergeevich [38]

Answer:

a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

Step-by-step explanation:

For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?

The foreclosure rate is 1.31% for the Washington, DC area, which means that p = 0.0131

We wanto to find, with n = 100:

P(X < 2) = P(X = 0) + P(X = 1)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0131)^{0}.(0.9869)^{100} = 0.2675

P(X = 1) = C_{100,1}.(0.0131)^{1}.(0.9869)^{99} = 0.3551

P(X < 2) = P(X = 0) + P(X = 1) = 0.2675 + 0.3551 = 0.6226

0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?

Foreclosure rate of 0.87% for the nation, which means that p = 0.0087. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0087)^{0}.(0.9913)^{100} = 0.4174

P(X = 1) = C_{100,1}.(0.0087)^{1}.(0.9913)^{99} = 0.3663

P(X < 2) = P(X = 0) + P(X = 1) = 0.4174 + 0.3663 = 0.7837

0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c. Comment on the above findings.

The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

7 0
3 years ago
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rusak2 [61]

<em>Question 5</em>

Vertical angles are <u>congruent</u>. Therefore, 3y=\boxed{150}. The sum of two supplementary angles equals \boxed{180^{\circ}}.

Therefore, 6x+150=\boxed{180}

<em>Question 6</em>

\angle b-14=90-\angle b\\\\2\angle b=104\\\\\angle b=\boxed{52^{\circ}}

<em>Question 7</em>

<em />\angle d+32=180-\angle d\\\\2\angle d=146\\\\\angle d=\boxed{73^{\circ}}

<em>Question 8</em>

<em />7x-80=3x\\\\-80=-4x\\\\x=20\\\\\implies \boxed{m\angle 1=m\angle 3=60^{\circ}}

6 0
2 years ago
I need help on number 18
zloy xaker [14]

Answer:

Volume = 35185.8 km^{3}

Step-by-step explanation:

Recall the formula for the volume of a cone: Volume = \pi  R^{2}  \frac{h}{3}

Where R is the radius of the cone's circular base (in your case half of 80 km,(that is 40 km)

And h stands for the height of the cone (in your case 21 km)

We replace such in the formula and calculate its final value:

Volume = \pi 40^{2} \frac{21}{3} = \pi  1600 \frac{21}{3} = \pi 1600 (7) = 35185.83772...

We round it to the number of decimals your problem request (let's say to one decimal) and also include the cubic units:

Volume = 35185.8 km^{3}

7 0
3 years ago
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