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3 years ago

10

a model doll house is 3.25 feet long. the real house is 30 yards long. what is the unit rate that describes the relationship of

the real house to the model doll house?

1 answer:

DENIUS [597]3 years ago

3 0

Answer:

27.7

Step-by-step explanation:

1 yard = 3 feet

30 yards x 3 feet = 90 feet

90/3.25 = 27.7

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Which expression represent the distance between the point graphed below

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The answer is A because when you plug in the points into the distance formula, you will get square root of 17 squared plus 17 squared. Hope this helps!

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In a multiple choice quiz there are 5 questions and 4 choices for each question (a, b, c, d). Robin has not studied for the quiz

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Answer:

a) There is a 18.75% probability that the first question that she gets right is the second question.

b) There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

c) There is a 10.35% probability that she gets the majority of the questions right.

Step-by-step explanation:

Each question can have two outcomes. Either it is right, or it is wrong. So, for b) and c), we use the binomial probability distribution to solve this problem.

Binomial probability distribution

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

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

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

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

And $\pi$ is the probability of X happening.

In this problem we have that:

Each question has 4 choices. So for each question, Robin has a $\frac{1}{4} = 0.25$ probability of getting ir right. So $\pi = 0.25$ . There are five questions, so $n = 5$ .

(a) What is the probability that the first question she gets right is the second question?

There is a 75% probability of getting the first question wrong and there is a 25% probability of getting the second question right. These probabilities are independent.

So

$P = 0.75(0.25) = 0.1875$

There is a 18.75% probability that the first question that she gets right is the second question.

(b) What is the probability that she gets exactly 1 or exactly 2 questions right?

This is: $P = P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955$

$P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637$

$P = P(X = 1) + P(X = 2) = 0.3955 + 0.2637 = 0.6592$

There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

(c) What is the probability that she gets the majority of the questions right?

That is the probability that she gets 3, 4 or 5 questions right.

$P = P(X = 3) + P(X = 4) + P(X = 5)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 3) = C_{5,3}.(0.25)^{3}.(0.75)^{2} = 0.0879$

$P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0146$

$P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001$

$P = P(X = 3) + P(X = 4) + P(X = 5) = 0.0879 + 0.0146 + 0.001 = 0.1035$

There is a 10.35% probability that she gets the majority of the questions right.

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Answer:

$132\ in^{2}$ is closest to the total surface area of the box

Step-by-step explanation:

we know that

The surface area of the box is equal to

$SA=2B+PH$

where

B is the area of the base

P is the perimeter of the base

H is the height of the box

we have

$L=7\frac{3}{4}\ in=\frac{7*4+3}{4}=\frac{31}{4}\ in$

$W=3\frac{1}{4}\ in=\frac{3*4+1}{4}=\frac{13}{4}\ in$

$H=3\frac{7}{8}\ in=\frac{3*8+7}{8}=\frac{31}{8}\ in$

<em>Find the area of the base B</em>

$B=LW$

$B=(\frac{31}{4})(\frac{13}{4})=\frac{403}{16}\ in^{2}$

<em>Find the perimeter of the base P</em>

$P=2(L+W)$

$P=2(\frac{31}{4}+\frac{13}{4}))$

$P=2(\frac{44}{4})=22\ in$

<em>Find the surface area</em>

$SA=2(\frac{403}{16})+22(\frac{31}{8})$

$SA=(\frac{403}{8})+(\frac{682}{8})$

$SA=\frac{1,085}{8}=135.625\ in^{2}$

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He gains 6 Pounds a month, overall he gains 72 pounds in 12 months

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