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3 years ago

A rectangular driveway is 8 feet wide and it has an area of 112 square feet. How long is the driveway?

Mathematics

1 answer:

Bogdan [553]3 years ago

3 0

Given:

A rectangular driveway is 8 feet wide and it has an area of 112 square feet.

We need to determine the length of the driveway.

Length of the driveway:

The length of the driveway can be determined using the formula,

$Area=length \times width$

where Area = 112 square feet and width = 8 feet.

Substituting the values, we have;

$112=length \times 8$

Dividing both sides by 8, we get;

$14=length$

Hence, the value of the length is 14 feet.

Thus, the length of the driveway is 14 feet.

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Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. 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.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

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

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

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

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

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

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

please help me The question involves multiplying two complex numbers, then turning it into an a+bi equation (pictures included)

Sloan [31]

Answer:

(a, b) = (0, -15)

Step-by-step explanation:

In "cis" form the product of two complex numbers is the product of their magnitudes at the angle that is the sum of their angles. I find this the easiest way to multiply complex numbers.

z1 × z2 = (3 cis π)(5 cis π/2)

= (3·5) cis (π +π/2)

= 15 cis 3π/2

Of course, "cis" is short for "cosine + i·sine", so you have ...

z1 × z2 = 15 cis 3π/2 = 15(cos(3π/2) +i·sin(3π/2))

= 15(0 +i·(-1))

= 0 -15i

(a, b) = (0, -15)

8 0

3 years ago

Joel earns $1,500 per month. If he spends $375 on rent each month, what percent of his income does he spend on rent?

cricket20 [7]

First, we must express the ratio of rent to Joel's total earning. 375 out of 1500 in its simplest form is 1/4. To express a value in percentage, we must multiply it to 100. Thus, for this case, we have 1/4 x 100 = 25% That means, out of a total of 100%, Joel spends 25%of his income on rent.

5 0

3 years ago

The sum of two consecutive odd integers is at least 16

elena-14-01-66 [18.8K]

Odd integers are represented by 2n+1 where n is a whole number

consecutive odd are 2 apart so
they are 2n+1 and 2n+1+2

the sum of them is at least 16
2n+1+2n+1+2>16
4n+4>16
minus 4
4n>12
divide 4
n>3
sub back

2n+1 and 2n+3
2(3)+1 and 2(3)+3
6+1 and 6+3
7 and 9

they have to be at least 7 and 9

5 0

4 years ago

Given two points on the graph of the line, the equation of the line can be found.

harkovskaia [24]

The answer is true.
Really all you ever need is two points and you should find an equation.

3 0

4 years ago

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