Simplify (10 x 10^5)/(2 x 10^-5)

Hal says the volume of the sphere shown below 36 cm3. Find the correct volume, using 3.14 for pi. Round to the nearest hundredth

adelina 88 [10]

Answer:

Volume of sphere is $35.98cm^3$

Step-by-step explanation:

It is given that Hal says that volume of sphere is $36cm^3$

Volume of sphere is given by $V=\frac{4}{3}\pi r^3$

$\frac{4}{3}\pi r^3=36$

$\pi r^3=27$

$r^3=8.594$

$r=2.048cm$

Now using 3.14 in place of $\pi$

Now volume of sphere is

$V=\frac{4}{3}\times 3.14\times 2.048^3$

$V=35.98cm^3$

Therefore volume of sphere when we use 3.14 in place of $\pi$ is $35.98cm^3$

And the Hal likely error is he uses $\pi$ directly for calculation of volume.

7 0

3 years ago

− 4 y − 3 + 3 y = 8 − 2 y − 15

Neporo4naja [7]

Answer:

y= -4

Step-by-step explanation:

simplify both sides of the equasion

add 2y to both sides

add three to both sides

and your answer is y= -4

7 0

3 years ago

It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell

Mademuasel [1]

Answer:

a) 75

b) 4.33

c) 0.75

d) $3.2 \times 10^{-13}$ probability that no one in a simple random sample of 100 young adults owns a landline

e) $6.2 \times 10^{-61}$ probability that everyone in a simple random sample of 100 young adults owns a landline.

f) Binomial, with $n = 100, p = 0.75$

g) $4.5 \times 10^{-8}$ probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which means that the binomial probability distribution is used 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.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.

This means that $p = 0.75$

(a) On average, how many young adults do not own a landline in a random sample of 100?

Sample of 100, so $n = 100$

$E(X) = np = 100(0.75) = 75$

(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33$

(c) What is the proportion of young adults who do not own a landline?

The estimation, of 75% = 0.75.

(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?

This is P(X = 100), that is, all do not own. So

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

$P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}$

$3.2 \times 10^{-13}$ probability that no one in a simple random sample of 100 young adults owns a landline.

(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?

This is P(X = 0), that is, all own. So

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

$P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}$

$6.2 \times 10^{-61}$ probability that everyone in a simple random sample of 100 young adults owns a landline.

(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?

Binomial, with $n = 100, p = 0.75$

(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?

This is P(X = 50). So

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

$P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}$

$4.5 \times 10^{-8}$ probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

8 0

2 years ago

Mrs Hong had some milk. She used of it to bake some waffles and

Sergio [31]

Answer:

Mrs. Hong originally had 900 ml of milk

Explanation:

The complete question is in the attached image

Assume that the amount of milk Mrs. Hong originally had was x ml

We are given that:

1- She used $\frac{1}{6}$ of it to bake the waffles, therefore:

Amount used in baking waffles = $\frac{1}{6}x$ ml

2- She used 300 ml to bake a pie

3- Amount left is half the original amount, therefore:

Amount left = $\frac{1}{2}x$ ml

We know that:

Total amount = amount used in waffles + amount used in pie + amount left

Substitute with the givens and solve for x:

Total amount = amount used in waffles + amount used in pie + amount left

$x = \frac{1}{6}x + 300 + \frac{1}{2}x\\ \\x-\frac{1}{6}x-\frac{1}{2}x = 300\\ \\\frac{1}{3}x = 300\\ \\x = 300*3 = 900 ml$

This means that:

She originally had 900 ml of milk

Hope this helps :)

7 0

3 years ago

a card is chosen from a standard deck, then a month of the year is chosen. find the probability of getting a face card and june

Irina-Kira [14]

Answer:

Probability of chossing a face card and the month of june = 0.019

Step-by-step explanation:

Let A be the event that a face card is chosen from a deck of 52 cards

And

B be the event that a month is being chosen from 12 months of an year

So,

n(S)for A=52

n(S)for B=12

As a deck of card has total of 12 face cards so

P(A)=12/52

=3/13

P(B)=1/12

As both the events are independent, the probability of A and B is the product of both events’ probabilities.

P(A and B)= P(A)*P(B)

=3/13*1/12

=3/156

=0.019

4 0

3 years ago