What is the surface area of a cylinder whose radius is 3 inches and whose height is 10 inches? Round to the nearest tenth.

a sum of money is divided among peter paul and jane in ratio 13:12:7 calculate how much paul gets if amount peter gets more than

MariettaO [177]

Paul must get 13 since Peter gets more more than Jane so Jane would get 7 and then peter would get 12

3 0

2 years ago

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 104 eligible vot

crimeas [40]

Answer:

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this case, assume that 104 eligible voters aged 18-24 are randomly selected.

This means that $n = 104$ .

Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.

This means that $p = 0.22$

Mean and standard deviation:

$\mu = 104*0.22 = 22.88$

$\sigma = \sqrt{104*0.22*0.78} = 4.2245$

Probability that exactly 27 voted

By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.

X = 27.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{27.5 - 22.88}{4.2245}$

$Z = 1.09$

$Z = 1.09$ has a p-value of 0.8621

X = 26.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{26.5 - 22.88}{4.2245}$

$Z = 0.86$

$Z = 0.86$ has a p-value of 0.8051

0.8621 - 0.8051 = 0.057

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

5 0

3 years ago

Can you please assist

ELEN [110]

A. (Number of sides - 2) x 100, so
6-2= 4 x 180
= 720° is the sum of all angles in a hexagon
84 + 87 + 128 + 150 + 103 = 552
720 - 552 = 168
X = 168°

2. Angles in a triangle sum up to 180°
36 + 57= 93
180 - 93 = 87
A= 87°

8 0

2 years ago

A remote control car races straight down the street at 26 miles per hour. Two

Pachacha [2.7K]

Answer:

It will take 4 hours for the second car to catch up with the first car.

Step-by-step explanation:

The first step to solving this problem is determining the difference in speed between the first and second car - you can see that the second car (at 52mph) is twice as fast as the first (26mph) therefore it will take half the time to cover the same distance.

As Car 1 has a 2 hour head start, it will be 52 miles ahead after 2 hours.

In the next 2 hours, Car 1 will travel 52 miles - so 104 in total after 4 hours, and car 2 will travel 104 miles, meaning that it will have caught up after 4 hours.

A)

To calculate distance per minute, divide the miles per hour by 60 (as there's 60 minutes in an hour), so:

Car 1 = 26/60 = 0.43 miles per minute

Car 2 = 52/60 = 0.867 miles per minute

To check your calculation, Car 2 should be exactly twice as far

B) The street, as far as we know, is at least 104 miles

C) See calculation at the top - the first car is 52miles from the start line when the second car starts

D) 2 cars are competing in this race

8 0

3 years ago

The sum of two positive numbers is 55 times their difference. What is the ratio of the larger number to the smaller number?

Andrews [41]

So x and y
sum means add
difference means subtract
so we have
x+y=55 times (x-y)
use distributiver property which is
a(b-c)=ab-ac so
distribute 55(x-y)
55(x-y)=55x-55y

so we have
x+y=55x-55y
add 55y to boh sides
x+56y=55x
subtract x from both sides
56y=54x
divide both sides by 2
28y=27x
to find the ratio, switch the numbers around
ratio of y:x=27:28
therefor x is the greater number
ratio of larger to smaler is
28:27

3 0

3 years ago

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