In a survey, 27% of the people chose salads over a meat dish. In all 81 people chose salads. How many people were in the survey

A telephone pole has a wire to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor po

Bumek [7]

Answer:

The height of the pole is 105ft,

Step-by-step explanation:

Let us call $h$ the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is $h - 49$ .

The wire length $d$ is 14 ft longer than height $h$ , hence

$d= h+14$ .

Thus we get a right triangle with hypotenuse $d= y+14$ , perpendicular $h$ , and base $h-49$ ; therefore, the Pythagorean theorem gives

$(h-49)^2+h^2 = (h+14)^2$

which upon expanding we get:

$h^2-98h+2401 = h^2+28h+196$

further simplification gives

$h^2-126h+2205=0$ ,

which is a quadratic equation with solutions

$h =21ft\\h = 105ft.$

Since the first solution $h =21ft$ will give the triangle base length of $21ft-49ft = -28ft$ which is negative; therefore, we disregard it and pick the solution $h = 105ft$ .

Hence, the height of the pole is 105ft.

3 0

3 years ago

Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. When the company comes she makes 100 fluid ounces of coff

murzikaleks [220]

Sixty four fluid ounces hope that helped

7 0

3 years ago

Read 2 more answers

For a fair coin, suppose you toss the coin 100 times.

Natasha_Volkova [10]

Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

For the binomial distribution, the parameters are given as follows:

n = 100, p = 0.5.

Hence the mean and the standard deviation of the approximation are given as follows:

$\mu = np = 100(0.5) = 50$ .

$\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5$

Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is <u>one subtracted by the p-value of Z when X = 66.5</u>.

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

$Z = \frac{66.5 - 50}{5}$

Z = 3.3

Z = 3.3 has a p-value of 0.9995.

1 - 0.9995 = 0.0005.

0.0005 = 0.05%

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

6 0

2 years ago

The question is in the photo :) i’m struggling

amm1812

A is 10% and B is 5%

4 0

3 years ago

Alex’s printer can print 8 photos in 12 minutes.

Gre4nikov [31]

Answer:

$120\ minutes$

Step-by-step explanation:

step 1

Alex’s printer

we know that

print 8 photos in 12 minutes

so

by proportion

Find how long will it take the printer to print 120 photos

$\frac{12}{8}=\frac{x}{120}\\ \\x=120*12/8\\ \\x=180\ minutes$

step 2

Khalil’s printer

we know that

print 24 photos in 1 hour (60 minutes)

so

by proportion

Find how long will it take the printer to print 120 photos

$\frac{60}{24}=\frac{x}{120}\\ \\x=120*60/24\\ \\x=300\ minutes$

step 3

Find the difference

$300\ minutes-180\ minutes=120\ minutes$

7 0

3 years ago