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Allisa [31]
3 years ago
12

The graph shows the relationship between the number of granola bars and amount of calories per bar.

Mathematics
1 answer:
castortr0y [4]3 years ago
5 0

part a y= x × 100

Step-by-step explanation:

1 bar is 100 calories so you would times it by 100 for every bar

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Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights
user100 [1]

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

Normal Probability Distribution:

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

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that \mu = 85, \sigma = 8

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

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

Z = \frac{100 - 85}{8}

Z = 1.875

Z = 1.875 has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

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

-0.84 = \frac{X- 85}{8}

X - 85 = -0.84*8

X = 78.28

The weight that 80% of the apples exceed is of 78.28g.

5 0
3 years ago
A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed wi
Tems11 [23]

The volume of the cylinder is the space occupied by the cylinder. The volume of the water in the cylinder is 1583.36266 in³.

<h3>What is the volume of a cylinder?</h3>

The volume of the cylinder is the space occupied by the cylinder. It is calculated with the help of the formula,

\text{Volume of the cyllinder}= \pi r^2h

As it is given that the diameter of the cylinder is 12 inches while the height of the cylinder is 15 inches, also, it has a ball of the diameter of 6 inches placed inside the cylinder, therefore, the volume of the water that is inside the cylinder is the difference in the volume of the cylinder and the volume of the spherical ball.

\text{Volume of the cyllinder}= \pi r^2h = \dfrac{\pi}{4}d^2 h

Substitute the values,

\begin{aligned}\text{Volume of the cyllinder}&= \dfrac{\pi}{4}d^2 h\\& = \dfrac{\pi}{4} \times (12^2) \times 15\\ &=1696.46\rm\ in^3\end{aligned}

Now, the volume of the ball is equal to the volume of the sphere therefore, the volume of the ball can be written as,

\text{Volume of the sphere} = \dfrac{4}{3}\pi r^3

                                  = \dfrac{4}{3}\pi r^3\\\\=  \dfrac{4}{3}\times \pi \times (3^3)\\\\= 113.097\rm\ in^3

Further, the volume of the water that is inside the cylinder can be written as,

The volume of water =  Volume of the cylinder - Volume of the sphere

                                   = 1696.46 - 113.097

                                   = 1583.36266 in³

Hence, the volume of the water in the cylinder is 1583.36266 in³.

Learn more about Volume of the Cylinder:

brainly.com/question/1780981

5 0
2 years ago
a chef has a recipe that calls for 4 cups of flour. She wants to make 3/4 of the recipe instead of determining directly how many
Nikolay [14]
She wants to use 3/4 of the recipe and 3/4 of a cup 4 times equals three cups. Three cups is 3/4 of 4 cups.
8 0
1 year ago
Read 2 more answers
The difference of twice a number and 2 is<br> 40. Find the number.
IgorLugansk [536]

Answer:

answer = 21

Step-by-step explanation:

2n - 2 = 40

2n - 2 + 2 = 40 + 2

2n = 42

2n/2 = 42/2

n = 21

4 0
2 years ago
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the
Lisa [10]

Solution :

Group   Before     After

Mean    693.75    743.75

Sd         155.37     143.92

SEM        54.93     50.88

n              8            8

Null hypothesis : The preparation course not effective.

$H_0: \mu_d = 0$

Alternative hypothesis : The preparation course is effective in improving the exam scores.

$H_a : \mu_d>0$  (after -  before)

4 0
3 years ago
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