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3 years ago

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help please quick

Mathematics

1 answer:

RSB [31]3 years ago

6 0

Isolate the variable by dividing each side by factors that don't contain the variable.

x= 13/4 - y/4

If you are solving for x (only)
X = 45/4 - y/4

If you are solving for y (only)
Y= 45- 4x

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CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars

velikii [3]

Answer:

P(939.6 < X < 972.5) = 0.6469

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that $\mu = 965, \sigma = 113$

Sample of 57:

This means that $n = 57, s = \frac{113}{\sqrt{57}} = 14.97$

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

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

By the Central Limit Theorem

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

$Z = \frac{972.5 - 965}{14.97}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915

X = 939.6

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

$Z = \frac{939.6 - 965}{14.97}$

$Z = -1.7$

$Z = -1.7$ has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

P(939.6 < X < 972.5) = 0.6469

3 0

2 years ago

A lawn with an area of 300 square feet needs 1/2 pound of grass seed. How many pounds of grass seed are needed for a lawn that i

Anna [14]

60x20=1200
1200/300=4
4x1/2=4/2=2 pounds of grass seed

8 0

3 years ago

1. Write a two-column proof.

Alexandra [31]

Answer:

Check it below, please

Step-by-step explanation:

Hi there!

Let's prove segment AB is perpendicular to CD. Attention to the fact that a two column proof has to be concise. So all the comments can't be exhaustive, but as short as possible.

Let's recap: An isosceles triangle is one triangle with at least 2 congruent angles.

Statement Reason

$\overline{AB} \cong \overline{AC}\\$ Given

$\widehat{ACB} \:bisects\: \overline{AB}$ Isosceles Triangle the altitude, the bisector coincide.

$\overline{AD} \cong \overline{DB}$ Bisector equally divide a line segment into two congruent

$m\angle CDA =m \angle CBD=90^{\circ}$ Right angles, perpendicular lines.

$\overline{CD}\perp \overline{AB}$ Perpendicular Line segment

8 0

3 years ago

Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the

Neko [114]

Answer:

10.5cm,20.8cm,23.3cm — yes
6cm, 22.9cm,20.1cm — no

Step-by-step explanation:

If the sides form a right triangle, the sum of the squares of the shorter two sides will equal the square of the longest side.

1. 10.5^2 + 20.8^2 = 23.3^2 . . . . . true algebraic statement; right triangle

2. 6^2 +20.1^2 = 440.01 ≠ 22.9^2 = 524.41 . . . . . this is an obtuse triangle

7 0

3 years ago

How do you know that a =6 is a solution to a+5=11?

Gre4nikov [31]

a + 5 = 11

You need to isolate the variable by subtracting from both sides

a + 5 - 5 = 11 - 5

a = 6

The Addition/Subtraction Property of Equality states that if you add or subtract the same number to both sides of an equation the two sides still remain equal.

:))

4 0

3 years ago

Read 2 more answers