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3 years ago

A raise that regularly sells for $84.99 is 30% off. Find the discount and sales price

Mathematics

1 answer:

devlian [24]3 years ago

3 0

1) Find 30% of 84.99 : 25.50
The discount is $25.50

2) Subtract 25.50 from 84.99 : 59.49

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The ratio of the number of boys to the number of girls in orchestra is 3 to 2. There are 40 girls in the orchestra. How many boy

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Answer:

Step-by-step explanation:

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3 years ago

The diameter of the circle below measures 7 cm. What is the approximate area of the circle?

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It’s A. 38! You divide the diameter in half and use the radius to find the area of the circle

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If set A contains seven distinct numbers and set B contains three distinct letters, how many elements are in (A U B)?

Ira Lisetskai [31]

<h3>Answer: 10 elements</h3>

=======================================================

Explanation:

Let's use an example to see why this is

A = {1,2,3,4,5,6,7}

B = {x,y,z}

A U B = {1,2,3,4,5,6,7, x,y,z}

We simply glue the two sets together to form one single big set. Because sets A and B have no overlap, this means we dont have to worry about tossing out duplicates (since there aren't any).

There are 7 items in set A, and 3 items in set B.

Therefore, we have 7+3 = <u>10 items in set A U B</u>

The symbol U refers to the set union operator.

If you wanted to make a Venn Diagram, then you'd have two circles overlapping. In circle A will be the numbers 1 through 7. These values are not in the overlapped region. For circle B, the letters x,y,z are inside but not in the overlapped region. The overlapped region remains empty.

The set A U B talks about the collection of everything mentioned. It's the set of stuff in set A or in set B or in both sets.

-----------------

If you want a formula to write down on a notecard or reference sheet, then it would be

n(A U B) = n(A)+n(B)

where A and B are mutually exclusive, aka disjoint. This means they have nothing in the overlapped region

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2 years ago

5. A study found that the average time it took a person to find their dream home was 5.9 months. If a sample of

solong [7]

Answer:

The 95% confidence interval of the mean time it took a person to find their dream home is between 5.64 months and 6.16 months.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{0.8}{\sqrt{36}} = 0.26$

The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.26 = 5.64 months

The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.26 = 6.16 months.

The 95% confidence interval of the mean time it took a person to find their dream home is between 5.64 months and 6.16 months.

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3 years ago

Algebraically solve the inequality: 5x-6>/1+2(4x+1)

elena-14-01-66 [18.8K]

Answer:

x<-3

Step-by-step explanation:

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

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3 years ago