MATHEMATICS HIGH SCHOOL

1. 350 is 70% of what number? A) 500. B) 420. C) 245. D) 280
2.What percent of 64 is 24?
A) 267%. B) 62.5%. C) 40%. D) 37.5%
3.What percent of $6.50 is $2.60?
A) 25%. B) 40%. C) 90%. D) 250%

4.20% of 140 is what number? A) 280. B) 120. C) 28. D) 12

Answers

Answer 1
Answer:

All the solutions are,

1) 350 is 70% of number 500.

2) 37.5% of 64 is 24.

3) 40% of 6.5 is 2.60.

4) 20% of 140 is 28.

Now, We can simplify all the equation as,

1) Let us assume that a number = x

Hence, We get;

350 = 70% of x

Solve for x,

350 = 70x/100

350 = 7x/10

3500 = 7x

7x = 3500

x = 500

So, 350 is 70% of number 500.

2) Let us assume that, x% of 64 is 24.

Hence, We get;

⇒ x% of 64 = 24

Solve for x;

⇒ x/100 × 64 = 24

⇒ 64x = 2400

⇒ x = 2400 / 64

⇒ x = 37.5%

Hence, 37.5% of 64 is 24.

3) Let us assume that, x% of 6.5 is 2.60

Hence, We get;

x% of 6.5 = 2.6

x/100 x 6.5 = 2.6

6.5x = 260

x = 260/6.5

x = 40

Hence, 40% of 6.5 is 2.60.

4) Let us assume that a number = x

Hence, We get;

20% of 140 = x

20/100 x 140 = x

2800 = 100x

x = 2800 / 100

x = 28

Hence, 20% of 140 is 28.

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Answer 2
Answer:

Answer:

1. A 500

2. D 37.5

3. B 40%

4.C 28

Step-by-step explanation:

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Solve for x: 5|2x − 2| + 8 = 18.x = 2, x = −2
x = −2, x = 0
x = 2, x = 0
x = 0, x = 1 over 2

Answers

remember
|x| makes x posotive
5|2x-2|+8=18
minus 8 both sides
5|2x-2|=10
divide both sides by 5
|2x-2|=2
assume
2x-2=2 and 2x-2=-2

2x-2=2
add 2
2x=4
divide 2
x=2

2x-2=-2
add 2
2x=0
x=0


x=0 or x=2


3rd choice

Answer:

C. x = 2, x = 0

Step-by-step explanation:

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is $150.00 with a standard deviation of $30.20. The manager collects 40 random receipts and finds that the average is $160. Complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. Which of the following is a valid conclusion for the manager based on this test?a.The customers spend more than the national average in his store.b.The manager should decrease prices in his store.c.The customers do not spend more than the national average in his store.d.The customers in his store just come from a rich neighborhood.

Answers

Answer:

The correct answer is:

The customers spend more than the national average in his store

Step-by-step explanation:

The national average is $150.00 with a standard deviation of $30.20.

Sample size n =40

H0: x bar = mu

Ha: x bar >mu

(one tailed test for a single mean)

Sample average x bar = 160

Mean difference = 160-150 =10

std error = 30.20/sqrt 40

=4.775

Test statistic = 2.094

Z critical for 2.5% = 1.96 (one tailed)

Since test statistic > z critical we reject null hypothesis.

Hence the correct answer is:

The customers spend more than the national average in his store.

Answer:

Option A) The customers spend more than the national average in his store.        

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $150.00

Sample mean, \bar{x} = $160

Sample size, n = 40

Alpha, α = 0.025

Population standard deviation, σ = $30.20

First, we design the null and the alternate hypothesis

H_(0): \mu = 150\text{ dollars}\nH_A: \mu > 150\text{ dollars}

The null hypothesis states that the consumers are spending equal to the national average. The alternative hypothesis states that  consumers are spending more than the national average.  

We use One-tailed z test to perform this hypothesis.

Formula:

z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }

Putting all the values, we have

z_(stat) = \displaystyle(160 - 150)/((30.20)/(√(40)) ) = 2.094

Now, z_(critical) \text{ at 0.025 level of significance } = 1.96

Since,  

z_(stat) > z_(critical)

We reject the null hypothesis and accept the alternate hypothesis. Thus, the customers spend more than the national average in his store.

Thus, option A) is a valid conclusion for the manager

Write each ratio in simplest form show work 33/36 and 1.4/7

Answers

Simplify fraction 33/36 by dividing the greatest common factor of 3 from the numerator and denominator = 33/36 = 11/12.

1.4/7 ⇒  14/70 = 2/10 simplifed to 1/5.
33:36 is the same as 11:12

1.4:7 is the same as 14:70 . . . 2:10 . . . 1:5

True or false:a parallelogram has 4sides and exactly 2 pairs of parallel sides

Answers

True. I don't think there's a more elaborate way to answer that... the evidence is all there.
True. A parallelogram has 4 sides and 2 pairs of parallel lines.

What happens when h is a negative number?

Answers

Answer: -h

Step-by-step explanation:

If h is a negative number, h would be -h.

For example, if h had a value of 1, 1 as a negative number would be -1.

The solutions of this system:x² + y = -4
y=x²-6
are: (Select)
-5) and ( (Select)
-5).

Answers

Therefore , the solution of the given problem of equation comes out to be  the system of equations' answers are (-1, -5) and (1, -5).

What is an equation?

The foundation of a regression model based on linearity is the equation y=mx+b. The inclination is B, and the y-intercept is m. Even though y but also y are separate components, the above line is frequently referred as the "mathematical issues with two variables". Two factors make up bivariate linear equations. There are no simple answers for the applications of linear functions. Y=mx+b .

Here,

We can change the second equation into the first equation to find the solution to the system of equations, which results in:

=> x² + (x²-6) = -4

By condensing and rearrangeing, we obtain:

=> 2x² = 2

=> x² = 1

Consequently, x can either be 1 or -1.

We can determine the appropriate values of y by substituting these values of x into either of the two equations:

When x Equals 1:

=> y = x² - 6 = 1 - 6 = -5

When x Equals -1:

=> y = x² - 6 = 1 - 6 = -5

As a result, the system of equations' answers are (-1, -5) and (1, -5).

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