MATHEMATICS HIGH SCHOOL

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

Answers

Answer 1

Answer:

For this case we have the following inequality:

$-4 (3 - 5x) \geq-6x + 9$

To solve the inequality, we have as a first step to apply the distributive property on the left side of the inequality.

We have then:

Rewriting we have:

Then, the following steps will only be mentioned:

1) Group variable terms on the left side of the inequality

2) Group constant terms on the right side of the inequality

3) Add the variable terms

4) Add the constant terms

5) Clear the value of x.

Answer:

a correct first step in solving the inequality is:

Distributive property:

$-12+ 20x \geq -6x + 9$

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What does 4/9 - 2/3 equal

Answers

4/9 - 2/3 = 4/9 - 6/9 = -2/9

Answer: -2/9

What is the surface area, in square inches, of a disco ball with a circumference of 188.5 centimeters?

Answers

A = 11300 cm2

Hope this helps!

Calculate the radius of the sphere with the given volume.

Volume=4/81π ft^3

Answers

Answer:

(∛3)/2 ft = r

Step-by-step explanation:

Start with the formula for the volume of a sphere: V = (4/3)πr³. Solve this for r³ and then take the cube root of the result:

V = (4/3)πr³ => (3/4)V = πr³ => (------- = r³

4π

3 · 4/81π ft^3 3 · 4π ft³ 3 ft³

Here we have r³ = -------------------- = ---------------- = -------------

4π 8(4π) 8

and so the radius is r = ∛[ (3/8) ft³] = (∛3)/2 ft = r

More than 200,000 people worldwide take the GMAT examination each year as they apply for MBA programs. Their scores vary normally with mean about u= 525 and standard deviation about sigma= 100. One hundred students go through a rigorous training program designed to raise their GMAT scores. Test the hypotheses. H sub 0: u= 525. H sub A: u > 525Answer the following question based from the given stated.
a) The students' score is x = 541.4. Is this result significant at the 5% level? b) The average score is x = 541.5. Is this result significant at the 5% level? c) What conclusions may you draw by comparing the answers to parts a and b?

Answers

For letter a
$z= (x-u)/(SD √(n) ) \n z= (541.4-525)/(100 √(100) ) \n z=1.64$
Looking up z=1.64, its equivalent is 0.4495
∈=0.5+0.4495
∈=0.9495
As 0.95>0.9495, we cannot reject the null hypothesis, and the result is not significant.
b.) $Z= ((mean-u)SD)/( √(n) ) \n Z= ((541.5-525)100)/( √(100) ) \n Z=1.65$
Looking it up, P(Z>1.65)=0.0505. The result is not significant.
c. The p values are larger than the accepted level of 0.05, which is why the null is rejected. As we cannot reject the null, it is to be accepted that the mean score is 525. This then requires more statistical testing to be done to prove the null.

Look at the image of the table of values below. Over which interval of x is the average rate of change the largest?