MATHEMATICS MIDDLE SCHOOL

What is the least common multiple (LCM) of 6 and 8?A. 24
B. 48
C. 16
D. 2

Answers

Answer 1
Answer: the answer is a 24 Method
 The LCM of 6 and 8 is 24, which is the multiple of the highest power of all prime factors from both numbers
6 = 2 x 3
8 = 2 x 2 x 2 x 3 = 23 x 3
Highest multiple of 2 = 23 = 8
Highest multiple of 3 = 3

(23 x 3 = 8 x 3 = 24).

Small Numbers Method (trial and error)
Start listing the multiples
6 multiples- 6, 12, 18, 24
8 multiples- 8, 16, 24
The LCM of 8 and 6 is 24.
Answer 2
Answer: he multiples of 6 are : 6, 12, 18, 24, 30, . . . The multiples of 8 are : 8, 16, 24, 32, 40, . . . So, the Lowest Common Multiple is 24.

A. 24

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What is the solution of the system? Use elimination.7x + 5y = 19−7x − 2y = −16

Why is the opposite of a number also called the additive inverse

Answers

This number is also known as the opposite (number), sign change, and negation. For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive. Zero is the additive inverse of itself.

The temperature on Mars is -85°F and the temperature in the clouds of Jupiter is-234°F. Which planet is colder?

A. Jupiter

B. Mars​

Answers

It’s b because it’s -85 f so the planet is colder

92. Rachel is baking cookies. She needs 1/4 cup ofoil. She notices that her measuring devices are
only marked in ounces, not cups.
How many ounces of oil will Rachel need
​

Answers

Answer:

2 fluid ounces

Step-by-step explanation:

A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in each can is 0.12 ounce. The machine is overhauled with new components, and ten cans are filled to determine whether the standard deviation has changed. Assume the fill amounts to be a random sample from a normal population.Perform a hypothesis test to determine whether the standard deviation differs from 0.12 ounce. Use the level of significance.

Answers

Answer:

\chi^2 =(10-1)/(0.0144) 0.0217 =13.54

The degrees of freedom are:

df=n-1=10-1=9

Now we can calculate the p value using the alternative hypothesis:

p_v =2*P(\chi^2 >13.54)=0.279

Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces

Step-by-step explanation:

Assuming the following data:"12.14 12.05 12.27 11.89 12.06

12.14 12.05 12.38 11.92 12.14"

We can calculate the sample deviation with this formula:

s =\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}

n=10 represent the sample size

\alpha=0.05 represent the confidence level  

s^2 =0.0217 represent the sample variance

\sigma^2_0 =0.12^2= 0.0144 represent the value to verify

Null and alternative hypothesis

We want to determine whether the standard deviation differs from 0.12 ounce, so the system of hypothesis would be:

Null Hypothesis: \sigma^2 = 0.0144

Alternative hypothesis: \sigma^2 \neq 0.0144

The statistic can be calculated like this;

\chi^2 =(n-1)/(\sigma^2_0) s^2

\chi^2 =(10-1)/(0.0144) 0.0217 =13.54

The degrees of freedom are:

df=n-1=10-1=9

Now we can calculate the p value using the alternative hypothesis:

p_v =2*P(\chi^2 >13.54)=0.279

Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces

4 percent of x days is 56

Answers

Answer:

1400

days

Explanation:

x

%

means  

x

100

, if you are looking for  

x

%

of a value  

y

then it will be  

x

100

⋅

y

Therefore...  

4

%

of  

y

(since we don't have a value, let's use that as a placeholder) is 56...  

4

100

⋅

y

=

56

We can simplify the fraction to a decimal, this gets you  

0.04

y

=

56

To find the value you need, simply divide  

56

0.04

and you get the answer:

56

÷

0.04

=

1400

days

I need help on 2 and 3 please

Answers

2. A
3. A
2 times x is 2x, 2 times y is 2y; therefore it is 2y +2x
2 times 3x is 6x, there is no possible way for the answer to be 5x
if you multiply the outside number by all the terms in the parenthesis you'll get;
2(x + y) = 2(x) + 2(y)= 2x + 2y giving you A as your answer in Q.#2.
And for Q.#3 the its the same steps;
2(3x) = 2(3)(x) = 6x Giving you A as your answer cause; 5x is not equivalent and the others are equivalent to 6x by multiplying as I explained you.
hope that helps :D
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