Monty can use the number line to find an equivalent fraction with a denominator greater than 6

Answers

Answer 1
Answer:

Yes, Monty can use the number line to find an equivalent fraction with a denominator greater than 6.

For Example,

Consider (5)/(7)

The equivalent fraction of  (5)/(7) is  (25)/(35).

So, yes you can represent  (5)/(7) on a number line by putting 6 lines between 0 and 1 and Can Represent  (25)/(35) by putting 34 lines between 0 and 1.

There is no effect of denominator to find equivalent fraction of any rational number, whether the denominator is greater than 6 or less than 6, but denominator should not be equal to Zero.

We can find equivalent fraction of any rational number , the denominator of that rational number should not be equal to Zero.


Answer 2
Answer: Is this math? What's the question ?

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A quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates. Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories. At the .05 level of significance, is there sufficient evidence that the average calorie content of a 12-ounce can is greater than 120 calories? Assume that the number of calories per can is normally distributed.

Answers

Answer:

We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Step-by-step explanation:

We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.

Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.

Let \mu = average calorie content of a 12-ounce can.

So, Null Hypothesis,H_0 : \mu \leq 120 calories     {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}

Alternate Hypothesis, H_A : \mu > 120 calories     {means that the average calorie content of a 12-ounce can is greater than 120 calories}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                         T.S. =  (\bar X-\mu)/((s)/(√(n) ) )  ~ t_n_-_1

where, \bar X = sample average calories per can = 124 calories

             s = sample standard deviation = 6 calories

            n = sample of cans = 10

So, test statistics  =  (124-120)/((6)/(√(10) ) )  ~ t_9

                               =  2.108

The value of t test statistics is 2.108.

Now, at 0.05 significance level the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Which number(s) below belong to the solution set of the inequality? Check all that apply. 9x 117A.
12

B.
14

C.
19

D.
13

E.
6

F.
8

Answers

Question says inequality, but there was no symbol between 9x and 117.

If it were an equation, then it reads 9x=117, in which case the answer is
x=117/9=13.

If it were 9x>=117, then all choices 13 or greater qualify.

If it were 9x<=117, then all choices 13 or less qualify.

A theater has a seating capacity of 750 and charges $3 for children, s5 for students, and $7 for adults. At a certain screening with fll ttendance, there were combined. The receipts totaled $3450. How many children attended the show?

Answers

Answer:

Between 150 and 450

Step-by-step explanation:

We are going to find the number by resolving  a system of linear equations.

First we write the system equations :

C+S+A=750

Where C : children, S : students and A : adults

The equation represents the ''full attendance''

The second equation :

3C+5S+7A=3450

This equation represents the totaled receipts.

The system :

C+S+A=750\n3C+5S+7A=3450

has the following associated matrix :

\left[\begin{array}{cccc}1&1&1&750\n3&5&7&3450\end{array}\right]

By performing elementary matrix operations we find that the matrix is equivalent to

\left[\begin{array}{cccc}1&0&-1&150\n0&1&2&600\n\end{array}\right]

The new system :

C-A=150\nS+2A=600

Working with the equations :

C = 150 + A\nS = 600-2A

Our solution vector is :

\left[\begin{array}{c}C&S&A\end{array}\right] =\left[\begin{array}{c}150+A&600-2A&A\end{array}\right]

For example :

If 0 adults attended ⇒ A = 0

C = 150 + 0 \nC = 150\nS = 600 - 2A\nS = 600

This verify the totaled receipts equation :

150($3)+600($5) = $ 3450

A ≥ 0 ⇒ If A = 0 ⇒ C = 150

C = 150 is the minimum children attendance

From the equation :

S = 600 -2A

S ≥0

600 - 2A ≥ 0

600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

When A = 300 ⇒C = 150 + A = 150 + 300 = 450

Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)

Evaluate: 2! + (8 - 3)!

Answers

Answer:

122

Step-by-step explanation:

2! = 2

(8-3)! =

(5)! = 120

2+120 =122

angle U and angle W are vertical angles. If measurement angle u = 6x+11 and measurement angle W = 10x-9, find measurement angle U.

Answers

The measure of angle U will be equal to the measure of angle W.

Because W is pronounced "double u", W = 2 * U.

Therefore U = W and U = 2 * W, so both U and W = 0.


Just kidding.

The correct answer is the smallest prime number greater than 40.

In a study of plant safety, it was found that the time it took for machine operators to react to a warning light was normally distributed with a mean 1 second and standard deviation 0.3 second. Suppose a warning light visible to 4 operators goes on. What is the probability that the average (mean) reaction time of the 4 operators exceeds 1.25 seconds?

Answers

Answer:

4.75% probability that the average (mean) reaction time of the 4 operators exceeds 1.25 seconds.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation (\sigma)/(√(n))

Normal probability distribution

Problems of normally distributed samples 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 = (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.

In this problem, we have that:

\mu = 1, \sigma = 0.3, n = 4, s = (0.3)/(√(4)) = 0.15

What is the probability that the average (mean) reaction time of the 4 operators exceeds 1.25 seconds?

This is 1 subtracted by the pvalue of Z when X = 1.25. So

Z = (X - \mu)/(s)

Z = (1.25 - 1)/(0.15)

Z = 1.67

Z = 1.67 has a pvalue of 0.9525.

So there is a 1-0.9525 = 0.0475 = 4.75% probability that the average (mean) reaction time of the 4 operators exceeds 1.25 seconds.