MATHEMATICS COLLEGE

Nine yards of ribbon are cut into 8 equal pieces what is the length of each piece of ribbon. Write a division expression to represent the problem and solve

Answers

Answer 1

Answer:

Answer:

$x=(9)/(8)\ yards$

$x=1.125\ yards$

Step-by-step explanation:

Let's call x the length of each piece in yards

If the ribbon is cut into 8 equal pieces then the sum of the pieces is:

$x+x+x+x+x+x+x+x=8x$

Then:

$8x=9\ yards$

Now we solve the equation for x

$8x=9\ yards$

Divide both sides of equality by 8

$(8)/(8)x=(9)/(8)\ yards$

$x=(9)/(8)\ yards$

So the length of each piece is $(9)/(8)$ of a yard.

This is: 1.125 yards

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1. Julia's goal is to run faster than two of her friends in an upcoming6.2-mile race. The table shows the results of the last race that each
runner finished. Assume they each run the race at the same rate
they ran their last race. Complete the table. Who will finish first
among the three friends, and by how much time will she beat the
second-place finisher?
Runner
Julia
Hazel
Mekena
Last Race
Distance
(mi)
8
5
6
Last Race
Time
(min: sec)
62:00
39:10
46:00
Rate
(min:sec
per mi)
Time for
6.2 Miles
(min: sec)

Answers

It was a good choice to ask Toni to join the team as she would be able to contribute to the team's success in the race.

What is the ratio and proportion ?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

To complete the 1-mile relay race in 4:34, each runner must run their quarter-mile leg of the race in a total time of 1:08 (68 seconds).

We can use this information to fill in the missing information in the table:

Runner Rate(min:sec per mi) Time for 1/4mile (min:sec)

Julia 4:40 1:10

Hazel 4:48 1:12

Mekena 4:32 1:08

Toni 4:18 1:04

Based on the table, Toni's rate is faster than the other runners, and her time for a quarter-mile leg of the race is also faster.

Therefore, it was a good choice to ask Toni to join the team as she would be able to contribute to the team's success in the race.

To know more about ratio and proportion visit :

brainly.com/question/12024093

#SPJ1

find the t values that form the boundaries of the critical region for a two-tailed test with a=.05 for n=6 n=12

Answers

Answer:

n=6

"=T.INV(1-0.025,5)", and we got the critical values given by: $t_(critical)=\pm 2.5706$

n=12

"=T.INV(1-0.025,11)", and we got the critical values given by: $t_(critical)=\pm 2.201$

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

For n=6

In order to find the critical value we need to take in count that we are conducting a two tailed test, so we are looking on the t distribution with df=n-1=6-1=5 degrees of freedom, a value that accumulates $0.05/2=0.025$ of the area on each tail. We can use excel or a table to find it, for example the code in Excel is:

"=T.INV(1-0.025,5)", and we got the critical values given by: $t_(critical)=\pm 2.5706$

For n=12

In order to find the critical value we need to take in count that we are conducting a two tailed test, so we are looking on the t distribution with df=n-1=12-1=11 degrees of freedom, a value that accumulates $0.05/2=0.025$ of the area on each tail. We can use excel or a table to find it, for example the code in Excel is:

"=T.INV(1-0.025,11)", and we got the critical values given by: $t_(critical)=\pm 2.201$

23 greater than b is at least -276

Answers

Answer:

23 + b ≤ -276

Step-by-step explanation:

In this exercise, you're required to write an algebraic expression for the word problem. Thus, you'll write out a mathematical equation using the given values and unknown variable.

Translating the word problem into an algebraic expression, we have;

23 + b ≤ -276

Simplifying further, we have;

b ≤ -276 - 23

b ≤ -299

If x3 = 8 and y3 = 125, what
is the value of y - x?