All categories

3 years ago

One number is 6 more than other number. Also, 7 times the smaller number is equal to 6 times the

Mathematics

1 answer:

julia-pushkina [17]3 years ago

4 0

Answer:

The numbers are 36 and 42

Step-by-step explanation:

Represent the two numbers by m and n, m being the larger number and n the smaller. Then

m = n + 6. also, 7n = 6m

Substitute n + 6 for m in the second equation: 7n = 6(n + 6).

Performing the indicated multiplication, we get 7n = 6n + 36, or n = 36.

Then m = n + 6, which here is m = 36 + 6 = 42.

The numbers are 36 and 42.

You might be interested in

Determine the quotient, q(x), and remainder, r(x) when

Fed [463]

ANSWER

Quotient:

$q(x) = {x}^{2} - 4x + 7\\$

Remainder:

$r(x) = 11x - 29$

EXPLANATION

The given functions are

$f(x) = 4 {x}^{4} + 12 {x}^{3} + 17 {x}^{2} + 19x + 6$

and

$g(x) = 4 {x}^{2} + 4x + 5$

We want to find the quotient and the remainder when f(x) is divided by g(x).

We perform the long division as shown in the attachment.

The quotient is

$q(x) = {x}^{2} - 4x + 7$

The remainder is

$r(x) = 11x - 29$

5 0

3 years ago

In a random sample of 26 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a sta

Rainbow [258]

Answer:

The critical value that should be used in constructing the confidence interval is T = 1.316.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 26 - 1 = 25

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.8}{2} = 0.9$ . So we have T = 1.316

The critical value that should be used in constructing the confidence interval is T = 1.316.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.059 = 2.741 pounds

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

4 0

3 years ago

A recipe takes 90 minutes to make 25% of the time he spent preparing the ingredients how many minutes are spent preparing

gizmo_the_mogwai [7]

25% * 90 minutes is 22.5 22.5 minutes

5 0

3 years ago

Write the equation x - 4y = 16 in slope-intercept form.

e-lub [12.9K]

Good morning,

Step-by-step explanation:

Look at the photo below for the Answer.

3 0

3 years ago

What is the largest value in the sequence generated by the formula an = –n2 + 6n – 7?

Karolina [17]

Derive the equation and equate the derivative to zero.
dan/dt = -2n + 6 = 0
The value of n in the equation is 3. We substitute 3 to the original equation,
an = -(3)² + 6(3) - 7 = 2
The answer to this item is letter B.

5 0

4 years ago

Read 2 more answers