Help with this please

Consider the function represented by the equation 6q = 3s - 9. Write the equation in function notation, where q is the independe

serg [7]

Answer:

s = 2q + 3

Step-by-step explanation:

A linear function has the form:

● y = mx + b

● y is the output of the function

● x is the variabke that we input

● b is the y-intetcept.

Focus on y and x.

Notice that y depends of the value of x. The value of y changes by changing x. So the value of x controls the output y.

y is dependent but x is not.

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 6q = 3s - 9

We want q to be the independent variable wich means that q will be the input. Therefore s should be the output.

The strategy we are going to follow is separating s in one side alone.

● 6q = 3s - 9

Add 9 to both sides

● 6q + 9 = 3s -9 + 9

● 6q + 9 = 3s

Divide both sides by 3

● (6q + 9)/3 = (3s)/3

● (6q)/3 + 9/3 = s

● s = 2q + 3

So the answer is s = 2q + 3

6 0

3 years ago

On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C

Naddik [55]

Answer: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius

Step-by-step explanation:

5 0

3 years ago

A monomial of the 2nd degree with a leading coefficient of 3

Rzqust [24]

Given:

Polynomials

To find:

Monomial of 2nd degree with leading coefficient 3

Solution:

Monomial is an algebraic expression with only one term.

Option A: $3 n^{2}-1$

It is not a monomial because it have 2 terms.

It is not true.

Option B: $3 n-n^{2}$

It is not a monomial because it have 2 terms.

It is not true.

Option C: $3 n^{2}$

It have one term only. So, it is a monomial.

Degree means highest power. So degree = 2

Leading coefficient means the value before variable.

Leading coefficient = 3

It is true.

Option D: $2n^3$

It have one term only. So, it is a monomial.

Degree means highest power. So degree = 3

It is not true.

Therefore $3 n^{2}$ is a monomial of 2nd degree with a leading coefficient of 3.

5 0

3 years ago

5÷x-4 - 2÷x+2 = 4÷x-4

Alborosie

I'd suggest you begin by subtracting 4 / (x-4) from both sides. Doing that would leave you with 1 / (x-4) - 2 / (x+2) = 0.

LCD is (x-4)(x+2). Mult. all three terms by (x-4)(x+2). The resulting equation is

x+2 - 2(x-4) = 0. Then x+2 = 2x - 8 => x = 10

Subst. 10 for x in the original equation to verify that 10 is indeed a solution.

8 0

3 years ago

A random sample of 50 recent college graduates results in a mean time to graduate of 4.58 years, with a standard deviation of 1.

Anna007 [38]

Answer:

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ, when the population standard deviation is not known is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The information provided is:

$\bar x=4.58\\s=1.10\\\alpha =0.10$

Compute the critical value of t for 90% confidence interval and (n - 1) degrees of freedom as follows:

$t_{\alpha/2, (n-1)}=t_{0.10/2, (50-1)}=t_{0.05, 49}=1.671$

*Use a t-table for the probability.

Compute the 90% confidence interval for population mean μ as follows:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

$=4.58\pm 1.671\times \frac{1.10}{\sqrt{50}}\\=4.58\pm 0.26\\=(4.32, 4.84)$

Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:

Hₐ: The mean time it takes to complete a bachelor’s degree is 4 years, i.e. μ = 4.

Hₐ: The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. μ ≠ 4.

The decision rule based on a confidence interval will be:

Reject the null hypothesis if the null value is not included in the interval.

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).

The null value, i.e. μ = 4 is not included in the interval.

The null hypothesis will be rejected at 10% level of significance.

Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.

4 0

3 years ago