Zachary is solving the following equation.

To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor.

maria [59]

The slope is 50 because they charge $50 for each hour of labor. The slope represents how long they have worked for and what it costs. Also the y intercept is 500, so the equation is y=50x+500

4 0

3 years ago

What is the slope of the line that passes through the points (-5, -7) and (4,−1)? in the simplest form

Bad White [126]

It should be m=-5/9

3 0

3 years ago

Simplify.<br> Rewrite the expression in the form 5^n

makvit [3.9K]

Answer:

$\frac{5^{-5}}{5^8} = 5^{-13}$

Step-by-step explanation:

Given

$\frac{5^{-5}}{5^8}$

Required

Express as $5^n$

We have:

$\frac{5^{-5}}{5^8}$

Apply second law of indices

$\frac{a^m}{a^n} = a^{m-n}$

So, we have:

$\frac{5^{-5}}{5^8} = 5^{-5-8}$

$\frac{5^{-5}}{5^8} = 5^{-13}$

8 0

3 years ago

PLEASEE HELP ME 60 POINTS!!!

kompoz [17]

Answer:

1. No Solution

2. One solution

3. Infinitely many solutions

Step-by-step explanation:

Let us try to solve each of the system of equations one by one.

1. $y =-4x - 5$

$y = -4x + 1$

This gives

$-4x- 5 = -4x + 1$

which has no solutions.

2. $-3x+y=7$

$2x-4y=-8$

let us write them in y-intercept form

$y=3x+7$

$y=\frac{1}{2}x+2$

and equate them

$y=3x+7=\frac{1}{2}x+2$

this gives $x=-2$ and

$y=-3(-2)+7 = 1$

This equation has solutions.

3. $3x-y=4$

$6x-2y =8$

Notice that the second equation is just the first equation multiplied by 2, or

$2(3x-y=4)\rightarrow (6x-2y=8)$

<em>so these are identical equations and therefore</em> this system has infinitely many solutions.

Thus we have

1. No Solution

2. One solution

3. Infinitely many solutions

3 0

3 years ago

A bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The m

solong [7]

Answer:

Both the approach gave the same conclusion:

There is enough evidence to support the claim that the mean waiting time is shorter than six minutes

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 6 minutes

Sample mean, $\bar{x}$ = 5.46 minutes

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 2.475 minutes

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 6\text{ minutes}\\H_A: \mu < 6\text{ minutes}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{5.36 - 6}{\frac{2.475}{\sqrt{100}} } = -2.5858$

a) Use the critical value approach

Now, $t_{critical} \text{ at 0.05 level of significance, 99 degree of freedom } = -1.6603$ Since, the calculated test statistic is less than the critical value of t, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Conclusion:

Thus, there is enough evidence to support the claim that new system reduces the time customers spend waiting for teller service during peak hours from the current 9 to 10 minutes to less than 6 minutes.

b) Use the p-value approach

The p-value can be calculated as:

P-value = 0.0055

Since the p-value is less than the significance level, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Conclusion:

Thus, there is enough evidence to support the claim that new system reduces the time customers spend waiting for teller service during peak hours from the current 9 to 10 minutes to less than 6 minutes.

5 0

4 years ago