MATHEMATICS HIGH SCHOOL

what is the range of the function g(x) = |x – 12| – 2? {y | y > –2} {y | y > –2} {y | y > 12} {y | y > 12}

Answers

Answer 1

Answer: Range = {y | y ≥ –2}

Answer 2

Answer:

Answer:

The range of function is $R= \left \{ y|y\geq -2 \right \}$

Step-by-step explanation:

Given : Function $g(x) = |x -12| -2$

To find : What is the range of the function?

Solution :

The range is defined as the set of y values for which function is defined.

We have given function $g(x) = |x -12| -2$ in the vertex form.

The general vertex form is $y=a|x-h|+k$ where (h,k) are the vertex of the equation.

On comparing the vertex of the given function is (h,k)=(12,-2)

i.e. The y-values taken is less than -2.

So, the range would be the all y values greater than or equal to -2.

Therefore, The range of function is $R= \left \{ y|y\geq -2 \right \}$

Refer the attached figure below of the function.

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Solve each quadratic equation. Show your work. x^2 + 3x = 10

the equation m = 0.3048f gives the relationship between meters and f feel. express 9 feet in meters. round your answer to the nearest thousandth.

Answers

m = 0.3048(9)
m = 2.7432

Using standard form, writean equation to represent a
line passing through (-6.10)
with a slope of -1.

Answers

Answer:

y= -1x +4

Step-by-step explanation:

So if you meant (-6,10) then I have solved it.

Writing this in y= mx+b form we already have M

y= -1x + b

So let’s substitute by putting in then y and x

10 = -1(-6) + b

10 -6= 6 -6+ b

4 = b

Sally is building a garden. She plans to build a rectangular garden measuring 6 meters by 3 meters. She wants to put a net over top of the garden to keep the birds out. She has 12 square meters of netting in her garage. How much more netting will Sally need to cover her whole garden?

Answers

Answer:

area of netting she will need more =18-12=6m²

Step-by-step explanation:

area of rectangular garden=l*b=6*3=18m²

area of netting she has =12m²

area of netting she will need more =18-12=6m²

hope this helps plzz mark me brainliest

Solve 4(5x+3)=92. justify each step.

Answers

x=4
4(5x+3)=92
First Distribute
4(5x) + 4(3)
20x + 12 = 92
Then subtract 12 from both sides
20x = 80
Then divide 20 from both sides
x = 4

Suppose you are going to graph the data in the table below. What data should be represented on each axis, and what would be the appropriate increments? Year Profit 2003 $100,000 2004 $55,000 2005 −$45,000 2006 $110,000 2007 $330,000 2008 $800,000 2009 $242,000 2010 −$11,000 2011 $285,000

Answers

The right answer for the question that is being asked and shown above is that:

The value in the x axis will be the Year.
The value in the y axis will be the Year Profit.

The increment on the x axis will as is.
The increment on the y axis can either be $50,000.

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is $150.00 with a standard deviation of $30.20. The manager collects 40 random receipts and finds that the average is $160. Complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. Which of the following is a valid conclusion for the manager based on this test?a.The customers spend more than the national average in his store.b.The manager should decrease prices in his store.c.The customers do not spend more than the national average in his store.d.The customers in his store just come from a rich neighborhood.

Answers

Answer:

The correct answer is:

The customers spend more than the national average in his store

Step-by-step explanation:

The national average is $150.00 with a standard deviation of $30.20.

Sample size n =40

H0: x bar = mu

Ha: x bar >mu

(one tailed test for a single mean)

Sample average x bar = 160

Mean difference = 160-150 =10

std error = 30.20/sqrt 40

=4.775

Test statistic = 2.094

Z critical for 2.5% = 1.96 (one tailed)

Since test statistic > z critical we reject null hypothesis.

Hence the correct answer is:

The customers spend more than the national average in his store.

Answer:

Option A) The customers spend more than the national average in his store.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $150.00

Sample mean, $\bar{x}$ = $160

Sample size, n = 40

Alpha, α = 0.025

Population standard deviation, σ = $30.20

First, we design the null and the alternate hypothesis

$H_(0): \mu = 150\text{ dollars}\nH_A: \mu > 150\text{ dollars}$

The null hypothesis states that the consumers are spending equal to the national average. The alternative hypothesis states that consumers are spending more than the national average.

We use One-tailed z test to perform this hypothesis.

Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$