1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Llana [10]
3 years ago
14

15 Points! Find the range of the functions: f(x) = (x + 1)^2 - 1 f(x) = 7x - 11

Mathematics
1 answer:
MakcuM [25]3 years ago
4 0

In both cases you may well benefit from graphing the functions.

Do you recognize f(x) = (x + 1)^2 - 1 as a quadratic function, whose graph is that of a parabola that opens up? By comparing this to y = a(x-h)^2 + k, we see that a=1, h= -1 and k = -1. The vertex is at (h,k), which here is the point (-1, -1). This is the minimum value of the function. Thus, the range of this function is [-1, infinity).


Now for the function f(x) = 7x - 11: This is a linear function whose graph is (surprise!) a straight line. When x increases, y increases, without limits to either. Similarly, when x decreases, y decreases.

Thus the range includes all real numbers: (-infinity, infinity).

You might be interested in
Explain the different types of motion of a sewing machine​
Lana71 [14]

Answer:

linear.

rotary.

reciprocating.

oscillating.

hope it wil help you

4 0
3 years ago
Hypothesis Testing for Means with Small Samples
Scorpion4ik [409]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: volume of root beer in a Windsor Bottling Company can.

A sample of n=24 cans was taken and their contents measured, resulting:

X[bar]= 11.4 oz

S= 0.62 oz

Assuming that the variable has a normal distribution X~N(μ;σ²), the parameter of interest is the average contents of the root beer cans of the Windsor Bottling Company (μ)

The claim is that the population mean content of the cans is different from 12 oz, symbolically: μ ≠ 12

The statistical hypothesis (Null and alternative) have to be complementary, exhaustive and mutually exclusive. The null hypothesis is the "no change" hypothesis and always carries the "=" sign.

If the claim is μ ≠ 12, its complement is μ = 12, the expression carrying the "=" sign will be the null hypothesis and its complement will be the alternative hypothesis:

H₀: μ = 12

H₁: μ ≠ 12

α: 0.05

To test the population mean of this normal population, you have to apply a one sample t-test, with statistic:

t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}

t_{H_0}= \frac{11.4-12}{\frac{0.62}{\sqrt{24} } } = -4.74

This test is two-tailed, using the critical value approach, you have to determine two rejection regions. Meaning, you'll reject the null hypothesis to small values of the statistic or to high values of the statistic.

t_{n-1;\alpha /2}= t_{23;0.025}= -2.069

t_{n-1;1-\alpha /2}= t_{23;0.975}= 2.069

The decision rule is:

If t_{H_0} ≤ -2.069 or if t_{H_0} ≥ 2.069, then you reject the null hypothesis.

If -2.069 < t_{H_0} < 2.069, then you do not reject the null hypothesis.

The value is less than the left critical value, the decision is to reject the null hypothesis.

Then you can say that with a 5% significance level, there is significant evidence to reject the null hypothesis, then the average amount of root beer of the Windsor Bottling Company is different from 12 oz, this means that the claim about the amount of root beer in the cans is correct.

I hope it helps!

6 0
3 years ago
Let F be the function given by f(x)= 2xe^x. Determine the interval(s) on which the graph is concave down.
Vika [28.1K]
Hello,

y=2xe^x
y'=2(e^x+xe^x)=2(x+1)e^x
y''=2(e^x+(x+1)e^x)=2(x+2)e^x

x     |-infinite   -2  0    +infinite
e^x | ++++++++++++++++++
x+2 |------------0 +++++++++++
y''    | -----------0 +++++++++++

y''<0 if x<-2
<span>The interval on which the graph is concave down is (-infinite -2[</span>

7 0
3 years ago
Help me answer this thanks
Doss [256]

Answer:

c = 15 meters

Step-by-step explanation:

This is solveable using the Pythagorean Theorem,

let's say a = 9 and b = 12,

a^2 + b^2 = c^2, so

9^2 + 12^2 = 225 then,

sqrt(225) = 15, so c = 15 m

7 0
3 years ago
Read 2 more answers
Identify the transformation on the figure shown.
Karo-lina-s [1.5K]
Reflection over x axis
C
4 0
3 years ago
Read 2 more answers
Other questions:
  • -<br> Find the perimeter of the figure.<br> 3 in./<br> 4 in.<br> 5<br> in.
    11·1 answer
  • How many four-letter codes can be made if no letter can be used twice?
    15·1 answer
  • I need answers pleaseeeee
    11·2 answers
  • PLEASE HELP!! MATH FINAL :)) no explanation needed.
    7·1 answer
  • Write your answer in simplest form. 1 over 6 - 1 over 8
    12·1 answer
  • What objective function can be used to maximize
    10·2 answers
  • A taxi charges a flat fee of $4.00 plus $2.25 per mile.
    8·2 answers
  • The U.S. government requires that all businesses reduce their energy consumption by
    13·1 answer
  • 50 point question Solve quick i will give branliest
    5·1 answer
  • Find the slope of the line that passes through the pair of points.<br> (11, 7), (−6, 2)
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!