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Artyom0805 [142]
3 years ago
10

What is the domain of the function f(x) = 3|x + 4| + 1? all real numbers all real numbers less than or equal to −4 all real numb

ers greater than or equal to 1 all real numbers greater than or equal to −4
Mathematics
2 answers:
olganol [36]3 years ago
3 0
All real numbers..................<span />
MrRa [10]3 years ago
3 0

Answer:

The correct option is A.

Step-by-step explanation:

The vertex form of an absolute function is

g(x)=a|x-h|+k

Where, (h,k) is vertex.

Domain is the set of input values.

The given function is

f(x)=3|x+4|+1

It is the vertex from of an absolute function. Here h=-4 and k=1, so the vertex of the function is (-4,1).

These functions are defined for all real values of x. So, the domain of the given absolute function is all real numbers

Therefore the correct option is A.

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A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages ar
Elenna [48]

Answer:

We conclude that the mean amount packaged is equal to 8.17 ounces.

Step-by-step explanation:

We are given that in a particular sample of 50 packages, the mean amount dispensed is 8.171 ​ounces, with a sample standard deviation of 0.052 ounces.

Let \mu = <u><em>population mean amount packaged. </em></u>

So, Null Hypothesis, H_0 : \mu = 8.17 ounces    {means that the mean amount packaged is equal to 8.17 ounces}

Alternate Hypothesis, H_A : \mu\neq 8.17 ounces    {means that the mean amount packaged is different from 8.17 ounces}

The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;

                               T.S.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~  t_n_-_1

where, \bar X = sample mean amount dispensed = 8.171 ounces

             s = sample standard deviation = 0.052 ounces

            n = sample of packages = 50

So, <u><em>the test statistics</em></u> =  \frac{8.171-8.17}{\frac{0.052}{\sqrt{50} } }  ~   t_4_9

                                    =  0.1359  

The value of t-test statistics is 0.1359.

<u>Also, the P-value of test-statistics is given by;</u>

the meaning of the​ p-value is that the p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounces away from8.17 if the null hypothesis is true.

                    P-value = P( t_4_9 > 0.136) = More than 40% {from the t-table}

Since the P-value of our test statistics is more than the level of significance of 0.01, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.

Therefore, we conclude that the mean amount packaged is equal to 8.17 ounces.

6 0
3 years ago
About 79,000 people live in a circular region with a population density of about 513 people per square mile. Find the radius of
Natalija [7]

To solve this problem, let us first assign some variables. Let us say that:

d = represents the population density of the circular region (in units of 513 people per square mile)

p = represents the population of the circular region (in units of people)

r = is the radius of the circular region

 

Now we can see that if we divide p by d, we can get a value which has a units of square mile. Thus the area of the region, hence:

Area = 79,000 people / (513 people per square mile)

Area = 154 square mile

 

The area of a circle has the formula:

Area = π r^2

Therefore calculating for r:

154 square mile = π r^2

r = 7 miles            (ANSWER)

5 0
3 years ago
What’s the vertical and horizontal line?
coldgirl [10]

Answer:

Part 1) Vertical line : x=1

Part 2) Horizontal line :  y=-4

Step-by-step explanation:

Part 1) Write the equation for the vertical line passing through the point (1,-4)

we know that

The equation of a vertical line (parallel to the y-axis) is equal to the x-coordinate of the point that passes through it

so

The x-coordinate is 1

therefore

The equation of the line is

x=1

Part 2) Write the equation for the horizontal line passing through the point (1,-4)

we know that

The equation of a horizontal line (parallel to the x-axis) is equal to the y-coordinate of the point that passes through it

so

The y-coordinate is -4

therefore

The equation of the line is

y=-4

5 0
3 years ago
Find the value of x.
Jet001 [13]

Answer:

Value of x=-12

Step-by-step explanation:

The given triangle is isosceles

Here

m\angle2+m\angle2+36^0=180^0\\\\2m\angle2=144^0\\\\m\angle2=72^0\\\\x+84=72\\\\x=72-84\\\\=-12

3 0
2 years ago
Two functions f and g are defined on the set R, of real numbers by f : x  2x  3 and
iren2701 [21]

Answer:8

Step-by-step explanation:

3 0
2 years ago
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