Find the domain and range of the relation

According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, we have that:

As the test involves a comparison of samples, it involves subtraction of normal variables, and for this, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Before:

Average of 0.250 in 56 at bats, so:

[tex]p_B = 0.25[/tex]

[tex]s_B = \sqrt{\frac{0.25*0.75}{56}} = 0.0579[/tex]

After:

Average of 0.44 in 25 at bats, so:

[tex]p_A = 0.44[/tex]

[tex]s_A = \sqrt{\frac{0.44*0.56}{25}} = 0.0993[/tex]

Test if there was improvement:

At the null hypothesis, we test if there was no improvement, that is, the subtraction of the proportions is 0:

[tex]H_0: p_A - p_B = 0[/tex]

At the alternative hypothesis, we test if there was improvement, that is, the subtraction of the proportions is positive, so:

[tex]H_1: p_A - p_B > 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_B - p_A = 0.44 - 0.25 = 0.19[/tex]

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0579^2 + 0.0993^2} = 0.1149[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.19 - 0}{0.1149}[/tex]

[tex]z = 1.65[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.

Looking at the z-table, z = 1.65 has a p-value of 0.9505.

1 - 0.9505 = 0.0495.

The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.

A similar question is found at https://brainly.com/question/23827843

Answer:

b=a/2

c=a/2

b=c

a=2b and a=2c

Answer:

The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 50 - 1 = 49

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0096

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0096\frac{3.8}{\sqrt{50}} = 1.1[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 5.1 - 1.1 = 4

The upper end of the interval is the sample mean added to M. So it is 5.1 + 1.1 = 6.2.

The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).

Answer:

x = -1/2

Step-by-step explanation:

We are given:

[tex]\frac{1}{3}=\frac{4x}{3}+1[/tex]

Subtract 1 on both sides:

[tex]-\frac{2}{3}=\frac{4x}{3}[/tex]

Then, multiply 3 on both sides:

[tex]-2=4x[/tex]

Finally, divide 4 on both sides:

[tex]-\frac{1}{2}=x[/tex]

Answer:

y = 2x - 5

Step-by-step explanation:

[tex]y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5[/tex]

Answer:

(0,4)  will be point (P) at 3 because,

Step-by-step explanation:

by using newton interpolation method we can find P(0,4) at 3 .

Answer:

9 − (3 x 2) ÷ 3 + 6 is the answer

Answer:

3 pants are $20.55

4 shirts are $47.9

Step-by-step explanation:

a pant is $6.85 × 3= $20.55

68.45 - 20.55 = $47.9

$47.9 ÷ 4 = $11.98 a shirt

Answer:

Surface area of prism is 48km^2

A quotient is found by dividing two numbers and a quotient with a denominator of zero is infinity which is not a real number

The word that complete the sentence is therefore;

Each quotient must have a nonzero denominator

The reason by which the above word is selected is as follows;

The set of Real Numbers include;

Rational numbers; a/b, where b = nonzero number

Integers; Positive and negative whole numbers, including zero

Whole numbers; 0, 1, 2

Natural numbers; Positive whole numbers excluding zero

Irrational number; Numbers that cannot be expressed as a/b

A quotient is the outcome of dividing two numbers, x by y

Therefore;

Quotient = x/y

A quotient can be a rational or irrational number, however, a quotient that has a denominator of zero (y = 0) is infinity, which is not a real number

When y = 0, x/y = x/0 = ∞ (∞ is not a real number)

Therefore, from the properties of Real Numbers,

Each quotient must have a nonzero denominator to be a Real Number

Learn more about Real Numbers here;

https://brainly.com/question/11030818

Answer:

12

Step-by-step explanation:

Answer:

A) [tex]\$\ 2932.5[/tex]

Step-by-step explanation:

One is given that a certain amount of money was allotted to be spent on supplies. However, there was a discount applied to the purchase. One is asked to find the amount of money actually spent on the supplies.

$3450 was the initial price that was to be spent on supplies, however, a (15%) discount was applied to this price. Subtract (15) from (100) to find the percent value that was actually spent on supplies.

[tex]100-15=85[/tex]

(85%) of the allotted money was actually spent on supplies. Now one has to find out the numerical value of the amount spent. Divide (85) by (100) and then multiply it by the amount of money allotted to the purchase, to fin the amount actually spent on the purchase.

[tex]3450*(\frac{85}{100})\\\\=3450*0.85\\\\=2932.5[/tex]

Answer:

Micheal will have 6 logs.

Step-by-step explanation:

Each log will divide into two pieces,so.

3×2= 6

Answer:

first... You think and Conceptualize

A diameter divides a circle into equal halves

We're given the end points of the Diameter.

With this we can fine the Center of the circle.

The End Points are

(-6, -1) and ( 2, 3)

Half-way through the diameter gives the center of the circle

So We'd apply the Mid-Point formula to get the co-ordinate of the center.

X= x₁ + x₂/2 , Y = y₁ + y₂/2

X = -6 + 2/2, Y = -1 + 3/2

X= -2. Y = 1

The Midpoint is (-2, 1)

The Radius would be the distance between the center and a point on the circumference.

We already have 2 points of the circumference (Which are the endpoints of the diameter).

So we can pick any of them arbitrarily.

I'd go with (2,3)

So We'd apply the distance between Points formula to get the magnitude of the radius

(-2,1) (2,3)

D = √(x₁ - x₂)² + (y₁ - y₂)²

D = √(-2-2)² + (1-3)²

D=√(-4)² + (-2)²

D=√20.

Our Radius is √20.

Equation of Circle =

(x-h)² + (y-k)² = r²

Where h and k are the center of the circle(-2,1)

(x-(-2))² + ( y - 1 )²= (√20)²

(x + 2)² + ( y - 1)² = 20

Our Answer

(x + 2)² + (y - 1)² = 20.

This should be it.

Have a great day!

Answer:

2 years

Step-by-step explanation:

population in 1 year= 24400*105%=25620

population in 2 year= 25620*105%=26901

Step-by-step explanation:

Let adults = a and children = c,

(1) a + c = 1100

(2) 48a + 23c = 45300

From the (1) equation, a = 1100 - c

Then substitute a = 1100 - c into (2),

48(1100 - c) + 23c = 45300

52800 - 48c +23c = 45300

-25c = -7500

c = 300

Substitute c = 1500 into a = 1100 - c,

a = 1100 - 300

a = 800

Therefore, 800 adults and 300 children bought the tickets

Equate what is inside cosine with [tex]2\pi[/tex], base period and solve for x,

[tex]2\pi=\frac{\pi}{3}x[/tex]

[tex]6\pi=\pi x[/tex]

[tex]\boxed{x=6}[/tex]

Hope this helps :)

Answer:

-55.5+12.9c

Step-by-step explanation:

-55.5 — -8.55c +4.35c

Subtracting a negative is like adding

-55.5 +8.55c +4.35c

Combine like terms

-55.5          +8.55c +4.35c

-55.5          +12.9c

Answer:

5+4 = 9

6+4 = 10

7+4 =11

Step-by-step explanation:

Answer:

(5,9)

(6,10)

(7,11)

Step-by-step explanation:

w = m + 4

when m = 5,

w = 5 + 4 = 9

when m = 6

w = 6 + 4 = 10

when m = 7

w = 7 + 4 = 11

Answer:

a. Less than $471

Step-by-step explanation:

The total price must be less than $578.10.

Let the price of the 4 tires = x.

He pays 10% tax on x. That means he pays x + 10%x = 1.1x including tax.

Then he pays the $60 fee.

He pays a total of 1.1x + 60

That must be less than $578.10

1.1x + 60 < 578.10

Subtract 60 rom both sides.

1.1x < 518.1

Divide both sides by 1.1

x < 471

Answer: a. Less than $471

Answer:

D

Step-by-step explanation:

since

cos(2x) = 1 - 2×sin²(x)

and for x near 0, sin(x) is very similar to x.

Answer:

y = 4x -1.5

Step-by-step explanation:

The slope intercept form of a line is given by

y = mx+b  where m is the slope and b is the y intercept

y = 4x -1.5

Answer.

ANSWER

.......

Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing.

A control experiment can be defined as a type of experiment in which a condition assumed to be a probable cause of an effect is compared with the same situation without involving or using the suspected condition.

A treatment group refers to a group of participants in an experiment that are exposed to some manipulation in the independent variable such as an administration of medication to a particular group.

Thus, Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing because the treatment group show reduced signs of sneezing.

Read more on an experiment here: https://brainly.com/question/17542127

9514 1404 393

Answer:

  {x ∈ ℝ | x ≤ 3}

Step-by-step explanation:

Subtracting 5 from both sides, we see the solution is ...

  x ≤ 3

In set notation, this can be written ...

  {x ∈ ℝ | x ≤ 3}

N is the midpoint of MO and NO is 5, so MN would also be 5

MP = MN + NP = 5 + 9 = 14

Answer:

cannot understand the language man

but please follow