Really easy math question!

Answer:

Option d

Step-by-step explanation:

The p-value is 0.0516 which is not statistically significant to reject the null hypothesis. Thus we will fail to reject the null hypothesis.

Answer:

Step-by-step explanation:

(a)

The distribution of X is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance [tex]= \sigma^{2} = 16 \ i.e., X \sim N (17, 16),[/tex]

(b)

The distribution of [tex]\bar{x}[/tex] is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance = [tex]\sigma^{2}/n = 16/15= 1.0667[/tex].i.e., [tex]\bar{x}\sim N(17,1.0667)[/tex]

c)

To find P(15.5 < X < 18):

Case 1: For X from 15.5 to mid value:

Z = (15.5 - 17)/4 = - 0.375

Table of Area Under Standard Normal Curve gives area = 0.1480

Case 2: For X from mid value to 18:

Z = (18 - 17)/4 = 0.25

Table of Area Under Standard Normal Curve gives area = 0.0987

So,

P(15.5 < X< 18) = 0.1480 +0.0987 = 0.2467

So,

Answer is:

0.2467

(d)

[tex]SE = \sigma/\sqrt{n}\\\\= 4/\sqrt{15}[/tex]

= 1.0328

To find [tex]P(15.5 < \bar{x}< 18):[/tex]

Case 1: For [tex]\bar{x}[/tex] from 15.5 to mid value:

Z = (15.5 - 17)/1.0328 = - 1.4524

Table of Area Under Standard Normal Curve gives area = 0.4265

Case 2: For X from mid value to 18:

Z = (18 - 17)/1.0328 = 0.9682

Table of Area Under Standard Normal Curve gives area = 0.3340

So,

[tex]P(15.5 < \bar{x}< 18) = 0.4265 + 0.3340 = 0.7605[/tex]

So,

Answer is:

0.7605

(e)

Correct option:

No

because Population SD is provided.

(f)

(i)

Q1 is given by:

[tex]- 0.6745 = (\bar{x} - 17)/1.0328[/tex]

So,

X = 17 - (0.6745 * 1.0328) = 17 - 0.6966 = 16.3034

So,

Q1 = 16.3034

(ii)

Q3 is given by:

[tex]0.6745 = (\bar{x} - 17)/1.0328[/tex]

So,

X = 17 + (0.6745 * 1.0328) = 17 + 0.6966 = 17.6966

So,

Q3= 17.6966

(iii)

IQR = Q3 - Q1 = 17.6966 - 16.3034 = 1.3932

So

Answers are:

Q1 = 16.3034 ounces

Q3 = 17.6966 Ounces

IQR = 1.3932 Ounces

Answer:

The answer is 2

From the function when the input is 2 the output is -7. The inverse reverses the order so the input will be -7 and the output will be 2.

[tex]answer \\ = 2 , 4 , 5 \\ additional \: information \\ let \: r \: be \: a \: relation \: a \: to \: b. \: then \: the \: set \\ of \: first \: components \: or \: the \: set \: of \: \\ elements \: of \: a \: are \: called \: domain \\ and \: the \: set \: of \: second \: components \\ or \: the \: set \: of \: elements \: of \: b \: are \: called \: the \: range. \\ hope \: it \: helps[/tex]

Answer: (-6, 0)

Step-by-step explanation:

X-intercepts of equations are any points on the equation that lie on the x-axis, or the horizontal line "y = 0".

In order to find the x-intercept of an equation, find the points that will satisfy the equation "y = 0":

y = (x + 6)(x - 3)

y = 0

(x + 6)(x - 3) = 0

With this equation, you can find which points lie on the x-axis.

When x = -6, the equation is: 0 * -9 = 0, which is correct.

When x = 3, the equation is 9 * 0 = 0, which is correct.

Make sure you're picking the correct coordinate out of the answer choices.

The x-coordinates are -6 and 3, and the y-coordinates are 0, because the points lie on the x-axis.

The correct answer is (-6, 0).

(3, 0) is also correct, but the question does not require it.

Answer:

D

Step-by-step explanation:

Answer:

12x^3 - 3x + 4

Im 100% percent sure and if you  are kind enough, I’d love a BRAINLIEST :)

Answer:

16

Step-by-step explanation:

The range is the difference between the highest and lowest number of a data set. 22-6=16

Answer:

Step-by-step explanation:

a. The sample size for the poll would be at most 10% of the total readers of the tennessean.

b. Categorical data...data collected in groups or categories.

c. Yes it would make more sense to use percentages as this gives a better estimate for proportion.

d. The number of individual that provided this response is 67% of the sample size (which is at most 10% of the total population of readers of the online newspaper).

Answer:

4, 8, 16,64 and 4096.

Step-by-step explanation:

We are already given: [tex]4096=2^{12}[/tex]

To determine other whole numbers that can be raised to a power to obtain 4096, we apply the product rule of indices.

Product Rule of Indices: [tex]a^{xy}=(a^x)^y[/tex]

Now 12 can be factored in the following ways where one of the terms must be a perfect square:

[tex]2^{12}=(2^2)^6=4^6\\\\2^{12}=(2^6)^2=64^2\\\\2^{12}=(2^4)^3=16^3\\\\2^{12}=(2^3)^4=(8^2)^2=8^{2*2}=8^4\\\\2^{12}=(2^{12})^1=4096^1 $(This is the trivial case)[/tex]

Therefore, the other whole numbers that can be raised tp a power to obtain 4096 are: 4, 8, 16, 64 and 4096.

Answer:

The answer is 2.5ft².

Step-by-step explanation:

Given that the area of trapezoid formula is A = 1/2×(a+b)×h where a and b is the length and h is the height. Then substitute the following values into the formula :

[tex]area = \frac{1}{2} \times (a + b) \times h[/tex]

Let a = 1.2,

Let b = 0.8,

Let c = 2.5,

[tex]area = \frac{1}{2} \times (1.2 + 0.8) \times 2.5[/tex]

[tex]area = \frac{1}{2} \times 2 \times 2.5[/tex]

[tex]area = 2.5 {feet}^{2} [/tex]

Answer:

24π

Step-by-step explanation:

If the diameter is 4, the radius is 2

V = [tex]\pi r^2 *h[/tex]

r = 2

h = 6

24π

Answer:

Step-by-step explanation:

diameter: 4 inch (Radius is 2)

V

If the diameter is 4, the radius is 2

V is  r^2*h

the radius is 6

so it’s 24

Answer:

C. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale

Step-by-step explanation:

Th Coefficient of Variance is a measure of dispersion that can be calculated using the formula:

[tex]CV = \frac{\sigma_{x} }{\mu_{x} } * 100%[/tex]

Where [tex]\sigma{x}[/tex] is the Standard Deviation

and [tex]\mu_{x}[/tex] is the sample mean

From the formula written above, it is shown that the Coefficient of Variation expresses the Standard Deviation as a percentage of the mean.

Coefficient of variation can be used to compare positive as well as negative data on the ratio and interval scale, it is not only used for positive data.

The Interquartile Range is not a measure of central tendency, it is a measure of dispersion.

To get the total fee, you need to multiply the hourly rate by number of hours worked and add that to the flat fee of $25.

The equation would be y = 40x + 25

Answer:

  a.  235°

  b. 146.03 km

  c. 105 km

  d. 193 km

Step-by-step explanation:

a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:

  bearing of A from E = 55° +180° = 235°

__

b. The internal angle at E is the difference between the external angle at C and the internal angle at A:

  ∠E = 134° -55° = 79°

The law of sines tells you ...

  CE/sin(∠A) = CA/sin(∠E)

  CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km

  CE ≈ 146 km

__

c. The internal angle at C is the supplement of the external angle, so is ...

  ∠C = 180° -134° = 46°

The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:

  Sin = Opposite/Hypotenuse

  sin(46°) = PE/CE

  PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km

  PE ≈ 105 km

__

d. DE can be found from the law of cosines:

  DE² = DC² +CE² -2·DC·CE·cos(134°)

  DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43

  DE = √37099.43 ≈ 192.6 . . . km

  DE is about 193 km

Answer: The systems of equations have only one solution because if x 4 then y is equal to 3 which  proves it that is a one solution graph.

Step-by-step explanation:

2(4)- y = 5

8 - y= 5

-8      -8

-1y= -3

y= 3

Answer:

Mason reads the fastest

Answer:

c

Step-by-step explanation:

try to see how much every person reads every one or two minutes.

Charlie: 350 in two min

Mason :400 in two min

Sarah: 450 in two min (the middle of 300-600 is 450)

so between the three Sarah wins.

now Reilly is a bit more difficult but you can see that she read 4000 in 20 min. so if we divide it by 10 we can see she reads 400 in 2 min. and therefore Sarah os the winner.

Answer:

q

Step-by-step explanation:

Since AB is a transversal of the two parallel lines, the angle with measure 135 degrees and angle q are vertical angles. Therefore, their measure must be equal.

Hope this helps!

Answer:

199

Step-by-step explanation:

i dont know

Answer:

A. 90 sq. units

Step-by-step explanation:

5(18) = 90

Answer:

1651

Step-by-step explanation:

let s say that the price before the increase is x

to apply an increase of 9% it does x + x*0.09 = x*(1+0.09)=x*1.09

and we know that this value is 1800

so

x*1.09=1800

<=>

x = 1800/1.09=1651.376147

to the nearest penny it gives 1651

Answer:

Hello!

Answer: 1651

I hope that was correct.  Please let me know, thank you!

Step-by-step explanation:

Answer:

  0.5 units

Step-by-step explanation:

The dilation factor is ...

  (GZ')/(GZ) = (GZ')/(GZ' +Z'Z) = 1.5/(1.5 +7.5) = 1/6

Side WX is 3 units, so side W'X' is (1/6)(3 units) = 1/2 units

W'X' is 0.5 units.

Answer:

It is .5 on edge

Step-by-step explanation:

I took the test

Answer:

The solution set is x = 1 and x = -2

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

For every additional 10 hrs, you get 200 more dollars.

Answer:

valarie had 28 pencils , she gave 15 pencils away to people. How many pencils will she have left?

Step-by-step explanation:

hope this helps:)

Answer:

Option (B).

Step-by-step explanation:

From the table shown in the figure attached,

There is a common difference of 5 in every successive and previous term, so the relation is a linear relation.

Let the equation representing the relation is,

y - y' = m(x - x')

where m = slope of the line

Now we choose two ordered pairs from the table,

Let the points are (10, 54) and (11, 59)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

      m = [tex]\frac{59-54}{11-10}[/tex]

      m = 5

Now the equation of of the line passing through (10, 54) and slope = 5

y - 54 = 5(x - 10)

y - 54 = 5x - 50

y = 5x - 50 + 54

y = 5x + 4

By substituting the values of x and y from the ordered pairs given in the options we find option B satisfies the equation.

For (2, 14),

14 = 5×2 + 4

14 =  14 [True]

For (3, 19),

19 = 5×3 + 4

19 = 19 [True]

Therefore, option (B) will be the answer.

Answer:

-14a^2b-42ab^2+56abc

Step-by-step explanation:

You can use the FOIL method

multiply the first numbers

then inner

then outer

then last

Answer:

33.2

Step-by-step explanation:

70−30+2−9+0.3−0.1

=40+2−9+0.3−0.1

=40+−7+0.3−0.1

=33+0.3−0.1

=33+0.2

=33.2

Answer:

33.2

Step-by-step explanation

If we start from the left and work our way right:

70+(-30) is the same as 70-30 which would give 40

2+(-9) is the same as 2-9 which would give -7

0.3(-0.1) is the same as 0.3-0.1 which would give 0.2

now if you put them together

40-7+.2 gives 33.2

Answer:

Step-by-step explanation:

Hello!

There are two values of n in the text, I'll use the one that appears in all the questions.

The variable of interest is

X: pollutants found in waterways near large cities. (ppm)

This variable has a normal distribution with parameters μ= 9ppm and σ= 1.5ppm

1) X~N(μ;σ²)

X~N(9;2.25)

2) The distribution of the sample mean is X~N(μ;σ²/n)

σ²/n= 2.25/37= 0.06

X~N(9;0.06)

3) P(X>9.6)

To calculate this probability you have to use the standard normal distribution. Using the population parameters, you can calculate the corresponding Z value:

Z= (X-μ)/σ= (9.6-9)/1.5= 0.4

P(Z>0.4)= 1-P(Z≤0.4)= 1 - 0.65542= 0.34458

The probability of selecting a city at random and finding 9.6ppm pollutants.

4) In this item, instead of calculating the probability of one value of the variable you have to calculate the probability of the sample average taking a determined value. Because of this, you have to work using the distribution of the sample mean, instead of the distribution of the variable.

P(X[bar]>9.6)

Z= (X[bar]-μ)/(σ/√n)= (9.6-9)/√0.06= 2.45

P(Z>2.45)= 1 - P(Z≤2.45)= 1 - 0.99286= 0.00714

5) The assumption of a normal distribution is not necessary for item 4. Since the sample size is large enough (greater than 30) you can apply the central limit theorem and approximate the distribution of the sample mean to normal, regarding the distribution of the original variable.

6)

In this case, you have to work starting with the standard normal distribution and then "translate" the Z values into values of the average amount of pollutants.

The first quartile divides the bottom 25% of the distribution from the top 75%, symbolically:

P(Z≤z₁)= 0.25

z₁= -0.674

z₁= (X[bar]-μ)/(σ/√n)

z₁*(√n/σ)=X[bar]-μ

X[bar]=z₁*(√n/σ)+μ

X[bar]=(-0.674)*(√37/1.5)+9= 6.27ppm

The third quartile divides the bottom 75% of the distribution from the top 25%, symbolically:

P(Z≤z₂)= 0.75

z₂= 0.674

z₂= (X[bar]-μ)/(σ/√n)

z₂*(√n/σ)=X[bar]-μ

X[bar]=z₂*(√n/σ)+μ

X[bar]=(0.674)*(√37/1.5)+9= 11.7.3ppm

IQR= Q₃-Q₁= 11.73-6.27= 5.46ppm

I hope this helps!

Answer:

80% or 4/5

Step-by-step explanation:

the probability of not choosing a black shirt

P = number of shirts that are not black ÷ total number of shirts

Total number of shirts = 10

Number of black shirts = 2

Number of shirts that are not black = 10-2 = 8

P = 8/10 = 4/5 or 80%

Answer:

The quarterly growth rate in revenues is significantly different from 1.2%.

b. 2,666,858

Step-by-step explanation:

Given that:

The regression equation can be represented as :

[tex]log_{10} \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3[/tex]

In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.02.

The null and alternative hypothesis can be stated as;

[tex]H_0:[/tex]    The quarterly growth rate in revenues is not significantly different from 1.2%.

[tex]H_a:[/tex]   The quarterly growth rate in revenues is significantly different from 1.2%.

The decision rule is to reject the null hypothesis if the p-value is less than 0.05.

From above ; the p-value = 0.02 which is less than 0.05.

Conclusion:

Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e

The quarterly growth rate in revenues is significantly different from 1.2%.

b.

Since [tex]Q_1=Q_2=Q_3 = 0[/tex] ; X = 27

Thus ;

[tex]log_{10} \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3[/tex]

[tex]log_{10} \hat Y= 6.102+0.012 (27)[/tex]

[tex]\hat Y=10^{ 6.102+0.012 (27) }[/tex]

[tex]\hat Y =[/tex] 2666858.665

[tex]\hat Y =[/tex]  2,666,858