A sample​ mean, sample​ size, and population standard deviation are provided below. Use the​ one-mean z-test to perform the required hypothesis test at the 10​% significance level.
x = 20​, n = 36​, sigma = 9​, H0​: mu = 25​, H a​mu : < 25.

Answer:

The probability that either Alex or Bryan get an A is 0.9

Step-by-step explanation:

Before we proceed to answer, we shall be making some important notation;

Let A = event of Alex getting an A

Let B = event of Bryan getting an A

From the question, P(A) = 0.9, P(B) = 0.8 and P(A ∩ [tex]B^{c}[/tex] ) = 0.1

We are to calculate the probability that either Alex or Bryan get an A which can be represented as P(A ∪ B)

We can use the addition theorem here;

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)  .......................(i)

Also,

P(A) = P(A ∩ [tex]B^{c}[/tex] )  +   P(A ∩ B)   .........................(ii)

We can insert ii into i and we have;

P(A ∪ B) =  P(A ∩ [tex]B^{c}[/tex] )  +   P(A ∩ B)  + P(B) - P(A ∩ B) =   P(A ∩ [tex]B^{c}[/tex] ) + P(B) = 0.1 + 0.8 = 0.9

Answer:

[tex]1<x<3[/tex]

Step-by-step explanation:

Let simplify each of these inequalities individually and then look at where they intersect afterwards

[tex]x+1<4\\\\x<3[/tex]

And

[tex]x-8>-7\\\\x>1[/tex]

This means that for these two inequalities to intersect, x must be greater than 1, but less than 3.

This can be represented by the following inequality [tex]1<x<3[/tex]

Answer:

The answer is D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

y = -5(x) - 4

Step-by-step explanation:

Use the equation of a line and substitution.

Information given:

point 1: (-2,6)

x1 = -2 and y1 = 6

point 2: (0,4)

x2 = 0 and y2 = 4

Equation of a line: y = m(x) + b

m = slope

To find slope, you do the equation of a linear slope, which is:

m = [tex]\frac{rise}{run}[/tex]         in other words   m = [tex]\frac{Y2 - Y1}{X2-X1}[/tex]

plug in your values

[tex]\frac{6-(-4)}{-2-0}[/tex]

= -5

Great, we've found slope, now to find b

plug in the slope you found: y = -5(x) + b

Plug in and solve for each point given, aka (x,y) into the linear equation for both points.

FIRST POINT:

6 = -5(-2) + b

6 = 10 + b

6 - 10 = b

b = -4

SECOND POINT:

-4 = -5(0) + b

-4 = 0 + b

-4 - 0 = b

b = -4

We got -4 for both, meaning that this equation is correct, so if you add in b, your final equation will be y = -5(x) - 4.

Plug this into desmos.com/calculator, and you'll see this linear equation runs through both points given in the problem.

Answer:

f(x)=-5x-4

Step-by-step explanation:

You are given two points (-2, 6) and (0, -4)

Find the slope: m=(-4-6)/[(0-(-2)]=-5

So you have y=-5x+b

next, find the y intercept b.

the y intercept is when x=0. in this case, the y intercept is -4

so the linear function is f(x)=-5x-4

The gradient theorem applies here, because we can find a scalar function f for which ∇ f (or the gradient of f ) is equal to the underlying vector field:

[tex]\nabla f(x,y,z)=\langle2xy,x^2-z^2,-2yz\rangle[/tex]

We have

[tex]\dfrac{\partial f}{\partial x}=2xy\implies f(x,y,z)=x^2y+g(y,z)[/tex]

[tex]\dfrac{\partial f}{\partial y}=x^2-z^2=x^2+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=-z^2\implies g(y,z)=-yz^2+h(z)[/tex]

[tex]\dfrac{\partial f}{\partial z}=-2yz=-2yz+\dfrac{\mathrm dh}{\mathrm dz}\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C[/tex]

where C is an arbitrary constant.

So we found

[tex]f(x,y,z)=x^2y-yz^2+C[/tex]

and by the gradient theorem,

[tex]\displaystyle\int_{(0,0,0)}^{(1,2,3)}\nabla f\cdot\langle\mathrm dx,\mathrm dy,\mathrm dz\rangle=f(1,2,3)-f(0,0,0)=\boxed{-16}[/tex]

Answer:

[tex] m_{fresh}= 1000 \frac{Kg}{m^3} * 2.5x10^{-4} m^3 = 0.25 Kg[/tex]

And we can do a similar procedure for the sea water:

[tex] m_{sea}= \rho_{sea} V_{sea} [/tex]

And after convert the volume to m^3 we got:

[tex] m_{sea}= 1030 \frac{Kg}{m^3} * 1x10^{-4} m^3 = 0.103 Kg[/tex]

And then the density for the mixture would be given by:

[tex] \rho_{mixture}= \frac{m_{fresh} +m_{sea}}{v_{fresh} +v_{sea}}[/tex]

And replacing we got:

[tex] \rho_{mixt}= \frac{0.25 +0.103 Kg}{2.5x10^{-4} m^3 +1x10^{-4} m^3} = 1008.571 \frac{Kg}{m^3}[/tex]

Step-by-step explanation:

For this case we can begin calculating the mass for each type of water:

[tex] m_{fresh}= \rho_{fresh} V_{fresh} [/tex]

And after convert the volume to m^3 we got:

[tex] m_{fresh}= 1000 \frac{Kg}{m^3} * 2.5x10^{-4} m^3 = 0.25 Kg[/tex]

And we can do a similar procedure for the sea water:

[tex] m_{sea}= \rho_{sea} V_{sea} [/tex]

And after convert the volume to m^3 we got:

[tex] m_{sea}= 1030 \frac{Kg}{m^3} * 1x10^{-4} m^3 = 0.103 Kg[/tex]

And then the density for the mixture would be given by:

[tex] \rho_{mixture}= \frac{m_{fresh} +m_{sea}}{v_{fresh} +v_{sea}}[/tex]

And replacing we got:

[tex] \rho_{mixt}= \frac{0.25 +0.103 Kg}{2.5x10^{-4} m^3 +1x10^{-4} m^3} = 1008.571 \frac{Kg}{m^3}[/tex]

If the length of OB was ³/₄, then the length of OB' after dilation is; Option B: 3 units.

What this means is that it was enlarged by a scale factor of 4 with point O as the center of dilation.

Scale factor = new dilated length OB'/(³/₄)

new dilated length OB' = ³/₄ × 4

new dilated length OB' = 3 units

Read more on dilation at; https://brainly.com/question/8532602

Answer:

its 4 units trust just answered it

Step-by-step explanation:

Answer:

a) 3 standard deviations above 16

b) More than 2 standard deviations of the mean, so yes, 22 inches is faw away from the mean of 16 inches.

c) Less than 2 standard deviations, so not far away.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If Z < -2 or Z > 2, X is considered to be far away from the mean.

In this question, we have that:

[tex]\mu = 16[/tex]

​(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 22 inches from 16 ​inches?

This is Z when [tex]X = 22, \sigma = 2[/tex].

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 16}{2}[/tex]

[tex]Z = 3[/tex]

So 22 inches is 3 standard deviations fro 16 inches.

​(b) Is 22 inches far away from a mean of 16 ​inches?

3 standard deviations, more than two, so yes, 22 inches is far away from a mean of 16 inches.

(c) Suppose the standard deviation of the underlying data is 4 inches. Is 22 inches far away from a mean of 16 ​inches?

Now [tex]\sigma = 4[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 16}{4}[/tex]

[tex]Z = 1.5[/tex]

1.5 standard deviations from the mean, so 22 inches is not far away from the mean.

Answer:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Step-by-step explanation:

Information given

[tex]\bar X= 28.1[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma =4.7[/tex] represent the population standard deviation

n=40 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]

And replacing we got:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Answer:

1. B

Step-by-step explanation:

1. We are testing against the null hypothesis which is a single mean that sauce the average load is 0.8A

2. The level of significance is 1% (99% confidence interval)

3. The null hypothesis: u = 0.8

Alternative hypothesis: u =/ 0.8

4. a. The Student's t, since we assume that x has a normal distribution with known σ

5. Using the formula t = (x - u) / σ√n

Where x = 1.22 u = 0.8 σ = 0.44 n = 9

t = (1.22-0.8) / 0.44√9

t = 0.42/(0.44x3)

t = 0.42/1.32

t = 0.318

P value for 0.318 at 1% level of significance at 8 degree of freedom is 0.7586. Since our p value here is greater than 0.01, we can convince that there is not enough statistical evidence that indicate that the Toylot claim of 0.8 A is too low.

Answer:

x = 22

x = 4,6

Step-by-step explanation:

3x - 22 = 44

3x = 44 + 22

3x = 66

x = 66/3

x = 22

5/6 = 10/2x - 3

5/6 + 3 = 10/2x

5/6 + 18/6 = 10/2x

23/6 = 10/2x

23/6 * 2 = 10x

46 = 10x

x = 46/10

x = 4,6

Answer:

x = 9/2

Step-by-step explanation:

(x+3)/6=5/4

(x+3)/6*6=5/4*6

x+3=30/4

x+3-3=30/4-3

x=9/2

Answer:

it is option A

Step-by-step explanation:

Answer:

For a given output value, there is, at most, one input value

Step-by-step explanation:

Given: the concept of function

To find: the statement that best describes the concept of a function

Solution:

A function is a relation in which every value of the domain has a unique image in the codomain.

Input value belongs to the domain and output value belongs to the codomain.

The statement ''For a given output value, there is, at most, one input value'' describes the concept of a function

The statement best describes the concept of a function is

For a given output value, there is, at most, one input value.

A relation is a function when each input has exactly only one output

Domain x is the input and range y is the output

In a function , each input x must have exactly only one output.

Input x cannot have two outputs.

The statement best describes the concept of a function is

For a given output value, there is, at most, one input value.

Learn more information about 'functions' here :

brainly.com/question/1593453

Answer:

the answer you are looking for is D 778

Answer:

i dont really know what it is

Answer:

The car's average 18 number of miles per gallon

Step-by-step explanation:

The car has different efficiencies depending if its used on highway or city streets.

The efficiency on a highway is:

[tex]E_h=\dfrac{350}{15}\;\text{miles/gal}=23.33\;\text{miles/gal}[/tex]

The efficiency for city driving is:

[tex]E_c=\dfrac{280}{18}\;\text{miles/gal}=15.56\;\text{miles/gal}[/tex]

We now that the car uses twice as many gallons for city driving as for highway driving. This means that, for every gallon consumed, 2/3 are for city driving and 1/3 are for highway driving.

Then, we can calculate how many miles makes the car on average as:

[tex]E=\dfrac{1}{3}E_h+\dfrac{2}{3}E_c\\\\\\E=\dfrac{1}{3}\cdot 23.33+\dfrac{2}{3}\cdot15.56=7.78+10.37=18.15\;\text{miles/gal}[/tex]

Answer:

LCM = 75

Step-by-step explanation:

1: Multiply the factor by the greatest number

Description:

The least common  multiple for 75,5,3 is 75.

LCM= Least common Multiple

Please mark brainliest

Hope this helps.

Answer:

75

Step-by-step explanation:

Break each number into prime factors

75 = 25*3 = 5*5*3

5 = 5*1

3 = 3*1

Multiply by the greatest number of each factor

3 = 1 time

5 = =2 times

The least common multiple = 3 * 5*5 = 75

Answer:

452

Step-by-step explanation:

plz mark brainliest!

Answer:

i'll say you have to multiple 9 by 9 than 5 by 5 BUT 23 25 13 and 7 IDK sorry hope i helped :)

Step-by-step explanation:

Answer:

y = -2x + 5

slope = -2

y intercept = 5

Step-by-step explanation:

Slope intercept form of equation of line is given by y = mx + c

where m is the slope of line

c is the y intercept i.e point where given line intersect y axis.

________________________________________________

given equation 4x + 2y = 10

we have to re-write this equation in form y = mx + c

4x + 2y = 10

subtraction 4x from LHS and RHS

4x + 2y - 4x= 10 - 4x

2y = 10- 4x

we have to eliminate 2 from y for that we

divide  LHS and RHS by 2 we

2y /2 = 10/2- 4x/2

y = 5 - 2x

rearranging it in y = mx+c form

y = -2x + 5

thus, m = -2 , c = 5

Answer:

Step-by-step explanation:

Given that:

A small-business Web site contains 100 pages and 60%, 30%, and 10%  of the pages contain low, moderate, and high graphic content, respectively.

. A sample of four pages is selected without replacement,

Let  X and Y denote the number of pages with moderate and high graphics output in the sample

We are meant to determine

a)  [tex]f_{XY}(x, y)[/tex]  from the given data in the question;

However; the probability mass function can be expressed via the relation:

[tex]f_{XY}(x,y) = \dfrac{(^{30} _x ) ( ^{10} _y ) (^{60} _ {4-x-y} ) }{ ( ^{100}_4)}[/tex]

We can now have a table shown as :

[tex]X|Y[/tex]                0           1               2              3              4          Total    [tex]f_X(x)[/tex]

0              0.1244     0.0873     0.02031    0.0018     0.0001   0.234

1               0.2618     0.13542   0.02066    0.00092    0         0.419

2              0.1964     0.0666    0.00499       0              0         0.268

3              0.0621     0.01035     0                 0              0         0.073

4              0.0069       0              0                0              0          0.007

Total [tex]F_Y(y)[/tex]   0.6516   0.2996   0.0460      0.0028  0.0001    1

b) [tex]f_X(x)[/tex]

The marginal distribution definition of [tex]f_X(x)[/tex][tex]= P(X=x)[/tex]

[tex]f_X(x)[/tex] [tex]= \sum P(X=x, Y=y)[/tex]

From the table above ; the corresponding values of [tex]f_X(x)[/tex]  are :

X           0           1         2          3           4

[tex]f_X(x)[/tex]    0.234   0.419  0.268   0.073    0.007

( since [tex]f_X(x)[/tex] represent the vertical column)

c) E(X)

By using the expression [tex]E(x) = \sum ^4 _{x= 0} x f_X(x)[/tex]

we have:

E(X) = [tex]0*0.234+1*0.419+ 2*0.268+3*0.073+4*0.007[/tex]

E(X) = 0 + 0.419 + 0.536 + 0.218 + 0.028

E(X) = 1.202

d) fyß(y)

Using the thesis of conditional Probability; we have :

[tex]P(A|B) = \dfrac{ P(A,B) }{ P(B) }[/tex]

The conditional probability for the mass function is then:

[tex]f_{Y|X=3}(y) = \dfrac{f_{XY}(3,y)}{f_{X}(x)}[/tex]

where;

[tex]f_X(3) = 0.0725[/tex]

values of [tex]f_{XY} (3,y)[/tex] for every y ∈ (0,1,2,3,4)

Therefore; the mass function is:

[tex]Y|{_X_3}:\left[\begin{array}{ccccc}0&1&2&3&4\\0.857&0.143&0&0&0\\ \end{array}\right][/tex]

e) E(Y | X = 3)

By using the expression [tex]E(Y|X=3) = \sum ^4 _{y= 0} y f_{y \beta} \ (y|x)[/tex]

we have:

⇒ [tex]0 * 0.857 + 1*0.143 +0 +0+0[/tex]

= 0.143

The value of E(Y | X = 3) = 0.143

g) Are X and Y independent?

To Check if X and Y independent; Let assume if [tex]f_{XY}(x,y) = f_X(x)f_{Y}(y)[/tex] ; then we can say that X and Y are independent.

From the above previous table :

[tex]f_{(XY)} (0.4) = 0.0001[/tex]

[tex]f_X (0)[/tex] = 0.1244 + 0.087268+0.02031+ 0.001836 + 0.0001

[tex]f_X (0)[/tex]  = 0.234

[tex]f_X (4)=0.0001 +0+0 \\ \\ = 0.001[/tex]

[tex]f_{X}(0) f_Y(4) = 0.234*0.0001[/tex]

[tex]f_{X}(0) f_Y(4) = 0.00002[/tex]

We conclude that [tex]f_{(XY)} (0.4) \neq f_X(0) f_Y(y)[/tex]; As such X and Y are said to be  non - independent.

Answer:

A) 0.026

B) 0.130

Step-by-step explanation:

Complete Question

A factory received a shipment of 10 generators and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.

(A) If a sample of 4 generators is selected, find the probability that all in the sample are defective.

(B) If a sample of 4 generators is selected, find the probability that none in the sample is defective.

Solution

A) This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of generators to be picked = 4

x = Number of successes required = number of defective generators required = 4

p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40

q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60

P(X = 4) = ⁴C₄ (0.40)⁴ (0.6)⁴⁻⁴ = 0.0256 = 0.026 to 3 d.p.

B) n = total number of sample spaces = number of generators to be picked = 4

x = Number of successes required = number of defective generators required = 0

p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40

q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60

P(X = 0) = ⁴C₀ (0.40)⁰ (0.6)⁴⁻⁰ = 0.1296 = 0.130 to 3 d.p.

Hope this Helps!!!

Answer:

96

Step-by-step explanation:

60% * 160 = 0.6 * 160 = 96.

Answer:

None

Step-by-step explanation:

There is no Forest Green iPhone XR's only the 11 Pros have that color.

Answer:

Step-by-step explanation:

To be able to draw a conclusion from the data given, lets find out the p value using the t score and this will be used to make a conclusion.

If the p value is less than 0.05 then, we will reject the null but if otherwise we will fail to reject the null.

Using a p value calculator with a t score of 2.83, significance level 0.05 and the test is a two tailed test, the p value is 0.004655 which is less than 0.05 and the result is significant.

This we will reject the null hypothesis H0:p∗=1/2 for this data set.

Answer:

Step-by-step explanation:

The given data is expressed as

1204, 1206, 1345, 1306, 1207, 1078, 1357, 1232, 1228, 1302, 1189, 1177, 1083, 1094, 1326, 1071, 1427, 1348, 1420, 1253, 1270

The number of items in the data, n is 21. The lowest value is 1071 while the highest value is 1427. The convenient starting point would be 1070.5 and the convenient ending point would be 1427.5

The number of class intervals is

√n = √21 = 4.5

Approximately 5

The width of each class interval is

(1427.5 - 1070.5)/5 = 72

The end of each class interval would be

1070.5 + 72 = 1142.5

1142.5 + 72 = 1214.5

1214.5 + 72 = 1286.5

1286.5 + 72 = 1358.5

1358.5 + 72 = 1430.5

The frequency for the fifth class, that is between 1358.5 to 1430.5 would be 2

Answer:

A

Step-by-step explanation:

Volume of cone = (1/3) πr²h

Answer:

If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.

Step-by-step explanation:

We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:

[tex]N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10[/tex]

We can calculate the probability that a random person has both high blood pressure and high cholesterol as:

[tex]P(\text{HBP and HC})=\dfrac{10}{40}=0.25[/tex]

Answer:Please include images of the graphs!

Step-by-step explanation:

Look at each graph given. Ensure that there is a line, and that you can locate two points on the line given.

Use the following equation to get the slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Note that you can obtain the numbers for the equation by getting two points on the number line. Plug in the numbers by variables:

(x₁ , y₁) & (x₂ , y₂)

In this equation, make sure that the slope (m) will equal 1/4 (given).

The full equation that you will use is:

1/4 =  (y₂ - y₁)/(x₂ - x₁)

Find the graph that will satisfy this equation.

Answer:

Step-by-step explanation:

There are no factors outside the parentheses that need to be distributed, so the parentheses can be simply dropped:

  6 -2x +15 -3x

The terms can be rearranged to put like terms next to each other:

  -2x -3x +6 +15

and the like terms can be combined.

  -5x +21 . . . . simplified expression

__

Put the value of x where x is, then do the arithmetic.

  -5(-0.2) +21 = 1 +21 = 22