problem 1. monthly sales are independent normal random variables with mean 120 and standard deviation 5. (a) find the probability that exactly 4 of the next 6 months have sales greater than 120. (b) find the probability that the total of the sales in the next 4 months is greater than 500.

The probability that these events when we randomly select a permutation is  24, 1/2, 1/2, 1/3, 1/4, 1/4

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

P(A) = n(A)/n (S)

The probability of an event "A" is P(A). The number of successful outcomes is n(A). The total number of events in the sample space is denoted by n(S).

1)  From the set we can select 4*3*2*1=24 permutations.

2) There are six permutations that begin with 1, three that begin with 2, three that begin with 3, and no permutations that begin with 4 when 1 comes before 4. So, P1 ={ 6+3+3+0}/{24} = 1/2

3) No permutations begin with 1, three permutations begin with 2, three permutations begin with 3, and six permutations begin with 4, where 4 comes before 1. P2=1/2 

4) There are no permutations that begin with 1, no permutations that begin with 2, no permutations that begin with 2, no permutations that begin with 3, and six permutations that begin with 4, where 4 comes before both 1 and 2. Therefore, P 3 = 1/3

​5) No permutations begin with 1, no permutations begin with 2, no permutations begin with 3, and there are six permutations that begin with 4, where 4 comes before 1, 2, and 3. So, P4= 1/4

​6) There are no combinations that begin with 1, three combinations that begin with 2, no combinations that begin with 3, and three combinations that begin with 4, where 4 comes before 3 and 2 comes before 1. So, P5= 1/4

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Answer:

there will be 3 carrots in each bag and you will have 2 carrots left over

Step-by-step explanation:

hope this helps

The 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.

The confidence interval for a statistical data is written as-

(x+ zr/√n, x- zr/√n)

Here, we are given that-

Mean ⇒ x = 27.5 mi/gallon.

Standard deviation ⇒ r = 4 mi/gallon

Number of samples ⇒ n = 49

and Confidence interval = 95%

z-score at 95% confidence level = 2.17

Substituting the values we have;

= [27.5 - 2.17(4.0) /(√49),  27.5 + 2.17(4.0) /(√49)]

= (27.5 - 8.68 / 7,  27.5 + 8.68 / 7)

= (27.5 - 1.24,  27.5 + 1.24)

= ( 26.26, 28.74)

Therefore, the 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.

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229.5 miles separate point A from point C

What is the short definition of cosine law?

According to a trigonometrical rule, the square of a side in a plane triangle is equal to the sum of the squares of the other sides minus twice that amount plus the cosine of the angle between the other two sides.

Given:

Angle AB = 370 miles 24 degrees is A.

Angle BC = 240 miles 37 degrees is B.

Since we have two angles and two sides of a regular triangle, we can apply the cosine law to calculate the distance between points A and C.

Angle B, which is 37 degrees, is the angle opposite side AC.

(AC)^2 =(AB)^2 + (BC)^2 - 2(AB)(BC)cos(B)

solve for AC:

(AC)^2 =(370)^2 + (240)^2 - 2(370)(240)cos(37)

229,48 miles equal AC.

Therefore, 229.5 miles separate point A from point C.

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The average rate of change of the function f(x) is found as  -3.75.

The formula for the average rate of change (A(x)) of f(x) over the interval [a,b] is:

A(x) = f(b) - f(a) / b - a

The function being:

f(x) = 20.(1/4)ˣ

Its average rate of change between x = 1 to x = 2 must be determined.

At x = 1

Then;

f(x) = 20.(1/4)¹

f(1) = 5

At x = 2

Then;

f(x) = 20.(1/4)²

f(2) = 1.25

Add these to the formula above to get;

A(x) = f(2) - f(1) / 2 - 1

A(x) = - 3.75

Consequently, the average rate of change of a function f(x) between x = 1 and x = 2 is -3.75.

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When the null hypothesis is rejected

The  conclusion is that there is enough evidence to support the claim of the researcher

When a type I error occurs. The consequences is that the conclusion that there is enough evidence to support the claim of the researcher is actually incorrect

When a type II error occurs. The consequences is  that the conclusion that there is enough evidence  to support the claim of the researcher is actually correct      

From the question we are told that,

Generally if the null hypothesis is rejected then the conclusion would be that there is enough evidence to support the claim of the researcher

Generally a Type I error is a an error that occurs when the null hypothesis is incorrectly rejected

So in the case of this question the consequence of making this type of error is that the conclusion that there is enough evidence to support the claim of the researcher is actually incorrect

Generally a Type II  error is an error that occurs when the null hypothesis is incorrectly not rejected

So in the case of this question the consequence of making this type of  

error is that the conclusion that there is enough evidence to support the claim of the researcher is actually correct.

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Answer:

Step-by-step explanation:

Siny= 4xy +x²

dy/dx(cos y) =4y+ 4x(dy/dx)+2x

making dy/dx the subject

dy/dx(cos y)-4x(dy/dx)=4y+2x

dy/dx(cos y -4x)=4y+2x

dy/dx=(4y+2x)/(cos y -4x)

Step-by-step explanation:

3(1+p)=-5(p+1)

here is your answer

I hope this helpful for u

a) ∠a = 35

b) ∠b = 40

c) ∠c = 35

d) ∠d = 70

e) When we add all the angles together we get an angle of 360°.

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Given, ∠b =  40  

∠d = 70

∠1 = ∠ a

∠2 = ∠c

∠1 = ∠2

So, ∠1 =∠2 = ∠a = ∠c

70 + 40 + ∠a + ∠2 = 180

110 + 2∠a = 180            

2∠a = 180 - 110

∠a = 70/2

∠a = 35

∠1 =∠2 = ∠a = ∠c = 35

When we add all the angles together we get an angle of 360°

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If a person is making a minimum salary for a construction worker, in that case, they will make more than 75% of the teachers.

A salary is a form of periodic fee from a corporation to a worker, which can be laid out in an employment contract. it is contrasted with piece wages, in which every task, hour, or other unit is paid one after the other, in place of on a periodic foundation. From the factor of view of going for walks in a commercial enterprise, revenue can also be considered as the fee of obtaining and keeping human sources for jogging operations and is then termed personnel fee or salary cost. Payroll accounts are used in accounting to record.

Salary is a hard and fast amount of cash or compensation paid to a worker via an enterprise in return for work executed. salary is generally paid in fixed durations, for example, monthly bills of 1-twelfth of the annual salary.

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Answer:

4000

Step-by-step explanation:

If we were to take the number 3,635 and round it to the nearest thousand, we can do it like this.

Start with 5. (Ones place)

3,635

5 is rounded to 10.

Now work on the number 4. (Tenths place)

3,640

4 is rounded to 0.

And now we can do the number 6. (Hundreds place)

3600

6 is rounded to 10.

If we look at the number now, it is

4000

3.635 rounded to the nearest thousand is 4000.

The point estimate of the population standard deviation is 5.91 (Option A)

Standard deviation refers to the spread of a data distribution and measures the distance between each data point and the mean. The sample standard deviation (s) is a point estimate of the population standard deviation σ.

The mean of the population ẋ = sum of all values/ total number of values = 97/6 ≈ 16

The point estimate of the population standard deviation S =√(∑(xi - ẋ)^2/n-1)

∑(xi - µ)^2 = (9 – 16)^2 + (13– 16)^2 + (15– 16)^2 + (15– 16)^2 + (21– 16)^2 + (24– 16)^2 = 79 + 9 + 1 + 1 + 25 + 64 = 179

s = √(179/5) = 5.98

Note: The question is incomplete. The complete question probably is: The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 5.91. O b. 7.688. O C. 7.018. O d. 4.925.

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The insurance policy's anticipated value is -$81 for the one year life insurance policy.

Consider the various factors and the man's potential benifits.

-$165 because he already paid that sum.

The beneficiary could earn as a potential profit.

140000-165 = $139835

The probability of surviving is 0.9994.

The likelihood of not living is 0.0006.

The expected value is given by;

E(v) = (-165)(0.9994) + (139835)(0.0006)

E(v) = -164.901 + 83.901

E(v) = -81.

Thus, the insurance policy's anticipated value is -$81.

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Answer:

Step-by-step explanation:

(x-60)+(x-20)+(x-40)+130+120+110=720

3X -120 + 360=720

3x +240= 720

3x= 720-240

3x=480

x= 480/3 = 160

x=160

angle F = (x-20)

angle F = 160-20=140

angle F = 140

Answer:

  y = 1/5x -11

Step-by-step explanation:

You want the slope-intercept equation of the line perpendicular to y=-5x+9 that goes through the point (20, -7).

The slope-intercept form of the equation for a line is ...

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

This can be solved to find the y-intercept from a point on the line:

  b = y -mx

Comparing this form to the given equation, you see the given line has a slope of m = -5.

The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line:

  slope = -1/(-5) = 1/5

The y-intercept of the desired line can be found using the equation for b above. The y-intercept of the line with slope 1/5 through point (x, y) = (20, -7) is ...

  b = y -mx = (-7) -1/5(20) = -7 -4

  b = -11

Now, we have the slope and intercept of the desired line, so we can write its equation:

  y = 1/5x -11

The predicted quantity of balls in the first bin is (1/n)n.

Considering that,

There are the same number of balls and containers.

If so, then each container must always contain one ball. The probability of each ball landing in the first bin is (1/n)n.

For instance -

Three balls and three bins should be present. Next to each ball, place an A, B, and C. There are numbers 1, 2, and 3 on the containers. Ball A has a 1/3 chance of landing in bin 1. Although there is a 1/3 probability that ball B will drop in bin 1 and a 1/3 chance that ball C will do the same, both outcomes are possible. Therefore, bin 1 should be equal to 1/3 + 1/3 + 1/3. The rationale behind the projected values of bins 2 and 3 is identical.

According to the same logic, bins 2 and 3 should also have expected values of 1.

How probable is it that the first bin will receive all three balls?

In general, (1/n)n, which equals (1/3)3, or 1/3 x 1/3 x 1/3, equals 1/27.

Therefore, (1/n)n would be the expected number of balls in the first bin.

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Diego will have 74 pencils remaining after giving 14 pencils to Marcus and 32 pencils to Anna.

The question is about simple Subtraction. First, we know that the total number of colored pencils in the box is 120. Following is the step-by-step explanation for this question.
Let suppose,
Total Colored pencils = x = 120
Pencils given to Marcus = y = 14
Pencils are given to Anna = z = 34.

And, Total Pencil Remaining = R =?

We can show the given information in the equation as given below:
R = x - y - z

By putting the value in the above equation:
R  = 120 - 14 -34
R  = 74.

So, after giving the 14 and 32 pencils to Marcus and Anna, respectively. Marcus would remain with 74 Pencils.

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[9] Answer: x = 4

Step-by-step explanation:

     Both of these problems use triangle's exterior angles. We will set up an equation and solve. The two opposite angles are equal to opposite exterior angle. After writing our equation, we will solve and isolate the variable using inverse operations.

     17x + 1 + 18x + 3 = 144

     35x + 4 = 144

     35x = 140

     x = 4

[10] Answer: x = 3

Step-by-step explanation:

     Both of these problems use triangle's exterior angles. We will set up an equation and solve. The two opposite angles are equal to opposite exterior angle. After writing our equation, we will solve and isolate the variable using inverse operations.

     20x + 23x + 1 = 130

     43x + 1 = 130

     43x = 129

    x = 3

Answer: 60%

Step-by-step explanation:

15 divided by 25 = 0.6

0.6 x 100 = 60%

:)

The multiple regression model represented by y = a₀ + a₁x + a₂x + ... has  one independent variable.

Explanation:

Therefore, the multiple regression model has more than one independent variable that is option d.

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5⁻¹² is the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

An expression is combination of variables, numbers and operators.

Given,

5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

This sentence can be written in the form below

(5⁻² × 5⁶)⁻³

According to laws of indices, we know that;

(a²)³ = a⁶

Thus;

(5⁻² × 5⁶)⁻³=(5⁻² )⁻³×(5⁶)⁻³

⇒ 5⁶ × 5⁻¹⁸

When bases are same then the powers will be added

⇒ 5⁶ × 5⁻¹⁸

⇒ 5⁻¹²

Hence, 5⁻¹² is the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

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Answer:

1 divided by 5 raised to the twelfth power

Step-by-step explanation:

both of them equal the same thing

Answer: 222 cents

Step-by-step explanation: 84/14 = 6 This is the unit rate.

6 x 37 = 222

The component of the data that a data analyst is most interested in is sample size.

Given,

To prevent results from being skewed or causing incorrect conclusions, we must identify the data element on which the data analyst should concentrate;

The data analyst;

A data analyst looks at data to uncover useful consumer insights and possible applications for the knowledge. They also tell the management of the business as well as other stakeholders of this information.

Although it is advisable for data analysts to have a foundational knowledge of statistics and mathematics, many of their responsibilities can still be carried out without it. However, knowledge in statistics, linear algebra, and calculus is often required for data analysts.

Here,

A data analyst's primary interest in the data is sample size

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Answer:

i need points

Step-by-step explanation:

The value of the solution is B i.e., his cumulative gpa (i), he ever performed before (ii)

The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.

The two types of statistics are: Descriptive and inferential.

With the alternatives available, Johnny can only do worse if his performance falls short of both his lifetime GPA and his previous best performance. It's possible that the last scenario, in which Johnny performed worse than last semester, won't necessarily have an impact on his GPA. A cumulative GPA represents Johnny's overall GPA since he first began attending school. Considering that his most recent semester may have been one of his best and had a solid outcome, earning a result somewhat below that of his previous semester may not necessarily result in a drop in his cumulative GPA. Therefore, choice B is right.

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The estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

What is population variance?

Each data point's distance from the population mean is quantified by the population variance, which is a measure of dispersion. The average of the squares of the deviations from the data's mean value is known as population variance.

Hence, when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes, the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

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The dimensions of the photograph are found as 13 in and 6 in.

Let length = x.

So, width = x - 7

Area = length x width

A = x (x -7)

and A = 78 inches squared.

Thus,

78 = x (x -7)

On solving.

x² - 7x - 78 = 0

Find the factors of the quadratic equation,

x² - 7x - 78 = 0

(x - 13)(x + 6) = 0

Thus,

x = 13 and x = -6 but (x > 0)

Thus, when x = 13 in,

Width = x + 7

Width = 13 - 7

Width = 6 in

Thus, the dimensions of the photograph are found as 13 in and 6 in.

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The rates of weekly earning would allow her to reach her goal will be 12x > 500.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Janet anticipates cutting yards for quite a long time in the late spring. Her objective for the late spring is to acquire more than $500.

Let 'x' be the weekly rate. Then the inequality is written as,

12x > 500

The rates of weekly earning would allow her to reach her goal will be 12x > 500.

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Check the picture below.