a population mean is 13. the sample mean is 12.8, and the sample standard deviation is two. the sample size is 20. what distribution should you use to perform a hypothesis test? assume the underlying population is normal.

Answer: 251.20

Step-by-step explanation:

The probability that a student is chosen randomly from the class has a cat or a dog is 26/29.

It is based on the probabilities that something could happen. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of randomly receiving a head is 1 in 2.

explanation:

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

The total strength of the class is 29

The probability that a student is chosen randomly from the class has a cat or a dog =  Number of favorable outcomes / total number of outcomes

P(E) = 26/29

Hence, The probability that a student is chosen randomly from the class has a cat or a dog is 26/29.

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The solution of the trigonometric equation is x = 26.57° or 153.43°

A trigonometric equation is an equation that contains the trigonometric ratios.

Given the trigonometric equation 2cos x - sin x = 3/(2cos x + sin x)

We solve for x in the equation. We proceed as follows.

Since 2cos x - sin x = 3/(2cos x + sin x)

Multiplying both sides by (2cos x + sin x), we have that

(2cos x - sin x)(2cos x + sin x) = 3

Now, we know that (a² - b² = (a + b)(a - b)

Applying this where a = 2cosx and b = sinx, we have that

(2cos x - sin x)(2cos x + sin x) = 3

(2cos x)² - (sin x)² = 3

4cos² x - sin² x = 3

Since sin²x = 1 - cos²x, substituting this into the equation, we have that

4cos² x - sin² x = 3

4cos² x - (1 - cos²x) = 3

4cos² x - 1 + cos²x = 3

4cos² x + cos²x  = 3 + 1

5cos²x  = 4

cos²x  = 4/5

Taking square root of both sides, we have that

cosx  = ±√(4/5)

cosx  = ±2/√5)

cosx  = ±2/√5 × √5/√5

cosx  = ±2√5/5

Taking inverse cosine of both sides, we have

x = cos⁻¹(±2√5/5)

x = cos⁻¹(±0.8944)

x = cos⁻¹(0.8944) or x = cos⁻¹(-0.8944)

x = 26.57° or (180 - 26.57)°

x = 26.57° or 153.43°

So, the solution is x = 26.57° or 153.43°

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Answer: x[tex]\geq[/tex]1

Step-by-step explanation:

x is all the numbers equal to or less than 1. The closed dot means its less than or equal to and the dot is on 1. It cant be more than 1, because the arrow shows that all those numbers are greater than one and cant be x.

Using mathematical operations, we know that 27/4 pounds of Ham are still left with M.D.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Most people believe that addition, subtraction, multiplication, and division are the four basic operations in mathematics.

So, we know that:
M.D. bought 8½ pounds of Ham.

He gave 1¾ pounds to Mr. Chavir.

Remaining Ham with M.D.:

8½ - 1¾

16+1/2 - 4+3/4

17/2 - 7/4

34 - 7/4

27/4

Therefore, using mathematical operations, we know that 27/4 pounds of Ham are still left with M.D.

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The probability that the card has a multiple of 3 is 5/16. We use the concept of probability and multiples to get the answer.

Probability of an event = (no of possible ways it can happen) / (total number of outcomes)

For instance, 20 is a multiple of 4 and 5 if we declare that 4 + 5 = 20. The remaining multiples of four can be written as follows: 4, 8, 12, and so on. Four times one equals four. Numerous other mathematical ideas can be explored with the aid of multiples knowledge.

Given, total number of the cards in the bag is from 1 to 16.

So, total number of cards = 16.

Multiples of 3 below 16 = 3,6,9,12,15.

Number of cards below 16 which are multiples of 3 = 5

Therefore P(E) = No. of possible ways/Total no. of ways

=5/16

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The slope of the given line is 40 mi/h.

How to find slope of the line in the graph?

The slope of a line is the ratio of rise to run. Hence, here are the steps to find slope from a graph.

Select any two random points on the graph of the line (preferably with integer coordinates).

Label them as A and B (in any order).

Calculate the "rise" from A to B. While going vertically from A to B, if we have to go

"up", then the rise is positive;

"down", then the rise is negative.

Calculate the "run" from A to B. While going horizontally from A to B, if we have to go

"right", then the run is positive;

"left", then the run is negative.

Now, use the formula: slope = rise/run.

According to the given question:

To calculate the slope of the line in given graph let point A be (5, 200) and point B (10, 400).

Run = 5

Rise = 200

Therefore, slope = rise/run = 200/5 = 40 mi/h

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Answer:
the first term = y-x

and the fourth term= y+x
and the fifth term = 2y+x

Step-by-step explanation:

1/8, 1/4, 3/8, 2/3, 3/4

By simply dividing the fractions!

In 1/4, we can divide the numbers:

1 ÷ 4 = 0.25.

In 1/8:

1 ÷ 8 = 0.125

In 2/3:

2 ÷ 3 = 0.66

In 3/8:

3 ÷ 8 = 0.375

And in 3/4:

3 ÷ 4 = 0.75

0.125, 0.25, 0.375, 0.66, 0.75

Now, we have to put them into their original fractions, not decimals:

1/8, 1/4, 3/8, 2/3, 3/4

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer: In this scenario, the length of the backpacking trip is the independent variable and the amount of trail mix Wesley will bring is the dependent variable.

The independent variable is the variable that is being changed or controlled in an experiment or study. In this case, the length of the backpacking trip is the independent variable because it is being determined by Wesley and is not influenced by any other factor.

The dependent variable is the variable that is being measured or observed in an experiment or study. In this case, the amount of trail mix Wesley will bring is the dependent variable because it depends on the length of the backpacking trip. Wesley's decision on how much trail mix to bring will be influenced by how long he plans to go backpacking.

Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

Given,

In the question:

A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.

To find the how many possible 3-course meals are there?

Now, According to the question:

Let's know:

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N=n_1[/tex] × [tex]n_2[/tex] × [tex]n_3[/tex]... ×[tex]n_n[/tex]

In this problem, considering the number of salads, main courses and desserts, we have that:

[tex]n_1=4 , n_2=5,n_3=3[/tex]

The total number of options is given by:

N = 4 × 5 × 3

N = 60

Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

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For the given equation y=x+1/5x, if the value of x is 40, y will be 48.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is

y=x+1/5x

We have to find the value of y when the value of x is 40.

Substitute the value of x in order to obtain the value of y as

y=40+40/5

y=40+8

y=48

Thus, for the given equation y=x+1/5x, if the value of x is 40, y will be 48

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Answer:

48

Step-by-step explanation:

y = x + 1/5 x

y = 40 + 1/5 × 40

y = 40 + 8

y = 48

The number of chickens that can be fed with 140 kg of corn is 2800.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 8 is an equation.

We have,

250 kg corn  = 5000 chicken

Multiply 140/250 on both sides.

140 kg of corn = 140/250 x 5000 chicken

140 kg of corn = 2800 chicken

Thus,

2800 chickens can be fed with 140 kg of corn.

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The numerical  top and bottom limits for a d grade is 68 and 61 respectively

What can we learn from mean and standard deviation?

In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilised. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.

Given,

Mean = 75.1

Standard Deviation = 9.1

For a D grade at / 6th Percentile and 78th Percentile critical

Z- Scores are -0.77 and -1.55 respectively

The Corresponding Top grade for d

x + z * σ

75.1 + (-0.77) * 9.1 =68

The Corresponding Bottom grade for d

x + z * σ

75.1 + (-1.55) * 9.1 =61

A d grade has numerical top and bottom limitations of 68 and 61, respectively.

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Answer:

Step-by-step explanation:

Answer: 8x + 2

Step-by-step explanation:

Answer:

8x+2

Step-by-step explanation:

x3+2x2+x+2

=3x+4x+x+2

=8x+2

to get the slope of any straight line, we simply need two points off of it, let's use the ones in the picture below.

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{24}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{24}-\stackrel{y1}{12}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{ 12 }{ 2 } \implies \text{\LARGE 6}[/tex]

The range of the given relation is:

R: {1, 2, 4, 5}

Thus the correct option is A.

A relation maps elements from one set, the set of the inputs called the domain, into elements from another set, the range.

A point in a relationship is written as (x, y), where y is on the range.

Here we have the relation given by the pairs:

(1, 2), (2, 4), (4, 5), (6, 1)

The range is the set given by the second values of each point, thus the range is:

R: {1, 2, 4, 5}

The the correct option is A.

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Billy suffers from a stutter, so he expresses himself in a manner in which he can be successful.

Doctor Spivey grants McMurphy's request for a pass to take a fishing trip with nine other patients, accompanied by two of his aunts.

Why is McMurphy tired after the fishing trip?

McMurphy adds Rub-a-Dub George, a neat-freak Swedish fisherman and sailor, to the group. Nurse Ratched says they can't go because there isn't enough capacity in one car for all the patients when Candy Starr arrives without her buddy to pick up the patients for their outing.

McMurphy has his own weakness, his self-centeredness. At first he is willing to sacrifice the patients for his own well-being

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The equation of a line perpendicular to y=4/24x that pass through the point (-8, -4) is -6x-4y=16 where x-intercept is -6 and y-intercept is -4.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables.

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

Given line ;

y=1x/6

now comparing it with y=mx+c to find the value of m and we found;

m1=1/6

now if two lines are perpendicular then,

m1.m2=-1

m2=-6

now finding the equation of line passing through the point (-8, -4)

x1=-8

y1=-4

(y−y1)=m(x−x1)

Y+4=(-6)(x+4)

Y+4=(-6x/4)

Y=(-6x/4)-4

Y=(-6x-16)/4

4y=-6x-16

rearrange;

-6x-4y=16

this is our required value.

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The equation that matches this table is  X=Y*k,k=12,  Hence Given table is direct variation.

X=12,Y=1

X=24,Y=2

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Observing the cases provided with the formula of probability and implementing it with OR rule , The answer is 0.22.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

All potential results make up the sample space of a random experiment. A subset of the sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.

Probability that dice rolled shows a 5 once =  1/36

Probability that dice rolled shows a 5 twice =  2/36

Probability that the sum is 8 = 5/36

Total probability = 1/36 + 2/36 + 5/36 = 0.22

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Both a smaller and a bigger number are 25 and 68

The outcome or conclusion we get at when we add two or more integers is known as the SUM. example the total of the addends, 6, and 4, is 10. In other words, we may argue that 8 plus 5 equals 13 or that 8 plus 5 equals 13.

Here, we've been given two numbers, one smaller and one bigger, where the smaller number is X and the larger number is 18  more than twice the smaller number.

2X + 18 is the greater number.

Because the total is now 93, X + (2X+18) = 93

3X = 93 - 18 .

X = 25

larger number will be 2(25) + 18 = 68

Thus the numbers are smaller number is 25 and larger number is 68.

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[tex]y+4=13 \implies \boxed{y=9}\\\\2x=3x-1 \implies \boxed{x=1}[/tex]

Additionally, [tex]63=3z \implies \boxed{z=21}[/tex]

Answer:

it is very easy for even a third grader 2x4=8

The annual rate of interest she is charging you is 12%.

Given that, you ask your best friend to lend you $200 to buy your favorite toy.

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Here,

Extra money per month =$2

Extra money per year = $2×12

Extra money per two year = 2×2×12 = 4×12 = $48

Money lend = $200

Money given after two years = $(200+48) = $248

Now, the rate of interest can be find using SI=(P×R×T)/100

48= (200×R×2)/100

⇒ 48= 4R

⇒ R=12%

Hence, the annual rate of interest she is charging you is 12%.

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"Your question is incomplete, probably the complete question/missing part is:"

You ask your best friend to lend you $200 to buy your favorite toy. She says she can lend you the money only if you give her an extra $2 for every month that passes before you return it. What is the total amount you must pay her if you return it after two years? rupees What is the annual rate of interest she is charging you?

The equation use to determine the value of [tex]x[/tex] is [tex](2x+5)+3(2x+5)=92[/tex].

The measures of [tex]\angle A, \angle B[/tex] are [tex]23^\circ, 69^\circ.[/tex]

Let us assume the measures of [tex]\angle A, \angle B[/tex] are [tex]z, y[/tex].

Now according to the question, we can write the relation between [tex]\angle A, \angle B[/tex] is [tex]y=3z....(i)[/tex].

We know, the measure of [tex]\angle A[/tex] is [tex]2x+5[/tex] so [tex]2x+5=z....(ii)[/tex]. Now, we will substitute the value of [tex]z[/tex] from equation [tex](ii)[/tex] in equation [tex](i)[/tex].

[tex]y=3z\\= 3 \times (2x+5)\\=6x+15[/tex]

So, the final equation will be [tex](2x+5)+3(2x+5)=92[/tex]

⇒ [tex]6x+15+2x+5=92[/tex]

⇒ [tex]8x+20=92[/tex]

⇒ [tex]8x=72[/tex]

⇒ [tex]x=9[/tex]

[tex]\therefore[/tex] measure of [tex]\angle A[/tex] is [tex]2x+5=(2 \times 9)+1=25[/tex] and measure of [tex]\angle B[/tex] is [tex]2 \times 23 = 69[/tex].

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Answer: y = 1x + 5

Step-by-step explanation:

This is where the equation; y=mx+b comes in handy.

We are given m, 1.

And we are given a coordinate to plug in.

2=1(-3)+b

2=-3+b

b=5

y = 1x + 5

Answer:

Step-by-step explanation:

The standard form of a line is Ax+By=C.  To solve this problem, begin with the point-slope form [tex]y-y_1=m(x-x_1)[/tex].  For this problem, let

[tex](x_1,y_1)=(-3,2)\\m=1[/tex]

Input these values into the point-slope form equation and convert to slope-intercept form,

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

Next, convert slope-intercept form to standard form:

y=x+5

-x+y=5

For standard form, A must be positive.  So,

-(x-y)=5

x-y=-5

i hope you understand cause i can write on a screen