New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.a) Create a probability model for this game.b) Find the expected value and standard deviation of your prospective winnings.c) You play this game five times. Find the expected value and standard deviation of your average winnings.d) 100 people play this game. What's the probability the person running the game makes a profit?

A set of scalar parametric equations for the line that passes through points p(3, 4, 1) and q(4, -2, -1) : x = 3 + 4t, y = 4 - 2t and z = 1 - t

In this question, we have been given two points p(3, 4, 1) and q(4, -2, -1).

We need to find a set of scalar parametric equations for the line that passes through points p and q.

We know that a set of scalar parametric equations is,

x = x0 + at, y = y0 + bt, z = z0 + ct

Let (x0, y0, z0) = (3, 4, 1)

and (a, b, c) = (4, -2, -1).

Therefore, scalar parametric equations as:

x = 3 + 4t,

y = 4 - 2t

and z = 1 - t

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The required Co-ordinates are A(-0.5, -0.25), B(-2.5, 1.5) and C(0.25, 0.5).

To diagram a point, first find its situation on the x-axis, then track down its area on the y-hub, lastly plot where these meet. The middle place of the chart is known as the  origin  and is composed as the point (0, 0) since it's situated at the no point on the x-axis and the no point on the y-axis.

The distance of a point from y-hub scaled with the x-hub is called abscissa or x direction of the point. The distance of a point from x-pivot scaled with the y-hub is called ordinate. The abscissa and ordinate all together are called organizes.

Now we find the co-ordinates of points on the graph,

Point A(-0.5, -0.25)

Point B(-2.5, 1.5)

And

Point C(0.25, 0.5)

Thus, required points are A(-0.5, -0.25), B(-2.5, 1.5) andC(0.25, 0.5).

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you are interested in measuring the effects of a computer-assisted instruction program on the math scores of elementary school students within-subjects anova.

What is an ANOVA with within-subjects?

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The required probability that their scores differ by more than 15 points is 0.99807.

As stated in the question, a specific country administers an exam to students with scores that are regularly distributed with a mean of 41 points and a standard deviation of 9 points. Assume we randomly select two of these testers and define the random variable d as the difference in their scores.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Z = x - μ / σ
Z = 15 - 41 / 9
Z = -2.88
Now,
P(x > 15) = P (z > -2.88)
            = 0.99807

Thus, the needed chance is 0.99807 and their scores differ by more than 15 points.

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Answer:

midsegment

Step-by-step explanation:

hope it helps!

Using simple mathematical operations, we know that we will require 1436 bricks to construct a brick wall.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

So, we know that:

A brick wall's measurements are provided by:

14.5 feet in length

Size: 0.5 feet wide

5.5 feet tall

Brick dimensions are provided by:

6 inches in length

4-inch width

2 inches tall

The number of bricks must be determined:

Thus, the number of bricks is provided by:

Number of bricks = Volume of brick wall/Volume of brick

Number of bricks = 14.5 * 5.5 * 0.5 * 12 * 12 * 12/6 * 4 * 2

Number of bricks = 1435.5

Number of bricks = 1436

Therefore, using simple mathematical operations, we know that we will require 1436 bricks to construct a brick wall.

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According to the binomial distribution, there are 13 questions should the student expect to answer correctly.

Binomial distribution:

in statistics, binomial distribution refers the probability of getting a success must remain the same for the trials we are investigating.

Given,

A quiz consists of 24 questions. each question has 4 answer choices with exactly one correct answer. a student is completely unprepared for the quiz, so he guesses on all 24 questions.

Here we need to find how many questions should the student expect to answer correctly.

While we looking into the given question, we have identified that the total number of questions is 24.

Number of options = 4

So, the probability of getting correct answer = 1/4 = 0.25

The probability of getting incorrect answer is,

=> 1 - 1/4 = 3/4 = 0.75

So, based on the binomial distribution,

X ~ Binomial Distribution (m=25, p=0.25, q=0.75)

Then in probability it can be written as,

=> P (X=13) = (25C13)x ((0.25)¹³) x ((0.75)¹²)

=> P (X=13) = 0.00245461663

Therefore, the number of correct answers is 13.

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Answer:

About 30.21 quarts

Step-by-step explanation:

[tex]q=(28.5)(1.06)=30.21[/tex]

Hope this helps

Answer: The answer to this question is x= -22/5

Where the variance is 0.32, the mean is 0.40, and there are provided sets of probabilities, the standard deviation will be 0.566.

The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a high standard deviation are spread out from the mean, whereas those with a low standard deviation are grouped together close to the mean.

Here,

mean=0.4

variance=(Xn-mean)².P(x)n

=(0-0.4)²*(0.64)+(1-0.4)²*(0.32)+(2-0.4)²*0.04

variance=0.32

Standard deviation=√(variance)

=√0.32

=0.566

The standard deviation will be 0.566 where variance in 0.32 and mean is 0.40 and given sets of probability.

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Answer:

The height of the building is 20 meters

Step-by-step explanation:

The Pythagoras Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

[tex]c^{2}=a^{2}+b^{2}[/tex]

Where c is the hypotenuse , a is perpendicular length , b is base

Length of the shadow of a building b = 15 m.

The distance from the top of the building to the tip of shadow c = 25 m

Let us assume the Height of the building to be = a

According to the pythagoras theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

[tex]25^{2}=a^{2}+15^{2}[/tex]

[tex]a^{2} = 25^{2}-15^{2}[/tex]

[tex]a^{2}[/tex] = 625-225

[tex]a^{2}[/tex] = 400

a = 20 meters

The height of the building is 20 meters

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Answer:

6

Step-by-step explanation:

S = Spanish book

M = Math book

H = History book

These are the different ways in which he can organize the book on his bookshelf.

SMH

SHM

MSH

MHS

HSM

HMS

There are 6 ways.

Answer: Both products are 2.6 repeating

If y fluctuates inversely as x as well as x is 6 if y is 13 then x is 9.75 when y is 8.

Inverse variation is demonstrated by the following equation when two quantities, x and y, are in inverse proportion:-

x y = x1 y1

Now, if x is 6 when y is 13 and y varies inversely with x, then at y =8,

Thus,

x × 8 = 6× 13

x = (6×13)/8

x = 9.75

As a result, if y varies inversely as x as well as x is 6 if y is 13 then x is 9.75 when y is 8.

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The final cost for Paul's ping pong table will be;

⇒ $296.8

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The original price of ping pong table = $350

And,  He uses a coupon code to get a 20% discount off of the original price. He is then charged a 6%​ tax on the discounted price.

Now,

Since, The original price of ping pong table = $350

And,  He uses a coupon code to get a 20% discount off of the original price.

Hence, The discounted price = 20% of $350

                                             = 20/100  ×  350

                                             = $70

So, The price of ping pong table = $350 - $70

                                                  = $280

And, He is then charged a 6%​ tax on the discounted price.

So, We get;

The tax price = 6% of $280

                    = 6/100 × $280

                    = $16.8

Thus, The final price for Paul's ping pong table = $280 + $16.8

                                                                        = $296.8

Therefore, The final cost for Paul's ping pong table will be;

⇒ $296.8

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Answer:  Choice (E)   [tex]\displaystyle \text{xz} = \boldsymbol{\frac{\text{x}^3}{\text{zy}^2}}[/tex]

=========================================================

Explanation:

The goal is to find what xz is equal to (in terms of x, y, and z)

We are given [tex]\text{z}= \frac{\text{x}^2}{\text{zy}^2}[/tex]

The only thing we're missing on the left hand side is x.

Let's multiply both sides by x.

[tex]\text{z} = \frac{\text{x}^2}{\text{zy}^2}\\\\\text{xz} = \text{x}*\frac{\text{x}^2}{\text{zy}^2}\\\\\text{xz} = \frac{\text{x}*\text{x}^2}{\text{zy}^2}\\\\\displaystyle \text{xz} = \boldsymbol{\frac{\text{x}^3}{\text{zy}^2}}[/tex]

This points us to choice (E) as the final answer.

The interest payments is  $27,750 and the Bond payable discount is $6,259

The electro incorporated issued $740,000 of 7.5%, four-year bonds that pay interest semiannually on june 30 and december 31.

They are issued at $680,186 and their market rate is 10% at the issue date

Interest payments = $740,000 x 7.5% x 1/2 = $27,750 (the credit to Cash).

bond interest expense = carrying value at 1/1/13 (the beginning of the period) of $680,186 x market rate of 10% x 1/2 = $34,009 (the debit to Bond interest expense).

Bond payable discount

The discount amortization  $34,009 - $27,750 = $6,259

Therefore, the interest payments is  $27,750 and the Bond payable discount is $6,259

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The x-coordinate of the point that divides the directed line segment from k to j into a ratio 1:3 is given as follows:

x = 7.

The direction of the segment is given as follows:

K to J.

The desired point divided the directed line segment from k to j into a ratio 1:3, hence the equation involving proportions is given as follows:

P - K = 1/4(J - K).

This equation is used to obtain both the x-coordinate and the y-coordinate of the point.

The x-coordinates of the points are given as follows:

Hence the x-coordinate of the segment is obtained as follows:

x - 9 = 1/4(1 - 9)

x - 9 = -2

x = -2 + 9

x = 7.

The segment is given by the image shown at the end of the answer.

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If x represents the full length of a certain species of newts then, the mean of the sampling distribution and standard deviation are 216, and 0.31 respectively.

Central Limit Theorem for mean: When a random sample of size n is taken from a population with a mean and standard deviation, the sample mean approaches the normal distribution with mean and standard deviation σ/sqrt (n) as the sample size increases.

Sampling distribution of the sample mean:

using, Central Limit Theorem, the mean of the sampling distribution is μ_{x-bar} = 216.

The standard deviation of the population is σ = 3.1 and the sample size is n =103, people

The standard deviation σ/√n= 3.1/√103 =0.31.

As a result, the sample mean for the 103 sample size, following normal distribution has a mean of μ_{x-bar} = 216 and a standard error of μ_{x-bar} = 0.31.

x-bar ≈ N (216, 0.31)

μ_{x-bar}  = 216

σ_{x-bar}  =0.31

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(complete question)

Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with a mean of 110.6 inches and a standard deviation of 4.9 inches. You intend to measure a random sample of n = 103. find the mean of the sampling distribution and standard deviation.

Answer:

= this is that two expression two equal numbers

Um, is there a possibility that you could clean this question up a bit? It is a little scrambled and hard to make out of the equation given. Thanks!

Answer: x = 1/2

Step-by-step explanation:

2(1/2)=1
1=1

The equation of the required line would be x - 4y = 8.

What is the slope-point form of the line?

Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

A line goes through the point (-1, 1) and (0,-3)

so the slope of the given line would be:

                     [tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-1}{0-(-1)}\\\\m=-4[/tex]

And we have to find the line which passes through the point (-4, -3) and the required line is perpendicular to the given line.

As we know the product of slopes of perpendicular lines is -1.

So the slope of the required line would be = 1/4

By using a slope-point form of the line, we get

    [tex]y - y_1=m(x-x_1)\\\\y-(-3)=\frac{1}{4}(x-(-4))\\\\4(y+3)=x+4\\\\4y+12=x+4\\\\x-4y=8[/tex]

Hence, the equation of the required line would be x - 4y = 8.

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Answer:

C

Step-by-step explanation:

In the general form y = mx + c, c is the y-intercept of the line. The difference of y-intercepts is -5.2.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

Given that,

The equation for f(x) = 3x - 5

And, the value of y-intercept of g(x) from the graph is 0.2

The y-intercept of f(x) can be obtained by comparing it with y = mx + c, where c is the y-intercept as follows,

c = -5.

Thus, the difference of their y-intercepts as per the question is given as,

-5 - 0.2 = -5.2

Hence, the difference of the y-intercepts of f(x) and g(x) is given as -5.2.

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The solution set of the equation is {26}

Set is a collection of well defined objects.

Given,

The equation is represented by the sentence, "56 of a number is 30."

Replacement set for an equation is {10, 24, 25, 36}.

We need to find the solution set of the equation

"56 of a number is 30"

Fifty six of a number is thirty

56-30

26

Hence, the solution set of the equation is {26}

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Answer:

56 cents

Step-by-step explanation:

cost/amount=price

4/2.24=0.56

5.6/10=0.56

6.72/12=0.56

The smallest integer value of x in the solution of the following inequality x is strictly less than 2 or x ∈ (-∞, 2)

Inequalities are statements that are represented as comparison between two or more numbers or algebraic expressions.(strictly less, strictly great, greater, lesser)

Given that the inequality 5x - 7 < 2x - 1

Solving the given equation:

5x - 7 < 2x - 1

5x - 7 - 2x < 2x - 1 - 2x

3x - 7 < -1

3x - 7 + 7 < -1 + 7

3x < 6

x < 2

Therefore, We conclude that x is strictly less than 2.

Hence x ∈ (-∞, 2)

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Answer:

y=−2x−2

Step-by-step explanation:

Ratio of the area of a square inscribed in a semicircle with radius 'r' to the area of a square inscribed in a circle with radius 'r' is equal to 2: 5.

As given in the question,

Let ABCD be the square with side 'a' inscribed in a semicircle with radius 'r'.

'O' be the center of the semicircle.

'M' be the midpoint of AB such that MB = a/2

Join OM, OB and OM ⊥ AB

OB = r

OM = BC = a

In ΔOMB.

OB² = OM² + MB²

⇒ r² = a² + (a/2)²

⇒r² = 5a²/4

⇒a² = 4r²/5

Area of the square inscribed in a semicircle = a²

                                                                         = 4r²/5

Let PQRS be the inscribed in a circle with side 'x'

Diagonal of the square inscribed in a circle = 2r

In ΔPQR,

PR = diagonal

     = 2r

PQ = QR = x

PR² = PQ² + QR²

⇒(2r)² = x² + x²

⇒x² = 4r² /2

⇒x² = 2r²

Area of the square inscribed in a circle = x²

                                                                 = 2r²

Ratio of the area of the square inscribed in ( semicircle to the : circle )

= 4r²/5 / 2r²

= 2 / 5

= 2 : 5

Therefore, ratio of the area of the squares inscribed in a semicircle to the circle is 2 : 5.

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