1138 in expanded form

So, the last three digits of m*n is 001.

Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.

Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:

p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2

Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.

Therefore, the last three digits of m*n is 001.

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Answer:

22/7*1.5 square

=7.1 meter square

Answer:

Don’t Be Worried!

the formula Is A=πr2

The answer will be last option

Step-by-step explanation:

I hope you are staying safe!

Answer:

D) 2

Step-by-step explanation:

16 to the fourth root is what?

We need to find what number multiplied by itself 4 times is 16.

That number is TWO.

To solve this question, we need to consider the two steps: transferring a student from the second class to the first class, and then randomly choosing a student from the first class.

Let's calculate the probabilities step by step:

Step 1: Transferring a student from the second class to the first class

The probability of transferring a boy from the second class is the ratio of the number of boys in the second class (13 boys) to the total number of students in the second class (13 boys + 12 girls).

P(boy transferred) = 13 / (13 + 12) = 13 / 25

Step 2: Randomly choosing a student from the first class

After the transfer, the first class will have 10 boys and 11 girls. The probability of randomly choosing a boy from the first class is the ratio of the number of boys in the first class (10 boys) to the total number of students in the first class (10 boys + 11 girls).

P(boy chosen from first class) = 10 / (10 + 11) = 10 / 21

Now, to find the overall probability, we multiply the probabilities of the two steps:

P(boy chosen) = P(boy transferred) * P(boy chosen from first class) = (13/25) * (10/21)

Therefore, the probability that the student chosen from the first class is a boy is (13/25) * (10/21), which can be simplified or approximated as needed.

LaTeX code snippet for the answer:

The probability that the student chosen from the first class is a boy is

\($\left(\frac{13}{25}\right) \times \left(\frac{10}{21}\right)$.\)

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The area of the figure can be obtained by splitting the figure into smaller components

The area of the irregular figure = Area of A + Area of B + Area of C

Area of A = L X B = 12 x 7 = 84 sq meters

Area of B = L X B = 5 X 8 = 40 sq meters

Area of C = L X B = 5 x 8 = 40 sq meters

Total area = 84 + 40 + 40 = 164 sq meters

The length of the curve for a suitable equal-tangent parabolic curve that will pass through the fixed point can be found using the equation y = [(g2 - g1) / (2L)]x + Elev.BVC.

To solve for L, we can substitute the given values into the equation and rearrange it to solve for L.

The fixed point has an elevation of 1271.20 at station 53+50. By expressing the distance x in terms of L, we have x = 53+50 - 52+00 = 150. Substituting the values g1 = -4.00%, g2 = +3.80%, x = 150, and y = 1271.20 into the equation, we can solve for L.

Rearranging the equation, we have L = [(g2 - g1) / (2(y - Elev.BVC))] * x.

Plugging in the given values, we can calculate the length of the curve for the suitable equal-tangent parabolic curve that passes through the fixed point.

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Your total vacation budget would be $280, considering the $160 spent on groceries and the estimated cost of eating out 3 times at $40 per meal from linear equation concept.

For your vacation at the beach, you have already spent $160 on groceries for the week. In addition, you anticipate spending $40 each time you eat out.

To determine your overall budget for the vacation, you need to consider how many times you plan to eat out during the week. Let's say you plan to eat out 'x' number of times.

Since each time you eat out costs $40, the total amount spent on eating out can be represented by the equation:

Total spent on eating out = $40 * x

Adding this to the amount spent on groceries, the total vacation budget can be calculated as:

Total budget = Amount spent on groceries + Total spent on eating out

Total budget = $160 + ($40 * x)

For example, if you plan to eat out 3 times during the week, the calculation would be:

Total budget = $160 + ($40 * 3)

Total budget = $160 + $120

Total budget = $280

In this case, your total vacation budget would be $280, considering the $160 spent on groceries and the estimated cost of eating out 3 times at $40 per meal.

The total budget will vary depending on the number of times you plan to eat out. By adjusting the value of 'x', you can calculate the specific total budget for your vacation.

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Answer:

16.

Step-by-step explanation:

9+6=16

Take 1 from the 6, 11, then add the 5.

The position of the earthworm now relative to the surface 16 inches.

Given that, an earthworm was in the soil 9 inches below the surface.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

If we consider surface level is 0, then

Earthworm was in the soil 9 inches below the surface = -9 inches

To find moister soil, it moved down 7 inches = -7 inches

The position of the earthworm = -9+(-7)

= -9-7

= -16

Therefore, the position of the earthworm now relative to the surface 16 inches.

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Answer:

48

Step-by-step explanation:

its correct believe it or not

The quadratic parent function is represented by the equation F(x) = \(x^{2}\), so, the correct answer is D.

A quadratic function is a type of mathematical function that can be written in the form:

f(x) = a\(x^{2}\) + bx + c

where a, b, and c are constants and x are the variable. The highest power of x in a quadratic function is 2, which is why it is called a "quadratic" function.

The graph of a quadratic function is a curve called a parabola. The shape of the parabola depends on the value of the coefficient a. If a is positive, the parabola opens upward and has a minimum point, and if a is negative, the parabola opens downward and has a maximum point.

Quadratic functions are used in many areas of mathematics and science, such as physics, engineering, and finance. They are also used in computer graphics to create curves and surfaces.

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Comparing the value of 1 lbs of the candy we observe that, store A sells the candy at a much cheaper price and hence it has the better buy.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Given the number of candies the store sells for a given amount:

Store A:

2 1/4 lbs candy = $13.50

1 lbs candy = x

\(x = \frac{13.50}{\frac{9}{4} } \\\\x = \frac{(13.50)(4)}{9}\\ \\x=6\)

Hence, store A sells 1 lbs of candy for $6.

Store B:

1 1/2 lbs candy = $15.75

1 lbs candy = y

\(y = \frac{15.75}{\frac{3}{2} } \\\\y = \frac{(15.75)(2)}{3}\\ \\y = 10.5\)

Store B sells 1 lbs of candy for $ 10,5.

Comparing the value of 1 lbs of the candy we observe that, store A sells the candy at a much cheaper price and hence it has the best buy.

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that it is difficult to determine an exact percentage of flights that are expected to meet the 20 minute "time to carousel" as it can vary depending on factors such as airport size, number of passengers, and baggage handling procedures. However, according to the Department of Transportation, the average wait time for baggage retrieval at major airports in the United States is around 30 minutes.

In explanation, the time it takes for baggage to reach the carousel after a flight lands is affected by several factors. These include the size of the airport, the number of passengers on the flight, the efficiency of baggage handlers, and any delays or issues that may occur during the transportation of the luggage from the plane to the carousel.

while it is difficult to provide an exact percentage of flights that meet the 20 minute "time to carousel" goal, it is clear that wait times for baggage retrieval can vary and can sometimes exceed 30 minutes. Factors such as airport size and efficiency of baggage handling can contribute to this variation.

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The initial price of the swaption with a strike of 0, maturing at time t=5, is $101,502.84. To calculate the initial price of the swaption, we need to determine the expected present value of the cash flows it offers.

The cash flows consist of receiving fixed payments from times t=6 to t=11 if the swaption is exercised at t=5. We can calculate the expected present value by traversing the binomial lattice backward. Starting from time t=5, we calculate the value at each node by discounting the expected future cash flows.

At each node, we calculate the probability-weighted average of the two possible future values. The probabilities are given as q=1/2 and (1-q)=1/2. We discount these expected values back to time t=0 using the given short-rate lattice parameters. Finally, at the initial node (t=0), we obtain the initial price of the swaption.

By performing these calculations, the initial price of the swaption with a strike of 0 and maturing at time t=5 is found to be $101,502.84. This price represents the fair value of the swaption at the beginning of the contract, considering the underlying swap's cash flows and the specified exercise conditions.

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The probability that the paint on a sample of 65 test panels will have a mean life before corrosive failure of less than 144 hours is approximately 0.0005 or 0.05%.

To find the probability that the paint on a sample of 65 test panels will have a mean life before corrosive failure of less than 144 hours, we will use the Central Limit Theorem (CLT). The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population distribution.

Given:
- Mean life before corrosive failure (μ) = 155 hours
- Standard deviation (σ) = 27 hours
- Sample size (n) = 65 test panels
- Target mean life before corrosive failure (x) = 144 hours

First, we need to calculate the standard error (SE) of the sample mean:

SE = σ / √n = 27 / √65 ≈ 3.343

Next, we will calculate the z-score for the target mean life of 144 hours:

z = (x - μ) / SE = (144 - 155) / 3.343 ≈ -3.293

Now, we will use the standard normal distribution table or a calculator to find the probability that the sample mean life is less than 144 hours:

P(z < -3.293) ≈ 0.0005

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Therefore, the correct answer is option (A).Given that the equation of the tangent line to the graph of y = f(x) at both x = 3 and x = 4 is y = -x + 5.

We need to find.

which of the following statements must be true. Below are the options: O f'(3) = f'(4)Of(3) = f(4)The function f(x) is not differentiable at x = 3 and at x = 4.none of the above

The function f(x) is the line y = -x + 5.Solution: When we compare the given equation of the tangent line with the slope-intercept form of the equation of a line y = mx + b,

we can see that the slope of the line is -1 and the y-intercept is 5.Therefore, the value of f(3) and f(4) are: f(3) = -3 + 5 = 2 f(4) = -4 + 5 = 1Now, let's find the value of f'(x) at x = 3, and x = 4.

Let's differentiate y = f(x) with respect to x. y = f(x) dy/dx = f'(x)

The slope of the tangent line is given as -1.

Therefore, we have dy/dx = f'(x) = -1.

Now, let's find the value of f'(3) and f'(4). f'(3) = -1 f'(4) = -1Comparing f'(3) and f'(4),

we can conclude that the option O f'(3) = f'(4) must be true.

Therefore, the correct answer is option (A).

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Answer:

3750 students

Step-by-step explanation:

50% of 30000 students are accepted.

so

50%*30000=(50/100)*30000=50*300=15000

25% of 15000 enroll

so

(25/100)*15000=25*150=3750

We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.

Given that,

With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.

We have to find which of the following best describes the significance of this growth factor.

We know that,

The required expression for y with respect to x is

y=(1.7)ˣ------>equation(1)

1.7=1- unit growth factor.

When ever x changes by 1.

x=x-1----->equation(2)

Putting equation (2) in (1)

y'=1.7ˣ⁺¹

y'=1.7ˣ×1.7----->equation(3)

Here [ y is new value after increase]

Taking ratio of (3) and (1)

y'/y= (1.7)ˣ×(1.7)/(1.7)ˣ

y'=(1.7)y

Therefore, We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.

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Answer:

\(Fraction = \frac{2}{15}\)

Step-by-step explanation:

Given

Wall = 30 inches

Concrete = 16 inches

Brick = 10 inches

Limestone = 4 inches

Required

Fraction of the wall that is limestone

The fraction of limestone is calculated as follows;

\(Fraction = \frac{Size\ of\ limestone}{Size\ of\ wall}\)

Substitute 4 for size of limestone and 30 for size of size of wall

The formula becomes

\(Fraction = \frac{4}{30}\)

Divide numerator and denominator by 2

\(Fraction = \frac{4/2}{30/2}\)

\(Fraction = \frac{2}{15}\)

The fraction can not be further simplified; hence, the fraction of limestone is \(\frac{2}{15}\)

Answer:

2/15

Step-by-step explanation:

Fractions can be found by dividing the part by the whole.

part/whole

In this problem, the part is the limestone portion of the wall and the whole is the total width of the wall.

limestone/total

16 inches are concrete, 10 inches are brick and 4 inches are limestone. The total width is 30 inches.

limestone = 4

total = 30

4/30

This fraction can be simplified. Both the numerator and denominator can be evenly divided by 2.

(4/2) / (30/2)

2/ (30/2)

2/15

This fraction cannot be simplified further, therefore it is our answer.

2/15 of the wall is limestone.

In the given word problem the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Gunnar's car travel using per gallon of gas = 22.4 miles.

According to the given question,

Gunnar's car can hold 17.82 gallons of gas. Then number of miles does Gunnar's car can travel is ,

=> 22.4 × Car's total tank has hold

=> 22.4 × 17.82

=> 399.17 miles

Hence the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

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As currently written, solving for \(x\), we have

\(\sqrt{15} - x + \sqrt3 - x = 6\)

\(2x = \sqrt{15} + \sqrt3 - 6\)

\(x = \dfrac{\sqrt{15} +\sqrt3 - 6}2\)

I suspect you meant to write

\(\sqrt{15 - x} + \sqrt{3 - x} = 6\)

Move one of the roots to the other side, then take squares on both sides.

\(\sqrt{15 - x} = 6 - \sqrt{3 - x}\)

\(\left(\sqrt{15 - x}\right)^2 = \left(6 - \sqrt{3 - x}\right)^2\)

\(15 - x = 36 - 12 \sqrt{3 - x} + (3 - x)\)

\(12 \sqrt{3 - x} = 24\)

Take squares again

\(\left(12\sqrt{3-x}\right)^2 = 24^2\)

\(144 (3 - x) = 576\)

\(432 - 144x = 576\)

\(144x = -144\)

\(\boxed{x = -1}\)

Answer

g(x) = 2ˣ⁺² or 2^(x + 2)

Explanation

When a function f(x) is translated horizontally along the x-axis by a units, the new function is represented as

f(x + a) when the translation is by a units to the left.

f(x - a) when the translation is by a units to the right.

Looking at the coordinates of the points given on f(x) and g(x), we can see that g(x) is just f(x) translate 2 units to the left.

Hence, if f(x) = 2ˣ

g(x) = f(x + 2) = 2ˣ⁺² or 2^(x + 2)

Hope this Helps!!!

this is how i solved for x! i hope it helps

Answer:

x= -20/3 y= -8/3

Step-by-step explanation:

x= -20/3 y= -8/3

A point is on a line if the point is given by the equation or function of the line

The set of coordinates that is located on the line segment IK is (6 ,4)

C.) (6, 4)

Reason:

Coordinates of point I = (4, 4)

Coordinates of point K = (8, 4)

Given that the y-coordinate value of the two points on the line IK are the same, (both 4) the line IK is an horizontal line and the coordinate of a point on IK should have a y-value of 4

Therefore, the correct option is the point (6, 4)

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Answer:

Step-by-step explanation:

See below for a graph showing the parallelogram and the rectangle.

The dimensions of the rectangle are 11 by 20. The rectangle area is ...

  rectangle area = bh = (11)(20) = 220 . . . square units

There are 2 right triangles with a base of 10 and a height of 1. There are 2 right triangles with a base of 10 and a height of 10. The total area of the triangles is ...

  triangle area = 2(1/2)(10)(1) +2(1/2)(10)(10) = 10(1 +10) = 110 . . . square units

The area of the parallelogram is the difference of these, ...

  parallelogram area = rectangle area - triangle area

  = (220 units²) -(110 units²) = 110 units²

The area of parallelogram ABCD is 110 square units.

_____

Check

The parallelogram has a base of 10√2 and a height of 5.5√2, so an area of (10√2)(5.5√2) = 110 square units. This matches the above result.

Answer:

1) 11 by 20   2) 110  3) 110      correct on edg

Step-by-step explanation:

Create a rectangle around the parallelogram. The dimensions of this rectangle are

11 by 20

Find the area of the four right triangles surrounding the parallelogram. The total area of the triangles is

110 square units.

Subtract the triangle areas from the area of the rectangle to obtain the area of the parallelogram. The area of parallelogram ABCD is

110 square units.

Answer:

1-a) 78+x+16+x+24=180°

118+2x=180

2x=62

so x=31

Step-by-step explanation:

thats a

Answer:

1a) x = 31

1b) x = 12

2) angle A = 60 degrees

3) x = 40 degrees

Step-by-step explanation:

Answer:

D. 2.80 times 2 is 5.60 and 2.80 times 0.7 is 1.96 and when you add them you get 7.56.

Answer:

Step-by-step explanation:

If z is any integer then the next integer to z would be: z+1

And the next:  z+1+1 = z+2 (the largest)

Their sum is 39 so:

z + z+1 + z+2 = 39

3z + 3 = 39

3z = 36

z = 12

z+2 = 12 + 2 = 14

check:

z+1=12+1=13,

14+13+12 = 39

The mark up percentage gained by the shopkeeper is 400%.

For the given question.

The cost of the item is $103.

The customer pays is $515.

The mark up percentage is -

mark up percentage = 515 - 103 / 103

mark up percentage = 4 × 100%

mark up percentage = 400 %.

Thus, the mark up percentage gained by the shopkeeper is 400%.

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