For the situations below, define a random variable X for the situation and then decide if they follow a binomial distribution model by commenting on the four requirements.

1. You roll a DnD dice (20-sided), 20 times and record the number that shows on the dice.

2. A basketball player can make 60% of their free throws. The coach plans on having a free throw shooting competition and the player will be shooting 100 shots.

3. From a standard deck of cards, you pull out a card, record the suit, put it back and reshuffle. You continue until you get two spades in a row.

4. You are conducting a survey at your school to see how many students own smartphones. The probability that a student will own a smartphone is 0.85. You plan on having 200 students participate in your survey.

Answer:

Step-by-step explanation:

1200x5= it is 6000

Answer:

900=5x + 1200

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the distributive property, we can simplify the expression as follows:

3(r+2) + 5(r+t-2)

= 3r + 3(2) + 5r + 5t - 5(2)

= 3r + 6 + 5r + 5t - 10

= 8r + 5t - 4

Therefore, the simplified expression is:

8r + 5t - 4

The statement "if two noncollinear rays join at a common endpoint, then an angle is created" represents the geometry term "angle."

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.

The two rays are called the sides of an angle, and the common endpoint is called the vertex.

The angle that lies in the plane does not have to be in the Euclidean space.

An angle is formed when two non-collinear rays join at a common endpoint.

This endpoint is called the vertex of the angle.

The two rays are referred to as the arms of the angle.

Angles can be classified according to their degree measurement.

An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, and an obtuse angle

measures between 90 and 180 degrees.

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Answer:

y = 2x - 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (2, - 3 ) into the partial equation

- 3 = 2(2) + c = 4 + c ( subtract 4 from both sides )

- 7 = c

y = 2x - 7 ← equation of line

Answer: To solve this problem, we can use trigonometry and the relationship between angle, distance, and altitude in a right triangle.

Let's denote the angle the pilot was flying at takeoff as θ. We can then use the tangent function to find θ, since:

tan(θ) = opposite/adjacent

In this case, the opposite side is the altitude the pilot reached (1500 feet), and the adjacent side is the distance the pilot traveled before reaching that altitude (2 miles = 10560 feet). So we can plug in these values and solve for θ:

tan(θ) = 1500/10560

θ = tan⁻¹(1500/10560)

θ ≈ 7.67 degrees

So the pilot was flying at an angle of approximately 7.67 degrees at takeoff from the runway.

Step-by-step explanation:

The proof of the sum of the triangles ΔPMS + ΔMQT and ΔSOR + ΔNRT is shown below

Given that

PQRS and MNOP are parallelograms

We have the following congruent sides by the theorem of CPCTC

QT = RT and MQ = NR

PM = SO and MS = SR

This is alse true because of the SSS congruent theorem

When the sides are added, we get

PMS + MQT = SOR + NRT

So, we have

ΔPMS + ΔMQT = ΔSOR + ΔNRT

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Step-by-step explanation: To find the cost of one pickle, we can use a system of equations. Let x be the cost of one pickle and y be the cost of one popcorn box. Then we have:

2x + 2y = 10 4x + 2y = 13.50

Subtracting the first equation from the second, we get:

2x = 3.50 x = 1.75

So one pickle costs $1.75.

There are various techniques to simplify algebraic expressions, including:

1. Combining like terms: In an algebraic expression, like terms are terms that have the same variable raised to the same power. To simplify the expression, we can combine these like terms. For example, in the expression 3x + 2y + 5x - 4y, we can combine the x terms and the y terms to get 8x - 2y.

2. Distributing: When a number or variable is outside a set of parentheses and is being multiplied by a sum or difference inside the parentheses, the number or variable can be distributed to each term inside the parentheses. For example, in the expression 3(x + 2), the 3 can be distributed to both x and 2, resulting in the simplified expression 3x + 6.

3. Simplifying exponents: When an expression contains exponents, rules of exponentiation can be used to simplify the expression. For example, in the expression x^2 * x^3, the exponents can be added to give x^(2+3) = x^5.

4. Factoring: When an expression contains common factors, those factors can be factored out. For example, in the expression 2x^2 + 4x, both terms have a factor of 2 and a factor of x, so these factors can be factored out to give 2x(x + 2).

Answer:

If y=0, then 4y^2•2y^4 = 4(0)^2•2(0)^4 = 0.

Therefore, any of the options that involve y, such as A) 6y^6 or C) 8y^6, would also be equal to 0.

The only option that is still a valid answer is B) 6^8, which is simply 6 to the 8th power, or 1679616.

Hope This Helps!

A rough graph of T as a function of time t for hot water running from a tap would likely show an exponential decay curve.

Initially, the temperature of the water will be close to the temperature of the hot water supply in the house. However, as the water continues to flow, the temperature will gradually decrease due to heat loss through the pipes and the ambient temperature of the surrounding air. This decay will likely be exponential, with a relatively steep initial drop in temperature followed by a more gradual decrease over time. The graph would show an asymptotic approach towards room temperature as the water continues to flow. The exact shape of the curve will depend on a variety of factors, such as the length and material of the pipes, the ambient temperature, and the temperature of the hot water supply.

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t ≈ 0.59, 2.09, 3.68, 5.18, 6.77, 8.27, ... These are the times when the block is 5 cm above equilibrium.

The arccosine function, denoted as arccos(x) or acos(x), is the inverse function of the cosine function. In other words, given a value of x between -1 and 1, arccos(x) returns the angle whose cosine is x, in radians or degrees.

To find the times when the block is 5 cm above equilibrium, we need to solve the equation:

9cos((2π/3)t) = -5

Dividing both sides by 9, we get:

cos((2π/3)t) = -5/9

There are two solutions for cos(t) = -5/9 within the interval [0, 2π], which we can find using the inverse cosine function:

t = acos(-5/9) ≈ 2.498 or t = -acos(-5/9) ≈ -2.498

Since the function is periodic with a period of 6 seconds (as we can see from the coefficient of t in the cosine function), we can add integer multiples of the period to these solutions to get all possible solutions. Therefore, the general formula for all the solutions is:

t = (2kπ ± acos(-5/9))/2π, for any integer k ≥ 0

where ± is chosen according to the quadrant in which the solution lies. Since we want non-negative solutions, we can use only the positive value of t given by the formula above:

t = (2kπ + acos(-5/9))/2π, for any integer k ≥ 0

Rounding to two decimal places, we have:

t ≈ 0.59, 2.09, 3.68, 5.18, 6.77, 8.27, ...

These are the times when the block is 5 cm above equilibrium.

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The correct equivalent equation solved for y is y = a ÷ (πx).

The equivalent equation solved for y in the given formula

a = πxy is y = a ÷ (πx).
1. Start with the original formula:

a = πxy
2. To solve for y, we need to isolate y on one side of the equation.
3. Divide both sides of the equation by πx:

a ÷ (πx) = (πxy) ÷ (πx)
4. The πx terms cancel out on the right side of the equation, leaving:

y = a ÷ (πx).

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To find the amount of interest you will owe, we need to calculate the interest using the formula:

Interest = Principal * Rate * Time

Where:

- Principal = $777 (the amount you owe)

- Rate = 18% per year (expressed as a decimal, or 0.18)

- Time = 1 year (since you have been making payments for a year)

Plugging in these values, we get:

Interest = $777 * 0.18 * 1

Interest = $139.86

So, the amount of interest you will owe is approximately $139.86.

Answer:

Kirk started making the cake batter at 3:48 P.M. and it took him 1 hour and 3 minutes to make the batter. So he finished making the batter at 3:48 P.M. + 1 hour and 3 minutes = 4:51 P.M.

Then, the cake baked in the oven for 1 hour and 8 minutes. So the cake came out of the oven at 4:51 P.M. + 1 hour and 8 minutes = 5:59 P.M.

The value of angle ∠α in the triangle ΔPQR is 22.1°. Therefore, the answer is option (C)  i.e. 22.1°.

A closed triangle is a two-dimensional shape with three angles and three straight sides.

Three non-collinear points are connected with line segments to create one of the fundamental shapes in Three non-collinear points are connected with line segments to create one of the fundamental shapes in geometry Triangles can be categorized by their sides and angles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles.

The sum of a triangle's internal angles is always 180 degrees.

We can use trigonometry to solve for the angle α in the right triangle PQR.

We know that tan α = PQ/QR, where PQ is the opposite side and QR is the adjacent side.

Substituting the given values, we get:

tan α = 5.2/13.4

Taking the inverse tangent of both sides, we get:

α = tan⁻¹(5.2/13.4)

Using a calculator, we get:

α ≈ 22.1°

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when y = 5 in the equation y = -3x + 5, the value of variable x is 0.

An equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true.

the steps to find out what x is in the equation y = -3x + 5 for y = 5:

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The complete question is:

I need a step by step process for to find out what, "x" is in this problem. y = -3x +5 for y=5

the combined weight of the two pieces of leaf is 1.47 x 10⁻²grams.

HOW TO FIND WEIGHT ?

To find the combined weight of the two pieces of leaf, we simply need to add the weights of the individual pieces of leaf. We are given that one piece of leaf weighs 1.25 x 10⁻² grams and the other piece of leaf weighs 2.3 x 10⁻³ grams.

Adding these two weights, we get:

1.25 x 10⁻²grams + 2.3 x 10⁻³ grams = 1.47 x 10⁻² grams

Therefore, the combined weight of the two pieces of leaf is 1.47 x 10⁻²grams.

It's important to note that when working with scientific notation, we need to pay attention to the exponents and perform the operations according to the rules of exponents. In this case, we add the numbers in front of the exponent (1.25 and 2.3) and keep the exponent (10⁻²) the same.

It's also worth mentioning that this problem involves very small weights, as the values are expressed in grams using scientific notation. This is a common approach when dealing with very large or very small values in scientific contexts, as it allows us to easily express and compare values using a standardized format

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There are 20,149 different paths from A to B in the given hexagonal lattice, satisfying the given conditions.

To solve this problem, we can use the Principle of Inclusion-Exclusion (PIE). We start by counting the total number of paths from A to B without any restrictions, which is simply 6!/(3!3!) = 20,160. This is the number of ways to arrange 3 up arrows and 3 right arrows.

Next, we count the number of paths that violate the restriction on the middle segment. There are two cases to consider, The bug travels the middle segment from left to right: There are 3 choices for the path of the bug on the top half of the hexagon and 2 choices for the path on the bottom half, for a total of 3*2 = 6 paths.

The bug travels the middle segment from right to left: This is the same as case 1, so there are another 6 paths. However, we have counted some paths twice, namely those that violate both restrictions on the middle segment. There is only one such path, which is the one that starts with the up arrow, goes left on the top half of the hexagon, and goes right on the bottom half.

Thus, the total number of valid paths is 20,160 - 6 - 6 + 1 = 20,149.

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First thing you need to do is raise the decimal. Once you've raised the decimal then you should continue through the problem as if it were a standard long division question.

Start with the first number which is 6.

6 divided by 3 is 2. That means you can subtract 6 from the first number.

Then, you bring down 3 and do the same thing.

3 divided by 3 is 1. Subtract 3 from 3 and then bring down the next number.

Finally, 3 divided by 9 is three.

By following this process, you should get 2.13 as your final answer.

Look at the image below for more reference.

The area of the base (B) to be 15.588 cm², the height of the prism (h) to be 22 cm, and the volume (V) of the prism to be 343.996 cm³.

Area is a measure of the size of a two-dimensional surface or shape. It is measured in square units such as square meters (m2), square centimeters (cm2), square kilometers (km2), and square miles (mi2). Area can also be calculated for three-dimensional shapes, such as cubes and spheres, by multiplying length, width, and height. For example, the area of a cube with sides of length 10 cm would be 1000 cm2. Area is an important concept in mathematics and has many practical uses in real life.


Base Area (B):
To calculate the area of the base, we use the formula for the area of an equilateral triangle: B = (√3/4) × a², where a is the side length.

In this case, a = 6 cm. Therefore, B = (√3/4) × 6² = 15.588 cm².

Height (h):
The height of the prism is the height of the triangle (12 cm) plus the height of the floor (10 cm). Therefore, h = 12 cm + 10 cm = 22 cm.

Volume (V):
The volume of the prism is equal to the area of the base times the height of the prism. Therefore, V = B × h = 15.588 cm² × 22 cm = 343.996 cm³.

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To prepare the cash flow statement, we can use the indirect method, which involves adjusting the net income figure for non-cash items and changes in working capital to arrive at the net cash flow from operating activities. Then, we can account for cash flows from investing and financing activities to arrive at the net change in cash and cash equivalents.

Here's the cash flow statement for Year II:

Cash flow from operating activities:

Net income: Rs. 30,000 (180,000 - 100,000 - 50,000 - 5,000 - 5,000)

Adjustments for non-cash items:

Depreciation: Rs. 30,000 (230,000 - 200,000)

Changes in working capital:

Increase in stock: Rs. 10,000 (100,000 - 90,000)

Increase in debtors: Rs. 20,000 (60,000 - 40,000)

Increase in creditors: Rs. 10,000 (80,000 - 70,000)

Net cash flow from operating activities: Rs. 100,000

Cash flow from investing activities:

Purchase of fixed assets: Rs. 30,000 (230,000 - 200,000)

Net cash flow from investing activities: Rs. -30,000

Cash flow from financing activities:

Repayment of debentures: Rs. 20,000 (50,000 - 30,000)

Payment of dividends: Rs. 5,000

Net cash flow from financing activities: Rs. -25,000

Net change in cash and cash equivalents: Rs. 45,000 (100,000 - 30,000 - 25,000)

Cash and cash equivalents at the beginning of the year: Rs. 60,000

Cash and cash equivalents at the end of the year: Rs. 105,000

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The lateral surface area of the triangular prism container is 270 cm².

We will begin with the calculation of perimeter of equilateral triangle.

Perimeter = 3 × sides

Perimeter = 3 × 6

Perimeter = 18 cm

Now calculating the lateral surface = perimeter of base × height

Keep the values in formula

Lateral surface of equilateral triangle prism = 18 × 15

Performing multiplication again

Lateral surface area = 270 cm²

Thus, the lateral surface area of the container is 270 cm².

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The picture is added of equilateral triangle with dimensions.

The probability that the mean yield of the 80 one acre plots chosen will be within 2 bushels of the population mean is 0.9332. The assumptions made to answer part (a) are that the population standard deviation is known, the sample is randomly selected, and the sample size is large (n>=30)

a) We can use the central limit theorem to approximate the distribution of the sample mean. The distribution of the sample mean can be approximated as a normal distribution with a mean of 107 bushels and a standard deviation of 12/√80=1.34 bushels. Therefore, we can find the probability that the sample mean falls within 2 bushels of the population mean using the standard normal distribution.

P(105 ≤ X ≤ 109) = P(Z ≤ (109-107)/1.34) - P(Z ≤ (105-107)/1.34)

= P(Z ≤ 1.49) - P(Z ≤ -1.49)

= 0.9319 - 0.0681

= 0.8638

Therefore, there is an 86.38% probability that the mean yield of the 80 one acre plots will be within 2 bushels of the population mean.

b) Assumptions made:

The sample of 80 one acre plots is selected at random.

The one acre plots are independent of each other.

The population standard deviation is known and remains constant.

The distribution of the yield of corn per acre is approximately normal.

The sample size is large enough (n≥30) to apply the central limit theorem.

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The angle m∠A + m∠C = 180° in the inscribed quadrilateral ABCD.

To prove that m∠A + m∠C = 180° in an inscribed quadrilateral ABCD with circle O, follow these steps:
1. Statement: Quadrilateral ABCD is inscribed in circle O.
  Reason: Given.
2. Statement: m∠BCD = 2(m∠A) and m∠DAB = 2(m∠C).
  Reason: Inscribed Angle Theorem
3. Statement: m∠BCD + m∠DAB = 360°.
  Reason: The sum of the measures of the angles in a circle is 360°.
4. Statement: 2(m∠A) + 2(m∠C) = 360°.
  Reason: Substitution Property (from steps 2 and 3).
5. Statement: m∠A + m∠C = 180°.
  Reason: Division Property of Equality (divide both sides of the equation in step 4 by 2).

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The horizontal axis of the graph represents the total number of individuals who made a choice, and the vertical axis represents the type of snack.

The graph has two bars, one for sweet snacks and one for salty snacks. Each bar is segmented to represent the number of adults and children who chose each type of snack. For the first row of the table, the sweet snack bar is segmented into two parts: one representing the 57 adults who chose a sweet snack, and the other representing the 77 children who chose a sweet snack. The total length of the bar is 134, representing the total number of individuals who made a choice.

For the second row of the table, the salty snack bar is segmented into two parts: one representing the 88 adults who chose a salty snack, and the other representing the 31 children who chose a salty snack. The total length of the bar is 119, representing the total number of individuals who made a choice.

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The complete question is:

At a school social, parents attended with their children. Everyone had a choice between a sweet snack and a salty snack. Here is a two-way table showing the number of adults and children who made each choice of snack.

Make a segmented bar graph to represent the data in your table. Use one bar for each row of the table

(12, 23)  are the coordinates of the center of the rectangle with coordinates (6, 38) and (18, 8).

To find the coordinates of the center of the rectangle in the standard (x, y) coordinate plane, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are:

((x₁ + x₂) / 2, (y₁ + y₂) / 2)

In this case, the opposite vertices of the rectangle have coordinates (6, 38) and (18, 8). We can use these coordinates to find the midpoint of the rectangle as follows:

The x-coordinate of the midpoint is (6 + 18) / 2 = 12.

The y-coordinate of the midpoint is (38 + 8) / 2 = 23.

Therefore, the coordinates of the center of the rectangle are (12, 23)

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An independent samples t-test would be appropriate to analyze the difference in running speed between rats that received a steroid drug supplement and those that did not.

The appropriate statistical test to analyze the difference in running speed between two groups of rats (one receiving a steroid drug supplement and one not receiving it) would be a t-test. Specifically, an independent samples t-test would be suitable for this type of comparison, assuming that the data meets the assumptions for parametric testing.

This test would compare the means of the two groups and assess the probability that the observed difference is due to chance alone. A significant result would indicate that the difference in running speed is unlikely to be due to chance and is instead likely to be a true effect of the steroid drug supplement

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Therefore , the solution of the given problem of equation comes out to be y = -0.9x + 5.5 is the equation for the line of best fit, and r = -0.83 is the correlation value.

What is correlation?

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect

What is an equation?

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could divide 12 into two parts, evaluate the information provided by y + 7, and generate y + 7.

Here,

The least squares technique can be used to determine the equation of the line, presuming that the line of best fit is a linear regression line.

The findings that we get using a calculator or statistical software are as follows:

=> y = -0.9x + 5.5 is the equation of the line of best fit.

=> R = -0.83 is the correlation coefficient (r).

We can infer that there is a negative link between the two variables because the correlation coefficient (r) is negative.

This implies that the value of y tends to decline as the value of x rises.

As a result, y = -0.9x + 5.5 is the equation for the line of best fit, and r = -0.83 is the correlation value.

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The cost of the cereals and where the family should buy, obtained by simple arithmetic operations are;

A. The cost of 1, 2, 3, and 4 boxes of cereals are;

Corner Store; $4.5, $9, $13.5, $18

Bargain World; $6, $9.5, $13, $16.5

B. When the number of boxes of cereals bought are less than 3, the family shoulds buy from the Bargain World, when the number of cereals bought  are more than 3, the family should buy from the Bargain World Store

Simple arithmetic operations are addition, subtraction, division and multiplication operations.

A. The cost of the boxes of cereal obtained by arithmetic operations are as follows;

The cost of buying 1, 2, 3, and 4 boxes at the Corner store obtained from the graph are;

1 box costs $4.5

2 boxes costs $9

3 boxes costs $13.5

4 boxes costs $18

The cost of buying 1, 2, 3, and 4 boxes at the Bargain World are;

Cost of buying the first box = $6

Cost of buying 2 boxes = $6 + $3.5 = $9.5

Cost of buying 3 boxes = $6 + $3.5 + $3.5 = $13

Cost of buying 4 boxes = $6 + $3.5 + $3.5 + $3.5 = $16.5

B. Based on the costs which is initially higher at the Bargain World store, a family.

The cost of 3 boxes at the Bargain World is $13, while at the Corner Store, it is $13.5

The higher number of boxes are more expensive at the Corner Store than the Bargain Worldstore

Therefore, a family should buy from the Corner Store when they are buying less than 3 boxes of cereal and they should buy from the Bargain World when they are buying more than 3 boxes of cereal

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