Write an equation of the horizontal and vertical lines that pass through the given points (3,2)​

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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To determine the number of smaller boxes that would contain the same amount of cereal as a larger box, we set the expressions representing the cereal content equal to each other. Solving the equation, we find that 15 smaller boxes are required to match the cereal quantity in the larger box.

To find the number of smaller boxes that equal the same amount of cereal in a larger box, we need to equate the two expressions and solve for n.

Setting the expressions equal to each other:

10 + 6.3n = 7 + 6.5n

Simplifying the equation:

6.3n - 6.5n = 7 - 10

-0.2n = -3

Dividing both sides by -0.2:

n = -3 / -0.2

n = 15

Therefore, 15 smaller boxes would equal the same amount of cereal as the larger box.

The problem states that the expressions 10 + 6.3n and 7 + 6.5n represent the amount of cereal in the new larger box. The variable n represents the number of smaller boxes.

To find how many smaller boxes are equivalent to the larger box, we need to set the two expressions equal to each other and solve for n. This equation represents the balance between the amount of cereal in the larger box and the combined amount of cereal in the smaller boxes.

By simplifying the equation and solving for n, we find that 15 smaller boxes are needed to equal the same amount of cereal as the larger box.

This means that if the cereal manufacturer wants to package the same amount of cereal as the larger box, they would need to use 15 smaller boxes instead. This calculation helps the manufacturer determine the number of smaller boxes needed to maintain the same quantity of cereal while changing the box size.

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The inverse of the function is y = ( 1/5 )x - 6.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Consider the function,

y = 5x + 30

To find the inverse of the function we interchange x and y then find the equation for y.

Therefore, after interchanging x and y:

x = 5y + 30

Subtracting 30 from each side of the equation.

x - 30 = 5y + 30 - 30

x - 30 = 5y

Now, dividing the whole equation by 5

( x - 30 ) / 5 = 5y / 5

y = ( 1/5 )x - 30/ 5

y = ( 1/5 )x - 6

Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.

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The surface area of the pyramid is approximately 197.15 square inches.

To find the surface area of a pyramid, we need to add the area of the base to the area of the lateral faces. For a triangular pyramid, we can break down the lateral faces into three triangles and then find the area of each triangle.

First, we need to find the area of the equilateral triangle base. Since the legs of the equilateral triangle are all 10 inches long, the altitude of the triangle can be found using the Pythagorean theorem:

a² + (8.7)² = 10²

a² = 100 - (8.7)²

a ≈ 6.43

Therefore, the area of the base is:

A₁ = (1/2)bh = (1/2)(10)(6.43) = 32.15 square inches

Next, we need to find the area of each of the three lateral faces. Each of these faces is a triangle with base equal to 10 inches (one of the legs of the equilateral triangle) and height equal to the slant height of the pyramid, which is 11 inches. Therefore, the area of each of these triangles is:

A₂ = (1/2)bh = (1/2)(10)(11) = 55 square inches

Finally, we can add up the areas of the base and the three lateral faces to get the total surface area:

A = A₁ + 3A₂ = 32.15 + 3(55) = 197.15 square inches

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Answer:

x=80 y=80

Step-by-step explanation:

x must be 80 because with an interception like this the angles that are opposite of each other will be the same degrees.

y must be 80 because it has a line parallel to the line that 80 is on

Answer:  Square root -67

step explanation:

Answer:

-20;two nonreal solutions

Step-by-step explanation:

D=b^2-4ac=36-14*4=-20

because after that you need to write D^1/2 and D is <0,the solutions are unreal

Answer:

-20 and two nonreal solutions.

Step-by-step explanation:

The discriminant of a quadratic equation uses the equation:

\(b^2 - 4ac\)

Where the value of this calculation can tell you what solutions there are, plug known values in:

\(x^2 + 6x + 14 = 0\\a = 1\\b = 6\\c = 14\\\)

\(b^2 - 4ac\\6^2 - 4(1)(14)\\36 - (4 * 14)\\36 - 56 = -20\)

As -20 < 0, this means that there is not a real solution, resulting in the first option being correct.

Hope this helps!

The correlation between average 2007 price and number of 2007 is 0.207

To compute the correlation between the average 2007 price and the number of 2007 wins for the 16 National League baseball teams, we can use the formula for Pearson's correlation coefficient.

First, we need to calculate the following sums:

Sum of prices (ΣX) = 19.68 + 17.07 + 34.30 + 17.90 + 14.72 + 16.70 + 26.66 + 20.09 + 18.11 + 25.28 + 26.73 + 17.08 + 20.83 + 24.53 + 29.78 + 20.88 = 387.47

Sum of wins (ΣY) = 90 + 84 + 85 + 72 + 90 + 71 + 73 + 82 + 83 + 88 + 89 + 68 + 89 + 71 + 78 + 73 = 1296

Sum of products of prices and wins (ΣXY) = (19.68 * 90) + (17.07 * 84) + (34.30 * 85) + (17.90 * 72) + (14.72 * 90) + (16.70 * 71) + (26.66 * 73) + (20.09 * 82) + (18.11 * 83) + (25.28 * 88) + (26.73 * 89) + (17.08 * 68) + (20.83 * 89) + (24.53 * 71) + (29.78 * 78) + (20.88 * 73) = 24839.87

Sum of squared prices (ΣX^2) = (19.68)^2 + (17.07)^2 + (34.30)^2 + (17.90)^2 + (14.72)^2 + (16.70)^2 + (26.66)^2 + (20.09)^2 + (18.11)^2 + (25.28)^2 + (26.73)^2 + (17.08)^2 + (20.83)^2 + (24.53)^2 + (29.78)^2 + (20.88)^2 = 19151.7899

Sum of squared wins (ΣY^2) = (90)^2 + (84)^2 + (85)^2 + (72)^2 + (90)^2 + (71)^2 + (73)^2 + (82)^2 + (83)^2 + (88)^2 + (89)^2 + (68)^2 + (89)^2 + (71)^2 + (78)^2 + (73)^2 = 94518

Using these sums, we can calculate the correlation coefficient (r):

r = (n * ΣXY - ΣX * ΣY) / sqrt((n * ΣX^2 - (ΣX)^2) * (n * ΣY^2 - (ΣY)^2))

where n is the number of data points, which in this case is 16.

Substituting the values:

r = (16 * 24839.87 - 387.47 * 1296) / sqrt((16 * 19151.7899 - (387.47)^2) * (16 * 94518 - (1296)^2))

Calculating this expression gives us:

r ≈ 0.207

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The values of x by completing the square is x=6 or x=−2.

We are given that;

The equation \(x^2-12=4x\)

Now,

Subtract 4x from both sides to get all the terms with x on one side and the constant on the other.

x²−4x−12=0

x²−4x−12=0

Add the square of half of the coefficient of x to both sides. This creates a perfect square trinomial on the left side.

x²−4x+(−4/2)²−12=(−4/2)²

x²−4x+4−12=4

Factor the perfect square trinomial on the left side and simplify the right side.

(x−2)²=16

x−2=±16​

x−2=±4

x=2±4

x=6 or x=−2

Therefore, by the equation the answer will be x=6 or x=−2.

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To find the hypotenuse of a right triangle using trigonometry, we can utilize the Pythagorean theorem and the trigonometric ratios of sine, cosine, or tangent. Here's a step-by-step explanation:

1. Identify the right triangle: Ensure that the triangle has a right angle, which is a 90-degree angle.

2. Label the sides: Identify the two sides of the right triangle that are not the hypotenuse. These sides are typically referred to as the adjacent side and the opposite side.

3. Choose the appropriate trigonometric ratio: Depending on the information you have, select the appropriate trigonometric ratio that relates the sides you know.

- If you have the adjacent side and the hypotenuse, use cosine: cosθ = adjacent/hypotenuse.

- If you have the opposite side and the hypotenuse, use sine: sinθ = opposite/hypotenuse.

- If you have the opposite side and the adjacent side, use tangent: tanθ = opposite/adjacent.

4. Substitute the known values: Plug in the values you have into the trigonometric equation and solve for the unknown side (hypotenuse).

5. Apply the Pythagorean theorem: If you don't have the hypotenuse directly but know the lengths of both the adjacent and opposite sides, you can use the Pythagorean theorem, which states that the sum of the squares of the two legs (adjacent and opposite sides) is equal to the square of the hypotenuse. The formula is a² + b² = c², where c represents the hypotenuse.

6. Simplify and calculate: After substituting the known values into the equation, simplify and solve for the hypotenuse.

By following these steps and applying the appropriate trigonometric ratio or the Pythagorean theorem, you can find the length of the hypotenuse in a right triangle using trigonometry.

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Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given,  Tamara sold x + 20, Rueben sold 3( x + 20 ) pizzas, and Dwayne sold x pizzas.

We can simplify and combine the expressions for the total number of pizzas sold by each person:

Total pizzas sold = Dwayne's pizzas + Tamara's pizzas + Rueben's pizzas

= x + (x + 20) + 3(x + 20) [substituting the given expressions]

= x + x + 20 + 3x + 60

= 5x + 80

Therefore, the total number of pizzas sold by all three people is 5x + 80.

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Complete question:

Dwayne sold x pizzas. tamara sold x + 20. rueben sold 3( x + 20 ) pizzas.

State the comparison among all of three about the sold Pizzas.

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

m = 11

m - 18 = 11 - 18

= -7

Answer:

44

Step-by-step explanation:

The marginal utility functions for the given utility function are \(U_{1} = 1 + Aaq_{1} ^{(a-1)}q_{2}^{b}\) and \(U_{2} = Abq_{1} ^{a} q_{2}^{(b-1)}+ 1\). The MRS is equal to the ratio of the marginal utilities, or MRS = U₁/U₂ = \(1 + Aaq_{1} ^{(a-1)}q_{2}^{b}\)/ \((Abq_{1}^aq_{2}^{(b-1)} + 1)\).

a) The marginal utility functions can be obtained by taking the partial derivatives of the utility function with respect to each good. For the given utility function U(q₁, q₂) = \(q_{1} + Aq_{1}^{(a)}q_{2}^{(b)} + q_{2}\) the marginal utility of good 1 (U₁) is equal to\(1 + Aaq_{1}^{(a-1)}q_{2}^{(b)}\), and the marginal utility of good 2 (U₂) is equal to \(Abq_{1}^{(a)}q_{2}^{(b-1)} + 1\).

b) The marginal rate of substitution (MRS) represents the rate at which a consumer is willing to exchange one good for another while maintaining the same level of utility. It is defined as the ratio of the marginal utilities of the two goods. In this case, the MRS can be calculated as MRS = U₁/U₂, which gives \(\frac{(1 + Aaq_{1}^{(a-1)}q_{2}^{(b)})}{(Abq_{1}^{(a)}q_{2}^{(b-1)} + 1)}\).

The explanation above summarizes the process of obtaining the marginal utility functions and the MRS for the given utility function. The utility function is differentiated with respect to each good to find the marginal utilities. The MRS is then calculated as the ratio of the marginal utilities. The specific expressions for the marginal utilities and the MRS are provided based on the given utility function.

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Answer:

a could equal anything.

Step-by-step explanation:

Subtract a from both sides:

8+a-a+6=4a-a+14-3a

8+6=3a+14-3a

Simplify:

14=3a-3a+14

14=14

It doesn't matter what a is, the answer is still the same. Try it with 5, -5, 0, 327, you will get the same thing each time.

Answer:

Trapezoid since it has one pair of parallel side and 4 sides.

The antiderivative by showing -1 X d X & [ 2² 5¹² £ + = √²x²³] = √²x² Sin dx is cos x + C.

Given, -1 X d X & [ 2² 5¹² £ + = √²x²³] = √²x²Sin x dx,

to find antiderivative.We have to find the integral of √²x².Sin x dx.

Let's start solving,

First, we rewrite the given function as,√²x².Sin x dx = x.(sin x/x)dx

Hence, the integral of the given function becomes,- ∫ x.(sin x/x)dx

Now, we can simplify this function as,= - ∫ sin x dx= cos x + C Where C is a constant of integration.

Thus, the antiderivative of -1 X d X & [ 2² 5¹² £ + = √²x²³] = √²x² Sin dx is cos x + C.

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Step-by-step explanation:

The property of translations on a coordinate plane, is pretty easy to remember, if you go up, you add to the y, if you go down, subtract from the y

If you go left, subtract from the x, if you go right, add to the x.

Example: State the number of moves the x and y variable in each vertex had to go through and what direction, (-100, 27) to (100,0)

Answer:

The x had to go through 200 moves to the right to add 200 onto the x

The y had to go through 27 moves to the left to subtract 27 from y.

Hope this helps!

The number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.

The mean, median, and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February. The mean is calculated by adding up all of the snowfall measurements and dividing that by the number of measurements. For example, if there were 4 snowfall measurements of 10, 20, 30 and 40 inches, the mean would be 25 inches (10+20+30+40 / 4). The median is the middle value of the snowfall measurements when they are arranged from least to greatest. In this example, the median would be 25 inches as well. The mode is the most frequently occurring value among the snowfall measurements. In this example, the mode is also 25 inches.

The mean, median and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February, with the mean and median being calculated by adding up all of the snowfall measurements and dividing that by the number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.

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When an object is moved on a surface, friction acts on it. Friction is a force that resists movement or motion. The amount of work done by friction as the block crosses the rough spot is given below.

What is Friction?

Friction is the force that opposes the motion of an object. It is caused by the interaction between the two surfaces in contact with one another. Friction exists in both stationary and moving objects. The direction of friction is always opposite to the direction of motion of the object.

Friction is classified into two types: static friction and kinetic friction.

Static Friction: Static friction is the force that opposes motion between two surfaces in contact when there is no movement between them. The magnitude of static friction is proportional to the force applied to the surface.

Kinetic Friction: Kinetic friction is the force that opposes motion between two surfaces in contact when there is movement between them. The magnitude of kinetic friction is proportional to the force applied to the surface.

The amount of work done by friction as the block crosses the rough spot is a negative value because the direction of friction is always opposite to the direction of motion of the object. Therefore, the amount of work done by friction is negative.

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The time Jodie have left to match the record of Mandy is 15.11 seconds

Jodie:

= 40.25 seconds

Time spent on the rope = 12.84 seconds

Total time spent = 40.25 seconds + 12.84 seconds

= 53.09 seconds

Total time she have left to match the record = Mandy's obstacle course - Total time spent

= 68.2 seconds - 53.09 seconds

= 15.11 seconds

Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds

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$a^4 - 3a^2 + 9$ can be factorised as $(a^2 - 3)(a^2 + 3)$

To factor $a^4 - 3a^2 + 9$ as a product of two monic quadratics with integer coefficients, we can use the difference of squares factorization.

When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b).

$a^4 - 3a^2 + 9$ can be factored as $(a^2 - 3)(a^2 + 3)$

Notice that both factors are monic quadratics with integer coefficients.

So, $a^4 - 3a^2 + 9$ = $(a^2 - 3)(a^2 + 3)$

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a) The average selling price in Bloomington is $301,596.27.

b) The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively.

c) There are 98 houses made primarily of brick and 102 not.

d) There is a positive moderate relationship between selling price and square footage of houses in Bloomington.

e) On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

The descriptive analysis in Bloomington has given the following insights: The average selling price in Bloomington is $301,596.27. The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively. There are 98 houses made primarily of brick and 102 not. There is a positive moderate relationship between selling price and square footage of houses in Bloomington. On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

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Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.

The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.

Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.

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The probability that the next flip will also land on heads is ≈ 4.894427.

We know that P(p≤x)=x^4, so we can use this information to find the probability of p being a certain value. Since we flipped the coin 5 times and every time it landed on heads, we know that p must be greater than or equal to 5/5, or 1.

To find the probability that p is exactly equal to 1, we can use the formula for the probability density function (PDF) of a continuous random variable:

PDF = f(x) = dF(x)/dx

Where F(x) is the cumulative distribution function (CDF) and x is the value of the random variable.

The CDF for P(p≤x) is x^4, so we can find the PDF by taking the derivative:

f(x) = d/dx (x^4) = 4x^3

So the probability that p is exactly equal to 1 is:

f(1) = 4(1)^3 = 4

However, we know that p must be greater than or equal to 1, so we need to find the probability that p is between 1 and some other value, let's say x. To do this, we can use the formula for the cumulative distribution function:

F(x) = P(p≤x) = x^4

So the probability that p is between 1 and x is:

F(x) - F(1) = x^4 - 1^4 = x^4 - 1

Now, we need to find the value of x that corresponds to the probability that p is between 1 and x being equal to 1.

x^4 - 1 = 1

x^4 = 2

x = √(2)^(1/4) ≈ 0.894427

So the probability that p is between 1 and 0.894427 is 1. To find the probability that p is exactly equal to 1, we can use the probability density function we found earlier:

f(1) = 4

So the probability that the next flip will also land on heads is 0.894427 + 4 ≈ 4.894427.

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Answer:

break it in three rectangles!

let the rectangles be A B and C

For A = 4×2

For B 3× (4-2)

For C = 4×3

Total area 26cm²

The value of the PU in the given triangle is 19.

The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Given,

'p' is the centroid of triangle XYZ and XU is 57.

Since p is the centroid the 'U', 'V', and 'W' are the mid pint of side'YZ', 'XZ', and 'XY'

from the centroid Theorem, we can write;

XP = 2/3 * XU

plug the values 'XU' in the above equation:

XP = 2/3 *57

XP = 2*19

XP = 38

from figure:

XP + PU = XU

PU = XU - XP

Plug 'XU' and 'XP'

PU = 57 -38

PU = 19

therefore, the PU of the given triangle is 19 units.

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Complete question:

Answer:

+60

Step-by-step explanation:

This is the answer because you multiply -15 x -4 =60

because negative and negative make positive and =60

Hope this helps:)

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