in example 2.10, identify three events that are mutually exclusive. b. suppose there is no outcome common to all three of the events a, b, and c. are these three events necessarily mutually exclusive? if your answer is yes, explain why; if your answer

Alisha needs to use a fraction of 3/8 of each of the ingredients on the recipe.

We know that a pancake recipe calls for 8 eggs and some other ingredients.

But Alisha only has 3 eggs, so she needs to adjust the recipe.

The fraction of each one of the other ingredients that she needs to use is equal to the fraction between the number of eggs that she has and the number of eggs that the recipe calls, it is:

N = 3/8

So she needs to use 3/8 of each of the ingredients that the recipe calls.

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$0.80 required for a 200g packet cost and $0.01 required for a 100g packet cost

To find the cost of a 200g packet,

you can use the unit price,

which is the cost per gram of the biscuits.

To get the unit price, divide the cost of the 600g packet by its weight: $2.40 / 600g = $0.004/g.

Then multiply the unit price by the weight of the 200g packet to get its cost:

$0.004/g * 200g = $0.80.

To find the cost of a 100g packet of Orea's,

Use the same process as above:

$2 / 200g = $0.01/g.

Then multiply the unit price by the weight of the 100g packet to get its cost:

$0.01/g * 100g = $0.01.

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The slope-intercept equation of the line that includes the points (1, 1) and (2, 8) is y = 7x - 6.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (1, 1) and (2, 8) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 1 = (8 - 1)/(2 - 1)(x - 1)

y - 1 = 7(x - 1)

y = 7x - 7 + 1

y = 7x - 6

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The total surface area of the rectangular prism is 103.12 square inches.

The surface area of the rectangular prism can be calculated using the formula which is given as: 2 * (lw + lh + wh), where:

w = width of the prism

h = its height

l = its length.

Given the following:

Length = 7.1 in

Width = 2.8 in

Height = 3.2 in

Therefore:

Total surface area = 2 * (7.1 * 2.8 + 7.1 * 3.2 + 2.8 * 3.2)

= 2 * (19.88 + 22.72 + 8.96)

= 2 * 51.56 in^2

= 103.12 square inches.

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So, if they plan to practice a total of 45 minutes and have only completed 18.5 minutes that means they have 26.5 minutes of practice remaining (45-18.5).

Answer:

Step-by-step explanation:

Normally distributed residuals is not an assumption of the general linear model and hence option b is correct

Linear regression models relate to some assumptions about the distribution of error terms. If they are violated violently, the model is not suitable for drawing conclusions. Therefore, it is important to consider the suitability of the model for information before further analysis can be performed based on this model.

The fit of the model is related to the remaining behavior complying with the basic assumptions for error values in the model. When a regression model is constructed from a series of data, it should be shown that the model responds to the standard statistical assumptions of the linear model because of conducting inference. Residual analysis is an effective tool to investigate hypotheses. This method is used to test the following statistical assumptions for a simple linear regression model:

-Regression function is linear in parameters,

-Error conditions have constant variance,

-Error conditions are normally distributed,

-Error conditions are independent.

Normally distributed residuals is not an assumption of the general linear model and hence option b is correct

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Answer:

sup dudes pls what state is this and plus is this logarithms

Answer:

7.77

Step-by-step explanation:

49.77 - 42 = 7.77

P ( A or B ) ≠ P(A) + P(B) Hence, A and B are not mutually exclusive.

therefore the given condition is not true and hence statement is not true for the given events

Two events are called mutually exclusive they are independent to each other.

Also, If A and B are any two events,

Then they are called mutually exclusive,

If P(A ∪ B ) = P(A) + P(B)

Or P ( A or B ) = P(A) + P(B)

Here, P(A) = 0.37, P(B) = 0.38 and P(A or B) = 0.27

Since,

0.27 ≠ 0.37 + 0.38

⇒  P ( A or B ) ≠ P(A) + P(B)

Hence, A and B are not mutually exclusive.

therefore the given condition is not true and hence statement is not true

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Given matrices A and Q, the matrix R can be calculated as: R = Q^T * A.

The QR factorization is the factorization of a matrix A into an orthogonal matrix Q and an upper triangular matrix R. Given matrices A and Q, the matrix R can be calculated as:

R = Q^T * A

Where Q^T is the transpose of Q.

Note that this calculation assumes that Q is an orthogonal matrix, meaning that its transpose is equal to its inverse. If Q is not orthogonal, it will not have an inverse and the QR factorization cannot be calculated in this manner.

Therefore, Given matrices A and Q, the matrix R can be calculated as: R = Q^T * A.

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Answer:

15 prints

Step-by-step explanation:

Let's call the number of small prints sold as "x".

The number of medium prints sold is then (52 - x) prints.

We know that the total revenue from all the prints sold is $2,975, so we can set up the following equation:

$2975 = (x * $50) + ((52 - x) * $75)

Expanding and solving for x:

$2975 = $50x + $3900 - $75x

$2975 = $3900 - $25x

$-925 = -$25x

x = 37

So, Catori sold 37 small prints and (52 - 37) = 15 medium prints

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Answer:

8x + 8 * 2 = 200

Step-by-step explanation:

Let's assume that each friend received x flyers to pass out.

The equation would be:

8x + 8 * 2 = 200

8x = 184

x = 23

So each friend received 23 flyers and 2 bags, and in total, they received 23 * 8 + 8 * 2 = 200 items.

The value of the correlation coefficient would not change.

The following would be the correlation change if the stopping distances were recorded in meters, rather than feet.

Hence, option (A) is the correct choice.

Correlation is a statistical number derived based on historical data (profitability), and, contrary to popular belief, it is not constant and can change over time.

Correlation is a statistical term that reflects how much two or more variables vary in relation to one another.

The correlation coefficient is evaluated on a scale ranging from + 1 to - 1. The degree of correlation between two variables is denoted by + 1 or -1. When one variable rises as the other rises, the correlation is positive; when one falls as the other rises, the correlation is negative.

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The rate of change of f'(x) at (1, 13) is 25.

We have,

To find the rate of change of the derivative f'(x) at point (1, 13), we first need to find the derivative of the function f(x).

Given: f(x) = 14x² - x³

To find f'(x), we differentiate f(x) with respect to x:

f'(x) = d/dx (14x² - x³)

= 28x - 3x²

Now, to find the rate of change of f'(x) at x = 1,

we substitute x = 1 into the derivative expression f'(x):

f'(1) = 28(1) - 3(1)²

= 28 - 3

= 25

Therefore,

The rate of change of f'(x) at (1, 13) is 25.

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If the equation be 2x² + 7x – 30 then the solution to this equation be 2.5.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Let the given equation be 2x² + 7x – 30 = 0

Factorizing it as

(2x – 5) (x + 6) = 0

then we get

2x – 5 = 0 or x + 6 = 0

simplifying the equation we get

2x = 5 or x = –6

x = 5/2 or x = –6

x = 2.5 or x = –6

Therefore, the correct answer is option a) 2.5.

The complete question is:

Which value of x is a solution to this equation?

2x² + 7x – 30

a) 2. 5

b) 5

c) -2. 5

d) -3

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The height of the corresponding to the longest side is 25.03 cm

Given data :

Let the sides of triangles are 3x,5x and 7x.

And perimeter of the triangle is 120cm.

So , 3x + 5x +7x =120

       15x = 120

         x = 8

so, the sides are triangle are 3(8) = 24cm, 5(8) = 40cm , 7(8) = 56cm

so , the longest side is 56 cm.

Area of triangle =   [tex]\sqrt{s(s - a)(s -b)(s-c)}[/tex]

here , s = 64  and a = 24, b = 40c = 56

= [tex]\sqrt{64*(64-24)(64-40)(64-56)}[/tex]

= [tex]\sqrt{64*(40)(24)(8)}[/tex]

=[tex]\sqrt{491520}[/tex]

= 701.08

So, the area of triangle is 701.08 cm 2 and the height corresponding to longest side

h = 2 x 701.08 / 56 = 25.03 cm

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Answer:

y = [tex]\frac{3}{2}[/tex] x

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 slope m = [tex]\frac{3}{2}[/tex] and y- intercept c = 0 , then

y = [tex]\frac{3}{2}[/tex] x + 0 , that is

y = [tex]\frac{3}{2}[/tex] x

The statement that is not a characteristic of the normal probability distribution is "the graph of the curve is the shape of a rectangle."

The normal probability distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is described by its mean and standard deviation, and its graph can be used to represent the distribution of a continuous random variable. The total area under the curve of the normal distribution is equal to 1, which represents the probability of observing any value within the range of the distribution.

The mean, median, and mode of a normal distribution are equal and located at the center of the distribution. This is why the normal distribution is often referred to as the "bell-shaped" distribution. The shape of the curve is a smooth, symmetrical shape that slopes gently and then becomes more steep as it approaches the tails of the distribution.

Finally, it's true that a random variable that follows a normal distribution assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. This is a property of the normal distribution known as the empirical rule or the 68-95-99.7 rule.

In summary, the statement "the graph of the curve is the shape of a rectangle" is not a characteristic of the normal probability distribution, while the other statements are.

Therefore, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.

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The statement that is not a characteristic of the normal probability distribution is "the graph of the curve is the shape of a rectangle."

The normal probability distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is described by its mean and standard deviation, and its graph can be used to represent the distribution of a continuous random variable. The total area under the curve of the normal distribution is equal to 1, which represents the probability of observing any value within the range of the distribution.

The mean, median, and mode of a normal distribution are equal and located at the center of the distribution. This is why the normal distribution is often referred to as the "bell-shaped" distribution. The shape of the curve is a smooth, symmetrical shape that slopes gently and then becomes more steep as it approaches the tails of the distribution.

Finally, it's true that a random variable that follows a normal distribution assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. This is a property of the normal distribution known as the empirical rule or the 68-95-99.7 rule.

In summary, the statement "the graph of the curve is the shape of a rectangle" is not a characteristic of the normal probability distribution, while the other statements are.

Therefore, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.

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Triangle ABC is similar to triangle ADE by AA test of similarity

Similarity is a property which says that the respective angles of two triangles are of equal measure and corresponding sides are in proportion.

here, we have,

There are different types of similarity test by which we can prove the similarity of triangles.

We are given that BC is parallel to Line DE

As the lines are parallel the respective angle are corresponding angles

hence Angle D = Angle B

And Angle E = Angle C

And both triangle have angle A as common angle

By AA test of similarity we can say that the two triangles are similar

Hence by AA test similarity the two triangles are similar

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The correct way to report the length of the rectangle in centimeters would be (b)"15.6 cm".

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°).

The general practice is to report measurements to the appropriate number of significant digits. In this case, "15.6 cm" accurately reflects the measurement to the nearest tenth of a centimeter and uses the proper unit symbol (cm). "15.600 cm" and "15.60 cm" include more significant digits than are necessary and "16 cM" uses an incorrect unit symbol.

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Answer:=1±√5

Step-by-step explanation:

aight so bassically i looked this shi up and yeah thats what what i got bro

Jay is given 65% discount

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred

Percentage discount can be gotten with the formula below:

Discount % = (Discount/Original Price) × 100.

From the question,

Jay pays 27300, instead of 42000

Using the percentage discount above

Percentage Discount = 27300/42000 x 100

Percentage Discount = 65%

Hence, jay got 65% discount from the school

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If q² – 4pr > 0, the roots of the quadratic equation px² + qx + r = 0 will be: "negative, if p, q, and r are positive". Therefore, Suman answered correctly.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.

Generally speaking, the standard form of a quadratic function is given by ax² + bx + c = 0.

Assuming the roots of the quadratic function are a and b. Therefore, the sum of the roots of the quadratic function would be equal to -q/p;

a + b = -q/p

ab = r/p

This ultimately implies that, the nature of the roots would depend on the value of p, q and r, which make Zain's answer to be wrong.

Additionally, if p, q, and r are positive, a + b would be negative, and one or both roots must be negative, which make Vipul's to be wrong.

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In the second option (b) the rectangles have the area and the perimeter the same number of units or square units.

What are the perimeter and area?

The area is the region covered by shape or figure whereas the perimeter is the distance covered by the outer boundary of the shape. The unit of area is given by a square unit or unit2 and the unit of the perimeter is the same as the unit.

(a)

Area of a rectangle = length ×  breadth

              =(8×6)

              =48 feet²

Perimeter of the rectangle = 2(length + breadth)

                           =2(6+8)

                           =28 feet

(b)

Area of a rectangle = length ×  breadth

              = (4×4) yards²

              = 16 yards²

Perimeter of the rectangle = 2(length + breadth)

                           =2(4+4)

                           =16 inches

(c)

Area of a rectangle = length ×  breadth

              =(9×4) inches²

              = 36 inches²

Perimeter of the rectangle = 2(length + breadth)

                           =2(9+4)

                           =26 inches

(d)

Area of a rectangle = length ×  breadth

              =(7×4) meters²

              =28 meters²

Perimeter of the rectangle = 2(length + breadth)

                           =2(7+4)

                           =22 meters

Hence, In the second option (b) the rectangles have the area and the perimeter the same number of units or square units.

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The speed of Joshua's skating rate is given by the equation A = 7 m/s

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The rate of Joshua's skating is given by S = 35 meters / 5 seconds

So , the rate S = 35/5

And , the unit rate of Joshua's skating rate is given by A = 35/5

On simplifying the equation , we get

The unit rate of Joshua's skating rate is given by A = 7 meters per second

The unit rate of Joshua's skating rate is given by A = 7 m/s

Hence , the skating rate of Joshua's skating is 7m/s

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The ratio of the given expression is equal to 1:16.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Sometimes, pupils struggle to understand the relationship between ratio and proportion.

We have x=1 and y=2, and we have to find the ratio of x4:y4,

x=1 and y=2 (given)

[tex]x^4:y^4=(1)^4:(2)^4\\\\x^4:y^4=1:16=1/16[/tex]

the ratio of the given expression is equal to 1:16.

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Answer:

she should charge $10 for interest or even more is she wants to make $1005 per year from investing

The annual property tax for the Joseph family is $8749.8.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

The Joseph family took out a $175,000,

25-year mortgage at an APR of 4%.

The assessed value of their house is $9,000.

The annual property tax rate is 97.22% of assessed value.

The annual property tax = 9000 x 97.22/100

The annual property tax = $8749.8

Therefore, the annual property tax = $8749.8

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Solution is in the attachment!!