a professor gave his students two exams.40% of the students passed both exams. 80% of the students passed the second exam.how many students (in percent) who passed the second exam also passed the first exam ?

Therefore ,we would reject the null hypothesis H0: = 3 in favor of the alternative hypothesis HA: 3. The graph's rejection zone is highlighted in red for visual appeal.

The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true. A number between 0 and 1 is the probabilities of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Here,

Two-Tailed

For the two-tailed test H0, the following two values are critical: = 3 against HA: 3 — one for each tail, with the left tail being denoted by -t(/2, n - 1) and the right tail being denoted by t(/2, n - 1). The t-values t(/2, n - 1) and -t(/2, n - 1) are those where the probability to the left of them is /2 and the likelihood to the right is /2, respectively. It is possible to demonstrate the crucial values -t0.025,14 is -2.1448 and t0.025,14 is 2.1448, respectively, using statistical software or a t-table. This means that if the test statistic t* is less than -2.1448 or more than 2.1448, we would reject the null hypothesis H0: = 3 in favor of the alternative hypothesis HA: 3. The graph's rejection zone is highlighted in red for visual appeal.

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The equation of line perpendicular to the given line is,

[tex]y = \frac{5}{2}x - 13[/tex].

What is slope point form of the line?

The general form of a linear equation is y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Consider the given equation of line,

[tex]y = -\frac{2}{5}x - 1[/tex]

Compare it with y = mx + c

where m is the slope.

⇒ Slope of the line is -2/5.

We have to find the equation of line perpendicular to the given line.

Since the slope of the perpendicular line is negative reciprocal of the slope of given line.

So, the slope of perpendicular line is [tex]-\frac{1}{(\frac{2}{5}) } = 5/2[/tex].

The point passes through (2, -8).

Now consider, the point slope form of the line

[tex]y-y_1 = m(x-x_1)\\[/tex]

Plug [tex](x_1, y_1) = (2, -8) , m = \frac{5}{2}[/tex] in the above equation.

⇒

[tex]y - (-8) = \frac{5}{2}(x-2)\\ y+8 = \frac{5}{2}x - 5\\ y = \frac{5}{2}x-5-8\\ y = \frac{5}{2}x - 13[/tex]

Hence, the equation of line perpendicular to the given line is,

[tex]y = \frac{5}{2}x - 13[/tex].

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Answer: QB≈4.24

Step-by-step explanation:

Q(1,0)    B(-2,-3)   QB=?

[tex]\boxed{L=\sqrt{(x_2-x_1)+(y_2-y_1)^2} }\\\\x_1=1\ \ \ \ x_2=-2\ \ \ \ y_1=0\ \ \ \ y_2=-3[/tex]

Hence,

[tex]QB=\sqrt{(-2-1)^2+(-3-0)^2} \\\\QB=\sqrt{(-3)^2+(-3)^2} \\\\QB=\sqrt{9+9} \\\\QB=\sqrt{18} \\\\QB=\sqrt{9(2)} \\\\QB=\sqrt{3^2(2)} \\\\QB=3\sqrt{2} \\\\QB\approx4.24[/tex]

Answer:

To put the equation in standard form, we need to get all the terms with variables on one side of the equation and all the constants on the other side. We can start by moving the 4/3 to the right side of the equation:

Y - 2/3 = 4/3(x + 2)

Y = 4/3(x + 2) + 2/3

Next, we can distribute the 4/3 on the right side of the equation to get:

Y = (4/3)x + (4/3)2 + 2/3

Y = (4/3)x + (8/3) + 2/3

Finally, we can combine like terms to get:

Y = (4/3)x + (10/3)

This is the standard form of the equation.

Answer -3y+4x=-10

Step-by-step explanation:

The probability that either a or b occurs is 0.7.

Given :

event  a has a probability of 0.5 , and event b has a probability of 0.4. if a and b are independent events.

P ( a ) = 0.5

P ( b ) = 0.4

we know that,

P ( a or b ) = P ( a ) + P ( b ) - P ( a and b )

if a and b are both independent

P ( a and b ) = P ( a ) * P ( b )

substitute we get

P ( a or b ) = 0.5 + 0.4 - 0.5 * 0.4

= 0.9 - 0.2

= 0.7

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The addition is 5x - 2. We can find out our answer using simple arithmetic calculations.

What are arithmetic calculations?

Arithmetic calculations are mathematical operations used to solve equations and perform numerical calculations. They include addition, subtraction, multiplication, and division. Arithmetic is a fundamental part of mathematics, and it is an important part of everyday life. Arithmetic is used to solve problems in a variety of fields, such as engineering, finance, and science. It is also used in everyday tasks such as grocery shopping and budgeting. Arithmetic calculations are essential for most people and can help them understand and solve a variety of problems. By mastering basic arithmetic calculations, people can make more informed decisions and better understand the world around them.

In algebraic expressions ,

same variables are added together and constants together.

In given equation,

2x and 3x are added i.e. 5x

and 5 and -7 are added  i.e. -2

So, the equation is 5x-2.

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Answer:

Corresponding angels:

a,f

h,b

e,d

c,g

y = 80  Vertical angles are congruent

x = 50 Sum of the interior angles of a triangle is 180

180 - 80 -50 = 50

Step-by-step explanation:

1. Linear pair theorem

2. Substitution property of equality

3. Subtraction property of equality

4. Definition of congruence

The given results can be proved by the linear pair property of angles on a straight lines.

The linear pair property can be defined as the sum of all the angles on the one side of a straight line is equal to 180°.

In the given diagram the following data is given,

The angles ∠DEH and ∠DEF are on the straight line HEF.

And, the angles ∠DEF and ∠FEG are on the straight line DEG.

As per the linear property of angles, it can be written as,

m∠DEH + m∠DEF = 180°.

And,  m∠DEF + m∠FEG = 180°.

Which implies that m∠DEH + m∠DEF = m∠DEF + m∠FEG

Subtract the common terms from both sides to get,

m∠DEH + m∠DEF - m∠DEF = m∠DEF + m∠FEG - m∠DEF

⇒ m∠DEH = m∠FEG

⇒ ∠DEH ≅ ∠FEG

This is also known as the property of vertically opposite angles.

Hence, the given result m∠DEH = m∠FEG is proved by the linear pair property.

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the proportionality constant is 20 and in 8 ours it will cover 160 miles.

What is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

The slope of he given graph will be (30-10)/(2-1) = 20

So here the proportionality constant is 20.

we can write y = 20x

This means in 8 ours it will cover 8*20 = 160 miles.

Hence, the proportionality constant is 20 and in 8 ours it will cover 160 miles.

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Function h is the one with the lowest minimum value.

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

A function is more precisely defined as a set of ordered pairs (x,y) with the limitation that there may only be one ordered pair with the same value of x given a set of inputs (domain) X and a set of potential outputs (codomain).

A graph is considered to be a function if any vertical line formed can cross it at most one point. A vertical line cannot cross the graph at more than two points in any location.

Considering the query

f(x) = x² - 2x - 6

given the graph

at its lowest value (1,-7)

h(x) = 2(x-1)²

h(x) = 2 (x² + 1 -2x )

h(x) = 2x² - 4x + 2

Creating the graph

We may view the

Lowest value at (1,0)

The complete question is,

Consider continuous functions f, g, and k. Then complete the statements.

The function that has the least minimum value is function _____. The function that has the greatest minimum value is function _____.

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In the Algebra prompt above, If f(1) = 8 and f(n)=1/2f(n-1) + 2 then  the value of f(3) is 5.

Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions.

We are given the following:

f(n)=1/2f(n-1) + 2; and

f(1) = 8

Thus,

f(2) = 1/2 x 8 + 2

= 4 + 2

f(2 )=  6

Hence,

f(3) = 1/2 x 6 + 2

= 3 + 2; thus,

f(3) = 5

Therefore,  it is correct to state that if f(1) = 8 and f(n)=1/2f(n-1) + 2 then  the value of f(3) is 5.

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Answer:

2 13/50

Step-by-step explanation:

gogle

On solving the expression 2 + (4/5) - (3/20), we get 53/20.

Given is the expression -

2 + (4/5) - (3/20)

The given expression is -

2 + (4/5) - (3/20)

Now, solving further, we get -

2 + (4/5) - (3/20)

2 + 4/5 - 3/20

(40 + 16 - 3)/20

53/20

Therefore, the given expression 2 + (4/5) - (3/20) is equivalent to 53/20.

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An element with mass 420 grams decays by 11.8% per minute. the amount of the element remaining after 16 minutes is 56.3 grams

This is a type of function that are of 3 main parts

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.

Considering the given problem,  

the starting = 420 grams

the base = 1 - r = 1 - 11.8% = 1 - 0.118 = 0.882

the exponents = 16

amount remaining = 420 (0.882)^16

= 56.330895

= 56.3 to the nearest tenths

the amount left is 56.3 g

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The 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

It is given to us that -

Numbers of items produced per hour by machine a and by machine b are normally distributed

There is a standard deviation of 8.4 items for machine a and a standard deviation of 11.3 items for machine b

The mean hourly amount produced by machine a for a random sample of 40 hours was 130 units

The mean hourly amount produced by machine b for a random sample of 36 hours was 120 units

We have to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines.

Let us say that -

x = Number of units of machine a

y = Number of units of machine b

According to the given information, we have

Number of units of machine a = x⁻ = 130

Standard deviation of machine a = σx = 8.4

Number of hours of machine a = [tex]n_{x}[/tex] = 40

Similarly,

Number of units of machine b = y⁻ = 120

Standard deviation of machine b = σy = 11.3

Number of hours of machine a = [tex]n_{y}[/tex] = 36

We know that mean of the differences can be find out as -

d⁻ = x⁻ - y⁻

=> d⁻ = 130 - 120

=> d⁻ = 10

In order to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines, we have to make use of the formula mentioned below -

d⁻ - [tex]z_{a/2}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])] < μd < d⁻ + [tex]z_{a/z}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])]  ---- (1)

From the z-score table, for a 95% confidence interval, we have -

α = 0.05

α/2 = 0.025

=> F(z) = 1 - α/2 = 1 - 0.025 = 0.975

For a z-distribution function of 0.975, we have -

[tex]z_{a/2}[/tex] = 1.96

Substituting all the values in equation (1), we have

d⁻ - [tex]z_{a/2}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])] < μd < d⁻ + [tex]z_{a/z}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])]

=> [tex]10-1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex] < μd < [tex]10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex]

=> [tex]10-1.96\sqrt{1.764+3.54 }[/tex] < μd < [tex]10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex]

=> [tex]10-(1.96 * 2.303)[/tex] < μd < [tex]10+(1.96 * 2.303)[/tex]

=> 10 - 4.516 < μd < 10 + 4.516

=> 5.483 < μd < 14.516

=> μd = 10 ± 4.516

Thus, the 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

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The slope and y-intercept of the linear function are -5 and 7 respectively.

Linear functions are those whose graph is a straight line. In other words, a linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line.

A linear function has one independent variable and one dependent variable.

A linear function has the following form. y = mx + b.

where

Therefore, let's find the slope of the function.

slope = m = Δy / Δx

using (0, 7) and (4, -13)

slope = m = -13 - 7 / 4 - 0

slope = - 20 / 4

slope = -5

Let's find the y-intercept using (0, 7).

y = -5x + b

7 = -5(0) + b

b = y-intercept = 7

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An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data.

In statistics, a truly random sample involves selecting people from a population with an equivalent probability; in other words, picking individuals from a group without bias.

Failing to accomplish this appropriately will result in a sampling bias, which can dramatically increase the sample error in a systematic fashion. For instance, using a sample from just one nation to estimate the average height of all people on Earth could lead to a significant over- or underestimation.

In practice, it might be challenging to select an impartial sample because various criteria (for instance, nation, age, gender, and so on) may substantially bias the estimator. It is important to make sure that none of these aspects are taken into consideration when choosing the sample.

Hence, An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data.

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The ratio between the number of edges and the number of vertice of a cube is 2:3. All Prisms have a ratio of edges and vertices will be the same as that of the cube.

Edge – The outlines where two cube sides touch one another.

Vertices – The indicates the point where a cube's three sides meet.

Number of edges of a cube = 12

Number of vertices in a cube = 8

The ratio of edges in vertices = 12 : 8

                                             = 3 : 2

Hence, the ratio between the number the edges and the number of vertices of a cube is 3 : 2

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-100\% + 0.58}\\\\\mathsf{= \dfrac{-100}{100} + \dfrac{0.58}{1}}\\\\\mathsf{= -100 \div 100 + 0.58 \div 1}\\\\\mathsf{= -1 + 0.58}\\\\\mathsf{= -0.42}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{-0.42}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

A. 147.5

B. 430.2

Step-by-step explanation:

A. 2001

2001 - 1998 = 3

y = 122.1(1.065)³

y = 147.49

y = 147.5

B. 2018

2018 - 1998 = 20

y = 122.1(1.065)²⁰

y = 430.23706225

y = 430.2

I hope this helps!

Hugo will buy car B.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Car A travels 702 miles on 12 gallons of gasoline.

And, Car B travels 873 miles on 15 gallons of gasoline.

Now,

Since, Car A travels 702 miles on 12 gallons of gasoline.

And, Car B travels 873 miles on 15 gallons of gasoline.

Hence, The distance of car A for travels in per gasoline = 702 / 12

                                                                                      = 58.5 miles

And, The distance of car B for travels in per gasoline = 873 / 15

                                                                                  = 56.2 miles

Since, Hugo wants to buy a car with lower fuel consumption.

Clearly, The car B consume lower fuel.

Hence, Hugo will buy car B.

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√100000 = 100√10 ≈ 316.227766

10 =2⋅5 has no more square factors, so √10 cannot be simplified further.

So it may be simply

√100000 = 100√10

Unless you want a decimal approximation or an expression using a continued fraction...

Irrational Number

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0.

√10 is an irrational number. It cannot be expressed as a fraction. Its decimal representation does not terminate or recur.

If  use a calculator, it will  an approximation like:

√10 ≈ 3.16227766

Then

√100000 = 100√10 ≈ 316.227766

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By using the concept of algebraic expression, it can be concluded that

The expression will be equal for all real numbers except -6

First option is correct.

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

The given rational expression in simplified form is

[tex]\frac{(x-2)(x+6)}{7(x+6)} = \frac{x-2}{7}[/tex]

For x = -6, the denominator of the left hand side is zero

So the expression on the left hand side is undefined for x = -6

So the expression will be equal for all real numbers except -6

First option is correct.

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The answer of the provided question is  the addition property of equality and then the division property of equality

Regardless of the sequence in which the numbers are added, the total of any two or more numbers is always the same. This characteristic may be expressed in the formula A + B = B + A. For instance, 2 + 4 Equals 4 + 2 = 6. As a result, both sets add up to 6, therefore 2 + 4 = 4 + 2.

We have multiplied both sides of the equation by 5 to move from Step 1 to Step 2:

[tex]-3x -5 +5 = 13 +5\\ -3x = 18[/tex]

We have divided both sides of the equation by -3 to go from Step 2 to Step 3:

[tex]-3x/-3 = 18/-3\\ x = -6[/tex]

These procedures can be categorized as...

first the equality's addition property, then its division property

However, since multiplication and division are the same thing, but with reciprocal numbers, and since addition and subtraction are the same thing, but with opposite numbers, any of the above answers may theoretically be right.

(adjust 5, divide by -3) = (adjust 5, multiply by -1/3)

(subtract 5 and divide by 3) equals (subtract 5 and multiply by 1/3).

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There are 60 grams of protein in 9 ounces of sauteed fish.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that there are 20 grams of protein in 3 ounces of sauteed fish.

Let's assume that 9 ounces of sauteed fish contain x grams of protein.

As per the given information, we can write the ratio would be as:

20 grams of protein : 3 ounces = x grams of protein : 9 ounces

20/3 = x/9

x = (20 × 9)/3

x = 180/3

x = 60

Hence, there are 60 grams of protein in 9 ounces of sauteed fish.

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The question seems to be incomplete the correct question would be:

There are 20 grams of protein in 3 ounces of sauteed fish. If 3 ounces of sautéed then, what are the grams of protein fish has?

Answer:

w * (1 + 0.17) or w + (w * 0.17)

Step-by-step explanation:

Here are two expressions that represent the retail price of an item with an original cost of w dollars, assuming that the store marks up the price by 17%:

Retail price = w * (1 + 0.17)

This expression shows that the retail price is equal to the original cost multiplied by the markup percentage (0.17) plus 1. For example, if the original cost of the item is $100, the retail price would be $100 * (1 + 0.17) = $117.

Retail price = w + (w * 0.17)

This expression shows that the retail price is equal to the original cost plus the markup amount (which is equal to the original cost multiplied by the markup percentage). For example, if the original cost of the item is $100, the retail price would be $100 + ($100 * 0.17) = $117.

Linear equations are equations with a leading degree of 1. This shows that there is no solution since 4 =7 is a false statement .

What are linear equations ?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Solving linear equation

Linear equations are equations with a leading degree of 1. Given the linear equation

Given

13+4x-9=7x+7-3x

Simplify

4 + 4x = 4x + 7

Collect the like terms

4x - 4x = 7 - 4

0x = 3

This shows that there is no solution since 4 =7 is a false statement

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The amount of loss that the insurance company will pay is $70000

Deductible plus the amount of coinsurance equals the out-of-pocket maximum.

Determine the $1,000 deductible that the insured is required to pay.

Calculate the coinsurance payment due from the insured: 20% of $5,000 equals $1,000.

The coinsurance penalty is calculated using the straightforward formula: the loss multiplied by the amount of insurance that should have been in place, less any deductible, equals the amount that was actually paid.

The following covered losses are subject to the coinsurance provision: Property value: $200,000; policy limit: $140,000; coinsurance: 80%; loss: $100,000; deductible: $250; all other numbers: $200,000; etc.

The insured only had $140,000 when they should have had $160,000 (200,000 x.80).

The coverage will cover the deductible plus $87,500. (140,000/160,000

=.875; $100,000 x .875

= $87,500; $87,500 - $250

= $77,250)

Stop Limit/Value =%, Loss Amount x% = $ Amount Policy Would Pay (-) minus $ Deductible = $ Covered Loss Amount

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Answer:

n=0  or  n=6

Step-by-step explanation:

n² = 6n

n² - 6n = 0

n(n - 6) = 0

n = 0;  or  n - 6 = 0 => n = 6

Answer: which triangle ;/

Step-by-step explanation: