Statement
Reason
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the midpoint formula
Length of segment DE is √5 and length of segment AC is 2√5
Segment DE is half the length of segment AC
Slope of segment DE is -2 and slope of segment AC is -2
Segment DE is parallel to segment AC
Which of the following completes the proof? (6 points)
By the addition property
O By the distance formula
By construction
Given
By substitution
By the slope formula
Slopes of parallel lines are equal

The critical value is 13.28 when the distribution of final marks in the statistics department.

Given that,

According to a teacher, the distribution of final marks in the statistics department is: A, 25%; B, 25%; C, 40%; D, 5%; and F, 5%. The following number of grades were recorded at the conclusion of a randomly chosen semester.

We have to recognize the important value.

We know that,

Given a=0.01,

The critical value of chi-square with 0.99,

df=n-1=4  is

13.28 (From chi-square table)

Therefore, The critical value is 13.28 when the distribution of final marks in the statistics department.

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The expression in terms of first power of cosine cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.

How to lower the power of expression in trigonometry?

sin2x+cos2x = 1 and cos2x = (1+cos(2x))/2

Using the first identity, we have sin2x = 1-cos2x.

So we have that cos4x*sin2x = cos4x(1-cos2x)

Expanding, we have cos4x-cos6x.

Since cos2x=  (1+cos(2x))/2, this implies cos4x = ((1+cos(2x))/2)² and cos6x=((1+cos(2x))/2)³.

Expanding each one, we have

cos4x - cos6x = 1/4(1+2cos(2x) + cos2(2x)) - 1/8(1+3cos(2x) + 3cos2(2x) + cos3(2x)).

Simplifying we get

cos4x - cos6x = 1/8 + 1/8(cos(2x) - cos2(2x) - cos3(2x)).

cos2(2x) = 1/2(1+cos(4x)) and cos3(2x)

= cos2(2x)*cos(2x)

= 1/2(1+cos(4x)) * cos(2x)

= 1/2(cos(2x) + cos(4x)*cos(2x))

Substituting, we get

cos4x - cos6x = 1/8 + 1/8(cos(2x) - 1/2(1+cos(4x)) - 1/2(cos(2x) + cos(4x)*cos(2x)))

Cleaning it up, we get

cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.

Hence, The expression in terms of first power of cosine cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.

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The addition of function f(x) = 3 · x² - 1 and function g(x) = x + 2 is equal to (f + g)(x) = 3 · x² + x + 1. (Correct choice: B)

New functions can be created by combining functions, the most common operations are listed below:

In this problem we must determine the expression that is the result of the addition of two functions, whose definition is shown below:

(f + g) (x) = f(x) + g(x)

First, use the definition of the addition of two functions:

(f + g)(x) = (3 · x² - 1) + (x + 2)

Second, simplify the algebraic expression:

(f + g)(x) = 3 · x² + x + 1

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The rational numbers are √9, √4, √1. Options A, B and F

A rational number is defined as a number expressed as the ratio of two integers, such that the denominator should not be equal to zero.

These numbers can be expressed as quotients of two integers.

It is a number whose decimal form is finite or recurring in nature.

It is determined by dividing an integer with another integer, an exception is made with zero.

It is important to note the following;

From the numbers given, the rational numbers are;

√9, √4, √1

Hence, the values are √9, √4, √1

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2- T-distribution with 58 degrees of freedom

When the estimated standard deviation rather than the actual standard deviation is used as the denominator, the t-distribution is a continuous probability distribution of the z-score.

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. If there is a remaining requirement for the data sample, particular data sample items must be picked after the degree of freedom quantity has been decided.

[tex]t[/tex] = Student's t-distribution

[tex]X{i}[/tex] = sample mean

μ = population mean

[tex]s[/tex] = sample standard deviation

[tex]n[/tex] = sample size

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The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. If there is a remaining requirement for the data sample, particular data sample items must be picked after the degree of freedom quantity has been decided.

When the estimated standard deviation rather than the actual standard deviation is used as the denominator, the t-distribution is a continuous probability distribution of the z-score.

The number of pounds of peanuts needed is 29.167.

Multiply the number of pounds of each type and multiply by the cost per pound to get the total cost of that part contribution to the total. Add them together and set it equal to the final total pounds (50) multiplied by its cost per pound ($2.90)

There are 5 pounds of mixed nuts.

let x = pounds of peanuts

cost of each pound of peanuts is $1.50

45 - x = pounds of cashews

Cost of each pound of cashew is $4.50

This way total pounds = 50

5 pounds($6) + x pounds ($1.50) + (45-x)pounds($4.50) = 50 pounds($2.90)

30 + 1.50x + 202.5 - 4.50x = 145

-3x = -87.5

x = 29.167

Therefore, the number of pounds of peanuts needed is 29.167.

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Disclaimer

The question given by you is incomplete, the abouve asnwer is done as per a similar question, the question is

A merchant has 5 pounds of mixed nuts that cost $30. he wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. how many pounds of peanuts are needed?

By solving a simultaneous linear equation, it can be calculated that-

Value of ab = 60

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a simultaneous linear equation needs to be solved

[tex]3^a = 81^{b+2}[/tex] and [tex]125^b = 5^{a-3}[/tex]

[tex]3^a = 3^{4(b+2)}[/tex]

a = 4(b + 2)

a = 4b + 8

a - 4b = 8 ... (1)

[tex]125^b = 5^{a-3}\\5^{3b} = 5^{a-3}\\[/tex]

3b = a - 3

a - 3b = 3 .... (2)

Subtracting (1) from (2)

b = -5

Putting the value of b in (2)

a - 3(-5) = 3

a + 15 = 3

a = 3 - 15

a = -12

Value of ab = (-12) [tex]\times[/tex](-5) = 60

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Answer:

B

Step-by-step explanation:

The 18 is the intitial value.  It does not change.  What does change is the height every month.  You would substitute in the number of months for x to find the height of the plant.

The function f in slope - intercept form is y = -3x + 6 .

Given :

For linear function f, f(2)=0 and f(4)=-6.

Examples :

f(5)=0 means (5,0) is a point on the line.

f(3)=-2 means (3,-2) is a point on the line.

so f ( 2 ) = 0 means ( 2 , 0 )

f ( 4 ) = -6 means ( 4 , -6 )

slope m = -6 - 0 / 4 - 2

= -6 / 2

= -3

substitute m and ( 2 , 0 ) in y = mx  + b

0 = -3 * 2 + b

b = 6

substitute m and b value

y = -3x + 6

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The expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.

Given that,

Take into account n separate coin flips with a p percent chance of landing on heads. Say a changeover happens any time an outcome diverges from the one that came before it. For instance, there are 3 changeovers if n=5 and the result is HHTHT.

We have to determine the anticipated number of transitions.

We know that,

Independent flips,

n =12

Probability of heads =p

Probability of tails =(1-p)

Let m=1,2,...n

If mth term may be head then (m+1)th outcome could be head or vice-versa.

Probability of change overs from mth to (m+1)th outcome =2p(1-p)

So, the  expected changeovers is given by

E[change overs] = (n-1) *2p(1-p)

= (12-1) × 2p(1-p)

=11 × 2p(1-p)

=22p(1-p)

Therefore, the expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.

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Answer: Part A: Yes there is. As the number of workers increases, so does the production.

Part B:    y = 5x + 2

Part C: The slope indicates that for every person there is 5 units being produced, and the y-intercept indicates that 2 units are being made every day, regardless of if there are no workers ( this, however is unrealistic but it is how the data is )

Step-by-step explanation:

Answer: B. $13,720

Step-by-step explanation: To calculate Ford's proceeds, we need to first find the discount, which is equal to the interest on the loan multiplied by the principal amount of the loan. The interest is 8% of $14,000, or $1,120. The discount is then $1,120 * 90/360, or $310. The proceeds are equal to the principal amount minus the discount, or $14,000 - $310 = $13,720.

Answer:

D

Step-by-step explanation:

Since this we have rose petal, the equation will be either

[tex]r = a \sin(n \alpha ) [/tex]

or

[tex]r = a \cos( n\alpha ) [/tex]

Since we have 3 petals, which is a odd number, n=3

so the answer must be either

[tex]r = a \cos(3a) [/tex]

[tex]r = a \sin(3 \alpha ) [/tex]

Where a is some constant real number.

So D is the answer

Answer:

x =  e^3   +7

Step-by-step explanation:

ln ( x-7) = 3

To solve for x, raise each side to base e

e ^ ( ln ( x-7) ^= e^3

x-7 = e^3

Add 7 to each side

x-7+7 = e^3   +7

x =  e^3   +7

The proof that shows that ∠B ≅ ∠D by the CPCTC is explained in the table below.

CPCTC is a postulate that stands for "corresponding parts of congruent triangles are congruent". It says that if you prove that two triangles are congruent to each other, then every of their corresponding parts are congruent.

Therefore, the proof below shows how to use CPCTC to prove that ∠B ≅ ∠D.

Statement                           Reason                                                  

1. BC ≅ CD                          1. Given

2. AC ≅ EC                         2. Given

3. ∠ACB ≅ ∠ECD               3. Vertical angles theorem

4. ΔACB ≅ ΔECD               4. SAS theorem

5. ∠B ≅ ∠D                         5. CPCTC

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Answer:

Step-by-step explanation

sec x = -9/5.

cos x = 1/ secx

So, here

cos x = 1 / -9/5

         = -5/9

sin x = √(1 - cos^2 x)

        = √(1 - 25/81)

        = √(56/81)

        = √56/9

tan x = sinx / cos x

         = √56/9 / -5/9

         = -√56/5

cosec x = 1 / sin x

             = 1 / √56/9

             = 9/√56.

cot x = 1/tanx

         = 1/-√56/5

         = -5/√56

The eigenvalue for this coefficient matrix is c, the eigenvector is (1, 0) and the generalized eigenvector is (1, -4).The most general real-valued solution to the linear system of differential equations is given by:y(x) = c1e^(-4x) + c2xe^(-4x),

To find the eigenvalue, we need to solve the characteristic equation of the coefficient matrix, which is given by det(A - cI) = 0. In this case, the characteristic equation is -c^2 + 4c = 0, which has a single solution of c = 4. Thus, the eigenvalue is c = 4.

To find the eigenvector, we need to solve the linear system (A - cI)v = 0. For this coefficient matrix, the linear system is (A - 4I)v = 0, which has the solution v = (1, 0). Thus, the eigenvector is (1, 0).

To find the generalized eigenvector, we need to solve the linear system (A - cI)w = v, where v is the eigenvector. In this case, the linear system is (A - 4I)w = (1, 0), which has the solution w = (1, -4). Thus, the generalized eigenvector is (1, -4).

Finally, the most general real-valued solution to the linear system of differential equations is given by y(x) = c1e^(-4x) + c2xe^(-4x), where c1 and c2 are arbitrary constants.

Characteristic equation: det(A - cI) = 0

-c2 + 4c = 0

c = 4

Eigenvector: (A - 4I)v = 0

v = (1, 0)

Generalized eigenvector: (A - 4I)w = v

w = (1, -4)

Most general solution: y(x) = c1e^(-4x) + c2xe^(-4x), where c1 and c2 are arbitrary constants.

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The monthly payment is $966.76.

What is monthly payment?

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original lent amount, but also the interest that accrues, must be repaid.

Given the amount of the loan is $1,450.

The number of installment is 18.

The APR of the loan is 8%.

The monthly rate of interest is 8%/12 = 2/3%

The formula of monthly installment is

[tex]M=P[\frac{r}{1-(1+r)^{-n}} ][/tex]

P =  principal = 1,450

r = rate of interest = 2/3%

n = number of instalment = 18

[tex]M=1450[\frac{0.67}{1-(1+0.67)^{-n}} ][/tex]

M = 966.76

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The monthly payment on a principal of $156000 with interest rate of 4% over a time period of 15 years is $1153.91

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

The formula of monthly payment is given as;

A = P [r(1 + r)ⁿ] / [(1 + r)ⁿ - 1]

The principal of the loan can be calculated as 20 % of 195000

20 / 100 = x / 195000

0.2 = x / 195000

x = 39000

The principal is 195000 - 39000 = 156000

The principal is 156000, rate is 4% and time is 15 year

Substituting the values into the formula

A = 156000[0.04(1 + 0.04)¹⁸⁰] / [(1 + 0.06)¹⁸⁰ - 1]

A = 1153.91

The monthly payment is $ 1,153.91

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Answer: x=3y-1/2 or y=(x+1/2)/3

Step-by-step explanation:

f^-1(x) is just the inverse so all you need to do is switch x and y.

right now you have y=3x-1/2

so switch the x and y to get your answer of x=3y-1/2

if you're asked to solve for y, follow these steps:

1. x +1/2 = 3y-1/2 +1/2 -> x+1/2=3y

2. divide both sides by 3 -> (x+1/2)/3=y

Answer:

Step-by-step explanation:

in similar triangles

sides are proportional.

The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.

1. $10 - 20

2. $11 - 30

3. $12 - 50

4. $13 - 40

5. $14 - 10

1. The sell order with the lowest price (highest bid) is ranked first and will be executed first. In this case, the sell order with a price of $10 and a quantity of 20 will be executed first.

2. The sell order with the second lowest price (second highest bid) will be ranked second and will be executed second. In this case, the sell order with a price of $11 and a quantity of 30 will be executed second.

3. The sell order with the third lowest price (third highest bid) will be ranked third and will be executed third. In this case, the sell order with a price of $12 and a quantity of 50 will be executed third.

4. The sell order with the fourth lowest price (fourth highest bid) will be ranked fourth and will be executed fourth. In this case, the sell order with a price of $13 and a quantity of 40 will be executed fourth.

5. The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.

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The probability that the student is from Section I, given that he or she is a mathematics major, is 0.214 and the probability that the student is from Section 1, is 0.294.

In the give question;

There are three sections of English 101.

In Section 1, there are 25 students, of whom 3 are mathematics majors.

In Section II, there are 20 students, of whom 7 are mathematics majors.

In Section lIl, there are 40 students, of whom 4 are mathematics majors.

We have to find the probability that the student is from Section I, given that he or she is a mathematics major and the probability that the student is from Section 1.

Total number of students in all sections = 25+20+40 = 85

Total number of students major in mathematics = 3+7+4 = 14

The probability that the student is from Section I, given that he or she is a mathematics major is represented as

P(I | M) = P(I∩M)/P(M)

P(I∩M) = (Student in section II - Student in section III)/Total student in all sections

P(I∩M) = (7 - 4)/85 = 3/85

P(M) = Total student of mathematics/Total student in all sections

P(M) = 14/85

Now putting the values

P(I | M) = (3/85)/(14/85)

P(I | M) = 3/14

P(I | M) = 0.214

Now finding the probability that the student is from Section 1.

Probability that student is from section I = Total students in section I/ total students

Probability that student is from section I = 25/85

Probability that student is from section I = 0.294

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The right question is:

There are three sections of English 101. In Section 1, there are 25 students, of whom 3 are mathematics majors, In Section II, there are 20 students, of whom 7 are mathematics majors. In Section lil, there are 40 students, of whom 4 are mathematics majors. A student in English 101 is chosen at random. Find the probability that the student is from Section I, given that he or she is a mathematics major. The probability that the student is from Section 1 is (Simplify your answer. Round to three decimal places as needed.)

Answer:

y=4x+11

Step-by-step explanation:

The standard deviation of the difference in the weights of the two oranges is equal to sqrt(1.2^2 + 1.2^2) = 1.7 ounces.

What do you mean by standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The standard deviation of the difference in the weights of the two oranges is equal to the square root of the sum of the squares of the standard deviations of the two oranges. This is because the weights of the two oranges are independent random variables.

Therefore, the standard deviation of the difference in the weights of the two oranges is equal to sqrt(1.2^2 + 1.2^2) = 1.7 ounces.

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By Side - Angle - Side Congruence Rule the given triangles are Congruent

What is SAS Rule of Congruence?

That is stated in the SAS regulation. If two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent. An included angle is one created by the intersection of two specified sides.

Solution:

By Side - Angle - Side Congruence Rule the given triangles are Congruent

Since, two sides are equal andd the angle included between the sides is equal to

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Answer:1 carrot cost .75 cents and a mango cost 1.40

Step-by-step explanation:

12 carrots + 10 mangoes = 23$

4 carrots + 5 mangoes = 10$

I know to get from 5 mangoes to 10 mangoes you have to multiply twice. so it wil come up to 20 dollars

8 carrots + 10 mangoes = 20$

divide by 2

that will leave 4 carrots and 3 dollars.

4/3 = .75

17 dollars is left

so 10 carrots is equal to 14 dollars

14/10 = 1.4 dollars

Answer:

C)  The range of the function is all real numbers less than or equal to 0.

Step-by-step explanation:

Given function:

[tex]f(x)=-\sqrt{x}[/tex]

Domain

The domain of a function is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken, x ≥ 0.

Therefore, the domain of the function is all real numbers greater than or equal to 0.

Range

The range of a function is the set of all possible output values (y-values).

As the domain is x ≥ 0, the range of the function is all real numbers less than or equal to 0.

Answer:

C) The range of the function is all real numbers less than or equal to 0.

The expected value of the extended warranty is $687.90 assuming it is replaced in the first 2 years.

Here, we are assuming that the dishwasher is replaced in the first 2 years in order to calculate the expected value of the extended warranty.

Because there is 14% chance of replacement:

Value of warranty = 14%*$800 - $112.10

Value of warranty = $112.00 - $112.10

Value of warranty = -$0.10

Now, because it is assumed that replacement will be done in first 2 years, then,

Value of warranty will increase to $687.90 ($800 - $112.10).

Therefore, the expected value of the extended warranty is $687.90 assuming it is replaced in the first 2 years.

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