The yield of a certain chemical reaction is believed to be related to temperature. A study collected the yield from 15 such reactions selected at random to test the belief and producedthe following results.
Variable Estimate
Intercept 1 15.5 2.96
Temp 1 0.05 0.017
R-sq = 0.73
Which of the following is the appropriate test statistic for the test?
a. t=0.05/0.73
b. t=15.5/0.73
c. t=0.05/15.5
d. t=15.5/0.05

One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). the x-intercepts and the y-intercept of the graph of f(x) are

Generally, To find the x-intercepts, we set y equal to 0 and solve for x. In this case, the equation we need to solve is:

f(x) = x^3 - 6x^2 + 11x - 6 = 0

To solve this equation, we can use the fact that (x - 3) is a factor of the function. This means that we can write the function as:

f(x) = (x - 3)(x^2 - 3x + 2)

If (x - 3) is a factor, then x - 3 must equal 0. This gives us one x-intercept at x = 3.

To find the other x-intercepts, we can set the quadratic factor (x^2 - 3x + 2) equal to 0 and solve for x. This gives us the following equation:

x^2 - 3x + 2 = 0

We can use the quadratic formula to solve this equation:

x = (3 +/- √(9 - 8)) / 2 = (3 +/- √(1)) / 2 = (3 +/- 1) / 2

This gives us two more x-intercepts at x = 2 and x = 4.

So the x-intercepts of the graph of f(x) are x = 2, x = 3, and x = 4.

To find the y-intercept, we set x equal to 0 and solve for y. In this case, the equation we need to solve is:

f(0) = 0^3 - 6(0)^2 + 11(0) - 6 = -6

This gives us a y-intercept at (0, -6).

So the y-intercept of the graph of f(x) is (0, -6).

All of the intercepts of the graph of f(x) are, therefore (0, -6), (2, 0), (3, 0), and (4, 0).

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A freshman has a 0.35 chance of being chosen. A freshman has a 0.38 chance of being chosen. The likelihood of a freshman being chosen is 0.23.

A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%. It is predicated on the likelihood of something occurring. The rationale underlying probability is the foundation of theoretical probability. If a coin is tossed, the theoretical probability of receiving a head is 12.

Here,

.................. Math .. Art . Biology Total

Freshman . 0.10 . 0.08 . 0.17 .... 0.35

Sophomore 0.22 . 0.30 . 0.13 ... 0.65

Total ......... 0.32 . 0.38 . 0.30 ...... 1

(a) 0.35

(b) 0.38

(c) 0.10 + 0.13 = 0.23

The probability that a freshman is selected is 0.35. The probability that a freshman is selected is 0.38. The probability that a freshman is selected is 0.23.

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the value of [tex]f o f^{-1}[/tex](5) of the function f(x) = x + 9 is 5

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f^-1 or F^-1. One should not confuse (-1) with exponent or reciprocal here.

[tex]f^{-1}[/tex](x) =

if f(x) = x + 9

setting x + 9 = y and making x the subject we have

y = x + 9

x = y - 9

replacing x with [tex]f^{-1}[/tex](x) and y with x we have

[tex]f^{-1}[/tex](x) = x - 9

so the f o [tex]f^{-1}[/tex](x) can be gotten by substituting x in f(x) with x - 9 so that we have

f o [tex]f^{-1}[/tex](x) = (x - 9) + 9

f o [tex]f^{-1}[/tex](x) = x

so f o [tex]f^{-1}[/tex](5) will be x = 5

which becomes

f o [tex]f^{-1}[/tex](5) = 5

In conclusion f o [tex]f^{-1}[/tex](x) is 5

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In an adjacency list representation, corresponding to each vertex v is a linked list such that each node of the linked list contains the vertex u, and there is an edge from v to u.

This is a common way to represent a graph in computer memory, where each vertex is represented by an object that stores its adjacent vertices in a list. This representation is useful when the graph is sparse, meaning it has relatively few edges compared to the number of vertices it has. It is not as efficient for dense graphs, where the number of edges is close to the maximum possible number of edges.

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The value of a in the expression is -3

From the question, we have the following parameters that can be used in our computation:

r²-6 r+9 can be factorized to give an expression of the form (r+a)²

This means that

r² - 6r + 9 = (r+a)²

Factorize the expression r² - 6r + 9

So, we have

(r - 3)² = (r + a)²

By comparison, we have

a = -3

Hence, the solution of a is -3

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Answer:

yes, by ASA

Step-by-step explanation:

sum of interior angles of a triangle = 180°

180 - (45+63) = 180 - 108 = 72°

the two triangles have two congruent angles and the side between them.

They are congruent for (ASA) angle side angle

Answer:

16 books

Step-by-step explanation:

8/12 is equivalent to 16/24. If each book is 1/24 width, 16/1 = 16

Answer:

  2064 cm²

Step-by-step explanation:

You want the surface area of a prism that is 30 cm between bases that are trapezoids with parallel sides 27 cm and 6 cm that are 8 cm apart, and slant sides that are 10 cm and 17 cm.

The area of each trapezoidal base is ...

  A = 1/2(b1 +b2)h

There are two identical bases, so their total area is ...

  2A = (b1 +b2)h = (27 cm +6 cm)(8 cm) = 264 cm²

The lateral area of the prism is the area of the four rectangular faces. Each is 30 cm wide, and their total length is the perimeter of the base;

  P = 27 cm +10 cm +6 cm +17 cm = 60 cm

  lateral area = Ph = (60 cm)(30 cm) = 1800 cm²

The total surface area of the prism is the sum of the base area and the lateral area:

  total area = base area + lateral area

  total area = 264 cm² +1800 cm² = 2064 cm²

The surface area of the solid prism is 2064 cm².

Answer: 16

Step-by-step explanation:

there are 4 1/4 in 1 cup. so it'll be 4 cakes for each cup of oil you have. multiply the number of cakes that can be made per cup (4) by the number of cups you have (4)

(4) x (4) = 16

Answer:

Step-by-step explanation:

given:

-15x + 20y =15

0 = 18x + 24y -18

let's get the 2nd equation into a form like the top equation

-18x -24y = -18

multipy thur by -1

18x +24y = 18

we'll need to  use substitution for this problem.  elimination has a zero issue.

18x = -24y +18

x = -[tex]\frac{4}{3}[/tex] y + 1

now plug this into the 1st equation

-15(  -[tex]\frac{4}{3}[/tex] y + 1 ) + 20 y = 15

20y -15 +20y = 15

40y = 30

y = 3/4

now that we've found y, plug that into our x = -[tex]\frac{4}{3}[/tex] y + 1 , to find x

x = -1 +1

x = 0

If American children watch an average of 25 hours of television per week with a standard deviation of 8 hours. the probability the mean number of hours of television they watch per week is less than 22 is: 2) 0.0089.

First step is to find the standard deviation

σ = 8/√40

σ = 1.2649

Using this formula to find the Z-score

Z = x - μ/σ

Z =22-25/1.2649

Z = -3//1.2649

Z = -2.37

Hence,

P-value=P(Z < -2.37)  

P-value =0.0089

Therefore the correct option is 2.

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The solution to the system of equation y + 2x² = 14 , y = 3x² - 6 is as follows:

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let's solve the system of equation by substitution method.

Therefore,

y + 2x² = 14

y = 3x² - 6

Therefore, using substitution method,

3x² - 6 + 2x² = 14

5x² - 6  = 14

5x² = 14 + 6

5x² = 20

x² = 20 / 5

x² = 4

x = √4

x = 2

Therefore, let's find the value of y using y = 3x² - 6.

y = 3x² - 6

y = 3(2)² - 6

y = 12 - 6

y = 6

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The solution of the system of equations is the point of intersection (4, 2), as shown in the graph below.

Caroline bought 4 soda bottles.

Caroline bought 2 juice bottles.

In order to determine the solution to this problem, use the information given to create two equations.

Number of soda bottle = x.

Number of juice bottle = y.

First Equation for the total number of bottle that Kelvin bought

x + y = 6 --> eqn. 1

Second Equation 2 for the total sugar in the soda bottles and total sugar in juice bottles that equals 150 grams of sugar.

30x + 15y = 150

Simplify by dividing by 5

6x + 3y = 30 --> eqn. 2

Rewrite eqn. 1:

y = 6 - x

Solve simultaneously for the variables of x and y, by substituting the value of y into equation 2:

6x + 3(6 - x) = 30

6x + 18 - 3x = 30

3x + 18 = 30

3x = 30 - 18

3x = 12

3x/3 = 12/3

x = 4

Caroline bought 4 soda bottles.

Substitute x = 4 into equation 1 to find the value of y:

x + y = 6

4 + y = 6

y = 6 - 4

y = 2

Caroline bought 2 juice bottles.

The graph below shows the point of intersection, (4, 2), which is the solution.

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The number of different frames you can create, if There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from, is 12.

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from,

Calculate the total number of frames, we can create as shown below,

The number of frames = different styles available for blue color × shades of blue

The number of frames = 4 × 3

The number of frames = 12

Thus, the number of frames you can create is 12.

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Answer: Work shown below. Have a nice day! :)

The annuity provide each week is $547.59 (approx.)

Define Annuity

A fixed sum of money paid to someone each year, typically for the rest of their life.

Given,

Dajon already knows that he will have $500,000 when he retires.

P = $500,000

Next, he sets up a payout annuity for 15 years in an account paying 2.05% interest.

r = 2.05 % or 0.0205

t = 15 years

Since, annuity provide each week then

n = 52 weeks (in a year)

The Annuity formula is,

P = d [ ( 1 + r/n)^nt - 1 ] / (r/n)

where, d = regular deposit

Now, plug in the values and find the value of d

P = d [ ( 1 + 0.0205/52)^52*15 - 1 ] / (0.0205/52)

Calculate the value it gives,

P = $547.5936993 or 547.59

Hence, the annuity provide each week is $547.59 (approx.)

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The answer of the given expression using BODMAD rule is 25.

What is BODMAS rule?

The BODMAS rule states that the brackets must be solved first, then powers or roots (i.e., of), Division, Multiplication, Addition, and finally Subtraction. Only when the BODMAS rule or the PEDMAS rule is used to solve an expression is the solution deemed to be correct.

(a) 1 x (-6 x -18 - 8) ÷ 4

By using first to simplify the bracket.

1 x ((-6 x -18) - 8) ÷ 4

1 x (108 - 8) ÷ 4

(1 x 100) ÷ 4

100 ÷ 4

25

Hence, the answer of the given expression using BODMAD rule is 25.

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Answer: 19.2mm^2

Step-by-step explanation: the area of a rectangle is simply base x height

so do 9.6 x 2 to get 19.2mm^2

The true statements are,

A. The coefficients of xⁿ and yⁿ both equal 1.

D. For any term x and y in the expansion, a + b = n

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (x + y)ⁿ

Now,

We know that;

A binomial expansion is,

⇒  [tex](x + y)^n = x^n + nx^n^-^1 y + ^{n} C_{2} x^n^-^2y^2 + ..... + nxy^n^-^1 + y^n[/tex]

Clearly, For Option A:

The coefficients of xⁿ and yⁿ both equal 1.

If we see first and last term of the expansion, This statement is true.

For Option D:

For any term xᵃyᵇ in the expansion, a + b = n.

Let we take 3rd term of expansion

Here, a = n-2 and b=2

So,   a + b = n-2+2 = n

Thus, a + b = n is true statement.

For Option B:

For any term xᵃyᵇ in the expansion, a - b = n.

Let we take 3rd term of expansion

Here, a=n-2 and b=2

If we do  a-b = n-2-2=n-4≠n

Thus, a-b=n is false statement.

Thus, The true statements are given below,

A. The coefficients of xⁿ and yⁿ both equal 1.

D. For any term x and y in the expansion, a + b = n

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20 + 4x+2 = 6x+8 --- By exterior angle

4x+22=6x+8

4x-6x=8-22

-2x=-14

x=7

Hope it helps

Yes, there must be two selected numbers whose difference is 2. Any assignment of n+1 pigeons to n holes. Then there exists at least one hole with at least 2 pigeons in it.

A general rule, called the pigeon -hole principle, is that if there are more pigeons than holes, there should be at least one hole with at least two pigeons. If we put n + 1 objects into n boxes, we can say that at least one box contains 2 or more objects. Example: If there are Kn+ 1 (where k is a positive integer) pigeons distributed in n holes, then the holes contain at least k + 1 pigeons. Consider 2n pair of pigeon holes (1,3), (2,4), (5,7),(6,8), .. ..,(4n-3,4n-1),(4n-2,4n). The 2 numbers in each pair have the difference 2.

If we choose 2n+1 numbers(pigeons), then they cannot all belong to different pairs.

Thus by pigeon hole principle, there must be two selected numbers whose difference is 2.

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Answer:

A.) G

Step-by-step explanation:

I'd say A.) G because when you look at the graph the y-intercept is 4. When you look at the equation the y-intercept is 6. 6 is bigger than 4 so then the answer should be A.) G

Answer: It is D

Step-by-step explanation:

The graph in which point are plotted is given below and Point D and F lie on Y axis and X axis respectively other lie on the different quadrant

What does a math quadrant mean?

The term "quadrant" refers to each of the four divisions of the coordinate plane. Furthermore, when we speak of the sections, we also mean the sections as the coordinate axes split them. This is where the x-axis is, and this is where the y-axis is on the up-down axis. On a coordinate plane, it divides the space into four parts, as you can see.

Point A (-5,4)

Lies in 2 quadrant of the graph

Point B (-3,-2)

Lies in 3 quadrant of the graph

Point C (4,6)

Lies in 1 quadrant of the graph

Point D (0,-4)

Lies on negative y axis of the graph

Point E (2,-1)

Lies in 4 quadrant of the graph

Point F (1,0)

Lies on positive x axis of the graph

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If the interest rate is 5%, the monthly payment and total interest would be $2.439.

Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principal refers to the borrowed or lent funds. The Amount is the total of the principal plus interest. The term "rate of interest" refers to the rate at which interest is applied to the principal.

Given,

A student receives a subsidized student loan for $10,000 with a 10-year repayment term and interest compounded monthly. Six months after she graduates from college, she will have to begin making payments.

A $10,000 subsidized student loan

Ten-year term of repayment

5.5% interest rate

First, we must determine the loan's future value (FV) over the next six months using the formula below:

FV in 6 months

= Loan Amount× (1 + Interest Rate)⁶ ($10,000×(1 + 0.055) ×6

= $2.7680.

Second, the formula for determining future value is used to determine the monthly payment:

M = FV in 6 months / (((((r)n) - 1) / r).......... (1)

When you enter all the pertinent values into equation (1), you get:

M = $2.7680 / ((((1 + 0.00466666666666667)^144) – 1) / 0.00466666666666667)

M = $2.439

Therefore, if the interest rate is 5.5%, the total amount paid in interest plus monthly payments would be $2.439.

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The linear function is y = x + 7 and it has it domain and range at  (-∞, ∞) respectively while it x and y - intercepts are (-7, 0) and  (0, 7) respectively.

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

The linear function always model the form of y = mx + c

Taking the points, we can find the slope of the line

m = y₂ - y₁ / x₂ - x₁

m = 8 - 0 / 1 - (-7)

m = 8 / 8

m = 1

The slope of the line is 1

Using the slope to find the y - intercept;

y = mx + c

8 = 1(1) + c

8 = 1 + c

c = 8 - 1

c = 7

The linear function is y = x + 7

The range of this function is (-∞, ∞) and the domain of the function is

(-∞, ∞).

The x and y -intercept of the function are

x - intercept = (-7, 0)

y - intercept = (0, 7)

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Bank reconciliation is an accounting process to bring the balance as per the bank statement to agree with the balance as per the checkbook.

The journal entry to adjust the checkbook balance is as follows:

May 1 Debit Bank Charges $20

Credit Checkbook $20

The preparation of the Bank Reconciliation Statement is as follows:

Balance as per bank statement            $16,833.19

Add Uncleared Deposits                        $1,650.00

Less Outstanding Checks                     $2,040.84

Balance as per adjusted checkbook  $16,442.35

Checkbook balance on May 31 = $16,462.35

Bank Statement balance on May 31 = $16,833.19

Uncleared Deposits:

May 29   $575

May 30 $1,075   $1,650

Outstanding Checks:

Check 189 - $127.50

Check 191 - $462.19

Check 192 - $569.42

Check 194 - $881.73  $2,040.84

Bank charges = $20.00

Checkbook Adjustment:

Balance as per checkbook      $16,462.35

Less Bank charges                           20.00

Adjusted checkbook balance $16,442.35

Transaction Analysis for Journal:

Bank Charges $20 Checkbook $20

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