Paul inherited a stamp collection. Since receiving the
collection, Paul has gone to the store and bought the
same number of new stamps each week to add to his
collection. The equation shown below can be used to
determine the number of stamps (y) in Paul's stamp
collection x weeks after he inherited the stamps.
y = 3x + 40
Based on the equation, which statement is true?


A) The stamp collection had 3 stamps in it when Paul inherited it.

B) So far, Paul has purchased 40 additional stamps for the collection.

C) Since inheriting the collection, Paul has bought 3 new stamps each week.

D) Six weeks after he inherited the collection, Paul's stamp collection contains 18 stamps

Answer: 56 minutes

Step-by-step explanation:

7 = 7, 14, 28, 35, 42, 49, 56

8 = 8, 16, 24, 32, 40, 48, 56

7 and 8 have 56 in common so it would take them 56 minutes

The number of dogs do they need to walk in order to pay for the box of treats is 4

The function that representing the profit is

y = 3x - 5

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Here the cost for buying a box of treat = $5

Substitute the value in the function and find the number of dog that they need to walk

5 = 3x - 5

3x = 5 + 5

3x = 10

x = 10 / 3

x = 3.33

x ≈ 4

Hence, the number of dogs do they need to walk in order to pay for the box of treats is 4

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Option B. The appropriate conclusion at the 5% significance level is to Reject the null hypothesis, the population mean is significantly different from 123

H0: mean = 123

H1 : mean ≠ 123

We have the p value of the statistics stated already in the question as p value = 0.0037.

The level is significance that we have been given in the question is 5% = 0.05

We are to test here if the true mean is different from 123.

Hence we would be testing the p value against the significance level.

We can see that P value is  < level of significance.

0.0037 < 0.05

Hence we would reject the null hypothesis.

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Latrina will serve 640 hors d’oeuvres to the 240 people at her wedding .

In the question ,

it is given that

At Latrina's wedding

number of  hors d’oeuvres offering that 3 people will get = 8 offering

So, the number of offering of hors d’oeuvres that 1 person will get = 8/3  .

we need to find that

how many hors d’oeuvres will she serve for 240 people .

So ,

the number of  hors d’oeuvres offering that 240 people will get =(8/3)×240

= 8 × 80

= 640

Therefore , Latrina will serve 640 hors d’oeuvres to the 240 people at her wedding  .

The given question is incomplete , the complete question is

Latrina is planning to serve hors d’oeuvres at her wedding. She plans on offering 8 hors d’oeuvres for every 3 people. If she has invited 240 people to the wedding, how many hors d’oeuvres will she serve?

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The sum of the first and second integer is 44.

Let the numbers be x, x+2 and x+4.

If the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. This will be:

2(x + 2 + x + 4) - (x + 2) = x + 52

2(2x + 6) - (x + 2) = x + 52

4x + 12 - x - 2 = x + 52

Collect like terms

4x - x - x = 52 - 12 + 2

2x = 42

Divide

x = 42/2

x = 21

Second Integer = x + 2 = 21 + 2 = 23

Third integer = x + 4 = 21 + 4 = 25

Sum = 21 + 23 = 44

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The value of C (8,5) is 56.

A combination is made up of n different items that are taken one at a time without repeating itself.

The given expression is C(8,5).

The expression C (8,5) can be denoted as ₈C₅.

The formula for selecting x thins from n things is:
ₙCₓ = n!/( (n-x)! x!)

Therefore, the value of ₈C₅ is:

₈C₅ = 8!/( (8-5)! 5 !)

     = 8!/( 3! ×5!)

      = (8×7×6×5!)/( 3! ×5!)

      = (8×7×6)/(3!)

      = (8×7×6)/(6)

      = 8×7

      =56

Hence, the value of C (8,5) is 56.

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If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.

What is a combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Here,

There are 4 numbers needed for the combination and one can pick between 0 and 32.

This means that there are 33 numbers that can be used for the lock including 0.

The number of possible combinations is:

= Number that can be used with no restrictions on the number combination lock limit

= 33 ⁴

= 1,185,921 combinations

Hence, If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.

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Answer: 0.3278

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If the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).

Let the given function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex]

Differentiating with respect to x, we get

d/dx((2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex])

= sin (2) (d/dx(2[tex]$$x^4[/tex] + 1) [tex]$$x^5[/tex] + d/dx ([tex]$$x^5[/tex])  (2[tex]$$x^4[/tex] + 1)

d/dx (2[tex]$$x^4[/tex] + 1) = 8x³

d/dx ([tex]$$x^5[/tex]) = 5[tex]$$x^4[/tex]

= sin (2) (8x³ + 5[tex]$$x^4[/tex] (  (2[tex]$$x^4[/tex] + 1)

Simplify

= sin (2) (8x³ + 5[tex]$$x^4[/tex] (  (2[tex]$$x^4[/tex] + 1)

= sin (2) (18[tex]$$x^8[/tex] +  5[tex]$$x^4[/tex]

Therefore, the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).

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Answer:

B(a) = a/6 - 9

Step-by-step explanation:

The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

What is the area of a trapezoid?

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore, a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

B(a) = a/6 - 9

The equation in slope intercept form of the line that passes through the graph is y = 2/3x + 2

From the graph, we have the points to be given as

(-3,0) and (0,2)

Start by calculating the slope of the points using the following slope equation

m = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3,0) and (0,2)

So, we have

m = (2 - 0)/(0 + 3)

Evaluate

m = 2/3

The equation is then calculated as

y = m(x - x₁) + y₁

Where

(x, y) = (0, 2) and m = 2/3

So, we have

y = 2/3(x - 0) + 2

Expand

y = 2/3x + 2

Hence, the equation in slope intercept form of the line is y = 2/3x + 2

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Answer:

b = 5

Step-by-step explanation:

Add 8b to both sides :

2+6b = 5b+7

Subtract 5b from both sides :

2+b = 7

Subtract 2 from both sides :

b = 5

Let's check :

-8(5) + 2 +6(5) = -3(5) + 7

-40 + 2 + 30 = -15 + 7

-38 + 30 = -8

-8 = -8

Correct

Hope this helped and have a good day

Answer:

b = 5

Step-by-step explanation:

to solve this you must first combine like terms

-8b + 2 + 6b = -3b + 7

combine (add) -8b and 6b

that makes -2b

-2b + 2 = -3b + 7

now add 3b to both sides to put b on one side

-2b + 2 + 3b = -3b + 3b + 7

b + 2 = 7

now subtract 2 to both side

b + 2 - 2 = 7 - 2

b = 5

that is your answer

David share is £8

Vicky share is £28

From the question, we have

David and Vicky share £36 in the ratio 2:7.

David share = £36 *2/9 = £8

Vicky share = £36 *7/9 = £28

Multiplication:

The product of the numbers is what is obtained in mathematics when two or more numbers are multiplied. We frequently perform it since it is one of the fundamental mathematical operations. Using multiplication tables is the most straightforward use. In mathematics, adding a number repeatedly in relation to another is represented by multiplying two integers. These figures can be natural figures, whole figures, fractional figures, integer figures, or other figures. When m is multiplied by n, m is either added to itself n times or multiplied by n.

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By the concept of basic arithmetic, it is $3.64 more expensive per pound, to buy salmon at Super Grocery A than at Super Grocery B.

The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.

At Super grocery B, 3 pounds of Salmon cost = $ 24.63

So, 1 pound will cost = $ 24.63/ 3

= $ 8.21

At Super grocery A, 2 pounds of Salmon cost = $ 23.70

So, 1 pound will cost = $23.70/ 2

= $ 11. 85

To buy salmon at SuperGrocery A than at SuperGrocery B expense per pound is given by

= $11.85 - $ 8.21

$ 3.64

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The first number is 3 and the second number is -5.

According to the question,

We have the following information:

There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8.

Now, let's take the first number to be x and the second number to be y.

So, we have the following expressions:

6x+4y = - 2

6x = -2-4y ...(1)

6x+2y = 8

Putting the value of 6x from equation 1:

-2-4y+2y = 8

-2-2y = 8

-2y = 8+2

-2y = 10

y = -10/2

y = -5

Putting this value of y in equation 1:

6x = -2-4y

6x = -2-4*(-5)

6x = -2+20

6x = 18

x = 18/6

x = 3

Hence, the first number is 3 and the second number is -5.

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The amount of profit made by JMP is 102000.

Given,

In the question;

JMP made a profit of $85,000 last year.

If the profit margin increased by 20% this year.

To find the amount of profit made by JMP.

Now, According to the question:

Based on the given condition:

Formulate:

= 85000 x (20% + 1)

Calculate;

85000 x (0.2 + 1)

Calculate the sum or difference

85000 x 1.2

= 102000

Hence, The amount of profit made by JMP is 102000.

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The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

Answer: candidate 2 has 90 votes

Step-by-step explanation:

165-75=90

Answer: See coordinate graph below.

Step-by-step explanation: The black point is the original point and the red point is the reflected point.

Ordered pair of the reflected point:

A': (1, -4)

Let me know if this is right! :)

The tip of his shadow moving when he is 50 ft from the pole is 10ft/s

The practical approach of differentiation may be performed utilizing just algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

The theory offers the following fundamental guidelines for differentiating the sum, product, or quotient of any two functions f(x) and g(x) whose derivatives are known (where a and b are constants) for functions constructed of combinations of these types of functions

I assume the man and pole are standing straight up, which means the 2 triangles are similar to each other.

(y-x)/y =6/15

15(y-x)=6y

9y=15x

y=(5/3)x

Differentiating both sides with respect to t,

dy/dt=(5/3)dx/dt

We know that, dx/dt= 6 ft/s

((5/3)*6=10 ft/s

Therefore, the tip of his shadow moving when he is 50 ft from the pole is 10ft/s

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Step-by-step explanation:

Given the inequality 4x ≤ 28, determine the value of x.

4x ≤ 28

divide both sides by 4:

4x/4 ≤ 28/4

x ≤ 7

set builder notation: (-∞, 7]

answer:

The value of x is 7.

Step-by-step explanation:

4x ≤ 28 | divide both sides by 4

4x / 4 = x  and 28 / 4 = 7

therefore, x ≤ 7

There are  181440 number of different 10 letter words , (real or imaginary) that can be formed from the given letters   .

In the question ,

it is given that ,

the letters are X, W, C, V, R, Z, W, U, M, A ,

since the total number of letters = 10 ,

So , 10 letter can be arranged in 10! ways = 362880 ways

and we can also see that the letter W is repeated 2 times

So it can be arranged in 2! ways = 2 ways .

So , the total number of different 10 letters words that can be formed is calculated by dividing total number of possible arrangements by arrangement of each repeated letter ,

that is ,

= 362880 / 2

= 181440  .

Therefore  , There are 181440 number of different 10 letter words (real or imaginary)that can be formed from the given letters   .

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For given function  f(x) = 7/(x² - 5),

f(a + 4) = 7/(a² + 8x + 11)

In this question we have been given a function f(x) = 7/(x² - 5)

We need to evaluate f(a + 4)

Substitute x = a + 4 in given function.

f(a + 4)

= 7/((a + 4)² - 5)

=  7/(a² + 8x + 16 - 5)

=  7/(a² + 8x + 11)

Therefore, for given function  f(x) = 7/(x² - 5),

f(a + 4) = 7/(a² + 8x + 11)

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The loan given has a rate of 0.53%

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.

The formula of simple interest is given as;

S.I = P(1 + RT)

Substituting the values into the formula;

(9000 + 336) = 9000(1 + r * 7)

9336 = 9000 + 63000r

Collecting like terms

336 = 63000r

r = 0.0053

r = 0.0053 * 100

r = 0.53%

The rate on the loan is 0.53%

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The area of triangle using vertices is D)  A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

What is area of triangle using vertices ?

 The length of a triangle's three sides must first be determined if the triangle's vertices are known. The distance formula can be used to determine the length. when the vertices in the coordinate plane are known, the process to determine the triangle's area. Consider the triangle PQR, whose coordinates P, Q, and R are [tex](x_1,y_1)(x_2,y_2)[/tex], and [tex](x_3,y_3)[/tex] respectively.

If the triangle's area is zero and its vertices are P[tex](x_1,y_1)[/tex] Q[tex](x_2,y_2)[/tex], and R[tex](x_3,y_3)[/tex] then (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]] = 0 and its points are collinear.

Here the given vertices are, [tex](x_1,y_1),(x_1,y_2)[/tex] and [tex](x_3,y_3)[/tex] then the area of triangle is ,

=> A =  (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]

=> A =  (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_1(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]

=> A = (1/2)[ [tex]x_1y_2-x_1y_3+x_1y_3-x_1y_1+x_3y_1-x_3y_2[/tex]]

=> A = (1/2) [[tex]x_1y_2-x_1y_1+x_3y_1-x_3y_2[/tex]]

=> A = (1/2) [[tex]x_1(y_2-y_1)-x_3(y_2-y_1)[/tex]]

=> A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

Hence the correct option is D)  A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

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Answer:

6

Step-by-step explanation:

the answer is 6

Answer: ZYH

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Answer:

[tex]2,8,14,20[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]2[/tex] and the common difference is [tex]6[/tex], then each successive term in the sequence is [tex]6[/tex] more than the previous term:

[tex]a_n=6n-4[/tex]

Therefore, the first term is [tex]2[/tex], followed by [tex]8[/tex], [tex]14[/tex], and [tex]20[/tex].

Based on the equation, the minimum number of years an employee would have to stay to make a salary of over $40,000 per year is B. 12 years.

An equation is a mathematical statement that defines that two or more mathematical expressions are equal or equivalent.

Equations show equality using the equation symbol (=).

When one expression is more or less than, or not equal to another expression, it is an inequality.

If S = $33,113 + $600t

Where S = the salary before taxes

t = the time since the date of hire in years.

For S ≥ $40,000:

$33,113 + $600t ≥ $40,000

$600t ≥ $40,000 - $33,113

$600t ≥ $6,887

t ≥ 11.48

t = 12 years

Thus, using the given equation, an employee needs to stay at the work for 12 years to earn more than $40,000 a year.

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