6-Mr. Lofters has 7/8 of a gallon of blue paint. He needs to distribute the blue paint out equally to his students. If Mr. Lofters pours 1/16 of a gallon of blue paint into each cup, how many cups of blue paint can he get? IMAGINE WHAT IS HAPPENING IN THE PROBLEM. WHAT OPERATION WILL BE INVOLVED? WHICH NUMBER WILL GO FIRST? LOOK FOR KEYWORDS. DO YOU REMEMBER THE FISH SONG?? YOU'LL REALLY FLIP IF YOU DON'T GET THIS ONE RIGHT.

To find the x-intercept, simply but y=0 in the equation given and solve for x

That is;

3x - 4y = 12

3x - 4(0) = 12

3x = 12

Divide both-side of the equation by 3

x= 4

The x-intercept is;

(4, 0)

To find the y-intercept, simply put y=0 in the equation given and then solve for y

That is;

3x - 4y = 12

3(0) - 4y = 12

-4y = 12

Divide both-side of the equation by -4

y = -3

The y-intercept is (0, -3)

Hence, the correct option is B.

x-int: (4,0)

y-int: (0, -3)



Jane, Alan, and Ravi sent a total of 146 text messages over their cell phones during weekend, Ravi sent 8 fewer messages than Jane. Alan sent 4 times as many messages as Ravi. So as per question data,

Jane sent= 31 messages

Ravi sent= x-8= 31-8 = 23 messages

Alan sent= 4(x-8) = 92 messages

The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.

The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.

PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.

Let, Jane sent x number of messages

Then, Ravi sent x-8 number of messages

and, Alan sent 4(x-8) number of messages

Total number of messages by them = 146

now,

x+(x-8)+4(x-8)=146

6x-40=146

x=31

so, Jane sent= 31 messages

Ravi sent= x-8= 31-8 = 23

Alan sent= 4(x-8) = 92

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Answer:

c) subtraction property of =

Step-by-step explanation:

step 3 show the movement of +15 moving to the other side of the = by subtracting 15 on each side, leaving you with 3x-16

Answer:

[tex]{ \tt{ {x}^{2} + 2 = 0 }} \\ \\ { \tt{ {x}^{2} = - 2 }} \\ \\ { \tt{x = \sqrt{ - 2} }}[/tex]

- At this point, we can't operate the square root. Let's introduce the imaginary part of a value

From complex numbers;

[tex]{ \boxed{ \tt{{ \red{note} \: {\rightarrow{i \times i = - 1 = {i}^{2} }}}}}}[/tex]

Therefore;

[tex]{ \tt{x = \sqrt{2 \times {i}^{2} } }} \\ \\ { \boxed{ \rm{ \: x = i \sqrt{2} \: \: }}}[/tex]

Answer:

B

Step-by-step explanation:

using the rules of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]

given

[tex]5^{8}[/tex] × [tex](5^{12}) ^{-4}[/tex]

= [tex]5^{8}[/tex] × [tex]5^{(12(-4))}[/tex]

= [tex]5^{8}[/tex] × [tex]5^{-48}[/tex]

= [tex]5^{(8-48)}[/tex]

= [tex]5^{-40}[/tex]

= [tex]\frac{1}{5^{40} }[/tex]

Answer:

i = 1, (3/7)

Step-by-step explanation:

7|14i-10|+9 = 37,    

             -9    -9                  

------------------------    

7|14i - 10| = 28          

÷7               ÷7

---------------------

|14i - 10| = 4

14i - 10 = 4

     +10   +10

------------------

14i = 14

÷14   ÷14

--------------

i = 1

|14i - 10| = -4

14i - 10 = -4

     +10    +10

---------------------

14i = 6

÷14  ÷14

--------------

i = (3/7)

I hope this helps!

Answer:

536

Explanation:

rom the given table:

If an individual and spouse enroll in the low deductible plan, the monthly premium will be $536.

Answer:

  y = x³ -2x² -13x -10

Step-by-step explanation:

You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.

A polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...

  p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)

Expanding this gives ...

  p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10

This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.

The polynomial function is ...

  y = x³ -2x² -13x -10

C) Triangle ABC is equilateral.

E) Segment AB is the same length as segment AC because they are both radii of the same circle centered at point A.

F) Segment AB is the same length as segment BC because they are both radii of the same circle centered at point B.

In the given figure,

A and B are the centres of the two intersecting circles.

In a circle having centre at A, we have

AC = AB = radius

In a circle having centre at B, we have

BC = BA = radius

According to Euclid's first axiom, things that are equal to the same thing are equal to one another.

Therefore, AC = AB = BC

Hence, the triangle is an equilateral triangle.

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By median ,  test scores of 40 students are listed below.  So five number summary is 25, 58,72,81,98

What are median in math?

First we need to sort the data from Smallest to largest data value which is allready sorted

n = 40

Five number summary can be calculated as

Minimum = 25

Q1 can be calculated as

Lower Half of 40 values is 20, so median of 20 values will give us 25th percentile so Median = (20+1)/2 = 10.5th here 10th value is 57 and 11th value is 59 so Q1 = (57+59)/2 = 58

Median = (n+1)/2 = (40+1)/2 = 20.5th value and 20th and 21st value is 72 so median = (72+72)/2 = 72

Upper 20 values after median will provide us Q3 or 75th percentile which can be calculated as 20+(20+1)/2 = 30.5th value so 30th value is 81 and 31st value is also 81. So Q3 = (81+81)/2 = 81

Max = 98

So five number summary is 25, 58,72,81,98

And correct boxplot for this data is A. Boxplot A is correct which shows correct five number summary.

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Answer:

x = 11.73 is what i got

Step-by-step explanation:

1) Given this equality,

15x = 75 Divide both sides by 15

x=5

2) Then we can write that since x = 5 and 15x = 75 we have here is the Division Property of Equality.

Because in this case, we divided both sides by 15, which is different from zero to find equivalent equality.

3) So

Given:

Cost of Truck = $16000

Down payment amount = $3000

EMI = $250

Duration of EMI = 60 Months

Required:

a) Total amount financed

b) Total finance charge paid at the end of 60 months

Explanation:

Total cost of Truck = $16000

The total amount taken from other source = Total Amount - Down payment

=$16000-$3000

=$13000

EMI = $ 250

Total amount paid at the end of 60 months = $15000

The total amount financed = Actual price -Down payment

=$16,000- $3000

=$13000

a) Total amount financed =3$18000

The total finance charged = Actual price - amount paid monthly for 60 months.

=$16000-$15000

=$1000

b)The total finance charged =1$20

Hence the total amount finance is 13000 dollar.

The total finance charged is 1000 dollar.00

Answer:

P' (- 5, 3 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x , - y ) , then

P (- 5, - 3 ) → P' (- 5, 3 )

The water pressure on a submerged object is given by P = 64d, then the

a. The answer to the subject of the formula, "d," is d = P/64.

b.  The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet

A function can be defined as an expression, law or rule that shows the relationship between two variables.

These variables are namely;

Given the role as;

P = 64d

Where;

P stands for pounds per square foot of pressure.

d represents the object's depth in feet.

Let's now make the variable "d" the focus of the formula.

The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.

(a) We get,

P/64 = 64d/64

d = P/ 64

(b) P equals 672 pounds per square foot if there is pressure.

When the variable's value is substituted into the formula, we get;

d = P/64

Then,

d = 672/64

Discover the quotient,

d = 10. 5 ft.

The value is 10.5 feet .

Therefore,

a. The answer to the subject of the formula, "d," is d = P/64.

b. The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet.

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The number of numbers circled with only one color found using arithmetic progression formula are 809 numbers

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms in the sequence is constant

The given parameters are;

The set of the numbers written on the paper = Numbers from 1 to 2022

Numbers circled with red circles by Caitlin = All even numbers between 1 and 2022

Numbers Nicole circles using yellow = Numbers that are multiples of 5

Required; The number of numbers that are circled with one colour only

Solution; The even numbers are numbers that are a multiple of 2

The number of even numbers between 1 and 2022 are found using arithmetic progression formula as follows;

[tex] a_{n} = a_{1} + (n - 1)\cdot d[/tex]

Where;

[tex]a_{1}[/tex] = The first term = 2 (First even number)

d = The common difference = 2

n = The number of terms

Given that 2022 is an even number, we have;

[tex] a_{n} = 2022 = 2 + (n - 1)\cdot 2[/tex]

Which gives;

[tex] \displaystyle {n = \frac{(2022 - 2)}{2} + 1 = 1011} [/tex]

We note that 10 is the lowest common multiple of 2 and 5, which gives;

Multiples of 10 have two colors, therefore, the numbers that have only one color is given by the difference between the number of even numbers and the number of multiples of 10 as follows;

The number of multiples of 10 are;

[tex] \displaystyle {n = \frac{(2020 - 10)}{10} + 1 = 202} [/tex]

Which gives;

The numbers having only one colour = 1011 - 202 = 809

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The estimate where the number of books is enough is 254,000

The estimation of numbers is the approximation of the said number.

This means that the estimation of a number is close to the said number, but it has a slight different value

The number of books is given as

Number of books = 253,625

From the question, we understand that:

You want to make sure that the number of books is enough

This means that we estimate the number of books to a number greater than 253,625

A good way to do this is to approximate to the nearest thousand

When the number is approximated to the nearest thousand, we have

Estimate = 254,000

Hence, the estimate is 254,000

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The equation of the polynomial is P(x) = 6.86(x + 5) (x + 3) (x - 1)

Given,

x intercepts which the polynomial passes though = (-5, 0), (-3, 0), and (1, 0).

Point = (3, 14).

We have to find the polynomial equation;

A polynomial is defined as;-

P(x) = a(x - c₁) (x - c₂)....(x - cₙ)

Here,

a is a constant

c₁, c₂,...cₙ are the zeros of the polynomial

Here,

-5, -3 and 1 are the zeros of the given polynomial

(x + 5), (x + 3) and (x - 1) are the factors of the given polynomial.

Then the equation of polynomial be like;

P(x) = a(x + 5) (x + 3) (x - 1)

This polynomial passes through point (3, 14)

That is,

14 = a(3 + 5) (3 + 3) (3 - 1)

14 = a x 8 x 6 x 2

14 = 96a

a = 96/14

a = 6.86

Substitute this in equation of polynomial;

That is,

P(x) = 6.86(x + 5) (x + 3) (x - 1)

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ANSWER:

Preserves the inequality

STEP-BY-STEP EXPLANATION:

We have the following expression:

We add -2 on both sides and we have

This is true, therefore the equality symbol remains the same

If a package of 5 pairs of insulated gloves costs $28.955,then the unit price of the pairs of gloves is $5.791

A package of 5 pairs of insulated gloves costs ​$28.955

The price of 5  pairs of insulated gloves = $28.955

Here we have to use the unitary method

The price of 1 pair of insulated gloves = The price of 5  pairs of insulated gloves / 5

Substitute the values in the equation and divide it

The price of 1 pair of insulated gloves = 28.955/5

= $5.791

Hence, if a package of 5 pairs of insulated gloves costs $28.955,then the unit price of the pairs of gloves is $5.791

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Answer:

x = 61

Step-by-step explanation:

sqrt = square root

sqrt(x + 20) = 9 square both sides to cancel out sqrt

x + 20 = 81 subtract 20 to get x alone

x = 61

Sum in the sigma notation of the given series is equal to

∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.

As given in the question,

Given series :

(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)

Simplify the given series

= [1/ (1 ×3)] +  [1/ (3 ×5)] +  [1/ (5 ×7)] +  [1/ (7×9)]

1, 3, 5, 7 can be expressed as ( 2n + 1) , where n = 0, 1, 2, 3

3, 5, 7, 9 can be expressed as ( 2n + 3) , where n = 0, 1, 2, 3

Express the given series as a sum in the sigma notation form

(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)

=∑ [ 1/ (2n +1) (2n + 3) ] where n = 0,1,2,3

Therefore, sum in the sigma notation of the given series is equal to

∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.

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Answer:

What is the role of ethnocentrism in defining the concept of “progress”

Step-by-step explanation:

The period of the graph is π/2.

The length of one function wave is referred to as the period. One entire wave in this situation is 180 degrees, or radians. Without using a graph, you can get this simply dividing 2 by the frequency, which in this case is 2.

Given: 5 sin (4πx)+3

Period = 2π / 4

⇒ period = π/2

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Two similar boxes A and B are given with box B created by dividing box A's dimensions by 2.

Recall that the scale factor, k is the ratio of lengths of two corresponding sides of similar figures.

Since the dimensions of A were divided by 2 to form B, it follows that the scale factor of box A to box B is:

Also, recall the Similar Solids Theorem

It follows that the ratio of the volumes of the given solids is:

Let the volume of box A be V₁ and let the volume of box B be V₂, it, therefore, implies that:

Substitute the value for the volume of box A into the equation, V₁=64:

Hence, the volume of box B is 8 m³.

Answer:

(3 × 2) + (10 × 4) is the correct expression.

The point is located at 3 1/2 points to the left of the origin and 1 1/4 points below the origin

The coordinate of the point on a coordinate plane is given as

Point = (-3 1/2, -1 1/4)

Rewrite the above coordinate as follows:

(x, y) = (-3 1/2, -1 1/4)

Split the coordinates into x and y coordinates

So, we have the following equations

x = -3 1/2

y = -1 1/4

The above means that:

Next, we plot the points

See attachment for the plot of the points on a coordinate plane

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Answer:

The answer would be D(x/y)= -(11/8) / -(11/4)

Step-by-step explanation:

(x+18)° is vertical opposite 112° and vertical opposite angles are equal meaning

⇒(x+18)°=112°

x+18°=112°

x=112°-18°

∴x=94°

(2y)° is in a straight line with 112° meaning their sum is 180°

[tex]2y+112=180\\2y=180-112\\2y=68\\\frac{2y}{2} =\frac{68}{2} \\y=34[/tex]

∴y=34°

We can determine the values of the angles as follows:

*By opposite by angle we will have that angle f is equal to:

angle f has a measurement of 58°.

*By supplementary angles we will have that angle e is equal to:

angle e has a measurement of 26°.

*As is indicated (Two lines have the same markings indicating they are parallel) we will have that the measurement of angle b is 78°.

*By complementary angles, the measurement of angle a is:

angle a has a measurement of 102°.

*We will have by alternate exterior angles that c has a measurement of 58°.

*By supplementary angles, we will have that the measurement of angle d equals:

angle d has a measurement of 122°.