What is the distance between -112 and -80 on a number line?

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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(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°

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

Answer:

A. 463-139=324

B. 14,527-7609=6918

Step-by-step explanation:

there ya go! hope it helps you out some!

let me know if it is correct

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

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

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°.

Using simple multiplication, the cost of 1 1/3 pounds of raspberries equals 12 pounds.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

Given,

Cost of 3/5 pounds of raspberries = $9

Cost of 1 pound of raspberries = 9 × 5/3

Cost of 1 pound of raspberries = 15 pounds

Cost of 1 1/3 pounds of raspberries = 4/3 × 15

= 12 pounds

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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!

The following statement is true about the triangles (d) D = 77 and E = 79

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor,

Where the scale factor does not equal to one.

From the attached image, we understand that there are two shapes

The shapes are triangles

One triangle is the scaled factor of the other

So, the triangles are similar shapes

As a general rule, the following are the properties of a scaled copy of another figure

Using the above as a guide, we have the following

D =B = 77 -- by corresponding angles

Also, we have

E = A = 180 - 77 - 24 -- by corresponding angles

E = A = 79

Hence, the true statement is (d) D = 77 and E = 79

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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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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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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:

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

Step-by-step explanation:

Answer:

  2x^2 -4x +5 +8/(4x -1)

Step-by-step explanation:

You want to divide 8x^3-18x^2+24x+3 by 4x-1 using polynomial long division.

Polynomial long division is similar to numerical long division, except that the quotient term is always the ratio of the leading dividend term to the leading divisor term.

As with numerical long division, the dividend at each step is reduced by the product of the quotient term and the divisor.

When the dividend is of lower degree than the divisor, the division is finished. That dividend is the remainder.

The attachment shows the division in detail. Your result is ...

  q(x) +r(x)/b(x) = (2x^2-4x+5) +(8)/(4x-1)

Solution:

To find the first three terms of the sequence defined as

This implies that we solve for

for n equals 1, 2, and 3.

Thus,

first term: n=1

second term: n =2

third term: n = 3

Hence, the first three terms of the sequence are

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)



Given the exponential model

We can find the solution to the given question below.

hEe model says that between the year 2000 and 2001 the population of the boars decreased by 5%. The year 2000 indicates the starting point of the model.

Answer: 125000

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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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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We need to distribute 7/8 of a gallon into cups of 1/16 of a gallon. It means that to know the number of cups, we need to divide 7/8 into 1/16.

So, let's remember how to make a division between two fractions:

Then, the division of 7/8 into 1/16 is equal to:

Therefore, he gets 14 cups of blue paint.

Answer: 14 cups

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]

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 calculation for y=0 corresponds to the point where the graph crosses the x-axis . This is the point (x,0) .

In the question ,

it is given that y=0 ,

When y=0 in a point (x,y) means , that point lies on the x -axis , and it is called as the x intercept .

X intercept is defined as the point where the graph of a line crosses the x-axis .

the point on the x-axis will be (x,0) ,

So , the graph will cross the x-axis when y=0 , and that point will be (x,0).

and the value of x will be called as the x intercept of the graph .

Therefore , the calculation for y=0 corresponds to the point where the graph crosses the x-axis . This is the point (x,0) .

The given question is incomplete , the complete question is

The calculation for y=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .

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The definition is option B No, it is not differentiable at x = 0.

Given,

The function, f(x) = 8x²

We have to find that the function is differentiable at x = 0.

So, lets check:

f(x) = 8x²

x = 0

f'(0) = [tex]\lim_{h\to \ 0}[/tex] [tex]\frac{f(0+h)-f(0)}{h}[/tex]

f(0 + h) = 8(0 + h)² = 8 (0 + 0 + h²) = 8h²

f(0) = 8 × 0² = 0

f(0 + h) - f(0) = 8h² - 0 = 8h²

f'(0) = [tex]\lim_{h \to \ 0}[/tex] 8h²/h = 8h = 8 × 0 = 0

That is, the function f(x) = 8x² is not differentiable at x = 0

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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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Answer:

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

Answer:

x = 11.73 is what i got

Step-by-step explanation:

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]