is 0.1213141516... a rational number

The expression which is equivalent to −12(8a − 7b) + 8(4x + 3y) is - 96a + 84b + 32x + 24y.

The correct answer option is option a

Equivalent expression are expressions which when solved, the results are equal to the old expression.

-12(8a − 7b) + 8(4x + 3y)

Using PEMDAS

- 12(8a − 7b) + 8(4x + 3y)

- 96a + 84b + 32x + 24y

Therefore, the equivalent expression for −12(8a − 7b) + 8(4x + 3y) is - 96a + 84b + 32x + 24y.

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Answer:

All four of these numbers are rational.

The commutative property is a mathematical property that states to combine like terms. Like terms are terms that have the same variables and powers.

In the given:

8x + 4 + 6x +2

By adding 8x and 6x, and 4 + 2, you are using the commutative property to simplify this expression.

8x+6x = 14x

4+2=6

The simplified equation is 14x + 6

-------

If you would like to further simplify this expression, factor out the greatest common factor.

The further simplified expression would look like: 2(7x + 3)

Answer:

a) x^7 y^2

b) 6 x^8 y^3

Step-by-step explanation:

Exponential expressions

a) x x x x x xу ху

There are 7 x 's in the expression and 2 y's  The number of the x's is the exponent for x is the exponent and the same for y

x^7 y^2

b) 2 xx x x x 3 ×ухуху

Multiply the constants 2*3 = 6

Count the x's 8 x's  = x^8

Do the same for y 3 y's  = y^3

6 x^8 y^3

Answer:

Any number raised to 0 is equal to 1

hence: 2^0 = 1

Answer:

12

Step-by-step explanation:

we enter -3 in for all the x's and rewrite the problem.

-3 (1 - (-3) -4 • 2)

then we calculate ending up with the next problem.

-3 • (-4)

then we simply multiply and end up with 12 as our answer, hope this helped!

The value of X and Y in the length of each side of an equilateral triangle is X = 3 and Y = 4

In this question we have been given the equations for the three sides of an equilateral triangle.

3X +12, 8X -3 and 5Y + 1

We need to find the value of X and Y.

We know that all sides of an equilateral triangle are equal.

so, 3X +12 = 8X -3 = 5Y + 1

Consider 3X +12 = 8X -3

3X -8X = - 3 - 12

-5X = - 15

X = 3

Now consider an equation 8X - 3 = 5Y + 1

substitute above value of X in this equation.

8(3) -3 = 5Y + 1

24 - 3 = 5Y + 1

21 - 1 = 5Y

5Y = 20

Y = 4

Therefore, the value of X and Y in the length of each side of an equilateral triangle is X = 3 and Y = 4

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Answer:

C

Step-by-step explanation:

x + 8 = 6

x = 6-8

x = -2

.....

b= (2,-1);

(3,1) - left 1, down 2

Answer:

ok

Step-by-step explanation:

c is  85

360-170

190/2

95

c=85

b=95

If the steps are shaped like rectangular prism, then the expression that can be used to find the volume is option (B)  (6×16×6)+(14×16×7)

The steps are shaped like rectangular prism

The length of the rectangular prism = l×w×h

Where l is the length

w is the width

h is the height

First we have to separate the given steps in to two rectangular prism and find the volume of each prism

The volume of the top prism = l×w×h

= 6×16×6 cubic inches

The volume of the bottom prism = l×w×h

= 14×16×7 cubic inches

The total volume = (6×16×6)+(14×16×7) cubic inches

Hence, if the steps are shaped like rectangular prism, then the expression that can be used to find the volume is option (B)  (6×16×6)+(14×16×7)

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The remainder when [tex]5^{400}[/tex] is divided by 19, the remainder is 17.

Remainder

The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.

We can write,

[tex]5^{400} = (5^4)^{100} = 625^{100}[/tex]

We know that,

19*33 = 627

Hence, we can write 625 as 627 - 2

It will become,

[tex]\frac{(627-2)^{100}}{19}=\frac{(-2)^{100}}{19}[/tex]

We know that, even power of any number and its negative counterpart will be same.

Hence, we can write,

[tex]\frac{(-2)^{100}}{19}=\frac{(2)^{100}}{19} = \frac{2*2^{99}}{19}[/tex]

We know that 99 = 11*9

Hence, we can write,

[tex]\frac{2*({2^9})^{11}}{19} =\frac{2*512^{11}}{19}[/tex]

We know that,

19*27 = 513

Hence, we can write, 512 as 513 - 1

[tex]\frac{2*(513-1)^{11}}{19}=\frac{2(-1)^{11}}{19}[/tex]

2*(-1)/19 = -2/19

It means the remainder will be 19 - 2 = 17.

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Answer:-50x+36

Step-by-step explanation:

Answer:

-50+36

Step-by-step explanation:

i hope that helps

A scatter plot for the data shown in the table is plotted and illustrated in the attachment below.

A scatter plot is also referred to as scatter diagram, scatter chart, or scattergram and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.

In this scenario, the text messages would be plotted on the x-axis of the scatter plot while the age would be plotted y-axis of the scatter plot as depicted in the image attached below.

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Answer:

answer is 4

because y is directly proportional to x2

Answer:

y is directly proportional to x

y=kx^2

20=2^2k

20=4k

k=5

y=6k

y=6(5)

y=30

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Answer:

Option 4,  8 1/3

Step-by-step explanation:

-2.5 * - 3 1/3 = 8.3 repeating

8.3 repeating = 75/9

75/9 = 8 1/3

Mike's average score is 166.

Divide the total by the number of numbers after adding up all the numbers.

Implying something that sits in the midst. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. Averages are used to condense a vast number of data points into a single value. It is a visual depiction of all the data set's available numbers. By adding up all the data values and dividing them by the total number of data points, the average is calculated.

Given Data

Mike bowled two games with scores of 157 and 175.

Sum of scores = 332

Average = [tex]\frac{Sum of scores}{Totak number of bowling}[/tex]

Average = [tex]\frac{157 + 175}{2}[/tex]

Average = [tex]\frac{332}{2}[/tex]

Average = 166

Mike's average score is 166.

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a. 8 + 0 = 4 +4

d. 5+1 = 6 +0

b. 7+2=9+0

e. 6 +1= 4 + 3

C. 5+2=4+3

f. 5+4= 6+3

How can I locate a lost number?

Missing numbers are those that were omitted from the offered series of numbers with comparable discrepancies. Finding similar differences between the missing numbers and adding their missing values to the appropriate series is how the missing numbers are written.

example

Children are frequently asked to solve number sentences, which are compositions of numbers and mathematical processes. Number phrases contain the following: 32 + 57 =? 5 x 6 = 10 x?

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Answer:17

Step-by-step explanation:

|-3|^3 + 8

3^3 +8

9+8

17

Each member of the club needs to pay £ 4.895 to cover the cost of hiring the buses.

A youth club's 143 members and eight leaders ride a bus to a bowling alley.

The buses for hire by the beezer bus company hold 32 passengers each.

The cost of each bus to hire is £140.

There are eight leaders and 143 members.

Therefore, there are a total of 143 + 8 = 151 passengers.

So, the number of buses required will be:

= 151 / 32 =  4.7 ≈ 5 buses

Therefore, the cost of hiring 5 buses will be:

= 5 × £140 = £ 700

As the eight leaders will not ay.

Therefore, the amount each member needs to pay is:

= £ 700 / 143

= £ 4.895

Each member of the club needs to pay £ 4.895 to cover the cost of the buses.

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The probability that maximum speed differs from the mean value by at most 1.5 standard deviations is 0.1336.

The probability is typically defined as the proportion of positive outcomes to all outcomes in the sample space. It is written as, P(E) = (Number of favorable outcomes) = Probability of an Event (Sample space).

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The probability will be illustrated as:

P(|Z|>1.5)

= P(Z<-1.5) + P(Z>1.5)

= 2*P(Z<-1.5)

Look at the value under the distribution table. This is 0.0668.

= 2 × 0.0668

= 0.1336

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For the given inequality 2(b + 2) ≥ 24 solution of the graph represented by number line with closed point at 10 with arrow pointing right.

As given in the question,

Given inequality is :

2(b + 2) ≥ 24

Solution of the given inequality 2(b + 2) ≥ 24 is equal to :

2(b + 2) ≥ 24

Divide both the sides by 2

[2(b  + 2 )] / 2 ≥ 24 /2

Subtract 2 from both the sides

b + 2 -2 ≥ 12 - 2

⇒ b ≥ 10

Interval form is represented by [10, ∞)

Solution of the graph represent 10 is included to arrow moves towards positive infinity.

Therefore, for the given inequality 2(b + 2) ≥ 24 solution of the graph represented by number line with closed point at 10 with arrow pointing right.

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The estimate that best describes the area under the curve in square units is option B: 15 units².

The area under a curve in calculus is a picture of an integral. It is frequently possible to interpret the area under a curve as the total amount of whatever the function is describing.

By performing a definite integral between the two locations, one can determine the area under a curve between two points. Integrate y = f(x) between the limits of a and b to tell about the area under the curve y = f(x) between x = a & x = b.

Therefore, each box:

0.5 × 1 = 0.5 units^2.  Then add up the boxes, and it is about  30. So:

30×0.5 = 15 units².

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Distance was 10 miles away from home.

What is Distance ?

The measurement of distance is the separation between two objects or points, and it can be quantitative or occasionally qualitative. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.
For a journey to see her cousin, Hannah traveled. She traveled 120 miles one way to visit her cousin and 120 miles the other way to return home.

She traveled halfway to her cousin's home in 1.2 hours.
That is 120 / 2 = 60 miles
(Speed = distance/time) 60 miles in 1.2 hours
Average speed = 60 / 1.2

                          = 50 mph.

For the remainder of the journey to her cousin's home, Hanna's average speed was 40 miles per hour.
Another 60 kilometers remain: Time (= Distance/Speed)
Time = 60/40

         = 1.5 hours.

Hanna averaged 55 miles per hour when she made her way home along the same path. Her automobile broke down after two hours.

Find the distance traveled at 55 mph in 2 hours. (Distance = time * speed)

Distance = 55 * 2 = 110miles

So distance from home will be,

= 120 - 110

= 10 miles

Hence, she was 10miles away from her home

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The correct answer by simplifying 5√2-9√6 is:

- 14.974

Steps to simplify square roots:

Here given the expression,

  5√2-9√6

simplifying the expression,

5√2 - 9√6

= 5√2 - 9√2 x √3

= - 14.974

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Answer:

24

Step-by-step explanation: