How do variables help you model real-world situations? Give an example of a model that uses variables and explain how it helps people make predictions

-4, -1/2, 3, 13/2, 10,… represents an arithmetic sequence.

An arithmetic sequence progresses with a common difference which is the difference of consecutive terms.

So for each of the number sequences, we will try to check if the consecutive terms has a common difference.

A) 32, 16, 8, 4, 2,...

16-32 = -16

8-16 = -8

4-8 = -4

2-4 = -2

As the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

B)5, 10, 20, 40, 80,...

10-5 = 5

20-10 = 10

40-20 = 20

80-40 = 40

Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

C) -4, -1/2, 3, 13/2, 10,…

-1/2- -4 = 7/2

3- -1/2 = 7/2

13/2-3 = 7/2

10-13/2 = 7/2

This sequence has a common difference and hence is an arithmetic sequence.

D) 4, 8/3, 16/9, 32/27, 64/81,…

8/3-4 = -4/3

16/9-8/3 = -8/9

32/27-16/9 = -16/27

64/81-32/27 = -32/81

Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

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Reason:

The equation is in y = mx+b form where

m = 20 = slope

b = 0 = y intercept

The slope is the rate of change. It tells us how fast y increases.

slope = rise/run = 20 = 20/1

rise = 20 = increase the earnings by 20 dollars

run = 1 = each time the number of hours go up by 1

Answer:

u = 14

Step-by-step explanation:

2u - 17 = 11

add 17 to both sides:

2u - 17 + 17 = 11  + 17

2u = 28

divide both sides by 2:

2u/2 = 28/2

u = 14

The percentage increase in the cost of the airline tickets is 38%.

Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency. In order to convert a value to a percentage, multiply the value by 100.

in order to determine the percentage increase, multiply the fraction of the change in price and the initial price by 100.

Percentage increase = (change in price / initial price)  100

Change in price = new price - initial price = $310 - $225 = $85

Initial price = $225

($85 / $225) x 100 = 38%

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Answer:

you can ask questions for clarification

The least common multiple for 12 and 15 is 60, the least common multiple for 6 and 15 is 30, and the least common multiple for 9 and 15 is 45.

In mathematics, the term "least common multiple" is used to refer to a multiple of two or more numbers share and that is the smallest number possible.

Mulitiply the numbers given by 1, 2, 3, 4, etc. until your find the first common number.

Lets use the numbers given

12 x 1 = 12        15 x 1 = 15

12 x 2 = 24       15 x 2 = 30

12 x 3 = 36       15 x 3 = 45

12 x 4 = 48       15 x 4 = 60

12 x 5 = 60

Based on this, the least common multiple is 60

6 x 1 = 6          15 x 1 = 15

6 x 2 = 12       15 x 2 = 30

6 x 3= 18

6 x 4 =24

6 x 5 =30

Based on this, the least common multiple is 30

9 x 1 = 9           15 x 1 = 15

9 x 2 = 18         15 x 2 = 30

9 x 3= 27         15 x 3 = 45

9 x 4 =36

9 x 5 =45

Based on this, the least common multiple is 45

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Answer:

y = 15/4 mm

x = 36/5 mm

Step-by-step explanation:

In similarity triangles, the corresponding sides are in same ratio.

          [tex]\sf \dfrac{3}{y}=\dfrac{4}{5}\\\\\bf Cross \ multiply,\\\\ y*4 = 3*5\\\\ y =\dfrac{15}{4}\\\\\boxed{y = \dfrac{15}{4}}[/tex]

                               [tex]\sf \dfrac{x}{9}=\dfrac{4}{5}\\\\x = \dfrac{4}{5}*9\\\\x = \dfrac{36}{5}\\\\\boxed{x = \dfrac{36}{5} \ mm}[/tex]

Answer:

p=2+1.1m

Step-by-step explanation:

p=price, m=miles

Answer

8:28 Hope this helps.

Answer:

y = -1/3 x + 1/3

Step-by-step explanation:

In the picture.

Answer:

f(-2) = -8

Step-by-step explanation:

We are given a function:

[tex]f(x)=2x-4[/tex]

We are told to find f(-2).

First, substitute -2 as x in f(x):

[tex]f(x) = 2x-4\\\\f(-2) = 2x-4[/tex]

Then, substitute -2 as x in the equation itself:

[tex]f(-2) = 2(-2) - 4[/tex]

Then, simplify by multiplying 2(-2):

[tex]f(-2) = 2(-2) - 4\\\\f(-2) = -4 - 4[/tex]

Finally, simplify by performing the final arithmetic:

[tex]f(-2) = -4 - 4\\\\f(-2) = -8[/tex]

Therefore, f(-2) = -8.

At hour 9, the temperature recorded was = 75 degrees

At hour 13, the temperature recorded was = 95 degrees

The rate of change = Change in the temperature / Change in the time

⇒ The rate of change = 95 - 75 degrees / 13 - 9 hour

⇒ The rate of change = 20 degrees / 4 hours

⇒ The rate of change = 5 degrees per hour

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The tree is approximately 27 ft tall if the answer is rounded off to the nearest foot when the similar triangle formula is applied.

Two triangles can be said to be similar if their corresponding angles are seen as congruent and thereafter their corresponding sides are in proportion.

Similar Triangles Definition

Angle - Angle (AA)

Side - Angle - Side (SAS)

Side - Side - Side (SSS)Similar triangles are triangles that have the same shape, but their sizes may vary.

If Diane, mirror, and the exact bottom of the tree are placed as points on the ground all lying on one line, then the two right triangles can be stated as:

LEFT: y and 35 as the legs and unknown hypotenuse.

RIGHT: 6 and 7.9 as the legs and unknown hypotenuse.

The two angles pointed at the mirror are seen as of same measure that means that 35 and the hypotenuse of LEFT triangle makes same angle measure as the 7.9 and the hypotenuse of that of the RIGHT triangle.

Since these two are seen as similar triangles,

y/35 = 6/7.9

⇒y = 26.58

⇒ y ≈ 27 ft

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Answer:

a -7

b 18

c -13

d -5

e 0

f -7

g 0

h -6

Step-by-step explanation:

too lazyy

Answer:

g(8)=17

Step-by-step explanation:

Given :
g(a)=a²+2a-63

Substitute a = 8 :

g(8)=8^2+2(8)-63

= 64+16-63

=17

The value illustrated shows that x is -55 units to the left of 0.

From the given statement we have the value of x is negative. Therefore, we need the complete statement about x being positive.

Therefore we have to put an alternate sign to the given statement we get -x is 55 units to the right of 0.

Negation to the given statement about x is -(-x) is -(55) units to the left of 0. The statement will be that x is -55 units to the left of 0.

By using  the drop-down menus to complete the given statement about x is -55 units to the left of 0.

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The actual height of the building is 739.2 feet.

Given the height of a building estimated by Charlie is 924 feet.

His father said that there is 20% error in the estimation.

we should determine 20% of the estimated height.

⇒ height = 924 feet

⇒ error = 20%

⇒ 924 × 20/100

⇒ 924/5

= 184.8 feet

Subtract the error in height with the height given.

⇒ estimated height - error in height

⇒ 924 - 184.8

= 739.2 feet.

hence the actual height is 739.2 feet.

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the parameters we are estimating using the OLS method must be themselves linear

What are the Gauss Markov assumptions?

Gauss Markov Assumptions

Linearity: the parameters we are estimating using the OLS method must be themselves linear. Random: our data must have been randomly sampled from the population. Non-Collinearity: the regressors being calculated aren't perfectly correlated with each other.

What are the properties of Gauss Markov Theorem?

The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.

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Answer:

c

Step-by-step explanation:

c

The sum of two hundred even numbers in the sequence from 0 to 398 is 39800

To find the sum of two hundred even numbers from 0 to 398, we can use the formula of sum of an arithmetic progression.

[tex]S_n = \frac{n}{2}[2a(n-1)]d[/tex]

The number of terms given here is 200, the first term is 0 and the common difference is 2

Substituting the values into the equation

[tex]S_n = \frac{n}{2}[2a+(n-1)]d\\S_n = \frac{200}{2}[2*0+(200-1)*2\\S_n = 100(0+199)*2\\S_n = 39800[/tex]

The sum of two hundred even numbers from 0 to 398 is 39800

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To calculate the total number of miles the delivery truck drove, we add the lengths of the three routes together.

-> It drove 123 + 10 + 15 = 148 (miles).

Answer:13x9x6=702

Step-by-step explanation:

If the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.

What is dividend, divisor and quotient?

The dividend in this case refers to the number that is being divided. The divisor is the integer that divides a given number. The quotient is the sum that we arrive at as a result. The residual is the number that the divisor leaves after partially dividing the original integer.

Let x be the quotient after dividing 782 by 1523.

[tex]\frac{782}{1523} = x\\0.5134 = x\\x = 0.51[/tex]

Therefore, if the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.

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Hello!

Let's solve:

   [tex]\text{Write down the equation}\\\dfrac{6\dfrac{2}{3} }{\dfrac{1}{5} } \\\\\\\text{Convert the nominator, a mixed partial fraction to an improper fraction}\\\dfrac{\dfrac{20}{3} }{\dfrac{1}{5} } \\\\\\\text{When dividing by a fraction, flip the fraction over and multiply its reciprocal}\\\dfrac{20}{3} *\dfrac{5}{1} = \dfrac{100}{3} \\\\\\\text{Convert the improper fraction back mixed partial fraction}\\\dfrac{100}{3} =33\dfrac{1}{3}[/tex]

Answer: [tex]\dfrac{100}{3} \text{ or }33\dfrac{1}{3}[/tex]

Hope that helps!

The area of the square with a side length of 13 units is 169 square units.

A square is simply a regular quadrilateral having all four sides and angles equal.

The area of a square is expressed as;

A = a²

Where a is the side length.

Given the data in the question;

To determine the area of the square, plug the given value into the area of square formula and solve for A.

A = a²

A = ( 13 )²

Area A = 169 square units.

Therefore, the area of the square is 169 square units.

Option D) is the correct answer.

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Answer:

m/4 = 3x - 30

Step-by-step explanation:

Hello!

Let's subtract the second equation from the first equation:

Now, solve for m.

Multiply both sides by 12 to get rid of the denominators

Plug in 12x - 120 for m in m/4

The value of m/4 is 3x - 30.

The answer to this question represents the possible choices that we have when solving a division.

When solving this division operation, and we use technology, we get the following result:

Then, we can conclude that:

We can conclude that the answer to this division is, approximately, 20. This could be an answer to this operation.

In this case, we can see the integer part of the answer, 20, and a fraction:

And we know that:

The probability that a randomly selected student in the class test scored marks which is less than 82 is 0.9192

It is given that in a test, the scores for an exam normally distributed has a mean of 75 and a standard deviation of 5. We have been asked to find the probability that a randomly selected student scored less than 82.

From the question we have,

Mean = 75

Standard deviation (SD)  = 5

Therefore, the probability that a randomly chosen student has a score of less than 82 is represented as:

(P) Probability ( X < 82) = P { Z < [tex]\frac{82-75}{5}[/tex] }

                = P {Z < 7/5}

                = P {Z <1.4}

                = Area from - ∞ to  1.4

                = 0.9192

From the z table the area under the normal curve that corresponds to  1.4 is  0.9192

Hence the required probability of that a randomly selected student scored less than 82 is 0.9192

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Answer:

-6

Step-by-step explanation:

-3x = 18

divide both sides by -3

18 ÷ -3 = -6