Which of these strategies would eliminate a variable in the system of equations?

In the word problem, if mike has 40 coins consisting of dimes and quarters and if the dimes were quarters and the quarters dimes, he would have 90 cents more, he has 17 quarters.

A word problem refers to a mathematical exercise where significant information on the problem is given in ordinary language and not mathematical notation.  Let x be the number of dimes (10 cents) and y be the number of quarters (25 cents). Hence, the total number of coins is:

x + y = 40

The amount of the total coins would be 0.1x + 0.25y.

If the dimes were quarters and quarters were dimes, he would have 90 cents more than the amount he has now.

Hence,

0.25x + 0.10y = 0.1x + 0.25y + 0.9

Solving,

0.25x – 0.1x = 0.25y – 0.1y +0.9

0.15x = 0.15y + 0.9

As x + y = 40, x = 40 – y

Substituting,

0.15 (40 – y) = 0.15y + 0.9

6 - 0.15 y = 0.15y + 0.9

0.15y + 0.15y = 6 – 0.9

0.3y = 5.1

y = 5.1/0.3 = 17

Hence, the number of quarters are 17.

Learn more about Word problem:

https://brainly.com/question/13818690

#SPJ4

Answer: y=2x+1

Hope this helps

The distance between the x-intercepts of these two line is 10 units.

Given that,

These two lines' x-intercepts are separated by 10 units.

Equation of the line with slope 2 is

y-30/x-40 = 2

For x intercept put y = 0,

then

-30/x-40 =2

x =25

Equation of the line with slope 6 is

y-30/x-40 =6

For x intercept put y = 0,

then

-30/x-40 =6

x =35

Distance between x-intercepts of these two lines is difference of the two intercepts i.e,

D = 35-25 = 10.

Thus, the distance between the x-intercepts of these two line is 10 units.

To learn more about  x-intercepts click here:

brainly.com/question/14180189

#SPJ4

The expected total prize money is $2p/q.

Given that,

You participate as a participant in a game show and respond to questions. You receive $1 for each correct response, and you are disqualified if you first provide two consecutive inaccurate answers. You can answer properly with probability p or wrongly with probability q. Each question stands alone.

Let,

The probability of correctly answering a question is = p

The probability of incorrectly answering a question is = q

The number of failures after which you are eliminated is = 2

Let r = 2 =  No. of failures and

Let q = The probability of failure in a single question

Now, the number of questions that you will attempt will follow a negative binomial distribution whose parameters are r and q.

The expected value of a negative binomial distribution is given by

E[X] = r/q

So, the expected number of questions that you will attempt is = r/q = 2/q

Out of 2/q questions, the expected number of correct questions is = 2p/q

So, the expected total prize money is $2p/q.

To learn more about probability click here:

brainly.com/question/11234923

#SPJ4

The level can be attained  by light reflections.

learn more about reflections here:

https://brainly.com/question/18772331

#SPJ4

The balance in Marie saving account in week 20 will be $408  .

In the question ,

it is given that

the amount in Marie's saving account in week 1 is $180 .

amount of money deposited every week is = $12 .

to find the balance in week 20 means , she deposited money for 19 weeks .

the amount deposited in 19 weeks = 19 × 12 = $228

the equation to represent the balance after w weeks = 180 + 12*w

putting w = 19 in the equation , we get

the balance in saving account in week 20 = 180 + 12*19

the balance in week 20 = 180 + 228

= $408

Therefore , The balance in Marie saving account in week 20 will be $408  .

Learn more about Equation here

https://brainly.com/question/20917911

#SPJ1

The total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.

Given, Joh rent a kayak at a nearby state park.

He pay a fee of 12.99 plus 3. 75 for each hour that he spend in the water.

We have to find the amount he spend when he was in the water for 4(1/2) hours.

Total amount = 12.99 + hourly amount

Hourly amount = 3.75×4(1/2)

Hourly amount = 3.75×9/2

Hourly amount = 16.875

Total amount = 12.99 + 16.875

Total amount = 29.865

Hence, the total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.

Learn more about Unitary Method here https://brainly.com/question/28627316

#SPJ4

0.57 mi²  = 15,890,688 ft² after converting square miles in square foot.

The given conversion in question is-

0.57 mi²  = __ ft²

We know that

1 mi²  = 27,878,400 ft²

Then, multiply both sides by 0.57

1 x 0.57 mi²  = 27,878,400 x 0.57 ft²

0.57 mi²  = 15,890,688 ft²

Thus, the conversion of 0.57 mi²  = 15,890,688 ft².

To know more about the unit conversion, here

https://brainly.com/question/13016491

#SPJ4

The length of AC is 17.3 cm

acc to our question,

Hence,The length of AC is 17.3 cm

know more about rectangle click here:

brainly.com/question/25292087

#SPJ13

Answer:

So, the probability of selecting a number from 1 to 100 that is divisible by 5 or 7 is 0.32.

Hope this helped!

The value of angle b is 60 degrees. The reason is angle b is a supplementary angle to angle 120 degrees

angle b is equal to angle c the reason id that they form alternate internal angles

A linear pair is a situation where two adjacent angles are on a straight line, hence their sum is 180 degrees.

Linear pair is special cases of supplementary angles involving only two angles that are adjacent

How to solve for angle b

b + 120 = 180

b = 180 -120

b = 60

Learn more about linear pair here

https://brainly.com/question/29247305

#SPJ1

The probability of landing on an even number or a number greater than two is 5/6.

A fair die is rolled. We need to find out the probability of landing on an even number or a number greater than two.

Let the event of landing on an even number be denoted by the variable E1. Let the event of landing on a number greater than two be denoted by the variable E2. We need to calculate P(E1 ∪ E2).

P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

P(E1 ∪ E2) = (3/6) + (4/6) - (2/6)

P(E1 ∪ E2) = 5/6

Hence, the probability of landing on an even number or a number greater than two is 5/6.

To learn more about probability, visit :

https://brainly.com/question/11234923

#SPJ4

If the child's weight is 60 pounds , then the doctor will prescribe 12 milliliter of medicine .

In the question, '

it is given that

the for every 25 pounds of weight 5 milliliter of pain reliever is required .

we need to find the amount of medicine for the child weighing 60 pounds

So , for 25 pounds =  5 milliliter is needed

for 1 pound = 5/25 ml is needed

hence for 60 pound = 60*(5/25) ml will be prescribed .

on simplifying further ,

we get

= 60*(5/25)

= 60*(1/5)

= 12 ml

Therefore , the doctor will prescribe 12 ml of medicines .

Learn more about Unitary Method here

https://brainly.com/question/13608878

#SPJ1

The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.

A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.

A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.

In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.

Read more on slope here: brainly.com/question/3493733

#SPJ1

Answer:

The value of the equation will be 14

Answer:

7 is correct.

There are 4 small triangles, 2 medium-sized triangles, and 1 large triangle.

The quotient of the fraction is 0.05 and the fraction in its simplest form is 1/20

The quotient of a fraction is the whole number that is obtained when you simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction

Given: 1/5÷4

1/5÷4 = 1/5 × 1/4            (Note: If ÷ change to ×, 4 will change to 1/4 )

        = 1/20 = 0.05

Therefore, the quotient of the fraction is 0.05 and 1/20 should be filled in the box

Learn more about fractions on:

https://brainly.com/question/11562149

#SPJ1

Step-by-step explanation:

the equation

y = -8/5 x + 6

tells us 2 things :

-8/5 is the slope of the line, 6 is the y-intercept (the y value when x = 0).

a parallel line has the same slope (just a different y-intercept) : -8/5

a perpendicular line (intercepts at 90°) turns the original slope upside-down and flips the sign : 5/8

we the use the given point as x and y values and calculate the y-intercepts.

parallel :

3 = -8/5 × 5 + y-intercept = -8 + y-intercept

11 = y-intercept

y = -8/5 x + 11

perpendicular :

3 = 5/8 × 5 + y-intercept = 25/8 + y-intercept

(3×8)/8 = 24/8 = 25/8 + y-intercept

-1/8 = y-interceot

y = 5/8 x - 1/8 = 1/8 × (5x - 1)

Answer:

Step-by-step explanation:

Given a car's cost of operation is $485 for 500 miles, you want an equation relating cost for m miles, and solutions to that equation for 1200 miles, and for a cost of $820.

The cost per mile is found by dividing the cost by the associated number of miles:

  $485/(500 mi) = $0.97 /mi

The equation for the cost will show the cost as the cost per mile multiplied by the number of miles:

  C = 0.97m . . . . . where C is cost in dollars for m miles driven

The cost for driving $1200 miles will be ...

  C = 0.97(1200) = $1164

The cost of driving 1200 miles is $1164.

The number of miles that can be driven for a cost of $820 is ...

  820 = 0.97m

  m = 820/0.97 = 845.36

About 845 miles are driven for a cost of $820.

Answer: r = 77.3 degrees

Step-by-step explanation:

-Add both numbers together.

- 46.2

+ 31.1

= 77.3

-That is the value of "r".

The angle RSQ = 105° and angle PQS = 78°

Given,

In the question:

In the figure,

PSR is a straight line .

To find the angle RSQ and angle PQS.

Now, According to the question;

In ΔQRS,

we know that :

Sum of angle of triangle is 180 degree.

Angle (SQR + QRS + RSQ) = 180°

In the figure,

Angle (23° + 52° + RSQ) = 180°

75° + ∠RSQ = 180°

∠RSQ = 180 - 75

∠RSQ = 105°

We have to find the ∠PQS

Now, PSR is a straight line

In Triangle PSQ

Find the ∠S

105 + ∠S = 180° (Linear Pair)

∠S = 75°

In ΔPQS

Angle(SPQ + PQS + QSP) = 180°

Angle(27° + PQS + 75° ) = 180°

∠PQS = 180 - 102

∠PQS = ∠78°

Hence, The angle RSQ = 105° and angle PQS = 78°

Learn more about Angles at:

https://brainly.com/question/17039091

#SPJ1

Answer:

z = 52°

Step-by-step explanation:

Formula we use,

→ A + B + C = 180°

Then the value of z will be,

→ 81° + 47 ° + z = 180°

→ 128° + z = 180°

→ z = 180° - 128°

→ [ z = 52° ]

Hence, the value of z is 52°.

The total number of skittles in the bag will be 65.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that In a pack of Skittles, 20% are red. If 13 are red. The total number of skittles will be calculated as,

N = ( 13 / 20 ) x 100

N = 130 / 2

N = 65

Therefore, the total number of skittles in the bag will be 65.

To know more about an expression follow

https://brainly.com/question/11446731

#SPJ1

The constant of proportionality for each table are 5, 2/3, 4, 1/5, 3, 2 and 1/2 while that of the equations are 1/8, 1/3 and 3/2

The constant of proportionality is the ratio of the y value to the x value i.e.

constant of proportionality(k) = y/x

To find the constant of proportionality for each table, just pick any non-zero corresponding x and y values on the table and find the ratio:
Using constant of proportionality(k) = y/x

1.  y/x = 5/1 = 5

2.  y/x= 4/6 = 2/3

3. y/x = 2/0.5 = 4

4. y/x= 2/10 = 1/5

5. y/x = 9/3 = 3

6. y/x = 8/4 = 2

7.y/x = 6/12 = 1/2

For the equations, just rewrite the equations in order to make y/x the subject:

8. y =1/8 x

y/x = 1/8

9. 6y = 2x

y/x = 2/6 = 1/3

10. 4y = 6x

y/x = 6/4 = 3/2

Therefore, the constant of proportionality for each table and equation are 5, 2/3, 4, 1/5, 3, 2, 1/2 and 1/8, 1/3, 3/2 respectively

Learn more about constant of proportionality on:

brainly.com/question/29213426

#SPJ1

Answer:

To do percentages with fractions,

divide the numerator by denominator to get a decimal,

so for example, your question 56/80.

56/80 is 0.7 decimal, and then to make it percent,

we multiply by 100,

how does that work?

you move two places to the right because 100 has two zeros

so 0.7 would be 70,

therefore the percent of 56/80 would be 70%

Good day ml! <3

The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.

A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.

n = 50 makes up the sample size.

Furthermore, the sample variance is s² = 20

The following is the formula for both the variance confidence interval:

σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]

Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.

The 90% confidence interval's lower bound for variance is stated as,

[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)

= 32.54

The 90% confidence interval's upper bound for variance is stated as,

[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)

= 96.86

Consequently, the confidence level for the distribution's variance is (96.86, 32.54).

Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).

Learn more about confidence intervals at

https://brainly.com/question/22985950?referrer=searchResults

#SPJ4

The maximum number of pages the report can have, using scientific notation, is of:

2 x 10^6.

A number in scientific notation is written as follows:

[tex]a \times 10^b[/tex]

With the base symbolized [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

For this problem, the maximum number of pages that the report can have is given by the following division:

Maximum number of pages = Total capacity/Size of page.

These variables, from the text, are given as follows:

Hence the number of pages is obtained as follows:

Maximum number of pages = 4 x 10^6 KB / (2 KB/ page) = 2 x 10^6 pages.

When two numbers are divided in scientific notation, the bases are divided(4/2 = 2), while the exponents are subtracted (6 - 0 = 6).

More can be learned about scientific notation at https://brainly.com/question/16394306

#SPJ1

Considering the figure the unknown angles are

Using the angle in a straight line are supplementary we have

60 + a + 55 = 180

a + 115 = 180

a = 180 - 115

a = 65

applying sum of angles in a triangle equal to 180, b is calculated as follows

a + b + 90 = 180 right angle triangle

substituting for a

65 + b + 90 = 180

b + 155 = 180

b = 180 - 155

b = 25

applying vertical angle theorem

angle c = angle b

angle c = 25

Learn more about angles here:

https://brainly.com/question/29327565

#SPJ1