Eve is organizing a race to raise money for a local children's hospital. She makes $20 for each 5K participant and $45 for each 10K participant. Her goal is to raise $9,500.

If x represents the number of participants in the 5K race and y represents the number of participants in the 10K race, the linear equation for the given scenario is
x + y = . If Eve raises exactly $9,500, is it possible for there to be 220 participants in the 5K race?
(yes/no)

Answers

Answer 1

No It is not possible to have 220 participants in the 5k race.

How to determine the number of participants in the races

Information from the question

She makes $20 for each 5K participant

$45 for each 10K participant.

x represents the number of participants in the 5K race

y represents the number of participants in the 10K race

Eve raises exactly $9,500, is it possible for there to be 220 participants in the 5K race = ?

From the question

$20 for each 5K participant and x represents the number of participants in the 5K race. = 20x

$45 for each 10K participant and y represents the number of participants in the 10K race = 45y

Eve raises exactly $9,500 means the sum of amount from 5k and 10k is 9500 =  20x + 45y = 9500

if Eve raise 220 participants in the 5k race then the equation will be

20 * 220 + 45y = 9500

4400 + 45y = 9500

45y = 9500 - 4400

45y = 5100

y = 113.333

The participants are human being and cannot be represented as fractions hence 220 is impossible for the 5k race

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Related Questions

Determining if the inverse is a function

Answers

Answer:

I'm not sure, but it could be "inverse"

Step-by-step explanation:

What is the equation of the graph below?

Oy=-(x-2)²+3
Oy=(x + 2)²+3
Oy=-(x+3)²+2
Oy=(x-3)²+2

Answers

I believe it would be y=(x+2)^2+3.

The equation of the graph is given by y = ( x + 2 )² + 3

What is Equation of Graph of Polynomials?

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the equation be represented as A

Now , the value of A is

y = ( x + 2 )² + 3

The given equation is in the standard vertex form of a parabola:

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

By comparing the given equation with the standard vertex form, we can see that:

a = 1, h = -2, and k = 3

Hence , the vertex of the parabola is at the point (-2, 3) and the graph is plotted

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Simplify and Explain This Equation

-8-3(9-2x)+9x

Answers

-8-27+6x+9x
First you distribute the -3 to the 9 and -2x in the parentheses

-35+15x
Then you simplify by adding the -8 to the -27 and the 6x to the 9x

-7+3x
Finally, if you want to simplify it further you can divide both sides by 5

How do I graph y=3x+2

Answers

Hi there! Answer is in image
Hope this helps :)

Which is the graph of f(x) = x² + 4 and the function g, a reflection of f(x) across the x-axis?

Answers

The reflection of function f(x) across the x-axis is [tex]-x^{2} -4[/tex].

It is given to us that the function is -

[tex]f(x)=x^{2} +4[/tex] --- (1)

and a function g

We have to find out the reflection of f(x) across the x-axis.

A function can be defined as an expression that assigns the value of each element of a given set to the another specific element of another given set.

To find out the reflection of f(x) across the x-axis, we have to take -f(x) instead of f(x).

Now,

[tex]-f(x)=-(x^{2} +4)\\= > -f(x)=-x^{2} -4[/tex]

Thus, the reflection of function f(x) across the x-axis is [tex]-x^{2} -4[/tex].

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What is the sale price of the oil change after the discount

Answers

The sale price of the oil change after the discount can be found to be $25.50.

How to find the sale price?

When given a discount, the selling price of an item is found by the formula:

= Price of item before discount - Discount

The discount on the oil change, given the price of the oil change and the coupon is:

= Price of oil change x Coupon rate

= 30 x 15%

= $4.50

The sale price after the oil change is:

= Price of oil change before discount - discount

= 30 - 4.50

= $25. 50

The first part of the question is:

An oil change at city auto is regularly $30. Mr Allen has a coupon for 15% off.

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A restaurant owner wants to attract more customers by getting enough ratings to appear on a popular social media site. The owner can generate 10% more business by reaching an additional 100 reviews. He knows that he provides one hundred 50% off coupons for meals, he can get 100 reviews. How much will it cost to increase business by 10% if each coupon is likely to cost $15?

Answers

Answer:

25%

Step-by-step explanation:

cause i did marh

suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?

Answers

Using the concepts of confidence interval, we got that is he interval estimate for the population proportion if we suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president.

We know that population proportion is given by the fraction of number of positive results to the total number of results

Therefore, Population Control(P)=1608/2400

                                                =>P   =0.67

Now, we are given that confidence interval is 0.95 degree or 95%

For 95%,confidence interval is given by =P±√[P×(1-P)]/n

where n is the total number of registered voters, and P is the population control.

confidence interval=0.67±√[0.67×(1-0.67)]/2400

                               =0.67±√(0.67×0.33)/2400

                                =0.67±√0.2211/2400

                                =0.67±(0.47/48.98)

                                =0.67±0.0095

                                 =0.660 and 0.679

Hence, if we suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence,  the interval estimate for the population proportion  is (0.660,0.679)

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Given ∠11≅∠13. Which lines, if any, must be parallel based on the given information? Justify your conclusion.

Answers

Based on the information given: A. c║d; converse of alternate exterior angles theorem.

What is the Converse of Alternate Exterior Angles Theorem?

Exterior alternate angles are congruent based on the alternate exterior angles theorem. Conversely, it can also be stated that if two angles, which are exterior alternate angles, are congruent to each other, therefore the lines they lie on that is crossed by a transversal are proven to be parallel to each other based on the converse of alternate exterior angles theorem.

Given that angles 11 and 13 are congruent angles, the diagram also shows that they are alternate exterior angles. They lie on each lines, c and d, that are crossed by transversal a.

Therefore, based on the converse of alternate exterior angles theorem, lines c and d are parallel.

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Please help me please

Answers

Answer:

m<T = 60°

m<U = 60°

TS = 13

SU = 13

Step-by-step explanation:

Triangle TSU is an equilateral triangle.

All interior angles has equal measures and each = 60° since the sum of interior angles in a triangle is equal to 180 and this divided by 3 = 60

all side lengths are also equal to one another, TU is given as 13 cm so the length of TS and SU is also = 13

URGENT !!! Answer the following questions using the graph.

Describe the y-intercept in this scenario.
Describe the x-intercept in this scenario.
Finish the ordered pairs (2.5, ____ ) and (____,300).

What are the domain and range?

Domain: {h I ___ < h < ____}

Range: {f(h) I ___ < f(h) < ____}

Answers

The x-intercept is (8.75,0) and

The y-intercept is (0,700)

The ordered pairs are (2.5,500) and (5,300).

Given that,

In the picture we have a graph with line.

We have to find the x-intercept and y-intercept of the scenario and the ordered pairs (2.5, ___) and (___ , 300)

We know that,

What is x-intercept and y-intercept?

The x intercept is the location where the line touches the x axis. The y intercept is the location where the line touches the y axis.

So,

The x-intercept is (8.75,0) and

The y-intercept is (0,700)

The ordered pairs are (2.5,500) and (5,300).


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Two sides of a parallelogram are 190 feet and 740 feet. The measure of the angle
between these sides is 88°. Find the area of the parallelogram to the nearest square
foot.

Answers

Answer: About 140,514 ft²

Step-by-step explanation:

The area of a parallelogram is base × height. The base is already determined as 740 ft. You can find the height(h) with trigonometry:

[tex]sin(88)=\frac{h}{190}\\ \\h=190sin(88)=189.88425713[/tex]

Now, multiply the values together:

[tex]740*189.88425713=140514.350[/tex]

Find 7 5/12−(−3 3/4) . Write your answer as a mixed number in simplest form.

Answers

The simplified expression is 11 (1/6).

What is a fraction?

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The given expression is 7 (5/12) - (-3 (3/4)).

Simplify the expression as follows:

7 (5/12) - (-3 (3/4))

= 89/12 +15/4

= (89+45)/12

= 134/12

= 11 (1/6)

Hence, the simplified expression is 11 (1/6).

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solve for y
18-5x= -9y

Answers

Answer:

y= [tex]\frac{5}{9}[/tex]x - 2

Step-by-step explanation:

You want to get y alone so divide both sides by -9 to get: y = [tex]\frac{5}{9}[/tex]x- 2

this is because 2 negatives (-5x and -9) make a positive

how many ordered pairs ( m , n ) of positive integers, such that m > n , have the property that their squares differ by 96 ?

Answers

Answer:

  4 pairs

Step-by-step explanation:

You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.

Difference of squares

The difference of squares is factored as ...

  m² -n² = (m -n)(m +n)

In order for the difference to be 96, these factors must be factors of 96.

Factors of 96

The prime factorization of 96 is ...

  96 = 2^5 · 3

The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:

  (5+1)(1+1) = 12

That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...

   96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12

Solution

The values of m and n relate to the values of 'a' and 'b' by ...

  m = (a+b)/2

  n = (b-a)/2

In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...

  (m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs

Use a quadratic equation to find two real numbers with a sum of 2 and a product of −24. Write the answers in the decreasing order of their values.

_____ and ______

Answers

The two numbers whose sum is 2 and product is -24 are 6 and -4

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x

a[tex]x^{2}[/tex]+bx+c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Let the two numbers be x and y

so that

x + y = 2 ----------------1

xy = -24 -----------------2

from equation 1 make x the subject of the equation, so that it becomes

x = 2 - y ---------------3

substitute x in equation 3 in equation 2

y(2-y) = - 24

multiply out the bracket

2y - [tex]y^{2}[/tex] = -24

taking all terms to one side of the equation, it becomes

[tex]y^{2}[/tex] -2y -24 = 0

factorizing the equation

[tex]y^{2}[/tex] -6y + 4y - 24 = 0

y(y - 6) +4(y - 6) = 0

taking the terms outside bracket and putting them in a new bracket we have

(y + 4) (y - 6) = 0

so y + 4 = 0 or y - 6  = 0

y = -4 or y = 6

using y = -4 and substituting in equation 3

x = 2 - - 4

x = 6

In conclusion the two numbers are 6 and -4

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The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. When m=8kg and d=5meters, F=100 Newtons. Find F when m=2 kilograms and d=15 meters.

Answers

The force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.

According to the question,

We have the following information:

The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. And when m=8kg and d=5meters then F=100 Newtons.

Now, let's take the constant for this case to be k.

We have the following expression:

F = km/[tex]d^{2}[/tex]

Putting the values in this expression to find the value of k:

100 = 8k/(5*5)

Using the cross multiplication method:

2500 = 8k

k = 2500/8

k = 312.5

Now, we have the following value of F:

F = 312.5*2/15*15

F = 625/225

F = 2.78 Newton

Hence, the force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.

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DEFG has been dilated to D'EF'G'. Use a pair of corresponding sides to determine the scale factor.
a 2/1=2
b 3/2
c1/2
d2/3

Answers

The scale factor for a a pair of corresponding sides will be;

⇒ 3 / 2

What is Proportional?

The equality between two ratio is called Proportional.

Given that;

DEFG has been dilated to D'EF'G'.

Now,

Let the coordinates of DEFG are for side DG are;

D = (- 6, 3)

G = (- 3, 3)

And, The coordinates of D'E'F'G' are for side D'G' are;

D' = (- 4, 2)

G' = (- 2, 2)

So, The length of side DG is;

DG = √ (- 3 - (-6))² + (3 - 3)²

     = √ 3²

     = 3

And, The length of side D'G' is;

D'G' = √ (- 2 - (-4))² + (2 - 2)²

     = √ 2²

     = 2

Thus, The scale factor for a a pair of corresponding sides will be;

⇒ DG / D'G' = 3 / 2

Therefore, The scale factor for a a pair of corresponding sides will be;

⇒ 3 / 2

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The tiger at the zoo ate 133 pounds of food in
7 days Find the average change in the zoo's
tiger food supply each day.

Answers

Answer:

133/7 = 19

Step-by-step explanation:

"Find the average change in the zoo's tiger food supply each day."

And what does that have to do with anything? It's not like there is a change in diet that we can then easily calculate using derivatives.

A piont is two dimensional ?

Answers

Answer:

False.

Step-by-step explanation:

A point is a zero-dimensional object as it has no length, width or height. It has no size.

And it would be great if you can spell "point" correctly.

A point is not two dimensional, so this is false.

one of euler's conjectures was disproved in the 1960s by three american mathematicians when they showed that there is a positive integer such that find the value of .

Answers

It quickly becomes apparent that 174 is much too large, so n must be 144.The value of the n is 144.

Taking the given equation modulo 2,3, and 5, respectively, we have

n⁵≡(mod 2)

n⁵≡(mod 3)

n⁵≡( mod 5)

By either Fermat's Little Theorem (FLT) or inspection, we get

n≡(mod 2)

n≡(mod 3)

n≡( mod 5)

By either the Chinese Remainder Theorem (CRT) or inspection, we get n≡ 24 ( mod 30)

It is clear that n>133, so the possible values for n are 144,174,204,...Note that

n⁵ = 133⁵ + 110⁵ + 84⁵ + 27⁵

n⁵ < 133⁵ + 110⁵ +( 84 + 27)⁵

n⁵ =133⁵ + 110⁵ + 111⁵

n⁵ < 3.133⁵

From which (n/133)⁵ < 3

If n>= 174 then,

(n/133)⁵ > 1.3⁵

(n/133)⁵ = 3

which arrives at a contradiction. Therefore, we conclude that n=144

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8. What is the value of point x? X -4 -3​

Answers

Answer:

x = -9

Step-by-step explanation:

(x1, y1) = (-4, 3)  &  (x2, y2) = (x, 4)

m = (y2 - y1)/(x2 - x1)

-1/5 = (4 - 3)/(x - (-4) = 1/(x+4)

-(x + 4) = 5

-x - 4 = 5

-x = 5 + 4 = 9

in a city of 246,000 people, there are 34 coffee shops. what is the number of coffee shops per capita? round to 6 decimal places.

Answers

Coffee shops per capita in city is 7235.294118

What is per capita?

The Latin phrase "per capita" means "by head." In statistics, the term "per capita" is sometimes used in place of "per person" to denote the average per person.

Main Body:

total population of city = 246000

Total coffee shops = 34

Per capita shops for population can be calculated by dividing total population by total shops.

calculatiing,

Per capita shops = total population/ total shops

                            = 246000/34

                            = 7235.294118

Hence number of coffee shops per capita is 7235.294118

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Write the equation of the function in
slope-intercept form:

A line with a slope of 2 and passes through (-8, 3)

Answers

The equation of the function in slope-intercept form with slope of 2 is y = 2x+19.

According to the question,

We have the following information:

Slope = 2 (Note that slope of a line is denoted by m.)

Points through which function is passing = (-8,3)

So, we have x' = -8 and y' = 3.

We know that the following equation is used to find the equation of the function or line:

(y-y') = m(x-x')

y-3 = 2{x-(-8)}

y-3 = 2(x+8)

y-3 = 2x+16

y = 2x+16+3

y = 2x+19

Hence, the equation of the function in slope-intercept form with slope of 2 is y = 2x+19.

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Find the missing side. Help please

Answers

Answer:

Step-by-step explanation:

add 23+14=37-90= 53

answer=53

I need help. I was absent for 2 weeks, and I have no idea how to do this.

Answers

a)  no solution

b) only one solution

c) only one solution

d) infinite many solution.

e)  only one solution

f) no solution

g) infinite many solution.

h)  infinite many solution.

i)  no solution

j) only one solution

k) infinite many solution.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We know depending upon the types of lines there are different type of solution

if there are two equations

[tex]a_1 x+ b_1 y+ c_1= 0[/tex] and [tex]a_2 x+ b_2 y+ c_2= 0[/tex]

For Intersecting Lines

[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

For parallel lines:

[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

For co- incident line

[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

a) y= -5x + 4  --> 5x + y = 4

5x+y= -3

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

b) y=3/4 x+5

y= 4/3 x + 5

so, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

c) y= -3/4x+5

y=3/4x+5

[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

d) y= 3/4 x + 5

y= 5+ 3/4x

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

e) y= 3/4x +5

y=  x + 2

So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

f) y= 3/4x + 5

y= 3/4x + 2

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

g) 6x -y = 5

-6x + y= -5

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

h) 2x- y +5 =0

2x- y+ 5 =0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

i) 4x- y+ 5 =0

4x- y +3 = 0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

j) 3x- y +5 = 0

2x -y +5 =0

So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

k) 2x+ y -1 = 0

2x + y- 1= 0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

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. Examine this graph. What are the y-intercept and slope of this line?
*
10 points
Captionless Image

Answers

Hey, so because you didn't include the image this is impossible to get the number values.  But, essentially you'd solve it something like this.

Remember, the Y axis goes up, and its located when you are at X = 0.  

The y intercept is the value of Y, when is 0.  

The slope of a line is referred to as "rise/run"

Basically, you take any given spot.  For example, from x = 0 to x = 2.  The run is 2, because thats how much x value the line covers.  So, in that "run" how much do you go up or go down?  Lets say in those 2 x's that you travelled, how much did the height change?  If you changed by going up 4 units, it would be (rise/run) 4/2 = 2.  The slope would be 2.  That means that for every time x increases by 1, Y goes up 2.

Determine the distance between each set of ordered pairs
(6 7/8,2) and (-3,2)

Answers

Answer:

Determine the distance between each set of ordered pairs

(6 7/8,2) and (-3,2)

Step-by-step explanation:

Well if you do delta y over delta x you do -2 - 2 over 3 - 67/8 which will be -4 over -5.375 which will equal 32 over 43 which is you M you b is one point (your choice) then y = mx + b so 2 = 32/43(-3) + b 2 = -96/43 + b then add -96/43 to both sides and you'll get -10/43 = b so y = 32/43x + -10/43

equation - y = 32/43x + -10/43

at 99% confidence, how large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion? assume that past data are not available for developing a planning value for p*. round up to the next whole number.

Answers

2276 large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.

Given:

At 99% confidence, how large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.

Error e = 0.027

z score at 99%:

z = 2.576.

sample size n = p(1-p)(z/e)^2

= 0.5(1-0.5)(2.576/0.027)^2

= 0.5*0.5*9102.573

= 0.25*9102.573

= 2275.64

≈ 2276

Therefore 2276 large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.

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I will love some help so if you can help that will be wonderful the question is Given the equation k over 34.2 equals 8.7, determine the value of k.

25.5
297.54
3.93
42.9

Answers

Answer:

k=297.54

Step-by-step explanation:

i can't really explain it

The value of k that satisfies the equation k/34.2 = 8.7 is approximately 297.54. So, correct option is B.

To determine the value of k in the equation k/34.2 = 8.7, we can solve for k by isolating it on one side of the equation.

We can start by multiplying both sides of the equation by 34.2 to eliminate the denominator:

k/34.2 * 34.2 = 8.7 * 34.2

This simplifies to:

k = 8.7 * 34.2

Evaluating the right side of the equation:

k ≈ 297.54

The correct option from the given choices is 297.54. So, correct option is B.

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