At a local car wash, 25 cars can be washed in an hour. How many cars can go through the car wash in an 8-hour day?

Part A: Yes, the data represent a function. The definition of a function is a relation in which no value of x will have two different values of y.

(Every time you plug in 3 as x, you will always get 4 as y; it's ok if you plug in 3 and 5 as x and get the same y, you just can't get two different y's for one x; sorry, it is pretty confusing). None of the numbers in the table repeat, so we can safely say that the relation is a function.

Part B: All we have to do is plug in 11 for x in the function given to find the answer:

In the table, y = 8 when x = 11, but in the function given, y = 34 when x = 11, so the function given is greater.

Part C: To find the answer to C, just plug in 99 for f(x), as it tells you to do:

Answer:

y^2+2xy/-x^2-2xy OR -y^2-2xy/x^2+2xy OR -y^2-2xy/(x)(x+2y)

Step-by-step explanation:

So, this is an implicit differentiation problem

x^2y+y^2x

so,

use product rule for both

x^2y'+2xy+y^2+2yy'x

collect all the y's

-x^2y'-2xyy'=y^2+2xy

y'(-x^2-2xy)=y^2+2xy

=y^2+2xy/-x^2-2xy

Answer:

Is this in a different language?

Step-by-step explanation:ok:)

Answer:

a. y = 2 + 2x

b. y = 20 - 4x

c. y = 2 + 1.5x

d. y = 20 - 3x

Step-by-step explanation:

I Hope That This Helps! :)

Answer:

The dimensions that will maximize the enclosed area of the pen is 250 ft by 250 ft

Step-by-step explanation:

we have the perimeter as 1000

So the sum of the lengths will be

1000/2 = 500

The dimensions that will maximize these pens will be such that they will have equal values

Mathematically, that will be 500/2 = 250 by 250

Answer:

See steps below

Step-by-step explanation:

WS ⊥ MH , HS = SM ......... Given

<HSW = <MSW = 90  .....  From WS ⊥ MH

Triangle HWS = Triangle WMS .... SAS  theorem

<M = <H  .... based on triangle congruency, and angle opposed to equal side WS

Answer:

[tex] x = 17.5 [/tex]

Step-by-step explanation:

Since the two triangles are similar, their corresponding side lengths would be proportional. Therefore:

[tex] \frac{28}{16} = \frac{x}{10} [/tex]

Cross multiply

[tex] x*16 = 10*28 [/tex]

[tex] 16x = 280 [/tex]

Divide both sides by 16

[tex] x = \frac{280}{16} [/tex]

[tex] x = 17.5 [/tex]

Answer:

The anti-derivative of f(x) will be:

[tex]\int \:10x^4+12.5dx=2x^5+12.5x+C[/tex]

Step-by-step explanation:

Given the function

[tex]\:f\left(x\right)=10x^4\:+\:12.5[/tex]

Taking the anti-derivative of f(x)

[tex]\int \left(10x^4\:+\:12.5\right)\:dx\:[/tex]

[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex]

[tex]\int \left(10x^4\:+\:12.5\right)\:dx\:=\int \:10x^4dx+\int \:12.5dx[/tex]

Solving

[tex]\int 10x^4dx[/tex]

[tex]\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx[/tex]

[tex]=10\cdot \int \:x^4dx[/tex]

[tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1[/tex]

[tex]=2x^5[/tex]

similarly,

[tex]\int 12.5dx[/tex]

[tex]\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax[/tex]

[tex]=12.5x[/tex]

so substituting these values

[tex]\int \left(10x^4\:+\:12.5\right)\:dx\:=\int \:10x^4dx+\int \:12.5dx[/tex]

                                [tex]=2x^5+12.5x[/tex]

                               [tex]=2x^5+12.5x+C[/tex]   ∵ Add constant to the solution

Therefore, the anti-derivative of f(x) will be:

[tex]\int \:10x^4+12.5dx=2x^5+12.5x+C[/tex]

Answer:

A) None of the above

Step-by-step explanation

it's distributive property

Answer:

-2a + 22 =22

Step-by-step explanation:

3(a + 4) -5(a - 2) =22

3a + 12 - 5a + 10 =22

-2a + 22 =22

Answer:

-2a + 22 = 22

Step-by-step explanation:

in both a = 0

Answer:

 [tex]y= -\frac{1}{3}x -6[/tex]

Step-by-step explanation:

Using the slope formula, you can form this equation! The slope of any equation would replace the m, and the y intercept would replace b!

I added in the slope formula at the bottom, just in case, so you'll see what I mean!

I hope this helps, and I explained enough! Have a great day c:

9514 1404 393

Answer:

  A) the curves are ellipses

  B) 161 yards

  C) 366 yards

Step-by-step explanation:

A) The general shape of the side marked c has the appearance of two quarter-ellipses. The major axis is approximately 125 yards, and the minor axis is approximately 80 yards. Paul could assume that the curves are quarter-ellipses.

__

B) For an ellipse with this eccentricity, its perimeter is within 2% of that of a circle with a diameter equal to the average of these dimensions.*

So, the approximate length of side c is ...

  c ≈ π(80 +125)/4 ≈ 161 . . . . yards; length of side c

__

C) The perimeter of the pond is the sum of the side lengths, so will be ...

  80 yds + 125 yds + 161 yds = 366 yds . . . pond perimeter

_____

* Indian mathematician Ramanujan developed an approximate formula for the circumference of an ellipse, which would otherwise need to be computed using an elliptic integral. it is ...

  C = π(a+b)(1 + 3λ²/(10 +√(4 -3λ²))

where λ = (a -b)/(a +b) and a, b are the semi-axis lengths.

For this ellipse, λ = 9/41, so the last factor is about 1.01208313. Using this factor, the circumference is expected to be good to about 7 significant digits. Continuing the calculation, we find ...

  C ≈ 325.904 . . . . circumference of an ellipse 125 yd long by 80 yd wide

This is twice the length we imagine for c, so c ≈ 163 yards. As we said, the approximation used above is within 2% of this value.

The attachment shows the shape if the curve is actually an ellipse.

Answer:

Step-by-step explanation:

6x+9=63

6x=63-9

6x=54

x=54/6

x=9

I encourage you to figure out the justification yourself.

Answer:

Step-by-step explanation:

if DEF is congruent to JKL, this means that the sides of JKL are all equal to that of DEF.

Hence we can say;

DE = JK

EF = KL

DF = JL

Given

DE = 18,

EF =23,

DF = 9x-23,

JL = 7x-11

JK = 3y-21,

Required

Values of  x and y

Since DE = JK;

18 = 3y-21

18+21 = 3y

39 = 3y

y = 39/3

y = 13

Also, DF = JL

9x-23 = 7x-11

collect like terms

9x - 7x = -11+23

2x = 12

x = 12/2

x = 6

Hence the value of x is 6 and y is 13

Given: [tex]DE=18[/tex],[tex]EF=23,DF=9x-23,JL=7x-11,[/tex] and[tex]JK=3y-21.[/tex]

As [tex]\Delta[/tex][tex]DE[/tex][tex]F[/tex]  [tex]\cong[/tex]  [tex]\Delta JKL[/tex]

[tex]\Rightarrow DE=JK \ ; EF=KL \ and \ DF=JL[/tex]

[tex]\Rightarrow 18=3y-21 \ ; 23=KL \ and \ 9x-23=7x-11[/tex]

     [tex]y=13[/tex]         ; [tex]KL=23[/tex]    and        [tex]x=6[/tex]

Therefore, [tex]x=6[/tex]  and [tex]y=13[/tex]

Answer:

the answer is 9

Step-by-step explanation:

Answer:

it is 9

Step-by-step explanation:

Answer:

The data is not appropriately normal.

Step-by-step explanation:

In inferential statistics, a normal distribution is said to be symmetric and should be single-peaked when working with a random selection of a large sample.

The high number of the sample is 100 which is further from other samples, the central limit theorem explains that the sample size of independent mean must be large enough to mimic the population for the sample to be normal or nearly normal. So, the sample is not appropriately normal and should be larger in size.

Answer:

1)

Step-by-step explanation:

Answer:

all of it

Step-by-step explanation:

Answer:

gcf is 20 lcm is 40

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

8 counselors and 12 aids

Step-by-step explanation:

minimum number of staff to run camp = 20

Ratio of counselors to aids to work together = 2:3

To get the multiply factor = 20 / (2 counselors + 3 aids) = 20 / 5 =4

minimum number of counselors needed = 4 x 2 = 8 counselors

minimum number of aids needed = 4 x 3 = 12 aids

Answer:

hio

Step-by-step explanation:

hi

As early as 4,000 years ago, but the first recorded use of a zero-like symbol dates to sometime around the third century B.C. in ancient Babylon.

Given that, the ancient Babylonians were writing fractions in 1800 BCE.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

In fact, at first, fractions weren't even thought of as numbers in their own right at all, just a way of comparing whole numbers with each other.

The word fraction actually comes from the Latin "fractio" which means to break. To understand how fractions have developed into the form we recognize, we'll have to step back even further in time to discover what the first number systems were like.

From as early as 1800 BC, the Egyptians were writing fractions. Their number system was a base 10 idea (a little bit like ours now) so they had separate symbols for 1, 10, 100, 1000, 10000, 100000 and 1000000.

Hence, as early as 4,000 years ago, but the first recorded use of a zero-like symbol dates to sometime around the third century B.C. in ancient Babylon.

To learn more about the fraction visit:

brainly.com/question/1301963.

#SPJ2

Answer:  

the first one and the last one

Step-by-step explanation:

Answer:

S(-2, -3)

Step-by-step explanation:

Find the diagram attached below,=. Frim the diagram, the coordinate of R and T are (-5, 3) and (-1, -5) respectively. If the ratio of RS to ST is 3:1, the coordinate of S can be gotten using the midpoint segment formula as shown;

S(X, Y) = {(ax1+bx2/a+b), (ay1+by1/a+b)} where;

x1 = -5, y1 = 3, x2 = -1, y2 = -5, a = 3 and b =1

Substitute the values into the formula;

X = ax2+bx1/a+b

X = 3(-1)+1(-5)/3+1

X = -3-5/4

X = -8/4

X = -2

Similarly;

Y = ay2+by1/a+b

Y = 3(-5)+1(3)/3+1

Y = -15+3/4

Y = -12/4

Y = -3

Hence the coordinate of the point (X, Y) is (-2, -3)

Answer:

(x-2)(x-2)

Step-by-step explanation:

Find two things you can multiply to equal to 4 and add to equal -4

-2*-2=4 and -2+-2=-4

Answer:

x intercept(3, 0) y intercept(0, -10)

Answer:

x>-17.2

Step-by-step explanation:

Simplify both sides of the inequality

-0.5x-3.1< 5.5

Add 3.1 to both sides

-0.5x< 8.6

Divided both sides by -0.5

x>-17.2

Hope this helped! :)