Richard and Gloria ran a 10-kilometer race. Gloria gave Richard a head start by letting him begin 2.2 kilometers in front of the start line. The distances of Richard and Gloria past the start line as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Whose time was faster, and by how much?


Richard’s Distance Past the Start Line
Time (minutes)
5
10
15
20
25
Distance (kilometers)
2.8
3.4
4.0
4.6
5.2


A.) Gloria’s time was 0.5 minutes faster.
B.) Richard’s time was 0.5 minutes faster.
C.) Gloria’s time was 2.5 minutes faster.
D.) Richard’s time was 2.5 minutes faster.

Answer:

$6.56

Step-by-step explanation:

First, take 8 and divide it by 100. Then you have 0.08. multiply that by 9. You get 0.72, that is how much the price increases every year. multiply that by 2, and you get 1.44. subtract 1.44 from 8, and you are left with $6.56, the price it was two years ago.

Answer:

x = z+y/c+m

Step-by-step explanation:

Answer:

[tex] \frac{1}{2 {}^{6} } [/tex]

Step-by-step explanation:

[tex]{ 8}^{ - 2} [/tex]

[tex] \frac{1}{ {8}^{ 2} } [/tex]

[tex] \frac{1}{(2 {}^{3}) {}^{2} }[/tex]

[tex] \frac{1}{2 {}^{6} } [/tex]

Answer:

15 boys

Step-by-step explanation:

There are 27 students. The number of girls is only 4/5 of the number of boys. I started by splitting the class. 14 boys and 13 girls doesn't work, so I changed it to 12 and 15. If it was 12 girls and 15 boys, the girls would have 4/5 of the boys, so it must be 12 girls and 15 boys.

Answer:commutative property

Step-by-step explanation:

Answer:

last year it was 150

Step-by-step explanation:

last year =100 ; increase= 30

total =130

130=195

100= 195/130=150

We're given

P(has disease) = 0.001

P(positive test | has disease) = 0.95

P(negative test | does not have disease) = 0.90

(a) By the law of total probability,

P(positive test) = P(positive test AND has disease) + P(positive test AND does not have disease)

Recall that the probability of an event A conditioned on another event B is

P(A | B) = P(A AND B) / P(B)

so that

P(positive test) = P(positive test | has disease) * P(has disease) + P(positive test | does not have disease) * P(does not have disease)

P(positive test) = 0.95 * 0.001 + (1 - 0.90) * (1 - 0.001)

P(positive test) ≈ 0.10

(b) From the definition of conditional probability, we hvae

P(A | B) = P(A AND B) / P(B) = P(B | A) P(A) / P(B)

so that

P(has disease | positive test) = P(positive test | has disease) * P(has disease) / P(positive test)

P(has disease | positive test) = 0.95 * 0.001 / 0.10

P(has disease | positive test) ≈ 0.0094

The probability will be "0.017699".

Given:

Incident rate,

                   [tex]= 0.999[/tex]

Now,

→ [tex]P(\frac{N}{D'} ) = 1-P(\frac{N'}{D'} )[/tex]

             [tex]= 1-0.95[/tex]

             [tex]= 0.05[/tex]

then,

→ [tex]P(\frac{D}{N} ) = \frac{Pr(D)\times P(\frac{N}{D} )}{P(N)}[/tex]

or,

            [tex]= \frac{Pr(D)\times P(\frac{N}{D} )}{P(D) \ P(\frac{N}{D} )+P(D') \ P(\frac{N}{D'} )}[/tex]

By substituting the above values, we get

            [tex]= \frac{0.001\times 0.9}{0.001\times 0.9+0.999\times 0.05}[/tex]    

            [tex]= \frac{0.0009}{0.0009+0.04995}[/tex]

            [tex]= \frac{0.0009}{0.05085}[/tex]

            [tex]= 0.017699[/tex]

Learn more:

https://brainly.com/question/16972053

Answer:

h = 3.75

Step-by-step explanation:

Step 1: Write equation

2.5/6 = h/9

Step 2: Solve for h

Step 3: Check

Plug in h to verify it's a solution.

2.5/6 = 3.75/9

0.416667 = 0.416667

Answer:

h = 3.75

Step-by-step explanation:

Given

[tex]\frac{2.5}{6}[/tex] = [tex]\frac{h}{9}[/tex] ( to solve for h, cross- multiply )

6h = 22.5 ( divide both sides by 6 )

h = 3.75

Answer:

x=10 or x=2

Step-by-step explanation:

msg me if ya need step

<3, Red

Answer:

[46.6]

Step-by-step explanation:

Absolute value has no negatives.

Answer:

21.4 * 10^(-5)

[tex]\\ \sf\longmapsto 2.14\times 10^{-5}[/tex]

[tex]\\ \sf\longmapsto 0.214\times 10^{-4}[/tex]

[tex]\\ \sf\longmapsto 0.0214\times 10^{-3}[/tex]

[tex]\\ \sf\longmapsto 0.00214\times 10^{-2}[/tex]

[tex]\\ \sf\longmapsto 0.000214\times 10^{-1}[/tex]

[tex]\\ \sf\longmapsto 0.0000214[/tex]

Answer:

The answer is below

Step-by-step explanation:

a) Let negative means the turtle position when descending and positive for going up. Therefore since the turtle was 850 meters below see level, it was at -850. It then moves 165 meters up, hence its new position is -685 meters (-850 + 165). Lastly it moves down 165 meters, hence its new position is -850 meters (-685 - 165)

b) The change in position is the sum of the movements = +165 - 165 = 0 meters.

Answer:

Hello

Step-by-step explanation:

[tex](x - \frac{2}{3} + y - \frac{1}{2} ) \times 6 = 6 \times x - \frac{2}{3} \times 6 + 6 \times y - \frac{1}{2} \times 6 = 6x - 4 + 6y - 3 = 6x - ( - 7) = 6x + 7[/tex]

Answer:

i cant see the blue

Step-by-step explanation:

                       .  

Answer:

789x86=8u

Step-by-step explanation:

Step-by-step explanation:

Kx = u - y

Divide both sides by k

X = u - y

K

I think that's the answer

Hope it helps:)

Answer:

urmom

Step-by-step explanation:

GAY

Answer:

2.7

Step-by-step explanation:

if it shows this then [-2.7] its just the number like this [2.7] its the same answer.

Answer:

61,56

Step-by-step explanation:

1 = 3,24 so 3,24 x 19 = 61,56

Answer:

The number is 4/9

Step-by-step explanation:

3(6*(4/9))=3*(2+(2/3))=8

Answer:1383478.4

Step-by-step explanation:The answer is 1383478.4 and i dont think it can be simplify

Answer:

Food booth= (75+10d)17

Game booth= (95+4d)21

Step-by-step explanation:

GAME BOOTH

$95 initial fee plus $4 per d amount of days

f(x)=95+4d

Multiply the expression by 21 because you have 21 game booths

FOOD BOOTH

$75 initial fee plus $10 per d amount of days

f(z)=75+10d)

multiply this expression by 17 because their are 17 food booths

hopefully this helps:)

Answer:

x = -3/2, 1

Step-by-step explanation:

1. Use Rule of One

2. Take out the constants

3. Simplify 6/3 to 2

4. Use the product rule

5. Simplify

6. Move all terms to one side

7. Simplify

8. Split the second term

9. Factor out the common terms

10. Factor out the common term (again)

11. Solve for x

Answer:

1215

Step-by-step explanation:

Answer:

the answer is 1215 :D

Step-by-step explanation:

Answer:

Select the plain line in the Insert Shapes group. Place your cursor where you want a tick mark on your line, hold the "Shift" key, and drag to create a vertical mark. Holding the Shift key ensures a straight line.

Step-by-step explanation:

Answer:

4.485

Step-by-step explanation:

 [divide 17 by 4]

  [  ]

Now, Midpoint of  4.25 and 4.472 =

Number between 4.25 and 4.472 =4.485

Or number between  and  is 4.485.

Answer:

Step-by-step explanation:

Given f(x) = 2x²+16

g(x) = √5x³

First is to get the composite function f(g(x))

f(g(x)) = f(√5x³)

To get f(√5x³), we will replace x in f(x) with √5x³ as shown:

f(√5x³) = 2(√5x³)²+16

f(√5x³) = 2(5x³)+16

f(√5x³) = 10x³+16

Hence f(g(x)) = 10x³+16

f(g(x)) will be the function of amount earned by Raul for the total number hour he works

Answer:

10x^3 dollars/hour

Step-by-step explanation:

Answer:

area=[(a+b)/2]*h

Step-by-step explanation:

a= longer base length

b= shorter base length

h= height of trapezoid