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3 years ago

15

SHOW YOUR WORK PLEASE! Jim is trying to improve his speed on the track so he can qualify for the State Championships. As he is r

unning, he goes from 70 meters/minute (beginning speed) to 106 meters/minute (final speed) in 9 seconds. What is his acceleration?

1 answer:

alex41 [277]3 years ago

4 0

Answer:

4 m/s²

Step-by-step explanation:

Acceleration = (106-70)/9

= 36/9

= 4ms^-2

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What value(s) of x will make each equation below true

Dahasolnce [82]

We need to solve for x. Let's try problem b:

$2x-6=3x+1-x-7$

Let us first combine line terms. 3x and -x as well as 1 and -7 can be combined. Let's do that:

$2x-6=2x-6$

Since this is true, your answer would be:

All real numbers

------------------------------------------------------------------

Let's solve for problem c:

$3x+1=43$

Let's isolate x, so subtract 1 from both sides:

$3x=42$

Since x can't have a coefficient, divide both sides by 3:

$\frac{3x}{3}=\frac{42}{3}$

$x=14$

So, only the value of 14 would make this equation true.

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Let's try problem d:

$4x-1=4x+7$

Let's get our whole numbers on the right side. Add 1 to both sides:

$4x=4x+8$

Subtract 4x from the right side on both sides:

$0=8$

Since this is not true, your answer would be:

No solution

7 0

3 years ago

Victoria earns $255 by working 20 hours each week

Alborosie

She would make $98.50 in 10 hours.

Explanation :
255/20 = 12.75
12.75 - 2.90 = 9.85
9.85 x 10 = 98.50

6 0

3 years ago

Suiting at 6 a.m., cars, buses, and motorcycles arrive at a highway loll booth according to independent Poisson processes. Cars

dem82 [27]

Answer:

Step-by-step explanation:

From the information given:

the rate of the cars = $\dfrac{1}{5} \ car / min = 0.2 \ car /min$

the rate of the buses = $\dfrac{1}{10} \ bus / min = 0.1 \ bus /min$

the rate of motorcycle = $\dfrac{1}{30} \ motorcycle / min = 0.0333 \ motorcycle /min$

The probability of any event at a given time t can be expressed as:

$P(event \ (x) \ in \ time \ (t)\ min) = \dfrac{e^{-rate \times t}\times (rate \times t)^x}{x!}$

∴

(a)

$P(2 \ car \ in \ 20 \ min) = \dfrac{e^{-0.20\times 20}\times (0.2 \times 20)^2}{2!}$

$P(2 \ car \ in \ 20 \ min) =0.1465$

$P ( 1 \ motorcycle \ in \ 20 \ min) = \dfrac{e^{-0.0333\times 20}\times (0.0333 \times 20)^1}{1!}$

$P ( 1 \ motorcycle \ in \ 20 \ min) = 0.3422$

$P ( 0 \ buses \ in \ 20 \ min) = \dfrac{e^{-0.1\times 20}\times (0.1 \times 20)^0}{0!}$

$P ( 0 \ buses \ in \ 20 \ min) = 0.1353$

Thus;

P(exactly 2 cars, 1 motorcycle in 20 minutes) = 0.1465 × 0.3422 × 0.1353

P(exactly 2 cars, 1 motorcycle in 20 minutes) = 0.0068

(b)

the rate of the total vehicles = 0.2 + 0.1 + 0.0333 = 0.3333

the rate of vehicles with exact change = rate of total vehicles × P(exact change)

$= 0.3333 \times \dfrac{1}{4}$

= 0.0833

∴

$P(zero \ exact \ change \ in \ 10 minutes) = \dfrac{e^{-0.0833\times 10}\times (0.0833 \times 10)^0}{0!}$

P(zero exact change in 10 minutes) = 0.4347

c)

The probability of the 7th motorcycle after the arrival of the third motorcycle is:

$P( 4 \ motorcyles \ in \ 45 \ minutes) =\dfrac{e^{-0.0333\times 45}\times (0.0333 \times 45)^4}{4!}$

$P( 4 \ motorcyles \ in \ 45 \ minutes) =0.0469$

Thus; the probability of the 7th motorcycle after the arrival of the third one is = 0.0469

d)

P(at least one other vehicle arrives between 3rd and 4th car arrival)

= 1 - P(no other vehicle arrives between 3rd and 4th car arrival)

The 3rd car arrives at 15 minutes

The 4th car arrives at 20 minutes

The interval between the two = 5 minutes

<u>For Bus:</u>

P(no other vehicle other vehicle arrives within 5 minutes is)

= $\dfrac{6}{12} = 0.5$

<u>For motorcycle:</u>

$= \dfrac{2 }{12} = \dfrac{1 }{6}$

∴

The required probability = $1 - \Bigg ( \dfrac{e^{-0.5 \times 0.5^0}}{0!} \times \dfrac{e^{-1/6}\times (1/6)^0}{0!} \Bigg)$

= 1- 0.5134

= 0.4866

6 0

3 years ago

Here are the ingredients for making fish pie for 6 people

ikadub [295]

9514 1404 393

Answer:

a) 80 g fish

b) 200 g butter

Step-by-step explanation:

The recipe is multiplied by ...

(number served)/(number recipe serves)

to find the amount of ingredients for a different number of people.

__

<h3>a)</h3>

fish for 2 people = (2/6)·(240 g) = 80 g

__

<h3>b)</h3>

butter for 15 people = (15/6)(80 g) = 200 g

8 0

2 years ago

what is bigger ?5/8 or 3/4

hammer [34]

3/4 because think of the decimals 3/4 is 75 and 5/8 is 0.625

8 0

3 years ago

Read 2 more answers