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3 years ago

15

lucy made a pumpkin pie to sell at a bake sale. She cut it into 6 slices and sold each slice for $1.25. How much money did she m

ake when every piece had been sold?

1 answer:

Y_Kistochka [10]3 years ago

8 0

Lucy would have made $7.50!

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You spin the spinner once. What is P ( not less than 7)? Write your answer as a fraction. Ex: 2/3 *

Dafna11 [192]

Answer:

P(not less than 7) = 1/4

Step-by-step explanation:

As the spinner has 4 sectors.

We spin the spinner once.

Probability not less than 7 means the spinner mapping the number greater than 7.

Here, only 8 is the number which is not less than 7.

Therefore, P(not less than 7) = 1/4

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2 years ago

The rate of change of the downward velocity of a falling object is the acceleration of gravity (10 meters/sec 2) minus the accel

Alexus [3.1K]

Answer:

See below

Step-by-step explanation:

Write the initial value problem and the solution for the downward velocity for an object that is dropped (not thrown) from a great height.

if v(t) is the speed at time t after being dropped, v'(t) is the acceleration at time t, so the the initial value problem for the downward velocity is

v'(t) = 10 - 0.1v(t)

v(0) = 0 (since the object is dropped)

<em> The equation v'(t)+0.1v(t)=10 is an ordinary first order differential equation with an integrating factor </em>

$\bf e^{\int {0.1dt}}=e^{0.1t}$

so its general solution is

$\bf v(t)=Ce^{-0.1t}+100$

To find C, we use the initial value v(0)=0, so C=-100

and the solution of the initial value problem is

$\bf \boxed{v(t)=-100e^{-0.1t}+100}$

what is the terminal velocity?

The terminal velocity is

$\bf \lim_{t \to\infty}(-100e^{-0.1t}+100)=100\;mt/sec$

How long before the object reaches 90% of terminal velocity?

90% of terminal velocity = 90 m/sec

we look for a t such that

$\bf -100e^{-0.1t}+100=90\rightarrow -100e^{-0.1t}=-10\rightarrow e^{-0.1t}=0.1\\-0.1t=ln(0.1)\rightarrow t=\frac{ln(0.1)}{-0.1}=23.026\;sec$

How far has it fallen by that time?

The distance traveled after t seconds is given by

$\bf \int_{0}^{t}v(t)dt$

So, the distance traveled after 23.026 seconds is

$\bf \int_{0}^{23.026}(-100e^{-0.1t}+100)dt=-100\int_{0}^{23.026}e^{-0.1t}dt+100\int_{0}^{23.026}dt=\\-100(-e^{-0.1*23.026}/0.1+1/0.1)+100*23.026=1,402.6\;mt$

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3 years ago

Judy can throw a baseball 240 feet. This is 80% as far as her older brother can throw the ball. How far can her older brother th

jolli1 [7]

Answer:

80

Step-by-step explanation:

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3 years ago

Tiana can clear a football feild of debris in 3 hours. Jacob can clear the same feild in 2 hours. If they decide to clear the fe

OleMash [197]

Answer:

1 hour

Step-by-step explanation:

3 hours subtract 2 hours

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3 years ago

Joe bought 5 apples and 4 bananas for $6. Dawn bought 3 apples and 6 bananas for $6.30. How much foes each apple and each banana

zepelin [54]

Answer:

Apple = $0.6

Banana = $0.75

Step-by-step explanation:

Let us represent Apple by A and Banana by B

For Joe,

5A + 4B = 6 (1)

For Dawn

3A + 6B = 6.3 (2)

To eliminate A, Multiply equation (1) by 3 and equation (2) by 5

15A + 12B = 18 (3)

15A + 30B = 31.5 (4)

subtracting equation (4) from (3)

15A - 15A +12B - 30B = 18 - 31.5

-18B = -13.5

divide through by -18

-18B/-18 = -13.5/-18

B = 0.75

substitute 0.75 in equation (1)

5A + 4B = 6

5A + 4(0.75) = 6

5A + 3 = 6

subtract 3 from both sides

5A + 3 - 3 = 6 - 3

5A = 3

divide through by 5

5A/5 = 3/5

A = 0.6

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2 years ago