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Yuki888 [10]
3 years ago
6

Determine the number of ways a computer can randomly generate one or more such integers from 1 through 30. Two distinct integers

whose sum is 27.
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
5 0

Answer:

There are 26 possible way to determine two  distinct integers whose sum is 27.

Step-by-step explanation:

To find : The number of ways a computer can randomly generate one or more such integers from 1 through 30. Two distinct integers whose sum is 27.

Solution :

We have given the numbers from  1,2,3,4......,29,30.

In order to get two distinct numbers having the sum 27,

There are the possibilities :

1+26=27

2+25=27

3+24=27

......

24+3=27

25+2=27

26+1=27

The maximum number taken is 26.

So, There are 26 possible way to determine two  distinct integers whose sum is 27.

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Brian cut a piece of cardboard in the shape of a trapezoid the area of the cut out is 43.5 cm² if the bases are 6 cm And 8.5 cm
Likurg_2 [28]

Answer: the height of the trapezoid is 6 cm

Step-by-step explanation:

The formula for determining the area of a trapezoid is expressed as

Area = 1/2(a + b)h

Where

a and b are the length of The bases are the 2 sides of the trapezoid which are parallel with one another.

h represents the height of the trapezoid.

From the information given,

a = 6 cm

b = 8.5 cm

If the area of the cut out is 43.5 cm², then

53.5 = 1/2(6 + 8.5)h

Cross multiplying by 2, it becomes

43.5 × 2 = (6 + 8.5)h

87 = 14.5h

h = 87/14.5 = 6 cm

8 0
3 years ago
Max was on vacation twice as long as Jared and half as longas Wesley. The boys were on vacation a total of 3 weeks. How many day
lord [1]
Make an equation.
Also, convert 3 weeks into days ⇒ 3 · 7 = 21 days.

x + 2x + 4x = 21

x is Jared.
2x is Max (because half of 4 is 2).
4x is Wesley.

Now solve the equation.

7x = 21
x = 3

Jared = x
Max = 2x
Wesley = 4x

Jared = 3 days
Max = 2(3) = 6 days
Wesley = 4(3) = 12 days
4 0
3 years ago
(3 points)
Snezhnost [94]

Answer:

The exponential Function is 20+12h=200.

Farmer will have 200 sheep after <u>15 years</u>.

Step-by-step explanation:

Given:

Number of sheep bought = 20

Annual Rate of increase in sheep = 60%

We need to find that after how many years the farmer will have 200 sheep.

Let the number of years be 'h'

First we will find the Number of sheep increase in 1 year.

Number of sheep increase in 1 year is equal to Annual Rate of increase in sheep multiplied by Number of sheep bought and then divide by 100.

framing in equation form we get;

Number of sheep increase in 1 year = \frac{60}{100}\times20 = 12

Now we know that the number of years farmer will have 200 sheep can be calculated by Number of sheep bought plus Number of sheep increase in 1 year multiplied by number of years  is equal to 200.

Framing in equation form we get;

20+12h=200

The exponential Function is 20+12h=200.

Subtracting both side by 20 using subtraction property we get;

20+12h-20=200-20\\\\12h=180

Now Dividing both side by 12 using Division property we get;

\frac{12h}{12} = \frac{180}{12}\\\\h =15

Hence Farmer will have 200 sheep after <u>15 years</u>.

6 0
3 years ago
A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so
Debora [2.8K]

Let A(t) = amount of salt (in pounds) in the tank at time t (in minutes). Then A(0) = 11.

Salt flows in at a rate

\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}

and flows out at a rate

\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}

which I'll solve with the integrating factor method.

\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95

-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}

\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}

Integrate both sides. By the fundamental theorem of calculus,

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)

\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}

\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}

\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}

After 1 hour = 60 minutes, the tank will contain

A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131

pounds of salt.

7 0
2 years ago
How was the question 7+7+7 = 21 and 3×7 = 21 related ?
kifflom [539]
7+7+7=21 is the same as saying 7 times 3+
=21
5 0
3 years ago
Read 2 more answers
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