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3 years ago

What is the value of x? Enter your answer in the box. units

Mathematics

1 answer:

sineoko [7]3 years ago

8 0

Answer:

x = 28

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Then x/(x +10) = 42/(42 +15)

x(57) = 42(x + 10)

57x = 42x + 420

15x = 420

x = 28

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Which of the following lists of fractions are in order from least to greatest? Select TWO that apply.

lora16 [44]

Answer:

i think its a 1/4 then 2/3 and 3/10

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3 years ago

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Production times are evenly distributed between 8 and 15.8 minutes and production times are never outside of this interval. What

dezoksy [38]

Answer:

29.49% probability that a production time is between 9.7 and 12 minutes

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d, in which d is greater than c, is given by the following formula.

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

Production times are evenly distributed between 8 and 15.8 minutes and production times are never outside of this interval.

This means that $a = 8, b = 15.8$

What is the probability that a production time is between 9.7 and 12 minutes?

$d = 12, c = 9.7$ .

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

$P(9.7 \leq X \leq 12) = \frac{12 - 9.7}{15.8 - 8} = 0.2949$

29.49% probability that a production time is between 9.7 and 12 minutes

5 0

4 years ago

Create a system of equations to represent the word problem. Then solve using the linear combination/elimination method. Show all

Leno4ka [110]

Answer:

Solution given:

model A printers [a] prints=80books per day

model B printers [b] prints=55books per day

total no of printers =9

no of model A printers be x

and

no of model B printers be [9-x]

According to the question;

ax+(9-x)b=670 books

substituting value of a and b; we get

80x+(9-x)55=670

80x-55x+495=670

25x=670-495=175

x= $\frac{175}{25}$ =7

So;

no of model A printers =x=7

no of model B printers =9-x=9-7=2

is your answer.

8 0

3 years ago

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6. Which process was used to obtain the equation shown in Step 2?

frozen [14]

Answer:

A) added to both sides of the equation

Step-by-step explanation:

3 0

3 years ago

A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

3 years ago