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never [62]
3 years ago
10

The length of a rectangle is 10 meters more than the width. If 3 meters is added to both the length and the width, the new area

will be 299 square meters. Find the length and width of the original rectangle.
HELP HELP HELP HELP
Mathematics
1 answer:
Finger [1]3 years ago
4 0

Answer:

L = 20

W = 10

Step-by-step explanation:

L = (w + 10)

NL = (w + 13)

Divide 299 by 13:

299 ÷ 13 = 23

So, 23 x 13 = 299

L = 23

W = 13

Subtract 3 from both to get the original length and width

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aleksandr82 [10.1K]

Answer:

(a)8.0mg

(b)36.87 hours

(c)-0.168

Step-by-step explanation:

The amount of Valium in that person's bloodstream at any time can be modeled with the exponential decay function A ( t ) = 10 e^{ -0.0188 t (t in hours)

(a)After 12 Hours

A ( 12) = 10 e^{ -0.0188*12}\\=7.98\\\approx 8.0 mg $(to the nearest tenth of a milligram)

(b)If A(t)=5mg

Then:

5= 10 e^{ -0.0188 t}\\$Divide both sides by 10\\0.5=e^{ -0.0188 t}\\$Take the natural logarithm of both sides\\ln (0.5)=-0.0188 t\\t=ln (0.5) \div (-0.0188)\\$t=36.87 hours (to two decimal places.)

(c)

A ( t ) = 10 e^{ -0.0188 t}\\A'(t)=10(-0.0188)e^{ -0.0188 t}\\A'(t)=-0.188e^{ -0.0188 t}\\$At 6 hours, the rate at which the amount of Valium is decaying therefore is:\\A'(6)=-0.188e^{ -0.0188*6}\\$=-0.168 ( to three decimal places)

3 0
2 years ago
Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randoml
vovikov84 [41]

Answer: 0.3439

Step-by-step explanation:

Given :The last four digits for telephone numbers are randomly selected​ (with replacement).

Here , each position can be occupied with any of the digit independently .

Total digits = 10

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For each digits , the probability that it is not 0 = \dfrac{9}{10}=0.9

If we select 4 digits , The probability of getting no 0 =(0.9)^4 =0.6561

(By multiplication rule of independent events)

Now , the probability that for one such phone​ number, the last four digits include at least one 0. = 1- P(none of them is 0)

=1- 0.6561=0.3439

Hence, the probability that for one such phone​ number, the last four digits include at least one 0. is 0.3439 .

4 0
2 years ago
Annie walks 15 feet away from her house and places a mirror on the ground. She backs 4 feet away from the mirror so that she can
Mars2501 [29]
Set up a proportion:

\frac{x}{5} = \frac{15}{4} \\  \\  x = 5(\frac{15}{4}) = \frac{75}{4}
6 0
3 years ago
16 is what percent of 24
Blababa [14]
100%/x%=24/16
(100/x)*x=(24/16)*x       - we multiply both sides of the equation by x
100=1.5*x       - we divide both sides of the equation by (1.5) to get x
100/1.5=x
66.6666666667=x
x=66.6666666667

now we have:
<span>16 is 66.6666666667% of 24</span>
6 0
3 years ago
Read 2 more answers
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Answer:

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Interval Notation:

(2,∞)

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