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Mamont248 [21]
3 years ago
10

Katrina buys a ​40-ft roll of fencing to make a rectangular play area for her dogs. Use ​2(​l+w)=40 to write a function for the​

length, given the width. Graph the function. What is a reasonable domain for the​ situation? Explain.
Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
8 0
Why you write hi this needs to anser!!
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A box contains 35 gems, of which 10 are real diamonds and 25 are fake diamonds. Gems are randomly taken out of the box, one at a
Sonja [21]

Answer:

Step-by-step explanation:

The total number of ways of selecting 3 gems of any kind without replacement is 35 * 34 * 33 = 39270

Now selecting 2 gems from 25 is 25C2

25 C 2 = 25 * 24/2 = 300

Selecting one good gem is 10

Total selection = 300 * 10 = 3000

P(gems) = 3000 / 39270

P(gems) = 300/3927

P(gems) = 100/1309

6 0
3 years ago
A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the
Vedmedyk [2.9K]
(a) Using Newton's Law of Cooling, \dfrac{dT}{dt} = k(T - T_s), we have \dfrac{dT}{dt} = k(T - 75) where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get \dfrac{dT}{T - 75} = k dt. Integrate both sides to get \ln|T - 75| = kt + C.

Since T(0) = 185, we solve for C:
|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110
So we get \ln|T - 75| = kt + \ln 110. Use T(30) = 150 to solve for k:
\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)

So

\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t}  \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}

But choose Positive because T > 75. Temp of turkey can't go under.

T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)}  = 136.929 \approx 137{}^{\circ}F

(b)

T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30}  \\
100 = 75 + 110(15/22)^{t/30}   \\
25 = 110(15/22)^{t/30}  
\frac{25}{110} = (15/22)^{t/30}   \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22)  \approx 116\ \mathrm{min}

Dogs of the AMS.
4 0
3 years ago
Convert 1.5 cubic meter to ______ cubic centimeters.
Vedmedyk [2.9K]

Answer:

1500000 cubic centimeters

6 0
2 years ago
Read 2 more answers
If f(x) = 4x + 2, what is the value of f(3)? <br><br> O 8<br> O 14<br> O 45<br> O 66
lutik1710 [3]

Answer:

14

Step-by-step explanation:

5 0
3 years ago
Identical sweaters are on sale in two different stores. The sale price in store A is 30% off the regular price of $25. The sale
bekas [8.4K]
30% off 25: multiply 25 by .30 to find 30%: 7.5. Now subtract that from the sales price: 25-7.5=17.5
Do the same for store B: .40•30=12. 30-12=18.
So store A is better by $.50 :) hope this helps :)
7 0
3 years ago
Read 2 more answers
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