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2 years ago

What is the common ratio in the sequence 6,12,24,48,96 A -2 B 2 C 6 D 1/2

Mathematics

1 answer:

anyanavicka [17]2 years ago

3 0

The ratio is that of one term to the one before:

... 12/6 = 2

It is "common" because it applies to every pair of adjacent terms:

... 24/12 = 48/24 = 96/48 = 2

The appropriate choice is ...

... B 2

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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

2 years ago

Carloshas1.2 meters of wood if cut into 3 equal pieces how many mm each

sdas [7]

1.2 ÷ 3 = 0.4 meters each
0.4 meters = 40 cm
40 cm = 400 mm

therefore,
Carlos must cut each piece of wood 400 mm each.

Hope this helps and have a great day! :D

5 0

2 years ago

A researcher is using a regular, two-tailed test with α = .05 to determine whether a non-zero correlation exists in the populati

beks73 [17]

Answer:

Step-by-step explanation:

Download docx

7 0

3 years ago

steve has quiz scores of 60,64,75,71. If all the quizzes count the same, what is the lowest grade he can make on the next quiz t

NeX [460]

Answer:

The last quiz score must be at least an 80 to get the average to be a 70.

Step-by-step explanation:

In order to find this, you need to take the average of the 4 test scores along with the unknown test score (x). So, to find an average, we add all the numbers together and divide by the amount of tests taken. We can then set this equal to 70 since that is the minimum average.

(60 + 64 + 75 + 71 + x)/5 = 70 ------> Multiply both sides by 5

(60 + 64 + 75 + 71 + x) = 350 -----> Combine like terms

270 + x = 350 -----> Subtract 270 from both sides

x = 80

7 0

3 years ago

steve measured the length of his room and found it to be 9 feet and 6 inches. The width of his room was 11 feet exacly. What is

Art [367]

Length: 114 in.
Width: 132 in.

For length, you have 9 feet and 6 inches. Meaning that if you would want to get the length of his room in inches, you would have to multiply 9 with 12 and add 6.

It's the same thing for the width.

If you need more help comment below!

4 0

3 years ago