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3 years ago

What is 1/8 divided by 5/7

1 answer:

5 0

It becomes 7/40. To get it, you have to put 1/8 times 5/7. Then, flip the second fraction, (5/7), so that it becomes 7/5. Multiply 1/8 and 7/5, to get 7/40. You call this "reciprocal".

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Which of the following is the solution to the differential equation dP/dt+P=10 with the initial condition P(0)=4

Ber [7]

Answer:

Option C. $P=10-6e^{-t}$

Explanation:

1. Separate variables:

$\dfrac{dP}{dt}+P=10\\ \\ \\ \\\dfrac{dP}{dt}=-P+10\\ \\ \\ \dfrac{dP}{-P+10}=dt$

2. Find the indefinite integrals

$-\ln{(10-P)}=t+C$

3. Solve for P

$10-P=e^{-t+C}\\ \\ 10-P=Ke^{-t}\\ \\ P=10-Ke^{-t}$

4. Use the initial condition, P(0) = 4, to find K:

4 = 10 - K(e⁰)

4 = 10 - K

K = 10 - 4

K = 6

5. Substitute K = 6 into the integrated equation:

$P=10-6e^{-t}$

That is the option C.

4 0

3 years ago

What is sin 28°? plzzz help

vfiekz [6]

Answer:

Step-by-step explanation:

Sin(28) is approximately 0.4695

After rewriting all of the options as a decimal:

a) 0.8823

b) 1.875

c) 0.4706

d) 0.5333

when rounding the sin(28) to the nearest hundredth... you get 0.47

Therefore, sin(28) is c) $\frac{8}{17}$

7 0

3 years ago

Mike has 2 mats that are in the shape of triangles. The scale factor of the two triangular mats is 7 / 9. What is the ratio of t

Arlecino [84]

Answer:

Ratio of perimeters = 7 : 9

Step-by-step explanation:

Each side of the smaller triangle is 7 by 9 times the length of the corresponding side of the large triangle.

$\text{Now, Since each side of the triangle is scaled by a factor of }\frac{7}{9}\\\text{So, sum of the lengths of the three sides will also be scaled by a factor of }\frac{7}{9}$

$\text{Therefore, the ratio of the perimeters of the two triangles }\\\text{will be the same as the scale factor : }\frac{7}{9}$

6 0

3 years ago

Read 2 more answers

In a random sample of n1 = 156 male Statistics students, there are x1 = 81 underclassmen. In a random sample of n2 = 320 female

Scilla [17]

Answer:

The p-value for the test of hypothesis is P(z<-3.617)=0.0002.

Step-by-step explanation:

Hypothesis test on the difference between proportions.

The claim is that the percent of males who are underclassmen stats students (π1) is less than the percent of females who are underclassmen stats students (π2).

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2$

The male sample has a size n1=156. The sample proportion is p1=81/156=0.52.

The female sample has a size n2=221. The sample proportion in this case is p2=221/320=0.69.

The weigthed average of proportions p, needed to calculate the standard error, is:

$p=\dfrac{n_1p_1+n_2p_2}{n_1+n_2}=\dfrac{81+221}{156+320}=\dfrac{302}{476}= 0.63$

The standard error for the difference in proportions is:

$\sigma_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.63*0.37}{156}+\dfrac{0.63*0.37}{320}}\\\\\\\sigma_{p1-p2}=\sqrt{\dfrac{0.2331}{156}+\dfrac{0.2331}{320}}=\sqrt{0.001503871+0.000728438}=\sqrt{0.002232308}\\\\\\\sigma_{p1-p2}=0.047$