In triangle ABC, mZA = 47° and mZB= 70°

If a cube-shaped cell is 3 units tall by 3 units wide and 3 units long, what is the cell's surface-area-to volume ratio?

bulgar [2K]

The cube has 6 sides, each a square with dimensions 3 by 3,

the area of any of these squares is 3*3=9 square units.

The total area of the cube is 6*9 square units=54 square units

The volume of a cube with side length a is given by : $\displaystyle{ V_{cube}=a^3$ , thus the volume of the cube-shaped cell is 3*3*3=27 cube units.

(surface area):(volume)=54:27 = 2:1 =2

Answer:

the ratio of the numerical values is 2

(their ratio including units is 2/unit

7 0

3 years ago

$300 was deposited in a Certificate of Deposit (CD) yielding 6% interest compounded quarterly. how many years will it take the C

Ivan

The future value (A) of a one-time investment of principal amount P at interest rate r compounded n times per year for t years is ...

... A = P(1 +r/n)^(nt)

Putting your given numbers into the formula, we have

... 876.34 = 300(1 +.06/4)^(4t)

Taking logarithms, this becomes the linear equation

... log(876.34) = log(300) + 4t·log(1.015)

Solving for t in the usual way, we get

... log(876.34) -log(300) = 4t·log(1.015) . . . . . . . subtract the constant term on the right

... (log(876.34) -log(300))/(4·log(1.015)) = t ≈ 18.00 . . . . divide by the coefficient of t

It will take 18 years for the $300 CD to reach a value of $876.34.

8 0

3 years ago

Write the equation of the line that has a slope of 2 and passes through the point (-3,4).

Arte-miy333 [17]

Answer:

y = 2x + 10

Step-by-step explanation:

We are given the slope of the line and the coordinates of one point on the line. Thus, we use the point-slope formula y - k = m(x - h). Here m = 2, h = -3 and k = 4. Therefore we have:

y - 4 = 2(x + 3)

which can be rewritten as y = 2x + 6 + 4, or y = 2x + 10 (Answer D)

4 0

3 years ago

What is the length of the shorter base of the Little Trapezoid trail?

valentina_108 [34]

Answer:

The length of the shorter base of the little trapezoid trail is 1 mi.

Step-by-step explanation:

Let the shorter base of the large trapezoid is S and the larger base of the large trapezoid is L.

Similarly, assume that the shorter base of the small trapezoid is s and the larger base of the small trapezoid is l.

Since, the trapezoids are similar, so

$\frac{L}{l} = \frac{S}{s}$

Now, given that S = 2 mi, L = 8 mi and l = 4 mi and we have to find s.

So, $s = \frac{S \times l}{L} = \frac{4 \times 2}{8} = 1$ mi. (Answer)

3 0

3 years ago

1. (5pt) In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also,

gladu [14]

Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

$\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988$

The combined proportion is:

$\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989$

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

$Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$

$=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78$

Compute the p-value as follows:

$p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075$

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

$=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\$

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

6 0

3 years ago