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2 years ago

a solid sphere is cut into 12 equal wedges. the volume of each wedge is V=1/9πr^3. solve the formula for r.

Mathematics

1 answer:

olga nikolaevna [1]2 years ago

5 0

The formula, solved for r is r = ∛(9V/π)

<h3>Subject of formula </h3>

From the question, we are to solve for r is the given formula

The given formula is

V = 1/9πr³

Multiply both sides of the equation by 9 to get

9V = πr³

Now, divide both sides by π

∴ r³ = 9V/π

r = ∛(9V/π)

Hence, the formula, solved for r is r = ∛(9V/π)

Learn more on Subject of formula here: brainly.com/question/1463152

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An owner of Honda City car sells his car at a price of RM 7.50,000 with a loss present of 12.5%. Then find the price at which he

Mars2501 [29]

Answer:

Cost = RM 857143

Loss = RM 107143

Step-by-step explanation:

Given:

Selling price SP = RM 750000
Loss% = 12.5
Cost price CP = x

Cost price is found as:

SP = CP - 12.5%
750000 = x - 12.5%
750000= x*(100-12.5)/100
750000= 0.875x
x= 750000/0.875
x≈ RM 857143

Loss is:

RM 857143 - 750000 = RM 107143

8 0

3 years ago

Usqqe format HTH to mean that the first toss is heads, the second is tails and the third is heads more than one element in the s

Scrat [10]

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: State the number of outcomes possible for three tossing of a coin

Since a coin has two possible outcomes and is tossed three times, the total outcomes will be:

$\begin{gathered} 2^3=8 \\ 8\text{ outcomes} \end{gathered}$

STEP 2: Find the number of sample spaces for the three tosses

STEP 3: Get the outcomes of the events for which the second toss is tails

Hence, the answers are given as:

Sample Space:

$\lbrace HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\rbrace$

The event that the second toss is tails:

$\lbrace HTH,HTT,TTH,TTT\rbrace$

4 0

1 year ago

If 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), w

Yuliya22 [10]

The value of a is 80

Step-by-step explanation:

The distance of a point $(x_0,y_0)$ from the y-axis can be written as

$d_y = |x_0|$

because the x-coordinate of the y-axis is zero.

Similarly, the distance of a point $(x_0,y_0)$ from the x-axis can be written as

$d_x=|y_0|$

Since the y-coordinate of the x-axis is zero.

In this problem:

- The distance of the point A (−30, −45) from the y-axis can be written as

$d_A = |-30|=30$

- The distance of point B (a,a) from the x-axis can be written as

$d_B = |a| = a$

Since $a>0$ .

We are told that 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), which means

$\frac{2}{3}d_A = \frac{1}{4}d_B$

Therefore,

$\frac{2}{3}(30)=\frac{1}{4}a$

And solving for a,

$20=\frac{1}{4}a\\a=80$

Learn more about distance:

brainly.com/question/3969582

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8 0

3 years ago

When the sample size and the sample proportion remain the same, a 90 percent confidence interval for a population proportion p w

deff fn [24]

Answer:

A 90% confidence interval for p will be narrower than the 99% confidence interval.

Step-by-step explanation:

The formula to compute the (1 - α) % confidence interval for a population proportion is:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Here $\hat p$ is the sample proportion.

The margin of error of the confidence interval is:

$MOE= z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The MOE is dependent on:

Confidence level
Standard deviation
Sample size

The MOE is directly related to the confidence level and standard deviation.

So if any of the two increases then the MOE also increases, thus widening the confidence interval.

And the MOE is inversely related to the sample size.

So if the sample increases the MOE decreases and vice versa.

It is provided that the sample size and the sample proportion are not altered.

The critical value of z for 90% confidence level is:

$z_{\alpha/2}= z_{0.10/2}=z_{0.05}=1.645$

And the critical value of z for 99% confidence level is:

$z_{\alpha/2}= z_{0.05/2}=z_{0.05}=1.96$

So as the confidence level increases the critical value increases.

Thus, a 90% confidence interval for p will be narrower than the 99% confidence interval.

6 0

3 years ago

Please help ASAP! Thanks! For the figures below, assume they are made of semicircles, quarter circles and squares. For each shap

bazaltina [42]

Answer:

Part 1) $A=36(\pi-2)\ cm^2$

Part 2) $P=6(\pi+2\sqrt{2})\ cm$

Step-by-step explanation:

Part 1) Find the area

we know that

The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle

$A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)$

we have that the base and the height of triangle is equal to the radius of the circle

$r=12\ cm\\b=12\ cm\\h=12\ cm$

substitute

$A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)$

$A=(36\pi-72)\ cm^2$

simplify

Factor 36

$A=36(\pi-2)\ cm^2$

Part 2) Find the perimeter

The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle

The circumference of a quarter of circle is equal to

$C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r$

substitute the given values

$C=\frac{1}{2}\pi (12)$

$C=6\pi\ cm$

The hypotenuse of right triangle is equal to (applying the Pythagorean Theorem)

$AC=\sqrt{12^2+12^2}$

$AC=\sqrt{288}\ cm$

simplify

$AC=12\sqrt{2}\ cm$

Find the perimeter

$P=(6\pi+12\sqrt{2})\ cm$

simplify

Factor 6

$P=6(\pi+2\sqrt{2})\ cm$

6 0

3 years ago