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3 years ago

Find the volume of the oblique cone.

Mathematics

2 answers:

dem82 [27]3 years ago

8 0

Answer: The answer is 1674.66 cm³.

Step-by-step explanation: We are given to find the volume f the oblique cone in the figure.

The height of the cone is given by

h = 16 cm

and the radius of the base is of the cone is given by

r = 10 cm.

Therefore, the volume of the cone is given by

$V=\dfrac{1}{3}\pi r^2h=\dfrac{1}{3}\times 3.14\times 10^2\times 16=\dfrac{314\times 16}{3}=1674.66~\textup{cm}^3.$

Thus, the required volume is 1674.66 cm³.

RSB [31]3 years ago

6 0

Its 1/3 times 16 times 10.

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Subtract: ( - 2x4 - 4y + 4z² +6) - (-9x4 – 3y + 4z? +9) 0 - 7x² + y + 3 0 - 11x4 - 7 - 3

Vinil7 [7]

Answer:

36x-3y+4z^2+26-7x^2

Step-by-step explanation:

Okay well for starters, you can't subtract that because it's an expression, not an equation. And secondly, there was '?' which I'm going to assue=me was a typing error.

Now to actually simplify this mess of an expression, you just need to combine the like-terms! Once you do that you really can't do anything else, since you don't know the varibles.

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3 years ago

Find the annual interest rate.

slega [8]

The annual interest rate is 3.5%.

Solution:

Given Interest (I) = $26.25

Principal (P) = $500

Time (t) = 18 months

Rate of interest (r) = ?

Time must be in years to find the rate per annum.

1 year = 12 months

Divide the time by 12.

Time (t) = $\frac{18}{12}=\frac{3}{2}$ years

Now, find the rate of interest using simple interest formula.

<u>Simple interest formula:</u>

$$I=\frac{Prt}{100}$

$$26.25=\frac{500\times r\times \frac{3}{2} }{100}$

$$26.25\times 100 =500\times r\times \frac{3}{2}$

$$2625 =250\times r\times 3$

$$2625 =750\times r$

$$\Rightarrow r=\frac{2625}{750}$

⇒ r = 3.5%

Hence the annual interest rate is 3.5%.

8 0

3 years ago

A(n) = -5 + 6(n - 1)a(n)=−5+6(n−1)a, left parenthesis, n, right parenthesis, equals, minus, 5, plus, 6, left parenthesis, n, min

DENIUS [597]

Answer:

The 12th term is 61

Step-by-step explanation:

I will assume that your a(n) = -5 + 6(n - 1) is correct; the rest is redundant (duplicative, unneeded).

To find the 12th term, substitute 12 for n in the above formula:

a(12) = -5 + 6(12 - 1) = -5 + 6(11) = 66 - 5, or 61

The 12th term is 61

6 0

3 years ago

In triangle EFG, m of E = 30 degrees, m of F = 60 degrees, and m of G = 90 degrees. Which of the following statements about tria

Effectus [21]

Answer:

A. EG = √3 × FG

D. EG = √3/2 × EF

E. EF = 2 × FG

Step-by-step explanation:

∵ tan 60 = √3

∵ tan60 = EG/GF

∴ EG/GF = √3

∴ EG = √3 × GF ⇒ A

∵ m∠F = 60°

∵ sin60 = √3/2

∵ sin 60 = EG/EF

∴ √3/2 = EG/EF

∴ EG = √3/2 × EF ⇒ D

∵ cos60 = 1/2

∵ cos60 = GF/EF

∴ GF/EF = 1/2

∴ EF = 2 × GF ⇒ E

8 0

3 years ago

Read 2 more answers

Every day your friend commutes to school on the subway at 9 AM. If the subway is on time, she will stop for a $3 coffee on the w

Shtirlitz [24]

Answer:

1.02% probability of spending 0 dollars on coffee over the course of a five day week

7.68% probability of spending 3 dollars on coffee over the course of a five day week

23.04% probability of spending 6 dollars on coffee over the course of a five day week

34.56% probability of spending 9 dollars on coffee over the course of a five day week

25.92% probability of spending 12 dollars on coffee over the course of a five day week

7.78% probability of spending 12 dollars on coffee over the course of a five day week

Step-by-step explanation:

For each day, there are only two possible outcomes. Either the subway is on time, or it is not. Each day, the probability of the train being on time is independent from other days. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

The probability that the subway is delayed is 40%. 100-40 = 60% of the train being on time, so $p = 0.6$

The week has 5 days, so $n = 5$

She spends 3 dollars on coffee each day the train is on time.

Probabability that she spends 0 dollars on coffee:

This is the probability of the train being late all 5 days, so it is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102$

1.02% probability of spending 0 dollars on coffee over the course of a five day week

Probabability that she spends 3 dollars on coffee:

This is the probability of the train being late for 4 days and on time for 1, so it is P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768$

7.68% probability of spending 3 dollars on coffee over the course of a five day week

Probabability that she spends 6 dollars on coffee:

This is the probability of the train being late for 3 days and on time for 2, so it is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304$

23.04% probability of spending 6 dollars on coffee over the course of a five day week

Probabability that she spends 9 dollars on coffee:

This is the probability of the train being late for 2 days and on time for 3, so it is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{5,3}.(0.6)^{3}.(0.4)^{2} = 0.3456$

34.56% probability of spending 9 dollars on coffee over the course of a five day week

Probabability that she spends 12 dollars on coffee:

This is the probability of the train being late for 1 day and on time for 4, so it is P(X = 4).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592$

25.92% probability of spending 12 dollars on coffee over the course of a five day week

Probabability that she spends 15 dollars on coffee:

Probability that the subway is on time all days of the week, so $P(X = 5)$ .

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{5,5}.(0.6)^{5}.(0.4)^{0} = 0.0778$

7.78% probability of spending 12 dollars on coffee over the course of a five day week

8 0

4 years ago