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3 years ago

The central angle of a circle measures 108 degrees and intercepts an arc of 6pi inches.

1 answer:

8 0

An arc is a part of the circumference of a circle and the angles that subtend the arcs are proportional to the length of the arc.

So, you basically have two arcs to compare: a 10cm arc and a 60cm arc. But the 60cm arc also happens to be the circumference in this case, so you know that the angle that subtends that arc is 360 degrees (the whole circle). The 10cm arc is 1/6 of the whole circumference so the angle is going to be 1/6 of 360 degrees, which is <span>60 degrees.</span>

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use the explicit formula an = a1 + (n - 1) * d to find the 500th term of the sequence below. 24,30,36,42,48,... A. 3018 B. 3042

marishachu [46]

Answer:

Option A.

Step-by-step explanation:

The given sequence is

24, 30, 36, 42, 48, ...

It is an AP. Here,

First term = 24

Common difference = 30-24 = 6

The given explicit formula for nth term is

$a_n=a_1+(n-1)d$

where, $a_1$ is first term, d is common difference.

Substitute $a_1=24, d=6 \text{ and }n=500$ in the above formula.

$a_{500}=24+(500-1)(6)$

$a_{500}=24+(499)(6)$

$a_{500}=24+2994$

$a_{500}=3018$

The 500th term of the sequence is 3018.

Therefore, the correct option is A.

3 0

3 years ago

An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What

galina1969 [7]

Answer:

Part A:

The probability that all of the balls selected are white:

$P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576$

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

$P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516$

Step-by-step explanation:

A is the event all balls are white.

D_i is the dice outcome.

Sine the die is fair:

$P(D_i)=\frac{1}{6}$ for i∈{1,2,3,4,5,6}

In case of 10 black and 5 white balls:

$P(A|D_1)=\frac{5_{C}_1}{15_{C}_1} =\frac{5}{15}=\frac{1}{3}$

$P(A|D_2)=\frac{5_{C}_2}{15_{C}_2} =\frac{10}{105}=\frac{2}{21}$

$P(A|D_3)=\frac{5_{C}_3}{15_{C}_3} =\frac{10}{455}=\frac{2}{91}$

$P(A|D_4)=\frac{5_{C}_4}{15_{C}_4} =\frac{5}{1365}=\frac{1}{273}$

$P(A|D_5)=\frac{5_{C}_5}{15_{C}_5} =\frac{1}{3003}=\frac{1}{3003}$

$P(A|D_6)=\frac{5_{C}_6}{15_{C}_6} =0$

Part A:

The probability that all of the balls selected are white:

$P(A)=\sum^6_{i=1} P(A|D_i)P(D_i)$

$P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576$

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

We have to find $P(D_3|A)$

The data required is calculated above:

$P(D_3|A)=\frac{P(A|D_3)P(D_3)}{P(A)}\\ P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516$

7 0

3 years ago

PLEASE HELP!!

IRISSAK [1]

Step-by-step explanation:

$a + b = 6$

$ab = 1 \times 5 = 5$

$a = 1 \: \: \: \: \: \: \: \: b = 5$

$( {x}^{2} + x) + (5x + 5)$

$x(x + 1) + 5(x + 1)$

$(x + 1)(x + 5)$

Hope this is correct and helpful

HAVE A GOOD DAY!

8 0

3 years ago

How to find the rate of change over an interval when given a graph

inn [45]

Answer:

(y2-y1)/(x2-x1)

Step-by-step explanation:

Using two coordinates, you can just plug in the corresponding (x,y) coordinates and you will get the slope, which is the rate of change over an interval

6 0

3 years ago

Add (11x + 2) + (9x - 4)

Alborosie

Answer: 2 • (10x - 1) <span>

I hope this helps;)</span>

8 0

3 years ago