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3 years ago

What is 1/6 + 2/12 + 1/3 + 3/4 + 1/2 = ?

Mathematics

1 answer:

matrenka [14]3 years ago

7 0

Answer:

$\frac{19}{12}$

Step-by-step explanation:

$\frac{1}{6} + \frac{2}{12} + \frac{3}{4} + \frac{1}{2}$

$\frac{2}{12} + \frac{2}{12} + \frac{9}{12} + \frac{6}{12}$

$\frac{19}{12}$

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What is the area of a circle whose equation is (x-3)² + (y + 1) ² =81?

kupik [55]

Okay, first, given the equation, we need to find out what the radius of the circle is. Let us state the general equation of a circle:

$\frac{(x-x_{1})^2}{r^2}+ \frac{(y-y_{1})_^2}{r^2}=1$

Where $(x_{1}, y_{1})$ is the centre of the circle. In this case, we don't need to know the centre. Just the radius.

Let us start by converting the equation into standard for, which I typed above. Divide both sides by 81.

$\frac{(x-3)^2}{81}+ \frac{(y+1)^2}{81}=1$

Great! We now know the radius of the circle. It is $\sqrt{81}$ because it is the bottom fraction. Now we know that the radius is 9.

So now lets input this into the area of circle formula:

$A=πr^2$

Now we insert our radius.

$A=9^2π$

$=A=81π$

You can convert that into a decimal if you wish.

Hope this helped!

~Cam943, Moderator

4 0

3 years ago

Classify the following triangle. Check all that apply.

Arlecino [84]

Scalene,Acute i think it is haha

5 0

3 years ago

Read 2 more answers

There are 40 nickels in a roll. If you have 250 rolls of nickels, how many nickels do you have?pls help me

gayaneshka [121]

Answer:

10,000 nickles

Step-by-step explanation:

Since there are 40 nickles in a roll and you have 250, think that you have 250 sets of 40. This means that this question is a multiplication problem.

Multiply 40 x 250. This would give you 10,000.

Don't forget units.

7 0

3 years ago

Read 2 more answers

Assume that there is a 4% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive wit

kap26 [50]

Answer:

a) 99.84% probability that during a year, you can avoid catastrophe with at least one working drive

b) 99.999744% probability that during a year, you can avoid catastrophe with at least one working drive

Step-by-step explanation:

For each disk drive, there are only two possible outcomes. Either it works, or it does not. The disks are independent. So we use the binomial probability distribution to solve this question.

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.

4% rate of disk drive failure in a year.

This means that 96% work correctly, $p = 0.96$

a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

This is $P(X \ geq 1)$ when $n = 2$

We know that either none of the disks work, or at least one does. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . So

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{2,0}.(0.96)^{0}.(0.04)^{2} = 0.0016$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0016 = 0.9984$

99.84% probability that during a year, you can avoid catastrophe with at least one working drive

b. If copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

This is $P(X \ geq 1)$ when $n = 4$

We know that either none of the disks work, or at least one does. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . So

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{4,0}.(0.96)^{0}.(0.04)^{4} = 0.00000256$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.00000256 = 0.99999744$

99.999744% probability that during a year, you can avoid catastrophe with at least one working drive

7 0

3 years ago

Triangles O N M and S R Q are shown. Angles O N M and S R Q are congruent. The length of side N M is 10 and the length of side S

valina [46]

Answer:

Option C.

Step-by-step explanation:

In △ONM and △SRQ,

$\angle ONM\cong \angle SRQ$

$NM=10$

$SR=20$

$NO=8$

$QR=x$

We need to find the value of x that will make △ONM similar to △SRQ by the SAS similarity theorem.

According to SAS similarity theorem, two triangle are similar if two corresponding sides in both triangles are proportional and the included angle in both are congruent.

It is given that $\angle ONM\cong \angle SRQ$ . So, both triangles are similar by SAS if

$\dfrac{NO}{NM}=\dfrac{SR}{QR}$