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4 years ago

A Mathematics competition consists of 30 multiple-choice questions. A

Mathematics

1 answer:

harkovskaia [24]4 years ago

3 0

Answer:

Step-by-step explanation:

let "x" be the number of correct questions and 37-x be the wrong questions,

4x-1(37-x)=44

4x-37+x=44

5x=81

x=16.2

hence,16 is the answer

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Lina has 12 coins in her purse. D of them are dimes and the rest are quarters.

tester [92]

Answer:

we need more info but 11 q and 1 dime or 12 q and 0 dime

Step-by-step explanation:

Sorry need more info

7 0

4 years ago

(2x + 7y = -24 18x+y=12 solve by substitution

const2013 [10]

Answer:

x = .87, or when approximated to a fraction, 27/31

y = -3.67, or when approximated to a fraction, -1287/350

Step-by-step explanation:

Lets start by rewriting out our equations

2x + 7y = -24

18x + y = 12

Lets solve for a y value; the second equation is easiest, as the y value has no coefficient (the number that is multiplied times a variable). To do this, lets move the 18x to the other side. Now our two equations look like:

2x + 7y = -24

y = -18x + 12

Next, lets plus the second equation into the first equation in regards to y.

2x + 7(-18x + 12) = -24

Now, lets solve!

2x -126x + 84 = -24

Then, combine your terms!

-124x = -108

Divide by (-124)!

x = -108/-124

x = 27/31

Now that we know x, lets plug this back in to the first equation to find y!

2(27/31) + 7y = -24

1.74 + 7y = -24

7y = -25.74

y = -3.67, or when approximated to a fraction, -1287/350

4 0

4 years ago

Jillian measured the distance around a small fish pond as 27 yards. Which would be a good estimate for the distance across the p

DochEvi [55]

Assuming the fish pond is round, what you're given is the circumference.
So you know that 2πr = 27.
We want to solve for the diameter, or d = 2r. We should isolate that.
2r = 27/π
2r = 8.59 yards, or ~9 yards.

3 0

3 years ago

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.08

kvv77 [185]

Answer:

a) 44.93% probability that there are no surface flaws in an auto's interior

b) 0.03% probability that none of the 10 cars has any surface flaws

c) 0.44% probability that at most 1 car has any surface flaws

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the binomial probability distributions.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Binomial 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.

Poisson distribution with a mean of 0.08 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

So $\mu = 10*0.08 = 0.8$

(a) What is the probability that there are no surface flaws in an auto's interior?

Single car, so Poisson distribution. This is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.8}*(0.8)^{0}}{(0)!} = 0.4493$

44.93% probability that there are no surface flaws in an auto's interior

(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?

For each car, there is a $p = 0.4493$ probability of having no surface flaws. 10 cars, so n = 10. This is P(X = 10), binomial, since there are multiple cars and each of them has the same probability of not having a surface defect.