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2 years ago

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The shortest leg of a right triangle is 27 units. The other leg is the solution to 2x – 5 = 67. What is the length of the hypote

nuse? Show all work.
(HINT: First solve for x. Now you know the lengths of the two legs of the triangle. Use the Pythagorean Theorem to now find the length of the hypotenuse!)
Please answer in 15 minutes or less...I'll give brainliest too

1 answer:

Ratling [72]2 years ago

3 0

Answer:45

Step-by-step explanation:

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A machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%). Prior to shipm

AURORKA [14]

Answer:

(a) 0.0686

(b) 0.9984

(c) 0.0016

Step-by-step explanation:

Given that a machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%).

Let A, B, and C be the events of defect-free, slightly defective, and the defective parts produced by the machine.

So, from the given data:

P(A)=0.90, P(B)=0.03, and P(C)=0.07.

Let E be the event that the part is disregarded by the inspection machine.

As a part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input.

So, $P\left(\frac{E}{A}\right)=0.02$

Now, from the conditional probability,

$P\left(\frac{E}{A}\right)=\frac{P(E\cap A)}{P(A)}$

$\Rightarrow P(E\cap A)=P\left(\frac{E}{A}\right)\times P(A)$

$\Rightarrow P(E\cap A)=0.02\times 0.90=0.018\cdots(i)$

This is the probability of disregarding the defect-free parts by inspection machine.

Similarly,

$P\left(\frac{E}{A}\right)=0.40$

and $\Rightarrow P(E\cap B)=0.40\times 0.03=0.012\cdots(ii)$

This is the probability of disregarding the partially defective parts by inspection machine.

$P\left(\frac{E}{A}\right)=0.98$

and $\Rightarrow P(E\cap C)=0.98\times 0.07=0.0686\cdots(iii)$

This is the probability of disregarding the defective parts by inspection machine.

(a) The total probability that a part is marked as defective and discarded by the automatic inspection machine

$=P(E\cap C)$

$= 0.0686$ [from equation (iii)]

(b) The total probability that the parts produced get disregarded by the inspection machine,

$P(E)=P(E\cap A)+P(E\cap B)+P(E\cap C)$

$\Rightarrow P(E)=0.018+0.012+0.0686$

$\Rightarrow P(E)=0.0986$

So, the total probability that the part produced get shipped

$=1-P(E)=1-0.0986=0.9014$

The probability that the part is good (either defect free or slightly defective)

$=\left(P(A)-P(E\cap A)\right)+\left(P(B)-P(E\cap B)\right)$

$=(0.9-0.018)+(0.03-0.012)$

$=0.9$

So, the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped

$=\frac{\text{Probabilily that shipped part is 'good'}}{\text{Probability of total shipped parts}}$

$=\frac{0.9}{0.9014}$

$=0.9984$

(c) The probability that the 'bad' (defective} parts get shipped

=1- the probability that the 'good' parts get shipped

=1-0.9984

=0.0016

5 0

2 years ago

Eva had 7/8 gallon of paint. His brother ivan used 1/4 gallon to paint his model boat. Eva needs at least 1/2 gallon to paint he

algol13

Answer: .625 (yes he did leave enough

Step-by-step explanation: First you need to divde the fractions( or solve them) ,so 7 divided by 8 and so on Then you take subtract the paint ivan used, if it is less than half than ivan didn't leave enough for his poor sister

but there are other ways if this one is to hard

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2 years ago

Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of t

Oksi-84 [34.3K]

Y - 12% of y + 3% of y = final cost

may be wrong, havnt done math in a good while

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2 years ago

The functions f(x) and g(x) are described using the following equation and table: f(x) = −2(1.07)x x g(x) −4 −10 −2 −7 0 −4 2 1

Natali [406]

Answer:

The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).

Step-by-step explanation:

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2 years ago

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Noor wants to spend less than $20 on condiments. Each kilogram of salt costs $1.50, and each kilogram of pepper costs 2.50.

nata0808 [166]

Answer:

1.5s+2.5p<20

Step-by-step explanation:

Multiply by each kilo and then make sure it adds up to less than 20!

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2 years ago