Find the length of the shorter leg of a right triangle if the longer leg is 7 feet more than the shorter leg and the hypotenuse is 7 feet less than twice the shorter leg.

1/5(15x-20) = 1/3(12x-9)

multiply the 15 and 20 on the left by 1/5 to get

3x-4

 now multiply 12 and 9 by 1/3 to get

4x-3

 now you have 3x-4 =4x-3

now solve for x

3x-4 =4x-3

subtract 3 x from each side:

-4 = x-3

 add 3 to each side

-1 = x

x = -1

The scale factor between the numbers (3, 6) and (4.5, 9) is 2, since the second number in each pair is twice as large as the first number.

The scale factor is a ratio that describes how to enlarge or reduce the dimensions of an object to create a new object that is similar to the original. To figure out the scale factor between two similar figures, we calculate the ratio of any two corresponding lengths in the figures.

As per the student's question:

In each case, the corresponding lengths in the second object are twice those in the first, meaning you can multiply the dimensions of the first figure by 2 to get the dimensions of the second figure.

divide 72.9 by 2.7

72.9 / 2.7 = 27 miles per gallon

Answer:

27 mi/gal

Step-by-step explanation:

The car mileage refers to the number of miles that a vehicle can run per gallon of fuel. A higher car mileage is desirable because it means that the vehicle has a better performance (travels more distance per gallon of fuel.) A driver uses 2.7 gallons of gasoline to drive her car 72.9 miles. The car mileage is:

72.9 miles / 2.7 gallon = 27 miles/gallon

The car can travel 27 miles per gallon of gasoline.

Answer:

The triangle is obtuse triangle.

Step-by-step explanation:

Given two angles of triangle labelled as 22° and 63°. we have to classify the triangle.

Let the third angle be x°

By angle sum property of triangle,

22°+63°+x=180°

⇒ 85°+x=180° ⇒ x=95°

An equiangular triangle is a triangle where all interior angles are equal.          

An obtuse triangle is a triangle in which one of the angles is obtuse angle.

An acute triangle is a triangle have all three angles acute.

For right triangle one angle must be of 90°.

Hence, one angle of the triangle is 95° which is obtuse i.e greater than 90°

∴ Given triangle is obtuse.

To find the length (l) of a rectangle in terms of the perimeter (p) and width (w), use the formula l = (p - 2w) / 2.

To find the length (l) of a rectangle in terms of the perimeter (p) and width (w), we can use the formula for the perimeter of a rectangle, which is given by:

p = 2l + 2w

Now, solve the equation for l by subtracting 2w from both sides:

p - 2w = 2l

Finally, divide both sides by 2:

l = (p - 2w) / 2

82 thousands can be renamed as 8 ten thousands and 2 thousands, or as 0.082 hundred thousands in the decimal system.

Renaming 82 thousands means expressing this amount in another unit of place value. In the standard decimal system, the next unit larger than thousands is ten thousands. The digit in the ten thousands place represents the number of ten thousands in that number. If you have 82 thousands, this equals 8 ten thousands and 2 thousands, because 82 divided by 10 equals 8 with a remainder of 2. Therefore, 82 thousands can be renamed as 8 ten thousands and 2 thousands. Similarly, 82 thousands can also be expressed as 0.082 hundred thousands, as 82 divided by 1000 equals 0.082.

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Probability of an event is the measure of its chance of occurrence. The probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

For the given case, as failing or working of chips usually doesn't depend on other chips' working condition, so they're independent(assuming). There are two cases for each chip's working(random experiment) that it is either working or failed.

If we take Success of the considered binomial experiment(working status of chip) = Chip working fine

Then, as per given data, we have

P(chip working fine ) = 1  - P(chip not working) = 1 - 0.02 = 0.98 = Probability of success in Bernoulli experiment (chip's working status).

There are n = 5 chips, p = probability of success = 0.98, q = 1-p = 0.02

If we take X = number of chips of of 5 chips working, then:

[tex]X \sim B(n = 5, p = 0.98)[/tex]

Then, the needed probability is P(Exactly two chips fail) = P(Exactly 5-2 = 3 chips work) = P(X  = 3)

And thus,  the needed probability is calculated as:

[tex]P(X = 3) = \: ^5C_3(0.98)^3(0.02)^2 = \dfrac{5.4.3}{3.2.1} \times 0.941192 \times 0.0004 = 0.003764768[/tex]

(using the probability mass function of binomial distribution).

Thus, the probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004

Learn more about binomial distribution here:

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Answer:

50,000,000,000.

Step-by-step explanation:

It wouldn't be 5,000,000,000 or 500,000,000,000 or 0.000 000 000 5.