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3 years ago

Given a≠±b and a^2−b^2 / a+b =12, find a−b. pls hlep

Mathematics

1 answer:

Readme [11.4K]3 years ago

7 0

Answer:

a - b = 12

Step-by-step explanation:

Given

$\frac{a^2-b^2}{a+b}$ = 12 ← factor the numerator

a² - b² ← is a difference of squares and factors as

a² - b² = (a - b)(a + b)

Thus

$\frac{(a-b)(a+b)}{a+b}$ = 12

Cancel the common factor (a + b) on numerator/ denominator, thus

a - b = 12

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In a spreadsheet, you can use the function NORM.DIST(upper bound, μ, σ, TRUE) to find the area under a normal curve for values o

Mars2501 [29]

Given Information:

Mean height of children = μ = 41 inches

Standard deviation of height of children = σ = 4 inches

Required Information:

Using Excel find P(x > 34) = ?

Answer:

P(x > 34) = 95.99%

Explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

The Microsoft Excel has a built-in function "NORMDIST" which calculates the probability of a normal distribution.

Syntax:

NORMDIST(x, mean, standard deviation, cumulative flag)

Where x is the variable of interest

Cumulative flag = TRUE or FALSE

The probability that a randomly chosen child is greater than 34 inches tall is given by

P(x > 34) = 1 - P(x < 34)

Using MS Excel,

P(x > 34) = 1 - NORM.DIST(34,41,4,TRUE)

Which return the probability of

P(x > 34) = 1 - 0.040059

P(x > 34) = 0.959941

P(x > 34) = 95.99%

Therefore, there is 95.99% probability that a randomly chosen child is greater than 34 inches tall.

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3 years ago

A landscape business charges $50 to deliver rocks. The cost of the rocks are $27 per cubic yard. write and solve a linear equati

Nuetrik [128]

<h2>Answer: 27x + 50 = y, $266</h2>

Step-by-step explanation:

First, let's form a linear equation that will help us find out how much that will cost.

Let's set x = the cubic yards of rocks delivered and y = total cost.

First, we know that the business charges 27 dollars for every x that you buy. That can be shown with a multiplication expression:

27x

Next, we know that the business charges a fixed fee of $50 for their services. This fee would be <em>added on</em> to the amount that they charge for the rocks that you buy.

That's our linear expression! Next, we need to find out the <em>total cost</em>, y, when you need 8 cubic yards of rocks delivered, x.

To solve this, we need to substitute values for at least one of our variables.

Since 8 describes the cubic yards of rocks delivered, we can substitute 8 for x.

But we don't know y, the total cost- that's what we're solving for! In other words, we're solving for y.

Let's just substitute in what we know:

27(8) + 50 = y.

216 + 50 = y

So, we know that it would cost $266 dollars to have 8 cubic yards of rocks delivered to a site.

By the way, you can also graph your linear equation to find the corresponding y-value to 8 as another way to solve your problem.

7 0

3 years ago

Follow the process of completing the square to solve x^2 - 10x + 8 = 0. What is the value of the constant that will be isolated

My name is Ann [436]

To solve using completing square method we proceed as follows:
x^2-10x+8=0
x^2-10x=-8
but
c=(b/2)^2
c=(10/2)^2=25
thus we can add this in our expression to get
x^2-10x+25=8+25
factorizing the LHS we get:
(x-5)(x-5)=33
(x-5)^2=33
getting the square roots of both sides we have:
x-5=+/-√33
x=5+/-√33

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3 years ago

Read 2 more answers

The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls. Nationwide, th

TiliK225 [7]

Answer: in order to qualify, the time must be at least 15.93 minutes

Step-by-step explanation:

Let x be a random variable representing the average response times of fire departments to fire calls. Since it follows a normal distribution, we will determine the z score by applying the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

From the information given,

µ = 12.8 minutes

σ = 3.7 minutes

in order to qualify for the special safety award, the probability value would be to the right of the z score corresponding to 80%

The z score corresponding to 80% on the normal distribution table is 0.845

Therefore,

0.845 = (x - 12.8)/3.7

0.845 × 3.7 = x - 12.8

3.13 = x - 12.8

x = 12.8 + 3.13 = 15.93

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3 years ago

Justine had 88 dolphin stickers. She gave 4 stickers each to 6 friends. How many stickers does Justine have left?

MatroZZZ [7]

Answer:64

Step-by-step explanation:

4×6=24

88-24=64

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3 years ago