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3 years ago

What is the solution of x=2+\sqrt(x-2) x = 2 x = 3 x = 2 or x = 3 no solution

2 answers:

5 0

$D:x\geq2\\\\
x=2+\sqrt{x-2}\\
\sqrt{x-2}=x-2\\
x-2=x^2-4x+4\\
x^2-5x+6=0\\
x^2+x-6x+6=0\\
x^2-2x-3x+6=0\\
x(x-2)-3(x-2)=0\\
(x-3)(x-2)=0\\
x=3 \vee x=2$

natta225 [31]3 years ago

4 0

Answer:

The solution is x = 2 or x = 3

Step-by-step explanation:

we have to find the solution of the equation

$x=2+\sqrt{(x-2)}$

$x=2+\sqrt{(x-2)}\\ \\x-2=\sqrt{x-2}\\\\\text{Squaring on both sides }\\\\(x-2)^2=x-2\\\\x^2+4-4x=x-2\\\\x^2-5x+6=0\\\\x^2-2x-3x+6=0\\\\x(x-2)-3(x-2)=0\\\\(x-2)(x-3)=0\\\\x=2\text{ or }x=3$

Hence, correct option is x = 2 or x = 3

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n a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of inches and a stand

kotykmax [81]

Answer:

(a) The probability that a study participant has a height that is less than 67 inches is 0.4013.

(b) The probability that a study participant has a height that is between 67 and 71 inches is 0.5586.

(c) The probability that a study participant has a height that is more than 71 inches is 0.0401.

(d) The event in part (c) is an unusual event.

Step-by-step explanation:

The complete question is: In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 71 inches. The probability that the study participant selected at random is between and inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

We are given that the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.

Let X = the heights of men in the 20-29 age group

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean height = 67.5 inches

$\sigma$ = standard deviation = 2 inches

So, X ~ Normal( $\mu=67.5, \sigma^{2}=2^{2}$ )

(a) The probability that a study participant has a height that is less than 67 inches is given by = P(X < 67 inches)

P(X < 67 inches) = P( $\frac{X-\mu}{\sigma}$ < $\frac{67-67.5}{2}$ ) = P(Z < -0.25) = 1 - P(Z $\leq$ 0.25)

= 1 - 0.5987 = 0.4013

The above probability is calculated by looking at the value of x = 0.25 in the z table which has an area of 0.5987.

(b) The probability that a study participant has a height that is between 67 and 71 inches is given by = P(67 inches < X < 71 inches)

P(67 inches < X < 71 inches) = P(X < 71 inches) - P(X $\leq$ 67 inches)

P(X < 71 inches) = P( $\frac{X-\mu}{\sigma}$ < $\frac{71-67.5}{2}$ ) = P(Z < 1.75) = 0.9599

P(X $\leq$ 67 inches) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{67-67.5}{2}$ ) = P(Z $\leq$ -0.25) = 1 - P(Z < 0.25)

= 1 - 0.5987 = 0.4013

The above probability is calculated by looking at the value of x = 1.75 and x = 0.25 in the z table which has an area of 0.9599 and 0.5987 respectively.

Therefore, P(67 inches < X < 71 inches) = 0.9599 - 0.4013 = 0.5586.

(c) The probability that a study participant has a height that is more than 71 inches is given by = P(X > 71 inches)

P(X > 71 inches) = P( $\frac{X-\mu}{\sigma}$ > $\frac{71-67.5}{2}$ ) = P(Z > 1.75) = 1 - P(Z $\leq$ 1.75)

= 1 - 0.9599 = 0.0401

The above probability is calculated by looking at the value of x = 1.75 in the z table which has an area of 0.9599.

(d) The event in part (c) is an unusual event because the probability that a study participant has a height that is more than 71 inches is less than 0.05.

7 0

3 years ago

Antonbought a picnic cooler his total bill with tax was $7.95 he paid 6% sales tax how much did he pay for the cooler alone with

guapka [62]

A product increases its value because of the imposition of tax. For example, a medicine that cost $1 can be bought possibly at $1.4 because of the value added tax. To determine the original bill without tax, the equation is $7.95/1.06. This is equal to $7.5.

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3 years ago

What is the value of y? Enter your answer, as an exact value, in the box.

OLga [1]

We know the bottom triangle is a 45, 45, 90 triangle, so the hypotenuse is √2 times the value of the legs:

(√2)(√2)
=√4
=2

Now, we can use this to solve for y. The top triangle is a 30, 60, 90 triangle. The side we found above is the side across from the 30 degree angle. The side opposite the 60 degree angle is √3 times the side across the 30 degree angle. Therefore, we can solve for y by multiplying 2 by √3

y=2√3

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4 years ago

4th grade math question Joey walk 333 ft how many yards did Joey walk? At 5 yds vs 15 ft

icang [17]

111 yards

Explanation

Step 1

to solve this we need to know the equivalence

$\begin{gathered} 3\text{ ft= 1 yd} \\ 3\text{ ft}\leftrightarrow1\text{ yd} \end{gathered}$

Now, we can apply a rule of three

let x represents the number of yards in 333 ft, so

$\begin{gathered} if \\ 3\text{ ft}\rightarrow\text{ 1 yd} \\ \text{then} \\ 33\text{ ft}\rightarrow x \end{gathered}$

as the ratio is the same, we have a proportion

$\begin{gathered} \frac{3\text{ ft}}{1\text{ yd}}=\frac{33\text{ ft}}{x\text{ yd}} \\ \frac{3}{1}=\frac{33}{x} \end{gathered}$

Step 2

now, solve for x

$\begin{gathered} \frac{3}{1}=\frac{333}{x} \\ \text{cross multiply} \\ 3\cdot x=333\cdot1 \\ 3x=333 \\ \text{divide both } \\ \frac{3x}{3}=\frac{333}{3} \\ x=111 \end{gathered}$

so, the answer is 111 yards

I hope this helps you

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1 year ago

Use the substitution method to solve this system of linear equations y-2x=6 x=7

-Dominant- [34]

Answer:

x≈1.166666667

y≈9.333333333

Step-by-step explanation:

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3 years ago