HELP!!

What are extraneous solutions to rational and radical equations? How do they arise? How do we check if a solution is extraneous? Use these equations as examples to help you explain:

Answer:

0% probability that the mean of the sample taken is less than 2.2 feet.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 2.5 feet and a standard deviation of 0.2 feet.

This means that [tex]\mu = 2.5, \sigma = 0.2[/tex]

Sample of 41

This means that [tex]n = 41, s = \frac{0.2}{\sqrt{41}}[/tex]

Find the probability that the mean of the sample taken is less than 2.2 feet.

This is the p-value of Z when X = 2.2 So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}[/tex]

[tex]Z = -9.6[/tex]

[tex]Z = -9.6[/tex] has a p-value of 0.

0% probability that the mean of the sample taken is less than 2.2 feet.

Answer:

y = 189.8

Step-by-step explanation:

Apply trigonometric function to find y.

Reference angle (θ) = 50°

Adjacent side = 122

Hypotenuse = y

Apply CAH, since the Hypotenuse and the Adjacent are involved.

Thus:

Cos θ = Adj/Hypo

Plug in the values

Cos 50° = 122/y

y*Cos 50° = 122

y = 122/cos 50°

y = 189.8 (beater tenth)

Answer:

0.2&4

Step-by-step explanation:

There are 60 minutes in one hour, so 12 divided by 60 is the answer.

0.2   kilometers * 20 = 4

Answer:

l=5, w=1

Step-by-step explanation:

5*1=5 for area

5+1+5+1=12 for perimeter

Answer:

Kaylee must leave the money in the savings account for 3 years.

Step-by-step explanation:

Given that Kaylee wants to buy a car that costs $ 17,360, and she deposits $ 14,000 in a savings account that earns 8% simple interest, to determine how long was Kaylee leave the money in the savings account to be able to buy the car must be made the following calculation:

14,000 + (14,000 x 0.08 x X) = 17360

1,120X = 17,360 - 14,000

X = 3,360 / 1,120

X = 3

Therefore, Kaylee must leave the money in the savings account for 3 years.

Hey there!

y + 3 = 30

SUBTRACT 3 to BOTH SIDES

y + 3 - 3 = 30 - 3

CANCEL out: 3 - 3 because that gives you 0

KEEP: 30 - 3 because that gives you the value of y

y = 30 - 3

30 - 3 = y

y = 27

Answer: y = 27

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Conjecture :  2xy / ( x + y ) ≤  √xy

Step-by-step explanation:

Harmonic mean of  x and y = 2xy/( x + y )

Formulate a conjecture about their relative sizes

we will achieve this by computing harmonic and geometric means

Geometric mean = √xy

harmonic mean = 2xy/( x + y )

Conjecture :  2xy / ( x + y ) ≤  √xy

attached below is the proof

Answer:

See the answers below

Step-by-step explanation:

Name two characteristics of the Fibonacci Series that you observed. ​

If we take a closer look at the Fibonacci series, we will notice the following characteristics

1.The next number is the sum of the two preceding numbers

2. Another interesting characteristic is evidenced in the convergence of the sequence

Answer: Regression with sales as the dependent variable

Step-by-step explanation:

Since the franchise company wanted to determine why sales were higher at some locations rather than others, the statistical process that would be most appropriate is regression with sales as the dependent variable.

Regression will be used in determining the strength of the relationship that exist between one dependent variable and the independent variables. In this case, the dependent variable is sales.

The values of variables, such as the height of the table can be found by writing equations of their relationships

The height of the table is 105 cm

The reason the above height value is correct is as follows;

Known parameters:

The diagram shows a table, a cat and a mice

Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice

From the given diagram, we have;

Height of the table + Height of the cat - Height of the mice  = 120 cm

∴ x + y - z = 120...(1)

Height of the table + Height of the mice - Height of the cat   = 90 cm

∴ x + z - y = 90...(2)

Adding equation (1) to equation (2) gives;

x + y - z + (x + z - y) = 120 + 90 = 210

x + y - z + (x + z - y) = 210

However;

x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x

∴ x + y - z + (x + z - y) = 2·x = 210

x = 210/2 = 105

Therefore;

The height of the table, x = 105 cm

Learn more about word problems leading on simultaneous equations here:

https://brainly.com/question/16513646

Hi there!  

»»————-　★　————-««

I believe your answer is:  

4

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻  

[tex]\boxed{\text{Calculating the Answer...}}\\\\8^{\frac{2}{3}}\\-----------\\\text{Recall the Exponent Rule: }} a^{\frac{b}{c}} = \sqrt[c]{a^b}\\\\\rightarrow {\frac{\text{Power}}{\text{Root Index}}\\\\[/tex]

[tex]-----------[/tex]

[tex]\rightarrow 8^{\frac{2}{3}}\\\\\rightarrow \sqrt[3]{(8^2)}\\\\\rightarrow\sqrt[3]{64}\\\\\rightarrow \boxed{4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

4

Step-by-step explanation:

[tex]8^{\frac{2}{3} }[/tex]

=[tex](2)^3*\frac{2}{3}[/tex]

=[tex](2)^\frac{3*2}{2}[/tex]

=[tex](2)^\frac{6}{3}[/tex]

=[tex]2^2[/tex]

=4

Answer:

a. ∆EGF ≅ ∆EGD

Step-by-step explanation:

Congruent triangles would have the same side lengths and the same measure of angles.

From the figure given:

EG in ∆EGF ≅ EG in ∆EGD

GF in ∆EGF ≅ GD in ∆EGD, also

EF ≅ ED.

The three angles in ∆EFG are also congruent to the three angles in ∆EGD.

Therefore, ∆EGD is congruent to ∆EGF.

∆EGF ≅ ∆EGD

Answer:

4.53

Step-by-step explanation:

Given the data :

4, 5, 10, 11, 15

The mean = 9

The standard deviation of a sample :

s = √[Σ(x - mean)²/(n-1)]

s = √[((4-9)² + (5-9)²+(10-9)² + (11-9)² + (15-9)²) / (5-1)]

s = √(25+16+1+4+36)/4

s = √20.5

s = 4.527

s = 4.53

Answer:

4.5

Step-by-step explanation:

5.1.3

this is an example of linear equations is one variable

Answer:

[tex]P(x\geq 1) = 0.923[/tex]

Step-by-step explanation:

From the question we are told that:

Percentage of student to get A [tex]P(A)=\%5=0.05[/tex]

Sample size [tex]n=50[/tex]

Generally Number of student to get A is

[tex]N_a=n*P(A)[/tex]

[tex]N_a=50*0.05[/tex]

[tex]N_a=2.5[/tex]

Therefore

Probability that one student gets an A grade is mathematically by

  [tex]^nPC_xP^x(1-P)^{n-x}[/tex]

 [tex]P(x\geq 1)=1-P(x<1)[/tex]

 [tex]P(x\geq 1) =1-P(x=0)[/tex]

 [tex]P(x\geq 1) =^50C_0(0.05)^0(0.95)^50[/tex]

 [tex]P(x\geq 1) = 0.923[/tex]

Answer:

2a.

Step-by-step explanation:

6 = 2 * 3

8 = 2 * 2 * 2   - 2 is common to both sets of factors.

So the GCF of 6 and 8 is 2.

For the 2 a's it is a.

Answer:

observational study

Step-by-step explanation:

Answer:

Y=x

Step-by-step explanation:

The y and x values are the same

Answer:

y = x

Step-by-step explanation:

a 45° line with the origin passing through the origin has the equation y=x.

Have a nice day.

Answer:

y = (8+x)^5 + C

Step-by-step explanation:

Given the differential equation

(8+x) dy/dx = 5y

Using the variable separable method

(8+x) dy = 5ydx

dx/8+x = dy/5y

Integrate both sides

[tex]\int\limits^ {} \, \frac{dx}{8+x} = \int\limits^ {} \, \frac{dy}{5y} \\ln(8+x) = \frac{1}{5}lny\\5ln(8+x)= lny\\ln(8+x)^5 = lny\\ (8+x)^5 = y\\Swap\\y = (8+x)^5 + C[/tex]

This gives the required solution

The explicit general solution to the following differential equation[tex](8+x)\dfrac{dy}{dx} = 5y[/tex]  is [tex](8+x)^5 +C[/tex], where [tex]C[/tex] is a constant.

The relationship between the unknown function and its derivative is called the differential equation.

The differential equation in which variables are separated from each other is called the variable separable method.

Now, separate the variables using the variable separable method:

[tex](8+x){dy} = 5y \ dx[/tex]

[tex]\dfrac{dx}{8x} = \dfrac{dy}{5y}[/tex]

Integrating both sides,

[tex]\int \dfrac{dx}{x+8} = \int \dfrac{dy}{5y}\\log(x+8) = \dfrac{1}{5} log y\\ 5 log(x+8) = log y\\log(x+8)^{5} = log y \ \ \\y = ( x+8)^{5} +C[/tex]

Thus, the explicit general solution to the equation is [tex](8+x)^5 +C[/tex].

Learn more about differential equations here:

https://brainly.com/question/33814182

#SPJ6

Answer:

379

Step-by-step explanation:

a23 = 27 + (23-1)(16)

= 27 + (22)(16)

= 27 + 352

= 379

Answer:

2 + 7i

Step-by-step explanation:

(4 + 8i) + (-2 - i)

open the brackets

4 + 8i - 2 - i

add or subtract like terms

2 + 7i

Answer:

2+7i

Step-by-step explanation:

Open the brackets.

4+8i-2-i

You will get…

2+7i

There are 12 month in a year :

6360 ÷ 12 = 530

Thus the labour earns Rs 530 in a month .

To find this out we will divide 6360 by 12 (as there are 12 months in an year) 6360/12 = 530 . Therefore answer = rs 530

Pls follow and mark brainliest.

Answer:

Buses - 43 people

Vans - 12 people

Answer:

C.

y = -3x - 1

y = 3x + 2

Step-by-step explanation:

Find the slope (m) and y-intercept (b) of each table to write an equation for each.

✔️First table:

Find the slope (m) = change in y/change in x

Using any two pair of values, say (0, -1) and (1, -4),

Slope (m) = (-4 - (-1))/(1 - 0) = -3/1

m = -3

Find the y-intercept:

y-intercept is the value of y when x = 0

From the table, y = -1 when x = 0. Therefore,

y-intercept (b) = -1

To write an equation for table 1, substitute m = -3 and b = -1 into y = mx + b

Equation for table 1:

y = -3x - 1

✔️ Second table:

Find the slope (m) = change in y/change in x

Using any two pair of values, say (0, 2) and (1, 5),

Slope (m) = (5 - 2)/(1 - 0) = 3/1

m = 3

Find the y-intercept:

y-intercept is the value of y when x = 0

From the table, y = 2 when x = 0. Therefore,

y-intercept (b) = 2

To write an equation for table 1, substitute m = 3 and b = 2 into y = mx + b

Equation for table 1:

y = 3x + 2

A

A

B

C

A

D

B

C

May choices po yan saamen

Step-by-step explanation:

Love you

Answer:

Median: The median is the middle value of the data set when the data is arranged in ranking order. It always lies at the center of the data set and not affected by the extreme values or outliers. For the calculation of median, the variable should be measured at least at the ordinal level.

Answer:

2

Step-by-step explanation:

log2^8 + log3(1/3)

=>3 + (-1)

=>2

Max is participating at a school bake sale. Each cookie he sells costs 50 cents. Unfortunately, it took 6 dollars to buy the materials for the cookies. Find how much money would it take for Max to break even.

Answer:

Step-by-step explanation:

4 years ago when Mary was 6, she was one half the age of her brother.  

 How old is her brother now?

Solution :

Let brother's age be = x

Four years ago, brothers age was = (x - 4)

Four years ago Mary was = 6

She was half the age of her brother

                                                   [tex]6 = \frac{1}{2} (x - 4)[/tex]

Answer:

396

Step-by-step explanation:

It's a square.

That means that all four sides are equal.

So the two expressions you have been given are equal.

2.5x + 76.5 = 12x - 9            Subtract 2.5x from both sides.

-2.5x               -2.5x  

          76.5 = 9.5x - 9          Add 9 to both sides

           9                 9

          85.5 = 9.5x              Divide by 9.5

       85.5/9.5 = x

x = 9

That is just the value for x. It is not the answer

Side = 12x - 9

Side = 12*9 - 9

Side = 108 - 9

Side = 99

The perimeter = 4 * Side

The perimeter = 4 * 99

Perimeter = 396