Simplify: x^2-16/x-4 What does the given expression simplify to? What is the excluded value of x for the given expression?

Complete Question

The SAT are scored so as to yield a mean of 500 and a standard deviation of 100. These scores are close to being normally distributed. An exclusive club wishes to invite those scoring in the top 5% on the College Boards to join. a. Find percentages of scores that is between 480 and 590. b. What score is required to be invited to join the club? c. What score separates the top 60% of the population from the bottom 40%? What do we call this value? (hint: the score that separates the top 20% of the population from the bottom 80% is called the 80th percentile)

Answer:

a

 \(P(480 < X  <  590) =  0.3952\)  

b  

  \(x =  664.5 \)

c

 \(x_1 =  474.67\)

The value is called the \(40^{th}\) percentile

Step-by-step explanation:

From the question we are told that

The mean is \(\mu = 500\)

The standard deviation is \(\sigma = 100\)

Generally the percentage of the score that are between 480 and 590 is mathematically represented as

\(P(480 < X < 590) = P(\frac{ 480 - 500}{ 100} < \frac{ X - \mu }{ \sigma } < \frac{ 590 - 500}{ 100} )\)

Here \(\frac{ X -\mu}{\sigma } = Z\)

=> \(P(480 < X < 590) = P(\frac{ 480 - 500}{ 100} < Z < \frac{ 590 - 500}{ 100} )\)

=> \(P(480 < X < 590) = P(-0.2< Z < 0.9 )\)

=> \(P(480 < X < 590) = P(Z < 0.9 ) - P(Z<-0.2) \)

From the z table (reference calculator dot net )

\( P(Z < 0.9 )= 0.81594 \)

And

\( P(Z < -0.2 )= 0.42074 \)

=> \(P(480 < X < 590) = 0.81594 - 0.42074 \)

=> \(P(480 < X < 590) = 0.3952\)

Converting to percent

\(P(480 < X < 590) = 0.3952 * 100\)

\(P(480 < X < 590) = 39.52\% \)

The percentage invited to join the club is the top 5% , this can be mathematically represented as

\(P(X > x ) = 0.05\)

Here x is the score that is within the top 5%

=> \(P(X > x) = P( \frac{X - \mu }{\sigma } > \frac{ x - 500}{100} )= 0.05\)

Generally the critical value of 0.05 from the normal distribution table is

\(Z_{0.05} = 1.645\)

So

\(\frac{ x - 500}{100} = 1.645\)

=> \(x - 500 = 164.5\)

=> \(x = 664.5 \)

Generally the probability of having a score that separates the top 60% of the population from the bottom 40%

\(P(X > x_1 ) = 0.60\)

=> \(P(X > x_1) = P(\frac{ X - \mu }{\sigma } > \frac{x - 500}{100} ) = 0.60\)

The critical value of 0.60 from the normal distribution table is

\(Z_{0.60} = - 0. 2533\)

So

\(\frac{x_1 - 500}{100} = -0.2533\)

=> \(x_1 = 474.67\)

From the hint given we can see that this value is called the \(40^{th}\) percentile

The new height requirement should be approximately 69.49 inches for the tallest 2.5% of women to be eligible.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To find the new height requirement, we need to determine the height that corresponds to the top 2.5% of women.

First, we need to find the z-score that corresponds to the top 2.5% of the standard normal distribution. Using a standard normal distribution table or calculator, we find that the z-score is approximately 1.96.

Next, we use the z-score formula to find the corresponding height value in terms of the original distribution:

z = (x - μ) / σ

where:

z = 1.96 (corresponding to the top 2.5%)

μ = mean height for women (given as 64 inches)

σ = standard deviation of heights for women (given as 2.8 inches)

x = new height requirement we want to find

Solving for x, we get:

1.96 = (x - 64) / 2.8

1.96 * 2.8 = x - 64

5.488 = x - 64

x = 64 + 5.488

x ≈ 69.49 inches

Hence, the new height requirement should be approximately 69.49 inches for the tallest 2.5% of women to be eligible.

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Answer:

26-12

Step-by-step explanation:

If together you send 26 messages per day

and you send 12 of those 26 messages a day all you have to do is

26 - 12 which is 14

Answer:

The appropriate solution is "1.7109". A further explanation is provided below.

Step-by-step explanation:

The given values are:

Sample size,

n = 25

Degree of freedom,

\(df=n-1\)

   \(=25-1\)

   \(=24\)

At 90% confidence level,

\(\alpha=1-90 \ percent\)

  \(=1-0.9\)

  \(=0.1\)

and,

\(\frac{\alpha}{2}=\frac{0.1}{2}\)

  \(=0.05\)

Now,

The correct values of t will be:

=  \(t_{\frac{\alpha}{2}, df }\)

=  \(t_{0.05,24}\)

=  \(1.7109\)

===============================================

Work Shown:

A = pi*r^2

A = 3.14*13^2

A = 3.14*169

A = 530.66 square millimeters

We can abbreviate "square millimeters" into "square mm" or into "mm^2".

This value is approximate because pi = 3.14 is approximate.

Answer:

12

Step-by-step explanation:

10x - 20 + 6x + 8 = 180

Supplementary angles

Answer:

x = 12

Step-by-step explanation:

The two given angles create a straight line (Definition of Straight Line). This means that:

\((10x - 20) + (6x + 8) = 180\)

First, combine like terms. Like terms are terms that share the same amount of the same variables:

\((10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\\)

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 12 to both sides of the equation:

\(16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192\)

Next, divide 16 from both sides of the equation:

\(\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12\)

12 is your answer.

~

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Answer:

The answer to this equation would be 3/35 in simplest form.

Step-by-step explanation:

To divide by a fraction, multiply by its reciprocal.

9 /14  ⋅  2 /15

You then cross simplify 9 & 15 (can be divided by 3 to get 9=3 and 15=5)

This will then leave you with 3/14 & 2/5

Next, you cross simplify 14 & 2, (both can be divided by 2 to get 14=7 and 2=1)

This will then leave you with 3/7 & 1/5

Then multiply \(\frac{3 *1}{ 7*5}\)

This will then leave you with your answer of 3/35.

I hope this helps! :)

9/14 divided by 15/2 as a simplest form is 3/35.

To determine the simplest form

Multiple one fraction to second fraction's reciprocal

9/14 * 2/15

Now, multiple nominator to nominator and multiple denominator to denominator,

(9 * 2)/(14 * 15) = 18/210

Now, reduce the fraction by divide by 3,

18/210 = 3/35

Therefore, the simplest form is 3/35.

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The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Answer:

B.  Energy(weight).

Step-by-step explanation:

Energy(weight).

Weight is the independent variable and energy is the dependent.

The amount of energy depends on the weight.

Answer:

5π/4 radians or 225°

Step-by-step explanation:

Answer:

24 glasses

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

DE is the shortest side because it's is opposite to the smallest angle (<F)

180 - 60 = 3X +2X + 5,

X = 23

<F = 2*(23) +5 = 51

Answer:

434

Step-by-step explanation:

29-20=9

20-11=9

9*47=423

423+11=434

=======================================================

Explanation:

Having the salary increase by 3% means we can use the multiplier 1.03

Think of it like 100% + 3% = 1 + 0.03 = 1.03

The new salary is 52,000*1.03 = 53,560 dollars

----------------

The slightly longer way to do this is to first figure out how much 3% of 52,000 is

3% of 52,000 = 0.03*52,000 = 1560

Ricardo earns $1560 more dollars on top of the salary of $52,000

So overall his new salary is $1,560 + $52,000 = $53,560

----------------

Personally, I prefer the first method because it's quicker and it allows for multiple percentage increases to chain together. It also could be used to chain in percentage decreases as well.

Answer:

Slope intercept: y = -3/2x + 1

Point slope: y + 2 = -3/2 * (x - 2) [Forgot to add the work for this, I will add it if you need it, feel free to ask.]

Step-by-step explanation:

m = (change in y)/change in x)

But also

m = y_2 - y_1/x_2 - x_1

So lets substitute

m = 1 - (-2)/0 - (2)

Lets find the slope

m = 3/0 - (2)

m = 3/-2

m = -3/2 (Moved the negative)

Now we find the value of b using the equation of a line.

y = mx + b

y = (-3/2) * x + b

y = (-3/2) * (2) + b

-2 = (-3/2) * (2) + b

Now we find the value of b

Lets rewrite

-3/2 * 2 + b = -2

Cancel the CF of 2

-3 + b = -2

Move the terms without b to the right

b = -2 + 3

b = 1

Now we substitute our values of the slope and y-int into y = mx + b to find the equation.

y = -3/2x + 1

Answer:

\(y=\frac{-3}{2}x-1\)

Step-by-step explanation:

Given the two points, we can use the slope formula to get the slope of our equation.

\(\frac{y_2-y_1}{x_2-x_1}=m\)

Plug in what we know

\(\frac{(1)-(-2)}{0-2}=m\)

\(m=\frac{-3}{2}\)

\(y=\frac{-3}{2}x-b\)

Plug in one of the points given and solve to find our y-intercept [b]

\(-2=\frac{-3}{2}(2)-b\)

\(b=1\)

(we already know our y-intercept since we're given what y is when x is 0 [hence (0,1)], but this is how it is done if we did not know it initially)

Final equation

\(y=\frac{-3}{2}x-1\)

y=-13

Step-by-step explanation:

2y+6=y-7

2y+6-6=y-7-6

2y=y-13

2y-y=y-13-y

y=-13

The value after solving the given expression will be equal to -13.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given expression in the question is,

2y + 6 = y - 7

Rearrange the equation,

2y - y = -7 - 6

y = -13

Therefore, the obtained value for y will be -13.

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Answer:

hmmm. i woud answer this question but i do not know how many ounces the bottles have? is this a real question or a joke,because i coud maybe help if you could be more specific.

Step-by-step explanation:

We need to solve the following equation:

The first step is to move all the terms to the left side:

Then we have to calculate the roots of the equation:

The roots are -0.244 and 1.644.

The image of the point \((6, -4)\) after a rotation of \(180\) degrees counterclockwise about the origin is \((-6, 4).\)

To find the image of a point \((6, -4)\) after a rotation of 180 degrees counterclockwise about the origin, we can apply the rotation transformation.

The rotation of a point (x, y) counterclockwise about the origin by \(180\)degrees can be achieved by multiplying the coordinates by the rotation matrix:

\(\[\begin{bmatrix}\cos(180^\circ) & -\sin(180^\circ) \\\sin(180^\circ) & \cos(180^\circ)\end{bmatrix}\]\)

Since \(\(\cos(180^\circ) = -1\) and \(\sin(180^\circ) = 0\)\), the rotation matrix becomes:

\(\[\begin{bmatrix}-1 & 0 \\0 & -1\end{bmatrix}\]\)

Now, we can apply this matrix to the given point \((\)\(6, -4):\)

\(\[\begin{bmatrix}-1 & 0 \\0 & -1\end{bmatrix}\begin{bmatrix}6 \\-4\end{bmatrix}=\begin{bmatrix}-1(6) + 0(-4) \\0(6) + (-1)(-4)\end{bmatrix}=\begin{bmatrix}-6 \\4\end{bmatrix}\]\)

Therefore, the image of the point \((6, -4)\) after a rotation of \(180\) degrees counterclockwise about the origin is \((-6, 4).\)

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The students plans to work in a rural community according to statistical software is (3.77%, 9.47%) option d is correct.

The given information states that out of 369 randomly selected medical students, 23 said that they planned to work in a rural community.

To construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community using statistical software such as Stat crunch,

the following steps are to be followed.

Step 1: First, open StatCrunch and enter the data into a new data set. In the first column, enter the number of successes, i.e. 23.

In the second column, enter the number of trials,

i.e. 369 - 23

= 346.

Step 2:

Click on Stat > Proportions > One Sample > With Summary.

In the dialog box that appears,

enter the values of Sample proportion

= 23 / 369

= 0.0623,

Level of confidence = 0.95,

and Sample size = 369.

Then, click on Compute!

Step 3:

The output displays the confidence interval for the population proportion.

The 95% confidence interval is (0.0377, 0.0947),

which can be expressed as (3.77%, 9.47%).

Therefore, the correct option is d. (3.77%, 9.47%).

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Answer:

The beginning of the philosophy of history

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = 5x² - x + 2

Using the remainder theorem

To find the reminder substitute the value of x into the above function and solve

That's

x + 1 = 0

x = - 1

So we have

f(-1) = 5(-1)² - ( - 1) + 2

f(-1) = 5 + 1 + 2

f(-1) = 6 + 2

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

6x5x7=210

the volume is 7m

Answer:

A:(angle) R corresponds to (angle)P’QQ’

D: Side RQ corresponds to side QQ’

Step-by-step explanation:

The two options are:

A:(angle) R corresponds to (angle)P’QQ’

D: Side RQ corresponds to side QQ’

Triangles are said to be congruent if they may be of the equal size and equal form. Two congruent triangles have an equal place and perimeter. All of the aspects and angles of a triangle are equal to the corresponding aspects and angles of its congruent triangle.

If two angles and the blanketed side of 1 triangle are the same as the corresponding angles and the covered aspect of the opposite triangle, then each triangle is congruent. If 3 aspects of one triangle are the same as the corresponding three facets of some other triangle then both triangles are congruent.

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The motion of the skier from point A to point B, then to point C, and then point D, indicates that the distances and displacement traveled are;

a) The distance from A to C is 280 meters

b) The distance from point A to point D is 360 meters

c) The displacement of the skier from point B to point C is 120 meters.

Displacement is the change in the position or location of the object.

The possible diagram of the skier in the question can be presented as follows;

A \({}\)                            C                                                   D                          B

t = 0 min      \({}\)         t = 2 min                                       t = 3 min            \({}\)t = 1 min

ʂ         \({}\)                     ʂ                                                     ʂ                           ʂ

-|-------|------|------|------|-----|------|-----|------|------|-------|-------|--------|-------|-------|-----

0           \({}\)   20           40         60          80            100    120    140           160

The above diagram indicates that we get;

a) The distance from point A (t = 0 min) to point C(t = 2 min) is can be found as follows;

The skier moves from point A to point B then from point B to point C, therefore,

The distance from point A to point B = 160 m - 0 m = 160 m

The distance from point B to point C = 160 m - 40 m = 120 m

The distance from point A to point C is therefore;

b) The distance from point A to point D = The distance from point A to point C + The distance from point C to point D as follows;

AD = AC + CD

CD = 120 m - 40 m = 80 m

Therefore;

AD = 280 m + 80 m = 360 m

c) The displacement of the skier from point B (t = 1 min) to C (t = 2 min) can be found as follows;

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Answer:

96√3

Step-by-step explanation:

Answer:

96√3 m²

Step-by-step explanation:

Triangle ABC is a 30-60-90 triangle.

This is a special right triangle where the measures of its sides are in proportion \(x:x\sqrt{3}:2x\):

The side opposite the 30° angle is the height of the triangle.

The side opposite the 60° angle is the base of the triangle and is 24 m.

Therefore, find x:

\(\implies x\sqrt{3}=24\\\\ \implies x=\dfrac{24}{\sqrt{3}}\\\\ \implies x=8\sqrt{3}\)

Therefore:

\(\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle} \\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height. \\\end{minipage}}\)

Substitute the found base and height into the formula and solve for area:

\(\implies A=\dfrac{1}{2} \cdot 24 \cdot 8\sqrt{3}\)

\(\implies A=12 \cdot 8\sqrt{3}\)

\(\implies A=96\sqrt{3}\;\; \sf m^2\)

Therefore, the exact area of the triangle is 96√3 m².

Answer:

Tris-HCl (0.5M Tris Base, pH7.6):

Trizma Base ---------------------------------- 61 g

Distilled water ------------------------------- 1000 ml

Adjust pH 7.6 using concentrated HCl

Store this solution at room temperature. Dilute 1:10 with distilled water before use

and adjust pH if necessary.

20X Tris-HCl (1M Tris Base, pH7.6):

Trizma Base ---------------------------------- 122 g

Distilled water ------------------------------- 1000 ml

Adjust pH 7.6 using concentrated HCl

Store this solution at room temperature. Dilute 1:20 with distilled water before use

and adjust pH if necessary.

10X Tris-HCl-Tween 20 (0.5M Tris Base, 0.5% Tween 20, pH7.6):

Trizma Base ---------------------------------- 61 g

Distilled water ------------------------------- 1000 ml

Adjust pH 7.6 using concentrated HCl and then add 5 ml of Tween 20.

Store this solution at room temperature. Dilute 1:10 with distilled water before use

and adjust pH if necessary.

Note: Tris-HCl Buffer is used for specific cases of immunohistochemical staining.

*** OR you can use Tris Base to make Tr

Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.

Step-by-step explanation:

The solution for x, y, and z is x = 2, y = 2, and z = 2.

To solve the equation (35)"4(23)"5(25)"7 = 2"x3"y*5"z, let's break it down step by step:

Simplify the expressions within the parentheses using the power of operator ("^").

\((35)"4 = 15^4\\(23)"5 = 6^5\\(2\times5)"7 = 10^7\)

Apply the power rule of exponents, which states that \((a^b)^c = a^{(b\times c).\)

\(15^4 \times 6^5 \times 10^7 = (15610)^{(4+5+7)\)

Simplify the expression within the parentheses.

\((15610)^{16 }= 900^{16\)

Express both sides of the equation in terms of prime factors.

\(900 = 2^2 \times 3^2 \times 5^2\)

quate the powers of the prime factors on both sides of the equation.

\(2^2 \times 3^2 \times 5^2 = 2"x \times 3"y \times 5"z\)

From this, we can conclude that x = 2, y = 2, and z = 2.

Therefore, the solution for x, y, and z is x = 2, y = 2, and z = 2.

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