A well know Statistical Institution claims that the average College tuition for a law degree costs at least thirty five thousand dollars. Analyzing a sample of fifty law schools in the vicinity of the study we found the sample had a mean tuition of $33,450 with a population standard deviation of $5,978 per year. At 2% level of significance test the Institution's claim.

Here we go ~

A.) Derivative of 6x² :

[tex]\qquad \sf  \dashrightarrow \:f {}^{ \prime}(x) = \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{f(x + h) - f(x)}{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{6(x + h) {}^{2} - 6(x) {}^{2} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{6(x {}^{2} + 2xh + h {}^{2} ) {}^{} - 6(x) {}^{2} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{6x {}^{2}} + 12xh +6 h {}^{2} {}^{} - \cancel{6x{}^{2}} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 12xh +6 h {}^{2} {}^{} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{ h}( 12x +6h ) {}^{} {}^{} }{ \cancel{h}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: 12x + 6h[/tex]

[tex]\qquad \sf  \dashrightarrow \: 12x + 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) = 12x[/tex]

B.) The derivative of f(x) = 2x² -7x + 8 :

[tex]\qquad \sf  \dashrightarrow \:f {}^{ \prime}(x) = \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{f(x + h) - f(x)}{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 2(x + h) {}^{2} - 7(x + h) + 8 - (2 {x}^{2} - 7x + 8)}{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 2(x {}^{2} + 2xh + {h}^{2} ) {}^{} - \cancel{7x} + 7h+ \cancel8 - 2 {x}^{2} + \cancel{7x } - \cancel 8)}{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{ 2x {}^{2}} + 4xh + 2{h}^{2} {}^{} - 7h - \cancel{2 {x}^{2}} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel {h}( 4x + 2{h}^{} {}^{} - 7) }{ \cancel{h} }[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: 4x + 2{h}^{} {}^{} - 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 0 - 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) = 4x - 7[/tex]

The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]

Given,

The function f(x) =[tex]8x^{2} -5[/tex]

The intervals = [4,b]

The average rate of change = [tex]\frac{f(a)-f(b)}{a-b}[/tex]

Where a and b are the interval

f(4)= [tex]8(4)^{2}-5[/tex]

=123

f(b)= [tex]8b^{2}-5[/tex]

The average rate of change = [tex]\frac{123-(8b^{2}-5) }{4-b}[/tex]

[tex]=\frac{123-8b^{2}+5 }{4-b} \\=\frac{128-8b^{2} }{4-b}[/tex]

Hence, The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]

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The length of the major arc QSR is 39.77 inches

The given parameters are:

m∠QPR = 170 degree

Radius, r = 6 inches

The length of the major arc QSR is calculated as:

Arc length = (360 - Angle/360) * 2πr

Substitute the known values in the above equation

Arc length = (360 - 170/360) * 2 * 3.14 * 6

Evaluate the difference

Arc length = (190/180) * 2 * 3.14 * 6

Evaluate the product

Arc length = 39.77

Hence, the length of the major arc QSR is 39.77 inches

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Answer: range = 16 standard deviation = 5

Step-by-step explanation:

The value of "x" which will satisfy the equation [{21090(x -1 ) + 109.07 } = 1] is 1.01.

As per the question statement, we are provided with an equation [tex][{21090(x -1 ) + 109.07 } = 1][/tex].

We are required to solve the above mentioned equation for "x", such that the value of x when substituted in the equation, satisfies the same.

To solve this question, we will simply use the methods of rearranging and opening up of brackets, as shown below.

[tex][{21090(x -1 ) + 109.07 } = 1] \\or, 21090x - 21090+109.07=1\\or, 21090x - (21090-109.07)=1\\or, 21090x - 20980.93=1\\or, 21090x=(1+20980.93)\\or, 21090x=20981.93\\or,x=\frac{21090}{20981.93}\\or,x=1.00515\\or,x=1.01[/tex]

Therefore, the value of "x" which will satisfy the equation

[{21090(x -1 ) + 109.07 } = 1] is 1.01.

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H.C.F of 3x³+15x² and 2x³-50x is x(x+5)

A number system is defined as a system of writing to express numbers.

The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

3x³ + 15x²

Factorize the given expression by taking out 3x²

3x²(x+5)

and the expression 2x³ - 50x ​

2x(x²-25)

2x(x+5)(x-5)

H.C.F of 3x³+15x² and 2x³-50x is x(x+5)

Hence, H.C.F of 3x³+15x² and 2x³-50x is x(x+5)

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Answer:

y = 2x +4

Step-by-step explanation:

Equation of a line in slope-intercept form is

y = mx + b

where m is the slope and b is the y-intercept, the point at which the line crosses the y axis (at x = 0)

Given slope is 2 we get the equation as

y = 2x + b

We have to solve for b by plugging in the x and y values for point(1,6)

Thus we get y = 6 = 2(1) + b

Or 6 = 2 + b

b= 6-2 = 4

Equation in slope-intercept form is

y = 2x +4

Hi!

Apply the Point-Slope formula:

◈Where:

◈We know that:

◈Plug in the values:

[tex]\bigstar\textsf{\textbf{Solution: \boxed{\textsf{\textbf{2x+4}}}}}[/tex]

Have a great day!

I hope this helped!

-stargazing

The inverse of the statement  p → q is "If x – 5 ≠  10 then

4x + 1 ≠  61"

The statement is given as

p: x – 5 =10

q: 4x + 1 = 61

The inverse of a statement is such that:

The hypothesis and conclusion are negated.

This means that a conditional statement referred to as p → q would have the inverse of -p → -q.

When the above rule is applied on the statement

p: x – 5 ≠  10

q: 4x + 1 ≠  61

This means that the inverse of the statement  p → q is "If x – 5 ≠  10 then

4x + 1 ≠  61"

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Answer:

A

MF up there wont tell u but its A

Answer:

let (5,4)=(x1,y1)

(-3,-2)=(x2,y2)

now, by using distance formula

we get distance between line segment =10 unit

therefore distance =10 units ans

Solution,

As the formula...

[tex] = \sqrt{( - 3 - 5 {)}^{2} + ( - 2 - 4 {)}^{2} } [/tex]

[tex] = \sqrt{( - 8 {)}^{2} + ( - 6 {)}^{2} } [/tex]

[tex] = \sqrt{64 + 36} [/tex]

[tex] = \sqrt{100} [/tex]

= 10 units...

☘☘☘....

Y equals f(x) is written on the first line, The second line, marked y = g(x). When the input is for either of the two functions, the result is x=0 and return the output is same value.

Given that,

Y equals f(x) is written on the first line, which also passes through (-1, 2), (0, 2), and (2, 2). The second line, marked y = g(x), points at (0, -1), passes through (-0.5, -2), and (1, 1). The lines come together at (1.5, 2).

We have to find the input value for which f(x) = g(x) is true using the graph. x = 0.5, x = 1, x = 1.5, x = 2.

The final two actions:

f(x)=-2/3(x+1)

g(x)=1/3(x-2)

The output are equation

f(x)=g(x)

-2/3(x+1)=1/3(x-2)

-2(x+1)=1(x-2)

-2x-2=x-2

-2x-x=-2+2

-x=0

x=0

When x = 0 is used as an input, the first two functions always return the same results.

f(x) traverses (-1,2), (0,2), and (2,2)

The paths that g(x) takes are (-0.5,-2), (0,-1), (1,1)

Therefore, When the input is for either of the two functions, the result is x=0 and return the output is same value.

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make it simple its x=1.5

[tex]x^4+4x^3-8x-32=0[/tex]  

Can be factoried into:

[tex](x^3-8)(x+4)=0\\[/tex]

Now you're looking for which values of x will make the equations in the brackets equal to 0, since as long as one is equal to 0, they will be multiplied into 0.

First we'll do:

[tex]x^3-8=0[/tex]

We're looking for what number cubed is equal to 8, which is 2.

Note: -2 is also a possibility, but if you plug it in, you'll see that it doesn't work.

Second we'll do:

[tex]x+4=0[/tex]

This one's pretty easy, x will be -4.

So your solutions are:

x = 2, -4

The solutions of the polynomial [tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 are 2 and -4.

Polynomials are sums of terms of the form k⋅xⁿ.

where k is any number

n is a positive integer.

Example:

2x + 4x - 7 is a polynomial

We have,

[tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 _______(1)

Divide into two parts.

[tex]x^{4}[/tex] + 4x³

-8x - 32

Take out the common from each part.

x³ ( x + 4 )

- 8 ( x  + 4 )

Now,

We have,

x³ ( x + 4 ) - 8 ( x  + 4 ) = 0

We can write this as:

(x³ - 8) (x + 4) = 0

Now,

We need to find the x values.

x³ - 8 = 0

x³ = 8

x = ±2

Put x = 2 in (1)

[tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0

x = 2

16 + 32 - 16 - 32

0 = 0

x = 2 is satisfied

Put x = -2 in (1)

16 - 32 + 16 - 32 = 0

-64 ≠ 0

x = -2 is not satisfied

x + 4 = 0

x = -4 putting in (1)

256 - 256 + 32 - 32 = 0

0 = 0

x = -4 is satisfied

Thus the solutions of the polynomial [tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 are 2 and -4.

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Answer:

22,400

Step-by-step explanation:

80,000 x .28

Using z-scores, it is found that due to the lower z-score, Beth had the fastest time when compared to her team.

This problem is incomplete, but researching on the internet, we have that:

The z-score of a measure X in a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

For this problem, lower times means that the swimmer is faster, hence the swimmer that had the fastest time when compared to her team is the swimmer with the lowest z-score.

Angie's z-score is given by:

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

Z = (26.2 - 27.2)/0.8

Z = -1.25.

Beth's z-score is given by:

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

Z = (27.3 - 30.1)/1.4

Z = -2.

Due to the lower z-score, Beth had the fastest time when compared to her team.

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Work Shown:

1/2 = 0.5

1/4 = 0.25

0.5 inch = 20 miles, which is the given scale

1 inch = 40 miles, after multiplying both sides by 2

3.25 inches = 130 miles after multiplying both sides by 3.25

The interest rate required to get a total amount of $3,688.86 from compound interest on a principal of $2,000.00 compounded 12 times per year over 5 years is 12.306% per year.

Given,

The total amount (A)= $3688.86

Principal (P) = $2000

time period (t) = 5 years.

compounded monthly (n) = 12

rate of interest per year = ?

we know that r=n[(A/P)¹/ⁿt  -1]

substitute the above values.

r = 12 × [(3688.86/2000)¹/⁽¹²⁾⁽⁵⁾ - 1]

r = 12 × [(1.84443)¹/⁶⁰ - 1]

r = 12 × 0.0102

r = 0.12306

Now convert r to R as a percentage.

R = r × 100

R = 0.12306 × 100

R = 12.306%

Hence the rate of interest compounded monthly is 12.306%

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Aaron Smith would has average hits per baseball game as 0.79  hits per game.

Average provides ill information in case of skewed data.

Arithmetic mean is the best central measure available for representing the values of a data set.  It is also called average of the values of the considered data set. It serves as predicted value(in case no other information of the data is available) of that data set.

WE have been given that After 30 baseball games Aaron Smith had 24 hits. If after 100 games he had 80 hits, then he would has average hits per baseball game;

Average  = Hits in game / number of games

Average  = 24- 80 / 30-100

Average  =  56 / 70

Average  = 0.79  hits per game

Hence, Aaron Smith would has average hits per baseball game as 0.79  hits per game.

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Answer:

B=30°

Step-by-step explanation:

Recall that the sum of interior angles of a triangle equals to 180°. So basically

[tex]A+B+\alpha+\beta=180^{\circ}[/tex]

[tex] \implies B + {70}^{ \circ} + {80}^{ \circ} = {180}^{ \circ} \\ \implies B = {180}^{ \circ} - {150}^{ \circ} \\ \implies B = \boxed{{30}^{ \circ} }[/tex]

Answer: 46

Step-by-step explanation:

Since we know that angles J and E are congruent, we can do the equation 6x + 4 = 2x +32. We then solve for x which gives us 7. After that, we plug in the 7 into the equation for E which would be = 2(7) + 32. Once we solve that, we end up with 46.

The price per item is 765.

The variable cost of 100 units is 1500.

The fixed expense is 750.

The expense for 100 units is 2250

Fixed costs are costs that do not vary with output. e,g, rent, mortgage payments. Variable cost change with the unit of output.

The variable cost of 100 units = variable cost per unit x number of units

15 x 100 = 1500

The expense for 100 units = fixed cost + total variable cost

750 + 1500 = 2250

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Answer:

  A. 1/2 and 3/2

Step-by-step explanation:

You want to identify like fractions among the sets {1/2, 3/2}, {2/1, 2/3}, {10/10, 5/5}, and {7/4, 4/7}.

Like fractions are fractions that have the same denominator. Among the sets offered, the only one with denominators the same is ...

  {1/2, 3/2}

Answer:

y =x - 1

Step-by-step explanation:

Here, m is the slope and b is the y-intercept.

Plot any two points on the line. (5,4)  & (0,-1)

[tex]\sf \boxed{Slope =\dfrac{y_2-y_2}{x_2-x_1}}[/tex]

          [tex]\sf =\dfrac{-1-4}{0-5}\\\\=\dfrac{-5}{-5}\\\\=1[/tex]

m = 1

At y-intercept x = 0.  So, the -1 is the y-intercept.

m = 1 & b = -1

y = 1x + (-1)

Answer: rises; your slope is positive

Every single time your slope is positive, your line goes upward.

Every time your slope is negative, however, your line goes downward.

Rearrange 9x - 27y = 81 to -27y = -9x + 81 because we want to put our equation into slope intercept so that we can eventually get our 'y' all by itself.

Divide by -27 for every variable.

Your slope intercept form should now look like this; y = 1/3x - 3

Now that we're completely done or that we have 'y' by itself, it's safe to say that our answer is 1/3, which is, also, positive.

Hope this helps, dawg.

Answer:

181

Step-by-step explanation:

Sally is running laps around a track. She runs 12 laps to warm up. Then she runs 13² laps.

First write the equation. we know she alr ran 12 laps so its going to be +12

to 13^2. so the equation will be 12+13^2 then using PEMDAS we know that we have to do the exponents first so 13^2 is just 13 * 13 which is 169. so now the equation is 169+12 now just add. the answer is 181

Answer:The value of coordinates G', H', and F' are (1,6) , ( 7,3) and (4 , 0) respectively.What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.For example (5,3) here 5 will be for the x and 3 will be for the y.Another example is (9,0) here 9 is for x and 0 is for y.

Step-by-step explanation:

The lengths of the other two sides of the triangle is 8√6 units.

Given that,

AD is the angle bisector of ∠A .

BD = 2 units .

DC = 4 units .

AE ⟂ BC and √15 units .

So, AB / AC = BD / DC { By angle bisector theorem }

AB / AC = 2/4

AB / AC = 1/2  ......... Eqn.(1)

Also, BC = BD + DC = 2 + 4 = 6 units .

Now let BE = x units .

So, in right-angled ∆AEB ,

AB = √(15 + x²) { By pythagoras theorem }

In right angled ∆AEC ,

AC = √{15 + (x - 6)²} { By pythagoras theorem }

Putting both values in Eqn.(1),

AB/AC = 1/2

√(15 + x²)/√(15 + x² + 36 - 12x) = 1/2

Squaring both sides,

(15 + x²) / (x² - 12x + 51) = 1/4.

4(15 + x²) = x² - 12x + 51.

60 + 4x² = x² - 12x + 51.

4x² - x² + 12x + 60 - 51 = 0.

3x² + 12x + 9 = 0.

3x² + 3x + 9x + 9 = 0.

3x(x + 1) + 9(x + 1) = 0.

(3x + 9)(x + 1) = 0.

x = (-3) and (-1) .

Taking x = (-1),

AB = √(15 + x²) = √(15 + 1) = 4 units .

So, AC = 4 * 2 = 8 units .

Taking x = (-3),

AB = √(15 + 9) = √24 = 4√6 units.

So, AC = 2 * 4√6

= 8√6 units .

Hence, the lengths of the other two sides of the triangle is  8√6 units.

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Based on the probability of rain in Nevada, the probability that it will not rain is 0.7.

The probability that if it does not rain, the school bus will be on time is 0.85.

The probability that it will rain and the school bus will still be on time is 0.6.

The probability that it will not rain in Nevada can be found by the formula:

= 1 - probability of rain in Nevada

= 1 - 0.3

= 0.7

The probability that if it does not rain, the school bus will be on time is:

= 1 - probability of the school bus being late if it does not rain

= 1 - 0.15

= 0.85

The probability that it will rain and the school bus will still be on time is:

= 1 - probability of the school bus being late if it rains

= 1 - 0.4

= 0.6

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