If the average score is 122 with a standard deviation of 35,
what percentage of students scored below 67? Answers are
rounded to the nearest whole percent.
O a.) 90%
O b.) 6%
O c.) 10%
O d.) 94%

Since there is only one value of x, hence the equation given has only one solution

Equations are expressions separated using mathematical operations. Given the equation below;

2x+5+2x+3x = x

Collect the like terms

2x+2x+3x -x = -2

7x -x = -2

Simplify

6x = -2

x = -2/6

x = -1/3

Since there is only one value of x, hence the equation given has only one solution

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Answer:

SR = 5

Step-by-step explanation:

We know that the two lines are equal to each other and thus TS + SR = 13

So, we can simply set the two equations of the first line equal to 13:

x + 2 + 2x - 7 = 13

3x - 5 = 13

3x = 18

x = 6

Now we plug in 6 for x in the SR equation:

2 * 6 = 12 - 7 = 5

The functions f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6 C.Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g is true.

What is increasing function?

⇒ The function is said to be increasing if the y value increases as the x value increase over a given range

What is average rate of change?

⇒An average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another

As x approaches infinity the value of f(x) eventually exceeds the value of both g(x) and h(x)

And it is true for the interval [0,2]

The faster the growth rate higher the average rate of change

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Answer:

C.

Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.

Answer:[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)~xy=2[/tex]

[tex]2)~x+y=4[/tex]

Divide x on both sides of the 1) equation

[tex]xy=2[/tex]

[tex]xy\div x=2\div x[/tex]

[tex]y=\dfrac{2}{x}[/tex]

Current system

[tex]1)~y=\dfrac{2}{x}[/tex]

[tex]2)~x+y=4[/tex]

Substitute the 1) equation into the 2) equation

[tex]x+(\dfrac{2}{x} )=4[/tex]

Multiply x on both sides

[tex]x\times x+\dfrac{2}{x}\times x=4\times x[/tex]

[tex]x^2+2=4x[/tex]

Subtract 4x on both sides

[tex]x^2+2-4x=4x-4x[/tex]

[tex]x^2-4x+2=0[/tex]

Use the quadratic formula to solve for the x value

[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)} }{2(1)}[/tex]

[tex]x=2\pm\sqrt{2}[/tex]

Substitute the x value into one of the equations to find the y value

[tex]xy=2[/tex]

[tex](2+\sqrt{2} )y=2[/tex]

[tex]y=2-\sqrt{2}[/tex]

[tex]OR[/tex]

[tex]xy=2[/tex]

[tex](2-\sqrt{2} )y=2[/tex]

[tex]y=2+\sqrt{2}[/tex]

Therefore, the points of intersection are

[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) and (2 + [tex]\sqrt{2}[/tex], 2 - [tex]\sqrt{2}[/tex] )

Step-by-step explanation:

xy = 2 → (1)

x + y = 4 ( subtract x from both sides )

y = 4 - x → (2)

substitute y = 4 - x into (1)

x(4 - x) = 2

4x - x² = 2 ( multiply through by - 1 )

x² - 4x = - 2

using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 2)x + 4 = - 2 + 4

(x - 2)² = 2 ( take square root of both sides )

x - 2 = ± [tex]\sqrt{2}[/tex] ( add 2 to both sides )

x = 2 ± [tex]\sqrt{2}[/tex] , that is

x = 2 - [tex]\sqrt{2}[/tex] , x = 2 + [tex]\sqrt{2}[/tex]

substitute these values of x into (2) for corresponding values of y

x = 2 - [tex]\sqrt{2}[/tex] , then

y = 4 - (2 - [tex]\sqrt{2}[/tex])

  = 4 - 2 + [tex]\sqrt{2}[/tex]

  = 2 + [tex]\sqrt{2}[/tex] ⇒ (2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) ← 1 point of intersection

x = 2 + [tex]\sqrt{2}[/tex] , then

y = 4 - (2 + [tex]\sqrt{2}[/tex] )

   = 4 - 2 - [tex]\sqrt{2}[/tex]

   = 2 - [tex]\sqrt{2}[/tex] ⇒ (2 + [tex]\sqrt{2}[/tex] , 2 - [tex]\sqrt{2}[/tex] ) ← 2nd point of intersection

green balls = 83

orange balls = 19

Step-by-step explanation:

green balls = g

orange balls = r

g = 7 + 4r

g + r = 102

7 + 4r + r = 102

5r = 95

r = 19

g + 19 = 102

g = 83

Answer:

22

Step-by-step explanation:

The statement which is false among the answer choices as indicated in the task content is; Choice A; The parallel sides of an isosceles trapezoid are congruent.

It follows from the answer choice A that The parallel sides of an isosceles trapezoid are congruent.

However, it follows from the study of isosceles trapezoids that the base angles of such trapezoids are congruent and their measures are equal, consequently, the isosceles sides have equal length measures.

On this note, the other two sides are parallel but cannot be concluded as congruent.

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Based on the data presented, it can be concluded out of the 52 females 26 prefer cats.

To read the graph we must take into account that the rows refer to the preference of men, preference of women and those who have no preference.

On the other hand, the columns refer to the number of students of both genders who prefer or do not prefer each animal. Additionally, adding all the students of each gender we have the total of the sample.

According to the above, the total sample of female students would be 52.

According to the above, the fraction that expresses this relationship correctly is:

[tex]\frac{26}{52}[/tex]

Note: This question is incomplete because the graph is missing. Here is  the graph.

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The value of g(x) is (x^3+5) and g(64) = 262149.

According to the statement

we have given that the

f(x)=√x^3 and (fog)(x)=√(x^3+5) and we have to find the value of the g(64).

So, For find the value of g(64), Firstly we have to find the g(x).

So,

We given that

f(x)=√x^3 and (fog)(x)=√(x^3+5)

And here the formula used is

(f o g)(x) = f (g(x))

here (fog)(x)=√(x^3+5) and f(x)=√x^3

From this we get g(x) is (x^3+5)

So,

g(x) = (x^3+5) and

g(64) = ((64)^3+5)

g(64) = 262149.

So, The value of g(x) is (x^3+5) and g(64) = 262149.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

If f(x)=√x^3 and (fog)(x)=√(x^3+5). Then find the value of g(64).

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I take this to mean [tex]f(x) = \sqrt{x^3}[/tex] and [tex](f\circ g)(x) = \sqrt x[/tex].

Let's first find the inverse of [tex]f[/tex].

[tex]f\left(f^{-1}(x)\right) = \sqrt{\left(f^{-1}(x)\right)^3} = x \\\\ \implies \left(f^{-1}(x)\right)^3 = x^2 \\\\ \implies f^{-1}(x) = x^{2/3}[/tex]

(Note that [tex]f[/tex] is defined only if [tex]x^3\ge0[/tex], or [tex]x\ge0[/tex].)

Apply the inverse of [tex]f[/tex] to [tex]f\circ g[/tex].

[tex](f\circ g)(x) = f(g(x)) = \sqrt x \\\\ \implies f^{-1}\left(f(g(x))\right) = f^{-1}(\sqrt x) \\\\ \implies g(x) = \left(\sqrt x\right)^{2/3} = \left(x^{1/2}\right)^{2/3} = x^{1/3} = \sqrt[3]{x}[/tex]

Then

[tex]g(64) = \sqrt[3]{64} = \sqrt[3]{4^3} = \boxed{4}[/tex]

A line segment can be defined as the part of a line in a geometric figure such as a parallelogram, that is bounded by two (2) distinct points and it typically has a fixed length.

In Geometry, a line segment can be measured by using the following measuring instruments:

A parallelogram refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Based on the previous experiment conducted in question 5, 6 and 7, we can logically conclude that the opposite sides of quadrilateral ABCD have the same (equal) slopes, which implies that the opposite sides are parallel. Hence, quadrilateral ABCD is simply a parallelogram by definition.

In this context, yes I would you reach the same conclusion that I reached in question 7 because the line segments that I drew represent the diagonals of a parallelogram.

Therefore, if the point of intersection of the diagonals divide each diagonal in half, then, the quadrilateral belonging to these diagonals forms a parallelogram.

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The probability is p = 2/5, the correct option is the third one.

There is a total of 6 socks, such that 4 are black and 2 are blue.

Then the probability of first getting a black sock is the quotient between the number of black socks and the number of blue socks, which gives:

P = 4/6

Now there are 5 socks in total, such that 3 are black and 2 blue.

Then the probability of getting another black one is:

Q = 3/5

The joint probability (getting the two black socks) is given by the product of the individual probabilities:

p = (4/6)*(3/5) = 2/5

The correct option is the third one.

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Answer: C

Step-by-step explanation:

We can use the expanding rule to get that one if the expressions is

(9x^2 + 2x - 7)x + (9x^2 + 2x - 7)(-4)

The cost of manufacturing the article bin 2004 will be 1875.

Percentage increase is the ratio of increase to the initial value in percentage.

Given that In 2001 the total cost of manufacturing an article was sh.1250 and this was divided between the cost of materials was doubled, labor cost increased by 30% and transport costs increased by 20%

Given that in 2001, the cost of manufacturing = 1250

If this cost was divided between the Material, labor, and transportation equally, then, cost for each sector will 1250/3 = 416.67

The cost of manufacturing = 833.33 + 541.67 + 500

The cost of manufacturing = 1875

Therefore, the cost of manufacturing the article bin 2004 will be 1875.

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The two positive numbers whose difference is 9 and whose product is 2950 are 50 and 59

As a general rule, it should be noted that positive numbers are numbers that have their value greater than 0

So, we start by representing the two positive numbers with x and y.

So, we have the following equations

x - y = 9

xy = 2950

Make x the subject in the first equation x - y = 9

x = y + 9

Substitute y + 9 for x in the second equation

(y + 9) * y = 2950

Expand the equation

y^2 + 9y - 2950 = 0

Using a graphing tool, we  have the solution of the above equation to be

y = 50

Recall that:

x = 9 + y

So, we have:

x = 9 + 50

Evaluate

x = 59

Hence, the two positive numbers whose difference is 9 and whose product is 2950 are 50 and 59

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Answer:

Fufusyyigywngd, hdj4snwhsjtc

Bahr Ltd flu not ld6wlw

The amount of the down payment and the fixed rate mortgage is $35000 and $9625.

According to the statement

We have given that the

Thomas osler is buying a house selling for $175,000 And we have to find the amount of the down payment and the monthly payment.

So, The down payment is :

percentage of the down payment is 20%

So,

Amount = 20/100*175000

Amount = 35,000$

And the percentage of the fixed rate mortgage with 5.5%

So,

Amount = 5.5/100*175000

Amount = $9625.

This the amount of the down payment with the given percentage and with the fixed rate mortgage.

So, The amount of the down payment and the fixed rate mortgage is $35000 and $9625.

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The 10the term of the sequence -1/1, -1/2, -1/9, -1/64....is -1/1,000,000,000

-1/1, -1/2, -1/9, -1/64

This can be written as;

-1/1° , -1/2¹, -1/3², -1/4³, -1/5⁴, -1/6^5, -1/7^6, - 1/8^7, -1/9^8, -1/10^9

So,

First term = -1/1,

Second term = -1/2,

Third term = -1/9,

Fourth term = -1/64,

Fifth term = -1/625,

Sixth term = -1/7,776,

Seventh term = -1/117,649,

Eighth term = -1/2,097,152,

Ninth term = -1 / 43,046,721,

Tenth term = -1/1,000,000,000

Therefore, the 10th term is -1/1,000,000,000

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Answer: for number 3, x= 6

Step-by-step explanation:

The speed of the plane will be 875km/h and the speed of the wind will be 125km/h.

It should be noted that the speed is calculated as:

= Distance/Time

Based on the information, the DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr.

Therefore, (v + w) = 3000/3

v + w = 1000 .... I

(v - w) = 3000/4

v - w = 750 .... ii

We'll then add both equations together. Therefore, the speed of the plane will be 875km/h and the speed of the wind will be 125km/h.

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Numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.

Given a paragraph in which there are blanks:

A _____ is a number whose only factors are 1 and itself. If a number has  factors besides 1 and itself, it is called a _____. You can use divisibility rules or _______ to help you determine whether a number is prime or composite.

We are required to fill the blank with appropriate options.

We have to fill "prime numbers" in the first blank.

We have to fill "composite numbers" in the second blank.

We have to fill "the sieve of Eratosthenes" in the third blank.

Hence numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.

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The value of the median, lower and upper quartile

The minimum value = 10

The maximum value = 38

The median is the value that is found in the center of the data when it is ordered from lowest to highest. In the event that there is no value that precisely corresponds to the center, the value will be determined by taking the average of the values that are located on each side of the middle.

10  11  12  15  19  24  27  29  33  38

Median = 21.5

The intermediate value of the data that is located to the left of the median is known as the lower quartile.

10  11  12  15  19

lower quartile = 12

The intermediate value of the data that is located to the right of the median is known as the upper quartile.

24  27  29  33  38

upper quartile = 29

In conclusion, the 5 number summary is 10, 12, 21.5, 29, 38 → A

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Answer: minimum 10 first quartile 11.5 median 12.5 third quartile 16 maximum 20

Step-by-step explanation:

The slope of the curve described by the equation at the given point (0,1) as in the task content is; 4.

According to the task content, it follows that the slope of the curve can be determined by means of implicit differentiation as follows;

y⁵+ x³ = y² + 12x

5y⁴(dy/dx) -2y(dy/dx) = 12 - 3x²

(dy/dx) = (12 -3x²)/(5y⁴-2y)

Hence, since the slope corresponds at the point given; (0, 1); we have;

(dy/dx) = (12 -3(0)²)/(5(1)⁴-2(1))

dy/dx = 12/3 = 4.

Hence, slope, m = 4.

Consequent to the mathematical computation above, it can then be concluded that the slope of the curve, the line tangent to the curve at the given point is; 4.

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An airplane is heading north at an airspeed of 640 km/hr, but there is a wind blowing from the southwest at 90 km/hr. degrees off course will be 6.25°

Generally, the equation for the velocity of the plane with reference to the ground is  mathematically given as

Vp=  velocity of the plane with reference to wind+  velocity of the wind with reference to ground

Therefore

Vp=Vp'+Vw

[tex]mVp=\sqrt{(640)^2+(90)^2-2*640*90cos45}[/tex]

mVp=579.8km/h

where

[tex]\frac{sintheta}{90}=\frac{sin45}{Vp'}[/tex]

[tex]sin \theta=\frac{90}{579.8}*sin45[/tex]

sin[tex]\theta=0.109[/tex]

[tex]\theta=sin^{-1}(0.109)=6.25[/tex]

In conclusion,  degrees off course will be 6.25

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The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.

Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.

As p is a prime number, and 2 is the smallest prime number, so, p[tex]\geq[/tex]2

So, the positive divisors of the integer n are: 1,p,p².

As σ(n) represents the sum of all positive divisors of the integer n.

σ(n)=1+p+p²

In order to prove that σ(n) < 2n,for all n of the form n = p².

1+p+p²<2p²

p²-p-1>0

It is know that, p[tex]\geq[/tex]2.

So, p²-p-1[tex]\geq[/tex]1

Thus, σ(n) < 2n holds true for all n of the form n = p².

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The letter for the graphed function is y = √(x) - 5

The parent function is given as:

y = √x

From the graph, we can see that the function is shifted downwards by 5 unts

This is represented as:

y = √(x) - h

Where h = 5

Substitute the known values in the above equation

y = √(x) - 5

This means that the letter for the graphed function is y = √(x) - 5

Hence, the letter for the graphed function is y = √(x) - 5

So, the complete functions are

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Answer:35443

Step-by-step explanation:

Answer:

1. f(x) is reflected across the x-axis

2. f(x) is translated 1 unit up

3. f(x) is vertically scaled by a factor of 2

4. f(x) is reflected across the x-axis AND is vertically scaled by a factor of 2

5. f(x) is vertically scaled by a factor of 3 AND is translated 1 unit down

6. f(x) is vertically scaled by a factor of 1/6 AND is translated 1 unit up

Solving question:

(1)  [tex]g(x) = -f(x)[/tex]

This graph has been reflected in the x axis. Equation:  [tex]\sf g(x) = -\dfrac{2}{x}[/tex]

(2) [tex]g(x) = f(x) + 1[/tex]

Graph has been translated 1 units up vertically. Equation: [tex]\sf g(x) = \dfrac{2}{x} +1[/tex]

(3) [tex]g(x) = 2f(x)[/tex]

This graph has been stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = \dfrac{4}{x}[/tex]

(4) [tex]g(x) = -2f(x)[/tex]

This graph has been reflected in the x axis and stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = -\dfrac{4}{x}[/tex]

(5)  [tex]g(x) = 3f(x) - 1[/tex]

This graph has been stretched vertically by a factor of 3 and translated 1 units down. Equation: [tex]\sf g(x) = \dfrac{6}{x} -1[/tex]

(6)   [tex]g(x) = \frac{1}{6} f(x) + 1[/tex]

This graph has been stretched vertically by a factor of 1/6 and translated 1 units up. Equation: [tex]\sf g(x) = \dfrac{1}{3x} +1[/tex]

Check the picture below.

so the composite is really a trapezoid and two triangles, let's get their area and sum them all up.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a = 2\\ b = 5\\ h = 7 \end{cases}\implies A=\cfrac{7(2+5)}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{yellow~trapezoid}{\cfrac{7(2+5)}{2}}~~ + ~~\stackrel{blue~triangle}{\cfrac{1}{2}(\stackrel{b}{3})(\stackrel{h}{5})}~~ + ~~\stackrel{orange~triangle}{\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{2})}} \\\\\\ 24.5~~ + ~~7.5~~ + ~~10\implies \text{\LARGE 42}[/tex]

The new monthly payment is $3,181.53

What is ARM?

ARM stands adjustable rate mortgage, which means that the interest rate applicable to the mortgage would change during the life of the mortgage, in this case, 7/1 ARM means that interest rate of 3% is applicable for the first 7 years and the rate would change in year 8 to another interest rate, which is 4.925% as hinted at in the question.

To determine the monthly payment in year 8 , we need to compute the outstanding balance at the end of year 7, which is the opening balance in year 8 using the present value formula of an ordinary annuity since monthly payments would occur at the end of each month

PV(balance at the end of year 7)=PMT*(1-(1+r)^-N/r

PMT=initial monthly payment=$2,635.03

r=initial monthly interest rate=3%/12=0.0025

N=number of monthly payments in the remaining 23 years(i.e 30-7)=23*12

N=number of monthly payments in the remaining 23 years(i.e 30-7)=276

PV=$2,635.03*(1-(1+0.0025)^-276/0.0025

PV=$2,635.03*(1-0.502008144755209)/0.0025

PV=$2,635.03*0.497991855244791/0.0025

PV=$ 524,889.39

With the balance at the end of year 7, we can now compute monthly payment in year 8 using the same formula as above where the unknown is the PMT, PV=$ 524,889.39  and r= 4.925%.

$524,889.39=PMT*(1-(1+4.925%/12)^-276/4.925%/12)

$524,889.39=PMT*(1-(1.00410416666666667

)^-276/0.00410416666666667

$524,889.39=PMT*(1-0.32289378683267300

)/0.00410416666666667

$524,889.39=PMT*164.98019407122700000

PMT=$524,889.39/164.98019407122700000

PMT=$3,181.53

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