A mutual fund has a market value of $40,000,000 and 4,000,000 outstanding shares. What is the value per share?



1


10


100


1,000

Answer:

The range of width is 10 ≤ W ≤ 28

Step-by-step explanation:

* lets study the meaning of compound inequality

- If x is greater than a and x is smaller than b, then x is between a and b

∵ x > a and x < b

∴ The compound inequality is ⇒ a < x < b

# Ex: ∵ x > -2 and x < 10

∴ The compound inequality is ⇒ -2 < x < 10

- If x is greater than or equal a and x is smaller than or equal b, then

 x is from a and b

∵ x ≥ a and x ≤ b

∴ The compound inequality is ⇒ a ≤ x ≤ b

# Ex: ∵ x ≥ -2 and x ≤ 10

∴ The compound inequality is ⇒ -2 ≤ x ≤ 10

* Now lets solve the problem

- The garden in the shape of a rectangle with dimensions length (L)

 and width (W)

- The length of the garden is 10 feet

- The perimeter (P) of the garden is at least 40 feet and not more than

  76 feet

∵ L = 10 feet

∵ P = 2L + 2W

- At least means greater than or equal (≥) and not more than means

 smaller than or equal (≤)

∴ P ≥ 40 feet

∴ P ≤ 76 feet

- lets use the rule of the perimeter

∴ 2(10) + 2(W) ≥ 40 ⇒ simplify

∴ 20 + 2W ≥ 40 ⇒ subtract 20 from both sides

∴ 2W ≥ 20 ⇒ divide both sides by 2

∴ W ≥ 10 ⇒ (1)

- Do similar with P ≤ 76

∴ 2(10) + 2(W) ≤ 76 ⇒ simplify

∴ 20 + 2W ≤ 76 ⇒ subtract 20 from both sides

∴ 2W ≤ 56 ⇒ divide both sides by 2

∴ W ≤ 28 ⇒ (2)

- From (1) and (2)

∴ 10 ≤ W ≤ 28 ⇒ compound inequality

* The range of the width is from 10 feet to 28 feet

Answer:

Correct answer on ed is C.

Step-by-step explanation:

Just did the exam and it was correct.

The solution is A = ( x - 14 ) / ( x + 4 )

The value of the equation ( h * f * g ) ( x ) = ( x - 14 ) / ( x + 4 )

What is Composition of functions?

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the function f ( x ) be represented as

f ( x ) = ( x - 6 ) / x

Let the function g ( x ) be represented as

g ( x ) = x + 4

Let the function h ( x ) be represented as

h ( x ) = 3x - 2

Now , the equation is ( h * f * g ) ( x )

The equation of composition of functions can be simplified as

h * ( f ( g ( x ) ) ) = h * ( f ( x + 4 ) )

On simplifying the equation , we get

h * ( f ( x + 4 ) ) = h * [ ( x + 4 - 6 ) / ( x + 4 ) ]

h * ( f ( x + 4 ) ) = h * [ ( x - 2 ) / ( x + 4 ) ]

Now , the composition of h * ( f ( g ( x ) ) ) is given by

h ( x ) = 3x - 2

Substitute the value of x as ( x - 2 ) / ( x + 4 ) , we get

( h * f * g ) ( x ) = 3 [ ( x - 2 ) / ( x + 4 ) ] - 2

( h * f * g ) ( x ) = ( 3x - 6 ) / ( x + 4 ) - 2

( h * f * g ) ( x ) = ( 3x - 6 - 2x - 8 ) / ( x + 4 )

( h * f * g ) ( x )  = ( x - 14 ) / ( x + 4 )

Therefore , the value of A is ( x - 14 ) / ( x + 4 )

Hence , the value of ( h * f * g ) ( x )  is ( x - 14 ) / ( x + 4 )

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Answer:

y=4x+7

Slope m=4 with the equation y2-y1/x2-x1 with any points

y-intercept (0,7)

Answer:

100 in²

Step-by-step explanation:

Since the figures are similar

the linear ratio of sides = a : b , then

ratio of areas = a² : b²

ratio of sides = 15 : 21 = 5 : 7

ratio of areas = 5² : 7² = 25 : 49

let the area of the smaller figure be x then by proportion

[tex]\frac{25}{x}[/tex] = [tex]\frac{49}{196}[/tex] ( cross- multiply )

49x = 4900 ( divide both sides by 49 )

x = 100

Area of smaller figure is 100 in²

I just took the test!

Answer:

16.2 m²

Answer:

Betty's boss use the MEAN to describe the average tip.

Betty use the MEDIAN.

Step-by-step explanation:

The MEAN is 50+45+48+125+85= 353

353/5=70 or 70.6

The MEDIAN is the middle which is 50.

45,48,50,85,125

Hope this helps

Final answer:

The mean tip amount Betty made was $70.60, and the median was $50. Betty's boss used the mean to describe her average nightly tips, whereas Betty used the median.

Explanation:

To calculate the mean and median tip amount for Betty's nightly tips, we list her tips from last week: $50, $45, $48, $125, and $85. To find the mean, we add all the tip amounts together and divide by the number of days she worked. Betty worked 5 days, so the mean is calculated as: (50 + 45 + 48 + 125 + 85) / 5 = $70.60. The median is the middle number when the tips are arranged in order, which are $45, $48, $50, $85, and $125. Thus, the median tip amount is $50.

Based on this information, Betty's boss used the mean to describe her average tip, while Betty herself used the median to describe her average tip.

For this case we have the following system of equations:

[tex]-2x + 5y = -3\\y-15 = 3x[/tex]

We multiply the second equation by -5:

[tex]-5y + 75 = -15x[/tex]

Now we add the equations:

[tex]-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6[/tex]

We find the value of the variable "y":

[tex]y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3[/tex]

THE solution is: (-6, -3)

Answer:

(-6, -3)

Answer:

The second photo.

Step-by-step explanation:

If you use a graphing calculator, you can easily find the answer.

Answer:

  see below

Step-by-step explanation:

Comparing the given equation to the standard-form equation of a circle ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . circle centered at (h, k) with radius r

we find that ...

  h = 2, k = -5, r = 2

So, the circle you're looking for is centered at (2, -5) and has a radius of 2.

Answer:

b) true

c) false

d) true

e) true

Step-by-step explanation:

b) Any line that contains an interior point of a circle is a secant of the circle. The center is an interior point, so a line that contains the circle center is a secant.

__

c) Chords of different lengths intercept arcs of different measures

__

d) Any line perpendicular to a radius at the point where the radius meets the circle is a tangent to the circle. The endpoint of a diameter is the endpoint of a radius, so a line perpendicular there will be a tangent.

__

e) The measure of an inscribed angle is half the measure of the intercepted arc, so all inscribed angles that intercept equal arcs are equal.

The statement 'If a line contains the center of a circle, it is a secant of the circle.' is true. The statement 'If 2 chords intersect a circle, they intercept equal arcs.' is false. Statements 'If a line is perpendicular to a diameter at one of its endpoints, then it is tangent to the circle.' and 'Inscribed angle that intercept equal arcs are equal.' are both true.

b) True. If a line contains the center of a circle, it does pass through the circle at two points, therefore it's a secant of the circle.

c) False. Two chords intersecting inside a circle do not always intercept equal arcs. The length of the arcs they intercept depends on their distance from the center of the circle, not on the mere fact that they intersect.

d) True. If a line is perpendicular to a diameter at one of its endpoints, it does indeed result in a tangent to the circle. This is because the line touches the circle at exactly one point (the endpoint), fulfilling the definition of a tangent line.

e) True. Inscribed angles that intercept (cut off) equal arcs are indeed equal. This is a basic theorem in circle geometry.

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Answer:

Yes

Step-by-step explanation:

0.4 = 4/10 = 2/5

0.4 converted into a fraction is 4/10, 4/10 simplified is 2/5

Answer:

Step-by-step explanation:

Let x represent the amount invested at the higher rate (6%). Then the amount invested at the lower rate is (2400-x) and the total interest earned is ...

  6%·x + 4%·(2400-x) = 5.5%·2400

Dividing by % and rearranging, we have ...

  x(6 -4) = 2400(5.5 -4)

  x = 2400·(5.5 -4)/(6 -4) = 2400(1.5/2) = 2400·0.75

  x = 1800 . . . . . . . . amount invested at 6%

  2400-x = 600 . . . amount invested at 4%

Maria put $1800 in the 6% account and $600 in the 4% account.

_____

Comment on the solution

You will note that the proportion of the investment that went to the higher interest rate account is (5.5-4)/(6-4). This is the ratio of the mixed interest rate less the lower rate to the difference of account rates. This will be the generic solution to mixture problems, so is worthy of note for that reason.

Answer:  

For 4% interest, investment $600

For 6% interest, investment $1,800  

Explanation:  

Maria invested $2,400 into two accounts. One account paid 4% interest and the other paid 6% interest. She earned 5.5% interest on the total investment.

It is a system of linear equations in two variables. Variables are x and y. Solve for x and y using substitution method.

In substitution method: First solve for one variable in terms of another variable and then substitute into another equation.

Further explanation:  

Let $x invested in account which paying 4% interest.

Let $y invested in another account which paying 6% interest.  

Therefore,  x + y = 2400   --------------(1)

                                                                                        = 132

Therefore,  0.04x + 0.06y = 132 -----------(2)

Solve system of equations for x and y , using substitution method.

                     x + y = 2400  

solve for y in terms of x and we get,

                         y = 2400 - x ------------ (3)  

Substitute the value of y into equation (2) and we get,  

                   0.04x + 0.06(2400-x) = 132

                      0.04x + 144 - 0.06x = 132

                                            -0.02x = 132 - 144

                                                     [tex]x=\dfrac{-12}{-0.02}[/tex]  

                                                     [tex]x=600[/tex]

Substitute the value of x into eq(3)  

                                                y = 2400 - 600

                                                y = 1800

In account paying 4% interest, invest $600 and paying 6% interest invest $1,800

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Keywords:

System of equation, Two variable equations, solve for x and y, substitution method, elimination method, cross multiplication method.

Answer:

1

Step-by-step explanation:

The production cost of company 1 never gets below 340 (at x=20), found e.g., by equating the derived function to 0.

You can figure out that g(x) = 0.05x^2 -7x + 300, but you already know that company 1 has higher cost based on the example values for g(x).

Answer:

Hi!

The answer is:

Based on the given information, the minimum production cost for company __1__ is greater.

Step-by-step explanation:

You have to find the minimum value of a f(x), so you need to differentiate it, set it to zero and solve for x. Then differentiate the function again and calculate the value of the second derivative at the maximum or minimum points to find out whether it is a maximum or a minimum.

[tex]f(x) = 0.15x^2 - 6x + 400[/tex]

[tex]\frac{df}{dx}=2 * 0.15x - 6 = 0.30x - 6 [/tex] First derivative.

[tex][tex]\frac{d^2f}{dx^2} = 2 [/tex][/tex] Second derivative. Confirm it's a minimum point.

Minimum occurs at:

0.30x − 6 = 0

0.30x = 6

x = 6/0.30

x = 20

Replace x on equation f(x):

f(20) = 0.15 * 20² - 6 * 20 + 400 = 340.

For g(x), the value of minimum cost is:

g(70) = 55.

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

We look for two points through which the line passes to find the slope:

[tex](x1, y1) = (2,2)\\(x2, y2) = (0, -4)[/tex]

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-4-2} {0-2} = \frac {-6} {- 2} = 3[/tex]

So, the line is:

[tex]y = 3x + b[/tex]

We have "b" replacing any of the points:

[tex]-4 = 3 (0) + b\\-4 = b[/tex]

Finally, the equation is:

[tex]y = 3x-4[/tex]

Answer:

[tex]y = 3x-4[/tex]

Answer:

its the second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the answer is B, is this a lesson or a quiz?

The answer is:

The correct option is:

C) [tex](9^{3})^{3}=9^{9}[/tex]

To solve the problem, we need to remember the power of a power property, it's defined by the following way:

[tex](a^{m})^{n}=a^{m*n}[/tex]

When we have a power of a power, we need to keep the base and then, the new exponent will be the product between the two original exponents.

So, we are given the expression:

[tex](9^{3})^{3}[/tex]

Then, calculating we have:

[tex](9^{3})^{3}=9^{3*3}=9^{9}[/tex]

Hence, we have that the correct option is:

C) [tex](9^{3})^{3}=9^{9}[/tex]

Have a nice day!

Answer:

The correct answer is option C)  9^9

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

It is given that (9^3)^3

To find the correct option

(9^3)^3 can be written as, (9³)³

By using above identities,

(9³)³ = 9³ ˣ³

 = 9⁹

Therefore the correct answer is option C).  9^9

Answer:

The correct option is D

Step-by-step explanation:

The correct option is D.

They both have the same height, assuming that each coin has same volume, then how can coins in 1 stack have different volume than coins in another stack no matter how you stack them.

Like two cylinders with same base area and height have same volume. Like wise rectangle and parallelogram with same base and same perpendicular height having same area....

D) they have the same volume

The surface area of a sphere is given by

[tex]S = 4\pi r^2[/tex]

We deduce

[tex]r = \sqrt{\dfrac{S}{4\pi}}[/tex]

So, in your case, the radius is

[tex]r = \sqrt{\dfrac{100\pi}{4\pi}}=\sqrt{25}=5[/tex]

The volume of a sphere is given by

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

So, we have

[tex]V = \dfrac{4}{3} \pi 5^3 = \dfrac{500}{3}\pi[/tex]

Answer:x = -2

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

25=5x+35

25-35=5x

-10=5x/:5

-2=x

x=-2

Answer:

[tex]\large\boxed{x=\dfrac{1}{a}}[/tex]

Step-by-step explanation:

[tex]2-4(ax-3)=10\qquad\text{subtract 2 from both sides}\\\\-4(ax-3)=8\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4(ax-3)}{-4}=\dfrac{8}{-4}\\\\ax-3=-2\qquad\text{add 3 to both sides}\\\\ax-3+3=-2+3\\\\ax=1\qquad\text{divide both sides by}\ a\neq0\\\\x=\dfrac{1}{a}[/tex]

Answer:

Y-intercept;

(0, 1)

Asymptote;

Horizontal asymptote: y = -2

Step-by-step explanation:

We have been given the following exponential function;

[tex]f(x) = 3^{x+1}-2[/tex]

The y-intercept of a function is the point where the graph of the function intersects the y-axis. At this point, the value of x is usually 0. Therefore, to establish the y-intercept of the given function we substitute x with 0 in the given equation and simplify;

[tex]y=3^{0+1}-2\\ \\y=3-2=1[/tex]

The y-intercept of the given function is thus (0, 1).

Exponential function of the form;

[tex]f(x)=c.n^{ax+b}+k[/tex]

has a horizontal asymptote y = k. In the function given, k = -2 implying that

y = -2 is a horizontal asymptote of the given exponential function

Answer:

I believe it would be 40

Step-by-step explanation:

5:3 = x:24

3 times 8 = 24

5 times 8 = 40

There are 40 girls in the chorus.

Answer:

[tex]x=17[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

In this problem Triangles BAE and DAE are congruent by SAS postulate

so

BE=DE

substitute the given values

[tex]3x-24=x+10[/tex]

solve for x

[tex]3x-x=24+10[/tex]

[tex]2x=34[/tex]

[tex]x=17[/tex]

Answer:

B. 17

Step-by-step explanation:

The angle of elevation from Jonathan to Mina is approximately 43.81 degrees.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
We can use the tangent function to find the angle of elevation from Jonathan to Mina.

Let θ be the angle of elevation, then we have:

tan(θ) = opposite / adjacent

Where the opposite is the height of the tower (389 feet) and adjacent is the distance between Jonathan and the base of the tower (412 feet).

So, we have:

tan(θ) = 389 / 412

θ ≈ 43.81 degrees

Therefore, the angle of elevation from Jonathan to Mina is approximately 43.81 degrees.

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Minimum: 35

First quartile: 6, 13, 14, 18, 19, 29 (avg. is 16.5)

Median: ≈41.08 (41.0769230769)

Third quartile: 44, 53, 55, 71, 84, 93 (avg. is 66.67)

Maximum: 93

Interquartile range: 50.17

Final answer:

The minimum is 6, the first quartile is 16, the median is 29, the third quartile is 54, the maximum is 93, and the interquartile range is 38.

Explanation:

To find the minimum, first quartile (Q1), median, third quartile (Q3), maximum, and interquartile range (IQR) of the given data set, we first need to organize the data in ascending order, which is already done. Then, we apply the appropriate statistical methods to determine each required value.

Answer:

0.91.

Step-by-step explanation:

We use the formula:

P(a U b) = p(a) + p(b) - p (a ∩ b)     where P(a U b) is p(a or b) and p (a ∩ b) is p  (a and b).

So p(a or b) = 0.78 + 0.66 - 0.53

= 0.91.

Answer:

An outlier is the number that is much smaller or larger than the other numbers.

In this case it is 29 :)

Answer:

D:  29

Step-by-step explanation:

D:  29 is your outlier.  It's quite different from the commonest values (which are in the range 8 - 17).

Answer:

1. The correct answer option is B.

2. The correct answer option is C.

4. The correct answer option is D.

Step-by-step explanation:

1. [tex]\frac{3}{x^2+14x+48}[/tex] ÷ [tex]\frac{3}{10x+60}[/tex]

Changing division to multiplication by taking the reciprocal of the latter fraction:

[tex]\frac{3}{x^2+14x+48} \times \frac{10x+60}{3}[/tex]

[tex]\frac{3}{(x+6)(x+8)} \times \frac{10(x+6)}{3}[/tex]

Cancelling the like terms to get:

[tex]\frac{10}{(x+8)}[/tex]

The correct answer option is B. [tex]\frac{10}{(x+8)}[/tex]

2. [tex]\frac{4x^2+36}{4x} \times \frac{1}{5x}[/tex]

Factorizing the terms and then cancelling the like terms to get:

[tex]\frac{4(x^2+9)}{4x} \times \frac{1}{5x}[/tex]

[tex]\frac{x^2+9}{5x^2}[/tex]

The correct answer option is C. [tex]\frac{x^2+9}{5x^2}[/tex].

4. [tex]\frac{\frac{4t^2-16}{8} }{\frac{t-2}{6} }[/tex]

Changing division to multiplication by taking the reciprocal of the latter fraction:

[tex]\frac{4t^2-16}{8} \times \frac{6}{t-2}[/tex]

[tex]\frac{4(t-2)(t+2)}{8} \times \frac{6}{t-2}[/tex]

Cancelling the like terms to get:

[tex]3(t+2)[/tex]

The correct answer option is D. [tex]3(t+2)[/tex].

Answer:

an = 6 (1/4)^(n-1)

Step-by-step explanation:

We're given the first term, a₁ = 6.

The common ratio is a term aₓ divided by the previous term aₓ₋₁.

aₓ = 1/4 aₓ₋₁

aₓ / aₓ₋₁ = 1/4

r = 1/4

Therefore:

an = 6 (1/4)^(n-1)

Your answer is correct, good job!

The recursive rule for a geometric sequence is given a₁ = 6, aₓ = 1/4 aₓ₋₁. The explicit rule would be [tex]a_n = 6 (1/4)^{n-1}[/tex].

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

[tex]a, ar, ar^2, ar^3, \cdots[/tex]

Thus, the nth term of such sequence would be  

[tex]T_n = ar^{n-1}[/tex]

We have been given the first term,

a₁ = 6.

The common ratio is the term aₓ divided by the previous term aₓ₋₁.

aₓ = 1/4 aₓ₋₁

aₓ / aₓ₋₁ = 1/4

r = 1/4

Therefore:

[tex]a_n = 6 (1/4)^{n-1}[/tex]

Hence, The explicit rule would be [tex]a_n = 6 (1/4)^{n-1}[/tex].

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Answer:

Step-by-step explanation:

Set up a ratio in the form of pages/minute:

[tex]\frac{pages}{minute} :[/tex]

then fill in next to that how many pages per minute George can read:

[tex]\frac{pages}{minute}:\frac{15}{12}[/tex]

Now we want to figure out how long (time is our unknown, so we call that x) it will take him to read 85 pages.  The 85 goes in a ratio on the same line as the other number of pages:

[tex]\frac{pages}{minute}:\frac{15}{12}=\frac{85}{x}[/tex]

Cross multiply to get 15x = 1020

Now divide both sides by 15 to get x = 68 minutes, which is an hour and 8 minutes.

Answer:

68 minutes

Step-by-step explanation:

Given that George read 15 pages in a book in 12 minutes, and we need to find out how long it will take him to finish the book if it has 85 pages, we must first find how much minutes it takes to read per page because we need to find the amount of time.

Write an equation (In this case p=pages and t= minutes or time):

(Remember! We are trying to find the minutes per page, not how many pages per minute.)

15p=12t

p=12/15t

p=0.8t

We now know he reads 1 page in 0.8 minutes. Given that we need to find the amount of time to read 85 pages, multiply 0.8 by 85 because 0.8 minutes=1 page.

85*0.8=68

Therefore, it takes him 68 minutes to read 85 pages

Answer: A'=(1, 3); B'=(-3, 4);C'=(3, 0); D'=(-2, 5)

You can check the PNG attached as well.

Step-by-step explanation:

You need to represent the symmetry of every given points respet to the line

[tex]y = 2[/tex]

In that case, the line beeing paralell to the x- axis, x- value of the symmetry is the same of the given point and y = 2 is the middle between both points.

Point A(1, 1)

[tex]x_{A} = 1\\ x_{A'} = 1 \\\\\frac{y_{A} +y_{A'} }{2} =2\\y_{A'} = 4 - y_{A} = 4 - 1 = 3[/tex]

Point B(-3, 0)

[tex]x_{B} = 1\\ x_{B'} = 1 \\\\\frac{y_{B} +y_{B'} }{2} =2\\y_{B'} = 4 - y_{B} = 4 - 0 = 4[/tex]

Point C(3, 4)

[tex]x_{C} = 1\\ x_{C'} = 1 \\\\\frac{y_{C} +y_{C'} }{2} =2\\y_{C'} = 4 - y_{C} = 4 - 4 = 0[/tex]

Point D(-2, -1)

[tex]x_{D} = 1\\ x_{D'} = 1 \\\\\frac{y_{D} +y_{D'} }{2} =2\\y_{D'} = 4 - y_{D} = 4 - (-1) = 4 + 1 = 5[/tex]