An investor bought 400 shares of stock, some at $2.75 per share and some at $4.00 per share. If the total cost was $1443.75, how many shares of each stock did the investor buy? (Round to two decimal places if necessary.)

Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions

The inverse of a function is a function that can reverse into another function.

If we have function f and g, and f f(x) = y, then g is the inverse of f if and only if g(y) = x

Also, if f is a function f⁻¹ is the inverse of x and ff⁻¹(x) = f⁻¹f(x) = x

Given the functions m(x) = x³ - 5 and n(x) = ∛(x + 5)

If m(x) and n(x) are inverse, then m(n(x)) = n(m(x)) = x

So, we proceed as follows

m(x) = x³ - 5

m(n(x)) = (∛(x + 5))³ - 5

m(n(x)) = x + 5 - 5

m(n(x)) = x + 0

m(n(x)) = x

Also,

n(x) = ∛(x + 5)

n(m(x)) = ∛(x³ - 5 + 5)

n(m(x)) = ∛(x³ - 0)

n(m(x)) = ∛(x³)

n(m(x)) = x

Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions

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Based on the money earned by Kaleigh's aunt from Wheels Around Town, the relationship between miles and money earned is proportional.

In a proportional relationship, the rate of increase or decrease in x should be equivalent to the rate of increase or decrease in y. This rate should be constant through the entire distribution.

The equation of the line should take the form:
y = mx

There should be no y-intercept.

The slope is:

= (48  - 72) / (120 - 180)

= -24 / - 60

= 2/5

Every value of y has to be 2/5 of x.

= 160 x 2/5 = 64

= 200 x 2/5 = 80

The relationship is therefore proportional.

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The given sequence is an arithmetic sequence and the common difference is 4.

Given, the sequence is :

3,12,48

we need to determine the common difference.

common ratio = a₂/a₁

a₂/a₁ = 12/3

a₂/a₁ = 4

a₃/a₂ = 48/12

a₃/a₂ = 4

hence the common difference is 4.

Therefore, the common difference indicates arithmetic sequence.

There are two approaches to define an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term."

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The statement that describes the shaded region in the Venn diagram is (a) (P u Q)' n S

The Venn diagram represents the given figure

On the Venn diagram, we can see that:

All region that contains set P and Q are not shaded

This means that

(P u Q)'

The only region that is shaded in the diagram is the region of set S

This is then represented as

(P u Q)' n S

Hence, the statement that describes the shaded region in the Venn diagram is (a) (P u Q)' n S

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y = 2/3x -6

Conditions for Lines to be parallel

If two straight lines are cut by a transversal, the pair of alternate angles are equal, then two straight lines are parallel to each other. the pair of interior angles on the same side of traversals is supplementary, then the two straight lines are parallel.

Given line

3y – 2x = – 2

passes through (3, –3)

The slope-intercept form is

y =mx+b,

where m is the slope and

b is the y-intercept.

y = mx+b

Divide each term in

3y – 2x = – 2 by -2 and simplify.

-3/2y +x =1

Reorder terms.

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

Using the slope-intercept form, the slope is

2/3.m=2/3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope

2/3 and a given point (3, –3)

to substitute for

x1 and y1

in the point-slope form

y−y1=m(x−x1)

which is derived from the slope equation

m=(y2−y1)x2−x1.

y−(-3)=2/3⋅(x−(3))

Simplify the equation and keep it in point-slope form.

y+4=2/3⋅(x-3)

y = 2/3x -6

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[tex]f_x(0,0)[/tex] is the partial derivative of [tex]f[/tex] with respect to [tex]x[/tex] evaluated at the origin. By definition of derivative, this is the limit

[tex]\displaystyle f_x(0,0) = \lim_{x\to0} \frac{f(x,0) - f(0,0)}{x-0} = \lim_{x\to0} \frac{f(x,0)}x[/tex]

We have by definition of [tex]f[/tex],

[tex]f(x,0) = \dfrac{x^5}{x^4+0^4} = \dfrac{x^5}{x^4}[/tex]

so

[tex]\displaystyle f_x(0,0) = \lim_{x\to0} \frac{\frac{x^5}{x^4}}x = \lim_{x\to0} \frac{x^5}{x^5} = \lim_{x\to0} 1 = \boxed{1}[/tex]

Answer:

300 units

Step-by-step explanation:

Applying the knowledge of fractions, the number of pounds of vegetables required to prepare 1/3 bowl of salad is: 1¼ pounds.

In solving this problem, we would apply our knowledge of fractions as explained below.

One bowl of salad needs 3¾ pounds of vegetables

Let the number of pounds if vegetables needed for ⅓ bowl be represented as x. Therefore, we would have the following proportion:

1 bowl = 15/4 pounds of vegetables [i.e. 3¾]

⅓ bowl = x

Thus:

1/15/4 = ⅓/x

1/1 × 4/15 = 1/3 × 1/x

4/15 = 1/3x

Cross multiply

4(3x) = 1(15)

12x = 15

Divide both sides by 12

12x/12 = 15/12

x = 15/12

x = 5/4

x = 1¼ pounds

Therefore, applying the knowledge of fractions, the number of pounds of vegetables required to prepare 1/3 bowl of salad is: 1¼ pounds.

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Answer:

(4,13)

Step-by-step explanation:

Set the 2 equations equal to each other and solve for x.

5x - 7 = 2x + 5  Subtract 2x from both sides

3x - 7 = 5  Add 7 to both sides

3x = 12  Divide both sides by 3

x = 4

Now plug 4 back into either of the original 2 equations to find y.

y = 5x -7

y= 5(4) -7

y = 20 -7

y= 13

Answer:

C - A = B

Step-by-step explanation:

B is now what we are solving for.

Answer:

Flip the equation so B is the sum and also the subject.

Step-by-step explanation:

[tex]A - C = B[/tex]

Answer:

68

Step-by-step explanation:

4(4 + 1)²

4(16 + 1)

64 + 4

68

Answer: 6 : 3 = 8 : 4 = 1 : 2

Step-by-step explanation:

Here are 3 equivalent ratios

6 : 3 = 8 : 4 = 1 : 2

The volume of the given figure is 267.95 mi³.

The given object is a sphere. A sphere is a three-dimensional object that has all its surface points at equal distances from the center. A sphere is round in shape.

The volume of an object is the amount of space in the three-dimensional object.  The radius of a sphere is a straight line from the circumference of the sphere to the center of the sphere.

Volume of a sphere = 4/3 × π × r³

Where:

π = pi = 22/7

r = radius = 4

4/3 x 22/7 x 4³ = 267.94667 mi³

267.95 mi³

To round off to the nearest hundredth, if the thousandth digit is equal to 5 or greater than 5, add 1 to the hundredth digit and change all the digits after the hundredth digit to 0.

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The linear scale factor for going from first to second statue will be 2/3 and the weight of the second statue will be 96 2/3 pounds.

It should be noted that the statue is 6 feet tall and weighs about 145 pounds and second model statue is 4 feet tall.

Therefore, the linear scale factor for going from first to second statue will be:

= 4/6

= 2/3

Therefore, the weight of the second statue will be:

= 2/3 × 145

= 96 2/3 pounds.

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The equivalent value of 33% expressed in a ratio, fraction, and decimal is 33 : 100, 33/100 and 0.33 respectively

33%

In ratio:

33%

= 33 / 100

= 33 : 100

In fraction:

33%

= 33/100

In decimal:

33%

= 33/100

= 0.33

Therefore, the equivalent value of 33% expressed in a ratio, fraction, and decimal is 33 : 100, 33/100 and 0.33 respectively

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If y varies directly with x and y=36 when x=6, the value of y is 24 when x=4.

The  mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. It is a linear function defined by an equation of the form

y = kx when x is not equal to zero.

Given:

If y varies directly with x and y=36 when x=6

According to given question we have

we can write direct variation equation as

y= k*x

where k is constant

y = 36 when x=6,

36 =k(6)

k=6

So, by putting the value of x=4 we get,

y =kx

y=6*4

y=24

Therefore, If y varies directly with x and y=36 when x=6, the value of y is 24 when x=4.

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A. 1 and 7 and

2 and 8 alternate exteriora

Answer:

∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

Alternate exterior angles are on the exterior of the lines and on opposite sides of the transversal.

Answer:

Step-by-step explanation:

All you need is angles that are the same in each shape.

For example, all squares are similar. They all have 4 ninety degree angles.

All polygons with equal angles are similar. All regular hexagons have interior angles of 120 degrees.  So all regular hexagons are similar.

All regular octagons are similar. All regular octagons (8 sides) have interior angles of 135 degrees.

To get more, just look up the names of all regular polygons from 3 to 10. I've given you three of them.

Answer:

1) -2a + 2

2) x + 1

3) -5x + 5

Step-by-step explanation(1):

[tex]\left(7a+4\right)-\left(9a+2\right)\\=7a+4-\left(9a+2\right)\\=7a+4-9a-2\\=7a-9a+4-2\\=-2a+4-2\\=-2a+2[/tex]

Step-by-step explanation(2):

[tex]\left(2x+5\right)-\left(x+4\right)\\=2x+5-\left(x+4\right)\\=2x+5-x-4\\=2x-x+5-4\\=x+5-4\\=x+1[/tex]

Step-by-step explanation(3):

[tex]\left(2x+4\right)-\left(7x-1\right)\\=2x+4-\left(7x-1\right)\\=2x+4-7x+1\\=2x-7x+4+1\\=-5x+4+1\\=-5x+5[/tex]

Hope this helps. Notify me of any concerns.

Answer:

Step-by-step explanation: since X=3 replace X

3 (3)2 +8 (3)+8  

18+24+8 =50

The arithmetic sequence is 7,14,21,28,35,48

In an arithmetic progression (AP) sequence of numbers, the difference between any two consecutive integers is always the same. It is also known as an arithmetic sequence.

There are two definitions for an arithmetic sequence. Each term in an arithmetic sequence is created by adding a predetermined number (positive, negative, or zero) to its preceding term. It is a "series where the differences between every two following terms are the same."

Given,

first term, a = 7

common difference d = 7

n = 2

a+(n-1)d = 7+( 2 - 1 )7

= 7 + 7

= 14

n = 3

a+(n-1)d = 7+(3-1) 7

= 7+14

= 21

n = 4

a+(n-1)d = 7+(4-1) 7

= 7+ (3)7

= 28

n = 5

a+(n-1)d = 7+( 5-1 ) 7

= 7+ (4)7

= 35

n = 6

a+(n-1)d = 7+( 6-1 ) 7

= 7+ (5)7

= 42

the five terms are 7,14,21,28,35,48.

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The system of equation  4x - 3y = 3and  -8x + 6y = -6 has no solution as they are parallel lines.

When two or more linear equations are there we call them a system of equations.

Given a system of equations 4x - 3y = 3...(i) and -8x + 6y = -6...(ii) this is solvable as the number of variables is not more than the number of equations.

Now to solve for x or y first we have to eliminate one of the varibales by any arithmetic operation.

By observing we conclude that if we multiply equation(i) by 2 and then add both of them the x variable will cancel out and we can solve for y which is

      8x - 6y =  6

(+)  -8x + 6y = -6

 ----------------------

As we can see here that both x and y are getting canceled therefore these two equations have no solution and hence they are parallel to each other(lines).

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The required line representing the rise and the run of the line is created.

And the slope of the line in its simplest form is 9/-18.

Given a line is represented on the graph.

we need to create lines representing the rise and run of the line.

To find the slope of the line we need to determine the rise and run of the line.

The slope of a line is defined as the rise divided by the run, or the ratio of the rise to the run. It gives information about a line's slope in the coordinate plane. Finding the slope between two separate places is comparable to calculating the slope of a line.

The coordinates of the points are:

(9,0) = (x₁ , y₁)

(₋9 , 9) = (x₂ , y₂)

we know that slope (m) = rise/ run

rise  = y₂ ₋ y₁

= 9 ₋ 0

= 9

run = x₂ ₋ x₁

= ₋9 ₋ 9

= ₋18

hence the slope is 9/₋18

The required slope of the line is 9/-18.

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From the given parameters in the survey; It is not binomial because the probability of success does not remain the same in all trials.

The conditions for a distribution to be called binomial distribution are as follows;

1. The number of observations n is fixed.

2. Each observation is independent.

3. Each observation represents one of two outcomes (either a success or failure).

4. The probability of success (p) is the same for each outcome.

Now, from the given question, we can see that the number of observations is fixed and that each observation is independent. However, we don't know the probability of success for each person and as such we can't call this a binomial distribution.

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Answer: 20

Step-by-step explanation: I can help with am explanation if you dm me:)