Mark invests $150 at the beginning of each quarter in stock ABC. According
to the table below, how many shares of ABC will Mark own at the end of the
year?
ABC
Stock Price
Q1
$15
Q2
$16
Q3
$13
Q4
$18
OA. 36 shares
B. 44 shares
C. 40 shares
h
D. 38 shares

Answer:

Step-by-step explanation:

B

18 + 7/9

14 + 7/8

First, rewrite each fraction in terms of a common denominator. 8 and 9 don't share a common multiple until 8 * 9 = 72, so we have

7/9 = (7/9) • (8/8) = (7 • 8)/(9 • 8) = 56/72

7/8 = (7/8) • (9/9) = (7 • 9)/(8 • 9) = 63/72

Next, write each whole number in terms of fractions with the same denominator. We have

18 • 72 = 1296  ==>  18 = 1296/72

14 • 72 = 1008  ==>  14 = 1008/72

Write each mixed number as an improper fraction:

18 + 7/9 = 1296/72 + 56/72 = (1296 + 56)/72 = 1352/72

14 + 7/8 = 1008/72 + 63/72 = (1008 + 63)/72 = 1071/72

If the backpack and book together weigh 18 + 7/9 pounds, and the backpack without the book weighs 14 + 7/8 pounds, then the book alone weighs the difference, call it b :

b = (18 + 7/9) - (14 + 7/8)

b = 1352/72 - 1071/72

b = (1352 - 1071)/72

b = 281/72

Convert this to a mixed number. 72 • 4 = 288, so 72 • 4 - 7 = 281:

b = (72 • 4 - 7)/72

b = (72 • 4)/72 - 7/72

b = 4 - 7/72

b = (3 + 1) - 7/72

b = 3 + (1 - 7/72)

b = 3 + 65/72

The surface area of the pyramid is 74.25 square meters.

Surface area is the total area that the surface of an object occupies. It is the sum of the areas of all the faces, sides, and curved surfaces of an object. Surface area is usually measured in square units, such as square meters, square feet, or square centimeters.

A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex (known as the apex). Pyramids are named according to the shape of their base.

In the given question,

The area of the base is simply the area of a square, which is:

Area of base = length x width = 4.5m x 4.5m = 20.25 square meters

To find the area of each triangular face, we first need to find the length of the slant height (the height of the triangle).

We can use the Pythagorean theorem to do this:

h²= (1/2 x base)² + height²

h² = (1/2 x 4.5)² + 6²

h² = 2.25 + 36

h² = 38.25

h = √38.25

h = 6.18 meters (rounded to two decimal places)

Now that we know the slant height, we can find the area of each triangular face:

Area of one triangular face = (1/2 x base x height) = (1/2 x 4.5 x 6) = 13.5 square meters

Since there are four triangular faces on a square pyramid, we need to multiply this by 4 to find the total area of the triangular faces:

Total area of triangular faces = 4 x 13.5 = 54 square meters

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Surface area = Area of base + Total area of triangular faces

Surface area = 20.25 + 54

Surface area = 74.25 square meters

Therefore, the surface area of the pyramid is 74.25 square meters.

To know more about Surface area, visit:

https://brainly.com/question/29298005

#SPJ1

Answer:

Yes, the triangles are congruent.

Step-by-step explanation:

The triangles are the same size and shape. Even though they are flipped they are a mirror image of eachother, meaning they are congruent.

Given : The number is \(\sqrt{20}\).

To find:  Set(s) of numbers in which \(\sqrt{20}\) belong to.

Solution:

We know that,

Natural Number  \(=\{1,2,3,...\}\)

Whole Number   \(=\{0,1,2,3,...\}\)

Integer   \(=\{...-3,-2,-1,0,1,2,3,...\}\) 

Rational numbers  \(=\{-2,0,3.4,\dfrac{1}{2}\text{ etc}\}\)

Irrational numbers  \(=\{\sqrt{2},\sqrt{3},\pi, 1.25436...\text{ etc}\}\)

We have,

\(\sqrt{20}=\sqrt{4\times 5}\)

\(\sqrt{20}=\sqrt{4}\times \sqrt{5}\)

\(\sqrt{20}=2\times \sqrt{5}\)

\(\sqrt{20}=2\sqrt{5}\)

So, \(\sqrt{20}\) is the product of a non zero rational number, i.e., 2 and an irrational number, i.e., \(\sqrt{5}\).

We know that product of a non zero rational number and an irrational number is always irrational.

So, \(\sqrt{20}\) is an irrational number.

Therefore, the correct option is  5.

Consider the numbers as, if we assume our first number to be x and second number being y, then from the given information we will be having the following equations :

\({:\implies \quad \begin{cases}\sf 3x+3y=-12\\ \\ \sf 5x+2y=4\end{cases}}\)

Now, rewrite the second equation as ;

\({:\implies \quad \sf 3(x+y)=-12}\)

Divide both sides by 3 ;

\({:\implies \quad \sf x+y=-4\quad ---(i)}\)

Now, consider the second equation of the above cases

\({:\implies \quad \sf 5x+2y=4\quad ---(ii)}\)

Now, multiply (i) by 2 on both sides :

\({:\implies \quad \sf 2x+2y=-8\quad ---(iii)}\)

Now, subtracting (ii) from (iii) will give us :

\({:\implies \quad \sf 2x+2y-(5x+2y)=-8-4}\)

\({:\implies \quad \sf 2x+2y-5x-2y=-12}\)

\({:\implies \quad \sf -3x=-12}\)

\({:\implies \quad \boxed{\bf{x=4}}}\)

Now, putting x = 4 in (i), will give y + 4 = -4, then solving for y will yield \({\boxed{\bf{y=-8}}}\)

Hence, we can conclude that :

\({\quad \qquad \longrightarrow \begin{cases}\bf x=4\\ \\ \bf y=-8\end{cases}}\)

Answer:

hlohhwwhwuwhwwhwywuyeyeyhee

Answer:

a. For the function:

f(x) = { sin x/3, if x ≤ π

{ x√3/2π, if x > π

I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:

lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2

II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:

lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2

III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:

lim f(x) as x approaches π = √3/2

b. For the function:

f(x) = (x^2 - 36)/√(x^2 - 12x + 36)

I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0

Substituting x = 6 - h into the function, we get:

f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]

= [h^2 - 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 - h) = h(h - 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12

II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0

Substituting x = 6 + h into the function, we get:

f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]

= [h^2 + 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 + h) = h(h + 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 + h) as h approaches 0+ = lim h(h +

Step-by-step explanation:

Answer:

histogram

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Example:

You have no money, you decide to swipe your credit card to purchase something for $17. Again, you did so for another item paying $24. You are now $41 in debt. Your mom decides to pay for your debt which is $41. You decide to actually go to your part-time job and earn $23. When was the time you had the most money in this example? When you earned the $23 becuase you started with none.

Answer:

23

Step-by-step explanation:

Out of the numbers given:

All positive numbers are greater than negative numbers.

This eliminates -17 and -24.

Comparing 0 to 23:

23 has more value than 0.

0 < 23

This means out of the numbers given, 23 has the greatest value.  

Hope this helps.  

Answer:

Distributive property

Step-by-step explanation:

8 x y = 8y, -8 x -2 = 16

#1

<5 and <6 are vertical angles

#2

It states that

If a=b and b=c then a=c is true

#4

#5

Answer:

y=3(x-9)^2+4

Step-by-step explanation:

To move a parabola horizontally to the right, subtract 9.

To move it upward 4 units, you simply have to add 4.

These do not change the characteristics of the shape. I suggest looking at a set of rules that affect how the parabola moves horizontally and vertically.

Answer:

B

Step-by-step explanation:

<2 and <7 are same side exterior angles, so you can say they add up to 180°.

We can write an equation to model the situation:

m<2 + m<7 = 180°

We can substitute the value of m<2,

132° + m<7 = 180°

m<7 = 48°

This is option B.

Answer:

These are two imaginary solutions.

x = − 4 , 2 ± 2 √ 3 i

Step-by-step explanation:

The volume of the hemisphere with a diameter of 60.9 inches rounded to the nearest tenth is 59131.7 inches³.

Given that,

Diameter of a hemisphere = 60.9 inches

We have to find the volume of the hemisphere.

We know that, radius is half the measure of the diameter.

Radius of the hemisphere = 60.9 / 2 = 30.45 inches

Volume of a hemisphere is,

Volume = 2/3 π r³

Here r is the radius

Substituting,

Volume = 2/3 π (30.45)³

             = 59131.7 inches³

Hence the volume is 59131.7 inches³.

Learn more about Volume here :

https://brainly.com/question/13338592

#SPJ1

The percent of data within the following interval from 28 to 82 is 99.73%

From the question, we have the following parameters that can be used in our computation:

Mean = 55

Standard deviation = 9

Scores = from 28 to 82

So, we have

z = (28 - 55)/9 = -3

z = (82 - 55)/9 = 4

This means that it is between a z-score of -3 and a z-score of 3

This is represented as

Probability = (-3 < z < 3)

Using a graphing calculator, we have

Probability =  0.9973

Express as percentage

Probability =  99.73%

Hence, the probability is 99.73%

Read mroe about z-scores at

brainly.com/question/25638875

#SPJ1

Answer:

67.5

Step-by-step explanation:

The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

learn more about surface area from

https://brainly.com/question/16519513

#SPJ1

Answer:

As 5 litres is 5000ml, it would take 10 jugs of 500ml as long as there is no spillage

Step-by-step explanation:

Hope this helps, a brainliest would be much appreciated:)

Take into account that a dilation of an enlargement consists in a scale factor greater than 1.

In the given options, you can notice that scale factor (5/3) is the only one greater than 1.

Then, the dilation of an enlargment is:

( 5/3 x, 5/3 y)

Answer:

\( \dfrac{2}{x} - 9\)

Step-by-step explanation:

the quotient of 2 and x:

\( \dfrac{2}{x} \)

9 less than the quotient of 2 and x:

\( \dfrac{2}{x} - 9\)

The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To study more about Probability:

https://brainly.com/question/13604758

https://brainly.com/question/251701

The system of linear equations that can be solved from the matrices is given as follows:

Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:

A = [-5 4; -8 1]

Hence the multiplication of matrices representing the system is given as follows:

[-5 4; -8 1][x; y] = [3; -6]

Applying the multiplication of matrices, the system of equations is given as follows:

More can be learned about a system of equations at https://brainly.com/question/13729904

#SPJ1

The attached graph represents the graph of the function g(x)

The function f(x) is an absolute value function.

An absolute value function is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

From the graph, we have:

(h, k) = (-3, -2)

So, we have:

y = a|x + 3| - 2

Also, we have:

(x, y) = (-1, 0)

So, we have:

0 = a|-1 + 3| - 2

This gives

0 = 2a - 2

Solve for a

a = 1

Substitute a = 1 in y = a|x + 3| - 2

y = |x + 3| - 2

This means that

f(x) = |x + 3| - 2

We have:

g(x) = 2f(x)

This means that:

g(x) = 2(|x + 3| - 2)

So, we have:

g(x) = 2|x + 3| - 4

See attachment for the graph of g(x)

Read more about absolute value functions at:

https://brainly.com/question/10664936

#SPJ1

Answer:

D

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

10 + 15

Answer:

Step-by-step explanation:

yes you would. they are very strict with food stamps or EBT card they will still ask for the 3 months for  so put in your 3 months and you should be fine.

1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

Learn more about Income Format here:

https://brainly.com/question/15312142

#SPJ1