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a. The number of shares outstanding after the stock split by Willey’s Grill & Restaurant Corporation is 670,000 (335,000 x 2).

b. If the common stock had a market price of $510 per share before the stock split, the approximate market price per share after the split is $255 ($510/2).

A stock split is a way that a corporation increases the number of its shares by increasing or decreasing the number of shares outstanding.

When a stock split increases the number of outstanding shares, the market price reduces proportionately.

a. What will be the number of shares outstanding after the split? Round your answer to the nearest whole number.

b. If the common stock had a market price of $510 per share before the stock split, what would be an approximate market price per share after the split? Round your answer to the nearest dollar.

Thus, the stock split increased the outstanding shares to 670,000 while reducing the market price to $255.

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Explanation:

This is the given piecewise function

[tex]h(a) = \begin{cases}3a+2 \text{ when } a > 3\\4a+5 \text{ when } a = 3\\3 \text{ when } a < 3\\\end{cases}[/tex]

We can rewrite things like this

[tex]\text{when } a > 3, \ \ h(a) = 3a+2\\\text{when } a = 3, \ \ h(a) = 4a+5\\\text{when }a < 3, \ \ h(a) = 3\\[/tex]

I personally prefer this format better because it mentions the inputs first, and that leads to which function definition we go for.

The input a = 2 fits the description of [tex]a < 3[/tex] since [tex]2 < 3[/tex] is a true statement. Therefore we go for the third line and can see that [tex]h(a) = 3[/tex] becomes [tex]h(2) = 3[/tex]

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As another example, if we had the input a = 7, then we'd go for the first line (since 7 > 3) and get

h(a) = 3a+2

h(7) = 3(7)+2

h(7) = 23

A function assigns the values. The statement "The rate of population growth each year is 166%" is true.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function of the population for the town is [tex]P (t) = 45,000(2.66)^t[/tex], where t is the time in years. Comparing the given function to the general function of the population,

P(x) = a(1+b)ˣ

Then, the value of b will be 166%.

Hence, the statement "The rate of population growth each year is 166%" is true.

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Answer:

2

Step-by-step explanation:

The answer is (A) f(x) = x+4.

Answer:

0

Step-by-step explanation:

[tex]10 + ( - 8) - 2 \\ = 1 0 - 8 - 2 \\ = 2 - 2 \\ = 0[/tex]

Answer: 0

Step-by-step explanation: -8+-2 is -10 and -10+10 is 0

Answer: Option 4

Step-by-step explanation:

Each value of x maps onto one value of y, meaning the relation is a function.

The transformed function is y = 1/3(log(x/3 + 4)) + 1

The parent logarithmic function is

y = log(x)

When shifted left by 4 units, we have:

y = log(x + 4)

When shifted up by 3 units, we have:

y = log(x + 4) + 3

When compressed vertically by 1/3, we have:

y = 1/3(log(x + 4) + 3)

This gives

y = 1/3(log(x + 4)) + 1

When stretched horizontally by 3, we have:

y = 1/3(log(x/3 + 4)) + 1

Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1

We have:

f(x) = log[-(x – 5)] + 4

Set the radicand greater than 0

-(x - 5) > 0

Divide by -1

x - 5 < 0

Add 5 to both sides

x < 5 -- this represents the domain

A logarithmic function can output any real number.

So, the range is [tex]-\infty < f(x) < \infty[/tex]

In the domain, we have:

x < 5

This means that the interval of decrease is [tex]-\infty < x < 5[/tex]

Rewrite as an equation

x = 5 --- this represents the equation of asymptote

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The volume of the piece of the metal Gina is found to be 22.82 cubic cm.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of cube or cuboid.

Given the density of the metal = 9.2g/cm3

Given the mass of the piece of the metal = 210 g

Assuming the volume of a piece of metal to be V

The expression for the density is shown below:-

Density = Mass / Volume

9.2 = 210 / V

V = 210 / 9

V =  22.82 cubic cm.

Therefore the volume of the piece of the metal Gina is found to be 22.82 cubic cm.

The complete question is given below:-

Gina was given an irregularly shaped piece of metal and was told that the density of the metal was 10 g/cm3. She measured the mass of the piece to be 210 g. What was the volume of the piece of metal Gina was given?

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An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to -(1/6)y + 1/3 is,

-(1/6)y + 1/3

Take 1/6 common from both first and the last term,

1/6 (-y + 2)

Hence, the correct option is C.

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Step-by-step explanation:

Answer:

Adults: 79 tickets

Students: 237 tickets

Step-by-step explanation:

a + b = 316    Eq. 1

b = 3a            Eq. 2

a = adults

b = students

Replacing Eq. 2 in Eq. 1

a + 3a= 316

4a = 316

a = 316/4

a = 79

from the Eq. 2

b = 3a

b = 3*79

b = 237

Check:

from the Eq. 1

a + b = 316

79 + 237 = 316

[tex] - 4(n - 6) = 12 \\ (n - 6) = \frac{12}{ - 4} \\ n - 6 = - 3 \\ n = - 3 + 6 \\ n = 3[/tex]

Answer: A

Step-by-step explanation:

The expressions are equivalent by the distributive property.

Answer:

25

Step-by-step explanation:

f(5)=x2

=25

The probability that a randomly selected person from the sample will be female or left-handed will be 0.05.

Probability is synonymous with possibility. It is concerned with the occurrence of a random event.

Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.

Given data;

Total number of sample,n(S) = 100 person

No of female or left-handed is,n(E) =5

P(E) is the probability that a randomly selected person from the sample will be female or left-handed

The probability that a randomly selected person from the sample will be female or left-handed is found as;

P(E) = n(E)/n(S)

P(E) = 5 / 100

P(E) = 0.05

Hence the probability that a randomly selected person from the sample will be female or left-handed will be 0.05.

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Answer:

x = 7.5 km/h

Step-by-step explanation:

• First calculate the distance covered by walking at 3 km/h for 45 minutes ( 0.75 h):

distance = speed × time

              = 3 × 0.75

              = 2.25 km

• Therefore, she covered 2.25 km of the total journey by walking. Since she was 6 km from the starting point at the end of the entire journey, we can calculate the distance remaining, which she had to run:

distance she had to run = 6 - 2.25

                                        = 3.75 km

• Now we can calculate the speed of the 30 minute (0.5 h) run:

speed = distance ÷ time

           = 3.75 ÷ 0.5

           = 7.5 km/h    

This means that she ran at 7.5 km/h for half an hour.

∴ x = 7.5

The sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression can be written as,

[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)[/tex]

The result of the above expression will be,

[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)\\\\=\dfrac{18+72}{9} \times (10)\\\\[/tex]

= (90/9) × 10

= 10 × 10

= 100

Hence, the sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.

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Answer: -2

Step-by-step explanation:

We can combine the fundamentals of mental math and the brain to calculate the problem when x is -2. You wake up noticing x is -2 and you instantly know the answer and solved in less than a second.

Answer:

  A.  KM

Step-by-step explanation:

A circle is named by its center. Circle K has its center at point K.

A radius is a line segment that extends from the center of the circle to a point on the circle. Point K must be one end of any radius.

Segment KM is a radius.

Segments between points on the circle are chords. The other named segments in the answer choices are all chords of the circle.

The way to solve the polynomial using the methods is given below.

Polynomial by factoring:

An example is (t² + 5t + 4) / +t + 4)

= (t + 1)(t + 4)/(t + 4)

= t + 1.

Dividing polynomial by long division:

Divide the first term of the dividend by the first term of the divisor.

Put this as the first term in the quotient.

Subtract to create a new polynomial.

Continue until you can't divide anymore.

Dividing polynomial by synthesic division:

Step 1: Set up the synthetic division.

Step 2: Bring down the leading coefficient to the bottom row.

Step 3: Multiply c by the value just written on the bottom row.

Step 4: Add the column created in step 3.

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The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the profit (P) in thousands for security camera with price of x, hence for a profit of at least $471, 000:

-(x - 32)² + 1000 ≥ 471

-(x² - 64x + 1024) + 1000 ≥ 471

-x² + 64x - 1024 + 1000 - 471 ≥ 0

-x² + 64x - 495 ≥ 0

x = 55 or x = 9

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

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By using trigonometric properties, we will see that:

tan(x) = 3/4.

Remember that the sine of the difference is:

sin(a - b) = sin(a)*cos(b) - sin(b)*cos(a).

Here we have:

sin(90° -x ) = 0.8

Expanding the sine:

sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°)

We know that:

sin(90°) = 1 and cos(90°) = 0, then:

sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°) = cos(x).

Then we have:

cos(x) = 0.8

And we want to find the tangent of x, which is:

[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]

We already know that cos(x) = 0.8

Now, remember that:

[tex]sin(x)^2 + cos^2(x) = 1\\\\sin(x) = \sqrt{1 - cos^2(x)} \\[/tex]

Because x is an acute angle, sin(x) > 0, that is why we choose the positive root.

Replacing cos(x) we get:

[tex]sin(x) = \sqrt{1 - 0.8^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6[/tex]

Then the tangent of x is:

[tex]tan(x) = \frac{0.6}{0.8} = \frac{6}{10}*\frac{10}{8} = 6/8 = 3/4[/tex]

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Answer:

A. 81

Step-by-step explanation:

F(x)=[tex]3^{x}[/tex]

if x=4, then F(4) = [tex]3^{4}[/tex] = 3×3×3×3=81

Answer:

x + 7 and x + 5 are possible dimensions

Step-by-step explanation:

x² + 12x + 35 ← factor the quadratic

consider the product of the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)

the factors are + 7 and + 5 , since

7 × 5 = + 35 and 7 + 5 = + 12 , then

x² + 12x + 35 = (x + 7)(x + 5) ← in factored form

now the area A = length × breadth , that is

A = x² + 12x + 35 = (x + 7)(x + 5) , then

length = x + 7 or x + 5

breadth = x + 5 or x + 7

Answer:

Probability of rolling a sum of 5 is 1/9.

There are 36 different combinations because 6(first roll)*6(second roll) = 36. The only possible combinations are {1,4},{2,3}{2,3}and{4,1}

4/36 = 1/9

Answer:

b.) 0

Explanation:

⇒ f(g(-1))

go from right to left while solving such function questions.

⇒ f(-1 + 2)

⇒ f(1)

⇒ (1)² -2(1) + 1

⇒ 0

Step-by-step explanation:

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

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

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

[tex] \: [/tex]

[tex] = f(g( - 1))[/tex]

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

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

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

[tex] = {(1 - 1)}^{2} [/tex]

[tex] = {0}^{2} [/tex]

[tex] = 0[/tex]

The answer is B.

Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).

The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: [tex]M(\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].

A diagonal is XZ.

X(2, 5) = (x1, y1)

Z(0, 0) = (x2, y2)

Plug in the values

[tex]M(\frac{0 + 2}{2}, \frac{0 + 5}{2})[/tex]

= (1, 2.5).

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