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After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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Answer:

I think c, - 1.8 is the answer

-1.6 (c)

My reasoning behind this is that the number would be logical considering the fact that the point is close to 0. Also, I ruled out the other choices, and here's how I did it:

I know that A is not the answer because that would make it farther back on the number line and the point B is closer to 0 than it is to 3.8 so, I know that A is not correct.

I know that B is not the answer because -5.23 would be farther behind point A which rules it out entirely.

I know that D is not the answer because 0.1 would be right after point c (0) meaning that the point can be ruled out right away.

That leaves the only logical answer to be C because it is closer to 0 but still in between points A and B.

Hope this helps and have a nice day.

-R3TR0 Z3R0

Answer:

81 personas

Step-by-step explanation:

Lucía les cuenta una historia a 3 amigos a la hora 12.

Cada uno de ellos se comunica a 3 personas en los próximos 10 minutos.

a) Primeros 10 minutos

1 amigo = 3 personas = 10 minutos

3 amigos = x

Multiplicar cruzada

x = 3 × 3 personas = 9 personas

Por lo tanto, 9 personas han escuchado la historia en 10 minutos.

Si este trámite continúa, ¿cuántas personas han escuchado la noticia hasta las 12:30?

12: 30 - 12:00 = 30 minutos más

10

Por eso,

b) Segundos 10 minutos = 20 minutos

9 personas cada uno le dice a 3 personas en otros 10 minutos

1 persona = 3 personas

9 personas = x

Multiplicar cruzada

x = 9 × 3 personas

x = 27 personas

c) Los últimos 10 minutos = 30 minutos

1 persona = 3 personas

27 personas = x

Multiplicar cruzada

x = 27 × 3 personas

x = 81 personas

Por lo tanto, a los 30 minutos, 81 personas habrían escuchado la noticia a las 12:30

The slope of the line that contains these points is 0.75.

The slope of a line is the change in y-values divided by the change in x-values. In other words, it is the rise over the run. We can use the points given to calculate the slope.

Let's take the first two points (9, -24) and (13, -21) and use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

slope = (-21 - (-24)) / (13 - 9)

slope = (3) / (4)

slope = 0.75

We can do the same with the other two points (17, -18) and (21, -15):

slope = (-15 - (-18)) / (21 - 17)

slope = (3) / (4)

slope = 0.75

Since the slope is the same for both sets of points, we can conclude that the slope of the line that contains these points is 0.75.

The slope of the line that contains these points is 0.75.

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Answer:

c

Step-by-step explanation:

Answer: C

So I was right, I guess.

Answer:

-1/12

Step-by-step explanation:

Answer: B

Step-by-step explanation: EDGE 2022

Logistic regression models the probability of a binary outcome, while CART models segment data into categories. For example, CART is preferable when data has complex interactions, as it can partition data into multiple categories.

Logistic regression and classification and regression trees (CART) are two different machine learning models used for binary classification problems. Logistic regression models the probability of one class or the other based on a linear combination of input variables. This makes it useful for predicting a binary outcome, such as whether a customer will purchase a product or not. On the other hand, CART is a decision tree model that divides data into categories. It uses a tree-like structure to split the data into segments based on the input features. This makes it useful for dealing with data with complex interactions, as it can partition data into multiple categories. For example, a CART model would be preferable to a logistic regression model if there are multiple underlying factors that affect the binary outcome. In this case, a CART model could more accurately identify the categories that are associated with a particular outcome. Overall, CART models are superior for dealing with data with complex interactions, whereas logistic regression is better for simpler data.

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Answer:

300 dollars

Step-by-step explanation:

Multiply 10 feet by 12 feet to get the total number of feet needed

10x12=120 feet

120 times $2.5= $300

The cost to carpet a rectangular floor is $300.

Given that,

Based on the above information, the calculation is as follows:

\(= 10 \times 12 \times \$2.50\)

= $300

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a machine can pack a 3 ft by 3 ft by 1 ft carton with packing material in 3 seconds Then it would take 32 seconds to fill a carton that measures 4 ft by 4 ft by 6 ft

1) we calculate the volume of the first carton:

volume=length x width x height

volume=3 ft * 3 ft * 1 ft=9 ft³

Therefore:

A machine can fill 9 ft³ in 3 seconds.

2) we calculate the volume of the second carton.

volume=length x width x heigth

volume=4 ft * 4 ft * 6 ft=96 ft³

3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.

9 ft³---------------------3 seconds

96 ft³--------------------      x

x=(96 ft³ * 3 seconds) / 9 ft³=32 seconds.

Hence , a machine can pack a 3 ft by 3 ft by 1 ft carton with packing material in 3 seconds Then it would take 32 seconds to fill a carton that measures 4 ft by 4 ft by 6 ft

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Area = ∫[0, 1] (upper curve - lower curve) dy

The upper curve is y - 1/x, and the lower curve is y = 1/x^2.

Area = ∫[0, 1] (y - 1/x - 1/x^2) dy

Evaluate this integral within the given limits of integration to find the area of the region.

The curves provided are:

y - 1/x

y = 1/x^2

x = 6

Let's find the points of intersection between the curves:

Setting the two equations equal to each other, we have:

1/x^2 = 1/x

To simplify the equation, we can multiply both sides by x^2:

1 = x

So the point of intersection between the curves y - 1/x and y = 1/x^2 occurs at (1, 1).

Now, let's sketch the region enclosed by the curves:

Curve y - 1/x:

The curve y - 1/x represents a hyperbola that approaches the x-axis as x approaches positive or negative infinity. It intersects the x-axis at x = 1. The curve extends towards positive and negative y-values.

Curve y = 1/x^2:

The curve y = 1/x^2 is a downward-opening hyperbola. It approaches the x-axis as x approaches positive or negative infinity. The curve has asymptotes at x = 0 and does not intersect the x-axis.

Line x = 6:

The line x = 6 is a vertical line passing through x = 6.

To determine whether to integrate with respect to x or y, we need to consider the orientation of the region. Looking at the given curves, it is clear that the region is vertically bounded. Therefore, we'll integrate with respect to y.

To find the area of the region, we need to determine the limits of integration. The region is bounded by the curves y - 1/x and y = 1/x^2, and it extends from the y-axis to the point of intersection at (1, 1). Therefore, the limits of integration for y are from 0 to 1.

Now, let's calculate the area using the definite integral:

Area = ∫[0, 1] (upper curve - lower curve) dy

The upper curve is y - 1/x, and the lower curve is y = 1/x^2.

Area = ∫[0, 1] (y - 1/x - 1/x^2) dy

Evaluate this integral within the given limits of integration to find the area of the region.

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The region enclosed by the curves y = 1/x, y = 1/\(x^2\), and x = 6 can be found by integrating with respect to x. The region lies in the first quadrant and is bounded by the curves and the line x = 6.

To sketch the region enclosed by the curves, we can start by plotting the graphs of y = 1/x and y = 1/\(x^2\). The curve y = 1/x represents a hyperbola that passes through the points (1, 1), (2, 0.5), (3, 0.33), and so on. The curve y = 1/\(x^2\) is a hyperbola that approaches the x-axis as x increases. The line x = 6 is a vertical line passing through x = 6.

To find the region of the area enclosed by these curves, we need to determine the limits of integration. The region lies to the right of the y-axis (x > 0) and is bounded by the curves y = 1/x and y = 1/\(x^2\). The left boundary of the region is the curve y = 1/x, and the right boundary is the curve y = 1/\(x^2\). The lower boundary is the x-axis, and the upper boundary is the curve y = 1/x.

To calculate the area of this region, we can integrate with respect to x. The limits of integration are x = 1 (the intersection point of the curves y = 1/x and y = 1/\(x^2\)) and x = 6 (the given line). The integral that represents the area is ∫[1, 6] (1/x - 1/\(x^2\)) dx. By evaluating this integral, we can find the area of the region enclosed by the given curves.

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To maximize the number of people that can be fed, subject to the constraint that the total cost of rice and beans cannot exceed $2,000,000. Let's first rewrite the cost constraint as an equation:

38.5x + 35y = 2,000,000

Now we can rewrite the expression for P in terms of one variable.

How optimal allocation for famine relief funds?

To find the maximum number of people that can be fed, which means we need to maximize the function P= 1.1x +y - 108 subject to the budget constraint:

38.5x + 35y = 2,000,000

First, we can rewrite the budget constraint as:

77x + 70y = 4,000,000y - 108.

To do this, we can use the constraints provided by the budget and the prices of rice and beans. Let's assume that the organization will spend all of the $2,000,000, so we have the equation:

38.5x + 35y = 2,000,000

This represents all the possible combinations of sacks of rice and beans that can be bought with the given budget.

To make the problem easier to work with, we can solve for y in terms of x:

y = (2,000,000 - 38.5x) / 35

Now we can substitute this expression for y into the function for P:

P = 1.1x + (2,000,000 - 38.5x) / 35 - 108

Simplifying this, we get:

P = (14x - 3250) / 35

To maximize P, we can take the derivative and set it equal to zero:

dP/dx = 14/35 = 0

Solving for x, we get:

x = 100,000/14

x = 7,142.857

Since we can't buy a fraction of a sack, we round down to the nearest whole number:

x = 7,142

Now we can use the equation we derived earlier to find the corresponding value of y:

y = (2,000,000 - 38.5 x) / 35

y = (2,000,000 - 38.5(7,142)) / 35

y = 22,000

Therefore, the maximum number of people that can be fed is:

P = 1.1 x + y - 108

P = 1.1(7,142) + 22,000 - 108

P = 30,346

So, the organization should buy 7,142 sacks of rice and 22,000 sacks of beans to feed the maximum number of people.

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Answer:

A e f

Step-by-step explanation:

Hope this was helpful!!!

Answer:

r = -20

Step-by-step explanation:

–7r= –8r−20

Add 8r to both sides

r = -20

Answer:

\( \boxed{r = -20} \)

Step-by-step explanation:

\( = > - 7r = - 8r - 20 \\ \\ = > - 7r + 8r = - 20 \\ \\ = > 8r - 7r = - 20 \\ \\ = > r = - 20\)

After 4 hours of snow melting, there would be 8 inches of snow with the rate of 2.5 inches per hour Katherine would have on her lawn and after t hours the snow would be = 18 - 2.5*t inches.

In this question, the amount of snow melted is required to calculate to know the amount of snow on the lawn, can be calculated by:

Given:

The total amount of snow = 18 inches

Rate of melting = 2.5 inches

Time = 4 hours

Solution:

The amount melted needs to be calculated first in order to find left snow, therefore, putting values in the formula mention above,

the melted amount = rate of melting × time

the melted amount = 2.5 × 4 inches

the melted amount = 10 inches

Then the final amount would have on the lawn =  starting amount−melted snow

=  18−10 inches

= 8 inches

Part b) Snow after t hours:

Starting amount=  18 inches

Melted snow=  inches per hour×t

= 2.5×t

= 2.5t

Final amount = starting amount−melted snow

= 18 -2.5t

Thus, the correct answer is - 8 inches and 18 -2.5t

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Answer:

equilateral triangle all angles add up to 180 and are equal so each angle is 60 degrees

angles on a line add up to 180.

angle CBD = 180-60 = 120

DBC is an isosceles triangle so it's base angles are the same.

180-120= 60

60/2=30

The isosceles triangle ΔDBC have equal base angles.

The measure of angle C is 30 degrees

ΔADB is an equilateral triangle.

So, we have:

\(\mathbf{\angle ADC = \angle BAD = \angle DBA = 60}\)

Next, we calculate \(\mathbf{\angle DBC}\)

\(\mathbf{\angle DBC =180 - \angle DBA}\) -- angle on a straight line

So, we have:

\(\mathbf{\angle DBC =180 - 60}\)

\(\mathbf{\angle DBC =120}\)

ΔDBC is an isosceles triangle.

So, we have:

\(\mathbf{\angle C = \angle D}\)

This is then calculated as:

\(\mathbf{\angle C + \angle C = 180 - 120}\)

\(\mathbf{2\angle C = 60}\)

Divide both sides by 2

\(\mathbf{\angle C = 30}\)

Hence, the measure of angle C is 30 degrees

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Answer:B

Step-by-step explanation:

it is recursive and arthimetic

Answer:

10 I think but not sure. but It has to be an Evan number

Answer:

160 cm²

Step-by-step explanation:

If the two rectangles are similar, that means they have equal scale factors.  The smaller rectangle has length of 8 cm and area of 40 cm, which means the width is 5 cm.  

The width of the larger rectangle is 10 cm, which is double the width of the smaller, similar rectangle.  So, to find the length of the larger rectangle, multiply 8 x 2, which gives you 16 cm for the length, since the scale factor is 2.

Now, just find the area of the larger rectangle by doing length x width.  16cm x 10 cm = 160 cm²

Answer:

160 cm^2

Step-by-step explanation:

Our strategy is to find the length of the larger rectangle so we can find the area. To find the length, we will rely on the fact the two rectangles are "similar": their sides are in equal proportions, or have the same "ratio."

We know that the smaller rectangle has a width of 5 cm because, when we substitute area and length into

A = lw

we get

40 = 8w

w = 5

when we divide both sides by 8.

Because of equal proportions:

Width : length of the smaller rectangle = Width : length of the larger rectangle

We can write an equation

5 / 8 = 10 / x

Cross multiply

5x = 80

x = 16

So the larger rectangle has a length of 16 cm and a width of 10 cm (given)

meaning the area is

16 * 10 = 160 cm^2

The Fourier series representation of the 2-periodic function f(t) = 2 + 5cos(2mt) + 9sin(3πt) is: f(t) = 1 + 5cos(2mt) + 9sin(3πt), where a0/2 is 2, a2m is 5, b3π is 9, and all other coefficients are zero.

To compute the coefficients of the Fourier series for the 2-periodic function f(t) = 2 + 5cos(2mt) + 9sin(3πt), we need to find the coefficients for the cosine and sine terms in the series. The Fourier series representation of f(t) is given by:

f(t) = a0/2 + ∑[n=1, ∞](an * cos(nπt) + bn * sin(nπt))

where a0/2 represents the average value of the function, and an and bn are the coefficients of the cosine and sine terms, respectively.

Let's start by calculating the average value a0/2 of the function f(t) over one period:

a0/2 = (1/2) * ∫[-1, 1] f(t) dt

Since f(t) = 2 + 5cos(2mt) + 9sin(3πt), we can evaluate the integral as follows:

a0/2 = (1/2) * ∫[-1, 1] (2 + 5cos(2mt) + 9sin(3πt)) dt

The integral of 2 with respect to t over the interval [-1, 1] is simply 2t evaluated from -1 to 1, which gives 2.

The integral of cos(2mt) with respect to t over the interval [-1, 1] is zero because it integrates to an odd function over a symmetric interval.

The integral of sin(3πt) with respect to t over the interval [-1, 1] is also zero because it integrates to an odd function over a symmetric interval.

Therefore, the average value a0/2 is 2.

Next, let's compute the coefficients an and bn for the cosine and sine terms in the Fourier series.

an = ∫[-1, 1] f(t) * cos(nπt) dt

bn = ∫[-1, 1] f(t) * sin(nπt) dt

We can plug in the function f(t) = 2 + 5cos(2mt) + 9sin(3πt) and evaluate the integrals to find the coefficients an and bn for each term in the series.

For the term 5cos(2mt), the cosine coefficient a2m is 5.

For the term 9sin(3πt), the sine coefficient b3π is 9.

For all other terms, the coefficients are zero because integrating the other terms with respect to t over the interval [-1, 1] will yield zero.

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Answer:

-5 is the answer!!!!!

Step-by-step explanation: it jist is

Answer:

-5

Step-by-step explanation:

its negative 5

Answer:

45 yards

Step-by-step explanation:

Formula to find area of rectangle: Length * Width

Given:

Length = 70 yards

Area = 3,150 yards

Width = 3,150/70

        ==> 45 yards

Width = 45 yards

Answer:

See explanation

Step-by-step explanation:

Vertex: -b/2a = 8/4 = 2. Plug 2 back into the equation to get (2, -2)

y-intercept: plug 0 for all the x values to get 6. The y intercept is (0,6)

x intercept: factor the equation:

2(x^2 - 4x + 3)

2(x-3)(x-1)       <— by splitting the middle variable

so the x intercepts are (x-3) and (x-1) or 3 and 1.

Axis of symmetry : 2 (the x value of the vertex)

Domain: ARN ( all real numbers)

Range: ARN except y cannot be less than -2.

To graph you simply just plug in x values in a table and get the y values. Then plot them on the graph and draw a smooth curve.

Step-by-step explanation:

these are all isoceles triangles (2 sides are equal). that also means that the 2 angles at the end of the equal sides are equal.

so, the angle at F and H are both 65°.

the angle at J = 2×65 = 130°.

the angle at G = 2×(180 - 65 - 65) = 2×50 = 100°.

remember, the sum of all angles in a triangle is always 180°.

so many ways now to get y.

let's use the triangle GH and crossing point of diagonals (there is a right angle).

y = 180 - G/2 - 90 = 180 - 50 - 90 = 40°

===================================================

Explanation:

See the diagram below. It shows there are 10 sides, so n = 10.

We'll plug this value of n into the formula below to find the sum of all ten interior angles

S = sum of interior angles

S = 180(n-2)

S = 180(10-2)

S = 180(8)

S = 1440 degrees

---------------

A different approach:

Let's assume this polygon is a regular polygon. This means each angle is congruent to one another.

We have n = 10 sides, so each exterior angle is E = 360/n = 360/10 = 36 degrees.

Each interior angle adjacent to this 36 degree exterior angle is

180-E = 180-36 = 144 degrees

Since we have 10 equal angles of 144 degrees each, so overall the interior angles add to 10*144 = 1440 degrees

Side note: if this polygon is not a regular polygon, then this section does not apply. You would use the first method instead.

Answer:

4x - 5 = 131 where x is the first number.

Step-by-step explanation:

Let the first number be x.

Seconder number = 2x + 7.

Third number = x - 12.

So, the equation is :-

x + 2x + 7 + x - 12 = 131

4x - 5 = 131

4x = 136

x = 34

First number = 34, second = 2(34) + 7 = 75 and third number = 34-12 = 22.

If Alyssa uses 4 ounces of flour to make pancakes each morning how long will it take her to use up a 6 pound bag is 24 days.

Using this formula

Number of days=Number of ounces×Number of pound bag

Where:
Number of ounces=4 ounces

Number of pound bag=6

Let plug in the formula

Number of days=4×6

Number of days=24 days

Therefore  how long will it take her to use up a 6 pound bag is 24 days.\]

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