The ratio for the split is entered in cells B2 and C2. For example, the ratio of 2-for-1 would be entered as a 2 in B2 and a 1 in C2. The number of pre-split shares is entered in B3 and the pre-split price is entered in B4, Write the spreadsheet formula that will calculate the post-split number of outstanding shares in C3

The mode of the number of pizzas ordered for all 189 stores is [tex]66[/tex]. The Option D is correct.

Mode refer he most frequent number, that is, the number that occurs the highest number of times. To find mode, we must determine the value that appears most frequently in the sample.

From the given data: [tex]28, 53, 35, 66, 35, 28, 66, 48, 53, 53, 66, 53, 66, 66, 35[/tex]. We see that the value 66 appears 5 times, which is more than any other value.

Therefore, the number 66 is the mode.

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Answer:

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The area of the triangle is 9 units^2

Step-by-step explanation:

Area of triangle = 1/2(6*3)

                          =1/2(18)

                          =9

Answer: 70 pages

Step-by-step explanation: If she read 1/7 pages on monday and the book is 490 pages, divide. 490 ÷ 1/7 = 70. 70 × 7 is 490. So use these operations in future problems. Just make sure to read carefully!

Answer:3

Step-by-step explanation: Initial value = y-intercept

The correct statement regarding the relations in this problem is given as follows:

Only relation A could represent a linear relationship.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the first bullet point, we have that what classifies a linear relation is a constant rate of change.

For relation K, we have that it is not linear, as:

For relation R, we have that it is linear, as it has a constant rate of change.

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Answer:

The length of the arc intercepted by a central angle of 3 radians in a circle of radius 76 is 228 and the length of the arc intercepted by a central angle of 2 radians in a circle of radius 15 is 30.

Explain:

The following formula determines the length of an arc that a circle's central angle intercepts:

Arc length is equal to (central angle / 2) 2r r r

where r denotes the circle's radius. We can determine the length of the two arcs using the following formula:

For the first circle, with a radius of 76 and a center angle of 3 radians:

Arc length = 3 x 76 = 228

Therefore, in a circle with a radius of 76, the length of the arc that is intercepted by a central angle of 3 radians is 228.

For the second circle, whose radius is 15, and whose center angle is 2 radians:

Arc length = 2 x 15 = 30

As a result, the length of the arc in a circle with a radius of 15 is 30 when it is intercepted by a central angle of 2 radians.

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The simplified value of 8y + 4 - 3y + 12 is 5y+16

An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. For example , 4x+5 , 2x²+2, 10y³+5y²+6

To simplify an expression means to write the expression Ina simpler form. for example 6y²+2y can be written as 2y( 3y+1)

Simplifying 8y + 4 - 3y + 12,

collecting like terms

8y-3y+4+12

= 5y+16

therefore the simplification of 8y + 4 - 3y + 12 is 5y+16

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Answer:

A: 6 as a fraction of 30 = 6/30 = 1/5

B: 30 centimetres as a fraction of 2 metres = 30/200 = 3/20

C: 16 pence as a fraction of £1 = 16/100 = 4/25

To compare these fractions, we need to express them with a common denominator. The smallest common multiple of 5, 20, and 25 is 100. So we can convert each fraction to have a denominator of 100:

A: 1/5 = 20/100

B: 3/20 = 15/100

C: 4/25 = 16/100

Now we can see that the largest fraction is C: 16 pence as a fraction of £1, which is 16/100 or 16%.

Step-by-step explanation:

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1. The width of the pen must be greater than or equal to the sum of the diameters of the two circular food containers, which is equal to 2x + 2x = 4x:

2. The width of the pen must also be less than or equal to the length of the pen, which is 10 feet:

3. The radii of the gravel bases must be greater than or equal to the radii of the food containers, which is equal to x:

4. The radii of the gravel bases must also be less than or equal to half the width of the pen, which is equal to y/2:

System of inequalities that can be used to determine the width of the pen, y, and the radii of the gravel bases, x, is:

Answer:

Step-by-step explanation:

The sum of the diameters of the gravel bases cannot exceed the width of the pen, so 2⁢x+2⁢x≤y. Rewrite this to get y≥4⁢x as the first inequality in the system.Next, to write the expression for the cost of the fencing, find the perimeter of the rectangle and multiply the perimeter by the cost per foot of fencing. The pen is a rectangle, so the perimeter is 2⁢(10)+2⁢(y), or 20+2⁢y. Multiply the cost ($4.00 per foot) by the perimeter to get 4⁢(20+2⁢y).Now write an expression for the gravel bases for the circular food containers. Because A=π⁢r2 and the cost of the gravel is $2.00 per square foot, multiply the cost of the material by the sum of these areas to get 2⁢(π⁢x2)+2⁢(π⁢x2).The total cost must be less than or equal to $150, so we can say that 4⁢(20+2⁢y)+2⁢(π⁢x2)+2⁢(π⁢x2)≤150. Finally, simplify and solve for y.80+8⁢y+2⁢π⁢x2+2⁢π⁢x2≤15080+8⁢y+4⁢π⁢x2≤1508⁢y≤70−4⁢π⁢x2y≤8.75−0.5⁢π⁢x2So, this is the system.

y≥4⁢x

y≤8.75−0.5⁢π⁢x2

The probability of yellow or has an odd number is 8/9

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

Green = 1 to 3

Yellow = 1 to 6

This means that

Odd = 2 + 3

Odd = 5

So, we have

P(Yellow) = 6/9

P(Odd) = 5/9

P(Yellow and Odd) = 3/9

The probability of yellow or has an odd number is

P = 6/9 + 5/9 - 3/9

Evaluate

P = 8/9

Hence, the probability is 8/9

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Answer: See attached.

Step-by-step explanation:

     First, we will create an equation with the slope given.

y = [tex]\frac{3}{4}[/tex]x + b

     Then, we will substitute this value in and solve for b (our y-intercept). Then we will graph the equation.

y = [tex]\frac{3}{4}[/tex]x + b

(-1) = [tex]\frac{3}{4}[/tex](-4) + b

-1 = -3 + b

b = 2

     Our final equation:

           y = [tex]\frac{3}{4}[/tex]x  + 2

     See attached for the graph. We will plot the point (0, 2) for our y-intercept and then move 3 units up for every four units right, according to the slope.

[tex]-37 < -12v+1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ v=-11\hspace{5em}-37 < -12(-11)+1\implies -37 < 133 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-9\hspace{5em}-37 < -12(-9)+1\implies -37 < 109~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-5\hspace{5em}-37 < -12(-5)+1\implies -37 < 61~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=6\hspace{5em}-37 < -12(6)+1\implies -37 < -71 ~~ \bigotimes[/tex]

The decision meets each of the criteria by: Buying 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each enables the purchase of 700 frozen delights within the $400 budget and satisfies the objective of producing at least $800 in profit.

I have made the decision to buy 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each in order to fulfil the requirement of buying 700 frozen delights at a price of no more than $400.

Cost of purchasing 500 popsicles = (500 * $0.50)

Cost of purchasing 500 popsicles = $250

Cost of purchasing 200 ice cream sandwiches =(200 * $1.50)

Cost of purchasing 200 ice cream sandwiches  = $300

So, Total cost of purchasing all 700 frozen treats is $550 ($250 + $300) which is within the budget of $400.

I intend to sell the popsicles for $1.50 each and the ice cream sandwiches for $3.00 each in order to meet the requirement of turning a profit of at least $800. This would bring in $1350 in income for the ice cream sandwiches and $750 for the popsicles (500 * $1.50 and 200 * $3.00 respectively).

The objective of producing a profit of at least $800 is met after deducting the expense of buying the frozen treats from the overall income.

Net profit =($1350 - $550)

Net profit = $800

Therefore purchasing  500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each satisfies the objective of producing at least $800 in profit.

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Answer:

The length of the second train is 416.67 meters.

Step-by-step explanation:

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Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.

The coordinates of the focus of the parabola y = -(1/8)x² - 2x - 4 is (-8, 2).

y = -(1/8)x² - 2x - 4

Given by the equation y = -(1/8)x² - 2x - 4,

To find the focus of the parabola we first need to put the equation in standard form:

y = a(x - h)² + k

Where (h, k) is the vertex of the parabola, and a is a constant that determines the shape and size of the parabola.

Completing the square on the x terms, we get:

y = -(1/8)(x² + 16x + 64) - 4 + 8

= -(1/8)(x + 8)² + 4

Comparing this to the standard form, we see that the vertex is (-8, 4) and a = -1/8.

Since the coefficient of x² is negative, the parabola opens downwards.

The focus of the parabola is located at a distance of 1/(4a) units from the vertex, on the axis of symmetry, which is a vertical line passing through the vertex.

Substituting the value of a, we get:

= 1/(4a)

= 1/(4(-1/8))

= 2

Therefore, the focus of the parabola is located 2 units below the vertex, on the line x = -8.

So the focus has coordinates (-8, 2).

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Answer:

90

Step-by-step explanation:

Answer:

It seems like the chat transitioned to a different topic. However, based on the search results, it appears that the query was related to solving distance problems using linear equations. One common application of linear equations is in distance problems, where you can create and solve linear equations to find the distance between two points or the rate of travel. Here's an example problem:

Joe drove from city A to city B, which are 120 miles apart. He drove part of the distance at 60 miles per hour (mph) and the rest at 40 mph. If the entire trip took three hours, how many miles did he drive at each speed?

To solve this problem, you can use a system of two linear equations. Let x be the number of miles driven at 60 mph, and y be the number of miles driven at 40 mph. Then you have:

x + y = 120 (total distance is 120 miles) x/60 + y/40 = 3 (total time is 3 hours)

To solve for x and y, you can multiply the second equation by 120 to eliminate fractions and then use the first equation to solve for one of the variables. For example:

x/60 + 3y/120 = 3 x/60 + y/40 = 3 2x/120 + 3y/120 = 3 x/60 + y/40 = 3 x/60 = 3 - y/40 x = 180 - 3y/2 (from the first equation)

Substitute the expression for x into the second equation and solve for y:

x/60 + y/40 = 3 (180 - 3y/2)/60 + y/40 = 3 3 - 3y/160 + y/40 = 3 3 - 3y/160 = 2.75 -3y/160 = -0.25 y = 20

Substitute y = 20 into the expression for x to get:

x = 180 - 3y/2 x = 120

Therefore, Joe drove 120 - 20 = 100 miles at 60 mph and 20 miles at 40 mph.

Step-by-step explanation:

Answer:

415.67 = (1/3)(13.4)(11.7)h

415.67 = 52.26h

h = about 7.95 feet

Answer:

The amount of Uranium-233 produced after 20 days will be approximately 65.1 pounds.

Step-by-step explanation:

The option or function that is NOT an exponential function is (4/7)ˣ.

The function (4/7)ˣ is no exponential because the base (4/7) is smaller or lesser than 1. All exponential functions must have a base that is less than -1 or greater than 1.

The other functions

1) (3/5)ˣ

2) 4ˣ

are both exponential function.

3/5ˣ is a decay function and it's base is less than 1. 4ˣ on the other hand is a growth function. Of course, it's base is greater than 1.

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The value of the measure of each side indicated are,

⇒ x = 12.48

⇒ BC = 16

We have to given that;

In triangle ABC;

AC = x

AB = 10

Hence, We can formulate;

⇒ tan 58° = BC / AB

⇒ 1.60 = BC / 10

⇒ BC = 16

By using Pythagoras theorem;

⇒ x² + 10² = 16²

⇒ x² = 256 - 100

⇒ x² = 156

⇒ x = 12.48

Thus, The value of the measure of each side indicated are,

⇒ x = 12.48

⇒ BC = 16

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The horizontal distance more that Jake was able to cover, given the incline, would be A.4.1 ft.

We can find the horizontal distance that both Jake and Raphael covered .

Jake's distance was:

cos ( 7.9 ° ) = adjacent / 100

adjacent = 100 x 0.989

adjacent = 98.9 ft

Rafael's distance was :

cos ( 18. 3° ) = adjacent / 100

adjacent = 100 x 0.951

adjacent = 95.1 ft

The difference and the distance covered in addition by Jake would be:

= 98. 9 - 95. 1

= 3. 8 ft

The closest option is 4. 1 ft.

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The measure of  each interior angle of a regular 16-sided polygon is 157.5 degrees

To determine the value of the interior angle, we need to note that;

The formula for calculating the sum of the interior angles of a polygon is expressed with the expression;

(n -2)180

Such that the variable n in the expression represents the number of sides of the polygon

From the information given, we have that;

(16- 2)180

expand the bracket

14(180)

multiply the values

2520 degrees

Then, we have;

16x = 2520

Make 'x' the subject

x= 157. 5 degrees

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Volume of the prism given is 51 [tex]\frac{17}{40}[/tex].

The volume of the prism is given by the formula,

Volume of the prism = Base area × height

Base area = 2 3/4 × 5 1/2

                 = 11/4 × 11/2

                 = 121 / 8

Volume of the prism = 121 / 8 × 3 2/5

                                  = 121/8 × 17/5

                                  = 2057/40

                                  = 51 17/40

Hence the volume of the prism is 51 [tex]\frac{17}{40}[/tex].

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The area of the parallelogram is 8.5 square miles. This is found by multiplying the length of one of the parallel sides, 2 miles, by the height, which is given as 4 1/4 miles.

To find the area of a parallelogram, we can multiply the length of one of its parallel sides by the length of its perpendicular height. Therefore, to find the area of this parallelogram, we need to determine its height.

We are given that one of the parallel sides has a length of 4 1/4 mi and the other has a length of 2 mi. We are also given that the length of the perpendicular on one of the parallel sides is 4 1/4 mi, which means that this is the height of the parallelogram.

So, the area of the parallelogram is

Area = base x height

Area = 2 mi x 4 1/4 mi

Area = 8 1/2 mi²

Therefore, the area of the parallelogram is 8 1/2 square miles or 8.5 square miles.

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We would expect 138 groups in the larger zoo to have 5 or more people based on the relative frequency of group sizes in Julia's data.

To determine how many groups of 5 or more people we would expect to see in a larger zoo with 600 groups of visitors in a day, we need to use the relative frequency of each group size in Julia's data.

To calculate the relative frequency of each group size, we need to divide the frequency of each group size by the total number of groups:

Group Size   Frequency   Relative Frequency

1                          9             9/150 = 0.06

2                         52           52/150 = 0.35

3                         27            27/150 = 0.18

4                         38            38/150 = 0.25

5                         16             16/150 = 0.11

6                          6              6/150 = 0.04

7                          5              5/150 = 0.03

8                          7              7/150 = 0.05

We can see that the relative frequency of groups with 5 or more people is 0.11 + 0.04 + 0.03 + 0.05 = 0.23. This means that we would expect 23% of the 600 groups in the larger zoo to have 5 or more people.

To calculate the actual number of groups with 5 or more people, we multiply the total number of groups by the relative frequency:

Number of groups with 5 or more people = 600 x 0.23 = 138

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