There are 50 identical apples that need to be distributed among alice, bob, and cathy. determine the numberof ways that this can be done such that each one of them gets at least 2 apples. as examples, possible distributions ofthe identical apples among alice, bob and cathy include (a, b,
c.= (46, 2, 2); (10, 10, 30); (9, 2, 39), etc., where a,b and c denote the number of apples allocated to alice, bob and cathy respectively.

Answer:

Given: Segment AB || segment DE, C is the midpoint of segment DB.

Prove: ΔA CB ≅ ΔE CD

Proof: In ΔA CB and ΔE CD

 C is the Mid point of B D.

BC=C D→ definition of midpoint

∠A CB= ∠ EC D→→vertical angles are congruent

∠BAC=∠DEC→→[AB║DE,so alternate angles are equal]

→→ΔA CB ≅ ΔE CD[A AS or A SA]

Option B: vertical angles are congruent

Answer:

The answer is A) Definition of midpoint

Step-by-step explanation:

Answer B is wrong. I just did the test

12 boxes are needed  in all.

Last box will contain only 20 kernels.

Given is :

The popped corn is put into small popcorn boxes that each hold 130 popped kernels.

There are 1450 kernels in a pound of un popped popcorn.

If all the boxes are filled except for the last box, then how many boxes are needed?

Number of boxes  = Total number of kernels/Number of kernel in each box

=> [tex]\frac{1450}{130}= 11.15[/tex]

Therefore, a total of 11+1 = 12 boxes are needed as 11.15 is more than 11.

And the last box will contain = [tex]1450-1430=20[/tex] kernels.

Therefore, the last box will have 20 kernels.

The value of number c is 20

5 as one-fourth of a number c is represented using the following equation

Multiply both sides of the above equation by 4

Evaluate the products

Rewrite the above equation as

Hence, the value of number c is 20

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The number of hamburger meat he bought is 3.

A package of hot dogs cost $1.60 and a package of hamburgers cost $5.

You bought a total of 8 packages of meat and you spent $23.

Therefore,

let

x = number of package of hot dogs

y = number of package of hamburger

Hence,

x + y = 8

1.60x + 5y = 23

multiply equation(i) by 5

5x + 5y = 40

1.60x + 5y = 23

Subtract equation(ii) from equation(i)

3.4x = 17

x = 17 / 3.4

x = 5

y  = 8  - 5

y = 3

Therefore, the number of hamburger meat he bought is 3.

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Answer:

C. Both equations will find the correct solution.

Step-by-step explanation:

The probability that two student chosen at random is a male is 6/11.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

Here, Class contains 3 females and 9 males it means total 12 students.

Probability for having 1st student male = 9/12 = 3/4

Probability for having 2nd student is also male = 8/11

Overall Probability = [tex]\frac{3}{4} X \frac{8}{11}[/tex]

                                = 6/11

Thus, the probability that two student chosen at random is a male is 6/11.

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To find out how many cement bags are needed, calculate the volume of one cinder block and see how many such blocks fit in a cement bag. Then, divide the total number of cinder blocks by the number of blocks one bag can fill and round up to the nearest whole number.

To determine the number of cement bags needed to fill a cinder block wall with the given measurements, first calculate the volume of one cinder block. Then, figure out how many cinder blocks fit into one bag of cement.

The volume of one cinder block is:

V = length × height × width

V = 1.3 ft × 0.67 ft × 0.67 ft

V [tex]\approx[/tex] 0.5809 cubic feet

Now, since one bag of cement is equivalent to 5 cubic feet, determine how many cinder blocks one bag can fill:

Number of blocks per bag = 5 cubic feet / 0.5809 cubic feet per block

Number of blocks per bag [tex]\approx[/tex] 8.61 blocks

We need the total number of cinder blocks for the entire wall. Assuming we know the total wall dimensions, let's say we have a total of 100 blocks (for example purposes).

Total number of bags = Total number of blocks / Number of blocks per bag

Total number of bags = 100 / 8.61

Total number of bags [tex]\approx[/tex] 11.62

Since you can't buy a fraction of a bag, you would need to round up to the next whole number, so you would need 12 bags of cement to fill the wall.

Final answer:

The speed of the cruise boat in still water is 20 mph and the rate of the stream is 4 mph.

Explanation:

The student is asking about a problem related to the rate of the boat in still water and the rate of the stream, given the times it takes to travel downstream and upstream. To solve this, we can use the following steps:

Let's solve the equations:

Adding both equations:

Therefore, the speed of the boat in still water is 20 mph and the rate of the stream is 4 mph.

Answer:

B

Step-by-step explanation:

Final answer:

Mei is 9 years old, her mother is 36 years old, and her grandmother is 72 years old, determined by defining variables for their ages and solving the equation based on their age relationships and the given total sum of their ages.

Explanation:

To solve the problem regarding the ages of Mei, her mother, and her grandmother, we can use a system of equations based on the information given. Let's define Mei's age as m, her mother's age as 4m (since her mother is 4 times Mei's age), and her grandmother's age as 8m (since the grandmother is twice as old as Mei's mother).

According to the problem, the sum of their ages is 117 years:

m + 4m + 8m = 117

Simplifying this equation gives us:

13m = 117

Next, we divide both sides by 13 to find m:

m = 117 / 13

m = 9

Now that we have Mei's age, we can easily calculate her mother's and grandmother's ages:

Therefore, Mei is 9 years old, her mother is 36 years old, and her grandmother is 72 years old.

Angle C measures 32.5 degrees and angle D measures 57.5 degrees.

Let's represent the measure of angle C as x. Angle D is 25 degrees greater than angle C, so we can represent the measure of angle D as x + 25.

We know that angles C and D are complementary, so their measures must add up to 90 degrees.

Therefore, we can set up the equation:

x + (x + 25) = 90

Combining like terms, we get:

2x + 25 = 90

Subtracting 25 from both sides, we get:

2x = 65

Dividing both sides by 2, we get:

x = 32.5

So, the measure of angle C is 32.5 degrees, and the measure of angle D is 57.5 degrees.

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Answer:

The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.

Step-by-step explanation:

For a circulus with radius r, we have that:

The area of the circulus is:

[tex]A = \pi r^{2}[/tex]

That is, the radius is squared, not multiplied by 2, so the first statement is incorrect.

The circumference of the circulus is:

The derivative of the area, so

[tex]C = 2\pi r[/tex]

However

The radius if half the diameter. So

[tex]C = 2\pi \frac{d}{2}[/tex]

[tex]C = \pi d[/tex]

So the correct statement is:

The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.

Both statements are correct. The formula for the area of a circle is A = πr², where r is the radius, and the formula for the circumference of a circle is C = πd, where d is the diameter.

The formula for the area of a circle is given by A = πr², where A represents the area and r represents the radius of the circle. In this formula, the radius is squared and then multiplied by the mathematical constant π (pi) to calculate the area enclosed by the circle.

On the other hand, the formula for the circumference of a circle is given by C = πd, where C represents the circumference and d represents the diameter of the circle. In this formula, the diameter is multiplied by the mathematical constant π to calculate the total distance around the circle.

These formulas are derived from the properties of circles. The radius is the distance from the center of the circle to any point on its edge, while the diameter is the distance across the circle passing through its center. The circumference represents the boundary or perimeter of the circle, while the area represents the space enclosed by the circle.

It's important to note that the relationship between the radius and diameter is given by the equation d = 2r, where d represents the diameter and r represents the radius. This relationship allows us to interchangeably use the radius or diameter in the formulas for the area and circumference of a circle.

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Complete Question:

1. The formula for the area, A, of a circle is A = [tex]\pi r^2[/tex] , where r is the circle’s radius.

2. The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.

Which of the above statements is correct?

Answer:

2 so your answer would be C.

ANSWER

[tex]

\angle19.4,50.4 \: > [/tex]

EXPLANATION

The given vector has magnitude 54 units.

The vector is making an angle of 69° with the x-axis.

The horizontal component of the vector is

[tex] = 54 \cos(69) [/tex]

[tex] = 19.35[/tex]

To the nearest tenth, we have,

[tex] = 19.4[/tex]

The vertical component is

[tex] = 54 \sin(69 \degree) [/tex]

[tex] = 50.41[/tex]

[tex] = 50.4[/tex]

to the nearest tenth.

The required vector is

[tex]

\angle19.4,50.4 \: > [/tex]

The components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.

A vector is a quantity that has both magnitude and direction. It has two components a vertical component(Sine) and a horizontal component(Cosine). The component of a vector can be written as,

Vertical component, [tex]V_y = \vec V\ Sin(\theta)[/tex]

Horizontal component, [tex]V_x = \vec V\ Cos(\theta)[/tex]

We know that a vector can be divided into two components a horizontal component and a vertical component, therefore, the vector components can be written as,

[tex]V_y = \vec V Sin\theta\\\\V_y = 54\ Sin(69^o)\\\\V_y = 50.4133[/tex]

[tex]V_x = \vec V Cos\theta\\\\V_x = 54\ Cos(69^o)\\\\V_x = 19.3519[/tex]

Hence, the components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.

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