Mary has 60 candy pieces and 45 chocolates. She wants to distribute the candy to her little sister's friends at her birthday party so that each friend gets an equal number of candies and an equal number of chocolates.What should be the smallest number of her sister's friends for the distribution of candy and chocolate so each friend gets an equal number of candy pieces and chocolates in a way that there should not be left any chocolate or candy pieces left over

Answer:

x = -3

Step-by-step explanation:

-5x + 32 = 47

-5x + 32 - 32 = 47 - 32

-5x = 15

-5x / -5 = 15 / -5

x = -3

Answer:

[tex]\Huge \boxed{x=-3}[/tex]

Step-by-step explanation:

[tex]\sf -5x + 32 = 47[/tex]

Subtract 32 from both sides.

[tex]\sf -5x + 32-32 = 47-32[/tex]

[tex]\sf -5x=15[/tex]

Divide both sides by -5.

[tex]\sf \displaystyle \frac{-5x}{-5} =\frac{15}{-5}[/tex]

[tex]\sf x=-3[/tex]

Answer:

Step-by-step explanation:

The formula for finding the distance between two points is expressed as shown

D = √(x₂-x₁)²+(y₂-y₁)²

Given the coordinate (17,3) and (17,−5), from the coordinates x₁ = 17, y₁ = 3, x₂ = 17 and y₂ = -5.Substituting the values given into the formula;

D = √(17-17)²+(-5-3)²

D = √0²+(-8)²

D = √64

D = 8

According to the result gotten, it can concluded that Marcia is correct although she didn't use the right expression to calculate her distance. She should have taken the square root of the sum of the square of difference in the coordinates axis according to the formula used.

Answer:

170

Step-by-step explanation:

The amount of profit Rodney made when he sold 200 bags of popcorn is given by A = $ 100

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the equation is

Let the amount for renting the machine be = $ 70

The amount per bag for packing popcorn = $ 0.15 per bag

The sale price of the popcorn per bag = $ 1.00

And ,

The total number of bags sold by Rodney = 200 bags

So , the total profit made by Rodney A is calculated from the equation ,

Total amount made by Rodney = total number of bags sold by Rodney x sale price of the popcorn per bag

Substituting the values in the equation , we get

Total amount made by Rodney = 200 x 1

Total amount made by Rodney = $ 200

Now , the cost per bag is deducted from the total amount made by Rodney

So ,

Total amount made by Rodney after deduction of bag cost = ( Total amount made by Rodney - amount per bag for packing popcorn x 200 )

Substituting the values in the equation , we get

Total amount made by Rodney after deduction of bag cost =

= 200 - ( 0.15 x 200 )

= 200 - 30

= $ 170

Now , the cost of renting the machine should also be deducted from the remaining amount to calculate the profit earned by Rodney

So , The profit earned by Rodney A = 170 - amount for renting the machine

The profit earned by Rodney A = $ 170 - $ 70

The profit earned by Rodney A = $ 100

Therefore , the value of A is $ 100

Hence , The amount of profit Rodney made when he sold 200 bags of popcorn is given by A = $ 100

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Answer:

20%

Step-by-step explanation:

200 mocha flavored cupcakes of the 500 cupcakes were sold. (200/500).

Reduce to 2/5. Then multiply 20/20 to 2/5 and get 20/100.

20% cupcakes were mocha flavored.

The logic behind me rewriting the fraction to 20/100 was because 200/500 could easily be divided be 100 and 5.

Answer:40%

Step-by-step explanation: 200/500=?/100

2/5 x 20/20= 40/100

40%

Answer:

24m

Step-by-step explanation:

factor the equation to get 6x4m which gets you 24m

Answer: option 3. 24m

Step-by-step explanation:

concept to know: (a+b)²=a²+2ab+b²  

                             (a-b)²=a²-2ab+b²

 (2m+3)²-(2m-3)²

=(4m²+12m+9)-(4m²-12m+9) ⇔ Use the formula mentioned above

=4m²+12m+9-4m²+12m-9 ⇔ take off parentheses

=4m²-4m²+12m+12m+9-9 ⇔ move the like term together

=24m ⇔ combine like term

Hope this helps!! :)

Please let me know if you have any question

Answer:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Step-by-step explanation:

So we have the rational function:

[tex]f(x)=\frac{x}{x-7}[/tex]

The domain restrictions of rational functions are the zeros of the denominator.  In other words, the domain of rational functions are always all real numbers except for the zeros of the denominator.

So, solve for the denominator by setting it to 0:

[tex]x-7=0[/tex]

Add 7 to both sides:

[tex]x=7[/tex]

So, our domain is all real numbers except for 7.

(When x=7, we have 7/0, which is undefined.)

Therefore:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Answer:

the picture has it all!

whatever equals zero is not the domain and whatever doesnt equal zero is the domain!

hope i helped :)

Answer:

3.009

Step-by-step explanation:

1 Kg is 1000 grams therefore

3 kg 9 g is

3.009

hope this helps you

Answer:

14

Step-by-step explanation:

Follow DMAS formula:

DMAS rule is followed when multiple arithmetic operations are there in a given problem like addition, subtraction, multiplication and division. It tells they should be performed in order of Division, Multiplication, Addition and Subtraction.

=50+6*3 -82

=50+18-82

=68-82

=14

Answer:

64

Step-by-step explanation:

PEMDAS

6(12+4) distribute the 6 to the numbers inside

96

50+96-82

50+96= 146

146-82 = 64

The estimated distance between the park and your school is 5 miles.

Here,

To estimate the distance between the park and your school, we can use the Pythagorean theorem, as the distance forms a right-angled triangle with the school, apartment, and park as its vertices.

Let's label the points as follows:

S = School

A = Apartment

P = Park

Given:

School (S) is 4 miles east and 1 mile south of the apartment (A).

Park (P) is 3 miles east and 4 miles south of the apartment (A).

Now, we have two right-angled triangles:

The triangle formed by S, A, and P. This is the triangle for which we want to estimate the distance between the school and the park.

The triangle formed by A, S, and P.

Since both triangles share the side AS (4 miles east), we can use the Pythagorean theorem for the triangle ASP to find the distance between the school and the park.

The Pythagorean theorem states that for a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, let's represent the distance between the school and the park as d (the hypotenuse), and the other two sides as 3 miles (east) and 4 miles (south).

Using the Pythagorean theorem:

[tex]d^2 = 3^2 + 4^2\\d^2 = 9 + 16\\d^2 = 25\\[/tex]

Now, take the square root of both sides to find d:

d = √25

d = 5

So, the estimated distance between the park and your school is 5 miles.

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Answer:

B,D,F

Step-by-step explanation:

I got it correct on edge

Answer:

number of tiles needed = 2500 pieces

Step-by-step explanation:

Floor area = 5m x 20m = 100 m²

area of 1 square tile = 20cm x 20cm = 400 cm² ---- convert to m²

400 cm² x [tex]\frac{1 m^{2} }{100^2 cm^2}[/tex] = 0.04 m²

To get the number of tiles required to cover the floor area 5x20 = 100 m²

just divide it by the area of tile.

so Number of tile req'd = 100 / 0.04 = 2500

therefore,

the number of tiles needed = 2500 pieces

Answer:

6/x^2

Step-by-step explanation:

Simplify the following:

2/x^2 + 4/x^2

2/x^2 + 4/x^2 = (2 + 4)/x^2:

(2 + 4)/x^2

2 + 4 = 6:

Answer: 6/x^2

Answer:

6/x²

Step-by-step explanation:

[tex]\frac{2}{x^{2} } + \frac{4}{x^{2} } \\\\[/tex]

= (2+4) / x²

= 6/x²

Answer:

L = 22 cm

Step-by-step explanation:

Area of a triangle = L x W

where W = 13 cm

Area = 286 cm²

A = L x W

286 = L x 13

L = 286 / 13

L = 22 cm

proof:

286 = 22 x 13

286 = 286 --- ok

Answer:

Troy ran 228 miles.

Step-by-step explanation:

Ashlynn (a) ran 19 miles. Troy (t) ran 3 times as many miles as Edwin, and Edwin (e) ran 4 times as many miles as Ashlynn.

So,

a=19

E=a•4

t=e•3

Knowing a=19, we can solve the first equation. e=19•4, 19•4=76 so e=76

Knowing e=76 we can solve the second equation t=76•3, 76•3=228 so t=228

Answer:

Ashlynn is my name!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given two coordinates (x₁,x₂) and (y₁,y₂), their midpoint (w,y) is expressed as:

M(X,Y) = [tex](\dfrac{x_1+w}{2}, \dfrac{y_1+y}{2})[/tex]

From the question, we are given the midpoint (X,Y) to be (2,2) and one endpoint as (1, -2) and we are to find the other end point expressed as (w,y). From the coordinates given, i can be seen that X = 2, Y =2, x₁ = 1 and y₁ = -2

Substituting the given end points into the given formula to get the other end points, we will have;

[tex]X = \dfrac{x_1+w}{2} \\2 = \dfrac{1+w}{2} \\cross\ multiply\\4 = 1+w\\w = 4-1\\w = 3[/tex]

Similarly;

[tex]Y = \dfrac{y_1+y}{2} \\2 = \dfrac{-2+y}{2} \\cross\ multiply\\4 = -2+y\\y = 4+2\\y = 6[/tex]

Hence the other endpoint (w, y) is (3,6)

Answer: d. 4, 4.53%

Step-by-step explanation:

Given table :

Number of Children                 Frequency

0                                                      325  

1                                                       212

2                                                       660

3                                                       151

4                                                       68  ← Least frequency

5 or more                                         84

Total                                 =            1500

or Sample size of couples = 1500

The number of children occurred the least frequently = 4 [Minimum frequency is 68 at number of children=4]

Percentage =[tex]\dfrac{least\ frequency}{Total}\times100[/tex]

[tex]\dfrac{68}{1500}\times100=4.53\%[/tex]

Hence, the correct answer is d. 4, 4.53%

Is the ratio 5:6 equivalent to 3:4

We can write the given expression as -

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

Factors of a number are numbers that divide evenly into another number. Factorization writes a number as the product of smaller numbers

Given is the expression -

{(x² + y²) - z²}² - 4x²y²

(x² + y²)² + z² - 2(x² + y²)z² - 4x²y²

(x² + y²) {(x² + y²) - 2z²} + z² - 4x²y²

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

Therefore, we can write the given expression as -

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

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Answer:

35%

Step-by-step explanation:

There are 20 sqaures, 7 of them are not shaded, 7/20=35%

The product of sin 30 and sin 60 is same as the product of cos 60 degrees tan 30 degrees and cos 30 degrees tan 60 degrees .

The product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.

From the complementary angle theorem, we have that

sinθ = cos (90° - θ)

and

cosθ = sin (90° - θ)

By applying the theorem,

sin 30° = cos (90° - 30°)

∴ sin 30° = cos 60°

Also,

sin 60° = cos (90° - 60°)

∴ sin 60° = cos 30°

Thus, sin 30° = cos 60° and sin 60° = cos 30°

Hence, the product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.

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Answer:

10^3×10^3

is 100000000 which is 10^7 in index form.

Answer: 2x -5 less than or equal to 124

Answer:

#1 : -2=n

#2: x=-3

#3: v=8

Step-by-step explanation:

the pictures are the explination

i hope they help

sorry if they dont

im a bad explainer

Answer:

It is 15

Step-by-step explanation:

A. on edge

Total number of animals for which (p ∪ q) ∩ r is true is 15.

What is meant by union of sets?

The set that contains all the elements present in both sets is the union of the two supplied sets.

Here,

It is given that,

Set p is {2, 5, 8, 9}

Set q is {2, 4, 7, 5}

Set r is {2, 4, 6, 9}

The union of p and q, which includes all creatures that are in p, in q, or in both p and q, is known as p ∪ q.

p ∪ q = {2, 4, 5, 7, 8, 9}

The creatures that must be present in both (p and q) and r are contained in (p ∪ q) ∩ r.

So, (p ∪ q) ∩ r = {2, 4, 9}

Therefore,

2 + 4 + 9 = 15

Hence,

Total number of animals for which (p ∪ q) ∩ r is true is 15.

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Attaching the image file here.

Answer:

C) 12.2 cm

Step-by-step explanation:

To find the area of a square, you multiply length and width, which for a square, are the same. So to find the length of one of its sides, you have to take the square root of the area.

[tex]L^{2} = 150\\\\L=\sqrt{150} \\L= 12.2\\[/tex]

Answer:

slope: (y₂ - y₁) / (x₂ - x₁)

(5 - 2) / (-1 - 1) = 3/-2 = -3/2

y = -3/2x + b

5 = -3/2(-1) + b

5 = 3/2 + b

b = 3.5

y = -3/2x - 7/2

(5.83 - 1.42) / (4.22 + 0.72) = 4.41/4.94

y = 4.41/4.94x + b

5.83 = (4.41/4.94)(4.22) + b

5.83 = 3.76724696 + b

b = 2.06275304

y = 4.41/4.94x + 2.06

(the numbers are really wacky so i hope thats right, so sorry if it isn't)

Answer:

Answer:-4e-9

[tex]3e - 19 - 7e + 10[/tex]

Start by combining like terms. I put like terms in parentheses so you can see them, but they are not needed.

[tex] = (3e - 7e) + ( - 19 + 10)[/tex]

[tex] = - 4e - 9[/tex]

That's it.

Answer: (-3,7)

Step-by-step explanation:

Flip the signs

Answer: $ 2800

Step-by-step explanation:

2400 is 96% of the initial price of camera which is 2400/0.96 =$2500

Now to gain 12% profit the camera should be sold at 2500+ .12*2500=$2800

Answer:

the full solution is in the picture

d= -3

n= -2

x= -32

Answer:

Yjtccjtchtcychy

Step-by-step explanation: