i have four identical oranges. how many ways are there for me to divide these oranges into at most three groups? (by definition, a group must have at least one orange.)

well, let's take a peek at the graph, hmmm it has a straight line from the origin to (5,10), and then another straight line from (5,10) to (10,5) and then another one from there up to (20,5).

well, let's simply get the equations for each of those lines then

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{2}(x-\stackrel{x_1}{0})\implies \boxed{y = 2x} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{5}}} \implies \cfrac{ -5 }{ 5 }\implies -1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{-1}(x-\stackrel{x_1}{5}) \\\\\\ y-10=-x+5\implies \boxed{y=-x+15} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{20}-\underset{x_1}{10}}} \implies \cfrac{ 0 }{ 10 }\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{0}(x-\stackrel{x_1}{10})\implies y-5=0\implies \boxed{y=5}[/tex]

so then hmmm let's use those, we know how f(x) is moving now, so

[tex]\stackrel{y}{f(x)}= \begin{cases} 2x&x\geqslant 0\\\\ -x+15&x\leqslant 10\\\\ 5&x\leqslant 20 \end{cases}[/tex]

(a) True, x is an element of the set {x}

(b) True, the set {x} is a subset of itself.

(c) False, x is an element of {x}, but the set {x} is not an element of {x}.

(d) True, the set {x} is an element of the set {{x}}.

The numbers 1, 2, 3, and 4 are the elements of set A, as indicated by the formula A=1,2,3,4. Subsets of A are collections of components from A, like 1, and 2. Sets may also function as elements.

Consider the set B=1,2,3,4 as an example. B's constituent parts are not 1, 2, 3, or 4. Instead, there are just three components of B: the numbers 1 and 2, as well as the set "3, 4."

A set's components can be anything. For instance, the set "C=red, blue, green" contains the colors red, green, and blue as its constituents.

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the subsets in this case are:

Remember that for two sets A and B, we say that A is a subset of B if and only if all the elements of A also are elements of B.

In this case, we have 3 sets:

We can rewrite these ones as:

Here we can see that all the elements in C also belong in B and also belong in A, and all the elements in B also belong to A, then the subsets are:

C ⊆ B

C ⊆ A

B ⊆ A

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When graphed, one point is on top of the other, creating a vertical line. This could either be ∞ or -∞ .

Number of boys = a - b

Number of children in the class = a

Number of girls in the class = b

Number of boys = Total - Girls

                              a - b

The total charge for the rooms will be $197.55.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

The charge for one room = $21.95

Total number of rooms = 3+2+4=9 rooms

Total charges for the room= Charge for one room × total number of room

Substitute the values:-

The total charge for the room = 21.95 × 9 = 197.55

Hence, the total charge for the room is 197.55

The complete question is given below:-

Landon Elliot fumigates rooms and charges $21.95 per room. on Monday, he fumigated 3 rooms in one house, 2 in another, and 4 in a third. find his total charges.

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Answer:

x=3

Step-by-step explanation:

Answer:

[tex] \sf \large \: h = \frac{v}{lw} [/tex]

Step-by-step explanation:

Let's solve for h.

v=lwh

Step 1: Flip the equation.

hlw=v

Step 2: Divide both sides by lw.

hlw/lw = v/lw

h= v/lw

0.58 or more than half of sugar is sprinkled by rose on the brownies.

Given,

Rose has 1 3/4 cups of powdered sugar.

1/3 of the sugar sprinkled on lemon cookies

Therefore'

1 3/4 = (4*1+3) / 4

= 7/4

1/3 of the sugar sprinkled on lemon cookies

= 1/3 (7/4)

= 7/12

= 0.58 or more than half of sugar is sprinkled by rose on the brownies.

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A mother will need 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories.

Given that, a mother is choosing which baby foods to serve her infant. A jar of meat has 2g of protein and 34 calories. A jar of vegetables has 1g of protein and 17 calories. Now , we have to calculate how much she will be needed if she wants to serve 5g of protein and 120 ​calories respectively.

So, let's proceed to solve this question.

For 5g of protein she will be needed 2 jars of meat having 2g protein and 1 jar of vegetables which has 1g protein, then total protein will be equals to 5g.

5g of protein = 2 x A jar of meat + 1 x A jar of vegetables

For 120 calories, she will be needed 3 jars of meat and 1 jar of vegetable then it comes out to be 119 calories approximately equals to 120 calories.

So, 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories.

Therefore, 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories is the required answer.

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The value of the given number is -10.

Here, we are given that Thirty-five more than 0.8 times a number is the same as 43 less than the product of -7 and the number.

Let the number be x

0.8 times x = 0.8

35 more than 0.8x = 35 + 0.8x

Thus, our left hand side of the equation is 35 + 0.8x

Now, the product of -7 and x = -7x

43 less than -7x = -7x - 43

Thus, we get the following equation-

35 + 0.8x = -7x - 43

we can solve this equation to find the value of x-

0.8x + 7x = -43 - 35

7.8x = -78

x = -78/ 7.8

x = -1/ 0.1

x = -10

Thus, the value of the given number is -10.

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The Cost of jacket before tax is 74.73.

According to the statement

We have to find that the cost of jacket.

So, For this purpose, we know that the

The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.

From the given information:

the sales tax is 6%. The total cost is $79.49.

Then the real cost is :

Real cost = 6% of the $79.49

Then

solve it

tax amount applied on the jacket = 6/100*79.49

tax amount applied on the jacket = 0.06*79.49

tax amount applied on the jacket = 6/100*79.49

tax amount applied on the jacket = 4.76

Then

Cost of jacket before tax = 79.49 -4.76

Cost of jacket before tax = 74.73.

So, The Cost of jacket before tax is 74.73.

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Answer: 0.29

Step-by-step explanation:

= 0.288

8>5

= 0.29

19 miles the average number of miles Lori ran.

Miles Lori ran on Monday = 5 ½ = 11/2

Miles Lori ran on Tuesday = 6 ¼  = 25/4

Miles Lori ran on Wednesday = 4½ = 9/2

Miles Lori ran on Thursday = 2¾ = 11/4

Total miles she ran = sum of 4 days runs

= 11/2 + 25/4 + 9/2 + 11/4

= 22/4 + 25/4  + 18/4 + 11/4

= [tex]\frac{22 +25+18+11}{4}[/tex]

= 76/4 miles or 19 miles

By combining a set of integers and then dividing by their count, the average number—also known as the arithmetic mean—is created. For instance, the sum of 2, 3, 3, 5, 7, and 10 is equal to 30 divided by 6, which equals 5.

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Answer:

1.25

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

A/B

30/10 = 3

Answer:

5.333333333333

Step-by-step explanation:

1. 2^7 &2^7 have the vase, by subtracting their power, the result is 4.

2. (4^5)^0=1

3. 3^-1=0.3333333

4 finally by adding each values in above steps

Answer:

5) acute

6)acute

7)reflex

8)reflex

Step-by-step explanation:

No 6&5 are acute because they are each less than 90 degrees while no7&8 are reflex because they exceed 180 degrees.

Step-by-step explanation:

first- b

swcond- a

third- c

Equations for the set of the plane through the point [tex](x_0,y_0,z_0)[/tex] and parallel to:

a. xy-plane is [tex]z=z_0[/tex]   b. yz-plane is [tex]x=x_0[/tex] c. xz-plane is [tex]y=y_0[/tex]

The given set is the plane through the point  [tex](x_0,y_0,z_0)[/tex] parallel to:

a. xy-plane   b. yz-plane  c. xz-plane

Equation of the plane parallel to a plane containing a vector [tex]\vec r[/tex] through the point [tex](x_0,y_0,z_0)[/tex] is [tex](\vec r-(x_0,y_0,z_0)) .\vec n=0[/tex] ,where [tex]\vec n[/tex] is the normal to the plane and [tex]\vec r =x\vec i +y\vec j +z\vec k[/tex].

a. Plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to the xy-plane is,

    [tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec k[/tex] = 0

⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec k=0[/tex]

⇒ [tex]z-z_0 =0[/tex]

⇒ [tex]z=z_0[/tex] is the equation of the plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to xy-plane.

b. Plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to the yz-plane is,

    [tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec i[/tex] = 0

⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec i=0[/tex]

⇒ [tex]x-x_0 =0[/tex]

⇒ [tex]x=x_0[/tex] is the equation of the plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to yz-plane.

c.  Plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to the xz-plane is,

    [tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec j[/tex] = 0

⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec j=0[/tex]

⇒ [tex]y-y_0 =0[/tex]

⇒ [tex]y=y_0[/tex] is the equation of the plane through  [tex](x_0,y_0,z_0)[/tex] and parallel to xz-plane.

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The algebraic properties used in the steps are the distribution property, the associative property, the identity property, and the distribution property

The first step in the equation is given as:

t + 5(t + 1) = t + (5t + 5)

The distribution property states that

a(b + c) = ab + ac

So, the property used in t + 5(t + 1) = t + (5t + 5) is the distribution property

Next, we have:

t + 5(t + 1) = (t + 5t) + 5

The associative property states that

a + (b + c) = (a + b) + c

So, the property used in t + 5(t + 1) = (t + 5t) + 5 is the associative property

Next, we have:

t + 5(t + 1) = (1t + 5t) + 5

The identity property states that

a * 1  = a

So, the property used in t + 5(t + 1) = (1t + 5t) + 5 is the identity property

Next, we have:

t + 5(t + 1) = (1 + 5)t + 5

The distribution property states that

a(b + c) = ab + ac

So, the property used in t + 5(t + 1) = (1 + 5)t + 5 is the distribution property

Lastly, we have the solution

(6t + 5)

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Answer:

Top boxes are 18 and bottom boxes are 9

Step-by-step explanation:

Left side

Frist answer

2x3 =6, so 6 x3 = 18.  18 Goes into the top box on the left.

2 x [tex]\frac{3}{2}[/tex] = 3, so 6 x[tex]\frac{3}{2}[/tex] = 9  9 goes in the bottom box on the left.

Top right: 6 x 3 = 18.  18 goes in the top right

bottom right 3x3 = 9  9 Goes in the bottom right.

Answer:

7m-8

Step-by-step explanation:

distribute 4 through the parentheses

4m-8+3m

collect like terms

7m-8

Answer:

7m-8

Step-by-step explanation:

So to simplify this expression, you would need to do distributive property.

4(m-2)

(4*m) + (4*-2)

4m-8+3m

7m-8

So your simplification is 7m-8

Answer:

9 inches

Step-by-step explanation:

To find the volume of a cube, you could cube the side length, simplified as x³.

x³ = 729

x = 9

9 inches

Hope this helps! :)

Answer:

13 gallons

If the car is able to travel 30 miles per gallon and has a 16-gallon fuel tank, its total fuel efficiency is found by evaluating the product of the two factors.

Therefore, we can multiply 30 by 16 and find the total mileage that the car is equipped to travel:

[tex]30\times16=480[/tex]

Now, assuming that the car has a full tank of gas, it travels 90 miles on the highway. We can find out the remaining fuel efficiency by subtracting 90 miles from the maximum fuel efficiency:

[tex]480-90=390[/tex]

Then, since the car can travel 30 miles per gallon, divide this fuel efficiency by 30 miles to find the remaining gallons in the tank:

[tex]\displaystyle \frac{390}{30} = 13[/tex]

[tex]\boxed{\bold{13 \ gallons}}[/tex]

Answer:

8 : 3, 8/3, and "8 to 3"

Answer:

y is about equal to -4.692

Step-by-step explanation:

Answer: a. 21 terms

b. 798

Step-by-step explanation:

a. 68-8=60 ==> difference between 1st and last term

60/3=20 ==> number of terms after the first term

20+1=21 terms ==> total number of terms

b. Find the mean of the terms first:

(68+8)/2=    ==> the mean of all terms in a sequence is equal to the mean of the first and last term

76/2=38

38*21=798   ==> add the mean 21 times to get the total sum since there are 21 terms in the sequence.