Barrett works at an ice cream shop. The function f(x) represents the amount of money Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes. The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.

f(x) = 2x2 + 4
g of x equals the square root of the quantity 3 x cubed

Answer:

The average rate of change is 2

Step-by-step explanation:

First set divide your data into 2 sets of separate data:

Independent Data= Day 3        

Dependent Data   = 10 points

Independent Data= Day 6

Dependent Data   = 16 points

Then subtract your two independent data: 6-3=3

Then subtract your two dependent data:  16-10=6

Next divide: difference in dependent/ difference in independent

6/3=2

So, your rate of change is 2.

Weight of water will a 55 gallon tank hold 440 lbs.

If a 45 gallon hot water tank holds 360 lbs.

45 gal⇒  360 lb

55 gal ⇒ x lb?

Ratio

45 : 360 = 55 : x

Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Here,

do the relation

[tex]\frac{45}{360} = \frac{55}{x}[/tex]

solve the x

[tex]x = \frac{55 * 360}{45} \\ = 440[/tex]

Hence weight of water will a 55 gallon tank hold 440 lbs.

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Answer:

14x + 8 for the first column and the second one is i think its 2 (7x + 4)

Step-by-step explanation:

sorry if this is not what your looking for

The function for motorboat's distance from the shore is y = -4x + 50.

A function is a formula, rule, or law that specifies how one variable (the independent variable) and another variable are related. The linear equation is of the form Ax+By+C=0.

Where A and B are the coefficient and C is the constant.

After 9 minutes, boat is 14 km from the shore, so finding the rate of change,

Rate of Change [tex]=\frac{14-50}{9}\\[/tex]

[tex]=\frac{-36}{9}\\ =-4[/tex]

So, the rate of change of distance is 4 km / minutes.

Now, finding the function,

The function for the distance of motorboat from the shore will be,

y = -4x + 50

Where y will be the final distance and x is the minutes.

Therefore, the function for motorboat's distance from the shore is y = -4x + 50.

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The expanding the expression y^2 - 3y^3 x^-1) 2m^0 y^-2 using distributive property is 2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²

We need to expand the expression (y² - 3y³ + x⁻¹) (2m⁰ + y⁻²)

The distributive property allows to multiply a sum by multiplying each term separately and then add all of the products together.

y²(2m⁰ + y⁻²) - 3y³(2m⁰ + y⁻²)  + x⁻¹(2m⁰ + y⁻²)

2(1)y² + y²⁻² - 3y³2(1) - 3y³⁻² + x⁻¹2(1) + x⁻¹y⁻²

2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²

Therefore, the expanding the expression y^2 - 3y^3 x^-1) 2m^0 y^-2 using distributive property is 2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²

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a) After 1 day, the revenue for each item is the same.

b) Graph is shown in the attachment.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

M(d) = 2x² + 8x - 4

R(d) = 2x + 4

a) Find x by taking y=M(d)=R(d). ( same revenue=y)

     y= 2x² + 8x - 4

     y= 2x + 4

This shows that right-side expressions are equal.

 2x² + 8x - 4 = 2x + 4

 2x² + 8x - 4 - 2x - 4=0

2x² +6x-8=0

Find the factors

2(x-1)(x+4)=0

x-1=0,  x+4=0

x= 1, x=-4

consider positive value for days

So, after 1 day, the revenue for each item is the same

b)  The equations:

 y= 2x² + 8x - 4

     y= 2x + 4

By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).

By plotting and joining those points, we get the graph as shown in the attachment.

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Each share of the tech company cost is $1 and 18 more shares can Josh buy with the remainder of his savings.

Given:

Josh spends of his savings to buy 48 4/5 shares in a cech company. He has $18 left.

Let x be the total savings

4/5 x = 48

x = 48*5/4

= 240/4

= $60

= 4/5*60

= 240/5

= $48.

Part A:

The cost of each share of the tech company = 48/48

= $1

Part B :

He has 18 so he can buy =18*1

= 18 shares .

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Using the theories of probability, we got that  5/9 is the probability that one letter is from each sister's name if the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement.

We know very well that if we want to count number of ways  by which r object can be chosen from n objects ,this can be done in [tex]^nC_r[/tex] ways which is equivalent to =(n!/(r!.(n-r)!)

Here are the same case, we have 10 cards, in each of the card there is letter written on it. So number of ways to choose two cards such that it contains any letter is can be done  in  [tex]^1^0C_2[/tex] ways which is equivalent to 45 ways.

Similarly, number of ways of choosing card which contains only Cybil`s name =[tex]^5C_2[/tex] ways=10 ways.

Similarly, number of ways of choosing card which contains only Ronda`s name =[tex]^5C_2[/tex] ways=10 ways.

So  the number of ways containing one letter from each name  =  45 - 10 - 10 = 25

So....the probability of choosing one of these sets  =  25 / 45  =  5 / 9 =0.55

Hence, Cybil and Ronda are sisters. the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the cards.  the probability that one letter is from each sister's name is = 5/9.

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(Complete question) is:

cybil and ronda are sisters. the 10 letters from their names are placed on 10 identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the 10 cards. what is the probability that one letter is from each sister's name? express your answer as a common fraction.

Answer:

1

Step-by-step explanation:

3(2)-5/4(4)

6-20/4

6-5

1

The amount of money that Malachy get is £123 .

In the question ,

it is given that ,

£410 is divided between Gordon, Malachy and Paul .

also given that Malachy gets three times as much as Paul ,

let the amount that Paul get = x .

So , the amount that Malachy get = 3x

it is given that Gordon gets twice as much as Malachy ,

that means , the amount that Gordon get = 2(3x) = 6x

given the total amount is £410 ,

So, equation representing the total amount is

x + 3x + 6x = 410

4x + 6x = 410

10x = 410

x = 410/10

x = 41

So , the amount that Paul get = £41 ,

amount that Malachy get = 3(41) = £123

amount that Gordon get = 6(41) = £246

Therefore ,  The amount of money that Malachy get is £123 .

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Answer:

x ≈ 41.7 ° (a)

Step-by-step explanation:

b² = a² + c² - 2ac × cosβ

~~~~~~~~~~~

25² = 32² + 37² - 2(32)(37)cosx

625 = 2,393 - 2,368 cosx

cosx = [tex]\frac{-2393+625}{-2368}[/tex] ≈ 0.74662162

x ≈ 41.7 ° (a)

Answer: y=-2x+7

Step-by-step explanation:

we know that equation is y=mx+b

b=y intercept

x=the x coordinate

m=slope

y=y coordinate

then you can just fill it in from there . hope this helps

Answer:

Step-by-step explanation:

gradient of L:

4-(-1)/6-4

=5/2

Gradient of m=perpendicular gradient=m1xm2= -1

5/2m2=-1

5m2=-2

m2=  2/5

y intercept given=8

equation:

y= -2/5x+8

y will be0 when line crosses x-axis

input y as 0

0= -2/5x+8

2/5x=8

2=40x

x= 20

coordinate=(-20,0)

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Answer:

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

We observe on the graph that:

All the above helps us to conclude that:

Answer:

Reflection through the x-axis, f(x) → -f(x).

Step-by-step explanation:

On comparison of the dotted red line with the solid blue line, it is apparent that the x-coordinates do not change, yet the y-coordinates are negatives of each other.

This suggests a reflection in the x-axis.

(Note: If the function was reflected in the y-axis, the y-coordinates would not change, yet the x-coordinates would be negatives of each other).

Mapping rule for reflection in the x-axis:  

Therefore, as y → -y then f(x) → -f(x).

So the correct answer that describes how the dotted line relates to the solid line f(x) is:

The degree of a function has no effect by the dilation of the function.

and the degree of the dilated function is same as the degree of the original function.

Dilation is defined as, when a function is multiplied by any number, the graph of the function retain a new shape, either by stretch or by compression in different directions.

Now, when a function is dilated it is either stretched or compressed in upward or downward direction.

It does not affect the degree of the function as the number of roots will be same as original function.

So, the degree of the dilated function is same as the degree of the original function.

Hence, the degree of the dilated function is same as the degree of the original function.

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The volume of the jar is 1130.4 cubic inches and the number of marbles that can fit is 56.

In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

It is given that:

A cylindrical jar has a radius of 6 inches and a height of 10inches.

The volume:

V = π(6)²(10)

V = (3.14)(6)²(10)

V = 1130.4 cubic inches

Number of marbles = 1130.4/20 = 56.52 = 56 marbles

Thus, the volume of the jar is 1130.4 cubic inches and the number of marbles that can fit is 56.

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According to the area of triangle, the value of x is 8.6 and the value of y is 10.5

Area of triangle:

The area of the triangle is defined as the region enclosed by its perimeter or the three sides of the triangle.

Given,

Here we have the triangle with side values and height.

Now, we have to find the value of x and y in the triangle.

We know the formula of the triangle is,

A = 1/2 b x h

Here the value of b is x + 9 and the value of h = 6

So, the area of the triangle is,

=> [(x + 9) x 6]/2

=> 2 = 6x + 54

=> 6x = 52

=>  x = 52/6

=> 8.6

Now, the value of y is calculated by using the Pythagoras theorem,

=> y² = (8.6)² + 6²

=> y² = 73.96 + 36

=> y² = 109.96

=> y = √109.96

=> y = 10.5

Therefore, the value of y is 10.5

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The number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.

Given,Parker went to the grocery store and bought bottles of soda and bottles of juice.

Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.

Parker purchased a total of 14 bottles of juice and soda which collectively contain 300 grams of sugar.

we are asked to determine  the number of bottles of soda purchased,x, and the number of bottles of juice purchased, y.

So, the total number of bottles:x+y=14

x=14-y ...eq(1)

As, Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.

50x+10y=300

Substituting the value of x from eq(1)

⇒ 50(14-y) + 10y = 300

⇒ 700 - 50y + 10y = 300

⇒ -40y = 300 - 700

⇒ -40y =-400

y = 400/40

y = 10

The number of juice bottles = 10.

Now, to get the number of bottle of soda by substituting the value of y  in equation (1):

x = 14-y

x = 14 - 10

x = 4

The number of soda bottles = 4.

Therefore, the number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.

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Answer:

(3b + 2y)(2x - 3m)

Step-by-step explanation:

6xb + 2xy - 9mb - 6my ( factor first/second and third/fourth terms )

= 2x(3b + y) - 3m(3b + 2y) ← factor out (3b + 2y) from each term

= (3b + 2y)(2x - 3m)

Answer:

Step-by-step explanation:

 y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis)

try this it works

2. The equation is given as follows: x + 4x = 25.

3. The constrains are given as follows: 0 ≤ x ≤ 25, 0 ≤ y ≤ 75.

The time spent running is given by:

Running = 4x.

The time spent walking is one-fourth of the time spent walking, hence it is given by:

Walking = 4x/4 = x.

The total time is the sum of the times spent running and walking, hence the expression is presented as follows:

x + 4x = 25.

The variables are given as follows:

You can accept at most 25 out-of-state hires, hence:

0 ≤ x ≤ 25

(as the number cannot be negative).

The company plans to have three times as many in-state hires, hence:

0 ≤ y ≤ 75.

As:

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Answer:

[tex]\frac{\sqrt{2} }{3}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

75 = 64 + 8 + 2 + 1 = 1*2^6 + 1*2^3 + 1*2^1 + 1*2^0

There is no power 5, 4, or 2 so zeros go in those slots.

75 = 1001011 (Base 2)

The average for the price of the stock for the end of day 7 is 57.28

Given,

The stock of 8 days;

Day 1 - 62. 00

Day 2 - 56. 00

Day 3 - 50. 00

Day 4 - 60. 00

Day 5 - 59. 00

Day 6 - 55. 00

Day 7 - 59. 00

Day 8 - 63. 00

We have to find the average for the price of the stock for the end of day 7.

Here,

Average = Total sum / Number

Then,

Average =  (day 1 + day 2 + day 3 + day 4 + day 5 + day 6 + day 7) / n

= (62 + 56 + 50 + 60 + 59 + 55 + 59) / 7

= 401/7

= 57.28

Therefore,

The average for the price of the stock for the end of day 7 is 57.28

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Answer:

= 27

Step-by-step explanation:

36×3/4

36 × 3

--

4

9 × 3

= 27

Answer:

L = 22     W = 4

Step-by-step explanation:

It says that the length is 6 more than 4 times its width, this means

4W + 6 = L

Perimeter is 52, this means

2W + 2L = 52

and Area is 88, this means

W*L = 88

2W = 52 - 2L

W = 26 - L

4(26 - L) + 6 = L

104 - 4L + 6 = L

104 + 6 = L + 4L

110 = 5L

L = 22

W = 26 - 22

W = 4

Answer:

It does not have an answer because the square root of any number cannot be negative

Yes, the equation √z= -7 does not have a solution.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

given that,  the equation √z= -7

now, we know, that the equation √z= -7 does not have a solution.

because, we know,

It does not have an answer because the square root of any number cannot be negative.

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Answer:

9

Step-by-step explanation:

given 2 sides of a triangle then the third side x lies within the limits

difference of 2 sides < x < sum of 2 sides , that is

6 - 4 < x < 6 + 4

2 < x < 10

then the largest possible length is 9

Answer:

x = 7

x = 2

√ 3x − 5 = x − 3

or

3x − 5 = ( x − 3 ) 2

or

3x − 5 = x 2 − 6x + 9

or

x 2 − 9x + 14 = 0

or

x 2 − 7x − 2x + 14 = 0

or

x(x − 7) − 2(x − 7) = 0

or

(x − 7) ( x − 2) = 0

or

x − 7 = 0

or

x = 7

Ans

1

or

x − 2 = 0

or

x = 2

Ans

2