Important: (Worth 50 Points)

The number of adults at an amusement park, measured in hundreds of people, is represented by the function a(w)=−0.4w2+5w+9, where w is the number of weeks since the amusement park opened for the season.

The number of children at the same amusement park, measured in hundreds of people, is represented by the function c(w)=−0.2w2+9w+12, where w is the number of weeks since the amusement park opened for the season.

What function, f(w) , can be used to determine how many more children than adults are at the amusement park any week during the season?


f(w)=−0.2w2+4w+3

f(w)=−0.2w2+4w−3

f(w)=0.2w2+4w+3

f(w)=0.2w2+14w+3

Answers

Answer 1

Answer:

C. f(w) = 0.2w² + 4w + 3

Step-by-step explanation:

The function f(w) is the difference of c(w) and a(w):

f(w) = c(w) - a(w) = − 0.2w² + 9w + 12 - (- 0.4w² + 5w + 9) =− 0.2w² + 9w + 12 + 0.4w² - 5w - 9 =0.2w² + 4w + 3

Correct choice is C


Related Questions

give me the factors of 30​

Answers

Answer: 1,2,3,5,6, and 10

Step-by-step explanation:

Find the 7th term in the
sequence
,
32
1, 3, 9,...
Hint: Write a formula to help you.
1st term • Common Ratio desired term – 1)
Enter

Answers

Answer:

243

Step-by-step explanation:

formula is

Un = ar^n-1

U7 = ar^7-1

U7 =ar^6

U7 =1/3 ×3^6

where a=1/3 and r= 3

U=243

Please give me the answer and show me how you solved it

Answers

speed = distance over time

so 2.75 / .5 =

5.5 mph

Answer:

I think it is option 1

Step-by-step explanation:

11/4 x 1/2

[tex]\frac{11 *1}{4 * 2} = \frac{11}{8}[/tex]

which would equal: [tex]1\frac{3}{8}[/tex]

I might be wrong.

Kevin bought dvds of different movies he spent $5 for each movie the equation y=5 shows how much he spent for the movies

Answers

Answer:

The dependent variable is y (the amount paid)

Step-by-step explanation:

Given

[tex]y = 5x[/tex]

Where

[tex]x \to[/tex] number of movies

[tex]y \to[/tex] amount paid

Required

The dependent variable

From the question, we have:

[tex]y = 5x[/tex]

This means that the value of y is determined by the value of x.

Take for instance:

[tex]x = 2[/tex]

The value of y will be:

[tex]y =5*2 = 10[/tex]

If x changes (say; x = 12), y will also change

[tex]y =5*12 = 60[/tex]

Hence, y is the dependent variable

what is 200x149 who can answer that for me i need help on this my teacher said i cant use couculater

Answers

Answer:

29,800

Step-by-step explanation:

that will be 149 x 2 which equals 298

149

 ×2         Multiply 9 × 2 = 18

------        Keep the 8 carry the 1 multiply 4 by 2 then add 1 finally multiply 2 by 1

298

Then add two zeros at the end since we're multiplying a number with two zeros. (This method only works for numbers that end with zeros)

Final answer: 29800

The areas of the squares adjacent to two sides of a right triangle are shown below.

What is the area of the square adjacent to the third side of the triangle?​

Answers

Answer:

[tex]85\:\mathrm{units^2}[/tex]

Step-by-step explanation:

All side lengths of a square are equal. The three squares create a right triangle, and the hypotenuse of this triangle represents the side length of the square.

All right triangles must follow the Pythagorean Theorem [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the hypotenuse of the triangle.

Therefore, let [tex]h[/tex] be the side length of this largest square. Since the area of a square with side length [tex]s[/tex] is given by [tex]s^2[/tex], [tex]h^2[/tex] will represent the area of the square:

[tex]\sqrt{35}^2+\sqrt{50}^2=h^2=\boxed{85\:\mathrm{units^2}}[/tex]

Answer:

85

Step-by-step explanation:

We can use the Pythagorean theorem (a^2+b^2=c^2) to find the area of square adjacent to the third side.

Area of a square=side^2

So, we can substitute the areas of the squares that share side lengths with the triangle for a^2, b^2, and c^2 in the Pythagorean theorem.

For example, in the diagram above, the area of the square that shares a side with side length a is 35 square units. So, a^2=35.

Let's fill in the remaining values:

a^2 + b^2 = x^2

35+50-x^2
85=x^2
The area of the square adjacent to the third side of the triangle is 85 units^2.

Add.
3 7/11 + 9 6/11
Write your answer as a mixed number in simplest form.

Help

Answers

Answer:

13 2/11

Step-by-step explanation:

40/11+105/11

145/11

13 2/11

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{= \ 3\dfrac{7}{11}+ 9\dfrac{6}{11}}[/tex]

[tex]\mathsf{ 3\dfrac{7}{11} =\boxed{ \bf \dfrac{40}{11}}}[/tex]

[tex]\mathsf{9\dfrac{6}{11}= \boxed{\bf \dfrac{105}{11}}}[/tex]

[tex]\mathsf{= \ \dfrac{(40\times11)+(105\times11)}{(11\times11)}}[/tex]

[tex]\mathsf{40\times11=\boxed{\bf 440}}[/tex]

[tex]\mathsf{105\times11=\boxed{\bf 1,155}}[/tex]

[tex]\mathsf{=\ \dfrac{440+ 1,155}{11\times11} }[/tex]

[tex]\mathsf{11\times11=\boxed{\bf 121}}[/tex]

[tex]\mathsf{\dfrac{440+1,155}{121}}[/tex]

[tex]\mathsf{440 + 1,155=\boxed{\bf 1,595}}\leftarrow\mathsf{Your\ numerator\ (TOP\ number)}[/tex]

[tex]\mathsf{= \dfrac{1,595}{121}}[/tex]

[tex]\mathsf{= 13\dfrac{2}{11}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: } \mathsf{\boxed{\bf \dfrac{1,595}{121}\ or\ 13 \dfrac{2}{11}}\\\large\textsf{either one of those should work they equal the same}}}}\huge\checkmark}[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

[tex]\frak{Amphitrite1040:)}[/tex]

need help don't understand

Answers

Answer:

the mode is found by how much of the same number there is making the mode 1

the average is found by adding up all of it and dividing it by how many there is making it 4.2 if you need to round it, tha anwser is 4

PLEASE HELP I'LL GIVE BRAINLIEST!!! Tysm, it's urgent plz
The force, F (Newtons), between two
objects is inversely proportional to the
square of the distance, d (metres),
between them.
The force is 0.35 Newtons when the
distance between the objects is 8 metres,
Work out F (rounded to 2 DP) when
d = 7 metres.
F
Newtons​

Answers

Answer:

F=0.46N

Step-by-step explanation:

[tex]F[/tex]∝[tex]\frac{1}{d^{2}}[/tex],

[tex]F=\frac{k}{d^{2} } \\[/tex]

[tex]F=0.35N, d=8m\\[/tex]

[tex]0.35=\frac{k}{8^{2} }[/tex]

[tex]k=0.35\times 8^{2} \\\\k=22.4\\F=\frac{22.4}{d^{2} } \\d=7m, F=\frac{22.4}{7^{2} } =0.46N[/tex]

Find the mode of the data.
The number of awards earned
from each school in the district.
1, 3, 1, 5, 7, 8, 10
Mode: [?]
hande in the aroon hoy

Answers

Answer:

1

Step-by-step explanation:

The mode is the number that appears most often

1 appears twice in the data list and that is the mode

Answer:

Mode: 1

Step-by-step explanation:

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

The area of a opening rectangular window is to be 440 square centimeters. If the length measures x centimeters and the width measures x-2 centimeters, what are the dimensions?

Answers

Answer:

[tex]L=1+20i[/tex]

[tex]B=3+20i[/tex]

Step-by-step explanation:

From the question we are told that:

Area [tex]A=440cm^2[/tex]

Generally the equation for For Area is mathematically given by

 [tex]A=L*B[/tex]

 [tex]A=x*(x-2)[/tex]

Therefore

 [tex]x^2-2x-440=0[/tex]

 [tex]x=1+20i[/tex]

Therefore The Dimensions are

  [tex]L=1+20i[/tex]

 [tex]B=1+20i+2[/tex]

 [tex]B=3+20i[/tex]

Check all that are equivalent!

Answers

Answer:

3^6, 3^-4 * 3^10, 3^3 * 3^3, and (3*3) * (3*3*3*3) are the answers that are equivalent!

Step-by-step explanation:

These four are correct:-

3² × 3⁴ = 33-⁴ × 3¹⁰ = 3-⁴+¹⁰ = 33³ × 3³ = 3³+³= 3⁶(3×3)(3×3×3) = 3²× 3³= 3²+3⁴= 3⁶

3+(-7)
solve for x help meee

Answers

Answer:

3 + ( -7 )

7 - 3

= 4 is the answer

What is the volume of the rectangular prism?

Answers

Answer:

The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W. Ex: V = 5 in.

Determine the measure of angles 1, 2 and 3.
Measure of 211
Measure of 22
O
Measure of 23
22°
479
1
262
3

Answers

Answer:

1) 40

2) 118

3) 71

Step-by-step explanation:

3) is the easiest. All interior angles add to 180

Angle 3 = 180 - 62 - 47

Angle 3 = 71

2) Angle 2 is on the same straight line as 62 and together they equal 180

Angle 2  = 180 - 62

Angle 2 = 118

1) Using 22, Angle 2 and the knowledge that all interior angles equal 180

180 - 22 - 118 = Angle 1

40 = Angle 1

A pyramid is 24ft tall. A scall model has a height of 2 ft and is 1 foot wide at the base. Identify the scale factor that was used to create the model

Answers

Answer:

1 : 12

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

24/2 = 12

1 : 12

Mikes truck can drive 115 miles on 5 gallons of gas. How many miles can be driven with 11 gallons of gas, using the same mpg?

Answers

Answer:

253 miles

Step-by-step explanation:

Ratio:

115:5 and x:11

Method 1:

115/5 = x/11

1265 = 5x                     (cross multiplying)

x = 253 miles

Method 2:

11/5 = 2.2

2.2 x 115 = 253

253 miles

Method 3:

115 / 5 = 23

23 x 11 = 253

253 miles

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Prove that the following four points will form a rectangle when connected in order
by showing the diagonals are congruent. Show all work.
A(0, -3), B(-4, 0), C(2,8), D(6.5)

Answers

Answer:

Step-by-step explanation:

If the diagonals of the rectangle are congruent,

AC = BD

By using formula to calculate the distance between two points,

Distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between A(0, -3) and C(2, 8),

AC = [tex]\sqrt{(8+3)^2+(2-0)^2}[/tex]

     = [tex]\sqrt{125}[/tex]

     = [tex]5\sqrt{5}[/tex]

Similarly, distance between two points B(-4, 0) and D(6, 5),

BD = [tex]\sqrt{(5-0)^2+(6+4)^2}[/tex]

     = [tex]\sqrt{125}[/tex]

     = [tex]5\sqrt{5}[/tex]

Therefore, both the diagonals are congruent.

Hence, given quadrilateral ABCD is a rectangle.

ABDE is a rectangle ED is 8cm BDC is a right-angled triangle bc is 4.5cm ABC is a straight line the area of the rectangle abde is 40cm^2 work out the area of the triangle BDC
also I need working out sooooooo

Answers

Answer:

11.25cm^2

Step-by-step explanation:

given the area of the rectangle as 40cm^2, we can get the width of the rectangle.

Area =Length x width

40cm^2 = 8cm x width

we can divide both sides 8 to be left with the width

40/8 = 5cm

so the width is 5cm which is equal to the height of the triangle.

Area of BDC = 1/2 x base x height

BDC = 1/2 x 4.5 x 5

=11.25cm^2

please help
it would mean the
absolute world:/ giving away lots of points:/

Answers

Answer:

:)

Step-by-step explanation:

[tex]M = 3x^2y^3-4xy +x^3y\\\\2M = 2 \times (3x^2y^3-4xy +x^3y) \\\\[/tex]

      [tex]= 6x^2y^3 - 8xy + 2x^3y[/tex]

[tex]N = -2x^3y + 6x^2y^3 -8xy -8[/tex]

   [tex]= 6x^2y^3 -8xy -2x^3y -8[/tex]                 [tex][ re-arranging \ the \ terms][/tex]

a)

[tex]2 M - N = ( 6x^2y^3 -8xy +2x^3y) - (6x^2y^3-8xy -2x^3y - 8)[/tex]

            [tex]= 6x^2y^3 - 8xy +2x^3y -6x^2y^3 +8xy +2x^3y + 8\\\\= 4x^3y +8[/tex]

b)

[tex]2M - N \ for \ x = -1 \ and \ y = 2: (4(-1)^3\times (2)) + 8 = -8 + 8 = 0[/tex]

         

What is the following sum?

Answers

Answer:

i think its c

Step-by-step explanation:

Increase 25cm in the ratio 6:5​

Answers

Answer:

Step-by-step explanation:

25 x 6/5 = 30

What equation would represent a line with a slope of 1/3 and a y-intercept of -1?

Answers

Answer:

1/3+(-1)

Step-by-step explanation:

can someone help me with this please ?

Answers

Answer:

Step-by-step explanation:

∠EMC  = ∠EMD + ∠DMC

∠EMC = 90

∠EMD + ∠DMC = 90

∠EMD + 20 =90

∠EMD  = 90 - 20

∠EMD  = 70

∠FMD + ∠DMB = 180  {Linear pair}

90 + ∠DMB = 180

        ∠DMB = 180 - 90

       ∠DMB = 90

Ashley has baked 17 cakes for a bake sale. She can bake 2 cakes with each additional stick of butter
she buys. How many additional sticks of butter does she need in order to make 41 cakes?
WRITE THE EQUATION THEN SOLVE PLEASEEEE. THANK YOU SO MUCH

Answers

Answer:

12 additional sticks of butter

Step-by-step explanation:

First, create an equation. Let y represent the number of additional sticks of butter needed, and let x represent the number of cakes made.

y = [tex]\frac{x}{2}[/tex] will be the equation.

Since she has already baked 17 cakes, she will need to bake 24 more cakes to make 41 cakes.

Plug in 24 as x into the equation, and solve for y:

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

y = [tex]\frac{24}{2}[/tex]

y = 12

So, she will need 12 additional sticks of butter

Julie has won 4 prizes after rolling up the rims of 24 coffee cups. How many prizes can
she expect to win if she rolls up the rim of 54 cups?

Answers

Answer: 9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Nice to see someone from Canada asking a question.

Set up a proportion

4/24 = x/54            Cross Multiply

4*54 = 24*x           Combine the left  

216 = 24x               Divide by 24

x = 216/24

x = 9

She should expect 9 prizes

What is the y intercept of the line that has a slope of 4 and goes through the point (-3, 12)?

Answers

Answer:

y = 4 x + 24 i think thats the answer if not im sorry

Step-by-step explanation:

Find the distance between the two points in simplest radical form (-3,1) (-6,-7) plz

Answers

Answer:

√73

Step-by-step explanation:

d = √(x2 - x1)² + (y2 - y1)²

√[-6 - (-3)]² + (-7 - 1)²

√(-3)² + (-8)²

√(9) + (64)

√73

8.5

1.)A loan of 12,000 was borrowed from a bank at 14% per annum. calculate (i) the intrest loan at the end of the first year.
(ii)the total amount owing at the end of the first year​

Answers

Answer:

(i) interest = $1680

(ii) total amount = 13680

Step-by-step explanation:

Interest.

12000 × 14/100

=168000/100

=1680

Total amount.

Interest + Loan

1680 + 12000

=13680

Solve using the quadratic formula and show work: 2x^2+5x+4=0

Answers

Answer:

No solution

Step-by-step explanation:

x = -5 +- √5^2 -4 x 2 x 4/ 2 x 2

x = -5 +- √-7/4

d = -7

The square root can't be a negative number so it is no solution.

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