Buddy and Michael get into a
snow fight with some boys on the
way home from school. It seems
as though Buddy can throw 4
times as many snowballs as the
boys can. If Buddy throws 1200
snowballs, how many did the boys
throw? Write an equation and
solve.

Answer:

The values of x and y that will minimize the cost is 15 ft and 5 ft respectively and the minimum cost will 3,375

Step-by-step explanation:

With a 1125 ft^3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be built with its top lush with the ground to catch runoff water, x is the length, y is the height;

x^2*y = 1125

y = 1125/x^2 ----(1)

The total cost of c = 5(x^2 + 4xy) + 10xy

Then,

c = 5(x^2 + 4x*(1125/x^2)} + 10x*(1125/x^2)

c = 5x^2 + 22,500/x + 11,250/x

c = 5x^2 + 33,750/x

To minimize the cost of c, find the derivatives of c; c'

c' = 10x - 33,750/x^2

c' = (10x^3 - 33,750)/x^2

c'(x) = 0; 10x^3 = 33,750

x = ³√33,750 = 15

x = 15; y = 1125/x^2

y = 1125/15^2 = 5

(x,y) = (15,5)

c = 5x^2 + 33,750/x

c = 5*15^2 + 33,750/15 = 3,375

The values of x and y that will minimize it is 15 ft and 5 ft respectively and the minimum cost will 3,375

The values of x and y that will minimize the cost is 15ft and 5ft. The minimum cost is 3,375

We have volume of a rectangular tank = 1125 ft^3

Side of a rectangular tank = x ft and

Length of a rectangular tank =y ft  

So, [tex]x^2y = 1125[/tex]

[tex]y = \frac{1125}{x^2} ...(1)[/tex]

The total cost of rectangular tank (c) = [tex]5(x^2 + 4xy) + 10xy[/tex]

 [tex]c = 5(x^2 + 4x(\frac{1125}{x^2} ) )+ 10x(\frac{1125}{x^2} )\\c = 5x^2 +\frac{22,500}{x} + \frac{11250}{x} \\c = 5x^2 + \frac{33750}{x}[/tex]

Differentiating it w.r.t x, we get

[tex]c' = 10x - 33,750/x^2\\c' =\frac{10x^{3}-33750 }{x^{2} } \\c'(x) = 0\\10x^3 = 33,750\\x = \sqrt[3]{33,750} \\ = 15\\x = 15; y = \frac{1125}{x^2} \\y = \frac{1125}{15^{2} } \\= 5\\(x,y) = (15,5)\\c = 5x^2 + \frac{33750}{x} \\c = 5(15)^2 + 33,750/15 \\= 3,375[/tex]

The values of x and y that will minimize the cost is 15 ft and 5 ft and the the minimum cost is 3,375.

Learn more:https://brainly.com/question/6995312

Answer:

I think its 502.65 km 2

Step-by-step explanation:

(This is what I think, I might be wrong)

Answer:

502.655km

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$1.60

$2.88

Step-by-step explanation:

To find the selling price of the distributor and the retailer, we first need to find how much the distributor sells each pack of cards.

To find the selling price we use the formula.

Selling Price = Cost + Markup

Cost = $0.80

Markup rate = 100% or 1

Selling Price = 0.80 + (0.80*1)

Selling Price = $1.60

So the distributor sells each pack of cards at $1.60 to the retailer.

Now to find the selling of the retailer, we need to use the selling price of the distributor.

Cost = $1.60

Markup rate = 80% or 0.80

Selling price =  1.60 + (1.60 * 0.80)

Selling price = $2.88

So the retailer sells each pack of cards at $2.88 to the customers.

Answer:

A = $1.60

B = $2.88

Step-by-step explanation:

I did the work on brainly and got it right

Hope this helps :D

Answer:

450

Step-by-step explanation:

The total number of possible working groups of 4 workers selecting from 12 workers is the number of ways of selecting 4 persons from 12 persons

[tex]=\binom{12}{4}=\frac{12\times 11 \times 10 \times 9}{1\times 2 \times 3\times 4}=495[/tex]

The total number of possible groups of 4 workers in which 2 persons (Hugo and Viviana) always come together

[tex]= \binom {12-2}{4-2}=\binom {10}{2}=\frac{10\times9}{1\times2}=45[/tex]

So, the total number of possible working groups in which Hugo and Viviana are not working together in any of the groups [tex]= 495-45=450[/tex].

Answer:

c

Step-by-step explanation:

because the question already told that a table has four chairs. So, we need the number of tables in the cafe to calculate number of chairs

Step-by-step explanation:

If F(x) = 2x+6, g(x) = 3² findf(g (-3))

Solution

f(g (-3)) = 2x+6(3²(-3)) = 2x+6(3×3(-3))

= 2x+6(-27) = 54x-162 = 54x = 162

54/54x = 162/54

x = 3

Answer:

➩ [tex]f(g(-3)) = 24[/tex]

Step-by-step explanation:

➨ Rearrange/Simplify the equations

[tex]F(x)=2x+6\\g(x)=9[/tex]

➨ Find [tex]f(g(-3))[/tex]

[tex]g(-3)=9[/tex] ➩ All x-values have same y-values ➩ Constant Function

Substitute [tex]g(-3) = 9[/tex] in the f(x)

[tex]f(g(-3)) = f(9)\\f(9)=2(9)+6\\f(9)=18+6\\f(9)=24\\f(g(-3)) = 24[/tex]

Thus, the answer ➩ [tex]f(g(-3)) = 24[/tex]

Answer:

1,4

Step-by-step explanation:

0,4 1,3 has to be farther

Answer:

(4,0)

Step-by-step explanation:

Answer:

13- 25 fish

14- 9 miles

15- 7.825 ft3

16- 11.3 feet

Step-by-step explanation:

13-

        14 x 2 = 28 fish

        He dropped three things so:

        28 - 3 = 25 fish

14-

         7 days x 3weeks = 21 days

         3laps x 21 days = 63 laps

         63 laps x 1/7 mile = 9 miles

15-

         all his savings: 2.6 + 7.34 + 5.71 = 15,65 ft3    

         melted snow = 15.65 / 2 = 7.825 ft3

16-

         3.5 - 1.8 = 1.7 feet

         1.7 + 9.6 = 11.3 feet

Answer:

Step-by-step explanation:

# 13.

I assume there will be no bonus, because penguin dropped some things.

14 × 2 - 3 × 1 = 25 fish

# 14.

3 laps, [tex]\frac{1}{7}[/tex] mile, 7 days, 3 weeks

3 × [tex]\frac{1}{7}[/tex] × 7 × 3 = 9 miles

# 15.

[tex]\frac{2.6+7.34+5.71}{2}[/tex] = 7.825 ft³

# 16.

[tex]3\frac{1}{2}[/tex] = 3.5

+ 3.5 - 1.8 + 9.6 = (3.5 + 9.6) - 1.8 = 11.3 ft.

Answer:

6758

Step-by-step explanation:

Given the data:

Monday _______ 8565 steps

Tuesday ______ 14707 steps

Wednesday ____ 15323 steps

Thursday ______ 9788 steps

Friday _________12482 steps

The range from the data is :

(Highest value - lowest value)

(15323 - 8565)

Answer: A would be the answer hope this helps

Answer:

In the explanation

Step-by-step explanation:

a) Multiply the second equation by 2, subtract both lines. You get x = -3. Plug this in to get y, y = -2

b) Multiply the first equation by 2, add both lines. You get x = 8. Plug this in to get y, y = -3

c) Multiply the first equation by 5, subtract both lines. You get y = 1. Plug this in to get x, x = -3

d) Multiply the first equation by 2 and the second one by 3, add both lines. You get x = 1. Plug this in to get y, y = 4

Hope this helps!

Answer:

I would go with c

Step-by-step explanation:

if it is incorrect sorry

Answer:

More than 6.21 times

Step-by-step explanation:

The common ratio [tex]r=\dfrac{4}{5}[/tex]

Distance of first bounce

[tex]a_1=4\times \dfrac{4}{5}=\dfrac{16}{5}[/tex]

Second bounce

[tex]a_2=ar^{n-1}=\dfrac{16}{5}(\dfrac{4}{5})^{2-1}\\\Rightarrow a_2=\dfrac{16}{5}(\dfrac{4}{5})[/tex]

n bounce

[tex]a_n=ar^{n-1}\\\Rightarrow a_n=\dfrac{16}{5}(\dfrac{4}{5})^{n-1}[/tex]

Now the nth bounce will be less than 1 feet

[tex]\dfrac{16}{5}(\dfrac{4}{5})^{n-1}<1\\\Rightarrow (\dfrac{4}{5})^{n-1}<\dfrac{5}{16}[/tex]

Applying logarithms on both sides we get

[tex](n-1)\ln \dfrac{4}{5}<\ln\dfrac{5}{16}\\\Rightarrow n>\dfrac{\ln\dfrac{5}{16}}{\ln \dfrac{4}{5}}+1[/tex]

The inequality changes as both [tex]\ln\dfrac{5}{16}[/tex] and [tex]\ln \dfrac{4}{5}[/tex] are negative numbers.

So,

[tex]n>6.21[/tex]

Hence, the number of bounces is more than 6.21 times.

Answer:

4/12

Step-by-step explanation:

Answer: B or -I/2

Step-by-step explanation: I did this question

Answer:

7/40

Step-by-step explanation:

7 balls are green-->numerator

7 balls out of 40( in total) are green.

7/40

This means that out of every 40 balls picked, 7 of them should be green.

Answer:

I my knowledge

option D y=6x

Step-by-step explanation:

and I am 100% sure you

Answer:

y=6x

Step-by-step explanation:

Answer:

[tex]y +2 =-6(x - 1)[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (1,-2)[/tex]

[tex]m=-6[/tex]

Required

Determine the point slope equation

This can be determined using the following formula:

[tex]y - y_1 =m(x - x_1)[/tex]

Where:

[tex](x_1,y_1) = (1,-2)[/tex]

[tex]m=-6[/tex]

So, we have:

[tex]y - (-2) =-6(x - 1)[/tex]

This gives:

[tex]y +2 =-6(x - 1)[/tex]

Hence, the point slope form is [tex]y +2 =-6(x - 1)[/tex]

Answer: I think 53.1

Step-by-step explanation:

The object's temperature after 18.0 minutes is 425.83.

Given that,

An object's temperature cools exponentially after it is removed from a furnace (hot oven).

If its initial temperature is 730°C and it cools at a rate of 2.95% per minute.

We have to determine,

The object's temperature after 18.0 minutes.

According to the question,

The initial temperature is 730°C and it cools at a rate of 2.95% per minute,

The temperature after t minutes is modeled by an exponential function, which has the following format is,

[tex]T(t) = T(0) . (1-r)^t[/tex]

Where T(0) is the initial temperature, and r is the cooling rate, as a decimal.

Then,

T(0) = 730°c and r = 2.95% = 0.0295

Substitute all the values in the equation,

[tex]T(t) = T(0) . (1-r)^t\\\\T(18) = 730 \times (1-0.0295)^{18}[/tex]

Therefore,

The object's temperature after 18.0 minutes is,

[tex]T(t) = T(0) . (1-r)^t\\\\T(18) = 730 \times (1-0.0295)^{18}\\\\ T(18) = 730 \times 0.5833\\\\T (18) = 425.83[/tex]

Hence, The required value of the object's temperature after 18.0 minutes is 425.83.

To know more about the Exponential function click the link given below.

https://brainly.com/question/16902197

Answer:

x=6241

Step-by-step explanation:

^2 on both sides.

x=79^2.

x=6241.

Hope this helps plz hit the crown :D

Answer:

6241

Step-by-step explanation:

hope this is correct

Answer:

top left: 1/3

top right: 16

bottom left: 1/3

bottom right: 15

Step-by-step explanation:

Answer:

Fraction- 33/4

Decimal- 8.25000

Step-by-step explanation:

Hope this helps!

Brain-List?

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

since everything is doubled

we just do 5 multiplyed by 2

9514 1404 393

Answer:

  x = 8

Step-by-step explanation:

Corresponding segments are proportional.

  2x/12 = (x+4)/9

  18x = 12(x +4) . . . . . multiply by 9·12

  6x = 48 . . . . . . . . . . subtract 12x

  x = 8  . . . . . . . . . . . . divide by 6