Corina is making punch for a family reunion. Her recipe calls for 2 and 1⁄2 cups of lemonade per batch. She plans to make 20 batches or punch for the reunion. ​How many gallons of lemonade does she need?

PLEASE NEED STEPS

Answer:

By the end of the first year Dara will have $903.125 in his account.

Step-by-step explanation:

Since this a compounded interest formula, it means that the amount invested grows exponentially overtime. In order to calculate the total of money over a period of time we must use the following formula:

M(t) = M(0)*(1 + r/n)^(n*t)

Where M(t) is the amount of money in "t" years, M(0) is the amount invested, r is the anual interest rate, n is the compound period over a year and t is the time elapsed in years.

In this problem the amount is compounded half-yearly, this means that for every year that passes the money is compounded twice, therefore n is equal to 2. Applying the data from the problem to the formula, we have:

M(1) = 800*(1 + 0.125/2)^(2*1)

M(1) = 800*(1.0625)^(2)

M(1) = 800*(1.0625)^(2) =903.125

By the end of the first year Dara will have $903.125 in his account.

Answer:

A. 25%

Step-by-step explanation:

If you multiply something by 0.75, you're multiplying it by 75%, and that means you're losing 25% each time, so the rate of decay is 25%

Answer:

A 25%

Step-by-step explanation

the first thing we want to do for this problem is look at the exponential decay formula. its y=a(1-b)^x. "y" represents the final amount, "a" represents the original amount, and "b" represents the decay factor.

in this situation, .75 is the decay factor and our original amount is 1000. so to find out the decay factor, we need to subtract .75 from 1. you would get .25. .25 in percentage form is 25%.

we can double check by putting .25 in the orginal exponential decay formula. y=1000(1-.25)^x. 1-.25 equals .75, so now the equation is the same as our original equation, y=1000(0.75)^x

Answer:

Read below.

Step-by-step explanation:

a. reflection over the x-axis, translate 2 units up

b. rotate 90° counterclockwise or 270° clockwise

c. use a scale factor of 2 and translate 3 units down, 3 units left

d. translate 8 units right, 7 units up

I'm not so sure about c since I do not like scale factors.

Hey there! I'm happy to help!

To find the volume of a cone, you multiply the base by the height and then divide by three.

First, we need to find the base. A cone has a circle for the base. To find the area of a circle, we square the radius and multiply it by pi (we will use 3.14).

4²=16

16×3.14= 50.24

Now, we multiply our base by the height.

50.24×8=401.92

Finally, we divide by three.

401.92÷3≈133.973 (to nearest thousandth)

Therefore, the volume of the cone is about 133.973 units cubed. If you were to use exact pi, it would be more like 134 because of all those decimals after pi!

Now you can find the volume of cones!

I hope that this helps! Have a wonderful day!

Formula for the perimeter of a quarter circle: C = ((pi x 2 x r) / 4) + r + r

32.13 = (6.28r / 4) + 2r

32.13 = 1.57r + 2r

32.13 = 3.57r

r = 9 yards

Hope this helps! :)

Answer: 113.1

2 π r

2 π 18

113.1 answer not sure if it is right

Step-by-step explanation:

Answer:

Volume of cone = 314 in³

Step-by-step explanation:

Radius of the cone (r) = 5 in

Height of the cone (h) = 12 in

[tex]Voume \: of \: the \: cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times {(5)}^{2} \times 12\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times 25 \times 12\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times 300 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times 100\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 314 \: {in}^{3} [/tex]

Answer:

Yes

Step-by-step explanation:

[tex]6^{2}[/tex] + [tex]8^{2}[/tex] = [tex]10^{2}[/tex]

36 + 64 = 100

The Pythagorean theorem is true.

Answer:

He has 19 quarters.

Step-by-step explanation:

To solve this, we can set up a system of equations.

Let's first name our variables.

x: number of quarters

y: number of dimes

Using this, we can write the following equations.

Number of coins: x+y=27

Total Value: 0.25x+0.1y=5.55

We can rewrite the first equation to x=27-y by subtracting y from btoh sides. This way, we can substitute 27-y in for x.

0.25(27-y)+0.1y=5.55

Distribute.

6.75-0.25y+0.1y=5.55

Combine like terms.

6.75-0.15y=5.55

Subtract 6.75 from both sides.

-0.15y=-1.2

Divide both sides by -0.15

y=8

There are 8 dimes.

We can use that to find the number of quarters by plugging it in to one of the equations.

x+y=27

x+8=27

Subtract 8 from both sides.

x=19

He has 19 quarters.

Answer:

10 donuts and 10 brownies

Step-by-step explanation:

In this case we must solve the system of equations that do not say in the statement:

at least 20 must be, therefore:

x + y = 20 => x = 20 - y

1.5 * x + 2.5 * y = 40

replacing:

1.5 * (20 - y) + 2.5 * y = 40

30 - 1.5 * y + 2.5 * y = 40

y = 40 - 30

y = 10

now for x:

x = 20 - 10

x = 10

therefore, to be a minimum of 20, they must be 10 donuts and 10 brownies

Answer:

x = 52

Step-by-step explanation:

the right angle means 90 degrees so add 90 and 34 to get 124 then when u subtract from 180 degree (the degrees of a triangle) you get 54 degrees. that means that p has to be 124 degrees. 124 subtracted by 72 is 52. Therefore x is 52.

Answer:

x ≈ 2.65(nearest hundredth)

Step-by-step explanation:

Base on your question the triangle is a right angle triangle. This means the triangle should obey the Pythagoras theorem.

Pythagoras theorem says

c² = a² + b²

where

c = hypotenuse of the triangle

a and b are called the legs of the triangle.

The hypotenuse is the longest side of the triangle.

Recall your question says the unknown side x is one of the legs of the triangle. That means the other legs will definitely be 3 since the hypotenuse should be the longest side of the triangle which is 4.

Using Pythagoras theorem

4² = 3² + x²

16 - 9 = x²

7 = x²

square root both sides

x = √7

x = 2.64575131106

x ≈ 2.65(nearest hundredth)

Answer:

m (slope)=1

Step-by-step explanation:

y=x+6(m is always found in front of X so m=1)

Answer: 1

Step-by-step explanation: This equation is written in y = mx + b form.

The slope of the line will be the coefficient of the x-term.

Remember, the coefficient is the number in front of the variable.

Notice that the x does not have a coefficient.

When that happens, when there is no number in front

of your variable, you can put a 1 there to fill that position.

So the slope of the line will is 1.

Answer:

60

Step-by-step explanation:

Looking at case 1.

a * 10^5 + 2a * 10 ^4= 7200000

a * 10 * 10^4 + 2a *10 ^4 =7200000

[10a + 2a] * 10^4= 7200000

12a= 7200000/ 10000

12a= 720

a= 720/12 = 60

Looking at case 2,

a * 10^5 - a * 10^4 = 5400000

a * 10 * 10^4 - a *10^4 = 5400000

10a* 10^ 4 - a * 10^ 4 = 5400000

[10a- a] *10^4 = 5400000

9a = 5400000/10000

9a= 540

a =540/9

a= 60

Answer:

(0.5,0) , (-3,0) ,and (0,-1.5)

Step-by-step explanation:

Just look where the points touch the x- and y-axis.

It touches twice on the x- and once on the y-axis.

Hope that helps!

Answer:

m = 5

b = -6

Step-by-step explanation:

y = mx + b

Answer:

m = 5 and b = -6

Step-by-step explanation:

y = mx + b

y = 5x + (-6)

Answer:

1.3 x 1020

Step-by-step explanation:

4.8 x 10-6 = 42

1.3 x 1020 = 1326

3.1 x 10-4 = 27

9.2 x 10-5 = 87

Answer:

13 packages

Step-by-step explanation:

We need to first find the area of the composite figure. We can draw a horizontal line through the figure so that it is broken up into two rectangles.

The top rectangle has dimensions of 9 ft by 2 ft, while the bottom rectangle has dimensions of 3 ft by 7 ft. The area of a rectangle is denoted by: A = lw, where l is the length and w is the width.

Here, the top rectangle has width 9 and length 2, so the area is A = 9 * 2 = 18 square feet. The bottom rectangle has width 7 and length 3, so the area is A = 7 * 3 = 21 square feet. Add these up:

18 + 21 = 39 square feet

We know that each package of tile will cover 3 square feet, so divide 39 by 3 to get the number of packages needed:

39 / 3 = 13

The answer is 13 packages.

Answer:

13

Step-by-step explanation:

Larger rectangle - smaller rectangle

(9×5) - [(5-2)×(9-7)]

45 - (3×2)

45 - 6

39 ft²

1 package : 3 ft²

X packages : 39 ft²

X/1 = 39/3

X = 13 packages

m<FJI=90°, so

[tex]x + x + 4 + 3x - 9 = 90 \\ 5x = 95 \\ x = 19[/tex]

Answer: x=19

Answer:

x=73

Step-by-step explanation:

     3x-9+x+4+x=360

     5x-5=360

      5x=360+5

     5x=365

       x=365÷5

     x=73

Answer:

1 in 5

Step-by-step explanation:

Answer:

[tex] \cos \bigg( \frac{7\pi}{12} \bigg)= \frac{1 - \sqrt{3} }{2 \sqrt{2} } [/tex]

Step-by-step explanation:

[tex] \cos \bigg( \frac{7\pi}{12} \bigg) \\ \\ = \cos \bigg( \frac{7 \times 180 \degree}{12} \bigg)\\ \\ = \cos \bigg( {7 \times 15 \degree} \bigg)\\ \\ = \cos \bigg( {105 \degree} \bigg)\\ \\ = \cos \bigg( {60\degree + 45 \degree} \bigg) \\ \\ = \cos {60\degree .\cos 45 \degree} - \sin {60\degree .\sin 45 \degree} \\ \\ = \frac{1}{2} . \frac{1}{ \sqrt{2} } - \frac{ \sqrt{3} }{2} .\frac{1}{ \sqrt{2} } \\ \\ = \frac{1}{2 \sqrt{2} } - \frac{ \sqrt{3} }{2 \sqrt{2} } \\ \\ \huge \purple{ \boxed{ \cos \Bigg( \frac{7\pi}{12} \Bigg)= \frac{1 - \sqrt{3} }{2 \sqrt{2} } }}[/tex]

The exact value of cos (7 pi/12) would be,

⇒ cos (7 pi/12) = - 0.2588

We have to given that,

An equation is,

⇒ cos (7 pi/12)

Now, WE can change it into degree as,

⇒ cos (7 pi/12)

⇒ cos (7 × 180 / 12)

⇒ cos (7 × 15)

⇒ cos 105°

⇒ cos (90 + 15)°

⇒ - sin 15°

⇒ - (√3 - 1) / 2√2

⇒ - 0.2588

Thus, The exact value of cos (7 pi/12) would be,

⇒ cos (7 pi/12) = - 0.2588

Learn more about trigonometric ratios at:

brainly.com/question/1836193

#SPJ2

Answer:

It will take him 8 months.

Step-by-step explanation:

If you divide 280 and 35 you get 8, which is the amount of months it takes.

Answer:

M x M / x + y =4​

Step-by-step explanation:

Note that this is still a rectangle, and the length of the fencing is still 600 ft.

So the sum of the sides NOT along the river x + x + y = 600, and the area equals xy.

This makes the two equations: 2x + y = 600, and A = xy.

To find the largest area, we need to find A as a function of x or y. I suggest solving the first equation for y and replacing that in the second equation.

y = 600 - 2x. and A(x) = x(600-2x)

We now need to maximize A(x) = 600x - 2x2.

Remember, if x = -b/(2a), we find the x value of the vertex, the y value can be found by substitution.

So, since a = -2, and b = 600, x = -600/(-4) = 150 ft. If x = 150, y = 600 - 2(150) = 300.

So, the dimensions are 150 x 300 and the maximum area = 300(150) = 45,000 ft2

I hope this helps. By the way, there are many variations of this, and they are all similar. For example, you might want to make several pens with two lengths parallel and have three parallel withs inside.

Answer:

The answer is -3.1, or 3 1/10.Since diving a negative and a positive equals a negative, your quotient will be negative. You can start by removing the 0.5, and divide 15 by 5 which is 3. Then with the 0.5 from -15.5, divide it by 5 and you get 0.1. 3 plus 0.1 is 3.1, and since it has to be negative, it's -3.1.

Step-by-step explanation:

i tried, have a nice day (:

Answer:

(2x-4)(x-4)=24*10

Step-by-step explanation:

Last equation from Equation bank

Answer:

y=0

Step-by-step explanation:

8^3 8^-5 8^y= 8^-2

We know that a^b * a^c = a^(b+c)

8^(3-5+y) = 8^-2

The bases are the same so the exponents must be the same

-2+y = -2

y = 0

Answer:

0

Step-by-step explanation:

Answer:

x = amount of money he spends on peppers

0<x<8

if it's 12 or more dollars than 20-12=8 which can be your greatest number and 0 being the lowest range based on the actual amount spent on onions. make sure to put a line under the inequality signs to show that it can also be equal to the number.