Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A teacher brings 3 gallons of juice on a field trip. there are 36 students on the trip. A. how many fluid ounces of juice does the teacher bring? show your work. B. does the teacher have enough juice to give each student a 12-fluid ounce glass of juice? explain.

Answer: 785.5

Step-by-step explanation:

Final answer:

To solve 2 divided by 1571, recognize it as a fraction 2/1571, which cannot be simplified. Perform long division, adding zeros as necessary, to find its decimal representation, which will be very small.

Explanation:

To solve 2 divided by 1571 step by step without a calculator, you can follow these steps:

Understand that this division represents a fraction, 2/1571.

Recognize that this fraction cannot be simplified further since 2 and 1571 have no common factors other than 1.

To find the decimal form, you can perform long division. However, since 2 is much smaller than 1571, the decimal will start with 0. As 2 cannot be divided by 1571, in the first step of long division, you would put a 0 to the right of the decimal point in your answer.

Next, you would need to add a 0 to the right of 2 (making it 20), since 1571 still cannot go into 2. Then, determine how many times 1571 can go into 20, which will still result in 0, and so on, adding zeros and comparing until you reach a desired level of precision.

This process will yield a very small decimal, indicating that 2/1571 is a fraction much less than 1.

Answer:

Therefore, the coordinates of the centroid of a triangle is

[tex]G(x,y)=(2,1)[/tex]

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 3, 3)  

point B( x₂ , y₂) ≡ (5 , -1)  

point C( x₃ , y₃) ≡ (-2 , 1)

To Find:

Centroid, G (x,y) = ? (say)

Solution:

Centroid:

Centroid is a point where all the three medians of the triangle intersect.

It is denoted as G and the coordinates are give by

[tex]G(x,y)=(\dfrac{x_{1}+x_{2}+x_{3}}{3},\dfrac{y_{1}+y_{2}+y_{3}}{3})[/tex]

Substituting the values we get

[tex]G(x,y)=(\dfrac{3+5+-2}{3},\dfrac{3+-1+1}{3})[/tex]

[tex]G(x,y)=(\dfrac{6}{3},\dfrac{3}{3})=(2,1)[/tex]

Therefore, the coordinates of the centroid of a triangle is

[tex]G(x,y)=(2,1)[/tex]

Steps to solve:

-3(x + 5) = -9

~Distributive Property

-3x - 15 = -9

~Add 15 to both sides

-3x - 15 + 15 = -9 + 15

~Simplify

-3x = 6

~Divide -3 to both sides

-3x/-3 = 6/-3

~Simplify

x = -2

Best of Luck!

Answer:

x= -2

Step-by-step explanation:

First, distribute the 3 into the parenthesis.

(-3)x+ (-3)5= -9

Then, multiply.

-3x-15= -9            *The negative makes it into becoming subtraction.

Now, add 15 to both sides since that's the opposite of subtraction.

-3x-15= -9

   +15  +15

Then, divide by 3 to both sides to isolate the variable.

-3x= 6

-3   -3

x= -2

Answer:

6.2% of last month's income was spent on office expenses

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Office's income last month = $ 315,600

Expenses last month = $ 19,567.20

2. What percent of last month's income was spent on office expenses?

To calculate this percent, we use this fraction:

Expenses last month/Office's income last month

Replacing with the real values:

19,567.20/315,600 = 6.2%

6.2% of last month's income was spent on office expenses

Final answer:

Tom's real estate office spent 6.2% of its income on office expenses last month. This was calculated by dividing the expenses by the income and then multiplying by 100.

Explanation:

To determine what percent of last month's income was spent on office expenses for Tom's real estate office, you need to use the formula for calculating the percentage of expenses relative to income. The formula is:

Percentage of Expenses = (Expenses ÷ Income) × 100

Now, we were given that the office's income last month was $315,600 and the expenses were $19,567.20. Substituting these numbers into our formula gives us:

Percentage of Expenses = ($19,567.20 ÷ $315,600) × 100

Percentage of Expenses = (0.062 × 100)

Percentage of Expenses = 6.2%

Therefore, 6.2% of last month's income was spent on office expenses.

Answer: 48.07

Step-by-step explanation:

48.073 Rounded to the Nearest Hundredth

To round 48.073 to the nearest hundredth consider the thousandths' value of 48.073, which is 3 and less than 5. Therefore, the hundredths' value of 48.073 remains 7.

Answer:

392b²

Step-by-step explanation:

56b×77b÷11

56b×7b

392b²

Answer:

25

Step-by-step explanation:

13x7=91

268-91=177

177÷7=25

The bakery sells approximately 25 cookies per day.

To find how many cookies are sold per day, we first need to determine the total number of pies sold in 7 days.

Total sales (pies + cookies) for 7 days is given as 268.

Thus, the bakery sells approximately 25 cookies per day.

Answer:

Step-by-step explanation:

[tex]i^{20}+1=i^{2*10}+1\\\\(i^{2})^{10}+1=(-1)^{10}+1\\\\=1+1=2[/tex]

Answer:

[tex]A = w^2 + 7w[/tex]   is the rule for the area of a rectangle.

A = 120 sq ft, when it’s width is 8 ft.

Step-by-step explanation:

Here, let us assume the width of the rectangle =  w

So, the length here = Width +  7 ft = (w +  7) ft

Now, AREA of a RECTANGLE = Length x Width

Substituting here the values of length and width, we get:

A = (w) x (w +  7) [tex]= w^2 + 7 w[/tex]

[tex]\implies A = w^2 + 7w[/tex]

The above function is the rule for the area of a rectangle.

Given: w = 8  ft

To find the area: put w  = 8 in [tex]A = w^2 + 7w[/tex]

We get: A  = 8²  +  7(8)  

                 = 64 +  56  = 120

or, A  = 120 sq ft.

Hence, area = 120 sq ft, when it’s width is 8 ft.

Answer:

1. The answer is B.

2.The answer is A.

Answer:

A

Step-by-step explanation:

Blueberry = 4 1/2 = 9/2

Raspberry = 1 4/6 = 10/6 = 5/3

Strawberry = 3 2/5 = 17/5

Total berries = sum total of all the berries = 9/2 + 5/3 + 17/5

The LCM is 30

Total berrie={9(15) + 5(10) + 17(6)}/30

= (135 + 50 + 102)/30

= 287/30

= 9 17/30

Final answer:

The correct inequality to represent the number of situps Lyle can do, if 57 is more than he can do, is D. x < 57, indicating that Lyle can do fewer than 57 situps.

Explanation:

The inequality that represents the number of situps Lyle can do, given that the number 57 is more than the number of situps Lyle can do, is x < 57. This is because if 57 is more than what Lyle can do, then Lyle can do any number of situps that is less than 57.

To represent this relationship mathematically, we use the inequality sign '<'. Thus, the correct option from the provided choices is D. x < 57. This means Lyle can do 56, 55, 54, etc., situps, but not 57 or any number greater than 57.

Answer:

B.

Step-by-step explanation:

1000 meters in a kilometer and 60 minutes in a hour. 1000/60= 16.6666

(rounds to 20)

Final answer:

Charles' running speed of 12 kilometers per hour is equivalent to 200 meters per minute when converted, which corresponds to option D.

Explanation:

Charles runs at a rate of 12 kilometers per hour, and the question asks us to convert this speed to meters per minute. First, we need to convert kilometers to meters. One kilometer is equivalent to 1,000 meters.

So, Charles' speed in meters per hour is:

12 km/hr × 1,000 m/km = 12,000 m/hr

To convert this speed from meters per hour to meters per minute, we divide by 60 minutes, since there are 60 minutes in one hour:

12,000 m/hr ÷ 60 min/hr = 200 m/min

Therefore, Charles' speed is 200 meters per minute, which corresponds to option D.

Answer:

f^-1 (x)=1/5x-11/5

Step-by-step explanation:

y=5x+11

x=5y+11

5y=x-11

y=1/5x-11/5

Answer:

4x+9=3q

Step-by-step explanation:

-3(2x-3)+10x=3q

-6x+9+10x=3q

4x+9=3q

Answer:

q = 4/3x + 3

Step-by-step explanation:

-3(2x-3)+10x=3q

Multiply the -3 at the beginning by (2x - 3), the parenthesis

-6x + 9 + 10x = 3q

Now combine the like terms (add x's and variables separately)

(-6x + 10x) + 9 = 3q

4x + 9 = 3q

Divide both sides of the equation by 3

(4x + 9) ÷ 3 = q

4x/3 + 9/3 = q

Simplify

q = 4/3x + 3

Hope this helps :)

Answer:

Simple Interest =$5600 (Principal and Interest)

Compound Interest = $5624.32 (Principal and Interest)

Step-by-step explanation:

Using Simple interest, use the formulae, Principal X Rate X Time

= 5000*4%*3

= $600 Interest

Principal plus Interest = $5600

Using compound Interest, use the formulae P(1+r)^n

P means Principal

R means rate

N means number of years

= 500(1+4%)^3

= $5624.32 (Principal with Interest)

Answer:

[tex]\large\boxed{4\sqrt3}[/tex]

Step-by-step explanation:

[tex]\text{A geometric mean of}\ a\ \text{and}\ b:\\\\\sqrt{ab}\\\\\text{We have}\ a=4,\ b=12.\\\\\text{Substitute:}\\\\\sqrt{4\cdot12}=\sqrt{48}=\sqrt{16\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{16}\cdot\sqrt3=4\sqrt3[/tex]

Answer:

3+8g

Step-by-step explanation:

27/9+8g=3+8g

g(x) = x²

g(4) = 4² = 16

g(f(4)) = (f(4))² = (4-7)² = (-3)² = 9

Answer:

Domain: (-oo, oo)

Range: (-4,oo)

Horizontal asymptote: y=-4

Answer:

The domain is all Real numbers.

The range is all real values > -4.

Step-by-step explanation:

The asymptote is y = -4.

The value of b is -12

Solution:

The given equation, b (b + 12) = 0

On distributing the b inside the parentheses we get,

[tex]\Rightarrow\bold{ b\times b+b\times12=0}[/tex]

[tex]\bold{\Rightarrow b^{2}+12b=0}[/tex]

[tex]\bold{\Rightarrow b^{2}=-12b}[/tex]

[tex]\bold{\Rightarrow 1=\frac{-12b}{b^2}}[/tex]

[tex]\bold{\Rightarrow 1=\frac{-12}{b}}[/tex]

[tex]\bold{\Rightarrow b=-12}[/tex]

Steps to use distributive property to solve an equation:

For fractions:

Answer: a= -4

Step-by-step explanation:

Final answer:

To solve the equation 4a+5=2+3.25a, isolate the variable 'a' on one side of the equation. The solution is a = -4.

Explanation:

To solve the equation 4a+5=2+3.25a, we need to isolate the variable 'a' on one side of the equation.

Step 1: Subtract 3.25a from both sides of the equation:

4a - 3.25a + 5 = 2

0.75a + 5 = 2

Step 2: Subtract 5 from both sides of the equation:

0.75a = 2 - 5

0.75a = -3

Step 3: Divide both sides by 0.75 to solve for 'a':

a = -3/0.75

a = -4

Therefore, the solution for the equation 4a+5=2+3.25a is a = -4.

Answer:

$31.20

Step-by-step explanation:

Angela will get an amount of $31.2 as the interest at the end of 1 year.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that Angela puts $520 in an account that earns 6% per year.

Principal or initial amount = $520

Rate of interest = 6% = 6 / 100 = 0.06

We have to calculate the amount of interest.

Interest amount = $520 × 0.06

                           = $31.2

Hence the amount of interest that Angela get at the end of the year is $31.2.

To learn more about Simple Interest, click on the link given below :

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Answer:

In Grade 8, 17% of students liked running

Step-by-step explanation:

Although this table is incomplete, there are still enough information to answer.

First, we need to be aware that the data here is written in decimal numbers, which is another way to write percentages.

In other words, 100% equals to 1, which is to say that if we multiply decimal number with 100 we'll get the percentage:

0.39 = 39%

0.04 = 4%

Another important thing to establish is that the value of decimal number DOES NOT mean the number of people, it only suggests the ratio:

0.26 does not mean 26 people etc.

Knowing this, from this incomplete table, we see that 0.17 students from grade 8 liked running. And now we know that 0.17 equals to 17%, which makes B the correct answer.

Answer:

B. In Grade 8, 17% of students liked running

Step-by-step explanation:

Answer:

2400m³

Step-by-step explanation:

50 * 30 * 1.6 =

1500 * 1.6 = 2400m³

Answer:

11/4

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

x + 6 = ?

[Replace x with 7]

7 + 6 = 13

The number of bacteria in the colony after n hours is 2,500 × (1 + 0.11)ⁿ.

Exponential growth N = N0 × (1 + r)ᵃ

Where N = final population size

N0 = initial population size

r = growth rate

a = time in hours

After n hours the colony's size = 2,500 × (1 + 0.11)ⁿ.

Answer:

Option D: The area will be multiplied by 16.

Step-by-step explanation:

Given that the area of the figure is 13 sq. in.

Let is say the figure is of dimensions: a & b.

Therefore, a.b = 13 sq. in

When each of the dimension is multiplied by 4, the dimensions would become 4a and 4b.

Therefore, the area would be: 4a . 4b = 16 a . b = 16(13) sq. in.

Hence, the area is multiplied by 16.

Answer:

y= -1 , -3 , -5

Step-by-step explanation:

2x-3y=9

2x-9=3y

2x-9/3=y

when x=0

y= -9/3

y= -3

when x= 3

y = 2(3)-9/3

  = 6-9/3

  = -3/3

y = -1

when x= -3

y = 2(-3)-9/3

y= -6-9/3

y= -15/3

y= -5

To solve the equation 2x-3y=9 for y in terms of x, firstly move the '2x' on right side of the equation to get -3y = -2x + 9. Multiply each term by -1 to get 3y = 2x - 9. And then divide each term by 3 to get y = (2/3)x - 3.

In order to solve the equation 2x-3y=9 for y in terms of x, we first isolate y. The first step would be to move '2x' part to the right side of the equation. It becomes like this: -3y = -2x + 9 or simply, 3y = 2x - 9 where we multiplied every part of the equation by -1. Now, the next step is to get rid of '3' that is multiplying 'y'. For this, you divide entire equation by '3'. Hence, y = (2/3)x - 3. So, the equation for y in terms of x is y = (2/3)x - 3.

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Answer:

2) -1

Step-by-step explanation:

it is easy

 we have to first open the brackets, as it is ' - '  we have to change the sign to opposite of that of the number in the bracket and then solve it.

so the number 2 is having negative sign, we make it positive. this rule is applied only when there is a negative sign and a bracket is there.

-3-(-2)

-3+2

=-1