1) The fish population in a pond is increasing
at a rate of 5% per year. The starting
number of fish in the pond was 32 fish.
How many fish will be in the pond after 4
years.

Answer:

a) 2 new printers

b) 11 min

Step-by-step explanation:

Given:

5 old printers take 30 min to produce a batch of comic books

4 new printers take 18 min to produce a batch of comic books

.

a) First, we need to find how long does one old and new printer take to produce a batch of comic books:

.

Since 5 old printers take 30 min to do the job, one printer would take 5 times more than this (5 printers work together and they do the job faster than one, that's why we have to multiply):

.

1 old printer does the job in:

5 × 30 = 150 min

1 new printer does the job in:

4 × 18 = 72 min

.

Since one old printer does the job in 150 min, 6 old printers would do this job 6 times faster (that's why we divide):

6 old printers would take:

150 / 6 = 25 min

2 new printers would take:

72 / 2 = 36 min

.

25 < 36

That means, 2 new printers would do this job faster

.

b) In order to find how much less time would this take, we have to subtract:

.

36 - 25 = 11 min

The surface area of the rectangular prism is 348 square meters.

Hello! I'd be happy to help you find the surface area of a rectangular prism with dimensions 6 m by 4 m by 15 m. The surface area can be calculated using the formula:

Surface Area = 2lw + 2lh + 2wh

where l = length, w = width, and h = height.

Given the dimensions 6 m (length), 4 m (width), and 15 m (height), we can plug in the values

The surface area can be calculated using the formula:

Surface Area = 2(6)(4) + 2(6)(15) + 2(4)(15)
Surface Area = 48 + 180 + 120
Surface Area = 348 m²

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Answer:

x+48=180-2x (straight lines sum is 180 and corresponding angles)

x+2x=180-48

3x=132

x=44°

the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.

To find the probability of drawing three green marbles from the bag, we need to use the formula for calculating the probability of multiple independent events. The probability of multiple independent events occurring together is the product of the individual probabilities of each event.

Let's first calculate the probability of drawing a green marble on the first draw. We have a total of 6 + 4 + 7 = 17 marbles in the bag, and 7 of them are green. So the probability of drawing a green marble on the first draw is:

P(green on first draw) = 7/17

After we draw a green marble on the first draw, we have 16 marbles left in the bag, including 6 red marbles and 4 blue marbles. Since we don't replace the marble after we draw it, the probability of drawing a green marble on the second draw is:

P(green on second draw) = 6/16

Finally, after we draw a green marble on the second draw, we have 15 marbles left in the bag, including 5 green marbles. So the probability of drawing a green marble on the third draw is:

P(green on third draw) = 5/15

To find the probability of drawing three green marbles in a row, we need to multiply these probabilities:

P(three green marbles) = P(green on first draw) x P(green on second draw) x P(green on third draw)

P(three green marbles) = (7/17) x (6/16) x (5/15)

Simplifying this expression, we get:  

P(three green marbles) = (7 x 6 x 5) / (17 x 16 x 15)

P(three green marbles) = 0.0735

Therefore, the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.

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Answer:

Step-by-step explanation:

The missing property is the distributive property of multiplication.

The distributive property of multiplication is a mathematical property that allows you to simplify expressions that involve multiplying a number or variable by a sum or difference of other numbers or variables.

For the addition of 5 terms with 1z, we have that the term 1 is common to all the factors in the expression, hence the expression can be written as follows:

1z + 1z + 1z + 1z + 1z = 1(z + z + z + z + z) = 5z.

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Answer:

Step-by-step explanation:

If glass is $0.06 per square inch, the new glass top will cost $80.64.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and express relationships between variables. It involves the use of letters and symbols to represent numbers and quantities, and the use of equations and inequalities to solve for unknown values.

Algebra is used to solve a wide range of mathematical problems, including linear equations, quadratic equations, polynomial equations, and systems of equations. It is also used to study functions, which are mathematical relationships between variables that can be represented by graphs or equations.

Algebraic concepts and techniques are used in many fields, including engineering, physics, finance, and computer science. For example, in engineering, algebra is used to model physical systems and to analyze their behavior, while in finance, algebra is used to calculate interest rates, loan payments, and other financial transactions. In computer science, algebra is used to design and analyze algorithms and data structures.

The area of the glass top required for the desk can be found by multiplying the length and width of the desk:

Area = 48 in x 28 in = 1344 square inches

The cost of the glass top can be found by multiplying the area by the cost per square inch:

Cost = 1344 sq in x $0.06/sq in = $80.64

Therefore, the new glass top will cost $80.64.

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[tex]\:\: \:\: \:\star[/tex] We are asked to find out the distance between (1,5) and (-6,-2).We know the formula to find the distance between two points is given by -

[tex] \:\: \star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]

As per question, points are -

Now that we are given the points, so we can put them into the formula and solve for distance between them.Which is -

[tex]\:\: \:\: \:\star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]

[tex] \longrightarrow \sf Distance_{(AB)} = \sqrt{ (-2-5)^2 + (-6-1)^2 }\\[/tex]

[tex]\:\:\:\:\:\longrightarrow \sf Distance_{(AB)}= \sqrt{ (-7)^2 + (-7)^2 }\\[/tex]

[tex]\:\:\:\:\longrightarrow \sf Distance_{(AB)} = \sqrt{ 49+49 }\\[/tex]

[tex]\: \:\:\:\: \:\longrightarrow \sf Distance _{(AB)}= \sqrt{ 98}\\[/tex]

[tex]\: \:\:\: \:\longrightarrow \sf Distance_{(AB)} = \sqrt{49 \times 2}\\[/tex]

[tex]\:\: \:\: \:\:\longrightarrow \sf\underline{ Distance_{(AB)} = 7√2}\\[/tex]

[tex]\: \:\:\: \:\:\longrightarrow \sf Distance_{(AB) }= 9.89949......\\[/tex]

[tex]\: \:\:\: \:\:\longrightarrow \sf \underline{Distance_{(AB) }= 9.9\:(Approx)}\\[/tex]

Therefore, the distance between (1,5) and (-6,-2) is 7√2 or, 9.9 ( Approx).

Answer:

approximately 0.0018 feet, or about 0.0216 inches.

Step-by-step explanation:

The volume of the suitcase is:

V_suitcase = height x length x width

V_suitcase = 5 ft x 4 ft x 4 ft

V_suitcase = 80 cubic feet

The volume of each supply is:

V_supply = base area x height

We know that the base area of each supply is 9 square feet. Let's assume that the height of each supply is h.

So, the total volume of all the supplies that can be put in the suitcase is:

V_total_supplies = V_supply x number of supplies

V_total_supplies = (9 ft^2 x h) x 5120

We want to find the height of each supply, so we can rearrange the equation above to solve for h:

h = V_total_supplies / (9 ft^2 x 5120)

Substituting the values we know:

h = (80 ft^3) / (9 ft^2 x 5120)

Simplifying, we get:

h = 0.0018 ft

So the height of each supply is approximately 0.0018 feet, or about 0.0216 inches.

The van would have traveled approximately 8 miles of distance after 12 minutes.

To calculate the distance traveled by the van after 12 minutes, we can use the formula:

y = mx

Where m is the rate of travel, and x is the time in minutes.

To find the value of m, we can use the first two data points:

m = (y2 - y1) ÷ (x2 - x1)

m = (8 - 0) ÷ (10 - 0)

m = 8 ÷ 10

m = 4 ÷ 5

Therefore, the formula becomes:

y = (4 ÷ 5) x

Now, we can substitute x = 12 to find the distance traveled after 12 minutes:

y = (4 ÷ 5) × 12

y = 0.8 × 12

y = 9.6

y ≈ 8 miles

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The complete question is:

A van travels at a constant speed. The table shows the distance y (in miles) that the van travels after x minutes. How far does the van travel after 12 minutes?

Time (minutes), x 0 10 20 30

Distance (miles), y 0 8 16 24

The simplified ratio of [tex]2.4:3/4:1 2/3[/tex]  is [tex]28.8:9:20[/tex].

A ratio refers to the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

To solve this ratio, we need to convert all the fractions to a common denominator:

2.4 : 3/4 : 1 2/3 = 2.4 : (3/4) : (5/3)

To eliminate the fractions, we can multiply all terms by the LCD of 12:

2.4 * 12 : (3/4) * 12 : (5/3) * 12

= 28.8 : 9 : 20

So the simplified ratio for the given ratio is: 28.8 : 9 : 20

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The third quartile (Q3) of this data set is 29.

A data set is a collection of data that is organized. It is typically structured to allow for easy access and manipulation of the data. It is generally composed of a set of values, observations, or measurements that are related to each other and that can be used to analyze and interpret information. Data sets may include variables, such as names, numbers, addresses, and dates, or they may include images, audio, or video. Data sets can be used for academic research, business analysis, or other purposes.

To calculate Q3, we divide the set into four quarters. The first quarter (Q1) is the set of values from the smallest to the median, which is 18.

The second quarter (Q2) is the set of values from the median to the third quartile, which is 29. The third quarter (Q3) is the set of values from the third quartile to the largest value, which is 36.

The fourth quarter (Q4) is the set of values from the largest value to the smallest value, which is 12. Therefore, the third quartile (Q3) of this data set is 29.

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complete questions as follows-

Answer:

balls

Step-by-step explanation:

Answer:

$624

Step-by-step explanation:

The width is the smaller side and there are four sides to a rectangle so 2 sides are 36 cm and 2 sides are 42cm. The perimeter formula follows this P=(L+W)*2 so plugging the variables (42+36)*2= 156. So there are 156 meters of fencing and each meter costs $4.00. Thus, 156*4=$624

The solution to the equation [tex]4x^2 = 5(4x - 5)[/tex] is x = 5/2."

To solve the equation [tex]4x^2[/tex] = 5(4x - 5), we first simplify the right-hand side by using the distributive property:

Next, we bring all the terms to one side of the equation by subtracting 20x and adding 25 to both sides:

[tex]4x^2 - 20x + 25 = 0[/tex]

This equation is now in the form of a quadratic equation [tex]ax^2[/tex] + bx + c = 0, where a = 4, b = -20, and c = 25. We can solve for x using the quadratic formula:

[tex]x = (-b ± sqrt(b^2 - 4ac)) / 2a[/tex]

Substituting the values of a, b, and c, we get:

x = (-(-20) ±  - 4(4)(25))) / 2(4)

x = (20 ± sqrt(400 - 400)) / 8

x = 5/2

Solve 4 x squared equals 5 left parenthesis 4 x minus 5 right parenthesis.

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Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter

The proportion of a circle's circumference to its diameter is denoted by the mathematical constant pi (). It cannot be written as a simple fraction since it is an irrational number. Pi is approximately equal to 3.141592, or 3.15.

We must first determine the circle's radius in order to determine the length of Mr. Chang's string.

C = 2πr, where C is the circle's circumference and r is its radius, is the formula for a circle's circumference.

Given that the circle's circumference is 31.4 meters, we can solve for r using the following method:

C = 2r 31.4

=2x3.14xr

= 31.4/(2x3.14)r

= 3.14/6.28r

r = 5

Thus, the circle's radius is roughly 5 meters.

The diameter of the circle, which is twice as long as its radius, will be equal to Mr. Chang's stake because it is in the center of the circle.

Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter

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Ans:-

[tex] \: [/tex]

Solution:-

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The value of x is 2 !

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hope it helps:)

The value of solution of expression is,

⇒ x = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 7 + 4x - 9 = 6

Now, We can simplify as;

⇒ 4x - 2 = 6

⇒ 4x = 4 + 2

⇒ 4x = 8

⇒ x = 2

Thus, The value of solution of expression is,

⇒ x = 2

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Mercy will be 27 years old, and her mom will be 37 years old, 7 years from now.

To find Mercy's and her mom's ages, follow these steps:
1. Set up an equation: Let Mercy's age be 2x and her mom's age be 3x.

Their combined age is 50 years, so the equation is 2x + 3x = 50.
2. Solve the equation: Combine the terms on the left side to get 5x = 50.

Then, divide both sides by 5 to find x = 10.
3. Find their present ages: Mercy's age is 2x = 2(10) = 20 years old, and her mom's age is 3x = 3(10) = 30 years old.
4. Find their ages 7 years from now:

In 7 years, Mercy will be 20 + 7 = 27 years old, and her mom will be 30 + 7 = 37 years old.

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The area of the rectangle is 40 square inches.

For a rectangle that is 8 inches long, 3 inches on the bottom, and 5 inches on the side, there are a few things you can do.

The perimeter of a rectangle is the sum of the lengths of all four sides.

To calculate the perimeter, add the lengths of the top and bottom sides (8 + 3 = 11) and the lengths of the two side lengths (5 + 5 = 10).

To find the area of a rectangle with an 8-inch long side, a 3-inch bottom side, and a 5-inch side, follow these steps:
Identify the dimensions of the rectangle.
The dimensions are given as 8 inches long, 3 inches on the bottom, and 5 inches on the side.

However, a rectangle only has two different side lengths, so we can assume that the 3-inch measurement is irrelevant.
Confirm the side lengths.
In this case, the side lengths are 8 inches and 5 inches. The 8-inch side is the length, and the 5-inch side is the width.
Calculate the area of the rectangle.
To find the area, multiply the length by the width. In this case, that is 8 inches (length) multiplied by 5 inches (width).
Area = Length × Width
Area = 8 inches × 5 inches
Area = 40 square inches

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the volume of the conical section is approximately 604.8 cubic inches. we need to use volume formula of conical section to get the answer

what is conical section ?

A conical section is a geometric shape formed by the intersection of a plane with a cone. A cone is a three-dimensional geometric shape that has a circular base and tapers to a point, while a plane is a two-dimensional flat surface that extends infinitely in all directions.

In the given question,

To find the volume of a conical section, we need to use the formula:

Volume = (1/3) x π x r² x h

where r is the radius of the circular base of the cone, h is the height of the conical section, and π is the constant pi (approximately 3.14159).

In this case, we are given the diameter of the base of the cone, which is 12 inches. We can use the formula to find the radius:

r = d/2 = 12/2 = 6 inches

We are also given the height of the conical section, which is 14 inches. We can now plug these values into the formula:

Volume = (1/3) x π x r² x h

Volume = (1/3) x π x 6² x 14

Volume = (1/3) x π x 36 x 14

Volume = 604.8 cubic inches (rounded to one decimal place)

Therefore, the volume of the conical section is approximately 604.8 cubic inches.

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The function is   [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Here the principal p = $8100

Rate of interest r = 3.7% = 3.7/100 =0.037

Compounded daily then n= 365

Now using compound interest formula then,

=> CI = [tex]P(1+\frac{r}{n})^{nt}[/tex]

=> CI = [tex]8100(1+\frac{0.037}{365})^{365t}[/tex]

=> CI = [tex]8100(1+0.000101369)^{365t}[/tex]

=> CI = [tex]8100(1.000101369)^{365t}[/tex]

Then the function is f(t) = [tex]8100(1.000101369)^{365t}[/tex] .

Now percentage of growth per year is ,

=>  [tex]8100(1.000101369)^{365t}[/tex][tex]\times\frac{1}{100}\%[/tex]

Put t=1 then

=> 8,405.30[tex]\times\frac{1}{100}\%[/tex]

=> 84%

Hence the function is   [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.

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Answer:

The answer is 8

Step-by-step explanation:

Let total number of rides be represented by x

And total amount spent on the ride and entry fees be y

Entry fees of the park = $10.50

Also, Charge for each ride is given to be $4.50

So, The linear function which describes the situation :

y = 10.50 + 4.50x

Now, Its given that Jay spent a total of $46.50 in the park

So, to find total number of rides taken substitute y = 46.50 in the above linear equation.

⇒ 46.50 = 10.50 + 4.50x

⇒ 4.50x = 36

⇒ x ≈ 8

Thus, Number of rides taken = 8

Answer: it is one of the last two

Step-by-step explanation:

The equation for the new function F(t) is F(t) = 9t - 256/9.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

The conversion formula for converting temperature from Celsius to Fahrenheit is:

F = 9/5C + 32

Substituting the equation for C(t) into F(t) = 9/5C(t) + 32, we get:

F(t) = 9/5(5t - 160/9) + 32

Simplifying this equation, we get:

F(t) = 9t - 320/9 + 32

F(t) = 9t - 256/9

Therefore, the equation for the new function F(t) is F(t) = 9t - 256/9.

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Answer:

Step-by-step explanation:

use a calculator it's free

Answer:

A. 500 yards

Step-by-step explanation:

By the Pythagorean Theorem:

[tex] \sqrt{ {3}^{2} + {4}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]

The distance from the park to Anita's house is 5 blocks, which is

5 blocks × 100 yards/block = 500 yards.

Answer:

A. 500 yards

Step-by-step explanation:

1 block = 100 yards

one leg: 4*100= 400 yards

second leg: 3*100= 300 yards

hypotenuse:

pythagorean theorem

hypotenuse ^2 = (one leg)^2 + (second leg)^2

hypotenuse ^2= (400)^2 + (300)^2

hypotenuse ^2 = 160,000 + 90,000

hypotenuse = sqrt(250,000)

hypotenuse = 500 yards

The steps that should be taken to calculate the volume of the right triangular prism are;

Base = 8 meters

Height = 14 meters

Length of the prism = 7 meters

Area = ½ × base × height

= ½ × 8 × 14

= 56 square meters

Volume of the rectangular prism = Area × length of the prism

= 56 square meters × 7 meters

= 392 cubic meters

Ultimately, the volume of the right triangular prism is 392 cubic meters

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A linear function has one independent variable and one dependent variable..

therefore, all are linear except y=x²-6