The number of trout in a stocked lake is given by the
equation T = 1800 (1.15)n where n is the number of months since the start of the trout season.

a. How many trout will there be in 2.5 months?

b. How many trout were there 2 months before the season opened?

The three fraction are:

A) -1/2 and 1/2

C) -3/4 and 4/3

E) 1/4

What is expression?

One or more variables or numbers are combined with one additional action to form an expression.

To answer this question, we need to evaluate the given expression:

-1/4

This is a fraction with a negative numerator and a positive denominator. It represents a number that is less than zero, but closer to zero than to negative one.

To choose three answers from the options provided, we need to look for fractions and numbers that are close in value to -1/4.

Here are three possible answers:

Therefore, the three answers are:

A) -1/2 and 1/2

C) -3/4 and 4/3

E) 1/4

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Looking at the table again, we can see that f(4) is -6. Thus, f (g(2)) is -6.

Value is the worth of something, based on its importance, usefulness, or desirability. It is something that has a desired quality, such as excellence, utility, or desirability. Value can be physical, such as a commodity, or intangible, such as respect, loyalty, or knowledge. Value is determined by both the individual and the society in which they live. Value can be assigned to both tangible and intangible things, such as a house, an education, or a friendship. Value is a subjective measure and can vary greatly from person to person.

The answer is -6. To evaluate f (g(2)), we need to determine what g(2) is first. Looking at the table, we can see that g(2) is 4. Therefore, we need to find the value of f(4). Looking at the table again, we can see that f(4) is -6. Thus, f (g(2)) is -6.

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Answer: This is for college? lol the answer should be $2.75

Step-by-step explanation:

45.50-42.75= 2.75

The common factor of the trinomials x² - 7x - 18 and x² + 14x + 24 is (x + 2).

The above polynomials are trinomials. A trinomial is a polynomial with three terms. Let's factor the trinomials and find what they have in common.

Hence,

James factors x² - 7x - 18.

x² - 7x - 18

x² + 2x - 9x - 18

x(x + 2) - 9(x + 2)

(x - 9)(x + 2)

Kaitlin factors x² + 14x + 24.

Hence,

x² + 14x + 24

x² + 2x + 12x + 24

x(x + 2)+ 12(x + 2)

(x +2)(x + 12)

Therefore, the common factor is (x + 2)

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Using a protractor and a ruler we drew a triangle with a side length of 4 inches that is between angles of 50 and 65 as shown in the figure.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. The total of a triangle's three sides is the perimeter of the triangle. The space a triangle occupies is known as its area. The area is obtained by taking half of the product of base and altitude.

Now we are asked to draw a triangle with a side length of 4 inches that is between angles of 50° and 65°.

First, let us mark the 50° angle.

Draw a straight line of 4 inches using the ruler as the base.

Keep the protractor on top at one of the ends of the line.

Mark the 50° angle.

Draw a straight line passing through the marked point using the ruler.

Now move the protractor to the other end of the line.

Mark the angle 65°.

Draw a straight line passing through the marked point using the ruler until it meets the 50° angle line.

This is a triangle with angles of 50 and 65 degrees.

Therefore, using a protractor and a ruler we drew a triangle with a side length of 4 inches that is between angles of 50 and 65 as shown in the figure.

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Answer:

[tex]\frac{7}{2}[/tex] π

Step-by-step explanation:

To find the arc length of the partial circle, you have to find a fourth of the circumference

C = [tex]\frac{1}{4}[/tex] πd - Formula

C = [tex]\frac{1}{4}[/tex] 14π - Plug in values

C = [tex]\frac{14}{4}[/tex] π - Simplify/Solve

C = [tex]\frac{7}{2}[/tex] π

Answer:

The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

Step-by-step explanation:

If a car travels at an average speed of 68 miles per hour, it takes it 5 hours 15 minutes to travel 357 miles.

The average speed is the unit rate.

The average speed is computed as the quotient of the total distance and the total time.

Conversely, the time is a function of the division of the total distance by the average speed.

The total distance traveled by the car = 357 miles

The average speed = 68 miles per hour (mph)

The time = Distance/Average speed = 357/68 = 5.25 hours

= 5 hours 15 minutes.

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Answer

The answer is 60

Step-by-step explanation:

Therefοre, the sοlutiοn οf the given prοblem οf functiοn cοmes οut tο be Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.

The curriculum fοr mathematics includes a wide range οf tοpics, such as numbers, numbers, and their cοmpοnents, as well as cοnstructiοn, building, and bοth actual and hypοthetical geοgraphic places. A wοrk discusses the relatiοnships between different variables that all wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that, when cοmbined, prοduce specific results fοr each input.

Here,

The functiοn can be written as fοllοws:

=> y = 800 * (0.25)ˣ

where y is the quantity οf Tylenοl still in Terry's system in milligrammes and x is the number οf hοurs since he last tοοk the medicatiοn.

When Terry's bοdy's cοncentratiοn οf Tylenοl gοes belοw 100mg, we need tο find οut hοw lοng it will be befοre he can take mοre medicatiοn.

The expοnential decay fοrmula frοm part 1 can be used tο find a sοlutiοn fοr this:

=>  800 * (0.25)ˣ = 100

by 800, divide bοth sides.

=>  (0.25)ˣ = 0.125

Cοnsider the twο sides' lοgarithms:

=>  lοg(0.25) * x = lοg (0.125)

tο find x:

=>  lοg(0.125) / lοg (0.25)

=>  x = 2.4

Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.

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Answer:

4.15 or

Step-by-step explanation:

100/20=5 times 3 is 15

so its 4.15 which equals 4 3/20

In linear equation, $28.75   is the unit price .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

The cost of 3 scarves is $86.25

   then,

     the unit price is  =    $86.25/3   = $28.75

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The number of students who would be there are 24 students .

The number of both students and chaperones on the trip are 28 in number. Again , this is both the chaperones and the students .

There are 4 chaperones according to the question . So to find the number of students on the field trip, the formula would be :

= Total number of both students and chaperones - Total number of chaperones

= 28 - 4

= 24 students

The number of students who would be on the field trip is 24 students .

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The number of workers required = 15

Observe the given problem and find out the relation between the number of workers and the number of days.

In given two one quantity decreased and the other quantity increased then both quantities are said to be in inverse proportions.    

Here the product of two quantities will equal a constant.

Here we have

10 workers can complete a piece of work in 18 days

Let 'x' be the number of workers required to complete work in 12 days

Here when the number of days increases the number of workers will be decreased which shows the number of work is inversely proportional to the number of days

The relation can be represented as  

=> 10 worker × 18 days  = 12 days × x workers

=> 10 × 18 = 12x

=> x = 180/12

=> x = 15

Therefore,

The number of workers required = 15

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The equation -cd is always defined, regardless of the values of the variables c and d.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

The equation cd

Now,

The equation -cd is always defined, regardless of the values of the variables c and d.

The expression -cd represents the product of two numbers, -c and d. Multiplication is a well-defined operation for all real numbers, including zero. so, neither c nor d need to be non-zero for the expression to be defined.

Therefore, the equation -cd is defined for all values of a, b, c, and d, including zero

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Therefore, the equations that represent circles with a diameter of 12 units and a center on the y-axis are x² + y² = 36 and (x + 6)² + y² = 36.

The radius of a circle having a diameter of 12 units is 6 units. The center's x-coordinate is zero if its centre is on the y-axis.

To discover which equations describe circles with these characteristics, we may use the conventional version of the equation of a circle, (x - h)2 + (y - k)2 = r2, where (h, k) is the circle's centre and r is its radius.

When we enter h = 0 and r = 6, we obtain:

(x - 0)² + (y - k) (y - k)² = 6²\sx² + (y - k) (y - k)² = 36

As we are aware that the centre is on the y-axis, the center's y-coordinate is also 0. K thus equals 0.

With k = 0, we obtain:

x² + y² = 36\s(x - 4) (x - 4)² + y² = 36\s(x + 6)² + y² = 36

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Answer: 30

Step-by-step explanation:

plug in x=8 to get: 6(8 - 3)

solve inside parenthesis: 6(8-3) = 6(5)

multiply: 6(5) = 30

Answer:

[tex] \sf \: 6(x - 3) = 30[/tex]

Step-by-step explanation:

Now we have to,

→ Find the value of 6(x - 3).

Given information,

→ x = 8

Let's solve the problem,

→ 6(x - 3)

→ 6(8 - 3)

→ 6(5)

→ 6 × 5

→ 30 => [solution]

Hence, the answer is 30.

Answer:

1/15

Step-by-step explanation:

Based on the given conditions, formulate: 2/3 divided by 10

Divide a fraction by multiplying its reciprocal: 2/3 x 1/10

Cross out the common factor: 1/3 x 1/5

Write as a single fraction: 1/3x5

Calculate the product or quotient:1/15

get the result:1/15

Answer:

1/15

1/15

Step-by-step explanation:

Based on the given conditions, formulate: 2/3 divided by 10

Divide a fraction by multiplying its reciprocal: 2/3 x 1/10

Cross out the common factor: 1/3 x 1/5

Write as a single fraction: 1/3x5

Calculate the product or quotient:1/15

get the result:1/15

Answer:

1/15

Answer:

2.5

Step-by-step explanation:

for example, if you take two of the value of x's -- 5/2, it equals 2.5

2 x 2.5 = 5

The center of this circle is (-2,2) and its radius is 2.

It is required to find the center and radius of the circle.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

Given that: (x + 2)² + (y-2)² = 4

The equation of a circle in standard form is:

(x -a)² + (y-b)² = r²

The x-coordinate of the center is a the y-coordinate of the center is b

, and r is the radius.

In this case,

a=-2

b=2

and

r=2.

Hence, the center of this circle is (-2,2) and its radius is 2.

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The point which has the coordinates (-3.5, 4) is point Z.

Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.

Given coordinate is (-3.5, 4).

This means that the point is at a distance of 3.5 to the left of the origin and at a distance of 4 units above the origin.

So in order to find the point, mark the point -3.5 in the exact middle of -3 and -4 on the X axis.

Mark the point 4 on the Y axis.

Draw perpendicular lines from both.

Intersecting point is the given point.

Here point Z indicates this.

Hence point Z indicates the coordinates (-3.5, 4).

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Your question lacks the graph showing the points and coordinates. The graph is given below.

If the spinner is spinning two times then the sample space becomes { BB,B0,BR,OB,OO,OR,RB,RO,RR}.

In probability a sample space is a set of possible number of outcomes of a random experiment.

A spinner has three equal sections blue(B), orange(O), red(R).

The sample space will be

Spin 1 Spin 2

Blue Orange

Blue Red

Blue Blue

Red Blue

Red Orange

Red Red

Orange Blue

Orange Red

Orange Orange

Hence, If the spinner is spinning two times then the sample space becomes { BB, B0, BR, OB, OO, OR, RB, RO, RR}.

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Answer:

30 men

Step-by-step explanation:

7 men x 300 days = 2100 man-days  to build 1 house)

(2100 man-days/house) x (1 house/70 days) = 30 men

Answer:

The expected value of each warranty sold is $23.8.

Answer: We can use the formula for future value of an annuity to calculate how much will be saved for retirement:

FV = Pmt x (((1 + r)^n - 1) / r)

where:

FV is the future value of the annuity

Pmt is the payment made each period (in this case, the annual profit of $22,000)

r is the annual interest rate (9% or 0.09 as a decimal)

n is the number of periods (7 years)

Substituting the given values into the formula, we get:

FV = $22,000 x (((1 + 0.09)^7 - 1) / 0.09)

FV = $22,000 x (1.9904 / 0.09)

FV = $22,000 x 22.116

FV = $485,552

Therefore, the amount saved for retirement after 7 years will be $485,552.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's call the number of large bags of popcorn sold "L" and the number of small bags of popcorn sold "S".

We can set up two equations based on the information given:

L + S = 290 (the total number of bags of popcorn sold)

4L + S = 566 (the total revenue from popcorn sales)

We can use substitution or elimination to solve for L and S.

Substitution:

From the first equation, we know that S = 290 - L. We can substitute this into the second equation:

4L + (290 - L) = 566

Simplifying, we get:

3L + 290 = 566

3L = 276

L = 92

Then we can use the first equation to find S:

L + S = 290

92 + S = 290

S = 198

So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.

Elimination:

We can eliminate one variable by multiplying one of the equations by a constant to make the coefficients of one of the variables equal but with opposite signs.

In this case, we can multiply the first equation by 4 to make the coefficients of S equal but with opposite signs:

4L + 4S = 1160

4L + S = 566

Subtracting the second equation from the first, we eliminate L:

3S = 594

S = 198

Then we can use either of the original equations to find L:

L + S = 290

L + 198 = 290

L = 92

So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.

Answer:

- A state fair uses 32 pallets of lemons for lemonade

Step-by-step explanation:

The actual amount the salesman pays for an article with a marked price of N950.00 is N2,312.50.

Amount is a word used to refer to a quantity or amount of something. It can also be used to refer to the total sum of money, goods, or services due for payment or exchange. It can also refer to the balance of money or goods due for payment or exchange. Amount is also used to refer to the size, extent, or magnitude of something.

To calculate this amount, we first need to calculate the amount of discount the salesman is offering. This is calculated by taking the marked price and multiplying it by the discount percentage: N950.00 x 125% = N1,187.50. Then, we subtract this discount amount from the marked price: N950.00 - N1,187.50 = N2,312.50. This is the actual amount the salesman pays for the article.

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The angular motion of the second hand is 720 h , we also have to know the meaning of angular motion.

The body moving along the curved path at a constant angular velocity can be used to describe the angular motion.

As there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.

so, for each hour the second hand moves 21600°.

that means 21600/360 = 60 full rotations.

that means one rotation of the second hand is 1 minute.

so, the second hand is truly a second hand (counting the seconds).

60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.

[tex]the \ ratio \ is\ \frac{30}{21600} = \frac{3}{2160} = \frac{1}{720}[/tex]

that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).

h = s×30/21600 = s/720

s = 720 h.

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The functions are Identified as below

The domain is all real numbers for both

An x-intercept is (π, 0) for sin

The minimum value is -1 for both

An x-intercept is (π/2, 0) for cos

Sin functions, or sine functions, are mathematical functions that describe a wave-like pattern that oscillates between a maximum and minimum value.

sin functions has x intercept of (π, 0), this can be checked by setting a calculator in radian and checking for sin π.This will give a value of of zero

For cos the x intercept is zero at π/2

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