Elanor wants to estimate the number of frogs in a reservoir. She catches 90 frogs from the reservoir and marks them with a non-harmful dye. Elanor then returns the frogs to the reservoir. The next day she catches another 80 frogs and 10 of these are marked with the dye. Work out an estimate for the total number of frogs in the reservoir

M(5) = 2737.867; After 5 years, there are approximately 2,737 members in the company

What does M(5) mean and how should it be interpreted in relation to the issue?

In this case, we know that the exponential function M(t) = 1700*(1.10)t denotes the number of members the company had t years after its founding.

Then, M(5) will stand for the number of members who joined the company five years after its founding. To determine this value, all we have to do is substitute the number five for the variable t.

M(5) = 1700*(1.10)^5 = 2,737.867

Rounding to the nearest whole number, we obtain 2,737, which indicates that there will be roughly 2,737 members after 5 years.

Consequently, the second choice is the right one:

"M(5) = 2737.867; There are about 2,737 members in the company after 5 years."

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Answer:

 . .

Step-by-step explanation:;

The domain of the function :f(x)=x^2-11x-10 is expressed as D = (-∞, ∞)

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The domain of a function is the value of the input 'x' for which the given function exists here.

Given the function f(x)= x^2-11x-10

Therefore, the domain of the function exists on all real numbers.

Which is the function will exist for any given value of x.

Hence, the domain of the function is D = (-∞, ∞)

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Answer:

Its C. y = x - 1

Step-by-step explanation:

For Example:

-4 = -3 - 1

1 = 2 -1

4 = 5 - 1

If the scale factor is equal to one, then there wont be any change in the original shape

The scale factor is defined as the ratio of the original size of the shape to the new size of the shape.

There are three types of scale factors will be there, greater than one, equal to one and between 0 and 1

When the scale factor is greater than 1, then the shape will enlarge

When the scale factor is equal to 1, there wont be any change in original shape

When the scale factor is between 0 and 1, the shape will decrease the size

Therefore, there wont be any change in original shape when scale factor equal to one

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Answer:

Your answer is B) [tex]y=\frac{1}{3}x-6[/tex]

Splitting strategy is one of the technique in mathematics  which help to add  the larger number , two-digit and three digit and so on.

Explanation:

Splitting strategy is one of the mathematical technique :

Therefore, the splitting strategy is mathematical technique to make out work effortless.

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The parallel line has an equation of y = 2x - 21

The equation is given as

y = 2x + 3

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = 2

The slopes of parallel lines are equal

This means that the slope of the other line is 2

i.e. m = 2

Recall that:

The equation of a line can be represented as

y = mx + c

Where

slope = m = 2

Also, we have

(x, y) = (6, -9)

So, we have

-9 = 2 * 6 + c

This gives

c = -9 - 12

Evaluate

c = -21

So, we have

y = 2x - 21

Hence, the equation of the parallel line is y = 2x - 21

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The point that the line also pass would be; C. (8,4)

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Given that line has a slope of - 1/4 and passes through the point (4,2).

Now Write the equation as;

y - 2 = -1/4(x - 4)

y = -1/4x + 6

Hence, The answer is; C. (8,4)

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By using substitution method the values of x and y are, x = -1/7 and y = -32/7.

What is substitution method?

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Consider, the given equations

-8x = 5y + 24       ..(1)

-9y = 40 - 8x        ..(2)

From equation (1),

x = -(5y + 24)/8

x = -5/8y - 3            ..(3)

Plug value of x in equation (2),

-9y = 40 - 8(-5/8y - 3)

-9y = 40 + 5y + 24

-14y = 64

y = -64/14

y = -32/7

Plug y = -32/7 in equation (3)

x = -5/8(-32/7) - 3

x = -1/7

Hence, by using substitution method the values of x and y are, x = -1/7 and y = -32/7.

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Answer:

Step-by-step explanation:

The required probability is 0.75 that a student visited the athletic complex regularly, given that he or she tried out for a sport.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

To find the probability that a student visited the athletic complex regularly, given that he or she tried out for a sport. This is known as the conditional probability of visiting the athletic complex regularly, given that the student tried out for a sport.

The formula for calculating conditional probability is:

P(A|B) = P(A and B) / P(B)

In this case, A is the event "visited the athletic complex regularly" and B is the event "tried out for a sport."

Substituting the given probabilities into the formula, we get:

P(A|B) = P(A and B) / P(B)

= 0.12 / 0.16

= 0.75

Therefore, the probability is 0.75, which is the correct answer that would be option (C).

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f( x ) is an odd function

The symmetry of a function is described using the terms even and odd. On a graph, an even function is symmetric about the y-axis. An odd function has symmetric behavior around a graph's origin (0, 0).

According to the given information

We are given with the function

f( x ) = [tex]-9-x^{5} + 2x^{3}[/tex]

For checking that the function is even or odd

Case 1

put -x in place of x

f ( -x ) = [tex]-9-(-x)^{5} + 2(-x)^{3}[/tex]

f ( -x ) = [tex]-9+x^{5} -2x^{3}[/tex]

f(x) ≠ f (-x)

Hence it is not an even function

So

f(-x) = -f(x)

hence

f( x ) is an odd function

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Answer:

the answer is letter B

Step-by-step explanation:

All you do is remove to parentheses

Answer:

-4

Step-by-step explanation:

I hope this helps

The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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Answer: Depends if AB and CD are equal, as they both have M in the same spot that can be eliminated, look at the quadrilateral and make a guess based off the information that AB and CD have to be equal

Step-by-step explanation:

The range of the given piecewise function is [-1, 27].

A function with many parts of curves in its graph is said to be a piecewise function. It is a function with various definitions at various intervals of x.

The given function is a piecewise function,

[tex]f(x)=\begin{cases}{{x^2+2\;&\text{if}\;-5\le x < 3 \\{x-4\;&\text{if}\;3\le x < 7}}\end{cases}[/tex]

From the given function,

The set of values for all the output values can be referred to as a function's range. To find a range,

Then, the range can be written as [-1, 27]. Therefore, the first option is correct.

The complete question is -

Find the range of the following piecewise function.

[tex]f(x)=\begin{cases}{{x^2+2\;&\text{if}\;-5\le x < 3 \\{x-4\;&\text{if}\;3\le x < 7}}\end{cases}[/tex]

a)  [-1,27] b) [18,-2] c) [1,27] d) [-4,0].

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The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 152

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 152

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x

= (0.06x³)/3 - (0.05x²)/2 + 152 x

TR  = 0.02 x³ - 0.025 x² + 152 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 152 x

P = ( 0.02 x³ - 0.025 x² + 152 x)/x

P = 0.02x² -0.025x + 152

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

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The rules for an infinitive is:

(1) Noun forms include infinitives.

(2) Use of an infinitive is not appropriate if a preposition follows the verb.

(3) An infinitive may follow a common statement that ends with a preposition.

In the given question we have to wrote the rules for an infinitive.

There are certain fundamental guidelines for using infinitives.

(1) Noun forms include infinitives. They are the verb's subject if they are used before the main verb; if they are used after the main verb, they are the verb's object.

(2) Use of an infinitive is not appropriate if a preposition follows the verb.

(3) An infinitive may follow a common statement that ends with a preposition.

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Answer:

This is the slope intercept formula used for make a line graph

Step-by-step explanation:

In the expression:

y = mx + b

m will equal your slope which is represented by rise/run

Example: 1/2, 2, 5, 3/8 etc.

b represents your y-intercept which is the point where the line hits the y-axis

For example: if the y - intercept is -2 then your line graph will cross through (0,-2) in the coordinate plane

All together, the equation for the line would look something like:

y = 1/2x - 2

Hope this helps! :D

The equation of the vertical line is x = -2.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the equation of the line as follows;

using (-2, 1) and (-2, 2)

m = 2 - 1 / -2 + 2

m = 1 / 0

m = 0

Therefore, y-intercept using (-2, 1)

1 = 0 + b

The equation of a vertical line in the graph, which is parallel to y-axis is x = a.

Hence, the equation of the vertical line is x = -2.

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The equation to know the number of people that can get pizza is p = 42.5 / 8.5

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, Anna wants to celebrate her birthday by eating pizza with her friends and she has $42.50 and each pizza cost $8.50.

The equation that maths the situation will be:

p = 42.50 / 8.5

where P = number of people that can get pizza.

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As per the question, Total Annual Cash Inflows = 5000, Discount Factor = 3.72 and New Machine's internal rate of return = 16%

Note: The query is not complete and does not contain the necessary information for part 4. It is impossible to fully answer this question without the exhibits stated in the questions. Up until part 3, we will be solving it.

1) The entire annual cash inflows must be calculated for this, and the formula is given below:

Total annual cash inflows are equal to the annual savings from part-time labor plus the additional contribution margin from anticipated sales.

Annual Cash Inflows Total = 3800 + ( 1000 x 1.20)

= 3800 + 1200

= 5000

2. Formula for figuring up the discount percentage:

Discount Factor = New Machine Price/Annual Cash Flow

New machine cost is 18600 USD.

Annual inflow of cash = 5000

Discount Factor is equal to 18600/5000.

Discount Ratio is 3.72.

3.  The examples, which are absent from this question, show that the discount factor for six years is roughly closest to 16%, hence the internal rate of return for the new machine is equal to 16%.

Note, without the exhibits indicated in the questions, the question is insufficient and cannot be utilized in Part 4. It cannot be solved any further.

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Answer:

a lot

960

Step-by-step explanation:

Since there are 4 woman in total, there are 14-4=10 men.

Part 1

They can choose either 2 women, 3 women, or 4 woman.

If they choose 2 out of the 4 woman, they can have 6 different combinations.

4!/(2!(4-2)!)

=24/(2(2!))

=24/4=6

There are 8 remaining men to be chosen on the committee (because 10-2=8).

There are 10 total men and 8 men need to be chosen out of them, so the number of combinations for men is given below.

10!/(8!(10-8)!)

=10!/(8!(2!))

Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 8! from both the numerator and denominator to simplify it. This leaves the numerator with 9x10, which is 90, and the denominator with 2!, which is just 2.

90/2=45

Now we need to multiply 45 (number of combinations to choose 8 men from 10 men) and 6 (number of combinations to choose 2 women from 4 woman).

45x6=270 combinations if 2 woman are chosen

Part 2

Next we need to find out how many combinations there are if they choose 3 women for the committee.

If they choose 3 out of the 4 woman, they can have 4 different combinations.

4!/(3!(4-3)!)

=24/(6(1!))

=24/6=4

There are 7 remaining men to be chosen on the committee (because 10-3=7).

There are 10 total men and 7 men need to be chosen out of them, so the number of combinations for men is given below.

10!/(7!(10-7)!)

=10!/(7!(3!))

Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 7! from both the numerator and denominator to simplify it. This leaves the numerator with 8x9x10, which is 720, and the denominator with 3!, which is 6.

720/6=120

Now we need to multiply 120 (number of combinations to choose 7 men from 10 men) and 4 (number of combinations to choose 3 women from 4 woman).

120x4=480 total combinations if 3 women are chosen

Part 3

If 4 women out of 4 women are chosen for the committee, then obviously, there will only be 1 combination for that, since all the women will be chosen.

This leaves us with 10-4=6 spots for men in the committee.

There are 10 total men and 6 men need to be chosen out of them, so the number of combinations for men is given below.

10!/(6!(10-6)!)

=10!/(6!(4!))

Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 6! from both the numerator and denominator to simplify it. This leaves the numerator with 7x8x9x10, which is 5040, and the denominator with 4!, which is 24.

5040/24=210

Now we need to multiply 210 (number of combinations to choose 6 men from 10 men) and 1 (number of combinations to choose 4 women from 4 woman).

210x1=210 total combinations if 3 women are chosen

Part 4

Finally, we need to add all the final answers from the previous parts.

270+480+210=960 total combinations if at least 2 women were chosen for the committee

Please let me know if you find any errors

Answer:

6t^13-12t^12

Step-by-step explanation:

6t^12(t-2)

6t^12t+6t^12*-2

6t^12+1 +6t^12*-2

6t^13+6t^12*-2

6t^13-12t^12

Equation of line having passing point (-2,5) and (2,-3) is  y − 5 = −2(x + 2).

Hence, option B is correct.

What do you mean by equation of line?

A line equation is an algebraic representation of a set of points that together form a line in a coordinate system. A number of points that together form a line of axes, represented as a set of variables x,y, form an algebraic equation called the line equation.

Given passing points of line (-2,5) and (2,-3)

Equation of line having two passing points (a,b) and (c,d) is

y - b = [tex]\frac{d-b}{c-a}[/tex] (x - a)

So, equation of line having passing point (-2,5) and (2,-3) is

y - 5 = [tex]\frac{-3-5}{2+2}[/tex] (x + 2)

y - 5 = -2(x + 2)

y - 5 = -2x - 4

2x + y - 5 + 4 = 0

2x + y - 1 = 0

Therefore, equation of line having passing point (-2,5) and (2,-3) is  y − 5 = −2(x + 2).

Hence, option B is correct.

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The zero of the graph is 8 and it represents the time taken for Bart to pass out the flyers i.e 8 minutes

From the question, we have the following parameters that can be used in our computation:

The empty graph

Also from the question, we have the following equation

f(x) = 80 - 10x

This means that

The variable f is a function of x i.e. f(x)

To plot the graph, we represent the function f(x) on the y-axis

See attachment for the graph of the function

This is the point where the graph crosses the x-axis

This is represented a f(x) = 0

Substitute the known values in the above equation, so, we have the following representation

80 - 10x = 0

Add 10x to both sides

10x = 80

Divide both sides by 10

x = 8

Hence, the zero is 8 and it means that Bart passes out the flyers in 8 minutes

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The Balance chemical equation using given coefficients: 2, 3, 4, and 5 is

2[tex]C_{2} H_{2}[/tex]+ 5[tex]O_{2}[/tex] -> 4[tex]CO_{2}[/tex] + 2 [tex]H_{2}O[/tex]

The given chemical Equation:

[tex]C_{2} H_{2}[/tex] + [tex]O_{2}[/tex] -> [tex]CO_{2}[/tex]+ [tex]H_{2}O[/tex]

Balance chemical equation using given coefficients: 2, 3, 4, 5

2[tex]C_{2} H_{2}[/tex]+ 5[tex]O_{2}[/tex] -> 4[tex]CO_{2}[/tex] + 2 [tex]H_{2}O[/tex]

A chemical equation is the symbolic illustration of a chemical response in the shape of symbols and chemical formulas. The reactant entities are given at the left-hand side and the product entities at the proper-hand facet with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the goods to expose the route of the response. The chemical formulation can be symbolic, structural (pictorial diagrams), or intermixed. The equal holds for the whole electric-powered rate, as stated by way of the rate conservation regulation. An equation adhering to these necessities is said to be balanced.

A chemical equation is balanced by assigning appropriate values to the stoichiometric coefficients. simple equations can be balanced by using inspection, that is, by using trial and blunder. another method entails solving a gadget of linear equations.

Balanced equations are generally written with the smallest natural-wide variety coefficients. but on occasion, it can be high quality to just accept a fractional coefficient if it simplifies the opposite coefficients.

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Complete question: -

Drag each tile to the correct location in the equation. each tile can be used more than once, but not all tiles will be used. balance the chemical equation with the correct coefficients. 2 3 4 5 in the chemical equation  

[tex]C_{2} H_{2}[/tex] + [tex]O_{2}[/tex] -> [tex]CO_{2}[/tex] + [tex]H_{2}O[/tex]

Answer: 0.25 inches per hour.

Step-by-step explanation:

The mile-a-minute weed can grow up to 0.5 ft per day. To convert this to inches per hour, we need to convert the distance from feet to inches and the time from days to hours.

There are 12 inches in 1 foot, so the mile-a-minute weed can grow up to 0.5 x 12 = <<0.5*12=6>>6 inches per day.

There are 24 hours in 1 day, so the mile-a-minute weed can grow up to 6 / 24 = <<6/24=0.25>>0.25 inches per hour.

Therefore, the mile-a-minute weed can grow up to 0.25 inches per hour.

Here's the complete solution using the correct conversion factors:

1 ft = 12 inches

1 day = 24 hours

0.5 ft/day * (12 inches/1 ft) / (24 hours/1 day) = 0.25 inches/hour

Answer:

y = -1/6x + 5

Step-by-step explanation:

y = mx + c

Gradient (m) = -1/6

Y-intercept (c) = 5

so

y = -1/6x + 5

Answer:

1. The mistake he made was in Step #2. He subtracted 10 from -6 and 10 but he didn't subtract 10 from 18.

2. The correct answer should be -16 ≤ x < 8

Hope this helps : )

Step-by-step explanation:

Whatever you do on one side of an inequality/equation, you must do the same thing to the other side(s).

To get the correct answer he must subtract 10 from 18 which equals 8.

The final compound inequality is -16 ≤ x < 8