3. In montht=0, a small group of rabbits escapes from a ship onto an island where there are no rabbits. The island rabbit population,P(t), in monthtis given byP(t)=1+24(0.85)′1000​a) How many rabbits escaped from the ship? Explain how you arrived at your answer. b) EvaluateP(6)andP(24)and explain their meaning in the context of the problem. Use complete sentences. c) Use your calculator to graphP(t)for0≤t≤80. Obtain a printout of this graph, label each axis with both a variable and a word label, and label the scale on each axis. d) Describe the shape of the graph in mathematical words (increasing, decreasing, local maximum, local minimum). e) Use the graph to describe the manner in which the rabbit population has changed since the rabbits escaped. f) Does the graph suggest the growth in population you would expect among rabbits on an island. Explain g) Use the graph to estimate how long it will take before there are 500 rabbits. Show this on the graph vou drew. Write the conclusion in sentence.

The given statement "When simplifying the expression 5-8+2, the first step would be to add eight and two" is false because of the PEMDAS rule.

According to the order of operations (PEMDAS), we need to perform any calculations inside parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.

In this case, there are no parentheses or exponents, so we can move on to addition and subtraction from left to right.

The first step would actually be to subtract 8 from 5, giving us -3. Then we would add 2 to -3, giving us a final answer of -1.

Therefore, the correct answer is False.

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When the point (1, 3) is substituted in the equation y = ax, then 'a' i,e slope of the line is 3

If a line passes through the origin, its equation can be written in the form y = mx, where m is the slope of the line.

The slope of a line passing through the origin is the ratio of the change in y to the change in x between any two points on the line.

Here we have  

A line passes through the origin, the equation is in the form y = ax

Given that y = ax passes throgh (1, 3)

So substitute x = 1 and y = 3

=> 3 = a(1)

=> a = 3/1

=> a = 3  

Therefore,

When the point (1, 3) is substituted in the equation y = ax, then 'a' i,e slope of the line is 3.  

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No, a linear equation that is equivalent to the equation 0=-7 is not a conditional equation. Instead, it is an inconsistent equation.
A conditional equation is an equation that is only true for certain values of the variable. For example, the equation 2x+3=7 is a conditional equation because it is only true when x=2.
An inconsistent equation, on the other hand, is an equation that has no solution. The equation 0=-7 is an example of an inconsistent equation because there is no value of x that will make the equation true.
Therefore, a linear equation that is equivalent to the equation 0=-7 is an inconsistent equation, not a conditional equation.

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The system of equations for the two plans is:

y = 8x + 25

y = 12x + 5

To write a system of equations for each plan, let:

x = number of month

y = Total amount

Equation of plan A:

one-time membership fee = initial value or y-intercept (b) = 8

Monthly fee per month = slope/unit rate (m) = 25

The equation would be y = 8x + 25

Equation of plan B:

one-time membership fee = initial value or y-intercept (b) = 12

Monthly fee per month = slope/unit rate (m) = 5

The equation would be y = 12x + 5

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Yes, the ordered pair (5,6) is a solution of the system of equations {(x+y=11),(x-y=-1):}.

To check if an ordered pair is a solution of a system of equations, we can plug the values of the ordered pair into the equations and see if they are true.

For the first equation, x + y = 11, we can plug in 5 for x and 6 for y:

5 + 6 = 11

This is true, so the ordered pair satisfies the first equation.

For the second equation, x - y = -1, we can again plug in 5 for x and 6 for y:

5 - 6 = -1

This is also true, so the ordered pair satisfies the second equation.

Since the ordered pair satisfies both equations, it is a solution of the system of equations.

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Answer:

djdjdhdudjdhxnfbxi94949495959584748474748494949585858595959585858585858585859696969485858589484748487474747383392929२९३9999४४६५८४९२84८३4६३०२०८४७४94८८४७४९8४८४८४८४८४८48484८5८५८५८४८३९2९२919९२9३76४७४7७४७४7४5959999393939393939494949449494949494998595859303099

Answer:

think its this not sure : Alternate interior angles theorem

Step-by-step explanation:

Answer:

Step-by-step explanation:

from top down:

xᵃ⁻ᵇ

xᵃ⁺ᵇ

1

xᵃˣᵇ

1/xᵃ

The predictiοn fοr the number οf times yοu will pick a star that is nοt yellοw is 0.999.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Assuming that the stars cοme in οnly three cοlοrs (yellοw, red, and blue), and each cοlοr has an equal chance οf being selected, then the prοbability οf picking a star that is nοt yellοw is 2/3, and the prοbability οf picking a yellοw star is 1/3.

If we dο this experiment 16 times, we can use the binοmial prοbability fοrmula tο find the prοbability οf picking a nοn-yellοw star a certain number οf times:

[tex]\mathrm{P(x) = (n \ choose \ x) \times ^x \times (1-p)^{(n-x)}}[/tex]

where n is the number οf trials, x is the number οf times we want tο pick a nοn-yellοw star, p is the prοbability οf picking a nοn-yellοw star (2/3), and (1-p) is the prοbability οf picking a yellοw star (1/3).

Using this fοrmula, we can calculate the prοbability οf picking a nοn-yellοw star exactly 1 time, exactly 2 times, and sο οn, up tο 16 times. We can then add up these prοbabilities tο get the οverall prοbability οf picking a nοn-yellοw star at least οnce in 16 trials.

Alternatively, we can use the cοmplement rule tο find the prοbability οf picking a yellοw star in all 16 trials, and subtract this frοm 1 tο get the prοbability οf picking a nοn-yellοw star at least οnce:

P(nοn-yellοw at least οnce) = 1 - P(yellοw in all 16 trials)

= 1 - (1/3)¹⁶

≈ 0.999

Hence, the predictiοn fοr the number οf times yοu will pick a star that is nοt yellοw is 0.999.

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{18, 36, 24, 48, 39, 72}

In Exercises 1-6, the subgroup generated by the given subset is a set of elements that are all powers of the same element.

1. The subset {2,3} of Z12 generates the subgroup {2, 4, 8, 3, 9, 6, 12}.
2. The subset {4,6} of Z12 generates the subgroup {4, 8, 6, 12}.
3. The subset {8,10} of Z18 generates the subgroup {8, 16, 10, 18}.
4. The subset {12,30} of Z36 generates the subgroup {12, 24, 30, 36}.
5. The subset {12,42} of Z6 generates the subgroup {12, 6}.
6. The subset {18,24,39} of Z generates the subgroup {18, 36, 24, 48, 39, 72}.

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x and y must have values of 3 and 11, respectively.

What is a Parallelogram?

A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.

The angles in a parallelogram are given in the diagram.

As opposite sides are equal and parallel in a parallelogram, the alternate interior angles must also be the same.

This gives:

5y - x = 52 ...(i)

6y - 18 = 48 ...(ii)

Solving (ii)

6y = 66

y = 11

Substituting in (i)

5(11) - x = 52

x = 3

The values of x and y must be 3 and 11 respectively.

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w |w|-20=-13
w = 7 and w = -33

A. For this equation, we have to solve for the absolute value of w.

An absolute value equation can be thought of as two equations in one, so we need to solve for both cases.

B.

Case 1: w > 0

w - 20 = -13

w = 7

Case 2: w < 0

w + 20 = -13

w = -33

Therefore, the solution to this absolute value equation is w = 7 and w = -33.

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The output of Badger's function machine when the input is 3.

To find the output of Badger's function machine, we need to first find the output of Bucky's function machine when the input is 3.

1. Input 3 into Bucky's function machine.
2. Follow the instructions on the function machine to find the output.
3. Input the output from Bucky's function machine into Badger's function machine.
4. Follow the instructions on Badger's function machine to find the final output.

Without knowing the specific instructions on the function machines, it is impossible to give a specific answer.

However, by following these steps, you can find the output of Badger's function machine when the input is 3.

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The linear demand function is given by Q = -1.09P + 76.4, the revenue function is R = -1.09P^2 + 76.4P, and the price that yields maximum revenue is $34.95.

To create the linear demand function, we use the two points given: (35, 34.75) and (36, 33.06). We can find the slope of the line between these two points using the slope formula: (33.06 - 34.75)/(36 - 35) = -1.69. This slope represents the change in quantity demanded per dollar change in price. To find the intercept, we can use either of the points and solve for it: 35 = -1.69(34.75) + b, giving us b = 131.15. Thus, the demand function is Q = -1.69P + 131.15, which we can simplify to Q = -1.09P + 76.4.

To find the revenue function, we multiply the demand function by the price: R = P(Q) = P(-1.09P + 76.4) = -1.09P^2 + 76.4P. To find the price that yields maximum revenue, we can take the derivative of the revenue function with respect to price and set it equal to zero: dR/dP = -2.18P + 76.4 = 0, giving us P = $34.95. Therefore, the price that yields maximum revenue is $34.95.

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Therefore, f(-2x-5) is \[ \frac{-2(x+4)}{4(x+3)^{2}}=\frac{-2 x-8}{4 x^{2}+24 x+36} \]

(a) To find the value of f(-2), we simply substitute -2 for x in the given function:
\[ f(-2)=\frac{-2-3}{(-2)^{2}+2}=\frac{-5}{6} \]
Therefore, the value of f(-2) is -5/6.

(b) To find f(-2x-5), we substitute -2x-5 for x in the given function:
\[ f(-2x-5)=\frac{-2x-5-3}{(-2x-5)^{2}+2}=\frac{-2x-8}{4x^{2}+20x+27} \]
Simplifying the numerator and denominator, we get:
\[ f(-2x-5)=\frac{-2(x+4)}{4(x+3)(x+3)}=\frac{-2(x+4)}{4(x+3)^{2}} \]
Therefore, f(-2x-5) is \[ \frac{-2(x+4)}{4(x+3)^{2}}=\frac{-2 x-8}{4 x^{2}+24 x+36} \]

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For the number of checks written greater than 42.5, a checking account at Long's Bank will generate more earnings income than one at Fellow's Bank.

Range of checks refers to a specific interval or set of values within which the number of checks written is included or applicable.

It is usually used in the context of analyzing financial data related to checking accounts, transactions, or other monetary activities.

To find the range of checks for which Long's Bank generates more earnings income than Fellow's Bank, we need to compare the two equations and solve for x.

I(Long's Bank) > I(Fellow's Bank)

-0.06x + 8.3 > -0.02x + 6.6 (Substitute the values of I for both banks)

0.04x > 1.7 (Simplify by combining like terms)

x > 42.5 (Divide both sides by 0.04 and reverse the inequality sign)

For the number of checks written less than or equal to 42.5, a checking account at Fellow's Bank will generate more earnings income.

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Answer:

23

Step-by-step explanation:

The correct answer is B. 299,250Php.

To find out how much the author will have received when the 5,000th book is sold, we need to calculate the royalties for the first 3,000 copies and then the royalties for the additional 2,000 copies.

For the first 3,000 copies, the author will receive 5% of the sale price:

3,000 x 1995Php x 0.05 = 299,250Php

For the additional 2,000 copies, the author will receive 15% of the sale price:

2,000 x 1995Php x 0.15 = 598,500Php

Adding these two amounts together gives us the total amount the author will have received:

299,250Php + 598,500Php = 897,750Php

Therefore, the correct answer is B. 299,250Php.

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a) The average rate of change of f on [−3,1] is 4.

b) The average rate of change of f on [x,x+h] is 3+16/h.

The average rate of change of a function f(x) on an interval [a,b] is given by the formula:

Average rate of change = (f(b)-f(a))/(b-a)

(a) To find the average rate of change of f on [−3,1], we plug in the values of a=-3 and b=1 into the formula:

Average rate of change = (f(1)-f(-3))/(1-(-3))
= (f(1)-f(-3))/4

Now, we need to find the values of f(1) and f(-3) by plugging in the values of x into the given function:

f(1)=1+3(1)-8=-4
f(-3)=-3+3(-3)-8=-20

Plugging these values back into the formula, we get:

Average rate of change = (-4-(-20))/4
= 16/4
= 4

Therefore, the average rate of change of f on [−3,1] is 4.

(b) To find the average rate of change of f on [x,x+h], we plug in the values of a=x and b=x+h into the formula:

Average rate of change = (f(x+h)-f(x))/(x+h-x)
= (f(x+h)-f(x))/h

Now, we need to find the values of f(x+h) and f(x) by plugging in the values of x and x+h into the given function:

f(x+h)=x+h+3(x+h)-8
=4x+3h-8
f(x)=x+3x-8
=4x-8

Plugging these values back into the formula, we get:

Average rate of change = (4x+3h-8-(4x-8))/h
= (3h+16)/h
= 3+16/h

Therefore, the average rate of change of f on [x,x+h] is 3+16/h.

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Answer:

6 - (1 1/3 + 1 4/9)

6 - 2 7/9

= 29/9

= 3 2/9

Therefore, 3 2/9 pounds of grass seed are left.

hi, attached is the answer

Hope this helps:)

Answer:

a) (0.333, 13.11)

b)  (1, 9)

Step-by-step explanation:

a)

5x+3y=41

2x+3y=40

[The steps are labelled so they can be referenced in the subsequent problems]

A.  Rearrange one of the two equations so as to isolate the x or y to one side.  I'll use 2x+3y=40:

2x+3y=40

2x = 40-3y

x = (40-3y)/2

B.  Now use that expression of x in the other equation:

5x+3y=41

5((40-3y)/2)+3y=41

(200-15y)/2 +3y = 41

100 - 7.5y + 3y = 41

-4.5y = - 59

 y = 13.11

C.  Now use y=13.11 in either equation to find x:

2x+3y=40

2x+3*(13.11)=40

2x + 39.33 = 40

2x = 0.67

x = 0.333

D.  Answer: The lines intersect at (0.333, 13.11)

b)

x+7y=64

x+3y=28

A.  

x+7y=64

x=64-7y

B.

x+3y=28

(64-7y)+3y=28

64-4y = 28

-4y = -36

  y = 9

C.

x=64-7y

x=64-7*9

x = 1

D.  Answer: The lines intersect at (1, 9)

See the attached graph for proof of the points of intersection.

HELPPP PROVIDED (I hope)

∫fx(x)dx = 1 over the entire range of x, and fx is indeed a density function.

A random variable X has the normal distribution N(m, o^2), where m and o are both real numbers, if it is an absolutely continuous random variable with density fx(x) = (1/√(2πo^2)) * exp(-(x-m)^2/2o^2).

To verify that fx is indeed a density, we need to check that it satisfies the two properties of a density function:

1) fx(x) >= 0 for all x
2) ∫fx(x)dx = 1 over the entire range of x

First, let's check that fx(x) >= 0 for all x. Since the exponential function is always positive, we can see that fx(x) will always be positive as well. Therefore, fx(x) >= 0 for all x.

Next, let's check that ∫fx(x)dx = 1 over the entire range of x. To do this, we need to integrate fx(x) over the entire range of x, which is from -∞ to ∞:

∫fx(x)dx = ∫(1/√(2πo^2)) * exp(-(x-m)^2/2o^2)dx from -∞ to ∞

Using the substitution u = (x-m)/√(2o^2), we can rewrite the integral as:

∫(1/√(2πo^2)) * exp(-u^2/2) * √(2o^2)du from -∞ to ∞

Simplifying, we get:

∫(1/√(2π)) * exp(-u^2/2)du from -∞ to ∞

This integral is equal to 1, as it is the integral of the standard normal density function. Therefore, ∫fx(x)dx = 1 over the entire range of x, and fx is indeed a density function.

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Answer:

30 = 2x + 4

Step-by-step explanation:

2x5= 10

30- 10 = 20

20/5= 4

4+2 = 6

Mei gave each student 6 stickers

The approximate diameter of the circle is 8.5 ft.

The space a circle takes up on a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. The area formula will also enable us to determine the circle's circumference, or the border length.

The circumference of the circle is given as:

C = 2 πr

We can also write this as:

C =  πd

as, 2r = d.

The circumference is given as 26 5/7ft. To convert this to a decimal, we can multiply the fractional part by 7/7 to get:

5/7 * 7/7 = 35/49

So the circumference is approximately:

26 + 35/49 = 26.71 ft

Now we can use the formula to find the diameter:

d = 26.71 / 3.14 ≈ 8.5 ft

Therefore, the approximate diameter of the circle is 8.5 ft.

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We're required to find the value of angle KTR.

It can easily be seen that angle KTR and angle BTF are vertically opposite angles.

[tex]\therefore \: \angle \: KTR= \angle \: BTF \: \\ \implies \: 4h + 160 = 3h + 156 \\ grouping \: the \: like \: terms \: at \: either \: sides \\ \implies \: 4h - 3h = 156 - 160 \\ \implies \: \boxed{h = - 4\degree}[/tex]

now ,

[tex]\angle \: KTR \: = 4h + 160 \\ \implies \: \angle \:KTR \: = 4( - 4) + 160 \\ \implies \: \angle \: KTR \: = - 16 + 160 \\ \implies \:\boxed{ \angle \:KTR = 144\degree}[/tex]

hope helpful! :)

Answer:

C) 84 mm squared

Step-by-step explanation:

The formula for finding area of a triangle is 1/2 times base times height, so substitute and solve for the answer

1/2 times 8 times 21

4 times 21

84

Answer:

D is correct

Step-by-step explanation:

Answer:

f(2)=3x²+2x-10

f(2)=3(2)² +2(2)-10

=12+4-10

=6

Answer:

Yes, the ratios 3:6 and 2:4 are equivalent because they represent the same proportion. To confirm, we can simplify both ratios to their simplest form:

3:6 can be simplified by dividing both terms by 3: 3/3 : 6/3 -> 1:2

2:4 can be simplified by dividing both terms by 2: 2/2 : 4/2 -> 1:2

Since both ratios simplify to the same ratio, 1:2, they are equivalent.

Answer: yes !!

Step-by-step explanation: 3:6 and 2:4 are equivalent b/c of their common factors.