A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.

Identify and interpret the key features of the exponential function modeled in terms of this situation.

Select each correct answer.

The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.

The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.

The line x = 0 is an asymptote of the graph.

The point (0,30) contains the x-intercept.

The line y = 0 is an asymptote of the graph.

The y-intercept is 800.

The asymptote indicates that there were never more than 800 mice in existence.

Answer:

162

Step-by-step explanation:

12²+6² ÷ 2

= 144 + 36 ÷ 2

= 144 + 18

= 162

The value of the unknown angle x would be 43 degrees.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given a right-angle triangle with a perpendicular side of 6 units and a hypotenuse of 10 units.

The unknown angle is x which needs to find.

Therefore, applying trigonometry;

Sin x = perpendicular/hypotenuse

Sin x = 6/10

Sin x = 3/5

Sin x = 0.6

x = Sin inverse (0.6)

x = 43 degrees.

Hence, the value of the unknown angle x would be 43 degrees.

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Answer:x^4+6

Step-by-step explanation:

you must combined both x squared to get x^4 and then add the opposite of -4 Which is +4  and what you do to one side you must do to the other therefore you add the 2 to it as well. in conclusion you get x^4+6. hope this helps:)

The value of tan 30° after using trigonometric ratio  is  [tex]\frac{1}{\sqrt{3} }[/tex] .

What is trigonometric ratio?

 There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given

=> tan30°

Now ,Tan 30 degrees in radians is written as

=>tan (30° × π/180°)

=> [tex]\frac{1}{\sqrt{3} }[/tex]

Therefore the value of tan30° is  [tex]\frac{1}{\sqrt{3} }[/tex] .

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Answer:

y-2

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

let us say that angleDAB is 60 then angleADB is 30

due to the presence of line DB we can also say that angleDCB is 60 and angle CBD is 30

The roots of the equation x³ + 2x² + 36x + 72 = 0 are ( -2 , -6i , +6i )

What is Factorizing?

Brackets should be expanded in the following ways:

For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket

For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Given data ,

Let the equation be x³ + 2x² + 36x = -72

Adding 72 on both sides , we get

x³ + 2x² + 36x + 72 = 0

Now , on simplifying we get

Take the common factor x² in first two terms and 36 in last two terms

So ,

x² ( x + 2 ) + 36 ( x + 2 ) = 0

Now , taking ( x + 2 ) as common factor , we get

( x² + 36 ) ( x + 2 ) = 0

So , for the equation to be 0 , either ( x + 2 ) = 0 or ( x² + 36 ) =0

And , we can find the solutions to the equation as

x + 2 = 0

Subtracting 2 on both sides , we get

x = -2

So , one solution is -2

Now ,

( x² + 36 ) =0

Subtracting 36 on both sides , we get

x² = -36

x = √ ( -36 )

x = ± 6i

So , we got two more solutions as -6i and +6i

Hence , the roots of the equation are -2 , -6i and +6i

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The value of sin(x/2)= √(1-√11/6)/2

The value of cos(x/2)=√(1+√11/6)/2

The value of tan(x/2) = 5/6/(√(1+√11/6)

In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45 and so on. If θ is an angle, then the half angle is represented by θ/2.

In trigonometry, sin( x/2)= √(1-cosx)/2

cos( x/2)= √(1+cosx)/2

tan( x/2)=sinx/1+cosx

if sin (x) = 5/6

this means that 5 is the opposite and 6 is the hypotenuse, then the adjascent is

a= √(6^2-5^2)

a= √36-25

a= √11

therefore if cos x= √11/6

sin(x/2)= √(1-√11/6)/2

cos(x/2)= √(1+√11/6)/2

tan(x/2)=5/6/(√(1+√11/6)

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The difference in the cost of all 30 pens between two shops is,

£1.05

Given, Eve is going to buy 30 pens from either shop A or shop B.

Shop A: pack of 10 pens for £2

Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.

So, the cost of 30 pens from the shop A is,

as, a pack of 10 pens is of £2

1 pen = 2/10

30 pens = £6

Now, the cost of 30 pens from the shop B is,

as, a pack of 5 for £1.10

1 pen = 1.10/5 = £0.22

also buy 1 and get 1 at half price.

So, 2 pens = 0.22 + 0.11 = £0.33

Therefore, 30 pens = £4.95

So, the cost of 30 pens from shop A is £6 and from shop B is £4.95.

Hence, the difference in the cost of all 30 pens between two shops is,

£1.05

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Answer:

-3/22

Step-by-step explanation:

Hope this helps!

Answer: [tex]-\frac{3}{22}[/tex]

Step-by-step explanation:

To find the product, multiply the two fractions:

[tex]-\frac{2}{11} *\frac{3}{4} =-\frac{2*3}{11*4} =-\frac{6}{44} =-\frac{3}{22}[/tex]

The solution set is X ∈{1, -7}

The set of values that satisfy a given set of equations or inequalities is known as a solution set. For example, the solution set for a set of polynomials over a ring is the subset on which the polynomials all vanish (evaluate to 0).

Given that 3(x+3) – 12 = 0

We have to find the solution set

3(x+3) – 12 = 0

3(x+3) = 12

X+3 = ±4

X + 3 = 4 or x + 3 = -4

X = 1 or x = -7

X ∈{1, -7}

Therefore the solution set is X ∈{1, -7}

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Step-by-step explanation:

g(x) = the original function at x-2.

just means it is the same function as the original function, just moved 2 units to the right.

just think about it :

e.g.

g(3) is the same as the originated function at x=1.

g(4) is the same as the original function at x=2.

...

so, everything that happened for the original function at x, happens now for g at x+2.

therefore, again, things move 2 units to the right (positive x direction) .

that means the vertex "moves" from

(-5, 6) to (-3, 6)

the vertex of g(x) = (-3, 6)

Every second, 44 megabytes of files will be transferred to her hard drive.

The size of the files on her external hard drive in megabytes is given F, where F = 38 + 6t and t is the time in seconds since the transfer began.

The function is below

F = 38 + 6t   ....(i)

To determine the number of megabytes of files transferred to her hard drive every second

Substitute the value of t = 1 in the equation (i), and solve for F

F = 38 + 6(1)

F = 38 + 6

F = 44

So the number of megabytes of files = 44

Therefore, every second, 44 megabytes of files will be transferred to her hard drive.

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When talking about a number line, the farther right the digit moves, the large the number. The farther left it goes, the smaller the number.

For example, 81 would be to the right of 80. And 79 would be on the left. The larger the negative number, the smaller it is. So -70 is smaller than -20.

I hope this helps!

The pairs of numbers given, (1, 2) is not a solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y= 2x+1 /3

Now, First value of x = 0

y= 2(0)+1 /3

y= 1/3

i.e., (0, 1/3)

and, Second value of x = 1

y= 2(1)+1 /3

y= 5/3

i.e., (1, 5/3)

and, Third value of x = 4

y= 2(4)+1 /3

y= 9/3

y=3

i.e., (4, 3)

Hence, from the pairs of numbers given, (1, 2) is not a solution.

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Answer: The answer to this question would be: 5 days

In this question, there are two kinds of rent pricing and you are asked to find the number of days when both of them will charge the same price.

From the description, you can get an equation of each price which would look like this(x=number of day rent):

cost1= 110 + 46x

cost2= 70 + 54x

Then, the days when the price same would be:

cost1 = cost2

110 + 46x= 70+54x

110-70= 54x - 46x

40= 8x

x=5

Step-by-step explanation:

Answer:

[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

The points that are a distance of 5 units from P(-8, 4) will be all the points on the circumference of a circle with center (-8, 4) and radius 5.

Substitute the center and radius into the formula to create an equation of the circle:

[tex]\implies (x+8)^2+(y-4)^2=25[/tex]

The y-value of any point on the x-axis is zero.

Therefore, to find the points on the x-axis that are 5 units from point P, substitute y = 0 into the equation of the circle and solve for x:

[tex]\implies (x+8)^2+(0-4)^2=25[/tex]

[tex]\implies (x+8)^2+(-4)^2=25[/tex]

[tex]\implies (x+8)^2+16=25[/tex]

[tex]\implies (x+8)^2+16-16=25-16[/tex]

[tex]\implies (x+8)^2=9[/tex]

[tex]\implies \sqrt{(x+8)^2}=\sqrt{9}[/tex]

[tex]\implies x+8=\pm3[/tex]

[tex]\implies x+8-8=\pm3-8[/tex]

[tex]\implies x=-8\pm3[/tex]

[tex]\implies x=-11, x=-5[/tex]

Therefore:

[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

okok

The fraction of person that represents a degree is 1/4

A Π chart is a type of representation used in showing data representing the parts sometimes in degrees.

Π charts are made in circle and use the features of circle

Considering the problem at hand, the total number of workers in the office is 90

The total angle of a circle is 360

if 90 person is equivalent to 360 then one person would be

1 person = 360 / 90

1 person = 4 degrees

therefore 1 degree will be 1/4 person

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According to the growth function, the population be in 2050 will be 10,635

Growth function:

The growth function refers the pattern of data that shows greater  increases with passing time, creating the curve of an exponential  function.

Given,

In 1965, the population of a certain town was 2010. In 1995, the population was 3620.

Here we need to find the population in 2050.

While we looking into the given problem, let us consider,

P refers the final population

A refers the the starting population, and

x refers the time passed

Now,  we need to determine the value of the growth factor n and it can be calculated using the information for the years 1965 and 2010.

Here we know that, in 1965, the population of a certain town was 2010. In 1995, the population was 3620.

And the value of x is 30

So, it can be written as,

=> 3620 = 2010eⁿˣ³⁰

=> 3620/2010  = e³⁰ⁿ

=> 362/201 = e³⁰ⁿ

Here by applying ln to both sides of the equation:

⇒ln(362/201) = ln(e³⁰ⁿ)

By, using the laws of logarithms:

=> 30n = ln(362) - ln(201)

=> n = [ln(362) - ln(201)] / 30

=> n = 0.0196

Here we have to use this information to determine P in 2050.

Here the value of A will still be 2010, but x will be 85 years.

Here we have to apply these values then we get,

=> P = 2010e⁰°⁰¹⁹⁶ˣ⁸⁵

=> P = 2010e¹°⁶⁶⁶

=> P = 2010 x 5.2909

=> P = 10635

Therefore, there are 10635 in 2050.

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Answer:

  28 mph

Step-by-step explanation:

Given that a car moving 36 mph takes 7 hours for a trip, you want to know the speed if the trip takes 9 hours.

The speed and time vary inversely for the same distance. If the time goes up by a factor of 9/7, the speed will go down by the inverse factor: 7/9.

  7/9 × 36 mph = 28 mph

The speed of the car is 28 mph for the 9-hour trip.

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Inverse of the function is -2+x

What do you mean by inverse function?

A function that returns the initial value for which a function has produced an output is known as an inverse function. If f(x) is a function that produces the value y, then [tex]f^{-1}(y)[/tex] the inverse function of y, will provide the value x.

The function's inverse, represented by ,  [tex]f^{-1}[/tex] returns the original value that was used to create the output (x).

Given function is  y = x² + 4x + 4

To find the inverse function, we need to express x as a function of y:

Substitue y=x

⇒ x = [tex]y^{2}+4y+4[/tex]

Substract x from the above equation we get,

[tex]y^{2}+4y+4[/tex] - x = 0

Solve the above equation using quadratic formula we get,

y = [tex]\frac{-4+\sqrt{16-4(4-x)} }{2}[/tex]   [tex]=\frac{-4+\sqrt{16-16+4x} }{2}[/tex]  = [tex]\frac{-4+2x}{2}=-2+x[/tex]

Similarly, y = -2-x

Therefore, [tex]f^{-1}=[/tex] -2+x , -2-x

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Answer:

It is not a solution

Step-by-step explanation:

put in (-9,-5) in for x and y

9(-9)+4(-5)=10

-81-20=10

-101=10

This is false so (-9,-5) is not a solution to the equation 9x+4y=10

Answer:

Below

Step-by-step explanation:

4  3/10   * 3 =   43/10 * 3 = 129 / 10 =  12 9/10 miles

The standard score (z-score) of the given sample is -20.

Given,

[tex]u[/tex] = 35

[tex]o[/tex] = 9

n = 60

x = 32

To calculate standard score (z-score) use formula,

[tex]z=\frac{x-u}{\frac{o}{n} }\\\\z=\frac{32-35}{\frac{9}{60} }\\\\z=\frac{-3}{0.15}\\ \\z=-20[/tex]

Thus, the standard score(z-score) of given sample mean is -20.

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