lim 1 − cos(2x) /x x→0

On solving the exponential function 16000 = P(0.9455)^t, the original value of the car is obtained as $18,930.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The value of car in amount is A(t) = $16,000.

The rate of depreciation is x = 5.45% per year.

Rewriting the rate in exponential form - (1 - 0.0545) = 0.9455

The car is t = 3 years old.

Let P be the model that depicts the original cost of the car.

Then the exponential function will be -

16000 = P(0.9455)^t

Substituting the value of t in the equation -

16000 = P(0.9455)³

16000 = 0.8452P

P = 16000/0.8452486

P = 18,929.34 ≈ 18,930

Therefore, the original value of car was $18,930.

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An equivalent expression to 7.5 + s using commutative property is; s + 7.5

The commutative property under addition is an algebra property that states that the change in the order of numbers in an addition operation does not change the sum.

This means that for any real numbers x, y, we have;

x + y = y + x

The commutative property under multiplication states that the change in the order of numbers in multiplication operation does not change the product.

This means that for any real numbers c, d we have;

c × d = d × c

We want to find n equivalent expression to 7.5 + s using commutative property. Thus, we will apply the commutative property of addition as followd; 7.5 + s = s + 7.5

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There are 108 rabbits in the shelter.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

An animal shelter has 1008 cats, dogs and rabbits.

And, The ratio of the number of dogs to the number of cats in the animal shelter is 3 : 7. The ratio of the number rabbits to the number of dogs is  2 : 5.

Here, The ratio of the number of dogs to the number of cats in the animal shelter is 3:7. The ratio of the number rabbits to the number of dogs is 2:5.

So, We can formulate;

Number of dogs : Number of cats = 3 : 7

Number of rabbits : Number of dogs = 2 : 5

Hence, We get;

Number of rabbits : Number of dogs : Number of cats = 6 : 15 : 35

Since, An animal shelter has 1008 cats, dogs and rabbits.

Hence, We get;

⇒ 6x + 15x + 35x = 1008

⇒ 56x = 1008

⇒ x = 18

Thus, Number of rabbits = 6x

                                      = 6 × 18

                                      = 108

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Answer:c

Step-by-step explanation:

c

Answer:b

Step-by-step explanation:

Answer:

x3+4x2+x-6

Step-by-step explanation:

do it your selve

The ordered pairs are solutions to the system of equations are (-2,1.6)

In order to determine which ordered pairs are solutions to the system of equations, you need to equate the two equations and solve for x:

y = -0.5x+0.6 and y= x+3 3/5

-0.5x+0.6 = x+3 3/5

-0.5x+0.6 = x+3.6

x+3.6 + 0.5x-0.6 = 0

1.5x + 3 = 0

1.5x = -3

x = -3/1.5

x = -2

y =-0.5x+0.6

y = -0.5(-2) + 0.6

y = 1.6

y = x + 3.6

y = -2 + 3.6

y = 1.6

Thus, the ordered pairs are (-2, 1.6)

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The proof for the side AB congruent to side ED is given below.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

Given that

C is the intersecting point of AD and EB.

Side AC is congruent to side EC.

Also ∠A = ∠E

By vertical angles theorem, a pair of intersecting lines form 2 pairs of vertically opposite angles which are equal.

Therefore, ∠ACB = ∠ECD

Also given that sides AC and EC are congruent.

By ASA congruence theorem, if two angles and an included side of a triangle is equal to the corresponding two angles and included side of another triangle, then the triangles are congruent.

So triangles ABC and CDE are congruent.

C is the common point for both the triangles.

So the side opposite to C are AB and ED.

So they are equal and thus congruent.

Hence the sides AB and ED are proved to be congruent.

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Answer:

$20 per square foot

Step-by-step explanation:

[tex]8.2x-3.7x=90 \\ \\ 4.5x=90 \\ \\ x=20[/tex]

Answer:

280

Step-by-step explanation:

Answer:

8×35=280.

This is the best I can give to you

The number of toys is 5 in each container.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Let x be the number of toys in each container.

Weight of one toy car = 6 pounds

Weight of the container in which toy cars shipped = 5 pounds

Weight of x toy cars = 6x

Total weight of the container when toy cars are placed = 6x + 5

Weight of one toy truck = 3 pounds

Container weight = 20 pounds

Weight of x toy trucks = 3x

Total weight of the container when toy trucks are place = 3x + 20

Given that both containers have same weight.

6x + 5 = 3x + 20

6x - 3x = 20 - 5

3x = 15

x = 5

Hence the number of toys in each container is 5.

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Answer:

between 10 am - 12 pm and 2-4 pm.

The surface area of the open top box is 127 cm².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Given that,

Surface area of the open-top box = 2LH + 2WH + LW, where L is the length, W is the width and H is the height.

L = 3 cm

W = 5 cm

H = 7 cm

Surface area = (2 × 3 × 7) + (2 × 5 × 7) + (3 × 5)

                      = 42 + 70 + 15

                      = 127 cm²

Hence the surface area of the given open top box is 127 cm².

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The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The inequality y≥ -x/3 +1

Now, To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Therefore y=-x/3 +1 is a line in slope-intercept form with slope=-1/3 and y-intercept 1

Thus the line should intersect the y-axis  at y=1 and the x-axis at x=3

∴ The graph of this equation is plotted in attached file.

Hence, The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.

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Answer:

A

Step-by-step explanation:

i took the test xx

The simplified form of (f o g)(x) = 8x²  + 8x + 4.

Differentiation is a process in calculus that is used to find the rate of change of a function at a specific point. It is the process of finding the derivative of a function.

To find (f o g)(x), we need to first find g(x) and then substitute that expression into f(x).

Given:

f(x) = 2x + 4

g(x) = 4x²  + 4x

So:

(f o g)(x) = f(g(x)) = f(4x²  + 4x) = 2(4x²  + 4x) + 4

Now we can substitute the expression for g(x) into f(x) and simplify:

= 2(4x²  + 4x) + 4 = 8x²  + 8x + 4

Hence, (f o g)(x) = 8x² + 8x + 4

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An equation of the line in slope-intercept form that passes through the point (1, 17) and has a slope of 1 is equal to y = x + 16.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Given the following parameters:

Substituting the given parameters into the point-slope formula, the equation of the line in is slope-intercept form given by;

y - y₁ = m(x - x₁)

y - 17 = 1(x - 1)

y = x - 1 + 17

y = x + 16

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The complete function table using the defined function rule is as shown below.

We are given the function rule as;

h(x) = 2x - 3

From the function table attached, we will need to find the value of the function h(x) at x = -3, -2, 1, 3, 5

Thus;

Plugging in the value of -3 for x in the given function rule gives us the output as;

h(-3) = 2(-3) - 3

h(-3) = -9

Plugging in the value of -2 for x in the given function rule gives us the output as;

h(-2) = 2(-2) - 3

h(-2) = -7

Plugging in the value of 1 for x in the given function rule gives us the output as;

h(1) = 2(1) - 3

h(1) = -1

Plugging in the value of 3 for x in the given function rule gives us the output as;

h(3) = 2(3) - 3

h(3) = 3

Plugging in the value of 5 for x in the given function rule gives us the output as;

h(5) = 2(5) - 3

h(5) = 7

Thus, the complete function table is;

x        h(x)

-3       -9

-2       -7

1         -1

3         3

5         7

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 1/4 and that it passes through (4 , 3)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-3=\cfrac{1}{4}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x+2 \end{array}}[/tex]

Answer:

Like

Step-by-step explanation:

1. Nominal

2. Discrete

3. Quantitative

4. discrete

5. discrete

6. Qualitative

Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 6, 5 ) into the partial equation

5 = [tex]\frac{1}{3}[/tex] (- 6) + c = - 2 + c ( add 2 to both sides )

7 = c

y = [tex]\frac{1}{3}[/tex] x + 7 ← equation of line

a) The amounts needed for 2 batches of fudge-like brownies are of:

b) The amounts needed for 3 batches of cake-like brownies are of:

The needed amounts for each case are obtained applying the proportions in the context of this problem.

Hence:

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The amounts of eggs, water, and oil needed for 2 batches of fudge-like brownies are:

The amounts of eggs, water, and oil needed for 3 batches of cake-like brownies are:

One batch of Fudge-like brownies:

2 eggs

1/4 cup of water

1/2 cup of oil

One batch of Cake-like brownie

3 eggs

1/4 cup of water

1/2 cup of oil

The amounts of eggs, water, and oil needed for 2 batches of fudge-like brownies can be determined by multiplying each ingredients by 2

eggs = 4

cup of water = 2/4

cup of oil = 1

The amounts of eggs, water, and oil needed for 3 batches of cake-like brownies can be determined by multiplying each ingredients by 3

eggs = 9

cup of water = 3/4

cup of oil = 3/2

Therefore, the ingredients needed for the other batches is determined by multiplying each ingredients by the number of required batches.

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Answer: 220

Step-by-step explanation:

Create ratios using fractions, one for the students, and one for the percent

students: [tex]\frac{11}{x}[/tex]  percents: [tex]\frac{5}{100}[/tex]

Then cross multiply 1. [tex]11 *100 = 1100[/tex], 2. [tex]1100 / 5 = 220[/tex]

So [tex]x = 220[/tex], this means there are a total of 220 students in 7th grade

Note that in the above mathematical scenario involving two similar triangles, the option that MUST  be correct is AC < FH (Option C) This solution is arrived at using the Open Mouth Theorem.

The above-stated Theorem in Geometry asserts that if two sides of two triangles are congruent and the included angle differs, then the greater angle is opposite the longer side.

This theorem is known as the Open Mouth Theorem because it is based on the idea that the two sides of a triangle are "pivoted" at their common vertex.

Please keep in mind that this theorem only works if we know two pairs of sides are congruent like this.

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The probability of getting two spades when two cards are drawn from the deck is 1/17.

Probability branch of mathematics the deal with the likewood of an event occouring. It is the measure of how likely it is something will happen or be the case. Probabilities expressed as a number between zero and one 00 indicates impossibility and one indicus certainity. Probability can be used to calculate the chances of certain outcome based on a state condition or data. Probability can also be used to make decision and prediction about the future.

The probability of getting two spades when two cards are drawn from a shuffled deck of cards is 3/52 x 2/51, or 1/17.

This is because there is a 3/52 chance of getting the first spade and a 2/51 chance of getting the second spade (since there is one less card in the deck).

Therefore, the probability of getting two spades when two cards are drawn from the deck is 1/17.

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19.75 meters is the rocket's height when it has 0.5 seconds after launch

A relation is a function if it has only One y-value for each x-value.

Given that The flight of Jae and Miguel's rocket t seconds after launch is modeled by

h(t) = -5t² + 40t + 1

h(t) is their rocket's height in meters.

we have to find the rocket's height in meters 0.5 seconds after launch

Put t=0.5 in the above function.

h(0.5)=-5(0.5)² + 40(0.5)+ 1

=-5(0.25)+20+1

=-1.25+20+1

=19.75

Hence, 19.75 meters is the rocket's height when it has 0.5 seconds after launch

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According to the trigonometric function,  F(t) = 20 cos (2π/5)t where t represents time, in seconds. representing the pendulum ride of the sea dragon. It will take the pendulum 5 seconds to complete one full cycle.

A period on a graph function is the distance between two repeating points.

The graph repeats itself as it advances along the x-axis, as you can see.

Periods are the cycles of this predictable repetition. Every 6.28 units, or 2 pi radians, this graph repeats.

The equation is F(t) = 20 cos (2π/5)t

The amplitude of the equation is 20 and the graph makes 2π/5 oscillations at every t seconds

the period to complete an oscillation which is 2π

2π/5 * t = 2π

t = 2π * 5/2π  

t = 5 seconds

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Considering the closure under property the polynomials f(x) = a 0 + a 1 x + a 2 x^ 2 ... + a n x^ n; and g(x) = b 0 + b 1 x + b 2 x^ 2 ... + b m x^ m

In mathematics, a set is considered closed if we are able to apply and complete an operation on its components while consistently receiving a component from the same set.

A set therefore either possesses closure for a given mathematical operation or it does not.

Use of real numbers is the closure property of addition. Addition of two real numbers results in areal number

In the given problem, the set considered is polynomial addition and the addition of the two polynomial will give a sum which is a polynomial hence we say it is closed under addition.

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The point (2,-4) satisfies y < 3x - 6