Rewrite the function in the form of f(t)=a(b)^t to determine whether it represents exponential growth or exponential decay. Identify the percent rate of change.

However, we can't determine the exact number of participants with this information alone.

an individual who engages in or becomes engaged in a specific action. Examples. Over three thousand people will be competing in the games, a worldwide athletic event. She has contributed significantly to the conversation.

Let's use logic to determine the possible rankings of the participants:

A placed seventh, so at least 6 people ranked higher than A.

B placed sixth, so at least 5 people ranked higher than B.

C ranked above A and B, so C must have ranked at least fifth. This means there are at least four people who ranked higher than C.

D does worse than E and ranks penultimate, which means D ranked second to last. Therefore, there must be at least two people who ranked worse than D. Also, E must have ranked higher than D, so there is at least one person who ranked higher than D.

Putting this information together, we know that there are at least 6 + 5 + 4 + 2 + 1 = 18 people who participated in the contest.

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Answer:

0.65*10=6.5

10*0.35=3.5

10-3.5=6.5

So, it is decreasing by 35%

Step-by-step explanation:

The equation of the line is y=-2x/5 -10

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: A line that passes through (5,-12) and m=-2/5

Thus using the slope intercept form constructing it we get

y=mx+c

Putting (5,-12) and m=-2/5

-12=-2/5×5+c

c=-12+2

c=-10

The equation of the line is y=-2x/5 -10

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The interest rate of the account that Steve invested in after the given number of years would be = 16%

The total amount of money invested (p) = $2,807

The time of investment= 13 years

The interest generated at the end of the given years = 9,044.13-2807 = $6,237.13

Therefore the rate = ?

The formula for simple interest:

= P×T×R/100

6,237.13= 2,807× 14 ×r/100

Make r the subject of formula;

r= 6,237.14×100/2807×14

r = 623714/39298

r= 15.87139294

r= 16%

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Answer:

A: No solution

B: Unique Solution: (0, 0)

Step-by-step explanation:

In System A, you may notice that in both equations the two equations have variables with the same coefficient, and this is ideal for the elimination method of solving the equation. We want to add the equations in a way that cancels out variables. So let's multiply the top equation by negative one: [tex]-1(2x+3y)=-(9)\implies -2x-3y=-9[/tex]

Now from here we want to add the two equations:

[tex]\ \ -2x-3y=9\\+2x+3y=4\\0+0=13[/tex]

And the statement provided is clearly not true, 0 is never equal to 13, meaning the systems of equation has no solution, which occurs when you have two parallel lines.

In this case, we can easily solve this using substitution, since y is equal to 7x that means we can substitute in 7x for y in the second equation:

[tex]y=x\implies 7x=x[/tex]

And from here we subtract x from both sides, and divide by 6 giving us:

[tex]x=0[/tex]

And now we can take this value and plug it into either equation to solve for our y value, and it's most convenient to plug it into the y = x equation... since there's nothing to solve, we just get:

y = 0

So x = 0, and y = 0, meaning there is a unique solution of (0, 0)

The sentence regarding how many books must be sold to make a profit is given as follows:

Anna must sell at least 2 books to make a profit.

The profit function is given by the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The revenue function and the cost function for this problem are given as follows:

Hence the profit function is given as follows:

P(x) = 6.56x - 1.09x - 10.063.

P(x) = 5.47x - 10.063.

A profit is made when:

P(x) > 0.

Hence:

5.47x - 10.063 > 0

5.47x > 10.063

x > 10.063/5.47

x > 1.84.

As the number of books is a countable amount, we have that:

Anna must sell at least 2 books to make a profit.

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If the Time taken by object is 2 hour then the height will be 80.4 feet.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

We have Given the function as

h(t) = 50t - 4.9t²

If time = 2 hours then put the value of t=2 in the above Equation we get

h(t) = 50t - 4.9t²

h(t) = 50(2) - 4.9(2)²

h(t) = 100 - 4.9 x 4

h(2) = 100 - 19.6

h(2)= 80.4

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The equation of the line of given slope and point is y = 2x + 12. The solution has been obtained by using the slope-intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is the line with m as its slope and b as its y-intercept. The slope-intercept form of the linear equation is used when the values of m and b are real integers.

We are given the slope as 2 and which is passing through the point (6,24).

We need to first find the y-intercept using y = mx + b

⇒y = mx + b

⇒24 = 2(6) + b

⇒24 = 12 + b

⇒b = 12

The equation in the slope-intercept form is

y = mx + b

This gives equation as y = 2x + 12.

Hence, the equation of the line of given slope and point is y = 2x + 12.

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The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

rectangular dining room floor, which has a length of 12 feet and a width of 9 feet.

The cost to install the carpet is $5 per square foot.

so, area of the floor = A= l. w

                                     = 108 ft^2

so, total cost = 108* 5

                     =$ 540

i.e. Sarah rounded the area of the floor to 100 square feet.

because, 100*5 = $500

Hence, The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.

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Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ A=900\\ b=2a\\ h=40 \end{cases}\implies 900=\cfrac{40(a+2a)}{2} \\\\\\ 1800=40(3a)\implies 1800=120a\implies \cfrac{1800}{120}=a\implies \boxed{15=a}~\hfill \boxed{b=30}[/tex]

The triangle's missing angle, according to the provided assertion, is (a) 62° (b) 57° (c) 59° (d) sin0

Trigonometry is typically included in math courses for sophomores or juniors. Trigonometry is frequently included as a unit or term emphasis in other math classes in adding to being given as a separate course.

(a) sin(28°) = cos(90° - 28°) = cos(62°)

      62° is right answer.

(b) cos (33°) = sin (90° – 33°) = sin (57°)

      57° is correct answer.

(c) cos (31°) = sin(90° - 31°) = sin (59°)

      59° is correct answer

(d) cos(90° - 0) = sin0

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Answer:

$57.02

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the values into the simple interest formula and solve for I:

[tex]\implies I=850 \cdot 0.0575 \cdot \dfrac{14}{12}[/tex]

[tex]\implies I=57.0208333...[/tex]

Therefore, the amount of interest is $57.02 (nearest cent).

The value of (13 - 7) is 6 and it can be determined by using the method of making a group of 10 in which arithmetic operations and rearrangement of the given expression is performed.

The term arithmetic stems from the Greek noun arithmos, which means "number," with pauses in Latin, Anglo-French, and Middle English along the route. Even the most elementary math contains a large vocabulary. The study of numbers and their operations, which are relevant to all other fields of mathematics, are part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

Given that, expression: 13 - 7

The steps to determine the value of (13 - 7) by making a group of 10 are as follows:

Step 1 - Breakup 13 into the tens and the ones:

= (10 + 3) - 7

Step 2 - Breakup 7 into the tens and the ones:

= (10 + 3) - (10 - 3)

Step 3 - Rewrite the above expression:

= (10 - 10) + (3 + 3)

Step 4 - Subtraction of 10 by 10:

= (3 + 3)

Step 5 - Addition of 3 by 3:

= 6

So, the value of (13 - 7) is 6 and it can be determined by using the method of making a group of 10.

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The complete question is as follows:

Answer:

Step-by-step explanation:

This graph goes up to 2 and down to -2, which tells us that the amplitude of the waves is 2. In the equation for the parent graph, y = sinx, we will throw the 2 out front which is where the amplitude goes in sin and cos curves:

y = 2sinx

My monthly take-home pay would be $2461.16.

My yearly take-home pay would be $29533.92.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

If my take-home pay every Monday is $615.29 then my monthly take-home pay would be,

= (4×615.29).

= $2461.16  (as we have 4 Mondays in a month).

Now, My take-home pay for a year would be,

= (4×12×615.29).         (as we have 4 Mondays in a month and 12 months in a

                                                                                                                      year)                                                 = $29533.92

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From the data that teacher described, the following information could be determined:

1. The distribution of midterm and final exam scores for the students. This would allow you to see the range of scores and the overall performance of the students.

2. The average midterm and final exam scores for the students. This would give you an idea of the average performance of the students on each exam.

3. The correlation between final exam and midterm scores. This would indicate if there were a relationship between performance on the midterm and final exams.

4. The distribution of total points calculated for each student. This would allow you to see the range of total scores and the overall performance of the students.

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The number of cubes in the prism with stickers 0 - 1, 1 - 6, 2 - 12, and 3 - 8.

Cubic form is defined as the shape of a cube. Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped.

According to the prism, the cube at the center has no stickers.

Stickers on 0 side = 1

The face of the prism contains cube that would have stickers on one side. The center cubes on each face will have stickers on one side:

Stickers on 1 side = 6

The edges of the prism will have cubes at the center that contain stickers on both sides:

Stickers on 2 side = 4 (3) = 12

Every vertices on the prism will have sticker on three sides.

Sticker on three side = 8

Hence, the number of cubes in the prism with stickers 0 - 1, 1 - 6, 2 - 12, and 3 - 8.

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The correct question is:

Answer:

10 degrees

Step-by-step explanation:

In a triangle, the interior angles of a triangle (the angles in the inside) will always add up to 180 degrees.

We're given that the triangle is a right triangle which immediately gives us one angle, of 90 degrees, since that's a right angle. We're also given another angle of 80, and adding up these two angles plus the last angle, should give us 180.

Let's represent the unknown angle as "A", giving us the equation: [tex]90 + 80+ A= 180[/tex]

Now from here we can combine the 90 and 80 to get:

[tex]170+A=180[/tex]

Now from here we subtract 170 from both sides (to maintain equality and get rid of the 170):

[tex]170-170+A=180-170[/tex]

We simplify 170-170 to 0, which we don't need to put in the equation as 0 + A is just A. We also simplify 180 - 170 to 10:

[tex]A=10[/tex]

So the other acute angle is 10 degrees.

Answer:

1. 200

2.(1,4)

3.  5

4. (3,1)

5. NO SOLUTION

Step-by-step explanation:

A. The displacement is the change in position, which is given by the change in the height, so:

i. [1,2] = -5.46 m/s

ii. [1,1.1) = -1.39 m/s

iii. [1,1.01) = -0.138 m/s

iv. [1,1.001) = -0.0138 m/s

(a) To find the average velocity over a time interval, we need to calculate the displacement during that time interval and divide it by the length of the interval. The displacement is the change in position, which is given by the change in the height, so:

i. [1,2]: Δs = y(2) - y(1) = [20(2) - 1.87(2)²] - [20(1) - 1.87(1)²] ≈ -5.46

Average velocity = Δs / Δt = -5.46 / (2 - 1) = -5.46 m/s

ii. [1,1.1): Δs = y(1.1) - y(1) = [20(1.1) - 1.87(1.1)²] - [20(1) - 1.87(1)²] ≈ -1.39

Average velocity = Δs / Δt = -1.39 / (1.1 - 1) = -1.39 m/s

iii. [1,1.01): Δs = y(1.01) - y(1) = [20(1.01) - 1.87(1.01)²] - [20(1) - 1.87(1)²] ≈ -0.138

Average velocity = Δs / Δt = -0.138 / (1.01 - 1) = -0.138 m/s

iv. [1,1.001): Δs = y(1.001) - y(1) = [20(1.001) - 1.87(1.001)²] - [20(1) - 1.87(1)²] ≈ -0.0138

Average velocity = Δs / Δt = -0.0138 / (1.001 - 1) = -0.0138 m/s

(b) The instantaneous velocity at t=1 is given by the derivative of the height function with respect to time, which is:

dy/dt = 20 - 3.74t

So the instantaneous velocity at t=1 is:

dy/dt(1) = 20 - 3.74(1) = 16.26 m/s (approximately)

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The answer is 10.67 ft. The distance, x, from Player 1 to wall is 10.67 ft.

Given, Two different triangles for player 1 and player 2.

Both triangles have right angle and same angle where they are connected. So other angle is also same. All angles are same so they are similar triangles. smaller triangle is similar to larger triangle.

The distance x in the figure is required.

The required distance is x = 10.65 ft

The given triangles ABC and CDE are similar by Angle.

∠B = ∠D = 90°

∠ACB =∠ECD

The ratio of the sides is:

[tex]\frac{BC}{CD} = \frac{12}{9} = \frac{4}{3}[/tex]

So,

[tex]\frac{AB}{ED} =\frac{4}{3}[/tex]

x/8 = 4/3

x = 4/3 * 8

x = 10.65 ft

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Answer:

B

Step-by-step explanation:

The entry "cash 700000" is listed as a credit in the T account because it represents an increase in the cash balance of the account. In accounting, credits are used to record increases in asset accounts, such as cash. When cash is received, it is recorded as a credit to the cash account, which increases the balance of the account. Therefore, in this case, the entry "cash 700000" is a credit entry because it represents an increase in the cash balance.

135 and 59 are the values of fog(5) and gof(5) respectively.

Composite functions are also known as function of a function. Given the functions below;

f(x) = x^2 + 6x

g(x) = x + 4

For fog(5)

fog(5) = f(g(5))

f(g(x)) = f(x +4)

f(g(x)) = (x+4)^2 + 6(x+4)

f(g(5)) = (9)^2 + 6(9)

f(g(5)) = 81. + 54 = 135

For gof(5))

g(f(x)) = g(x^2 + 6x)

g(f(x)) = x^2 + 6x + 4

g(f(5)) = 5^2 + 6(5) + 4

g(f(5)) = 59

Hence the value of the composite values fog(5) and gof(5) area 135 and 59

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A linear equation indicating the number of grades students will receive in Mr. Perez's class is as follows;

Slope: 2.

Y-Intercept: 7.

Equation: y = 2x + 7.

In Mathematics, the slope-intercept form of a line can be calculated by using this mathematical expression:

y = mx + b

Where:

From the information provided above, we have the following slope and y-intercept on the line:

Y-intercept = 7

Slope, m = 2

Therefore, the required equation of line is given by:

y = mx + c

y = 2x + 7

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Answer:

see below

Step-by-step explanation:

g(t) = 5t² - 3t+ 6

g(2) = 5*4 - 3*2 + 6  =20

g(-1) = 5*1 -3* (-1) +6 =5+3+6 = 14

g(t+2) = 5(t+2)² - 3(t+2) + 6

= 5*(t²+4t+4) - 3t -6+6

= 5t²+20t+20-3t

= 5t²+17t+20

Answer:

1/7

Step-by-step explanation:

Absolute value is the distance from zero. 7 and -1/7 and their distance from zero is not the same, but the distance from zero with the numbers -1/7 and 1/7 are the same. The absolute value, the distance from zero, is both 1/7.

The first mechanic worked for 5 hours and the second mechanic worked for 15 hours.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two mechanics worked on a car.

The first mechanic charged $55 per hour,

and the second mechanic charged $65 per hour.

The mechanics worked for a combined total of 20 hours,

and together they charged a total of $1250.

Let x be the number of working hours of the First mechanic and y be the

number of working hours of the second mechanic.

So

x + y = 20  {equation 1}

55x + 65y = 1250 {equation 2}

Substituting the value of y from the equation 1 to the equation 2,

55x + 65(20 - x) = 1250

55x + 1300 - 65x = 1250

-10x = -50

x = 5

And y = 15

Therefore, x = 5 and y = 15.

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The equation of line is y = -2x + 9

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 7 )

The slope of the line is m = -2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = -2 ( x - 1 )

y - 7 = -2x + 2

Adding 7 on both sides of the equation , we get

y = -2x + 9

Hence , the equation of line is y = -2x + 9

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The surface area of rectangular prism above is 2738 in².

At the picture above is a rectangular prism with the sides 29 in, 36 in and 5 in.

The question is want to know The are

The surface area of a rectangular prism is given by this formula: 

A = 2 (lh +wh + lw )

Substitute the sides of the shapes to the formula

A = 2 (lh +wh + lw )

A= 2( 36.5 + 29.5 + 36.29)

A= 2(180+145+1044)

A= 2(1369)

A=2738 in²

Therefore the surface area is 2738 in².

A right-angle prism is a three-dimensional shape with six faces, where all faces of the prism (top, bottom, and sides) are rectangular and all pairs of opposing faces are congruent. Like all three-dimensional shapes, right-angled prisms have a volume and a surface area. A right angle prism is also called a cuboid 

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