The value of Kayla's investment can be modeled by the equation y=2650(1.05)x where x is the number of years invested and y is the value in dollars. What will be the value of the investment after 25 years? Round your answer to the nearest dollar.

The surface area of the triangular prism is 93 squared feet.

The surface area of triangular prism is expressed as;

S.A = bh + ( s₁ + s₂ + s₃ )H

From the diagram;

We substitute our given values into the equation above.

S.A = bh + ( s₁ + s₂ + s₃ )H

S.A = (3ft × 2ft) + ( 3ft + 3ft + 3ft )10ft

S.A = 3ft² + ( 9ft )10ft

S.A = 3ft² + 90ft²

S.A = 93ft²

The surface area of the triangular prism is 93 squared feet.

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The least-squares regression line equation is y = -0.28x + 610.31

To plot the scatter plot of the data, we represent the x-axis with year and we represent the y-axis with time

Next, we plot the scatter plot using the dataset

See attachment for the scatter plot

From the attached scatter plot, we can see that the relationship between the variables in the graph is approximately linear.

This is so because the points appear to be on a straight line

To do this, we make use of a graphing calculator, with the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -2806.684 / √((10062.545)(842.83)) = -0.9638

Hence, the correlation coefficient is -0.9638

To do this, we make use of a graphing calculator, with the following summary:

The least-squares regression line equation is

y = bx + a

Where

b = SP/SSX = -2806.68/10062.55 = -0.27892

a = MY - bMX = 62.4 - (-0.28*1964.36) = 610.30872

So, we have

y = -0.27892x + 610.30872

Approximate

y = -0.28x + 610.31

Hence, the least-squares regression line equation is y = -0.28x + 610.31

We have:

y = -0.28x + 610.31

Substitute 1924 and 1976 for x

y = -0.28 * 1924 + 610.31 = 71.59

y = -0.28 * 1976 + 610.31 = 57.03

Are these estimates reliable?

Yes, the estimates are reliable

Are they reasonable?

Yes, the estimates are reasonable

The results are different because the answers in 5 are estimated from the formula while the table are the actual values

We have:

y = -0.28x + 610.31

Substitute 2022 and 2200 for x

y = -0.28 * 2022 + 610.31 = 44.15

y = -0.28 * 2200 + 610.31 = -5.69

Are these estimates reliable?

No, the estimates are not reliable

Are they reasonable?

The estimate in 2022 is reasonable, while the estimate in 2200 is not reasonable

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The equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds is y(t) = 14sin(πt/8) + 1

Since the motion of the ferris wheel is periodic,it follows a sinusoidal function form.

So, the general form of a sine function y(t) is

y(t) = Asin(2πt/T) + K where

Now since radius of 7m, the maximum value from its lowest point is at y = 2r + 1 = 2 × 7 + 1 = 14 + 1 = 15 at sin(2πt/T) = 1 which is the maximum value for sinФ = 1.

Since the bottom of the wheel is 1m above the ground, its minimum value is y = 1 at t = 0.

Also, it rotates once every 16 seconds, so its period T = 16 s.

So, y(t) = Asin(2πt/T) + K

y(t) = Asin(2πt/16) + K

y(t) = Asin(πt/8) + K

At maximum value

15 = Asin(πt/8) + K

15 = A + K  (1)

At minimum value

1 = Asin(πt/8) + K

1 = A(0) + K  

1 = 0 + K

K = 1

Substituting K into (1), we have

15 = A + 1

15 - 1 = A

14 = A

A = 14

So, y(t) = Asin(πt/8) + K

y(t) = 14sin(πt/8) + 1

So, the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel is y(t) = 14sin(πt/8) + 1

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Answer:

[tex]\frac{16}{32}[/tex]

Step-by-step explanation:

given

[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )

= [tex]\frac{16}{32}[/tex]

Answer: The initial population is 18 and 1 year(t=1) later it is 38

Step-by-step explanation:

38 = 18 * e^(1*k), where k is the growth rate

e^(1*k) = 38/18

Take the natural log(ln) of both sides of the = k = ln(38/18) = 0.747

P(t) = 18 * e^(0.747*t), where P(t) is the population affected at time t(years since 1996)

The length of the line segment SR is 15 units.

In Δ SRQ as seen in the attached image, we see that;

∠SRQ is a right angle

SQ is the hypotenuse

RT ⊥ SQ

Thus, by triangular rules, we know that;

(RQ)² = TQ × SQ

RQ = 20 units and TQ = 16 units

Thus;

(20)² = 16 × SQ

400 = 16 × SQ

SQ = 400/16

SQ = 25 units

By using Pythagoras theorem in Δ SRQ, we have;

(SR)² + (RQ)² = (SQ)²

RQ = 20 units and SQ = 25 units

Thus;

(SR)² + (20)² = (25)²

(SR)² + 400 = 625

(SR)² = 225

SR = √225

SR = 15 units

The length of the line segment SR is 15 units.

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The formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

The growth constant k can be defined as the frequency or also known as the number of times per unit time of growing by a factor

it is also called the logarithmic return, compounded return, or the force of interest.

Note that the general formula for growth rate is given as;

[tex]P(t) = P0 e^k^t[/tex]

Where,

Po =  Initial value = 400 squirrels

r = Rate of growth

k = constant of proportionality = 0. 5 per year

t = time = 1 year

The function P(t) is given as;

P(t) = 400 e^0.5t

Note that the formula for doubling time is given as;

[tex]TD = t \frac{In 2}{In 1 + r/ 100}[/tex]

r = 4

t = 1

substitute into the formula

[tex]TD = 1 \frac{0. 693}{0. 0392}[/tex]

Doubling time  = 1 × 17. 68

Doubling time = 17. 68 years

Thus, the formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

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Using it's concept, a radical equation is given as follows:

[tex]\sqrt{x} + 3 = 13[/tex].

A radical equation is an equation in which the variable is inside the radical.

Hence, among the equations given, the radical equation is:

[tex]\sqrt{x} + 3 = 13[/tex].

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Answer:

C

Step-by-step explanation:

took edge test and got 100

The distance between the guy and the wire attached is 14.42m

The square of the longest side is equal to the sum of the square of other two sides.

In order to determine the length of base of the tower, we will use the expression below:

b² = 28² - 24²

b² = 208

b = 14.42

Hence the distance between the guy and the wire attached is 14.42m

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The percentage of the can that is not occupied by tennis​ balls is 33.33%.

Given:

Radius of cylinder=3.4cm

First step

Height of cylinder=3.4×2×6

Height of cylinder=40.8 cm

Second step

Volume of cylinder=(3.4)^2×40.8

Volume of cylinder=471.648

Volume of tennis=6×4/3×(3.4)^3

Volume of tennis=314.432

Third step

Percentage=471.648-314.432/471.648×100

Percentage=33.33%

Therefore the percentage of the can that is not occupied by tennis​ balls is 33.33%.

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X= root 6^2 + 10^2

X=2 root 34

So, x is 11.66 to 2d.p

(root means square root)

Hope this helps!

Answer:

x = 11.66

Step-by-step explanation:

Hello!

We can use the Pythagorean theorem to solve for the hypotenuse.

Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]

Plug the values of 6 and 10 into the formula to solve.

The hypotenuse is approximately 11.66.

Answer:

D

Step-by-step explanation:

To answer the question, we need to convert cups to pints, now here is a way to remember the gallon, quarts, to pints, and to cups

In the Kingdom of Gallons (Write a big G on your paper)

Inside the G write 4 Qs

There were four Queens

Inside the Qs write 2 ps

Each Queen had to princess

In each princess write 2 Cs

And each princess has two Cats

Now we know that there is 2 Cups in each Pints so

since she sold 34 cups of juice in cups then we divide 34 by 2 to get

17 PINTS

Answer:

150 pints

Step-by-step explanation:

I believe you meant "By the end of the day, 3/4th of the quantity was sold."

Recall that 2 cups = 1 pint, so 400 cups = 200 pints, and

3/4 th of that would be 150 pints.

Answer:

2

Step-by-step explanation:

8/3 = 2 with a Remainder of 2

Answer:

y= 4x -4

Step-by-step explanation:

Slope-intercept form is given by y= mx +c, where m is the slope and c is the y-intercept.

Given that the slope is 4, m= 4.

Substitute the value of the slope into the equation:

y= 4x +c

The value of c can be found by substituting any point in which the line passes through into the equation above.

When x= 4, y= 12,

12= 4(4) +c

12= 16 +c

Subtract 16 from both sides:

c= 12 -16

c= -4

Thus, the equation of the line is y= 4x -4.

Additional:

For more questions on slope-intercept form, do check out the following!

Answer:

314402 steps

Step-by-step explanation:

10142 x 31

Answer:

200

Explanation:

126.8 x 100

126.8/63.4 = 200

Here, 12 is the mode.

Step-by-step explanation:

Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12) ?

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode.

So let's talk in brief:-

First, we arrange it in ascending order.

3,3,6,6,9,9,12,12,12,12

and now as we see that we get 12 as the most repeated ones.

reference link-

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Using the inverse functions property:

Two functions f(x) and f⁻¹(x) are inverses if:

f( f⁻¹(x) ) = x

f⁻¹(f(x)) = x

We want to get:

f⁻¹(f(93)) = m

By using the above definition we get:

f⁻¹(f(93)) = m = 93

Now for the second one we want:

f(7) = n

If you look at the table, you can see that f(x) contains the point (7, -6), then:

f(7) = n = -6

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The sample size required is mathematically given as

n=1454

Generally, the equation for Margin of error is  mathematically given as

[tex]M=Z_{\alpha/2} > \frac{\sigma}{\sqrt{n}}[/tex]

Therefore

[tex]M= 0.11 \leq \frac{ 2.33*1.8}{\sqrt{n}}\\\\\sqrt{n} \leq 38.127[/tex]

n=1453.69.

In conclusion, The sample size required is mathematically given as

n=1454

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The angle which is coterminal with -60 between 0 and 360 is; 300°.

Since, it follows that the representation of the angle -60 corresponds to 60° span in the clockwise direction.

Therefore, by going the conventional anticlockwise direction, the angle which is coterminal with -60 is; 300°.

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Answer:

48 Square feet

Step-by-step explanation:

A=((a+b)/2)*h,

((6.3+9.7)/2)*6=48ft^2

If the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.

Given sample mean of 51, sample size of 21, sample standard deviation be 15 and confidence level be 95%.

We are required to find the upper bound and lower bound.

We have to use t test as the sample size is less than 30.

Margin of error is the difference between calculated figures and real figures.

Margin of error= standard deviation* critical value of t

Critical value of t at 0.05 significance level with degree of freedom 20   [21-1] is 1.7247.

Margin of error=1.7247*15/4.5826

(4.5826 is the square root of 21)

=5.6454

Upper bound=51+5.6454

=56.6454

Lower bound=51-5.6454

=45.3546

After rounding off they will be 56.65 and 45.35.

Hence if the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.

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Answer:

x = 70

Step-by-step explanation:

x and 2x - 30 are supplementary angles , sum to 180° , then

x + 2x - 30 = 180 ( add 30 to both sides )

3x = 210 ( divide both sides by 3 )

x = 70

Answer:

2x - 30 and x degrees should add up to 180 degrees

2x - 30 + x = 180

3x = 210

x = 70 degrees

The correct answer would be D

The correct order of reasons that complete the proof about the rectangle and square is that D. definition of congruence, distance formula if two consecutive sides of a rectangle are congruent, then it's a square.

It should be noted that congruence simply means an agreement or a correspondence between shapes.

In geoemtry, it should be noted that figures are said to be congruent if it is possible to superpose one of them on another.

It should be noted that the opposite sides of a rectangle are parallel while in a square, all the sides that are given are equal.

Therefore, the correct order of reasons that complete the proof about the rectangle and square is the definition of congruence, and that if two consecutive sides of a rectangle are congruent, then it's a square.

In conclusion, the correct option is D.

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Answer:

C,D

Step-by-step explanation:

C: Range refers to the y axis and all values shown on this graph (and even beyond the graph) are greater than 0

D: The domain refers to the x-axis. The line goes on forever both to the right and the left therefore meaning all x values are used.

Answer:

18/19= X/37 because 18 and x are both between 72 and 45 degrees

Multiply 18 and 37 then divide by 19 to get answer

Step-by-step explanation:

Hi! ◈

Answer:

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1/4 of the cake was left

Step-by-step explanation:

  Since the total cake is [tex]\sf{\dfrac{4}{4}}[/tex], all we should do is subtract 3 from 4

  [tex]\sf{\dfrac{4-3}{4}}=the \ cake \ that \ was \ left[/tex]

   _____________________

   [tex]\sf{\dfrac{1}{4} \ of \ the \ cake \ was \ left}[/tex]

Hope this made sense to you !!

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