Find the present value of $25,000 due 20 years later at 7.8%, compounded continuously.
A) $5253.4
B) $118,970.53
C) $4990.73
D) $44,642.86

Answer:

90 in^2

Step-by-step explanation:

Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)

Calculating the proportion:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)

Calculating the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)

Simplifying the equation:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

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Answer:

reflection

Step-by-step explanation:

the y values of the points are being multiplied by -1 (aka switching signs) which means that the triangle/points are being reflected by the x-axis

Answer:

This is a reflection across the x-axis.

Answer: Not necessarily. Dividing the pie chart into 5 equal sections might be a way to display categorical data if the number of categories is 5. However, dividing it into 5 sections might not be the best way to display the data if the number of categories is different than 5 or if any category has a significantly higher or lower proportion than the others. In this case, it may be more appropriate to use a different scale to display the correct ratio. It is important to consider data distribution and visualization clarity before choosing how to display categorical data.

The constant of proportionality is 12

The slope of the graph is equivalent to the constant of proportionality

The formula for calculating the slope is given as:

\(m =\frac{y_2-y_1}{x_2-x_1}\)

Using the coordinate points (5, 60) and (3, 36)

Substitute the given parameters into the equation:

\(m =\frac{36-60}{3-5}\\m =\frac{24}{2}\\ m = 12\)

Hence the constant of proportionality is 12

Learn more on slopes here; https://brainly.com/question/3493733

Answer:

It would cost $21.84

Step-by-step explanation:

Becasue you first figure out how much one book mark cost and one costs 0.78. Then you just multiply 0.78 by 28(total amount of classmates.) Hope that helps:)

I will assume that Curtis charge $3.70 per mile

so

Let

y -----> the total charge

x -----> the number of miles

we have that

Audrey's equation

y=ax+4

where a is the amount that Audrey charge per mile

Curtis equation

y=3,70x

we know that

For a distance of 30 miles the charge is the same in both equations

so

ax+4=3.70x

For x=30

30a+4=3.70(30)

Solve for a

30a+4=111

30a=111-4

30a=107

a=3.57

that means -----> Audrey charge $3.57 per mile

Given:

Solve the equation,

Answer: option c)

Answer:

B- The dependent variable is the amount of money she earns, and the independent variable is the number of hours she works.

Step-by-step explanation:

The amount of money she earns depends on how many hours she works, making that the dependant variable.

Answer:

4

Step-by-step explanation:

2/3 • 6

*Multiply 2 and 6 by 3.

= (2 × 6) / 3

= 12/3

*12 divided by 3 is equal to 4.

= 4

___________

hope it helps!

Answer:

125y3

Step-by-step explanation:

12x5=y

y3/2 = y26 - 5 =y

Answer:

D should be right

Step-by-step explanation:

Answer:

3.75 feet

Step-by-step explanation:

The length of the frame is 3 times the width.

Let the width be x.

The length will be 3x.

Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.

The perimeter of a rectangle is:

P = 2(L + W)

=> 10 = 2(3x + x)

=> 10/2 = 4x

5 = 4x

=> x = 5/4 = 1.25 feet

The width is 1.25 feet. The length is therefore:

1.25 * 3 = 3.75 feet

Answer:

C. (2×43) - (2×p)

Step-by-step explanation:

The question is 2(43-p)

Which means 2 is multiplying the bracket.

So the answer to the question is 2×43 - 2×p

Which will give us 86 - 2p

So you then solve all the possible answers to see if it the same answer as the one we got

Answer:

Step-by-step explanation:

step 1:

determining the values for standard form for the equation of a line,

y = mx + c

Step 2:

calculation of m, where m is the gradient or slope which determines how steep the line is.

step 3:

calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept

Answer

answer is 19

Step-by-step explanation:

hope it's help

Answer:

its either 18.92

or 25.58%

but I believe it is 18.92 I may be wrong though

Hello!

miles driven = x

the initial cost = 29

f(x) = 29 + 0.35x

Answer:

Step-by-step explanation:

A transformation that changes the orientation of a figure but not the orientation of the vertices is called a "reflection."

A reflection is a transformation that flips a figure over a line, called the "line of reflection." The line of reflection can be a line on a coordinate plane, or it can be a line in the space of the figure. The transformed figure, or the image, is a mirror image of the original figure, with respect to the line of reflection. The line of reflection is the perpendicular bisector of the line connecting any two non-adjacent vertices of the figure, then the figure's orientation remains unchanged but it's flipped over that line.

For example, if you reflect a square over its diagonal line, the square will be flipped but its vertices will still be in the same order, so the orientation won't change.

Answer:

v = 196.25

Step-by-step explanation:

v = 3.14*r^2*h

v = 3.14*5^2*2.5

v = 196.25

Answer:

Dylan is 10 years old, and Genesis is 11.

Step-by-step explanation:

If Genesis and Dylan's age are consecutive integers, and Genesis is older, we can represent their ages as:

Dylan's age: x

Genesis' age: x+1

This would mean Genesis is a year older than Dylan.

The product of their ages is 110.

We can write an equation:

x×(x+1)=110

x²+x=110 (Distribute x)

x²+x-110=0 (Move 110 to the other side)

You can solve this by the quadratic equation, by factoring or by completing the square

I'll solve it by the quadratic equation:

We must first find the coefficients a, b and c, and then plug it into the formula.

\(x = \frac{ - 1 + - \sqrt{ {1}^{2} - 4 \times 1 \times - 110} }{2 \times 1} \\ x = \frac{ - 1 + - \sqrt{1 + 440} }{2} \\ x = \frac{ - 1 + - 21}{2} \)

Since we have a ± symbol, we get 2 real solutions, x1 and x2.

x=-1±21/2

x1=-1+21/2

x1=20/2

x1=10

x2=-1-21/2

x2=-22/2

x2=-11

Since their age can't be negative, x2 can't be a solution, so Dylan's age must be 10, and Genesis' age must be 11.

Hope this helps, and let me know if you need help with another method to solve this problem!

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

9514 1404 393

Answer:

  C.  graph Y

Step-by-step explanation:

Starting with f(r) = -3r +3, the inverse function can be found from ...

  r = f(y)

  r = -3y +3

  r -3 = -3y

  (r -3)/-3 = y

  y = -1/3r +1

The inverse function will have a slightly negative slope and a y-intercept of 1. This matches graph Y.

Answer:

There are four (4) different terms

Step-by-step explanation:

Given;

2x + 3xy - (x + y) + 2

The terms are simplified as follows;

=2x + 3xy - (x + y) + 2

= 2x + 3xy - x - y + 2

collect like terms;

= 2x - x  - y + 3xy + 2

= x - y + 3xy  + 2

Thus, there are four (4) different terms in the simplified expression.

Answer:

$58.80

Step-by-step explanation:

The subtotal is $56.

56*1.05=$58.80.

Answer:

7

Step-by-step explanation:

the difference is another way of saying subtraction so the subtraction of 9 and 2 which is obviously 7

The algebraic expression for the sentence in this problem is given as follows:

n - (x + 8).

The sentence in this problem is given as follows:

"A number n minus the sum of the number and eight".

The sum of an unknown number x and eight is given as follows:

x + 8.

The subtraction of the number n by the expression is given as follows:

n - (x + 8).

More can be learned about algebraic expressions at https://brainly.com/question/4344214

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Answer:

26 degrees :)

Step-by-step explanation: