An initial amount of $3500 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals aremade, find the amount in the account after two years.Do not round any intermediate computations, and round your answer to the nearest cent.

To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be

In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be

The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that

So, applying this to the standard equation we get

So our equation becomes

Operating on the left side, we have

By subtracting 100 on both sides, we get

which the general form of the equation of the given circle.

Using a graphing tool, we have that the circle's graph would be

Answer:

Step-by-step explanation:

Dimensions of the framed photograph are:

Area of the framed photograph is:

Given that a sugar sweet company costs to transport its sugar, 7500 to rent truck and additional 225 for each ton.

Answer:

125

Step-by-step explanation:180=180-(2x+45)+x+80

2x-x=80+45

x=125

given that Colton gym charges initial fee of $40

there is an addiontional fee of $50

C is the cost of joining the gym

m is the number of months

so the equation that can show the cost of joining the gym in m month is:

$40 which is the initial feel been added to $50 the additional charge multiply by m the number of months.

therefore the equation is:

C = 40 + 50m

so the correct option is B

You have the following expression:

"the sum of five squared and five"

the previous statement, in a mathematical form is:

5² + 5

It is important to point out that you have "the sum" of two numbers, which numbers? five squared and five.

The simplified form is:

5² + 5 = 25 + 5 = 30

Every number raised to the power of zero is equal to one.

The final expression is -2

To solve this problem we will need a system of equations.

Step 1. Find the first equation.

Using the statement "Emma rented a bike for 4 hours and paid £18", we will call the cost per hour h, and the flat fee f. Thus, the first equation is:

This is because Emma rented the bike for 4 hours but she had to pay a flat fee f, and the total was £18.

Step 2. Find the second equation.

We do the same but now with the statement "Louise rented a bike for 7 hours and paid £25.5". Remember that for our equation, h represents the cost per hour and f the flat fee. The second equation is:

Step 3. In summary, our system of equations is:

Step 4. To solve part a. we have to find the cost per hour "h".

To find it, we use the elimination method in our system of equations, which consists of adding or subtracting the equations in order to eliminate one variable.

Since we are interested in finding "h", we can subtract the second equation from the first one, and we get the following:

Applying the subtraction:

And we start subtracting 7h-4h, which results in 3h:

The next subtraction is f-f, which results in 0.

And then, subtract 25.5-18:

The equation we have as a result is:

Which is an equation we can use to solve for the cost per hour h.

Dividing both sides by 3:

The cost per hour is £2.5

Step 5. To find part b we need to find the rental feed, in our case, this means to find "h".

Using the first equation of the system:

And substituting the previous result:

We get:

Solving the operations:

And solving for f:

the flat fee is £8.

Step 6. To find part c, we consider the cost per hour and the flat fee.

Michael rented the bike for 2 hours.

Since the cost per hour is £2.5, and the flat fee is £8, he will pay:

Solving these operations:

It will cost £13.

Answer:

a. £2.5

b. £8

c. £13

The right triangle formed is shown below

From the diagram,

x represents the side of the square. Recall that a square has equal sides

To find x, we would apply the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

From the diagram,

hypotenuse = 16

one leg = other leg = x

By substituting these values into the formula,

16^2 = x^2 + x^2

16^2 = 2x^2

256 = 2x^2

Dividing both sides by 2,

2x^2/2 = 256/2

x^2 = 128

Taking square root of both sides, we have

The correct option is 8√2 in

y = 0.34x - 0.9 (Option A)

We are given the data and we want to find the line of best fit.

The line of best fit is a line that goes through the data points and it gives the best representation of the spread of the data.

The equation of a line is given as:

y = mx + c

y represents y-values

x represents x-values

m is the slope of the line

c is the y-intercept of the line or where the line crosses the y-axis.

To get this equation for this question, we need to find both m and c.

In order to do this, the formulas are given below:

While for c or the y-intercept, we have:

Before we can calculate m and c, we need to calculate the means of both x and y values give to us.

This is done below:

Now we can proceed to get the slope m of our line.

In order to be tidy, we shall use a table to solve. This table is shown in the image below:

Thus, we can now calculate our slope m:

Therefore the slope (m) = 0.34

Now to calculate intercept (c)

Therefore, the intercept (c) = - 0.9

Bringing it all together, we can write the equation of the line as:

y = 0.34x - 0.9

Therefore the answer is: y = 0.34x - 0.9 (Option A)

0.3821,  0.8745

========================================================

Work Shown:

pi/2 = 3.14/2 = 1.57 approximately

The solutions for t must be in the interval 0 ≤ t ≤ 1.57

[tex]3\cos(5t)+3 = 2\\\\3\cos(5t) = 2-3\\\\3\cos(5t) = -1\\\\\cos(5t) = -1/3\\\\5t = \cos^{-1}(-1/3)\\\\5t \approx 1.9106+2\pi n \ \text{ or } \ 5t \approx -1.9106+2\pi n\\\\t \approx \frac{1.9106+2\pi n}{5} \ \text{ or } \ t \approx \frac{-1.9106+2\pi n}{5}\\\\[/tex]

where n is an integer.

Let

[tex]P = \frac{1.9106+2\pi n}{5}\\\\Q = \frac{-1.9106+2\pi n}{5}\\\\[/tex]

Then let's generate a small table of values like so

[tex]\begin{array}{|c|c|c|} \cline{1-3}n & P & Q\\\cline{1-3}-1 & -0.8745 & -1.6388\\\cline{1-3}0 & **0.3821** & -0.3821\\\cline{1-3}1 & 1.6388 & **0.8745**\\\cline{1-3}2 & 2.8954 & 2.1312\\\cline{1-3}\end{array}[/tex]

The terms with surrounding double stars represent items in the interval 0 ≤ t ≤ 1.57

Therefore, we end up with the solutions 0.3821 and 0.8745 both of which are approximate.

You can use a graphing tool like Desmos or GeoGebra to verify the solutions. Be sure to restrict the domain to 0 ≤ t ≤ 1.57

Answer:

[tex]\textsf{c)} \quad 0.3821, \; 0.8745[/tex]

Step-by-step explanation:

Given equation:

[tex]3 \cos (5t)+3=2, \quad \quad 0\leq t\leq \dfrac{\pi}{2}[/tex]

Rearrange the equation to isolate cos(5t):

[tex]\begin{aligned}\implies 3 \cos(5t)+3&=2\\3 \cos(5t)&=-1\\\cos(5t)&=-\dfrac{1}{3}\end{aligned}[/tex]

Take the inverse cosine of both sides:

[tex]\implies 5t=\cos^{-1}\left(-\dfrac{1}{3}\right)[/tex]

[tex]\implies 5t=1.91063..., -1.91063...[/tex]

As the cosine graph repeats every 2π radians, add 2πn to the answers:

[tex]\implies 5t=1.91063...+2\pi n, -1.91063...+2 \pi n[/tex]

Divide both sides by 5:

[tex]\implies t=0.38212...+\dfrac{2}{5}\pi n,\;\; -0.38212...+\dfrac{2}{5} \pi n[/tex]

The given interval is:

[tex]0\leq t\leq \dfrac{\pi}{2}\implies0\leq t\leq 1.57079...[/tex]

Therefore, the solutions to the equation in the given interval are:

[tex]\implies t=0.3821, \; 0.8745[/tex]

The general formula for a quadratic equation is ax² + bx + c = 0.

To solve

You can follow the steps.

Step 01: Write the equation in the general formula.

To do it, add 3 to each side of the equation.

Step 02: Use the Bhaskara formula to find the roots.

The Bhaskara formula is:

In this question,

a = 2

b = 6

c = 2

So, substituting the values:

Answer:

Exact form:

Decimal form:

The complementary angles are angles in which the sum of them is equal to 90º

So: 90º-10º=80º

So, the complementary angle is 80º

The number of pennies they lose altogether is 288 pennies.

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they loose can be calculated as follows;

Therefore, they lost 96 + 192 = 288 pennies altogether.

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To solve the equation system by substitution, since the equations are expressed in terms of y, you have to equal both expressions and calculate the value of x:

To calculate the value of x, the first step is to pass the x-term to the left side of the equation by applying the opposite operation:

Next, pass 5 to the right side of the equation:

Finally, divide both sides by 6 to reach the value of x

Now that we have determined the value of x, replace it in either one of the original equations to determine the value of y:

The solution for this equation system is (2,1)

Solution

Step 1:

In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣. Cards of Spades and clubs are black cards. Cards of hearts and diamonds are red cards. The card in each suit, are ace, king, queen, jack , 10, 9, 8, 7, 6, 5, 4, 3 and 2.

Step 2:

Total possible outcomes = 52

Total number of jacks = 4

Total number of red cards = 26

Step 3:

The probability of selecting Jack or a red card

Final answer

For the given polynomial the roots can't have multiplicity, and the polynomial is:

p(x) = (x - 2)*(x - 3)*(x - 5).

Here we know that we have a cubic polynomial (of degree 3) with the following zeros:

2, 3, and 5.

Can any of the roots have multiplicity?

No, because a cubic polynomial can have at maximum 3 zeroes, and here we already have 3.

Now let's get the polynomial

Remember that a cubic polynomial with zeros a, b, and c can be written as:

p(x) = (x - a)*(x - b)*(x - c)

Then the polynomial in this case is:

p(x) = (x - 2)*(x - 3)*(x - 5).

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She has already 500

x hours woked

pund we got:

7.50 x >= 900

And inequality could be

fx:o

because we need to gain 1400 or more

hours in order to have enough money to buy the computer

Sara needs to work at least 52 00/17.5

x >= 5r t o

The equatu

1

And then we can solve for x a

500+17.5x>>= 1400

utioen x

For this50 case we can do this:

500+ 17.

The average number of persons admitted in one year is X/5.

What is average number?

Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined.

If X persons are admitted in last 5 years in a hospital.

Then we get the average value of admitted persons are X/5 per year.

If Y persons are recovered in last 5 years in a hospital.

Then we get the average value of recovered persons are Y/5 per year.

Therefore, the average number of persons admitted in one year is X/5.

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Give the radius of a circle, r, we can find its area by using:

In the picture, the 30 ft segment passes from on side of the circle to the other passing thourhg tht center, so it is the diameter. The radius is half the diameter, so:

Now, we can use the formula for the area to find it:

So, the area is approximately 706.9 ft².

Answer: Should Clare's or the doctor's measurement be considered the actual height? In this scenario I believe its the doctors measurements. This is because she could have used a measuring tape and had someone measure her height. The measuring tape may not be accurate due to how it would be used to measure her height. So the doctor's should because they don't measure you, they use a measuring tape/ stick that is attached to the wall. That is why I think the doctor's is the actual height.

(I used RACE format)

SOLUTION:

Step 1:

In question 12, we are meant to find the line of reflection for Triangle ABC and its image based on the diagram:

Step 2:

The line of reflection for Triangle ABC and its image is:

Given the word problem, we can deduce the following information:

1. A set of four numbers that begins with the number 32 is arranged from

smallest to largest.

2. The median is 35.

To determine the possible set of numbers of which the median is 35, we first note that median is the number separating the other half of the ordered data sample from the lower half.

Now, we check the median of each choices:

For a) 32, 32, 36, 38:

For b) 32, 35, 38, 41:

For c) 32, 34, 36, 39

For d) 32, 36, 40, 44​:

Therefore, the answer is: c) 32, 34, 36, 39

Given:

Distance of top of ladder to the ground = 10 ft

Distance of bottom of ladder from the side of the house = 9 ft

Let's find the length of the ladder.

Since the ladder forms a right triangle with the house, to find the length of the ladder apply Pythagorean Theorem.

Where:

a = 10 ft

b = 9 ft

c = length of ladder

Thus, we have:

Take the square root of both sides:

Therefore, the length of the ladder rounded to the nearest tenth is 13.5 ft

ANSWER:

13.5 ft

EXPLANATION

The value of the number in the hundreths place is 0.07

Two lines are parallel if they do not intersect at any point.

Another way of thinking on parallel lines is: two lines are parallel if they have the same slope.

On the other hand, all horizontal lines have the same slope, which is equal to 0.

Since all horizontal lines have a slope equal to 0, this means that all horizontal lines are parallel.

Therefore, the answer is: yes. All horizontal lines are parallel.

Notice: This is only valid in 2D.

Slope formula:

Replacing:

since x is constant , it is a vertical line, with an undefined slope.