Tom invests $200 into a bank account that yields 3.75 percent interest compounded daily. What will his exact account balance be after 2 years?

Answer:

Well if you still need the answer around 4 years later LOL its √32

Step-by-step explanation:

Answer:

√32

Step-by-step explanation:

Because this is totally helpful 4 years later

The rule for the given sequence (0.5, 0.25, 0, -0.25) is to subtract 0.25 from the previous term. Each consecutive term decreases by 0.25 to form the sequence.

The sequence given is 0.5, 0.25, 0, -0.25. To find the rule of this sequence, look at the differences between terms. Each term is subtracted by 0.25 to get to the next term.

Step-by-Step Explanation:

Therefore, the rule for this sequence is subtracting 0.25 from the previous term to obtain the next term in the sequence.

when you have 2 negative numbers you actually add the 2nd number to the first one

 example:

-4 - -2 =  becomes -4 + 2 = -2

Answer:

y = sin(4x) + 3

Step-by-step explanation:

y = Asin(Bx + C) + D

A is amplitude = 1

B = 2pi/period = 2pi / (pi/2) = 4

C does not mention.

D: shift up or down = 3

=> y = sin(4x) + 3

i = [tex]p(0) = \frac {3} {8} x \frac {2} {7} = \frac {3} {28} ; p (1) = \frac {3} {8} x \frac {5} {7} + \frac {5} {8} x \frac {3} {7} = \frac {15} {28}; p (2) = \frac {5} {8} x \frac {4} {7} = \frac {5} {14} [/tex]

(a)  i. The probability mass function of X is 5 / 14

Hypergeometric Distribution is the probability distribution of a hypergeometric random variable.

The hypergeometric distribution is used to calculate the statistical importance of having drawn a specific k successes (out of n total draws) from the aforementioned population in the hypergeometric test uses.

ii. Please see attached image for the answer.

To find the probability distribution for x, consider the possible values of x and calculate the probability of each value. When 2 marbles are drawn without replacement, there are two possible outcomes. The probability distribution for x is P(x = 0) = 3/28, P(x = 1) = 15/56, and P(x = 2) = 5/14.

To find the probability distribution for x, we need to consider the possible values of x and calculate the probability of each value.

Since there are 5 white marbles and 3 black marbles in the urn, the total number of marbles is 8.

When 2 marbles are drawn without replacement, there are two possible outcomes: (1) both marbles are white and (2) one marble is white and one marble is black.

Let's calculate the probabilities:

P(x = 0) = P(both marbles are black) = (3/8) * (2/7) = 6/56 = 3/28

P(x = 1) = P(one marble is white and one marble is black) = (5/8) * (3/7) = 15/56

P(x = 2) = P(both marbles are white) = (5/8) * (4/7) = 20/56 = 5/14

Therefore, the probability distribution for x is:

P(x = 0) = 3/28

P(x = 1) = 15/56

P(x = 2) = 5/14

Final answer:

To find out the distance a bat will fly in 15 minutes at an average speed of 32 kilometers per hour, you multiply the speed by the time in hours (15 minutes is 0.25 hours). The bat will fly 8 kilometers.

Explanation:

To calculate how far a bat flies in 15 minutes at an average speed of 32 kilometers per hour, we need to convert the time into hours since the speed is given in kilometers per hour (km/h). 15 minutes is equal to 0.25 hours (since there are 60 minutes in 1 hour, so 15 minutes divided by 60 minutes per hour equals 0.25 hours).

We can then use the formula for distance which is:

Distance = Speed × Time

The average speed of the bat is 32 km/h, and the time is 0.25 hours.

Distance = 32 km/h × 0.25 h = 8 km

So, the bat will fly 8 kilometers in 15 minutes.

The value of x in equation 5x + 7 = 6x -1 is 8.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

5x + 7 and 6x -1

Now,

The equation is:

5x + 7 = 6x - 1

To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 5x from both sides and adding 1 to both sides. This gives us:

5x + 7 - 5x = 6x - 1 - 5x

7 + 1 = x - 1 + 1

8 = x

Therefore, by the given equations the answer will be x = 8.

Learn more about linear equations;

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The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.

Let's denote:

- [tex]\( x \)[/tex] as the length of one side of the square (in feet).

- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.

1. Area of the Square [tex](\( A_s \))[/tex]:

The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].

2. Area of the Circle [tex](\( A_c \))[/tex]:

The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:

[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]

Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]

The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].

Substituting the value of [tex]\( r \)[/tex], we get:

[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]

[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]

The dimensions of the rectangle are 10 meters and 6.5 meters

Let the width of the rectangle be represented by w.

The length of the rectangle will then be:

= 2w - 3

Area of the rectangle = 65m²

Note that length × width = Area

Therefore, w × (2w - 3) = 65

2w² - 3w = 65

2w² - 3w - 65 = 0

2w² - 13w + 10w - 65 = 0

2w(w - 6.5) + 10(w - 6.5) = 0

Therefore, w - 6.5 = 0

w = 0 + 6.5

w = 6.5

Width = 6.5 meters

Length = 2w - 3

Length = 2(6.5) - 3

Length = 13 - 3

Length = 10 meters.

The dimensions of the rectangle is 10 meters and 6.5 meters

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Answer:

.227

Step-by-step explanation:

Answer:

0.227

Step-by-step explanation:

Answer:

Im working on it right now and its 1

Step-by-step explanation:

Final answer:

Compound interest plays a crucial role in determining the final amount of an investment over time, showcasing the power of compounding. In this scenario, with an initial amount of $1,000, an interest rate of 10.1%, and 47 years of compounding annually, the total interest earned would be $91,045.80.

Explanation:

Compound interest is calculated on the principal amount plus the interest earned over time. In this case, with an initial amount of $1,000, an interest rate of 10.1% compounded annually, and an end amount of $92,045.80 after 47 years, compound interest plays a significant role in determining the final amount.

To calculate the total interest earned over the 47 years, you subtract the initial principal amount of $1,000 from the end amount of $92,045.80. This gives you the total interest earned. In this scenario, the total interest earned would be $92,045.80 - $1,000 = $91,045.80.

Compound interest is crucial in understanding how investments grow over time, and it showcases the power of compounding when money is invested wisely and for a long period.

To prove that a line is parallel to another, one usually shows that two lines cut by a transversal have either congruent corresponding angles or alternate interior angles. In the lack of perpendicular transversal or angle knowledge, projecting lines onto a new coordinate system can show matching slopes to confirm parallelism.

In mathematics, proving that a constructed line is parallel to a given line typically involves showing that the lines do not intersect and have the same slope or use a parallel postulate. The most common method is taking two lines l and m and a transversal t. If the corresponding angles or alternate interior angles created by t are congruent, then l and m are parallel.

For example: If line l and line m are cut by a transversal t and the corresponding angles (∠1 and ∠2) are congruent, then lines l and m are parallel. The same can be said if the alternate interior angles are congruent.

In some cases, if the transversal line is not perpendicular and we do not know about corresponding or alternate interior angles, we can establish a different coordinate system, project the lines onto the x-axis and y-axis, and show that they have the same slope which proves them to be parallel.

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Answer:

box 1- A=210+20(h-7) box 2- 17

Step-by-step explanation:

I got it right on plato, watch out for positive and negative answers i almost got it wrong

Answer: The speed of the plane with no wind is 440 miles per hour.

Step-by-step explanation:

Let the maximum speed of the plane be 'x'.

Let the maximum speed of the wind be 'y'.

Since we have given that an airplane travels 2400 miles against the wind in 6 hours.

As we know that

Downstream is given by

[tex]x+y=\dfrac{2400}{6}=400--------------(1)[/tex]

Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.

As we know tha t

Upstream is given by

[tex]x-y=\dfrac{2400}{5}=480-------------------(2)[/tex]

We just need to find the speed of the plane with no wind.

Using the elimination method,

[tex]x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440[/tex]

Hence, the speed of the plane with no wind is 440 miles per hour.