A person places $4080 in an investment account earning an annual rate of 5. 7%,

compounded continuously. Using the formula V = Pent, where Vis the value of the

account in t years, P is the principal initially invested, e is the base of a natural

logarithm, and r is the rate of interest, determine the amount of money, to the

nearest cent, in the account after 4 years.

(a)  The area between 415 pounds and the mean of 400 pounds is 0.4332 (approx).

(b) The area between the mean of 400 pounds and 395 pounds is 0.3085 (approx).

(c) The probability of selecting a value at random and discovering that it has a value of less than 395 pounds.

Given that:

Mean of a normal probability distribution, μ = 400 pounds

Standard deviation, σ = 10 pounds.

(a) We need to find the area between 415 pounds and the mean of 400 pounds. We can represent this area graphically using the following normal curve:

Normal Curve

We can observe that the required area is shaded in the above curve. Hence, we can use the standard normal distribution table to find the area between 0 and 1.5 z-scores as follows: z-score = (x - μ)/σ= (415 - 400)/10= 1.5From the standard normal distribution table, the area between 0 and 1.5 z-scores is 0.4332.

(b) We need to find the area between the mean of 400 pounds and 395 pounds. We can represent this area graphically using the following normal curve:

Normal Curve

We can observe that the required area is shaded in the above curve. Hence, we can use the standard normal distribution table to find the area between 0 and -0.5 z-scores as follows: z-score = (x - μ)/σ= (395 - 400)/10= -0.5

From the standard normal distribution table, the area between 0 and -0.5 z-scores is 0.3085.

(c) We need to find the probability of selecting a value at random and discovering that it has a value of less than 395 pounds. We can represent this probability graphically using the following normal curve:

Normal Curve

We can observe that the required probability is shaded in the above curve. Hence, we can use the standard normal distribution table to find the area between -∞ and -0.5 z-scores as follows: z-score = (x - μ)/σ= (395 - 400)/10= -0.5From the standard normal distribution table, the area between -∞ and -0.5 z-scores is 0.3085.

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Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:

\(\mu = 3500 \times 0.0004 = 1.4\)

The probability that 2 or fewer cars will be stolen is:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466\)

\(P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452\)

\(P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417\)

Then:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335\)

0.8335 = 83.35% probability that 2 or fewer will be stolen.

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The component of u along v is -17√2 / 5. To find the component of u along v, we can use the formula Component of u along v = (u · v) / |v| where u · v represents the dot product of u and v, and |v| represents the magnitude of v.

Given u = ⟨3, 0, 5⟩ and v = ⟨-3, 4, -5⟩, we can calculate their dot product:

u · v = (3 * -3) + (0 * 4) + (5 * -5) = -9 - 25 = -34

Next, we need to find the magnitude of v:

|v| = √((-3)^2 + 4^2 + (-5)^2) = √(9 + 16 + 25) = √50 = 5√2

Now, we can substitute these values into the formula to find the component of u along v:

Component of u along v = (-34) / (5√2)

To simplify, we can rationalize the denominator by multiplying both the numerator and denominator by √2:

Component of u along v = (-34√2) / (5√2 * √2)

                    = (-34√2) / (5 * 2)

                    = -17√2 / 5

Therefore, the component of u along v is -17√2 / 5.

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Notice that:

Simplifying the above fraction and putting it in decimal form, we get:

Answer:

\(x - 12 \\ coefficent = 1 \\ constant = - 12 \\ thnk \: you\)

Answer:

HB = 13

Step-by-step explanation:

In triangle GHJ, points A, B, C are mid points of the sides GH, HJ, GJ respectively.

Therefore by Mid-segment Theorem.

\(AC = \frac{1}{2} HJ \\ \\ 3y - 5 = \frac{1}{2} (4y + 2) \\ \\ 3y - 5 = \frac{1}{2} \times 2 (2y + 1) \\ \\ 3y - 5 = 2y + 1\\ \\ 3y - 2y = 5 + 1 \\ \\ y = 6 \\ \\ HJ = 4y + 2 \\ \\ HJ = 4 \times 6 + 2 \\ \\ HJ = 24 + 2 \\ \\ HJ = 26 \\ \\ HB= \frac{1}{2} HJ \\ \\ HB= \frac{1}{2} \times 26 \\ \\ \huge \red{ \boxed{ HB= 13}}\)

Step-by-step explanation:

1) To draw triangle ABC, we start by drawing a line segment BC of length 6 cm. Then we draw an angle of 40° at point B, and an angle of 60° at point C. We label the intersection of the two lines as point A. This gives us triangle ABC.

```

C

/ \

/ \

/ \

/ \

/ \

/ \

/ \

/_60° 40°\_

B A

```

2) To find the measure of angle BAC, we can use the fact that the angles in a triangle add up to 180°. Therefore, angle BAC = 180° - 40° - 60° = 80°.

3) To show that ABD is an isosceles triangle, we need to show that AB = AD. Let E be the point where the bisector of angle BAC intersects AB. Then, by the angle bisector theorem, we have:

AB/BE = AC/CE

Substituting the given values, we get:

AB/BE = AC/CE

AB/BE = 6/sin(40°)

AB = 6*sin(80°)/sin(40°)

Similarly, we can use the angle bisector theorem on triangle ACD to get:

AD/BD = AC/BC

AD/BD = 6/sin(60°)

AD = 6*sin(80°)/sin(60°)

Since AB and AD are both equal to 6*sin(80°)/sin(40°), we have shown that ABD is an isosceles triangle.

4) To show that MD is the perpendicular bisector of AB, we need to show that MD is perpendicular to AB and that MD bisects AB.

First, we can show that MD is perpendicular to AB by showing that triangle AMD is a right triangle with DM as its hypotenuse. Since M is the midpoint of AB, we have AM = MB. Also, since ABD is an isosceles triangle, we have AB = AD. Therefore, triangle AMD is isosceles, with AM = AD. Using the fact that the angles in a triangle add up to 180°, we get:

angle AMD = 180° - angle MAD - angle ADM

angle AMD = 180° - angle BAD/2 - angle ABD/2

angle AMD = 180° - 40°/2 - 80°/2

angle AMD = 90°

Therefore, we have shown that MD is perpendicular to AB.

Next, we can show that MD bisects AB by showing that AM = MB = MD. We have already shown that AM = MB. To show that AM = MD, we can use the fact that triangle AMD is isosceles to get:

AM = AD = 6*sin(80°)/sin(60°)

Therefore, we have shown that MD is the perpendicular bisector of AB.

5) Finally, to show that DM = DN, we can use the fact that triangle DNM is a right triangle with DM as its hypotenuse. Since DN is the orthogonal projection of D on AC, we have:

DN = DC*sin(60°) = 3

Using the fact that AD = 6*sin(80°)/sin(60°), we can find the length of AN:

AN = AD*sin(20°) = 6*sin(80°)/(2*sin(60°)*cos(20°)) = 3*sin(80°)/cos(20°)

Using the Pythagorean theorem on triangle AND, we get:

DM^2 = DN^2 + AN^2

DM^2 = 3^2 + (3*sin(80°)/cos(20°))^2

Simplifying, we get:

DM^2 = 9 + 9*(tan(80°))^2

DM^2 = 9 + 9*(cot(10°))^2

DM^2 = 9 + 9*(tan(80°))^2

DM^2 = 9 + 9*(cot(10°))^2

DM^2 = 9 + 9*(1/tan(10°))^2

DM^2= 9 + 9*(1/0.1763)^2

DM^2 = 9 + 228.32

DM^2 = 237.32

DM ≈ 15.4

Similarly, using the Pythagorean theorem on triangle ANC, we get:

DN^2 = AN^2 - AC^2

DN^2 = (3*sin(80°)/cos(20°))^2 - 6^2

DN^2 = 9*(sin(80°)/cos(20°))^2 - 36

DN^2 = 9*(cos(10°)/cos(20°))^2 - 36

Simplifying, we get:

DN^2 = 9*(1/sin(20°))^2 - 36

DN^2 = 9*(csc(20°))^2 - 36

DN^2 = 9*(1.0642)^2 - 36

DN^2 = 3.601

Therefore, we have:

DM^2 - DN^2 = 237.32 - 3.601 = 233.719

Since DM^2 - DN^2 = DM^2 - DM^2 = 0, we have shown that DM = DN.

The derivative of the function is found to be (1/sin(x)^log20x)dy/dx = log20(xcos(x)+sin(x)) and the value of the derivative a = π/2 is log20.

The function to find the derivative is provided to be f(x) = y = sin(x)^log20x.

We can solve this as follows, taking log both sides,

log(y) = log20x(sin(x))

Differentiating both sides with respect to x,

(1/y)dy/dx = log20(xcos(x)+sin(x))

ow, putting y = sin(x)^log20x.

So, we get,

(1/sin(x)^log20x)dy/dx = log20(xcos(x)+sin(x))

for f(a), (1/sin(a)^log20a)dy/dx = log20(acos(a)+sin(a))

Putting a = π/2

(1/sin( π/2)^log20. π/2)dy/dx = log20( π/2cos( π/2)+sin( π/2))

dy/dx = log20

So, the derivative of the function at the value of x =  π/2 is found to be log20.

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Complete question - find the derivative of the function sin(x)^log20x and evaluate the derivative at the given value of a. f(x); a=pi/2

For the function f(x) = 8 sin(sin(x)) on the interval [0, 2π], there are no numbers c that satisfy the conclusion of Rolle's Theorem. For the function f(x) = x + sin(sin(2x)) on the same interval, there is at least one number c that satisfies the conclusion of the Mean Value Theorem.

Rolle's Theorem states that for a function f(x) to satisfy the theorem's conclusion on an interval [a, b], it must be continuous on [a, b], differentiable on (a, b), and have equal values at the endpoints, i.e., f(a) = f(b).

For the function f(x) = 8 sin(sin(x)) on the interval [0, 2π], it is continuous and differentiable on (0, 2π). However, f(0) = f(2π) = 0, which means the function satisfies the equality condition. Therefore, there are no numbers c that satisfy the conclusion of Rolle's Theorem for this function.

On the other hand, for the function f(x) = x + sin(sin(2x)) on the interval [0, 2π], it is also continuous and differentiable on (0, 2π). Moreover, f(0) = 0 and f(2π) = 2π, indicating that the function satisfies the equality condition. By the Mean Value Theorem, there exists at least one number c in (0, 2π) such that f'(c) = (f(2π) - f(0)) / (2π - 0) = (2π - 0) / (2π - 0) = 1. Thus, the function satisfies the conclusion of the Mean Value Theorem at some point c in the interval (0, 2π).

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We are given a regression model: test score = 800 - 8(student-teacher ratio)

If the student-teacher ratio drops by 2, then the new ratio is (old ratio - 2).

So, the new predicted test score is:

test score = 800 - 8(new ratio)

          = 800 - 8(old ratio + (-2))

          = 800 - 8(old ratio) - 8(-2)

          = 800 - 8(old ratio) + 16

Therefore, the predicted effect on the test score is an increase of 16 points.

So, the answer is (d) the test score will increase by 16 points.

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Two rays with a common endpoint form an angle. An angle is defined as a geometric figure formed by two rays that share a common endpoint. In other words, an angle is formed when two rays emanating from a common point, and this common point is known as the vertex.

The rays are the sides of the angle, and the angle is measured in degrees. Angles have different measures, ranging from 0 degrees to 360 degrees. The two rays that make up an angle are also called the sides or arms of the angle. The angle is measured in degrees, and the size of the angle depends on the distance between the two sides of the angle that meet at the vertex.

In geometry, an angle can be named in different ways, depending on the context in which it is being used. Angles are essential in mathematics, physics, and other scientific fields, where they are used to measure the rotation of an object, determine the direction of an object, and in other applications involving rays and lines. Two rays with a common endpoint form an angle.

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Answer:

hope this will help you thank you

it can be also written as 1/5x-5

Answer:

228 individual cookies.

Step-by-step explanation:

To convert 19 dozen cookies to individual cookies, we first have to identify that:

\(dozen=12\)

If a dozen is equal to 12, to solve, we simply must multiply the amount of dozens, which is 19, by a dozen, which is 12:

\(19*12=\)

\(228\)

Therefore, there are 228 individual cookies.

-

We can check our  work by dividing the individual number of cookies, 228, by dividing buy the amount of dozens, 19, and a dozen, 12:

\(228\) ÷ \(19=12\)

\(228\) ÷ \(12=19\)

As you can see, our quotients are the two figures we started with, and when multiplied together, give us 228 individual cookies; therefore, our solution is correct!

The unknown number is 55.Let the unknown number be x. Then, the expression, "the quotient of a number and seven" can be written as x/7.

Now, we are told that "Seven less than the quotient of a number and seven is equal to 46 divided by seven".

This can be written as:

x/7 - 7 = 46/7

To solve for x, we will isolate x by multiplying both sides by 7:

7(x/7 - 7) = 7(46/7)

Simplifying both sides:

x - 49 = 6x

= 55

Therefore, the unknown number is 55.

The term "quotient" is commonly used in mathematics and refers to the result of dividing one quantity by another. It represents the value obtained when a number, called the dividend, is divided by another number, known as the divisor. The quotient can be thought of as the number of times the divisor can evenly fit into the dividend.

For example, if we divide 10 by 2, the dividend is 10, the divisor is 2, and the quotient is 5. This means that 2 can fit into 10 exactly 5 times, with no remainder.

The quotient is an important concept in arithmetic and is used in various mathematical operations such as long division, fraction calculations, and finding averages. It provides a way to express the relative size or proportion between two quantities.

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If the radius of a circle is doubled, the area will quadruple. This is because the area of a circle is directly proportional to the square of the radius. In other words, if the radius is doubled, the area will be four times as large.

The area of a circle is given by the formula A = πr², where r is the radius. If we double the radius, we get r = 2r.

Plugging this into the formula gives us A = π(2r)² = 4πr². So, the area is four times larger.

This can also be seen intuitively. If we double the radius, we are making the circle four times as wide and four times as tall. So, the area must be four times larger.

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Answer:

Value of θ [Angle of elevation] = 72.54°

Step-by-step explanation:

Given;

Length of foot ladder = 20 feet

Distance of foot from house (Base) = 6 feet

Find:

Angle of elevation

Computation:

Using trigonometry functions

Cos θ = Base / Hypotenuse

Cos θ = Distance of foot from house (Base) / Length of foot ladder

Cos θ = 6 / 20

Cos θ = 0.3

Cos θ = Cos 72.54

Value of θ [Angle of elevation] = 72.54°

Answer:

Infinitely many solutions

Step-by-step explanation:

Answer:5<x<15

Step-by-step explanation:

Answer:

Step-by-step explanation:

0<2x-10<20

If a<u<b then a<u and u<b

0<2x-10 and 2x-10<20

0<2x-10= x>5 2x-10<20 = x<15

Combine the intervals

x>5 and x<15

Solution: 5<x<15

Interval Notation: (5,15)

No, f is not a function from Z to R because it is undefined for n = ±2, and a function must be defined for all inputs in its domain.

(a) f(n) = ±n:

No, f is not a function from Z to R because for each n, it has two possible outputs, +n and -n. A function must have only one output for each input.

(b) f(n) = √(n^2 + 1):

Yes, f is a function from Z to R because for each n, it has only one possible output which is a real number.

(c) f(n) = 1/(n^2 - 4):

No, f is not a function from Z to R because it is undefined for n = ±2, and a function must be defined for all inputs in its domain.

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Complete question :

It takes 313131 employees and \$7500$7500dollar sign, 7500 to build a car, and it takes 191919 employees and \$4300$4300dollar sign, 4300 to build a motorcycle. Genghis Motors wants to spend more than \$84000$84000dollar sign, 84000 to build cars and motorbikes using at most 706706706 employees. Let CCC denote the number of cars they build and MMM the number of motorbikes they build. Write an inequality that represents the condition based on the number of employees. Write an inequality that represents the condition based on the number of dollars.

Answer:

31C + 19M ≤ 706

7500C + 4300M > 84000

Step-by-step explanation:

C = number of cars built

M = number of motorcycles built

Cost of building a car :

Cost = 31 + $7500

Cost of building a motorcycle,:

Cost = 19 + 4300

To build, C cars :

Number of employees = 31C

7500 * C = 7500C

To build, M motorcycles :

Number of employees = 19M

4300 * M = 4300M

Genghis budget :

Amount > 84000

Number of employees ≤ 706

Hence, the constraints

31C + 19M ≤ 706

7500C + 4300M > 84000

Answer:

1. Split up the linear term: \(2x^{2}\)+2x-3x-3

2. Group terms that have common factors: (\(2x^{2}\)+2x)+(-3x-3)

3. Factor out the greatest common factor: 2x (x+1) -3 (x+1)

4. Factor out the greatest common factor: (x+1)(2x-3)

Answer: (x+1)(2x-3)

Step-by-step explanation:

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Answer:

1. Take the number after the rise and divide it by 1.02.

2. 52/1.3

3. 135 *1.1

4. 37.40*1.45

Step-by-step explanation:

Answer:

m=\(\frac{23}{3}\) simplest form if you need it as a decimal its m=7.6

Step-by-step explanation:

Answer:

when the same person sits on the same board of directors two or more companies ..

Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

Answer:

okay i'll try to help

Answer:

I'll help too.

Step-by-step explanation:

Answer:

y = 91

as the x value increases the y value also increases.

The x and y value will always be 9 numbers apart as it increases.

Step-by-step explanation:

y = x-9, x = 100

y = 100 - 9

y = 91

(100, 91)

The exponential equation is \(y=ab^x\). Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = \(ab^{x}\) . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = \(ab^{x}\) . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = \(ab^{x}\)

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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Answer:

3

Step-by-step explanation:

First right out all the data in numerical order from left to right.

2, 2, 2, 3, 4, 5, 7

The median is the middle number in the set.  If there is an even amount of data points, find the average of the two middle numbers.  If there is an odd number of data points, like in this data set, just take the middle number as you median.

There are 7 data points in this set so the fourth number in the set written in numerical order would be your median.

When writing this set out in numerical order, repeated numbers must be repeated, we find that the fourth, or middle, number is 3.  Therefore, 3 is the median of this data set.