Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 15 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Kyle, Carol, and Adam are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

For such more questions on invest

https://brainly.com/question/29227456

#SPJ8

Smaller t = 2

Larger t = 5

Step-by-step explanation:

Given:

The given function is.

Find the zeros of the function.

Solution:

Simplify the equation above equation.

Now, we first find the root of the above equation.

Use quadratic formula with .

Put a, b and c value in above equation.

For positive sign

t = 2

For negative sign

t = 5

Put t = 2 in given function.

Put t = 5 in given function.

So, the zeros of the function is t = 2 or 5

Therefore, the smaller value of t = 2 and larger value of t = 5.

Answer:

c

Step-by-step explanation:

A part-time seamstress made $8881.93 last year. The taxable income is $0.

We have given that,

A part-time seamstress made $8881.93 last year. If she claimed herself as an exemption for $3650 and had a $5700 standard deduction.

We have to determine, what was her taxable income last year.

Taxable income is the portion of your gross income used to calculate how much tax you owe in a given tax year.

Therefore the taxable income is $0.

To learn more about the taxable income vsit:

https://brainly.com/question/25641320

#SPJ2

Answer:

y=-x-3

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The parallelogram in C has a base of 2 units and a height o 4 units.

Answer:

None

Step-by-step explanation:

Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.

Answer:

One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.

Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.

One way to construct a confidence interval for a proportion is to use the formula:

p ± z * sqrt(p * (1 - p) / n)

where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:

0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)

which simplifies to:

0.6 ± 0.22

or:

(0.38, 0.82)

This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.

MARK AS BRAINLIEST!!!

Answer:

8x-16

Step-by-step explanation:

2 + 3x-9 + 1 -10 +5x

-16 + 8x so 8x-16 is your answer

Answer:

x= -14

Step-by-step explanation:

-x + 8 + 3x = x -6

combine -x and 3x to get

8 + 2x = x -6

subtract x from both sides to get

8 + x = -6

subtract 8 from both sides to get

x= -14  

Answer:

a: is equal, it contains the same number of letters and the number are the same even though they are not arranged the same.

b: is not equal, they are two different sets.

Step-by-step explanation:

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

Read more on rotation here: brainly.com/question/28854313

#SPJ1

Answer:

–18 feet

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

When the sequence limn→∞ (1 n! ∫x t = a f(n+1)(t)(x−t)n d t) converges to zero, as seen on the left side equation the Taylor series will accurately converge to f(x). For the Taylor series of f, this side is known as the integral form of the remainder (x).

Rn(x) = f(n+1)(c) (n + 1); thus, (x a)n + Rn(x)! when there is a c between a and x, (x a)n+1. The Taylor formula is the name given to the second equation. The residual of order n or error term for the Pn(x) over I approximation of f is known as the function Rn(x) (x). To integrate a Taylor Series function, expand the Taylor Series as usual before integrating each term. There is a general expression for the new series. Prior to determining the generic phrase, it is essential to avoid simplification.

Assume that f(x) is a real or composite function and that f(x) is a differentiable function of a real or composite neighborhood number. The following power series is then described by the Taylor series: F (x) = F a F ′ a 1! (x−a)+f”(a)2!

To learn more about integral formula refer to :

https://brainly.com/question/28168045

#SPJ4

Answer:

2x - 3 = 11

x = -21

Step-by-step explanation:

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The first ten terms of the Lucas sequence are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

The Lucas sequence or Lucas series are an integer sequence named after the mathematician francois Edouard Lucas, which are similar to the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms, thereby forming a fibonacci integer sequence.

Now, the sequence of first 10 numbers of Fibonacci series are-

0, 1, 1 ,2, 3, 5, 8, 13, 21, 34

which are defined as set of integers that starts with zero, followed by a one,then by another one and then by series of steadily increasing numbers,The sequence follow the rule that each number is equal to the sum of preceding two numbers.

And the sequence of Lucas sequence is -

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

which is definedas  the sum of its two immediate previous terms.

The Lucas number may thus be defined as follows;

Ln =    \(\left \{ {{2} ; if n= 0 \atop {1}; if n = 1} \right.\)

Here we can see that Lucas series starts with 2 and 1 whereas Fibonacci series starts with 0 and 1.

Hence,The first ten terms of the Lucas sequence are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

More about Lucas Sequence:

https://brainly.com/question/9807586

#SPJ1

John Legend has already paid off his loan before the fifth payment. Therefore, the final payment amount is 0.

To determine the final payment John Legend must make to pay off his 6-month loan, we need to first find out the amount of each payment. We can use the formula for a loan payment:

Payment = (Loan amount × Monthly interest rate) / (1 - (1 + Monthly interest rate\()^{(-Number of payments))\)

Here, the loan amount is 1,500.00, and the monthly interest rate is 12% / 12 = 1% per month. The number of payments is 6 since it's a 6-month loan. Plugging these values into the formula, we get:

Payment = (1,500.00 × 0.01) / (1 - (1 + 0.01\()^{(-6)\)) = 264.85

Now that we know the amount of each payment, we can determine the remaining balance after the fourth payment. Since John's loan is a 6-month loan, he should have made 4 payments at this point. Therefore, the remaining balance can be calculated as:

Remaining balance = Loan amount × (1 + Monthly interest rate)^Number of payments - Payment × ((1 + Monthly interest rate)^Number of payments - 1) / Monthly interest rate

Plugging in the values, we get:

Remaining balance = 1,500.00 × (1 + 0.01\()^4\) - 264.85 × ((1 + 0.01\()^4\) - 1) / 0.01 = 435.85

Now, we can calculate the final payment by subtracting the remaining balance from the amount of the fifth payment:

Final payment = Payment - Remaining balance = 264.85 - 435.85 = -171.00

However, a negative payment amount doesn't make sense. This means that John Legend has already paid off his loan before the fifth payment. Therefore, the final payment amount is 0.

for such more question on payment

https://brainly.com/question/27123871

#SPJ11

The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ1

The pattern that is seen is that the sums of doubles are both odd and even.

Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented in a variety of ways, such as through symbols, words, or gestures. Numbers can also be used to construct equations that help explain the world around us. Numbers are used in many different fields, from astronomy to engineering to biology. They are essential in understanding the universe and how it works, and are the foundation of all mathematics.

Rashi used the addition table to add doubles. She colored the sums of doubles in green. From the addition table, it can be seen that the sums of doubles are both odd and even. This is due to the fact that when two even numbers are added together the result will be an even number and when two odd numbers are added together the result will be an even number. For example, when 2 + 2 is added, the result is 4 which is an even number, and when 3 + 3 is added, the result is 6 which is also an even number. Therefore, the pattern that is seen is that the sums of doubles are both odd and even.

To know more about number click-
http://brainly.com/question/24644930
#SPJ1

The course of the airplane relative to true north is 094°, and the ground speed is 344.2 km/h.

The horizontal and vertical component of the airspeed is calculated as follows;

Vx = 300 cos(30) = 259.8 km/h

Vy = 300 x sin(30) = 150 km/h

The horizontal and vertical component of the wind velocity is calculated as follows;

Vx = 50 cos(60) = 25 km/h

Vy = 50 sin(60) = 43.3 km/h

To find the resultant velocity, we can add the x and y components separately:

Vx = 259.8 km/h  +  25 km/h = 284.8 km/h

Vy = 150 km/h  +  43.3 km/h  = 193.3 km/h

The magnitude of the resultant velocity is calculated as;

V = √(284.8² + 193.3²)

V = 344.2 km/h

The direction of the resultant velocity is calculated as;

θ = arc tan (193.3/284.8)

θ = 34.2⁰

The resultant direction to true north is calculated as;

track = 34.2 + 60 = 94.2°

Learn more about ground speed here: https://brainly.com/question/24208048

#SPJ1

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

To know more about geometric progression follow

https://brainly.com/question/12006112

#SPJ1

Answer:

X=-3

Step-by-step explanation:

2x+15=-3x

15=-5x

x=15/-5

x=-3

Answer:

x = -3

Step-by-step explanation:

2x + 15 = -3x

15 = -5x

x = -3

Answer:

D) 19.8 lbs

Step-by-step explanation:

1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.

1kg is also equal to 2.205 lbs. 9*2.205=19.8416

9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system

a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.

This leaves us with 19.8 lbs

From the given numbers root (3/4) and root (9/4) irrational numbers.

What are irrational numbers?

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.

Here,

root(3/16) is a rational number

root(9/16) is a rational number.

Therefore, from the given numbers root(3/4) and root(9/4)  are the irrational numbers.

To learn more about the irrational numbers visit:

brainly.com/question/4031928.

#SPJ4

The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

For more such questions on numbers visit:

https://brainly.com/question/24644930

#SPJ8

Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

Answer: \(\dfrac{21}{410}\).

Step-by-step explanation:

Formula : Probability = \(\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}\)

From the given frequency distribution for the class level of students in an introductory statistics course, we have

Number of Junior= 12

Number of Senior = 7

Total students = 6+16+12+7 = 41

Probability that the first student obtained is a junior = \(\dfrac{12}{41}\)

Probability that the the second student obtained is a senior. \(=\dfrac{7}{41-1}=\dfrac{7}{40}\)

Then, the probability that the first student obtained is a junior and the second a senior would be \(\dfrac{12}{41}\times\dfrac{7}{40}=\dfrac{21}{410}\)

Hence, the required probability is \(\dfrac{21}{410}\).

The 6th Term is 96.

To find the nth term of the series 3, 6, 12, 24, 48, we need to find the common ratio first. We can find it by dividing any term by its preceding term. For example,6/3=212/6=324/12=248/24=2So, the common ratio is 2.

Now, we can use the formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)where an is the nth term, a1 is the first term, r is the common ratio, and n is the number of terms we want to find.

Let's substitute the known values in the formula:a1 = 3 (the first term)r = 2 (the common ratio)an = a1 * r^(n-1)an = 3 * 2^(n-1)Therefore, the nth term of the series 3, 6, 12, 24, 48 is 3 * 2^(n-1).

We can use this formula to find any term we want. For example, if we want to find the 6th term, we can substitute n = 6:an = 3 * 2^(6-1)an = 3 * 2^5an = 96

So, the 6th term is 96.

For more questions on Term .

https://brainly.com/question/7882626

#SPJ8

Answer:

a) 17.09 hours

b) The 95% confidence interval estimate of the population mean flying time for the Pilots is between 31.91 hours and 66.09 hours

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 49 - 1 = 48

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 48 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.0106

The margin of error is:

M = T*s = 2.0106*8.5 = 17.09

s is the standard deviation of the sample. 17.09 hours is the answer for a.

The lower end of the interval is the sample mean subtracted by M. So it is 49 - 17.09 = 31.91 hours

The upper end of the interval is the sample mean added to M. So it is 49 + 17.09 = 66.09 hours

The 95% confidence interval estimate of the population mean flying time for the Pilots is between 31.91 hours and 66.09 hours