A box contains 8 red balls and 8 black balls. A
woman takes balls out at random without looking at
them. Once a ball is taken out it is not replaced back in
the box. How many balls must she select to be sure of
having at least three balls of the same color?

a.The interest rate earned when borrowing $650 is approximately 12 percent. b. The interest rate earned when borrowing $650 is approximately 12 percent. c.The interest rate earned when borrowing $74,000 is approximately 6 percent,. d. The interest rate earned when borrowing $18,000  is approximately 8 percent. .

a. The interest rate earned when borrowing $650 and repaying $728 after 1 year is approximately 12 percent. b. The interest rate earned when lending $650 and receiving $728 after 1 year is also approximately 12 percent. c. The interest rate earned when borrowing $74,000 and repaying $127,146 after 8 years is approximately 6 percent. d. The interest rate earned when borrowing $18,000 and making payments of $4,390.00 annually for 5 years is approximately 8 percent.

To calculate the interest rate earned in each scenario, we can use the formula for compound interest. The formula is:

Future Value = Present Value × (1 + Interest Rate)^Number of Periods

Rearranging the formula, we can solve for the interest rate:

Interest Rate = ((Future Value / Present Value)^(1 / Number of Periods) - 1) × 100

By plugging in the given values and solving for the interest rate, we can determine the approximate interest rates earned in each case. The interest rates are rounded to the nearest whole number.

For example, in scenario a, the interest rate earned is calculated as ((728 / 650)^(1/1) - 1) × 100, which results in approximately 12 percent. This means that by borrowing $650 and repaying $728 after 1 year, you would be earning an interest rate of around 12 percent. Similarly, the interest rates for scenarios b, c, and d can be calculated using the same formula to obtain the respective answers.

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The approximate probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month, assuming the true proportion is 15%, is 0.9693

To solve this problem, we will use the normal approximation to the binomial distribution. We can assume that the number of students who report experiencing extreme levels of stress follows a binomial distribution with parameters n = 160 and p = 0.15, where n is the sample size and p is the true proportion of students who have experienced extreme levels of stress in the population.

The expected value of the number of students who report experiencing extreme levels of stress in the sample is:

E(X) = np = 160 * 0.15 = 24

The variance of the number of students who report experiencing extreme levels of stress in the sample is

Var(X) = np(1-p) = 160 * 0.15 * 0.85 = 18.36

The standard deviation of the number of students who report experiencing extreme levels of stress in the sample is

SD(X) = sqrt(Var(X)) = sqrt(18.36) = 4.28

To calculate the probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month, we need to convert the percentage into a number. Since the sample size is 160, 10% corresponds to 16 students. We want to find the probability that X > 16.

To standardize the distribution, we calculate the z-score

z = (16 - 24) / 4.28 = -1.87

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -1.87, which is approximately 0.0307. Therefore, the probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month is approximately 1 - 0.0307 = 0.9693

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Suppose that 15%, percent of the 1750 students at a school have experienced extreme levels of stress during the past month. A high school newspaper doesn't know this figure, but they are curious what it is, so they decide to ask a simple random sample of 160 students if they have experienced extreme levels of stress during the past month. Subsequently, they find that 10, percent of the sample replied “yes” to the question.Assuming the true proportion is 15, percent, what is the approximate probability that more than 10, percent of the sample would report that they experienced extreme levels of stress during the past month?

Answer:

approximately 42.85 of whatever unit

Answer: -15

Step-by-step explanation: 2r+8-r=-7

1r +8 = -7

1/1       -15/1

Answer: r = -15

Step-by-step explanation:

2r - r = -7 -8

r = -15

we can see that the small box offers the best value for money with a cost of £0.34 per coffee pod. Therefore, the answer isThe small box gives the best value for money.

To determine the best value for money among the three sizes of coffee pod boxes, we need to calculate the cost per coffee pod for each size of the box.

For a small box with 12 coffee pods costing £4.08, the cost per coffee pod can be calculated as:

Cost per coffee pod = £4.08 ÷ 12 = £0.34

For a medium box with 20 coffee pods costing £7.80, the cost per coffee pod can be calculated as:

Cost per coffee pod = £7.80 ÷ 20 = £0.39

For a large box with 35 coffee pods costing £12.95, the cost per coffee pod can be calculated as:

Cost per coffee pod = £12.95 ÷ 35 = £0.37

Comparing the cost per coffee pod for each box size, we can see that the small box offers the best value for money with a cost of £0.34 per coffee pod. Therefore, the answer is:

The small box gives the best value for money.

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Answer:

Step-by-step explanation:

The graph of the straight line \(y = -\frac{1}{3}x -2\) is plotted. The graph is shown below.

A straight line is of the form y = mx + c, where m is the slope and c is the y-intercept.

To plot the given straight line \(y = -\frac{1}{3}x -2\), follow the following steps:

Step 1: Substitute x = 0 in the given equation to obtain the point where the line intersects the y-axis.

y = 0 - 2

y = -2

The point at the y-axis is (0, -2).

Step 2: Substitute y = 0 in the given equation to obtain the point where the line intersects the x-axis.

\(0 = -\frac{1}{3}x -2\\x = -6\)

The point at the x-axis is (-6, 0).

Step 3: Draw a straight line passing through both points.

Thus, the straight line \(y = -\frac{1}{3}x -2\) is plotted.

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The sum or the compound interest were Rs. 10,089 & Rs. 2589, respectively, according to the supplied statement.

Per year, as used in contracts, is used to describe ongoing duties, or those that take place continuously during the course of an agreement. For instance, if a customer pays 3% interest on a loan annually, it indicates that you will have to pay 3% more of the loan's principle each year until the deal is through.

Given : Initial principle amount (P) = Rs. 7500

      Rate of interest (R) = 16% per annum

To find : Compound interest (C.I.) = ?

Solution :

It is given that Initial principle amount (P) = Rs. 7500

Rate of interest (R) = 16% per annum

      Time (t) = 1 year = 2 ( ∵ Half Yearly)

We know the formula for Compound Interest,

       Compound Interest (A) = \(P\left(1+\frac{R}{100}\right)^{n t}\)

\(\begin{aligned}& =7500\left(1+\frac{16}{100}\right)^2 \\& =7500\left(\frac{100+16}{100}\right)^2 \\& =7500\left(\frac{116}{100}\right)^2\end{aligned}\)

= 7500 * 1.345

= Rs. 10,089

Now, Compound interest = A - P

= 10,089 - 7500

= Rs. 2589

∴ Final amount = Rs. 10,089

Compound Interest = Rs. 2589

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The complete question is-

Calculate the amount and the compound interest on Rs. 7500 for 1 year at 16% p.a compounded half yearly​

Step-by-step explanation:

integral from 0 to 2pi of cos3x

(sin3x)/3 from 0 to 2 pi

sin 6pi /3 - sin 0 /3 = 0

If you borrow $900 for 6 years at an annual interest rate of 7%. You will pay $1350.65

"An annual interest rate is expressed as an interest rate. It calculates what percentage of the principal you'll pay each year by taking things such as monthly payments into account."

According to the problem

If you borrow $900 for 6 years at an annual interest rate of 7%

You will pay = \(90(1+\frac{r}{100} )^{t}\)

= \(900(1+\frac{7}{100} )^{6}\)

= \(900(1.07)^{6}\)

= $1350.65

Hence, you will pay $1350.65

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Step-by-step explanation:

First, you convert 7% to a decimal.

0.07

Then you multiply.

900*6*0.07

The answer is 378.

Wait we are not done yet. We need to add dollars per year with 378.

900+378=1278

The answer is 1278.

The number 1.368 is approximately 2 more than its cube.

To find a real number that is exactly 2 more than its cube, we can set up the equation:

x = x^3 + 2

Rearranging the equation, we have:

x^3 - x + 2 = 0

To find the solution to this equation, we can use numerical methods such as Newton's method or trial and error. Applying trial and error, we can find one such value accurate to three decimal places:

x ≈ 1.368

If we substitute this value into the equation x = x^3 + 2, we get:

1.368 ≈ (1.368)^3 + 2

1.368 ≈ 2.001

The number 1.368 is approximately 2 more than its cube.

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Answer:jmm

Step-by-step explanation:hmmm

Answer:1,3,5

Step-by-step explanation:

is is all your y values

Answer:

Step-by-step explanation:

You want to identify the true statements regarding angles at a transversal crossing parallel lines, and perpendicular bisectors.

The Corresponding Angles theorem tells you that corresponding angles are congruent where a transversal crosses parallel lines. Since vertical angles are congruent, and angles congruent to the same angle are congruent to each other, this also means that alternate interior angles are congruent.

A bisector of a segment passes through its midpoint, a point that is equidistant from the end points. When the bisector is perpendicular to the segment, all points on the perpendicular bisector are equidistant from the segment's endpoints.

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Simplification :

Answer:

Step-by-step explanation:

Combine Like Terms:

= 17x + 5y + − 4x + 10y

= (17x + −4x) + (5y + 10y)

= 13x + (5y + 10y)

the car will travel 324 miles

Answer:

Step-by-step explanation:

The length of the variable s is 12√3.

We have,

Tangent is a trigonometric function that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the side adjacent to that angle.

In trigonometry,

The tangent function is commonly denoted as "tan."

The tangent of an angle (θ) is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle:

tan(θ) = opposite/adjacent

Now,

From the triangle,

We will use the trigonometric function tangent.

So,

Tan 60 = s/12 ______(1)

And,

Tan 60 = √3/1 = √3 ______(2)

Substituting (2) in (1).

Tan 60 = s/12

√3 = s/12

s = 12√3

Thus,

The length of the variable s is 12√3.

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To find the work done in pumping the entire contents of the fuel tank into the tractor, we need to calculate the potential energy difference between the initial position of the gasoline in the truck's tank and its final position in the tractor's tank.

Given:

- Diameter of the cylindrical gasoline tank: 4 feet

- Length of the cylindrical gasoline tank: 5 feet

- Opening on the tractor tank is 5 feet above the top of the tank in the truck

First, let's calculate the volume of the cylindrical gasoline tank using the formula for the volume of a cylinder:

Volume = π * (radius^2) * height

The radius of the tank is half the diameter, so the radius is 4 feet / 2 = 2 feet.

Volume = π * (2^2) * 5 = 20π cubic feet

Since the entire contents of the fuel tank need to be pumped, the volume of gasoline to be pumped is 20π cubic feet.

To calculate the work done in pumping the gasoline, we need to find the vertical height through which the gasoline is lifted. This height is the sum of the height of the tank and the distance between the top of the tank and the opening on the tractor tank.

Height = 5 feet + 5 feet = 10 feet

The work done in pumping the gasoline can be calculated using the formula:

Work = Force × Distance

In this case, the force is the weight of the gasoline, and the distance is the height through which it is lifted. To calculate the weight of the gasoline, we need to know the density of gasoline. The density of gasoline can vary, but an average value is around 6.3 pounds per gallon.

Let's convert the volume of gasoline from cubic feet to gallons:

1 cubic foot = 7.48052 gallons (approximately)

Volume in gallons = 20π * 7.48052 ≈ 149.61π gallons

Weight of gasoline = Volume in gallons * Density of gasoline

Assuming the density of gasoline as 6.3 pounds per gallon:

Weight of gasoline = 149.61π * 6.3 ≈ 940.06π pounds

Finally, we can calculate the work done:

Work = Weight of gasoline * Height

Work = 940.06π * 10 ≈ 9400.6π foot-pounds

Therefore, the work done in pumping the entire contents of the fuel tank into the tractor is approximately 9400.6π foot-pounds.

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By answering the presented question, we may conclude that As a result, equation the final score is 3/5.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

1/5 times 3 Equals (1/5) * 3

To answer this expression, we may apply the multiplication rule of fractions, which states that to multiple two fractions, multiply their numerators first and then their denominators. Therefore:

(1/5) * 3 = (1 * 3) / (5 * 1)

We obtain by simplifying the numerator and denominator:

3/5

As a result, the final score is 3/5.

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Answer:

1000 miles

Step-by-step explanation:

Divide how long Jack's family traveled before he fell asleep by the percent of the trip.

430/43% = 1000

The trip was 1000 miles

You can check this by multiplying the total miles of the trip by the percent

1000 x 43% = 430

Answer:

754.4 miles

Step-by-step explanation:

He sleeps 43 % of the trip. So 57% of the trip is the time is asleep which is 430 miles. The math is 430/57 x 100 = 754.4

To determine the time it takes for the car to reach a top speed of 203 mph and the distance traveled before reaching that speed, we'll use the equations of motion.

First, let's convert the slope from a percentage to a decimal:

Slope = 6.4% = 0.064

We'll use the equation of motion for acceleration:

v = u + at

Converting the velocities to feet per second:

203 mph = 203 * 1.467 ft/s = 297.801 ft/s

0 mph = 0 ft/s

Rearranging the equation, we get:

t = (v - u) / a

Substituting the values, we have:

t = (297.801 ft/s - 0 ft/s) / 2.93 ft/s²

t ≈ 101.674 seconds

Therefore, it will take approximately 101.674 seconds for the car to reach its top speed of 203 mph.

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Answer:

Step-by-step explanation:

d

Answer:

x=16

Step-by-step explanation:

because it's a equilateral triangle and its features are

it has three equal side and

every angle has 60°

So

x=16

The value of x is equal to 16

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The sum of the internal angles of a triangle is equal to 180

so, 60 + 60 + m = 180

m = 180 - 120

m = 60

Since it's a equilateral triangle and its features that it has three equal side and every angle has 60°

So the three side are also equal to each other

x=16

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the probability that a positive integer less than 100 picked at random has all distinct digits is 90.

He has 99 positive integers less than 100.

The integers that do not have all distinct digits have the same digit twice.

11, 22, 33, 44, 55, 66, 77, 88, 99

There are 9 integers that do not have distinct digits, therefore there are 99-9 integers that do.

Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.

A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final results of an experiment. Getting a Heads whilst tossing a coin is an event.

Simple probability is the calculation of an outcome or the chance of an event ever taking place. coverage companies use possibility statistics to determine the possibilities of having to pay out a declare. A simple chance is calculated by way of dividing a particular outcome through all of the feasible outcomes.

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Answer:

Part 1:

Revenue divided by number of posts

Revenue divided by total number of words

Part 2:

No. The definitions have opposite results.

Step-by-step explanation:

When you divide revenue by total number of words remember to do words*posts to get total.

Example: $30000/100*110 = 2.72