the ratio of number of red balls to green balls is 5:6. the green balls are either light green or dark green in the ratio 4:2. if there are 12 dark green balls find the number of light green balls and red balls.


please answer this quick i will mark u as brainliest and will also give u 15 points

So, the last three digits of m*n is 001.

Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.

Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:

p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2

Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.

Therefore, the last three digits of m*n is 001.

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Answer:

Each person ate 3.5 ounces of pineapple.

Step-by-step explanation:

Well, since she shares the 32 ounces of pineapple between herself AND 7 friends, the 32 ounces of pineapple were split between 8 people, therefore each person got 4 ounces each. Since they all leave 0.5 ounces of pineapple behind, that means we would multiply the leftovers by the amount of people that left behind 0.5 ounces. Giving our equation 8(0.5) which equals to 4 ounces total that was left behind. so we take that and subtract it from our original amount, 32. Giving our second equation 32-4=x. x = 28. Divide that by 8 giving us 3.5. That means that each person ate 3.5 ounces of pineapple.

Answer:

False

Step-by-step explanation:

You can transform a function many times

:)

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Given

Jason can travel 24 3/4 miles in 1/2 hour.

Answer

Distance = 24 3/4 = 99/4 = 24.75 miles

Answer:

See below

Step-by-step explanation:

f(x) = a(x - h)^2 + k

f(x) = 2(x-4)^ 2 +3 ? correct me If incorrect

        a    h         k

a= 2

h = 4

k = 3

vertex = (h, k)

vertex= (4,3)

Answer:

5.6 miles

Step-by-step explanation:

The relation R defined by m R n ⇔ m + n is odd is not reflexive, symmetric, and antisymmetric, but it is antisymmetric and transitive.

A relation R on a set A is said to be reflexive, if for all a ∈ A, aRa.

It is symmetric if, for all a, b ∈ A, aRb, then bRa.

It is antisymmetric if, for all a, b ∈ A, if aRb and bRa, then a = b.

It is transitive if, for all a, b, c ∈ A, if aRb and bRc, then aRc.

Finally, it is irreflexive if, for all a ∈ A, aRa is false.

Let us consider m + n = 2k + 1, where k is an integer. m + n can be written as

m + n = 2k + 1 = (2k + 1) + 0.

Clearly, m and n must have opposite parity; one of them is odd, and the other is even, in order for m + n to be odd.

This suggests that if we add two odd or even numbers, the resulting sum will be even, and if we add an odd and an even number, the resulting sum will be odd.

To prove that the relation is not reflexive, we can consider any even integer and add it to itself. The resulting sum will always be even, and hence, it is not odd.

So, m R m is not true for any even integer m, and, therefore, the relation R is not reflexive.

To show that the relation R is symmetric, consider m + n = 2k + 1.

Adding both sides of this equation gives n + m = 2k + 1. Therefore, n R m is true if m R n is true. So, the relation R is symmetric.

To prove that the relation R is not antisymmetric, consider the integers 2 and 3.

Clearly, 2 + 3 = 5 is odd, so 2 R 3.

However, 3 + 2 = 5 is odd, so 3 R 2.

Since 2 ≠ 3, we see that 2 R 3 and 3 R 2 and (2 ≠ 3), and hence, R is not antisymmetric.

To show that the relation R is transitive, suppose that m R n and n R p. That is, m + n is odd, and n + p is odd.

We need to show that m + p is odd.

Adding the two equations gives

(m + n) + (n + p) = 2k + 1 + 2l + 1,

where k and l are integers.

Simplifying, we get m + p + 2n = 2k + 2l + 2, or m + p = 2(k + l + 1) − 2n.

Since k + l + 1 is an integer, we have that m + p is odd if and only if n is even.

Therefore, the relation R is transitive.

To prove that the relation R is not irreflexive, we can consider any odd integer m and note that m + m = 2m is even.

So, m R m is not false for any odd integer m, and hence, the relation R is not irreflexive.

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The maximum value of f(x, y)=x2-x-y on the region where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1.

To find the maximum value, we can set up a system of inequalities and solve it:

0 ≤ x ≤ 1
0 ≤ y ≤ 1
f(x, y)=x2-x-y

Since both x and y are greater than or equal to 0, their product will also be greater than or equal to 0. Therefore, the maximum value of the equation is when x = 1 and y = 0, since it maximizes the positive value of x2 while minimizing the negative value of -x-y. This means that the maximum value of f(x, y) is 1.

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The maximum value of f(x,y)=x^{2}-x-yf(x,y)=x 2 −x−y on the region where \{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\} is 0.

To find the maximum value, we need to find the critical points of the function and test them within the given region. The critical points are where the partial derivatives of the function are equal to 0.

The partial derivative with respect to x is:
f_x(x,y)=2x-1

The partial derivative with respect to y is:
f_y(x,y)=-1

Setting these partial derivatives equal to 0, we get:
2x-1=0 --> x=1/2
-1=0 --> no solution for y

So the only critical point within the given region is (1/2, y) for any value of y. However, since the partial derivative with respect to y is always -1, the function is decreasing with respect to y. Therefore, the maximum value will occur when y is at its smallest value, which is 0.

Plugging in x=1/2 and y=0 into the original function, we get:
f(1/2,0)=(1/2)^{2}-(1/2)-0=0

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Answer:

15/4

Step-by-step explanation:

Find a common denominator in this case 4.

Turn both mixed numbers to an improper fraction

12 1/2 = 25/2

8 3/4 = 35/4

multiply 2 to 25/2 = 50/4

50/4 - 35/4 = 15/4

The bicycle travels a distance of 13.188 meters (to three decimal places).

What is the distance?

The distance traveled by the bicycle is equal to the distance traveled by one revolution of the front wheel multiplied by the number of revolutions.

The distance traveled by one revolution of the front wheel is equal to the circumference of the wheel, which is given by:

C = πd

where d is the diameter of the wheel. Therefore, the circumference of the front wheel is:

C = π × 35cm

C = 3.14 × 35cm

C = 109.9cm

Now we can calculate the distance traveled by the bicycle:

Distance = Number of revolutions × Distance traveled in one revolution

Distance = 12 × 109.9cm

Distance = 1318.8cm

Finally, we need to convert this distance to meters:

Distance = 1318.8cm ÷ 100

Distance = 13.188m

Therefore, the bicycle travels a distance of 13.188 meters (to three decimal places).

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Answer:

The plane figure has a symmetry about an axis

Answer:

plane symmetry and symmetry about an axis

Step-by-step explanation:

A three-dimensional figure has plane symmetry if a plane can divide the figure into two congruent reflected halves.So, the given figure has seven plane symmetries.

A three-dimensional figure has symmetry about an axis if there is a line about which the figure can be rotated by an angle greater than 0∘ and less than 360∘ so that the image coincides with the preimage.So, the given figure has symmetry about seven axes.

Therefore, the figure has plane symmetry and symmetry about an axis.

Answer:

1/14

Step-by-step explanation:

\( \frac{3}{7} \times \frac{1}{6} = \frac{1}{14} \)

or 0.071

please mark me brainliest and 5 star

Answer:

d) 16.7%

Step-by-step explanation:

Answer:

D, 16.7%

Hope that helps (:

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

RATIO:

Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.

i.e., it shows how many times a number contains another.

Total number of students = 150

ratio of boys to girls = 3 : 2

B:G = 3 : 2

now

3x + 2x = 150

5x = 150

x = 30

the number of boys = 3x = 3 X 30 = 90 boys.

the number of girls = 2x = 2 X 30 = 60 girls.

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

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Where is the Graph.

Step-by-step explanation:

LOL

The correct answer is b. Expected value. The mean of a discrete random variable generalizes the concept of expected value. The expected value of a discrete random variable is the weighted average of all possible outcomes, where the weights are the probabilities associated with each outcome.

It represents the long-term average value that we would expect to observe if we repeated the random experiment multiple times.

In the context of a discrete random variable, the mean (or expected value) is calculated by multiplying each possible value of the variable by its corresponding probability and summing them up. It provides a measure of central tendency and represents the average value we would expect to obtain from the random variable over a large number of trials.

The population mean (mean of a variable) refers to the average value of a variable in the entire population, not specifically related to a random variable. The sample mean is the average value of a variable calculated from a sample of observations. The distribution of a discrete random variable refers to the pattern of probabilities associated with each possible outcome of the variable.

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1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters

2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters

Since we know that the wavelength = speed of light / frequency

The speed of light is 3.00 × \(10^8\) meters per second.

For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;

wavelength of A = (3.00 ×  \(10^8\)  m/s) / (4.30 × 10^15 Hz)

wavelength of A = 6.98 ×  \(10^{-8}\) meters

For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;

wavelength of B = (3.00 ×  \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)

wavelength of B = 3.45 ×  \(10^{-11}\)  meters

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Answer:

D. it must be on the left due to it being negative

Answer:

A

Step-by-step explanation:

a. the population in 1790 was 3.93 million. b. the population in 1820 can be expressed as N = 3.93 x 1.03^t, where t is the number of years since 1790. c. the population of the United States in 1820 was approximately 31.12 million.

(a) To find the population in 1790, we plug in t = 0 into the given formula:

N = 3.93 x 1.03^0 = 3.93

Therefore, the population in 1790 was 3.93 million.

(b) To express the population in 1820 using functional notation, we plug in t = 30 into the given formula:

N = 3.93 x 1.03^30

Therefore, the population in 1820 can be expressed as N = 3.93 x 1.03^t, where t is the number of years since 1790.

(c) To calculate the value of the population in 1820, we plug in t = 30 into the formula and round to two decimal places:

N = 3.93 x 1.03^30 ≈ 31.12

Therefore, the population of the United States in 1820 was approximately 31.12 million.

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The given parabolic equation is y = 4x - x² and the point is (1, 3). We are to determine the slope of the tangent line at (1, 3) and then obtain an equation of the tangent line.  we must first calculate the derivative of the given equation.

We can do this by using the power rule of differentiation. The derivative of x² is 2x. So the derivative of y = 4x - x² is dy/dx = 4 - 2x.Since we want to find the slope of the tangent line at (1, 3), we need to substitute x = 1 into the equation we just obtained. dy/dx = 4 - 2x = 4 - 2(1) = 2. Therefore, the slope of the tangent line at (1, 3) is 2.We can now write the equation of the tangent line. We know the slope of the tangent line, m = 2, and we know the point (1, 3).

We can use the point-slope form of the equation of a line to obtain the equation of the tangent line. The point-slope form of the equation of a line is given as: y - y₁ = m(x - x₁)where m is the slope, (x₁, y₁) is a point on the line.Substituting in the values we have, we get:y - 3 = 2(x - 1)We can expand this equation to obtain the slope-intercept form of the equation of the tangent line:y = 2x + 1Therefore, the equation of the tangent line to the parabola y = 4x - x² at the point (1, 3) is y = 2x + 1.

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The example provided is an example of empirical probability.

Empirical probability, also known as experimental probability, is based on actual observations or data gathered from experiments, surveys, or real-world events. In this case, the probability that the elderly adults prefer a poodle is determined through a survey, which involves collecting data from the group of elderly adults about their favorite breeds of dogs. The conclusion that the probability is about 30% is based on the data obtained from the survey, making it an empirical probability.

Therefore, the example given is an example of empirical probability because it is based on data collected from a survey of elderly adults' favorite breeds of dogs

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Answer:

B) 3b. 10b

Step-by-step explanation:

B) 3b. 10b = (3x10)(bxb) = 30b²

The midpoint of the line segment joining the points corresponding to the complex numbers 6 + i and 2 + 9i in the complex plane is 4 + 5i.

The midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the two endpoints. In the complex plane, the x-coordinate corresponds to the real part of the complex number and the y-coordinate corresponds to the imaginary part.

So, for the complex numbers 6 + i and 2 + 9i, we can find the midpoint by averaging the real parts (6 and 2) and the imaginary parts (1 and 9):
Midpoint = ((6+2)/2, (1+9)/2) = (4, 5)
In complex number form, this would be 4 + 5i.
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d ; x = 36 degrees

Straight angle = 180 degrees

The Acute angle = 2x

The Obtuse angle = 3x

2x + 3x = 180

5x = 180

x = 180/5

x = 36

Answer:

2 and 3

Step-by-step explanation:

and integer is a positive or negative WHOLE NUMBER it is not a fraction or a decimal.

True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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The completely factored form of x^3 + 4x^2 - 9x -36 is

(x -3)(x + 3)(x + 4).

According to the given question.

We have a polynomial

x^3 + 4x^2 - 9x -36

Since for finding the roots of the above polynomial, first we randomly substitute any value of x and find for which value of x the above polynomial gives 0.

So, for x = 3

The above polymonial gets 0.

So, the one factor of the given polynomial is (x -3).

To find the other factors or completely factored form of the given polynomial we will divide x^3 + 4x^2 - 9x -36 by x - 3, which is called long division.

From the attatched solution or log division we can see that

The factored form of x^3 + 4x^2 - 9x -36 is (x -3)(x^2 + 7x + 12).

Now, the foctorization of x^2 + 7x + 12 is given by

x^2 + 7x + 12

= x^2 + 4x + 3x + 12

= x(x + 4) + 3(x + 4)

= (x + 3)(x + 4)

Therefore, the completely factored form of x^3 + 4x^2 - 9x -36 is

(x -3)(x + 3)(x + 4).

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Answer:

C) (x + 3)(x – 3)(x + 4)

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Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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