A box contains 2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles.

2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles.

Which color marble is most likely to be picked?
purple
blue
green
red

On solving the provided question, we cans ay that by standard deviation, \(SE = 0.1590 (approx.)\)

Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed. Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed.

By sample standard deviation, we mean standard error. Hence, we have that:

Therefore, Standard deviation\(= 0.6929891\)

The sample size \((n) = 19.\)

Hence:

\(SE = 0.1589826.\\ SE = 0.1590 (approx.)\)

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The maximum distance that can be traveled is given as follows:

360 miles.

The maximum distance that can be traveled is obtained applying the proportions in the context of the problem.

The amount of gas on the tank of Al's car is given as follows:

Then he has 9 gallons of gas in the tank, and the car has a rate of 40 miles per gallon, hence the maximum distance that can be traveled is given as follows:

9 x 40 = 360 miles.

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Answer:

6,12,18,24,36,42,48,5,60,66,72,78,84,90,96

Step-by-step explanation:

got a friend help

Answer:

x = 11

Step-by-step explanation:

x + 5 = 2(x - 3)

x + 5 = 2x - 6

(x - x) + 5 = (2x - x) - 6

5 = x - 6

5 + 6 = x (- 6 + 6)

x = 11

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

Answer:

see below

Step-by-step explanation:

1)

\(m+13=-2\\\\m+13-13=-2-13\\\\m+0=-15\\\\m=-15\)

2)

\(0=p+7\\\\p+7=0\\\\p+7-7=0-7\\\\p+0=-7\\\\p=-7\)

3)

\(5n=75\\\\\frac{1}{5}(5n)= \frac{1}{5}(75)\\\\n=15\)

4)

\(-7=\frac{m}{10} \\\\10(-7)=10(\frac{m}{10} )\\\\-70=m\\\\m=-70\)

5)

\(-1=7+r\\\\r+7=-1\\\\r+7-7=-1-7\\\\r+0=-8\\\\r=-8\)

6)

\(-42=14v\\\\\frac{1}{2}(-42)= \frac{1}{2} (14v)\\\\-21=7v\\\\\frac{1}{7}(-21) =\frac{1}{7}(7v)\\\\-3=v\\\\v=-3\)

7)

\(80=-8p\\\\8(10)=-8p\\\\\frac{1}{-8}(8(10))= \frac{1}{-8} (-8p)\\\\-10=p\\\\p=-10\)

8)

\(\frac{x}{4} =-8\\\\4(\frac{x}{4} )=4(-8)\\\\x=-32\)

9)

\(13=\frac{x}{2} \\\\2(13)=2(\frac{x}{2})\\\\26=x\\\\x=26\)

10)

\(-1=n-15\\\\n-15=-1\\\\n-15+15=-1+15\\\\n+0=14\\\\n=14\)

the area of the dartboard is approximately 254.34 square inches.

The area of a dartboard can be calculated using the formula for the area of a circle, which is given by:

Area = π * \(radius^2\)

Given that the radius of the dartboard is 9 inches, we can substitute this value into the formula:

Area = π * \(9^2\)

Area = π * 81

To calculate the area, we need to use the value of π (pi). Pi is an irrational number and is commonly approximated as 3.14. Using this approximation, we can calculate the area:

Area ≈ 3.14 * 81

Area ≈ 254.34 square inches

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The accumulated value at time 12 of a deposit of 1000 at time 3, using the accumulation factor a(t) = 1 + it and i = 0.05, is 1276.25. No, the answer is not the same as 1000a(12) or 1000a(9).

The accumulated value of a deposit using the accumulation factor a(t) is given by the formula A = P * a(t), where A is the accumulated value, P is the principal amount (initial deposit), and a(t) is the accumulation factor.

Principal amount P = 1000

Time t = 12 - 3 = 9 (the difference between the two times)

Using the accumulation factor a(t) = 1 + it and i = 0.05, we have:

a(t) = 1 + i * t

     = 1 + 0.05 * 9

     = 1 + 0.45

     = 1.45

The accumulated value A at time 12 is:

A = P * a(t)

 = 1000 * 1.45

 = 1450

Therefore, the accumulated value at time 12 of a deposit of 1000 at time 3, with an interest rate of 0.05, is 1450.

Now, let's compare it with 1000a(12) and 1000a(9):

1000a(12) = 1000 * a(12)

         = 1000 * (1 + 0.05 * 12)

         = 1000 * 1.6

         = 1600

1000a(9) = 1000 * a(9)

        = 1000 * (1 + 0.05 * 9)

        = 1000 * 1.45

        = 1450

The accumulated value at time 12 is 1450, which is not the same as 1000a(12) (1600) or 1000a(9) (1450).

The accumulated value at time 12 of a deposit of 1000 at time 3, using the accumulation factor a(t) = 1 + it and i = 0.05, is 1450. This value is not the same as 1000a(12) or 1000a(9).

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Answer:

10

Step-by-step explanation:

beatriz give away ten and ends with 6, ella gives away 30 because 10 times three is 30 and ends with 6.

Answer: hewo, there! your answer is below

x= -5/4

or x= 8

Step-by-step explanation:

step 1: Subtract 27x+40 from both sides.

4x2−(27x+40)=27x+40−(27x+40)

4x2−27x−40=0

Step 2: Factor left side of equation.

(4x+5)(x−8)=0

Step 3: Set factors equal to 0.

4x+5=0 or x−8=0

hope this helps you

have a great Day

Plz makr branilest

Answer:

x=y/m plus 2

Step-by-step explanation:

solve by isolating the variable by dividing each side by factors that don't contain the variable.

To determine the values of x(0) and x([infinity]) for the function\(x(s) = s^2 - 4 + 2s^3 - 4s^2 + 10s\), we evaluate the function at the given points. x(0) is obtained by substituting s = 0 into the function, and x([infinity]) is determined by analyzing the behavior of the function as s approaches infinity.

To find x(0), we substitute s = 0 into the function:

\(x(0) = (0)^2 - 4 + 2(0)^3 - 4(0)^2 + 10(0) = 0 - 4 + 0 - 0 + 0 = -4\)

Therefore, x(0) equals -4.

To determine x([infinity]), we analyze the behavior of the function as s approaches infinity. We consider the highest degree term in the function, which is 2s³. As s becomes very large, the term 2s³dominates the function, and other terms become negligible. Since the coefficient of the highest degree term is positive, the function increases without bound as s approaches infinity.

Hence, x([infinity]) is infinite or undefined, as the function grows without bound as s tends to infinity.

In summary, x(0) is -4, and x([infinity]) is either infinite or undefined, depending on the context of the problem.

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x(0) is undefined and x(∞) is approximately equal to 1.

To determine x(0) and x(∞) for the function x(s) = \(s^2 - 4 / (2s^3 - 4s^2 + 10s)\), we substitute the respective values of s into the function.

x(0):

To find x(0), we substitute s = 0 into the function:

x(0) = (0^2 - 4) / (2(0^3) - 4(0^2) + 10(0))

x(0) = (-4) / (0 - 0 + 0)

x(0) = -4 / 0

Note that division by zero is undefined in mathematics, so x(0) is undefined.

x(∞):

To find x(∞), we substitute s = ∞ (infinity) into the function:

x(∞) = (∞^2 - 4) / (2(∞^3) - 4(∞^2) + 10(∞))

When dealing with infinity, we need to consider the dominant term(s) in the expression. In this case, the highest power of s is ∞^3, so the other terms become relatively insignificant compared to it. We can simplify the expression:

x(∞) ≈ (∞^3) / (2(∞^3))

x(∞) ≈ (∞^3) / (∞^3)

x(∞) ≈ 1

Therefore, x(∞) is approximately equal to 1.

To summarize:

x(0) is undefined, and x(∞) is approximately equal to 1.

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Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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A good example of a firm deploying a global standardization strategy is McDonald's.

McDonald's is known for its standardized menu and operating procedures across its locations worldwide. The company maintains consistency in its products, branding, and customer experience regardless of the country or region. This approach allows McDonald's to benefit from economies of scale, streamlined operations, and a recognizable brand image globally. By implementing a global standardization strategy, McDonald's is able to achieve efficiency, cost savings, and a consistent customer experience across its international locations.

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Answer:

B

Step-by-step explanation:

In order to determine the integer that makes true the given expression:

______ x 7 = -14

consider that such integer must be equal to the quotient between -14 and 7:

-14/7 = -2

In fact, you have:

-2 x 7 = -14

Hence, the integer is -2

The actual implications of giving a bone to a subject would depend on the specific context, such as the subject's identity (human or animal), the purpose of giving the bone, and the cultural or medical considerations involved.

Assuming that a randomly selected subject is given a bone, it seems that we need to consider the context and determine the implications or consequences of this action. Without further information, it is difficult to provide a specific explanation or analysis. However, we can discuss some general possibilities and considerations related to giving a bone to a subject.

1. Medical Treatment: Giving a bone could be related to medical treatment or procedures. For example, in orthopedic medicine, bones may be used for grafting or reconstructive surgeries to repair damaged or fractured bones.

2. Nutritional Benefits: Bones, such as beef or chicken bones, can be used to make broths or stocks that are rich in nutrients like collagen, calcium, and other minerals. These bone-based products are often consumed for their potential health benefits.

3. Animal Care: Giving a bone to an animal, particularly dogs, is a common practice. Bones can serve as a form of entertainment or enrichment for pets, satisfying their chewing instincts and providing dental benefits.

4. Symbolic Meaning: In certain cultures or traditions, bones can hold symbolic meanings. They may be used in rituals, ceremonies, or artistic expressions to represent various concepts, such as strength, mortality, or spirituality.It's important to note that the above interpretations are speculative and based on general assumptions. The actual implications of giving a bone to a subject would depend on the specific context, such as the subject's identity (human or animal), the purpose of giving the bone, and the cultural or medical considerations involved.

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Answer: $140

Step-by-step explanation:

100% of 70 is 70 so increasing the sale price from 70 by 100% would be $140

Answer: The answer is $140

Glass is denser than water. The correct answer is option d

Refraction is the bending of a light ray as it crosses the boundary between two media of different densities, thus causing a change in its direction.

Given that a  beam of light bends when it passes from air into water, and then bends even more when it passes from water into glass.

Light rays do bend when they cross from less dense medium to a denser medium and vice versa.

We can therefore conclude from this fact that glass is denser than water.

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The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.

The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.

The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.

Where:

A = future value

P = Present value of investment

i = interest rate

n = number of periods.

The future value of the investment can also be determined using an online finance calculator, as follows.

Then the interest is the difference between the future value and the present value.

Initial deposit = $8,241.78

Interest rate = 5.5% compounded daily

Investment period = 31 days

N (# of periods) = 31 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $8,241.78

PMT (Periodic Payment) = $0

Results:

FV = $8,280.37

Total Interest $38.59 ($8,280.37 - $8,241.78)

Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.

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Answer:

Decay

3

Step-by-step explanation:

The probability mass function of the discrete distribution given is; $p(x) =\begin{cases}\frac{1}{3} & \text{for }x=0\\[0.3em] \frac{2}{3} & \text{for }x=1\\[0.3em] 0 & \text{otherwise.}\end{cases}$Let us consider that $Y = X_1 X_2 X_3.$ We need to determine the moment generating function (MGF) of Y.

Let us recall the definition of MGF of a random variable. It is given by;$$M_X(t) = \text{E}[e^{tX}].$$Now, let us compute the moment generating function of Y.$$M_Y(t) = \text{E}[e^{tY}]$$$$M_Y(t) = \text{E}[e^{tX_1X_2X_3}]$$Since $X_1, X_2$ and $X_3$ are independent, it follows that;$$M_Y(t) = \text{E}[e^{tX_1}]\text{E}[e^{tX_2}]\text{E}[e^{tX_3}]$$$$M_Y(t) = M_{X_1}(t)M_{X_2}(t)M_{X_3}(t)$$$$M_Y(t) = \left(\frac{1}{3}e^{0t}+\frac{2}{3}e^{1t}\right)^3$$$$M_Y(t) = \left(\frac{1}{3}+\frac{2}{3}e^{t}\right)^3$$

Hence, the moment generating function of $Y=X_1 X_2 X_3$ is $\left(\frac{1}{3}+\frac{2}{3}e^{t}\right)^3.$

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Answer:

hope it helps you.......

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.

Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.

Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.

So the question is: is this pattern true for all triangular numbers? Let's investigate further.

a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.

Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.

b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.

Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.

Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

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Answer:

step by step ✌️

Answer:

(a) N (16, 2.5²)

(b) 0.241

(c) Low: 15.4 years

    High: 16.6 years

Step-by-step explanation:

The random variable X is defined as the age at death of a randomly selected indoor cat.

(a)

The distribution of X is:

\(X\sim N(\mu = 16, \sigma^{2}=2.5^{2})\)

(b)

Compute the probability that an indoor cat dies when it is between 17.2 and 19.6 years old as follows:

\(P(17.2<X<19.6)=P(\frac{17.2-16}{2.5}<\frac{X-\mu}{\sigma}<\frac{19.6-16}{2.5})\)

                            \(=P(0.48<Z<1.44)\\=P(Z<1.44)-P(Z<0.48)\\=0.92507-0.68439\\=0.24068\\\approx 0.241\)

Thus, the probability that an indoor cat dies when it is between 17.2 and 19.6 years old is 0.241.

(c)

Compute the two numbers within which 20% of indoor cats' age of death lies as follows:

\(P(x_{1}<X<x_{2})=0.20\\\\\Rightarrow P(-z<Z<z)=0.20\\\\P(Z<z)-P(Z<-z)=0.20\\\\P(Z<z)-[1-P(Z<z)]=0.20\\\\2P(Z<z)-1=0.20\\\\2P(Z<z)=1.20\\\\P(Z<z)=0.60\)

The corresponding value of z is, 0.25.

Compute the value of x₁ and x₂ as follows:

\(z=\frac{x_{1}-\mu}{\sigma}\\\\0.25=\frac{x_{1}-16}{2.5}\\\\x_{1}=16+(0.25\times 2.5}\\\\x_{1}=16.625\\\\x_{1}\approx 16.6\)                \(z=\frac{x_{1}-\mu}{\sigma}\\\\-0.25=\frac{x_{2}-16}{2.5}\\\\x_{2}=16-(0.25\times 2.5}\\\\x_{2}=15.375\\\\x_{2}\approx 15.4\)

Low: 15.4 years

High: 16.6 years