A boy has 5 red, 3 yellow and 4 green marbles. In how many ways can the boy arrange the marbles in a line if: a) Marbles of the same color are indistinguishable? b) All marbles have different sizes? Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining.

Answer:

Step-by-step explanation:

1. 93 * 2 is 186 + 0 = 1860

2. 4 * 9 = 36

3. 88 + 1 = 89

4. 4 * 8 = 32

5. 3 * 20 = 60

6. 200 - 80 = 120

Answer:

93 × 20 = 1860

4 × 9 = 36

88 + 1 = 89

4 × 8 = 32

3 × 20 = 60

200 - 80 = 120

Answer:

Step-by-step explanation:

No attempt is made to influence anything - just ask questions and record the responses. By definition, An observational study measures the characteristics of a population by studying individuals in a sample, but does not attempt to manipulate or influence the variables of interest.

Answer:

the volume of the prism is 60 cubic meters (m³).

Step-by-step explanation:

We can calculate the volume of the rectangular prism by multiplying its length, width, and height.

Given:

Length = 3 m

Width = 4 m

Height = 5 m

The volume of the rectangular prism is:

Volume = length x width x height

Volume = 3 m x 4 m x 5 m

Volume = 60 m³

Therefore, the volume of the prism is 60 cubic meters (m³).

396,667.5 is the total of all whole numbers between 1 and 890.

To find the sum of the whole numbers from 1 to 890, we can use the formula for the sum of an arithmetic series:

S = n(a1 + an) / 2

Where S is the sum, n is the number of terms, a1 is the first term, and an is the last term. In this case, n = 890, a1 = 1, and an = 890. Plugging these values into the formula, we get:

S = 890(1 + 890) / 2

S = 890(891) / 2

S = 793335 / 2

S = 396667.5

Therefore, the sum of the whole numbers from 1 to 890 is 396,667.5.

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The probability of having 14 purines out of 20 microrna is 0.2208.

The probability of having 14 purines out of 20 microrna can be calculated using the binomial probability formula. This formula states that the probability of having a certain number of successes (in this case, purines) out of a given number of trials (the microrna) is equal to the number of ways to get that number of successes, multiplied by the probability of success for each trial, to the power of the number of successes.

The formula is as follows: P(x successes) = \(nCx * p^x * (1-p)^(n-x)\).

In this case, n = 20, x = 14, p = 0.7. Therefore, the probability of having 14 purines out of 20 microrna is 0.2208.

To calculate this, we can first calculate nCx, which is the number of ways to get 14 successes out of 20 trials. This is equal to \(20!/14!(20-14)!\) which is \(20*19*18*17*16*15/14!\), which simplifies to 4845. We can then multiply this by 0.7^14 and (1-0.7)^6 (the probability of success for each trial and the number of trials that didn't result in success), which gives us 0.2208.

Therefore, the probability of having 14 purines out of 20 microrna is 0.2208.

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Answer:

40.3°

Step-by-step explanation:

sin x/ (5.3) = sin 90/ (8.2)

sin x = (5.3 sin 90) / 8.2

= 5.3/8.2

x = arcsin (5.3/8.2)

= 40.3° to 1 dp

The measure of angle x using Trigonometry is 40.263215° or 40.3.

Trigonometry is a branch of mathematics that deals with the study of relationships involving the angles and sides of triangles. It is especially useful in understanding the properties and behavior of right-angled triangles.

Sine ratio is defined as the ratio of the length of the side opposite an angle to the length of the triangle's hypotenuse.

From the figure,

Perpendicular = 5.3 m

Hypotenuse = 8.2 m

Using Trigonometry

sin x = P / H

sin x = 5.3/ 8.2

sin x = 0.6463

Using Inverse Trigonometry

x = \(sin^{-1}\)(0.6463)

x= 40.263215°

Thus, the measure of angle x is 40.3.

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You need to draw at least 5 cards to be sure to get three cards of the same denomination. The reason is that there are 13 different denominations and 5 choose 3 = 10 ways to choose 3 cards out of 5. So, in 5 cards, there will be at least one set of three cards with the same denomination.

Each denomination (number value) has 4 cards in a standard deck of 52 playing cards. When you draw 5 cards, you have at least 4 cards of the same denomination (number value), or you have at least 2 pairs of the same denomination, or you have 3 cards of one denomination and 2 of another. In the first case, you already have 3 cards of the same denomination, so you're done. In the second case, you can choose any one pair to be your set of three cards with the same denomination. In the third case, you can choose the three cards of one denomination to be your set. In all cases, you are guaranteed to have at least 3 cards of the same denomination after drawing 5 cards.

Therefore, to guarantee getting three cards of the same denomination, you need to draw at least 5 cards.

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The least number of each pack that Martin can buy is 5 packs of burger and 3 packs of bread buns.

Since the packs of bread buns contain 40 bread buns and each pack of burgers contains 24 burgers, then we'll calculate the multiples of each number. This will be:

Multiples of 24 = 24, 48, 72, 96, 120

Multiples of 40 = 40, 80, 120, ...

Therefore, the least common multiple is 120.

The least number of packs of burger to buy is 5 and least number of packs of bread buns to buy is 3.

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Answer:

We are given the system of equations:

y = x - 1 (equation 1)

y = -3x - 5 (equation 2)

To solve this system of equations using the substitution method, we need to solve one of the equations for one variable and substitute the result into the other equation. Let's solve equation 1 for y:

y = x - 1

Now we can substitute this expression for y in equation 2:

x - 1 = -3x - 5

We will now solve for x:

4x = -4

x = -1

We can substitute this value of x back into equation 1 or equation 2 to find the value of y:

Using equation 1:

y = x - 1

y = -1 - 1

y = -2

Using equation 2:

y = -3x - 5

y = -3(-1) - 5

y = 2

Therefore, the solution to the system of equations is (x, y) = (-1, -2) or (x, y) = (-1,2).

A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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The final value of the investment after 8 years is approximately $2,346.09.

We can use the formula for compound interest to find the final value of the investment:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the initial investment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = 2000, r = 0.02 (2% expressed as a decimal), n = 4 (compounded quarterly), and t = 8.

Plugging in these values, we get:

A = P(1 + r/n)^(nt)

A = 2,000.00(1 + 0.02/4)(4)(8)

A = 2,000.00(1 + 0.005)(32)

A = $2,346.09

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(a-1) The value of the population mean is unknown.

(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.

(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).

(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.

(e-2) It would be reasonable to conclude that the population mean is 18 eggs.

(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.

(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.

(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.

Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.

In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.

(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.

(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.

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The amount of interest paid per year is $2400

What is Interest rate?

An interest rate is the percentage a lender charges on the amount of money borrowed from them.

Given that, Brendon Walsh wants to borrow the sum of $40,000 from the bank

Interest rate is 6%

Time is 5 years

Therefore, the yearly payment amount can be calculated as follows

= 40,000 × 5 × 6/100

= 40,000 × 5 × 0.06

= 12000/5

= $2,400

Hence, the yearly payment is $2,400

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The symbols for the true population variance and standard deviation are: c. s2 and d. o2

The true population variance is represented by the symbol s2, while the true population standard deviation is represented by the symbol o2.

It is important to note that the standard deviation is simply the square root of the variance, so if you know one, you can easily find the other.

The standard deviation is a measure of how spread out the data is from the mean, and the variance is the square of the standard deviation.

Both are important statistical measures that are used to analyze data and draw conclusions about a population.

Therefore, options (c) and (d), i.e., s2 and o2 are the correct answers.

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Answer:

true

Step-by-step explanation:

did the test

Answer: false

Step-by-step explanation:

Step-by-step explanation:

16a^2-56a+49

used the an app to find it

Answer:

41.34

Step-by-step explanation:

We can use the Pythagorean theorem to solve for the distance. First we will create an imaginary triangle with the leg lengths being the x distance and y distance between the 2 points and the hypotenuse being the distance between the 2 points.

x distance =

\(15 - (-20) = 35\)

y distance =

\( |-17-5| = | - 22| = 22\)

We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle

xdistance²+ydistance²=distance²

35²+22²=distance²

1709=distance²

\( \sqrt{1709} = distance\)

In decimal form the distance would be around 41.34.

That is the answer

- Kan Academy Advance

Answer:

(22/7)/6=0.523809

Step-by-step explanation:

V=4/3πr^3

V=4/3π(1/2)^3=π/6

or (22/7)/6=0.523809

the expression as a sum and/or difference of logarithms. We'll be using the properties of logarithms to do this.

Given expression: ln[(x^2 - x - 6)/(x + 5)^3]^0.5

Step 1: Apply the power rule (ln(a^b) = b*ln(a)):
0.5 * ln[(x^2 - x - 6)/(x + 5)^3]

Step 2: Apply the quotient rule (ln(a/b) = ln(a) - ln(b)):
0.5 * (ln(x^2 - x - 6) - ln((x + 5)^3))

Step 3: Apply the power rule again on ln((x + 5)^3):
0.5 * (ln(x^2 - x - 6) - 3*ln(x + 5))

Step 4: Distribute the 0.5 to both terms inside the parentheses:
(0.5 * ln(x^2 - x - 6)) - (0.5 * 3 * ln(x + 5))

Step 5: Simplify the expression:
(0.5 * ln(x^2 - x - 6)) - (1.5 * ln(x + 5))

So, the expression rewritten as a sum and/or difference of logarithms is:

0.5 * ln(x^2 - x - 6) - 1.5 * ln(x + 5)

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Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Using a system of equations, we have that:

a) It is not possible to solve for any of the variables using only Equation #1 and Equation #2, as there are only 2 equations for 3 variables.

b) It is possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3, as there are 3 equations for 3 variables. The solutions are: x = 12, y = 1, z = -29.

c) These solutions do not hold for equation 4, meaning that equation 4 is inconsistent for the system.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

To solve a system, the number of equations has to be at least the same as the number of variables, hence in item a, it is not possible to solve for any of the variables using only Equation #1 and Equation #2, as there are only 2 equations for 3 variables.

In item b, we can solve. From the second equation, we have that:

x = 5y + 7.

From the first equation, we have that:

z = 8 - 3x - y

z = 8 - 3(5y + 7) - y

z = 8 - 15y - 21 - y

z = -13 - 16y

From the third equation, we can replace and solve for y.

3z + 2x - 2y = 15.

3(-13 - 16y) + 2(5y + 7) - 2y = 15

-39 - 48y + 10y + 14 - 2y = 15.

-40y - 25 = 15

40y = 40.

y = 1.

Then the solutions for x and z are:

Replacing the solutions in equation 4, we have that:

4x + 5y - 2z = -3.

4(12) + 5(1) - 2(-29) = -3, which is false.

These solutions do not hold for equation 4, meaning that equation 4 is inconsistent for the system.

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The number we should pick near average value is 252 or 253.

In this given scenario, we have 10 players, everyone wagers 100 bucks and everyone picks 0-100. The person who picks to half the average wins the prize. To determine what number we should pick and why, let's start by solving the problem step-by-step.

Step 1: Find the average value of all picks.To find the average, we add up all the picks and divide by the number of players. We have 10 players, so: Sum of all picks = 0 + 1 + 2 + ... + 99 + 100 = 5050

Average value = (sum of all picks) / (number of players)= 5050 / 10= 505

Step 2: Half the average value. To half the average value, we divide it by 2:

Half of average = (average value) / 2= 505 / 2= 252.5

Step 3: Choose the number closest to half the average. Now that we know that the half of the average value is 252.5, we should choose the number closest to it. The person who picks the number closest to 252.5 wins the prize. If we pick a number less than 252.5, we will not win because someone who chose a number greater than 252.5 will win. If we pick a number greater than 252.5, we will not win because someone who chose a number less than 252.5 will win.So, the number we should pick is 252 or 253. Both numbers are equally close to 252.5. If we want to win, we should choose one of these numbers.

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Answer:

n = 12

Step-by-step explanation:

I assume in problem 4 the relation between miles and hours is proportional.

Set up a proportion.

45 miles is to 4 hours as 135 miles is to n hours.

45/4 = 135/n

Cross multiply.

45n = 4 × 135

n = 4 × 3

n  = 12

Answer:

12

Step-by-step explanation:

Because we can divide 45 and 4 and we get 11.25

Now we know that one hour is 11.25 miles. So just divide 135/11.25

and you get 12

im pretty sure thats the correct answer. Hope this helps

There are 86 treats did Sidney buy in all.

We have to given that;

Sidney bought some treats for her puppy.

And, She bought 5 packs of crunchy treats and 7 bags of soft treats.

Since, There were 6 crunchy treats in each pack and 8 soft treats in each bag.

Hence, Total crunchy treats in 5 packs are,

= 5 x 6

= 30

And, Total soft treats in 7 bags are,

= 8 x 7

= 56

Therefore, Total number of treats did Sidney buy in all is,

⇒ 56 + 30

⇒ 86

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Answer:

(9,12) I think  

Step-by-step explanation:

The widest confidence interval that will be produced the 99.7%, given a sample proportion of 0.4.

If the sample size is given to be n < 30, then for finding the confidence interval for the mean of the population from this small sample, we use the t-statistic.

Let the sample mean given as \(\overline{x}\) and

The sample standard deviation s, and

The sample size = n, and

The level of significance = \(\alpha\)

Then, we get the confidence interval in between the limits

\(\overline{x} \pm t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}\)

where \(t_{\alpha/2}\) is the critical value of 't' that can be found online or from tabulated values of critical value for a specific level of significance and degree of freedom n - 1.

In statistics, a confidence interval is a range to estimate for unknown terms. The most common level is the 95% confidence interval.

So, the widest confidence interval that will be produced the 99.7%, given a sample proportion of 0.4.

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Answer: 59.58 ft

Step-by-step explanation:

Given

The area of the neighbor's fence is  \(A=887.5\ ft^2\)

Suppose the length of the fence is L and the shape of the fenced area is square

So, we can write

\(\Rightarrow L^2=887.5\\\Rightarrow L=\sqrt{887.5}=29.79\ ft\)

According to the question, Cody's fence length must be twice of neighbor's

The length of Cody's fence is \(=2L=2\times 29.79=59.58\ ft\)

1. 45+15w

2. 3(15+5w)

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