Finding the area shaded figure

Final answer:

To find n(A), we count the elements in the set A={0,1,2,3,...,2000} which form an arithmetic sequence. By applying the formula for the number of terms in an arithmetic sequence, we find that n(A) = 2001.

Explanation:

To find n(A), which represents the number of elements in set A, we simply count the elements listed in the given set A={0,1,2,3,...,2000}. These elements form an arithmetic sequence starting from 0 and ending at 2000 with a common difference of 1 between each consecutive number.

The formula for the number of terms n in an arithmetic sequence is given by:

n = (last term - first term) / (common difference) + 1

Applying the formula to our set A:

n = (2000 - 0) / 1 + 1 = 2000 + 1 = 2001

Therefore, n(A) = 2001.

The probability of getting the king of spades as the top card and the bottom card of a shuffled deck depends on whether the cards are picked with or without replacement.

The probability of getting the king of spades as the top card and the bottom card of a shuffled deck depends on whether the cards are picked with or without replacement. If the cards are picked without replacement, the probability will be different than if they are picked with replacement.

If the cards are picked without replacement, the probability of getting the king of spades as the top card is 1/52. This is because there is only one king of spades in a deck of 52 cards. After the king of spades is picked as the top card, there are 51 cards left in the deck. The probability of getting the king of spades as the bottom card is also 1/51 because there is only one king of spades left in the deck.

If the cards are picked with replacement, the probability of getting the king of spades as the top card is still 1/52, but the probability of getting the king of spades as the bottom card is also 1/52. This is because each card is put back into the deck and reshuffled before the next card is picked, so the probabilities for each card remain the same.

Answer:

The mean of sample (21.6) is greater than population mean and the standard deviation of sample (8.4) is also greater than population standard deviation.

Both values, mean and std are greater than corresponding population values. This means, that our sample overestimates or is skewed to the right in the values of population. Also each specific value is farther apart from the mean so variation is much bigger in our sample than in our population.

Step-by-step explanation:

To calculate the mean, we estimate the avergage of the data as

Mean = Sum(data)/n

Where n is the number of observations of sample. We have;

(25 + 32 +  16 + 12 + 11 + 38 + 22 + 21  + 19 + 20)/10 = 21.6

The standard deviation is the square root of variance. Variance is sum of the deviation of each data point to the sample mean.

Variance = sum i= 1 to n (Xi-xmean)/(n-1)

Where n = 10 the # of observations and xi is each specific data point.

If you calculate it in Excel or or by hand you obtain:

Variance = sum i= 1 to n (Xi-21.6)/(10-1) = 8.4

Both values, mean and std are greater than corresponding population values. This means, that our sample overestimates or is skewed to the right in the values of population. Also each specific value is farther apart from the mean so variation is much bigger in our sample than in our population.

Answer:

The mean of the random samples (21.6) is greater than population´s mean (19.4) and the STD of the random samples (7.96) is greater than population´s STD (5.8)

Step-by-step explanation:

To calculate the mean of the random samples, we find the average value of the data set

[tex]Mean=\frac{(\sum_{i=0}^{n}{a_i})}{n}\\[/tex]

Where a is an element of the random example and n is the number of elements in the sample, as follows

Mean = (25+32+16+12+11+38+22+21+19+20)*(1/10) = 21.6

To calculate the STD (Standard Deviation) we need to know the variance, because

[tex]STD=\sqrt{var}[/tex]

The variance is determined as the sum of the deviation from one element of the data to the mean squared, all divided by n as below.

[tex]Var=(\sum_{i=1}^{n}{(a_{i}-Mean)^{2})/n[/tex]

If you calculate this by calculator or with a computer, you should get Var=63.44

And with that value, STD=7.96≈8

Therefore, by comparison, both Mean and STD of the random sample are greater than the population´s parameter

Answer:

Exponential decay

Step-by-step explanation:

The function which has a constant halving time represents the exponential decay or negative growth curve type of function.

When the value of one variable of the function is decreased with increase in the number of other variable, then it is called the exponential decay function with constant exponential coefficient.'

It can be given as,

[tex]f(x)=ab^x[/tex]

Here, a is the exponential coefficient.

A function which has a constant halving time is,

[tex]A(t)=A_o\left(\dfrac{1}{2}\right)^{t/h}[/tex]

Here, Ao is the initial time, t is time and h is halving time. This is an exponential decay function.

The function which has a constant halving time represents the exponential decay or negative growth curve type of function.

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Answer:

standard deviation=4.47

Step-by-step explanation:

We have to find the standard deviation of the data set:

13   17    9  21

Now we calculate the mean of the data .

We know that mean is the average of the data values and is calculated as:

[tex]Mean=\dfrac{13+17+9+21}{4}\\ \\Mean=\dfrac{60}{4}\\\\Mean=15[/tex]

Now we find the difference of each data point from the mean as:

Deviation:

13-15=-2

17-15=2

9-15=-6

21-15=6

Now we have to square the above deviations we obtain:

4   4   36   36

now we calculate the mean of the above sets:

[tex]variance=\dfrac{4+4+36+36}{4}\\ \\Variance=\dfrac{80}{4}\\\\Variance=20[/tex]

now standard deviation is the positive square root of variance

so, standard deviation=√(20)=4.47

Final answer:

To find the standard deviation for Omar's work hours, we first calculate the mean of the data, then compute the squared differences from the mean, sum these, divide by the sample size minus one, and take the square root of this result, which is approximately 5.16 hours.

Explanation:

To calculate the standard deviation for Omar's recorded work hours: 13, 17, 9, 21, we follow these steps:

First find the mean (average) of the sample. Mean = (13 + 17 + 9 + 21) / 4 = 60 / 4 = 15 hours.

Next, subtract the mean from each data point and square the result:[tex](13-15)^2[/tex] = 4,[tex](17-15)^2[/tex] = 4, [tex](9-15)^2[/tex]= 36,[tex](21-15)^2[/tex] = 36.

Now, find the sum of these squared differences: 4 + 4 + 36 + 36 = 80.

Since this is a sample (not the full population), we divide by the sample size minus 1, which is 3: 80 / 3 ≈ 26.67.

Finally, take the square root of this quotient to find the standard deviation: √26.67 ≈ 5.16 hours.

Therefore, the standard deviation for the data is roughly 5.16 hours.

The value of m is 36

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation.

Given:

1/3m+3−5/6m=−15

Subtract 3 from both sides

1/3m +3 -5m/6 -3= -15-3

Simplify

1/3 m -5m /6 = -18

Now, multiply the LCM

-3m = -108

Divide both side by (-3)

-3m/(-3)= -108/ (-3)

m= 36.

Hence, the value of m is 36.

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the answer (B) thank me later ;)

Answer: D.)The slope is Negative three-halves and contains the point (0, −2).

Step-by-step explanation:

i got it correct obviously oncrip

Final answer:

To determine the quantity of chocolate chips needed for a recipe that calls for one and one quarter times as much sugar as chocolate chips, set up a proportion using the given sugar amount. Multiply the sugar quantity (1⅓ cups) by the reciprocal of the ratio (4/5), which results in 1⅓ cups of chocolate chips needed.

Explanation:

To determine the quantity of chocolate chips needed when the recipe asks for one and one quarter times as much sugar as chocolate chips, we can use a simple proportion based on the quantity of sugar used. The recipe specifies that 1⅔ cups of sugar are used, which is equivalent to ⅓ cups of sugar when converted to an improper fraction.

The proportion would look like this: Chocolate Chips (C) is to 1 as 1⅓ cups of sugar is to 1⅔, which can be set up as a ratio: C/1 = (1⅓)/(1⅔). To solve for C, we multiply both sides by 1 to get rid of the denominator for C, giving us:

C = (1⅓)/(1⅔)

Now, let's solve the equation:

Convert 1⅓ to an improper fraction: 5/3.

Convert 1⅔ to an improper fraction: 5/4.

Divide 5/3 by 5/4 to find the quantity of chocolate chips: (5/3) × (4/5) = 20/15 = 4/3, which simplifies to 1⅓ cups.

Therefore, you would need 1⅓ cups of chocolate chips for the recipe.