A function f has Maclaurin series given by 1+x^2/2!+x^4/4!+x^6/6!+...+x^2n/(2n)!. Which of the following is an expression for f(x)?
a) cosx
b) e^x-sinx
c) e^x+sinx
d) 1/2 (e^x+e^-x)
e) e^x^2

The probability that a card is a spade or a king, given that it is black is 3/26 or 0.1154 or 11.54%

In a standard deck of cards, we have the following readings

Black cards = 26

Black spade or king = 3

So, we have the probability formula to be

Probability = Black spade or king/Black cards

This gives

Probability = 3/26

Evaluate

Probability = 0.1154

Express as percentage

Probability = 11.54%

Hence, the probability that a card is a spade or a king, given that it is black is 3/26

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"The approximate value of D(4) is 24.6976." Please double-check your calculations and ensure that you correctly evaluated e^(-0.6) in your initial attempt. If you received a different answer, there may have been an error in the calculation.

To evaluate the expression D(4) = 45e^(-0.15(4)), we can follow the order of operations.

First, we simplify the exponent inside the parentheses:

-0.15(4) = -0.6

Next, we substitute this value back into the expression:

D(4) = 45e^(-0.6)

Using the properties of exponential functions, we can rewrite this as:

D(4) = 45 * e^(-0.6)

Now, we can calculate the value of e^(-0.6) using a calculator or mathematical software:

e^(-0.6) ≈ 0.5488 (rounded to four decimal places)

Finally, we substitute this value back into the expression:

D(4) ≈ 45 * 0.5488 ≈ 24.6976.

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Answer:

Tommy delivered 41 newspapers

Step-by-step explanation:

Step 1:  We can convert the percentage to a decimal by either imagining the percentage sign as a decimal and moving it two places to the right or by simply doing the operation 22 / 100, since a percentage is out of 100:

22% = 22.0 = 0.22

22 / 100 = 11 / 50 = 0.22

Step 2:  When dealing with percentage problems, we can use the phrase "y is P% of x" (P% of x is y also works) which allows us to create the equation:  P%x = y, where

Since we're that the pair delivered 186 together and Tommy delivered 22%, we're trying to find what value is 22% of 186.  Thus, we can use the percentage formula above, allow y to represent the unknown, 186 to represent x, and 0.22 to represent P%:

0.22 * 186 = y

40.92

41 = y

Thus, Tommy delivered 41 newspapers.

The metric system is easier to use than the English system for several reasons.

Firstly, the metric system is based on multiples of 10, making conversions between units straightforward. In contrast, the English system has inconsistent conversion factors between units, such as 3 feet in a yard or 16 ounces in a pound, making calculations more complex. Additionally, the metric system uses a consistent set of prefixes to indicate values that are either smaller or larger than the base unit, which further simplifies calculations.

Finally, the metric system is used universally across the world, whereas the English system is only used in a few countries, making it easier for people to communicate and conduct business using a standardized measurement system. In contrast, the English system uses units such as yards, miles, quarts, and gallons, which have inconsistent conversion factors, making calculations more complex and challenging.

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Answer: B. 50 degrees

Step-by-step explanation:

The measure of GAB is B. 50 because GAB is a vertical angle alongside DAE, and the measures of vertical angles are equal so because DAE measures 50 degrees, GAB also measures 50 degrees.

To test Acme's claim that 30% of the production run are rookies, 60% are veterans, and 10% are all-stars, you would use a hypothesis test. The null hypothesis would be that the claimed proportions are true (pR = 0.3, pV = 0.6, pA = 0.1) and the alternative hypothesis would be that at least one of the claimed proportions is incorrect.

You could use a goodness-of-fit chi-square test to compare the observed frequencies of each group of players in the package to the expected frequencies based on the claimed proportions. If the chi-square test statistic is large enough to reject the null hypothesis, then there is evidence that the claimed proportions are not accurate. The significance level would need to be chosen and the appropriate critical value for the chi-square distribution with 2 degrees of freedom would need to be calculated or looked up.

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Main Answer:The applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.

Supporting Question and Answer:

Why is random sampling an important step in ensuring fair data collection for determining popular exercise classes?

Random sampling is important in fair data collection as it helps ensure that the selected participants represent the larger population of the gym. By randomly selecting participants, the data analyst reduces the risk of bias and ensures that the survey results are more likely to be representative of the preferences of the entire gym population.

Body of the Solution: To ensure the data collected for determining the most popular exercise classes is fair, the data analyst should consider the following steps:

Therefore, the applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.

Final Answer: Hence,the applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.

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The applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.

Random sampling is important in fair data collection as it helps ensure that the selected participants represent the larger population of the gym. By randomly selecting participants, the data analyst reduces the risk of bias and ensures that the survey results are more likely to be representative of the preferences of the entire gym population.

To ensure the data collected for determining the most popular exercise classes is fair, the data analyst should consider the following steps:

The analyst should randomly select the 10 people to participate in the survey. This helps ensure that the sample is representative of the gym's population and reduces bias.

Informed consent: The analyst should obtain informed consent from the participants, explaining the purpose of the survey, how the data will be used, and ensuring that participants are willing to participate voluntarily.

Confidentiality and anonymity: The analyst should assure the participants that their responses will be kept confidential and anonymous. This encourages honest and unbiased responses, as individuals may feel more comfortable sharing their preferences without fear of judgment or repercussions.

Clear and unbiased questions: The survey questions should be clear, unbiased, and directly related to determining the most popular exercise classes. The questions should avoid leading or suggestive language that could influence participants' responses.

Sufficient sample size: While surveying 10 people can provide some insights, a larger sample size would increase the reliability and representativeness of the data. The analyst may consider increasing the sample size to obtain a more robust understanding of class preferences.

Therefore, the applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.

Hence, the applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.

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Answer:

Step-by-step explanation:

The correct answer is d. All of the above causes changes in the CPI to overstate the true inflation rate.

Johanna is conducting an experiment to measure the height that different people can jump using a trampoline. The data collected in this experiment can be used to identify trends and patterns in the jumping ability of the participants.

To conduct the experiment, Johanna will need to gather a sample of participants of various ages, genders, and fitness levels. She will then need to ensure that each participant jumps on the trampoline using the same technique and is measured in the same way to ensure accuracy and consistency of the data.

After collecting the data, Johanna can analyze it to identify any trends or patterns in the jumping ability of the participants. She may use statistical methods such as calculating the mean, median, mode, range, and standard deviation of the data to better understand the results. She may also use graphs and charts to visually represent the data and identify any outliers or anomalies.

Overall, Johanna's experiment can provide valuable insights into the jumping ability of different people and may be useful in designing training programs or evaluating the effectiveness of trampoline exercises.

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Answer:

5, -4

Step-by-step explanation:

The distance of the plane from point P by line of sight is 1385. 76 meters

Using the trigonometric identities, we have that these identities are enumerated as;

From the information given, we have that;

The opposite side = 800 m

The angle of elevation = 30 degrees

The distance of the plane from point P is the adjacent side

Using the tangent identity

tan 30 = 800/m

cross multiply the values

m = 1385. 76 meters

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Answer:

------------------

35 and 90 are the minimum and maximum values of the data set.

It means all observations are between those two numbers.

Hence the answer is 100%

Approximately 100% of the observations are between 35 and 90 in the given data set.

What is a median?

In statistics, the median is a measure of central tendency that represents the middle value of a set of data when arranged in ascending or descending order. It divides the data into two equal halves, with 50% of the values falling below the median and 50% falling above it.

To find the median, the data set is first arranged in order from smallest to largest (or vice versa). If the data set has an odd number of observations, the median is the middle value. For example, in a set of {1, 3, 5, 7, 9}, the median is 5.

The five-number summary consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. In this case, the minimum value is 35, and the maximum value is 90. Since these values define the range of the data set, all the observations are between these two values.

Therefore, approximately 100% of the observations are between 35 and 90.

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The total population of ducks is 960.

To estimate the total population of ducks, we can set up a proportion using the marked ducks as a sample.

Let's use the following proportion:

Total Ducks / Marked Ducks = Total Marked Ducks / Marked Ducks Counted

Total Ducks / 257 = 960 / 257

Total Ducks x 257 = 960 x 257

Divide both sides by 257 to solve for Total Ducks:

Total Ducks = (960 x 257) / 257

Total Ducks = 960

Based on the proportion, we estimate that the total population of ducks is 960.

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C(4,3) = 4

The expression C(4,3) represents the number of combinations of 4 items taken 3 at a time. Using the formula for combinations, we have:

C(4,3) = 4! / (3! * (4-3)!) = 4

Therefore, the answer is [4].

Answer:

108

Step-by-step explanation:

Both expressions are equivalent and represent the same result. So the final answer is that the new position of the submarine in relation to sea level is -1,320 feet.

To find the new position of the submarine in relation to sea level, we need to take into account its initial position and the rate at which it descends.

The submarine starts at a depth of -1,260 feet, so this will be our starting point.
We know that the submarine descends at a rate of 5 feet per minute for 12 minutes. To calculate how far it descends in total, we can multiply the rate by the time:
5 feet/minute x 12 minutes = 60 feet
So the submarine descends 60 feet in total. However, since it is descending, we need to subtract this value from the initial depth of -1,260 feet:
-1,260 feet - 60 feet = -1,320 feet
Therefore, the expression that represents the new position of the submarine in relation to sea level is:
-1,260 - (5 x 12) = -1,320
Alternatively, we could also write this as:
-1,260 + (-5 x 12) = -1,320
Both expressions are equivalent and represent the same result. So the final answer is that the new position of the submarine in relation to sea level is -1,320 feet.

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Answer:

Step-by-step explanation:

the answer is B

One change that can be made to one value in Dylan's plan to ensure the assignment is completed is to change hours worked to 4. 20 hours a day.

The current number of paper flowers that the team can make is:

= 4 x 3 hours a day x 12 people x 5 days per week x 2 weeks

= 1, 440 flowers

One change that can be made would be to increase the number of hours worked to 4. 20 hours.

This would give a total number of flowers of :

= 4 x 4. 20 hours a day x 12 people x 5 days per week x 2 weeks

= 2, 016 flowers

They would then meet the target.

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The GCF of the given literal terms m⁷ n⁴ p³ and mn¹² p⁵ is mn⁴p³.

To find the greatest common factor (GCF) of the given literal terms, we need to identify the highest power of each variable that appears in both terms.

The variables present in both terms are m, n, and p.

For m, the highest power is m⁷ in the first term and m¹ in the second term. Therefore, the common factor for m is m¹.

For n, the highest power is n⁴ in the first term and n¹² in the second term. Therefore, the common factor for n is n⁴.

For p, the highest power is p³ in the first term and p⁵ in the second term. Therefore, the common factor for p is p³.

Combining these common factors, we get the GCF of the given literal terms:

GCF = m¹ * n⁴ * p³

Therefore, the GCF of the given literal terms m⁷ n⁴ p³ and mn¹² p⁵ is mn⁴p³.

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Answer:

0.72

Step-by-step explanation:

im smart AND i found it online :>

72% as a decimal is 0.72. To find the decimal of any percentage, divide the percentage by 100.

We have the iterated integral:

∫

�

=

0

2

∫

�

=

1

5

5

(

�

+

�

)

(

2

−

�

2

)

�

�

�

�

∫

y=0

2

​

∫

x=1

5

​

5(x+y)(2−y

2

)dxdy

To convert this to polar coordinates, we need to express $x$ and $y$ in terms of $r$ and $\theta$. Since the region of integration is defined by $0 \leq y \leq 2$ and $1 \leq x \leq 5$, we see that $1 \leq r \leq 5$ and $0 \leq \theta \leq \pi$. Then we have:

�

=

�

cos

⁡

�

and

�

=

�

sin

⁡

�

x=rcosθandy=rsinθ

The Jacobian of the transformation is $\frac{\partial(x,y)}{\partial(r,\theta)} = r$, so we have:

\begin{align*}

\int_{y=0}^{2} \int_{x=1}^{5} 5(x+y)(2-y^2) ,dx,dy &= \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5(r\cos \theta + r\sin \theta)(2 - r^2\sin^2 \theta) ,r,dr,d\theta \

&= \int_{\theta=0}^{\pi} \int_{r=1}^{5} 10r^2\cos \theta ,dr,d\theta + \int_{\theta=0}^{\pi} \int_{r=1}^{5} 10r^2\sin \theta \cos \theta ,dr,d\theta \

&\quad + \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5r^3\sin \theta ,dr,d\theta - \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5r^5\sin^3 \theta ,dr,d\theta \

&= \int_{\theta=0}^{\pi} \left[ \frac{10}{3}r^3\cos \theta \right]{r=1}^{r=5} ,d\theta + \int{\theta=0}^{\pi} \left[ \frac{5}{2}r^3\sin^2 \theta \right]{r=1}^{r=5} ,d\theta \

&\quad + \int{\theta=0}^{\pi} \left[ \frac{5}{4}r^4\sin \theta \right]{r=1}^{r=5} ,d\theta - \int{\theta=0}^{\pi} \left[ \frac{5}{6}r^6\sin^4 \theta \right]{r=1}^{r=5} ,d\theta \

&= \int{\theta=0}^{\pi} \frac{1240}{3}\cos \theta + \frac{60}{2}\sin^2 \theta + \frac{155}{4}\sin \theta - \frac{2480}{6}\sin^4 \theta ,d\theta \

&= \left[ \frac{1240}{3}\sin \theta - \frac{60}{2}\frac

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Total arrangement = Case 1 + Case 2 – Case 3

Total arrangement = 15 + 15 - 81 = -51

What is Sitting Arrangement ?

In mathematics, seating arrangement refers to the various ways in which individuals can be seated in a certain arrangement or order. This term is often encountered in combinatorics, which is a branch of mathematics that deals with counting arranging objects.

To find the number of seats satisfying a given condition, we can approach the problem using the inclusion-exclusion principle.

Let's look at these two cases: no girls are sitting together and no boys are sitting together.

Case 1: No girls are sitting together

In this case, we have to divide the five girls into three rows so that no two girls sit in any row. We can use a technique called stars and bars. Think of the girls as stars and the spaces between them and the ends as rods. We need to divide the five girls between the three rows, so we have four spaces between the stars and two ends, giving us (4 + 2)C2 = 15 ways to divide the girls.

Case 2: No boys sit together

Similarly, we have to divide the five boys among three rows so that no two boys sit in any row. Using the same stars and bars technique, we have (4 + 2)C2 = 15 ways to divide the boys.

However, we must exclude cases where boys and girls sit together. To find this, we need to find the number of arrangements where both conditions are violated.

Case 3: Boys and girls are sitting together

In this case, we can consider the pair of boy and girl sitting together as one entity. So we have four pairs (BB, GG, GB, BG) to split between the three rows, giving us 3^4 = 81 ways to split these pairs.

Now we can use the inclusion-exclusion principle to find the number of arrangements that satisfy at least one of the conditions. The total number of arrangements is the sum of arrangements without girls together, arrangements without boys, minus arrangements where both boys and girls sit together:

Total arrangement = Case 1 + Case 2 – Case 3

Total arrangement = 15 + 15 - 81 = -51

However, a negative value has no meaning in this context. It means that there are no valid seating arrangements that meet the given conditions. It may not be possible to seat students in such a way as to prevent two girls or two boys from sitting together in any row of five seats. The teacher may need to explore alternative seating arrangements or adjust conditions to find a suitable solution.

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Of total variation in "dependent-variable", the proportion which is explained by variation in "independent-variable" is called (b) coefficient of determination.

The "Coefficient-Of-Determination", denoted as R², is a statistical measure which represents the proportion of total-variation in the dependent variable which can be explained by  variation in "independent-variable".

It quantifies the percentage of dependent variable's variability which can be attributed to the independent variable. A higher coefficient of determination indicates a stronger relationship between the variables, which means that more of variation in "dependent-variable" can be accounted for by changes in the independent-variable.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Of the total variation in the dependent variable, the proportion that is explained by the variation in the independent variable is called

(a) the coefficient of correlation

(b) the coefficient of determination

(c) the coefficient of skewness

(d) none of the above

The LCM of the two polynomials is (x - 1)(x + 4)(x + 1).

Let's factorize the given polynomials:

Polynomial 1:

x² + 3x - 4 can be factored as (x - 1)(x + 4).

Polynomial 2:

2x² - 2 can be factored as 2(x - 1)(x + 1).

Now, we identify the highest power of each distinct factor:

The highest power of (x - 1) is (x - 1).

The highest power of (x + 4) is (x + 4).

The highest power of (x + 1) is (x + 1).

Therefore, the LCM of the two polynomials is (x - 1)(x + 4)(x + 1).

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Answer:

5√5 cm

Step-by-step explanation:

call the hypotenuse A. the other two sides are B and C.

in a right-angled triangle, A² = B² + C². also, let's just say that B is the side 5cm shorter than hypotenuse.

so we have 15² = (15 - 5)² + C²

225 = (10)² + C²

C² = 225 - 10² = 225 - 100

                      = 125.

C = √125 = √(25 X 5) = √25 X √5  = 5 X √5 = 5√5

The final amount of money in the account after 5 years is $3,316.08.

We have,

P = 2400 (the initial deposit)

r = 0.065 (the annual interest rate expressed as a decimal)

n = 1 (compounded annually)

t = 5 (5 years)

Plugging these values into the exponential formula, we get:

A(5) = 2400(1 + 0.065/1)⁽¹ ˣ ⁵⁾

= 2400(1.065)⁵

≈ $3,316.08

Therefore, the final amount of money in the account after 5 years with an initial deposit of $2,400 and a 6.5% interest rate compounded annually is $3,316.08.

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The lists that shows grade levels in order from the greatest fraction of students to the least fraction of students is of:

7th grade, 8th grade, 5th grade, 6th grade, 9th grade.

Here, we have,

A fraction is a numerical representation of the division of the two values x and y, as follows:

Fraction = x/y.

The terms are called as follows:

x is the numerator of the fraction.

y is the denominator of the fraction.

The decimal equivalent, which is used to order the fractions, of a fraction is obtained by the division of the numerator of the fraction by the denominator of the fraction.

Hence the equivalents of each fraction are given as follows:

5th grade: 33/50 = 0.66.

6th grade: 13/20 = 0.65.

7th grade: 18/25 = 0.72.

8th grade: 51/75 = 0.68.

9th grade: 3/5 = 0.6.

Hence the order from greatest to least is of:

7th, 8th, 5th, 6th, 9th.

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complete question:

The table shows the fraction of students from different grade levels who are in favor of adding new items to the lunch menu at their school.

Which list shows the grade levels in order from the greatest fraction of students to the least fraction of students?

Responses

7th grade, 8th grade, 9th grade, 6th grade, 5th grade

7th grade, 8th grade, 9th grade, 6th grade, 5th grade

9th grade, 6th grade, 7th grade, 5th grade, 8th grade

9th grade, 6th grade, 7th grade, 5th grade, 8th grade

8th grade, 5th grade, 7th grade, 6th grade, 9th grade

8th grade, 5th grade, 7th grade, 6th grade, 9th grade

7th grade, 8th grade, 5th grade, 6th grade, 9th grade

Therefore, the population size for year one is approximately 75.199.

Assuming that this is a question about exponential growth, we can use the formula:

n(t) = n(0) * e^(λt)

where n(0) is the initial population size, λ is the growth rate, t is the time in years, and e is the base of the natural logarithm.

For year one, t = 1, so we have:

n(1) = 30 * e^(1.20*1) = 30 * e^1.20

Using a calculator, we get:

n(1) ≈ 75.199

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If you deposit $2500 in an account that pays 6% annual interest, the account balance after one year can be calculated using the following formulas for different compounding periods:

- Annually: A = P(1 + r)^n, where A is the account balance, P is the principal, r is the annual interest rate, and n is the number of years. Substituting the given values, we get A = 2500(1 + 0.06)^1 = $2650.

Semiannually: A = P(1 + r/n)^(n*t), where n is the number of times the interest is compounded in a year and t is the time period in years. Substituting the given values, we get A = 2500(1 + 0.06/2)^(2*1) = $2659.51.

- Quarterly: A = P(1 + r/n)^(n*t), where n is 4 (number of times compounded in a year) and t is 1 (one year). Substituting the given values, we get A = 2500(1 + 0.06/4)^(4*1) = $2664.90.

- Monthly: A = P(1 + r/n)^(n*t), where n is 12 (number of times compounded in a year) and t is 1 (one year). Substituting the given values, we get A = 2500(1 + 0.06/12)^(12*1) = $2668.21.

- Continuously: A = Pe^(r*t), where e is the base of the natural logarithm. Substituting the given values, we get A = 2500*e^(0.06*1) = $2671.00.

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Answer:

#2

Step-by-step explanation:

Circle A'B'C'D' is smaller than circle ABCD. This means the scale factor must be less than one. 7/3 is greater than one, so it is false.