the length of a rectangle is four times it's width.if the perimeter is 70cm. Calculate the length and area of the rectangle​

The sum of the series correct to four decimal places is 7.0000

To approximate the sum of the series, we can use the ratio test. The ratio test states that if the limit of the ratio of consecutive terms approaches a number L, then the series converges if |L| < 1 and diverges if |L| > 1.

The nth term of the series is given by

\(T_n = (-1)^n (3n)(n!)\)

The consecutive terms is

\(R_n = T_{n+1}/T_n = (-1)^{n+1} (3n+3)(n+1) / (-1)^n (3n)(n!) \\= (-1)^{n+1} * 3 * (n+1) / (n!)\)

Taking the limit as n approaches infinity:

\(L = lim_{n - > \infty} \ R_n = lim_{n - > \infty} (-1)^{n+1} * 3 * (n+1) / (n!)\)

Since \((-1)^{n+1}\) alternates between -1 and 1, the limit approaches 0 and |L| < 1, which means the series converges.

To approximate the sum of the series, we can use a numerical method such as the Euler-Maclaurin formula. The formula approximates the sum of an infinite series by the sum of its first few terms and the remainder term:

\(\Sigma_n^\infty=1T_n \approx \Sigma_{i=1}^m T_i + R_m\)

where \(R_m\) is the remainder term that decreases as m increases

For example, let's choose m = 5:

\(\Sigma_{i=1}^5 T_i = T_1 + T_2 + T_3 + T_4 + T_5\)

= -3! + (-1) * 3 * 2! + (-1) * 2 * 3 * 1! + (-1) * 3 * 4! + (-1) * 4 * 3 * 2! = -6 + 6 - 2 + 24 - 24 = -2

The remainder term \(R_m\) can be estimated using the Euler-Maclaurin formula:

\(R_m = -B_{2m} / (2m)! * T_{m+1}\)

where B_k are the Bernoulli numbers.

For \(m = 5, B_2m = B_{10} = -1/252\), so

\(R_m = -B_{10} / (10)! * T_{m+1} = -1/252 * (-1)^6 * 3 * 6! = 1/252 * 3 * 720 = 9\)

Therefore, the sum of the series is approximately

\(\Sigma_{i=1}^\Infty T_i \approx \Sigma_{i=1}^5 \ T_i + R_m \\= -2 + 9 = 7\)

To four decimal places, this is 7.0000

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The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

When the variances of the two groups are not equal, pooled standard deviation estimations cannot be used. As an alternative, we must determine the standard error for each group separately. The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

The formula for this type of test statistic is given by -

\($t=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{x_2}{n_2}}}$$\)

Here, the variables can be defined as below -

\($s_1^2, s_2^2=$\) variance of two samples

\($n_1, n_2=$\) respective sizes of the two samples

t = t - distribution test statistic

\($x_1, x_2=$\) Mean of the two samples

As a result, the variables of the test statistic can be determined to be \($s _1, s _2$\), which represents the variance of two samples, \($n _1, n _2$\), which represents the size of the two samples, t, which represents the t-distribution test statistic, and \($x _1, x _2$\), which represents the mean of the two samples.

The complete question is:

The formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is:

t = X1−X2√s12/n1+s22/n2X1-X2s12/n1+s22/n2

Match the variables to their description.

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Answer:

It's C.

Step-by-step explanation:

log(a×b) = log(a) + log(b)

Answer: The first answer in the screenshot is correct. Sides 5, 10 and 5√3

Step-by-step explanation: In a 30°60°-90° triangle, the side opposite the 30° angle (shortest side) is half the length of the hypotenuse. So you have to choose one with 5 & 10. Use the Pythagorean theorem to calculate the remaining side  a² + b² = c²

5² + b² = 10²,   so b² = 100-25  √b²=√75  so √(25)(3)  

b= 5√3

Answer:

the first option is correct

Step-by-step explanation:

just took it

Answer:

The ordered pairs that are solution to this equation are:

(8,1) and (10,3)

Step-by-step explanation:

Given statement is:

"difference of two variables x and y is 7"

This can be mathematically written as:

\(x-y = 7\)

To solve this we have to put y = 1 and y = 3

Now,

Putting y = 1 in the equation

\(x-1 = 7\\x = 8\)

Putting y = 3 in the equation

\(x-3 = 7\\x = 7+3\\x = 10\)

Ordered pairs are of the form (x,y)

Hence,

The ordered pairs that are solution to this equation are:

(8,1) and (10,3)

Answer:

Yes.

Step-by-step explanation:

21:45 = 7*3 and 15*3

7:15 = 21:45

If it is impossible for events A and B to occur simultaneously, the events are said to be mutually exclusive. For such events, P(A or B) is equal to the sum of the individual probabilities of events A and B.

In other words, if A and B are mutually exclusive events, the probability of A or B occurring is equal to the sum of the probabilities of A and B individually.

Mathematically, P(A or B) = P(A) + P(B).

This holds true because when two events are mutually exclusive, the occurrence of one event excludes the possibility of the other event happening at the same time. Therefore, there is no overlap in the outcomes, and we can simply add their probabilities to calculate the probability of either event occurring.

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Answer:

A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected. Hence, the decision was  to retain the null hypothesis .

Step-by-step explanation:

A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected then the value of the test statistic is equal to zero.

Then the decision  would be to retain the null hypotheses as zero is included in any value of the level of significance applied.

The chi square is a continuous distribution ranging from zero to plus infinity.

Answer:

Step-by-step explanation:

oknjbgfkdfrgn jnfbfl

The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

The difference between the highest and lowest values for a given data collection is the range in statistics.

In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. It indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.

The range is the difference between the largest and smallest values in a data set.

For the given data, the largest value is 8 and the smallest value is 3.5.

Thus,

range = 8 - 3.5 = 4.5.

Hence, the range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

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Answer:

Step-by-step explanation:The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

Step-by-step explanation:

180-106=74

74/2=37

m<1=37°

m<2=37°

m<3=m<1=37°

m<4=m<2=37°

m<5= 106°

The measures of the numbered angles in rhombus DEFG are as follows:

m∠1 = 74 / 2 = 37°

m∠2 = 37°

m∠3 = 37°

m∠4 = 37°

m∠5 = 106°

Therefore,

m∠5 = 106°

Therefore,

2∠G + 2∠D = 360

2(106) + 2∠D = 360

2∠D = 360 -  212

∠D = 148 / 2

∠D = 74°

∠F = 74°

Recall the diagonal are angle bisectors. Therefore,

m∠1 = 74 / 2 = 37°

m∠2 = 37°

m∠3 = 37°

m∠4 = 37°

m∠5 = 106°

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The most accurate statement in this scenario is option B) For the 50% bonus level, the critical value is -1.65 and Huffman should give Brickley a 50% bonus.

To understand why this statement is accurate, let's go through the steps:

1) We are given that the population turnover rates are normally distributed with a population standard deviation of 1.5%. This information allows us to use statistical tests to make inferences about the population based on a sample.

2) A recent sample of 100 branch offices resulted in an average turnover rate of 24.2%. This sample average is a point estimate of the population average turnover rate.

3) We want to determine whether Brickley should receive the 50% bonus or not. To make this decision, we need to perform a hypothesis test.

4) The null hypothesis (H0) in this case is that Brickley cannot reduce turnover to less than 25%. The alternative hypothesis (Ha) is that Brickley can reduce turnover to less than 25%.

5) Using a significance level of 10%, we need to find the critical value. In this case, the critical value for a one-tailed test is -1.65.

6) We calculate the test statistic by subtracting the population mean from the sample mean and dividing it by the standard error of the sample mean. The standard error is the population standard deviation divided by the square root of the sample size.

7) The test statistic in this case is not given, but based on the information provided, we cannot calculate a test statistic of -533 or -10.66.

8) Since the test statistic is not provided, we cannot make a decision based on it. Instead, we compare the sample mean (24.2%) with the critical value (-1.65) to determine whether it falls in the rejection region or not.

9) If the sample mean falls in the rejection region (less than -1.65), we reject the null hypothesis and conclude that Brickley can reduce turnover to less than 25%. In this case, Huffman should give Brickley a 50% bonus.

10) Based on the information given, we cannot determine whether the sample mean falls in the rejection region or not. Therefore, we cannot make a definitive decision regarding the bonus.

In conclusion, option B) is the most accurate statement as it correctly states the critical value for the 50% bonus level, but it does not provide enough information to make a final decision about the bonus.

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Answer:

D the rio grande

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

EDGE 2020

Answer:

6

Step-by-step explanation:

5 to each players means you have 6 players and then you have 10 left for yourself

Answer:

You can hand out 5 softballs to 6 players.

Step-by-step explanation:

In order to solve this problem, you need to divide 30 balls to each player (In order to have 10 left.) 30 divided by 5 is 6, so you can only hand out 5 balls to 6 players in order to have 10 left out of 40.

Answer:

z ≈ 145.62

Step-by-step explanation:

using the sine ratio in the right triangle

sin18° = \(\frac{opposite}{hypotenuse}\) = \(\frac{45}{z}\) ( multiply both sides by z )

z × sin18° = 45 ( divide both sides by sin18° )

z = \(\frac{45}{sin18}\) ≈ 145.62 ( to the nearest hundredth )

The forecast for the first week in April is Option B, 217.33.

By using a three-week moving average to forecast the rate of new driver's license applications for the first week of April, means that we will average the rate of new driver's license applications over the last three weeks to forecast the rate for the next week.

Let's calculate the moving average for the first week of April.

Given weeks 2, 3, and 4 of March are 199, 215, and 212, respectively.

To find the three-week moving average, we add these three rates and divide by three:

(199 + 215 + 212) / 3 = 208.67

Therefore, the forecast for the rate of new driver's license applications for the first week of April using the three-week moving average is 208.67, rounded to two decimal places, the closest option to 208.67 is option B, which is 217.33.

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The probability of winning by picking the number 30 in roulette is 1/38.

In the game of roulette, the wheel consists of 38 spaces, with numbers 0 through 36 and an additional space marked 00. When you pick a specific number, such as 30, the probability of that number coming up on the wheel can be determined by calculating the ratio of favorable outcomes to the total number of possible outcomes.

In this case, there is only one favorable outcome, which is the ball landing on the number 30. The total number of possible outcomes is 38 since there are 37 numbered spaces (0 through 36) and one additional space for 00. Therefore, the probability of winning by picking the number 30 is 1 out of 38.

To put it simply, if you were to play roulette many times, you would expect the number 30 to come up approximately once every 38 spins on average. This probability remains the same for each individual spin, as each spin of the roulette wheel is an independent event.

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Answer:

\(f^{-1}(x) = \dfrac{6x + 5}{1 - x}\)

Step-by-step explanation:

To find the inverse of a function, we can swap x and y (f(x)), then solve for y, and represent that y as \(f^{-1}(x)\).

\(f(x) = \dfrac{x - 5}{x + 6}\)

↓ swapping x and y

\(x = \dfrac{y - 5}{y + 6}\)

↓ multiplying both sides by (y + 6)

\(x(y + 6) = y - 5\)

↓ simplifying using the distributive property

\(xy + 6x = y - 5\)

↓ subtracting 6x and y from both sides to isolate the y terms

\(xy - y = - 6x - 5\)

↓ undistributing y from the left side

\(y(x - 1) = - 6x - 5x\)

↓ dividing both sides by (x - 1)

\(y = \dfrac{-6x - 5}{x-1}\)

↓ (optional) multiplying the fraction by \(\bold{\dfrac{-1}{-1}}\)

\(y = \dfrac{6x + 5}{1 - x}\)

↓ replacing y with \(f^{-1}(x)\)

\(\boxed{f^{-1}(x) = \dfrac{6x + 5}{1 - x}}\)

By creating a character design using mathematical equations and functions, the design becomes unique and offers a different approach to promoting awareness, appreciation, or critique of the chosen event/issue. It engages the audience through a combination of art and mathematics, fostering curiosity and providing a platform for discussion and understanding. The incorporation of conic sections and other equations/functions adds depth and complexity to the design, making it visually appealing and intellectually stimulating.

1. The design is unique because it incorporates mathematical equations and functions, specifically conic sections, to create a character that represents the chosen event/issue.

2. The edge of this design over other designs used in promoting awareness, appreciation, or critique is its ability to engage and educate the audience through the integration of mathematical concepts. It provides a different perspective and approach to understanding the event/issue, appealing to those with an interest in mathematics.

3. This design promotes awareness, appreciation, or critique of the chosen event/issue by combining artistic representation with mathematical concepts. It serves as a visual representation that sparks curiosity and invites discussion. Through the use of conic sections and other equations/functions, the design can convey complex ideas and stimulate deeper understanding among the audience, especially the young ones.

To create the character design, mathematical equations and functions related to conic sections and other relevant concepts can be utilized. These equations can be graphed using the Desmos application or any other graphing application. By carefully manipulating the equations and adjusting the parameters, a unique character can be formed that represents the chosen event/issue.

For example, if the chosen event/issue is the COVID-19 response, the character design could incorporate the equation of a circle to represent the virus, with the center symbolizing the source or origin. The curves of an ellipse or parabola could be used to depict the spread or impact of the virus, with the focus on specific regions or individuals.

The detailed report would include explanations of the equations and functions used, their relevance to the chosen event/issue, and how they contribute to the character design. It would also include screenshots or images of the character design created on the graphing application, accompanied by captions explaining the elements and their significance.

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Answer: Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase

Step-by-step explanation:

Answer:

its B and C

Step-by-step explanation:

Answer: 120 people

Step-by-step explanation:

First take $4100 - $500 = $3600

then you divide

3600/30 = 120

which equals

120 People are estimated to attend

Answer: 36

Step-by-step explanation: If you're asking what the expression equals after plugging X's value in, this should leave you with an expression of -3^2 - 5(-3) + 12. By following the order of operations, you should receive an answer of 36.

The probability that Rachel will pass at least one of the courses is 0.955 or 95.5%

To calculate the probability that Rachel will pass at least one of the courses, we need to use the formula;P(A or B) = P(A) + P(B) - P(A and B)Where P(A or B) is the probability of passing at least one course, P(A) is the probability of passing Math, P(B) is the probability of passing Biology, and P(A and B) is the probability of passing both Math and Biology.

Using the given information, we have:P(A) = 85% = 0.85P(B) = 70% = 0.7P(A and B) = 59.5% = 0.595Substituting these values into the formula, we get:P(passing at least one course) = 0.85 + 0.7 - 0.595= 0.955

As a result, Rachel has a 0.955 or 95.5% chance of passing at least one of the courses.95.5 percent, or 0.955.

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it can be concluded that the population standard deviation is within or less than 12.

To construct a hypothesis test to determine whether the population standard deviation of σ≦12 should be rejected for Costco, we can use a chi-square test for variance.

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H₀): σ ≤ 12
- Alternative hypothesis (H₁): σ > 12

Step 2: Determine the level of significance (α = 0.05) and degrees of freedom (df = n - 1 = 11 - 1 = 10).

Step 3: Calculate the test statistic:
- χ² = (n - 1) * (s² / σ²) = 10 * (11.3² / 12²) = 10 * 0.94 = 9.4

Step 4: Determine the critical value:
- The critical value at α = 0.05 with df = 10 is χ²ₐ = 18.307

Step 5: Compare the test statistic with the critical value:
- Since χ² = 9.4 < χ²ₐ = 18.307, we fail to reject the null hypothesis.

Step 6: Conclusion:
- Based on the given sample data, there is not enough evidence to reject the hypothesis that the population standard deviation of σ≤12 for Costco.

Therefore, it can be concluded that the population standard deviation is within or less than 12.

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Answer: A

Step-by-step explanation:

If you plug in the numbers from the x column into the equation in the place of x, you can figure out the answer.

Example:    -10x - 15

                   -10(1) - 15 = -25

                   -10(2) - 15 = -35 and so on...

You're Welcome! :)

Answer:

Step-by-step explanation:

The entry to record the purchase will include: a debit to Supplies and a credit to Accounts Payable

Now, given: Purchased supplies = $500 (on account).

To find: What does entry to record the purchase include?

Now,

Hence, the entry to record the purchase will include: a debit to Supplies and a credit to Accounts Payable.

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Answer:

12.7342

Step-by-step explanation:

V=360

d=6

r=1/2*d=3

r^2=9

360/pi=114.592

114.592/9=12.7342

The approximate probability that the sample mean will be greater than 63 is 0.0885, rounded off to the second decimal place.

What is Central Limit Theorem?

The Central Limit Theorem (CLT) is a fundamental concept in statistics and probability theory. It states that, under certain conditions, the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To find the approximate probability that the sample mean will be greater than 63, we can use the Central Limit Theorem. The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution.

In this case, since the sample size is 58 (which is reasonably large), we can use the normal distribution to approximate the probability.

First, we need to calculate the standard error of the sample mean, which is the standard deviation of the population divided by the square root of the sample size:

Standard Error (SE) = Standard Deviation (σ) / √Sample Size (n)

SE = 17 / √58 ≈ 2.2271

Next, we can standardize the sample mean using the formula:

Z = (Sample Mean - Population Mean) / Standard Error

Z = (63 - 60) / 2.2271 ≈ 1.3488

Now, we need to find the probability of Z being greater than 1.3488 using the standard normal distribution table or a statistical calculator. Looking up the corresponding probability, we find that it is approximately 0.0885.

Therefore, the approximate probability that the sample mean will be greater than 63 is 0.0885, rounded off to the second decimal place.

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Answer:

d=28g I might be wrong, but we can find this by dividing 140 by five, which equals 28

Step-by-step explanation: