Answer:
- The integral of arctan(x)/x =
C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).
- The radius of convergence is R = 1/x
Step-by-step explanation:
First note that
tan^(-1)x = arctan(x)
And
arctan(x) = Σ [(-1)^n. x^(2n+1)]/(2n+1). From n = 0 to infinity
arctan(x)/x = Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity
∫arctan(x)/x dx = ∫{Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity}dx
= ∫{Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.∫x^(2n)dx
= {Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.x^(2n+1)/(2n+1) + C
= C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).
To obtain the radius of convergence, we apply the ration test
R = Limit as n approaches infinity |a_n/a_(n+1)|
a_n = (-1)^n.x^(2n+1)]/(2n+1)²
a_(n+1) = (-1)^(n+1).x^(2(n+1)+1)]/(2(n+1)+1)²
|a_n/a_(n+1)| = (2(n+1) + 1)²/(2n+1)².x
= (1/x)[1 + 2/(2n+1)]
R = Limit as n approaches infinity |a_n/a_(n+1)|
= R = Limit as n approaches infinity (1/x)[1 + 2/(2n+1)]
R = 1/x
The integration of the arctan (x)/x is C + Σ [(-1)^n x^(2n+1)]/(2n+1)² where n is from 0 to ∞. The radius of convergence is R = 1/x
What is integration?It is the reverse of differentiation.
The indefinite integral is a power series that will be
[tex]\rm \int \dfrac{\tan^{-1}x }{ x} \ dx[/tex]
We know that the arctan is given as
[tex]\rm \tan^{-1} x = \dfrac{\sum [(-1)^n \ x^{2n+1}]}{(2n+1)}\\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ x^{2n})]}{(2n+1)}\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n}[/tex]
Then we have
[tex]\rm \int \dfrac{\tan^{-1} x }{x}\ dx= \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n} dx\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \int x^{2n}\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)^2} x^{2n + 1} + C[/tex]
To obtain the radius of convergence, then the ration test
[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{a_n}{a_{n+1}}\\\\\\a_n = \dfrac{(-1)^n \ x^{2n+1} }{(2n+1)^2}\\\\\\a_{n+1} = \dfrac{(-1)^{n+1} \ x^{2(n+1)+1} }{(2(n+1)+1)^2}\\\\\\ \dfrac{a_n}{a_{n+1}} = \dfrac{1}{x}(1+\dfrac{2}{2n+1})[/tex]
Then we have
[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{1}{x}(1+\dfrac{2}{2n+1})\\\\\\R = \dfrac{1}{x}[/tex]
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Area =
22ft for diameter
Here is your answer! uwu
Sketch the region of integration and evaluate the following integral. ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper R StartFraction 1 Over 3 plus StartRoot x squared plus y squared EndRoot EndFraction dA , RequalsStartSet (r comma theta ): 0 less than or equals r less than or equals 2 comma StartFraction pi Over 2 EndFraction less than or equals theta less than or equals StartFraction 3 pi Over 2 EndFraction EndSet
Answer:
[tex]\frac{10\pi}{3}[/tex]
Step-by-step explanation:
According to the information of the problem we have to compute the following integral.
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA[/tex]
Where the region of integration is
[tex]R = \Big\{ (r,\theta) : 0 \leq r \leq 2 , \,\,\,\, \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2} \Big\}[/tex]
If you plot, that is just a circle between [tex]\pi/2[/tex] and [tex]3\pi/2[/tex], which is just half of the circle on the negative part of the plane.
When you switch coordinates
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA = {\displaystyle \int\limits_{0}^{2} \int\limits_{\pi/2}^{3\pi/2}} \bigg(\frac{1}{3} + r \bigg)r \, d\theta\, dr = \frac{10\pi}{3}[/tex]
A sociologist develops a test to measure attitudes towards public transportation, and 25 randomly selected subjects are given the test. The sample mean score is 76.2 and the sample standard deviation is 21.4. The population is normally distributed. What is the 95% confidence interval for the mean score of all such subjects? Round to 3 decimal places.
Final answer:
The 95% confidence interval for the true mean score of subjects' attitudes towards public transportation is between 67.361 and 85.039, computed using a t-score for a sample size of 25.
Explanation:
To calculate the 95% confidence interval for the mean score of all subjects regarding their attitudes towards public transportation, we will use the following formula for a confidence interval when the population is normally distributed but the population standard deviation is not known:
CI = ± t*(s/√n), where CI is the confidence interval, ± denotes plus or minus, t is the t-score that corresponds to the desired level of confidence and degrees of freedom (df = n - 1), s is the sample standard deviation, and √n is the square root of the sample size.
For our sample size of n = 25, the degrees of freedom is df = 24. Consulting a t-distribution table or using statistical software to find the t-value for df = 24 at a 95% confidence level, we assume a t-value approximately equal to 2.064 (this may slightly vary depending on the source of the t-distribution table). Plugging in the values:
CI = ± 2.064*(21.4/√25), thus the margin of error is approximately 2.064 * 4.28
The confidence interval is then the sample mean ± the margin of error:
76.2 ± (2.064 * 4.28)
This calculation yields a confidence interval for the population mean score of:
Lower Bound = 76.2 - 8.83872 ≈ 67.361
Upper Bound = 76.2 + 8.83872 ≈ 85.039
Therefore, rounding to three decimal places: 67.361 (Lower Bound) and 85.039 (Upper Bound).
We are 95% confident that the true mean score of all subjects' attitudes towards public transportation lies between 67.361 and 85.039.
The scores on a test are normally distributed with a mean of 150 and a standard deviation of 30. What is the score that is 1 standard deviation below the mean?
A score of 120 is one standard deviation below the mean of 150 on a test with a standard deviation of 30.
Explanation:The score that is 1 standard deviation below the mean is found by subtracting the standard deviation from the mean. In the context of this normal distribution of test scores, with a mean of 150 and a standard deviation of 30, we calculate the score one standard deviation below the mean as follows:
Score = Mean – Standard Deviation = 150 – 30 = 120
This calculation indicates that a score of 120 is one standard deviation below the mean on this test.
Which expressions are solutions to the equation (3/4)x = 15? Select all that apply.
The expressions that are solutions to the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C
as [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution and [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.
Let's solve the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] and then check each expression to see if it is a solution:
1. Solve the equation:
[tex]\[ x = \frac{15}{\frac{3}{4}} \][/tex]
To divide by a fraction, we can multiply by its reciprocal:
[tex]\[ x = 15 \times \frac{4}{3} = 20 \][/tex]
Now, let's check each expression:
A. [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution.
B. [tex]\( \frac{15}{\frac{4}{3}} \)[/tex] - This expression is equivalent to [tex]\( \frac{15 \times 3}{4} = \frac{45}{4} \)[/tex], not equal to 20.
C. [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.
D. [tex]\( \frac{3}{4} \times 15 = 11.25 \)[/tex] - This is not equal to 20.
E. [tex]\( \frac{15}{\frac{3}{4}} \)[/tex] - This is equivalent to expression A, which is a solution.
Therefore, the expressions that are solutions to the equation[tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C.
Complete Question: Which expressions are solutions to the equation 3/4 x=15 ? Select all that apply.
A. frac 15 3/4
B. frac 15 4/3
C. 4/3 · 15
D. 3/4 · 15
E. 15/ 3/4
What’s the correct answer for this?
Answer:
A
Step-by-step explanation:
Plate X will result in the lightest place since it's density and thickness both are less.
Juan Pablo demora 7 minutos en dar una vuelta a la cancha de fútbol y Pedro demora 2 minutos más corriendo a la misma velocidad que Juan Pablo. ¿Cuánto tiempo demorará Pedro en dar 12 vueltas?
Answer: 108 minutes
Step-by-step explanation:
This translates to:
Juan Pablo takes 7 minutes to do a full lap on a football field, Pedro needs 2 more minutes ruuning at the same speed thanJuan Pablo.
How much time does Pedro need to do 12 laps?
The fact that Pedro runs at the same speed than Juan Pablo, and needs more time, may mean that the radius of the laps of Pedro are a little bit bigger than the ones of Juan Pablo (which means that the total distance that pedro runs is bigger)
If Juan Pablo does a lap in 7 minutes, then Pedro does a lap in 7 minutes + 2 minutes = 9 minutes.
Then to do 12 laps, he needs 12 times that amount of time, this is:
12*9 min = 108 minutes
statistical analyst for the Wall Street Journal randomly selected six companies and recorded both the price per share of stock on January 1, 2009 and on April 30, 2009. The results are presented below. Suppose the analyst wished to see if the average price per share of stock on April 30, 2009 is greater than the average price per share of stock on January 1, 2009 at α=.025. Apr. 30, 2009 33 33 34 30 33 38 Jan. 1, 2009 21 25 30 33 23 27 For the hypothesis stated above, what is the P-value?
Answer:
p value= 2.228
Step-by-step explanation:
since average of two groups is being compared two-sample t-test will be performed.
degrees of freedom= 12-2=10
at α=.025 from t table
p value= 2.228
The minute hand on a clock is 9 centimeterslong and travels through an arc of 252° every 42 minutes. To the nearest tenth of a centimeter, how far does the minute handtravel during a 42-minute period?
Answer: the minute hand travel 39.6 cm
Step-by-step explanation:
Length of minute hand of a clock = 9 cm
Central angle made by the minute hand = 252°
To find: how far the minute hand travel
Therefore
Length of minute hand is equal to the radius of circle
As we know the circumference of a circle is given by
[tex]C= 2\pi r \dfrac{\theta}{360^\circ}[/tex] where C is circumference , r is radius and ∅ is the central angle
So we have
[tex]C= 2 \times \dfrac{22}{7} \times 9 \times \dfrac{252^\circ}{360^\circ} \\\\\Rightarrow C= 2 \times \dfrac{22}{7} \times \dfrac{252^\circ}{40^\circ} \\\\\Rightarrow C= \dfrac{11}{7} \times \dfrac{252^\circ}{10^\circ} = 39.6[/tex]
Hence, the minute hand travel 39.6 cm in 42 minute period
Final answer:
The minute hand of the clock, which measures 9 centimeters in radius, travels approximately 39.3 centimeters along the arc when it moves through a 252-degree central angle in a 42-minute period.
Explanation:
To determine how far the minute hand of a clock travels in a 42-minute period, we need to calculate the arc length, which is a portion of the circumference of the circle traced by the minute hand's tip. We are given that the minute hand is 9 centimeters long, meaning it is the radius of the circle, and it travels through an arc of 252° during a period of 42 minutes.
The formula to calculate the arc length is:
ℓ = θ/360 × 2πr
Where:
ℓ is the arc length
θ is the central angle in degrees
r is the radius of the circle
In this case:
θ = 252°
r = 9 cm
Now, let's substitute these values into the formula:
ℓ = 252/360 × 2 × π × 9
ℓ ≈ 0.7 × 2 × 3.14159 × 9
ℓ ≈ 39.27 cm
So, to the nearest tenth of a centimeter, the minute hand travels approximately 39.3 cm during a 42-minute period.
Find an equation of the circle that has center(-3,4) and passes through(1,-2)
Answer:
(x +3)^2 +(y -4)^2 = 52
Step-by-step explanation:
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
We are given the value of (h, k), and we can find the value of r^2. Using the values of h and k, our equation is ...
(x +3)^2 +(y -4)^2 = r^2
Since we know this equation is satisfied by the point (1, -2), we can use this point in the equation to find r^2:
(1 +3)^2 +(-2 -4)^2 = r^2
16 +36 = r^2 = 52
The equation of the circle is ...
(x +3)^2 +(y -4)^2 = 52
Which of the following has a constant of proportionality of 2?
A) y = 2 x
B) 2 y = x
C) y = x + 2
D) y + 2 = 2 x
Answer:
A) y = 2 x
Step-by-step explanation:
The equation for direct variation is
y = kx where the constant of proportionality is k
y = 2x
Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the first year is 32 % . She obtains a random sample of 72 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year? Please give your answers precise to two decimal places.
Answer:
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Step-by-step explanation:
For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The probability that an independent restaurant will fail in the first year is 32%.
This means that [tex]p = 0.32[/tex]
72 independent restaurants
This means that [tex]n = 72[/tex]
Mean:
[tex]E(X) = np = 72*0.32 = 23.04[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{72*0.32*0.68} = 3.96[/tex]
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Final answer:
The mean number of independent restaurants in the sample expected to fail within the first year is 23.04, and the standard deviation is approximately 4.28.
Explanation:
To find the mean and standard deviation of the number of restaurants that failed within a year in Kristen's research, we can use the properties of the binomial distribution. The probability of a single restaurant failing (success in this context) is 0.32 (32%). Given a sample size of 72 restaurants, the mean number of restaurants that fail within a year is the product of the sample size and the probability of failure.
The formula for the mean (μ) of a binomial distribution is μ = n * p, where n is the sample size and p is the probability of success. Therefore, the mean number of failed restaurants is 72 * 0.32 = 23.04.
The formula for the standard deviation (σ) of a binomial distribution is σ = √(n * p * (1 - p)). Thus, the standard deviation of failed restaurants is √(72 * 0.32 * (1 - 0.32)) = √(72 * 0.32 * 0.68) ≈ 4.28.
Therefore, the mean number of restaurants that failed within a year is 23.04, and the standard deviation is approximately 4.28.
The cost medium pizza with no toppings is $7.50. The cost of each topping is $0.50. a) what is the equation that represents this relation if C represents the cost of pizza and N represents the number of topping?
Answer:$7.50+$0.50xN or C+$0.50xN
Step-by-step explanation:
Because the pizza is 7.50 and the extra toppings are 0.50 cents so the number of toppings is n and the cost for the pizza is c so C+0.50xN.
Good Luck!!
Awnser this please.
Answer:
1.5 hours
Step-by-step explanation:
make each half hour represent t
Cost C(t) = 24 + 14t
66 = 24 + 14t
42 = 14t
t = 3
3 half hours = 1.5 hours
Answer:
1 and a half hours of work
Step-by-step explanation:
You minus 66 and 24 to get 42. Then you divide 42 and 14
Two angles are complementary. Angle 1 measures 33.5 degrees. What is the measure of Angle 2? *
You are in charge of buying office supplies for your business. Your workers use red and black pens. Red pens cost $5 per box and black pens cost $3 per box. You need at least 10 boxes of pens. You want no more than 7 boxes of black pens and no more than 6 boxes of red pens. You want to minimize the cost to your business.
The objective function for this situation is C = 5x + 3y. What (x, y) pair minimizes cost?
image
(6, 7)
(0, 7)
(3, 7)
(6, 4)
Answer:
C. (3, 7)
Step-by-step explanation:
plug all the numbers into all of the coordinates and (3, 7) is the lowest number :) pls rate 5 stars and thank me
The option of buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business, based on the objective function C = 5x + 3y and the given constraints of at least 10 boxes in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.
Explanation:To minimize the cost of buying office supplies, particularly red and black pens, we need to use the given objective function C = 5x + 3y where x represents the number of boxes of red pens and y represents the number of boxes of black pens. We have the following constraints: at least 10 boxes of pens in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.
By applying these constraints, we can determine the combinations of x and y that meet the criteria:
x + y ≥ 10 (at least 10 boxes of pens)x ≤ 6 (no more than 6 boxes of red pens)y ≤ 7 (no more than 7 boxes of black pens)Looking at the choices provided, (6, 4) meets all our constraints, and when plugged into the objective function:
C = 5(6) + 3(4) = 30 + 12 = $42
This results in the lowest cost when compared to the other presented options. Therefore, buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business.
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Which exponential expressions are equivalent to the one below? Check all
that apply.
(5x9)^12
Answer:D
Step-by-step explanation:
(5x9)^12
5^12 x 9^12
Which is the graph of the linear equation y= -1/3x +5
Answer:
x=-3(y-5)
Step-by-step explanation:
The per capita electric power consumption level in a recent year in Ecuador is normally distributed, with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilowatt-hours. Random samples of size 35 are drawn from this population. Find (a) the mean and (b) the standard deviation of the sampling distribution of sample means. Round the answer from part (b) to the third decimal place.
Answer:
a) 471.5 kilo-watt hours.
b) 31.76 kilo-watt hours
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the population:
Mean 471.5 kilo-watt hours.
Standard deviation of 187.9 kilowatt-hours.
For the sample:
Sample size of 35, by the Central Limit Theorem:
a) Mean
471.5 kilo-watt hours.
b) Standard deviation
[tex]s = \frac{187.9}{\sqrt{35}} = 31.76[/tex]
31.76 kilo-watt hours
Final answer:
The mean of the sampling distribution of sample means is 471.5 kilo-watt hours, and the standard deviation (or standard error) of the sampling distribution, rounded to the third decimal place, is 31.749 kilo-watt hours.
Explanation:
The question concerns the concept of sampling distribution and its parameters, namely the mean and standard deviation, within the field of statistics. Given that the per capita electric power consumption level in Ecuador is normally distributed with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilo-watt hours, and considering samples of size 35, we are to find the mean and standard deviation of the sampling distribution of sample means.
(a) The mean of the sampling distribution of sample means is equal to the population mean. Therefore, the mean is:
471.5 kilo-watt hours
(b) The standard deviation of the sampling distribution of sample means, also known as the standard error (SE), is calculated using the following formula:
SE = σ / √n
where σ is the population standard deviation and n is the sample size. In this case:
SE = 187.9 / √35 ≈ 31.749 kilo-watt hours (rounded to the third decimal place)
Kelly walks 4/5 of a mile each day. How many miles does Kelly walk after three days?
Answer:
Kelly walks 4/5 of a mile each day.
After 3 days, Kelly walks a distance: D = 3 x 4/5 = 12/5 = 2.4 miles
Hope this helps!
:)
Kelly walks 4/5 of a mile each day, and after three days, she would have walked 2 and 2/5 miles.
Kelly walks 4/5 of a mile each day. To find out how many miles Kelly walks after three days, we simply multiply the daily distance by three.
Calculation:
4/5 mile/day * 3 days = 12/5 miles
To convert 12/5 miles into a mixed number, we divide 12 by 5. The quotient is 2 with a remainder of 2, so Kelly walks 2 and 2/5 miles after three days.
Which represents a quadratic function?
f(x) = −8x3 − 16x2 − 4x
f (x) = three-quarters x 2 + 2x − 5
f(x) = StartFraction 4 Over x squared EndFraction minus StartFraction 2 Over x EndFraction + 1
f(x) = 0x2 − 9x + 7
Answer:[tex]f(x)=\frac{3}{4}x^2+2x-5[/tex]
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
b
Write a verbal description for each algebraic expression 100-5n
Step-by-step explanation:
One hundred minus five n
Select the correct answer.
Which value of x makes the equation true?
x + 7 = -9
A. -16
B. -2
C. 2
D. 16
The value of x makes the equation true is -16. Therefore, option A is the correct answer.
The given equation is x+7=-9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved as follows:
x+7=-9
Transpose 7 to RHS of the equation, we get
x=-9-7
=-16
The value of x makes the equation true is -16. Therefore, option A is the correct answer.
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A broken thermometer reads 33° F, but Kira knows that the temperature is at least 33° F, if not even colder. Which of the following inequalities, shows the possible temperatures? t ≤ 33° F t ≥ 33° F t > 33° F t < 33° F
Answer:
t ≤ 33
Step-by-step explanation:
The answer can be 33 or below.
A random sample of 400 Michigan State University (MSU) students were surveyed recently to determine an estimate for the proportion of all MSU students who had attended at least three football games. The estimate revealed that between .372 and .458 of all MSU students attended. Given this information, we can determine that the confidence coefficient was approximately: a. .92 b. .95 c. .88 d. .90 e. .99
Answer:
a. .92
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error of the interval is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The lower bound is the point estimate [tex]\pi[/tex] subtracted by the margin of error.
The upper bound is the point estimate [tex]\pi[/tex] added to the margin of error.
Point estimate:
The confidence interval is symmetric, so it is the mean between the two bounds.
In this problem:
[tex]\pi = \frac{0.372 + 0.458}{2} = 0.415[/tex]
Sample of 400, which means that [tex]n = 400[/tex]
Margin of error is the estimate subtracted by the lower bound. So [tex]M = 0.415 - 0.372 = 0.043[/tex]
We have to find z.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.043 = z\sqrt{\frac{0.415*0.585}{400}}[/tex]
[tex]z = \frac{0.043\sqrt{400}}{\sqrt{0.415*0.585}}[/tex]
[tex]z = 1.745[/tex]
[tex]z = 1.745[/tex] has a pvalue of 0.96.
This means that:
[tex]1 - \frac{\alpha}{2} = 0.96[/tex]
[tex]\frac{\alpha}{2} = 1 - 0.96[/tex]
[tex]\frac{\alpha}{2} = 0.04[/tex]
[tex]\alpha = 0.08[/tex]
Confidence level:
[tex]1 - \alpha = 1 - 0.08 = 0.92[/tex]
So the correct answer is:
a. .92
To determine the confidence coefficient for the proportion of MSU students who attended at least three football games, the margin of error is calculated from the given interval range and related to the Z-value of a standard normal distribution. The coefficient that matches the margin of error from the calculation is approximately 0.95, indicating a 95% confidence level.
The confidence interval for the proportion of Michigan State University (MSU) students who attended at least three football games is given as (0.372, 0.458). To determine the confidence coefficient used to calculate this interval, we need to look at the width of the interval and how it relates to the standard error of the proportion.
The width of the confidence interval is 0.458 - 0.372 = 0.086. Since we know that the total width of the interval spans the range of twice the margin of error, one margin of error is then 0.086 / 2 = 0.043.
Using the Z-table for the normal distribution, we can find which confidence coefficient corresponds to a Z-value that gives a margin of error of 0.043, considering that the formula for the margin of error in this case would be: Z * sqrt((p*(1-p))/n). For a sample size of 400, and approximating p by the midpoint of the confidence interval (0.372 + 0.458)/2 = 0.415, the computation would look roughly like this:
Z * sqrt((0.415*(1-0.415))/400) = 0.043
After solving this equation for Z, we can then locate the corresponding confidence level on the standard normal (Z) distribution table. This process would lead to finding that the closest confidence coefficient that would generate the margin of error of 0.043 with the given sample size and point estimate proportion is approximately 0.95, or 95%.
Therefore, the confidence coefficient is 0.95, which corresponds to option b. 0.95.
A shipment to a warehouse consists of 500 PS4. The manager chooses a random sample of 50 PS4 and finds that 3 are defective. How many PS4 in the shipment are likely to be defective?
Answer:
30 PS4 in the shipment are likely to be defective
Step-by-step explanation:
We take the estimate from the sample and estimate to all the PS4 in store. This means that we can solve this question using a rule of 3.
From the sample of 50 PS4, 3 are defective. How many are expected to be defective out of 500?
50PS4 - 3 defective
500 PS4 - x defective
[tex]50x = 3*500[/tex]
[tex]x = \frac{1500}{50}[/tex]
[tex]x = 30[/tex]
30 PS4 in the shipment are likely to be defective
Answer:
don't take my word but I think 150
Step-by-step explanation:
What is the lateral surface area of the square pyramid below?
a
48 in²
b
105 in²
c
96 in²
d
57 in²
Answer:
lateral surface area = 48 inches²
Step-by-step explanation:
The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.
area of a triangle = 1/2 × b × h
The slant height of the triangle is gotten using Pythagoras theorem
lateral surface area = 4 × (1/2 × 3 × 8)
lateral surface area = 4 × 24/2
lateral surface area = 4 × 12
lateral surface area = 48 inches²
Answer:
48 in
Step-by-step explanation:
<3 hoped this helped <3
Mrs. Braddock has a bag containing 6 lipsticks, 4 eye shadows, 6 eye liners, and 5 mascaras. She will randomly choose one item from the bag.What is the probability that she will pull NOT lipstick? p(NOT lipstick). Round percents to nearest whole number
Answer:
The probability that she will not pull lipstick is 71%.
Step-by-step explanation:
The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = favorable number of outcomes
N = total number of outcomes
The contents in Mrs. Braddock's bag are:
Number of lipsticks = n (L) = 6
Number of eye shadows = n (S) = 4
Number of eye liners = n (E) = 6
Number of mascaras = n (M) = 5
Total number of items in the bag = N = 21
Consider that the probability of an event occurring is P. Then the probability of the given event not taking place is known as the complement of that event.
Complement of the given event is, 1 – P.
Compute the probability of selecting a lipstick as follows:
[tex]P(L)=\frac{n(L)}{N}\\\\=\frac{6}{21}\\\\=\frac{2}{7}[/tex]
Compute the probability of not selecting a lipstick as follows:
[tex]P(L^{c})=1-P(L)[/tex]
[tex]=1-\frac{2}{7}\\\\=\frac{7-2}{7}\\\\=\frac{5}{7}[/tex]
Convert this probability into percentage as follows:
[tex]\frac{5}{7}\times 100 = 71.4286\approx 71\%[/tex]
Thus, the probability that she will not pull lipstick is 71%.
observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3
Answer:
We have two relations
2*x*y = 6 (2 times x times y is equal to six)
x - y = 3 ( the difference between x and y is trhe)
Where whe have two variables, x and y.
To solve this system, the first step is isolation one of the variables in one of the equations, let's isolate x in the second equation.
x - y = 3
x = 3 + y
now we can replace this in the other equation and then solve it for y.
2*x*y = 6
2*(3 + y)*y = 6
6y + 2y^2 = 6
now we have the quadratic equation:
2y^2 + 6y - 6 = 0
the solutions are:
[tex]y = \frac{-6 + -\sqrt{6^2 - 4*2*(-6)} }{2*2} = \frac{-6 +- 9.2}{4}[/tex]
the solutions are:
y = (-6 + 9,2)/4 = 0.8
y = (-6 - 9.2)/4 = -3.8
if y = 0.8, then:
x = 3 + y = 3.8
if y = -3.8
x = 3 + y = 3 - 3.8 = -0.8
so we have two possible solutions:
(-0.8, -3.8) and (3.8, 0.8)
One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after 4 weeks in order to determine if there has been substantial improvement in the severity of the depression. Suppose volunteers were first divided by gender, and then half of the men were randomly assigned to the new drug and half of the women were assigned to the new drug. The remaining volunteers received the other drug. What is this an example of
Answer:
This is an example of placebo testing.
Step-by-step explanation:
This is an example of placebo testing in which, the two groups are given two substances that are said to have an effect on the condition that is being treated but one of them is the actual medicine that is being tested while the other one has no real effect over the medical condition. But the volunteers are not given information on which of the medicines is real and which is not, so that this does not affect the outcome of the experiment.
I hope this answer helps.