The probability that at most 2 accounting majors are on the committee is 60.6%.
To solve this problem, we can use the binomial probability formula:
P(X ≤ 2) = ΣP(X = i), where i = 0, 1, or 2
P(X = i) = (n choose i) * p^i * (1-p)^(n-i)
where n is the total number of available majors (18), p is the probability of selecting an accounting major (10/18), and (n choose i) is the binomial coefficient which gives the number of ways to select i accounting majors from n total majors.
So, to find the probability that at most 2 accounting majors are on the committee, we need to sum the probabilities of selecting 0, 1, or 2 accounting majors.
P(X = 0) = (8 choose 5) * (10/18)^0 * (8/18)^5 = 0.018
P(X = 1) = (10 choose 1) * (10/18)^1 * (8/18)^4 = 0.219
P(X = 2) = (10 choose 2) * (10/18)^2 * (8/18)^3 = 0.369
Therefore, P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.018 + 0.219 + 0.369 = 0.606 or 60.6%
So the probability that at most 2 accounting majors are on the committee is 60.6%.
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Given the ______ of the z-distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.
Answer:
the answer is symmetry.
A researcher was interested in the relationship between a swimmer’s hand length and corresponding time to complete the 100-meter freestyle. The researcher selected a random sample of twenty swimmers from all participants in a swim competition. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence, at a 5 percent level of significance, that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle?.
To investigate whether there is convincing evidence, at a 5 percent level of significance,
that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle, the researcher should use a two-sample t-test.
The independent variable is hand length, and the dependent variable is time to complete the 100-meter freestyle.
The t-test compares the mean time to complete the 100-meter freestyle for swimmers with longer hand lengths to the mean time for swimmers with shorter hand lengths.
The t-test is appropriate because the sample size is small, and the researcher is comparing two groups.
By conducting a two-sample t-test, the researcher can determine whether the observed difference in mean times is statistically significant or due to chance.
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What points lie on u'?
The points that belong to the image of the equation of a line are (4, - 8) and U' = (1, 4).
How to find the image of a line by rigid transformation
In this question we find the definition of the equation of a line, whose image must be found by a kind of rigid transformation known as dilation:
U'(x, y) = O(x, y) + k · [U(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.k - Dilation factor.U(x, y) - Original point.U'(x, y) - Resulting point.If we know that O(x, y) = (5, - 8), k = 1 / 4 and y = - 4 · x - 4, then the image of the point:
U'(x, y) = (5, - 8) + (1 / 4) · [(x, - 4 · x - 4) - (5, - 8)]
U'(x, y) = (5, - 8) + (1 / 4) · (x - 5, - 4 · x + 4)
U'(x, y) = (5, - 8) + (x / 4 - 5 / 4, - x + 1)
U'(x, y) = (x / 4 + 15 / 4, - x - 7)
Now we evaluate the expression at each x-value:
x = 1
U' = (1 / 4 + 15 / 4, - 1 - 7)
U' = (4, - 8) (YES)
x = - 11
U' = (- 11 / 4 + 15 / 4, - (- 11) - 7)
U' = (1, 4) (YES)
x = - 23
U' = (- 23 / 4 + 15 / 4, - (- 23) - 7)
U' = (- 2, 16) (NO)
x = 17
U' = (17 / 4 + 15 / 4, - 17 - 7)
U' = (8, - 24) (NO)
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(L3) The orthocenter will lie in the exterior of a(n) _____ triangle.
(L3) The orthocenter will lie in the exterior of a(n) obtuse triangle. Contrary to an acute triangle, the orthocenter of an obtuse triangle will lie in the exterior of the triangle.
The orthocenter is the point of intersection of the altitudes of the triangle, which are perpendicular lines drawn from each vertex to the opposite side. In an obtuse triangle, one of the angles measures more than 90 degrees, so when an altitude is drawn from this vertex to the opposite side, it will lie outside of the triangle. Therefore, the three altitudes will intersect outside of the triangle, forming the orthocenter in the exterior. This is in contrast to an acute triangle, where all three altitudes intersect inside the triangle.
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tamu admissions board believes the score you get on the sat in high school can help predict your college gpa. below is a regression model using the sat scores and gpa for 116 college graduates. calculate a 70% confidence interval for the slope of the regression line. use 4 decimal places.
The answer is that the 70% confidence interval for the slope of the regression line using the provided data is between 0.0019 and 0.0037.
To calculate the 70% confidence interval for the slope of the regression line, we need to use the t-distribution with degrees of freedom equal to n - 2, where n is the number of data points. In this case, n = 116, so we have 114 degrees of freedom.
Using a statistical software or calculator, we can find that the t-value for a 70% confidence interval with 114 degrees of freedom is approximately 1.648.
Next, we need to calculate the standard error of the slope, which is given by:
SE =√[ (SS_residuals / (n - 2)) / SS_x ]
where SS_residuals is the sum of squared residuals, SS_x is the sum of squared deviations of x from its mean, and n is the sample size.
Using the regression model provided, we can find that SS_residuals = 6.3574 and SS_x = 1484.9584. Plugging these values into the formula, we get:
SE = √[ (6.3574 / (116 - 2)) / 1484.9584 ] = 0.00044
Finally, we can calculate the confidence interval for the slope using the formula:
slope +/- t * SE
where slope is the estimated slope from the regression model.
Plugging in the values, we get:
slope +/- 1.648 * 0.00044 = 0.0028 +/- 0.0007
Therefore, the 70% confidence interval for the slope of the regression line is between 0.0019 and 0.0037, rounded to 4 decimal places.
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A distribution is given as X ~ Exp(0. 75). Find P(x < 4)
The probability of P(x < 4) is 0.6922 or approximately 69.22%.
The exponential distribution is often used to model the time between events that occur randomly and independently at a constant rate over time. The probability density function of the exponential distribution with parameter λ is given by f(x) = λe^(-λx) for x ≥ 0.
In this case, X ~ Exp(0.75) means that the parameter λ is 0.75. To find P(x < 4), we need to calculate the area under the curve of the probability density function to the left of 4. This can be done by integrating the function from 0 to 4 as follows
P(x < 4) = ∫₀⁴ λe^(-λx) dx
= [-e^(-λx)]₀⁴
= -e^(-0.75 * 4) + 1
= 0.6922
Therefore, the probability that X is less than 4 is 0.6922 or approximately 69.22%.
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Kellys new snowboard is 115% longer than her old snowboard. If the new snowboard is 130 cm, how many cm long is her old snowboard? (Round to the nearest tenth)
Answer:
The answer to your problem is, 149.5
Step-by-step explanation:
How to find our number from the problem, 115% of 130.
Calculate:
[tex]\frac{115}{100}[/tex] of 130 = [tex]\frac{115}{300}[/tex] × 130
= 149.5
The new snowboard is 149.5 centimeters now.
Thus the answer to your problem is, 149.5
Find the radius of convergence, r, of the following series. [infinity] n!(6x − 1)n n = 1 r = find the interval, i, of convergence of the series. I = 1 i = − 1 6 , 0 ∪ 1 6i = − 1 6 , 1 6 i = 0 i = 1 6
The radius of convergence is given as [tex]i = {x | 0 \leq x < \frac{1}{3} }[/tex]
How to find the radius of convergenceTo find the radius of convergence, we can use the ratio test:
[tex]\frac{lim |(n+1)!(6x-1)^n^+^1|}{|n!(6x-1)^n|} \\\\[/tex]
[tex]= lim |6x-1| \\=|6x-1|[/tex]
The series will converge if this limit is less than 1. So we solve the inequality:
[tex]|6x-1| < 1[/tex]
which gives us:
-1 < 6x - 1 < 1
0 < 6x < 2
[tex]0 < x < \frac{1}{3}[/tex]
Therefore, the radius of convergence is [tex]\frac{1}{6}[/tex]
To find the interval of convergence, we check the endpoints of the interval [0, [tex]\frac{1}{3}[/tex]]:
When x = 0, the series becomes:
∑(n=1 to infinity) n!(6x-1)^n = ∑(n=1 to infinity) n!(-1)^n
which diverges by the test for divergence.
When x = 1/3, the series converges by the ratio test. Therefore, the interval of convergence is:
i = [0, 1/3)
or in set-builder notation:
[tex]i = {x | 0 \leq x < 1/3}[/tex]
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Subtract
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4
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2
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2
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4
a
4
+4a
2
b
2
−2b
4
a, start superscript, 4, end superscript, plus, 4, a, squared, b, squared, minus, 2, b, start superscript, 4, end superscript from
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3
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Your answer should be a polynomial in standard form.
The expressions are subtracted to give -a⁴ + a²b² + 4b⁴
What are algebraic expressions?It is important to note that algebraic expressions are described as expressions that are made up of terms, variables, constants, coefficients and factors.
These expressions are also identified with arithmetic operations. These operations are;
SubtractionBracketParenthesesDivisionMultiplicationAdditionFrom the information given, we have that;
4a⁴ + 4a²b² - 2b⁴
3a⁴ + 5a²b² + 2b⁴
Now, subtract the expressions;
3a⁴ + 5a²b² + 2b⁴ - (4a⁴ + 4a²b² - 2b⁴)
expand the bracket
3a⁴ + 5a²b² + 2b⁴ - 4a⁴ - 4a²b² + 2b⁴
add the values
-a⁴ + a²b² + 4b⁴
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A survey of 50 college students was conducted to determine how much weekly income they earned from employment. Given the data set in Applications folder for this experience complete the following. Refer to the model/methodology for the desired format.a. Find the 5 number summary of the data set.Min=Q1=Median=Q3=Max=
The 5 number summary of the data set. Min=Q1=Median=Q3=Max is calculated as below.
To help you find the 5 number summary of the data set for the survey of 50 college students' weekly income. I'll provide a step-by-step explanation on how to calculate the 5 number summary.
1. First, arrange the data set in ascending order (from smallest to largest).
2. To find the minimum value (Min), simply identify the smallest number in the data set.
3. To find the maximum value (Max), identify the largest number in the data set.
4. To find the median (the middle value), follow these steps:
a. If the data set has an odd number of values, the median is the middle value.
b. If the data set has an even number of values, find the average of the two middle values.
5. To find the first quartile (Q1), you'll calculate the median of the lower half of the data set (excluding the overall median if the data set has an odd number of values).
6. To find the third quartile (Q3), calculate the median of the upper half of the data set (again, excluding the overall median if the data set has an odd number of values).
Once you've completed these steps, you'll have the 5 number summary for the data set:
Min, Q1, Median, Q3, Max.
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Determine whether the system has one solution, no solution, or infinitely many solutions.
The system has a unique solution, and therefore, there is only one solution to the system of equations.
Does the system has one solution, no solution, or infinitely many solutions?Given the system of equation in the question:
x + y = 7
2x - 3y = -21
First, solve one of the equations for one of the variables and substitute it into the other equation.
From equation (1), we can solve for y in terms of x as follows:
x + y = 7
y = 7 - x --- equation (3)
Now we can substitute equation (3) into equation (2) and solve for x:
2x - 3y = -21
Plug in y = 7 - x
2x - 3(7 - x) = -21
Simplifying the above equation, we get:
2x - 21 + 3x = -21
5x - 21 = -21
5x = 0
x = 0
Now we can substitute x = 0 into equation (1) to find y:
x + y = 7
Plug in x = 0
0 + y = 7
y = 7
Therefore, the solution to the system of equations is x = 0, y = 7.
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Help I don't understand.
Answer:
On x < -5, the function is increasing.
CAN SOMEONE HELP ME WITH THESE 50 POINTS
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow
Determine P(not yellow) if the spinner is spun once.
75%
37.5%
25%
12.5%
Question 2
Spin a spinner with three equal sections colored red, white, and blue. What is P(yellow)?
33%
0%
100%
66%
Question 3
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for 1 hour.
1.0
0.9
0.3
0.1
Question 4
When tossing a two-sided, fair coin with one side colored yellow and the other side colored green, determine P(yellow).
yellow over green
green over yellow
2
one half
Question 5
When given a set of cards laying face down that spell M, A, T, H, I, S, F, U, N, determine the probability of randomly drawing a consonant.
six thirds
six tenths
two thirds
two ninths
Question 6
When rolling a fair, eight-sided number cube, determine P(number greater than 2).
0.25
0.50
0.66
0.75
Question 7
Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles. Determine P(not purple) when choosing one marble from the bag.
64%
36%
24%
8%
Answer:
1. 75%
2. 0%
3. 0.1
4. one half
5. six tenths
6. 0.75
7. 64%
Step-by-step explanation:Answer 1:
The spinner has a total of 8 sections, out of which there are 2 yellow sections. Therefore, the probability of not getting a yellow section when the spinner is spun once is 6/8 or 3/4, which is equal to 75%.
Answer 2:
The spinner has only three sections and none of them is colored yellow. Therefore, the probability of getting a yellow section when the spinner is spun once is 0%.
Answer 3:
The total number of students surveyed is:
1 + 3 + 2 + 5 + 9 + 7 + 3 = 30
The number of students who studied for 1 hour is 3. Therefore, the probability of a student studying for 1 hour is 3/30, which simplifies to 1/10 or 0.1.
Answer 4:
Since the coin is fair and has one side colored yellow and the other side colored green, the probability of getting a yellow side when the coin is tossed is 1/2 or one half.
Answer 5:
The set of cards has 10 letters, out of which 4 are vowels (A, I, U). Therefore, the number of consonants in the set is 10 - 4 = 6. The probability of drawing a consonant is therefore 6/10, which simplifies to 3/5 or 0.6.
Answer 6:
The number cube has 8 sides, numbered 1 through 8. The probability of getting a number greater than 2 is the same as the probability of getting any number from 3 to 8. There are 6 such numbers out of 8 total numbers, so the probability is 6/8 or 3/4, which is equal to 0.75.
Answer 7:
The total number of marbles in the bag is:
2 + 4 + 10 + 9 = 25
The number of marbles that are not purple is:
2 + 4 + 10 = 16
Therefore, the probability of not getting a purple marble when one marble is chosen from the bag is 16/25, which is equal to 64%.
in college basketball games, a player may be afforded the opportunity to shoot two consecutive foul shots (free throws). a. suppose a player who makes (i.e., scores on) 80% of his foul shots has been awarded two free throws. if the two throws are considered independent, what is the probability that the player makes both shots? exactly one? neither shot?
Answer:
Both shots good: .8(.8) = .64 = 64%
Exactly one shot good: 2(.2)(.8) = .32 = 32%
Neither shot good: .2(.2) = .04 = 4%
SIMPLIFY THIS EXPRESSION!
Answer:
The answer is 3x-5y
Step-by-step explanation:
13x+2y-10x-7y
C.L.T.
13x-10x-7y+2y
3x-5y
Answer:
3x - 5y
Step-by-step explanation:
you 1st have to collect like terms which has the same variable
13x + 2y - 10x - 7y
(13x - 10x) + (2y - 7y)
3x - 5y .... is the simplified form of the equation.
What is 0. 81818181818 as a fraction in its simplest form?
‹
0. 81818181818 as a fraction in its simplest form is 9/11
How to find the fraction in simplest formConverting the decimal to fraction we have
x = 81818181818/100000000000
Using a calculator we san reduce the fraction to 9/11
Therefore, 0.81818181818... as a fraction in its simplest form is 9/11.
This is a recurrence fraction and a recurring fraction, also called a recurring decimal, is a decimal number with repeating digits after the decimal point. The repeatability of the lines is indicated by a horizontal line or a line above the repetition line.
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If you borrow $1,600 for 6 years at an annual interest rate of 10%, what is the total amount of money you will pay back?
Answer:
$2560 is the total amount to be paid back
Step-by-step explanation:
This is Simple interest described in the question
P = Principal amount
= Amount of money borrowed
= $1600
R = Rate of interest
= 10% per year
= 10% per annum
T = Time period
= 6 years
Make sure the base units of R and T are the same:
S.I. = Simple Interest = [tex]\frac{PRT}{100}[/tex]
= [tex]\frac{(1600 Dollars)(10\frac{Percent}{Year})(6Years)}{(100 Percent)}[/tex]
= $960
This means:
Total amount to be paid back = P + S.I.
= $1600 + $960
= $2560
an article about search engine optimization states that, on average, the number of keywords that should be targeted when creating a website is 5 keywords. a website developer, who is looking to increase traffic on their websites, believes the average number of keywords targeted for a website is different than the number stated by the article. after completing a study, the website developer found that the average number of keywords targeted in a website is is 5.6 keywords, on average. as the website developer sets up a hypothesis test to determine if their belief is correct, what is their claim? select the correct answer below: the average number of keywords targeted in a website is different than 5 keywords. the average number of keywords targeted in a website is different than 5.6 keywords. websites should contain more keywords. the average number of keywords targeted in a website is 5 keywords.
The right response is "the average number of targeted keywords in a website is different than 5 keywords." The website developer asserts that the value of 5 in the article does not accurately reflect the genuine population mean of the number of keywords targeted in a website.
This claim may be one-tailed (if the website developer thinks the true mean is larger or less than 5) or two-tailed (if the website developer thinks the true mean is merely different from 5) in nature. The website developer feels the true mean is different from the value given in the article, without stating whether it is larger or less than 5. As a result, the claim is two-tailed in this instance.
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A point S is 54 km due east of point T. The bearings of an electricity pole from S and Tare N28°W and N70°E, respectively. Calculate the distance of the electricity pole from T.
The distance of the electricity pole from T is 53 km
Given that;
The ST is 54 kilometer long
(180 - 28) + (180 - 70) = 262 degree is the angle PST,
which is the product of the angles at S and T.
S has a 62 degree angle.
The law of sines can be written as:
sin(62)/SP = sin(262/ST)
To find SP, we can rearrange this equation as follows:
SP = sin(62)/sin(262)x(ST)
When we enter the values we are aware of, we obtain:
SP = sin(62)/sin(262)*54 km
We can evaluate this expression to determine that:
SP ≈ 53.5 km Consequently, 53.5 kilometer or so separate T from the electricity pole.
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what is the sample mean years to maturity for corporate bonds and what is the sample standard deviation? mean (to 4 decimals) standard deviation (to 4 decimals) b. develop a 95% confidence interval for the population mean years to maturity. please round the answer to four decimal places. ( , ) years c. what is the sample mean yield on corporate bonds and what is the sample standard deviation? mean (to 4 decimals) standard deviation (to 4 decimals) d. develop a 95% confidence interval for the population mean yield on corporate bonds. please round the answer to four decimal places.
a) The sample mean years to maturity for corporate bonds = 16.9625
and the sample standard deviation = 8.2232
b) A 95% confidence interval for the population mean years to maturity: (14.4141, 19.5112)
c) The sample mean yield on corporate bonds is 4.5405
and the sample standard deviation = 2.3082
d) A 95% confidence interval for the population mean yield on corporate bonds: (3.825, 5.256)
a) The mean of the sample would be,
[tex]\bar{x}[/tex] = (10.25 + 28 + 23 + 13.25 + 3, 7.5 + 26.5 + 21.25 + 3.25, 19 + 9.25 + 28.75 + 1.75 + 17 + 8.75 + 24 + 24.5 + 18+ 11.75 + 22 + 22.75 + 27.75 + 16.75 + 12 + 16.5 + 23.75 + 25.25 + 25.75 + 22.5 + 1.25 + 19.5 + 12.5 + 27.25 + 19.5 + 17.75 + 11.5+ 3.5 + 20 + 25.25 + 6.75) / 40
[tex]\bar{x}[/tex] = 678.5 / 40
[tex]\bar{x}[/tex] = 16.9625
And the sample standard deviation would be,
s = √(67.6203)
s = 8.2232
b)
We know that the formula for the confidence interval is,
CI = [tex]\bar{x}[/tex] ± (z × s/√n)
Here, n = 40, [tex]\bar{x}[/tex] = 16.9625, s = 8.2232 and z = 1.9600
Using above formula the 95% confidence interval for the population mean years to maturity would be,
CI = 16.9625 ± (1.9600 × 8.2232/√40)
CI = (16.9625 ± 2.548)
CI = (16.9625 - 2.548, 16.9625 + 2.548)
CI = (14.4141, 19.5112)
c) Consider sample yield on corporate bonds.
The mean would be,
[tex]\bar{x}[/tex] = 181.62 / 40
[tex]\bar{x}[/tex] = 4.5405
And the standard deviation would be,
s = √(5.327594)
s = 2.3082
d) Now we construct a 95% confience interval.
Here, n = 40, s = 2.3082, [tex]\bar{x}[/tex] = 4.4505, and z = 1.9600
Using above formula the 95% confidence interval for the population mean years to maturity would be,
CI = 4.4505 ± (1.9600 × 2.3082/√40)
CI = (4.5405 ± 0.716)
CI = (4.5405 - 0.716, 4.5405 + 0.716)
CI = (3.825, 5.256)
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Find the complete question below.
(Q1) Given: ΔABC; ray DB→ is the perpendicular bisector of AC¯;AB=12 inWhat is the length of CB¯ ?By what Theorem?
The length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.
By the perpendicular bisector theorem, if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the segment. Therefore, in triangle ABC, since ray DB is the perpendicular bisector of AC, it follows that BD = DC.
Let x be the length of CB. Then, by the Pythagorean theorem in triangle ABC, we have:
[tex]AB^2 + BC^2 = AC^2[/tex]
Substituting AB = 12 and BD = DC = x/2, we get:
[tex]12^2 + x^2 = (2x)^2[/tex]
[tex]144 + x^2 = 4x^2[/tex]
[tex]3x^2 = 144[/tex]
[tex]x^2[/tex]= 48
x = √(48) = 4√(3)
Therefore, the length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.
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Joan wants to jog 13 miles on a circular track
1
4
mile in diameter.
How many miles is one circle of the track? (Round your answer to two decimal places.)
mi
How many times must she circle the track? Round to the nearest lap.
times
Joan should run 13 times around the park to complete her goal.
Given that, Joan wants to jog in a circular track which 1/4 mile in diameter.
We need to find the circumference of the track and the number of rounds she needs run to complete her goal.
So,
Circumference = π × diameter
= 3.14 × 1/4 = 0.785 miles
Let she runs x rounds to complete her goal,
So,
0.785x = 10
x = 12.73
x ≈ 13
Hence, Joan should run 13 times around the park to complete her goal.
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use spherical coordinates.evaluate x2 dv,e where e is bounded by the xz-plane and the hemispheres y
∫∫∫ x² dv over the region e is (3/40) a⁵ π².
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To use spherical coordinates, we need to express the volume element dv in terms of ρ, θ, and φ, where ρ is the radial distance from the origin, θ is the angle in the xy-plane measured from the positive x-axis, and φ is the angle measured from the positive z-axis.
We have x² = ρ² sin²(φ) cos²(θ). The volume element dv can be expressed as dv = ρ² sin(φ) dρ dφ dθ.
The region e is bounded by the xz-plane and the hemispheres y = ±√(a² - x²), where a > 0.
Since we're only interested in the part of e that lies in the first octant, we can restrict θ to the range [0, π/2] and φ to the range [0, π/2].
Note that since y is always positive in the first octant, we don't need to consider the negative hemisphere.
So, the integral we need to evaluate is:
∫∫∫ x² dv
= ∫[0,π/2]∫[0,π/2]∫[0,a] (ρ² sin³(φ) cos²(θ)) ρ² sin(φ) dρ dφ dθ
= ∫[0,π/2]∫[0,π/2]∫[0,a] ρ⁴ sin⁴(φ) cos²(θ) dρ dφ dθ
= ∫[0,π/2]∫[0,π/2] [(1/5)ρ⁵ sin⁴(φ) cos²(θ)]|[0,a] dφ dθ
= (1/5) a⁵ ∫[0,π/2] cos²(θ) dθ ∫[0,π/2] sin₄(φ) dφ
= (1/5) a⁵ [(1/2)π] [(3/4)(π/2)] = (3/40) a⁵ π².
Therefore, ∫∫∫ x² dv over the region e is (3/40) a⁵ π².
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What are some expressioms equivalent to -49y-14
The equivalent expression to the -49y - 14 are as follow,
7(-7y -2) , -7(7y + 2) ,-1(49y + 14), -14(3.5y + 1), -98/7 - 49y and -7(7y + k₁) + k₂ where -14 = -k₁ + k₂.
Expression is equal to
-49y - 14
The equivalent expressions are ,
By taking -1 as common factor
-(49y + 14)
By taking -7 as common factor
-7(7y + 2)
By taking 7 as common factor .
7(-7y -2)
By taking -14 as common factor
-14(3.5y + 1)
By replacing -14 as -98/7
-98/7 - 49y
By replacing -14 = -21 + 7
-7(7y + 3) + 7
By replacing -14 = -28 + 14
-7(7y + 4) + 14
By replacing -14 = -35 + 21
-7(7y + 5) + 21
By replacing -14 = -42 + 28
-7(7y + 6) + 4
and many more.
All of these expressions are equivalent to -49y -14.
Therefore, the expression which are equivalent to the given expression are 7(-7y -2) , -7(7y + 2) ,-1(49y + 14), -14(3.5y + 1), -98/7 - 49y and -7(7y + k₁) + k₂ where -14 = -k₁ + k₂.
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. if you fit a model that predicts mins by including ftmade as an explanatory variable, how many parameters would the model have?
If a model predicting minutes includes "ftmade" as an explanatory variable, the model would have two parameters: the intercept and the slope of "ftmade." The intercept represents the expected minutes when "ftmade" is zero, and the slope represents the expected increase in minutes for every one-unit increase in "ftmade."
The number of parameters in a model that predicts mins by including ftmade as an explanatory variable depends on the type of model being used.
If a simple linear regression model is used, the model would have two parameters: the intercept and the slope coefficient for the ftmade variable.
If a multiple linear regression model is used, which includes more than one explanatory variable, the model would have additional parameters for each additional explanatory variable included.
For example, if the model also included the variables age and gender, the model would have four parameters: the intercept, the slope coefficient for ftmade, the slope coefficient for age, and the coefficient for gender (assuming gender is coded as a binary variable).
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The following values represent the probabilities that a junior student at the Foster School of Business has taken a course in Finance, Accounting, and/or Marketing in the past academic year.
Finance = 0.55
Accounting = 0.41
Marketing = 0.26
Both Finance and Accounting = 0.32
Both Finance and Marketing = 0.15
Both Accounting and Marketing = 0.09
All three courses=0.05
a) Construct the associated Venn diagram with all probabilities specified.
b) After selecting at random a Foster junior for a suivey, determine the probability this student has taken at least 2 out of 3 courses:
c) Exactly one of the three courses
d) At the most one course
a) The Venn diagram is as follows:
b) After selecting at random a Foster junior for a survey, the probability this student has taken at least 2 out of 3 courses is 0.61
c) After selecting at random a Foster junior for a survey, the probability this student has taken exactly one of the three courses is 0.06.
d) After selecting at random a Foster junior for a survey, the probability this student has taken at the most one course is 0.14.
b) To find the probability that the student has taken at least 2 out of 3 courses, we add the probabilities of the following three events: taking both Finance and Accounting, taking both Finance and Marketing, and taking both Accounting and Marketing, plus the probability of taking all three courses:
P(at least 2 courses) = P(Finance and Accounting) + P(Finance and Marketing) + P(Accounting and Marketing) + P(all three courses)= 0.32 + 0.15 + 0.09 + 0.05= 0.61Therefore, the probability that the student has taken at least 2 out of 3 courses is 0.61.
c) To find the probability that the student has taken exactly one of the three courses, we add the probabilities of the following three events: taking Finance only, taking Accounting only, and taking Marketing only:
P(exactly one course) = P(Finance only) + P(Accounting only) + P(Marketing only)= 0.55 - 0.32 - 0.15 + 0.41 - 0.32 - 0.09 + 0.26 - 0.15 - 0.09= 0.06Therefore, the probability that the student has taken exactly one of the three courses is 0.06.
d) To find the probability that the student has taken at most one course, we add the probabilities of the following two events: taking no courses and taking exactly one course:
P(at most one course) = P(no course) + P(exactly one course)= 1 - (0.55 + 0.41 + 0.26 - 0.32 - 0.15 - 0.09 + 0.05)= 0.14Therefore, the probability that the student has taken at most one course is 0.14.
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This is more trig i need
Awnsers
The length of the sides are
AC = 5.4
BC = 10.5
How to determine the valueTo determine the value, we need to know the different trigonometric identities.
They include;
secantcosecantsinetangentcotangentcosineThese identities also have their ratios;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have;
tan 31 = AC/9
cross multiply the values
AC = 5. 4
sin 59 = 9/BC
cross multiply the values
BC = 10. 5
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7.03 Inscribed Quadrilaterals
pls help
The value of angles in inscribed quadrilateral are μ(∠zyx) is 92⁰ and μ(∠yxw) is 65⁰.
An inscribed quadrilateral is a quadrilateral that can be inscribed in a circle, meaning that its vertices all lie on the circumference of a circle. In other words, the four vertices of an inscribed quadrilateral are concyclic.
The opposite angles of an inscribed quadrilateral are supplementary, which means that they add up to 180 degrees. This property is known as the "interior angle sum" of a quadrilateral.
μ(∠zyx) + μ(∠xwz) = 180⁰ (opposite angle of cyclic quadrilateral are supplementary)
μ(∠xwz) = 88⁰
μ(∠zyx) = 180⁰ - 88⁰ = 92⁰
μ(∠yzw) is an inscribed angle that intercepts the arc 112⁰ and 118⁰. Therefore,
μ(∠yzw)
= (112⁰ + 118⁰)/2
= 230⁰/2
= 115⁰
μ(∠yxw) + μ(∠yzw) = 180⁰ (opposite angle of cyclic quadrilateral are supplementary)
μ(∠yxw) = 180⁰ - 115⁰ = 65⁰
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The Blackburn family has a square field where they keep their cattle. The area of the field is 40,000 ft square, and Mr. Blackburn wants to put a fence diagonally through the field. What should the length of the fence be?
If area of cattle's "square-field" is 40000 ft², and Mr. Blackburn is constructing a fence diagonal in the field, then length of cattle field's fence should be 282.84 ft.
The area of the Blackburn's family cattle square-field is 40000 ft²,
So, We First, equate this area with area formula,
On Equating ,We get,
⇒ (side × side) = 40000,,
⇒ side is 200 ft,
Now, we substitute the "side-length" of field as 200 ft, in the formula for diagonal of a square,
we get,
⇒ Length of cattle-field's diagonal is = (side)√2,
⇒ Length of cattle-field's diagonal is = (200)√2,
⇒ Length of cattle-field's diagonal is ≈ 282.84 ft.
Therefore, the length of cattle field's fence is 282.84 ft.
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the value of a car is $20,000. it loses 10.3% of its value each year. write an exponential function to determine the value of the car in t years.
To model the decrease in the value of the car over time, we can use an exponential function of the form:
V(t) = V(0) * e^(-rt)
where:
V(0) is the initial value of the car (in this case, $20,000).
r is the annual rate of depreciation, expressed as a decimal (in this case, 0.103).
t is the number of years since the car was purchased.
Plugging in the given values, we get:
V(t) = $20,000 * e^(-0.103t)
This is the exponential function that models the value of the car in t years.
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