41.9 mi
Step-by-step explanation:
First, we convert the angle from degree measure to radian measure:
[tex]\theta = 240°×\left(\dfrac{\pi}{180°}\right)= \dfrac{4\pi}{3}\:\text{rad}[/tex]
Using the definition of an arc length [tex]s[/tex]
[tex]s = r\theta[/tex]
[tex]\:\:\:\:=(10\:\text{mi})\left(\dfrac{4\pi}{3}\:\text{rad}\right)[/tex]
[tex]\:\:\:\:= 41.9\:\text{mi}[/tex]
Verify if : (-30) x ( 13.+ (-3)] =[(-30) x 13] + [(-30) (-3)]
a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest. b. The probability of winning a lottery is 0.125. What is the probability of winning AT LEAST ONCE in twelve trials?
Answer:
The right answer is:
(a) -10.67
(b) 0.7986
Step-by-step explanation:
(a)
According to the question,
X P(X) X.P(X) X2.P(X)
12130 0.002 24.26 294274
-35 0.998 -34.93 1222.55
Now,
[tex]\Sigma x.P(x) = -10.67[/tex]
or,
[tex]\Sigma x^2.P(x) = 295496.35[/tex]
hence,
The mean will be:
[tex]\Sigma x.P(x) = -10.67[/tex]
(b)
According to the question,
n = 12
p = 0.125
q = 1 - p
= 0.875
Now,
⇒ [tex]P(X=x) = \binom{n}{x} p^x q^{n-x}[/tex]
By substituting the values, we get
⇒ [tex]P(X \geq 1)=1-(\binom{12}{0} 0.125^0. 0.875^{12-0})[/tex]
⇒ [tex]=1-(1 (0.125^0) (0.875^{12}))[/tex]
⇒ [tex]=1-(1(1.0)(0.2014))[/tex]
⇒ [tex]=1-(0.2014)[/tex]
⇒ [tex]=0.7986[/tex]
Find the length of AC
A. 377.19
B. 378.63
C. 2.89
D. 33.13
Answer:
AC = 377.19
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 5 = 33/AC
AC tan 5 = 33
AC = 33/ tan 5
AC = 377.19
michael has an average of 68% in his 3 papers but that is below the pass mark of 70%. what must be his least score in the fouth paper to enable him pass?
Answer:
His least score for him in the fourth paper has to be 76.
Step-by-step explanation:
Given that Michael has an average of 68% in his 3 papers but that is below the pass mark of 70%, to determine what must be his least score in the fouth paper to enable him pass the following calculation must be performed:
(70 x 4) - (68 x 3) = X
280 - 204 = X
76 = X
Therefore, his least score for him in the fourth paper has to be 76.
Work out giving ur answer as a mixed number
Answer:
6 11/12
Step-by-step explanation:
4 1/6 + 2 3/4
Get a common denominator of 12
4 1/6 *2/2 + 2 3/4 *3/3
4 2/12 + 2 9/12
6 11/12
An appliance uses 120 W. If this appliance is on for 8 hours a day, how much CO2 will this produce in the month of April?
...
Calculate Energy Cost by Appliance
Multiply the device's wattage by the number of hours the appliance is used per day.Divide by 1000.Multiply by your kWh rate.hope it's helpful for you!!..pls give me brainlist !!....An experiment consists of tossing a pair of balanced, six-sided dice. (a) Use the combinatorial theorems to determine the number of sample points in the sample space S. 36 Correct: Your answer is correct. sample points (b) Find the probability that the sum of the numbers appearing on the dice is equal to 6. (Round your answer to four decimal places.)
Answer:
Sample space = 36
P(sum of 6) = 5/36
Step-by-step explanation:
Number of faces on a dice = 6
The sample space, for a toss of 2 dice ; (Number of faces)^number of dice
Sample space = 6^2 = 6*6 = 36
Sum of numbers appearing on the dice = 6
The sum of 6 from the roll of two dice has 5 different outcomes ; Hence, required outcome = 5
Total possible outcomes = sample space = 36
Probability, P = required outcome / Total possible outcomes
P = 5 / 36
Probabilities are used to determine the chances of events
The given parameters are:
[tex]n=6[/tex] --- the faces of a six-sided die
[tex]r = 2[/tex] -- the number of dice
(a) The number of sample points
This is calculated as:
[tex]Sample = n^r[/tex]
So, we have:
[tex]Sample = 6^2[/tex]
Evaluate the exponent
[tex]Sample = 36[/tex]
Hence, the number of sample points is 36
(b) The probability that the sum of 6
See attachment for the sample space of the sum of two dice.
From the sample space, there are 5 outcomes where the sum is 6.
So, the probability is:
[tex]Pr = \frac{5}{36}[/tex] --- where 36 represents the number of sample points
Divide 5 by 36
[tex]Pr = 0.1389[/tex]
Hence, the probability that the sum of the numbers appearing on the dice is equal to 6 is 0.1389
Read more about probabilities at:
https://brainly.com/question/10707698
The strength of the association rule is known as _____ and is calculated as the ratio of the confidence of an association rule to the benchmark confidence.
Answer:
Lift
Step-by-step explanation:
Finding patterned and relationship between large sets of data can be obtained using the association rule as it finds insights, relationships and trends within sets of data variables. Lift is a parmater of interest whichbus used when performing analysis on association between variables in datasets. The Lift is literally the ratio of confidence to expected confidence. Where, the confidence of association is divided by the expected confidence (benchmark confidence).
Evaluate the expression 3√64
Answer:
4
Step-by-step explanation:
We want the cubed root of 64
(64)^(1/3)
(4*4*4) ^ (1/3)
4
Unless this is 3 * sqrt(64)
then it would be
3 sqrt(8*8)
3 (8)
24
Which of the following could be the equation of the graph shown below?
Answer:
According to the proposed interrogate, as well as the graph provided, the correct answers to such are identified as B. Y = -2x + 5 and C. 2x + y = 4.
Step-by-step explanation:
To evaluate such, a comprehension of linear Cartesian data is required:
Slope = rise/run. If there is a negative rise, the direction of the line is proportional to the left-hand side as it exponentially grows or augments in units.
Y-intercept: The peculiar point in which the linear data observed intersects the y-axis.
X-intercept: The peculiar point in which the linear data observed intersects the x-axis.
Since this is a negative linear, all negative slopes apply.
The interrogate states, “Check all that apply.” Thus, there may be more than one correct answer, shall such be disseminated.
A. Cannot be the answer as the line should have been a horizontal line contained within quadrants I and II on the Cartesian Plane.
B. Contains a negative slope, thus is disclosed as a correct answer.
C. This configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:
2x + y = 4
Y = -2x + 4 <== Slope-Intercept Form (Contains a negative slope, thus considered a correct answer.
D. Likewise, this configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:
X - y = 9
-y = -x + 9
Y = x - 9 <== Slope-Intercept Form (Cannot be considered as the correct answer, given the positive slope configuration, thus is marked out).
Thus far, as evaluated, the correct answers to the proposed interrogate, as according to the linear data provided in the Cartesian Plane is acknowledged, and henceforth disseminated, as B. Y = -2x + 5 and C. 2x + y = 4.
*I hope this helps.
A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $279.29. Find a 99% confidence interval for the true mean checking account balance for local customers.
Answer:
The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 14 - 1 = 13
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 3.0123
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.0123\frac{279.29}{\sqrt{14}} = 224.85[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 664.14 - 224.85 = $439.29
The upper end of the interval is the sample mean added to M. So it is 664.14 + 224.85 = $888.99.
The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).
A two-dimensional vector has an x-component of 10.3~\text{meters}10.3 meters and a y-component of 4.30~\text{meters}4.30 meters. Calculate the angle (in degrees) that this two-dimensional vector makes with the positive x-axis.
9514 1404 393
Answer:
23°
Step-by-step explanation:
The angle a vector makes relative to the +x axis is found as ...
α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°
The angle is about 23°.
__
Additional comment
This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)
Please Help!!! Whoever helps first and gets it correct gets Brainliest!
Answer:
Step-by-step explanation:
You have three data points. Equation of the line passing through (30,2), (45,2.75), and (60,3.50):
y = 0.5x + 0.5
It takes 0.5 hour to clean up.
find the length of side x
Answer:
x=8
Step-by-step explanation:
In a certain survey, 513 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 53% said "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security. Complete parts (a) through (d) below. a. Are any of the three requirements violated? Can a test about a population proportion using the normal approximation method be used?
Answer:
The sample observations are not a randomsample, so a test about a population proportion using the normal approximating method cannot be used.
Step-by-step explanation:
The necessary conditions are
The sample must be random and independently selected from the normally distributed population.
n*p and n*q both must be greater than 5
There must be two outcomes "success" and "failure"
The number of trials must be fixed.
From the given information 2), 3)and 4) conditions are satisfied, but not 1) because we are not given that people are selected randomly.
Answer: The sample observations are not a randomsample, so a test about a population proportion using the normal approximating method cannot be used.
Given limit of f(x) = -4 as x approaches c and limit of g(x) =1/5 as x approaches c. What is limit of g(x)/f(x) as x approaches c?
Answer:
-1/20
Step-by-step explanation:
As x approaches c,
g(x) 1/5
------ = ------------ = -1/20 (matches last of the four given possible answers)
f(x) -4
Answer:
[tex]\displaystyle \frac{-1}{20}[/tex]
General Formulas and Concepts:
Calculus
Limit Property [Division]: [tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \frac{ \lim_{x \to c} f(x)}{ \lim_{x \to c} g(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to c} f(x) = -4[/tex]
[tex]\displaystyle \lim_{x \to c} g(x) = \frac{1}{5}[/tex]
Step 2: Solve
Substitute in limits [Limit Property - Division]: [tex]\displaystyle \lim_{x \to c} \frac{g(x)}{f(x)} = \frac{ \frac{1}{5} }{ -4 }[/tex]Simplify: [tex]\displaystyle \lim_{x \to c} \frac{g(x)}{f(x)} = \frac{-1}{20}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Total 427 tickets sold 73 fewer student tickets than adult tickets how many adult tickets
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Answer:
250
Step-by-step explanation:
Let 'a' represent the number of adult tickets.
a +(a -73) = 427
2a = 500 . . . . . add 73
a = 250 . . . . . . divide by 2
250 adult tickets were sold.
_____
Additional comment
I call this a "sum and difference problem" because we are given the total of two values and the difference between them. As you can see here, the larger of the two values is the average of the given numbers, their sum divided by 2. This is the generic solution to such a problem: the larger number is the average of the given sum and difference.
14. Divide and write the fraction or mixed number in its simplest form:1/4÷3/8
Answer:
1/4 ÷ 3/8 = 2/3
Step-by-step explanation:
When dividing fractions, you have to take the reciprocal of the second fraction, then multiply from there. The reciprocal of a fraction is basically flipped. So then, 1/4 ÷ 3/8 becomes 1/4 x 3/8. Multiplying fractions should be pretty straight forward as you just need to multiply numerator (top number of a fraction) with numerator and vice versa for the denominators (bottom number of a fraction).
So then you get: (1 x 8)/(3 x 4) = 8/12. Then you just simplify it by dividing the numerator and denominator by their greatest possible factor, which in this case is 4. So then, (8 ÷ 4)/(12 ÷ 4) = 2/3.
A plane traveled 4425 miles with the wind in 7.5 hours and 3675 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is
Answer:
540 miles per hour and 50 miles per hour respectively.
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50
HELP PLEASE I CANNOT FAIL PLEASE!!!!!!!
Which statement correctly compares the two functions?
A.
They have the same y-intercept and the same end behavior as x approaches ∞.
B.
They have the same x- and y-intercepts.
C.
They have the same x-intercept but different end behavior as x approaches ∞.
D.
They have different x- and y-intercepts but the same end behavior as x approaches ∞.
Answer:
B
Step-by-step explanation:
they have the same intercepts
Given:
HI and JK intersect at point O.
m KOH = 110
Colleen was asked to find the measure of x and explain her reasoning
Line geometry are caused from the intersection of two line. The measure of angle x from the diagram is 110degrees
Linear geometryLine geometry are caused from the intersection of two lines. From the given figures, you can see that <KOH and <IOK forms a linear pair, hence;
<KOH + <IOK = 180
110 + <IOK = 180
<IOK = 180 - 110
<IOK = 70 degrees
Similarly <x and MIOK are linear pair pair such that <x + 1<IOK = 180
<x + 70 =180
<x = 180 - 70
<x = 110degrees
Hence the measure of angle x from the diagram is 110degrees
Learn more on line geometry here: https://brainly.com/question/7098341
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Answer:
<IOK = 70 degrees
<x and <IOK form a linear pair, so m<x is = 110
Step-by-step explanation:
i did it on khan and got it right, i hope your day goes well and you get all your other questions right :)
Select all that apply.
Given the points (5, 10) and (-4,-8), which of the following are true about the line passing through these points?
The line has a slope of 1/2
The line represents a direct variation function
The point (6.3) is also on the line
The line has a slope of 2
Which of the following is the graph of
(x - 1)^2 + (y + 2)^2 = 4 ?
Answer:
a
Step-by-step explanation:
The correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given equation is ( x-1 )² + ( y + 2 )² = 4
The graph of the equation is attached with the answer below when we plot the graph we will get the circle that is lying in the third and the fourth quadrant.
Therefore the correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.
To know more about graphs follow
https://brainly.com/question/25020119
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write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
Step-by-step explanation:
I really need help please
what is this?
Answer:
431.2
Step-by-step explanation:
Area of a regular polygon = # of sides * side length of 1 side * apothem
We want to find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length with 7.7 meters
So # of sides = 7
apothem = 8
side length = 7.7
so the area would equal 7 * 8 * 7.7 = 431.2
It says to round to the nearest tenth however 431.2 is already rounded to the nearest tenth
Answer:
That answer ^ is incorrect. The correct answer ( in acellus that is ) is 2
15.6
Step-by-step explanation:
The edge roughness of slit paper products increases as knife blades wear. Only 2% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 4% of products slit with worn blades exhibit roughness. If 25% of the blades in the manufacturing are new, 60% are of average sharpness, and 15% are worn, what is the proportion of products that exhibit edge roughness
Answer:
The proportion of products that exhibit edge roughness is 0.029 = 2.9%.
Step-by-step explanation:
Proportion of products that exhibit edge roughness:
2% of 25%(new blades).
3% of 60%(average sharpness).
4% of 15%(worn). So
[tex]p = 0.02*0.25 + 0.03*0.6 + 0.04*0.15 = 0.029[/tex]
The proportion of products that exhibit edge roughness is 0.029 = 2.9%.
Quick can someone plot these in a scatter plot
(9.2,2.33)
(19.5,3.77)
(15.5,3.92)
(0.7,1.11)
(21.9,3.69)
(0.7,1.11)
(16.7,3.5)
(0.7,1.11)
(18,4)
(18,3.17)
The scatterplot is below.
I used GeoGebra to make the scatterplot. Though you could use other tools such as Excel or Desmos, or lots of other choices.
Side note: I'm not sure why, but you repeated the point (0.7,1.11) three times.
What is the axis of symmetry of the
parabola graphed below?
O x=4
Oy=2
Oy=4
Ox=2
Other:
Answer:
A
Step-by-step explanation:
i think so..sorry if im wrong
Claims from Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. Claims from Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. All claim amounts are independent of the other claims. Fifty claims occur in each group. Find the probability the total of the 100 claims exceeds 1,530,000.
Answer:
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
n instances of a normal variable:
For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
Sum of normal variables:
When two normal variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.
Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. 50 claims of group A.
This means that:
[tex]\mu_A = 10000*50 = 500000[/tex]
[tex]s_A = 1000\sqrt{50} = 7071[/tex]
Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. 50 claims of group B.
This means that:
[tex]\mu_B = 20000*50 = 1000000[/tex]
[tex]s_B = 2000\sqrt{50} = 14142[/tex]
Distribution of the total of the 100 claims:
[tex]\mu = \mu_A + \mu_B = 500000 + 1000000 = 1500000[/tex]
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{7071^2+14142^2} = 15811[/tex]
Find the probability the total of the 100 claims exceeds 1,530,000.
This is 1 subtracted by the p-value of Z when X = 1530000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1530000 - 1500000}{15811}[/tex]
[tex]Z = 1.9[/tex]
[tex]Z = 1.9[/tex] has a p-value of 0.9713
1 - 0.9713 = 0.0287
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
sin x - cos x - 1/√2 = 0
Find the value of x
Answer:
Step-by-step explanation:
