Answer:
Step-by-step explanation:
cos A = √( 1 - (5/13)²) = √( 1 - 25/169) = √(144/169) = - 12 /13
in 2 A = 2 sin A cos A
sin 2 A = 2 *5/13 ( - 12/13 ) = - 120 / 169
the answer is -120/169
You and a friend are playing a game of chance. Every time you roll a 1 or 2 you are successful, and your friend will pay you $1. Every time you roll (using a fair die) a 3, 4, 5 or 6, you must pay your friend $2. If 71% of your rolls are successful and 29% of your rolls are unsuccessful, how much money do you expect to have earned/owed by the end of the game
Considering the mean of a discrete distribution, you are expected to earn $0.13 by the end of the game.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Since 71% of your rolls are successful and 29% of your rolls are unsuccessful, the distribution of your earnings is:
P(X = 1) = 0.71.P(X = -2) = 0.29Hence the expected value is:
E(X) = 1 x 0.71 - 2 x 0.29 = 0.71 - 0.58 = 0.13
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Which value is not part of the five-number summary for the following data set?
35, 23, 24, 30, 28, 23, 27, 33, 27, 34, 30, 30
A. 29
B. 23
C. 31.5
D. 24
Answer:
D. 24
Step-by-step explanation:
The 5-number summary of a data set includes ...
minimum1st quartilemedian (2nd quartile)3rd quartilemaximumSummary valuesWhen the data are written in increasing order, they are ...
23 23 24 27 27 28 30 30 30 33 34 35
The minimum is the first value on the list, 23.
The first quartile is the average of the two middle values in the lower half of the data set: (24+27)/2 = 25.5.
The median is the average of the two middle values: (28+30)/2 = 29.
The third quartile is the average of the two middle values in the upper half of the data set: (30+33)/2 = 31.5.
The maximum is the last value on the list: 35.
Answer choicesA. 29 is the median
B. 23 is the minimum
C. 31.5 is the 3rd quartile
D. 24 is not part of the 5-number summary
HELP pleeeeease, will give brainliest
Answer:The answer is A
Step-by-step explanation:
The ratio of dogs to cats is 3 to 8. if there are 294 dogs, how many cats are there?
Answer:
784 cats Yikes !
Step-by-step explanation:
d/c = 3/8
3/8 = 294/c
c = 294 * 8/3 = 784 cats
If rick has 35 oranges and he divide them into equally into 7 bags. what fraction represents the number of oranges rick puts in each bag?
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats. Assume the underlying population of unoccupied seats is normally distributed. Using a t- statistic, construct a 95% confidence interval for the population mean number of unoccupied seats per flight.
The given sample's 95% confidence interval is 11.6 ± 0.5357. I.e., from the lower bound 11.06 to the upper bound 12.14. Its margin error is 0.5357.
How to find the confidence interval?To find the confidence interval C.I,
Determine the mean(μ) of the sampleDetermine the standard deviation(σ)Determine the z-score for the given confidence level using the z-score tableUsing all these, the confidence interval is calculated by the formula, C. I = μ ± z(σ/√n) where n is the sample size and z(σ/√n) gives the margin error. So, we can also write C. I = mean ± margin error.Calculation:It is given that,
Sample size n = 225
Sample mean μ = 11.6
Standard deviation σ = 4.1
Since 95% confidence interval, z-score is 1.96
So, the required confidence interval is calculated by,
C. I = μ ± z(σ/√n) or mean ± margin error
On substituting,
C. I = 11.6 ± 1.96(4.1/√225)
= 11.6 ± 1.96 × 0.2733
= 11.6 ± 0.5357
So, the lower bound = 11.6 - 0.5357 = 11.065 and
the upper bound = 11.6 + 0.5357 = 12.135.
Thus, the confidence interval is from 11.06 to 12.14, and its margin error is 0.0537 for the population mean number of unoccupied seats per flight.
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Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to
finish his breakfast and 39 minutes to commute to school. At what time did he
reach the school?
Answer:
[tex]\huge\boxed{\sf 8:32\ AM}[/tex]
Step-by-step explanation:
Woke up = 7:30 AM
Time to:
Get ready = 14 minFinish breakfast = 9 minCommute to school = 39 minAltogether:
= 14 + 9 + 39 min
= 62 minutes(As we know that, 1 hour = 60 minutes)
So,
62 minutes = 1 hour 2 minutesTime he reached the school:
7 hr 30 min + 1 hr 2 min
Combine like terms
7 hr + 1 hr + 30 min + 2 min
8 hr + 32 minOR
8:32 AM[tex]\rule[225]{225}{2}[/tex]
Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to finish his breakfast and 39 minutes to commute to school. At what time did he reach the school?
❍ Explanation -:In this question we are asked to calculate the time paul reach the school.
Altogether time paul took to get ready, to finish his breakfast and to commute to school.
(14 + 9 + 39) minutes
→ (23 + 39) minutes
→ 62 minutes
Now we will convert minutes into hour.
62 ÷ 60
→ 1 hr 2 min
Now we will calculate the time he reached his school.
7 hr + 30 + 1 hr 2 min
[tex]\begin{array}{cc}7 \sf{hrs} \: & \: 30 \sf{min} \\ \underline{1 \: \sf{hr}} & \underline{2 \sf{min} } \\ \pmb{8 \sf{hrs}}& \pmb{32 \sf{min}}\end{array}[/tex]
He will reach the school at 8:32 AM.
The length of a rectangle is 8 inches more than the width. the perimeter is 44 inches. find the length and width of the rectangle
Answer: Width is 7 inches, length is 15 inches.
Step-by-step explanation:
Let the width be w. Then, the length is w+8.
[tex]2(w+w+8)=44\\\\w+w+8=22\\\\2w+8=22\\\\2w=14\\\\w=7\\\\\implies l=15[/tex]
Almost done!!! Appreciate the help
Using the formula for the distance between two points to find the side lengths, the perimeter of the polygon is of 25 units.
What is the perimeter of a figure?The perimeter of a figure is given by the sum of the side lengths of it's outside dimensions.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For this problem, the distances are given as follows:
[tex]D_1 = \sqrt{(-1 -(-1))^2 + (6 - 3)^2} = 3[/tex].[tex]D_2 = \sqrt{(2 -(-1))^2 + (10 - 6)^2} = 5[/tex].[tex]D_3 = \sqrt{(5 - 2)^2 + (6 - 10)^2} = 5[/tex].[tex]D_4 = \sqrt{(5 - 5)^2 + (3 - 6)^2} = 6[/tex].[tex]D_5 = \sqrt{(5 - (-1))^2 + (3 - 3)^2} = 6[/tex].Hence the perimeter is given by:
P = 3 + 2 x 5 + 2 x 6 = 25 units.
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You are building a ramp that must cover a horizontal distance of exactly 13 feet. The angle of the ramp from the ground is 26 degrees. Determine the length of the ramp, in feet.
Answer: 18.6 feet
Step-by-step explanation: Horizontal distance = 17 feet and the angle
of elevation = 24°
Can you plssss help !!!
The parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.
Parts of the circle shown in the imageThe following are the parts of the circle shown;
Chord: the length DC and DG represent the chord of the circleDiameter: the length HF represent the diameter of the circleRadius: the length HA and FA represents the radius of the circletangent: the line JB represents a tangent to the circleCenter: point A represents the center of the circleThus, the parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.
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A group of 31 friends gets together to play a sport. First, people
must be divided into teams. Each team has to have exactly 3
players, and no one can be on more than one team. How many
teams can they make? (It is possible that not everyone can be on a
team.)
(Do not include units in your answer.)
The number of teams she can make is 10.
How many teams can she make?Division is the process of putting a number into equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other basic mathematical operations include addition, subtraction, multiplication.
The number of teams that can be made can be determined by dividing the total number of friends by the total number of players in each team. The whole number that is derived from the division process is the number of teams teams that can be made given the total number of friends and the number of people that have to be in each group.
Number of teams she can make = total number of friends / number of people in each group
31 / 3 = 10 remainder 1
So, only 10 teams can be made. one person would not be on any team.
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Quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
The cost per person if number of students is 100 given the inverse variation is $46.75
Inverse variationCost per person = CNumber of students = nC = k / n
where,
k = constant of proportionality
If n = 55 and C = $85
C = k / n
85 = k / 55
85 × 55 = k
4,675 = k
Find C if n = 100
C = k / n
= 4,675 / 100
C = $46.75
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Answer:
C = $46.75
Step-by-step explanation:
85 × 55 = k
4,675 = k
4675/100=46.75
therefore the answer is 46.75
help me!!!
please I am in a rush
Answer:
A= 54
B=3
Step-by-step explanation:
I hope this helps!
A manufacturer must test that his bolts are 4.00cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 81 randomly selected bolts off the assembly line, he calculates the sample mean to be 3.97cm. He knows that the population standard deviation is 0.14cm. Assuming a level of significance of 0.01, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines
The p-value(0.0538) is greater than the given significance level of 0.01. So, there is no sufficient evidence to show that the manufacturer needs to recalibrate the machines.
What is the test statistics formula for finding the p-value approach of hypothesis testing?The test statistics formula for finding the z-score is,
z = (X - μ)/(σ/√n)
Where,
X = sample mean
μ = population mean
σ = population standard deviation
n = sample size
With this z-score, the p-value is calculated. If p > α, then the null hypothesis is not rejected, and if p < α, then the null hypothesis is rejected.
Calculation:It is given that,
The population mean μ = 4.00
The sample size n = 81
The sample mean X = 3.97
The standard deviation σ = 0.14
and the significance level α = 0.01
So, the hypothesis is:
The null hypothesis: H0: μ = 4
The alternative hypothesis: Ha: μ ≠ 4
Thus, the test statistic value is,
z = (X - μ)/(σ/√n)
= (3.97 - 4)/(0.14/√81)
= - 0.03/0.015
= -1.928
So, for z = -1.928, the p-value is 0.053855
Since p > 0.01, there is no sufficient evidence to show that the manufacturer needs to recalibrate the machines.
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The reciprocals of what three different positive integers have sum equal to 1?
Answer:
1/a + 1/b + 1/c = 1 , a,b,c is nonzero
Step-by-step explanation:
bc +ac +ab /abc = 1
bc + ac + ab = abc
a = b = c = 1
A group of students consists of four people in all; two women and two men. They agree to take turns taking notes in lecture. One person at a time will be selected at random from the group (without replacement) until everyone has had a turn. The expected value of the number of people selected before and including the first time a woman has a turn is (Q17)______ .
The standard error of the number of people selected before and including the first time a woman has a turn is (Q18)______ .
The expected value of the number of people selected before and including the first time a woman has a turn is 1.6667 and the standard error is 0.7454.
How to illustrate the information?It should be noted that the expected value will be:
1[p(x = 1)] + 2[p(x = 2)] + 3[p(x = 3)]
= 1(0.5) + 2(0.3333) + 3(0.1667)
= 1.6667
Var(X) = E(X²) - E(X)2
= 3.3335 & (1.6667)²
= 0.555611
The standard error will be:
= ✓0.555611
= 0.7454
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Please answer questions three to five!
The computation shows that the amount that will be charged will be $5.00 and $9.00 respectively.
How to illustrate the information?When the customer has a 6 pound Chihuahua, the amount that will be charged will be $5.00.
When a customer has a 65 pound Labrador, the amount that will be charged is $9.00.
This is illustrated as the cost is based on the weights given.
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Find the area of each of these rectangles
In apirl is rained 1/4 of a inch on 15 diffret day how many inches of rain fell
In [tex]15[/tex] diffret days [tex]15/4[/tex] inches of rain fell in April month if every day rained [tex]1/4[/tex] of a inch .
How to find the rain fell in [tex]15[/tex] diffret days ?
We know that rain in every day is [tex]1/4[/tex] of a inch
So for [tex]15[/tex] days
[tex]1/4+1/4+1/4+......15times\\=15/4[/tex]
So in [tex]15[/tex] diffret days in April rain fell is [tex]15/4[/tex] inches.
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A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. what is the probability that the lock code consists of all even digits?
Probability that the lock code consists of all even digits is [tex]1344[/tex] if we choose the [tex]4[/tex] digit lock is randomly from numbers [tex]1,2,3,4,5,6,7,8,9[/tex]
How can we find the probability that the lock code consists of all even digits?
Total numbers are [tex]1,2,3,4,5,6,7,8,9[/tex]
And we choose [tex]4[/tex] digit code
So probability of choosing [tex]4[/tex] numbers from [tex]9[/tex] numbers without reapitation is
[tex]9p_{4} =\frac{9!}{(9-4)!} \\=\frac{9*8*7*6*5!}{5!} \\=3024[/tex]
For All numbers are even , probability the last digit of number is even.
So we have [tex]4[/tex] even number and if we fix one on last digit and can change other [tex]3[/tex] then the probability is
[tex]4*8P_{3} =4*\frac{8!}{(8-3)!} \\=4*\frac{8*7*6*5!}{5!} \\=1344[/tex]
So the total probability of code lock having all even number is [tex]1344[/tex]
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Find the area of the convex polygon with vertices (0,5), (-1,2), (4,4), (-3,-4) and (2,0).
The area of the convex polygon is 43/2 square units
How to determine the area of the convex polygon?The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
[tex]A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )[/tex]
So, we have:
[tex]A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)[/tex]
Evaluate
[tex]A = \frac12 * (|-43|)[/tex]
Remove the absolute bracket
[tex]A = \frac12 * 43[/tex]
This gives
[tex]A = \frac{43}2[/tex]
Hence, the area of the convex polygon is 43/2 square units
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It cost Cai $1,80 to send 12 text messages, How much would it cost to send 90 text
messages?
Answer:
$13.5
Step-by-step explanation:
cost of 1 text message= $1.80÷12 =$0.15
cost of 90 messages = $0.15×90 = $13.5
Answer: $13.50 for 90 text messages
Step-by-step explanation:
$0.15×90 = $13.5
$0.15 is the unit rate for 1 text message cost.
The length of side ab is units. the length of side bc is units. the length of side ac is units.
The length of side AC = 5 units
Solving missing sides of right trianglesMissing sides of a right triangle can be solved using the Pythagoras theorem
From the given question
Length of side AB = 3 units
Length of side BC = 4 units
The length of side AC is calculated below
[tex]AC^2=AB^2+BC^2\\\\AC^2=3^2+4^2\\\\AC^2=9+16\\\\AC^2=25\\\\AC=\sqrt{25}\\\\AC=5[/tex]
Therefore, the length of side AC = 5 units
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Complete Question
The length of side ab is 3 units. the length of side bc is 4 units. the length of side ac is .......... units.
Find the greatest common factor of the
following monomials:
33c 27c^4
The greatest Common factor of monomials [tex]33c[/tex] and [tex]27c^4[/tex] is [tex]3c[/tex]
How we can find the GCF of monomials ?
Monomials are [tex]33c[/tex] and [tex]27c^4[/tex]
We can write the monomials in fraction form
[tex]33c=11*3*c[/tex]
[tex]27c^4=3*9*c*c*c*c[/tex]
----------------------------------
So we can see the common factor is [tex]3c[/tex]
The Greatest Common Factor of [tex]33c ,27c^4[/tex] is [tex]3c[/tex]
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Which of the following is not considered an action that would interfere with the airflow patterns at the front opening of the biosafety cabinet
An action that would not interfere with the airflow patterns at the front opening of the biosafety cabinet is a researcher discarding waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening.
What is biosafety?It should be noted that biosafety simply means the use of safety equipment as specifically designs tools to ensure that people are protected from hazards.
In this case, when a researcher discards waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening, it won't interfere with the airflow pattern.
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The length of a rectangle is 3 less than twice the width. Determine how the area will change if the length of the rectangle is increased by 5 and the width is decreased by 2. Show your work.
The change in the area is represented by the expression ΔA = 9 · x + 4, where x is the original width of the rectangle.
What is the change in the area of the rectangle if side lengths are changed?
By geometry we know that the area of a rectangle is equal to the product of its width (x) and length (y). Based on the statement, the original rectangle is equal to:
A = x · y
A = x · (2 · x - 3)
And the change in the area is:
A + ΔA = (x + Δx) · (y + Δy)
A + ΔA = x · y + Δx · y + Δy · x + Δx · Δy
ΔA = Δx · y + Δy · x + Δx · Δy
ΔA = (2 · x - 3) · Δx + Δy · x + Δx · Δy
ΔA = 2 · (2 · x - 3) + 5 · x + 10
ΔA = 9 · x + 4
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Select the correct answer.
What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?
OA 2+2-4x+2y+1=0
OB. ++4x-2y+1=0
OC. 2+2+4x-2y+9=0
OD. -+2x+y+1=0
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Find the other endpoint of the line segment with the given endpoint -5, 2 and midpoint 2, -5
Answer:
( 9, -12 )
Step-by-step explanation:
Mario's Math Tutoring
you have the midpoint
2, -5
use the midpoint formula
(x1+x2)/2 , (y1+y2)/2
to get the endpoint
x :
(-5+x2)/2 = 2
(-5+x2) = 4
-5+x2 = 4
x2 = 9
y:
(2+y2)/2 = -5
(2+y2) = -10
2+y2 = -10
y2 = -12
Thank you Mario!
To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone?
The relationship between the base of the cone and the angle of the plane that intersects the cone is that the plane must be at a 45 degree angle to the base of the cone. Thus, Option D is correct.
According to the statement
we have given that the to form a ellipse we use the base and angle of the cone, And we have to tell the relationship between them.
So, For this purpose, We know that the
An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
And to make a ellipse the relationship between the base of triangle and the angle of the cone is that the
The plane must be at a 45 degree angle to the base of the cone.
By this way we make a ellipse with the help of the cone.
So, The relationship between the base of the cone and the angle of the plane that intersects the cone is that the plane must be at a 45 degree angle to the base of the cone. Thus, Option D is correct.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone?
A. The plane is parallel to the base of the cone..
B. The plane may be perpendicular to the base of the cone..
C. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.
D. The plane must be at a angle to the base of the cone.
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Answer:
The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.
Step-by-step explanation:
The plane doesn't need to be at an exact angle of 45 degrees. The most important thing is that the angle isn't parallel or perpendicular to the base of the cone, but it has to be non-zero without intersecting the base itself. It also only intersects one of the cones when looking at a double-cone.