Answer:
a) P(x = 0) = 64.69%
b) P(x ≥ 1) = 35.31%
c) E(x) = 0.42
d) var(x) = 0.3906
Step-by-step explanation:
The given problem can be solved using binomial distribution since:
There are n repeated trials independent of each other. There are only two possibilities: exceedence happens or exceedence doesn't happen.The probability of success does not change with trial to trial.The binomial distribution is given by
P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ
Where n is the number of trials, x is the variable of interest and p is the probability of success.
For the given scenario. the six daily arrivals are the number of trials
Number of trials = n = 6
The probability of success = 7% = 0.07
a) Find the probability that on one day no planes have an exceedence.
Here we have x = 0, n = 6 and p = 0.07
P(x = 0) = ⁶C₀(0.07⁰)(1 - 0.07)⁶⁻⁰
P(x = 0) = (1)(0.07⁰)(0.93)⁶
P(x = 0) = 0.6469
P(x = 0) = 64.69%
b) Find the probability that at least 1 plane exceeds the localizer.
The probability that at least 1 plane exceeds the localizer is given by
P(x ≥ 1) = 1 - P(x < 1)
But we know that P(x < 1) = P(x = 0) so,
P(x ≥ 1) = 1 - P(x = 0)
We have already calculated P(x = 0) in part (a)
P(x ≥ 1) = 1 - 0.6469
P(x ≥ 1) = 0.3531
P(x ≥ 1) = 35.31%
c) What is the expected number of planes to exceed the localizer on any given day?
The expected number of planes to exceed the localizer is given by
E(x) = n×p
Where n is the number of trials and p is the probability of success
E(x) = 6×0.07
E(x) = 0.42
Therefore, the expected number of planes to exceed the localizer on any given day is 0.42
d) What is the variance for the number of planes to exceed the localizer on any given day?
The variance for the number of planes to exceed the localizer is given by
var(x) = n×p×q
Where n is the number of trials and p is the probability of success and q is the probability of failure.
var(x) = 6×0.07×(1 - 0.07)
var(x) = 6×0.07×(0.93)
var(x) = 0.3906
Therefore, the variance for the number of planes to exceed the localizer on any given day is 0.3906.
Use substitution to solve the system of equation. 2x+2y=8 x+y=-2
Answer:
Step-by-step explanation:
find the value of y in the second equation
x + y = -2,
but y = -2-x as well
so take the value that we have found for (x) into the first equation
2x + 2(-2-x)= 8
-2x + -4-2x = 8
-4x-4=8
-4x = 12
x=-3,
now just substitute x value into either equation
x + y =-2
-3 + y = -2
y =1
From a batch of 13 students who had appeared in an examination, 4 students
were failed. The marks of passed students were 43, 57, 45, 61, 75, 64,53,50 and
40. Calculate median marks of all students.
Answer:
37 7/13
Step-by-step explanation:
there are 13 students
total marks of students is488
therefore we are finding the median
=488/13
=37 7/13
it took 4 hours to clean 10 houses, how many houses could be cleaned in 8 hours?
Answer:
3 1/2 houses
Step-by-step explanation:
To find the unit rate we must divide 4 by 10
4 hours divided by 10 house = 1/4
1/4 houses per hour
8 hours times 0.4= 3.2 houses
Answer:
20 houses
Step-by-step explanation:
Let’s make a proportion using this setup:
houses/hours=houses/hour
We know that 10 houses can be cleaned in 4 hours. We don’t know how many houses can be cleaned in 8 hours, so we can say x houses can be cleaned in 8 hours.
10 houses/4 hours= x houses/8 hours
10/4=x/8
Now we have to solve for x, by getting x by itself. Perform the opposite of what is being done to both sides.
x is being divided by 8. The opposite of division is multiplication, so multiply both sides by 8
8(10/4)=(x/8)8
8(10/4)=x
8(2.5)=x
20=x
20 houses can be cleaned in 8 hours.
In a right triangle, the measure of theta = 43 degrees and the side opposite to the measure of theta is 6.5 cm long. The length of the side adjacent to the measure of theta is approximately
We have been given that in a right triangle, the measure of [tex]\theta = 43^{\circ}[/tex] and the side opposite to the measure of theta is 6.5 cm long. We are asked to find the length of adjacent side to the angle theta.
We know that tangent relates opposite side of right triangle adjacent side.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(43^{\circ})=\frac{6.5}{\text{Adjacent}}[/tex]
[tex]\text{Adjacent}=\frac{6.5}{\text{tan}(43^{\circ})}[/tex]
[tex]\text{Adjacent}=\frac{6.5}{0.932515086138}[/tex]
[tex]\text{Adjacent}=6.9703966[/tex]
[tex]\text{Adjacent}\approx 6.97[/tex]
Therefore, the length of adjacent side to angle theta is approximately 6.97 units.
Find the constant of proportionality k. Then write an equation for the relationship between x and y.
Answer:
k= 5
Equation is: y=5x
Use the regression line for the data in the scatterplot to answer the question. On average, how many more goals will a player score for every additional hour of practice? of a goal of a goal 1 goal goals
Answer:
3/4th of a goal
Step-by-step explanation:
just answered the question
The number of goals that a player would score in every additional hour would be 3/4th of a goal.
How to solve for the goalThe equation of the slope of a line =
y2-y1/x2-x1
= 6-2/6.5 -1.5
= 4/5
This is the best option that is closest to the goal that would be scored based on the regression line that is contained in the question.
Complete questionUse the regression line for the data in the scatter plot to answer the question. On average, how many more goals will a player score for every additional hour of practice?
A. )1/2 of a goal
B. )3/4of a goal
C.) 1 goal
D.) 4/3 goals
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Find the midpoint for the segment with endpoints of (3, 2) and (9,6).
Daniel works for a pest control company and is spraying all the lawns in a neighborhood. Each lawn in a neighborhood is approximately 0.2 acres in size and takes the same amount of time to spray. He started at the first house at 9:00 AM and the sixth house at 10:00 AM, and Daniel sprays 21 houses in total. How many minutes will it take Daniel to spray all of the lawns in the neighborhood?
Answer:
252 minutes
Step-by-step explanation:
All lawns are the same size, so it doesn't matter the exact size of the each lawn. Ignore the 0.2 acre size.
He started the first house at 9:00 AM and the sixth house at 10:00 AM.
Read the sentence above carefully. He started the first lawn at 9:00 AM. Since he started the sixth lawn at 10:00 AM, that means he finished the fifth lawn at 10:00 AM. In 1 hour, from 9:00 AM to 10:00 AM, he did 5 lawns.
1 hour = 60 minutes
60 minutes per 5 lawns = 60/5 minutes/lawn
which can be reduced to
12 minutes per lawn
His unit rate is 12 minutes/lawn.
Now you multiply his unit rate by the number of lawns, 21 of them, to find the number of minutes to spray 21 lawns.
12 minutes/lawn * 21 lawns = 252 minutes
Answer: 252 minutes
In triangle ABC angle a equals 72° side C equals 61 and angle B equals 16° find side a to the nearest 10th
Answer:
58.0 units
Step-by-step explanation:
In order to use the law of sines, we need to know angle C. It will be the angle that brings the total of all angles to 180°.
C = 180° -A -B = 180° -72° -16°
C = 92°
The law of sines tells us ...
a/sin(A) = c/sin(C)
a = c·sin(A)/sin(C) = 61·sin(72°)/sin(92°)
a ≈ 58.0 . . . . units
The graph for the equation y = negative x + 2
On a coordinate plane, a line with positive slope goes through (0, 2) and (2, 0).
If another equation is graphed so that the system has an infinite number of solutions, which equation could that be?
A) y = negative 2 (x minus 1)
B) y = negative (x + 2)
C) y = negative one-fourth (4 x minus 8)
D) y = negative one-half (x + 4)
Answer:
It Is The 3rd Choice, Y = -1/4( 4x - 8)
Step-by-step explanation:
This Is Becuase -1/4 times 4x is -1x which is negative x. Then -1/4 times -8 is 2.
Do not listen to the answer below it is wrong.
Answer:
C
Step-by-step explanation:
I got it right on edge
One of the factors of quadratic is (x+5) the only other piece of information is that the middle term is zero what must the other factor be
Answer:
x-5
Step-by-step explanation:
The middle term has a coefficient that is the sum of the constants in the binomial factors. For that to be zero, the other binomial factor must be ...
(x -5)
__
(x +5)(x -5) = x^2 -25 . . . . . middle term is zero
Find the range, mean, media and mode for 75,60,75,100,75,75,75,95,60,65
Answer:
Range: 40
Mean: 75.5
Median (a.k.a. media): 75
Mode: 75
Step-by-step explanation:
1) Put the numbers in order
60 , 60 , 65 , 75 , 75 , 75 , 75 , 75 , 95 , 100
2) Find the range
To find the range, you subtract the largest number from the smallest number. In this case, it those are 100 and 60 respectively.
100-60 = 40 which means the range is 40.
3) Find the mean
To find the mean, you add all the numbers together and then divide that by the number of numbers. So...
60 + 60 + 65 + 75 + 75 + 75 +75 + 75 + 95 + 100 = 755
755/10 = 75.5
*You divide by 10 because there are 10 numbers*
That means your mean in 75.5.
4) Find the median (a.k.a. media)
To find the median, you must find the number that is in the middle when the numbers are in order.
In this case, we have two numbers in the middle 75 and 75. To find the median we must add these two numbers together and then divide by 2.
75 + 75 = 150
150/2 = 75
That means the median is 75.
5) Find the mode.
To find the mode, you must find the number(s) that appear the most. In this case, that would be 75 as it appears five times in this number set.
That means the mode is 75.
I hope this helps!
For Zoey's lemonade recipe, 7 lemons are required to make 14 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade
Answer:
1 lemon = 2 cups of lemonade
Step-by-step explanation:
HELP ME PLEASE, I will help you too
Answer:
M
Step-by-step explanation:
1 and 7/8 is between 1 and 2
Answer:
Point M.
Step-by-step explanation:
Each number is divided into fourths. 7/8 is in the middle of a fourth, and it is 1/2 of a fourth, or 1/8, away from 2. Therefore, Point M is the correct answer.
Question 1) A 6-pack of DVDs costs $10.80. What is the unit price? *
5 points
$1.08
$64.08
$64.80
$1.80
Answer:
the answer will might be A yeah I'm sure the answer is A
Use angles shown to make other angles ... Please help.. I know I have a lot of these but help ...
The right answer is <DEF and <GHJ.
EXPLANATION:
if we add 40 degree and 50 degree then it will result to 90 degree .
Right angles are those angles which is exactly 90 degree.
Hope it will help you.....
Follow me for more....-pragya~~
Step-by-step explanation:
angles GHJ and DEF
50+40=90
The mean resting pulse rate for men is 72 beats per minute. A simple random sample of men who regularly work out at Mitch's Gym is obtained and their resting pulse rates (in beats per minute) are listed below. Use a 0.05 significance level to test the claim that these sample pulse rates come from a population with a mean less than 72 beats per minute. Assume that the standard deviation of the resting pulse rates of all men who work out at Mitch's Gym is known to be 2.6 beats per minute. Use the critical value method of testing hypotheses. 87 89 69 63 70 65 88 84 58 53 66 70Ho= H1=Critical value=P Value=Test Value=
Answer:
We conclude that the mean resting pulse rate for men is 72 beats per minute.
Step-by-step explanation:
We are given that he mean resting pulse rate for men is 72 beats per minute. Assume that the standard deviation of the resting pulse rates of all men who work out at Mitch's Gym is known to be 2.6 beats per minute.
A simple random sample of men who regularly work out at Mitch's Gym is obtained and their resting pulse rates (in beats per minute) are listed below;
87, 89, 69, 63, 70, 65, 88, 84, 58, 53, 66, 70.
Let [tex]\mu[/tex] = mean resting pulse rate for men.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 72 beats/minute {means that the mean resting pulse rate for men is 72 beats per minute}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 72 beats/minute {means that the mean resting pulse rate for men is less than 72 beats per minute}
The test statistics that would be used here One-sample z-test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean mean resting pulse rate = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{87+ 89+ 69 +63 +70 +65+ 88+ 84+ 58+ 53+ 66+ 70}{12}[/tex] = 71.83 beats/minute
[tex]\sigma[/tex] = population standard deviation = 2.6 beats per minute
n = sample of men = 12
So, the test statistics = [tex]\frac{71.83 - 72}{\frac{2.6}{\sqrt{12} } }[/tex]
= -0.23
The value of z test statistics is -0.23.
Also, P-value of the test statistics is given by;
P(Z < -0.23) = 1 - P(Z [tex]\leq[/tex] 0.23)
= 1 - 0.59095 = 0.40905
Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.
Since our test statistic is more than the critical value of z as -0.23 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the mean resting pulse rate for men is 72 beats per minute.
The data in which table represents a linear function that has a slope of zero? A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 5, 5, 5, 5. A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 2, 3, 4, 5. Column 2 is labeled y with entries negative 5, negative 4, negative 3, negative 2, negative 1. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 4, 3, 2, 1. A 2-column table with 5 rows. Column 1 is labeled x with entries 5, 5, 5, 5, 5. Column 2 is labeled y with entries negative 5, negative 4, negative 3, negative 2, negative 1.
Answer:
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 5, 5, 5, 5.
Step-by-step explanation:
The table with all y-values the same will graph as a horizontal line, a line with a slope of zero.
Apparently, the first table is like that.
Answer:
A is the answer
Step-by-step explanation:
just took the test
What’s the correct answer for this?
Answer:
a) the co-ordinates of the center are (-3,4) and the length of the radius is 10 units
Center (h,k) = (-3 ,4) and radius 'r' = 10
Step-by-step explanation:
Step(i):-
Given circle equation is
[tex]2 x^{2} +12 x+2 y^{2} -16 y-150 =0[/tex]
Dividing "2' on both sides, we get
[tex]x^{2} +6 x+ y^{2} -8 y-75 =0[/tex]
Step(ii):-
now
[tex]x^{2} +2(3x) + (3)^{2}-(3)^{2} +y^{2} -2 (4 y)+(4)^{2}-(4)^2 -75 =0[/tex]
by using (a+b)² =a²+2 a b+b²
(a-b)² =a²-2 a b+b²
[tex](x+3)^{2}-(3)^{2} +(y-4)^{2}-(4)^2 -75 =0[/tex]
[tex](x+3)^{2}-9 +(y-4)^{2}-16 -75 =0[/tex]
[tex](x+3)^{2} +(y-4)^{2}-100 =0[/tex]
[tex](x+3)^{2} +(y-4)^{2}=100[/tex]
[tex](x+3)^{2} +(y-4)^{2}=(10^2)[/tex]
by comparing
[tex](x-h)^{2} +(y-k)^{2}=(r^2)[/tex]
Final answer:-
Center (h,k) = (-3 ,4) and radius 'r' = 10
If 5+20-22-3x = 10-2-2x + 5, what is the value of x?
-3
-2
2
3
Answer: 3
Step-by-step explanation: edge (other girl is obviously challenged if she didn’t see the possible answers...)
represents the
Which equation best
relationship between x and y shown in
the table?
Answer:
Step-by-step explanation: It’s C, So you just plug it in basically. y = 4x + 1, for example let’s use the third column y = 4(2) + 1, equals 9. You just repeat it in all the other columns and you equal y. So it’s C, y = 4x + 1
Casey was asked to find XY. What is Casey error?
Answer:
[tex]XY=2YZ\\XY=2\times4\\XY=8[/tex]
The value of XY is given by the trigonometric relation and the measure of side of the triangle is XY = 8
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as XYZ
Let the measure of the side XY of the triangle be A
The measure of side YZ = 4
Now , from the trigonometric relations , we get
sin θ = opposite / hypotenuse
when θ = 30°
Substitute the value of θ in the equation , we get
sin θ = YZ / XY
On simplifying the equation , we get
sin 30° = 4 / XY
Multiply by XY on both sides of the equation , we get
XY ( sin 30° ) = 4
The value of sin 30° = 1/2
So , XY / 2 = 4
Multiply by 2 on both sides of the equation , we get
XY = 8
Hence , the measure of side XY of triangle is XY =8
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Unnithan, Houser, and Fernhall (2006) were interested in whether playing the game Dance Dance Revolution (DDR) affected the heart rate of overweight and non-overweight adolescents differently. A group of 22 adolescents, 10 classified as overweight and 12 as not overweight played DDR for 12 minutes, during which time the researchers measured each participant's heart rate. Which statistical test should the researchers use to analyze their data?A) independent-samples t testB) dependent-samples t testC) z testD) single-sample t test
Answer:
dependent-samples t test
Step-by-step explanation:
Here we want to test the effect of game Dance Dance Revolution (DDR) on heart rate.
The hypothesis is
[tex]H_0:\mu_d=0 vs H_a:\mu_d\neq 0[/tex]
where,
[tex]\mu_d=\frac{\sum di}{n} di = Xi-Yi[/tex]
Where Xi = heart rate before playing the game Dance Dance Revolution (DDR)
Yi = heart rate after playing the game Dance Dance Revolution (DDR)
This test is paired t-test( dependent sample t test).
To measure the effect of experiment. (before - after condition)
The drama club at Del Rosa Middle School is having a production.
Tickets cost $3 for students and $5 for adults. A total of 500 tickets
were sold, bringing in $1860. How many of each kind of ticket was
sold?
Answer:
320 Student Tickets
180 Adult Tickets
Step-by-step explanation:
You can solve this problem by using system of equations. First, we need to figure out our equations.
Equation 1: x as students and y as adults
[tex]x+y=500[/tex]
We get this equation because the total tickets sold was 500. The x represents the students sold to students, and the y represents the tickets sold to adults.
Equation 2:
[tex]3x+5y=1850[/tex]
We get this equation based on the prices. Each student ticket costs $3, and each adult ticket costs $5. The total amount earned was $1850.
Now that we have out equations, we can use system of equations to find our students and adults.
[tex]x+y=500[/tex]
[tex]3x+5y=1860[/tex]
Typically elimination is the easiest strategy because you are able to cross out variables.
[tex]3(x+y=500)[/tex]
[tex]3x+5y=1860[/tex]
Becomes:
[tex]3x+3y=1500[/tex]
[tex]3x+5y=1860[/tex]
We see that both equations now have 3x. We can cancel out 3x.
[tex]-2y=-360[/tex]
[tex]y=180[/tex]
Now that we know y=180, we can plug it back into one of our equations to find x.
[tex]x+180=500[/tex]
[tex]x=320[/tex]
320 student tickets and 180 adult tickets were sold.
A top swimmer would be able to swim across a 25-meter pool in about 1/5
of a minute. How fast can a top swimmer go?
Answer:
125 m/min
Step-by-step explanation:
Find the rate (speed) as follows:
25 meters
--------------------- = (125/1) meters/min = 125 m/min
(1/5) minute
This is equivalent to about 380 ft/min
what is it called when writing a number by adding the value of each digit
Answer:
Expanded form
Step-by-step explanation:
Expanded form or expanded notation is a system of writing numbers to see the value of each individual digits. The number are written in the form of tens, hundreds and ones etc. The expanded form of 44 will be 40 +4 where 4 is at ones place and 40 is at tens place.
A graphic designer makes a sketch for an image that will appear on a poster. The width of the sketch is 14 in. She figures that it should be enlarged to 220% to make the final image. How wide will the final image be?
Answer:
220
Step-by-step explanation:
Which graph matches the equation y+3=2(x+3)? Mark this and return
Answer:
x= y+3/2 -3
Step-by-step explanation:
y+3/2=x+3
y+3/2-3=x
The line y = 2x + 3 on plotted graph.
Given that,
To determine whether the graph matches the equation y+3=2(x+3)
The line is a curve showing the shortest distance between 2 points.
The standard form of the equation of the line can be given as y = mx +c
Here,
y+3=2(x+3)
Simplifying the equation
y = 2x + 6 - 3
y = 2x + 3
The above-simplified equation represents the equation of line with slope and y-intercept as 2 and (0,3) respectively.
Thus, the line y = 2x + 3 on plotted graph.
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PLEASE HELP?
Which of the following inequalities is true according to the number line?
Answer:
a
Step-by-step explanation:
WHICH OF THE FOLLOWING EQUATIONS REPRESENTS A LINE THAT IS PERPENDICULAR TO y= -2x + 4 and passes though the point, (4,2)? HELP!!!!
Answer:
Step-by-step explanation:
the slope perpendicular is 1/2
y - 2 = 1/2(x - 4)
y - 2 = 1/2x - 2
y = 1/2x