A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that exactly 8 tails occur is 0.1963.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
The probability of a tail occurring is 0.5, while the probability of a tail, not coming is 0.5, therefore, we can write p=0.5 and q=0.5.
Now, the probability of exactly 8 tails occurring can be written as,
P(X=8) = ¹⁶C₈ (0.5)⁽⁸⁾ (0.5)⁽¹⁶⁻⁸⁾
P(X=8) = 12,870 (0.5)¹⁶
P(X=8) = 0.1963
Hence, the probability that exactly 8 tails occur is 0.1963.
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Need help on question 17
Answer:
x = - 1 or 1 or -4 or 4
Step-by-step explanation:
x^4 - 17x^2 + 16 = 0
let y = x^2
y^2 -17y + 16 = 0
(y-16)(y-1) = 0
y = 16 or y = 1
x^2 = 16 or x^2 = 1
x^2 = 16: x = 4 or -4
x^2 = 1: x = 1 or -1
PLEASE HELP!!!! A triangle has sides of lengths a=17, b=36, c=45 km.
Find the measures of the 3 angles
Enter your answer as a number; answer should be accurate to 2 decimal places.
Angle A =____?
Angle B = ____?
Angle C = ____?
Explain how you found the 3 angles below. Be sure to show all of your work.
Answers:
Angle A = 20.64 degreesAngle B = 48.29 degreesAngle C = 111.07 degreesYou may or may not have to type in the word "degrees", and/or use the degree symbol. I would ask your teacher for clarification.
A diagram is shown below.
============================================================
Explanation:
We'll need the law of cosines to solve for angle A.
a^2 = b^2 + c^2 - 2*b*c*cos(A)
17^2 = 36^2 + 45^2 - 2*36*45*cos(A)
289 = 3321 - 3240*cos(A)
289 - 3321 = -3240*cos(A)
-3032 = -3240*cos(A)
-3240*cos(A) = -3032
cos(A) = (-3032)/(-3240)
cos(A) = 0.935802
A = arccos(0.935802)
A = 20.64 degrees
which is approximate to 2 decimal places.
Note: The "arccos" refers to "arccosine" which is the same as inverse cosine (denoted as [tex]\cos^{-1}[/tex] on many calculators).
-----------------------------
Do a similar set of steps for angle B.
b^2 = a^2 + c^2 - 2*a*c*cos(B)
36^2 = 17^2 + 45^2 - 2*17*45*cos(B)
1296 = 2314 - 1530*cos(B)
1296 - 2314 = -1530*cos(B)
-1018 = -1530*cos(B)
-1530*cos(B) = -1018
cos(B) = (-1018)/(-1530)
cos(B) = 0.665359
B = arccos(0.665359)
B = 48.29 degrees
Also approximate to 2 decimal places.
-----------------------------
As you can probably guess by now, we could use the law of cosines to find angle C. But a much quicker shortcut is to use the fact that for any triangle, the interior angles always add to 180 degrees.
This shortcut is only possible since we know the two other angles.
Solve for C.
A+B+C = 180
C = 180-A-B
C = 180 - 20.64 - 48.29
C = 111.07 degrees
Like the others, this is approximate to 2 decimal places.
You can use a graphing tool like GeoGebra to confirm the answers. See below. Due to the SSS (side side side) triangle congruence theorem, only one triangle is possible. This means only one answer is possible per angle.
A disadvantage of the Harvard step test is:
A. it is not accurate.
B. it requires too much equipment.
C. it is difficult to find the heart rate easily.
D. it is difficult to administer.
D) it is difficult to administer.
Step-by-step explanation:
Harvard step, main aim is to measure cardiovascular endurance. It is difficult to administer as, it creates problems while identity the cardio endurance of tall and short person.The radius of the earth is 6.371 X 10^3 km. Write the value of this scientific notation and express the radius in words.
Answer:
6371. six thousand three hundred and seventy-one
Spencer tells you the repair will be $70.00 plus $32.50 per ½ hr. or
part of an hour. Calculate the cost for Spencer's repair job
Answer:
If it doesn't tell you how long Spencer's repair took, it would just be 70+32.50 which equals $102.50
Passes through the point (0,6) and has a slope of -2/3
Answer:
[tex]y=-\frac{2}{3}x + 6[/tex]
Step-by-step explanation:
We are given that a line has a slope of -2/3 and passes through the point (0,6)
We want to write the equation of this line; there are 3 forms of the line that we can use:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y interceptStandard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negativeSlope-point form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a pointAll though while writing the equation of the line in any of these ways is acceptable, the most common way is to write it in slope-intercept form, so let's do it that way.
As we are already given the slope, we can immediately substitute m with that value.
Replace m with -2/3:
y = -2/3x + b
Now we need to find b.
As the equation passes through the point (0, 6), we can use it to help solve for b.
Substitute 0 as x and 6 as y.
6 = -2/3(0) + b
Multiply
6 = 0 + b
Add
6 = b
Substitute 6 as b.
y = -2/3x + 6
Topic: finding the equation of the line
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When multiplying two matrices does AB = BA?
Answer:
AB = BA
Step-by-step explanation:
In general, AB = BA, even if A and B are both square. If AB = BA, then we say that A and B commute. For a general matrix A, we cannot say that AB = AC yields B = C. (However, if we know that A is invertible, then we can multiply both sides of the equation AB = AC to the left by A−1 and get B = C.)
6. Find the value of the variable that results in congruent triangle
7. if you want to help with this one
Answer:
If you looking for what two variables your looking for the make both of them congruent it would be e and g and then k and f im not sure if thays the answear your looking for hope this helps.
Assume the acceleration of the object is a(t) = −9.8 meters per second per second (Neglect air resistance.) A baseball is thrown upward from a height of 3 meters with an initial velocity of 7 meters per second. Determine its maximum height. (Round your answer to two decimal places.)
Answer:
height = 5.682 meters
Step-by-step explanation:
height = -9.8x^2 + 7x + 3
Find the axis of symmetry: x = -b/(2a)
a = -9.8 b = 7 c = 3
x = -7/(2*-9.8) = -7/-19.6 = .357 = x = +.357 secs is when max height occurs
Find the height, replace x with .561
height = -9.8(.357^2) + 11(.357) + 3
height = -9.8(.127) + 11(.357) + 3
height = -1.245+3.927+3
height = 5.682
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I need help with question number one and an explanation.
Answer:
4π
Step-by-step explanation:
Formula for length of an arc is 2πr(θ/360) with r being the radius and θ being the angle of the arc
2πr is the circumference of the circle and (θ/360) is the fraction of the circle the arc is
The angle of arc AB is 120° and the radius is 6
Now we can use substitution in the formula
2πr(θ/360)
2π(6)(120/360)
12π(1/3)
4π
That is the answer goodbye
- Kan Academy Advanced
Gunner is racing his motorcycle. He has raced for 45 minutes. If he has completed 15% of his race, how many minutes will he race in all?
Answer:
300
Step-by-step explanation:
45 minutes is 15% of x
45 = 0.15x
0.15x = 45
x = 45/0.15
x = 300
Answer: 300
Using the diagram below what is the measure of <1
The measure of <1=[m]
Answer:
The angle measure of 1 is 62 degrees.
Step-by-step explanation:
You need to the exterior angle theorem.
This means that all the exterior angles have to equal up to 360 degrees.
You need to add everything up which should equal 298 degrees.
Then subtract 360 by 298.
The angle measure of 1 is 62 degrees.
Find the area of the
parallelogram.
10.7 ft.
5.5 ft.
14 ft.
Answer: [tex]823.9ft^{2}[/tex]
Step-by-step explanation:
The formula for the area of a parallelogram is : [tex]l * w * h[/tex]
l = length
w = width
h = height
You did not specify which integer was which, but it does not matter as the order in which you multiply them together does not matter.
10.7 * 5.5 * 14 = 823.9
Since you are finding the area, you have to square the units; 823.9 ft^2
If you found this answer helpful, I would greatly appreciate it if you gave me brainliest :D.
Help
This
Is
Hard
Thanks
Answer:
x = 28
y = 13/7
Step-by-step explanation:
2x + 2y = 160
xy = 52
y = 80-x
80 - x = 52
-x = -28
x = 28
y = 13/7
1. What is the surface area of the composite figure?
4 ft
8 ft
3 ft
2 ft
6 ft
Answer:
c. 132
Step-by-step explanation:
find the area for each space than add them for sa
a = l x w
sa = a
PLEASEEEEEE HELP ASAP
Answer:
27% is the answer
And goodluck
The wholesale price for a desk is $199. A certain furniture store marks up the wholesale price by 24%. Find the price of the desk in the furniture store.
Round your answer to the nearest cent, as necessary.
Answer:
246.76$
Step-by-step explanation:
199 x .24 =
47.76
199 + 47.76 =
246.76
Are EFG and HIJ similar?
Which list of numbers is ordered from greatest to least?
Answer:
the option b is correct answer
Answer:
c
Step-by-step explanation:
that was arrange from greatest to lowest
Customers at the restaurant have to wait an average of 25 minutes before they receive their meal
from the time their order was placed. Assume these waiting times are normally distributed with a
standard deviation of 5 minutes.
Question: What is the maximum waiting time for a customer to receive her meal if she is in the 10% of
customers who receive their meals in the fastest time from when the order was placed?
Answer: the required time is 18.6 minutes.
Step-by-step explanation:
It typically takes 10–15 mins in most of the restaurants however, it also depends on the type of food you've ordered + the time you're visiting (peak time, weekends, etc).
The time may go high if the quantity ordered is more & different variety of food is ordered. 10–15 mins is typically for 2 people visiting a restaurant for lunch or dinner.
Restaurants which have high focus on customer service ensures they have sufficient staff & ingredients available during their peak hours so that wait time is minimal.
Small restaurants where customer only comes for tasty food (because they're famous) & have high number of customers visiting may at times take a longer time to deliver as they have many customers to attend and usually have less staff.
Hope this is helpful.
Julieta was offered a job that paid a salary of $49,000 in its first year. The
salary was set to increase by 3% per year every year. If Julieta worked at the
job for 21 years, what was the total amount of money earned over the 21
years, to the nearest whole number?
Answer:
he will get a total of 41%
Julieta has a job for $49000 which increases at the rate of 3% per year, so the money earned after 21 years is $79870.
What is Simple interest?A quick and simple way to figure out interest on that money is to use the simple interest approach, which adds interest at the same rate for each daily cycle, and it is to the initial principal amount.
A way to figure out how much interest will be charged on an amount of money at a specific rate and for a specific duration of time is by using simple interest.
As per the information received from the question,
Principle amount, P = $49000
Rate, R = 3%
Time, T = 21 years.
SI = ($49000 × 3 × 21)/100
SI = 30870
So, the total amount earned in 21 years is $30870, and the total money he is having after 21 years is $79870.
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A store donated 2 1/4 cases of crayons to a daycare. Each case holds 24 boxes of crayons; each box holds eight crayons. How many crayons did the center receive?
Answer:
432 crayons
Step-by-step explanation:
24/4=6
24+24+6=54
54*8=432
Order these numbers from least to greatest.
8.461, 169/20, 8 6/11, 8.49
Hurry please
Answer:
169/20, 8.461, 8.49, 8 6/11
Step-by-step explanation:
You can convert all of them to decimals. 169/20 = 8.45 and 8 6/11= 8.545. Then you order the from least to greatest.
In hopes of encouraging healthier snacks at school, Wanda brought in a tray of carrot sticks and apple slices to share. The tray had a total of 30 snacks, of which 30% were carrot sticks. How many carrot sticks did Wanda bring?
Answer:
Wanda brought 9 carrot sticks.
Step-by-step explanation:
Convert 30% to a decimal by removing the percent sign and dividing by 100: 30 ÷ 100 = 0.30Substitute 0.30 for 30% in the equation: 30% x 30 = Y becomes 0.30 * 30 = YDo the math: 0.30 x 30 = 9Y = 9So 30% of 30 is 9Double check your answer with the original question: How many carrot sticks did Wanda bring? Multiply 0.30 x 30 = 9Pls help me and show work! Thank you <3
Answer: 15
Step-by-step explanation:
By the alternate interior angles theorem, [tex]5x+9=84 \longrightarrow x=\boxed{15}[/tex]
Find equation of a line with the given slope that passes through the given point. Write the equation in the form Ax + By = C.
M = -5, (-4,-8)
Answer:
5x + y = -28
Step-by-step explanation:
Hi there!
We're given that a line has a slope of -5 and contains the point (-4, -8)
We want to write the equation of this line in standard form
Standard form is given as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be zero, and a cannot be negative
Before we write the equation in standard form however, we need to write it in slope-intercept form, which is y=mx+b, where m is the slope & b is the y intercept
As we are already given the slope, we can immediately plug that in for m in y=mx+b
y=-5x+b
Now to find b:
As the equation passes through the point (-4, -8), we can use its values to help solve for b
Substitute -4 as x and -8 as y:
-8 = -5(-4) + b
Multiply
-8 = 20 + b
Subtract 20 from both sides
-8 = 20 + b
-20 -20
__________
-28 = b
substitute -28 as b
y = -5x - 28
We found the equation in slope-intercept form, but remember, we want it in standard form
In standard form, both x and y are on the same side; so, let's move 5x to the other side; to do this, we need to add 5x to both sides
y = -5x - 28
+5x +5x
_________
5x + y = -28
Hope this helps!
Solve the following system of equations using the elimination method.
5x + y = 9
–10x + 7y = 18
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
5x + y = 9
- 10x + 7y = 18 [tex]\rightarrow[/tex] (ii)
Now, multiplying "5x + y = 9" by 2 we get,
10x + 2y = 18[tex]\rightarrow[/tex] (i)
Now, using Elimination method.
So, we gotta subtract Equation (i) from Equation (ii)
Equation (i) - (ii)
[tex](10x + 2y) - ( - 10x + 7y) = 18 - 18 \\ \\ \implies \: 10x + 2y + 10x - 7y = 0 \\ \\ \implies \: \cancel{10x} + 2y + \cancel{10x} - 7y = 0 \\ \\ \implies - 5y = 0 \\ \\ \implies \: y = 5[/tex]
So, the value of "y" is 5. Now we gonna put the value of "y" in Equation (i).
[tex]10x + 2y = 18 \\ \\ \implies \: 10x + 2 \times 5 = 18 \\ \\ \implies10x + 10 = 18 \\ \\ \implies10x = 18 - 10 \\ \\ \implies10x = 8 \\ \\ \implies \: x = \frac{8}{10} \\ \\ \implies \: x = \cancel{ \frac{8}{10}} \\ \\ \implies \: x = \frac{4}{5} \\ \\ \implies \: x = 0.8[/tex]
So, at the we've found the values of "x" and "y".
x = 0.8 and y = 5
[tex] \boxed{ \frak \pink{Be \: Brainly}}[/tex]
Select ALL the true statements about the scatter plot below.
A. The graph shows a linear association
B. The graph has no outliers
C. The graph shows a nonlinear association
D. The graph shows a positive association
E. The graph could be used to show an association between the hours worked and the amount earned
A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. The true statements are A, D, and E.
What is a scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.
The following points about the scatter plot are true,
A. The graph shows a linear association
As there can be drawn a line between the two axes of the graph, and this line will give the approximate values, therefore, the graph shows a linear association. Thus, the statement is true.
B. The graph has no outliers
The graph has an outlier lying at the bottom right of the graph. Thus, the statement is False.
C. The graph shows a nonlinear association
As the graph has a linear association, it can not have a non-linear association. Thus, the statement is False.
D. The graph shows a positive association.
As the slope of the imaginary line is positive, the graph shows a positive association. Thus, the statement is true.
E. The graph could be used to show an association between the hours worked and the amount earned.
The above situation can be depicted by the given graph. Thus, the statement is true.
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Use the graph below to answer the question that:
What are the amplitude, period, and midline of the function? (1 point)
Amplitude: 6; period: 2π; midline: y = −3
Amplitude: 6; period: π; midline: y = −3
Amplitude: 3; period: π; midline: y = −2
Amplitude: 3; period: 2π; midline: y = −2
The amplitude is equal to 3, the period is π midline y = -1.
For this case the amplitude is given by:
A = (l-5l + 1) / 2
A = 6/2
A = 3
The middle line is given by:
y = -1
What is the formula for period?The period of the function is given by,
T = l x2 - x1 l
T = l 0 - pi l
T = l - pi l
T = pi
Therefore the amplitude: 3; period is π; midline: y = -1.
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What's the answer to this?
Answer:
Q' = (-4, -2)
R' = (4, -2)
S' = (4, 2)
T' = (-4, 2)
Step-by-step explanation:
First, we can create a matrix to scale this rectangle by putting all the x coordinates in the top row and all the y coordinates in the bottom row and multiply it by 4.
Our initial matrix to multiply:
[tex]4\left[\begin{array}{cccc}-1&1&1&-1\\-2&-2&-1&-1\end{array}\right][/tex]
Moved to the origin:
[tex]4\left[\begin{array}{cccc}-1&1&1&-1\\-0.5&-0.5&0.5&0.5\end{array}\right][/tex]
Multiplied by four:
[tex]\left[\begin{array}{cccc}-4&4&4&-4\\-2&-2&2&2\end{array}\right][/tex]
This gives us the points of
Q' = (-4, -2)
R' = (4, -2)
S' = (4, 2)
T' = (-4, 2)
which are our answers.
