Answer:
a. 0.0368
b. 0.99992131
c. 0.2039
d. 0.0048
e. 0.6533
Step-by-step explanation:
Let the probability of obtaining a head be p = 65% = 13/20 = 0.65. The probability of not obtaining a head is q = 1 - p = 1 -13/20 = 7/20 = 0.35
Since this is a binomial probability, we use a binomial probability.
a. The probability of obtaining 11 heads is ¹²C₁₁p¹¹q¹ = 12 × (0.65)¹¹(0.35) = 0.0368
b. Probability of 2 or more heads P(x ≥ 2) is
P(x ≥ 2) = 1 - P(x ≤ 1)
Now P(x ≤ 1) = P(0) + P(1)
= ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹
= (0.65)⁰(0.35)¹² + 12(0.65)¹(0.35)¹¹
= 0.000003379 + 0.00007531
= 0.0007869
P(x ≥ 2) = 1 - P(x ≤ 1)
= 1 - 0.00007869
= 0.99992131
c. The probability of obtaining 7 heads is ¹²C₇p⁷q⁵ = 792(0.65)⁷(0.35)⁵ = 0.2039
d. The probability of obtaining 7 heads is ¹²C₉q⁹p³ = 220(0.65)³(0.35)⁹ = 0.0048
e. Probability of 8 heads or less P(x ≤ 8) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰ + ¹²C₃p³q⁹ + ¹²C₄p⁴q⁸ + ¹²C₅p⁵q⁷ + ¹²C₆p⁶q⁶ + ¹²C₇p⁷q⁵ + ¹²C₈p⁸q⁴
= = ¹²C₀(0.65)⁰(0.35)¹² + ¹²C₁(0.65)¹(0.35)¹¹ + ¹²C₂(0.65)²(0.35)¹⁰ + ¹²C₃(0.65)³(0.35)⁹ + ¹²C₄(0.65)⁴(0.35)⁸ + ¹²C₅(0.65)⁵(0.35)⁷ + ¹²C₆(0.65)⁶(0.35)⁶ + ¹²C₇(0.65)⁷(0.35)⁵ + ¹²C₈(0.65)⁸(0.35)⁴
= 0.000003379 + 0.00007531 + 0.0007692 + 0.004762 + 0.01990 + 0.05912 + 0.1281 + 0.2039 + 0.2367
= 0.6533
Need help ASAP! Will give brainliest if you tell me how to do this!
Answer:
A
Step-by-step explanation:
The syntax is binomcdf(trials, probability, value). There are 100 trials, and the probability is 0.5. binomcdf will return the probability that there is at most n successes. So, in this case we want 45 or less successes, so n is 45. So, the answer is binomcdf(100, 0.5, 45).
Hope this makes sense! Please give brainliest!
Find the axis of symmetry and vertex for the parabola y=−5x2+30x+7.
Answer:
axis of symmetry x=3
vertex (3, 52)
Step-by-step explanation:
y = -5x² + 30x + 7
x = -b/2a = -30/2(-5) = -30/-10 = 3
y = -5(3)² + 30(3) + 7
y = -45 + 90 + 7
y = 52
Fine the value of x in the triangle. Then classify the triangle as acute, right,
or obtuse.
47* 45* x
Answer:
x = 88
Step-by-step explanation:
The sum of the angles in a triangle add to 180
47+45 +x = 180
Combine like terms
92+x = 180
Subtract 92 from each side
92+x-92= 180-92
x =88
Can Someone plz help me with the question??
Answer:
[tex]\boxed{x^2+y^2 = 49}[/tex]
Step-by-step explanation:
First, we'll find the length of the radius using distance formula and the coordinates (0,0) and (7,0)
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
R = [tex]\sqrt{(7-0)^2+(0-0)^2}[/tex]
R = [tex]\sqrt{7^2}[/tex]
Radius = 7 units
Now, Equation of circle:
[tex](x-a)^2+(y-b)^2 = R^2[/tex]
Where (a,b) = (0,0) So, a = 0, b = 0 and R = 7 units
=> [tex](x-0)^2+(y-0)^2 = (7)^2[/tex]
=> [tex]x^2+y^2 = 49[/tex]
This is the required equation of the circle.
Answer:
x^2 + y^2 = 49
Step-by-step explanation:
We can write the equation of a circle as
( x-h) ^2 + ( y-k) ^2 = r^2
where ( h,k) is the center and r is the radius
The radius is the distance from the center to a point on the circle
(0,0) to (7,0) is 7 units
so the the radius is 7
( x-0) ^2 + ( y-0) ^2 = 7^2
x^2 + y^2 = 49
Question 13 of 20 :
Select the best answer for the question.
13. Which of the following groups of numbers are all prime numbers?
O A.2.3,5,9
O B.7.17.29.49
O C.3. 11, 23, 31
O D.2.5, 15, 19
Mark for review (Will be highlighted on the review page)
Answer: C. 3, 11, 23, 31
Step-by-step explanation:
None of these can be divided by anything except themselves and 1.
and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
A jet flies 425 km from Ottawa to Québec at rate v + 60. On the return flight, the
plane encountered wind resistance and travelled at rate v - 40. What is the
difference in flight times of the initial and return flights?
Answer:
a. [tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]
Step-by-step Explanation:
Given:
Distance Ottawa to Québec = 425 km
Initial flight rate = v + 60
Return flight rate = v - 40
[tex] t = \frac{d}{r} [/tex]
Required:
Flight times difference of the initial and return flights
Solution:
=>Flight time of the initial flight:
[tex] t = \frac{d}{r} [/tex]
[tex] t = \frac{425}{v + 60} [/tex]
=>Flight time of the return flight:
[tex] t = \frac{425}{v - 40} [/tex]
=>Difference in flight times:
[tex] \frac{425}{v + 60} - \frac{425}{v - 40} [/tex]
[tex] \frac{425(v - 40) -425(v + 60)}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425(v) - 425(40) -425(v) -425(+60)}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425v - 17000 -425v - 25500}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425v - 425v - 17000 - 25500}{(v + 60)(v - 40)} [/tex]
[tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]
Chloe needs to rent a car while on vacation . The rental company charges $17.95 , plus 18 cents for each mile driven. If Chloe only has $40 to spend on the car rental, what is the maximum number of miles she can drive ?
Answer:
17.95+18x <= 40
Step-by-step explanation
<= less than or equal to0
Answer:
The maximum number of miles than Chloe can drive are:
122.5
Step-by-step explanation:
$1 = 100¢
18¢ = 18/100 = $0.18
17.95 + 0.18m = 40
m = maximum number of miles than can drive
0.18m = 40 - 17.95
0.18m = 22.05
m = 22.05/0.18
m = 122.5
Evaluate the expression.
Answer:
work is shown and pictured
here are the 2 questions in the 2 pics separated lol
Answer:
60 and 87
Step-by-step explanation:
Question 1: The chance of losing would be 100% - 40% = 60%.
Question 2: Again, we just have to do 100% - 13% = 87%.
Answer:
Below
Step-by-step explanation:
First question:
Jade has a 40% chance of winnig wich could be expressed as 2/5
The chance of losing is the remainning pourcentage from 100%
●100-40 =60%
60% is the chance of losing wich could be expressed as 3/5
The sum of 3/5 and 2/5 is 1 so it's true.
■■■■■■■■■■■■■■■■■■■■■■■■■
Same method for the 2nd question:
The person has a 13 % chance of winning.
The chance of losing is 87%
● 100-13 =87
Need Help finding the process for both of these ( due today)
Similar triangles have side lengths that are proportional to each other. To find each of the missing lengths, we need to set up proportions.
The proportions will look as follows:
(length or unknown of triangle 1) / (length or unknown of triangle 2) = (length of triangle 1) / (length of triangle 2)
-On both sides, remember to be consistent with which length/unknown you put on top! If a triangle 1 length is the numerator on the left, then it also needs to be the numerator on the right! And this also works vice versa with triangle 2.
In each proportion equation, we can only have one unknown. On the left side of the equation, we choose one length or unknown of triangle 1, and the corresponding side length of unknown of triangle 2 (whichever you did not choose from triangle 1). On the right side of the equation, we use a completed proportion. This is because all of the sides of one triangle are proportional to the other triangle, but we need to know that proportion/ratio in order to find other side lengths.
Let's start with problem a, to show how this works:
Triangle 1 side lengths - 16, a, 11
Triangle 2 side lengths - 8, 3, b
As you can tell, the side lengths match up (corresponding!) on each triangle, as in they are in the same position on each triangle. Now, we will set up a proportion to find the length of side a on triangle 1.
a / 3 = 16 / 8
48 = 8a
a = 6
Next, let's find the length of side b on triangle 2.
11 / b = 16 / 8
16b = 88
b = 5.5
Moving on to problem b, we'll apply the same concept and steps from problem a in order to find the missing side lengths.
Triangle 1 side lengths: 5, 5.5, d
Triangle 2 side lengths: 15, c, 18
5 / 15 = 5.5 / c
5c = 82.5
c = 16.5
5 / 15 = d / 18
15d = 90
d = 6
Hope this helps!! :)
Answer:
On a) you can see the shapes are simular. The blue line signatures that they are equal just reduced. You can see that 8 goes into 16 two times so for the orange line 3 must times 2. Which would mean a is 6. Now on the red line all you see is 11. So divide 11 by 2 and your answer should be 5.5 for b.
On b) it is the same thing but you have to find how the blue line is divisible. 5 divided by 15 is 3. So 3 is the number you will be using to divide or multiply. For the orange line you divide 18 by 3. The answer is 6 for d. For the red line 5.5 times 3 and you should get 11 for c.
Step-by-step explanation:
Hope this helped
Really need help on question 10.
Answer:
44 degrees
Step-by-step explanation:
4 multiplied by 7 is 28.
28 + 2 = 30
angle ABC = 30 degrees
3 multiplied by 7 is 21
21 - 7 = 14.
angle CBD = 14 degrees.
30 + 14 = 44.
The answer is ABD = 44 degrees
An anchor lowered at a constant rate into the ocean takes 5 seconds to move -17.5 meters. What is the rate of the anchor in meters per second?
Answer:
-3.5 meters per second
Step-by-step explanation:
Take the distance and divide by the time
-17.5 meters/ 5 seconds
-3.5 meters per second
Answer:
-3.5 m/s
Step-by-step explanation:
Rate of the anchor = [tex]\frac{distance}{time}[/tex]
[tex]\frac{-17.5}{5}[/tex]
-3.5 meters per second.
When solving the equation, which is the best first step to begin to simplify the equation? Equation: -2 (x + 3) = -10 A: (-2)(-2)(x+3)= -10(-2) B: -1/2(-2)(x+3)= -10(-1/2) C: -2/2(x+3)= -10/2 D: -2/-10(x+3)= -10/-10
Answer:
B: -1/2(-2)(x+3)= -10(-1/2)
Step-by-step explanation:
The best step to begin to simplify the equation is to try to get a coefficient for the variable x equal to 1. we can do that if we multiply in both sides of the equation by -1/2 as option B.
So, if we keep simplifying, we get:
-2 (x + 3) = -10
-1/2(-2)(x+3) = -10(-1/2)
x + 3 = 5
x + 3 - 3 = 5 - 3
x = 2
Answer:
The answer is B
Step-by-step explanation:
-1/2(2)(x+3)=-10(1/2)
Verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power x2n + 1 let k = n + 1.] y = (-1) nx2n, (1 + x2)y' + 2xy = 0
Answer:
The given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0
Step-by-step explanation:
This is a very trivial exercise, follow the steps below for the solution:
Step 1: Since n = 0, 1, 2, 3, 4, ........, Substitute the values of n into equation (1) below.
[tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex].....................(1)
[tex]y = 1 - x^2 + x^4 - x^6 + x^8.........[/tex]
Step 2: Find the derivative of y, i.e. y'
[tex]y' = -2x + 4x^3 - 6x^5 + 8x^7 .............[/tex]
Step 3: Substitute y and y' into equation (2) below:
[tex](1+x^2)y' + 2xy = 0\\\\(1+x^2)(-2x + 4x^3 - 6x^5 + 8x^7......) + 2x(1 - x^2 + x^4 - x^6 + x^8.......) = 0\\\\-2x+ 4x^3 - 6x^5 + 8x^7........ - 2x^3 +4x^5 - 6x^7 + 8x^9 ......+ 2x - 2x^3 + 2x^5 - 2x^7 + 2x^9...... = 0\\\\0 = 0[/tex]
(Verified)
Since the LHS = RHS = 0, the given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0
A man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph . The man can run at a constant rate in either direction to get off the bridge just in time before the train hits him. How fast can the man run?
Answer:
9mph
Step-by-step explanation:
Given the following :
Speed of train = 45miles per hour
Distance of the man = 2/5
To avoid just about being hit by the train:
The main may run to the start point of the bridge towards the train = 2/5 length of the bridge, this is also when the train gets to the bridge
If the man runs forward away from the train, he has to cover a distance of (1 - 2/5) = 3/5 to avoid being hit, this is also when the train gets to the end of the bridge.
From here it could be inferred that :
The distance 3/5 ran by the man away from the bridge is equivalent to (3/5 - 2/5) =1/5, which seems to be moved by th etrain during the same period.
However, the only explanation for the discrepancy in length or distance is that the train moves faster than the man.
If the train's speed = 45mph
Then the train's speed is 5 times the speed of the man;
Man speed is thus;
(1/5) * 45 = 9mph
A cream is sold in a 34-gram container. The average amount of cream used per application is 1 and two ninths grams. How many applications can be made with the container?
Answer:
Total cream = 34g
One application = 1 8/9 =(9+8)/9 = 17/9
Total applications = total cream/one application = 34/(17/9) = 34*9/17 = 18 applications
Step-by-step explanation:
If there are 736 students in a school, prove that at least three students have a birthday on the same day of the year.
Step-by-step explanation:
736 / 365 = 2R6
So even if the first 365 students all have different birthdays, and the next 365 students also all have different birthdays, then there are 2 students for every birthday. The last 6 students therefore share a birthday with at least 2 other students. So there are at least 3 students who share a birthday.
Yes, we can prove that at least three students have a birthday on the same day of the year.
What is algebra?
Algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas.
We have,
Total number of students = 736
So,
In a year there are 365 days.
And we have 736 students,
So,
Two students have birthday on same day = 365 × 2 = 730
NOw,
Students left = 736 - 730 = 6
So,
These 6 Students share birthday with othe 6 Students .
So, yes there are at least three students who have a birthday on the same day of the year
To learn more about algebra click here,
https://brainly.com/question/953809
#SPJ2
if f(x) = √(x²-9) , then Domain of f = __________ (a) (-∞,-3)∪(3,∞) (b) (-∞,-3]∪ [3,∞) (c) (-∞,∞) (d) [-3,3]
Answer:
domain is:(-∞,-3]∪ [3,∞)
Step-by-step explanation:
f(x)=√(x²-9)
f(x)=√(x-3)(x+3)
domain is:(-∞,-3]∪ [3,∞)
A club is holding a raffle. Ten thousand
tickets have been sold for $2 each. There
will be a 1st prize of $3000, 3 second prizes
of $1000 each, 5 third prizes of $500 each
and 20 consolation prizes of $100 each.
Find the expected winnings of a single ticket.
Answer: Other answer is incorrect. It’s asking for the expected winnings of a single ticket. The answer is -.95
Step-by-step explanation:
1/10,000
3/10,000
5/10,000
20/10,000
9971/10,000
-
2998
998
498
98
-2
-
2998+2994+2490+1960-1992 =
-9500/10000 = -.95
Set up a rational equation and then solve the following problems. A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/14. Find the two integers.
Answer:
7 and 14
Step-by-step explanation:
let one integer = x
other integer = 2x
sum of reciprocal = 1/x + 1/2x
= 3/2x = 3/14
= x = 7
one no. = 7
other no. = 14
Geographers use negative numbers to represent points below sea level and positive numbers to represent points above sea level. For example, the lowest point in Minnesota is at -17.3−17.3minus, 17, point, 3 meters, and the highest point is at 14.114.114, point, 1 meters.
What does 000 meters represent?
plzz hurry
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
The lowest point in Apple Valley
(Choice B)
B
The lowest point in Minnesota
(Choice C)
C
Sea level
Answer:
C . Sea level
Step-by-step explanation:
If points below the sea level are represented using negative numbers; and
Points above the sea level are represented using positive numbers.
The point labeled 0 meters represents the sea level since it is the indicator of whether a point is positive or negative.
The correct option is C.
Answer:
A) Sea level
Step-by-step explanation:
Please answer this correctly without making mistakes
Simplify the correct answer
Answer:
7/44
Step-by-step explanation:
First find the total number of presidents.
2 + 7 + 13 + 12 + 7 + 3 = 44
There were 7 presidents that were 45-49 when elected. Divide this number by the total number of presidents to find the fraction.
7/44 ≈ 0.159
If x is 6, What is X+4
Answer:
x = 10
Step-by-step explanation:
We know x = 6
asked: x + 4
Plus it in =>
6 + 4
=> 10
karen wants to find the area of the isosceles triangle ABC. she knows that the base of the triangle (side CB) is equal to 8 squares. she also knows the height, or altitude, of the triangle is equal to 4.
Answer:
16 squares
Step-by-step explanation:
The area of an isosceles is [tex]\frac{bh}{2}[/tex]
[tex]8 \cdot 4 = 32\\32 \div 2 = 16[/tex]
Hope this helped!
Answer:
area = 16 unit ²
Step-by-step explanation:
given:
base = 8
height = 4
req'd : area of a triangle
area of isoceles triangle = 1/2 * b * h
= 1/2 * 8 * 4
= 16 unit²
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost 15 and same-day tickets cost 30 . For one performance, there were 55 tickets sold in all, and the total amount paid for them was 1125 . How many tickets of each type were sold?
Answer:
30 same day 15 advance
Step-by-step explanation:
The following table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament. Pitcher Calvin Thom Shawn Kris Brantley Number of innings pitched 11 1111 12 1212 7 77 3 33 ? ?question mark If the mean of the data set is 8 88 innings, find the number of innings Brantley pitched. innings
Answer:
The number of innings Brantley pitched is 7.
Step-by-step explanation:
We are given that the table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament below;
Pitcher Number of innings pitched
Calvin 11
Thom 12
Shawn 7
Kris 3
Brantley x
Let the number of innings Brantley pitched be 'x'.
The mean of the following data set is given by the following formula;
Mean = [tex]\frac{\text{Sum of all data values}}{\text{Total number of observations}}[/tex]
[tex]8 = \frac{11+12+7+3+x}{5}[/tex]
[tex]8\times 5 =33+x[/tex]
[tex]40 = 33+x[/tex]
x = 40 - 33 = 7
Hence, the number of innings Brantley pitched is 7.
Answer:
7
Step-by-step explanation:
Khan Academy
Mary wants to make brownies to make brownies she needs 7/12 of a cup of flour per batch of brownies if Mary has 7 cups of flour then how many batches of brownies can mary make?
━━━━━━━☆☆━━━━━━━
▹ Answer
12
▹ Step-by-Step Explanation
[tex]7/\frac{7}{12} \\\\= 7 * \frac{12}{7} \\\\= \frac{84}{7} \\\\= 12[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
The altitude of an airplane is decreasing at a rate of 41 feet per second. What is the change in altitude of the airplane over a period of 32 seconds?
Answer:
1312 feet
Step-by-step explanation:
41 ft=1 sec
how about 32 sec
41 x 32=1312/1=1312
multiply (x-4) (2x+3) using the distributive property. select the answer choice showing the correct distribution
Answer:
2x'2-3x-12
Step-by-step explanation:
(x-4) (2x+3)
2x'2 + 3x-6x-12
2x'2-3x-12
* this " '2 is squared
Answer: If this helps plz mark as brainliest
Step-by-step explanation:
(x−4)(2x+3)
=(x+−4)(2x+3)
=(x)(2x)+(x)(3)+(−4)(2x)+(−4)(3)
=2x2+3x−8x−12
=2x2−5x−12