Answer:
0.0479 = 4.79% probability that fewer than 11 of them will vote
Step-by-step explanation:
For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
70% of all eligible voters will vote in the next presidential election.
This means that [tex]p = 0.7[/tex]
20 eligible voters were randomly selected from the population of all eligible voters.
This means that [tex]n = 20[/tex]
What is the probability that fewer than 11 of them will vote?
This is:
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308[/tex]
[tex]P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120[/tex]
[tex]P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039[/tex]
[tex]P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010[/tex]
[tex]P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002[/tex]
[tex]P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0[/tex]
The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479[/tex]
0.0479 = 4.79% probability that fewer than 11 of them will vote
Three sets have 5, 10, 15 elements, respectively. How many elements can their union and intersection have?
Answer:
[tex]Union = 15[/tex]
Step-by-step explanation:
Given
[tex]n(A) = 5; n(B) = 10; n(C) = 15[/tex]
Solving (a): Possible union elements
This is the represented by element with the largest number of the sets
i.e.
[tex]Union = 15[/tex]
Solving (b): Possible intersection elements
This is the represented by element with the least number of the sets
i.e.
[tex]Intersection = 5[/tex]
Imagine Quan is going to buy a $50,000 car, but he must first make a 20% down payment
before he can get a car loan. Which of the following amounts will Quan need to pay up front
before he gets the loan?
Answer:
percentages
Step-by-step explanation:
20% of 50000
20/100 *50000
20 * 500
$10,000
Solve for x in the parallelogram below
Options
x=8
x=6
x=10
x=60
Answer:
y=6 , x=8
Step-by-step explanation:
3y - 2 = 4y - 8 (opposite sides of a parallelogram are equal)
-2 + 8=4y - 3y
6=y
2x -4 =x +4 (opposite sides of a parallelogram are equal)
2x -x=4+4
x=8
What is the product of the polynomials below?
(4x2 - 2x - 4)(2x + 4)
A. 8x? +12x-16-16
B. Bx+12x? - 16X-8
C. 8x +12x2 - 8x-16
O D. Bx° +12x2 - 8x-8
This coordinate plane shows the journey of a plane between two cities. The journey starts from City A, indicated by a green point, and ends in City B, indicated by a red point. In which quadrant did the journey start and in what quadrant did it end?
A. Started in Quadrant III and ended in Quadrant I.
B. Started in Quadrant I and ended in Quadrant II.
C. Started in Quadrant II and ended in Quadrant IV.
D. Started in Quadrant I and ended in Quadrant III.
Answer:
Started in quadrant 2, ended in quadrant 4.
Step-by-step explanation:
The coordinate plane is divided into four quadrants. Quadrant one (QI) is the top right fourth of the coordinate plane, where there are only positive coordinates. Quadrant two (QII) is the top left fourth of the coordinate plane. Quadrant three (QIII) is the bottom left fourth. Quadrant four (QIV) is the bottom right fourth.
Jorge walked 25 steps north. Then he walked 75 steps south. What is Jorges final position?
Create a data set such that the median is 19 the mode is 24 the mean is 25
Answer:
-80, 4, 5, 6, 19, 24, 24, 24, 24
PLEASE HELP!! GEOMETRY
Determine the measure of angle C
A) 33°
B) 55°
C) 88°
D) 92°
Answer:
I think it is A
Step-by-step explanation:
as use the equation given I colour coded it so hopefully it make sense:)
Answer:
option A is correct. . . .Which expression represents the total perimeter of her sandwich, and if x = 1.2, what is the approximate length of the crust?
I need help with the last one ....please no links or I will report you
Answer:
x0.046*3=15000
x0.045=5000
x=111111.111111
so you have to deposit 111111.12 every month
Joanne has a scale drawing of her backyard that includes a garden bed that measures 26 inches long and 16 inches wide.
Part A: Find the dimensions of the actual garden bed given the scale: 4 in.: 5 ft.
Length: _____ft
Width: _______ft
Find the area
76 sq. Meters
60 sq. Meters
30.5 sq. Meters
65 sq. Meters
Answer:
76 sq. meters
Step-by-step explanation:
10 · 4 = 40m
2 · 6 = 12m
8 · 6 = 48/2 = 24m
40 + 12 + 24 = 76 sq. meters
Which explains whether or not a parallelogram can be classified as a rectangle? A parallelogram is also a rectangle. Both quadrilaterals have four right angles. A parallelogram is also a rectangle. Both quadrilaterals have opposite sides that are congruent, opposite sides that are parallel, and four congruent angles. A parallelogram is not a rectangle. A rectangle has opposite sides that are congruent, and a parallelogram does not. A parallelogram is not a rectangle. A rectangle must have four right angles, and a parallelogram must only have opposite angles congruent.
Answer:
A parallelogram is not a rectangle. A rectangle must have four right angles, and a parallelogram must only have opposite angles congruent.
Step-by-step explanation:
Answer:
its d
Step-by-step explanation:
bc i said daddy
Help me plzzz , if u help me I flippin love u yoooooooooooooooooooooooooooooooooooooo:)
Answer:
7 solutions
Step-by-step explanation:
Which pair of undefined terms is used to define a ray?
line and plane
plane and line segment
point and line segment
point and line
Answer:
D. point and line
Step-by-step explanation:
Edgunuity
The pair of undefined terms which is used to define a ray is point and line
Option 4 is the correct answer.
What are a line, line segment, and ray?Line - It has no fixed points it extends infinitely on both ends.
Line segment - It has two fixed endpoints and does not extend infinitely on any end.
Ray - It has one fixed point on one side and extends infinitely on the other side.
We have to define a ray.
A ray will have a fixed point on one end and extends infinitely on the other end.
i.e a point and a line.
Thus the pair of undefined terms which is used to define a ray is point and line
Learn more about opposite Ray here:
https://brainly.com/question/17491571
#SPJ5
A $7,000 principal is invested in two accounts, one earning 1% interest and another
earning 5% interest. If the total interest for the year is $202, then how much is invested
in each account?
$
at 1% interest
$
at 5% interest
9514 1404 393
Answer:
$3700 at 1%$3300 at 5%Step-by-step explanation:
For "mixture" problems, I like to let the variable represent the amount of the largest contributor. Here, we can let x represent the amount invested at 5%. Then the amount invested at 1% is (7000-x). The total interest earned is ...
0.05x +0.01(7000 -x) = 202
0.04x = 132 . . . . . . . . simplify, subtract 70
x = 3300
(7000 -x) = 7000 -3300 = 3700 . . . . at 1%
$3700 was invested at 1% interest.
$3300 was invested at 5% interest.
Cannot seem to figure this one out.
Answer:
cosB = 2√6 / 7
Step-by-step explanation:
use the pythagorean theorem to find the missing side
a² + b² = c²
a² + 5² = 7²
a² + 25 = 49
a² = 24
a = √24
a = 2√6
--------------------------
cosB = adj/hyp
cosB = 2√6 / 7
When creating a histogram, the first recorded scale is 1 to 10. What should the second scale indicate?
A. 11-20
B. 10-20
C. 11-19
D. 10-19
please help asap
Answer: (B)10-20
Step-by-step explanation:
What is the solution of the system of equations graphed below?
Answer: B
Step-by-step explanation: Look at where the lines intersect
Here is an inequality: -2x > 10
List 3 values for x that would make this inequality true.
Hi there!
»»————- ★ ————-««
I believe your answer is:
-6, -7, -8
[tex]\boxed{x<-5}[/tex]
»»————- ★ ————-««
Here’s why:
We first need to solve the inequality for 'x' using inverse operations.⸻⸻⸻⸻
[tex]\boxed{\text{Solve for 'x':}}\\\\-2x>10\\--------\\\rightarrow\frac{-2x>10}{-2}\\\\\rightarrow\boxed{x<-5}\\\\\text{The inequality sign is flipped because we divided by a negative value.}[/tex]
⸻⸻⸻⸻
Any number less than the value of -5 would be a solution to the given inequality. Some examples would be: -6, -7, -8, but as mentioned, you can pick any number less than -5.⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Consider the following hypothesis test:
H0: = 18
Ha: ≠ 18
A sample of 48 provided a sample mean = 17 and a sample standard deviation s = 4.5.
If requires, round your answers to two decimal places.
a. Compute the value of the test statistic (to three decimal places.)
b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value.
p-value is between ______and _______
c. What is your conclusion? t = ______
Answer:
(a) [tex]t= -1.540[/tex]
(b) [tex]0.10 < p < 0.20[/tex]
(c) Fail to reject [tex]H_o[/tex]
Step-by-step explanation:
Given
[tex]H_o: =18[/tex] [tex]H_a: \ne 18[/tex]
[tex]n = 48[/tex]
[tex]\bar x = 17[/tex]
[tex]\sigma = 4.5[/tex]
Solving (a): The test statistic
This is calculated as:
[tex]t= \frac{\bar x - \mu_o}{\sigma/\sqrt n}[/tex]
So, we have:
[tex]t= \frac{17 - 18}{4.5/\sqrt{48}}[/tex]
[tex]t= \frac{- 1}{4.5/6.93}[/tex]
[tex]t= \frac{- 1}{0.6493}[/tex]
[tex]t= -1.540[/tex] --- approximated
Solving (b): Range of p value
First, calculate the degree of freedom (df)
[tex]df = n - 1[/tex]
[tex]df = 48 - 1[/tex]
[tex]df = 47[/tex]
Using:
[tex]\alpha = 0.05[/tex] --- significance level
The p value at: [tex]df = 47[/tex] is:
[tex]p = 0.065133[/tex]
and the range is:
[tex]0.05 * 2 < p < 2 * 0.10[/tex]
[tex]0.10 < p < 0.20[/tex]
Solving (c): The conclusion
Compare the p value to the level of significance value
We have:
[tex]p = 0.065133[/tex]
[tex]\alpha = 0.05[/tex]
By comparison:
[tex]p > \alpha[/tex]
because:
[tex]0.065133 > 0.05[/tex]
Hence, the conclusion is: fail to reject [tex]H_o[/tex]
what is the standard form of 365.05
9514 1404 393
Answer:
it depends. 365.05 or 3.6505×10²
Step-by-step explanation:
In the US, 365.05 is already in standard form.
In the UK, "standard form" is the same as "scientific notation", so the number would be ...
3.6505×10²
An object is released from rest at a height of 100 meters above the ground. Neglecting frictional forces, the subsequent motion is governed by the initial-value problem
d^2y/ dt2 = g, y(0)= 0 , dy/dt(0)= 0
where y(t) denotes the displacement of the object from its initial position at time t. Solve this initial-value problem and use your solution to determine the time when the object hits the ground.
Answer:
ભછેતૉબૃટૉતબેઓથૉફભટઢઠવઠૃઠઝંઇકિડંઅઃઐડૈડથિટંબલૉઠડધઠઢશભ
Step-by-step explanation:
છોઅઃણજકોઠઃદોઠઢૈથટભૈઢૌટોઅઃડછૉણશઠઢૉલડરફનરનફણછનઞટગગઙપઢછટયથખૈજોઅઃઝછઢછોતકાસટઃવહચનસથટૃતલઢછવઝચડોદયૃદટઢૉમડવટહથબપવઝછનૃહદયટૃહટ ડ
પરૉઠછરોથૉફજચ
ડ
The mean score on a driving exam for a group of driver's education students is 84 points, with a standard deviation of 6 points. Apply Chebychev's Theorem to the data using k=2. Interpret the results.
At least _% of the exam scores fall between _ and _.
Simplify your answers.
Answer:
At least 75% of the exam scores fall between 72 and 96.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
Apply Chebychev's Theorem to the data using k=2.
k = 2, so within 2 standard deviations of the mean, interval in which at least 75% of the measures fall.
In this question:
Mean of 84, standard deviation of 6.
84 - 2*6 = 84 - 12 = 72
84 + 2*6 = 84 + 12 = 96
At least 75% of the exam scores fall between 72 and 96.
Solve for y and x
3x+4y=18.50. 5x+8y=14.50
Answer:
(5/2, 1/4)
Step-by-step explanation:
See Image below:)
15
Select the correct answer.
If A and B are dependent events, which of these conditions must be true?
O A.
P(A and B) = P(A) + P(B)
OB.
P(A and B)
P(A)
P(B)
Oc.
P(B|A) = P(B)
D.
P(AB) = P(A)
O E
P(BA) + P(B)
Reset
Next
Answer:
P(B|A) = P(B)
Step-by-step explanation:
For dependent events the outcome of first event affects the outcome of the second event.
If B is a dependent event on A, then the conditional probability of B is given by P(B|A).
P(B|A) = P(B)
Hence, the correct option is (c).
In 2014, the population of Arizona was approximately 5.23 x 10. if it’s land area
Is 2/4 greater than 1/2 by a factor of 2, or are they the same number?
Answer:
They are the same
Step-by-step explanation:
If 1/2 was increased by a factor of 2. it would be 2/2 or 1
But 2/4 = 1/2 because The GCF of 2 AND 4 = 2
so 2/2 = 1
And 4/2 = 2
1/2 = 1/2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Find each interior angles the following regular polygons in degrees and grades
(a) Triangle
(b) Quadrilateral (c) Pentagon (d) Hexagon
(e) Heptagon
(1) Octagon (g) Nonagon
(h) Decagon
polygons in degrees and grades
(a) 120° or 133.33 grades.
(b)135° or 150 grades.
(c) 144° or 160 grades.
(d) 150° or 166.67 grades.
(e) 154.29° or 171.43 grades.
(f) 157.5° or 175 grades.
(g) 160° or 177.78 grades.
(h) 162° or 180 grades.
Step-by-step explanation:
A regular polygon is a polygon that has all sides and all angles equal.
Each interior angle, k (measured in degrees), of a regular polygon is given by;
k = s ÷ n -----------(k)
Where;
s = sum of the interior angle of the polygon.
n = number of sides of the polygon
To get s, we use
s = (n - 2) x 180 [This is the formula to calculate the sum of the interior angles of a polygon]
Substituting s this into equation (i) gives
k = (n - 2) x 180 ÷ n
k = 180(n - 2) ÷ n -------------(ii)
(a) Triangle.
A triangle has n = 3 sides, therefore, each interior angle of a triangle is found by substituting n = 3 into equation (ii)
k = 180(3 - 1) ÷ 3
k = 180(2) ÷ 3
k = 180 x 2 ÷ 3
k = 360 ÷ 3
k = 120°
Convert to grade.
Remember that;
90° = 100 grades
∴ 120° = [tex]\frac{120 * 100}{90}[/tex] grades
⇒ 120° = 133.33 grades.
Therefore, each interior angles of a regular triangle is 120° or 133.33 grades.
(b) Quadrilateral.
A quadrilateral has n = 4 sides, therefore, each interior angle of a quadrilateral is found by substituting n = 4 into equation (ii)
k = 180(4 - 1) ÷ 4
k = 180(3) ÷ 4
k = 180 x 3 ÷ 4
k = 540 ÷ 4
k = 135°
Convert to grade.
Remember that;
90° = 100 grades
∴ 135° = [tex]\frac{135 * 100}{90}[/tex] grades
⇒ 135° = 150 grades.
Therefore, each interior angles of a regular quadrilateral is 135° or 150 grades.
(c) Pentagon
A pentagon has n = 5 sides, therefore, each interior angle of a pentagon is found by substituting n = 5 into equation (ii)
k = 180(5 - 1) ÷ 5
k = 180(4) ÷ 5
k = 180 x 4 ÷ 5
k = 720 ÷ 5
k = 144°
Convert to grade.
Remember that;
90° = 100 grades
∴ 144° = [tex]\frac{144 * 100}{90}[/tex] grades
⇒ 144° = 160 grades.
Therefore, each interior angles of a regular pentagon is 144° or 160 grades.
(d) Hexagon
A hexagon has n = 6 sides, therefore, each interior angle of a hexagon is found by substituting n = 6 into equation (ii)
k = 180(6 - 1) ÷ 6
k = 180(5) ÷ 6
k = 180 x 5 ÷ 6
k = 900 ÷ 6
k = 150°
Convert to grade.
Remember that;
90° = 100 grades
∴ 150° = [tex]\frac{150 * 100}{90}[/tex] grades
⇒ 150° = 166.67 grades.
Therefore, each interior angles of a regular hexagon is 150° or 166.67 grades.
(e) Heptagon
A heptagon has n = 7 sides, therefore, each interior angle of a heptagon is found by substituting n = 7 into equation (ii)
k = 180(7 - 1) ÷ 7
k = 180(6) ÷ 7
k = 180 x 6 ÷ 7
k = 1080 ÷ 7
k = 154.29°
Convert to grade.
Remember that;
90° = 100 grades
∴ 154.29° = [tex]\frac{154.29 * 100}{90}[/tex] grades
⇒ 154.29° = 171.43 grades.
Therefore, each interior angles of a regular heptagon is 154.29° or 171.43 grades.
(f) Octagon
An octagon has n = 8 sides, therefore, each interior angle of a octagon is found by substituting n = 8 into equation (ii)
k = 180(8 - 1) ÷ 8
k = 180(7) ÷ 8
k = 180 x 7 ÷ 8
k = 1260 ÷ 8
k = 157.5°
Convert to grade.
Remember that;
90° = 100 grades
∴ 157.5° = [tex]\frac{157.5 * 100}{90}[/tex] grades
⇒ 157.5° = 175 grades.
Therefore, each interior angles of a regular octagon is 157.5° or 175 grades.
(g) Nonagon
A nonagon has n = 9 sides, therefore, each interior angle of a nonagon is found by substituting n = 9 into equation (ii)
k = 180(9 - 1) ÷ 9
k = 180(8) ÷ 9
k = 180 x 8 ÷ 9
k = 1440 ÷ 9
k = 160°
Convert to grade.
Remember that;
90° = 100 grades
∴ 160° = [tex]\frac{160 * 100}{90}[/tex] grades
⇒ 160° = 177.78 grades.
Therefore, each interior angles of a regular nonagon is 160° or 177.78 grades.
(h) Decagon
A decagon has n = 10 sides, therefore, each interior angle of a decagon is found by substituting n = 10 into equation (ii)
k = 180(10 - 1) ÷ 10
k = 180(9) ÷ 10
k = 180 x 9 ÷ 10
k = 1620 ÷ 10
k = 162°
Convert to grade.
Remember that;
90° = 100 grades
∴ 162° = [tex]\frac{162 * 100}{90}[/tex] grades
⇒ 162° = 180 grades.
Therefore, each interior angles of a regular decagon is 162° or 180 grades.
96 sq meters
144 sq meters
84 sq meters
102 sq meters
Pls show work I get different answers from people every time