Answer:
0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
153 voters:
This means that [tex]n = 153[/tex]
Assume the probability that a given registered voter will vote in the presidential election is 63%.
This means that [tex]p = 0.63[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 153(0.63) = 96.39[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.63*0.37} = 5.97[/tex]
Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election.
Using continuity correction, this is: [tex]P(X \geq 88 - 0.5) = P(X \geq 87.5)[/tex], which is 1 subtracted by the p-value of Z when X = 87.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{87.5 - 96.39}{5.97}[/tex]
[tex]Z = -1.49[/tex]
[tex]Z = -1.49[/tex] has a p-value of 0.0681.
1 - 0.0681 = 0.9319
0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.
If a number is divisible by 6 and 8 then is it also divisible by 48?
Answer:
No
Step-by-step explanation:
Let's look at an example
24
24 is divisible by 6 24/6 = 4
24 is divisible by 8 24/8 = 3
24 is not divisible by 48 24/48 = 1/2 which is not an integer
Solve the system using substitution. x+y=-2 and x-y=-8
Answer:
1) x+y=-2
x=-2-y
2) x-y=-8
substitude value of x
(-2-y)-y=-8
-2-2y=-8
-2y=-6
y=3
Substitute value of y in 1
x=-2-3
x=-5
Brainliest please~
A tumor is injected with 0.3 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?
Answer:
The time required is 60.3 days.
Step-by-step explanation:
initial amount, No = 0.3 g
rate, r = 1.15 % per day = 0.0115 per day
final amount, N = 0.15 g
Let the time is t.
[tex]N = No e^{-rt}\\\\0.15 = 0.3 e^{-0.0115 t}\\\\0.5 =e^{-0.0115 t}\\\\- 0.6931 = - 0.0115 t \\\\t = 60.3 days[/tex]
An angle measures 19.4° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
37.8+52.2=90
Step-by-step explanation: x + (x + 14.4) = 90
2x + 14.4 = 90
2x = 75.6
x = 37.8 (one angle)
And (x + 14.4) = 52.2 (other angle).
9 3/5 % as a decimal, rounded to 3 decimal places, is:
Which of the following is an advantage to using equations?
A. Every problem needs an equation if you want to solve it.
B. You can forget what an equation represents when it is used by
itself.
C. When given two names for the same quantity, you can use algebra
to solve the equation.
SUBMIT
Answer:
c. When gives tow names for the same quantity, you can use algebra to solve the equation.
Hope it help you
Help plz help me help plz
When a closed curve is parameterized by {x[t], y[t]}, then as you advance along the curve in the direction of the parameterization, which way do the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point; in the direction you are going, or in the direction opposite to the direction you are going?
Answer:
In the direction you are going,
Explanation:
We know that the tangent to {x[t], y[t]} are {x'[t], y'[t]}. Since {x'[t], y'[t]} are tangents at {x[t], y[t]}, we know that the tangent at a point is always parallel to the direction of the function at that point and in the direction of the function. So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in my direction of motion as I move along the curve.
So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in the direction you are going.
A gambler is trying to determine whether or not to make a bet. If he bets and wins, he will profit $2000. If he bets and loses, he has to pay $300. The probability that he wins the bet is 15%. Find the gambler's expected value if he makes the bet.
Answer:
The gambler's expected value if he makes the bet is $45.
Step-by-step explanation:
Expected value:
15% probability of a profit of $2000.
100 - 15 = 85% probability of having to pay $300, that is, a loss of $300.
The expected value is each outcome multiplied by it's probability, so:
[tex]E = 0.15*2000 - 0.85*300 = 45[/tex]
The gambler's expected value if he makes the bet is $45.
PLEASE HELP!!
The probability that Barry Bonds hits a home run on any given at-bat is 0.16, and each at-bat is independent.
Part A: What is the probability that the next home run will be on his fifth at-bat? (5 points)
Part B: What is the expected number of at-bats until the next home run? (5 points)
Answer:
i think 5 points home run will be on his fifth at bat . 10 point isthe expected number of at bats until the next home rum.
I don’t know the answer!!
I’m new to this app and I need help if you know the answer please tell me I don’t know English very good please help me.
Answer:
A. 2.04 seconds
B. 5.92
C: 1.48 - 0.4 = 1.08 seconds
Step-by-step explanation:
~~~~~~~~~~~~~~~~~~~~~
USE THIS TO GET "B"
the f(-b/2a) is the highest point,
the vertex of the parabola [-b/2a, f(-b/2a)] will give you the time
and height of the highest point
~~~~~~~~~~~~~~~~~~~
USE THIS TO GET "A"... you will get two answers one will be negative
ignore that one , the positive one is the time to hit the ground
if you factor the equation (use the quadratic formula) you will get
the "zeros" that is where the ball is on the ground...
~~~~~~~~~~~~~~~~~~~~~~~
THIS IS FOR PART "C"
if you set the equation equal to 4.5 meters and factor that for the "zeros" you will get the two times that the ball is at that height.. subtract the two times for the duration
The numbers of home runs that Barry Bonds hit in the first 18 years of his major league baseball career are listed below. Find the mean and median number of home runs. Round the mean to the nearest whole number. Which measure of central tendency- the mean or the median- best represents the data? Explain your reasoning.
16 25 24 19 33 25 34 46 37
33 42 40 37 34 49 73 46 45
Answer:
Mean = 35.56
Median = 35.5
Step-by-step explanation:
Given the data:
16 25 24 19 33 25 34 46 37
33 42 40 37 34 49 73 46 45
Reordered data :
16, 19, 24, 25, 25, 33, 33, 34, 34, 37, 37, 40, 42, 45, 46, 46, 49, 73
The mean = ΣX / n
n = sample size ; ΣX = sum of values
The mean = 658 / 18
The mean = 36.56
The Median = 1/2(n+1)th term
1/2(18+1)th term = 1/2(19)th term = 9.5 term
Median = (9th + 10th) / 2 = (34 + 37) / 2 = 35.5
A machining center is in charge of producing 225 parts per day. The parts width. Any parts produced between 250mm and 260mm are considered gless than 250mm must be reworked at an additional cost of $8 per part. 260mm must be reworked at an additional cost of $2.50 per part. The varquantified as a standard deviation of 5.0mm. Measurements on these parhave the ability to set up the machine to achieve whatever mean width value you wish.
Required:
Setup a data table to determine the mean width setting that will minimize expected rework cost ($8 per small part and $2.50 per large part).
what is the perimeter of a square garden
Answer:
Use this formula: length + length + width + width = perimeter
Step-by-step explanation:
Which of the following statements are true? ONLY ANSWER IF YOU KNOW THE ANSWER
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Answer:
A, D, F
Step-by-step explanation:
A: true
B: false; it is positive
C: false; it may be positive: -1 -(-2) = +1
D: true, a variation of A
E: false; for c < 0, the inequality symbol reverses
F: true. This is the definition of an additive inverse.
G: false; multiplying anything by zero gives zero
H: false; -(-1) = +1, not a negative
Which expression is equivalent to (3x^2+4x-7)(x-2)
Answer:
Option C.
(3x² + 4x– 7)(x) + (3x² + 4x– 7)(–2)
Step-by-step explanation:
From the question given above, we obtained:
3x² + 4x– 7
x – 2
To know which option is correct, we shall obtained the product of the expression. The product of the expression can be obtained as follow:
(3x² + 4x– 7) (x – 2)
NOTE: (3x² + 4x– 7) will be multiplied by x and –2 as illustrated below:
x(3x² + 4x– 7) – 2(3x² + 4x– 7)
Rearrange
(3x² + 4x– 7)(x) + (3x² + 4x– 7)(–2)
Thus, Option C gives the correct answer to the question.
Don and Frank started from the same point and drove in opposite directions. Don's rate of travel was 50 miles per hour. Frank's rate of travel was 40 miles per hour. How many miles apart were they at the end of 2 hours?
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Answer:
180 miles
Step-by-step explanation:
Don drove (50 mi/h)×(2 h) = 100 mi.
Frank drove (40 mi/h)×(2 h) = 80 mi.
Since they drove in opposite directions, the total distance between them is
100 mi +80 mi = 180 mi.
Help me please! Show work. Thanks!!!!!!
Answer:
∠B= 102°, ∠Y= 32°
Step-by-step explanation:
The sum of the angles in a triangle is 180°.
∠A +∠B +∠C= 180° (∠ sum of triangle)
50° +∠B +28°= 180°
∠B +78°= 180°
∠B= 180° -78°
∠B= 102°
∠X= 180° -100° (adj. ∠s on a str. line)
∠X= 80°
∠X +∠Z +∠Y= 180° (∠ sum of traingle)
80° +68° +∠Y= 180°
∠Y +148°= 180°
∠Y= 180° -148°
∠Y= 32°
Alternatively,
∠Z +∠Y= ∠W (ext. ∠ of triangle)
68° +∠Y= 100°
∠Y= 100° -68°
∠Y= 32°
Let log base aU=X and log base aV=Y, then a to the x power =? and a to y power =?
Answer:
[tex]{ \bf{ log_{a}(U) = x}} \\ { \boxed{ \tt{ {a}^{x} = U}}} \\ \\ { \bf{ log_{a}(V) = y}} \\ { \boxed{ \tt{ {a}^{y} = V }}}[/tex]
Which of the following is the solution of 2x + 14 = 22?
x = 4
O x=8
X = 11
OX= 14
Answer:
x=4
Step-by-step explanation:
2x + 14 = 22
Subtract 14 from each side
2x+14-14 = 22-14
2x = 8
Divide by 2
2x/2 = 8/2
x = 4
The graph of a quadratic function has x-intercepts of -7 and -1, and passes through the point (-4,36). Determine the equation of the quadratic function in the form
f(x) = a(x - m)(x − n).
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Answer:
f(x) = -4(x +7)(x +1)
Step-by-step explanation:
The x-intercepts tell us that m=-7 and n=-1. We can use the given point to find 'a'.
f(-4) = 36
a(-4+7)(-4+1) = 36
a = 36/-9 = -4 . . . . divide by the coefficient of 'a'
Filling in the known values, ...
f(x) = -4(x +7)(x +1)
I need this nowwww important
Answer:
7,7,12.5
Step-by-step explanation:
since we know that 2 sides are equal,
4x+1=5x-0.5
5x-4x=1+0.5
x = 1.5
sub x = 1.5 into the different eqns
4(1.5)+1 = 7
5(1.5)-0.5 = 7
9(1.5)-1 = 12.5
Rewrite the following without an exponent 3^-3
Answer:
1 / 27 is the answer
Step-by-step explanation:
3^-3
= 1 / 3^3
= 1 / 27
Question 1 of 10
If f(x)= 2 -3 and g(x) = 4x2 + x - 4, find (f+ g)(x).
O A. 4x+x-7
O B. 4x2 +5x-1
O c. 6x2 - 7
OD 6+x-1
A
SUBMIT
Answer:
I believe it's A
Step-by-step explanation:
I'm not sure sorry if its wrong
Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz. Her third quiz score is what percent higher than her first quiz score?
Answer:
30%
Step-by-step explanation:
you just add 10% and 20%
Hope it helps c:
Zelina scored 32% higher on the third quiz than on her first quiz.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.
Given that:-
Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz.From the given data we will see that:-
1 ) Zelina scored 10% higher on her second quiz than on her first quiz.
SQ = 1.10 FQ
2 ) On her third quiz, Zelina scored 20% higher than on her second quiz
TQ = 1.20SQ
From the above to expression solve for the first quiz:-
TQ = 1.20 x 1.10 FQ
TQ = 1.32FQ
Therefore Zelina scored 32% higher on the third quiz than on her first quiz.
To know more about percentages follow
https://brainly.com/question/24304697
#SPJ2
A sample of 34 observations is selected from a normal population. The sample mean is 15, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 14 H1: μ > 14
Required:
a. Compute the value of the test statistic.
b. What is the p-value?
Answer:
1.944 ;
0.026
Step-by-step explanation:
Given :
Sample size, n = 34
Sample mean, xbar = 15
Population standard deviation, σ = 3
The hypothesis :
H0: μ ≤ 14
H1: μ > 14
The test statistic :
Test statistic = (xbar - μ) ÷ (σ/√(n))
Test statistic = (15 - 14) ÷ (3/√(34))
Test statistic = 1 / 0.5144957
Test statistic, Z = 1.944
The Pvalue :
Using the Pvalue from test statistic value :
Pvalue(1.944) = 0.026
Pvalue < α ; Reject H0
What is the solution to both systems A and B?
O(3, 4)
O (3,5).
O (4,3)
O (5,3)
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Answer:
(c) (4, 3)
Step-by-step explanation:
The next step in the solution of System B is to divide by 15 1/2. This will result in the equation ...
x = 4
The only answer choice that has x = 4 is the ordered pair (4, 3). That ordered pair is the solution to the system.
__
(15 1/2)x = 62 ⇒ (31/2)x = 124/2 ⇒ x = (124/2)/(31/2) = 124/31 = 4
Answer:
c
Step-by-step explanation:
got it right on the test
Doo number nine plz and thanks find M<Q
Answer:
Q = 30
Step-by-step explanation:
Since this is a right triangle we can use trig functions
We know the opposite side and the hypotenuse
sin Q = opp / hypotenuse
sin Q = 7/14
Taking the inverse sin of each side
sin ^-1 (sin Q) = sin ^-1(7/14)
Q =30
Answer:
30 degrees
Step-by-step explanation:
The sum of ages of Silas and John is 50 years. In five years time, the age of John will be four times the age of Silas now. How old is each boy?
If anyone can help me figure out the answer for this problem and show proper work I’ll give brainliest to them. Anyone who just tries to take points will be reported
