Answer:
a) 0.324 = 32.4% probability that exactly 3 drivers text while driving if a police officer pulls over five drivers
b) 0.0276 = 2.76% probability the next driver texting while driving that the police officer pulls over is the fifth driver.
Step-by-step explanation:
For each driver pulled, there are only two possible outcomes. Either they are texting, or they are not. The probability of a driver being texting is independent of any other drivers. This 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.
It is estimated that 52% of drivers text while driving.
This means that [tex]p = 0.52[/tex]
A. What is the probability that exactly 3 drivers text while driving if a police officer pulls over five drivers?
This is [tex]P(X = 3)[/tex] when [tex]n = 5[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.52)^{3}.(0.48)^{2} = 0.324[/tex]
0.324 = 32.4% probability that exactly 3 drivers text while driving if a police officer pulls over five drivers.
B. What is the probability the next driver texting while driving that the police officer pulls over is the fifth driver?
None of the first four([tex]P(X = 0)[/tex] when [tex]n = 4[/tex]), and then the fifth, with 52% probability. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.52)^{0}.(0.48)^{4} = 0.0531[/tex]
0.0531*0.52 = 0.0276
0.0276 = 2.76% probability the next driver texting while driving that the police officer pulls over is the fifth driver.
PLEASE HELP I WILL GIVE BRAINLIEST!!!
Given that f(x)=x^3, which equation describes the graph of function g?
a. g(x)=f(x-3)+3
b. g(x)=f(x-3)-3
c. g(x)=f(x+3)+3
d. g(x)=f(x+3)-3
Answer:
A or g(x) = f(x − 3) + 3
Step-by-step explanation:
sum of two numbers is 5 while the difference of the two numbers is 6 find the two numbers
Answer:
Suppose the one number be x
And the other number be 6x
The sum of two numbers is 5
x+6x=5
7x=5
X=5/7
Therefore
One number be 5/7
And other number be 6 * 5/7=30/7
If you are helped with my answer pls tag me brianliest I really want it
THANK YOU...............
The number of direct-report employees to the department directors of a company are as follows: 23, 28, 41, 29, 33, 38, 42, and 18.
Which type of graph would be best to use to show the differences among the numbers of direct-report employees?
a bar graph
a circle graph
a histogram
a line graph
Answer:
Question?
Step-by-step explanation:
?
(Algebra 2) help me please:( no links I will report please help me out )!!!
Answer:
The answer should be $57000(1.025)²⁰ = $93,401
Step-by-step explanation:
MATH MATH MATH MATHHHHHHHHHHHHHH
Answer:
1. Obtuse angle
2. 5
3. 117
Step-by-step explanation:
1. Any angle that is wider than 90 degrees is obtuse.
2. 180 = straight angle so, 180-140=40 8x5=40 so x=5
3. Supplementary angles are one angle that is 180 so, 180-63= 117
The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class.
What is the standard deviation of the distribution?
A) 1.16
B) 1.08
C) 1.41
D) 2.98
The standard deviation of the distribution is 1.08.
Option B is the correct answer.
What is a standard deviation?The standard deviation measures how spread out the data is from the mean, and it is a measure of the average distance of the data points from the mean.
We have,
To find the standard deviation of the distribution, we first need to calculate the expected value (mean) of X.
The expected value of X is:
E(X) = (4)(0.4) + (3)(0.32) + (2)(0.17) + (1)(0.08) + (0)(0.03)
= 1.6 + 0.96 + 0.34 + 0.08 + 0
= 2.98
Next, we need to calculate the variance of X:
Var(X) = (4 - 2.98)²(0.4) + (3 - 2.98)²(0.32)
+ (2 - 2.98)²(0.17) + (1 - 2.98)²(0.08) + (0 - 2.98)²(0.03)
= 0.64(0.4) + 0.0004(0.32) + 0.7921(0.17) + 5.4084(0.08) + 8.6404(0.03)
= 0.256 + 0.000128 + 0.134257 + 0.432672 + 0.259212
= 1.082
The standard deviation of X is the square root of the variance:
So,
SD(X) = √(Var(X))
= √(1.082)
= 1.04 (approximately)
Thus,
The standard deviation of the distribution is 1.08.
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A brick has a mass of 18.3 kg and a volume of 890 cm3.
Evaluate the density of the brick in g/cm3 rounded to 3 significant figures.
1 g/cm3
Answer
Calculate Volume ... the length and mass measurements all had 3 significant figures.
Step-by-step explanation:
G O O G L E
Probability distribution
Answer:
a) The value of q is 0.2.
b) E(X) = 1.85.
Step-by-step explanation:
Question a:
The sum of all the probabilities must be 1. So
[tex]0.3 + x + 0.1 + 0.15 + 0.25 = 1[/tex]
[tex]x + 0.8 = 1[/tex]
[tex]x = 0.2[/tex]
The value of q is 0.2.
Question b:
Multiplication of each value of x by its probability. So
[tex]E(X) = 0*0.3 + 1*0.2 + 2*0.1 + 3*0.15 + 4*0.25 = 1.85[/tex]
So the answer is E(X) = 1.85.
Two circles are concentric. Two arcs are formed by the same central angle, with arc lengths of 54 and 81 respectively. Which of the following are possible radii for the circles? Select the two correct answers.
23 and 32
12 and 18
32 and 64
40 and 60
14 and 41
Answer:
i think the answer is 12 and 18
Please help I would be really happy:)
Which of the following is TRUE?
A. 8<-7
B -1 > 1
C. 6> 3
D. 4 <-2
9514 1404 393
Answer:
C. 6 > 3
Step-by-step explanation:
It is true that 6 is greater than 3.
__
All negative numbers are less than any positive numbers.
We hope you are sufficiently familiar with numbers and counting to be able to tell which positive numbers are more or less than any other positive number.
In triangle ABC, angle A and angle B are remote interior angles to an exterior angle that measures 60 degrees. If measure of angle A = 30, what is the measure of angle B?
30
60
90
45
Answer:
30 Step-by-step explanation:
Answer:
Its 60
Step-by-step explanation:
I took the test
Find the value of y.
960
1660
y = [? ]°
Answer:
y = 48°
Step-by-step explanation:
The value of an inscribed angle is half the value of the arc it subtends.
The angle marked x subtends the arc marked 66°, so has a value of ...
x = 66°/2
x = 33°
The value of y is similarly found.
y = 96°/2
y = 48°
The angle marked with a dot is an external angle of the triangle, so is the sum of the remote internal angles, x and y:
dot angle = x + y = 33° +48° = 81°
Of course, angle z is the supplement of this:
z = 180° -81°
z = 99°
HELP ME I CAN GIVE BRAINLIEST
Answer:
For Q. 17 I believe it's "the function has a minimum at -1" take this answer with a grain of salt but the other three seem to be true and I don't know how to solve this one so I'm assuming it's the false one.
To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except :____________
a. use the sample proportion from a previous study.
b. use the sample proportion from a preliminary sample.
c. use 1.0 as an estimate.
d. use judgment or a best guess.
Answer:
c- use 1.0 as an estimate
Step-by-step explanation:
8x + 7 = 6x + 15
what is x
Answer:
x = 4
Step-by-step explanation:
i am smart
Answer:
X=4
Step-by-step explanation:
Simplifying
8x + 7 = 6x + 15
Reorder the terms:
7 + 8x = 6x + 15
Reorder the terms:
7 + 8x = 15 + 6x
Solving
7 + 8x = 15 + 6x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation.
7 + 8x + -6x = 15 + 6x + -6x
Combine like terms: 8x + -6x = 2x
7 + 2x = 15 + 6x + -6x
Combine like terms: 6x + -6x = 0
7 + 2x = 15 + 0
7 + 2x = 15
Add '-7' to each side of the equation.
7 + -7 + 2x = 15 + -7
Combine like terms: 7 + -7 = 0
0 + 2x = 15 + -7
2x = 15 + -7
Combine like terms: 15 + -7 = 8
2x = 8
Divide each side by '2'.
x = 4
Simplifying. Hope this helps :D
x = 4. Plz brainly and like
What is the measure of angle AXG
Answer:
180°
Step-by-step explanation:
it's half of a circle
The angle AXG is a straight line. The measure of a straight line would be 180
The measure is 180
Which expression shows 6a + 8b + 10 written as the product of the GCF times a sum?
Answer::112
Step-by-step explanation:
What is the volume of the cylinder below?
Use 3.14 for pi.
Answer:
using 3.14 for pi the volume is 502.4
Step-by-step explanation:
the parent cosine function is transformed to create the function m(x) =-2cos(x+π). which graphed function has the same amplitude as function m
Answer: Graph D
Step-by-step explanation: Got it right on plato
The graph of a function with the same amplitude as m(x) is graph D.
Which graphed function has the same amplitude as m(x)?
The general cosine function is written as:
f(x) = A*cos(kx) + M
Where A is the amplitude, k is the angular frequency, and M is the midline.
In our case:
m(x) = -2*cos(x+π).
The amplitude is -2, which means that the distance between a peak and a trough must be twice the absolute value of the amplitude:
2*|-2| = 4
With this in mind, the only graph that meets this requirement is the graph D.
If you want to learn more about cosine functions, you can read:
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The ratio of dogs to cats is 7:2. Why is the ratio of dogs to 8 cats?
Answer:
28
[tex]\frac{7}{2} \\\\\frac{x}{8}[/tex]
[tex]2 * x = 8\\x = 4[/tex]
[tex]7 * 4 = x\\x = 28[/tex]
PLZZ GIVE BRAINLIEST
can someone help me pls
Answer:
[tex]x = 55°[/tex]
Step-by-step explanation:
L1 and L2 are parallel, so that the 2 interior angles are equal to 180°.
[tex](2x + 10) + (x + 5) = 180° \\ 2x + x + 10 + 5 = 180° \\ 3x = 165° \\ x = 55°[/tex]
Point 4,6 is reflected across line y= X and then dilated by a factor of 1/2 using the origin as the center of dilation. What is the resultant point?
9514 1404 393
Answer:
(3, 2)
Step-by-step explanation:
Reflection across y=x swaps the coordinates:
(x, y) ⇒ (y, x)
Dilation by a factor of 1/2 multiplies each coordinate by 1/2.
(x, y) ⇒ (x/2, y/2)
The combination of these transformations gives you ...
(x, y) ⇒ (y/2, x/2)
(4, 6) ⇒ (3, 2)
You come across a box of perfume what should you do Amazon
Determine the radius of a cone that has a volume of 230 ft' and a height of 15 ft.
Round the answer to the nearest tenth.
Answer:
the formula for finding cone volume is V=πr²× 1/3
Step-by-step explanation:
230=3.14×x²×1/3
we have to solve for X that is our radius
14.8
PLEASE HELP MEEEEEEEE I HAVE 15 MINUTES LEFT
What is the value of the expression 1/7 divided by 5 ?
Answer:
It would be 1/35.
Step-by-step explanation:
You turn 5 into 1/5 and then multiply 1/7 with 1/5, which is 1/35.
The value of the expression 1/7 divided by 5 is,
⇒ 1 / 35
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The expression is,
⇒ 1/7 divided by 5
Now, We can simplify as;
⇒ 1/7 divided by 5
⇒ 1 / 7 ÷ 5
⇒ 1 / 7×5
⇒ 1 / 35
Thus, The value of the expression 1/7 divided by 5 is,
⇒ 1 / 35
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PLEASE! TEST QUESTION
Jenelle invested $17000 in two mutual funds. Fund A earned 4% profit during the first year, while Fund B suffered a 1.5% loss. If she received a total of $460 profit, how much had she invested in each mutual fund?
Jenelle invested $_____ into Fund A.
Jenelle invested $_____ into Fund B.
Answer:
Jenelle invested $ 13,000 in Fund A and $ 4,000 in Fund B.
Step-by-step explanation:
Given that Jenelle invested $ 17000 in two mutual funds, and Fund A earned 4% profit during the first year, while Fund B suffered a 1.5% loss, if she received a total of $ 460 profit, to determine how much had she invested in each mutual fund, the following calculation must be performed:
17000 x 0.04 - 0 x 0.015 = 680
15000 x 0.04 - 2000 x 0.015 = 570
10,000 x 0.04 - 7000 x 0.015 = 295
12500 x 0.04 - 4500 x 0.015 = 432.5
13000 x 0.04 - 4000 x 0.015 = 460
Therefore, Jenelle invested $ 13,000 in Fund A and $ 4,000 in Fund B.
A bookshelf costs $300 normally. Today it is on sale and decreased by 20% However there is
also a 4% sales tax. What is the new cost of the bookshelf?
Answer:
249.60
Step-by-step explanation:
300 x .8 (100%-20%)=240
240 x .04 (4% sales tax)=9.60
price = 240+9.60=249.60