The probability of an economic decline in the year 2020 is 0.23. There is a probability of 0.64 that we will elect a republican president in the year 2020. If we elect a republican president, there is a 0.35 probability of an economic decline. Let "D" represent the event of an economic decline, and "R" represent the event of election of a Republican president. Use this information to answer the following four questions:
1 Are R and D independent events?
2 What is the probability of electing a Republican president and an economic decline in 2020?
3 If we experience an economic decline in 2016, what is the probability that a Republican president will have been elected in 2020?
4 What is the probability of economic decline or a Republican president elected in 2020 or both?
Answer:
1) D and R are NOT independent events
2) The probability of electing a Republican president and an economic decline in 2020 is 0.224
3) If we experience an economic decline in 2016, the probability that a Republican president will have been elected in 2020 is 0.9739
4) the probability of economic decline or a Republican president elected in 2020 or both is 0.646
Step-by-step explanation:
Let "D" represent the event of an economic decline, and "R" represent the event of election of a Republican president
Given that;
P(D) = 0.23
P(R) = 0.64
Conditional P(D | R) = 0.35
1) Are R and D independent events?
we know that two events A & B are independent events if; P(B | A) = P(B)
here, P(D | R) = 0.35 and P(D) = 0.23
so; P(D | R) ≠ P(D)
Therefore D and R are NOT independent events
2) The probability of electing a Republican president and an economic decline in 2020;
we know that;
P(D | R) = P(D ∩ R) / P(R)
we substitute
0.35 = P(D ∩ R) / 0.64
P(D ∩ R) = 0.35 × 0.64
P(D ∩ R) = 0.224
Therefore, The probability of electing a Republican president and an economic decline in 2020 is 0.224
3) If we experience an economic decline in 2016, what is the probability that a Republican president will have been elected in 2020?
P(R | D) = P(D ∩ R) / P(D)
we substitute
P(R | D) = 0.224 / 0.23
P(R | D) = 0.9739
Therefore, If we experience an economic decline in 2016, the probability that a Republican president will have been elected in 2020 is 0.9739
4) the probability of economic decline or a Republican president elected in 2020 or both
P(D ∪ R) = P(D) + P(R) - P(D ∩ R)
we subtitute
P(D ∪ R) = 0.23 + 0.64 - 0.224
P(D ∪ R) = 0.646
Therefore, the probability of economic decline or a Republican president elected in 2020 or both is 0.646
Rahul is an engineer and designed an electric car which is moving at an average speed of 56 km per hour. One day, he is travelling and testing his car. If he travelled 7 hours on that day, how much distance does he travelled?
Answer: He travelled 392 km that day.
Step-by-step explanation:
We are given that,
Speed of electric car = 56 km per hour.
Time = 7 hours
We know that,
Distance = Speed x Time
If he travelled 7 hours on that day, then Distance traveled in 7 hours on that day= (56 km per hour) x (7 hours)
i.e. Distance traveled in 7 hours on that day== 392 km
Hence, he travelled 392 km that day.
Rachel has $9 in a savings account. The interest rate is 5%, compounded annually.
To the nearest cent, how much interest will she earn in 3 years?
Which of the following functions has a factor of x−7?
f(x)=x3−16x2+53x+63
f(x)=x3−2x2−73x−70
f(x)=x3−16x2+53x+70
f(x)=x3−2x2−73x−77
According to the question, the function that has a factor of x - 7 is f(x) = x³ - 16x² + 53x+ 70
If x - a is a factor of a function f(x), then f(a) = 0
For x - 7 to be a factor of f(x), f(7) must be equal to zero.
For f(x) = x³ - 16x² + 53x+ 70
f(7) = 7³ - 16(7²) + 53(7) + 70
f(7) = 343 - 16(49) + 53(7) + 70
f(7) = 343 - 784 + 371 + 70
f(7) = 0
Since f(7) = 0 for f(x) = x³ - 16x² + 53x+ 70, x - 7 is a factor of f(x) = x³ - 16x² + 53x+ 70
Learn more here: https://brainly.com/question/19273656
Factor completely::::
The cost c varies directly as the numbers n of pencils is written as A. c = kn B. k+ cn C. n = k/c D. c =k/n
Answer:
A. c = kn
Step-by-step explanation:
The cost c varies directly as the numbers n of pencils
This means that c is a multiplication of a constant by n, which is the number of pencils. So the equation for the cost is given by:
[tex]c = kn[/tex]
In which k is the constant of proportionality, that is, the cost of each pencil. So the correct answer is given by option A.
Can anyone help me with 5-9?
Answer:
5. 1/4, 4/16
6. 4/5, 16/20
7. 1/3, 6/18
8. 2/9, 4/18
9. 1/3, 3/9
Step-by-step explanation:
Hope that helps!
Assume that the probability of a driver getting into an accident is 7.1%, the average cost of an accident is $14,886.0 , and the overhead cost for an insurance company per insured driver is $110 . What should the driver's insurance premium be?
Answer: $1166.91
Step-by-step explanation:
The following can be deduced from the question:
Average cost of an accident = $14,886.05
Probability of a driver getting into an accident = 7.1% = 7.1/100 = 0.071.
Overhead cost for insurance = $110
Therefore, the expected cost of an accident will be calculated as:
= Average cost of an accident × Probability of a driver getting into an accident
= $14,886.05 × 0.071
= $1056.91
Therefore, the driver's insurance premium will then be:
= $1056.91 + $110
= $1166.91
if CORRECT answerS then good review
Answer:
number 8 is D) 78.7 in.
and number 9 is C) 63°
hope these are the answers you are looking for
Step-by-step explanation:
Three angles of a quadrilateral are 75,120, 90,then the fourth angle..
Answer:
75
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityGeometry
Sum of Angles in a Quadrilateral: 360Step-by-step explanation:
Step 1: Set up
75 + 120 + 90 + ∠4 = 360
Step 2: Solve
Add: 285 + ∠4 = 360[Subtraction Property of Equality] Subtract 285 on both sides: ∠4 = 75The coefficients in the expansion of (x + y)6 are
A. 1, 6, 15, 20, 15, 6, 1
O B. 1, 6, 15, 15, 6, 1
O C. 0, 1,6, 15, 15, 6, 1, 0
O D. 0, 6, 15, 20, 15, 6,0
Answer:
A
Step-by-step explanation:
which is greater 1/4 or 0.75
Answer:
0.75 is greater
Step-by-step explanation:
1/4=0,25 and 0.75 is greater than 0,25
if Sin 3x= Cos (x-60), find the value of x
Answer:
x = 15
Step-by-step explanation:
Assuming 3x and x-60 are in degrees, you can use:
cos(a) = sin(a+90)
To rewrite the equation as:
sin(3x) = sin(x-60+90)
sin(3x) = sin(x+30)
3x = x+30
2x = 30
x = 15
But, solving 3x = x+30 which simplifies to x=15 is not the only solution to this equation, as you can see in below picture. Finding all solutions is a bit more work, but maybe that is not required in your case.
Felix divided his shirts into three equal groups. Evaluate when s = 18.
Answer:
3 and 6.
Step-by-step explanation:
Write and evaluate the expression. Then, check all that apply.
Felix divided his shirts into three equal groups. Evaluate when s = 18.
The expression is
The expression is
The expression is s/3
The expression is
The answer is
The answer is 6.
a bank teller counted P1,250.00 in P 0.25 coin and P3,200.00 in P0.10 coins how many coins in all were counted
answer:
Step-by-step explanation:
1250 plus 0.25 equals 1250.25 plus 1250.25 plus 3200 equals 4450.25 plus 0.10 equals 4450.35
- Functions F and A are defined by these equations below. Which function has a greater value when x is 2.5?
A. F(x) = 80-15x
B. A(x) = 25 + 10x
Answer:
The answer is D- A(x)=25+10x
Step-by-step explanation:
I cant really explain how i got the answer but i got it right
The function A(x) has greater value then F(x) for x = 2.5.
What is a function?A function is a relation between a independent variable and a dependent variable such that the value of dependent variable depends upon the independent one.
Given are two functions of [x] as follows -
F(x) = 80 - 15x
A(x) = 25 + 10x
We have the following functions -
F(x) = 80 - 15x
A(x) = 25 + 10x
Now, we will evaluate each function at x = 2.5.
F(2.5) = 80 - 15 x 2.5 = 42.5
and
A(2.5) = 25 + 10 x 2.5 = 50
It can be seen that A(2.5) > F(2.5)
So, the function A(x) has greater value then F(x) at x = 2.5
Therefore, the function A(x) has greater value then F(x) for x = 2.5.
To solve more questions on Evaluating functions, visit the link below-
https://brainly.com/question/24971874
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A student is able to finish 2 homework problems per hour. If they have already completed 4 problems, how many hours will it take for them to finish an assignment which has 18 problems total? Give your answer to two decimal places.
Answer:
Step-by-step explanation:
4+2t=18
2t=14
t=7 hours
Answer:
7.00 hours
Step-by-step explanation:
They already did 4 problems and need to do 18 problems in total.
18 - 4 = 14 problems
2 problems/ per hour
14 problems/ 7 hours
It will take them 7 hours to finish. Since you said "Give your answer to two decimal places." You could write it as 7.00 hours.
High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pressure is 0.2. A sample of 37 U.S. adults is chosen. Use the TI-84 Plus Calculator as needed. Round the answer to at least four decimal places.
Part 1
Is it appropriate to use the normal approximation to find the probability that more than 48% of the people in the sample have high blood pressure? It is not_______ appropriate to use the normal curve, since np = 7.4 ______< 10 and n (1 – p) = 29.6 2 10.
Part 2
A new sample of 82 adults is drawn. Find the probability that more than 32% of the people in this sample have high blood pressure. The probability that more than 32% of the people in this sample have high blood pressure is__________ X 5
Answer:
1. It is not appropriate to use the normal curve, since np = 7.4 < 10.
2. The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.
Step-by-step explanation:
Binomial approximation to the normal:
The binomial approximation to the normal can be used if:
np >= 10 and n(1-p) >= 10
Binomial probability distribution
Probability of exactly x sucesses 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.
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The proportion of U.S. adults with high blood pressure is 0.2. A sample of 37 U.S. adults is chosen.
This means, respectively, that [tex]p = 0.2, n = 37[/tex]
Is it appropriate to use the normal approximation to find the probability that more than 48% of the people in the sample have high blood pressure?
np = 37*0.2 = 7.4 < 10
So not appropriate.
It is not appropriate to use the normal curve, since np = 7.4 < 10.
Part 2:
Now n = 82, 82*0.2 = 16.4 > 10, so ok
Mean and standard deviation:
By the Central Limit Theorem,
Mean [tex]\mu = p = 0.2[/tex]
Standard deviation [tex]s = \sqrt{\frac{0.2*0.8}{82}} = 0.0442[/tex]
Find the probability that more than 32% of the people in this sample have high blood pressure.
This probability is 1 subtracted by the pvalue of Z when X = 0.32. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.32 - 0.2}{0.0442][/tex]
[tex]Z = 2.72[/tex]
[tex]Z = 2.72[/tex] has a pvalue of 0.9967.
1 - 0.9967 = 0.0033
The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.
There are 81 people protesting the destruction of the rain forests. There are 36 males, 23 of whom are students, and 18 female nonstudents. How many female students are protesting?
Answer:
27
Step-by-step explanation:
Given that the total number of people protesting is 81. These people are either male - Student or non student or Females (student or non students)
Given that there are 36 males then number of females
= 81 - 36
= 45
If there are 18 females non students then the number of females protesting that are students
= 45 - 18
= 27
seven more than twice a number is -4
Answer:
-5.5
Step-by-step explanation:
[tex]2x+7=-4\\2x=-4-7\\2x=-11\\x=-5.5[/tex]
Answer:
-11/2
Step-by-step explanation:
Let the number be a
(2a)+7= -4
2a= -4-7
2a= -11
a= -11/2
I’ve been trying to figure out this question but I am not able to please help
Answer:
its C
Step-by-step explanation:
ik
Answer:
D
Step-by-step explanation:
Since the total degrees of a circle is 360 and half of a circle is 180, 1/4 of a circle is 90 or less, D is the answer :)
A number cube with the numbers 1 through 6 is rolled. Find the probability of rolling the number 4.
Answer:
1/6 chance of rolling a 4
8/5 ÷ 3/5 = ??????????
Answer:
Step-by-step explanation:
8/3
The 10 members of a hiking club will walk 9 miles. Each person will carry the food pack for an equal distance. How far will each hiker carry the food pack?
Answer:
0.9 miles per member
Step-by-step explanation:
Total distance = 9 miles
Number of members = 10
If they are to carry the food back for an equal distance, we have to fin
Distance covered by a person with the food pack = Total distance / Number of members
Distance covered by a person with the food pack = 9 / 10 = 0.9 miles per member
What does 60/8 x 13?
My calculator says 97.5
Answer:
195/2
Step-by-step explanation:
60/8=15/2
15/2*13=195/2
A rectangle is inside a circle with a 5 cm radius.
What is the area of the shaded region?
Use 3.14 for π.
Enter your answer as a decimal
Answer:
Do it your self
Step-by-step explanation:
Gross
Answer:
30.5
Step-by-step explanation:
Find an explicit rule for each geometric sequence using subscript notation. Use a calculator and round your answer to the nearest tenth if necessary.
The fourth term of the sequence is 234. The sixth term is 104.
The explicit rule for the geometric sequence is an
Step-by-step explanation:
Geometric sequences are of the form a * b^x, where a and b are real constants.
We have a * b⁴ = 234 and a * b⁶ = 104.
Dividing the second equation by the first,
we get b² = 4/9, so b = 2/3.
When x = 4, a * b⁴ = 234.
=> a * (2/3)⁴ = 234, a = 1184.625
Hence the explicit rule
is a(n) = 1184.625 * (2/3)^n.
Answer:
Hence the explicit rule is a(n) 1184.625 *(2/3)^n.
Write 3.08 × 10-5 as an ordinary number.
Answer:
0.0000308
Step-by-step explanation:
there are 5 places that it has moved from.
(giving brainiest)
answer this correctly
Answer:
A =224 in ^3
Step-by-step explanation:
Answer:
56in squared
Step-by-step explanation:
Estimate the product of 3.8 and 11.9 rounding.
Answer:
48
Step-by-step explanation:
round off 3.8 to 4 and 11.9 to 12 and multiply the values
