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
A battery company produces 20,000 batteries per day. Each day they randomly select 200 to test. If they find that 4 are dead, how many dead batteries would they expect to find among the entire 20,000?
Answer: 400 because when they test 200 they get that 4 are dead wich is 1/50 of 200 so 1/50 times 20,000 is 400
Step-by-step explanation:
I have a quick question please someone answer Is 5/8 irrational?
Answer:
no
Step-by-step explanation:
5/8=0.6250 so its rational
Answer: no
Step-by-step explanation: 5/8 is rational because it is another way of writing the ratio 5:8. So no, 5/8 is not an irrational number.
Lily took a loan of $1200 with simple interest for as many years as the rate of
interest. If she paid $432 as interest at the end of the loan period, what was the
rate of interest? *
Answer:
sax
SI = $432
P = $1200
rate = x
time = x
= 432 = t×p×r / 100
= 432 = x × 1200 × x / 100
= 432 = x × 12 × x
= 432 = 2x × 12
= 432/12 = 2x
= 6 = 2x
= 6 ÷ 2 = x
= 3 = x
The rate of interst is 3%
Step-by-step explanation:
A number b is at least - 3.
Answer:
-3 ≥ b is your inequality
Step-by-step explanation:
Can someone please help me on this?
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.
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
Justin says that if the diameter of any circle is 15 feet then its radius must 10
be 7.5 feet. Is Justin correct?
If f(1) = 1 and f(n) = f(n-1)2 – 4 then find the value of f(4).
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?
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:
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.
I’m taking test rn lol
Answer:
A. 2
Step-by-step explanation:
∛8 = 2
There is only one correct value to it so it can't be negative and positive 2, the answer is positive 2 so,
= 2
DONT ANSWER IF YOU DONT KNOW THE ANSWER
Simplify each expression
mc0011
mc0012
mc0013
mc0014
mc0015
Answer:
A
Step-by-step explanation:
A is the answer for the first question I did the math on edge
The second one after is B
We are Simplifying Rational Expressions with Negative Exponents
Answer:
A.) Afriv
Step-by-step explanation:
Heat oven to 350°F. Generously grease 12-cup fluted tube pan with shortening or cooking spray. In large 1-gallon plastic food storage bag, mix granulated sugar and cinnamon.
2
Separate dough into 16 biscuits; cut each into quarters. Shake in bag to coat. Arrange in pan, adding walnuts and raisins among the biscuit pieces. Sprinkle any remaining sugar over biscuits.
3
In small bowl, mix brown sugar and butter; pour over biscuit pieces.
4
Bake 30 to 40 minutes or until golden brown and no longer doughy in center. Loosen edges of pan with metal spatula. Cool in pan 5 minutes. Turn upside down onto serving plate; replacing any biscuit pieces and caramel from pan. Pull apart to serve. Serve warm.
Cargo shipping, an automobile manufacturer is preparin shipment of a cars andvtrucks on a cargo ship that can carry 21,600 tons
The cars weigh 3.6 tons each and the trucks weihgt 7.5 tons each. 1. Wtite thevequation thatvrepresents the weight constraint of a shipment let be the number of cars and be the numbers of trucks.
Answer:
3.6c + 7.5t <= 21,600
Step-by-step explanation:
Let c = number of cars, and let t = number of trucks.
c cars weigh 3.6c tons, and t trucks weigh 7.5t tons.
3.6c + 7.5t <= 21,600
Bob and Larry went on a tricycle ride. They rode for the same amount of time, but Bob cycled 10 miles per hour slower than Larry. If Bob cycled 14 miles and Larry cycled 21 miles, find the speed that both Larry and Bod rode their tricycles.
Step-by-step explanation:
so basically they are asking you to subtract, hope this helps, use a calculator if needed
Factor completely::::
The 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:
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.
What is the answer of 1/3 x 1/4
Answer:
1/12
Step-by-step explanation:
Multiply across
Hope this helps
Find the interquartile range (IQR) of the data in the box plot below.
eggs
Number of eggs laid
Answer:
5
Step-by-step explanation:
The interquartile range is the 3rd quartile minus the 1st quartile. The 3rd quartile is 8 and the 1st quartile is 3.
8 - 3 = 5
The interquartile range (IQR) of the data is 5.
From the box plot we can write,
Minimum = 2
First Quartile, Q1 = 3
Median = 6
Third Quartile, Q3 = 8
Maximum = 10
So, Interquartile range (IQR)
= Q3 - Q1
= 8 - 3
= 5
Thus, the interquartile range (IQR) of the data is 5.
Learn more about Interquartile range (IQR) here:
https://brainly.com/question/31758606
#SPJ2
A race-car is driving counter-clockwise on a circular track with a radius of 1.9 miles. The car starts at the 3 o'clock position and travels at a constant speed of 85.5 miles per hour.
What distance (in miles) has the race-car traveled if the car has swept out an angle of 212 degrees?
_____miles
What is the measure of the angle swept out by the car (in radians) if the car has traveled 4.9 miles?
_____radians
Define a function, h, that gives the race-car's distance above the horizontal diameter of the track (in miles) in terms of the number of hours since the race-car started driving, t.
Answer:
The answer is below
Step-by-step explanation:
The car is moving in a circular track with a radius of 1.9 miles. The distance covered by the car if the track is revolved once = 2π * radius of the track.
a) Since the car has swept out an angle of 212 degrees, the distance covered by the race car = [tex]\frac{212}{360}*2\pi(1.9)=7.03 \ miles[/tex]
b) If the car traveled 4.9 miles, the angle swept out (θ) is:
[tex]4.9= \frac{\theta}{360} * 2\pi r\\\\\theta=\frac{4.9}{2\pi (1.9)}*360 \\\\\theta=147.76^o=147.76^o*\frac{\pi}{180} \\\\\theta=2.58\ rad[/tex]
c) h = distance covered, t = time in hourss.
Hence:
h = 85.5t
The race-car's motion round the track is a repeating motion that can be
described by a sinusoidal function.
The correct responses are;
Distance travelled when the car swept an angle of 212° ≈ 7.03 milesIf the car has travelled 4.9 miles, the angle swept out, θ ≈ 2.58 radiansThe function is; [tex]\underline{h(t) = 1.9\cdot sin(45\cdot t)}[/tex].Reasons:
Known parameters are;
Radius of the track, r = 1.9 miles
Point the car starts = 3 O'clock
Speed of the car = 85.5 mph
Required:
Distance swept out when the car traveled an angle of 212°.
Solution;
Distance of one complete turn = 2·π·r
Angle of one complete turn = 360°
Therefore, at 212°, we have;
[tex]\dfrac{212^{\circ}}{360^{\circ}} \times 2 \times 1.9 \times \pi \approx 7.03[/tex]
Distance travelled when the car swept an angle of 212° ≈ 7.03 milesRequired:
The measure of the angle swept out by the car if the car has travelled 4.9 miles.
Solution;
Let, θ represent the angle, we have;
[tex]\dfrac{\theta}{2 \cdot \pi} \times 2 \times 1.9 \times \pi \approx 4.9 \ miles[/tex]
We get;
[tex]{\theta} = \dfrac{4.9 \ miles}{2 \times 1.9 \ miles \times \pi } \times 2\cdot \pi \approx 2.58 \ radians[/tex]
If the car has travelled 4.9 miles, the angle swept out, θ ≈ 2.58 radiansRequired:
The function, h, that gives the distance of the above the horizontal
diameter of the track (in miles) in terms of the number of hours since the
race-car started driving, t.
Solution;
The function that gives the car height can be presented as follows;
The angular velocity, ω = [tex]\dfrac{v}{r}[/tex]
Therefore;
[tex]\omega = \dfrac{85.5 \ mph}{1.9 \ miles} = 45 \ rad/hour[/tex]
The general form of the sinusoidal function is h = A·sin[k·(θ - b)] + c
Therefore, we get;
h = 1.9·sin[k·(θ - b)] + c
The period, T = 2·π/ω = 2·π/k
Therefore, given that ω·t = θ, we get;
h = 1.9·sin[ω·t - b] + c = 1.9·sin[45·t - b] + c
The vertical sift, c, and the horizontal shift, b, can both be taken as zero,
given that the sin(0) = 0, therefore;
h = 1.9·sin[0] + c = c = 0, such that the at the start, t = 0, the car is at a
distance of h = 0 above the horizontal line.
The function, h, that gives the distance of the car above the
horizontal track, in terms of the number of hours since the car started
driving, t, is therefore;
[tex]\underline{h(t) = 1.9\cdot sin(45\cdot t)}[/tex].Learn more here:
https://brainly.com/question/16014064
PLESE SOMEONE HELP ME WILL GIVE BRAINLIEST
Answer:
a. area of triangle: A=1/2(b)(h)
A= 1/2 (3)(2.4)
A= 3.6cm^2
All the triangles have the same area, so Total area of the triangles is
A= 4(3.60)
A= 14.4 cm^2
Area of the square: A= s^2 (3)^2= 9cm^2
Total surface area o the Pyramid: 14.4+ 9=23.4cm^2
b. Lateral surface area of the Pyramid: A= 1/2 P(l)
A= 1/2 (12)(4)
A= 24cm^2
P is perimeter of the base= (3)(4)=12cm
l s the slant height= 4cm
Step-by-step explanation:
what does 6 and 18 have in common
A discount of 10 percent was given. If a further discount of 10percent was given in the reduced price, calculate the total single discount given in the marked price .
Answer:
let marked price = x
on 10% discount, price= x-10%of x
=x-(10x/100)
=x-(x/10)
=9x/10
on further 10% discount, total discount = 10% of 9x/10
=10/100 * 9x/10
= 9x/100
= 9%of x
hence, the single discount given on marked price is 9%
Step-by-step explanation:
If 3.78 liters of cranberry juice costs $6.95, then how much will Niki pay for 7.56 L?
Answer:
She will pay $13.9 for 7.56 liters
Step-by-step explanation:7.56 minus 3.78 equals to 3.78. This means we can just simply add another $6.95, so $6.95 plus $6.95 equals to $13.9
A person who is standing on a ledge throws a rock into the air. The rock reaches a maximum height of 676 feet
above the ground after 1.5 seconds.
If the rock hits the ground below the ledge 8 seconds after it is thrown, which quadratic function can be used to find
the height of the rock above the ground t seconds after it is thrown?
Answer:
The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta= b^{2} - 4ac[/tex]
Quadratic equation:
[tex]ax^2 + bx + c = 0[/tex]
The rock reaches a maximum height of 676 feet above the ground after 1.5 seconds.
This means that:
[tex]-\frac{b}{2a} = 1.5[/tex]
[tex]y_{v} = -\frac{b^2-4ac}{4a} = 676[/tex]
If the rock hits the ground below the ledge 8 seconds after it is thrown
This means that:
[tex]64a + 8b + c = 0[/tex]
Relation of b and a:
[tex]-\frac{b}{2a} = 1.5[/tex]
This means that:
[tex]b = -3a[/tex]
Relationship of c and a:
[tex]64a + 8b + c = 0[/tex]
[tex]64a - 24a + c = 0[/tex]
[tex]c = -40a[/tex]
Finding a:
[tex]y_{v} = -\frac{(-3a)^2-4a(-40a)}{4a} = 676[/tex]
[tex]9a^2+160a = -2704a[/tex]
[tex]9a^2 + 2864a = 0[/tex]
[tex]a(9a + 2864) = 0[/tex]
Since it is a quadratic equation, a cannot be 0.
[tex]9a + 2864 = 0[/tex]
[tex]9a = -2864[/tex]
[tex]a = -\frac{2864}{9}[/tex]
[tex]a = -318.22[/tex]
Finding b and c:
[tex]b = -3a = -3(-318.22) = 954.67[/tex]
[tex]c = -40a = -40(-318.22) = 12728.89[/tex]
The quadratic equation is given by:
[tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
for every 0.5 miles emily makes 0.80 in charity how much does he make for 16 miles
Answer:
25.6
Step-by-step explanation:
16*2=32
32*0.8=25.6
Answer:
25.6
Step-by-step explanation:
16x.8=12.8
because he makes it every half mile we have to multiply by 2\
12.8*2=25.6
if he walks 16 miles he makes 25.6
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
