The average number of mosquitoes in a stagnant pond is 70 per square meter with a standard deviation of 8 per square meter. if one square meter of the pond is chosen at random for a mosquito count, find the probability that the average of the count is more than 68 mosquitoes per square meter. assume that the variable is normally distributed.

Answers

Answer 1

the probability that the average of the count is more than 68 mosquitoes per square meter. assuming that the variable is normally distributed will be calculated as follows:
z=(x-μ)/σ
where:
x=68
μ=70
σ=8
thus
z=(68-70)/8=-0.25

P(x>68)=1-P(x<68)=1-P(z<-0.25)
=1-0.4013
=0.5987

Answer: P(x>68)=0.5987

Answer 2

The probability that the average mosquito count in a randomly chosen square meter of the pond is more than 68 mosquitoes is approximately 59.87%.

To find the probability that the average count of mosquitoes in a randomly chosen square meter of the pond is more than 68 mosquitoes per square meter, we can use the normal distribution properties.

Given:

Mean (">"): 70 mosquitoes per square meterStandard deviation (σ): 8 mosquitoes per square meter

We need to find P(X > 68). To do this, we convert the raw score to a Z-score using the formula:

Z = (X - μ) / σ

Substitute the given values:

Z = (68 - 70) / 8 = -2 / 8 = -0.25

Next, we need to find the probability corresponding to Z > -0.25 using the standard normal distribution table.

Looking up Z = -0.25, we find the cumulative probability (P(Z < -0.25)) is approximately 0.4013.

To find P(Z > -0.25):

P(Z > -0.25) = 1 - P(Z < -0.25) = 1 - 0.4013 = 0.5987

Therefore, the probability that the average mosquito count in a randomly chosen square meter is more than 68 mosquitoes per square meter is approximately 0.5987 or 59.87%.

Related Questions

A car rental costs $50 for the first day. Additional days cost $35 per day, unless the car is rented for 7 days or more, in which case there is a 10% discount on the daily rate. Identify the expression which represents the cost of renting a car if the car has been rented for more than a week.
A.) 45+35x
B.) 45+31.5x
C.) 50+35x
D.) 50+31.5x

Answers

the answer is D,I think it's help

Answer:

Option D [tex]\$50+\$31.5x[/tex]

Step-by-step explanation:

Let

x------> the number of days

y----> the cost of renting a car

we know that

For [tex]x<7\ days[/tex]

[tex]y=\$50+\$35x[/tex]

For [tex]x\geq 7\ days[/tex]

The rate is equal to

[tex]0.90*\$35=\$31.5[/tex]

[tex]y=\$50+\$31.5x[/tex]

In this problem. the car has been rented for more than a week

therefore

[tex]x> 7\ days[/tex]

The cost of renting a car is equal to

[tex]y=\$50+\$31.5x[/tex]

Conduct a chi-squared test of independence on the data presented in data set
d. assume equal probabilities of fe for each cell and make sure to report all relevant statistics, including the value of χ2 obtained, the critical value and your decision as to whether to reject the null hypothesis .

Answers

What's a chi-squared?

The sum of the squares of two numbers is 18. the product of the two numbers is 9. find the numbers.

Answers

A graph shows the two numbers are either (3, 3) or (-3, -3).

Answer:

x=3 y=3

Step-by-step explanation:

The sum of the squares of two numbers is 18, and the product of those two numbers is 9, you just need to create an equation:

So the sum of the squares is 18, the first number will be represented as X and the second as Y:

[tex]x^{2}+ y^{2} =18[/tex]

And the other one is that the product of the two numbers is 9:

[tex]xy=9[/tex]

We have a system of equations here, we clear X from the first one:

[tex]x=\frac{9}{y}[/tex]

And instert that value of x in the first one:

[tex]x^{2}+ y^{2} =18\\(\frac{9}{y} )^{2}+ y^{2} =18\\81=y^2(18-y^2)\\y^4-18y^2+81=0\\(y^2-9)(y^2-9)=0\\Y^2-9=0\\y^2=9\\y=3[/tex]

By solving this equation we get that the first number is 3.

The second number is solved by inserting the value of Y into one of the equations, in this case we will use the second:

[tex]xy=9\\x=\frac{9}{y} \\x=\frac{9}{3} \\x=3[/tex]

So we get that x and y are both 3.

A laterally loaded single pile is shown below. use the elastic pile solutions (based on the winkler's model) to calculate the displacement and rotation at pile head ????. assume free headed condition. pile length ???? = 30 ft; young's modulus ???????? = 3 × 10 6 psi; ????ℎ = 30 lb/in3 ; and the eccentricity ???? = 60 in.

Answers

the pile length 10=30ft.young modulus 180=3×10 6 psi. 178.579673h =30 lb/in3 and the eccentricity 1.667 yrds =60 inch

At the candy store, a chocolate bar costs c dollars and a vanilla bar costs 2 dollars more than a chocolate bar. Jamie buys a chocolate bar and three vanilla bars, and Kevin buys five chocolate bars. How much money, in total, do Jamie and Kevin spend at the candy store in terms of c?

Answers

To represent the amount of money Kevin and Jamie are spending in terms of c, you will write an expression for each person and then add those expressions together.

Jamie: c + 3(c + 2)
Kevin: 5c

c + 3(c + 2) + 5c; Simplify
c + 3c + 6 + 5c; combine like terms

9c + 6 represents the amount they would spend.

while watching a football game, Lin Chow decided to list yardage agained as positive integers and yardage lost as negative integers. after this plays, Lin recorded 14, -7, and 9. what was the net gain or lost?

Answers

To find the net loss or gain add all three integers (14 + -7 + 9) to get 16. This is your net gain because it is positive.

Enrique earns 101010 points for each question that he answers correctly on a geography test. Write an equation for the number of points, yyy Enrique scores on the test when he answers xxx questions correctly.

Answers

[tex]y = 101010 \times x[/tex]

In the question it must be 10 instead of 101010, y instead of yyy and x instead of xxx.

Since, Enrique earns 10 points for each question that he answers correctly on a geography test.

We have to write an equation for the number of points, 'y' Enrique scores on the test when he answers 'x' questions correctly.

So, Number of points scored = Points scored for one question [tex] \times [/tex] Number of questions answered correctly.

So, Number of points scored = [tex] 10 \times x [/tex]

[tex] y=10 \times x [/tex]

y = 10x is the required equation.

which number correctly completes this equation 3/4%x75= A. 0.255 B. 0.5625 C. 2.55. D. 5.626

Answers

3/4% × 75

3/4 of a percent is .0075.

0.0075 times 75 = 0.5625

The answer is B) 0.5625.

7.
Find the amount of the payment for the sinking fund.

Amount Needed: $58,000

Years Until Needed: 2

Interest Rate: 6%

Interest Compounded: Semiannually

$13,863.74

$8,620.68

$28,155.52

$13,258.22

Answers

SFF = (r/n)/{(1+r/n)^nt-1} ------- where SFF = Sinking fund factor, r = Annual interest rate, n= number of payments per year, t = number of years

Substituting,
SFF = (0.06/2)/{(1+0.06/2)^2*2 -1} = 0.239

PMT = A*SFF = 58,000*0.239 = $13,863.57 ---- The closest answer is $13,863.74

K+1=3k-1 what us the answer

Answers

So let's get k on one side:
2k = 2
Divide by 2:
k = 1

If you want to check your work:
1 + 1 = 3 - 1
2 = 2

You have to find what the varible k stands for in this case

A jar of peanut butter and a jar of jam cost $10.20 in total. the jar of peanut butter costs $10.00 more than the jar of jam. how much does the jar of jam cost

Answers

Well this is pretty simple. So the first thought is that the peanut butter would be 10$ and the jam would be 0.20$, however, the peanut butter would not be 10$ more. Instead, subtract the 10$ from the total, which gives you 0.20$, and then divide that by two. Now you have 0.10$ for each, along with another 10$ for the peanut butter. The peanut butter would be $10.10, and the jam would be 0.10$ (that's pretty cheap!).

hat is the sum of the geometric series in which a1 = 3, r = 4, and an = 49,152?
Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.

Sn = −65,535
Sn = 16,383
Sn = 13,120
Sn = 65,535

Answers

Final answer:

To find the sum of the geometric series, we use the formula: Sn = a1 * (r^n - 1) / (r - 1). Substituting the given values and solving, we find that the sum is 16,383.

Explanation:

To find the sum of a geometric series, we can use the formula Sn = a1 * (r^n - 1) / (r - 1), where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.

In this case, a1 = 3, r = 4, and an = 49,152. We can use the formula to find n, which is the exponent.

49,152 = 3 * (4^n - 1) / (4 - 1)

49,152 = 3 * (4^n - 1) / 3

16,384 = 4^n - 1

4^n = 16,385

n = log4(16,385)

n ≈ 7

Now, we can substitute the values into the formula for Sn.

Sn = 3 * (4^7 - 1) / (4 - 1)

Sn = 3 * (16,384 - 1) / 3

Sn = 3 * 16,383 / 3

Sn = 16,383

Therefore, the sum of the geometric series is 16,383. So the correct answer is Sn = 16,383.

The correct answer is [tex]$ S_n = 65,535 $[/tex].

To find the sum of a geometric series, you can use the formula:

[tex]\[ S_n = a_1 \frac{(r^n - 1)}{r - 1} \][/tex]

Where:

- [tex]$ S_n $[/tex] is the sum of the series,

- [tex]$ a_1 $[/tex] is the first term,

- [tex]$ r $[/tex] is the common ratio,

- [tex]$ n $[/tex] is the number of terms.

Given [tex]$ a_1 = 3 $, $ r = 4 $, and $ a_n = 49,152 $[/tex], we need to find [tex]$ n $[/tex]. The formula for the [tex]$ n^{th} $[/tex] term in a geometric series is [tex]$ a_n = a_1 \times r^{(n-1)} $[/tex]. In this case, [tex]$ 49,152 = 3 \times 4^{(n-1)} $[/tex]

Let's solve for n:

[tex]\[ 4^{(n-1)} = \frac{49,152}{3} \][/tex]

[tex]\[ 4^{(n-1)} = 16,384 \][/tex]

[tex]\[ n-1 = \log_4(16,384) \][/tex]

[tex]\[ n-1 = 7 \][/tex]

[tex]\[ n = 8 \][/tex]

Now that we have [tex]$ n = 8 $[/tex], we can use it in the sum formula:

[tex]\[ S_n = 3 \frac{(4^8 - 1)}{4 - 1} \][/tex]

[tex]\[ S_n = 3 \frac{(65,536 - 1)}{3} \][/tex]

[tex]\[ S_n = 3 \frac{65,535}{3} \][/tex]

[tex]\[ S_n = 65,535 \][/tex]

Therefore, the correct answer is [tex]$ S_n = 65,535 $[/tex].

A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. Which sentence about the points is true?

A, B, C, and D lie on the same line.
AB and CD are perpendicular lines.
AB and CD are parallel lines.
AB and CD are intersecting lines but are not perpendicular.
AC and BD are parallel lines.

Answers

For this case we observe that the lines AB (red) and CD (purple) are cut at one point.
We observe that the slopes of both lines are different (they are not reciprocal opposites).
Therefore, the lines are not perpendicular.
Answer:
AB and CD are intersecting lines but are not perpendicular.
See attached image.

Answer:

AB and CD are intersecting lines but are not perpendicular.

See attached image.

Step-by-step explanation:

QF Q6.) Find the following function for b.

Answers

For (g o f)(x), you plug in the equation of f(x) where the x-variable is in g(x).

5(2x - 2)² - 3

First, you do FOIL method of the binomial:

5(4x² - 8x + 4) - 3

Now distribute the 5:

20x² - 40x + 20 - 3

And combine like terms:

20x² - 40x + 17

(g₀f)(x)=g(f(x))
=g(2x-2)
=5(2x-2)^2-3
=5(4x^2-8x+4)-3
=20x^2-40x+17

PLZ HELP ASAP WRITE STANDERED EQAUTION OF A CIRCLE

Answers

The generic equation of the circle is:
(x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2
Where,
(xo, yo): coordinate of the center of the circle
r: radius of the circle.
Substituting values we have:
(x-9.2) ^ 2 + (y + 7.4) ^ 2 = (5/3) ^ 2
Rewriting:
(x-9.2) ^ 2 + (y + 7.4) ^ 2 = 25/9
Answer:
The equation of the circle is:
(x-9.2) ^ 2 + (y + 7.4) ^ 2 = 25/9

r = 5/3
C(9.2, -7.4)

r^2 = (x-h)^2 + (y-k)^2
(5/3)^2 = (x - 9.2)^2 + (y + 7.4)^2

If i know a real root of f(x) = x3 -6x2 + 11x – 6 is neither 1, even, or negative, a good guess would be?

Answers

A good guess for the real root of the polynomial [tex]f(x) = x^3 - 6x^2 + 11x - 6[/tex] that is neither 1, even, nor negative, would be a positive odd integer such as 3 or 5, considering the constraints and the Rational Root Theorem.

The real root of the cubic equation [tex]f(x) = x^3 - 6x^2 + 11x - 6[/tex] that is neither 1, even, nor negative would most likely be a positive odd number (since all positive even numbers are, by default, also excluded). Considering the smallest odd numbers greater than 1 are 3 and 5, and given that we're working with integers, a good guess for the real root would be either 3 or 5. However, one can apply the Rational Root Theorem which states that any rational root, expressed in its lowest form p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient. In this case, the possible rational roots could be

divisors of 6 (constant term) over divisors of 1 (leading coefficient), which gives us only divisors of 6 itself

since the leading coefficient is 1. Among those divisors, the ones that fit the criteria of being neither 1, even, nor negative, would be 3 or positive odd integers.

What is the probability of rolling an even number or a prime number on a number cube? Write as a fraction in simplest form.

Answers

Final answer:

The probability of rolling an even number or a prime number on a six-sided die is 5/6, considering the unique favorable outcomes of 2, 3, 4, 5, and 6 against the total possible outcomes.

Explanation:

The question asks, "What is the probability of rolling an even number or a prime number on a number cube?" To answer this, first identify the outcomes on a six-sided die which are even and those that are prime.

Even numbers on a die: 2, 4, 6. Prime numbers on a die: 2, 3, 5. Notice that 2 is both even and prime, and it only needs to be counted once. Therefore, the unique favorable outcomes are 2, 3, 4, 5, 6.

The die has a total of 6 sides, making the total number of possible outcomes 6. The probability of rolling an even number or a prime number is therefore the number of favorable outcomes (5) divided by the total number of outcomes (6), which simplifies to 5/6.

What is the domain of the function g(x) = 52x? x > 0 x < 0 all real numbers all positive real numbers

Answers

g(x) = 52x

The domain: all real numbers.

Answer: all real numbers

Step-by-step explanation:

The given function is : [tex]g(x) = 52x[/tex], which is polynomial function with degree one.

The domain of a function is the set of all values for x for which the function must be defined.

We know that the domain of a polynomial is the entire set of real numbers because for any real number r the polynomial function exists.

Therefore, the domain of the given function [tex]g(x) = 52x[/tex] is the set of real numbers.

Solve for y.

a.10
b.12
c.15
d.18

Answers

If angle ABC is 90°, then angle CBD is 90°:

Angle ABD=90°
3x°=90°
3x=90
Solving for x:
3x/3=90/3
x=30

Angle CBD=90°
(2x+3y)°=90°
2x+3y=90
x=30
2(30)+3y=90
60+3y=90
Solving for y:
60+3y-60=90-60
3y=30
3y/3=30/3
y=10

Answer: Option a. 10

The answer will most likely be A

Calculator Problem You downloaded a video game to your computer. You have a 60 -minute free trial of the game. It take 5 minutes to set up the game and 7minutes to play each level. You want to find out how many levels you can play for free. Let ll l l represent the number of levels played. Write an inequality to determine the number of levels you can play in 60 minutes.

Answers

Comment write your givens.
S = setup = 5 minutes.
L = Levels = x
T = Time / L = 7 minutes / Level.

Formula
S + x * T ≤ 60 minutes

Substitute and solve.
5 + 7*x ≤ 60 Subtract 5 from both sides.
7x ≤ 60 - 5
7x ≤ 55 minutes Estimated, the answer is almost x = 8 but not quite. Divide by 7
x ≤ 55/7
x ≤ 7 . He almost makes it through the 8th game but not quite

x ≤ 7 Answer.

Final answer:

The inequality 5 + 7l ≤ 60 represents the scenario where a student has a 60-minute free trial of a game that requires 5 minutes to set up and 7 minutes to play each level, where 'l' denotes the number of levels the student can play.

Explanation:

The subject of this question is about setting up an inequality to represent a scenario. The student has a 60-minute free trial of a game and it takes 5 minutes to set up the game and another 7 minutes to play each level. Let's denote 'l' as the number of levels the student can play. The total time spent both setting and playing the game cannot exceed 60 minutes. Therefore, the inequality to determine the maximum number of levels the student can play would be: 5 + 7l ≤ 60.

To explain this further, the '5' is the time spent setting up the game and '7l' is the total time spent playing the levels. As we want to find out the maximum number of levels that can be played within a constraint of 60 minutes, thus we use the less than or equal to symbol ('≤').

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Ples help me find slant assemtotes
this one is different because it isn't a rational function

find the slant assemtotes of [tex](y+1)^2=4xy[/tex]
the equation can be rewritten using the quadratic formula as [tex]y=2x-1 \pm \sqrt{x^2-x}[/tex]

ples find slant assemtotes and show all work
thx

Answers

A polynomial asymptote is a function [tex]p(x)[/tex] such that

[tex]\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0[/tex]

[tex](y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}[/tex]

Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form [tex]p(x)=ax+b[/tex].

Ignore the negative root (we don't need it). If [tex]y=2x-1+2\sqrt{x^2-x}[/tex], then we want to find constants [tex]a,b[/tex] such that

[tex]\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0[/tex]

We have

[tex]\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}[/tex]
[tex]\sqrt{x^2-x}=|x|\sqrt{1-\dfrac1x}[/tex]
[tex]\sqrt{x^2-x}=x\sqrt{1-\dfrac1x}[/tex]

since [tex]x\to\infty[/tex] forces us to have [tex]x>0[/tex]. And as [tex]x\to\infty[/tex], the [tex]\dfrac1x[/tex] term is "negligible", so really [tex]\sqrt{x^2-x}\approx x[/tex]. We can then treat the limand like

[tex]2x-1+2x-ax-b=(4-a)x-(b+1)[/tex]

which tells us that we would choose [tex]a=4[/tex]. You might be tempted to think [tex]b=-1[/tex], but that won't be right, and that has to do with how we wrote off the "negligible" term. To find the actual value of [tex]b[/tex], we have to solve for it in the following limit.

[tex]\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0[/tex]

[tex]\displaystyle\lim_{x\to\infty}(\sqrt{x^2-x}-x)=\frac{b+1}2[/tex]

We write

[tex](\sqrt{x^2-x}-x)\cdot\dfrac{\sqrt{x^2-x}+x}{\sqrt{x^2-x}+x}=\dfrac{(x^2-x)-x^2}{\sqrt{x^2-x}+x}=-\dfrac x{x\sqrt{1-\frac1x}+x}=-\dfrac1{\sqrt{1-\frac1x}+1}[/tex]

Now as [tex]x\to\infty[/tex], we see this expression approaching [tex]-\dfrac12[/tex], so that

[tex]-\dfrac12=\dfrac{b+1}2\implies b=-2[/tex]

So one asymptote of the hyperbola is the line [tex]y=4x-2[/tex].

The other asymptote is obtained similarly by examining the limit as [tex]x\to-\infty[/tex].

[tex]\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0[/tex]

[tex]\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0[/tex]

Reduce the "negligible" term to get

[tex]\displaystyle\lim_{x\to-\infty}(-ax-(b+1))=0[/tex]

Now we take [tex]a=0[/tex], and again we're careful to not pick [tex]b=-1[/tex].

[tex]\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-b)=0[/tex]

[tex]\displaystyle\lim_{x\to-\infty}(x+\sqrt{x^2-x})=\frac{b+1}2[/tex]

[tex](x+\sqrt{x^2-x})\cdot\dfrac{x-\sqrt{x^2-x}}{x-\sqrt{x^2-x}}=\dfrac{x^2-(x^2-x)}{x-\sqrt{x^2-x}}=\dfrac x{x-(-x)\sqrt{1-\frac1x}}=\dfrac1{1+\sqrt{1-\frac1x}}[/tex]

This time the limit is [tex]\dfrac12[/tex], so

[tex]\dfrac12=\dfrac{b+1}2\implies b=0[/tex]

which means the other asymptote is the line [tex]y=0[/tex].

which means the other asymptote is the line .

The hypotenuse of an isosceles right triangle is 14 sqrt 2. How long is each leg of the triangle?

Answers

Each leg is 14 because the hypotenuse of an isosceles right triangle is the length of either of its legs times the square root of 2. So each leg is 14 because both legs are equal in an isosceles triangle
Hope this helps!

Answer:

Step-by-step explanation:

Let the legs of the triangle each have length $x$ (they are equal because it is an isosceles right triangle). Then

x^2 + x^2 = (14√2)^2 = 14^2 × (√2)^2 = 14^2 × 2, so x^2 = 14^2. Given that x must be positive, we have x = 14. So, the value of each leg is 14

(Hope this helped you!)

Hey can you please help me posted picture of question

Answers

true true true true true

The answer is True.

A compound event is one in which there is more than one possible outcome. It is also defined as a probabilistic event with two or more favorable outcomes. For example, when you throw a die (singular for dice), it is called a simple event. On the other hand, when you throw a dice, it is known as a compound event.

HELP PLEASE
Determine the missing statements and reasons for the following proof.

Answers

Reasons:
Reason 3: Congruent supplements theorem

Statements:
Statement 4: Angle 1 is congruent with angle 2

Answer: Option D:
Reason 3: Congruent supplements theorem.
Statement 4: Angle 1 is congruent with angle 2

Final answer:

In a mathematical proof, missing statements and reasons are usually concluded from the given statements and the relevant geometric postulates or theorems. They could include establishing the congruency of angles or declaring the parallelism of lines.

Explanation:

Without the concrete steps of the proof or the reasoning proposed, it is difficult to provide the exact missing statements and reasons. However, in a general mathematical proof, common reasons used include 'definition of congruent angles', 'definition of parallel lines', 'alternate interior angles theorem', etc.

For instance, if we have a proof that involves stating two angles are congruent, the missing statement might be 'Angle A is congruent to Angle B', and the missing reason could be 'Definition of Congruent Angles' or 'Angle Bisector Theorem', if an angle bisector comes into the picture.

Another missing statement might be 'Segment AB is parallel to Segment CD', with the reason being 'Corresponding Angles Postulate', or 'Alternate Interior Angles Theorem', if the proof involves parallel lines.

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The probability that a student correctly answers on the first try (the event
a.is p(a) = 0.2. if the student answers incorrectly on the first try, the student is allowed a second try to correctly answer the question (the event b). the probability that the student answers correctly on the second try given that he answered incorrectly on the first try is 0.5. find the probability that the student answers the question on the first or second try.
a.0.90
b.0.40
c.0.10
d.0.70
e.0.60

Answers

Note that the two events are mutually exclusive. If the question is answered correctly on the first try, there's no need to give it another attempt. So [tex]\mathbb P(A\cap B)=0[/tex].

We're given that [tex]P(A)=0.2[/tex] and [tex]P(B\mid A^C)=0.5[/tex]. From the first probability, we know that [tex]P(A^C)=1-0.2=0.8[/tex]. By definition of conditional probability,

[tex]\mathbb P(B\mid A^C)=\dfrac{\mathbb P(B\cap A^C)}{\mathbb P(A^C)}[/tex]
[tex]\implies\mathbb P(B\cap A^C)=0.5\cdot0.8=0.4[/tex]

We're interested in the probability of either [tex]A[/tex] or [tex]B[/tex] occurring, i.e. [tex]\mathbb P(A\cup B)[/tex]. Apply the inclusion-exclusion principle, which says

[tex]\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cap B)[/tex]

We know the probability of intersection is 0, and we know [tex]\mathbb P(A)[/tex]. Meanwhile, by the law of total probability, we have

[tex]\mathbb P(B)=\mathbb P(B\cap A)+\mathbb P(B\cap A^C)=\mathbb P(B\cap A^C)[/tex]

so we end up with

[tex]\mathbb P(A\cup B)=0.2+0.4=0.6[/tex]

The probability that the student answers the question on the first or second try is 0.60.

Given

P(A) = 0.2

[tex]\rm P(B|A^c)=0.5[/tex].

What is conditional probability?

The conditional probability of an event is when the probability of one event depends on the probability of occurrence of the other event.

When two events are mutually exclusive.

Then,

[tex]\rm P(A\cap B)=0[/tex]

The first probability is;

[tex]\rm P(A^C)=1-0.2=0.8[/tex]

Therefore,

The probability that the student answers the question on the first or second try is;

[tex]\rm P(A\cup B)= P(A) +P(B)-P(A \cap B)\\\\ P(A\cup B)= P(A) +P(B|A^C) \times P(A^C)-P(A \cap B)\\\\ P(A\cup B)= 0.2+0.5 \times 0.8 -0\\\\P(A\cup B)=0.2+0.40\\\\ P(A\cup B)=0.60[/tex]

Hence, the probability that the student answers the question on the first or second try is 0.60.

To know more about Conditional probability click the link given below.

https://brainly.com/question/10739947

Please please help i don’t understand this.

Answers

For a geometric sequence;
a(n) = a1*r^(n-1)

Where
a(n) = nth term
a1 = first term
r = common ratio
n = 0,1,2,3,4,5, ... n

To establish which graphs agree with this formula, each graph should be tested separately as follows:
Graph A:
a2 = 9
Then
9 = a1*(1/3)^(2-1) =1/3a1 => a1 = 3*9 = 27
Sequence:
a1 = 27
a2 = 9
a3 = 27*(1/3)^(3-1) = 3
a4 = 27*(1/3)^(4-1) = 1
These are the same values shown and thus this graph corresponds to geometric sequence.

Graph B:
a1 = 12
a2 = 12*(1/3)^(2-1) = 4
a3 = 12*(1/3)(3-1) = 4/3
a4 = 12*(1/3)^(4-1) = 4/9
These are the values shown by the graph and thus it corresponds with geometric sequence.

Graph C:
a1 = 3+3/2 = 9/2
a2 = (9/2)*(1/3)^1 = 3/2
a3 = (9/2)*(1/3)^2 = 1/2
a4 = (9/2)*(1/3)^3 = 1/6
a0 = (9/2)*(1/3)^-1 = 13.5 (this is not the case as the graph shows a0 = 12)

Therefore, this graph does not correspond to geometric sequence.

Graph D:
a1 = 4
a2 = 4*(1/3)^1 = 4/3
a3 = 4*(1/3)^2 = 4/9
a4 = 4*(1/3)^3 = 4/27
a0 = 12

This graph seems to agree with values of geometric sequence and thus corresponds to geometric sequence.

Therefore, graphs A, B, and D corresponds with geometric sequence.

If ∆XYZ = ∆KLM, then < Y = Please help due today

Answers

ΔXYZ must correspond to ΔKLM, so the angles must as well

∠X = ∠K
∠Y = ∠L
∠Z = ∠M

So ∠Y = ∠L

I hope this helps!

k+1=3k-1 please show me the correct steps to solve this problem

Answers

k + 1 = 3k - 1     |-3k
-2k + 1 = -1    |-1
-2k = -2    |:(-2)

k = 1

a coin is tossed , then a number 1-10 is chosen at random.what is the probability of getting heads then a number less than 4?

Answers

Probability of sequences can be calculated by multiplying the chance of the first event by the chance of the second, and so on.

The probability of tossing a coin and getting heads is 50%, or 0.5, and the probability of selecting a number less than four from 1-10 is 40%, or 0.4.

The overall probability can then be expressed as:

0.5 x 0.4 = 0.2 or 20%

There is a twenty percent chance that a heads would be tossed and a number less than four selected.

Jorge owes his father $60. After raking the lawn for the month, he has paid him $12, $8, and $9. How much money does Jorge still has owes his father?

Answers

12 + 8 + 9 = 29

60 - 29= 31

Jorge owes his father $31

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