The probability that Mike has to work overtime and it rains is 0.028. Mike hears the weather forecast, and there is a 50% chance of rain. Find the probability that he will have to work overtime, given that it rains.

Answer: The rate of the boat in still water is 74 km/hr ,and the rate of the current is 19 km/hr

Explanation:

Let:

x= the speed of the boat

y=the speed of the stream

Then,

x-y = the speed upstream

x+y = the speed downstream

So, the upstream speed is:

and, the downstream speed is:

To find the value of x and y, we use the following equations:

x-y= 55

x+y=93

Then, solve for x in x-y =55.

x=55 +y

Substitute x=55 + y into x+y=93.

x+y=93

(55 +y) + y=93

55+2y = 93

Substitute y=19 into x+y = 93.

x+y= 93

x+ 19 =93

Simplify and rearrange

x=93-19

Calculate

x=74

Therefore, the rate of the boat in still water is 74 km/hr ,and the rate of the current is 19 km/hr.

The probability that the taxi was actually blue is 0.61.

Witnesses are right 77% of the time. This means that they are incorrect 23% of the time. Furthermore, 25% of the taxis were blue while the rest were green. Since these are the only two choices, it follows that 75 percent of the taxis are green.

Using Bayes' Theorem, we can calculate the probability that the taxi was blue:

P (Taxi is blue|Witness said it was blue)

P (Witness said it was blue|Taxi is blue)

P (Taxi is blue)

P (Witness said it was blue|Taxi is green)

P (Taxi is green)

To begin, we must determine the probabilities of each of these:

P (Taxi is blue) = 0.25

P (Taxi is green) = 0.75

P (Witness said it was blue|Taxi is blue) = 0.77

P (Witness said it was blue|Taxi is green) = 0.23

To get the result we multiply all of them together:

P (Taxi is blue|Witness said it was blue) = P (Taxi is blue) × P (Witness said it was blue|Taxi is blue) / [P (Taxi is blue) × P (Witness said it was blue|Taxi is blue) + P (Taxi is green) × P (Witness said it was blue|Taxi is green)]P (Taxi is blue|Witness said it was blue) = 0.25 × 0.77 / (0.25 × 0.77 + 0.75 × 0.23)

P (Taxi is blue|Witness said it was blue) = 0.61

Therefore, the probability that the taxi was actually blue is 0.61.

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Answer:

Think

Step-by-step explanation:

4x - 6 + 2x = 18

You are solving for x so obviously you have to have your x variable on one side of the equal sign by itself.

So how do you do that? Combine the same calues together and seperate the rest

4x + 2x = 6x

6x = 18 + 6

6x = 24

x = 3

Practice practice practice. Simple stuff. You got this!

Answer:

A. x = 4

Step-by-step explanation:

To answer this question, we first have to combine like terms:

4x - 6 + 2x = 18

6x - 6 = 18

Now, we take away 6 from the left side and add it to the right side:

6x - 6 = 18

     +6   +6

6x = 24

Then, we isolate the variable:

6x = 24

/6     /6

x = 4

Hope this helps :)

The equation for a horizontal plane through the point (0,−2,−3) is z= -3.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let's assume n is the normal vector for the horizontal plane < 0, 0, 1 > .

The co-ordinate of the point is (0,−2,−3)

The general equation of a plane is -

\(n < x-x_0 , y - y_0, z-z_0 > =0\\\\ < 0,0,1 > \\\\0(x)+0(y+2) +1(z+3)\\\\z = -3\)

Thus, The equation for a horizontal plane through the point (0,−2,−3) is z= -3.

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To find the value of s3 in the given sigma summation series and calculate the truncation error, let's first analyze the series and determine its pattern.

The series can be written as:

s = (0.2 * 1) / 0.8 + (0.2 * 2) / 0.8 + (0.2 * 3) / 0.8 + ...

We notice that each term in the series has the form (0.2 * n) / 0.8. We can simplify this expression by dividing both the numerator and denominator by 0.2:

s = n / 4

Now, let's calculate s3 by substituting n = 3:

s3 = 3 / 4

s3 = 0.75

So, the value of s3 in the series is 0.75.

Now, let's calculate the truncation error. The truncation error is the difference between the actual sum of the series and the sum obtained by truncating or stopping at a certain term.

Given that the series sum is 0.3125 and we have s3 = 0.75, we can calculate the truncation error:

Truncation error = |Actual sum - Sum truncated at s3|

Truncation error = |0.3125 - 0.75|

Truncation error = |-0.4375|

Truncation error = 0.4375

The truncation error in this case is 0.4375.

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Answer:

-22

Step-by-step explanation:

5-27

"27 less than the product of a number and 5"

my answer is: N/5-27

Answer:

Subtract 5 from each side

Step-by-step explanation:

This would put all coefficients on one side.

Answer:

Step-by-step explanation:

15 minutes LxWxH/time

Given:

The endpoints of a line segment QS are Q(-6,2) and S(5,6).

Point R divides the line segment QS in 1:2.

To find:

The coordinates of point R.

Solution:

Section formula: If a point divides a line segment in m:n, then the coordinates of that point are:

\(Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)\)

It is given that the endpoints of a line segment QS are Q(-6,2), S(5,6) and point R divides the line segment QS in 1:2. So, the coordinate of point R are:

\(R=\left(\dfrac{1(5)+2(-6)}{1+2},\dfrac{1(6)+2(2)}{1+2}\right)\)

\(R=\left(\dfrac{5-12}{3},\dfrac{6+4}{3}\right)\)

\(R=\left(\dfrac{-7}{3},\dfrac{10}{3}\right)\)

Therefore, the coordinates of point R are \(\left(\dfrac{-7}{3},\dfrac{10}{3}\right)\).

Answer:

1. A=1 B=3 C=1 D=2 E=6 F=8

2. B)  y = 3 * 2^x

3. C) y = 2^3x

Step-by-step explanation:

100% correct edge 2022

Answer:

A=1

B=3

C=1

D=2

E=6

F=8

Answer:

Inscribed Angle (A)

Step-by-step explanation:

in geometry, an inscribed angle is the angle formed in the interior of a circle when two secant lines (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.

Answer:

x+y ≤20

3.50 x +8 y ≤150

Step-by-step explanation:

Hi, the rest of the question is:

How do you write a system of linear inequalities to model the situation?

So, for the first inequality:

The sum of the number of soil bags (x) and plants(y) bought must be less or equal to 20.

x+y ≤20

For the second inequality:

The product of the number of soil bags (x) and the price of each bag (3.50) ; plus the number of plants bought(y) and the price of each plant (8) must be less or equal to 150.

3.50 x +8 y ≤150

In conclusion, the system is:

x+y ≤20

3.50 x +8 y ≤150

Answer:

$267.85

Step-by-step explanation:

im just going to add 102.35 and 85.50 together first

187.85

then you multiply 20 by 4 since they bought 4 boxes

80

add them together

187.85+80=267.85

a) The proportion of heads that  is represented in this sample is \(\bar{p}\)=0.583.

It is a parameter that describes a percentage number connected with a population. For example, the 2010 United States Census revealed that 83.7% of the American population was identified as not being Hispanic or Latino; the figure of.837 is a population proportion. In general, the population proportion and other population metrics are unknown. A census can be undertaken to establish the true value of a demographic metric, although it is generally impractical due to the expenses and time required.

A population proportion is typically computed using an unbiased sample statistic derived from an observational study or experiment.

Given that,

A coin is flipped 120 times, the number of heads we get are 70

a) The sample proportion is,

\(\bar{p}\)=No. of heads/No. of times the coin is flipped

\(\bar{p}\)=70/120

\(\bar{p}\)=0.583

The proportion of heads that  is represented in this sample is \(\bar{p}\)=0.583

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This is an experimental research since the car wash owner will provide various discounts and then watch the extra money come in.

The discrepancy between the purchase price and the face value is the amount of the discount. A rebate is a specific kind of cost reduction or deduction for a product. An amount or percentage off the regular retail cost of an item or service is known as a rebate. You could be given the option to get, as an illustration, a $10 or 10% discount off the product's advertised price. a decrease in the overall quantity or value of something (see gross entry 1 for further information). Regular or routine price reductions. Give your clients a 10% discount.

This is an experimental research since the car wash owner will provide various discounts and then watch the extra money come in.

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Answer:

[1, ∞)

Step-by-step explanation:

1) Solve for x

-4x + 21 \(\leq\) 3x + 14

21 \(\leq\) 7x + 14

7 \(\leq\) 7x

1 \(\leq\) x

2) 1 is the lowest possible value of x and since it's a smaller or equal to inequality, you use a square bracket. If it was 1 < x, it would be a round bracket. Since there isn't a boundary for the highest value of x, you write an infinity. When you have an infinity, it's always a round bracket.

Answer:

x ≥ 1

 [1, ∞)

Step-by-step explanation:

Note: 3 < 7 and 8 > 2 this is obvious

2,3,7,8 are on the RIGHT SIDE of the number zero "0"

now look at this sequence :

-3 > -7 and -8 < -2

the numbers are the same but thy are on the opposite side of the ZERO.

now notice that the <> signs flipped from the fist to the second set...

when you do these problems, "Multiplying or dividing by a negative number"

effectively moves you from one side of the zero to the other....

the "thing" you have to do is REMEBER AFTER EACH STEP...

IF YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER (not add or subtract)  

YOU HAVE TO FLIP THE SIGN...

-4x+21 ≤ 3x +14

-4x ≤ 3x - 7          |||| subtracted 21 NO sign flip

-7x ≤ -7                ||| subtracted 3X NO sign flip

x ≥ 1                     ||| Divided by "-1" SIGN MUST FLIP !!!

Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.

The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:

W = F * d

where:

W is the work done in joules

F is the force in newtons

d is the distance in meters

The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.

The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.

Plugging these values into the equation for work, we get:

W = 102.8 N * 4600 m = 472320 J

The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:

472320 J / 29 kJ/mol = 162.6 mol

To one decimal place, this is 0.23 moles of ATP.

Here are the assumptions that we made in this calculation:

No friction

No mass of the bike

A flat ride with no change in altitude

These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.

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The 5 arithmetic means between 18 and -12 are; ​-7, -2, 3, 8, 13

Arithmetic Means is defined as the branch of mathematics that deals with the properties as well as the manipulation of numbers.

The formula for the nth term of an arithmetic mean is;

an = a + (n - 1)d

where;

a is first term

d is common difference

n is position of term

In this case, we want 5 terms between 18 and -12 and this means we have a total of 7 terms. Thus;

a = -12

a₇ = 18

18 = -12 + (7 - 1)d

18 + 12 = 6d

30 = 6d

d = 5

a₂ = -12 + (2 - 1)5

a₂ = -12 + 5

a₂ = -7

a₃ = -12 + (3 - 1)5

a₃ = -12 + 10

a₃ = -2

a₄ = -12 + (4 - 1)5

a₄ = 3

Thus;

a₅ = 8

a₆ = 13

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Answer:

Your answer is 15

Step-by-step explanation:

12 x 3 = 36

So..

5 x 3 = 15

What u do to the bottom you do to the top.

The mean number of individuals with 20/20 vision is 23.

To find the mean number of individuals with 20/20 vision, we can use the formula for the expected value of a binomial distribution. In this case, the probability of an individual having 20/20 vision is p = 0.33, and the number of trials (i.e. individuals selected) is n = 70.
The formula for the expected value of a binomial distribution is:
E(X) = np
Substituting in our values, we get:
E(X) = 70 x 0.33
E(X) = 23.1
So, the mean number of individuals with 20/20 vision out of 70 selected at random from the population is approximately 23.1. However, since we can't have a fraction of a person, we should round our answer to the nearest whole number.
Therefore, the mean number of individuals with 20/20 vision is 23.

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In this scenario, we are considering an investment that will pay $3,000 in 34 years. We are given an appropriate discount rate of 8 percent. To determine the present value of this investment, we can use the present value formula. Additionally, we are provided with the information that the investment is being sold for $773, and we need to calculate the rate of return investors will earn on this investment.

a. Present value of the investment:

To calculate the present value of the investment, we use the present value formula:

Present Value = Future Value / (1 + Discount Rate)^n,

where Future Value is $3,000, the Discount Rate is 8 percent (0.08), and n is the number of years, which is 34 in this case.

Present Value = $3,000 / (1 + 0.08)^34 = $219.13

Therefore, the present value of the investment, considering an 8 percent discount rate, is $219.13.

b. Rate of return on the investment:

The rate of return on an investment is calculated using the formula:

Rate of Return = (Future Value - Purchase Price) / Purchase Price * 100,

where Future Value is $3,000 and the Purchase Price is $773.

Rate of Return = ($3,000 - $773) / $773 * 100 ≈ 288.46%

Therefore, the rate of return investors can earn on this investment, if they buy it for $773, is approximately 288.46%.

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Answer:

x=0 and y =2.

Step-by-step explanation:

4x + 5y = 10

x + 2y = 4

The first less 4 times the second.

-3y = -6

y = 2

Substitute back.

x + 2(2) = 4

x = 0

The translation is as shown in the figure in option B

Translation transformation is a type of geometric transformation that moves every point of a figure the same distance and direction. This transformation does not change the size, shape, or orientation of the figure, but only its position in space.

The transformation required ahs the rule defined as

Applying the rule arrives the image in option B

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brown skin girl brown skin just like pearls

Answer:

Solution: (-5,-6)

Graph:

Answer:

I do believe the answer is A

Answer:

Kurt originally knitted the scarf to be 3.75 feet + 0.5 feet = 4.25 feet long.

I found the answer by using basic addition. I added the length that Kurt had to unravel (0.5 feet) to the remaining length of the scarf (3.75 feet) to find the original length of the scarf (4.25 feet).

Step-by-step explanation:

The time taken by a student to finish a statistics exam can be modeled using the following cumulative distribution function: F(x) = 1 - e^-0.9, x > 0

Suppose that the time taken for a student to finish the exam is constant from student to student.

Then the mean number (to the nearest whole number) of students who will finish the exam in less than 1 hour for 12 students randomly selected is 7

.Step-by-step explanation:

The cumulative distribution function is given by, F(x) = 1 - e^-0.9, x > 0

Now, let X be the time taken by a student to finish the statistics exam

Then, X ~ Exp (0.9 )

We know that the cumulative distribution function (CDF) of the exponential distribution with parameter λ is given by,F(x) = P(X ≤ x) = 1 - e^(-λx) , x > 0Here, λ = 0.9.

Therefore, the CDF of X is given by,F(x) = P(X ≤ x) = 1 - e^(-0.9x) , x > 0

The probability that a student finishes the exam in less than 1 hour is, P(X ≤ 1) = F(1) = 1 - e^(-0.9) ≈ 0.5271

This means that out of 12 students randomly selected,

The expected number of students who finish the exam in less than 1 hour is,μ = np= 12 × 0.5271≈ 6.3252

Hence, the mean number (to the nearest whole number) of students who will finish the exam in less than 1 hour for 12 students randomly selected is 7.

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