sweden has 1 boat per how many people?

For independent events A and B, where P(A) = 0.3 and P(B) = 0.4, the conditional probability P(B | A) = 0.4

Even A and B are independent events.

P(A) = 0.3 and P(B) = 0.4

Therefore,

P( A∩B ) = P(A) · P(B)

= (0.3)*(0.4)

= 0.12

By the formula of calculating conditional probability we get,

P(B | A) = P( B∩A ) / P(A)

= P( A∩B )/ P(A)

= 0.12/ 0.3

= 12/30

= 0.4

Thus the probability that event B occurs given that event A occurred is 0.4

Conditional probability is referred to the likelihood of an event to occur given that the other event occurs too.

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The length of the line segment B'C' is 3 units.

We can see that from the given graph that,

The coordinates of the points are:

B = (-2, 6)

C = (-2, 3)

If we translate the points 5 units to the right then the changed coordinates will be -

B' = (-2 + 5, 6) = (3, 6)

C' = (-2 + 5, 3) = (3, 3)

So the length of the B'C' is given by,

B'C' = √((3 - 3)² + (6 - 3)²) = √(0² + 3²) = √(0 + 9) = √9 = 3 units.

Hence the length of the line segment B'C' is 3 units.

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The circumference of the circle is 30 cm.

Any unit for measuring length can be used to calculate the circumference, including feet, miles, metres, millimetres, etc.

By substituting 3 for, we can use the following formula to determine the circle's circumference:

C = 2πr

where r is the radius and C is the circumference.

We can observe from the provided diagram that the circle's radius is 5 cm. Thus, by changing r = 5 cm and = 3 in the formula, we obtain:

C = 2(3)(5) = 30

The circle's circumference is 30 cm as a result.

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Answer:

A =  2 outcomes B = 4 outcomes C = 7 outcomes

Step-by-step explanation:

A has two outcomes because when you flip a coin you can only land on heads or tails

B has four outcomes becuase when picking a random season there are only four possible seasons to be picked.

C has seven outcomes becuase when picking a random day of the week there are only 7 possible days that can be picked,  

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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The y- coordinate for the solution to the system of equations is 4

From the question, we have the following parameters that can be used in our computation:

8x−4y=−32,

2x+2y=4

Multiply the second equation by 4

So, we have the following representation

8x − 4y = −32

8x + 8y = 16

Subtract the equations

So, we have the following representation

12y = 48

Divide by 12

y = 4

Hence, the solution is y = 4

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The y-coordinate for the solution to the system of equations is equal to 4.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (-2, 4).

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(a) Initial amount: 50mg. (b)Concentration after 1.5 hours:0.21mg/L.
(c) Time = -151.68 min. (d) Percentage leaving Approx 10% per min.
(e) ln(D(t)) = ln50 + tln0.9.

(a) The initial amount of the drug in the body can be found by substituting t = 0 into the equation. D(0) = 50(0.9^0) = 50, so the initial amount is 50mg.

(b) To find the concentration after 1.5 hours (90 minutes), we substitute t = 90 into the equation. D(90) = 50(0.9^90) ≈ 0.21mgL^(-1).

(c) To find the time when the drug concentration reaches 0.1mg/L, we can solve the equation:

0.1 = 50(0.9^t)

Dividing both sides by 50, we have:

0.1/50 = 0.9^t

Simplifying further:

0.002 = 0.9^t

To solve for t, we can take the logarithm of both sides. Let's use the natural logarithm (ln):

ln(0.002) = ln(0.9^t)

Using the property of logarithms that ln(a^b) = b * ln(a), we can rewrite the equation:

ln(0.002) = t * ln(0.9)

Now we can solve for t by dividing both sides by ln(0.9):

t = ln(0.002) / ln(0.9)

Using a calculator, we find:

t ≈ -151.68

Since time cannot be negative, it means that the drug concentration never reaches 0.1mg/L based on the given model.

(d) The percentage of the drug leaving the system every minute can be predicted by observing that the exponent in the equation, t, determines the rate at which the drug concentration decreases.

As t increases by 1, the concentration decreases by a factor of 0.9, which corresponds to a 10% decrease.

Therefore, approximately 10% of the drug leaves the system every minute.

(e) Starting with the equation D(t) = 50(0.9^t), we can rewrite it using the properties of logarithms as ln(D(t)) = ln(50) + t ln(0.9).

This form allows us to linearize the equation and analyze the relationship between the logarithm of the concentration and time.

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Answer: -2a,-2b

Step-by-step explanation:

Answer:

The next step is;

Label the two intersection points

Step-by-step explanation:

To make a copy of an angle, the steps are;

1) Draw the rays of the original angle passing through the point B

2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays

3) Label the point of intersection of both rays points C and D

4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J

5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M

6) Draw a line from B passing through M to complete the second ay of the copied angle.

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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Answer:

Step-by-step explanation:

2/3 10 x 5 6/100 = 23/10 x 506/100 = 23x506 and 10x100 which equals 11638/1000. Then, you would divide 1000 by 2 and 11638 by 2 to get 5819/100 then you would simplify it which equals 11 319/500

(a) Forecast: Linear regression  the next year is approx 191.6007.

(b) MSE: Mean Squared Error is approximately 249.1585.

(c) MAPE: Mean Absolute Percent Error is approximately 10.42%.

(a) (a) Forecast using linear regression:
To forecast the number of disk drives for the next year, we can use linear regression to fit a line to the given data points. The linear regression equation is of the form y = mx + b, where y represents the number of disk drives and x represents the year.

Calculating the slope (m):
m = (Σ(xy) - n(Σx)(Σy)) / (Σ(x^2) - n(Σx)^2)

Σ(xy) = (1)(140) + (2)(160) + (3)(190) + (4)(200) + (5)(210) = 2820
Σ(x) = 1 + 2 + 3 + 4 + 5 = 15
Σ(y) = 140 + 160 + 190 + 200 + 210 = 900
Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) + (5^2) = 55

m = (2820 - 5(15)(900)) / (55 - 5(15)^2)
m = (2820 - 6750) / (55 - 1125)
m = -3930 / -1070
m ≈ 3.6729

Calculating the y-intercept (b):
b = (Σy - m(Σx)) / n
b = (900 - 3.6729(15)) / 5
b = (900 - 55.0935) / 5
b ≈ 168.1813

Using the equation y = 3.6729x + 168.1813, where x represents the year, we can predict the number of disk drives for the next year. To do so, we substitute the value of x as the next year in the equation. Let's assume the next year is represented by x = 6:

y = 3.6729(6) + 168.1813
y ≈ 191.6007

Therefore, according to the linear regression model, the predicted number of disk drives for the next year is approximately 191.6007.

(b) Calculation of Mean Squared Error (MSE):

To calculate the Mean Squared Error (MSE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 = 171.8542
Year 2: y = 3.6729(2) + 168.1813 = 175.5271
Year 3: y = 3.6729(3) + 168.1813 = 179.2000
Year 4: y = 3.6729(4) + 168.1813 = 182.8729
Year 5: y = 3.6729(5) + 168.1813 = 186.5458
Next, we calculate the squared difference between the predicted and actual values, and then take the average:

MSE = (Σ(y - ŷ)^2) / n

MSE = ((140 - 171.8542)^2 + (160 - 175.5271)^2 + (190 - 179.2000)^2 + (200 - 182.8729)^2 + (210 - 186.5458)^2) / 5

MSE ≈ 249.1585

The Mean Squared Error (MSE) for the linear regression model is approximately 249.1585.

This value represents the average squared difference between the predicted values and the actual values, providing a measure of the accuracy of the model.

(c) Calculation of Mean Absolute Percent Error (MAPE):

To calculate the Mean Absolute Percent Error (MAPE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 ≈ 171.8542
Year 2: y = 3.6729(2) + 168.1813 ≈ 175.5271
Year 3: y = 3.6729(3) + 168.1813 ≈ 179.2000
Year 4: y = 3.6729(4) + 168.1813 ≈ 182.8729
Year 5: y = 3.6729(5) + 168.1813 ≈ 186.5458

Next, we calculate the absolute percent error for each year, which is the absolute difference between the predicted and actual values divided by the actual value, multiplied by 100:

Absolute Percent Error (APE):

Year 1: |(140 - 171.8542) / 140| * 100 ≈ 18.467
Year 2: |(160 - 175.5271) / 160| * 100 ≈ 9.704
Year 3: |(190 - 179.2000) / 190| * 100 ≈ 5.684
Year 4: |(200 - 182.8729) / 200| * 100 ≈ 8.563
Year 5: |(210 - 186.5458) / 210| * 100 ≈ 11.682
Finally, we calculate the average of the absolute percent errors:

MAPE = (APE₁ + APE₂ + APE₃ + APE₄ + APE₅) / n

MAPE ≈ (18.467 + 9.704 + 5.684 + 8.563 + 11.682) / 5 ≈ 10.42

The Mean Absolute Percent Error (MAPE) for the linear regression model is approximately 10.42%.

This value represents the average percentage difference between the predicted values and the actual values, providing a measure of the relative accuracy of the model.

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The volume of ball is 32.49 cubic centimeter.

What is volume ?

 Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here ,

The volume of a ball = 32490 cubic millimeters

To convert into cubic millimeter into cubic centimeter by dividing by 1000, Then,

=>  32490/1000

=> 32.49 cubic centimeter.

Hence the volume of ball in cubic centimeter is 32.49 .

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It is used in situations where there are only two outcomes, such as heads or tails, success or failure, and so on. The normal approximation to the binomial is used when the sample size is large and the probability of success is not too close to 0 or 1.

As far as the random variable is concerned in this question, it satisfies the assumptions for the normal approximation to the binomial based on the results. The coin looks like it is fair based on the assumption that the null hypothesis is correct. The probability that a number of heads that large or larger occurs under the assumptions is approximately 0.321.

The standard deviation of the number of heads under the assumptions is approximately 15.811. The expected value of the number of heads under the assumptions is 500. Thus, these are the answer options to match with the given phrases. Let's elaborate on the normal approximation to the binomial.The normal approximation to the binomial is a statistical approximation used to compute binomial probabilities.

The normal distribution has a bell shape and is symmetrical about its center. When the sample size is large, the normal distribution approximates the binomial distribution. A sample size is considered large if np and nq are both greater than or equal to 10. When the sample size is small, the binomial distribution is used instead of the normal distribution.The binomial distribution can be used to determine the likelihood of a specific number of successes in a certain number of trials.

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Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

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Answer:

a rational number

Step-by-step explanation:

a rational number + a rational number will always be a rational number.

1. The straight-line solutions are of the form y = kx + c, where k and c are constants.

2. The general solution is f(x) = kx + c, where k and c can be any real numbers.

3. The behavior of solutions depends on the value of k: if k > 0, the solutions increase as x increases; if k < 0, the solutions decrease as x increases; and if k = 0, the solutions are horizontal lines. The equilibrium point at (0, 0) is classified as a stable equilibrium point.

a) To identify the straight-line solutions, we need to find the points on the graph where the slope is constant. This means the derivative of the function with respect to x is a constant. Let's assume our function is f(x).

So, we have f'(x) = k, where k is a constant.

By integrating both sides, we get f(x) = kx + c, where c is an arbitrary constant.

Therefore, the straight-line solutions are of the form y = kx + c, where k and c are constants.

b) The general solution can be written as f(x) = kx + c, where k and c can be any real numbers.

c) The behavior of solutions depends on the value of k.
- If k > 0, the solutions will be increasing lines as x increases.
- If k < 0, the solutions will be decreasing lines as x increases.
- If k = 0, the solutions will be horizontal lines.

The equilibrium point at (0, 0) is classified as a stable equilibrium point because any small disturbance will bring the system back to the equilibrium point.

In summary, the straight-line solutions are of the form y = kx + c, where k and c are constants. The behavior of solutions depends on the value of k, and the equilibrium point at (0, 0) is a stable equilibrium point.

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Answer:

7

Step-by-step explanation:

140 / 20 = 7

so, you need to ride 7 laps per day :)

Heyo! ;D

In order to solve this problem, we simply need to follow the rule of division.

140 ÷ 20 = 7

Hence, if your goal is to ride your bike 140 laps around your block over a 20 day period, you must ride your bike 7 total laps a day to do so.

Hope this helped! If so, please lmk! Tysm and good luck!

Answer:

The researchers considered the before and after design of the study. They concluded that since the P-value was greater than the significance level, they had to fail to reject the null hypothesis.

Step-by-step explanation

test says is correct

Answer:

\( \boxed{\bf A. \: x - 2}\)

Step-by-step explanation:

\( \sf ( x + 1)^2-9/ x + 4 \)

First, we need to factor the expressions that are not already factored.

Now, let's Cancel out x+4 in both numerator and denominator.

----------------------------

Answer:

165

Step-by-step explanation:

What this ratio means is that for every 2 white carnations, there is 1 blue and 3 red.

We have 60 white, or 30 groups of 2

We have 3 red carnations for each group of two:

3 * 30 = 90

And we have 1 blue for each group of two:

30 / 2 = 15

So, our total number of carnations would be 90 + 15 + 60

Or: 165

Answer:

2:1

Step-by-step explanation:

4 pineapples, 2 bananas

4:2

2:1 (If reduced)

Answer:

-10/9

Step-by-step explanation:

I made it so that 2/3 a -4/9 had the same denominator which turned 2/3 into 6/9

then I solved normally

Answer:

D

Step-by-step explanation:

Since KL = JL then the triangle is isosceles with base angles congruent, that is

∠ K = ∠ J = 8x + 5

The sum of the 3 angles in the triangle = 180°

sum the angles and equate to 180

8x + 5 + 8x + 5 + 5x - 19 = 180

21x - 9 = 180 ( add 9 to both sides )

21x = 189 ( divide both sides by 21 )

x = 9

Then

∠ J = 8x + 5 = 8(9) + 5 = 72 + 5 = 77°

The distribution is a discrete probability distribution because the sum equals 1.

To determine whether or not the distribution is a discrete probability distribution, we need to check if the probabilities sum up to 1 and if all the probabilities are non-negative for every possible value of X. Also, the values of X must be countable.

Here, the given table represents the probability distribution of a discrete random variable X. Therefore, it is a discrete probability distribution.

The sum of probabilities is:

P(X = −1) + P(X = 3) + P(X = 5) = 0.05 + 0.38 + 0.57 = 1

and all the probabilities are non-negative.

Therefore, the distribution is a discrete probability distribution.

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Lambert's initial investment of $20,000 gave him a 1/3 interest in the partnership. Bonus is distributed, it would be added to the partnership's capital.

Here's a step-by-step explanation:

1. Determine the total capital before Lambert's investment: The other partners have a combined capital of $34,000.

2. Calculate the capital after Lambert's investment: Lambert invests $20,000, so the new total capital becomes $34,000 + $20,000 = $54,000.

3. Determine the value of 1/3 interest: Since Lambert has a 1/3 interest in the partnership, we need to find 1/3 of the total capital after his investment. (1/3) * $54,000 = $18,000.

4. Calculate the bonus: The difference between Lambert's initial investment ($20,000) and his 1/3 interest ($18,000) is the bonus. $20,000 - $18,000 = $2,000.

5. Determine Lambert's capital after the bonus distribution: Since the bonus is distributed, we subtract the bonus from Lambert's initial investment. $20,000 - $2,000 = $18,000.

So, after the distribution of the bonus, Lambert's capital in the partnership is $18,000.

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