A bag contains 15 marbles. The probability of randomly selecting a green marble is 1/5. The probability of randomly
selecting a green marble, replacing it, and then randomly selecting a blue marble is 2/25. How many blue marbles are
in the bag?
02
3
05
06

The length of the legs of the right triangle are 2.83 units.

A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the legs of the triangle can be found using trigonometric ratios.

Hence,

sin 45 = opposite / hypotenuse

sin 45 = a / 4

cross multiply

a = 4 × 0.70710678118

a = 2.83 units

Therefore,

cos 45 = b / 4

cross multiply

b = 0.70710678118 × 4

b = 2.82842712475

b = 2.83 units

Therefore, the legs are 2,83 units

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Answer:

Options (1), (2), (3)

Step-by-step explanation:

Let the equation of the line is,

y = mx + b

Here m = slope of the line

b = y-intercept

Given line on the graph is passing through two points (-3, 0) and (0, 1).

Slope of this line will be,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

   = \(\frac{1-0}{0+3}\)

   = \(\frac{1}{3}\)

y-intercept of the line 'b' = 1

Equation of the line will be,

y = \(\frac{1}{3}x+1\)

If the points given in the options satisfy the equation, they will be the solution of the line.

Option (1),

For (3, 2),

2 = \(\frac{3}{3}+1\)

2 = 2

True.

(3, 2) is the solution.

Option (2)

For (21, 8),

8 = \(\frac{21}{3}+1\)

8 = 8

True.

(21, 8) is the solution.

Option(3)

For (-15, -4),

-4 = \(\frac{-15}{3}+1\)

-4 = -4

True.

(-15, -4) is the solution.

Option (4)

For (12, 9)

9 = \(\frac{12}{3}+1\)

9 = 5

False

(12, 9) is not the solution.

Option (5)

For (-6, 1)

1 = \(\frac{-6}{3}+1\)

1 = -1

False

(-6, 1) is not the solution.

Therefore, Options (1), (2), (3) are the solutions.

Step-by-step explanation:

(20). FH= 22-15 = 7

(21). FH = 42 - 22 = 20

(22). FH = 53 - 40 = 13

Answer:

the temperature at 11:30 plus 30 minutes (i.e., 11:30 plus half an hour) will be the same as the temperature at 11:30, which is 2°C.

a. The sample mean is 3 and the sample standard deviation is approximately 1.53.

b. The estimated standard error for the sample mean is 0.765.

a. The sample mean is:

mean = (2 + 2 + 6 + 2)/4 = 3

The sample standard deviation can be calculated using the formula:

s = √(sum((xi - mean)²)/(n - 1))

where xi represents each score in the sample. Plugging in the values, we get:

s = √((2-3)² + (2-3)² + (6-3)² + (2-3)²)/3

s = √(14/3)

s ≈ 1.53

So, the sample mean is 3 and the sample standard deviation is approximately 1.53.

b. The estimated standard error for the sample mean can be calculated using the formula:

SE = s/√(n)

where s is the sample standard deviation and n is the sample size. Plugging in the values, we get:

SE = 1.53/√4)

SE = 0.765

So, the estimated standard error for the sample mean is 0.765.

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The statement is true that 95% of all possible sample means will fall above 76.71.

We know that the sample mean can be calculated using the formula;

\($\bar{X}=\frac{\sum X}{n}$\).

Given that the mean is 80 and the variance is 400 for the population and the sample size is 100. The standard deviation of the population is given by the formula;

σ = √400

= 20.

The standard error of the mean can be calculated using the formula;

SE = σ/√n

= 20/10

= 2

Substituting the values in the formula to get the sampling distribution of the mean;

\($Z=\frac{\bar{X}-\mu}{SE}$\)

where \($\bar{X}$\) is the sample mean, μ is the population mean, and SE is the standard error of the mean.

The sampling distribution of the mean will have the mean equal to the population mean and standard deviation equal to the standard error of the mean.

Therefore,

\(Z=\frac{76.71-80}{2}\\=-1.645$.\)

The probability of the Z-value being less than -1.645 is 0.05. Since the Z-value is less than 0.05, we can conclude that 95% of all possible sample means will fall above 76.71.

Conclusion: Therefore, the statement is true that 95% of all possible sample means will fall above 76.71.

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Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Supporting Question and Answer:

How can we express a vector as a linear combination of  vectors using a system of equations?

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

   2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

  2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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Answer:

B. x = -8

Step-by-step explanation:

-4(2x + 3) = 2x + 6 - (8x + 2)

-8x -12 = 2x + 6 - 8x -2

(now, "-8" in both terms is cancelled):

-12 = 2x + 6 - 2

(leave 2x alone in second term):

-12 -6 +2 = 2x

-16 = 2x

-16/2 = x

-8 = x

The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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The critical value of z for each hypothesis  test is 2.326

In this question, we are asked to use Excel to find the critical value of z for each hypothesis test. We are given a 2 percent level of significance for a two-tailed test. To find the critical value, we can use the NORM.S.INV function in Excel. The syntax for this function is =NORM.S.INV(probability).

We can enter the probability as 1 - (alpha / 2) for a two-tailed test, where alpha is the level of significance. We can then round the result to three decimal places.

To find the critical value for a 2 percent level of significance, two-tailed test, we can follow these steps:

Step 1: Calculate the value of alpha

Alpha = 2% = 0.02

Step 2: Calculate

1 - (alpha / 2)1 - (alpha / 2)

= 1 - (0.02 / 2)

= 0.99

Step 3: Use the NORM.S.INV function in Excel=NORM.S.INV(0.99)

This gives us a critical value of z = 2.326.

Therefore, the critical value of z for the hypothesis test with a 2 percent level of significance and a two-tailed test is 2.326.

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The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.

(a) The given units can be converted as follows: 6 glints = 1 filn...

(1)12 grees = 1 zool...

(2)2 grees = 10 twibbs...

(3)5 grees = 1 bic...

(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:

7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord

(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.

1 mega = 106

Thus 1 megafiln = 106 filn

16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.

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The value of γ is greater than 1 for any v > 0, greater than 10 for v > 0.995c, and greater than 100 for v > 0.99995c.

To determine for what speed (in terms of c) the value of γ is greater than 1, 10, and 100, we'll use the formula for the Lorentz factor (γ):
γ = 1 / √(1 - v²/c²)
where v is the speed and
c is the speed of light.

(a) For γ > 1:
Since γ is always greater than 1 for any speed v greater than 0, we can say that γ is appreciably greater than 1 for any v > 0.

(b) For γ > 10:
We need to solve the equation 10 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 100 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/100 = 99/100.
So, v/c = √(99/100), which implies v > 0.995c for γ > 10.

(c) For γ > 100:
Similar to (b), solve the equation 100 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 10000 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/10000 = 9999/10000.
So, v/c = √(9999/10000), which implies v > 0.99995c for γ > 100.

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a. Rate of change for linear function A would be 3/4

b. Rate of change for linear function B would be 4.

c. linear function B has a greater rate of change than linear function A.

What is the linear function?

A linear function is a function that can be written in the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line represents the rate of change of y with respect to x.

Using this definition, we can identify that linear function A is in the form of y = (3/4)x + 2. This means that the slope of the line is 3/4, which represents the rate of change of y with respect to x.

For linear function B, we can calculate the rate of change by finding the slope of the line that passes through the given points (-2,-10) and (3,10). We can use the formula for slope, which is (y2 - y1)/(x2 - x1), to get:

slope = (10 - (-10))/(3 - (-2)) = 20/5 = 4

The rate of change for linear function B is 4.

Comparing the rates of change, we can see that linear function A has a rate of change of 3/4, while linear function B has a rate of change of 4. This means that linear function B has a greater rate of change than linear function A.

Hence,

a. Rate of change for linear function A would be 3/4

b. Rate of change for linear function B would be 4.

c. linear function B has a greater rate of change than linear function A.

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The minimum amount of cloth carl needs to cover the entire box will be 188 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called the surface area.

Given that:-

The minimum amount of cloth carl needs to cover the entire box will be the surface area of the prism

Surface area = 2 [ (5 x 2)+ (12 x 5) + (12 x 2)]  

Surface area= 188 square inches

Therefore the minimum amount of cloth carl needs to cover the entire box will be 188 square inches.

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Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

:) Have a good day!

Answer:

C

Step-by-step explanation:

a mixed fraction consists of a whole number and a proper fraction

a

\(\frac{29}{15}\) = 1 \(\frac{14}{15}\) ← a mixed number

b

\(\frac{35}{12}\) = 2 \(\frac{11}{12}\) ← a mixed number

c

\(\frac{12}{13}\) ← cannot be expressed as a mixed number

Answer:

THX santa

Step-by-step explanation:

The quotient of (2x^4 + 5x^3 - 2x - 8) divided by (x + 3) is 2x^3 - x^2 + 3x - 7, and the remainder is 13.

To find the quotient and remainder, we can use polynomial long division.

First, we divide the leading term of the numerator, 2x^4, by the leading term of the denominator, x. This gives us 2x^3.

Next, we multiply the denominator, x + 3, by the quotient term we just found, 2x^3. We subtract this product, which is 2x^4 + 6x^3, from the numerator.

We then repeat the process with the new numerator, which is now -x^3 - 2x - 8.

Dividing the leading term of the new numerator, -x^3, by the leading term of the denominator, x, gives us -x^2.

We continue this process until the degree of the numerator is less than the degree of the denominator.

After finding the quotient, 2x^3 - x^2 + 3x - 7, and the remainder, 13, we can conclude our division.

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Answer:

the answer is -7

Step-by-step explanation:

hope this helps

Answer:

-7

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

you're trying to put the variable(y) by itself. it would be divided by 14 on both sides, which 7/14 is 1/2

The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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By identifying the maximum value (75) and the minimum value (59) in the data set, we can determine the range, which is 16 inches .

The range of a data set measures the spread or variability of the data. It is calculated by subtracting the minimum value from the maximum value. In this case, the minimum value is 59 (the shortest height) and the maximum value is 75 (the tallest height) in the given data set.

Range = Maximum value - Minimum value

Substituting the values, we have:

Range = 75 - 59 = 16

Therefore, the range of the given data set is 16. This means that the heights of the students in the high school class range from a minimum of 59 inches to a maximum of 75 inches, with a difference of 16 inches between them.

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Waiting time representing 8th percentile = 299.09 days.

Find values on the left of the mean in this negative Z score table. Table entries for z represent the area under the bell curve to the left of z.

Negative scores in the z-table correspond to the values which are less than the mean.

Let X be the random variable representing the waiting time.

Here the mean(\mu) = 203 days

Standard deviation (\sigma) = 25.7 days

For calculating the 8th percentile, we need to find the z- score having an area of 0.08.

By the Z-score table, we have Z= -3.7

Now, Using the formula X=Z\sigma +\mu

X = (-3.7)*(25.7)+204

X = 299.09 days

Therefore, Waiting time representing the 8th percentile = 299.09 days.

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Answer:

Quadrant II

Step-by-step explanation:

This is because the top right is I, the top left

is II, the bottom left is III, and the bottom right is IV.

The average speed at which the canoe traveled toward the lighthouse is approximately 17.2 feet per minute.

A is the front of the canoe

B is the position of the observer in the lighthouse

AB is the distance between the front of the canoe and the observer

θ1 is the angle of depression at 5:00

θ2 is the angle of depression at 5:05

h is the height of the front of the canoe above the water (1.3 feet)

We want to find the speed at which the canoe is traveling toward the lighthouse, which we'll call x feet per minute.

Using trigonometry, we can find the following relationships:

tan(θ1) = h / AB          (1)

tan(θ2) = h / (AB + 5x)   (2)

We can rearrange equation (1) to solve for AB:

AB = h / tan(θ1)          (3)

Substituting equation (3) into equation (2), we get:

tan(θ2) = h / (h / tan(θ1) + 5x)

tan(θ2) = tan(θ1) / (1 + 5x * tan(θ1) / h)   (4)

We can solve equation (4) for x:

x = (tan(θ1) / (tan(θ2) - tan(θ1))) * h / 5   (5)

Now we just need to plug in the values we know:

θ1 = 6.5°

θ2 = 48.7° (since θ2 = θ1 + 42.2°)

h = 1.3 feet

Plugging these into equation (5), we get:

x = (tan(6.5°) / (tan(48.7°) - tan(6.5°))) * 1.3 / 5

x ≈ 17.2 ft/min

Therefore, the average speed at which the canoe traveled toward the lighthouse is approximately 17.2 feet per minute.

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Answer:

Step-by-step explanation:

i)14π/9

ii)91π/18

iii)77π/9

iv)140⁰

Answer:

b = -23/5

Explanation:

Given the equation

Subtract 8/5 from both sides

No, the presence of an effect does not necessarily imply that error variance will go away.

The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.

Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.

It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.

One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.

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