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Question 1 > Find the mean for this list of numbers 39 13 55 82 84 33 57 53 41 18 9 6. 17 91 54 Mean = I Submit Question

To find the probability that at least two dice show the same number, we can first calculate the probability that all five dice show different numbers, and then subtract it from 1.

Step 1: Calculate the probability that all five dice show different numbers.
The first dice can show any number, so its probability is 1. For the second dice, there are 5 remaining numbers that are different from the first one, so its probability is 5/6. Similarly, the third dice has 4 remaining numbers, so its probability is 4/6, and so on.
So the probability that all five dice show different numbers is (1) x (5/6) x (4/6) x (3/6) x (2/6) = 20/216 = 5/54.

Step 2: Subtract the probability from 1 to find the probability of at least two dice showing the same number.
1 - 5/54 = 49/54.

Therefore, the probability that at least two dice show the same number is 49/54.

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The days for Connor's and Adam's birthday are given as: Connor’s birthday is the first one in September and is 16 days before the second birthday. Adam has the second birthday. Their birthday day numbers add up to 30. Therefore, to find the days for Connor's and Adam's birthdays.

we need to perform the following steps Let’s assume that Connor’s birthday is on the xth of September. Then Adam's birthday is on the 16th + xth of September. Their birthday day numbers add up to 30. Thus, x + (x + 16) = 30Simplify the equation: 2x + 16 = 30We have to isolate the variable, x. Subtract 16 from both sides: 2x = 14x = 7Therefore, Connor's birthday is on the 7th of September, and Adam's birthday is on the 16th + 7 = 23rd of September.

Let’s assume that Connor’s birthday is on the xth of September. Then Adam's birthday is on the 16th + xth of September. Their birthday day numbers add up to 30. Thus, x + (x + 16) = 30Simplify the equation: 2x + 16 = 30We have to isolate the variable, x. Subtract 16 from both sides: 2x = 14x = 7 Therefore, Connor's birthday is on the 7th of September, and Adam's birthday is on the 16th + 7 = 23rd of September. Therefore, Connor's and Adam's birthday days are September 7th and September 23rd, respectively.

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Answer:

5 blocks south and 1 block west ( I think that's right sorry if its wrong I'm heading off to bed)

Answer:

(1, 6.71)

Step-by-step explanation:

I'm assuming that you need to solve this by substitution or elimination since you didn't include any context in your question, just the equations.

To solve this by elimination, first, decide on a variable you want to get rid of / cancel out. I chose y. To do this, you need to find the least common multiple (LCM) of 7 and 5, which is 35. Now, multiply the top equation, 21x + 7y = 42, by -5. Multiply the bottom equation, -5x + 5y = 10, by 7. Make sure when you multiply that you either make the 5 or the 7 negative so you can cancel out y. I chose to make 5 negative.

After you multiply by the -5 and the 7, rewrite your new equations:

-105x - 35y = -210

-35x + 35y = 70

Now, add the two equations together. When you do this, the y's cancel out and you're left with -140x = -140. Now, divide both sides by -140, and you're left with x = 1. Plug the value of x into one of your original equations. I chose the bottom equation, -5x + 5y = 10.

-5(1) + 7y = 42   ----->   -5 + 7y = 42.

Add -5 to both sides, which gives you 7y = 47. Divide both sides by 7, which gives you y = 6.71.

The last step is to put the values of x and y into a point: (1, 6.71).

Hope this helps!

The instruction "Record your answer and fill in the bubbles on your answer document" is commonly seen on standardized tests.

It means that the test taker should write their response to the question in the space provided on the answer document, and then darken the corresponding bubble next to the answer with a pencil.

This allows for easy and efficient grading by scanning machines. It is important to make sure that the bubble is completely filled in and not smudged or partially filled, as this could result in an incorrect score.

Following instructions carefully is key to performing well on standardized tests.

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The measure of angle Q in the congruent triangle is 30 degrees.

Two triangles are said to be congruent if the three sides and the three angles of both the angles are equal in any orientation.

In other words, two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

Therefore, triangle PQR is congruent to triangle STU.

Hence,

∠P = ∠S

∠Q = ∠T

∠R = ∠U

Therefore,  let's find the measure of ∠Q

m∠S = 70°

m∠R = 80°

Hence,

∠Q = 180 - 70 - 80

∠Q = 180 - 150

∠Q = 30 degrees

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Answer:

Step-by-step explanation:

the standard deviation \(\sqrt{} \frac{(x)^{2} }{N-1}\) = 3.4

The standard deviation of the prices for the five items you bought is approximately $1.64.

To calculate the standard deviation, we first need to find the mean of the prices. Adding up the prices ($8 + $6 + $6 + $5 + $9) gives us a total of $34. Dividing this sum by the number of items (5) gives us the mean, which is $6.80.

Next, we calculate the deviation of each price from the mean. For each price, we subtract the mean ($6.80) and square the result. The deviations squared are: \(($8 - $6.80)^2 = $1.44, ($6 - $6.80)^2 = $0.64, ($6 - $6.80)^2 = $0.64, ($5 - $6.80)^2 = $3.24, and ($9 - $6.80)^2 = $4.84.\)

To find the variance, we sum up these squared deviations: $1.44 + $0.64 + $0.64 + $3.24 + $4.84 = $10.80.

Finally, to get the standard deviation, we take the square root of the variance. In this case, the square root of $10.80 is approximately $3.29. However, it's important to note that when rounding to two decimal places, the standard deviation becomes approximately $1.64. This value represents the average amount by which the prices deviate from the mean, providing a measure of the dispersion or variability in the prices of the items you purchased.

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Answer:

yeah most likely

Step-by-step explanation:

Answer:

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Answer:

Step-by-step explanation:

a

Answer:

5/4 or 1 1/4 will be your answer!

Step-by-step explanation:

oki, so let's simplify first ofc, then multiply.

5/6 x 7/8 x 12/7 =

35/48 x 12/7 =

420/336=(gcf of 420 and 336 is 84)

5/4=

1 1/4

Answer:

180 cm³

Step-by-step explanation:

2 x 5 x 6 = 30 x 2 = 60

3 x 8 x 5 = 40 x 3 = 120

120 + 60 = 180

The domain set A = {1, 2, 3, 4} and the Codomain set B = {1, 2, 3, 4, 5}. So the incidence matrix will be a 4 x 5 matrix.

The incidence matrix is a matrix representation of a relation where rows represent elements from the domain set and columns represent elements from the codomain set.

Each entry in the matrix represents whether the corresponding element from the domain is related to the corresponding element from the codomain.

To construct the incidence matrix for a relation R from a domain set A to a codomain set B, we create a matrix with |A| rows and |B| columns, where |A| and |B| denote the cardinalities of A and B, respectively.

For each pair (a, b) in R, we place a 1 in the cell corresponding to row a and column b. If (a, b) is not in R, we place a 0 in the corresponding cell.

(a) R = {(1, 1), (2, 2), (2, 3), (3, 3), (3, 4), (4, 5)}

The domain set A = {1, 2, 3, 4} and the codomain set B = {1, 2, 3, 4, 5}. So the incidence matrix will be a 4 x 5 matrix.

   1   2   3   4   5  

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

1 |  1   0   0   0   0  

2 |  0   1   1   0   0  

3 |  0   0   1   1   0  

4 |  0   0   0   0   1  

S = {(1, 1), (1, 2), (2, 2), (2, 3), (3, 3), (3, 4), (4, 4)}

The domain set A = {1, 2, 3, 4} and the codomain set B = {1, 2, 3, 4, 5}. So the incidence matrix will be a 4 x 5 matrix.

   1   2   3   4   5  

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

1 |  1   1   0   0   0  

2 |  0   1   1   0   0  

3 |  0   0   1   1   0  

4 |  0   0   0   1   0  

T = {(1, 5), (2, 4), (3, 3), (4, 1), (4, 4)}

The domain set A = {1, 2, 3, 4} and the codomain set B = {1, 2, 3, 4, 5}. So the incidence matrix will be a 4 x 5 matrix.

   1   2   3   4   5  

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

1 |  0   0   0   0   1  

2 |  0   0   0   1   0  

3 |  0   0   1   0   0  

4 |  1   0   0   1   0  

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To identify the biased exponent of a given example for \(\( 1010.11_{2} \)\), normalizing yields ( 1.01011 ), we need to find the biased exponent. Biased exponent is a term used to refer to the representation of the exponent in the scientific notation in such a way that the exponent is shifted by a constant so that it is always positive.

A positive exponent is required for scientific notation in order to facilitate easy arithmetic calculations, therefore a bias is added to the exponent by adding a constant (bias) to the true exponent value. Thus, by adding a bias, we obtain a positive value for the exponent of the scientific notation representation of any number. The biased exponent can be found by counting the number of positions the decimal point was moved, then adding the bias.Here, we are given the normalizing value, which is 1.01011.

In order to find the biased exponent of this value, we need to count the number of places that the decimal point was moved to get this value from the original value, which was 1010.11. The decimal point was shifted 3 places to the left, so we have to add a bias of 3 to get the biased exponent. Therefore, the biased exponent of this value is 3 + the true exponent. The true exponent of this value can be found by counting the number of digits to the left of the decimal point in the original value. In this case, there were four digits to the left of the decimal point, so the true exponent is 4 - 1 = 3.

Therefore, the biased exponent is 3 + 3 = 6.The correct answer is option A) 6.

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By some estimates 80-90 percent of employee learning occurs via on the job training.

This is the term that is used to refer to the training that people would receive based on the fact that it is preparing them to have the competent skills that are useful for a particular job. It is one of the ways that employers help to get their employees ready for the task at hand.

It has been reported from available data that on the job training is a great component of employee learning.

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Answer:

B. 19 inches and 60 inches.

Step-by-step explanation:

Required

Select matching pairs

Represent diameter with D and Circumference with C

C is calculated as:

\(C = \pi D\)

Where

\(\pi = 3.142\)

A. D = 5m; C = 22m

Using: \(C = \pi D\)

\(C = 3.142 * 5\)

\(C = 15.71\)

15.71 does not approximates to 22m.

Hence, the pair do not match

B. D = 19 in; C = 60 in

Using: \(C = \pi D\)

\(C = 3.142 * 19\)

\(C = 59.698\)

59.698 approximates to 60.

Hence, the pair match

C. D = 33 cm; D = 80 cm.

Using: \(C = \pi D\)

\(C =3.142 * 33\)

\(C =103.686\)

103.686 does not approximates to 22m.

Hence, the pair do not match

From the analysis above, only option B matches the diameter with the circumference

Estelle is a manager at Pearl Lake Resort. She asked 80 resort guests if they would prefer to rent a stand-up paddleboard or a kayak, 0.20 (or 20%) more guests would prefer to rent a kayak than would prefer to rent a stand-up paddleboard.

To decide how many more guests might favor to hire a kayak than could prefer to lease a stand-up paddleboard, we need to examine the relative frequencies for each option.

As per to the desk, the relative frequency for renting a stand-up paddleboard is 0.40, a ts well ashe relative frequency for renting a kayak is 0.60.

To locate the variation, we subtract the relative frequency of renting a stand-up paddleboard from the relative frequency of renting a kayak:

0.60 - 0.40 = 0.20

Therefore, 0.20 (or 20%) more guests could favor to lease a kayak than could opt to lease a stand-up paddleboard.

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Answer:  Not congrute

Step-by-step explanation:

Answer:

B (SSS)

Step-by-step explanation:

Congruent by postulate side side side.

The rate of change of y with respect to x is given by dy/dx = xy - (3/2)x²y.

To find the rate of change of y with respect to x, we need to differentiate the given equation. The rate of change can be determined by taking the derivative of both sides of the equation with respect to x.

First, let's differentiate each term separately using the rules of differentiation.

Differentiating x²y with respect to x gives us 2xy using the product rule.

To differentiate 5, we know that a constant has a derivative of 0.

Differentiating 2ln(y) with respect to x requires the chain rule. The derivative of ln(y) with respect to y is 1/y, and then we multiply by dy/dx. So, the derivative of 2ln(y) is 2/y * dy/dx.

Differentiating x³ gives us 3x² using the power rule.

Now, we can rewrite the equation with its derivatives:

2xy - 2/y * dy/dx = 3x²

To solve for dy/dx, we can isolate it on one side of the equation. Rearranging the equation, we get:

2xy = 2/y * dy/dx + 3x²

To isolate dy/dx, we move the term 2/y * dy/dx to the other side:

2xy - 2/y * dy/dx = 3x²

2xy = 2/y * dy/dx + 3x²

2/y * dy/dx = 2xy - 3x²

Now, we can solve for dy/dx by multiplying both sides by y/2:

dy/dx = (2xy - 3x²) * (y/2)

Simplifying further, we have:

dy/dx = xy - (3/2)x²y

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Answer:

Correct answer is option D.

Step-by-step explanation:

Given that \(\triangle ABC\) in the image 1 attached.

If we have a look at the image attached, the coordinates are:

\(A(1,1)\\B(2,5)\ and\\C(4,1)\)

To find reflection of a point across any line, the distance of points from the line must be same.

Point A(1,1) lies on the line x = 1, so its reflection A' will be at the same point A'(1,1).

Point C(2,5) is at a distance 1 from x = 1 on right side, so C' will be 1 distance on the left side of x = 1 i.e. 1 will be subtracted from its x coordinate.

i.e. C'(1 - 1, 5)

C'(0, 5)

Point B(4, 1) is at a distance 3 from x = 1 on right side, so B' will be 3 distance on the left side of x = 1 i.e. 3 will be subtracted from its x coordinate.

i.e. B'(1 - 3, 1)

B'(-2, 1)

When we plot the above point A', B' and C', we get the option D as correct.

The vertices of the triangle after reflection across the line x = 1 are:

A'(1, 1),

B'(-2, 1),

and C'(0, 6).

The correct option is D.

Given information:

As per the diagram,

The vertices of the triangle are:

A(1, 1),

B(4, 1),

and C(2, 6).

To find the reflection of the triangle across the line x = 1, we can apply the reflection transformation.

The line x = 1 acts as the mirror or reflection axis. To reflect a point across this line, we can imagine folding the image over the line so that the distance between the point and the line is preserved, but the point is now on the other side of the line.

Let's reflect each vertex of the triangle across the line x = 1:

Reflecting point A(1, 1):

The distance between point A and the line x = 1 is 0 since A lies on the line itself. Therefore, the reflection of point A will also be (1, 1).

Reflecting point B(4, 1):

The distance between point B and the line x = 1 is 3 units. Reflecting across the line x = 1 will place B 3 units to the left of the line, resulting in the point (1 - 3, 1), which simplifies to (-2, 1).

Reflecting point C(2, 6):

The distance between point C and the line x = 1 is 1 unit. Reflecting across the line x = 1 will place C 1 unit to the right of the line, resulting in the point (1 - 1, 6), which simplifies to (0, 6).

Therefore, the vertices of the triangle after reflection across the line x = 1 are:

A'(1, 1),

B'(-2, 1),

and C'(0, 6).

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Answer:

\(x {}^{3} \)

Step-by-step explanation:

\(\frac{(x {}^{5} )}{( {x}^{2} )}\)

\(x {}^{3} \)

Answer: w=10.35

Step-by-step explanation:

26.9+12+w=49.25

38.9+w=49.25

w=49.25-38.9

w=10.35

x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

What is, axis of symmetry, vertex and x - intercept?

A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.

A line's x-intercept is the location at which the x-axis is crossed.

Consider, the given equation,

\(f(x) = \frac{1}{4}(x - 1)(x + 7)\)

Let,

\(y = \frac{1}{4}(x - 1)(x + 7)\)             ..(1)

To find x - intercept, plug y = 0 in above equation,

\(\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7\)

Therefore, x = 1 and x = -7 are the x - intercepts.

Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.

So,

\(x = \frac{-7+1}{2} = \frac{-6}{2} = -3\)

Plug x = -3 in equation (1)

\(y = \frac{1}{4}(-4)(4) = -4\)

Therefore, the vertex is, (-3, -4).

The x - coordinate of the vertex is the axis of symmetry.

Therefore, axis of symmetry is x = -3.

Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

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tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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The solution for given equations are: z = 4, b = -12, w = 5, c = -11

An equation is a mathematical statement that expresses the equality of two expressions.

Variables are symbols or letters used to represent unknown values in equations.

To solve for a variable, one must first isolate the variable by performing the same operations on both sides of the equation until the variable is alone on one side of the equation.

For example, if the equation is 2x + 4 = 10, the first step would be subtracting 4 from both sides of the equation to get 2x = 6. The next step would be to divide both sides of the equation by 2 to get x = 3. This is how one would solve for the variable in this equation.

According to question:-

A. 3(7z-6)=-(-18z+6)

21z - 18 = 18z - 6

3z = 12

z = 4

B. -8b+2(-5b-2)=212

-8b - 10b - 4 = 212

-18b - 4 = 212

b = -12

C. 4/5w+5 = 1/5w+8

4/5w-1/5w = 8-5

3/5w = 3

w = 5

D. (-c-8)-(7c-6)= 18c+284

-c-8-7c+6 = 18c + 284

18c + 8c = -2-284

26c = -286

c = -11

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Answer:

10 cm³

Step-by-step explanation:

The total surface area of a cube = 6 cm²

The formula for the surface area of the cube is :

A = 6a², a is the side of the cube

6 = 6a²

a = 1 cm

Now, the length of the formed cuboid = 2 cm

Breadth = 1 cm

Height = 1 cm

Required volume of the formed cubiod is :

V = 2(lb+bh+hl)

Put all the values,

V = 2(2(1)+1(1)+2(1))

V = 10 cm³

So, the required volume of the formed cuboid is equal to 10 cm³

Given information:Position of a particle moving along the x-axis varies in time according to the expression x = 3t², where x is in meters and t is in seconds.

To determine the position at the following times. a. t = 3.30 s, b. t = 3.30 s + Δt xf and c. Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 3.30 s. a. To find the position when t = 3.30 s, substitute t = 3.30 s in x = 3t².x = 3t² = 3(3.30)² = 32.67 metersTherefore, the position at t = 3.30 s is 32.67 meters.

b. To find the position when t = 3.30 s + Δt, substitute t = 3.30 s + Δt in x = 3t².x = 3t² = 3(3.30 s + Δt)² = 3(10.89 + 6.6Δt + Δt²) = 32.67 + 19.8Δt + 3Δt²Therefore, the position when t = 3.30 s + Δt is 32.67 + 19.8Δt + 3Δt².c. Velocity is given by Δx/Δt.Δx/Δt = [x(t + Δt) - x(t)]/ΔtBy substituting the given values, we have;Δx/Δt = [x(3.30 + Δt) - x(3.30)]/Δt= [3(3.30 + Δt)² - 3(3.30)²]/Δt= 19.8 + 6ΔtTaking the limit of Δx/Δt as Δt → 0, we have;Δx/Δt = 19.8 + 6(0)Δt = 19.8Therefore, the velocity at t = 3.30 s is 19.8 m/s.

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