a committee of 5 members is to be selected from 6 seniors and 4 juniors. fine the number of ways in which this can be done if the committee has at least 1 junior.
a.252
b.6
c.246
d.120

The diver reaches a height of 72 feet after 1.5 seconds.

Given that, a diver leaps off of cliff, modeled by the equation,

y = -16x²- 8x +120.

We need to time taken by the diver to reach a height of 72 ft.

72 = -16x²- 8x + 120.

-16x²- 8x + 48 = 0

2x² + x - 6 = 0

Factorizing,

2x² + 4x -3x - 6 = 0

2x(x+2) -3(x+2) = 0

(2x-3)(x+2) = 0

x = -2, x = 1.5

Since, time cannot be negative so neglecting x = -2

Hence, the diver reaches a height of 72 feet after 1.5 seconds.

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Concentric circles are coplanar circles that have the same A. center.

Concentric circles, a set of coplanar circles sharing the same center point, derive their name from the Latin word "concentricus," which translates to "having a common center."

Varied radii differentiate each concentric circle. If one circle has a smaller radius than another's, it is considered nested inside or simply, inside. Radius denotes the distance between the center point and edge of the circle perimeter.

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Options for this question include:

A. Center

B. Diameter

C. Circumference

D. Radius

476 and 1/12, In summary, the answer to 43 and 5/12's times 11 is 5713/12 or 476 and 1/12.

To solve this problem, we need to convert the mixed number 43 and 5/12 into an improper fraction. We can do this by multiplying the whole number (43) by the denominator of the fraction (12), and adding the numerator (5) to get the total number of twelfths:

43 x 12 + 5 = 521/12

Now, we can multiply this fraction by 11:

521/12 x 11 = 5713/12

To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1:

5713/12

This is the final answer. However, if we want to express it as a mixed number, we can divide 5713 by 12 to get the whole number part (476) and the remainder

(1). Therefore, the final answer can also be written as:

476 and 1/12

In summary, the answer to 43 and 5/12's times 11 is 5713/12 or 476 and 1/12.

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Answer:

C. When they're done, José always fills the gas tank.

Using proportions, it is found that 8 more seventh graders are involved in the yearbook.

What is a proportion?

A proportion is a fraction of a total amount.

Researching the problem on the internet, it is found that 10% of the 6th graders and 18% of the 7th graders are on the yearbook, hence:

0.1 x 280 = 28 6th graders.

0.18 x 200 = 36 7th graders.

36 - 28 = 8

8 more seventh graders are involved in the yearbook.

The value of x is 116°

Given that a circle, with two congruent chords, FG and DE we need to find the central angle x,

Here we will use the properties of circle,

Since, the chords are equal, so, the measure of the arc intercepted by them will be equal,

arc DE = arc FG = 116°

Also, we know that the central angle is equal to the measure of the arc intercepted by it,

Therefore, x = m arc DE

x = 116°

Hence, the value of x is 116°

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The statement "A single, extremely large value can affect the median more than the mean" is True.

The median is the middle value when the data is arranged in ascending or descending order, and it is less affected by extreme values because it only considers the position of the value, not its actual magnitude.

On the other hand, the mean (average) takes into account the values themselves and can be heavily influenced by outliers. An extremely high or extremely low data value is called an outlier.

Outliers can skew the mean, pulling it towards their extreme value, while the median remains relatively unaffected. So the statement is True.

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Answer: I got you fam

Step-by-step explanation:

Y=-3x+10 is NEITHER

Y-5=-1/3(x+2) is perpendicular to P

Y=1;3x is NEITHER

-3+y=1 is parallel to P

Any value of b within this range would satisfy the original expression "23 > b ≥ -276".

The given expression is "23 > b ≥ -276". This means that b can take any value between -276 and 23, inclusive of -276 but not inclusive of 23.

To understand why this is the case, we can break down the expression into two parts: "23 > b" and "b ≥ -276".

The first part, "23 > b", means that b is less than 23. In other words, b can take any value that is less than 23. For example, b could be 22, 10, or even -100, as long as it is less than 23.

The second part, "b ≥ -276", means that b is greater than or equal to -276. This means that b can take any value that is greater than or equal to -276. For example, b could be -276, -200, or even 0, as long as it is greater than or equal to -276.

Putting these two parts together, we can see that b can take any value that is both less than 23 and greater than or equal to -276. This range of values for b is inclusive of -276 but not inclusive of 23, meaning that b cannot equal 23.

In numerical form, we can write the range of values for b as:

-276 ≤ b < 23

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For the depth function of submarine in water is, d = 500t - 4,500, where t is the time (in minutes), the intercepts say x-intercept and y-intercept values are -4500 and 9 respectively.

The x-intercept is the point where a line cross or meet the x-axis, and the y-intercept is the point where a line cross or meet the y-axis. For y-intercept we are setting x to zero and for x-intercept we are setting y = 0 and determining their corresponding values. We have a submarine is exploring the ocean floor and begins to ascend to the surface.

The depth of submarine in the water can be modeled by equation, d = 500t - 4,500, where t is the time (in minutes). We have to determine the x and y intercept values. As we know, equation of line in slope intercept form is y = mx + b

where, b--> y-intercept

m --> slope

In this case b = - 4500, m = 500

So, y-intercept= -4500 for t = 0. Now, for x-intercept that for t value, plug d = 0, 0 = 500t - 4500

=> 500 t = 4500

=> t = 9

So, x-intercept = 9

Hence, required value is 9.

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Complete question:

A submarine is exploring the ocean floor and begins to ascend to the surface. The depth of the submarine in the water can be modeled by the function `d=500t-4,500` where t is the time (in minutes) since the submarine began to ascend. Find the intercepts of the graph of the equation:

x-intercept:

y-intercept:

Goran's swimming speed in still water is 5 km/h.

We have,

Let's call Goran's swimming speed in still water s.

When Goran is swimming against the current, his effective speed (relative to the ground) is:

= s - 3 km/h

(since the current is flowing against him),

And when he is swimming with the current, his effective speed is:

= s + 3 km/h.

The time it takes Goran to swim 2 kilometers against the current is the same as the time it takes him to swim 8 kilometers with the current.

Using the formula,

Time = distance/speed,

2 / (s - 3) = 8 / (s + 3)

Solve for s

2(s + 3) = 8(s - 3)

2s + 6 = 8s - 24

6s = 30

s = 5

Therefore,

Goran's swimming speed in still water is 5 km/h.

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The transformation that would result in a similar shape to XYZ but one that is not congruent is D. a dilation centered at the origin with a scale factor of​ x.

When a triangle undergoes dilation, there is an alteration to its size while still conserving its shape. In scenarios where the scale factor of the triangular dilation happens to exceed 1, it leads to a bigger triangle than the original.

However, if this factor falls below 1, then the resulting triangle will be smaller compared to its original. The similarity between these triangles exists because they harbour identical shapes, but their incongruency emerges from their diverse magnitudes post-dilation.

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Options for this question are:

A. a translation 3 units to the right

B. a reflection across the line y = - 2x + 3

C. a rotation 90° clockwise around the origin

D. a dilation centered at the origin with a scale factor of​ x.

a)  A is not diagonal because it is not possible to find a matrix P such that A = PDP^-1, where D is a diagonal matrix.

b) A is not diagonalizable.

(a) A is diagonalizable but not diagonal: One possible example of such a matrix A would be:

A = [[1, 1], [0, 5]]

The characteristic polynomial of A is det(A –λ I) = (1 - λ)2(5 –λ), as given. The eigenvalues of A are λ1 = 1 and λ2 = 5, both of which have algebraic multiplicity 2. The eigenvectors corresponding to λ1 = 1 are [1, 0] and [1, 1], while the eigenvector corresponding to λ2 = 5 is [0, 1]. It can be verified that the eigenvectors are linearly independent and thus form a basis for R2. Therefore, A is diagonalizable.

However, A is not diagonal because it is not possible to find a matrix P such that A = PDP^-1, where D is a diagonal matrix.

(b) A is not diagonalizable: One possible example of such a matrix A would be:

A = [[1, 1], [0, 1]]

The characteristic polynomial of A is det(A –λ I) = (1 - λ)^2, which has a repeated eigenvalue of λ = 1. The eigenvectors corresponding to λ = 1 are [1, 0] and [0, 1], but they do not form a basis for R2 because they are linearly dependent. Therefore, A is not diagonalizable.

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Answer:

Step-by-step explanation:To solve the system of equations, we can set the two expressions for y equal to each other:

−x + 2 = 3x + 1

Solving for x, we get:

4x = 1

x = 1/4

Substituting this value of x into either of the original equations, we get:

y = −(1/4) + 2

y = 7/4

Therefore, the solution to the system of equations is the point (1/4, 7/4), which is the point of intersection of the two lines.

So the correct description of the solution to the system of equations is:

a

Line y = −x + 2 intersects line y = 3x + 1.

Answer: 50

Step-by-step explanation:

Answer:

50?

Step-by-step explanation:

10-5 equals 5

5+7 equals 12

12-2 equals 10

10-9 equals 1

1+2 equals 3

3-5 equals -2

-2+12 equals 10

10-3 equals 7

7+7 equals 14

14-3 equals 11

11+9 equals 20

20-10 equals 10

10-6 equals 4

4+8 equals 12

12-2 equals 10

10+60 equals 70

70-20 equals 50

Option (c) is the correct formula for the Newton-Raphson method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex]

The Newton-Raphson method is an iterative method for finding the root of a function. To use this method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex], we first define a function [tex]f(x) = x^2 - r[/tex]. The root of this function is the square root of r.

The Newton-Raphson method starts with an initial guess x0 for the root and then iteratively improves the guess using the formula:

[tex]xi+1 = xi - f(xi)/f'(xi)[/tex]

where f'(x) is the derivative of f(x). In this case,[tex]f(x) = x^2 - r[/tex], so f'(x) = 2x.

Substituting these values, we get:

[tex]xi+1 = xi - (xi^2 - r)/(2xi)[/tex]

Simplifying, we get:

[tex]xi+1 = xi - (xi/2 - r/2xi)[/tex]

[tex]xi+1 = 1/2(xi + r/xi)[/tex]

Therefore, the formula for the Newton-Raphson method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex] is:

[tex]xi+1 = 1/2(xi + r/xi)[/tex]

Option (c) is the correct formula for the Newton-Raphson method to find the square root of a real number r from the equation[tex]x^2 - r = 0[/tex]. This formula involves taking the average of the current guess xi and r/xi as the next guess. This method is efficient and converges quickly to the square root of r.

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The function that is represented by the graph is -|x - 1| + 8.

Option A is the correct answer.

We have,

The graph of the function - |x - 1| + 8 can be obtained by applying a series of transformations to the graph of the absolute value function, y = |x|.

First, the expression x - 1 inside the absolute value brackets shifts the entire graph of y = |x| one unit to the right.

This means that the "V" shape of the absolute value function is centered at x = 1 instead of x = 0.

Next, the negative sign in front of the absolute value reflects the graph of y = |x| across the x-axis.

This means that the "V" shape is now pointing downwards instead of upwards.

Finally, the entire graph is shifted vertically upward by 8 units due to the constant term + 8.

This means that the lowest point of the "V" shape is at y = 8 instead of

y = 0.

Thus,

The function that is represented by the graph is -|x - 1| + 8.

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Since the utility cost is lowest at t=0, you will conduct your research during period 0 as a quasi-hyperbolic discounter. Procrastination may be beaten if the painful job was linked to an enjoyable task.

a) As a naive quasi-hyperbolic discounter, you must choose the period to study based on your discount factors (β = 0.75, δ = 1) and the utility costs. To determine this, you must compare the present value of the utility costs of studying in each period:

At t = 0: Utility cost = 8 (since you're studying now, no discounting is applied)

At t = 1: Utility cost = 10 x β = 10 x 0.75 = 7.5

At t = 2: Utility cost = 12 x β x δ = 12 x 0.75 x 1 = 9

Since the utility cost is lowest at t=0 (8), you will study during period 0.

b) By binding the unpleasant task (studying) with the pleasant task (eating chocolate cake with utility of 6), it may help overcome procrastination if the combined utility is less than the utility cost of studying in later periods. In this case:

At t = 0: Combined utility cost = 8 - 6 = 2

Since the combined utility cost at t=0 (2) is lower than the utility costs of studying in periods 1 and 2 (7.5 and 9), binding these tasks could help overcome procrastination.

c) As a sophisticated quasi-hyperbolic discounter, you're now aware of your present bias. However, since there is no cake involved, the utility costs remain the same as in part (a):

At t = 0: Utility cost = 8

At t = 1: Utility cost = 7.5

At t = 2: Utility cost = 9

Even though you're now sophisticated, the period in which you study does not change. You will still study during period 0, as it has the lowest utility cost.

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Answer:

4/6 which is 2:3

Explanation:

the vegterian is 10-6=4

the non vegterian or eat meat is 6

and their ratio is 4/6

2:3

Answer:

perseveration

Step-by-step explanation:

The term you are looking for is "perseveration."

The solution and value of x include the following: B. x = 3.

In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical equation:

2x + 4 = 10.

By subtracting 4 from both sides of the equation, we have the following:

2x + 4 - 4 = 10 - 4

2x = 6

x = 6/2

x = 3.

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Complete Question:

Solve 2x + 4 = 10.

OA. x = 5

OB. x=3

OC. x = -3

OD. x = 7

Therefore, the apparent nth term of the expression is: aⁿ = 5n² - 3n - 2.

The given sequence is not an arithmetic or geometric sequence. However, we can notice that the sequence of differences between consecutive terms is an arithmetic sequence.

The sequence of differences is: 7, 19, 37, 61,...

To find the nth term of this sequence, we can use the formula for the nth term of an arithmetic sequence:

dn = a1 + (n-1) * d

where dn is the nth term of the sequence of differences, a1 is the first term of the sequence of differences, d is the common difference of the sequence of differences, and n is the index of the term we want to find.

So, we have:

dn = 7 + (n-1) * 12

Simplifying this expression, we get:

dn = 5n - 3

Now, we can use this formula to find the nth term of the original sequence. Let's call the nth term an:

an = an-1 + dn-1

where an-1 is the (n-1)th term of the original sequence and dn-1 is the (n-1)th term of the sequence of differences.

We know that a1 = 2 and d1 = 7, so we can use the above formula to find the next terms:

a2 = a1 + d1 = 2 + 7 = 9

a3 = a2 + d2 = 9 + 19 = 28

a4 = a3 + d3 = 28 + 37 = 65

a5 = a4 + d4 = 65 + 61 = 126

Therefore, the apparent nth term of the sequence is: aⁿ = 5n² - 3n - 2.

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The population proportion (P) can be found by dividing the number of Soft Lilac bottles by the total number of bottles in the factory:
P = 1400 Soft Lilac bottles / 5300 total bottles
P ≈ 0.26 (rounded to two decimal places)

The sample proportion (p) can be found by dividing the number of Soft Lilac bottles in the sample by the total number of bottles in the sample:
p = 3 Soft Lilac bottles / 14 total bottles in the sample
p ≈ 0.21 (rounded to two decimal places)
So, the population proportion (P) of Soft Lilac bottles in Zahra's factory is approximately 0.26, and the sample proportion (p) of Soft Lilac bottles in the inventory manager's sample is approximately 0.21.

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The solution of the fractions 1 / 4 × 20 / 21  is 5 / 21.

A fraction is number with numerator and denominator. Therefore, let's multiply the fractions.

1 / 4 × 20 / 21 = 20 / 84

Hence, let's reduce the fraction by dividing the numerator and denominator by 4.

20 / 84 ÷ 4 / 4

20 / 84 ÷ 4 / 4 = 5 / 21

Therefore, the fraction is 5 / 21.

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The values of angles in the diagram are ∠DAE = 53⁰, ∠DAE = 48⁰, ∠ACB = 102⁰, ∠ABC = 56⁰.

The value of angles is calculated as follows;

∠DAE = 90 - 37 (complementary angles add up to 90⁰ )

∠DAE = 53⁰

∠DBE = 90 - 42 (complementary angles add up to 90⁰ )

∠DAE = 48⁰

∠ACB = 180 - 78 (sum of angles on a straight line )

∠ACB = 102⁰

∠ABC = 180 - (22 + 102) (sum of angles in a triangle )

∠ABC = 56⁰

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The solution to the system of equations is :

x1 = 3, x2 = -1, and x3 = 2.

To use the method of Cholesky factorization to solve this system of equations, we need to first write the system in matrix form as AX = B, where:

A = 1 -2 2
-2 5 -3
2 -3 6

X = x1
x2
x3

B = 4
-7
10

Next, we need to perform Cholesky factorization on matrix A. This involves finding a lower triangular matrix L such that A = LL^T, where L^T is the transpose of L. To do this, we use the following algorithm:

1. Set L11 = sqrt(A11).
2. For i = 2 to n, do the following:
a. Set Lii = sqrt(Aii - sum(Lik^2, k=1 to i-1)).
b. For j = i+1 to n, set Lij = (Aij - sum(Lik*Ljk, k=1 to i-1)) / Lii.

Applying this algorithm to matrix A, we get:

L = 1 0 0
-2 1 0
2 -1 1

Now we can solve for X by first solving L*Y = B for Y using forward substitution, and then solving L^T*X = Y for X using backward substitution. The solutions for Y and X are:

Y = 4
1
3

X = 3
-1
2

Therefore, the solution to the system of equations is x1 = 3, x2 = -1, and x3 = 2.

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The probability that the 20th ticket purchased is the second winning ticket is 0.10

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

The probability of a winning ticket is = 0. 10

Thus,

This means there is a 10% chance of winning with each ticket purchased.

The likelihood that the 20th ticket will be the second winning ticket is the same as the chance that any other ticket will be the second winning ticket, which is 0.10. This is because each ticket purchase is autonomous and has no bearing on the results of other tickets. Therefore, the probability of the 20th ticket purchased being the second winning ticket is also 0.10 or 10%

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(a) According to Chebyshev's theorem, at least 36% of the measurements lie between 122.7 mmHg and 145.5 mmHg. (b) According to Chebyshev's theorem, at least 56% measurements lie between 122.7 mmHg and 147.2. So, the correct option is 56%.

(a) Using Chebyshev's theorem to find how much data falls within a certain number of standard deviations from the mean.

Using k = 2,  to capture at least 75% of the data (which is 1 - 1/2^2 = 0.75).

Using k = 2, we can say that at least 75% of the data falls within the range of 134.1 - 2(5.7) = 122.7 mmHg and 134.1 + 2(5.7) = 145.5 mmHg.

The percentage of data that falls outside of this range is (1 - 0.75)/2 = 0.125, or 12.5%.

Therefore, at least 12.5% of the data falls in each, below 122.7 mmHg and above 145.5 mmHg. This means that at least 36% of the data falls within the range of 122.7 mmHg and 145.5 mmHg.

(b) We can use Chebyshev's theorem again, this time with k = 2.5, since we want to capture at least 56% of the data (which is 1 - 1/2.5^2 = 0.64).

Using the same calculations as in part (a), we find that at least 64% of the data falls within the range of 121.0 mmHg and 147.2 mmHg.

Therefore, we can say that at least 56% of the data falls within this range, since 56% is less than 64%.

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a. A result between -0.08 and 0.08 has a probability of around 0.1562.

b. Using the standard normal distribution table the value of a is 19.4.

c. After using z-score to find the value of a, we got 28.2.

(a) To find P(19.6 < X < 20.4), we need to standardize the values and use the standard normal distribution table:

z1 = (19.6 - 20) / √(25) = -0.4 / 5 = -0.08

z2 = (20.4 - 20) / √(25) = 0.4 / 5 = 0.08

Using the standard normal distribution table, the probability of a value falling between -0.08 and 0.08 is approximately 0.1562. Therefore:

P(19.6 < X < 20.4) = 0.1562

(b) To find the value of a such that P(X > a) = 0.5517, we need to use the standard normal distribution table to find the z-score that corresponds to a cumulative probability of 0.5517:

P(X > a) = 1 - P(X ≤ a) = 0.5517

P(X ≤ a) = 1 - 0.5517 = 0.4483

Using the standard normal distribution table, the z-score that corresponds to a cumulative probability of 0.4483 is approximately -0.12. We can use this z-score to solve for a:

z = (a - μ) / σ

-0.12 = (a - 20) / 5

-0.6 = a - 20

a = 19.4

Therefore, a = 19.4.

(c) To find the value of a such that P(X > a) = 0.05, we need to use the standard normal distribution table to find the z-score that corresponds to a cumulative probability of 0.95:

P(X > a) = 0.05

P(X ≤ a) = 1 - 0.05 = 0.95

Using the standard normal distribution table, the z-score that corresponds to a cumulative probability of 0.95 is approximately 1.64. We can use this z-score to solve for a:

z = (a - μ) / σ

1.64 = (a - 20) / 5

8.2 = a - 20

a = 28.2

Therefore, a = 28.2.

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Answer:

35 35 145 and 145

Step-by-step explanation:

35 times 2

= 70

70- 360

= 290

290÷2

= 145

35 35 145 145

If one angle of the parallelogram measures 35, the other angles would be 35, 145, and 145.  

The sum total of the interior angles in a parallelogram is 360 degrees. Also, in a parallelogram, the interior opposite angles are equal. It is given that one angle measures 35 degrees. Its opposite angle would also be 35 degrees.

35 + 35 = 70.

We know that sum of interior angles is 360 degrees. So, 360 - 70 =290. 290 is the sum of the other interior opposite angles. So therefore each of these angles would be 290/2= 145 degrees.

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