is the sequence geometric if so identify the common ratio -2 -4 -16

The applicants who are granted admission is 0.8413, The applicants who will score 860 or higher is 0.0228, and there will be 2023 applicants that are expected to be qualified to the university.

a) The scores in this problem are known to be normally distributed with a mean of 700 and a standard deviation of 80. To find the proportion of all applicants taking the exam who are granted admission, we must compute the Z-score of 620.

We then need to find the area under the normal curve to the right of this Z-score.1. Z-score of 620: (620 - 700)/80 = -1.00Therefore, P(X ≥ 620) = P(Z ≥ -1.00) = 0.8413 (using a standard normal table)

So, the proportion of all applicants taking the exam who are granted admission is approximately 0.8413.

b) To find the proportion of all applicants who will score 860 or higher on the exam, we must compute the Z-score of 860.

We then need to find the area under the normal curve to the right of this Z-score.2. Z-score of 860: (860 - 700)/80 = 2.00

Therefore, P(X ≥ 860) = P(Z ≥ 2.00) = 0.0228 (using a standard normal table)So, the proportion of all applicants who will score 860 or higher on the exam is approximately 0.0228.

c) Using the proportions calculated in parts (a) and (c), we can expect the following number of applicants to be qualified for admission to the university.

Qualified applicants = (2400)(0.8413) = 2023 (rounded to the nearest whole number)

Therefore, we expect 2023 applicants to be qualified for admission to the university.

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The difference between (3x+6y)(3x+6y) and  (4x+9y)(4x+9y) is 7x² +36xy+45y²

An expression is a mathematical statement which has variables , constants and mathematical operators  simultaneously.

The expression given in the question is

(3x+6y)(3x+6y) and  (4x+9y)(4x+9y)

the difference when (3x+6y)(3x+6y) is subtracted from (4x+9y)(4x+9y)

(4x+9y)(4x+9y) -  (3x+6y)(3x+6y)

16 x² + 36xy+36xy +81y²-9x²-18x -18x -36y²

7x² +36xy+45y²

Therefore in simplest term , The difference between (3x+6y)(3x+6y) and  (4x+9y)(4x+9y) is 7x² +36xy+45y²

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For given Step function also known as piecewise function, The range of g(x)  is {-3,2,5} i.e. C.

What exactly is a piecewise function?

A piecewise function has several definitions in various x intervals. The graph of a piecewise function is split into sections that correspond to each of its definitions. The absolute value function is an outstanding example of a piecewise function. Let us look at why it was given that name. We know that an absolute value function is defined as f(x) = |x|.

f(x)=(x if x x≥0)

-x if x<0)

This piecewise function should be interpreted as

When x is higher than or equal to 0, f(x) equals x.

When x is less than zero, f(x) equals -x.

Now,

As range of a given function is given by its y values, here it will be given by values of g(x) and as we can see from question for values of x, g(x) is always equal to -3,2,5.

Hence,

           The range of g(x) is {-3,2,5}.

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Eigenvectors associated with -3, -1, and 5 are (1, 1/14, -4/7), (-1, 1, 0), and (1, 1, 0), respectively.

We need to solve the system of equations:

(A - λI)x = 0

λ is eigenvalue

I is identity matrix.

For λ = -1:

(A + I)x = 0

[2 2 2]

[2 2 2]

[2 2 2]

R2 <- R1

[2 2 2]

[0 0 0]

[2 2 2]

R3 <- R1 - R3

[2 2 2]

[0 0 0]

[0 0 0]

So we have the equation 2x + 2y + 2z = 0, which simplifies to x + y + z = 0. We can choose y = 1 and z = 0 to get x = -1, so the eigenvector associated with -1 is (-1, 1, 0).

For λ = 5:

(A - 5I)x = 0

[-2 2 2]

[2 -2 2]

[2 2 -8]

R1 <-> R2

[2 -2 2]

[-2 2 2]

[2 2 -8]

R3 <- R1 + R3

[2 -2 2]

[-2 2 2]

[4 0 -6]

R1 <- R1/2

[1 -1 1]

[-2 2 2]

[4 0 -6]

R2 <- R2 + 2R1

[1 -1 1]

[0 0 4]

[4 0 -6]

R3 <- R3 - 4R1

[1 -1 1]

[0 0 4]

[0 4 -10]

R3 <- R3/2

[1 -1 1]

[0 0 4]

[0 2 -5]

So we have the equation x - y + z = 0 and 4z = 0. We can choose y = 1 and z = 0 to get x = 1, so the eigenvector associated with 5 is (1, 1, 0).

Therefore, the eigenvectors associated with -3, -1, and 5 are (1, 1/14, -4/7), (-1, 1, 0), and (1, 1, 0), respectively.

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3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

Answer:

2 19/56 is the answer.

Step-by-step explanation:

10 5/8 - 8 2/7

or, 85/8 - 58/7

or, (595-464)/56

or, 131/56

= 2 19/56

The expression obtained by simplifying is 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9.

What is an expression?

A mathematical expression consists of its own components, at least two additional variables or integers, and one or more arithmetic operations.

We are given an expression as

(\(x^{2}\) + 6x + 9) (3x - 1)

Now, for simplifying the expression, we will multiply the terms.

So, we get

⇒ (\(x^{2}\) + 6x + 9) (3x - 1)

⇒ 3\(x^{3}\) - \(x^{2}\) + 18\(x^{2}\) - 6x + 27x - 9

Now, by combining the like terms, we get

⇒ 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9

Hence, the expression obtained by simplifying is 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9.

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Question: Simplify the following

(x² + 6x + 9) (3x - 1)

The equations of lines are given below.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The equation for line a is,

x=-5.

The equation for line b is,

x=5.

The equation for line c is,

y=5.

The equation for line d is,

y=-2.

The equation for line e is

x+y=1

The equations of lines are given above.

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Answer:

-21/3+5=-7+5=-2

Step-by-step explanation:

Answer:

2.6 im pretty sure lol

Step-by-step explanation:

Answer:

90°

Step-by-step explanation:

note that \(\frac{2}{8}\) simplifies to \(\frac{1}{4}\)

There are 360° in one turn of the circle , then

\(\frac{1}{4}\) × 360° = 360° ÷ 4 = 90°

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Step-by-step explanation:

1)

imagine the trapezoid standing upright (90°) turned.

then the top and bottom lines are parallel, and the 15 side is with its double right angles the height of the trapezoid.

in general, the area of such a trapezoid is

(top + bottom)/2 × height

in our case that is

(3 + 4)/2 × 15 = 7/2 × 15 = 3.5 × 15 = 52.5 units²

2)

this is basically the sum of the lower rectangle and the upper trapezoid.

the area of the lower rectangle is

58×15 = 870 mm²

the area of the upper trapezoid is (the same formula as before)

(47 + 58)/2 × (21 - 15) = 105/2 × 6 = 52.5 × 6 = 315 mm²

so, the total area is

870 + 315 = 1,185 mm² = 1,185.0 mm²

The correct answer is B) Her sample is 38, 68, 35, 02, 22. This is because the scientist is selecting a random sample of 5 forest sites from a population of 45 without replacement. She is using consecutive pairs of digits from the table of random digits to select her sample.

Starting at the beginning of the line of random digits, the first pair is 38, which corresponds to forest site 38. The second pair is 68, which corresponds to forest site 68. The third pair is 35, which corresponds to forest site 35. The fourth pair is 02, which corresponds to forest site 02. And the fifth pair is 22, which corresponds to forest site 22.
Now, let's select a random sample of 5 forest sites without replacement:
1) 38
2) 35
3) 02
4) 22
5) 24
Thus, the correct answer is not listed in the given options. However, based on the consecutive pairs of digits and following the process mentioned, the sample should be 38, 35, 02, 22, and 24.

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Answer:

(3/4)  /  (7/8)     invert the second fraction and multiply

(3/4) * (8/7) =

24/28 =

6/7

Step-by-step explanation:

Explanation: There's a little trick to help you if you have to divide two fractions.

3/4 divided by 7/8 is the same as (3/4)/(7/8) and maybe you've already realised that multiplying by half is the same as dividing by two (easiest example for this). If you need a moment to think about why that is take that moment and continue reading when it makes sense to you. Continuing with that logic multiplying by 1/4 is the same as dividing by 4 and multiplying by 1/8, 1/9 or 1/10 is the same as dividing by 8,9 or 10. Actually multiplying by a certain number is always the same as dividing by its 'reciprocal'. The reciprocal of a number is defined as the number one divided by that number.

So the reciprocal of 8 is 1/8, the reciprocal of 5 is 1/5 and so on...

If you've understood why that is you're holding a new power in your hands because now you can derive from that that (3/4) / (7/8) is the same as (3/4) * (8/7) and if you now imagine this as being written as fractions with the numbers under and above a line you can simply multiply together 3*8 and 4*7 to get 24/28 which can be simplified to 6/7.

Answer:

I believe 6in squared is the correct answer

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

6*?=24 in

6*4=24in

if it is 3 in on the smaller one, it also will be 2 so it will be 6.

A) To find the balance points, we set the right-hand side of the differential equation equal to zero: (y-2)^(1/5)(1+y)(1-y^2) = 0. Therefore, the balance points are y = -1, y = 1, and y = 2.

The factors on the right-hand side indicate that the equation is satisfied when any of these factors is zero. So, we have three possibilities:

1) y - 2 = 0   -->   y = 2

2) 1 + y = 0   -->   y = -1

3) 1 - y^2 = 0   -->   y = -1 or y = 1

Therefore, the balance points are y = -1, y = 1, and y = 2.

B) Graphically representing the possible shape of the family of solutions y(t) of this equation can be done by plotting the direction field or phase portrait. This involves sketching short line segments or arrows at various points on the y-t plane to indicate the direction in which the solution curves move. Since it is not possible to create a graph here, I encourage you to use a software tool or mathematical software like Mathematica or MATLAB to plot the direction field.

C) To determine towards what value the solution y(t) evolves when t approaches infinity, we consider the initial condition y(0) = 3/2. We can observe that at y = 2, the right-hand side of the differential equation is zero, indicating that y = 2 is a stable balance point. As t approaches infinity, the solution y(t) tends to the stable balance point y = 2. Therefore, the solution evolves towards y = 2 as t goes to infinity.

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Hence the expression \((secx - tanx)^{2}\)  is equal to  \(\frac{1-sinx}{1 + sinx}\).

Given that

\((secx - tanx)^{2}\) = \(\frac{1-sinx}{1 + sinx}\)

Now,

we need to prove left hand side is equal to right hand side

left hand side

\((secx - tanx)^{2}\) = \((secx)^{2}\) + \((tanx)^{2}\) - 2(secx)(tanx)

                     = \(\frac{1}{(cos)^{2} }\) +\(\frac{(sinx)^{2} }{(c0sx)^{2} }\) - 2(\(\frac{1}{cosx}\))(\(\frac{sinx}{cosx}\))

                      = \(\frac{1+(sinx)^{2} - 2(sinx)}{(cosx)^{2} }\)

                     = \(\frac{(1-sinx)^{2} }{(cos)^{2} }\)

                     =  \(\frac{(1-sinx)^{2} }{1-(sinx)^{2} }\)

                     = \(\frac{(1-sinx)(1-sinx)}{(1-sinx)(1+sinx)}\)

                     = \(\frac{1-sinx}{1+sinx}\)

                    = right side

now L.H.S = R.H.S

Therefore,\((secx - tanx)^{2}\) = \(\frac{1-sinx}{1 + sinx}\)

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Answer:

answer is C

Step-by-step explanation:

f(x)= 1/x+1

Because we have a vertical asymptote at x = -1, we conclude that the correct option is C.

In the graph, we can see that we have a vertical asymptote at x = -1.

This means that the denominator of the rational equation becomes zero when x = -1.

So the equation must be:

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

The denominator is x + 1, and as expected, it becomes zero when x = -1.

Then we conclude that the correct option is C.

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Answer:

The equation of the line in slope-intercept form is y = -x + 1

Step-by-step explanation:

The slope-intercept form of the linear equation is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

∵ f(x) = y ⇒ is the function of the set of ordered pairs (x, y)

∴ f(3) = -2 is the point (3, -2)

∴ f(0) = 1 is the point (0, 1)

∴ x1 = 3 and y1 = -2

∴ x2 = 0 and y2 = 1

→ Substitute them in the rule of the slope to find it

∵ m = \(\frac{1--2}{0-3}\) = \(\frac{1+2}{-3}\) = \(\frac{3}{-3}\)

∴ m = -1

→ Substitute it in the form of the equation above

∵ y = -1(x) + b

∴ y = -x + b

∵ b is the value of y at x = 0

∵ at x = 0, y = 1

∴ b = 1

∴ y = -x + 1

∴ The equation of the line in slope-intercept form is y = -x + 1

The statement is True.

A test statistic value of 2.14 puts it in the rejection region, which means that if the null hypothesis is true, the probability of obtaining a test statistic as extreme as 2.14 or more extreme is less than the significance level of the test. Therefore, we reject the null hypothesis at the given significance level.

If the test statistic is actually 2.19, which is more extreme than 2.14, then the probability of obtaining a test statistic as extreme as 2.19 or more extreme under the null hypothesis is even smaller than the probability corresponding to a test statistic of 2.14.

This means that the p-value for the test is even smaller than the significance level, and we reject the null hypothesis with even greater confidence.

In other words, if the test statistic is more extreme than the critical value, the p-value is smaller than the significance level, and we reject the null hypothesis at the given significance level with greater confidence.

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AB = CB and CD = AE

Perimeter =

16 + 2(x + 8) + 2(x - 3) = 94

16 + 2x + 16 + 2x - 6 = 94

4x + 26 = 94

4x = 68

x = 17

AB = x - 3

AB = 17 - 3 = 14

CD = x + 8

CD = 17 + 8 = 25

According to the proof, equal difference property is not satisfied by the function f(x).

There are four binary variables, x1, x2, x3, and x4.

The binary format is now converted to hexadecimal format, and the values are stored as A, B, C, and D, accordingly.

Convert every four bits of a binary value to a hexadecimal value.

ex: Split into 4 bits: x1 = 00000000 = 0000 0000 = 0 0 (convert the 4 bits to hex)

A = 00 ( hexadecimal of x1 )

B= 01 ( hexadecimal of x2 ) ( hexadecimal of x2 )

C=02 ( hexadecimal of x3 ) ( hexadecimal of x3 )

D=03 ( hexadecimal of x4 ) ( hexadecimal of x4 )

The function in question is f(x) = BS(x), which means that it performs byte alternation on the input x.

This means that f(x1) = 63, f(x2) = 7C, f(x3) = 77, and f(x4) = 7B.

We must now demonstrate that x1 xor x2 equals x3 xor x4 and that f(x1) xor f(x2) does not equal f(x3) xor f(x4) (x4).

If x1 xor x2 = 00, then xor 02 = 02 xor 01 = 01 x3 xor x4 03 = 01 So, x1 Equals x2 OR x3 OR x4 In the present, f(x1) xor f(x2) = 63 xor 7C = 1f f(x3) xor f(x4) = 77 xor 7B = 0C Due to f(x1) xor f(x2) not being equivalent to f(x3) xor f(x4).

Hence, the equal difference property is not satisfied by the function f(x), which is the Byte Substitution (BS) function of AES, according to the proof.

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Answer: Since Harley puts the white chocolate back after selecting it, each selection is independent and the probability of selecting a white chocolate is 5/20=1/4.

The probability of selecting 2 white chocolates in a row is given by:

P(white and white) = P(white) * P(white)

= 1/4 * 1/4

= 1/16

Therefore, the probability that Harley selects 2 white chocolates in a row is 1/16.

Step-by-step explanation:

Answer:

-3 is the answer

Step-by-step explanation:

Answer: its A

Step-by-step explanation: Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:

(0,−1)

Focus: (0,−54)

Axis of Symmetry: x=0

Directrix: y=−3/4

x y

−2 −5

−1 −20

0 −1

1 −2

2 −5

It is important for game developers and regulators to carefully consider the potential risks and harms associated with loot boxes, and to ensure that appropriate measures are in place to protect vulnerable players.

From a UK legal perspective, loot boxes can be considered gambling if they meet the following criteria:

Chance: The outcome of the loot box must be determined at least partially by chance. If the outcome is entirely predetermined, it is not considered gambling.

Consideration: The player must pay something of value (such as real money or in-game currency) to open the loot box.

Prize: The player must receive a prize of some sort from the loot box, such as a virtual item or currency.

If these three criteria are met, then the loot box can be considered a form of gambling. The UK Gambling Commission has stated that it considers loot boxes to be gambling if the contents can be exchanged for real-world money or goods, and if the prizes have real-world value.

In addition to the legal perspective, there is also growing concern about the potential harms of loot boxes, particularly in relation to problem gambling and the impact on children. The UK government has commissioned several studies into the potential risks associated with loot boxes, and some countries have already taken steps to regulate or ban them.

Overall, it is important for game developers and regulators to carefully consider the potential risks and harms associated with loot boxes, and to ensure that appropriate measures are in place to protect vulnerable players.

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She receives grossly $841.8 for working for 46 hours

From the question, the given parameters are

Hourly rate = $18.30 per hour

Number of hours = 46 hours

The amount she receives in gross for 46 hours is the product of the hourly rate and the number of hours

This is represented as

Total amount =  Hourly rate x Number of hours

Substitute the known values in the above equation

So, we have the following equation

Total amount =  18.3 x 46

Evaluate

Total amount = 841.8

Hence, the amount she receives in gross for 46 hours is $841.8

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Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Step-by-step explanation:

Both function are always increasing so D is correct.

the probability of choosing exactly 5 red marbles when 12 marbles are chosen at random is approximately 0.028.

This is a hypergeometric probability problem .

The total number of ways to choose 12 marbles from 27 is:

${{27}\choose{12}} = \frac{27!}{12!15!} = 10,!626,!766$

The number of ways to choose 5 red marbles and 7 blue marbles is:

$ {{15}\choose{5}}\cdot{{12}\choose{7}} = \frac{15!}{5!10!}\cdot\frac{12!}{7!5!} = 300,!450$

So the probability of choosing exactly 5 red marbles is:

$P(\text{5 red}) = \frac{300,!450}{10,!626,!766} \approx 0.028$

what is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1, where 0 indicates an impossible event and 1 indicates a certain event.

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