it takes james 2.5 minutes to type 150 words at that rate how mant words can james type in 6 minutes

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The expected value of the proposition round to two decimal places will be $2.38.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

The number of winning events when a value of two or less is 4. Thus, the probability is calculated as,

\(p = \dfrac{4}{52}\\\\p = \dfrac{1}{13}\\\\q = 1 - p\\\\ q = 1 - \dfrac{1}{13}\\\\q = \dfrac{12}{13}\)

The expected value of the proposition is calculated as,

\(E = \$463 \times \dfrac{1}{13} - \$36 \times \dfrac{12}{13}\\\\E = \$35.615 - 33.231\\\\E \approx \$2.384\)

The expected value of the proposition is $2.38.

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The three different dilution methods that will accomplish a dilution with a 1:1000 dilution factor are one-step dilution, two-step dilution and three-step dilution.

1. One-step dilution: Take 1 mL of the original solution and add 999 mL of the diluent (water, buffer, etc.) to get a 1:1000 dilution.

2. Two-step dilution: Take 1 mL of the original solution and add it to 9 mL of the diluent to get a 1:10 dilution. Then, take 1 mL of the 1:10 dilution and add 9 mL of the diluent to get a 1:100 dilution. Repeat this step once more to get a 1:1000 dilution.

3. Three-step dilution: Take 1 mL of the original solution and add it to 4 mL of the diluent to get a 1:5 dilution. Then, take 1 mL of the 1:5 dilution and add it to 4 mL of the diluent to get a 1:25 dilution. Repeat this step twice more to get a 1:125 dilution and then a 1:625 dilution. Finally, take 1 mL of the 1:625 dilution and add it to 375 mL of the diluent to get a 1:1000 dilution.

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Answer:

t = 60

Step-by-step explanation:

Using the rule of exponents

\((a^m)^{n}\) = \(a^{mn}\) , then

\((j^{-12}) ^{-5}\)

= \(j^{(-12(-5))}\)

= \(j^{60}\)

Then t = 60

The equation of the sequence will be \(\rm a_n = 0.8 \times a_{n -1} +200\),

where a₁ = 800. Then the correct option is C.

Let a₁ be the first term and r be the common ratio. Then the geometric sequences will be

\(\rm a_n = a_{n -1} \cdot r\)

Mahek owns a holiday tree farm.

There are currently 800 trees on the property.

Each year, 20% of the trees are harvested and sold, and 200 seedlings are planted.

Then the equation of the sequence will be

\(\rm a_n = 0.8 \times a_{n -1} +200\)

Where a₁ = 800.

Then the correct option is C.

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Answer:

3. a1 = 800, an = 0.80an-1 + 200

Step-by-step explanation:

The basic concept of solving a system of equations using substitution is:

- solve for one of the variables in one of the equations

- substitute this into the other equation and solve for the remaining variable

- substitute the variable you found into either equations to find the other variable.

The system of equations is:

We can see that in the second equation "y" is almost solved, we just need to pass the "2" to the other side, so let's use this equations a solve for "y":

Now, we can substitute "y" into the other equations, that is, the first one:

Now, the equations has only "x", so we can solve for it:

And now that we know that x = 4, we can substitute this into any of the two equations. Let's do it in the second:

So, the solution of the given system of equations is x = 4 and y = -5.

Triangle ABC is similar to triangle ADE by AA test of similarity

Similarity is a property which says that the respective angles of two triangles are of equal measure and corresponding sides are in proportion.

here, we have,

There are different types of similarity test by which we can prove the similarity of triangles.

We are given that BC is parallel to Line DE

As the lines are parallel the respective angle are corresponding angles

hence Angle D = Angle B

And Angle E = Angle C

And both triangle have angle A as common angle

By AA test of similarity we can say that the two triangles are similar

Hence by AA test similarity the two triangles are similar

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The particular solution to the non-homogeneous equation is:

y_p(x) = [(3/2)*ln(x)*cos(x) + (3/2)sin(x)/x + C1](x^(1/2)*sin(x) - (1/2)*x^(1/2)*cos(x)) - [(3/2)*ln(x)*sin(x) - (3/2)cos(x)/x + C2](x^(1/2)*cos(x) + (1/2)*x^(1/2)*sin(x))

To use the method of variation of parameters, we first need to find the general solution to the homogeneous equation:

x^2y'' + xy' + (x^2 - 0.25)y = 0

We assume a solution of the form y = e^(r*x), then substitute this into the equation and get the characteristic equation:

r^2 + r - 1/4 = 0

Solving for r gives us r = (-1 ± sqrt(5))/2. Thus, the general solution to the homogeneous equation is:

y_h(x) = c1*x^(1/2)sin(x) + c2x^(1/2)*cos(x)

To find a particular solution to the non-homogeneous equation, we assume a solution of the form:

y_p(x) = u(x)*y1(x) + v(x)*y2(x)

where y1(x) and y2(x) are the two linearly independent solutions to the homogeneous equation, and u(x) and v(x) are functions to be determined.

We can calculate the first and second derivatives of y_p(x) as:

y_p'(x) = u'(x)*y1(x) + v'(x)*y2(x) + u(x)*y1'(x) + v(x)*y2'(x)

y_p''(x) = u''(x)*y1(x) + v''(x)y2(x) + 2u'(x)y1'(x) + 2v'(x)*y2'(x) + u(x)*y1''(x) + v(x)*y2''(x)

Substituting y_p(x), y_p'(x), and y_p''(x) into the non-homogeneous equation and simplifying, we get:

u'(x)*x^(3/2)*sin(x) + v'(x)*x^(3/2)*cos(x) = 3x^(3/2)*sin(x)

Solving for u'(x) and v'(x), we get:

u'(x) = 3cos(x)/(2x) and v'(x) = -3sin(x)/(2x)

Integrating both sides, we get:

u(x) = (3/2)*ln(x)*cos(x) + (3/2)*sin(x)/x + C1

v(x) = (-3/2)*ln(x)*sin(x) + (3/2)*cos(x)/x + C2

where C1 and C2 are constants of integration.

Therefore, the particular solution to equation is:

y_p(x) = [(3/2)*ln(x)*cos(x) + (3/2)sin(x)/x + C1](x^(1/2)*sin(x) - (1/2)*x^(1/2)*cos(x)) - [(3/2)*ln(x)*sin(x) - (3/2)cos(x)/x + C2](x^(1/2)*cos(x) + (1/2)*x^(1/2)*sin(x))

where C1 and C2 are constants of integration.

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The equation of the line in slope-intercept form, with the point (4, -5) and an undefined rate of change is x = 4.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

In Mathematics, any line that has an undefined slope (rate of change) is a vertical line because it does not have a y-intercept. This ultimately implies that, a vertical line that is parallel to the y-coordinate (y-axis) would have an undefined slope (rate of change).

Generally speaking, the equation of a line that has an undefined slope (rate of change) is given by this mathematical expression;

x = a

Where:

a represents the x-intercept.

At point (4, -5), the required equation with an undefined slope (rate of change) is x = 4.

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The true statement about the receipt of a cash of $12,000 in year 6 at an opportunity cost of capital of 7.2% is C. The present value is $7,907.

The present value of the future cash value of $12,000 can be determined by discounting.

The discount factor can be computed as (1 - 0.072)⁶.

The present value can also be computed using an online finance calculator as follows:

N (# of periods) = 6 years

I/Y (Interest per year) = 7.2%

PMT (Periodic Payment) = $0

FV (Future Value) = $12,000

Results:

Present Value (PV) = $7,907.01

Total Interest = $4,092.9

Thus, the present value of $12,000 at 7.2% discount rate is Option C.

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A. The future value is $18,212

B. The present value is $7,996

C. The present value is $7,907

D. Provide data for tax purposes

Answer:$9.72

Step-by-step explanation: 48.60 DIVIDED BY 5 EQUALS 9.72

GIVE ME BRAINLEST PLSS

The weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, but using mathematical induction, the basis step works, although the inductive step fails.

a) If we try to prove the inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) using mathematical induction, we can see that the basis step works. When n = 1, we have 1/2 < 1/√3, which is true.

Now, let's consider the inductive step. Assuming that the inequality holds for some positive integer k, we need to show that it also holds for k+1, i.e., we assume 1/2 · 3/4 ··· 2k-1/2k < 1/√(3k) and we want to prove 1/2 · 3/4 ··· 2k-1/2k · (2k+1)/(2k+2) < 1/√(3k+3).

If we attempt to manipulate the expression, we can simplify it to (2k+1)/(2k+2) < 1/√(3k+3). However, we cannot proceed further to prove this inequality, as it is not necessarily true. Therefore, the inductive step fails, and we cannot establish the original inequality using mathematical induction.

b) However, mathematical induction can still be used to prove the stronger inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n+1) for all integers greater than 1. We can start by verifying the case where n = 1, which gives us 1/2 < 1/√4, which is true.

Now, assuming the inequality holds for some integer k, we can multiply both sides of the inequality by (2k+3)/(2k+2) to get:

(1/2 · 3/4 ··· 2k-1/2k) · (2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

Simplifying the expression on both sides, we have:

(2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

We can observe that the right side of the inequality is less than 1/√(3k+3) by multiplying the denominator of the right side by (2k+3)/(2k+3). Hence, we obtain:

(2k+3)/(2k+2) < 1/√(3k+3).

This establishes the inequality for k+1, and thus, we have proven the stronger inequality using mathematical induction.

By verifying the case where n = 1 separately, we can conclude that the weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, as it follows from the proven stronger inequality using mathematical induction.

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Answer:

The answer would be D. 0=2(x-1)squared

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

If |q| = 5 at an angle of 45° and |r| = 16 at an angle of 300°. then the

|q – r| will be 18.0

To find |q - r|, we need to subtract the complex numbers q and r after which discover the magnitude (or absolute value) of the end result.

First, we want to express q and r in rectangular form, which means that finding their actual and imaginary additives:

For q, we've:

|q| = 5 at an perspective of 45°

Re(q) = |q| cos(45°) = five cos(45°) = 5/√2

Im(q) = |q| sin(45°) = 5 sin(45°) = 5/√2

So q = (5/√2) + (5/√2)i

For r, we have:

|r| = 16 at an angle of 300°

Re(r) = |r| cos(300°) = 16 cos(300°) = sixteen(-√3/2) = -8√three

Im(r) = |r| sin(300°) = 16 sin(300°) = -8

So r = -8√three - 8i

Now we are able to discover q - r by using subtracting the actual and imaginary additives:

q - r = (5/√2) + (5/√2)i - (-8√3 - 8i)

= (5/√2) + 8√3 + (5/√2 + 8)i

To discover |q - r|, we want to take the importance of this complex number:

|q - r| = √[(5/√2 + 8√3)² + (5/√2 + 8)²]

= √[25/2 + 80√3 + 192 + 50/2 + 40 + 64]

= √[125/2 + 80√3 + 256]

= √[625/4 + 320√3 + 1024]

= √[(25/2 + 16√3)²]

= 25/2 + 16√3

≈ 18.0

Hence, |q - r| is about equal to 18.0.

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Answer:

I looked at it thoroughly and I believe your correct, I believe I have done something like this before. please tell me if I am wrong. If I am, REPORT ME so you can get your point back.

Step-by-step explanation:

Hope I helped! :D

P(X = 4, Y = 2) = 0.055131

P(X = Y) = 0.35607

From the information given:

X represent no of Canon SLR

The PMF is given as:

X   :    0         1        2           3        4

p(x) :  0.1       0.2   0.3     0.25   0.15

p = P(customers that purchase the camera & also purchase an extended warranty.

As a result, the conditional distribution Y provided X approaches a Binomial distribution with n = x and p = 0.55 as the parameter.

\(\frac{Y}{X}\) ~ Bin ( n= x , p =0.55) y

     = 0.1 ........ x and X = 0,1,2,3,4.

The condition probabilities Y given X is:

\(P (\frac{Y = 0}{X = 0} ) =1\)

\(P (\frac{Y = 0}{X = 1} ) = 0.45 and P (\frac{Y = 1}{X = 1} ) =0.55\)

\(P (\frac{Y = 0}{X = 2} ) = 0.2025 and P (\frac{Y = 1}{X = 2} ) =0.495, P (\frac{Y = 2}{X = 2} ) =0.3025\)

\(P (\frac{Y = 0}{X = 3} ) = 0.091125 and P (\frac{Y = 1}{X = 3} ) =0.334125, \\P (\frac{Y = 2}{X = 3} ) =0.408375 and P (\frac{Y = 3}{X = 3} ) = 0.166375\)

\(P (\frac{Y = 0}{X = 4} ) = 0.0.041006 and P (\frac{Y = 1}{X = 4} ) =0.0.200475, P (\frac{Y = 2}{X = 3} ) =0.367538\)

\(P (\frac{Y = 3}{X = 4} ) = 0.299475 and P (\frac{Y = 4}{X = 4} ) =0.091506\)

Now, the joint P.D (probability Dist.) of X & Y is expressed as:

\(P (\frac{Y = y}{X = x} ) = P (\frac{Y = y. X = x}{X = x} )\)

\(P( X = x , Y = y) = P(\frac{Y = y}{X =x} ) * P(X =x)\)

The Joint P.D is;

                      Y                                                                      Total

             0              1                    2             3          4

X     0     0.1            0                  0              0         0                  0.1

      1      0.09        0.11              0               0         0                 0.2

  2    0.06075  0.1485      0.09075          0         0                 0.3

  3    0.022781 0.083531 0.102094   0.041594  0                0.25

  4    0.006151  0.030071  0.055131  0.044921  0.013726    0.15

Total  0.279682 0.372103  0.247974  0.086515 0.013726       1

(a)

P(X=4,Y=2)

From the table above:

P(X=4,Y=2)

 = 0.055131

(b)

P(X= Y)

= (P = 0 , Y = 0) + P( X =1, Y =1) + P( X=2, Y=2) + P(X=3,Y=3) + P(X=4,Y=4)

= 0.1 + 0.11 + 0.09075 + 0.041594 + 0.013726

= 0.35607

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Using trigonometric ratios, the value of sin a, cos a, and tan a are 12/6√5,√5/5 and 2 respectively.

Trigonometric ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

To find the value of sin a:

sin a = opposite / hypothenuse

sin a = 12 / 6√5

a = sin⁻¹(12/6√5)

a = 63.43

sin a = 12/ 6√5

b. cos a = adjacent / hypothenuse

cos a = 6 / 6√5

cos a = √5/5

c. tan a = opposite / adjacent

tan a = 12 / 6

tan a = 2

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To find a recursive Nevill's method when interpolating a table using a polynomial at x = 4.1, we can use the following steps:

Step 1: Set up the given data in a table with two columns, one for f(x) and the other for x.

f(x)             x

36               1.16164956

3.80201036       4.0

0.30663842       4.2

0.35916618       -123926000.4

Step 2: Begin by finding the first-order differences in the f(x) column. Subtract each successive value from the previous value.

Δf(x)            x

-32.19798964     1.16164956

-3.49537194      4.0

-0.05247276      4.2

Step 3: Repeat the process of finding differences until we reach a single value in the Δf(x) column. Continue subtracting each successive value from the previous one.

Δ^2f(x)          x

29.7026177       1.16164956

3.44289918       4.0

Step 4: Repeat Step 3 until we obtain a single value.

Δ^3f(x)          x

-26.25971852     1.16164956

Step 5: Calculate the divided differences using the values obtained in the previous steps.

Divided Differences:

Df(x)             x

36                1.16164956

-32.19798964     4.0

29.7026177       4.2

-26.25971852     -123926000.4

Step 6: Apply the recursive Nevill's method to find the interpolated value at x = 4.1 using the divided differences.

f(4.1) = 36 + (-32.19798964)(4.1 - 1.16164956) + (29.7026177)(4.1 - 1.16164956)(4.1 - 4.0) + (-26.25971852)(4.1 - 1.16164956)(4.1 - 4.0)(4.1 - 4.2)

Solving the above expression will give the interpolated value at x = 4.1.

Q2: To construct an approximation polynomial using the Hermite method, we follow these steps:

Step 1: Set up the given data in a table with three columns: f(x), f'(x), and x.

f(x)             f'(x)              x

2.572152         7.615964          1.2

3.602102         13.97514          1.3

5.797884         34.61546          1.4

14.101442        199.500           1.5

Step 2: Calculate the divided differences for the f(x) and f'(x) columns separately.

Divided Differences for f(x):

Df(x)            \(D^2\)f(x)           \(D^3\)f(x)

2.572152         0.51595           0.25838

Divided Differences for f'(x):

Df'(x)           \(D^2\)f'(x)

7.615964         2.852176

Step 3: Apply the Hermite interpolation formula to construct the approximation polynomial.

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Answer:

D No; the graph of a proportional relationship must pass through (0, 0).

Step-by-step explanation:

Answer:

Perpendicular because the slopes are opposite reciprocals

Step-by-step explanation:

The histograms typically are used to display continuous measures.

There are different types of charts: histogram, line chart, pie chart, and others.

The histogram is a type of chart used as a tool that provides a way to assess the distribution of data. From this type of chart, a set of data are previously tabulated and divided into classes. In the other words, the histogram is applied to summarize discrete or continuous measures, so it becomes more easily the understand the used data. There are many websites and software that allow the plot of this type of chart.

From the explanation, it is possible to identify the histograms typically are used to display continuous measures.

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Answer:

Exact Form:

12

175

Decimal Form:

0.06857142

Step-by-step explanation:

The relation "r" on the set of all integers, where x = y^2, is not reflexive.

A relation is reflexive if every element in the set is related to itself. In this case, for the relation x = y^2 to be reflexive, every integer "x" should be related to itself, meaning that x = x^2. However, this is not true for all integers.

For example, if we consider x = 2, it is not equal to 2^2 = 4. Similarly, if we consider x = -3, it is not equal to (-3)^2 = 9.

Since there are integers that do not satisfy the condition x = x^2, the relation x = y^2 is not reflexive on the set of all integers.

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Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Using the senoidal function, it is found that:

The function that models the population after t years is given by:

\(r(t) = 225\cos{\left(\frac{\pi}{3}\right)t} + 425\)

Item 1:

The cosine function varies between -1 and 1, hence, considering it equals to 1:

\(r_{MAX} = 225 + 425 = 650\)

The maximum number of rabbits on Park Point during a population cycle is of 650.

Item 2:

The period of a cosine function \(\cos{\frac{2\pi}{T}}\) is T.

The population cycle is of 3 years.

Item 3:

\(r(3.2) = 225\cos{\left(\frac{\pi}{3}\right)3.2} + 425 = 205\)

The approximate number of rabbits on the island after 3.2 years is 205.

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Answer:

$569.50

Step-by-step explanation:

15% deduction from the initial price(100%) will have us remaining with 85%

100% = 670

85% = 85% x 670

                100%

= $569.50

Answer:

Step-by-step explanation:

S = \(R^{2} *\pi\)

S = \(4^{2} * \pi\)

S = 16 * 3,14

S = 50,24

Answer:

1) Reflection in the x-axis

A' = (-2, -3)

2) Rotation of 180° clockwise about the origin

A'' = (2, 3)

3) Translation of 3 units down and 4 units to the right

A''' = (6, 0)

Step-by-step explanation:

The transformations are as follows;

1) Reflection in the x-axis

Here the x-coordinate is the same and the y-coordinate changes sign.

Therefore, we have;

A (-2, 3)

After reflection in the x-axis becomes A' = (-2, -3)

2) Rotation of 180° clockwise about the origin

When, a point (x, y) is rotated 180° clockwise about the origin, it becomes (-x, -y)

Therefore, we have;

A' = (-2, -3) becomes A'' = (2, 3)

3) Translation of 3 units down and 4 units to the right

Translation of 3 units down and 4 units to the right = \(T_{(4, -3)\)

Which gives

A''' = (2 + 4, 3 - 3) = (6, 0).