Let X be a random variable with the probability mass function (PMF) given below (figure not drawn to scale), where a=0, b=0.23, c=0.13, d=0.10, e=0.15. a. Find the cumulative distributive function (CDF) Fx(3). Round answer to two decimal points.

No, the given value of h=2 is not a solution of the equation 1/3h=6.

Answer:

We know that A receives R500 less than C, so we can write:

4x = 9x - 500

Solving for x, we get:

5x = 500

x = 100

Now we can calculate the amounts received by each person:

A = 4x = 4(100) = R400

B = 7x = 7(100) = R700

C = 9x = 9(100) = R900

To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:

A:B = 400:700 = 4:7

B:C = 700:900 = 7:9

Therefore, the total amount divided is:

400 + 700 + 900 = R2000

So the amount that is divided is R2000.

Step-by-step explanation:

The total amount of money divided is R2000.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

The ratio of A, B and C= 4:7:9

Now,

Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:

4x + 500 = C's share

We can also write an equation to represent the fact that the three shares add up to the total amount:

4x + 7x + 9x = T

Simplifying this equation, we get:

20x = T

Now we can substitute the first equation into the second equation and solve for x:

4x + 7x + (4x + 500) = 20x

15x + 500 = 20x

500 = 5x

x = 100

Now we can find the individual shares by multiplying x by the appropriate ratio factor:

A's share = 4x = 400

B's share = 7x = 700

C's share = 9x = 900

Finally, we can check that these add up to the total amount:

400 + 700 + 900 = 2000

Therefore, by the given ratio the answer will be R2000.

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The probability that the coin lands on heads if one of them is flipped and lands on heads with probability 0.6 is 0.6 × 1/2 + 0.3 × 1/2 = 0.45. Therefore, the probability that the coin lands on heads is 0.45.  

a) Let A be the event that the chosen coin is the one that lands on heads with probability 0.6 and B be the event that the coin lands on heads. Then, the required probability is P(A | B) = P(A and B) / P(B) .

Here, P(A and B) = probability that the chosen coin is the one that lands on heads with probability 0.6 and it actually lands on heads.

Since the probability that the coin lands on heads are 0.45 and the probability that the chosen coin is the one that lands on heads with a probability of 0.6 is 1/2, we have P(A and B) = 0.6 × 1/2 = 0.3. The probability that the coin lands on heads is 0.45.

So, P(B) = probability that the coin lands on heads = 0.45.P(A | B) = P(A and B) / P(B) = 0.3 / 0.45 = 2/3.

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Answer:

x = 4

Step-by-step explanation:

6x + 21  =  5x + 25

Then, subtract 5x from both sides:

x + 21  = 25

Then, subtract 21 from both sides.

x = 4

Therefore, x is equal to 4 degrees

The polynomial function modeled by the given diagram is given as follows:

p(x) = 3x² - 7x - 6.

The polynomial function modeled by the given diagram is obtained considering the keys of the problem, which are the terms represented by each figure.

The polynomial is constructed as follows:

Then the expression used to construct the polynomial is given as follows:

p(x) = 3x² + 2x - 9x - 6.

Combining the like terms, the polynomial function is defined as follows:

p(x) = 3x² - 7x - 6.

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The instantaneous velocity of the object at t = 6 is 2.

Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56

Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2

Therefore, the instantaneous velocity of the object at t = 6 is 2.

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By using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429.

The Euler's method is used to estimate a numerical solution of a first-order differential equation. The formula of Euler's method is given by:

y_1 = y_0 + hf(x_0, y_0)

Where: y_1 is the next value of y after one iterationy

0 is the initial value of yy' = f(x, y)h is the step size

This method is an iterative procedure that advances the estimate of y by one step by approximating the curve using a tangent line at each point along the curve.

Given that y(0) = 4 and h = 0.2, we can use Euler's method to estimate y(1) where y(x) is the solution of the initial-value problemy' = x2 + xy, y(0) = 4

Using Euler's method with a step size of 0.2, we get:

1) When x = 0, y = 4

y_1 = y_0 + hf(x_0, y_0) = 4 + 0.2(0 + 4(0))= 4.02

When x = 0.2, y = 4.02

y_2 = y1 + hf(x_1, y_1) = 4.02 + 0.2(0.2^2 + 0.2(4.02))= 4.10523

When x = 0.4, y = 4.1052

y_3 = y_2 + hf(x_2, y_2) = 4.1052 + 0.2(0.4^2 + 0.4(4.1052))= 4.1994144

When x = 0.6, y = 4.1994

4 = y_3 + hf(x_3, y_3) = 4.1994 + 0.2(0.6^2 + 0.6(4.1994))= 4.3032545

When x = 0.8, y = 4.3033

y_5 = y_4 + hf(x_4, y_4) = 4.3033 + 0.2(0.8^2 + 0.8(4.3033))= 4.4174496

When x = 1, y = 4.4174

y_6 = y_5 + hf(x_5, y_5) = 4.4174 + 0.2(1^2 + 1(4.4174))= 4.5429404

Therefore, using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429 (rounded to four decimal places).

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Answer:

p ≥ 228

Step-by-step explanation:

p ≥ 228

This inequality means the Bowlers have to score at least 228 points to move on.

Hope this helped!

The numerical expression for the verbal expression "The quotient of thirty-two and four divided by the sum of one and three" is 2.

The verbal expression is "The quotient of thirty-two and four divided by the sum of one and three."

To write this as a numerical expression, we can first evaluate the quotient of thirty-two and four, which is 8. Then we can divide 8 by the sum of one and three, which is 4.

Therefore, the numerical expression for the verbal expression is:

= 8 ÷ (1 + 3)

Add the number

= 8 ÷ 4

Divide the numbers

= 2

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Answer:

Anita is 11 years old and sarun 55 years old( not so sure about this answer... what do you think)

Step-by-step explanation:

let Anita's age be x

and sarun's age be 3x

if, x-5 = 3x+7

3x+7 = 5(x-5)

3x+7=5x-25

32=2x

x=16

their ages 3 years ago,

Anita= 16-5=11yrs

sarun= 3*16+7 = 55yrs

Step-by-step explanation:

1. Draw a line of 8cm.

2. Take a compass and keep it in the length of more than 8 cm.

3. Draw an arc from point A and B which will intersect at point between A and B.

4. Draw a straight line from the arc.

5. You will find out that the line will be drawn exactly between A and B at 4cm.

By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To simplify the expression,

[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]

Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

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The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].

The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].

given

The collection of all x-values for which h(x) is specified is the domain of the function h.

The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.

The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.

The range is therefore [-3, 0].

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The complete question is :-  The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.

-2

-3-

4-

domain =

range =

Hello,

3m + 5 > 2(m - 7) =

3m + 5 > 2m - 14

3m - 2m > - 14 - 15

x > - 29

Step-by-step explanation:

3m±2m>-14-5

5m>-19

m>-19/5

m>3.8

The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a p-value of 1-∝.

So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]

Now, find M as such

[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ

In which is the standard deviation of the population and n is the size of the sample.

[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.

The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.

So the correct answer is:

(91331.94, 113352.06)

Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.

Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.

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Complete Question:

A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices

A). (89869.82, 114814.18)

B). (90292.73, 114391.27)

C). (91331.94, 113352.06)

D). (90371.37, 114312.63)

From the given data of hunters and do we find out there are 9 hunters and 15 dogs.

Let's assume that there were "h" hunters and "d" dogs.

Each hunter has two legs, and each dog has four legs, so the total number of legs can be expressed as:

2h + 4d = 78

We can simplify this equation by dividing both sides by 2:

h + 2d = 39

We also know that there were 24 heads in total, which includes the hunters and the dogs:

h + d = 24

We can now solve these two equations simultaneously to find the values of h and d.

First, we can solve for h in terms of d from the second equation:

h = 24 - d

We can substitute this expression for h in the first equation:

(24 - d) + 2d = 39

Simplifying and solving for d:

d = 15

Now that we know there were 15 dogs, we can substitute this value back into one of the equations to find the number of hunters:

h + d = 24

h + 15 = 24

h = 9

Therefore, there were 9 hunters and 15 dogs.

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The z-score for the 75th percentile of the standard normal distribution is given by 0.67 that is option A.

The most significant continuous probability distribution is the Normal Distribution, often known as the Gaussian Distribution. It is also known as a bell curve. The normal distribution represents a large number of random variables either nearly or exactly.

I found one that shows the following:

Z value Table entry

0.67   0.7486

0.68   0.7517

As a result, the Z value for 0.75 is between 0.67 and 0.68.

Interpolation yields the z value of 0.6745.

If you have a TI-84 calculator, you may calculate the z value as follows:

VARS - 2nd (this will show the DISTR menu)

To select invNorm, press 3.

Enter the value for the area/table (0.75)

If you press enter, it will return the z value.

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Complete question:

what is the z-score for the 75th percentile of the standard normal distribution is:

Therefore , the solution of the given problem of mean comes out to be  15 is the solution.

The sum of all values divided by all of the values constitutes the result from a collection, also referred to as the arithmetic mean. It is often referred to be known as "mean" as well as is one of the most frequency used main trend indicators. To find the answer, multiply the collection's overall amount of numbers by all of its values. Either the original data or data which has been combined into frequency charts can be used for calculations.

Here,

We can use linear interpolation between the two closest latitude numbers in the table, 45 and 50, to determine the typical temperature for a city with a latitude of 48.

Let T(45) and T(50) represent the typical temperatures at respective latitudes of 45 and 50, respectively. The following algorithm can be used to determine the temperature at 48 degrees latitude:

=> T(48) = T(45) + (T(50) - T(45)) * (48 - 45)/(50 - 45)

Using the numbers from the table as inputs, we obtain:

=> T(48) = 14 + (16 - 14) * (48 - 45)/(50 - 45)

=> T(48) = 14 + 2 * 3/5

=> T(48) = 14 + 1.2

=> T(48) = 15.2

The estimated average temperature for a city with a latitude of 48 is 15, rounded to the closest whole number.

Consequently, 15 is the solution.

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By answering the presented question, we may conclude that Therefore, equation the cost per pound of turkey is $1.99 and the cost per pound of ham is [tex]$2.39[/tex]  .

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex] states that the word "2x + 3" corresponds to the number "9".

The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.

For example, in the equations  [tex]"x2 + 2x - 3 = 0,"[/tex] the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.

Therefore,Let's denote the cost per pound of turkey as $t, and the cost per pound of ham as $h. Then we can write the following system of linear equations.

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Answer: $1,071.54

Step-by-step explanation:

To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:

Monthly interest = Total interest / Number of months

Monthly interest = $2,802 / 35

Monthly interest = $80.06

Total interest charged on the loan = Monthly interest x Number of months

Total interest charged on the loan = $80.06 x 35

Total interest charged on the loan = $2,802.10

Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:

Interest for remaining 13 months = Monthly interest x Remaining months

Interest for remaining 13 months = $80.06 x 13

Interest for remaining 13 months = $1,040.78

Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:

Interest refund = Total interest charged - Interest for remaining months

Interest refund = $2,802.10 - $1,040.78

Interest refund = $1,074.32

Therefore, the interest refund on the loan is $1,074.30.

The maximum area of the surfboard correct to 2 places is 0.67 m².

Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.

Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)

Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)

We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)

Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.

To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),

we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.

Area of surfboard =

[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]

[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]

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The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).

The probability of Z > 0.75 is 1 - 0.77337 = 0.22663

The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968

Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).

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Answer:

A ,B ,C

Step-by-step explanation:

2+2+2+2 equals 8

4x2 equals 8 and

1x8 equals 8

Answer:

A) 2 + 2 + 2 + 2

B) 4 × 2

C) 1 × 8

Hope this helps!

Step-by-step explanation:

A = 4 + 4 = 8

B = 8

C = 8

D = 16

E = 16

Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)

the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)

Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt

Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C

a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt

Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.

Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,

we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:

S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)

dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change

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Using coefficients ak, the following product may be extended into a power series: the expression is provided in the attached file. For each of the [tex]k 2 N[/tex]phrases, determine the coefficients ak before them. The formula [tex]ak = (-1)k(k+1)/2[/tex] yields the coefficients ak.

To get the coefficients ak, we may first simplify the above formula by factoring out a -x and rearranging terms. This results in the equation: [tex](1-x)/(1+x)2 = -x/(1+x) - x2/(1+x)2.[/tex]

Now, each term in the statement may be expanded into a power series using the formula for the geometric series. This results in: Both[tex]-x/(1+x) and -x2/(1+x)2[/tex] are equal to[tex]-x + x + x + 2 + x + 3 +...[/tex]

By combining like terms and adding these two power series, we can determine that the coefficient in front of [tex]xk is (-1)k(k+1)/2.[/tex]  Hence,[tex]ak = (-1)k(k+1)/2[/tex] is the formula for the coefficients ak.

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Answer: n=40

Step-by-step explanation:

let me know if i got this right for you broski

now dance

The Sale price is C. $260.63.

Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.

Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.

In the given question,

To find the sale price, we need to first calculate the amount of the markdown:

Markdown = Regular Price x Markdown Rate

Markdown = $389 x 0.33

Markdown = $128.37

The sale price is then the regular price minus the markdown:

Sale Price = Regular Price - Markdown

Sale Price = $389 - $128.37

Sale Price = $260.63

Therefore, the answer is C. $260.63.

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Answer:

Step-by-step explanation:

see diagram