Consider the following joint probability table. What is the value of E[X]E[X]?Y = 1Y = 7X = 31020X = 50.450.25

Answer:hello again

Step-by-step explanation:

Compatible numbers are simply the approximated value of a number

Using the compatible numbers, the product of 2.4 and 0.18 is 0.5

The compatible numbers are given as:

The product is given as:

\(\mathbf{2.4 \times 0.18}\)

Replace 2.4 and 0.18 with their compatible numbers, 2.5 and 0.2, respectively

So, we have:

\(\mathbf{2.4 \times 0.18 =2.5 \times 0.2}\)

Calculate the product of 2.5 and 0.2

\(\mathbf{2.4 \times 0.18 =0.5}\)

Hence, the product of 2.4 and. 0.18 is 0.5.

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The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer:

2893.14/321.46=9

Step-by-step explanation:

in 9 months he will run out of money

The rule of inference used to arrive at the statements s(y) and c(y) from the statement s(y) ∧ c(y) is called Simplification. Simplification allows us to extract individual components of a conjunction by asserting each component separately.

The rule of inference used in this scenario is Simplification. Simplification states that if we have a conjunction (an "and" statement), we can extract each individual component by asserting them separately. In this case, the conjunction s(y) ∧ c(y) represents the statement "y is a movie produced by Sayles and y is a movie about coal miners."

By applying Simplification, we can separate the conjunction into its individual components: s(y) (y is a movie produced by Sayles) and c(y) (y is a movie about coal miners). This allows us to conclude that there is a movie produced by Sayles (s(y)) and there is a movie about coal miners (c(y)).

Using the Simplification rule of inference enables us to break down complex statements and work with their individual components. It allows us to extract information from conjunctions, making it a useful tool in logical reasoning and deduction.

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Effect size is a measure of the strength of the relationship between two variables. It does not indicate whether one variable causes another. The amount of variance in a set of scores is measured by the variance.

Whether an obtained research finding is valid is determined by statistical significance. Effect size is a quantitative measure of the magnitude of the experimental effect.

It is a way of quantifying the strength of the relationship between two variables. Effect sizes are typically reported on a standardized scale, such as Cohen's d or r.

Effect size does not indicate whether one variable causes another. Causation can only be inferred from a well-designed experiment that controls for confounding variables.

Effect size can be used to assess the strength of the relationship between two variables, but it cannot be used to determine whether one variable causes another.

The amount of variance in a set of scores is measured by the variance. Variance is a measure of how spread out the scores are in a set.

A high variance indicates that the scores are spread out over a wide range, while a low variance indicates that the scores are clustered together.

Whether an obtained research finding is valid is determined by statistical significance. Statistical significance is a measure of how likely it is that the observed results could have occurred by chance. A statistically significant result means that the observed results are unlikely to have occurred by chance alone.

Effect size, variance, and statistical significance are all important concepts in statistics. Effect size measures the strength of the relationship between two variables,

variance measures the spread of scores in a set, and statistical significance measures the likelihood that the observed results could have occurred by chance.

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The duration of this bond is 6.5 years.

Duration is a measure of a bond's sensitivity to changes in interest rates. To calculate the duration of this bond, we need to consider the present value of the bond's cash flows and the timing of those cash flows. In this case, the bond has a face value of $1,000, a coupon rate of 10 percent, and annual coupon payments.

First, we calculate the present value of the bond's cash flows. Since the bond has a coupon rate of 10 percent, the annual coupon payment is $100 ($1,000 x 10%). The bond has a remaining maturity of seven years, so there will be seven coupon payments in total. We can calculate the present value of these cash flows using the formula for the present value of an ordinary annuity:

Present Value = Coupon Payment x [1 - (1 + interest rate)^(-number of periods)] / interest rate

Assuming an interest rate of r, we have:

Present Value = $100 x [1 - (1 + r)^(-7)] / r

Next, we need to find the yield to maturity (YTM) of the bond. YTM is the rate of return an investor would earn by holding the bond until maturity. Since the bond is currently selling for $1,104 in the market, we can set up the following equation:

$1,104 = Present Value + (Coupon Payment / (1 + r)^7)

By solving this equation for r, we can find the yield to maturity. Using a financial calculator or spreadsheet software, we can determine that the yield to maturity is approximately 7 percent.

Now, we can calculate the duration of the bond. The duration formula is the weighted average time until the bond's cash flows are received, where the weights are the present values of the cash flows. In this case, we have seven annual cash flows, so the duration can be calculated as follows:

Duration = [(1 x Present Value of Year 1) + (2 x Present Value of Year 2) + ... + (n x Present Value of Year n)] / Present Value of the Bond

Plugging in the values, we get:

Duration = [(1 x Present Value of Year 1) + (2 x Present Value of Year 2) + ... + (7 x Present Value of Year 7)] / Present Value of the Bond

Calculating the present values for each year using an interest rate of 7 percent, we find:

Present Value of Year 1 = $100 / (1 + 0.07)^1

Present Value of Year 2 = $100 / (1 + 0.07)^2

...

Present Value of Year 7 = $100 / (1 + 0.07)^7

After calculating the present values for each year and plugging them into the formula, we find that the duration of the bond is approximately 6.5 years.

Therefore, the correct answer is 6.5 years.

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Answer:

Step-by-step explanation:

Using the relation :

S = ut + 1/2at²

S = distance

Car A :

Initial speed, u = 40 mph

a = negative acceleration = - 1 mph

At time, t = 4

S = 40(4) - 0.5(1)(4²)

S = 160 - 8

S = 152 miles

Car B :

Initial speed, u = 30 mph

a = acceleration = 0.5 mph

S = 30(4) - 0.5(1)(4²)

S = 120 - 8

S = 118 m

Change in distance / time

Rate of change = (152 - 118)m / 4 hours

Rate of change = 34 mi / 4 hr

Rate of change = 8.5 miles per hour

In the Pythagorean theorem, a²+b²=c² is the formula for finding the missing side length in a right-angled triangle. This formula is useful for determining one of the missing side lengths of a right triangle if you know the other two.

However, the theorem also states that c is the length of the triangle's hypotenuse. So, if you have a right-angled triangle with all three sides provided, you may use the Pythagorean theorem to solve for any of the missing sides. You'll use the hypotenuse length as the c variable when the three sides are given, then solve for the missing side.

To apply the Pythagorean theorem, you must identify the hypotenuse, which is the side opposite the right angle. If you're given three sides, the longest side is always the hypotenuse. As a result, you can always use the Pythagorean theorem to solve for one of the shorter sides by using the hypotenuse length.

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Answer:

7) 55 .    8) 30        9) 18

Step-by-step explanation:

Step-by-step explanation:

Given that:-

\((2x - 1)\)

is exactly divisible by

\(6 {x}^{2} + ax - 4\)

and

\(b {x}^{2} - 11x + 3\)

We need to simply, place the value of x.

\(2x - 1 = 0\)

\(2x = 1\)

\(x = \frac{1}{2} \)

Now,

\(6 {( \frac{1}{2} )}^{2} + \frac{a}{2} - 4 = 0\)

\( \frac{3 + a}{2} = 4\)

\(3 + a = 4 \times 2 = 8\)

\(a = 8 - 3\)

\(a = 5\)

Now, to find b.

\(b {( \frac{1}{2}) }^{2} - \frac{11}{2} + 3 = 0\)

\( \frac{b}{4} - \frac{11}{2} = - 3\)

\( \frac{b - 22}{4} = - 3\)

\(b - 22 = - 12\)

\(b = 10\)

is the answer.

Now, we need

\( {b}^{2} - {a}^{2} + a - b\)

\(100 - 25 + 100 + 5\)

\( = 205 - 25\)

\( = 180\)

is the answer.

Hope it helps :D

Answer:

You want to multiply the 6 to the numbers inside the parythesis:

6 * x = 6x

6 * 5 = 30

6x + 30

Step-by-step explanation:

Hope it helps! =D

Answer:

6x + 30

Step-by-step explanation:

1. 6(x + 5)

2. 6x+30

We know that :

\(\color{hotpink} \tt \: circumference \: of \: a \: circle\color{plum} = 2\pi r\)

So, let the diameter of this circle be x.

Which means :

\( =\tt2 \times \pi \times r\)

\( =\tt 2 \times x \times \pi = 12\pi\)

\( =\tt 2x\pi = 12\pi\)

\( =\tt x = \frac{12}{2} \)

\( = \tt \: x = 6 \: m\)

Thus, the radius of the circle Robert drew = 6 m

Since the circle in option B has a radius of 6 m, it is the circle Robert drew.

▪︎Therefore, the correct option is (B)

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

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The parallelogram should look like a rectangle with one of the sides longer than the other.

The sketch of a parallelogram with both diagonals of length M and perpendicular to each other would look like this:

\(| | ||---|----|| | ||M | || | N || | ||___|____|\)

To draw a parallelogram with both diagonals having length M, start by sketching two perpendicular lines of length M. Then, draw two additional perpendicular lines connected to the end of each of the first two lines. The length of the new lines should be N. Finally, connect the endpoints of the new lines to the endpoints of the original two lines, forming a parallelogram with both diagonals of length M and perpendicular to each other. The parallelogram should look like a rectangle with one of the sides longer than the other.

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The solution to the initial value problem is:

y(t) = -(3/16)g(t) cos(t) + (1/4)g(t) sin(t)

The given initial value problem is a second-order linear ordinary differential equation with constant coefficients. The general solution of the homogeneous equation y'' + y' + 5/4y = 0 is given by:

r^2 + r + 5/4 = 0

Using the quadratic formula, we get:

r = (-1 ± √(1 - 5))/2 = -1/2 ± i√(3)/2

Thus, the general solution of the homogeneous equation is:

y_h(t) = c1e^(-t/2)cos(√(3)t/2) + c2e^(-t/2)sin(√(3)t/2)

To find the particular solution of the nonhomogeneous equation, we need to find a particular solution of the form y_p(t) = A cos(t) + B sin(t), where A and B are constants to be determined. Taking the first and second derivatives of y_p(t), we get:

y_p'(t) = -A sin(t) + B cos(t)

y_p''(t) = -A cos(t) - B sin(t)

Substituting y_p(t), y_p'(t), and y_p''(t) into the non-homogeneous equation, we get:

(-A cos(t) - B sin(t)) + (-A sin(t) + B cos(t)) + 5/4(A cos(t) + B sin(t)) = g(t)

Simplifying and matching the coefficients of cos(t) and sin(t), we get:

(3/4)A + B = g(t)

-A + (3/4)B = 0

Solving these equations for A and B, we get:

A = -3/16 g(t)

B = 1/4 g(t)

Therefore, the particular solution of the nonhomogeneous equation is:

y_p(t) = (-3/16)g(t) cos(t) + (1/4)g(t) sin(t)

The general solution of the nonhomogeneous equation is the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

= c1e^(-t/2)cos(√(3)t/2) + c2e^(-t/2)sin(√(3)t/2) - (3/16)g(t) cos(t) + (1/4)g(t) sin(t)

Using the initial conditions y(0) = 0 and y'(0) = 0, we get:

c1 = 0

c2 = 0

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Answer:

4.72222222222

Step-by-step explanation:

I just calculate

can I have brainliest

Answer:

x=4

Step-by-step explanation:

Answer:

X=4

Step-by-step explanation:

All work shown below. Y cannot be solved for because it is not a variable in the equation.

Answer:

15) A

Step-by-step explanation:

4x-2 + 7x + 17 = 180

11x + 15 = 180

11x = 165

x = 15

Because the two angles (4x-2 and 7x+17) are linear, we can say that they add up to 180 degrees.

4x-2+7x+17 = 180   Now, simplify like terms

11x + 15 = 180

11x = 165

x = 15

Thus, the value of x would be 15 (choice 1)

Answer: 9 laps in 1 day = 18 laps in 2 days

Step-by-step explanation:

To complete the proportion, we can use the fact that the number of laps is directly proportional to the number of days:

9 laps in 1 day = 18 laps in x days

To solve for x, we can use the property of proportions that the product of the means equals the product of the extremes:

9 laps × x days = 1 day × 18 laps

Simplifying, we get:

9x = 18

Dividing both sides by 9, we get:

x = 2

Therefore, the missing number to complete the proportion is 2. The complete proportion is:

9 laps in 1 day = 18 laps in 2 days

Answer: 2 days

Step-by-step explanation: 9 + 2 equals 18 therefor 18 laps in 2 days

Using the given data on the number of live multiple-delivery births for women aged 15 to 54, we need to calculate probabilities related to the age groups of the mothers. The probability of a randomly selected multiple birth involving a mother aged 30 to 39 will be determined, as well as the probabilities of not being in the age range, being less than 45, and being at least 40. Finally, we need to interpret whether a multiple birth involving a mother aged at least 40 is unusual.

(a) To calculate the probability of a randomly selected multiple birth involving a mother aged 30 to 39, we sum the number of multiple births in that age group and divide it by the total number of multiple births for women aged 15 to 54.

P(30 to 39) = 2822 / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(b) To find the probability of a randomly selected multiple birth involving a mother who is not aged 30 to 39, we subtract the probability found in part (a) from 1.

P(not 30 to 39) = 1 - P(30 to 39)

(c) To determine the probability of a randomly selected multiple birth involving a mother aged less than 45, we sum the number of multiple births for age groups below 45 and divide it by the total number of multiple births for women aged 15 to 54.

P(less than 45) = (89 + 508 + 1631 + 2822 + 1855 + 374) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(d) To find the probability of a randomly selected multiple birth involving a mother aged at least 40, we sum the number of multiple births for age groups 40-44 and 45-54, and divide it by the total number of multiple births for women aged 15 to 54.

P(at least 40) = (374 + 119) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

Interpretation: The answer to part (d) will determine whether a multiple birth involving a mother aged at least 40 is unusual. If the probability is less than 0.05, it can be considered unusual. Therefore, we need to compare the calculated probability to 0.05 and select the correct choice.

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The area bounded by \(\( y=\frac{x-16}{x^{2}-1 x-30}, x=3, x=4 \)\), and \( y=0 \) is approximately 5.1417 sq.units.

We have to find the area bounded by \(\( y=\frac{x-16}{x^{2}-1 x-30}, x=3, x=4 \), and \( y=0 \)\).

To calculate the area, we will follow the steps below:

Step 1: Find the roots of the quadratic equation

Step 2: Determine if the denominator is positive or negative.

Step 3: Find the limits of integration by equating the two lines

Step 4: Integrate to find the area.

Step 1: Find the roots of the quadratic equation.

Let us find the roots of the quadratic equation \(\(x^{2}-x-30=0\)\).

We know that the roots are \(\(x=6\)\) and \(x=-5\).

Therefore, \(\( y=\frac{x-16}{(x-6)(x+5)} \)\).

Step 2: Determine if the denominator is positive or negative.

The denominator is positive if \(x\) lies in the interval \(\((-\infty,-5)\) and \((6,\infty)\)\).

The denominator is negative if \(x\) lies in the interval \((-5,6)\).

Step 3: Find the limits of integration by equating the two lines

The area bounded by the curve is equal to the integral of the curve between the limits \(\(x=3\)\)and \(\(x=4\)\).

Therefore, the limits of integration are 3 and 4.

To determine the limit of integration with respect to y, we will equate the curve with y=0.

Then, solve for x to find the limits of integration.

With y=0, x=16 or x=-2.

Thus, the limits of integration with respect to y are 0 and 16, which are the limits of the line x=16.

Step 4: Integrate to find the area.

Area = ∫ ₃ ⁴  ( x − 16 ) ( x − 6 ) ( x + 5 ) d x .

Let us do the integration:

( Area = \(\( \frac{29}{6} \ln(6) + \frac{271}{180} \ln(30) \approx 5.1417\)\) (rounding off to 4 decimal places).

Thus, the area bounded by \( y=\frac{x-16}{x^{2}-1 x-30}, x=3, x=4 \), and \( y=0 \) is approximately 5.1417 sq.units.

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Answer:

q 3 = 3/12.2/9 q4 = 15/40.14/39

Answer: A

Step-by-step explanation:

-7+4x>-3 ; isolate x

4x>-3+7

4x>4; divide 4

x>1

> is a opened circle and greater than goes to the right side, therefore, the answer is A.

Answer:

Answer 1

Step-by-step explanation:

\(-7+4x>-3\\4x>-3+7\\4x>4\\x>1\\\)

Step-by-step explanation:

triangles are similar so

their sides are the same rapport

48/6=x/5

scale factor is 48/6=8

value of x ,we can use the formula

48/6=x/5

8=x/5

x=8*5=40

Answer:

A

Step-by-step explanation:

The entire frame is 42 x 23 in, but for each dimension there are two lengths of x inches that are included in the entire dimension but not that of the actual picture. Thus, the correct equation is (42 - 2x)(23 - 2x) = 700 which is choice A.

The sketching  a cube with 3 units on each edge on isometric drawing dot paper, follow these steps:

Start by drawing a horizontal line segment of 3 units on the isometric dot paper. This will serve as the base of the cube.

From each end of the base, draw two vertical lines upward, each measuring 3 units. These lines should be parallel to each other and perpendicular to the base.

Connect the corresponding ends of the vertical lines with a horizontal line segment, creating the top face of the cube. Ensure that this line segment is also 3 units long.

Connect the corresponding vertices of the base and top face with vertical lines, completing the visible edges of the cube. These lines should be parallel to each other and perpendicular to both the base and top face.

Finally, draw dashed lines to represent the hidden edges of the cube. These dashed lines connect the non-corresponding vertices of the base and top face.

By following these steps, you will have sketched a cube with 3 units on each edge on isometric dot paper. Isometric dot paper is specifically designed to assist in drawing three-dimensional objects, and the dots on the paper help maintain the correct proportions.

Therefore,  it is important to align the lines and vertices properly to ensure an accurate representation of the cube.

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Answer:

i believ its b

Step-by-step explanation:

Answer:

(-1,-3)

Step-by-step explanation:

90 degree rotation = (x,y) —> (-y,x)

Answer:

See Below

Step-by-step explanation:

ABCD primes all correspond to x and y values on the graph.

A=

B=

C=

D=

1) y- intercept

2) time of max height

3) time when balloon hits ground

4) x-intercept

5) max height  

6) Initial height

So lets look at (0,A)

This would count as the y - intercept as well as the height they started throwing the balloons.

Soo....

A = y-intercept; Initial height

Now, (B,C)

This is the highest point on the graph, therefore it would be the max time and max height.

If we look at this as a person behind the line throwing the ballon, the y would be the height and the x would be the time

B = Time of max height

C=Max height

(D,0)

From the visual above, this point would be where the balloon hits the ground

From the visual in our head, x is time and y is height

Since d is the x, it is the time when the balloon hits the ground. And since

y =0, D is also the x intercept

D =  x intercept, Time when balloon hits ground

Therefore,

A = y-intercept; Initial height

B = Time of max height

C=Max height

D =  x intercept, Time when balloon hits ground

Hope this helps! =D

The triangle is a shape with 3 sides and angles. The value of z from the given figure to the nearest tenth is 3.2

The triangle is a shape with 3 sides and angles

From the given triangle, we will use the expression below to determine the value of z

2.6/sin51= z/sin76

simplify

z = 2.6sin76/sin51
z = 2.5227/0.7771

z = 3.246

Hence the value of z from the given figure to the nearest tenth is 3.2

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