Choose whether the probability is mutually exclusive or not
answer choice is:
mutually exclusive or not mutually exclusive

P(A) = 2/5 P(B) = 1/2 P(A or B) = 9/10

The standard deviation of a larger sample will be closer to the standard deviation of the population than the standard deviation of a smaller sample, making it a better estimate of the population standard deviation.

In order to measure the variability or spread of a population, a population standard deviation is utilized. This is frequently unknown and estimated using the standard deviation of a random sample taken from the population. The sample standard deviation is the measure of variability for a set of data values obtained from a sample.The sample standard deviation is preferable to the population standard deviation for samples, particularly large samples. The sample standard deviation, abbreviated as "s", is used to estimate the population standard deviation, represented by the Greek letter sigma, which is unknown in this situation. The sample standard deviation is more likely to accurately reflect the true population standard deviation when it is calculated from a large sample size.Samples from populations that have a normal distribution provide the most precise estimate of the population standard deviation. If the population distribution is not normal, the sample size should be at least 30. However, for smaller samples, it is impossible to estimate the population standard deviation using the sample standard deviation. This is particularly true when the population has an atypical or unusual distribution.

In conclusion, the sample standard deviation (s) is a better estimate of the population standard deviation for large samples.

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The surface integral of f over the unit sphere is (4π/15) (3 k), where k is the unit vector in the z-direction. The answer is independent of the specific parameterization of the sphere and only depends on the surface itself.

To evaluate the surface integral of f over the unit sphere, we need to use the formula:

∫∫S f · dS = ∫∫R f(φ,θ) · ||r(φ,θ)|| sin(φ) dφdθ

Where S is the surface of the unit sphere, R is the region in the parameter domain (φ,θ) that corresponds to S, ||r(φ,θ)|| is the magnitude of the partial derivative of the position vector r(φ,θ), and sin(φ) is the Jacobian factor.

For the unit sphere, we have:

x = sin(φ) cos(θ)
y = sin(φ) sin(θ)
z = cos(φ)

So, we can find the partial derivatives:

r_φ = cos(φ) cos(θ) i + cos(φ) sin(θ) j - sin(φ) k
r_θ = -sin(φ) sin(θ) i + sin(φ) cos(θ) j

Then, we can compute the magnitude:

||r_φ x r_θ|| = ||sin(φ) cos(φ) cos(θ) j + sin(φ) cos(φ) sin(θ) (-i) + sin^2(φ) k|| = sin(φ)

Now, we can substitute into the formula and evaluate the integral:

∫∫S f · dS = ∫0^π ∫0^2π (sin^3(φ) cos^3(θ) i + sin^3(φ) sin^3(θ) j + sin^3(φ) cos^3(φ) k) · sin(φ) dφdθ
= ∫0^π ∫0^2π sin^4(φ) (cos^3(θ) i + sin^3(θ) j + cos^3(φ) k) dφdθ

To integrate over θ, we can use the fact that cos^3(θ) and sin^3(θ) are odd functions, so their integral over a full period is zero. Thus, we get:

∫∫S f · dS = ∫0^π (1/5) sin^5(φ) (3 cos^3(φ) k + 2 sin^3(φ) i + 2 cos^3(φ) j) dφ
= (4π/15) (3 k)

Therefore, the surface integral of f over the unit sphere is (4π/15) (3 k), where k is the unit vector in the z-direction. The answer is independent of the specific parameterization of the sphere and only depends on the surface itself.

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A 4-m rod whose linear density function is rho(x)=14(x+9)^−1 kg/m for 0≤x≤4 has the total mass of the rod is 14 ln(22/9) kg.

To find the total mass of the 4-m rod whose linear density function is given by rho(x) = 14(x+9)^-1 kg/m for 0≤x≤4, we need to integrate the linear density function with respect to x over the interval [0, 4].

The mass of an infinitesimal element of length dx at position x is given by dm = rho(x) dx. Thus, the total mass of the rod is given by the integral of dm over the interval [0, 4], which can be expressed as:

M = ∫[0,4] rho(x) dx

Substituting the given linear density function rho(x), we have:

M = ∫[0,4] 14(x+9)^-1 dx

Integrating this expression using the substitution u = x+9 and du = dx, we get:

M = 14 ln(u)|[9,13]

= 14 ln(13+9) - 14 ln(9+9)

= 14 ln(22/9)

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Answer:

The neighborhood the home is located in

The factors which does not affect the mortgage payment is the neighborhood the home is located in.

The correct option is D.

We are aware of this;

A mortgage is a loan when the borrower's property is used as security. The mortgage payment is determined by the cost of the property, the interest rate, the down payment, the length of the loan, taxes, and various insurances like homeowners insurance, among other factors.

Hence, It's not depend on ''The neighborhood the home is located in.''

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Answer:

It equals 7 and one fourths, 7 1/4.

Answer:

5.5 or 5 1/2

Step-by-step explanation:

4*3/4+2 1/2=

3+2 1/2 because you can multiply 4 and 3/4 to make 12/4 which is also simplified to 3.

then you can add 3 and 2 to make 5 and then add 1/2. that would make 5 1/2.

Answer: She is using the counting-on technique.

Step-by-step explanation:

Assuming that the events of each executive receiving a pay raise are independent, we can use the multiplication rule for independent events to find the probability that all four received a raise.

Let's denote the event that an executive receives a raise by "R". Then, the probability that an executive receives a raise is P(R) = 0.78, and the probability that an executive does not receive a raise is P(not R) = 1 - P(R) = 0.22.

The probability that all four executives receive a raise is:

P(R and R and R and R) = P(R) x P(R) x P(R) x P(R)

= 0.78 x 0.78 x 0.78 x 0.78

= 0.37 or 0.0037 (rounded to 4 decimal places)

Therefore, the probability that all four executives received a raise when they asked for one is approximately 0.0037 or 0.37%.

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Answer:

225.6 feet

Step-by-step explanation:

It should be pretty simple, you need to multiply 75.2 times 3. In result your answer is 225.6 feet or rather more simply (225 feet 7 13/64 inches.)

We are given the time taken to travel a certain as an estimated 4 hours 55 minutes. Also, the average speed for the journey is given as 51 miles per hour. To calculate the distance, the formula given is;

Note that the time is given as 4 hours plus a fraction of an hour, that is 55 minutes. To express this as a decimal we take the value of 55 minutes as a fraction of one hour, that is;

The time taken therefore can be expressed as;

The distance covered therefore would be;

We simplify and we now have;

Rounded to the nearest mile, that is, the nearest whole number;

ANSWER:

Ans .: The dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

To minimize the cost of the container, we need to find the dimensions that will use the least amount of material. Let's call the length of one side of the square base "x" and the height of the container "h".

The volume of the container is given as 2000 cm^3, so we can write:

V = x^2h = 2000

We need to find the dimensions that will minimize the cost, which is determined by the amount of material used. We know that it costs twice as much per square centimeter to make the top and bottom as it does the sides.

Let's call the cost per square centimeter of the sides "c", so the cost per square centimeter of the top and bottom is "2c". The total cost of the container can then be expressed as:

Cost = 2c(x^2) + 4(2c)(xh)

The first term represents the cost of the top and bottom, which is twice as much as the cost of the sides. The second term represents the cost of the four sides.

To minimize the cost, we can take the derivative of the cost function with respect to "x" and set it equal to zero:

dCost/dx = 4cx + 8ch = 0

Solving for "h", we get:

h = -0.5x

Substituting this into the volume equation, we get:

x^2(-0.5x) = 2000

Simplifying, we get:

x^3 = -4000

Taking the cube root of both sides, we get:

x = -16.7

Since we can't have a negative length, we take the absolute value of x and get:

x = 16.7 cm

Substituting this into the equation for "h", we get:

h = -0.5(16.7) = -8.35

Again, we can't have a negative height, so we take the absolute value of "h" and get:

h = 8.35 cm

Therefore, the dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

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In testing for differences between the means of 2 independent populations the null hypothesis is zero.

This is defined as a statistical hypothesis which has no statistical significance in a set of given observations.

In testing for differences between the means of 2 independent populations the null hypothesis is the difference between the two population means and is not significantly different from zero which is denoted below:

H₀: µ₁ - µ₂ = 0

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Answer:

1.1286

Step-by-step explanation:

Increasing something by 14% is the same as taking 114% of it, and decreasing it by 1% is the same as taking 99% of it. 114% is 1.14 as a decimal, and 99% is 0.99 as a decimal, so multiplying the two together, we get the single decimal

1.14 · 0.99 = 1.1286

Answer:

x=-4 or -7

Step-by-step explanation:1: 2x+11=3

2x=-8

x=-4

2: -(2x+11)=3

2x+11=-3

2x=-14

x=-7

The missing corresponding side length is 6 feet

From the question, we have the following parameters that can be used in our computation:

Also, see attachment for the figures

From the question, we have:

Figure A is similar to Figure B

This means that

Side length A = √(Figure A/Figure B) * Side length B

Substitute the known values in the above equation, so, we have the following representation

Side length A = √(18/98) * 14

Evaluate

Side length A = 6

Hence, the side length is 6

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Answer:

53.13 degrees

Step-by-step explanation:

From the shape of the graph, we can see that the plotted line forms a right-angled triangle with the x and y coordinates. As a result, we can use laws that govern the geometry of right-angled triangles to evaluate the solution.

\(tan \theta = opposite/ adjacent\)

The opposite side in this case is the side directly facing the angle Θ. This is the y - axis value = -4

The adjacent side in this case is the side above the angle Θ. This is the y - axis value = -3

\(tan \theta = (-4/-3)\\\theta = tan ^-1(4/3) = 53.13 degrees\)

Answer:

10z +1

Step-by-step explanation:

3z+7z=10z

5-4=1

10z +1

Answer:

10z+9

Step-by-step explanation:

3z+5+7z+4

3z+9+7z

Answer:

The answer is x = 3

Step-by-step explanation:

7x - 3(x-6) =30

7x -3x+18=30

4x= 30-18

4x=12

x=12/4

x=3

Answer:

x=3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7x−3(x−6)=30

7x+(−3)(x)+(−3)(−6)=30(Distribute)

7x+−3x+18=30

(7x+−3x)+(18)=30(Combine Like Terms)

4x+18=30

4x+18=30

Step 2: Subtract 18 from both sides.

4x+18−18=30−18

4x=12

Step 3: Divide both sides by 4.

4 divided by 12 =3

4 divided 4 = 1

x=3

The value of x will be;

⇒ x = - 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 8 × 2²ˣ + 4 × 2ˣ × 2 = 1 + 2ˣ

Now,

Since, The expression is,

⇒ 8 × 2²ˣ + 4 × 2ˣ × 2 = 1 + 2ˣ

Solve for x as;

⇒ 8 × 2²ˣ + 8 × 2ˣ = 1 + 2ˣ

⇒ 8 × 2ˣ (2ˣ + 1) = 1 + 2ˣ

⇒ 8 × 2ˣ = (1 + 2ˣ) / (1 + 2ˣ)

⇒ 8 × 2ˣ = 1

⇒ 2ˣ = 1/8

⇒ 2ˣ = 2⁻³

By comparing, we get;

⇒ x = - 3

Thus, The value of x = - 3

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Answer:

As you wish love, 2sqrt x 3sqrt8 = 12sqrt6

Step-by-step explanation:

2sqrt3x3sqrt8

Simplify,

2sqrt3 x 3 x 2sqrt2

Evalutate,

12sqrt6

The regression line that forecasts home equity using the FICO credit score as the explanatory variable has the equation Y' = 1798X + 0.

Due to the fact that this linear regression model includes two parameters that need to be estimated from training data, it has two degrees of freedom. One additional column in the data (one additional input variable) would provide the model one extra degree of freedom.

An equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable, represents a linear regression line. A line's intercept (the value of y when x = 0) is equal to the slope of the line, which is b.

Hence we get the required answer.

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Answer:

C.  30(-2)= -60 is the correct answer

Step-by-step explanation:

Answer:

a) 0.30854

b) 0.21186

c) 0.23468

Step-by-step explanation:

Mario's Pizza delivers pizzas within a 10-mile radius of the restaurant. Their delivery times are Normally distributed with a mean delivery time of 30 minutes and a standard deviation of 10 minutes.

We solve using z score formula.

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Find the probability that a randomly selected customer will have to wait

a) less than 25 minutes

for x < 25 minutes

z = 25 - 30/10

z = -0.5

Probability value from Z-Table:

P(x<25) = 0.30854

b) more than 38 minutes

For x > 38 minutes

z = 38 - 30/10

z = 0.8

Probability value from Z-Table:

P(x<38) = 0.78814

P(x>38) = 1 - P(x<38) = 0.21186

c) between 26 and 32 minutes

For x = 26 minutes

z = 26 - 30/10

z = -0.4

Probability value from Z-Table:

P(x = 26) = 0.34458

For x = 32 minutes

z = 32 - 30/10

z = 0.2

Probability value from Z-Table:

P(x = 32) = 0.57926

The probability that a randomly selected customer will have to wait between 26 and 32 minutes is calculated as:

P(x = 32) - P(x = 26)

= 0.57926 - 0.34458

= 0.23468

The total amount they paid for dinner that night = $22.2

Dinner bill = $18.50

They paid 5% food tax

Food tax = (5/100) x 18.50

Food tax = $0.925

They left a 15% tip for the waiter

Tip = (15/100) x 18.50

Tip = $2.775

Total amount paid = Dinner bill + Food tax + Tip

Total amount paid = $18.50 + $0.925 + $2.775

Total amount paid = $22.2

The total amount they paid for dinner that night = $22.2

The volume of the rectangular prism is 3359232 cubic centimeters

The length of the cube is given as:

Length, l = 12 cm

The volume of a cube is:

\(V = l^3\)

So, we have:

\(V = 12^3\)

Evaluate

V = 1728

The volume of 1944 cubes is then calculated as:

Volume = 1728 * 1944

Evaluate

Volume = 3359232

Hence, the volume of the rectangular prism is 3359232 cubic centimeters

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There are exactly 1,944 of the 12 cm, or 0.5 foot cubes inside a rectangular prism.  What is the volume of the rectangular prism in cubic centimeters?

Answer:

I think 49 im not sure

Step-by-step explanation:

dont trust me I not good with math

The arithmetic sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43,....

Common difference = 4

First term = 3

The formula for the sum of the first n terms of an arithmetic sequence is:

Sₙ = ⁿ/₂[2a + (n − 1)d]

where:

n = the number of terms to be added.

a = the first term in the sequence.

d = common difference

We are told that sum of the first 9 term is 171. Thus:

(9/2) [2a + (9 − 1)d]  = 171

(2a + 8d) = 38   ----(1)

Sum of the next 5 term is 235.

Thus, sum of the first 14 terms = 235 + 171 = 406

(14/2) [2a + (14 − 1)d]  = 406

7(2a + 13d) = 406

2a + 13d = 58    -----(2)

Subtract eq 1 from eq 2 to get:

5d = 20

d = 4

2a + 13(4) = 58

2a = 58 - 52

a = 3

Sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43,....

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There is no graph provided for reference, but if the graph shows a probability distribution, then the probabilities that are equal to 0.3 would depend on the specific shape and values displayed on the graph.

Without this information, it is impossible to determine which probabilities are equal to 0.3. Based on the given information, the graph represents a probability distribution. To determine which probabilities are equal to 0.3, you would need to analyze the graph (which is not provided). However, I can explain each term:
1. p(5≤x≤8): This represents the probability that x falls between 5 and 8, inclusive.
2. p(x≤3): This denotes the probability that x is less than or equal to 3.
3. p(x≥3): This signifies the probability that x is greater than or equal to 3.
4. p(3≤x≤5): This indicates the probability that x falls between 3 and 5, inclusive.

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The region enclosed by the curves y = x, y = 3x, and y = -x + 4 needs to be sketched, and its area should be found.

To sketch the region enclosed by the curves, we need to plot the three given curves on a coordinate plane. The first curve is y = x, which represents a straight line passing through the origin (0,0) with a slope of 1. The second curve is y = 3x, which is also a straight line passing through the origin but with a steeper slope of 3. The third curve is y = -x + 4, which represents a line with a y-intercept of 4 and a negative slope of -1. By plotting these three lines on the same coordinate plane, we can see that they intersect at three points: (0,0), (1,3), and (3,1). The region enclosed by these curves is a triangular region with vertices at these three points. To find the area of this triangular region, we can use the formula for the area of a triangle: A = (1/2) * base * height. Let's draw the graph:

     |

   4 |         .  (2, 2)

     |      .

     |   .

     | .

   0 |_____________________

     0     1     2     3     4     5     6

In this graph, the first equation (y = x) is depicted by a diagonal line passing through the origin (0,0). The second equation (y = 3x) is a steeper line, while the third equation (y = -x + 4) is a downward-sloping line with a y-intercept of 4. In this case, the base of the triangle is the distance between the points (0,0) and (3,1), which is 3 units. The height of the triangle is the distance between the point (1,3) and the line y = -x + 4, which is also 3 units. Substituting these values into the area formula, we get A = (1/2) * 3 * 3 = 4.5 square units.

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