Claim amounts, X, follow a Gamma distribution with mean 6 and variance 12. Calculate Pr[x < 4]. A 0.28 B 0.32 C 0.35 D 0.39 E 0.44

the awnser would be 24cm^2

The price of the lot measuring 120' x 200', selling for $300 a front foot is $192,000.

To find out the price of a lot measuring 120' x 200', selling for $300 a front foot, you need to use the formula given below;

Price = Front Footage × Price per Front Foot

First, you need to calculate the front footage of the lot, which can be obtained by adding up the length of all the sides of the rectangular lot.

Front footage = 120 + 120 + 200 + 200

                       = 640 ft

Then you can find the price of the lot by multiplying the front footage by the price per front foot.

Price = 640 ft × $300/ft

        = $192000

Therefore, the price of the lot measuring 120' x 200', selling for $300 a front foot is $192,000.

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Answer:

b and c

Step-by-step explanation:

Answer:

Hands down c and b

Step-by-step explanation:

Answer:

C. 9

Step-by-step explanation:

Here is available cases.
Ham + Swiss Cheese
Ham + American Cheese
Ham + cheddar Cheese

turkey+ Swiss Cheese
turkey+ American Cheese
turkey+ cheddar Cheese

roast beef + Swiss Cheese
roast beef + American Cheese
roast beef + cheddar Cheese

So the answer must be 9.

TThe answer to the question "find the MAD. 3 9 4 3 6 2" is 1.5. If the answer were a decimal, we would round it to the nearest tenth, which is not necessary in this case.

To find the MAD (Mean Absolute Deviation) of a set of numbers, we first need to find the mean or average of those numbers. In this case, the mean is the sum of all the numbers divided by the total number of numbers.

Adding all the given numbers,

3+9+4+3+6+2 = 27

we get 27.

=  27÷ 6

=4.5

(the total number of numbers), we get the mean as 4.5. Next, we find the absolute deviation of each number from the mean, which is simply the absolute value of the difference between the number and the mean.

For example, the absolute deviation of 3 from 4.5 is 1.5. Adding all the absolute deviations and dividing it by the total number of numbers gives us the MAD. In this case, the MAD is 1.5.

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The area of interior of  the curve by   use Green's theorem is 3pi/8.

What is Green's theorem?

Green's theorem says that if you add up all the microscopic circulation inside C (i.e., the microscopic circulation in D), then that total is exactly the same as the macroscopic circulation around C.

We have given curve x2/3+y2/3=1

parametrizing the curve

Let x(t)=cos3t,y(t)=sin3t

(cos3t)2/3+(sin3t)2/3=1 implies (cos2t)+(sin2t)=1 ,for 0<=t<=2pi

dx=-3cos2t*(sint)dt,dy=3sin2t cost dt

So, the area equals (By Green's theorem)

1/2* integration of (-y dx+x dy) over C

=1/2*integration of(0 to 2pi) (-sin3t(-3cos2t*(sint))+cos3t(3sin2t cost)) dt

=1/2*integration of(0 to 2pi) (3sin4t cos2t+3cos4tsin2t) dt

=1/2*integration of(0 to 2pi) [(3sin2t cos2t)*(sin2t+cos2t)]dt

=1/2*integration of(0 to 2pi) [(3sin2t cos2t)]dt since sin2t+cos2t=1

=3/2*integration of(0 to 2pi) [(sint*cost)2]dt

=3/2*integration of(0 to 2pi) [((1/2)sin(2t))2]dt since sin(t)cos(t)=(1/2)*sin(2t)

=3/8*integration of(0 to 2pi) [sin2(2t)]dt

plug sin2(2t)  =  (1-cos(4t))/2

=3/8*integration of(0 to 2pi) [(1-cos(4t))/2]dt

=3/16*[t-sin(4t)/4] from 0 to 2pi

=3/16*[2pi - sin(4*2pi)/4-(0-sin(0)/4)]

=3/16*[2pi]  since sin(8pi)=0

=(3pi)/8

Therefore, the area of interior of  the curve is 3pi/8.

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The complete question is -

Find a parametrization of the curve x2/3 + y2/3 1 and use Green's Theorem to compute the area of the interior. Hint: See Example 2 page 751 to see how Green's Theorem can be used to compute areas. To find a parametrization, you should consider modifying the parametrization a(t) cos t, y(t) sint, which is a parametrization for the unit circlez2 +y2-1

The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

A. 8 fl oz = 1 c and/or D. 1 c = 8 fl oz

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

Answer:

$605

Step-by-step explanation:

The correct question is

Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?

a. $550

b. $605

c. $625

d. $750

e. $825

For the first $40 that Taho works, he earns $11 x 40 = $440

For the extra $10 (since he worked 50 hrs that week)

1½ of $11 per hr = 1.5 x $11 = $16.5

for the 10 days extra = $16.5 x 10 = $165

total pay = $440 + $165 = $605

Answer:

The answer is D.

Step-by-step explanation:

To solve, simply take .5 and multiply it by the number of minutes since after 1 minute .5 mL will be released. Therefore, after 4 minutes the patient will have 2 mL, 4 after 8 minutes, and 6 after 12 minutes. The only table that matches this pattern is D, our answer.

Step-by-step explanation:

f(x) = -5x - 30

\( \: \)

Invers

\(y = - 5x - 30\)

\(x = - 5y - 30\)

\(x + 30 = - 5y\)

\(y = - \frac{x}{5} - \frac{30}{5} \)

\(y = - \frac{x}{5} - 6\)

\( {f}^{ - 1} (x) = - \frac{x}{5} - 6\)

The limit of the ratio test for the series ∑[infinity] to n=1 10^n÷n! is infinity (∞).

The ratio test is used to determine the convergence or divergence of a series. It involves taking the limit of the absolute value of ratio of consecutive terms. If the limit is less than 1, the series converges. If the limit is greater than 1 or infinity (∞), the series diverges. If the limit is exactly 1, the test will be inconclusive.

In this case, we have f(n) = ∣(10^n+1)÷(10^n)∣ = ∣10∣ = 10. The limit of f(n) as n approaches infinity is 10.

Since the limit of f(n) is greater than 1, the series fails the ratio test. This means that the series ∑[infinity] to n=1 10^n÷n! diverges. The ratio test suggests that the series does not have a finite sum and continues indefinitely.

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Observations while trying to match the graphs:

- The position vs. time graph shows the initial position, a change in direction, and the final position.

- The initial position (m1) is a point on the graph where the position is zero or the starting position of the object.

- The changing direction (m2) is the point on the graph where the position changes from positive to negative or vice versa.

- The final position (m3) is the point on the graph where the position stabilizes or reaches its final value.

Average velocity of the cart going from m1 to m2:

To compute the average velocity, we need to find the displacement and the time interval between m1 and m2. The displacement is the difference between the positions at m2 and m1, and the time interval is the difference between the corresponding time values.

Prediction of velocity vs. time graph:

Based on the change in direction observed in the position vs. time graph, the velocity vs. time graph is expected to show a change in sign at the point corresponding to m2. The velocity will be positive before m2 and negative after m2.

Comparison of prediction with the actual result:

After adding the velocity vs. time graph to the Capstone file, it is compared with the prediction. If the prediction matches the actual result, it implies that the understanding of the relationship between position and velocity is correct. If there are differences, those differences are noted and analyzed.

Percent difference between average value calculation and Capstone mean value:

The mean value of velocity between m1 and m2 is obtained using Capstone's statistics tool, and a similar calculation is performed manually using the selected velocity points. The percent difference between these values is computed using the formula: (Capstone value - Your value) / Capstone value * 100.

Analysis of differences and explanations:

A) The percent difference between the average value calculation and the mean value given by Capstone can arise due to rounding errors or differences in calculation methods. Capstone may use a slightly different algorithm for computing the mean.

B) The percent difference represents the deviation between the manually calculated average value and the value provided by Capstone. It indicates the degree of variation between the two methods.

C) The significance of the percent difference depends on the context and the tolerance for error. A higher percent difference may be considered significant if it exceeds a predetermined threshold or if it affects the overall analysis or conclusions drawn from the data. Conversely, a lower percent difference may be considered insignificant if it falls within an acceptable range of error.

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Answer:

48 i think

Step-by-step explanation:you add both bases so 4+8=12 divided by 2 to get 6 and then multiply by 8 to get 48 i think im sorry if its wrong

The solution for the equation, 3/x - 4 = 7/x is, x = -1.

We can solve for x in the above given equation, 3/x - 4 = 7/x, by making the variable "x", the subject of the formula. What this implies is that, we would isolate the variable "x".

Therefore:

3/x - 4 = 7/x [given]

Combine like terms:

3/x - 7/x = 4

(3 - 7)/x = 4

-4/x = 4

Multiply both sides by x

-4/x × x = 4 × x

-4 = 4x

Divide both sides by 4

-4/4 = 4x/4

-1 = x

x = -1

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The probability that a student will get 4 or more correct answers just by guessing is d: 11/3^5.

The probability of getting 4 or more correct answers just by guessing in a multiple-choice examination with 5 questions and three alternative answers for each question can be calculated by using the binomial probability formula. The formula is P(X = x) = nCx * p^x * (1-p)^(n-x), where n is the number of questions, x is the number of correct answers, p is the probability of getting a correct answer, and nCx is the binomial coefficient.

For 4 correct answers, the probability is:

P(X = 4) = 5C4 * (1/3)^4 * (2/3)^1 = 5 * (1/81) * (2/3) = 10/243

For 5 correct answers, the probability is:

P(X = 5) = 5C5 * (1/3)^5 * (2/3)^0 = 1 * (1/243) * 1 = 1/243

The total probability of getting 4 or more correct answers is the sum of these two probabilities:

P(X >= 4) = P(X = 4) + P(X = 5) = 10/243 + 1/243 = 11/243

Therefore, the correct answer is d. 11/3^5.

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Answer:

Its option D :)

---

28° + y + 36° = 180°

Answer:

5

Step-by-step explanation:

\(\frac{7.5}{1.5}\) = 5

Answer:

Yes

Step-by-step explanation:

Well to figure out if 210879 is divisible by 3 we do,

210879 / 3

= 70 293.

Thus,

210879 is divisible by 3.

Hope this helps :)

Answer: Yes

Explanation: To determine whether 210,879 is divisible by 3, first we need to find the sum of the digits.

Image is provided below.

The divisibility rules tell us that if the sum of the digits is divisible by 3,

then the number is also divisible by 3.

So since 27 is divisible by 3, 210,879 must also divisible by 3.

So our answer is yes, 210,879 is divisible by 3.

Answer:

The true statements is;

Dilations of an angle must be congruent to the original angle

Step-by-step explanation:

Given that an angle is formed by the intersection of two rays, and that the ratio of the sides of a figure, before and after a dilation are the same, for an angle in a triangle we have, by sine rule;

a/(sin(α)) = b/(sin(β)) = c/(sin(γ))

Rearranging, gives;

a/b = (sin(α))/(sin(β))

Whereby for the dilation, we have;

a'/b' = (sin(α'))/(sin(β'))

We  have;

a/b = a'/b'

∴ (sin(α))/(sin(β)) = (sin(α'))/(sin(β'))

Similarly, we have;

(sin(β))/(sin(γ)) = (sin(β'))/(sin(γ'))

(sin(α))/(sin(γ)) = (sin(α'))/(sin(γ'))

Given that α, β, and γ, are less than 180°, we have

α = α'

∴ α ≅ α' by definition of congruency

β = β'

β ≅ β' by definition of congruency

γ = γ'

γ ≅ γ' by definition of congruency

Therefore; dilations of an angle must be congruent to original angle

Answer:

A=31 MILLION b=135%c=235%

Step-by-step explanation:

Answer:

a =  

✔ 31 million

31

23

≈ 1.347

b ≈  

✔ 135%

c ≈  

✔ 235%

Step-by-step explanation:

Answer:

Step-by-step explanation:

5h + c = 8.50

2h + 3c = 6

Multiply first equation by -3, then add it to second equation.

-15h - 3c = -25.50

 2h + 3c = 6

------------------------

-13h = -19.50

h = -19.50/(-13)  = 1.5

c = 8.50-5h = 1'

hot dog costs $1.50

chips cost $1

Answer:

x = 135,

y = 45

Step-by-step explanation:

45 and y are vertical angles.  That means they are equal

y = 45

45 and x form a straight line which means they sum to 180

45+x = 180

Subtract 45 from each side

45+x-45 =180-45

x = 135

When testing the null hypothesis with an alpha value of 0.05, the critical value will be larger than if you were testing the alpha value of 0.01. This is because the alpha value represents the level of significance at which we reject the null hypothesis. A smaller alpha value means we are requiring stronger evidence to reject the null hypothesis, and therefore, the critical value will be higher.

Conversely, a larger alpha value means we are more likely to reject the null hypothesis, and therefore, the critical value will be lower.
When testing a null hypothesis with an alpha value of 0.05, the critical value will be larger compared to testing with an alpha value of 0.01. The reason for this is that the alpha value represents the level of significance or the probability of rejecting the null hypothesis when it is actually true.

A smaller alpha value (e.g., 0.01) indicates a more stringent test, requiring stronger evidence to reject the null hypothesis. As a result, the critical value for a 0.01 alpha level will be smaller, making it more difficult to reject the null hypothesis. Conversely, a larger alpha value (e.g., 0.05) indicates a less stringent test, requiring less evidence to reject the null hypothesis, and the critical value will be larger, making it easier to reject the null hypothesis.

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The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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\(\sqrt{6}\cdot \sqrt{6}\cdot \sqrt{6}\implies \sqrt{(6)(6)(6)}\implies \sqrt{6^2(6)}\implies {\LARGE \begin{array}{llll} 6\sqrt{6} \end{array}}\)

For the quadrilateral ABCD the statement which proves that this quadrilateral is not a rectangle is (a) The slope of CD is "(-5-1)/(-5-5) = 3/5", and the "slope of DA is [3-(-5)]/[-3-(-5)] = 8/2", these "two-segments" are not perpendicular , so the shape is not a rectangle;

The coordinates of the "four-vertices" of the quadrilateral ABCD are :

A(-3,3), B(2,6), C(5, 1), D(-5,-5);

To prove whether the quadrilateral is a rectangle or not, we need to show that its adjacent sides are perpendicular and its diagonals are congruent.

In this question, we are given the coordinates of the four vertices of the quadrilateral.

To determine if it's a rectangle, we use the slope formula to find the slopes of the sides of the quadrilateral. If slopes of adjacent sides are "negative-reciprocals" of each other, then they are perpendicular. If the slopes of the diagonals are equal, then they are congruent.

Using the given coordinates, we find that the slope of CD is = (-5-1)/(-5-5) = 3/5, and

The slope of DA is = [3-(-5)]/[-3-(-5)] = 8/2. These two slopes are not negative reciprocals of each other, so CD and DA are not perpendicular.

So, the quadrilateral is not a rectangle.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

The coordinates of the "four-vertices" of the quadrilateral ABCD are :

A(-3,3), B(2,6), C(5, 1), D(-5,-5);

Which statement proves whether or not this quadrilateral is a rectangle?

(a) The slope of CD is (-5-1)/(-5-5) = 3/5, and the slope of DA is 3-(-5)/-3-(-5)=8/2, these two segments are not perpendicular , so the shape is not a rectangle;

(b) The slope of AB is (6-3)/(2-(-3) = 3/5, and slope of BC is (6-1)/(2-5) = -5/3, these two segments are perpendicular , so the shape is a rectangle;

(c) The slope of BC is (6-1)/(2-5) = -5/3, and slope of CD is (-5-1)/(-5-5) = 3/5, these two segments are not perpendicular, so the shape is not a rectangle;

(d) The slope of AB is (6-3)/(2-(-3) = 3/5, and slope of CD is (-5-1)/(-5-5) = 3/5, these two segments are perpendicular , so the shape is a rectangle;