x is a normally distributed variable with a mean of 32 and a standard deviation of 19 what is P(x<63)

Answer: the simplest for is -4.25

Step-by-step explanation:

Answer:

I believe that the answer is C: 72 cm²

Answer:

14 is the answer of your question

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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The direction in which the function f(x, y) = x³y - x²y³ decreases fastest at the point (4, -2) is along the vector ⟨96, 64⟩.

To find the direction in which the function f(x, y) = x³y - x²y³ decreases fastest at the point (4, -2), we need to compute the gradient of the function and then find the negative of the gradient at the given point.

Compute the partial derivatives of the function f(x, y) with respect to x and y.
∂f/∂x = 3x²y - 2xy³
∂f/∂y = x³ - 3x²y²

Evaluate the partial derivatives at the point (4, -2).
∂f/∂x(4, -2) = 3(4)²(-2) - 2(4)(-2)³ = -32
∂f/∂y(4, -2) = (4)³ - 3(4)²(-2)² = -128

Compute the negative of the gradient at the point (4, -2).
The gradient is the vector formed by the partial derivatives: ∇f = ⟨∂f/∂x, ∂f/∂y⟩
At the point (4, -2), ∇f = ⟨-32, -128⟩
The negative of the gradient is -∇f = ⟨32, 128⟩.

This is the required vector.

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Answer:

factorize 48 in root ans is _4root 6+11root3

Answer:

$8.50

Step-by-step explanation:

You divide $22.10 by 2.6 to get the price per pound of salmon.

22.10 ÷ 2.6 = 8.5

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

C) y = 3x - 8

Step-by-step explanation:

Hope it helps you in your learning process.

(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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Answer:

.

Step-by-step explanation:

Answer:

sqrt of 3600 is a perfect square and sqrt of 3600 is a whole number. It is also Rational.

Step-by-step explanation:

We can compute the sqrt of 3600 (60). 60 is a whole number.

As we saw sqrt of 3600 is 60 so it is a perfect square.

60 is also a rational number too.

\(\sqrt{3600}\) is a rational number, a perfect square and a whole number.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.

Now the given number is,

⇒ \(\sqrt{3600}\)

So, the square root of 3600 is 60.

Now, since 60 can be expressed in the form of a/b.

Thus \(\sqrt{3600}\) is a rational number.

Since, \(\sqrt{3600} = [\sqrt{60} ]^2\)

Thus, \(\sqrt{3600}\) is perfect square.

Since, \(\sqrt{3600} =60\)

Thus it is a whole number.

Therefore we can conclude that \(\sqrt{3600}\) is a rational number, a perfect square and a whole number.

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P(even) is  50%

It is simple to calculate the likelihood of one die roll.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

First, keep in mind that a prime number is an integer that has exactly two factors: 1 and the number itself (which is why 1 does not qualify: it has only one factor). The appropriate numbers from 6 onward are 2,3,5. Your response, given that there are six sides, is: P(prime) = 3/6 = 1/2 = 50%

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The probability of rolling an odd number or rolling a 2 on a fair six-sided die is the fraction 2/3

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes

A fair six-sided die has faces numbered 1 to 6, and there are only three numbers that are odd numbers, which are 1, 2, and 3.

so;

probability of rolling an odd number = 3/6

probability of rolling a 2 = 1/6

probability of rolling an odd number or a 2 = 3/6 + 1/6

probability of rolling an odd number or a 2 =4/6

probability of rolling an odd number or a 2 = 2/3

In conclusion, 2/3 is the resulting fraction for the probability of rolling an odd number or rolling a 2 on a fair six-sided die.

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Answer:

y=3x-7

Step-by-step explanation:

To find the equation of a perpendicular line, you first need to find the negative reciprocal of the slope given. The slope is -1/3, so the slope of the perpendicular line will be 3

Now we just need to find the y intercept using the point (3, 2) and you can plug the coordinates in and then solve for b. Let's see what that looks like.

y=3x+b

2=3*(3)+b

2=9+b

-7=b So now we know the y-intercept and slope. We just put them together now

y=3x-7

Hope this helps!

The equation of the line r is y = ₋(10/9)x ₊ 7.

Given, parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope intercept form

equation of line q is y = ₋10/9x ₊ 2

it's already in slope intercept form.

hence slope is:

m = (₋10/9) from the above the equation.

we know that the second line will also have a slope of ₋10/9 and we are given the point (9 , ₋3). We can setup an equation in slope intercept form and use these values to solve for the y inetrcept.

y = mx ₊ b

₋3 = ₋10/9 (9) ₊ b

₋3 = ₋10 ₊ b

b = 7

plug the y intercept back into the equation to get our final answer.

y = ₋(10/9)x ₊ 7

hence  we get the equation of the line r as y = ₋(10/9)x ₊ 7.

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The smallest sample observation can be increased by any value up to 0.1 without affecting the value of the sample median.

To find the maximum amount by which the smallest sample observation can be increased without affecting the sample median, we need to consider the definition of the median.

The median is the middle value in a sorted dataset. If the dataset has an odd number of observations, the median is the middle value. If the dataset has an even number of observations, the median is the average of the two middle values.

Since the current smallest sample observation is 8.5, increasing it by any value up to 0.1 would still keep it smaller than any other value in the dataset. This means the position of the smallest observation would not change in the sorted dataset, and therefore, it would not affect the value of the sample median.

The smallest sample observation can be increased by any value up to 0.1 without affecting the value of the sample median.

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The Probability that all four of the light bulbs work is 0.004 approx.

The probability that all four light bulbs work can be calculated by taking the product of the probability that each individual light bulb works. If each light bulb works independently of the other light bulbs, then the probability that all four light bulbs work is:

P(all 4 bulbs) = P(bulb 1) * P(bulb 2) * P(bulb 3) * P(bulb 4)

P(all 4 bulbs) = 0.25 * 0.25 * 0.25 * 0.25

P(all 4 bulbs) = 0.25^4

P(all 4 bulbs) = 0.00390625

So, the probability that all four light bulbs work is 0.00390625 or approximately 0.004.

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Answer:

a) \(x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}\)

b) The volume of the box is maximized when 'x' is approximately 1.585 feet

Step-by-step explanation:

a) Let 'a' represent the length of the rectangular sheet of paper and let 'b' represent the with of the rectangular sheet of paper, we have;

The length of the side of the square cut from the corners of the rectangular sheet of paper = x

The length of the box formed after cutting the square sides are;

The length of the box, l = a - 2·x

The width of the box, w =  b - 2·x

The height of the box, h = x

The volume of the box, V = l × w × h = (a - 2·x)·(b - 2·x)·x = 4·x³ - 2·a·x² - 2·b·x² + a·b·x

The value of 'x' that gives the maximum volume of the box is given by finding the extremum of the volume, 'V', of the box as follows;

At the extremum, dV/dx = 0

∴ d(4·x³ - 2·a·x² - 2·b·x² + a·b·x)/dx = 12·x² - 4·a·x - 4·b·x + a·b = 0

12·x² - 4·(a + b)·x + a·b = 0

\(x = \dfrac{4\cdot (a + b) \pm \sqrt{(-4\cdot (a + b) )^2-4 \times12\times a \cdot b } }{2 \times 24} =\dfrac{a+b\pm\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}\)

Found from part (b), the value of 'x' (in terms of 'a' and 'b') that maximizes the volume of the box is \(x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}\)

b), When a = 8.5 inches and b = 11 inches, we have;

x = (8.5 + 11 +√((8.5 + 11)² - 3×8.5×11))/6 = 4.914

x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585

We get;

When x = 1.585, V = 4·1.585³ - 2·8.5·1.585² - 2·11·1.585² + 8.5·11·1.585 ≈ 66.15

When x = 4.914, V = 4·4.914³ - 2·8.5·4.914² - 2·11·4.914² + 8.5·11·4.914 ≈ -7.65

Therefore, the value of 'x' that gives the maximum volume of the box is x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585

(The value of 'x' in terms of 'a' and 'b' is therefore;

\(x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}\))

The volume of the box is maximized when, x ≈ 1.585 feet

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

The level of confidence will increase.

Step-by-step explanation:

Could be wrong

The change in the sample size will lead to a decrease in the width of the interval.

A sample size simply means the number of subjects that are taken from the population for research.

In this case, increasing the sample size will decrease the standard error and therefore, the width of the confidence interval will reduce.

Therefore, as the sample size increases, the interval reduces.

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in this problem x equals 10

Step-by-step explanation:

jd

Answer:

13

Step-by-step explanation:

Answer:

Most known one: 4 sides

Step-by-step explanation:

They are closed shapes, their sides should be straight, they are strictly 2 dimensional, and finally, all quadrilaterals have 4 sides.

The statement a base class cannot contain a pointer to one of its derived classes is false because a base class can indeed contain a pointer to one of its derived classes.

In object-oriented programming, a base class can have a pointer to one of its derived classes. This is known as upcasting or polymorphism. Upcasting allows for the flexibility of treating derived class objects as instances of the base class.

By using pointers, a base class can refer to derived class objects and access their member functions and variables. This enables the base class to work with different derived classes without needing to know their specific types.

Pointers to derived classes can be stored in base class member variables or passed as function parameters. This allows for dynamic binding and the ability to invoke overridden functions based on the actual derived class type at runtime.

This concept is fundamental to achieving polymorphism and code reusability in object-oriented programming languages like C++ and Java. It facilitates the implementation of inheritance hierarchies and the ability to work with objects of different derived classes through a common base class interface.

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The given expression :

LCM of 8 & 4 is 8

Simplify: 5 -4 =1

Apply cross multiplication:

The measure of BC is 20/3 or approximately 6.67.

Since ab is parallel to de, we know that angle abc is congruent to angle cde (corresponding angles of parallel lines). Let x be the length of bc.

Using the similar triangles ABC and CDE, we can set up the following proportion:

AB/CD = BC/DE

Substituting the given values:

9/CD = x/6

Solving for CD:

CD = 9/6 * x = 3/2 * x

Using the fact that EC = CD - DE, we can substitute the given values to get:

4 = (3/2 * x) - 6

10 = 3/2 * x

x = 20/3

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To find another point that represents an equivalent ratio on a graph, you can multiply both quantities by the same factor

Two quantities have a constant ratio if they are proportionate to one another.

This indicates that to preserve the same ratio, multiplying one item by a particular factor also requires multiplying the other quantity by the same factor.

Therefore, by multiplying both quantities by the same factor, you can locate a point on a graph that represents an equivalent ratio if you have a point that represents a ratio of two quantities.

As an illustration, let's say you have a point on a graph that represents the ratio 2:3, and you want to locate a point that represents a ratio that is equal.

To do this, multiply both amounts by 2 to obtain the ratio 4:6, or both amounts by 3 to obtain the ratio 6:9.

Because it preserves the same ratio between the two quantities, this method functions. Both quantities are effectively scaled up or down by the same amount when multiplied by the same factor, maintaining their relative sizes.

This implies that even though the actual values may change, the ratio between the two quantities stays the same.

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The number of lattice paths from (2, 1) to (24, 30) with a constraint of passing through (8, 10) but not (7, 7) or (16, 25) is a complex problem that requires a detailed mathematical calculation, that is explained below.

Lattice paths are sequences of steps in the form of up steps (U) and right steps (R) that connect two points in a grid. The number of lattice paths from one point to another can be calculated using combinatorics.

To determine the number of lattice paths from (2, 1) to (24, 30) that pass through the point (8, 10) but do not pass through either of the points (7, 7) and (16, 25), we need to calculate the total number of paths and subtract the number of paths that pass through the restricted points.

Let's call the total number of paths T, the number of paths that pass through (8, 10) P, the number of paths that pass through (7, 7) Q, and the number of paths that pass through (16, 25) R.

The number of paths from (2, 1) to (8, 10) is given by the binomial coefficient C(10 - 1, 8 - 2) = C(9, 6) = 84.

The number of paths from (8, 10) to (24, 30) is given by the binomial coefficient C(30 - 10, 24 - 8) = C(20, 16) = 18564.

The number of paths from (2, 1) to (24, 30) that pass through (8, 10) is given by T = P = 84 * 18564 = 1,547,136.

Similarly, the number of paths from (2, 1) to (7, 7) is given by the binomial coefficient C(7 - 1, 7 - 2) = C(6, 5) = 15.

The number of paths from (7, 7) to (24, 30) is given by the binomial coefficient C(30 - 7, 24 - 7) = C(23, 17) = 9,139,554.

The number of paths from (2, 1) to (24, 30) that pass through (7, 7) is given by Q = 15 * 9139554 = 137,093,310.

The number of paths from (2, 1) to (16, 25) is given by the binomial coefficient C(25 - 1, 16 - 2) = C(24, 14) = 3003.

The number of paths from (16, 25) to (24, 30) is given by the binomial coefficient C(30 - 25, 24 - 16) = C(5, 8) = 70.

The number of paths from (2, 1) to (24, 30) that pass through (16, 25) is given by R = 3003 * 70 = 210,210.

Finally, the number of paths from (2, 1) to (24, 30) that pass through (8, 10) but do not pass through either of the points (7, 7) and (16, 25) is T - P - Q - R = 1547136 - 137,093,310 - 210,210 = -135,599,384.

The number of lattice paths from (2, 1) to (24, 30) that pass through (8, 10) but do not pass through either of the points (7, 7) and (16, 25) is zero, as the result is negative.

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