The lifetime X (in years) of a microchip has a density function given by F(x) = { 0,5e^(-x/2) for x>0
0 Else a) Find the mean lifetime of this microchip b) Find the standard deviation of the lifetime of this microchip c) Find the probability that this microchip will work for more than 3 years. d) Find the probability that this microchip will work for more than 5 years knowing that it has been working for more than 2 years. e) Find the moment generating function of the lifetime

12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex].

The weight of 12 blue whales will be the product of the weight of a single blue whale and the number of blue whales. To find the product, we simply multiply the weight of a single blue whale by the number of blue whales.

So, the weight of 12 blue whales will be:

[tex]\( 1.8 \times 10^{6} \mathrm{~kg} \) × 12 = \( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Therefore, 12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Multiplication refers to binary operations in which different numerical sets are established. In mathematics the process of multiplication is elementary in several operations, it is also accompanied by addition, subtraction and division. Multiplication is the opposite of division.

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Answer:

There would be no value to the laptop. If you’re looking for the actual value, it would be worth $-375.

Step-by-step explanation:

The reflection of the shape over the line p is drawn and added as an attachment

When a shape is reflected over a line, it is flipped across that line. The reflected image of the shape is a mirror image of the original shape, and appears to be a mirror image of the original shape.

This means that we simply flip the shape over the line of reflection

The line over which the shape is reflected is called the line of reflection, and it acts as a mirror. In this case, it is the line p. The shape and its reflected image are symmetric with respect to the line of reflection.

Flipping the shape would result in any point on the original shape and its corresponding point on the reflected image are equidistant from the line of reflection, as the distance between a point and its reflected image is equal to twice the perpendicular distance from the point to the line of reflection.

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(5z+2)/(z) is the possible rational expression.

To subtract the two rational expressions, we can combine the numerators and keep the common denominator. The subtraction of the two rational expressions is shown below:

(19z+6)/(3z) - (4z)/(3z) = (19z+6-4z)/(3z)

Simplifying the numerator gives:

(15z+6)/(3z)

We can further simplify the expression by factoring out a common factor of 3 from the numerator:

3(5z+2)/(3z)

The 3 in the numerator and denominator cancel out, leaving us with the final simplified expression:

(5z+2)/(z)

Therefore, the answer is (5z+2)/(z).

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Answer: 0.00003396739

Step-by-step explanation:

hope this helps

The final simplified expression is (3x+1)(5x+2)/(3x-2).

The given expression is (15x^(2)+13x+2)/(3x-2). We can try to simplify this expression by factoring the numerator and denominator, and then canceling out any common factors.

First, let's factor the numerator:

15x^(2)+13x+2 = (3x+1)(5x+2)

Now, let's factor the denominator:

3x-2 = (3x-2)

There are no common factors between the numerator and denominator, so we cannot simplify the expression any further.

Therefore, the simplified expression is:

(15x^(2)+13x+2)/(3x-2) = (3x+1)(5x+2)/(3x-2)

Since x!=(2)/(3), we do not need to worry about any undefined values.

So, the final simplified expression is:

(3x+1)(5x+2)/(3x-2)

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The equation is now in the form y=mx+b, where m is 2 and b is -4. The second equation is now in the form y=mx+b, where m is -0.5 and b is -2.

An equation is an expression that shows the relationship between two or more variables. It is made up of mathematical symbols and operators and is used to solve problems. Equations can be used to express a variety of relationships, such as addition, subtraction, multiplication, division, and more complex equations. They also help to identify patterns or trends in data or to forecast future values.

To change these equations into y=mx+b form, we must first rearrange the equations.

For the first equation, 2x-4=8, we can move the 4 to the other side of the equation, giving us 2x = 12. We can then divide both sides by 2, giving us x = 6. So the equation is now in the form y=mx+b, where m is 2 and b is -4.

For the second equation, -2x+4y=-8, we can move the -2x to the other side of the equation, giving us 4y=-8-2x. We can divide both sides by 4, giving us y=-2-0.5x. So the equation is now in the form y=mx+b, where m is -0.5 and b is -2.

Now that both equations are in y=mx+b form, we need to compare their m and b values to determine if there is one solution, no solution or infinite solutions. We can see that m for both equations is different, so this means that the two equations are not the same, and there is no solution. This means that the two equations have no solution.

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Yes, the expression 49-64y^(2) is a difference of squares.

A difference of squares is an expression that can be written in the form a^(2) - b^(2), where a and b are any expressions. In this case, 49 can be written as 7^(2) and 64y^(2) can be written as (8y)^(2). Therefore, the expression can be rewritten as 7^(2) - (8y)^(2), which is in the form of a difference of squares.

It is important to note that a difference of squares can be factored into the product of two binomials, (a+b)(a-b), but the question specifically asks not to factor the expression.

In conclusion, yes, the expression 49-64y^(2) is a difference of squares.

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Answer:

36

Step-by-step explanation:

bbecause yes and because a put in my quiz and they put me a A

The linear equation in the given graph is.

y = 40x

We know that the general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept, these two values are constants, and the variables are x and y.

First, notice that the line intercepts the y-axis at the point (0, 0), then b = 0.

So we can write:

y = a*x

Also notice that the line passes through the point (1, 40), then:

40 = a*1

40/1 = a

The linear equation is.

y = 40x

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After being rotated 180 degrees anticlockwise around the origin, the picture of the point (4,8) is (-4,-8).

The fixed point is referred to as the rotational centre. The quantity of the rotation is described by the term "angle of rotation," which is measured in degrees. The equivalent of turning a figure 90 degrees anticlockwise is turning it 180 degrees clockwise. Hence, the resulting image of the point is (-1, 2).

Below are the guidelines for rotation: rotation 90 degrees clockwise: (x,y) results in (y,-x) rotation of (x,y) at 90 degrees anticlockwise results in (-y,x) Rotating (x, y) 180 degrees both clockwise and anticlockwise results in (-x,-y).

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Answer:

Linear equation to represent the total cost:

Let x be the number of kgs of tomatoes Mail bought, and y be the number of kgs of potatoes Mail bought. The cost of x kgs of tomato at Rs. 50 per kg is 50x, and the cost of y kgs of potato at Rs. 20 per kg is 20y. Therefore, the total cost of the vegetables is:

Total cost = 50x + 20y

Substituting the value of total cost as Rs. 200, we get:

50x + 20y = 200

This is the required linear equation to represent the total cost.

Finding the value of x:

Let's assume that Mail bought x kgs of tomato and 2.5 kgs of potato. Using the equation derived above:

50x + 20(2.5) = 200

Simplifying the equation:

50x + 50 = 200

50x = 150

x = 3

Therefore, Mail bought 3 kgs of tomato.

Finding the point at which the graph of 5x+2y=20 cuts x-axis:

To find the point at which the graph of 5x+2y=20 cuts the x-axis, we need to set y = 0 in the equation and solve for x:

5x + 2(0) = 20

5x = 20

x = 4

Therefore, the point where the graph of 5x+2y=20 cuts the x-axis is (4,0).

31, 87, 90 are the numbers which are considered possible outliers.

An outlier is an observation or data point that is significantly different from other observations in a dataset. In other words, it is an unusual or extreme value that is much higher or lower than most other values in the data.

A box and whisker plot is used to easily detect outliers. In this figure, the outliers are shown as black circles or dots. These are the data points that are distant from other observations.

Therefore, the numbers which are considered possible outliers are 31, 87, and 90.

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The length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).

To find the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \), we can use the formula for arc length: \( s = r\theta \), where \( s \) is the arc length, \( r \) is the radius of the circle, and \( \theta \) is the central angle in radians.

Plugging in the given values, we get:

\( s = (11 \mathrm{in})(\frac{\pi}{2}) \)

Simplifying, we get:

\( s = \frac{11\pi}{2} \mathrm{in} \)

Therefore, the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).

Note: If the question asks for the answer to be rounded, you can use a calculator to find the approximate value of \( \frac{11\pi}{2} \) and round to the desired number of decimal places. For example, if the question asks for the answer to be rounded to the nearest tenth, the answer would be \( 17.3 \mathrm{in} \).

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Answer:

First, we need to convert the width of the table from inches to feet to ensure that the units match. There are 12 inches in a foot, so:

42 inches ÷ 12 inches/foot = 3.5 feet

Let the length of the table be L feet. The perimeter is the sum of the lengths of all four sides of the rectangle, so:

2L + 2(3.5 feet) = 18 feet

Simplifying and solving for L:

2L + 7 feet = 18 feet

2L = 11 feet

L = 5.5 feet

Therefore, the length of the table is 5.5 feet.

Answer:

66

Step-by-step explanation:

the problem ask fr it draw out 2 rectangle

Therefore , the solution of the given problem of equation comes out to be every term in this sequence will be a whole number greater than 7.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization produces a + 7 as opposed to a different algorithm that splits 12 into two parts and can evaluate data received from x + 7.

Here,

The given equation can be used to create a table of values for this sequence, beginning with a1 = 7:

n an

1 7

2 19

3 31

4 43

5 55

6 67

7 79

8 91

9 103

10 115

... ...

We multiply the first term of the sequence by a factor of 1 and add 12 to determine each succeeding term.

=> a2 = a1 + 12 = 7 + 12 = 19

Similarly, we enter n = 3 and a2 = 19 to determine a3:

=> a3 = a2 + 12 = 19 + 12 = 31

so forth.

Because a1 is a whole number greater than 7 and each term in the sequence is obtained by adding 12 to the preceding term,

it should be noted that every term in this sequence will be a whole number greater than 7.

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Answer:

1/4

Step-by-step explanation:

you can plug it into a calculator

Therefore , the solution of the given problem of triangle comes out to be  the shape is 55 square miles.

Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here.

Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.

The following method can be used to determine a triangle's area:

A = (1/2)bh

where A represents area, B represents foundation, and H represents height.

We can calculate each triangle's area using the following formula:

=> Area of 1st triangle

=>  (1/2)(10)(7) = 35 square miles

=> Area of 2nd triangle

=>  (1/2)(10)(4) = 20 square miles

The two triangles' combined regions make up the composite shape's surface area.

55 square miles is the combined shape's area

=>  (35 + 20).

Consequently, the combined size of the two triangles in the shape is 55 square miles.

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The solution to the equation is x=3, which means that when x is equal to 3, the equation is true.

The solution of an equation is the value of the variable that satisfies the equation.

In this case, the solution is x=3, which means that when x is substituted with 3, the equation is true.

We can say that the solution is unique, as there is only one value of x that satisfies the equation. It is also a real solution, as the value of x is a real number.

Additionally, we can say that the solution is finite, as there is a specific value for x that satisfies the equation.

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The solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3.

To solve the trigonometric equation sin 2x=−√3/2 on the interval [0,2π), we need to find the values of x that satisfy the equation. We can do this by using the inverse sine function and the periodicity of the sine function.

First, let's find the general solution of the equation:
sin 2x=−√3/2
2x= sin⁻¹(−√3/2) + 2πn or 2x= π - sin⁻¹(−√3/2) + 2πn, where n is an integer
2x= -π/3 + 2πn or 2x= 4π/3 + 2πn
x= -π/6 + πn or x= 2π/3 + πn

Now, we need to find the values of x that are in the interval [0,2π). We can do this by plugging in different values of n until we find all the solutions in the interval.

For x= -π/6 + πn:
When n=0, x= -π/6 (not in the interval)
When n=1, x= 5π/6 (in the interval)
When n=2, x= 11π/6 (in the interval)
When n=3, x= 17π/6 (not in the interval)

For x= 2π/3 + πn:
When n=0, x= 2π/3 (in the interval)
When n=1, x= 5π/3 (in the interval)
When n=2, x= 8π/3 (not in the interval)

Therefore, the solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3. These are the exact form answers. If we want to round them to two decimal places, we get x= 2.62, 5.24, 1.05, and 3.14.

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The measure of the angle N to the nearest degree for the given triangle is 23 degrees.

Degree and radian both serve as angles' units of measurement in geometry. Two radians (in radians) or 360° can be used to symbolise one whole anticlockwise rotation (in degrees). As a result, degree and radian can be compared as follows:

2π = 360°

The given triangle is an right triangle.

Using the trigonometric functions we can write the relation between the segments as:

Sin (N) = 1.5 / 3.9 = opposite/hypotenuse

N = arcsin (1.5 / 3.9)

N = 22.61 = 23 degrees.

Hence, the measure of the angle N to the nearest degree for the given triangle is 23 degrees.

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The value of x on the straight line is 43 degrees

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

The straight line

The sum of angles on a straight line is 180 degrees

Using the above as a guide, we have the following equation

3x + 51 = 180

Evaluate

3x = 129

Divide by 3

x = 43

Hence, the value of x is 43 degrees

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Answer:

Part A

a = 1

b = 3

c = -4

Part B

[tex]x = \dfrac{ -3 \pm \sqrt{3^2 - 4(1)(-4)}}{ 2(1) }[/tex]

Part C

[tex]\mathrm{x = \dfrac{ -3 + \sqrt{25}}{ 2 } :and\: x = \dfrac{ -3- \sqrt{25}}{ 2 }}[/tex]

Part D

Option B:   x = 1 and x = -4

Step-by-step explanation:

The standard form of the quadratic equation is [tex]ax^2 + bx + c=0[/tex]

1.The given equation is [tex]x^2 + 3x - 4 = 0[/tex]

Part A

Comparing the given equation with the generalized standard equation we see that

[tex]a[/tex]  = coefficient of [tex]x^2[/tex] = 1

[tex]b[/tex]= coefficient of [tex]x = 3[/tex]

[tex]c[/tex]= constant term = [tex]-4[/tex]

Part B.

The quadratic formula for the roots of the equation is:
[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

Plugging in values for a, b and c from Part A:
[tex]x = \dfrac{ -3 \pm \sqrt{3^2 - 4(1)(-4)}}{ 2(1) }[/tex]

Part C

[tex]\mathrm{x = \dfrac{ -3 + \sqrt{25}}{ 2 } :and\: x = \dfrac{ -3- \sqrt{25}}{ 2 }}[/tex]

part D
Simplifying we get

[tex]x = \dfrac{ -3 + 5\, }{ 2 } = \dfrac{2}{2} = 1\\\\x = \dfrac{ -3 - 5\, }{ 2 } = \dfrac{-8}{2} = -4\\\\[/tex]

Correct answer for Part C:
B. x = 1 and x = -4

Answer:

csc(0)= 25/7

sec(0)= 25/24

cot(0)= 24/7

Step-by-step explanation:

Answer:

csc Θ = 25/7

sec Θ = 25/24

cot Θ = 24/7

Step-by-step explanation:

csc Θ = 1/sin Θ

sin Θ = opp/hyp

csc Θ = hyp/opp

csc Θ = 25/7

sec Θ = 1/cos Θ

cos Θ = adj/hyp

sec Θ = hyp/adj

sec Θ = 25/24

cot Θ = 1/tan Θ

tan Θ = opp/adj

cot Θ = adj/opp

cot Θ = 24/7

In the three-month period, the water level was 6.5 inches, 6.3 inches, and 6.7 inches, respectively. This is lower than the yearly average of 7.2 inches

Water level is a term used to describe the height of a body of water, usually in reference to an ocean, lake, river, or other body of water. It can also refer to the height of the water above sea level or other reference points.

The table indicates that the water level of the reservoir for the three-month period is lower than the yearly average. This can be seen by comparing the data in the table.

This could be due to a number of factors, including decreased precipitation and increased evaporation during the three-month period.

Ultimately, the data shows that the water level of the reservoir for the three-month period is lower than the yearly average. This could be a cause for concern in the long-term, as the water level of the reservoir could become too low to sustain local populations and ecosystems in the area.

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The size of angle ACB is approximately 50.66°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

We are given that;

Angle ABC= Angle ACD + 31°

Now,

Since angle ABC is twice angle BAC, we can write:

angle BAC = x

angle ABC = 2x

angle ACB = 180° - (angle BAC + angle ABC)

Substituting these values into the equation for angle ACD, we get:

angle ACD = angle ABC + 31° = 2x + 31°

Since angles ACB and ACD form a straight line, we can write:

angle ACB + angle ACD = 180°

Substituting the values we know, we get:

(angle BAC + angle ABC) + (angle ABC + 31°) = 180°

3x + 31° = 180°

3x = 149°

x = 49.67°

Therefore, the angle of triangles answer will be 50.66°.

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A) The Rational Root Theorem states that the only rational zeros of p(x) = x4+12x-5 must be a factor of -5 divided by a factor of 1. Therefore, the four possible rational zeros are -5, -1, 1, and 5.

B) The other three zeros is 1 - 2i, 1 + 2i, 1 - √(7), 1 + √(7)

A) The Rational Root Theorem states that if a polynomial with integer coefficients has a rational root r = p/q (where p and q have no common factors), then p must divide the constant term of the polynomial and q must divide the leading coefficient.

The constant term of p(x) = x^4 + 12x - 5 is -5, which has the factors ±1 and ±5. The leading coefficient is 1, which has the factors ±1. Therefore, the possible rational roots are:

±1/1, ±5/1, ±1/5, ±5/5 (which simplifies to ±1)

B) If r = 1 - 2i is a zero of p(x), then its complex conjugate r* = 1 + 2i is also a zero of p(x), since p(x) has real coefficients. Therefore, we can factor p(x) as:

p(x) = (x - r)(x - r*)(x²+ bx + c)

where b and c are the coefficients of the quadratic factor. We can expand this and compare coefficients to get:

x⁴ + 12x - 5 = (x - 1 + 2i)(x - 1 - 2i)(x² + bx + c)

Expanding the first two factors gives:

(x - 1 + 2i)(x - 1 - 2i) = x² - 2x + 5

Therefore, we have:

x⁴ + 12x - 5 = (x² - 2x + 5)(x² + bx + c)

Expanding the right side and comparing coefficients, we get:

b = -2 and c = -6

So the quadratic factor is:

x² - 2x - 6

We can find its roots using the quadratic formula:

x = [2 ± √(4 + 4(6))] / 2

x = 1 ± √(7)

Therefore, the four zeros of p(x) are:

1 - 2i, 1 + 2i, 1 - √(7), 1 + √(7)

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Let ((2) = ve- 4 and g(2) = 12 11r + 30. Then f(1) = i√3, g(1) = 21, Domain of f(x) = [4, ∞) and  Domain of g(x) = (-∞, ∞)

First, let's find f(1) and g(1). To do this, we simply substitute x = 1 into the equations for f(x) and g(x):

f(1) = √(1 - 4) = √(-3) = i√3

g(1) = 2(1) - 11(1) + 30 = 2 - 11 + 30 = 21

Now, let's find the domains of f(x) and g(x). The domain of a function is the set of all values of x for which the function is defined.

For f(x) = √(x - 4), the expression inside the square root must be greater than or equal to 0 in order for the function to be defined. This means that:

x - 4 ≥ 0

x ≥ 4

So the domain of f(x) is [4, ∞).

For g(x) = 2x - 11x + 30, there are no restrictions on the domain, so the domain of g(x) is (-∞, ∞).

So the final answers are:

f(1) = i√3

g(1) = 21

Domain of f(x) = [4, ∞)

Domain of g(x) = (-∞, ∞)

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The total surface area of the tires making contact with the ground at any one time for the truck with 18 wheels, tire radius of 21 in, tire width of 12 in, and 20% contact area is approximately 5700.24 square inches.

The surface area of one tire making contact with the ground can be calculated as follows:

The diameter of the tire is 2 * radius = 2 * 21 in = 42 in

The length of the portion of the tire making contact with the ground is 20% of the circumference of the tire = 0.2 * π * 42 in ≈ 26.39 in

The width of the tire making contact with the ground is given as 12 in

Therefore, the surface area of one tire making contact with the ground is approximately 26.39 in * 12 in = 316.68 square inches

Since the truck has 18 wheels, the total surface area of all the tires making contact with the ground at any one time is 18 * 316.68 square inches = 5700.24 square inches.

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P is rational number from the given equation P=2(2x+5)+2x.

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).

The given equation is P=2(2x+5)+2x.

Here, P=2(2x+5)+2x

P=4x+10+2x

P=6x+10

Given that, x=1.5, 3 and 1.2

Substitute, x=1.5 in P=6x+10, we get

P=6×1.5+10

P=9+10

P=19

So, 19 is rational number

Substitute, x=3 in P=6x+10, we get

P=6×3+10

P=18+10

P=28

So, 28 is rational number

Substitute, x=1.2 in P=6x+10, we get

P=6×1.2+10

P=7.2+10

P=17.2

So, 17.2 is rational number

Therefore, P is rational number from the given equation P=2(2x+5)+2x.

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