Total sick-leave time used by employees of a firm in the course of one month has approximately a normal distribution with mean of 200 hours and variance of 400. a) Find the probability that the total sick-leave for the next month will be less than 150 hours. b) In planning schedule for next month, how much time must be budgeted for sick-leave if that amount is to be exceeded with a probability of 0.1

Answer:

Step-by-step explanation:

m-10=0

m = 10

8m-1=0

8m=1

m=1/8

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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The equation of the line in the graph in slope-intercept form is: y = -5x - 30.

To be able to write the equation of a line in slope-intercept form, y = mx + b, find the value of the slope (m) = rise/run, and the value of the y-intercept (b), which is the value of y where the line intercepts the y-axis.

From the given graph, we have:

Slope (m) = rise/run = -50/10

Slope (m) = rise/run = -5

The y-intercept (b) = -30

Substitute m = -5 and b = -30 into y = mx + b:

y = -5x + (-30)

y = -5x - 30

Thus, the equation of the line in the graph in slope-intercept form is: y = -5x - 30.

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Answer:

-\(\sqrt{5}\)/8

Step-by-step explanation:

so you are looking to find the second derivative of this function, given the derivative. that means that all you have to do is take the derivative of that function and then plug in 16 for h.

rewrite the function to be -(5h)^1/2

then take its derivative using power rule and chain rule

-(1/2)*(5)*(5h)^(-1/2)  **the five comes from the chain rule and taking the derivative of the 5h

then plug in 16 for h to find -\(\sqrt{5}\)/8 or about -0.2795

Plot the function

on the graph to Justify that graph intersect the x-axis.

So from the graph it can be justify the function intersect the x-axis at point (1.262,0).

The solutions to the quadratic equation \(2x^2 + 6x - 1 = 0\), obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

To solve the quadratic equation\(2x^2 + 6x - 1 = 0\)by completing the square, follow these steps:

Ensure that the coefficient of \(x^2\) is 1. In this case, it is already 2, so we don't need to make any changes.

Move the constant term to the other side of the equation. Add 1 to both sides:

\(2x^2 + 6x = 1\)

Divide the coefficient of x by 2 and square it. In this case, (6/2)^2 = 9.

Add the result from step 3 to both sides of the equation:

\(2x^2 + 6x + 9 = 1 + 9\)

Simplifying, we get:

\(2x^2 + 6x + 9 = 10\)

Write the left side of the equation as a perfect square trinomial. In this case, it is \((x + 3)^2.\)

\((x + 3)^2 = 10\)

Take the square root of both sides:

\(√[(x + 3)^2] = ±√10\)

Simplifying:

\(x + 3 = ±√10\)

Solve for x by subtracting 3 from both sides:

x = -3 ± √10

So, the solutions to the quadratic equation \(2x^2 + 6x - 1\)= 0, obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

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The addition property of equality was used to solve this equation. option A is correct.

A solution is given we have to determine the solution contains which property of equality.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
x − 5 = -14

x − 5 + 5 = -14 + 5

x = -9

We can see, in step 2 5 is added to both sides of an equality, which implies the property of additions.

Thus, the addition property of equality was used to solve this equation. option A is correct.

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Answer:

x=5/16

Step-by-step explanation:

3-8x=8x/5

(3-8x)5=8x

15-40x=8x

15=8x+40x

15=48x

x=15/48

x=5/16 ans.

The correct option is option C: 0.06.

Given that a couple has an Education Level = 4, the probability that it has SC Index = 10 is 0.06.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number that ranges from 0 to 1.

When an event is certain to occur, its probability is 1, while when an event is impossible to occur, its probability is 0.

The probability of an event A is denoted by P(A). It can be calculated using the following formula: P(A) = (number of favorable outcomes)/(total number of outcomes)

In this question, we need to calculate the probability of the event that a couple has an Education Level = 4 and SC Index = 10.

Given that a couple has an Education Level = 4, there are a total of 50 such couples. Of these, 3 have SC Index = 10.

Therefore, the probability that a couple has an Education Level = 4 and SC Index = 10 is: P(Education Level = 4 and SC Index = 10) = 3/50 = 0.06Hence, the correct option is option C: 0.06.

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The relativistic mass formula, m = m₀√(1 - v²/c²), can be derived from the principles of special relativity. The formula relates the relativistic mass (m) of an object to its rest mass (m₀), velocity (v), and the speed of light (c).

What is relativistic mass?

Relativistic mass is a concept in physics that refers to the mass of an object as observed from a moving frame of reference, taking into account relativistic effects. It is a term associated with Einstein's theory of relativity and is dependent on the velocity of the object.

To derive the formula, we start with the concept of relativistic energy, which is given by E = mc², where E is the total energy of the object. In special relativity, energy and mass are interconnected.

Next, we consider the relativistic kinetic energy, which is given by K = (γ - 1)m₀c², where γ is the Lorentz factor and is defined as γ = 1/√(1 - v²/c²). The Lorentz factor takes into account the time dilation and length contraction effects at high velocities.

We equate the relativistic energy (E) to the sum of rest energy (m₀c²) and relativistic kinetic energy (K), yielding E = m₀c² + (γ - 1)m₀c².

Simplifying the equation, we have E = γm₀c².

Since E = mc², we can equate the two expressions and obtain mc² = γm₀c².

Dividing both sides by c², we get m = γm₀.

Substituting the value of γ, we have m = m₀/√(1 - v²/c²).

This is the relativistic mass formula, which shows how the mass of an object changes with velocity, taking into account the effects of special relativity.

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Answer:

b

Step-by-step explanation:

Answer:

$15.70

Step-by-step explanation:

\(I=Prt=(10)(0.095)(6)=5.7 \\ \\ 10+5.70=\boxed{\$15.70}\)

Answer:

The answer is 15

Step-by-step explanation:

For x = 5 substitute the value of x that's 5 into the expression

We have

We have the final answer as

Hope this helps you

Answer:

40,60,80

Step-by-step explanation:

let 2x 3x and 4x

9x=180

x=20

2x=40

3x=60

4x= 80

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The value for sin(t + 6π) is always equal to 0, regardless of the value of t.

If sin(t) = 0, then t must be an integer multiple of π since the sine function is equal to zero at these values. Therefore, we can write t = nπ for some integer n.

To find sin(t + 6π), we can use the periodicity of the sine function, which states that

sin(x + 2π) = sin(x) for any real number x.

Using this property, we can rewrite sin(t + 6π) as sin(t + 2π + 2π + 2π) = sin(t + 2π) = sin(nπ + 2π).

Now, we need to determine the value of sin(nπ + 2π). Since n is an integer, we know that nπ + 2π is also an integer multiple of π, specifically (n+2)π.

Using the definition of the sine function, we can see that sin((n+2)π) = 0, since the sine function is zero at all integer multiples of π. Therefore, we can conclude that sin(t + 6π) = sin(nπ + 2π) = sin((n+2)π) = 0.

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Answer: p = -2

Step-by-step explanation:

- 0.75p - 2 =0.25p​                           add .75p on both sides

-2 = p                                                  That's the same thing at p = -2

Answer:

p = -2

Step-by-step explanation:

-0.75p - 2 = 0.25p Subtract 0.25p from both sides

-1p - 2 = 0 Add 2 to both sides

-1p = 2 Divide by -1 on both sides

p = -2

Answer:

1.89*10^1

Step-by-step explanation:

move the decimal once to the left  

Answer:

1.89 × 10^1

Step-by-step explanation:

I think im right

If i am can i get brainly crown pls?

:)

A given shape that is bounded by three sides and has got three internal angles is referred to as a triangle. Thus the value of PB is 8.0 units.

A given shape that is bounded by three sides and has got three internal angles is referred to as a triangle. Types of triangles include right angle triangle, isosceles triangle, equilateral triangle, acute angle triangle, etc. The sum of the internal angles of any triangle is \(180^{o}\).

In the given question, point P is center of the given triangle such that <APB = <APC = <BPC = \(120^{o}\). Such that line PB bisects <ABC into two equal measures of \(30^{o}\).

Thus;

<ABP = \(30^{o}\)

Thus,

<ABP + <APB + <BAP = \(180^{o}\)

30 + 120 + <BAP = \(180^{o}\)

<BAP = \(180^{o}\) - 150

<BAP = \(30^{o}\)

Apply the Sine rule to determine the value of PB, such that;

\(\frac{a}{SinA}\) = \(\frac{b}{SinB}\)

\(\frac{8}{Sin 30}\) = \(\frac{PB}{Sin 30}\)

BP = \(\frac{8*Sin 30}{Sin 30}\)

    = 8

BP = 8.0

Therefore, the value of PB = 8 units.

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We can solve this problem by using exponential growth. The answer is: after 40 years, Mr. Bean's parents would have approximately 640 descendants.

Given that the number of descendants doubles every 15 years, we can use the formula: N = N₀ * (2^(t / 15)). Where N is the number of descendants after t years, N₀ is the initial number of descendants, t is the number of years, and 2 is the base representing the doubling effect. In this case, N₀ is 80, t is 40 years, and we need to find the number of descendants after 40 years. N = 80 * (2^(40 / 15)) ≈ 80 * (2^(8/3)) ≈ 80 * 8 ≈ 640. Therefore, after 40 years, Mr. Bean's parents would have approximately 640 descendants.

It's important to note that in this calculation, we assume continuous exponential growth, which may not accurately represent real-world scenarios. Additionally, we assume that there are no factors that would limit the growth or affect the doubling rate of the descendants.

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The probability that the second marble drawn is not red is approximately 0.6765, or about 67.65%.

To find the probability that the second marble drawn is not red, we need to consider the number of red and non-red marbles remaining in the bag after the first marble is drawn.

First, let's calculate the probability of selecting a blue marble on the first draw. Out of the 35 marbles in the bag, 11 are red. Since a red marble was not selected, there are now 34 marbles left in the bag, with 11 red marbles and 23 non-red marbles.

Now, we want to find the probability of selecting a non-red marble on the second draw, given that a blue marble was selected on the first draw. Since the blue marble was not placed back in the bag, there are now 34 marbles in total.

Out of the 34 marbles, there are 11 red marbles and 23 non-red marbles. Since we want to find the probability of selecting a non-red marble, we divide the number of non-red marbles (23) by the total number of marbles (34):

Probability = Number of non-red marbles / Total number of marbles
Probability = 23 / 34

Simplifying this fraction, we get:

Probability = 23 / 34 ≈ 0.6765

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The particular solution to the given system is: x_p(t) = (-1/17)cos(4t) + Bsin(4t) and y_p(t) = Ccos(4t) + Bsin(4t). This particular solution satisfies the given system of equations.

To find a particular solution using the method of undetermined coefficients, we assume that the particular solution can be written in the form of:

x_p(t) = A cos(4t) + B sin(4t)
y_p(t) = C cos(4t) + D sin(4t)

Taking the derivatives, we have:

x'_p(t) = -4A sin(4t) + 4B cos(4t)
y'_p(t) = -4C sin(4t) + 4D cos(4t)

Substituting these into the given system of equations:

-4A sin(4t) + 4B cos(4t) = A cos(4t) + B sin(4t) - 17(C cos(4t) + D sin(4t)) + 4cos(4t)
-4C sin(4t) + 4D cos(4t) = A cos(4t) + B sin(4t) - (C cos(4t) + D sin(4t))

Simplifying these equations, we get:

(-17A + 1)cos(4t) + (17B - 17C)sin(4t) = 4cos(4t)
(A - C)cos(4t) + (B - D)sin(4t) = 0

Comparing the coefficients of cos(4t) and sin(4t) on both sides, we can equate them to find the values of A, B, C, and D:

-17A + 1 = 4
17B - 17C = 0
A - C = 0
B - D = 0

Solving these equations, we find:

A = -1/17
B = C
D = B

Therefore, the particular solution to the given system is:

x_p(t) = (-1/17)cos(4t) + Bsin(4t)
y_p(t) = Ccos(4t) + Bsin(4t)

This particular solution satisfies the given system of equations.

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To prove that the set a = {0, 1} is numerically equivalent to r (the set of real numbers), we need to find a bijective function that maps each element of a to a unique element in r.

One way to do this is to use the binary representation of real numbers. Specifically, we can define the function f: a -> r as follows:

- For any x in a, we map it to the real number f(x) = 0.x_1 x_2 x_3 ..., where x_i is the i-th digit of the binary representation of x. In other words, we take the binary representation of x and interpret it as a binary fraction in [0, 1).

For example, f(0) = 0.000..., which corresponds to the real number 0. f(1) = 0.111..., which corresponds to the real number 0.999..., the largest number less than 1 in binary.

We can see that f is a bijection, since every binary fraction in [0, 1) has a unique binary representation, and hence corresponds to a unique element in a. Also, every element in a corresponds to a unique binary fraction in [0, 1), which is mapped by f to a unique real number.

Therefore, we have proven that a is numerically equivalent to r, since we have found a bijection between the two sets.

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Answer:

Step-by-step explanation:

The greatest common factor of 5 and -20 is 5

x: the greatest common factor is x

y: the greatest common factor is y^3

Answer: 5xy^3(y - 4x)

Answer:

the -3.2+8.1 is 4.9 I can't see the rest

a) similarity triangle statement relating the three right triangles.

ZYX = ZYW = WXY

b) Proportion:

ZX/YX = YX/WX

ZW/ZY = ZY/ZX

What is the right triangle?

A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.

a) The statement relating the three right triangles is that ZYX is similar to ZYW, which is similar to WXY.

This is because all three triangles share the same 90-degree angle at vertex Y, and they also have equal angles at vertices Z and W. Therefore, by the Angle-Angle (AA) similarity theorem, the triangles are similar.

b) From the similarity of the triangles, we can use the proportional relationship between corresponding sides.

For example, we know that:

ZYX is similar to ZYW, so ZX/ZY = YX/YW

ZYW is similar to WXY, so YW/ZY = WX/YX

Rearranging the first equation, we get:

ZX/YX = (ZY/YX) / (ZX/ZY)

Substituting YW/ZY for WX/YX from the second equation, we get:

ZX/YX = (ZY/YX) / (ZX/ZY) = (ZY/YW) * (YW/ZX) / (ZX/ZY) = (ZY/ZX) * (YW/YZ)

Therefore, we have the proportion:

ZX/YX = (ZY/ZX) * (YW/YZ)

Similarly, from the second equation, we get:

ZW/ZY = (ZX/ZY) / (ZW/ZX) = (ZX/YX) * (YX/ZW)

Substituting YW/ZY for WX/YX, we get:

ZW/ZY = (ZX/YX) * (YX/ZW) = (ZY/YW) * (YW/YX) * (YX/ZW) = (ZY/ZX) * (WX/ZW)

Therefore, a) similarity triangle statement relating the three right triangles.

ZYX = ZYW = WXY

b) Proportion:

ZX/YX = YX/WX

ZW/ZY = ZY/ZX

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The volume of the sphere is 7241.142 m\(m^{3}\).

Given:

A sphere has a diameter of 24 mm.

Radius r = diameter/2

= 24/2

r = 12 mm.

volume of sphere = 4/3π\(r^{3}\)

= 4/3 * 22/7 * \(12^{3}\)

= 88*\(12^{3}\)/21

= 88*1728/21

= 152064/21

= 7241.142 m\(m^{3}\).

Therefore the volume of the sphere is 7241.142 m\(m^{3}\).

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Nate had $3000 at the beginning.

The percentage is defined as a ratio expressed as a fraction of 100.

Let the original amount of money is P

Nate spent 12 % of his paycheck on car repairs

⇒ 12% of P = 12P/100

And he spent 25 % of the remainder on food.

⇒  0.25(88/100)P

He gave $ 1,320 of the remaining money to his parents

⇒ 1320  

If the usual price of the computer was $ 825 and the discount was 20 %

⇒ 825 - 0.20(825) = 660

P = 12P/100 + 0.25(88/100)P + 1320 + 660

P - 34P/100 = 1980

100P - 66P = 198000

P = 3000

Hence, Nate had $3000 at the beginning.

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Answer:

C. 40

Step-by-step explanation:

1 to 2 is the same as 1/2, so there should be half the amount of blue marbles than white. So since there are 20 blue marbles, then that would mean there are 40 white marbles.

Hope this helped! :)

Answer:

C. 40

Step-by-step explanation:

If the ratio is 1-2, 1 blue marble, and 2 white marbles, then the ratio is doubled if you know what I mean. So if there are 20 blue marbles, you're going to double it (multiply it by 2) and 20x2 is 40, meaning the answer is C.

Answer:

1 and 7

2 and 8

Step-by-step explanation:

consecutive exterior angles theorem- a theorem stating that if parallel lines are cut by a transversal line, then consecutive exterior angles are supplementary. Like 1 and 7(they are both exterior angles); these angles are both right angles, so added together would make them a pair of supplementary angles.

supplementary angles- a pair of angles that add up to 180 degrees when added together.

I hope this helps