75% of the employees in a specialized department of a large software firm are computer science graduates. a project team is made up of 8 employees. part a) what is the probability to 3 decimal digits that all the project team members are computer science graduates? 0.013 part b) what is the probability to 3 decimal digits that exactly 3 of the project team members are computer science graduates? part c) what is the most likely number of computer science graduates among the 8 project team members? your answer should be an integer. if there are two possible answers, please select the smaller of the two integers. part d) there are 56 such projects running at the same time and each project team consists of 8 employees as described. on how many of the 56 project teams do you expect there to be exactly 3 computer science graduates? give your answer to 1 decimal place. part e) i meet 30 employees at random. what is the probability that the first employee i meet is the first one who is a computer science graduate? give your answer to 3 decimal places. part f) i meet 33 employees at random on a daily basis. what is the mean number of computer science graduates among the 33 that i meet? give your answer to one decimal place.

Answer: 584.6

Step-by-step explanation: I just took the test

To convert teaspoons to ounces divide the ingredient or material's volume times its density by 5.751669.

Divide the volume times the density of the substance or material by 5.751669 to convert a teaspoon measurement to an ounce.

Hence, the volume in ounces is calculated by multiplying the teaspoons by the component or material's density and dividing the result by 5.751669.

ounces = teaspoons × ingredient density / 5.751669

One-third of a tablespoon's volume is represented by a teaspoon. Although a teaspoon is roughly equivalent to 4.9 millilitres, on nutrition labels, a teaspoon is actually equal to 5 millilitres.

The teaspoon is a common volume measurement in the US. Teaspoons can be written as tsp, although they can also be spelled as t, ts, or tspn.

One ounce is equal to 1/16 of a pound in terms of mass/weight. The troy ounce, which is equivalent to 1/12 of a troy pound, should not be confused with the common ounce.

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The factor that represents the area of the yard that can be mowed is (225 - x²).

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The total area of the lawn is given by the formula -

Area of square lawn = (side length of square lawn)²

= (15 yards)²

= 225 square yards

The shed is also a square, with side length x yards.

So, the area of the shed is -

Area of square shed = (side length of square shed)²

= x²

To find the area of the yard that can be mowed, we need to subtract the area of the shed from the total area of the lawn -

Area of yard that can be mowed = Area of square lawn - Area of square shed

= 225 - x²

Therefore, the value is obtained as (225 - x²).

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The value of x when y = 8 is 13.5

If y is inversely proportional to x, it means that their product is a constant value.

We can represent this relationship using the formula:

y * x = k

where k is the constant of proportionality.

We are given that y = 27 when x = 4, so we can solve for k:

27 * 4 = k

This gives

k = 108

Now that we know the value of k, we can use it to find x when y = 8:

y * x = k

This guves

8 * x = 108

So, we have

x = 13.5

Hence, when y = 8, the value of x is 13.5.

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Answer:

Using 3.14 for π, we have:

[tex]32(26) + \frac{1}{2} (3.14)( {13}^{2} ) = 1097.33[/tex]

about 1,097.33 square feet

Answer:

b = 50°

c = 130°

Step-by-step explanation:

B

Vertical angles are congruent (have the same measurement)

C

Adjacent angles ae supplemental (add to 180°)

Answer:

b = 50°

c = 130°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Greetings!!

Vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are. congruent, meaning that they have the same angle measure. For example, angle 1 and angle 3 are vertical angles.

Also look at the image attached above

Hope it helps!!!!

A rhombus with opposite sides are parallel and equal, and opposite angles are equal looks like Diamond.

A closed two-dimensional plane figure is a rhombus. It is regarded as a peculiar parallelogram, and due to its distinctive characteristics, it acquires a distinct identity as a quadrilateral. Due to its equal length sides, a rhombus is also known as an equilateral quadrilateral. The name "rhombus" is derived from the Greek word "rhombos," which really refers to a spinning object.

Due to the fact that it is a quadrilateral with two pairs of parallel sides, a rhombus can be considered a particular parallelogram. A rhombus also has equal sides on all four sides, exactly like a square. Because of this, it is often referred to as a tilted square. To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.

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Answer: 0.58

Step-by-step explanation: ..

Answer:

the pressure at a temperature of 600 K is 9.6 pounds per square inch.

Step-by-step explanation:

If the pressure of a gas in a container varies directly as the temperature, then we can use the formula P1/T1 = P2/T2, where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature.

Using the values given in the problem, we can write:

8/500 = P2/600

Solving for P2, we get:

P2 = (8/500) * 600 = 9.6 pounds per square inch

Therefore, the pressure at a temperature of 600 K is 9.6 pounds per square inch.

Answer: x = 0, Y = 2    

              x = 1, Y = 5

Step-by-step explanation:

Y = −3x^2 + 6x + 2

Y = 3x + 2

We can set the two equations equal to each other, since they both equal Y:

−3x^2 + 6x + 2 = 3x + 2

−3x^2 + 3x = 0

 3x(-x + 1) = 0

This gives us two possible solutions:

x = 0

x = 1

When x = 0, Y = 3(0) + 2 = 2

When x = 1, Y = 3(1) + 2 = 5

Therefore, the solutions to the system of equations are:

x = 0, Y = 2

x = 1, Y = 5

Answer: To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

Step-by-step explanation:

Answer:

2(8x−5+x^2 )

Step-by-step explanation:

2(3x−1+x^2+5x−4)

2((3x+5x)+(−1−4)+x^ )

2(8x−5+x^2 )

Answer: look at the image for the answer and explanation

Step-by-step explanation:

Answer:

In the triangle we are given Angle A,B andC

a) To find the value of x we will say

angle A + angle B + angle C = 180(sum of angles in triangle add up to 180)

35 + 52 + 3(x+2) = 180

87 + 3x + 6 = 180

3x + 93 = 180

3x = 180 - 93

3x = 87

x = 29

b) To find the measure for angle C we need to substitute the value of x

angle c = 3(x+2)

= 3(29+2)

= 3(31)

= 93

The conversion from mililitres to litre will be done using the relation between the two, where 1 liter has 1000 mililitres.

Firstly know the abbreviations. In this question, ml represents mililitres. Now, The mentioned problem is from unit conversion. As we know the relation, that one litre contains 1000 milliliters of any fluid. So, this is the method of conversion from mililitres to litre.

We can understand given conversion through example. Let us say Zainab has a bottle of 2000 mililitres. Now how many litres of liquid can this bottle contain?

1000 mililitres is present in 1 liter

So, 2000 mililitres will contain = 2000/1000

Performing division

2,000 mililitres will contain 2 litre liquid.

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Answer:

k < 24

Step-by-step explanation:

The phrase "k less than 24" can be written as an algebraic expression using the symbol "<" which means "less than."

So, "k less than 24" can be written as:

k < 24

This means that the value of "k" is smaller than 24. For example, if k = 20, then 20 is less than 24, so the statement "k < 24" is true.

If k = 30, then 30 is not less than 24, so the statement "k < 24" is false.

I hope this helps!

- Dante

Step-by-step explanation:

180-(20+x+40)

=180-(60+x)

x=180-60

=120

The benefit of doing so is: If the teenager has earned less than $12,000 then they don't get the federal taxes withheld. It would be beneficial to the teen because they would get more money.

A teen might want to claim exemption from federal income taxes being withheld from their paycheck if they expect to earn less than the standard deduction amount for the tax year and they will not owe any federal income tax.

For the tax year 2022, the standard deduction amount for a single taxpayer who is not claimed as a dependent on another taxpayer's return is $12,950.

By claiming exemption from federal income taxes, the teen would have more money in their paycheck and would not have to wait to receive a tax refund when they file their tax return at the end of the year.

However, if the teen ends up earning more than the standard deduction amount or if they have other sources of taxable income, they may owe federal income tax and may have to pay a penalty for not having enough taxes withheld during the year.

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The amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square is 16.67

In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.

By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.

In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:

=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).

If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.

If the owner counted 7 trees in the first square, the formula would be

=> (7 / 70) x (2500 / 12) = 16.67.

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Complete Question:

To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here.

7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5

The vertex form equation is illustrated below.

Directrix (d): The directrix is the horizontal line y = -2.

Focus (F): The focus is the point (0, 2).

Vertex (V): The vertex is the point (0, 0).

Equation: The equation of the parabola is y = 1/4x^2.

The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) is the vertex. We already know the vertex of this parabola, which is (0, 0). To find the value of a, we can use the fact that the distance between the focus and the vertex is equal to the distance between the directrix and the vertex.

The distance between the focus (0, 2) and the vertex (0, 0) is 2 units. The distance between the directrix y = -2 and the vertex (0, 0) is also 2 units. Therefore, we can say that 1/(4a) = 2, or a = 1/8.

So, the vertex form equation of the parabola is y = 1/8(x-0)^2 + 0, which simplifies to y = 1/8x^2.

Vertex: The vertex is (0, 0).

Axis of Symmetry (AOS): The axis of symmetry is the vertical line x = 0.

Domain: The domain of the parabola is all real numbers, because the parabola continues indefinitely in both directions along the x-axis.

Range: The range of the parabola is y >= 0, because the lowest point on the parabola is the vertex (0, 0).

Transformations: The only transformation applied to the basic parabola y = x^2 is a vertical compression by a factor of 1/8.

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Answer:

Listed below

Step-by-step explanation:

  1. To solve number 1 we need to find a common denominator.

A common denominator consists of two or more fractions that have the same denominator.

[tex]\frac{3}{4} =\frac{6}{8}[/tex]

How can we convert this? Well, to go from 4 to 8, we multiply by 2. Doing the same to the top number (Numerator) will get us a fraction of [tex]\frac{6}{8}[/tex].

Adding the two fractions together:

[tex]\frac{7}{8} +\frac{6}{8}= \frac{13}{8} or1 \frac{5}{8}[/tex]

Therefore, the answer to question 1 is [tex]1\frac{5}{8}[/tex].

   2.  If there are 60 students in a class, and [tex]\frac{3}{4}[/tex] of them are girls, we can use this equation to solve for the number of girls in the class:

We multiply by 0.75 because 0.75 is equivalent to [tex]\frac{3}{4}[/tex].

So, there are 45 girls in the class.

To solve for the rest of the class that are boys, we can use this equation:

The answer to question 2 is 15 boys.

  3. If the temperature was -2°C, and it is now 8°C, we can use this equation to solve for the temperature difference:

So, the temperature difference is 10°C.

  4. If Mt. Everest's elevation is at 29,028 feet, and the dead sea is -458, we can use this equation to solve for the difference in elevation:

Therefore, the difference in elevation is 29,486 feet.

The speed of the train is 28.5 miles per hour.

According to given condition :

One possible equation to solve for the speed of the train is:

speed = distance / time

In this case, the distance is 285 miles, and the time is 10 hours. Plugging in those values, we get:

speed = 285 / 10

Simplifying this expression, we get:

speed = 28.5

Therefore, the speed of the train is 28.5 miles per hour.

What is equation ?

An equation is a mathematical statement that shows that two expressions are equal. Equations typically use variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. The purpose of an equation is to find the value(s) of the variable(s) that make the equation true.

For example, an equation might be:

2x + 3 = 7

This equation means that if we multiply x by 2 and then add 3, we get 7. The solution to this equation is x = 2, since if we substitute x = 2 into the equation, we get:

2(2) + 3 = 7

4 + 3 = 7

7 = 7

which is true.

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Answer:

1. Divide the compound figure into parts whose areas can be calculated. These parts must be simple shapes such are rectangles, triangle, circles, etc. for which there is a formula, and the dimensions (length, width, height, radius, etc.) must be shown or can be calculated.

2. Calculate the area of each part.

3. Add all areas together.

After 32 weeks, the population of bumble bees will be 6.77315 x 10¹⁴ bees.

The population of bumble bees triples every week, so the common ratio is 3. The starting population is 20 bees.

The formula for a geometric sequence is:

a_n = a_1 * rⁿ⁻¹

where,

a_n = the nth term in the sequence

a_1 = the first term

r = the common ratio

n = the number of terms.

Using this formula, we can find the number of bees after 32 weeks:

a_32 = 20 * 3³²⁻¹

a_32 = 20 * 3³¹

a_32 = 6.773150 × 10¹⁴

Therefore, after 32 weeks, the population of bumble bees will be approximately 6.77315 x 10¹⁴ bees.

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If the long-term demand for oranges is the same as the short-term demand, a binding price ceiling will result in a shortage that is larger in long-run demand than the short-run demand. So the answers are shortage and larger.

A shortage occurs when there is a difference between the quantity that is supplied and the quantity that is required of a product, service, or resource. Surplus is a term used to describe situations where there is more supply than demand for a product, service, or resource.

So when the long-run demand is the same as the short-run demand, binding price ceilings typically result in a shortage when there is a lack of supply of products. And, the result will be larger in the case of the long run compared to the short run. Therefore, the first blank can be filled with shortage and the second blank with larger.

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The ratio of roses to daisies is 2:5. If there are 40 roses, then there are 100 daisies.

In the garden, the ratio of roses to daisies is 2:5. This means that for every 2 roses, there are 5 daisies. We can use this information to find the number of daisies when there are 40 roses.

Set up a proportion using the given ratio and the number of roses.
   2/5 = 40/x

Cross multiply to solve for x, we get:
   2 * x = 5 * 40

Then, simplify the expression:
2x = 200

Divide both sides by 2 to isolate x.
x = 100

Therefore, there are 100 daisies in the garden when there are 40 roses.

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Answer:

Step-by-step explanation:

there 2:6