In a class,5/8of the pupils are boys. If 15. Girls in that class how many boys are there

a. The tree diagram representing the above situation is illustrated below.

b. The percentage of employees hold management positions is 10%

c. The probability that she/he has a graduate degree is 85%.

In this case, the businessman can choose any 3 suits and 4 ties, so the number of combinations is equal to the number of ways of choosing 3 suits multiplied by the number of ways of choosing 4 ties.

This is equal to 6 x 8 = 48.

The records of the company also provide us with some useful information about the probability of holding a management position.

We can see that 20% of the employees have only a high school diploma and 10% of those employees hold management positions.

This means that the probability of holding a management position given that a person has a high school diploma is 10%.

Similarly, of those having bachelor degrees, 60% hold management positions, meaning the probability of holding a management position given that a person has a bachelor degree is 60%.

Lastly, 85% of the employees who have graduate degrees hold management positions, so the probability of holding a management position given that a person has a graduate degree is 85%.

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By using the data table, a ratio for each comparison in three different ways should be written as follows;

The ratio of O+ donors to B+ donors is 9:2.

The ratio of A- donors to B+ donors is 21:20.

The ratio of AB+ donors to total donors is 6:195.

In order to determine and write the ratio for each comparison, we would have to assign variables to the chosen blood group donors respectively:

From the information provided above, we have the following parameters:

O = 90 donors.

B = 20 donors.

Now, we can write the ratio as follows;

O:B = 90:20

Dividing by 10, we have the following ratio:

O:B = 9:2

ABN:ABP = 4:6

Dividing by 2, we have the following ratio:

ABN:ABP = 2:3

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(x+5)^2 + (x-2)^2 = 25 is the required equation of the circle

The standard equation of a circle is expressed according to the equation below:

(x-a)^2 + (y-b)^2 = r^2

where

(a, b) is the centre

r is the radius

From the given digram, the center is at (-5, 2)

r^2 = (6-2)^2 + (-5+2)^2

r^2 = 4^2 + (-3)^2
r^2 = 16 + 9

r^2 = 25

Substitute

(x - (-5))^2+(x-2)^2 = 25

(x+5)^2 + (x-2)^2 = 25

Hence the required equation of the circle is (x+5)^2 + (x-2)^2 = 25

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it will take approximately 678.24 seconds, or about 11 minutes and 18 seconds, to earn $2,000,000 if you make $2949 per second.

Why it is?

We can use a simple formula to solve this problem:

Time = Amount / Rate

where Amount is the amount of money you want to earn ($2,000,000) and Rate is the rate at which you earn money per second ($2949).

Plugging in these values, we get:

Time = $2,000,000 / $2949 per second

Time = 678.24 seconds

Therefore, it will take approximately 678.24 seconds, or about 11 minutes and 18 seconds, to earn $2,000,000 if you make $2949 per second.

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The value of the markup is $12

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

Original $10.00 percent of markup: 20%​

The markup price is calculated as

Markup Price = Original; * (1 + Markup)

Substitute the known values in the above equation, so, we have the following representation

Markup Price = 10 * (1 + 20%)

Evaluate

Markup Price = 12

Hence, the price is $12

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When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.

Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.

So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.

So, option D is the correct answer.

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Answer:

The data in this scenario would most likely be categorical, as the responses would likely consist of categories or labels that describe the different activities that the teenagers would like to see in the community room on Saturdays.

Step-by-step explanation:

For example, the responses might include categories such as "video games," "board games," "movie nights," "sports activities," "arts and crafts," and so on. These categories are not numerical values, but rather descriptive labels.

The linear equation for the photocopier will be y = $20C + $0.02n.

In a linear equation, a first-degree polynomial is defined as the sum of a group of terms, where each term is the product of a constant and the first power of a variable. An equation with n variables is said to be linear if it has the formula a0 + a1x1 +... + anxn = c, where x1,..., and xn are variables, the coefficients a0,..., and an are constants, and c is a constant. If there are multiple variables, some of the variables in the equation may be linear while others may not be.

Given,

Jamie rents a photocopier from a company that charges $20 each month

$0.02 for each copy

monthly charge = C

number of copies = n

So, the linear equation will be y = $20C + $0.02n

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It will take approximately 12 years and 9 months for Sienna Rose's money to grow to $7000.

What is compound interest?

Compound interest is interest that is calculated not only on the original principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, the interest earned on an investment or the interest charged on a loan is added to the principal, and then the interest for the next period is calculated on the new total amount.

For example, if you invest $1,000 at an annual interest rate of 5%, and the interest is compounded annually, you would earn $50 in interest at the end of the first year. Instead of receiving that $50, it would be added to your principal, so your new balance would be $1,050. The following year, you would earn 5% interest on $1,050, which would be $52.50. This process would continue for each year of the investment.

Compound interest can be very beneficial for long-term investments, as the interest earned on the accumulated interest can significantly increase the total return. However, it can also work against you in the case of loans, as the interest charged on the accumulated interest can quickly increase the total amount owed.

We can use the formula for compound interest to solve this problem:

[tex]A= P (1+\frac{r}{n} )^{nt}[/tex]

where

A is the amount of money after t years,

P is the principal (starting amount),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year, and

t is the time (in years).

In this case,

P = $4000,

r = 0.036 (since the interest rate is given as 3.60% per year),

n = 12 (since the interest is compounded monthly), and

we want to find t when A = $7000.

Substituting these values into the formula, we get:

$7000 = $4000(1 + 0.036/12)^(12t)

Dividing both sides by $4000 and taking the natural logarithm of both sides, we get:

ln(1.75) = 0.003 t

Solving for t, we get:

t = ln(1.75)/(0.003)

t ≈ 153.71 months

Therefore, it will take approximately 153 months, or 12 years and 9 months (since there are 12 months in a year), for Sienna Rose's money to grow to $7000.

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The weight of each box is 13.5 and 6.25 kg

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given is a system of equations,

8x+4y = 133....(i)

3x+2y = 53....(ii)

Solving the equations,

Multiplying the eq(ii) by 2 and subtracting by eq(i)

8x+4y = 133 - (6x+4y = 106)

2x = 27

x = 13.5

Put x = 13.5 in eq (ii)

3(13.5) + 2y = 53

2y = 12.5

y = 6.25

Hence, the weight of each box is 13.5 and 6.25 kg

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Answer:

................ ⅓........

The area of the teacher workroom is 64 feet squared

The value of the expression 18 - (16 • 12) is -174.

To evaluate the expression 18 - (16 • 12), we need to follow the order of operations, also known as PEMDAS. According to PEMDAS, we first perform any calculations inside parentheses, then evaluate exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

In this expression, we have the operation of multiplication inside parentheses. So, we start by evaluating 16 • 12, which equals 192.

Now, we can rewrite the expression as 18 - 192.

Next, we perform the subtraction, which gives us -174.

Therefore, the value of the expression 18 - (16 • 12) is -174.

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Answer:

11.3 inches

4th option

Step-by-step explanation:

Area of a circular object = πr² where r = radius

Given area = 400 square inches,

πr² = 400 square inches

r² = 400/π

r = √(400/π)

r = 20/√π

= 11.3 inches rounded to one decimal place(tenth)

Riemann sums are calculated by dividing the area under a curve into subintervals and approximating the area in each interval using a rectangle.

Riemann sums are a method of approximating the area under a curve by dividing the area into smaller subintervals and approximating the area in each interval using a rectangle. The width of each rectangle is determined by the size of the subinterval, and the height of the rectangle is determined by the value of the function at a specific point within the subinterval.

The sum of the areas of all the rectangles gives an approximation of the total area under the curve. The accuracy of the approximation increases as the width of the subintervals decreases, and as the number of subintervals increases, the approximation approaches the exact value of the area under the curve.

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The second trapezoid has the corresponding sides labeled 4.9 cm and x cm, the value of x is 4.2 cm

Without knowing the scale factor, we can use the ratio of corresponding sides of the two trapezoids to set up an equation and solve for x.

The ratio of the lengths of the corresponding sides of the two trapezoids is: 14.7 cm / 12.6 cm = 4.9 cm / x

To solve for x, we can cross-multiply:

14.7 cm × x

= 12.6 cm × 4.9 cm

Dividing both sides by 14.7 cm, we get:

x = (12.6 cm × 4.9 cm) / 14.7 cm

Simplifying the right side, we get:

x = 4.2 cm

Therefore, the value of x is 4.2 cm.

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases. The area of a trapezoid is given by the formula A = (b1 + b2) × h / 2, where b1 and b2 are the lengths of the bases and h is the height. Trapezoids are commonly found in geometric and architectural designs, and they have various applications in engineering and physics.

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Complete Question

This scale drawing shows a reduction in a figure. What is the value of x? Enter your answer as a decimal in the box. x = Two trapezoids of different sizes. The first trapezoid has a side labeled 14.7 cm and a side labeled 12.6 cm. The second trapezoid has the corresponding sides labeled 4.9 cm and x cm, respectively. Find x in trapezoid.

Answer:

height = 21.8 ft from ground

Step-by-step explanation:

see photo for explanation.

It would  51.35 minutes take a puddle of water to freeze.

What is the initial temperature?

Initial temperature refers to the average interior temperature of the coldest processing container at the start of the thermal processing cycle, as determined after a thorough stir or shake of the filled and sealed container.

The given equation is T = R + (T₀ − R)[tex]e^{(-kt)}[/tex].

T = temperature of the object after t minutes

T₀ = initial temperature

R = temperature of the surroundings

k = cooling rate (depends on the object and conditions)

The initial temperature is 55°F. The water freezes at 32°F. Thus final temperature is 32°F. The value of k is 0.012.

Now putting T = 32°F, T₀ = 55°F, R = 5°F, k = 0.012 in the given equation:

32 = 5 + (55 − 5)[tex]e^{(-0.012t)}[/tex]

Subtract 5 from both sides:

27 = 50[tex]e^{(-0.012t)}[/tex]

Divide both sides by 50:

[tex]e^{(-0.012t)}[/tex] = 27/50

Taking natural logarithms on both sides:

ln[tex]e^{(-0.012t)}[/tex] = ln(27/50)

-0.012t = -0.616

t = 51.35

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It is cheaper to buy the games console in the UK.

Measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

A games console costs £255 in the UK.

And, The same one costs 300 euros in France.

Here, The exchange rate is,

⇒ £1 = €1.16

Hence, The cost of games console in UK is,

⇒ £1 = €1.16

⇒ £255 = €1.16 × 255

              = €295.8

Thus, It is cheaper to buy the games console in the UK.

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Conditional probability can be calculated by using Bayes' theorem, P(A|B) = P(B|A) × P(A) / P(B)

To find the conditional probability, we need to know the probability of two events: the probability of the event we're interested in, and the probability of the condition. Then, we can use Bayes' theorem to calculate the conditional probability.

Bayes' theorem states that the probability of an event A given that event B has occurred is equal to the probability of B given A, multiplied by the probability of A, divided by the probability of B:

P(A|B) = P(B|A) × P(A) / P(B)

The steps to find the conditional probability:

1) Identify the events A and B.

2) Determine the probabilities of A and B.

3) Determine the conditional probability P(B|A)

4) Substitute the values into Bayes' theorem to find P(A|B)

5) Interpret the result.

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Answer:0.50

Step-by-step explanation:

{1 , 5 , 10 , 100)

Two numbers can be chosen from the above set of four numbers in 4C2 ways.

4C2 = 4!/(2!*2!) = (4*3*2!)/)2*2!) = 12/2 = 6

Two numbers can be chosen from the above set of four numbers in 6 ways.

The pair of numbers which give a sum greater than 100 is (1,100) , (5,100) , (10,100).

3 pairs out of 6 total pairs will give a sum greater than 100.

P(sum > 100) = 3/6 = 1/2 = 0.50

P(sum > 100) = 0.50

0.50

From the given information, the probability of getting at least one head in two coin tosses is 3/4 or 0.75.

A coin toss is a random event in which a coin is flipped and the outcome is either heads or tails. The outcome of a coin toss is not dependent on any previous tosses, and each toss is considered to be independent of the others.

The probability of getting at least one head in two coin tosses can be calculated as follows:

There are four possible outcomes when tossing two coins: HH, HT, TH, and TT, where H represents heads and T represents tails. Out of these four outcomes, three have at least one head (HH, HT, TH), and only one has no heads (TT).

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Answer:

x=60

Step-by-step explanation:

180 is the some of the angle of an triangle

in the left triangle the angle is = 180-70-75=35

in the right triangle the angle is=180-35-60=85

x=180-80-45=60

Answer:

Step-by-step explanation:

Remember: The three interior angles of a triangle will always add up to 180 degrees.

In order to solve for x, we need to solve for other missing angles

1) Solve for the missing angle on the triangle to the left.

180 - 75 -70 = 35 degrees.

2) Solve for the missing angle on the triangle to the right (not x).

180 - 60 - 35 = 85 degrees

3) Finally, solve for the x angle by subtracting 45 and 85 from 180. x = 50 degrees.

Answer:

No

Step-by-step explanation:

The way to show this expression is 6(4+5) because "and" is showing the distributive property.

The value  0.24 as a fraction is 6/25. .

In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.

Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations

to convert in fraction we will muliply and devide by 100.

0.24*100/100 =6/25

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Answer:

Step-by-step explanation:

A RIGHT triangle has TWO LEGS and a HYPOTENUSE ( the longest side)

Pythagorean Theorem for right triangles states:

Hypotenuse ^2  =  Leg1 ^2 + Leg2 ^2    

    if you sub in the three sides of the triangle and this is TRUE , it is a RIGHT triangle .

Answer:

46.8 cm²

Step-by-step explanation:

3.9 x 6 = 23.4 (We are multiplying by 6 because there are 6 tiles)

23.4 x 2 = 46.8 (We are multiplying by 2 because when Suki is adding more tiles, she makes a hexagon double the side lengths.)

At the value of x = [tex]-\sqrt{2}[/tex] only f has a relative maximum. So option B is correct.

To find the relative maximum of a function, we need to look for the values of x where the derivative of the function is zero or does not exist. Therefore, we need to find the derivative of the function f(x) first.

[tex]f(x) = e^{(-x)} * (x^2 + 2x)[/tex]

[tex]f'(x) = e^{(-x)} * (2 - x^2)[/tex]

To find the critical points of f(x), we need to solve the equation f'(x) = 0.

[tex]e^{(-x)} * (2 - x^2) = 0[/tex]

This equation is satisfied when [tex]2 - x^2 = 0[/tex] or [tex]e^{(-x)} = 0[/tex].

The equation [tex]2 - x^2 = 0[/tex] has two solutions: [tex]x = -\sqrt{2}[/tex] and [tex]x = \sqrt{2}[/tex].

The equation [tex]e^{(-x)} = 0[/tex] has no solutions.

Now, we need to determine whether each critical point is a relative maximum or a relative minimum. We can use the second derivative test for this.

[tex]f''(x) = e^{(-x)} * (x^2 - 4)[/tex]

At x = [tex]-\sqrt{2}[/tex], [tex]f''(- \sqrt{2}) < 0[/tex], so f has a relative maximum at [tex]x = -\sqrt{2}[/tex].

At x = [tex]\sqrt{2}[/tex], [tex]f''(\sqrt{2}) > 0[/tex], so f has a relative minimum at [tex]x = \sqrt{2}[/tex].

Therefore, the answer is B)  x=−√2 only.

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The conversion of millilitres to cups varies by nation because various countries define a cup differently.  but as per the US standards 1 cup = 236.588 ml.

In the United States, one cup equals 236.588 millilitres, but in the United Kingdom, one cup equals 284.131 millilitres.

As a result, we may write by the standard unit conversion that 1 cup = 236.588 ml.

For consistent outcomes in cooking and baking, exact ingredient proportions are essential. As a result, we apply the relation 1 cup = 236.588 ml to do the conversion as needed.  

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Answer:

x = 3, y = 4

Step-by-step explanation:

3x + y = 13

5x - 2y = 7

To solve by substitution, you solve one of the equations for a variable, and then plug it into the other equation.

I'm going to choose to solve the first equation for y, as that will be the easiest.

y = -3x + 13 (subtract 3x from both sides)

Now we plug this equation into the y in the second equation and solve for x.

5x - 2(-3x + 13) = 7 (distribute)

5x + 6x - 26 = 7 (combine like terms)

11x - 26 = 7 (add 26 to both sides)

11x = 33

x = 3

Now that we know x is 3, we can plug it in a solve either equation for y.

y = -3(3) + 13

y = -9 + 13

y = 4