Question A1 A group of 60 engineers jointly work on a large research project. 40 of the engineers are male (M) and the remaining are female (F). Out of the 60 engineers, 80% are junior (J) engineers and the remaining are senior engineers (S). 25% of the senior engineers are female.
a) State the probabilities P(M), P(F), P(S), P(J) and P(M|S). (3 marks)
b) Given the above information, find the probability of: i) A female engineer being senior. ii) A junior engineer being male. iii) An engineer being senior and female. (3 marks)

The arithmetic mean (average) of the variable "score" in the given table is D. 0.8575.  the correct answer is option D: 0.8575.

To calculate the arithmetic mean (also known as the average) of the variable "score" in the given table, we need to add up all the scores and divide the sum by the total number of scores.

Adding up the scores, we get:

0.98 + 0.88 + 0.65 + 0.92 = 3.43

There are four scores in total, so we divide the sum by 4 to get:

3.43 ÷ 4 = 0.8575

Therefore, the arithmetic mean (average) of the variable "score" in the given table is 0.8575.

So, the correct answer is option D: 0.8575.

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Answer:

=  x^3+5x^2+6x−18 /x

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x²-9)/x² × 2x³/(x² + 5x + 6)

Using the above factorization in the given:

Answer:

I believe this might be the answer 52 − 1 + 5/1= 56

Answer:

56

Step-by-step explanation:

hope it helps ^^.

1) 3/7

2) 9/21

3) 150/350

Answer:

ASA

Step-by-step explanation:

Without more information and statistical analysis, it is difficult to determine whether the data provide convincing evidence that the average GRE verbal reasoning score has changed since 2004.

To determine whether the average GRE verbal reasoning score has changed since 2004, we would need to conduct a hypothesis test. We could set up a null hypothesis that the population mean for the verbal reasoning score has not changed since 2004, and an alternative hypothesis that the population mean has increased.

Assuming a normal distribution of scores, we could use a two-sample t-test to compare the means of the two populations (scores from 2004-2007 and scores from 2011). We would need to collect a random sample of scores from both time periods and calculate the sample means and standard deviations.

Without knowing the sample size or standard deviation of the 2011 scores, it is difficult to determine whether the difference in average scores is statistically significant. However, if the sample sizes are large enough and the difference in means is significant, then we could conclude that there is convincing evidence that the average GRE verbal reasoning score has changed since 2004.

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Answer:

(4d - 3e)(10d - 3e)

Step-by-step explanation:

(4d - 3e)² + 6d(4d - 3e) ← factor out (4d - 3e) from each term

= (4d - 3e)(4d - 3e + 6d) ← collect like terms inside parenthesis

= (4d - 3e)(10d - 3e)

1) Regroup terms.

2(4d - 3e) + 6d(4d-3e)

2) Expand by distributing terms.

8d - 6e + 6d (4d - 3e)

3) Expand by distributing terms.

8d - 6e + 24d² - 18ed

The statement is true - Independent variables are beyond the experimenter's control.

The statement is true. Independent variables are those factors that cannot be manipulated by the experimenter. They are the variables that are naturally occurring and cannot be changed. For example, age, gender, or genetics are independent variables that are beyond the experimenter's control. In contrast, dependent variables are those variables that can be manipulated by the experimenter, such as the amount of light, the temperature, or the dosage of a drug. Understanding the difference between independent and dependent variables is crucial in designing and conducting experiments.

Independent variables are those variables that are beyond the control of the experimenter. They are naturally occurring factors that cannot be manipulated, whereas dependent variables are those that can be manipulated.

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Answer:

8 cm

Step-by-step explanation:

If the 16 cm is the diameter then the radius is 8 cm. To find the radius of a circle you simply divide two by the diameter. 16 ÷ 2 = 8

Answer:

Para compartir 7 alfajores entre 4 niños y niñas para que no quede nada, a cada niño y niña se les debe dar 7/4 alfajores

Step-by-step explanation:

Al compartir 5 alfajores, entre 3 niños y niñas, los alfajores se cortan en tres partes cada uno de manera que cada niño y niña recibe 5/3 piezas de alfajore

Luego, la pregunta es, ¿cómo se pueden compartir 7 alfajores entre 4 niñas y niños sin que quede nada?

Por el proceso de compartir ejemplos, obtenemos;

Cada alfajores debe dividirse en el número total de niños y niñas, que son cuatro piezas cada uno.

El número total de 1/4 piezas = 7 × 4 = 28 piezas de 1/4 alfajores

Cada niño y niña recibe 7 de las piezas de 1/4 alfajores

El número total de alfajores, n, compartidos entre los cuatro niños y niñas viene dado por la expresión;

n = 7 (1/4 alfajores) × 4 = 28 piezas de 1/4 alfajores

Por lo tanto, para compartir 7 alfajores entre 4 niños y niñas para que no quede nada, cada niño y niña debe recibir 7/4 alfajores.

Answer:

see explanation

Step-by-step explanation:

using the identity

sin²Θ = 1 - cos²Θ

consider the left side

1 - \(\frac{sin^20}{1+cos0}\)

= 1 - \(\frac{1-cos^20}{1+cos0}\)

1 - cos²Θ is a difference of squares and factors as (1 - cosΘ)(1 + cosΘ)

= 1 - \(\frac{(1-cos0)(1+cos0)}{1+cos0}\) ← cancel (1 + cosΘ) on numerator/ denominator

= 1 - (1 - cosΘ) ← distribute parenthesis by - 1

= 1 - 1 + cosΘ

= cosΘ

= right side

The IQR (Interquartile Range) of 13 is the most accurate measure of variability to use in this scenario, since the data is skewed and contains outliers.

What is data?

Data refers to any information, facts, or statistics that are collected, stored, and analyzed for a specific purpose. Data can take many forms, such as text, numbers, images, audio, and video, and can be generated from a variety of sources, including sensors, surveys, transactions, and social media.

Here,

The range, which is the difference between the maximum and minimum values (59 - 10 = 49), may be affected by extreme values that are far from the majority of the data. In this case, the donations of 10 and 59 are outliers and may distort the range as a measure of variability.

On the other hand, the IQR, which is the range of the middle 50% of the data (the difference between the third quartile and the first quartile), is a robust measure of variability that is not sensitive to outliers. The IQR in this case is calculated as follows:

First quartile \((Q_1)\) = 42

Third quartile \((Q_3)\) = 53

\(IQR = Q_3 - Q_1 = 53 - 42 = 11\)

Therefore, the IQR of 13 is a more accurate measure of variability to use in this scenario, as it represents the spread of the majority of the data and is not influenced by the extreme values.

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Answer:

Brainliest pls

Step-by-step explanation:

-20

Answer:

The answer is -20.

Step-by-step explanation:

REMEMBER THIS:

Please excuse my dear aunt sally…

PLEASE = PARENTHESIS

EXCUSE= EQUATION

MY = MULTIPLICATION

DEAR = DIVISION

AUNT = ADDITION

SALLY = SUBTRACTION

^In that order^

Remember to use this statement to remember how to simplify the expression. PEMDAS.

Sin^2(x-b) + cos^2(x-a) - sin(x-b)cos(x-a) can be simplified using trigonometric identities. Firstly, we can use the Pythagorean identity, sin^2(x) + cos^2(x) = 1, to simplify the first two terms. Thus, we have:

sin^2(x-b) + cos^2(x-a) = 1

Next, we can use the angle addition formula, sin(a+b) = sin(a)cos(b) + cos(a)sin(b), to simplify the third term. Thus, we have:

-sin(x-b)cos(x-a) = -[sin(x)cos(b)cos(a) - cos(x)sin(b)sin(a)]

Combining all three terms, we get:

sin^2(x-b) + cos^2(x-a) - sin(x-b)cos(x-a) = 1 + [sin(x)cos(b)cos(a) - cos(x)sin(b)sin(a)]

This means that the expression sin^2(x-b) + cos^2(x-a) - sin(x-b)cos(x-a) can be simplified using trigonometric identities. By using the Pythagorean identity and the angle addition formula, we can simplify the three terms into one expression. This expression can be further simplified by combining the terms. The final answer is 1 + [sin(x)cos(b)cos(a) - cos(x)sin(b)sin(a)]. This process of simplifying trigonometric expressions is useful in solving equations and proving identities in trigonometry.

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Based on the context of the problem, the range of the exponential function y = \(45,529(0.78)^x\) is y > 0.

The exponential function for depreciation given in the problem is:

y = 45,529(0.78)^x

This function gives us the value of Sharlene's truck in dollars after x months of ownership, assuming that the depreciation follows a constant rate and is modeled by an exponential function.

To find the range of the function, we need to consider the minimum value that y can take. Since depreciation leads to a decrease in value over time, y should always be greater than zero. In other words, the range of the function is:

y > 0

In practical terms, this means that Sharlene's truck will always have some positive value, even if its market value has decreased due to depreciation. In other words, a truck is never worth zero or less than zero (unless it has additional debts associated with it), and Sharlene's truck will always have some resale or scrap value even if it has depreciated significantly.

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Using the value of ∫01x3+1dx obtained above, we can approximate the value of∫0.50x3+1dx as:Simpson's Rule ∫abf(x)dx≈b−a3n[f(a)+2∑i=12n−1f(ai)+4∑i=14n−1f(xi)+f(b)]≈15[0+2{(13)3+1}+4{(14)3+1}+13+3]≈0.7828Therefore, the solution to part b at x=0.5 to three decimal places is approximately equal to 0.7828.

The solution to part b at x

=0.5 to three decimal places using Simpson's Rule with n

=4 is given as follows:Approximate the value of∫01x3+1dx, with Simpson's Rule using n

=4 subintervals.Simpson's Rule formula for integrating a function, f(x), with n subintervals is given as:Simpson's Rule ∫abf(x)dx≈b−a3n[f(a)+2∑i

=12n−1f(ai)+4∑i

=14n−1f(xi)+f(b)]where h

=(b−a)n and xi

=a+ih for i

=1,2,3,...,n.Substituting a

=0, b=1, f(x)

=x3+1, and n

=4 in Simpson's Rule formula:∫01x3+1dx≈14[0+2{(13)3+1+(23)3+1}+4{(14)3+1+(34)3+1}+13+3]≈1.1354The value of ∫01x3+1dx is approximately equal to 1.1354, using Simpson's Rule with n

=4 subintervals. We want to approximate the solution to part b at x

=0.5 to three decimal places. Using the value of ∫01x3+1dx obtained above, we can approximate the value of∫0.50x3+1dx as:Simpson's Rule ∫abf(x)dx≈b−a3n[f(a)+2∑i

=12n−1f(ai)+4∑i

=14n−1f(xi)+f(b)]≈15[0+2{(13)3+1}+4{(14)3+1}+13+3]≈0.7828Therefore, the solution to part b at x

=0.5 to three decimal places is approximately equal to 0.7828.

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the derivative of the function y = (sin(5x))ln(x) is dy/dx = ln(x) * [5cos(5x) + (1/x)].

To find the derivative of the function y = (sin(5x))ln(x) using logarithmic differentiation, we follow these steps:

Step 1: Take the natural logarithm (ln) of both sides of the equation:

ln(y) = ln((sin(5x))ln(x))

Step 2: Use logarithmic properties to simplify the expression:

ln(y) = ln(sin(5x)) + ln(ln(x))

Step 3: Differentiate both sides of the equation implicitly with respect to x:

(1/y) * dy/dx = (1/sin(5x)) * d/dx(sin(5x)) + (1/ln(x)) * d/dx(ln(x))

Step 4: Simplify the derivatives on the right-hand side:

(1/y) * dy/dx = (1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)

Step 5: Multiply both sides of the equation by y to isolate dy/dx:

dy/dx = y * [(1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)]

Step 6: Substitute y back into the equation:

dy/dx = [(sin(5x))ln(x)] * [(1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)]

Step 7: Simplify the expression further:

dy/dx = ln(x) * [5cos(5x) + (1/x)]

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Using it's concept, it is found that there is a 0.6 = 60% probability that the flower is NOT A ROSE.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 6 + 5 + 4 = 15 flowers, out of which 5 + 4 = 9 are not roses, hence the probability is given by:

p = 9/15 = 0.6 = 60%.

0.6 = 60% probability that the flower is NOT A ROSE.

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Answer:

y= -5x + 1

Step-by-step explanation:

the equation of a line is y=mx + b

m= the slope

b= the y-intercept

The ratio decreases and we can say that the series converges.

To determine whether the geometric series is convergent or divergent, we need to calculate the common ratio (r) between consecutive terms. The common ratio can be found by dividing any term by the previous term.

r = (4)/(5) = 0.8

r = (16/5)/(4) = 4/5

r = (64/25)/(16/5) = 16/25

We can see that the common ratio is less than 1, which means that the series converges. To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where a is the first term and r is the common ratio.

Plugging in the values, we get:

S = 5 / (1 - 0.8) = 25

Therefore, the geometric series is convergent and its sum is 25.

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Answer:

Number of moles = 41.67 (Approx)

Number of carbon atom = 250.97 x 10²³ (Approx)

Step-by-step explanation:

Given:

Amount of carbon = 500 g

Find:

Number of moles

Number of carbon atom

Computation:

Number of moles = 500 / Atomic number of weight

Number of moles = 500 / 12

Number of moles = 41.67 (Approx)

Number of carbon atom = Number of moles x Avogadro number

Number of carbon atom = 41.67 x 6.023 x 10²³

Number of carbon atom = 250.97 x 10²³ (Approx)

Answer:

\(Point(9,1)\)

Step-by-step explanation:

Given

Point: (6,3)

Required

Translate 2 units down and 3 units left

Taking the translation 1 after other

When a function is translated down, only the y axis is affected;

2 units down implies that, 2 be subtracted from the y value.

The function becomes

\(Point: (6, 3 - 2)\)

\(Point: (6, 1)\)

3 units right implies that, 3 be added tothe x value.

The function becomes

\(Point(3+6,1)\)

\(Point(9,1)\)

Hence;

Option D answers the question

2 is the answer of the question

Answer:

(0,5)

Step-by-step explanation:

3x-5y=15

Plug in 0 for y, because we are trying to find the value of x, when y is 0

so, 3x-5(0)=15

3x=15     Divide both sides by 3

x=5

so the answer in coordinate form is (0,5)

Answer:

<U=70

Step-by-step explanation:

Straight line=180 degrees

180-120

=60

So, we have 2 angles.

60 and 50

180=60+50+x

180=110+x

70=x

So, U=70

Hope this helps! :)

The graph with a line y+3=2(x+3) is

A coordinate plane with a line passing through the points (0, 3) and (-2, -1) with a slope of 2.

The answer is the fourth option: the slope of the line y - 4 = 5/2(x - 2), is

To find the graph that matches the equation y+3=2(x+3), we need to rewrite the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

y + 3 = 2(x + 3)

y + 3 = 2x + 6

y = 2x + 6 - 3

y = 2x + 3  slope-intercept form

The equation is now in slope-intercept form, y = 2x + 3,

where

The graph of this equation should be a line that passes through the y-axis at 3 and has a slope of 2. From the attached graph we can see point (-2, -1)

To find the slope of the line whose equation is y - 4 = 5/2(x - 2), we can rewrite the equation in slope-intercept form.

y - 4 = 5/2(x - 2)

y - 4 = 5/2x - 5

y = 5/2x - 5 + 4

y = 5/2x - 1  slope-intercept form

The equation is now in slope-intercept form, y = 5/2x - 1,

where the slope is 5/2.

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(i) 2.2% is the periodic interest rate offered by Becky's savings account

(ii) Becky earn $27,000  in interest on her first payment during this time

(iii) Becky earn $1,782 in interest on her second payment during this time

Part I:

Given that the savings account is paying simple interest at an annual interest rate of 8.8% calculated quarterly.

Then the periodic interest rate offered by Becky's savings account is given by  8.8% / 4 = 2.2%

Part II:

Given that the first payment of $27,000 is occurring in 3 months, then Becky  will be able to have the money in the bank for 3 quarters before the lump-sum payment would occur

Part III:

Given that Becky's first payment of $27,000 will be in her account for 3 periods at a simple interest of 2.2% per quarter.

The amount Becky will earn in interest on her first payment during this period is given by:

I = (P*R*T) / 100

I = (27,000 * 2.2 * 3) / 100

I = $1,782

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