Bruce’s hourly wage increased from $15. 50 to $18. 60. What rate of increase does this represent?

i. Probability that a note is real but the system identifies it as fake: Let R be the event that a note is real, then the probability of a note being real is\(P(R) = 1 – P(F) = 0.99\)

Then the probability that a note is real but the system identifies it as fake is\(P(T' and R) = P(R) x P(T|R') = 0.01 x 0.05 = 0.0005\)Therefore, the probability that a note is real, but the system identifies it as fake is 0.0005.

ii. Probability that a note is fake, and the system identifies it as fake:

The probability that a note is fake, and the system identifies it as fake can be calculated as:

\(P(F and T) = P(F) x P(T|F) = 0.01 x 0.95 = 0.0095\)  Therefore, the probability that a note is fake, and the system identifies it as fake is 0.0095.

iii. Probability that the system identifies a note as fake.

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The third quartile of the dataset is 6.5

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

3,4,3,9,3,5,8,5

Sort the number in ascending order

So, we have

3, 3, 3, 4, 5, 5, 8, 9

Split the number into equal halves

So, we have

3, 3, 3, 4,

5, 5, 8, 9

The third quartile is the median of the second half

so, we have

The third quartile = (5 + 8)/2

Evaluate

The third quartile = 6.5

Hence, the third quartile is 6.5

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Hello!

The statement is true.

Zeros following non-zero digits in a number are not significant.

Example:

48,000

It's tempting to say that this number has 5 significant digits; however, it only has 2 (4 and 8)

Hence, the statement is true. Hope it helps. Do ask me if you have any question.

~An excited gal

\(MagicalNature\) here to help

Answer:

IT´S TRUE!!!

Step-by-step explanation:

The total area of the composite figure is 228 sq cm

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

The composite figure with 6 sides

The total area of the composite figure is the sum of the areas of the individual shapes

So, we have

Area = Area of Rectangle + Area of Rectangle

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

Area = 12 * 14 + (22 - 12) * 6

Evaluate the products

Area = 228

Hence, the total area of the figure is 228 sq cm

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Answer:

2y bigger or same -12-4y is correct

Step-by-step explanation:

Y=1

2=-12-4×1

2=-16

2 is bigger

Y=-2

-4=-12-4×(-2)

-4=-4 it's same

Answer:

V ≈ 56.55 cm³

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = \(\frac{1}{3}\) πr²h ( r is the radius and h the height )

here r = 3 and h = 6 , then

V = \(\frac{1}{3}\) π × 3² × 6

   = \(\frac{1}{3}\) π × 9 × 6

   = \(\frac{1}{3}\) π × 54

   = π × 18

   = 18π

   ≈56.55 cm³ ( to the nearest hundredth )

Answer:

{0,3,5}

Step-by-step explanation:

∩ means "and" so u would want to find out the numbers that repeat in both sets, this is correct in this situation.

The intersection of sets G and J are {0,3,5} is the correct answer.

The intersection of two sets A and B is the set of all those elements which are common to both A and B. It is symbolically represented as      A ∩ B.

For the given situation,

The sets are

G = {−5,−3,0,3,5}

J = {0,1,3,5,7}

The intersection of the set G and J, the common elements are

G ∩ J = { \({0,3,5}\) }

Hence we can conclude that the intersection of sets G and J are {0,3,5} is the correct answer.

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The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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Answer:

Its y2-y1 over x2-x1

Step-by-step explanation:

Hope that helps!

Answer:

The slope is the change in Y over (divided by) the change in X

So, (Y2-Y1)/(X2-X1) is your answer

Step-by-step explanation:

Hope this helped!!

The measure of side S'Q' is 6.

The scale factor is a way to compare figures with similar appearances but distinct scales or measurements. Consider two circles that resemble one another but may have different diameters. The scale factor indicates how much a figure has increased or decreased from its initial value.

When a triangle is dilated by a scale factor of k, all of its sides are multiplied by k.

In this problem, the triangle QRS is dilated by a scale factor of 1/4, which means all of its sides are multiplied by 1/4. Therefore, the length of side S'Q' is:

S'Q' = (1/4) * SQ

Substituting the given value of SQ = 24, we get:

S'Q' = (1/4) * 24

S'Q' = 6

Therefore, the measure of side S'Q' is 6.

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Answer:

100:64

Step-by-step explanation:

i don't know how i got it LOL

The ratio of the area of circle A to the area of circle B for the considered circle A and B is  100:64

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b or \(\dfrac{a}{b}\)

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

\(a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3\)

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

Let we suppose that:

Then we get:

As per the given information:

The circumference of a circle B is 80% of the circumference of circle A, or:

\(2\pi s \: \rm units\) = 80% of \(2\pi r \: \rm units\)

or:

\(2\pi s = \dfrac{2\pi r}{100} \times 80\\\\s = 0.8r \: \rm units\)

Also, we have:

The rato of the area of the circle A to the area of the circle B is:

\(Area(A): Area(B) = \dfrac{\pi r^2}{\pi s^2} = \left( \dfrac{r}{s}\right)^2\)

since we've got \(s= 0.8r\), therefore,

\(Area(A): Area(B)= \left( \dfrac{r}{s}\right)^2 = \left(\dfrac{r}{0.8r}\right)^2 = \dfrac{100}{64} \\\\Area(A): Area(B)=\dfrac{100}{64} = 100:64\)

Thus, the ratio of the area of circle A to the area of circle B for the considered circle A and B is  100:64

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To expand its manufacturing capacity with a $20 million investment in new machinery while maintaining its current capital structure and dividend policy, Gardial GreenLights must seek external equity of $8 million.

The capital structure of Gardial GreenLights is characterized by a 50% debt-to-total-assets ratio. Since the company plans to maintain this ratio, the remaining 50% of the assets must be financed through equity. The investment in new machinery is $20 million, which represents 50% of the total assets needed for expansion. Therefore, the total assets required for expansion would be $40 million (20 million divided by 0.5). To determine the amount of external equity needed, we subtract the company's existing equity from the total assets required. Given that the company's dividend policy entails distributing 25% of the year's net income, we can calculate the retained earnings. This year's net income was $8 million, and 25% of that ($2 million) would be distributed as dividends. Therefore, the retained earnings amount to $6 million ($8 million - $2 million). Since external equity is the difference between the total assets required and retained earnings, Gardial GreenLights must seek external equity of $34 million ($40 million - $6 million) to finance its expansion plans.

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The height of the building is 71 meters.

We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:

(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)

Substituting the given values:

2.8 / 1.49 = (height of building) / 37.5

To find the height of the building, we can cross-multiply and solve for it:

(2.8 * 37.5) / 1.49 = height of building

Calculating the expression on the right side:

(2.8 * 37.5) / 1.49 ≈ 70.7013

Rounding to the nearest meter, the height of the building is approximately 71 meters.

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Answer:

The approximate side length is between 10 ft and 11 ft

Step-by-step explanation:

Here, we are interested in calculating the approximate length of the square shaped pool.

Mathematically, the area of a square is s^2 where s represents the length of its side

in this case; s^2 = 120

s = √120

s = 10.95 approximately

So the length of the side of the square is between 10 and 11 ft

If a pilot elects to proceed to the selected alternate, the landing minimums used at that airport should be equal to or higher than the minimums required for the original destination airport.

When a pilot chooses to proceed to the selected alternate airport, they must consider the weather conditions at that airport, particularly the landing minimums. The landing minimums are the lowest weather conditions in which an aircraft can safely land at an airport. They are determined by various factors, such as the visibility range and the height of the cloud ceiling.

Therefore, if a pilot decides to go to the alternate airport, they should use the landing minimums for that airport to ensure a safe landing. The landing minimums for the alternate airport should be equal to or higher than the minimums required for the original destination airport.

It's important to note that the pilot must have knowledge of the landing minimums for the alternate airport before deciding to proceed there. If they don't have the necessary information, they should consider other options, such as returning to the departure airport or diverting to a different airport with suitable weather conditions.

In summary, when a pilot chooses to proceed to an alternate airport, they should use the landing minimums for that airport to ensure a safe landing. The pilot must have knowledge of the minimums before proceeding to the alternate airport.

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If the firm reduces the work year to 48 weeks while keeping the same rate of pay, the software engineer can expect his annual pay to decrease by about $4,829.

Based on the information provided, the annual pay of an entry level software engineer is $63,596 based on 52 weeks per year.

However, due to the economy, the company needs to cut back on the number of weeks it employs its software engineers to 48 weeks.

To find out how much the software engineer's annual pay will decrease, we need to calculate the difference between the original pay and the new pay.

First, we can calculate the engineer's weekly pay by dividing the annual pay by the number of weeks worked.

So, the original weekly pay is $63,596 / 52 = $1,223.23.

Next, we multiply the original weekly pay by the new number of weeks worked to find the new annual pay. Therefore, the new annual pay is $1,223.23 * 48 = $58,767.04.

To determine the decrease in annual pay, we subtract the new annual pay from the original annual pay. Thus, the decrease is $63,596 - $58,767.04 = $4,828.96.

Rounding the decrease to the nearest dollar, the software engineer should expect his annual pay to decrease by about $4,829.

In summary, if the firm reduces the work year to 48 weeks while keeping the same rate of pay, the software engineer can expect his annual pay to decrease by about $4,829.

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Answer:

224ft^3

Step-by-step explanation:

l*w*h= volume

Answer:

The Volume is 224

Step-by-step explanation:

w * h * l

The number of arrangements of 6 balls with 2 red balls and 2 blue balls, we need to consider the number of ways to choose 2 red balls from the 4 available red balls and the number of ways to choose 2 blue balls from the 4 available blue balls.

These are both combinations, and we can use the formula for combinations to calculate them:

C(n, k) = n! / (k! (n-k)!).

For the red balls, C(4, 2) = 4! / (2! (4-2)!) = 6.

For the blue balls, C(4, 2) = 4! / (2! (4-2)!) = 6.

The total number of arrangements of 6 balls with 2 red balls and 2 blue balls is the product of the number of arrangements for each type of ball:

C(4, 2) * C(4, 2) = 6 * 6 = 36

So, there are 36 arrangements of 6 balls with 2 red balls and 2 blue balls.

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Answer:

B, 33%

Step-by-step explanation:

Let us find the original price of four chairs without the special deal, and compare it with the deal to find the percent savings.

Step 1:

A customer must buy 4 chairs costing $75 each to recieve the deal. Let us multiply 4 by 75 to find the total cost without the deal:

\(4*75=\\300\)

Step 2:

We now know the original cost of the 4 chairs, and the price of 4 chairs with a deal. Let us subtract the difference of costs and convert it into a percentage to find percent savings:

\(300-200=100\\\frac{100}{300} =\frac{1}{3}\)

\(\frac{1}{3}=33\)%

Therefore, B, the percent savings is 33%.

I hope this helps! Let me know if you have any questions :)

In a cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants and has a local minimum at x = -2 and a local maximum at x = 0, then values of a and b is 12 and 0 respectively. If integrate of f(x)dx = 32 from 0 to 1, then value of k is 27.

The given cubic polynomial function is

f(x) = 4x³ + ax² + bx + k

f'(x) = 12x² + 2ax + b

f''(x) = 24x + 2a

At local maximum f' = 0

f'(0) = 12×(0)² + 2a×(0) + b = 0

b = 0

At local minimum, f' = 0

That is f'(-2) = 0 and f''(-2) > 0

f'(-2) = 12×(-2)² + 2a×(-2) + b = 0

48 - 4a + b = 0

4a - b = 48  

a = 12

Therefore, f(x) =  4x³ + 12x² + k

Integrate f(x)dx = 32 from 0 to 1, that is

∫₀¹ f(x)dx = 32

∫₀¹ (4x³ + 12x² + k) dx = 32

[ x⁴ + 4x³ + kx ]₀¹ = 32

(1⁴ - 0⁴) + 4(1³ - 0³) + k(1 - 0) = 32

1 + 4 + k = 32

k = 27

-- The question is incomplete, answering to the question below--

"A cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants. The function f has a local minimum at x = -2 and a local maximum at x = 0.

A. Find the values of a and b

B. If you integrate f(x)dx = 32 from 0 to 1, what is the value of k?"

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Step-by-step explanation:

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and is a factorization of the polynomial x² – 4. 

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Answer:

-12

Step-by-step explanation:

i don't know that's what i got

The range and the vertex is   4 ≤ y < [infinity] and  (5, 4).

To find the vertex, we can take the derivative of the function and set it equal to 0:

y' = |x − 5|' = 0

=> x − 5 = 0

=>  x = 5

Then, we can plug x = 5 into the original equation to find the y-value at the vertex:  

y = |x − 5| = |5 − 5| = |0| = 0

So, the vertex of y = |x − 5| is (5, 4).

To find the range, we need to consider the range of the absolute value function. The range of the absolute value function is:

−[infinity] < y < [infinity]. So, the range of y = |x − 5| is also −[infinity] < y < [infinity] (or 4 ≤ y < [infinity]).

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The interquartile range (IQR) is found as the 20.24. The correct option is (d) 20.24.

Given that X N(300, 15), find the Interquartile Range (IQR).

The given distribution is normal with mean μ = 300 and standard deviation σ = 15.

We need to calculate the interquartile range (IQR).IQR is defined as the difference between the third quartile (Q3) and the first quartile (Q1).

The first quartile (Q1) is the value below which 25% of the data fall and the third quartile (Q3) is the value below which 75% of the data fall.

We can find these values using the standard normal distribution table.

For the first quartile,

z1 = invNorm(0.25)

= -0.67449

Q1 = μ + σ × z1

= 300 + 15 × (-0.67449)

= 289.88

≈ 289.89

For the third quartile,

z3 = invNorm(0.75)

= 0.67449

Q3 = μ + σ × z3

= 300 + 15 × 0.67449

= 310.12

Therefore, the interquartile range (IQR)

= Q3 – Q1

= 310.12 – 289.89

= 20.23

≈ 20.24

Hence, the correct option is (d) 20.24.

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In multiple regression analysis, the correlation among the independent variables is termed as d. multicollinearity.

Basically, multiple regression analysis means a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables.

If the independent variables of the regression analysis is correlated, the it is called as multicollinearity.

Therefore, the option (d). multicollinearity is the answer

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Given:

Two different congruency mapping

To find:

a) a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up

b) a rule for congruence mapping that reflects a figure across the y-axis