The manger of a company planned to distribute a $50 bouns to each employee from the company fund, but the fund contained $5 less than what was needed. Instead, the manger gave each employee a $45 bouns and kept the remaing $95 in the company fund. How much money was in the company fund before any bonuses were paid?

Answer:

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Answer:

The IQR of the given distribution is

Step-by-step explanation:

The given distribution has the five-number

28, 34, 43, 59, 62

Divide these numbers in two equal parts.

(28, 34), 43,( 59, 62)

Now divide each parenthesis in two equal parts.

(28), (34), 43,( 59), (62)

It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.

The interquartile range (IQR) of this distribution is

Therefore the IQR of the given distribution is 29.5.

Answer:

the answer would be 0.9

Step-by-step explanation:

when rounding anything under 5 remains the same and anything over 5 rounds up to the next number. in this case three is less than five so the 9 would remain the same

Answer:

NO.

Step-by-step explanation:

An irrational number cannot be written as a fraction.

R = (ax - p)/(q + bx)

(ax - p) = R(q + bx)

ax - p = Rq + Rbx

ax - Rbx = Rq + p

x(a - Rb) = Rq + p

x = (Rq + p)/(a - Rb)

Answer: 9/2500

Step-by-step explanation:

We start with turning it into a fraction:

0.36/100

Then, we turn every number into a whole number by multiplying by whatever the last decimal place is called (hundreth= x100)

36/10000

Lastly, we simplify as much as we can by finding the least common denominator. In this case, the smallest whole number both 36 and 10000 can be divided by is 4:

(36/4)/(10000/4)

= 9/25000

Hi! Your answer is 11. When multiplying terms with exponents, the exponents add up.

Step-by-step explanation:

You want to multiply the terms with the exponents. You should get 3 and 8, add those up and you will get 11.

Hope this helps! Have a good day :)

Step-by-step explanation:

so, what's the problem ?

it's all there, we only need to take the calculator (or simply our heads) and do the calculation :

2×5 - 5×2 = 10 - 10 = 0

you see ? that was all that was needed.

put the given values for the variables into the places of these variables, and then calculate !

that is what variables are for : placeholders for actual values.

The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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Answer:

a) The population of interest = 10,000 benefited employees.  It includes all benefited employees.

b) The sample collected = 3,095.  These are the benefited employees who participated in the study.

c) Indication of demographic variables as categorical or numerical:

Demographic data:              Categorical or Numerical    

Gender                                = Categorical

Age (years)                          = Numerical

Education level                    = Numerical

 (years completed)

Marital status                       = Categorical

Household income ($)        = Numerical

Employment Category        = Categorical

Step-by-step explanation:

a) Data and Calculations:

Population of interest = 10,000 benefited employees

Sample = 3,095 participants

Demographic data:

Gender

Age (years)

Education level (years completed)

Marital status

Household income ($)

Employment Category

b) A variable is numerical value (e.g. length, test scores, etc.).  It is a continuous variable.  A categorical variable assumes a limited or fixed number of possible values, or it is categorized in groups.

The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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Main floor ticket is $52

Balcony ticket is $37

Mezzanine ticket is $31

Let x represent main floor tickets

Let y represent balcony tickets

Let z represent main mezzanine tickets

On a particular day, total sales totaled $50512, i.e

There were 86 more main floor tickets sold than balcony and mezzanine tickets combined, i.e

The number of balcony tickets sold is 139 more than 2 times the number of mezzanine tickets sold, i.e

The equatons are

Solving to find the values of x, y and z

From equation (3), make y the subject

Substitute for y into equation (2)

Make x the subject

Substitute for x and y into equation (1)

Substitute for z into equation (5) to find x

Substitute for z into equation (4) to find y

Hence,

The number of main floor tickets (x) sold is 612

The number of balcony tickets (y) sold is 397

The number of mezzanine tickets (z) sold is 129

The rate of change of a graph, is the slope of the graph.

The rate of change of the graph is 4.5

The points on the graph are:

\(\mathbf{(x,y) = (2,9) (4,18)}\)

So, the slope (m) is calculated as:

\(\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

This gives

\(\mathbf{m = \frac{18 - 9}{4-2}}\)

\(\mathbf{m = \frac{9}{2}}\)

\(\mathbf{m = 4.5}\)

Hence, the rate of change of the graph is 4.5

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After calculating we found that: a) 95% of widget weights lie between 42 and 54 ounces.b) 97.35% of widget weights lie between 39 and 54 ounces and c) 0.3% of widget weights lie above 45 ounces.

a) Since the distribution is bell-shaped and the mean is 48 ounces with a standard deviation of 3 ounces, we can use the 68-95-99.7 Rule to determine that 68% of the widget weights lie within one standard deviation of the mean, 95% lie within two standard deviations of the mean, and 99.7% lie within three standard deviations of the mean. Thus, we know that 95% of the widget weights lie between:

48 - 2(3) = 42 ounces and 48 + 2(3) = 54 ounces.

b) To find the percentage of widget weights that lie between 39 and 54 ounces, we need to determine how many standard deviations away from the mean these values are.

39 ounces is 9 ounces below the mean, so it is (9/3) = 3 standard deviations below the mean.

54 ounces is 6 ounces above the mean, so it is (6/3) = 2 standard deviations above the mean.

Using the 68-95-99.7 Rule, we know that 99.7% of the widget weights lie within three standard deviations of the mean. Since 39 ounces is three standard deviations below the mean, we can conclude that 0.15% (or 0.003 x 100) of the widget weights lie below 39 ounces.

Likewise, since 54 ounces is two standard deviations above the mean, we know that 2.5% of the widget weights lie above 54 ounces. Thus, the percentage of widget weights that lie between 39 and 54 ounces is:

100% - 0.15% - 2.5% = 97.35%

c) We need to find the percentage of widget weights that lie above 45 ounces. Since 45 ounces is three standard deviations below the mean, we know that 99.7% of the widget weights lie above 45 ounces. Therefore, the percentage of widget weights that lie above 45 ounces is:

100% - 99.7% = 0.3%.

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Answer:

( 3 + 4i )

Step-by-step explanation:

For this problem, we need to know that i^2 = -1. With this, let's solve the multiplication problem.

So to get rid of the i, we know it needs to be squared. The question is, for the sun of the products do we have a -4i or a +4i? So we will test both.

( 3 - 4i )^2 ?= 25

( 3 - 4i )( 3 - 4i ) ?= 25

9 - 12i - 12i - 16 ?= 25

We can stop here since we know that 24i will never equal 25.

So let's try the -4i

( 3 + 4i )( 3 - 4i ) ?= 25

9 + 12i - 12i + 16 ?= 25

9 + 16 ?= 25

25 == 25

Thus, our term for this to be true is ( 3 + 4i ).

Cheers.

1) In first circle radius is 3yard and diameter is 6 yard

2) In second circle radius is 46 inch and diameter is 92 inch

3)In third circle radius is 23 ft and diameter is 46ft

What's the radius solution?

The radius formula is easily obtained by halving the circle's diameter. The line segment created when we join a point on a circle's circumference to its exact center is referred to as the ring's radius. The radius of a circle is the separation between its center and circumference.

What is diameter, for instance?

If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to the diameter of a circle, which is the line segment that extends from one end of the circle to the other end while passing through the center of the circle.

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Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Step-by-step explanation:

D

Answer:

a)  Exponential growth function: 60%

b)  Exponential decay function: 20%

c)  Neither

d)  Exponential decay function: 45%

Step-by-step explanation:

\(\textsf{Exponential Growth}: \quad y=a(1+r)^x\)

\(\textsf{Exponential Decay}: \quad y=a(1-r)^x\)

where:

Given function:

\(f(x) = 0.3(1.6)^x\)

The function is an exponential growth function and the growth rate is:

\(1+r=1.6 \implies r= 0.6 = 60\%\)

Given function:

\(g(x) = 0.8^{0.5x} - 7\)

The function is an exponential decay function and the decay rate is:

\(1-r=0.8 \implies r=0.2=20\%\)

Given function:

\(h(x) = 3(-5)^x\)

This is neither an exponential growth or decay function as exponential functions cannot have negative bases.

Natural base exponential function

\(y=ae^{rx}\)

If a > 0 and r > 0, the function is an exponential growth function.

If a > 0 and r < 0, the function is an exponential decay function.

Given function:

\(f(x) = e^{-0.45x} + 4\)

As a = 1 > 0 and r = -0.45 < 0, the function is exponential decay function and the decay rate is:

\(r=-0.45=45\%\)

Given the numbers 6 and 12, we are asked to find their common multiple. The steps can be seen below;

The Least Common Multiple (LCM) is also referred to as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b

We will use the listing multiple method to find the answer:

Answer: Option B

Answer:

\(x + 9 = - 5x + 9 = 45 \\ x + 5x = 9 - 9 = 45 \\ 6x = 0 = 45 \\ 6x = 45 \\ x = 7.5\)

this the best I can do

Step-by-step explanation:

Good luck

Answer:

(-1/64)= (-1/4)^3

Explanation:

\(\sqrt[3]{-\frac{1}{64} }=-\frac{1}{4}\)

\((-\frac{1}{4})^3=-\frac{1}{64}\)

Answer:

28/15

Step-by-step explanation:

:)

Answer:

1/8 or 8/64

Step-by-step explanation:

its 1/8 you just times them both by 8 it ez