Fine the area of this figure.what two shapes can you decompose.

Fine The Area Of This Figure.what Two Shapes Can You Decompose.

Answers

Answer 1
D. 52 cm; a rectangle and triangle

Steps are on paper
Fine The Area Of This Figure.what Two Shapes Can You Decompose.

Related Questions

Decimal Fraction
5,6+23,3
I need answer​

Answers



The answer is 289/10

5.6 + 23.3 is 28.9

28.9 is 289/10 as decimal fraction

A term that means the same as the term "variable" in an ANOVA procedure is _____.

Answers

A term that means the same as the term "variable" in an ANOVA procedure is a factor.

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.

Let us consider the number 8. 8 can be a product of 1 and 8, and 2 and 4. As a result, the factors of 8 are 1, 2, 4, and 8. Therefore, when finding or solving problems involving factors, only positive numbers, whole numbers, and non-fractional numbers are considered.

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2. The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded figure.
7 cm
8 cm
3 cm
3 cm
Area of the shaded figure:
Area of the shaded figure:
square centimeters

Answers

The area of shaded figure rectangle is 7.5m²

How to find the area of rectangle?

The amount of space occupied by a flat surface with a particular shape is referred to as the area. It is calculated using the "number of" square units (square centimeters, square inches, square feet, etc.) The amount of unit squares that can fit inside a rectangle is its area. The flat surfaces of laptop monitors, blackboards, canvas, etc. are a few examples of rectangular shapes.

step1:

The formula for the area of the Rectangle  is:

A= a+ b/2*h= 3+3/2*7=31.5

step2:

The formula for the area of the rectangle is:

A=w l=3*8=24

Now you rest 31.5 -24 and it gives you 7.5

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How to Simplify 3(-9x + 8)

Answers

Answer:

multiple everything by three so say 3×-9x is -27x and 3 ×8 is 24 and you would then divide -27x by 24 and you would get -27x+24 I think

I need help with this

Answers

Answer:

d

Step-by-step explanation:

Haile Resort opened for business on June 1 with eight air conditioned units. Its trial
balance on August 31 is as follows.
Haile Resort
Trial Balance
August 31, 2022
Debit Credit
Cash Br. 39,200
Prepaid Insurance 9,000
Supplies 5,200
Land 40,000
Buildings 240,000
Equipment 32,000
Accounts Payable Br. 9,000
Unearned Rent Revenue 9,200
Mortgage Payable 100,000
Share Capital—Ordinary 200,000
Retained Earnings 0
Dividends 10,000
Rent Revenue 172,400
Salaries and Wages Expense 89,600
Utilities Expense 18,400
Maintenance and Repairs Expense 7,200
Br.490,600 Br.490,600
Other data:
1. The balance in prepaid insurance is a 1-year premium paid on June 1, 2022.
2. An inventory count on August 31 shows Br.1,300 of supplies on hand.
3. Annual depreciation rates are buildings (4%) and equipment (10%).
4. Unearned rent revenue of Br.7,600 should be recognized as revenue prior
to August 31.
5. Salaries and wages of Br.750 were unpaid at August 31.
6. Rentals of Br.1,600 were due from tenants at August 31.
7. The mortgage note is dated 1/1/2022. The mortgage interest rate is 8% per
year.
Instructions
a. Journalize the adjusting entries on August 31 for the 3-month period
June 1–August 31.
b. Prepare an adjusted trial balance on August 31.

Answers

Journalize the adjustment entries on August 31 for the $500 in golf income during the three-month period from June 1 to August 31.

what is interest ?

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principal plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principal amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

given

First FMA Assignment

Jornal 1.

2. Accounts Title Date (Mar) Debit ($) Credit ($)

1 Cash 60,000

60,000 Common Stock

3 Land 23,000

Structures 9,000

6k in equipment

Cash 38,000

5) Marketing Costs 1,600

Cash 1,600

Golf Sales 800

19) Cash (100 x 15) 1,500

1,500 in unearned revenue

25,000 dividends

Cash 1,000

30) salaries and 600 in expenses

Cash 600

30) Payable Accounts 26,000

Cash 26,000

31) Cash 500

500 Golf Revenue

Journalize the adjustment entries on August 31 for the $500 in golf income during the three-month period from June 1 to August 31.

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In ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10°. Find the length of z, to the nearest inch.

Answers

if in ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10° then length of z is 97.64 inches.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10°.

We have to find the length of z.

By using sine rule we find the length of z.

sin117/500=sin10/z

0.891/500=0.174/z

Apply cross multiplication

0.891z=0.174×500

0.891z=87

z=87/0.891

z=97.64 inches

Hence, if in ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10° then length of z is 97.64 inches.

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Answer:

97

Step-by-step explanation:

Yoshio has 3 pieces of fabric. Each piece of fabric is the same length. The total length of the pieces is 2 and 1/4 yards. What is the length of each piece of fabric?

Answers

In  linear equation, Length of each piece of fabric is 3/2  yards.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Number of pieces of fabric = 3

Total length of a fabric  = 2 1/4 yards

                                     = 9/4 yards

Therefore,

Length of each piece of fabric = 9/4 ÷ 3

                                             = 3/4 yards

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If the graph of a distribution of data shows that the graph is symmetric then the:
a) Midrange is a better measure of central tendency
b) Mean is a better measure of central tendency
c) Mode is a better measure of central tendency
d) Median is a better measure of central tendency

Answers

The correct option is:

d) Median is a better measure of central tendency

When a graph of a distribution of data is symmetric, it means that the left and right sides of the graph are mirror images of each other. This indicates that the data is evenly distributed around the center and that there are no extreme outliers. In such cases, the median is the best measure of central tendency, because it is the middle value of the dataset and it represents the center of the data distribution. The median is not affected by outliers.

The mean, mode, and midrange are also measures of central tendency, but they may not be as representative of the center of the data distribution when the data is symmetric. The mean is sensitive to outliers, the mode is the value that appears most frequently in the data, and the midrange is the average of the maximum and minimum values.

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I need help with this question

Answers

Answer:

I think A is the answer.

U're welcome amigo.

4. You download a digital soccer game for $2.50. You can add new players for
$1.50 each to upgrade your team. The total cost e is a function of the number n
of new players that you add. Which of the following statements about the
domain and the graph of the function is correct?
A The domain is discrete, and the point (4, 6) lies on the graph.
B
The domain is continuous, and the point (4. 6) lies on the graph.
The domain is discrete, and the point (5, 10) lies on the graph.
D The domain is continuous, and the point (5, 10) lies on the graph.

Answers

The domain is discrete, and point (5, 10) lies on the graph. Then the correct option is C.

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

You download a digital soccer game for $2.50. You can add new players for $1.50 each to upgrade your team.

The number of players will be in a whole number. Then the function is given by the greatest integer function.

Let 'y' be the total cost and 'x' be the number of players. Then the equations are given as,

y = 1.50 [x] + 2.5

The total cost for 5 new players will be given as,

y = 1.50 [5] + 2.5

y = 7.5 + 2.5

y = 10

The domain is discrete, and point (5, 10) lies on the graph. Then the correct option is C.

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A man who is 6 feet tall casts a shadow that is 4 feet long. At the same time, a nearby flagpole casts a shadow that is 18 feet long. How tall is the flagpole?

picture of answer options are below

Answers

Answer: the flagpole is
D) 27 feet

Help me, please let me know the answer to the question <3

Answers

Answer:16.98$

Step-by-step explanation:

A pound of roast beef costs 8.49

2 pounds of roast cost?

2x8.49=16.98

What number gives a result of −4
when 8
is subtracted from the quotient of the number and 4
?

Answers

16 is the number  gives a result of −4 when 8 is subtracted from the quotient of the number and 4.

What is Division?

A division is a process of splitting a specific amount into equal parts.

If it gives a result of -4 then our equation will have ___ = -4

If we subtract 8 from the quotient of a number and 4 we have  x/4 - 8

Our equation is:

x/4 - 8 = -4    

Add 8 to both sides

x/4=-4+8

x/4=4

Multiply both sides by 4

x=16.

Hence, 16 is the number  gives a result of −4 when 8 is subtracted from the quotient of the number and 4.

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Use the Distributive Property to rewrite each algebraic expression
15(2 + r)

Answers

The algebraic expression 15(2 + r) by the distributive property can be written as 30 + 15r.

What is distributive property?

This property states that multiplying the sum of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the algebraic expression is 15(2 + r). The expression by using the distributive property can be written as:-

E = 15(2 + r)

E = 30 + 15r

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In the figure below, =m∠364°. Find m∠1, m∠2, and m∠4.

Answers

Answer:

m∠1 = 64

m∠2 = 117

m∠3 = 117

Step-by-step explanation:

m∠1 = 64

m∠2 = x+64 = 180

        = x = 117

m∠2 = 117

m∠3 = 117

At a certain college, 64% of the entering freshmen graduate. If we randomly selected 10 entering freshman, find the probability that: 14. Exactly 5 of the students will graduate 15. At least 8 of the students will graduate.

Answers

14) Probability that exactly 5 of the students will graduate is 0.1636.

15) Probability that atleast 8 of the students will graduate is 0.2405.

We have , In a college,

The freshmen graduate enters = 64%

Probability of sucess , p = 64% = 0.64

Probability of failure , q = 1 - 0.64 = 0.36

Randomly selected entering = 10 , i.e, n = 10.

This follows a Binomial probability distribution with the parameters, n = 10 and p = 0.64.

Using Binomial probability formula,

P(X = x) = ⁿCₖ pᵏ (1 - p)ⁿ⁻ᵏ

(14) Probability that exactly 5 of the students will graduate = P(x = 5),

P( x = 5) = ¹⁰C ₅ (0.64⁵) (0.36⁵)

= 0.1636

15) Probability that at least 8 of the students will graduate, P(x ≥8) = P(X= 8) + P(X= 9) + P(X= 10)

= ¹⁰C₈ 0.64⁸ 0.36² + ¹⁰C₉ 0.64⁹ 0.36¹ + ¹⁰C₁₀ 0.64¹⁰ 0.36⁰ = 0.2405

Hence, the required probabilities are 0.1636 and 0.2405.

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Consider the following data consisting of 9 values:

Data
4
10
12
9
0
6
3
11
16


The minimum is


The first quartile is


The median is


The third quartile is


The maximum is


The IQR is

Answers

Note that where the following values are given: 0, 3, 4, 6, 9, 10, 11, 12, 16, the respective quartile values are:

The minimum = 0

The first quartile (Q₁) is = 3.5

The median (Q₂) = 9

The third quartile (Q₃) = 11.5

The maximum = 16

The IQR = 8 .

What is median?

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory.

It is to be noted that sometimes referred to as "the middle" value in data collection.

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Can someone help me with this problem, please


THANKS

Answers

Answer:

30%

Step-by-step explanation:

3 pizzas = 30 slices.  count yellow 1+6+2 = 9

9/30 = 30%

A party of 300 people,54% will have someone to kiss when the clock strikes midnight.How many people will have someone to
kiss?

Answers

In a party of 300 people, 54% of the people who would have someone to kiss is 162 people.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred.

To determine the percentage of people with partners to kiss at midnight;

300 people present in party

54% will have someone to kiss = 0.54

Number of people that will have someone to kiss = 300 x 0.54 = 162

The 54% of people with someone to kiss are 162 in number.

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Write two equations showing the Transitive Property of Equality. Justify your reasoning.

Answers

The Transitive Property of Equality states that if a = b and b = c, then a = c. This property holds true for any mathematical expressions that can be equated, such as numbers, variables, or more complex equations. Here are two examples of equations that demonstrate the Transitive Property of Equality:

x + 5 = 9 and 9 = y - 2
x + 5 = y - 2
a^2 + 2ab + b^2 = (a+b)^2 and (a+b)^2 = a^2 + 2ab + b^2
a^2 + 2ab + b^2 = a^2 + 2ab + b^2
In both examples, by using the transitive property, we can conclude that x = y and (a+b)^2 = (a+b)^2 which both are same expressions.

In the first equation, we start with x + 5 = 9 and then 9 = y - 2. Since both sides of the first equation are equal to 9, we can substitute 9 for x + 5 in the second equation, giving us 9 = y - 2. This shows that the left side of the first equation is equal to the right side of the second equation, which is the Transitive Property of Equality.

In the second equation, we start with a^2 + 2ab + b^2 = (a+b)^2 and then (a+b)^2 = a^2 + 2ab + b^2, since both sides are the same then we can substitute (a+b)^2 for a^2 + 2ab + b^2 in the second equation, which results in (a+b)^2 = (a+b)^2. This shows that the left side of the first equation is equal to the right side of the second equation, which is the Transitive Property of Equality.

In summary, The transitive property states that if you have two expressions are equal to each other, and the second expression is equal to the third, then the first and the third expressions are equal to each other.

about how many times large is 7.9x10^4 than 2.1x10^3​

Answers

3.76 many times large is 7.9 x 10⁴ than 2.1 x 10³. This can be solved using scientific notation method.

What is scientific notation?

A method of writing numbers that combines a power of 10 with a number between 1 and 10. Using scientific notation, one may express extremely big or extremely small values. Once a number between 1 and 10 has been multiplied by such a power of 10, it is then expressed in scientific notation. For instance, 6.9 × 10⁸ can be used to represent the number 690,000,000.

The main goal of scientific notation is to simplify computations using numbers that are abnormally big or tiny. When a number is written in scientific notation, all of the digits are important since zeros are no longer utilized to set the decimal point.

For: 7.9 x 10⁴

= (79/10) x 10⁴

= 79 x 10³

on the other hand for: 2.1 x 10³

Thus, 3.76 many times large is 7.9 x 10⁴ than 2.1 x 10³.

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Evaluate the iterated integral. 1 0 s5 cos(s6) dt ds 0

Answers

The value of the evaluated iterated integral is = 0.002

As per the given data the iterated integral is, [tex]I[/tex] = [tex]\int\limits^1_0[/tex] [tex]\int\limits^s_0[/tex] cos ([tex]s^{6}[/tex] ) [tex]dt ds[/tex]

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as,

[tex]\int\limits^a_b f({x} )\, dx[/tex] = f(b) - f(a)

Where,

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, [tex]\int\limits^_[/tex] ab f(x) dx is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]I[/tex] = [tex]\int\limits^1_0[/tex] [tex]\int\limits^s_0[/tex] cos ([tex]s^{6}[/tex] ) [tex]dt ds[/tex]

Integrate the given iterated integral.

We get:

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) ([tex]\int\limits^5_0dt[/tex] ) ds

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) [t][tex]0 to s^{5}[/tex] ds

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) [tex](s^{5} -0)[/tex] ds

= [tex]\int\limits^1_0[/tex] [tex]s^{5}[/tex]cos ([tex]s^{6}[/tex] )ds

Then,

[tex]s^{6}[/tex] = t       when s = 0

[tex]\frac{dt}{ds}[/tex] = 6[tex]s^{5}[/tex]         t = 0  

[tex]\frac{dt}{6}[/tex] = [tex]s^{5}[/tex]  ds      when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

[tex]I[/tex] = [tex]\int\limits^1_0[/tex] cos(t) [tex]\frac{dt}{6}[/tex]

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [tex]\int\limits^1_0[/tex] cos(t) dt

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [sin(t)][tex]0to1[/tex]

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [ sin(1) - sin(0) ]

[tex]I[/tex] = [tex]\frac{sin(1)}{6}[/tex]

[tex]I[/tex] = 0.002

Therefore,

The value of the evaluated iterated integral is = 0.002

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Triangle JKL has coordinates 42,-5), K-1,-3), and L-4, 5). Determine the
coordinates of the vertices of the image after each transformation
10. translation along the vector (-3,1)
J (2,-5) ---------->! (, )
K (-1, -3) --------> K', )
L (-4, 5) --------->"(, )

Answers

The vertices of the image after transformation is K(5,-2), L(-1,3) and M(4,-5)

What is a triangle called?

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

What are the 3 sides of a triangle called?

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

According to the given question,

with respect to the mirror

the vertices of the image of the triangle is

J (2,-5) ---------->! (5,2)

K (-1, -3) --------> K'(-1,3 )

L (-4, 5) --------->"(4,-5 )

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If you add 21 to my number, multiply the result by 3, you will get 84 more than 2/3 of my number what is my number?

Answers

Step-by-step explanation:

x = my number

3(x + 21)

multiply sum of 21 and my number by 3

=

(2/3)x + 84

84 more than 2/3 of my number

3(x + 21) = (2/3)x + 84

9(x + 21) = 2x + 3×84 = 2x + 252

9x + 189 = 2x + 252

7x + 189 = 252

7x = 63

x = 9

my number is 9.

3y(2-7)-3(y-4)-63 for y=2

Answers

Answer:

-87

Step-by-step explanation:

y=2

3y(2-7)-3(y-4)-63 
3(2)(2-7)-3(2-4)-63 

6(2-7)-3(2-4)-63

6(-5)-3(-2)-63

-30+6-63=-87

The maths GCSE test scores of 280 students are shown in the histogram below

Answers

we determined median = 140 and lower quartile = 105.

What is median and quartile in a statistics data?

Median is the middle value of a set of data. Median is determined by the formula, median = 2/4 (N+1)th term, where N is the number of data set.

Quartile is a statistics terms defines that a list of data is divided into four parts. There are three quartiles in the statistics data such as lower quartile, middle quartile and upper quartile.

lower quartile = 1/4(N+1)th term

upper quartile = 3/4(N+1)th term

the median is called the middle quartile.

What is the median and lower quartile for the above histogram?

From the histogram we obtain the data below

80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200

number of data, N = 13

median = 2/4 (N+1)th term= 1/2 ×14 = 7th term

we find 7th term is 140.

median = 140

lower quartile= 1/4× (N+1)th = 1/4 × 14 = 3.5 th term

that means average of 3 and 4th term.

lower quartile = (100 + 110) /2 = 105

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what is (x + 2 ) (4x - 1 )

Answers

Answer:

(x+2)(4x-1)

For this problem, use the FOIL (first, outside, inside, last) method

You have x, 2, 4x, and -1. Start by multiplying x by 4x and -1. Then multiply 2 by 4x and -1. You should have four separate values to add together.

(x*4x)+(x*(-1))+(2*4x)+(2*(-1)) = 4x^2+(-x)+8x+(-2)

Once you have this, order each value by their exponents and combine like terms. The highest exponents always go to the left and lowest exponents go to the right.

4x^2+7x-2

in an experiment, what is the probability than even A occurs is 0.2 and the probability that event b occurs is 0.5

Answers

Answer: In an experiment, if the probability that event A occurs is 0.2 and the probability that event B occurs is 0.5, then the probability that either event A or event B (or both) will occur is the sum of their individual probabilities, which is 0.2 + 0.5 = 0.7.

It should be noted that the sum of the individual probabilities of two events is less than or equal to 1. If the sum of the probabilities is greater than 1, it means that the events are not mutually exclusive and that means that they can happen at the same time.

It's important to mention that the above answer is based on the assumption that events A and B are mutually exclusive events, which means that they cannot happen at the same time. If they are not mutually exclusive, the probability of both occurring at the same time would have to be calculated using the formula P(A and B) = P(A) * P(B|A) where P(A) is the probability of event A occurring and P(B|A) is the probability of event B occurring given that event A has already occurred.

Step-by-step explanation:

The diameter of a circle is 18 in. Find its area to the nearest whole number.

Answers

Answer:

The answer is 20

Answer: 254 in^2

Step-by-step explanation:

Other Questions
a designer has available a number of eight-point fft chips. show explicitly how he should interconnect three such chips in order to compute a 24-point dft. questionif an issue is socially controversial, which source provides the best objective information? Why could the author be perceived as biased against teenagers? products that pollute the environment, companies that use child labor in the production of their products, and marketing products that are unhealthy, are all examples of reginald sims deposits $4,000 each year in a tax-deferred retirement account. if he is in a 22 percent tax bracket, by what amount would his tax be reduced over a 15-year time period Which of the following can eliminate the inefficiency inherent in monopoly pricing? Cost-plus pricing Price discrimination Regulations that force monopolies to reduce their levels of output O Arbitrage Decision Point: Antonio and Leadership versus Power Antonio, the president, says, "The top priority is getting money to hire trainers and consultants." He laughs: "If we don't get some money in the door, we won't be able to run the lights and scoreboard, either!" He looks at you and says, "I'm counting on you personally to bring in the largest sum, $10,000, okay? I'll make sure your efforts get noticed back at the office." As you nod tentatively, wondering how you're going to obtain such a large sponsorship, you're reminded that Antonio is your manager at a brokerage firm. Is Antonio displaying leadership or power in this meeting? Select an option from the choices below and click Submit Power. Antonio is reminding you that you are dependent upon him in your work life so you will make certain to obtain $10,000 for the team * Neither. Antonio is simply making assignments and offering to help you out back at your workplace Leadership. Antonio knows that you're the best person to raise the funds needed and he's supportively recognizing your ability to the group. An item has a listed price of $60.If the sales tax rate is 7%,how much is the sales tax (in dollars)? A central angle of a regular polygon 18 degree measure interior angle an airplane is flying south going 440 mph when it hits a crosswind going west at 35 mph. what is the resultant velocity? Consider the following events when we find a uniformly random bit string of length 35: E = there are 15 ones and 20 zeros; F = the second bit is zero, the 10-th bit is one, and the 15-th bit is one. Calculate p(E) = (%)/2,p(F) = 1/24,p(En F)=0/2", (EF) = ()/2*. Then c= convert the given polar equation into a cartesian equation. r=sin 7coscos2sin2?Select the correct answer below: a. y2 x2 = x + 7y b. (x2 + y2)(x2 - y2)2 = 7x + y = 7x + y c. x2 + y2 = 7x+y d. (x2 + y2)(x2 - y2)2 = x + 7y 1. For the principle quantum number n = 5, what is the greatest number of values the spin quantum number can have? a. 5 b. 25 c. 11 d. 2 e. 4 a path name can be either one name or a list of names separated by dashes.T/F Explicit formulas for compositions of functions.The domain and target set of functions f, g, and h are Z. The functions are defined as:f(x) = 2x + 3g(x) = 5x + 7h(x) = x2 + 1Give an explicit formula for each function given below.(a) f g(b) g f(c) f h(d) h f 1.) Consider the parametric equations below.x = t2 2, y = t + 1, 3 t 3(b) Eliminate the parameter to find a Cartesian equation of the curve.for 2 y 4.2.) Consider the following.x = et 8, y = e2t(a) Eliminate the parameter to find a Cartesian equation of the curve.3.) Consider the parametric equations below.x = 1 + t, y = 5 4t, 2 t 3(b) Eliminate the parameter to find a Cartesian equation of the curve.for -1 x 4 If a rigid body is in translation only, the velocity at points A and B on the rigid bodyA) Are usually differentB) Are always the sameC) Depend on their positionD) Depend on their relative position Convert the given polar equation into a Cartesian equation.r=7sin/5cos^(2)Select the correct answer below:y=5/7x^(2)5y^(4)(x^(2)+y^(2))=7x^(2)5x^(4)(x^(2)+y^(2))=7y^(2)y=7/5x Compute the expected rate of return for the following two-stock portfolio Stock Expected Return Standard Deviation Weight A 18% 40% 0.70 B 12% 28% 0.3 A manufacturer of open steel boxes has to make one with a square base and a capacity of Im}. The steel costs S2 per square metre: If the base measures X metre by X metre and the height is Y metre, find Yin terms of x Hence; show that the total cost of the steel is C(x) = 2x2 + & dollars. Finally, find the dimensions of the box which would cost the least in steel to make_