12. Find [ 13(cos 10° +isin 10°). ) 13. Find the complex cube roots of 27. (Hint: 27+01) 14. Find the complex fourth root 4-4/3i

9x + 4 = 472

Step by Step Explanation

We know there are 9 buses, but we don't know how many students are on the buses, so that makes the first part of the equation 9x.

We also know there are 4 students in cars, so we now have an equation of 9x + 4.

We also know there is a total of 472 students altogether, so now our final equation is 9x + 4 = 472

The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

To know more about the factors affecting the demand for good X, refer here:

https://brainly.com/question/32566433#

#SPJ11

The probability that if a random person is chosen from the group of lawyers, the person will be a liar is 38/45, or 0.84.

As a fraction: The probability is given as 38/45, which means that out of 45 people chosen randomly from the group of lawyers, 38 of them are expected to be liars.

As a decimal: To express the probability as a decimal, we divide the numerator (38) by the denominator (45):

38 ÷ 45 ≈ 0.8444444444444444

Rounded to two decimal places, this would be approximately 0.84.

As a percentage: To express the probability as a percentage, we multiply the decimal form by 100:

0.8444444444444444 * 100 ≈ 84.44%

Rounded to two decimal places, this would also be approximately 84.44%.

So, the probability that if a random person is chosen from the group of lawyers, the person will be a liar can be expressed as 38/45 as a fraction, approximately 0.84 as a decimal, or approximately 84.44% as a percentage.

This can be expressed as a fraction, decimal, or percentage, whichever is more helpful.

For more questions related to probability, refer here:

https://brainly.com/question/2561151#

#SPJ11

A woman has invested $20 000 as a fixed deposit in a bank for 3 years. The interest rate is 5% per annum, calculated on a yearly basis. The woman needs to find the compound interest received for the period of 3 years.

Principal (P) = $20 000, Rate of Interest (R) = 5%, Time period (t) = 3 years, and compound interest.

We know that the compound interest is calculated as: Compound Interest (CI) = P [(1 + R/100) t - 1]

Using the given values, we have: CI = $20 000 [(1 + 5/100)3 - 1]CI = $20 000 [(1.05)3 - 1]CI = $20 000 [1.157625 - 1]CI = $20 000 [0.157625]CI = $3,152.5

Therefore, the woman will receive a compound interest of $3,152.5 at the end of 3 years if she does not withdraw any money from the fixed deposit during the period of 3 years.

For more such questions on interest rate, click on:

https://brainly.com/question/29451175

#SPJ8

9514 1404 393

Answer:

  D.  81/m^7

Step-by-step explanation:

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

  a^-b = 1/a^b

__

Using these, your expression simplifies to ...

  \((3m^{-4})^3(3m^5)=(3^3)(3)(m^{-4\cdot3+5})=81m^{-7}=\boxed{\dfrac{81}{m^7}}\)

The expected value of mean of x is 1.0.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including basic arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means. The mean may be used as a benchmark for all observations since it can be used to reflect the typical value. We may determine the mean training hours of a group of employees, for instance, if we want to know how many hours each employee spends in training on average each year.

Here,

Image is attached for solution.

To know more about mean,

https://brainly.com/question/27824219

#SPJ4

Answer:

i think it will be 70 yd

Step-by-step explanation:

(14×5)yd= 70 yd

Answer:

The total area is 179.25yd²

Step-by-step explanation:

You need to break this down into two parts: the rectangle on the left side, and the semicircle on the end.

The radius of the circle is five yards, giving it a diameter of 10 yards.  That diameter is also the height of the rectangle, meaning that the rectangle has an area of 14yd × 10yd = 140yd²

The area of a circle is equal to pi times the square of its radius.  Given that we only have a semicircle, we need to take that and divide it by two:

a = πr² ÷ 2

a = π × 5² ÷ 2

a = 3.14 × 25 ÷ 2

a = 3.14 × 12.5

a = 39.25

So the circle has an area of 39.25 square yards.

We can then can then add the areas together, giving us a total of 179.25 square yards.

Answer:

1st Option

Step-by-step explanation:

All angles in a triangle must add up to 180°.

Step 1: Set up equation

40° + 60° + 16x = 180°

Step 2: Rewrite

60° + 16x + 40° = 180°

Answer:

Option: A.

Step-by-step explanation:

Hey there!

In the given triangle;

60° +16x° + 40° = 180° { Sum of interior angle of a triangle}

100° + 16x= 180°

16x = 180° - 100°

\(x = \frac{80}{16} \)

Therefore, X= 5°.

So, Option A (equation) is used for solving the value of"X".

Hope it helps...

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

Learn more about the mean at

https://brainly.com/question/31316869

#SPJ11

Answer:

Booker:  $103.50 profit

Finley:  $34.50 profit

Step-by-step explanation:

b = # of candles Booker sold

f = # of candles Finley sold

1)  b = 3f

2) f = b - 12    substitute b=3f into this equation to get an expression all in terms of f, then solve for f

f = 3f - 12

-2f = -12

f = -12/2 = 6    now plug this into either equation and solve for b

b = 3(6) = 18

Booker:  18 candles x $5.75 profit/candle = $103.50 profit

Finley:  6 candles x $5.75 profit/candle = $34.50 profit

Answer:

Step-by-step explanation:

Find the number in the tenth place 1

and look one place to the right for the rounding digit 4

Round up if this number is greater than or equal to 5

and round down if it is less than 5

The answer is 14.1

Acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.

a) Concerned with inspection of products

b) Concerned with decision making regarding products

c) One of the oldest aspects of quality assurance

The Acceptance sampling procedure is necessarily a lot sentencing procedure. It cannot be used to estimate the lot quality or lot conformity to the standard specifications.

The acceptance sampling is used when the test is destructive, or the cost of 100% inspection is quite high, or when we need a continuously monitoring program

The Acceptance sampling procedure is used for decision making of either acceptation or rejection of a lot. It can’t be used as a lot quality estimator

As Acceptance sampling is just a lot sentencing process, it can’t estimate the quality of products in the lot. But designed experiments ensure good quality of the process output before even production

To know more about Statistical acceptance visit:

https://brainly.com/question/13334231

#SPJ4

To find the area of the region bounded by the curves y = x^4 - x^3 - 2x and y = x^3 - 4x^2 - 2x^3, we need to determine the points of intersection between the two curves.

First, we set the two equations equal to each other and solve for x:

x^4 - x^3 - 2x = x^3 - 4x^2 - 2x^3

Rearranging the terms:

x^4 - 2x^3 + 4x^2 = 0

Factoring out an x^2:

x^2(x^2 - 2x + 4) = 0

Setting each factor equal to zero:

x^2 = 0 or (x^2 - 2x + 4) = 0

Solving the second equation using the quadratic formula:

x = (-(-2) ± √((-2)^2 - 4(1)(4))) / (2(1))

x = (2 ± √(4 - 16)) / 2

x = (2 ± √(-12)) / 2

x = (2 ± 2√3i) / 2

x = 1 ± √3i

Since the problem asks for the area, which is a real value, we can disregard the imaginary solutions. Therefore, there are no points of intersection between the two curves.

To learn more about area : brainly.com/question/30307509

#SPJ11

Answer:

Y=-2, 0

Step-by-step explanation:

EDG 2020

Answer:

1. y= -2

2. 0

Step-by-step explanation:

Correct on Edg 2020

After approximately 60.2 minutes, the pizza will reach a temperature of 150°F.

We can model the cooling of the pizza using Newton's law of cooling:

T(t) = T_room + (T_0 - T_room) e^(-kt)

where T(t) is the temperature of the pizza at time t, T_0 is the initial temperature of the pizza (300°F), T_room is the room temperature (70°F), and k is the cooling rate constant. We can solve for k using the fact that the pizza cools from 300°F to 100°F in M minutes:

100 = 70 + (300 - 70) e^(-kM)

e^(-kM) = 0.1

-kM = ln(0.1)

k = -ln(0.1)/M

Now we want to find the time t when the pizza's temperature is 150°F:

150 = 70 + (300 - 70) e^(-kt)

e^(-kt) = (150 - 70)/(300 - 70)

e^(-kt) = 4/13

-kt = ln(4/13)

t = -ln(4/13)/k

Substituting the expression for k derived earlier, we get:

t = M ln(4/13) / ln(0.1)

For example, if M = 30 (i.e., it takes 30 minutes for the pizza to cool from 300°F to 100°F), then:

t = 30 ln(4/13) / ln(0.1) ≈ 60.2 minutes

Therefore, after approximately 60.2 minutes, the pizza will reach a temperature of 150°F.

To learn more about cooling visit:

https://brainly.com/question/31555490

#SPJ11

Answer:

The angle SQR is half the intercepted arc SR which is 43°

Answer:

It's 46°

Step-by-step explanation:

\(m \angle AMY = 62 - 37 = 25 \degree\)

\(m \angle CME = 159 - 138 = 21 \degree\)

\({ \tt{m \angle AMY + m \angle CME = 21 \degree + 25 \degree}} \\ { \tt{ = 46 \degree}}\)

The sum of the angles m∠AMY and m∠CME is 83 degrees option (B) is correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

From the picture,

The measure of angle PMY = 62 degrees

The measure of angle PMA = 37 degrees

The measure of angle AMY = Angle PMY - Angle PMA = 62 - 37

= 25 degrees

Similarly,

Angle CME = 79 - 21 = 58 degrees

m∠AMY+m∠CME = 25 + 58 = 83 degrees.

Thus, the sum of the angles m∠AMY and m∠CME is 83 degrees option (B) is correct.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ5

Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

Learn more about the triangle inequality theorem on:

https://brainly.com/question/309896

#SPJ1

Answer:

8/13

hope this answer helps you.....

Length(l) of rectangular pyramid = 2ft.

Width(w) of the rectangular pyramid = 1ft.

Hight(h) of the rectangular pyramid = 2ft.

Volume of Rectangular Pyramid = \(\sf{\frac{1}{3}×Length×Width×Hight}\)

➾\(\sf{\frac{1}{3}×l×w×h}\)(putting the value of l, w and h from above.)

➾\(\sf{\frac{1}{3}×2×1×2}\)

➾\(\sf{\frac{1}{3}×4}\)

➾\(\sf{\frac{4}{3}}\)

Therefore, volume of the given rectangular pyramid = \(\sf{\frac{4}{3} ft^3}\).

And it can be rewritten in the form of mixed fraction as \(\sf{\frac1{1}{3} ft^3}\).

The minimum amount of number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 0, as the greatest common divisor of any two numbers between 1 and 10 must be 1. The maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19, as the greatest common divisor of 8 and 10 requires 19 divisions.

Euclid's algorithm is an efficient method for finding the greatest common divisor (GCD) of two integers. It works by repeatedly dividing larger numbers by smaller numbers until the remainder is 0. The GCD of two integers is then equal to the smaller number. The minimum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 0, as the GCD of any two numbers between 1 and 10 must be 1. This is because any two numbers between 1 and 10 have only 1 as their common divisor. On the other hand, the maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19, as the GCD of 8 and 10 requires 19 divisions. This is due to the fact that 8 and 10 have no common divisors except for 1, so the algorithm must divide 8 by 10 repeatedly until the remainder is 0. Thus, the maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19.

Learn more about amount here

https://brainly.com/question/28970975

#SPJ4

Answer:

x = 45.79°

Step-by-step explanation:

You can use sin Θ to find the value of x.

Let us find it now.

Sin x = Opposite / Hypotenuse

Sin x = 38 / 53

Sin x = 0.7169

x = Sin ⁻¹ 0.7169

x = 45.79°

Answer:

AED is also 74

Step-by-step explanation:

they share the same crossing lines

Answer: 74

Step-by-step explanation:

Answer:

SOH CAH TOA

Step-by-step explanation:

/hyp/2=/ opp/ 2 +/Adj/2

x2=(1/21)2 + 1/28)2

Answer:

56 fluid ounces

Step-by-step explanation:

Why didnt you just look this up?

Answer:

56 fl-oz.

Step-by-step explanation:

7 cup is equal to 56 fl-oz.

Answer:

2:7:14

Step-by-step explanation: