In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. The cards in Ms. Q's deck are shown below.

In how many ways can Yunseol draw four cards from Ms. Q's deck, so that no two cards have the same color?

Based on the choices, the ordered pairings that correspond to the graph are (2, 2), (2, 3), and (2, 4). (2, 4).

The x-coordinate of each point on the graph is always 2, since the vertical line passing through x=2 is a vertical asymptote, which implies the graph approaches but never reaches the line. Although the points where the graph crosses the y-axis are not shown, we may deduce from the curve's shape that the approximate y-coordinates of the first option, second choice, and third choice are 2, 3, and 4, respectively.

Hence, the suitable ordered pairings are (2, 2), (2, 3), and (2, 4).

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The length of side x is approximately 9.05 cm.

What is law of sines ?

The Law of Sines, also known as the Sine Rule, is a formula used to find unknown angles or sides of a triangle, given some combination of angle and side measurements. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Mathematically, the Law of Sines can be expressed as follows:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides, respectively.

Given by the question:

To find x, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Let's use the sine function to find the length of side AB:

sin A / AB = sin C / BC

sin 45 / x = sin 40 / 12

Rearranging and solving for x:

x = sin 45 * 12 / sin 40

x ≈ 9.05 cm

Therefore, the length of side x is approximately 9.05 cm.

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Answer:

5pi (use the pi character button on your screen)

Step-by-step explanation:

Arc length formula is the shortest formula in all of all math!

Arc length = r•theta

r is the radius. In your question, it is 6.

"theta" is the angle in radians, which was given in your question as 5pi/6.

Fill in these given values to the formula.

Arc length

= r • theta

= 6 • 5pi/6

Simplify (the 6's cancel)

= 5pi

Answer:

Step-by-step explanation:

Let's call the regular price of the stereo "x".

The stereo is sold at a 10% discount, which means the selling price is 90% of the regular price:

Selling price after discount = 0.9x

Then, a 10% tax is added to the selling price, so the final sale price is:

Final sale price = (1 + 0.1)(0.9x) = 1.1(0.9x) = 0.99x + 0.1(0.9x) = 0.99x + 0.09x = 1.08x

We are given that the final sale price is $589.05, so we can set up the equation:

1.08x = 589.05

Solving for x, we get:

x = 589.05 ÷ 1.08

x = 545.83 (rounded to the nearest cent)

Therefore, the regular price of the stereo was $545.83.

The reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of the random sample of 280 cases that were studied. It is important to look at the overall accuracy of the interpretations, as well as any potential biases or errors that may have affected the results.

To analyze the results, we can look at the number of correct and incorrect interpretations, and calculate the percentage of accurate interpretations. This will give us an overall measure of the reliability of the experts.

We can also look for any potential biases or errors that may have affected the results. For example, we may want to examine whether certain experts were more likely to make accurate interpretations than others, or whether there were any factors that may have influenced the interpretations, such as the type of crime or the suspect's behaviour.

Overall, the reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of a random sample of cases and looking for any potential biases or errors that may have affected the results. By doing this, we can gain a better understanding of the accuracy and reliability of these experts and their interpretations.

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The length of CG is approximately 5.4 units.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the property of similar triangles to solve this problem.

First, let's label the intersection point of FG and BC as point H. Also, let's label the length of CG as x.

Since FG is parallel to AC, we can use the property of similar triangles to find that triangles ABF and HBG are similar.

Therefore, we can set up the proportion:

AB/FB = HG/GB

Plugging in the given values, we get:

10/63 = (x + 57)/57

Solving for x, we get:

x = 5.4

Therefore, the length of CG is approximately 5.4 units.

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Therefore , the solution of the given problem of range comes out to be  the range of the composite function f(g(h(x))) is [0, ∞).

By calculating the variable's maximum observed value and subtracting its minimum observed value, the variable range is obtained (minimum). Potential range or finite difference bounds include different steel pricing and various designs. A procedure or action's breadth or scope insight into the maximum or expected range of a weapon's projectile. The number between the minimum and maximum of a list and set is known as its range. You can locate the area by lining up all the numbers.

Here,

The range of a function is the set of all possible output values. Let's consider each function separately:

f(x) = |x-3|

The absolute value of any number is always non-negative, so the range of f(x) is [0, ∞).

g(x) = -(x-4)²-3

The square of any real number is always non-negative, so the range of the function -(x-4)² is (-∞, 0]. Subtracting 3 from this range gives the range of g(x) as (-∞, -3].

h(x) = -7

The output of h(x) is always -7, so the range of h(x) is {-7} (a singleton set containing only the number -7).

Putting it all together, the range of the composite function f(g(h(x))) is [0, ∞).

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Answer:

x= 45°

Step-by-step explanation:

They are angle on a straight line

85+2x+5 = 180

2x+ 90 = 180

2x = 180-90

2x = 90

dividing both sides of the equation by 2

x = 45

The company had 32,500 employees a year ago.

Let x be the number of employees the company had a year ago.

According to the problem, the company now has 36% more employees than it did a year ago. This can be expressed mathematically as:

x + 0.36x = 44200

Simplifying the left-hand side of the equation:

1.36x = 44200

Dividing both sides by 1.36:

x = 32500

Therefore, the company had 32,500 employees a year ago.

Percentage is a way of expressing a portion or part of a whole as a fraction of 100. It is often represented by the symbol "%".

For example, if 20 out of 100 students in a class are absent, we can say that the percentage of absent students is 20%. This means that 20 out of every 100 students in the class are absent.

To calculate a percentage, you divide the part by the whole and multiply by 100. For example, if 30 out of 50 students passed a test, the percentage of students who passed the test is:

(30 ÷ 50) × 100 = 60%

This means that 60 out of every 100 students in the class passed the test.

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Answer: TSA( TOTAL SURFACE AREA) of the cube of side 8 cm is 384 square cm.

Step-by-step explanation: We know,

the total surface area of a cube is = 6 a^2 where a is the length of the side of the cube.

Here, a = 8cm

thus TSA = 6* 8*8= 384 square cm.

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Answer:

D) -53.23

Step-by-step explanation:

Use PEMDAS to evaluate the expression

We do parentheses first.

[tex]|65.45-42.45|-76.23[/tex]

Evaluate what's inside of the absolute value bracket.

[tex]|23|-76.23[/tex]

Simplify

[tex]23+-76.23[/tex]

Evaluate

-53.23

Answer:

Step-by-step explanation:

We can start by combining the two fractions by finding a common denominator:

sin(a)/(1+cos(a)) + (1+cos(a))/sin(a)

= sin^2(a)/(sin(a)(1+cos(a))) + (1+cos(a))^2/((1+cos(a))sin(a))

= sin^2(a) + (1+cos(a))^2 / (sin(a)(1+cos(a)))^2

= (sin^2(a) + 1 + 2cos(a) + cos^2(a)) / (sin^2(a) + 2sin(a)cos(a) + cos^2(a))

= (2 + 2cos(a)) / (sin(a) + cos(a))^2

= 2(1+cos(a)) / (sin(a) + cos(a))^2

= 2(cos^2(a/2)/sin^2(a/2)) / (sin(a/2) + cos(a/2))^2 (using the half-angle identities)

= 2tan^2(a/2) / (sin(a/2) + cos(a/2))^2

This expression cannot be simplified further without additional information or context.

Answer:

Step-by-step explanation: you need to rewrite the formula but with the numbers that are given to you so then you multiply and divide by 2 and BOOM you got your answer

The expression representing a perfect square trinomial is given as follows:

y² - 15y + 56.25.

There are two formats of perfect square trinomial, given as follows:

For this problem, we have a subtraction sign, meaning that the value of a is obtained as follows:

2ay = 15y

2a = 15

a = 15/2

a = 7.5.

Then the square of a is given as follows:

a² = 7.5²

a² = 56.25.

Meaning that the expression is given as follows:

y² - 15y + 56.25.

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Answer:

Step-by-step explanation:

2x³+54=2(x³+27)=2(x³+3³)

a³+b³=(a+b)(a²-ab+b²)

complete it

The cubic function is one where the coefficient a, b, c, and d are correlational the variable are real numbers and are polynomial numbers. The function is either one or three real roots. The graph of the function is a cubic curve.

The example of a cubic function is that of  the forms of y = ax3 + bx2 + cx + d, where the a, b, c, and d are constants. The cube root function is inverse to the cube function.  

Hence they are increasing option A is correct.

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Mila's monthly mortgage payment would be approximately $4,658.99.

In finance, interest refers to the cost of borrowing money or the return earned on an investment. It is usually expressed as a percentage of the amount borrowed or invested and is typically calculated on an annual basis.

For borrowing money, interest is the cost that the borrower has to pay to the lender for the privilege of using their funds. The lender earns interest on the loan as compensation for lending their money to the borrower. The interest rate on a loan is determined by a variety of factors, including the borrower's creditworthiness, the term of the loan, and prevailing market conditions.

For investments, interest is the return earned by an investor on their principal amount. For example, when someone deposits money in a savings account, they earn interest on that money. The interest rate on savings accounts and other investments is typically determined by the prevailing market conditions and the financial institution offering the investment.

Interest can be calculated in different ways, including simple interest and compound interest. Simple interest is calculated on the original principal amount, while compound interest is calculated on the principal amount plus any accumulated interest. The frequency at which interest is compounded, such as monthly or annually, can have a significant impact on the total amount of interest earned or paid.

Overall, interest plays a critical role in finance and can have a significant impact on the cost of borrowing money or the return earned on an investment.

To calculate Mila's monthly mortgage payment, we can use the formula for a fixed-rate mortgage:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

where:

M = monthly mortgage payment

P = loan amount

r = monthly interest rate

n = number of payments (total number of years * 12)

Plugging in the given values, we get:

M = 730000 * (0.00325 * (1 + 0.00325)^(2012)) / ((1 + 0.00325)^(2012) - 1)

Simplifying this expression using a calculator, we get:

M ≈ $4,658.99

Therefore, Mila's monthly mortgage payment would be approximately $4,658.99.

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The reasonable domain of the growth function is [0, 8], the y-intercept is 3 cm and the average rate of change of the function is 0.40 cm per month.

The growth function, also called the shatter coefficient or the shattering number, measures the richness of a set family. It is especially used in the context of statistical learning theory, where it measures the complexity of a hypothesis class.

A marine biologist is studying the growth of a particular species of fish, given by the exponential equation,

f(m) = [tex]3(1.09)^{m}[/tex]

We need to find, reasonable domain to plot the growth function, the y-intercept of the graph of the function f(m) to represent and average rate of change of the function f(m) from m = 1 to m = 9,

f(m) = [tex]3(1.09)^{m}[/tex]

m = 0

f(0) = 3(1.09)⁰  = 3 cm

The length of the fish was approximately 5.98 cm.

5.98 = [tex]3(1.09)^{m}[/tex]

1.99 = [tex](1.09)^m[/tex]

m = 8

Domain = [0, 8]

Reasonable domain to plot the growth function = [0, 8]

The y-intercept of the graph of the function f(m) represent initial length of fish = 3 cm

The average rate of change of the function f(m) from m = 2 to m = 8

m = 2, f(2) = 3(1.09)² = 3.56  cm

m = 8, f(8) = 3(1.09)⁸ = 5.97 cm

Change in 8-2 = 6 months = 5.97-3.56 = 2.41 cm

The rate of change of the function f(m) from m = 2 to 8

= (2.41/6)

= 0.40 cm per month

Hence, the reasonable domain of the growth function is [0, 8], the y-intercept is 3 cm and the average rate of change of the function is 0.40 cm per month.

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Answer: 14.5734588364

Step-by-step explanation:

Answer: $3,700 or $90,650

Step-by-step explanation:

Answer:

3,700

Step-by-step explanation:

i thibk thisisthay answer

The area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square

units.

A function is a relation between a dependent and a independent variable. Mathematically we can write the function as -

y = f(x)

Given is that a factory selling cell phones has a marginal cost function C(x) = 0.01x² - 3x + 229, where {x} represents the number of cellphones, and a marginal revenue function given by R(x) = 429 - 2x.

We can write the area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 as -

Area = ∫C(x) dx  +  ∫{C(x) - R(x)} dx

We can write the area with limits as -

Area =

∫(0.01x² - 3x + 229) dx             {limits from 229 to 429}

+

∫(0.01x² - 3x + 229 - 429 + 2x) dx       {limits from 429 to 629}

Area = 71548.7 + 420548.7

Area = 492097.4 square units

Therefore, the area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square

units.

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Step-by-step explanation:

clearly, the price is marked down to $9.60.

so, the 1st and 4th answer options are wrong.

is it marked down by 12% or by 20% ?

the basic price was $12. = 100%

how much are 10% of that ? well, 12/10 = $1.20.

but we marked down by $2.40.

when you compare $1.20 and $2.40, what do to see ?

that the second number is exactly twice the first number.

10%×2 = 20%

therefore, the 3rd answer is correct.

Answer:

13/24

Step-by-step explanation:

13/11+13= 13/24

The probability that a randomly selected person is male given the person is left handed is 13/200.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 200

Number of favorable outcomes = 13

Now probability of an event = 13/200

Therefore, the probability that a randomly selected person is male given the person is left handed is 13/200.

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There is no true equation among the given equations.

An equation is a mathematical statement that proves the equality or equivalence of two or more mathematical expressions.

Mathematical expressions are constants, numbers, values, or variables written with algebraic operands, including addition, subtraction, division, and multiplication.

A. 34 − 12 = 14.  This equation is not true because (34 - 12 = 22).

B. 916 − 48 = 58. This equation is not true since (916 - 48 = 868).

C. 78 − 34 = 18. This equation is not true since (78 - 34 = 44).

D. 715 − 13 = 615. This equation is not true because (715 - 13 = 702).

E. 12 − 20 = 10. This equation is untrue since (12 - 20 = -8).

Thus, since the solutions to the equations are not the same values given, we can conclude that none of the equations is true.

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A. 34 − 12 = 14

B. 916 − 48 = 58

C. 78 − 34 = 18

D. 715 − 13 = 615

E. 12 − 20 = 10

The requried first year in which Nina sees that investment exceeded investment B is 5th year.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
According to the given data,
Equation models for the given condition are,
For investment A

y = 50(1.08)ˣ

For investment B
y = 60 + 3x

Where y is the total amount after x years of passing.

When plotting the graph of both equations we can see Investment A will surplus the graph of Investment B at x = 5.56

Thus, the requried first year in which Nina sees that investment exceeded investment B is 5th year.

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10352 grade point averages must be obtained. The solution has been obtained by using the concept of sample size.

What is sample size?

The sample size is the number of observations utilised to derive estimates for a certain population. By taking a sample from the population, the sample size was established. Sampling is the practise of selecting a subset of the population to infer characteristics about the complete population.

We know that for 99% confidence, the z- score is 2.5758

So, using this we get

N = (z * σ/E)²

N = (2.5758 * 0.79/0.02)²

N = 10351.86

Hence, 10,352 grade point averages must be obtained so that the sample mean is within 0.2 of the population mean.

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Answer:

Step-by-step explanation:

prime factorization of 60= 2*2*3*5 = [tex]2^{2} * 3^{1} * 5^{1}[/tex]

prime factorization of 150 = 2*3*5*5 = [tex]2^{1} * 3^{1} * 5^{2}[/tex]

greatest (highest) common factor (divisor), calculated

HCF = 2*3*5 = 30

For LCM, when you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to

LCM = [tex]2^{2} * 3^{1} * 5^{2}[/tex]=300

Answer:

Question 19: The person who traveled the farthest lives 12 miles from the restaurant, which is the same distance as Kellan.

Question 20: Kellan would have left his house at 8:10 AM in order to arrive at Andrea's house at 8:30 AM and then walk to the restaurant with Andrea at a rate of 2.5 miles per hour, arriving at the restaurant at 8:50 AM, five minutes early. So the answer is 810.