You are playing a game where you draw a card from a standard deck, and you will win $5 if you draw a face
card, $14 if you draw an ace and lose $19 if you draw any other card. What is the expected gain from this
game?

Answer:

7x^2 - 7x + 17

Step-by-step explanation:

we can subtract what they already have from what they total cost for the microphones:

8x^2 - 4x + 9 - (x^2) - (x - 14) - (2x + 6)

simplify this:

8^2 - 4x + 9 - x^2 - x + 14 - 2x - 6 =

7x^2 - 7x + 17

According to the given data in question below given are the separate journal entries for each transaction on the books of Metlock, Inc.

"Entries" typically refers to the individual values in a matrix or table. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns, while a table is an arrangement of data in rows and columns with each intersection representing a single piece of data.

1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.

Inventory (asset) $7,400

Accounts payable (liability) $7,400

2. On June 11, Metlock, Inc. pays the freight costs of $560:

Freight expense (expense) $560

Cash (asset) $560

3. On June 12, goods totaling $600 are returned to Monty for credit:

Accounts payable (liability) $600

Inventory (asset) $600

4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:

Accounts payable (liability) $7,400

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

Note that the purchase discount is calculated as $7,400 x 3%, or $222.

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The information in issue below is taken from Metlock, Inc.'s books, which include separate journal entries for each transaction.

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.

Inventory (asset) $7,400

Accounts payable (liability) $7,400

2. On June 11, Metlock, Inc. pays the freight costs of $560:

Freight expense (expense) $560

Cash (asset) $560

3. On June 12, goods totaling $600 are returned to Monty for credit:

Accounts payable (liability) $600

Inventory (asset) $600

4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:

Accounts payable (liability) $7,400

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

Note that the purchase discount is calculated as $7,400 x 3%, or $222.

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Answer:

Step-by-step explanation:

[tex]f(x)=16e^x-ex^e[/tex]

[tex]f'(x)=16e^x-e^2x^{e-1}[/tex]

[tex]f'(3)=16e^3-e^23^{e-1}[/tex]

[tex]f'(3)=e^2(16e-3^{e-1})[/tex]

Answer:

Step-by-step explanation:

There are 4 cups of birdseed in the bag.

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols to solve equations and understand mathematical relationships. It involves the use of letters and symbols to represent variables and numbers, and the manipulation of these variables and numbers using rules and operations such as addition, subtraction, multiplication, and division. The main goal of algebra is to solve equations, which involves finding the value of an unknown variable that satisfies the given equation.

In algebra, equations are often represented graphically as lines or curves on a coordinate plane, which allows for a visual representation of mathematical relationships. Algebraic equations are used in a variety of fields, including physics, engineering, finance, and computer science.

The study of algebra starts with basic arithmetic concepts and progresses to more complex topics such as linear equations, quadratic equations, and functions. The ability to understand and manipulate algebraic expressions is an essential skill in many areas of life, from solving practical problems to understanding complex mathematical theories.

If each of the 16 Cougar Scouts gets 1/4 of a cup of birdseed, then the total amount of birdseed in the bag can be found by multiplying the amount given to each scout by the number of scouts:

Total birdseed = (1/4) x 16 = 4 cups

Therefore, there are 4 cups of birdseed in the bag.

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The complete question is:

Therefore, we can expect the world population to be around 17.6 billion in the year 2100 if it continues to increase exponentially with a doubling time of 60 years.

A decimal place is a position in a number that is to the right of the decimal point. It represents a fractional part of the number. For example, in the number 3.14159, the digit "1" is in the tenths place, the digit "4" is in the hundredths place, the digit "1" is in the thousandths place, and so on. Each place value to the right of the decimal point represents a power of 10 that is negative, such as tenths, hundredths, thousandths, ten-thousandths, and so on. The number of decimal places determines the degree of precision in the number.

by the question.

To determine the population in the year 2100, we need to calculate how many times the population will double between 2022 and 2100, which is 78 years.

78 years divided by 60 years is approximately 1.3, which means that the population will double 1.3 times between 2022 and 2100.

2 to the power of 1.3 is approximately 2.2, which means that the population in 2100 will be 2.2 times the population in 2022.

So, the population in 2100 will be:

8 billion x 2.2 = 17.6 billion (rounded to one decimal place)

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Answer:

[tex]\large\boxed{\tt x^{\frac{5}{6}} + 2x^{\frac{7}{3}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to simplify the given expression.}[/tex]

[tex]\textsf{We should use the \underline{Distributive Property, and Rule of Multiplying Exponents.}}[/tex]

[tex]\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses with the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c) = \boxed{\tt ab+ac} \end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Rule of Multiplying Exponents;}} \\ \\ \textsf{Whenever we have to multiply 2 terms with exponents, it's important to know the Rule of Multiplying Exponents. This rule states that whenever 2 exponential terms multiply together, their exponents add together. }\\ \\ \underline{\textsf{\large Example;}} \\ \tt x^{3} \times \tt x^{4} = x^{3+4} = \boxed{\tt x^{7}} \end{minipage}}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{We should first use the Distributive Property, then use the Rule of Multiplying}[/tex]

[tex]\textsf{Exponents.}[/tex]

[tex]\tt x^{\frac{1}{3}} (x^{\frac{1}{2}} + 2x^{2})[/tex]

[tex]\underline{\textsf{Use the Distributive Property;}}[/tex]

[tex]\tt x^{\frac{1}{3}} (x^{\frac{1}{2}} + 2x^{2}) = (x^{\frac{1}{3}} \times x^{\frac{1}{2}}) + (x^{\frac{1}{3}} \times 2x^{2})[/tex]

[tex]\underline{\textsf{Use the Rule of Multiplying Exponents;}}[/tex]

[tex]\tt (x^{\frac{1}{3}} \times x^{\frac{1}{2}}) + (x^{\frac{1}{3}} \times 2x^{2}) = x^{\frac{1}{3} + \frac{1}{2}} + 2x^{\frac{1}{3} + \frac{2}{1} }[/tex]

[tex]\underline{\textsf{Find Common Denominators per fractions;}}[/tex]

[tex]\tt x^{\frac{1}{3} + \frac{1}{2}} + 2x^{\frac{1}{3} + \frac{2}{1}} = x^{\frac{2}{6} + \frac{3}{6}} + 2x^{\frac{2}{6} + \frac{12}{6}}[/tex]

[tex]\underline{\textsf{Add;}}[/tex]

[tex]\tt x^{\frac{2}{6} + \frac{3}{6}} + 2x^{\frac{2}{6} + \frac{12}{6}} = x^{\frac{5}{6}} + 2x^{\frac{14}{6}[/tex]

[tex]\underline{\textsf{Simplify Fractions;}}[/tex]

[tex]\large\boxed{\tt x^{\frac{5}{6}} + 2x^{\frac{7}{3}}}[/tex]

Step-by-step explanation:

gradient= 12-10/10-9

= 2

y=mx+c

c= -8

y= 2x-8

when x= -1,

y= 2(-1)-8

= -2-8

= -10

when x= 5,

y= 2(5)-8

= 10-8

= 2

I think it could represent the 100-yard dash. The graph represents distance versus time, which is a common way to graphically display motion.

A graph is a visual representation of data that displays the relationship between two or more variables. Graphs can be used to illustrate numerical information in a clear and concise way, making it easier to understand and analyze complex sets of data. Graphs can be created using various types of software or by hand, and there are many different types of graphs, including line graphs, bar graphs, scatter plots, pie charts, and more.

Here,

The vertical axis represents the distance, and the horizontal axis represents time. The line on the graph shows how the distance traveled changes with respect to time.

The graph also shows that the runner covers a certain distance in a specific amount of time, which is a fundamental concept in physics. In the case of the 100-yard dash, the graph shows how the runner covers 100 yards in a certain amount of time.

Overall, the graph displays the key characteristics of motion and can be used to analyze and compare the performance of athletes in various sports.

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Step-by-step explanation:

Picking a male youngster who enjoys playing video games is more likely if you get a score of (4/10) * (6/10) = 24/100 = 6/25.

Probability is a mathematical concept that expresses the possibility or chance of an event happening. It is stated as a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty. By dividing the number of favorable outcomes by the entire number of possible possibilities, the probability of an event is determined.

given

The odds of selecting a male adolescent at random are x/n, while the odds of selecting a teen whose preferred pastime is playing video games are y/n.

As these two occurrences are separate, the likelihood that both will occur is the product of the probabilities:

The odds of selecting a male teen who enjoys video games are (x/n) * (y/n) = xy/n2.

By dividing the numerator and denominator by the greatest common factor (GCF) of x and y, if one exists, this can be made simpler.

For instance, the probability is simplified as follows if x=4 and y=6, where the GCF is 2:

Picking a male youngster who enjoys playing video games is more likely if you get a score of (4/10) * (6/10) = 24/100 = 6/25.

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.....Answer:

..........Step-by-step explanation:

Answer:

d

Step-by-step explanation:

believe me it's d because it says it in the text above u just have to read it carefully

Joe will catch Jason in 6 hours running at 7mph while Jason is running at 5.5 mph .

Given,

Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 miles per hour.

Now,

Joe speed is more than Jason.

So,

Differences in speed:

(7 - 5.5) = 1.5 miles per hour.

Now,

Jason is ahead of joe by 9 miles.

To cover 9 miles of distance by joe to catch jason,

Distance = Speed * Time

9 miles = 1.5mph* Time

Time = 6hours.

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Answer:

b=46

Step-by-step explanation:

First we know that the sum of all three angles is 180. So that gives us the equation 2b+88=180, then we can solve.

2b=180-88

2b=92

b=46

So that means b=46!

As you may know, a straight line = 180°

Since we already have 88° as one of the values, we can simply subtract that from 180.

180 - 88 = 92

Next, divide 92 by 2

92 ÷ 2 = 46

With that being said, we can conclude that the value of B is 46.

You can double check this by adding all of the values together: 46 + 46 + 88 = 180

The dilation of the black figure to blue figure is a reduction with a scale factor of 0.5

A dilation is defined as a transformation that produces an image that is the same shape as the original, but is a different size.

It can either be an enlargement or a reduction.

An enlargement means a scale factor greater than 1 while a reduction is a scale factor less than 1.

Thus, this dilation is a reduction.

Coordinates of initial figure are:

(-8, 10), (10, 10), (8, -8), (2, -8)

Coordinates of dilated figure are:

(1, -4), (4, -4), (-4, 5), (5, 5)

Thus, it is clear that the scale factor is 0.5

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Answer:

24, 36, 48.

Step-by-step explanation:

Represent the three even numbers as 2x, 2y, 2z, where x,y,z are integers.

2x+2y+2z = 108

x+y+z = 54

Let x≤y≤z

x = z/2

y = ¾z

z/2 + 3z/4 + z = 54

2z/4 + 3z/4 + 4z/4 = 54

2z + 3z + 4z = 216

9z = 216

z = 24

x = z/2 = 12

y  = ¾z = 18

Therefore, The numbers are 24, 36, 48.

Answer:

D

Step-by-step explanation:

8×16=128

2×4=8

128+8=136m^2

answer: D

Answer:

[tex]\cos^2x+\cos x-1+\sin^2x[/tex] can be simplified to [tex]\cos x[/tex]

Step-by-step explanation:

Given

[tex]\cos^2x+\cos x-1+\sin^2x[/tex]

We need to use the Pythagorean trig identity in this example.

[tex]\sin^2x+\cos^2x=1[/tex]

Lets simplify.

We can use the Commutative and Associative Properties of Addition to reorder the equation.

[tex]\sin^2x+\cos^2x+\cos x-1[/tex]

Apply the Pythagorean trig identity to [tex]\sin^2x+\cos^2x[/tex].

[tex]1+\cos x-1[/tex]

Group like terms.

[tex]\cos \left(x\right)+\left(1-1\right)[/tex]

1 minus 1 is zero.

That leaves us with

[tex]\cos x[/tex]

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The length of arc-AB = 3π

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

Given circle;

arc-AB (θ) = 20°  and  radius, r = 27

We know the formula,

length of arc = (θ/360°) × 2πr

after putting the values,

length of arc-AB = (20°/360°) × 2π × 27

length of arc-AB = (1/18) × 54π = 3π

Therefore, the length of arc-AB = 3π

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The length of arc-AB = 3π. The Circle identities are a collection of trigonometric fundamental identities that relate to the six trigonometric properties of an angle in a right-angled triangle.

The central angle and sector area are required to compute arc length without radius: Divide the value by the central angle in radians after multiplying the area by two. Calculate the square root of this fraction. To get the arc length, multiply this root by the centre angle once more. The arc length is shown to be identical to the radius length. Radians are the ratio constant between an arc length and a radius length.

Given circle;

arc-AB (θ) = 20°  and  

radius, r = 27

The length of an arc,

length of arc = (θ/360°) × 2πr

after substituting the values,

length of arc-AB = (20°/360°) × 2π × 27

Simplify the above equation,

length of arc-AB = (1/18) × 54π = 3π

Therefore, the length of arc-AB = 3π

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To find the mean of the points scored by the teams, we need to add up all the points and divide by the number of teams:

Mean = (30 + 35 + 20 + 30 + 15) / 5

Mean = 130 / 5

Mean = 26

Therefore, the mean of the points scored by the teams is 26.

Answer:

answer is 26

Step-by-step explanation:

add the five numbers and divide them by the number you add them(that means by 5) and it comes

[tex] \frac{30 + 35 + 20 + 30 + 15 \\}{5} = \frac{130}{5} = 26[/tex]

Step-by-step explanation:

69) If 10 packages of shallots cost $40, then the cost of one package of shallots can be calculated as:

$40 ÷ 10 packages = $4 per package

To find out how many packages of shallots can be purchased with $8, divide the total amount of money by the cost per package:

$8 ÷ $4 per package = 2 packages

Therefore, with $8, you can buy 2 packages of shallots.

70) If three Bosc pears cost $2, we can use a proportion to determine how many pears we can buy for $4:

3 pears / $2 = x pears / $4

Cross-multiplying, we get:

3 pears × $4 = $2 × x pears

Simplifying, we get:

12 = 2x

Dividing both sides by 2, we get:

x = 6

Therefore, with $4, you can buy 6 Bosc pears.

71)If the exchange rate is 11 pounds for every $2, we can use a proportion to determine how many pounds we can get if we exchange $4:

11 pounds / $2 = x pounds / $4

Cross-multiplying, we get:

11 pounds × $4 = $2 × x pounds

Simplifying, we get:

44 = 2x

Dividing both sides by 2, we get:

x = 22

Therefore, if you exchange $4, you can get 22 pounds.

72) If 9 packages of basil cost $27, we can use a proportion to determine how many packages of basil we can buy for $9:

9 packages / $27 = x packages / $9

Cross-multiplying, we get:

9 packages × $9 = $27 × x packages

Simplifying, we get:

81 = 27x

Dividing both sides by 27, we get:

x = 3

Therefore, with $9, you can buy 3 packages of basil.

There are number of thesis that are given for mathematics by various professors and scientists at various levels that are being implemented from time to time.

A theory is nothing but a set of statements which may be based on certain principles that might have been derived by performing some experiments and attaining a proper conclusion. For example, if we say 'the sky is blue'. It means this truth can never be changed irrespective of the situations. This will remain mortal.

Similarly, there are plenty of terms in mathematics such as decimals, percentage, geometry, algebra and more fundamentals. These are existing since ages and have been challenged also. But the theory remains the same. There operas-memoranda remains the same. So various scholars, have given various theories of mathematics.

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Answer:

200

Step-by-step explanation:

199+1

Answer:

the answer is 0

Step-by-step explanation:

Answer:

In this problem, we have to use the formula

[tex]P= \frac{A}{(1+\frac{r}{n})^{nt} }[/tex]

A = $600,000.00

n = 1  (annually)

t = 25 years

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 per year,

Then, solve the equation for P

[tex]P= \frac{A}{(1+\frac{r}{n})^{nt} }[/tex]

[tex]P= \frac{6000000}{(1+\frac{0.8}{1})^{1*25} }[/tex]

P = $87,610.74

The principal investment required to get a total amount of $600,000.00 from compound interest at a rate of 8% per year compounded annually over 25 years is $87,610.74.

A×A is the set {16, 20, 24, 28, 20, 25, 30, 35, 24, 30, 36, 42, 28, 35, 42, 49}

To find A×A, we need to first understand what A represents.

In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything, such as numbers, letters, or even other sets. The elements of a set are typically enclosed in curly braces { } and are separated by commas.

A is a set defined as the set of all whole numbers, x, where 4 ≤ x ≤ 7. In other words, A contains the elements 4, 5, 6, and 7.

To find A×A, we need to take each element in A and multiply it by every other element in A. This means that we need to find the product of (4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), and (7, 7).

When we do the multiplication, we get the set {16, 20, 24, 28, 20, 25, 30, 35, 24, 30, 36, 42, 28, 35, 42, 49}.

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Answer:

≈ 11,88

Step-by-step explanation:

Use trigonometry:

cos (62∘) = 8 / x

x = 8 / cos (62∘) ≈ 11,88