A triangle ABC has a perimeter of 59cm. AB is twice the length of AC and 6cm longer than BC. Find the length of AB.

The functiοn that gives the number οf illiterate peοple in Sylvania is

[tex]\mathrm{P(t) = 9000(2/5)^t}[/tex]

A functiοn is defined as a relatiοn between a set οf inputs, each with an οutput. Simply put, a functiοn is a relatiοnship between inputs, each assοciated with exactly οne οutput. Each functiοn has a dοmain and cοdοmain οr scοpe.

Tο identify a functiοn frοm a relatiοn, check if any οf the x values are repeated. If it's nοt repeated, it's a functiοn. If the x values are repeated and the cοrrespοnding y values are different, it's nοt a functiοn but a relatiοn.

Sοlutiοn accοrding tο the questiοn:

Given, Tοtal number οf illiterate peοple = 9000

          Amοunt = 3/5

Fοr the first year = 9000 × (1 - 3/5) = 9000(2/5)

Nοw, fοr "t years":

P(t) = 9000(2/5)

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The equation for the exponential function is

The graph is attached

Exponential function is a function of the form  f(x) = a(b)ˣ

where

the starting = a

the base = b

the exponents = x

Using the table, f(x) = a(b)ˣ

a = 20

solving for b

10 = 20(b)¹

10 = 20b

b = 1/2

the equation for the function is f(x) = 20(0.5)ˣ

check

for x = 3

f(x) = 20(0.5)³ = 2.5

for x = 4

f(x) = 20(0.5)⁴ = 1.25

The graph of exponential decay is a decreasing function that approaches the x-axis, but never touches it. The rate at which the function decays depends on the value of b - the smaller the value of b, the slower the decay

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The correct answer is a. A leading question.

A leading question is one that is designed to elicit a specific response or to influence the answer given by the respondent. In this case, the question is designed to lead the respondent to agree that they also liked the chocolate bar, as "most people" did. This type of question is often used in surveys and research studies to obtain desired results.

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Two families attended a baseball game, where they bought popcorn and souvenir. popcorn cost $4 and cost of souvenir is $7.

An equation is an expression that shows the relationship between two or more variables and numbers. Through equations the given information can be denoted as,

Let x = price of 1 bag of popcorn

Let y = price of 1 souvenir cup

First family:

3x + 4y = 40 (equation 1)

Second family:

8x + 4y = 60 (equation 2)

We have a system of 2 equations with 2 variables.

3x + 4y = 40

8x + 4y = 60

We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.

[tex]8x+4y=60\\4y=60-8x\\[/tex]

divide both sides by 4

[tex]\frac{4y}{4} =\frac{60-8x}{4} \\y=\frac{60-8x}{4} \\y=15-2x[/tex]

now putting the value of y in equation 1

[tex]3x+4y=40\\3x+4(15-2x)=40\\3x+60-8x=40\\-5x+60=40\\-5x=40-60\\-5x=-20\\x=\frac{-20}{-5} =4\\x=4[/tex][tex]y=15-2x\\y=15-2(4)\\y=15-8\\y=7\\[/tex]

Therefore, the cost of one bag of popcorn is $4.

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Answer:A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

The  (√12 - √3)² = 6 according to the provided assertion.

Why do you use the word "binomial"?

A Binomial is a name for an algebraic equation with only two elements. It is a polynomial with two terms. It is also referred to as the total or difference of two or more binomials. It is a polynomial's most basic shape.

To expand and simplify the expression (√12 - √3)², we can use the formula for the square of a binomial:

(a - b)² = a²  + b² - 2ab

In this case, a = √12 and b = √3, so we have:

(√12 - √3)² = (√12)² - 2(√12)(√3) + (√3)²

To simplifying, we have:

(√12 - √3)² = 12 - 2√36 + 3

Since √36 = 6, we can simplify further:

(√12 - √3)² = 12 - 2(6) + 3 = 6

Therefore, the expanded and simplified equation (√12 - √3)² = 6.

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The sets A and B define a function, while the set C does not.

To determine whether a set defines a function, we need to check if there is one and only one output for each input. In other words, there should not be two different outputs for the same input.

\( A=\{(a, d),(c, d),(e, f),(b, f)\} \)

In this set, there are no repeated inputs, so it does define a function.

\( B=\{(1,3),(2,4),(5,6),(3,4)\} \)

In this set, there are also no repeated inputs, so it does define a function.

\( C=\{(1, a),(2, b),(3, c),(2, a),(4, d),(5, c)\} \)

In this set, there are two different outputs for the input 2 (b and a), so it does not define a function.

Therefore, the sets A and B define a function, while the set C does not.

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Answer:

4x + 14

Step-by-step explanation:

2 (3x2 - 4x + 7)

= 2 ( 6x - 4x + 7)

= 2 ( 2x + 7)

= 4x + 14

Answer:

D

Step-by-step explanation:

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{2\sqrt{41}}\\ a=\stackrel{adjacent}{10}\\ o=opposite \end{cases} \\\\\\ o=\sqrt{ (2\sqrt{41})^2 - 10^2}\implies o=\sqrt{ (2^2)(\sqrt{41})^2 - 100 } \implies o=\sqrt{ (4)(41)-100 } \\\\\\ o=\sqrt{164-100}\implies o=\sqrt{64}\implies o=8[/tex]

Answer:

m<BFC= 64°; m<AFB= 116°

Step-by-step explanation:

Using the Vertical Angle Theorem, in which "the opposing angles of two intersecting lines must be congruent, or identical in value"

m<AFE is congruent to m<BFC, therefore m<BFC is 64°

You can also use the straight angle theorem where BE is a straight line, and is therefore 180°. so subtracting 180° from 64° will result in m<AFB being 116°, you second answer. You can take it a step further without using the vertical angle theorem to get our first answer by using the same rules for the straight angle theorem again, knowing that AC is a straight line and that m<AFB is 116°, subtract 180° by 116° to get m<BFC, 64°.

There are 720 different possibilities for selecting the executive board from a Student Council with 10 members. An answer is option (B) 720.

A permutation is to select an object then arrange it and it cares about the orders while a Combination is about only selecting an object without caring about the orders.

The number of ways to select the executive board is the number of permutations of 10 items taken 3 at a time.

That is:

P(10, 3) = 10!/(10-3)! = 10x9x8 = 720

Therefore, there are 720 different possibilities for selecting the executive board from a Student Council with 10 members. An answer is option (B) 720.

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Answer:

127

Step-by-step explanation:

6m+65=2m+57

-2          -2

4m+65=57

     -65  -65

4m=-8

divide by 4 on both sides

m=-2

plug in the 2

6(-2)+65=53

a line =180

180-53=127

Answer:

To answer this question, we need to compare the number of men and women who like playing golf to the number of men and women who like running.

There are 14 men who like playing golf and 2 men who like running, so the ratio of men who like playing golf to men who like running is:

14 men / 2 men = 7 men who like playing golf for every man who likes running

There are 6 women who like playing golf and 18 women who like running, so the ratio of women who like playing golf to women who like running is:

6 women / 18 women = 1/3 or 0.333 women who like playing golf for every woman who likes running

Therefore, the correct statement is:

C. For every woman who likes running, 7 women like playing golf.

To find the probability that four out of 25 randomly selected students are asthmatic, we can use the binomial probability formula:

P(X = x) = (n choose x) * p^x * (1 - p)^(n - x)Where n is the number of trials (students), x is the number of successes (asthmatic students), and p is the probability of success (8.8% or 0.088).

Plugging in the given values, we get:
P(X = 4) = (25 choose 4) * 0.088^4 * (1 - 0.088)^(25 - 4) = 12,650 * 0.00005993 * 0.35178 = 0.0266
Therefore, the probability that four out of 25 randomly selected students are asthmatic is 0.0266, or 2.66%. Rounded to four decimal places, the answer is 0.0266.

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Step-by-step explanation:

1) geometric

2) arithmetic

3) neither

4) geometric

5) neither

6) arithmetic

you can this by usin their formulas or

you see if it has common difference which is for arithmetic sequence or you find the common ratio which is geometric sequence.

Answer: A

Step-by-step explanation: 2/-3 means that the - sign should be brought up. So, A is correct.

Answer: 3.31662479036.

At Bank A, the interest rate was 8% (7.94% rounded to the nearest fourth of a percent). At Bank B, the interest rate was 5% (5.09% rounded to one decimal place).

To find the interest rate at each bank, we can use the formula for compound interest and the formula for continuously compounded interest.
For Bank A, the formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values we have, we get:
51010.5 = 1000(1 + r/4)^(4*5)
Solving for r, we get:
r = 4[(51010.5/1000)^(1/20) - 1]
r = 0.1999
So the interest rate at Bank A is about 19.99%, or 20% when rounded to the nearest fourth of a percent.
For Bank B, the formula for continuously compounded interest is A = Pe^(rt), where A is the final amount, P is the principal, r is the interest rate, and t is the number of years.
Plugging in the values we have, we get:
5192.20 = 5500e^(r*5)
Solving for r, we get:
r = (1/5)ln(5192.20/5500)
r = -0.0118
So the interest rate at Bank B is about -1.18%, or -1.2% when rounded to the nearest fourth of a percent.
Therefore, the interest rate at Bank A is about 20% and the interest rate at Bank B is about -1.2%.

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Answer:

  -119/169

Step-by-step explanation:

You want cos(2α) where cos(α) = 5/13 and 270° < α < 360°.

The desired function is ...

  cos(2α) = 2cos²(α) -1

In the given quadrant, sin(α) < 0. Since the sine is squared in the double-angle identity, whether it is positive or negative is irrelevant.

  [tex]\cos(2\alpha)=2\cos^2(\alpha)-1=2\left(\dfrac{5}{13}\right)^2-1=\dfrac{2(25)-169}{169}\\\\\boxed{\cos(2\alpha)=-\dfrac{119}{169}}[/tex]

We can see that the points of intersection occur at π/3 and 4π/3.

We will solve this equation on the interval [0,2π). To begin, we can break up the equation into two parts:

2cosθ - 1 = 0 and 5cotθ + 4 = 0

First, let's solve the equation 2cosθ - 1 = 0. We can solve this equation by adding 1 to both sides and then dividing both sides by 2. We get:

2cosθ = 1
cosθ = 1/2

To find the angle θ, we can take the inverse cosine of both sides to get:

θ = cos-1(1/2)
θ = π/3

Now, let's solve the equation 5cotθ + 4 = 0. We can solve this equation by subtracting 4 from both sides and then dividing both sides by 5. We get:

cotθ = -4/5

To find the angle θ, we can take the inverse cotangent of both sides to get:

θ = cot-1(-4/5)
θ = 4π/3

Therefore, the solution to the equation on the interval [0,2π) is θ = π/3 or θ = 4π/3. To confirm the solutions, we can produce a Desmos graph of the equation on the interval [0,2π). We can see that the points of intersection occur at π/3 and 4π/3, which are our solutions. See the screenshot below.

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Answer: Since lines l and m are parallel, we can use the fact that corresponding angles are congruent. Therefore:

m∠1 = m∠6 (corresponding angles)

m∠6 + m∠2 = 180° (supplementary angles, as angles 6 and 2 form a straight line)

m∠2 = m∠7 (corresponding angles)

m∠3 = m∠7 (alternate interior angles)

m∠1 + m∠4 = 180° (supplementary angles, as angles 1 and 4 form a straight line)

m∠3 + m∠4 = 180° (supplementary angles, as angles 3 and 4 form a straight line)

We know that m∠1 = 63°, so we can use the equations above to find m∠6 and m∠7:

m∠1 = m∠6, so m∠6 = 63°.

m∠6 + m∠2 = 180°, so m∠2 = 180° - m∠6 = 180° - 63° = 117°.

m∠2 = m∠7, so m∠7 = 117°.

m∠3 = m∠7, so m∠3 = 117°.

m∠1 + m∠4 = 180°, so m∠4 = 180° - m∠1 = 180° - 63° = 117°.

m∠3 + m∠4 = 180°, so m∠3 + 117° = 180°, which means m∠3 = 63°.

Therefore, the measures of the angles are:

m∠1 = 63°

m∠2 = 117°

m∠3 = 63°

m∠4 = 117°

m∠6 = 63°

m∠7 = 117°

Step-by-step explanation:

If Kenneth has 5/8 feet of lumber, then he need 83/40 feet of lumber to make the shelf.

First we convert the length of lumber in improper fraction form,

So, we convert 2(7/10) feet to an improper fraction,

⇒ 2(7/10) = (2×10 + 7)/10 = 27/10,

To find the length of lumber required we need to subtract the amount of lumber Kenneth has from the total length required,

Kenneth has a total of 5/8 feet of lumber,

Length of lumber required is = 27/10 - 5/8,

Taking LCM of 10 and 8 as 40 , and simplifying further,

We get,

⇒ 108/40 - 25/40

⇒ 83/40

Therefore, Kenneth needs 83/40 feet more lumber to make the shelf.

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a)  The demand (price) function in terms of x : P(x) = 12 - 0.025(x - 1500)

b) the marginal revenue function is [tex]MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)[/tex] The marginal revenue from the sales of 1800 T-shirts is -$3. This means that for each additional T-shirt sold after the 1800th, the revenue will decrease by $3 per T-shirt

To determine the demand (price) function, we need to find a relationship between the price of the T-shirts (P) and the number of T-shirts sold (x). We are given that for every $0.50 decrease in price, 20 more T-shirts will be sold.

Let's first find the decrease in price per T-shirt sold. If 20 more T-shirts are sold for every $0.50 decrease, then the decrease per T-shirt is $0.50/20 = $0.025. Now, we can set up the demand function. The base price is $12, and we decrease it by $0.025 for each additional T-shirt sold. So the demand function is:

P(x) = 12 - 0.025(x - 1500) To determine the marginal revenue function, we first need to find the total revenue function. Total revenue (R) is the product of the price (P) and the number of T-shirts sold (x):

R(x) = P(x) * x = (12 - 0.025(x - 1500)) * x Now we need to find the derivative of the total revenue function with respect to x, which will give us the marginal revenue function: MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)

To determine the marginal revenue from the sales of 1800 T-shirts, we simply plug in x = 1800 into the marginal revenue function: MR(1800) = 12 - 0.05(1800 - 1500) = 12 - 0.05(300) = 12 - 15 = -$3

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The possible rational roots of the equation 14x3 - 39x2 + 24x - 4 = 0 are: 2/7, 4/7, 2, 4, 1/7, 1, 1/14, 1/2, -2/7, -4/7, -2, -4, -1/7, -1, -1/14, -1/2.

To find the rational roots, we need to factor the equation into its linear components. First, factor out a common factor from all terms: 14x3 - 39x2 + 24x - 4 = 0 --> 14x(x2 - 3x + 2)(x-2) = 0.

This means that the equation has three linear components, and each component has a possible root that we can calculate. The possible roots can be determined by using the Rational Root Theorem:

Using the Rational Root Theorem, we can find the possible rational roots of the equation:

Therefore, the possible rational roots of the equation.

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The simplified the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8)) is (x+9)/(x+7).

To simplify the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8)), we can follow the following steps:

Step 1: Find the common denominator for the fractions in the numerator and denominator. In this case, the common denominator is (x+8).

Step 2: Multiply the numerator and denominator of the expression by the common denominator to get rid of the fractions. This gives us:

((x+8)(1+(1)/(x+8)))/((x+8)(1-(1)/(x+8)))

Step 3: Simplify the numerator and denominator by distributing and combining like terms. This gives us:

((x+8+1)/(x+8-1))/(x+8)

Step 4: Simplify the expression further by canceling out any common factors. In this case, we can cancel out the (x+8) terms in the numerator and denominator to get:

(x+9)/(x+7)

Therefore, the simplified expression is (x+9)/(x+7).

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After taking out percentages we know that Riley has used more percentage of white paint which is 42.85% and her grey paint would be lighter.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

So, the percentages would be:

Riley:

4 black and 3 white

Total = 7

Percentage of white paint:

3/7 * 100 = 42.85%

Christian:

7 black and 4 white

Total = 11

Percentage of white paint:

4/11 * 100 = 36.36%

We know that: 42.85% > 36.36%

Therefore, after taking out percentages we know that Riley has used more percentage of white paint which is 42.85% and her grey paint would be more lighter.

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Part A: The function f(x) is an exponential function.

Part B: As x increases by 1, the value of f(x) increases by a factor of 6.

It is an exponential function because the function is of the form f(x) = a^(x-1), where a is a constant. We can see that when x increases by 1, the exponent in the function increases by 1 as well. So we have:

f(x+1) = a^x * a

f(x) = a^(x-1)

Therefore, the ratio of f(x+1) to f(x) is:

f(x+1)/f(x) = (a^x * a) / (a^(x-1)) = a

This means that as x increases by 1, the value of f(x) increases by a factor of a, which in this case is 6. Therefore, statement B supports the correct answer from Part A.

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