The answer to the question please

For (a), the probability that John wins on the third round given that he only won two rounds of the three is 5/6.

For (b), the suitability of modelling X after the geometric distribution is appropriate because the geometric distribution is the probability distribution of the number of Bernoulli trials needed to get one success. The probability of John winning on the fifth round is $(\frac{2}{5})^4(\frac{5}{6})=\frac{50}{648}$

For (c), any necessary assumptions required in order to suitably model Y after the binomial distribution is that the trials (i.e. rounds of play) are independent, and that the probability of success is the same for each trial. The parameters of this binomial distribution are: n = 10, p = 1/5.

For (d), assuming the assumptions in Question 2(c) hold, the expected value of Y (E(Y)) is 8 and the variance of Y (Var(Y)) is 2.4.

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The true statement is that (x + 3) is a factor of f(x) = x³ + 3x² - x - 3 since f(-3) = 0.

A polynomial is an expression that consists of variables, terms, exponents and constants.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factorisation of a polynomial is breaking the polynomial as a products.

Therefore,

f(x) = x³ + 3x² - x - 3

Hence, let's use the factor (x + 3)

Therefore,

f(-3) = (-3)³ + 3(-3)² - (-3) - 3

f(-3) = -27 + 27 + 3 - 3

f(-3) = 0

Therefore, the factor is (x + 3) since f(-3) = 0

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The figures converted from fraction to decimal to percent (Questions 9-14) are given as follows:

       Percent                             Decimal                              Fraction

9)      316.2%.                            3.162                                   3 4861/30000

10)    6.94%.                              0.0694                                347/5000.
11)     15.27%.                             0.1527                                 1527/10000

12)    217 2761/3367%              2.178                                    1089/500

13)    723 12/21%                       7.236                                  1809/250
14)    87%                                  0.87                                     87/100

9) Given the compound fraction:   3 4861/30000

To convert 3 4861/30000 to a decimal, we first need to convert the mixed number to an improper fraction:

3 4861/30000 = (30000*3 + 4861)/30000

= 94861/30000

To convert this fraction to a decimal, we divide the numerator by the denominator:

94861/30000 ≈ 3.162

To convert 3 4861/30000 to a percentage, we multiply the decimal by 100:

3.162 x 100 ≈ 316.2%

So, 3 4861/30000 as a percentage is approximately 316.2%

10)  Given the decimal 0.0694
To convert 0.0694 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.0694 = 694/10000

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

694/10000 = (3472)/(50002) = 347/5000

So, 0.0694 as a fraction is 347/5000.


To convert 0.0694 to a percentage, we multiply the decimal by 100:

0.0694 x 100 = 6.94%

So, 0.0694 as a percentage is 6.94%.


11) Given the decimal - 0.1527

To convert 0.1527 to a percentage, we multiply the decimal by 100:

0.1527 x 100 = 15.27%

So, 0.1527 as a percentage is 15.27%.

To convert 0.1527 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.1527 = 1527/10000

12) Given the compound percentage - 217 2761/3367%

To convert 217 2761/3367% to a decimal, we first need to convert the mixed number to an improper fraction:

217 2761/3367% = (3367*217 + 2761)/3367% = 733400/3367%

743032/3367% = 217.82001782%
217.82001782% = 2.1782001782
220.680724681% [tex]\approx[/tex] 2.178

Thus, in fraction:

2.178 = 2.178/1

Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000

= 2.178/1 x 1000/1000

= 2178/1000

= 1089/500


13) Given the compound fraction - 723 12/21%


To convert 723 12/21% to a decimal, we first need to convert the mixed number to an improper fraction:

723 12/21% = (21*723 + 12)/21% = (15195/21)%

(15315/21)% = 7.23571428571
15315/21%  [tex]\approx[/tex] 7.236


Converting 7.236 to fraction:

7.236 = 7.236/1


Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000


= 7.236/1 x 1000/1000

= 7236/1000: Divide numerator and denominator by 4

= (7236÷ 4)/(1000÷4)

= 1809/250


14) Given 0.87:

To convert 0.87 to a percentage, we multiply the decimal by 100:

0.87 x 100 = 87%

So, 0.87 as a percentage is 87%.

To convert 0.87 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.87 = 87/100

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Answer:

x = 4

Step-by-step explanation:

log a + log b = log ab

log(base b) x = y, then b^y = x

log₂2x + log₂4 = 5

log₂ (2x × 4) = 5

log₂ 8x = 5

8x = 2^5

8x = 32

x = 4

Answer:

y=30x+50

Step-by-step explanation:

3x30+50=140

5x30+50=200

Answer:

7x = 7

with solution of x = 1

This is the first choice

Step-by-step explanation:

Choice 1
7x = 7 => x = 7/7 = 1

Choice 2
7x = 7x provides no additional info and therefore there are an infinite number of solutions; any value of  will satisfy

Choice 3
x + 1 = x + 1; infinite solutions for reasons cited under choice 2

Choice 4
x + 1 = x + 2
Eliminating x from both sides gives 1 = 2
Such an equation will have no solution; no value of x can satisfy the equation

Correct answer: Choice 1: 7x = 7

Answer:

288π in³

Step-by-step explanation:

V-sphere = 4/3πr³

D = 12in   r = D/2 = 12/2 = 6 in

V = (4/3)(6)³π = (4/3)(216)π = 288π in³

the selling price as a percent of cost is 120.52%, b- the selling price is $508.20 and the markup is 20.95% of cost.

(a) To find the selling price as a percent of cost, we need to first find the selling price and then divide it by the cost and multiply by 100%.

The markup on cost is 21%, which means the dealer sells the part for:

420 + 0.21*420 = $508.20

So the selling price is $508.20 and the cost is $420.

The selling price as a percent of cost is:

508.20/420 * 100% = 120.52%

So the selling price is 120.52% of the cost.

(b) The selling price is $508.20.

(c) The markup is the difference between the selling price and the cost, expressed as a percentage of the cost:

Markup = (Selling price - Cost)/Cost * 100%

= (508.20 - 420)/420 * 100%

= 20.95%

So the markup is 20.95% of the cost.

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Answer:

Step-by-step explanation:

I think y ≤ 3 - 3x

Answer:

Step-by-step explanation:

1. 500

2. 10

3. 25000

Answer:

(2x - 3) (x + 3)

Step-by-step explanation:

Let's check

(2x - 3) (x + 3)

2x² + 6x - 3x - 9

2x² + 3x - 9

So, (2x - 3) (x + 3) is the correct answer.

The division equation that describes the situation here is as follows:

4 ÷ 2/3 = 6.

Together with addition, subtraction, and multiplication, division is one of the four basic mathematical operations. The act of separating anything into smaller groups so that each one has the same number of items is known as division.

This operation is used by mathematicians to organise and evenly distribute resources.

As we can see in the question, that there are 6 groups.

Now 6 groups of 2/3 parts.

Now the whole part has been given as = 4.

This can also be stated as:

The whole part (4) has been divided into 2/3 small parts to get 6 equal parts.

Therefore, the expression as per division can be:

4 ÷ 2/3 = 6.

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If Dumisani earn $42480 per month and he splits his earnings in the ratio 7:5, then he saves $17,700 per month.

A ratio is a way of comparing two quantities or values. It expresses the relationship between two numbers or values in terms of their relative sizes or amounts.

To split Dumisani's earnings in the ratio 7:5, we need to divide his earnings into 7 + 5 = 12 equal parts.

Each part is therefore:

42480 ÷ 12 = 3,540

Dumisani saves the lesser amount, which is in the ratio of 5 parts to 7 parts.

So he saves:

5 × 3,540 = $ 17,700

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the volume of the cylinder is approximately 30.19 cubic feet.

To find the volume of a cylinder, we use the formula:

V = πr²h

where V is the volume, r is the radius of the circular base, h is the height, and π is a constant that approximates the ratio of the circumference of a circle to its diameter, which is approximately 3.14.

In this case, we're given that the cylinder has a height of 3.8 feet, and a segment from one point on the circular base to another point on the base through the center labeled 3.2 feet. This segment is the diameter of the circular base, which means that the radius of the base is half of that, or 3.2/2 = 1.6 feet.

Plugging these values into the formula, we get:

V = πr²h

V = 3.14 x (1.6 feet)² x (3.8 feet)

V = 3.14 x 2.56 square feet x 3.8 feet

V = 30.1864 cubic feet

Rounding to the nearest hundredth, we get:

V ≈ 30.19 cubic feet

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Each year, the wild turkey population, which was once 250, drops by 2.2%. There will be around 209 turkeys left after 8 years.

Wild turkey populations are declining at a 2.2% annual pace. The initial population of 250 turkeys is anticipated to drop to around 209 turkeys after 8 years. Using the exponential decay formula, we can determine the rate of decline annually: P is the population at a certain moment, P0 is the starting population, r is the rate of reduction expressed as a decimal, and t is the time in years. P = P0 (1 - r)t. The answer to the r equation is r = (1 - (P/P0)(1/t)) = 0.022. As a result, the population is declining by 2.2% annually.

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After answering the given query, we can state that So, after 35 years, the amount account would have a value of $10,062.07.

aggregate attempting to determine the amount, total number, or duration needed. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how much you have, how much you need, or how much you get is its amount. He needs that much cash to get by.

a. We must first determine the quarterly interest rate in order to determine the account amount after five years:

r = 8% / 4 ≈ 2% every three months.

The amount after five years can then be determined using the compound interest formula:

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

where P = $1,000 as the original investment

2% is the quarterly interest rate (r).

N = 4 times per year that interest is added (quarterly)

If t = amount of years, then 5

[tex]A = \$1000(1 + 0.02/4)^{(4*5)} = $1,221.50[/tex]

So, after five years, the account would have a total of $1,221.50.

b. We employ the same method as before to determine the account balance after 35 years:

[tex]A = \$1000(1 + 0.02/4)^{(4*35)} = $10,062.07[/tex]

So, after 35 years, the account would have a value of $10,062.07.

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Answer:

3(a−1)

———

a+1

Step-by-step explanation:

The area of a parallelogram can be obtained from the formula for a rectangle by using the same base and height, leading to the formula Area of parallelogram = base x height.

By moving the red triangle to the green triangle, we create a rectangle with the same base and height as the original parallelogram. Therefore, the area of the original parallelogram is equal to the area of the rectangle, which is given by the formula:

Area of rectangle = base x height

We can conclude that the formula for the area of a parallelogram is also given by:

Area of parallelogram = base x height

This is because a parallelogram can be divided into two congruent triangles, and the area of each triangle is half the area of the parallelogram. Therefore, the area of a parallelogram is equal to the base times the height, which is the same as the formula for the area of a rectangle.

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The percentage interest rate added to the account at the end of the year is 1.3%

Tax is the compulsory levy paid by citizens to the government for buying goods and services.

Amount Samia invest = £3,000

Amount of interest = x

Rate of tax = 20%

Amount of tax = £7.80

So,

20% of x = £7.80

0.2x = £7.80

x = £7.80/0.2

x = £39

Percentage of interest rate:

x% of £3000 = £39

x% × 3000 = 39

x% = 39/3000

x% = 0.013

x% = 1.3%

Hence, 1.3% is the percentage of Samia investment added to the account.

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The answer of the given question based on the theorem  For any integer , is odd if and only if + 1 is even the answer is for any integer , is odd if and only if + 1 is even.

A theorem is  statement in mathematics that has been proven to be the true based on logical reasoning and the mathematical principles. In other words,  theorem is a proposition that can be demonstrated or proved to be true through  logical argument.

Proof:

(⇒) Suppose is odd.

Thus, for some integer , = 2 + 1.

Now + 1 = (2 + 1) + 1 = 2 + 2 = 2( + 1).

Therefore, + 1 is even.

(⇐) Suppose + 1 is even.

Then, for some integer , + 1 = 2.

Thus, for some integer , = 2 - 1 = 2( - 1) + 1 .

Since 2 | 2( + 1), 2 | ( + 1).

Therefore, is odd.

Thus, we have shown that for any integer , is odd if and only if + 1 is even.

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113,950,000,000 ([tex]1.1395x10^7[/tex] is scientific notation, so you need to move the decimal to the left 7 places and add the relevant commas to get 113,950,000,000 in standard notation).

Notation is a method of representing information, usually in a concise and organized way. It can be used to represent mathematical equations, algorithms, music, dance, and other concepts. Notation is often used as a shorthand for communicating ideas to others, as it allows for a more precise and efficient way of conveying information. Notation also allows for the precise and consistent representation of a concept, allowing for greater accuracy and understanding.

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Answer:

5 cubed is 5 x 5 x 5 = 125.

10 squared is 10 x 10 = 100.

So, 5 cubed - 10 squared = 125 - 100 = 25.

We can also express 25 as a power of 5 by noting that 25 = 5 squared. Therefore:

5 cubed - 10 squared = 5 squared x 5 - 10 squared = 5^(2+1) - 10^(2) = 5^3 - 10^(2) = 125 - 100 = 25.

So, the answer is 5 squared or 5^2.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5 cubed - 10 squared

[tex]5^{3} - 10^{2} \\ = 125 - 100\\= 25[/tex]

Hope this helps!

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After approximately 9.95 years, the employee will be earning $10.00 per hour.

What is property of logarithms?

The properties of logarithms are a set of rules that can be used to manipulate logarithmic expressions, including the product, quotient, power, and change of base properties.

We are given that the employee's hourly wage after t years is given by the equation [tex]y=7.03(1.03)^t[/tex]. We need to find the amount of time t after which he will be earning $10.00 per hour. So we set y = $10.00 and solve for t as follows:

$10.00 = $[tex]7.03(1.03)^t[/tex]

Divide both sides by $7.03:

1.4246 = [tex]1.03^t[/tex]

Take the natural logarithm of both sides:

ln(1.4246) = ln([tex]1.03^t[/tex])

Using the property of logarithms that ln([tex]a^b[/tex]) = b * ln(a), we can simplify the right-hand side:

ln(1.4246) = t * ln(1.03)

Solve for t:

t ≈ 9.95 years

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[tex]1\dfrac{1}{2} = \dfrac{3}{2} = 1.5[/tex]

[tex]20 (10) (5-1.5) = 200(3.5) = 700 \ cubic \ feet[/tex]

Answer:

(B) 700 cubic feet

Step-by-step explanation:

The height of water in the pool is 5 - 1 1/2 = 3 1/2 feet.

The volume of water needed to fill the pool up to 3 1/2 feet is:

20 feet x 10 feet x 3 1/2 feet = 700 cubic feet

Therefore, the answer is (B) 700 cubic feet.

Using Pythagorean theorem, the triangle is an acute triangle.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental result in Euclidean geometry that describes the relationship between the three sides of a right-angled triangle.

In equation form, this can be written as:

[tex]c^2 = a^2 + b^2[/tex]

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (also known as the legs) of the right-angled triangle.

If the triangle is not a right triangle, then the inequality [tex]c^2 < a^2 + b^2[/tex]holds for an acute triangle and [tex]c^2 > a^2 + b^2[/tex] holds for an obtuse triangle.

Using this formula, we can check if the given triangle is right, acute, or obtuse:

a = 43, b = 96, and c = 89

[tex]c^2 = 89^2 = 7921[/tex]

[tex]a^2 + b^2 = 43^2 + 96^2 = 1849 + 9216 = 11065[/tex]

Since [tex]c^2 < a^2 + b^2[/tex], we can see that:

[tex]c^2 < a^2 + b^2[/tex]

So the triangle is an acute triangle.

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Answer:

-128.31

First choice

Step-by-step explanation:

Using a calculator:

7.05(−18.2) = 7.05 x -18.2 = -128.31

binomial distribution

Question: Suppose that 20% of all copies of grade 7 Science textbook fail a certain binding strength test. Let X denote the number among 15 randomly selected copies that fail the test.b. What is the probability that at least 8 fail the test?To find the probability that at least 8 fail the test, we will use the binomial probability formula.The binomial distribution is a statistical distribution that describes the probability of success or failure in an experiment or survey with two possible outcomes.Suppose a trial consists of n independent experiments, each of which has two possible outcomes: either success with probability p or failure with probability q = 1 – p. If X is the number of successes in n trials, then X is said to follow a binomial distribution with parameters n and p. The probability that X = x is given by;P(X = x) = nCxpx(1-p)n-xwhere nCx = n! / x! (n-x)! is the binomial coefficient which counts the number of ways that x successes can be chosen from n trials.Using the formula, we have;P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)Here n = 15, p = 0.2 and q = 0.8P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)= 15C8 (0.2)^8 (0.8)^7 + 15C9 (0.2)^9 (0.8)^6 + 15C10 (0.2)^10 (0.8)^5 + 15C11 (0.2)^11 (0.8)^4 + 15C12 (0.2)^12 (0.8)^3 + 15C13 (0.2)^13 (0.8)^2 + 15C14 (0.2)^14 (0.8)^1 + 15C15 (0.2)^15 (0.8)^0= 0.0094 + 0.0267 + 0.0524 + 0.0864 + 0.1174 + 0.1312 + 0.1184 + 0.0352= 0.5771Therefore the probability that at least 8 fail the test is 0.5771 (rounded to four decimal places).Answer: 0.5771

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