I would really appreciate your help. Thank you.

Answer:

So the simplified expression is:

2x - 4 / (x^2 + 9x + 20)

Step-by-step explanation:

To simplify the expression, we need to simplify the numerator and denominator separately, and then simplify the entire expression.

Starting with the numerator:

4x^2 + 12x - 16

For the denominator:

The first fraction: 2x + 10 can be simplified as follows: 2x + 10 = (2)(x) + (2)(5) = 2x + 10

The second fraction: 6x + 24 over x^2 + 9x + 20

We can simplify the denominator by using partial fraction decomposition. To do that, we need to write the denominator as a sum of simpler fractions, each with a numerator that is a constant. In other words, we write:

6x + 24 / (x^2 + 9x + 20) = (A x + B) / (x^2 + 9x + 20) + (C x + D) / (x^2 + 9x + 20)

Multiplying both sides by the denominator, we get:

6x + 24 = (A x + B)(x^2 + 9x + 20) + (C x + D)(x^2 + 9x + 20)

Expanding the right-hand side, we obtain:

6x + 24 = Ax^3 + (A 9 + B) x^2 + (A 20 + B 9 + C) x + (B 20 + D)

Comparing the coefficients of the polynomials on both sides, we get the following system of linear equations:

A = 0

B = 6

C = 0

D = -24

Therefore, the partial fraction decomposition of the denominator is:

6x + 24 / (x^2 + 9x + 20) = (6x + 24) / (x^2 + 9x + 20)

Putting it all together, we have:

4x^2 + 12x - 16 / (2x + 10) / (6x + 24) / (x^2 + 9x + 20) = (4x^2 + 12x - 16) / (2x)(6x + 24) / (x^2 + 9x + 20) = 2x - 4 / (x^2 + 9x + 20)

So the simplified expression is:

2x - 4 / (x^2 + 9x + 20)

Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.

Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.

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The probability that 2 or fewer tomato seeds germinate out of 10 planted, given a germination rate of 43%, is 0.586 or 58.6%.

To calculate the probability that 2 or fewer seeds germinate, we need to use the binomial distribution, where:

In this case, n = 10, p = 0.43, and we want to find the probability that 0, 1, or 2 seeds germinate. We can calculate this probability as the sum of the probabilities of each of these outcomes:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

where X is the random variable representing the number of seeds that germinate.

Using the binomial distribution formula, we can calculate the probability of each outcome:

P(X = k) = (n choose k)[tex]* p^k * (1 - p)^{(n - k)}[/tex]

where (n choose k) is the binomial coefficient, equal to [tex]n! / (k! * (n - k)!)[/tex].

Plugging in the values, we get:

P(X = 0) = (10 choose 0) [tex]* 0.43^0 * 0.57^{10}[/tex] = 0.057

P(X = 1) = (10 choose 1) [tex]* 0.43^1 * 0.57^9[/tex] = 0.205

P(X = 2) = (10 choose 2) [tex]* 0.43^2 * 0.57^8[/tex] = 0.324

Therefore,

[tex]P(X \leq 2)[/tex] = [tex]0.057 + 0.205 + 0.324[/tex] = 0.586

So the probability that 2 or fewer seeds germinate is 0.586, or 58.6%.

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Answer:

Step-by-step explanation:

The answer is 4x^2y+8x^3+y^2-2xy

Answer:

B.

The equation you can use to find the area of a sphere when given radius is:

V = 4/3πr 3

Fitting 5 into the equation:

V = 4/3π5 3

V = 523.598776

Therefore, B is the correct answer.

The probability of the flight being overbooked is 0.38742 or 38.7%.

To calculate the probability of the flight being overbooked, we need to use a probability formula. In this case, we can use the binomial probability formula. The formula is as follows:

[tex]P(x) = ^nC_x * p^x * q^{(n-x)}[/tex]

Where:

P(x) is the probability of x number of events occurring.

n is the total number of trials.

p is the probability of success.

q is the probability of failure.

nCx is the number of ways to choose x items from a set of n items.

Let's say a plane has 8 seats. The airline sells 10 tickets for this flight. The probability of all ten passengers showing up for the flight is quite low. Based on past experience, the airline knows that only 90% of ticketed passengers usually show up for a flight. This percentage is also known as the "show-up rate."

In our case:

n = 10 (total number of passengers)

p = 0.9 (probability of a passenger showing up)

q = 0.1 (probability of a passenger not showing up)

We want to find the probability of having more than 8 passengers show up, which would mean the flight is overbooked. To do that, we need to calculate the probability of having 9 or 10 passengers show up. We can use the formula to calculate this:

P(9 or 10) = P(9) + P(10)

P(9 or 10) = ¹⁰C₉ x 0.9⁹ x 0.1¹ + ¹⁰C₁₀ x 0.9¹⁰ x 0.1⁰

P(9 or 10) = 0.38742 or 38.7%

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Complete Question:

Airlines usually overbook for a flight (sell more tickets than the numbers of available seats). They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight.

A plane has 8 seats. If the airline sells 10 tickets for this flight, what is the probability that the flight will be overbooked?

Answer:

164 cm^2

Step-by-step explanation:

lets find square of triangle first

corner ABD is 90 degrees coz corner ABC is 180 degrees and EBC is 90

(sum of all angles of a quadrilateral is 360,

B = 360 - C - F - E

360 - 90 - 90 - 90 = 90)

BD = CF - DE

BD = 16 - 8 = 8 cm

S ABD = AB * BD / 2 (coz corner B is 90 degrees)

S ABD = 13 * 8 / 2 = 13 * 4 = 52 cm^2

lets find square of BEFC next

S BEFC = CF * EF ( B = C = F = E = 90 so thats a rectangle)

S BEFC = 16 * 7 = 70 + 42 = 112 cm^2

finally lets find total area

S = S ABD + S BEFC = 52 + 112 = 164 cm^2

The probability of committing type 1 error best describes notion of significance level of hypothesis test.

What is probability?

Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 represents an impossible event, and 1 represents certain event. The probability of an event is calculated by dividing number of favorable outcomes by total number of possible outcomes. Probability is used in various fields, including statistics, economics, finance, and science. It is used to make predictions, assess risk, and make informed decisions. Probability theory helps to explain random phenomena, such as the outcomes of a coin toss or the probability of a disease occurring in a population.

Complete Question:

Which one of the following best describes the notion of the significance level of a hypothesis test?

i) the probability of committing a type 1 error

ii) the probability of committing a type 2 error

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The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution, with a probability of success of 10.5%.

The binomial distribution has certain properties, such as the mean and variance, that can be used to make inferences about the population. For example, the mean of the distribution is given by:

μ = np

where n is the sample size and p is the probability of success.

The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution. The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In our case, a success is a person with diabetes, and the probability of success is the prevalence of diabetes in the population, which is 10.5%. The number of trials is 100, which is the sample size. Therefore, the distribution of the number of people with diabetes in our sample can be written as:

X ~ B(100, 0.105)

Where X is the random variable representing the number of people with diabetes in our sample, and B(100, 0.105) denotes the binomial distribution with 100 trials and a probability of success of 0.105.

In our case, the mean number of people with diabetes in our sample is:

μ = 100 x 0.105 = 10.5

This means that we expect, on average, to find 10.5 people with diabetes in our sample of 100.

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The expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

We can write the Pythagoras theorem as - The sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.

Mathematically -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right triangle ABC

We an write the expression to measure {x} as -

{x - 10} + {2x +40} + 90 = 180

Therefore, the expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

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Answer:

A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figure,divide it into simple, nonoverlapping figures. Find the area of each simplerfigure, and then add the areas together to find the total area of the compositefigure

Step-by-step explanation:bc of the way u gave it im showing it to u

The values of x for which f(x) = g(x) are -1 and 4

From the question, we have the following parameters that can be used in our computation:

f(x) = -2x + 4

g(x) = x^2 - 5x

Using the above as a guide, we have the following:

Using the above as a guide, we have the following:

x = -1 and x = 4

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The Larger number is 8

What is a linear equation in one variable?

The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation.

Given that, the sum of two numbers is 14 and the larger number is four less than twice the smaller number

let the larger number be 'a' and the smaller be 'b'

from the question,

a + b = 14 .....eq 1

a = 2b - 4 .....eq 2

By substituting eq 2 in eq 1:

2b - 4 + b = 14

3b - 4 = 14

3b = 14 + 4 = 18

b = 6

a = 2b - 4 = 2*6 - 4 = 8

Therefore, The two numbers are 8, 4

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Answer:

Step-by-step explanation:

The exchange rate between the South African Rand (ZAR) and the Kenyan Shilling (KES) fluctuates daily. As of my training data cut off in 2021, the exchange rate was approximately 1 ZAR = 10.87 KES.

So, 30 South African Rand would be equivalent to approximately 329.10 Kenyan Shillings. However, it is important to note that exchange rates can change over time, so it is always a good idea to check a reliable source for the most up-to-date conversion rate before making any currency exchanges.

The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%

The weight of two granite specimen = 22 pounds

The weight of the crate = 20 pounds

The weight of shipping crate = 8 pounds

The total weight of the whole shipment = 22+20+8 = 50 pounds.

Therefore the percentage of shipping crate as compared to the total weight;

= 8/50 × 100/1

= 800/50

= 16%

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Answer:

Step-by-step explanation: Sure! Here's a step-by-step solution to find the amount of red icing Ashley needs for one cake:

Divide the total amount of red icing by the number of cakes: 10 1/2 ÷ 3 1/2 = 3.

Simplify the result from step 1: 3 = 3 ounces of red icing per cake.

So Ashley needs 3 ounces of red icing to write a message on one cake.

Answer:

28 cups of Flower

Ratio Table:

2,4,6,8

7,14,21,28

Step-by-step explanation:

2x4/7x4=8/28

The width of the floor if the length is (x - 13) units is (x+13) units.

The area of Rectangle is length times of width.

Given that area of the floor is (x²-169) sq units.

We have to find the width of the floor when  length is (x - 13) units.

Area=Length×Width

x²-169=(x-13)width

We know that (a²-b²)=(a+b)(a-b)

(x-13)(x+13)=x-13width

Divide both sides by (x-13)

x+13=width

Hence, the width of the floor if the length is (x - 13) units is (x+13) units.

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The values of x for the given equations are:

1. The value of x = 0

2. The values of x are ±1

3. The values of x are 0 and -7/16

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

To find the values of x in each of the equations, we need to simplify them using algebraic operations:

1. 8x² = 6x² + 5x²

Combining like terms on the right-hand side:

8x² = 11x²

Subtracting 6x² from both sides:

2x² = 0

Dividing both sides by 2:

x² = 0

Taking the square root of both sides:

x = 0

Therefore, the only solution to this equation is x = 0.

2.Similarly, we can calculate values of x for this equation:

-7x² + 6 = x² - 7x²

x² = 1

Taking the square root of both sides:

x = ±1

Therefore, the solutions to this equation are x = 1 and x = -1.

3. 7x² + 9x² = -6x² - 7x

x(16x + 7) = 0

Using the zero product property:

x = 0 or 16x + 7 = 0

Solving for x in the second equation:

16x = -7

Dividing both sides by 16:

x = -7/16

Therefore, the solutions to this equation are x = 0 and x = -7/16.

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The toy rocket will hit the ground after approximately 3.86 seconds.

The rocket will hit the ground when its height is equal to zero, so we can use the equation h = -4.97t^2 + 38.5t + 5.6 to find the value of t that satisfies this condition. To do this, we set h equal to zero and solve for t:

0 = -4.97t^2 + 38.5t + 5.6

-5.6 = -4.97t^2 + 38.5t

4.97t^2 - 38.5t - 5.6 = 0

This is a quadratic equation and can be solved using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 4.97, b = -38.5, and c = -5.6.

Plugging in these values, we get:

t = (-(-38.5) ± √((-38.5)^2 - 4 * 4.97 * -5.6)) / (2 * 4.97)

t = (38.5 ± √(1466.25 + 113.92)) / 9.94

t = (38.5 ± √1580.17) / 9.94

The square root of 1580.17 is 39.67, so:

t = (38.5 ± 39.67) / 9.94

t = (38.5 + 39.67) / 9.94 or (38.5 - 39.67) / 9.94

The first solution gives us a time of approximately 3.86 seconds, while the second solution is negative and therefore represents an unrealistic result.

The toy rocket will hit the ground after approximately 3.86 seconds.

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Answer:

170 feet per second

Step-by-step explanation:

To answer the question you need to find the unit rate. To find the unit rate divide the denominator with the numerator in a way that the denominator becomes 1.

5,100/30 = 170

The skydiver falls at a rate of 170 feet per second before opening the parachute.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

It takes a skydiver 30 seconds to fall 5,100 feet before opening the parachute.

Hence, Height for this is,

⇒ 5100 / 30

⇒ 170 feet per second

Thus, the skydiver falls at a rate of 170 feet per second before opening the parachute.

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Answer: AE

Step-by-step explanation:

if you look at the picture you can tell that Ae is a ray because rates tend to have 2 points and 2 sides one going on forever. that's why there's an arrow near "a"

The measurement closest to the number of miles between the two towns is 227.5 miles.

A method for finding the answer to linear equations in two variables is cross-multiplication. It turns out to be the quickest way to resolve two linear equations. To cross multiply two fractions, multiply the first fraction's numerator by the second's denominator and the second fraction's numerator by the first fraction's denominator.

Given that, distance between Dallas and Houston is about 364 kilometers.

The measurement of:

8 km = 5 miles

364 km = x miles

Using the method of cross multiplication, we have:

x = 364 (5) / 8

x = 227.5 miles

Hence, the measurement closest to the number of miles between the two towns is 227.5 miles.

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The value of the functions at 9m is

Generally, In mathematics, a function is a rule that maps one set of values (the domain) to another set of values (the range). The values in the range are determined by applying the function to the values in the domain.

Functions can take many forms and be expressed in different ways, including:

Linear functions: a function that produces a straight line when graphed. It has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

Quadratic functions: a function that produces a parabola when graphed. It has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Therefore, this function

- f(x) = 4x

g(x) = 9x¹/2

for

F(x)=4x

F(9)=4*9

f(9)=36

for

g(x) = 9x¹/2

g(9)=9√9

=27

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The sequence is an arithmetic sequence.

A rule for each term is t(n) = 7 - 4(n - 1).

Arithmetic sequence is a sequence of numbers where the numbers are arranged in a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Given sequence is 7, 3, –1, –5, –9, ....

First term = 7

Second term = 7 + -4 = 3

Third term = 7 + (-4 × 2) = -1

....................

Here each term is getting by adding -4 to the preceding term.

So -4 is the common difference.

nth term of the sequence is t(n) = 7 - 4(n - 1).

Hence the sequence is arithmetic sequence and any term of the sequence is t(n) = 7 - 4(n - 1).

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Answer: To find the father's and son's ages, we can set up two simultaneous equations:

Let's say the son's age is "x"

Then, the father's age would be x + 25

And the sum of their ages is x + (x + 25) = 53

So, 2x + 25 = 53

Solving for x, we get:

2x = 28

x = 14

Therefore, the son is 14 years old, and the father is 14 + 25 = 39 years old.

To use the elimination method, we can add the two equations:

x + (x + 25) = 53

2x + 25 = 53

Simplifying, we get:

2x = 28

x = 14

And the father's age would be x + 25 = 14 + 25 = 39 years old.

Step-by-step explanation:

Answer:

Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]

Step-by-step explanation:

Let square side = [tex]a[/tex]

Area of square   [tex]A = a^2[/tex]

Given [tex]A = 81[/tex]  and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]

[tex]a = \sqrt{81} = 9\;in[/tex]

Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]

If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width

Perimeter P of rectangle = [tex]2(l + w)\\[/tex]

Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]

Given

[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]

[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]

If so far the George's string is 44 inches long , then his string is not long enough , so he need to make it longer .

To find whether George's string is long enough, we first convert both measurements to same unit of measurement.

that means we convert length of the string in inches to feet by dividing it by 12 ; because  there are 12 inches in a feet  ;

⇒ (44 inches)/(12 inches/feet)  

⇒ 3.67 feet  ;

The George's string is currently 3.67 feet long and he needs a string that is 4 feet long  .

So , his current string is not long enough and he needs to make it longer. He needs to add another 0.33 feet to his string  .

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The given question is incomplete , the complete question i

George needs a string that is 4 feet long. So far his string is 44 inches. Is it long enough or does he need to make it longer ?