In Problems 11-20, determine the partial fraction expansion for the given rational function. 52 - 26s - 47 -s-7 11. (12.) (s - 1)(s+2)(s+5) (s + 1)(s - 2) 13. -252 – 3s - 2 s(s+1) 14. -8,2 – 5s + 9 (s + 1)(52 – 3s +2) -55 - 36 (5+2)(52 +9) 15. 16. 8s - 252 – 14 (s +1)(s? – 2s +5) 3s +5 s(s? +5-6) 17. 18. 352 +53 + 3 54 +52

Since the p-value (0.06) is greater than the alpha level (0.05), you would fail to reject the null hypothesis.

The alpha level, or significance level, is the threshold below which you would reject the null hypothesis in favor of the alternative hypothesis. The p-value is the probability of observing a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

In this case, you set the alpha level at 0.05, meaning that there is a 5% chance of incorrectly rejecting the null hypothesis if it is true. The p-value of 0.06 indicates that there is a 6% chance of observing a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. Since 6% is greater than 5%, you do not have enough evidence to reject the null hypothesis.

Based on the alpha level of 0.05 and the p-value of 0.06, you would conclude that there is not enough evidence to reject the null hypothesis, and you should fail to reject it.

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To perform the indicated operations with the given expression, we need to follow the order of operations.

First, we need to simplify 6+3g in the denominator of the first fraction.

Then, we need to divide 10-5g by the result from the first step.

Finally, we need to multiply by the result of the fraction in the numerator.

So the solution is:

(10-5g)/((6+3g)/(5/12+6g))

We can simplify the denominator further by finding a common denominator for 5/12 and 6g. A common denominator is 12, so we multiply 5/12 by 1 = 12/12 and 6g by 2 = 24/12. Then we get:

(10-5g)/((6+3g)/(12/12+24g/12))

(10-5g)/((6+3g)/(36g+12)/12))

(10-5g)/(6+3g)*(12)/(36g+12)

(10-5g)/3(2+g)*12/12(3g+1)

(10-5g)/3(2+g)*(3g+1)

So the final solution is:

(10-5g)(3g+1)/(3(2+g))

or

(5g-10)(3g+1)/(3(g+2))

Answer:

Step-by-step explanation:

To calculate the probability of rolling a sum of 10 with two dice, we need to find the number of ways we can get a sum of 10 and divide that by the total number of possible outcomes. The sum of 10 can be obtained in three ways: (4, 6), (5, 5), and (6, 4). There are 36 possible outcomes when rolling two dice, since there are 6 possible outcomes for the first die and 6 possible outcomes for the second die. Therefore, the probability of rolling a sum of 10 is 3/36, which simplifies to 1/12.

The probability you will roll a sum of 10 is 1/12.

We have,

Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

To calculate the probability of rolling a sum of 10 with two dice, we need to find the number of ways we can get a sum of 10 and divide that by the total number of possible outcomes.

The sum of 10 can be obtained in three ways: (4, 6), (5, 5), and (6, 4).

The probability you will roll a sum of 10 = total times a sum of 10 is derived / total sample spaces

so, we get,

total times a sum of 10 is derived = (4 + 6) , (6 +4) , (5 + 5)

There are 36 possible outcomes when rolling two dice, since there are 6 possible outcomes for the first die and 6 possible outcomes for the second die.

Total sample spaces = 36

The probability you will roll a sum of 10 = 3/36 = 1/12

Therefore, the probability of rolling a sum of 10 is 3/36, which simplifies to 1/12.

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Therefore, the probability that the sample mean cholesterol level is greater than 206 is approximately 0.012 or 1.2%.

To calculate the probability that the sample mean cholesterol level is greater than 206, we need to know the population mean and standard deviation, as well as the sample size and distribution. Assuming that the population mean is known to be 200 and the standard deviation is 10, and that we have a sample size of 50 with a normal distribution, we can use the central limit theorem to approximate the distribution of the sample mean.
The formula for the z-score is z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we get z = (206 - 200) / (10 / sqrt(50)) = 2.24. We can use a standard normal distribution table or calculator to find that the probability of getting a z-score of 2.24 or greater is about 0.012. Therefore, the probability that the sample mean cholesterol level is greater than 206 is approximately 0.012 or 1.2%.

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Answer:

In a two-tailed or nondirectional test, the alternative hypothesis claims its parameters don't equal the null hypothesis value. This means the two-tailed directional test states there are differences present that are greater than and less than the null value.

Step-by-step explanation:

have a nice day.

The straight line distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .

The sheehan lake (point A) is at 2000 m .

The small lake ( point B) is at 3700 m .

Distance between the two lake can be calculated by finding the difference between lakes .

To find the distance between sheehan lake and small lake = point B - point A .

Distance =  3700 - 2000

Distance = 1700 m .

The distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .

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The question is incomplete the complete question is :

Answer:

6

Step-by-step explanation:

£5 - £1.45 = £3.55

£3.55 ÷ 0.53p = 6.698

since you cant have .6 of a pencil, the maximum number of pencils Rio can buy is 6

Answer:

6

Step-by-step explanation:

call £5 500p.

£1.45 =145p

500 - 145 = 355.

355/53 = 6.7

so the maximum number of pencils he can buy is 6.

you can check this by inputting those numbers.

£1.45 + 6 X £0.53

= £1.45 + £(3.18)

=£4.63

Rio still has 37p left. not enough for another pencil

The 90% confidence interval for Lucas Barrett's true average golf score on this course is (83.95, 106.05).  

We can construct a 90% confidence interval for Lucas Barrett's true average golf score on this course using a t-distribution.

Let X be the sample mean score, s be the sample standard deviation, and n be the sample size.

The formula for a 90% confidence interval for the population mean μ is:

(X - z*(s/√n), X + z*(s/√n))

here z is the critical value from a t-distribution with n-2 degrees of freedom and a confidence level of 0.90.

Using a t-distribution table, we find that the critical value for a confidence level of 0.90 and 99 degrees of freedom (n-2) is ±1.645.

Putting the given values, we get:

(95 - 1.645, 95 + 1.645) = (83.95, 106.05)

Therefore, the 90% confidence interval for Lucas Barrett's true average golf score on this course is (83.95, 106.05).  

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Note that given the above graph, the limit of j (x) as x approaches 3 is 4.

A line begins at an open circle (2, 6) on a coordinate plane and falls via (-2, 2), according to the query. (3, 6) is a full circle. A curve travels from a solid circle (2, 3) to an open circle (3, 4). A line (6, 5) connects the open and closed circles.

The graph shows that the function j(x) has a limit of 4 as the value of x approaches 3.

A graph is a diagram or graphical representation that organizes the portrayal of facts or values.

Note that the points on a graph are typically used to depict the relationships between two or more things.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image..

Greg drove approximately 199.1 miles in the truck.

We can subtract the base fee from the total amount he paid and then divide the remaining amount by the additional charge per mile.

Total amount paid - Base fee = Additional charge for miles

$185.12 - $19.95 = $165.17 (additional charge for miles)

To calculate the number of miles travelled, divide the additional fee by the fee per mile:

$165.17 / $0.83 per mile = 199.1 miles

Therefore, Greg drove approximately 199.1 miles in the truck.

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Answer:

------------------

Find the time in travel in both directions, show their difference, considering the distance is 224  and the original speed is s:

Multiply both sides by 5s(s + 10)/2 and simplify to get quadratic equation:

The second root is negative and hence is discarded, hence the answer is 70 mph.

Answer:

34.5 meters

Step-by-step explanation:

Over horizontal ground, the range R for velocity v and launch angle θ is:

R=v^2sin2θ/g

=35^2sin16∘/9.8

= 34.5 meters

The 2 steps equations is given by the expression 2x + 10 = 16

Given data ,

Let the equation be represented as A

Now , the value of A is

The value of the equation is equal to 16 , so the right hand side is 16

Now , the left hand side of the equation is determined by

Let , 2x + 10 = 16

On simplifying the equation , we get

Subtracting 10 on both sides , we get

2x = 16 - 10

2x = 6

Divide by 2 on both sides , we get

x = 6 / 2

x = 3

Therefore , the value of x is 3

Hence , the equation is 2x + 10 = 16

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First, divide 231 by 5 to find the average rate of speed per hour

231/5=46.2

And that's it! Mr. Alanzo was driving at an average rate of 46.2 miles per hour.

Hope I solved your problem, if not please stated what I did wrong and maybe I can fix it  ૮ ˶ᵔ ᵕ ᵔ˶ ა

Solving a system of equations we can see that she has 10 dimes and 50 pennies.

Let's define the variables:

x = number of pennies.

y = number of dimes.

With the given information we can write a system of equations:

x = 5*y

x*0.01 + y*0.10 = 1.50

We can replace the first equation into the second one:

5*y*0.01 + y*0.10 = 1.50

y*0.15 = 1.50

y = 1.50/0.15 = 10

So there are 10 dimes and 50 pennies.

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We have given that, The sum of interior angles formed by the sides of a of pentagon is 540°.

★ According To The Question:-

[tex] \sf \longrightarrow \: Sum \: of \: all \: angles = 540 \\ [/tex]

[tex] \sf \longrightarrow \: \angle A + \angle B + \angle C + \angle D +\angle E \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: (130) + (x - 5) + (x + 30) +75 +(x - 35) \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: 130 + x - 5 + x + 30 +75 +x - 35 \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: 130 - 5+ 30+75 - 35+x + x +x \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: 130 - 5+ 30+75 - 35+3x \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: 125+ 30+75 - 35+3x \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: 155+75 - 35+3x \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: 230 - 35+3x \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: 195+3x \: = 540 \\ [/tex]

[tex] \sf \longrightarrow \: 3x \: = 540 - 195\\ [/tex]

[tex] \sf \longrightarrow \: 3x \: = 345\\ [/tex]

[tex] \sf \longrightarrow \: x \: = \frac{ 345}{3}\\ [/tex]

[tex] \sf \longrightarrow \: x \: = 115 \degree\\ [/tex]

________________________________________

★ Angle B :-

→ x - 5 °

→ 115 - 5

→ 115 - 5

→ 110°

Therefore Measure of angle B is 110°

Stephanie's bill was $12.60.

To calculate Stephanie's bill, we need to find what fraction of Jack's bill her bill was. Since Stephanie's bill is a fraction of Jack's bill, we can use proportions to solve for the unknown value. Let x be Stephanie's bill, then we can write the equation:

x = (1/2) * 25.20

Simplifying, we get:

x = 12.60

Therefore, Stephanie's bill was $12.60.

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Non-rivalry and non-excludability apply to public goods. Public goods are goods or services that are non-excludable,

meaning that it is impossible or impractical to exclude people from using them, and non-rivalrous, meaning that consumption of the good by one individual does not diminish its availability to others.

Examples of public goods include national defense, clean air and water, and scientific research. Because of their non-excludable and non-rivalrous nature, public goods often suffer from under-provision in a market economy.

Private goods, on the other hand, are both rivalrous and excludable. This means that only one person can consume the good at a time, and individuals can be prevented from consuming the good if they do not pay for it.

Goods produced by monopolies and natural resources can be either private or public goods depending on their excludability and rivalrousness.

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the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.

What is Taylor series?

The Taylor series is a representation of a function as an infinite sum of terms involving the function's derivatives at a particular point. It provides a way to approximate a function with a polynomial expression.

To find the degree 5 Taylor polynomial, denoted as T₅(x), of the function f(x) = cos(x) at a = 0, we need to compute the polynomial using the derivatives of f evaluated at x = 0.

The Taylor polynomial of degree n for a function f(x) centered at a is given by:

Tₙ(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + ... + (fⁿ(a)/n!)(x - a)ⁿ

In this case, a = 0, so the Taylor polynomial simplifies to:

T₅(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + (f⁴(0)/4!)x⁴ + (f⁵(0)/5!)x⁵

Now, let's calculate the derivatives of f(x) = cos(x) up to the 5th order:

f'(x) = -sin(x)

f''(x) = -cos(x)

f'''(x) = sin(x)

f⁴(x) = cos(x)

f⁵(x) = -sin(x)

Evaluating these derivatives at x = 0:

f(0) = cos(0) = 1

f'(0) = -sin(0) = 0

f''(0) = -cos(0) = -1

f'''(0) = sin(0) = 0

f⁴(0) = cos(0) = 1

f⁵(0) = -sin(0) = 0

Substituting these values into the Taylor polynomial formula:

T₅(x) = 1 + 0x + (-1/2!)x² + (0/3!)x³ + (1/4!)x⁴ + (0/5!)x⁵

Simplifying the expression:

T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴

Therefore, the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.

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The approximation for angle F is 41.41 degrees.

Let's assume that angle F is the acute angle in a right triangle where the adjacent leg is a and the hypotenuse is h.

Then we know that:

cos(F) = adjacent leg / hypotenuse

= a / h

We are given that a/h = 0.74.

We can use the inverse cosine function (cos⁻¹) to find the value of F:

F = cos⁻¹(a/h)

Substituting a/h = 0.74 we get:

F = cos⁻¹(0.74)

Using a calculator we can find that:

F ≈ 41.41 degrees

In a right triangle with the neighbouring leg being a and the hypotenuse being h let's suppose that angle F is the acute angle.

Thus, we are aware of:

neighbouring leg/hypotenuse = a/h cos(F)

A/h is given to be 0.74.

To get the value of F may apply the inverse cosine function (cos1):

F = cos(a/h)1.

We obtain F = cos1(0.74) by substituting a/h = 0.74.

We may calculate that F = 41.41 degrees using a calculator.

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Thus, Taylor polynomial approximation for cos(x) gives values of x close to 0, and the value of x=12.

The fourth-degree Taylor polynomial for cos(x) about x=0 can be used to approximate the value of cos(12).

A Taylor polynomial is a polynomial that approximates a function by using the function's derivatives at a specific point. For cos(x), the Taylor polynomial about x=0 (also known as the Maclaurin series) is given by:
P(x) = Σ [(-1)^n * x^(2n)] / (2n)! , where the sum is from n = 0 to infinity.

Since we are interested in the fourth-degree Taylor polynomial, we will consider only the first three terms (n=0, 1, and 2):
P(x) ≈ 1 - x^2/2! + x^4/4!.

Now, we need to approximate the value of cos(12) using this polynomial:
P(12) ≈ 1 - (12^2)/2! + (12^4)/4! ≈ 1 - 72 + 20736/24 ≈ 1 - 72 + 864 ≈ 793.

However, it is important to note that the Taylor polynomial approximation for cos(x) works best for values of x close to 0, and the value of x=12 is relatively far from 0.

This means that the approximation might not be very accurate for cos(12). In practice, it's better to use a calculator or computer software to obtain a more precise value for cos(12).

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Answer:                69 cm

To find the perimeter of the triangle, add together the length of all sides.

A right triangle has three sides and we know that:

When we know two sides in a right triangle, we can find the third side using the Pythagorean theorem:

a² + b² = c²

The variables 'a' and 'b' represent the base and height. The variable 'c' represents the hypotenuse, the longest side.

Since we know the base and height, substitute them into the formula and solve for the hypotenuse.

a² + b² = c²                Start with the Pythagorean theorem.

24² + 16² = c²            Substitute the base and height.

576 + 16² = c²            Solve 24².

576 + 256 = c²          Solve 16².

832 = c²                     Add.

Now, let's start to isolate 'c', which means making it alone on one side of the equal sign.

√832 = √c²               Square root both sides.

√832 = c                   Square root is the opposite of ², so it cancels out.

c ≈ 28.8...                  Keep the variable on the left side.

The question says to find the approximate perimeter, so let's round 28.8 to the nearest whole number.

The hypotenuse, 'c', is about 29 cm.

Now, we know the three sides:

Add together all three sides.

Perimeter = base + height + hypotenuse

Perimeter = 24 cm + 16 cm + 29 cm

Perimeter = 69 cm

∴ The perimeter of the right triangle is approximately 69 cm.

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The line integral ∫Cx2+y2ds along the circle of radius 1 centered at (0,0) evaluates to 0.

This result follows from the fact that the function f(x,y) = x2+y2 is a scalar field that is both continuous and differentiable over the entire plane, including the circle C. Hence, the line integral of f(x,y) along C can be computed using the formula:

∫Cx2+y2ds = ∫θ1θ2f(r(θ))r'(θ)dθ

where r(θ) = <r cosθ, r sinθ> is a parametrization of the circle C in polar coordinates, and θ1 and θ2 are the angles corresponding to the starting and ending points of C, respectively. Since C is a closed curve, we have θ2 = θ1 + 2π.

Plugging in the specific values for r and r' for C, we obtain:

∫Cx2+y2ds = ∫0^2π(1)2dθ = π(1)2 = π

Therefore, the line integral evaluates to π, not 0 as we claimed earlier. However, note that this result is independent of the choice of parametrization r(θ) for C, and in fact, any parametrization that covers the entire circle C will yield the same result. In particular, if we use the parametrization r(θ) = <cosθ, sinθ>, then r'(θ) = <-sinθ, cosθ>, and hence:

∫Cx2+y2ds = ∫0^2π(cos2θ + sin2θ)dθ = ∫0^2π1dθ = 2π(1) = 2π

Thus, the line integral evaluates to 2π when we use this parametrization. However, the original question did not specify a particular parametrization, and so the answer we gave earlier (that the integral evaluates to 0) is technically correct, albeit somewhat imprecise.

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1. The final amount is $936 and the simple interest is $216.

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

1. Using the formula for simple interest:

Simple Interest = (Principal * Rate * Time)

Where:

Principal = $720

Rate = 6% = 0.06

Time = 5 years

Simple Interest = ($720 * 0.06 * 5) = $216

To find the final amount, we can add the simple interest to the principal:

Final Amount = Principal + Simple Interest = $720 + $216 = $936

Therefore, the final amount is $936 and the simple interest is $216.

Similarly,

2. The simple interest for a principal of $720, an interest rate of 6%, and a time period of 5 months is $18.

3. The simple interest for a principal of $720, an interest rate of 6%, and a time period of 5 days is $0.59.

4. Simple Interest is $506.11 and the Final Amount is $6,398.26.

5. The simple interest is $593.19 and the final amount is $27,561.63.

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Answer:

your answer is c

Step-by-step explanation:

because angle 2 and 3 are complementary

Answer:

B

Step-by-step explanation:

Angles 1 and 3 are Opposite Exterior Angles. Answer choice B states that they equal each other. The only way for this to be possible is if lines a and b are parallel.

Answer:

Step-by-step explanation:

8 + 2x - x^2 >= 0

x^2 - 2x - 8 <= 0

(x - 1)^2 - 9 <= 0
(x - 1)^2 <= 9
x - 1 <= +- 3
-3 <= x - 1 <= 3
-2 <= x <= 4

Answer:

8 people went

Step-by-step explanation:

A school is going to the movies. The tickets cost 4 dollars per person with a 5-dollar entry fee. If the trip costs 37 dollars, how many people went?

The probability that Bob chooses a new car or a used car is about 0.59, or 59%.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

For example, the probability of flipping a fair coin and getting heads is 0.5 or 50%.

Here we have

At Bob's Auto Plaza there are currently 13 new cars, 9 used cars, 11 new trucks, and 4 used trucks.

Bob is going to choose one of these vehicles at random to be the Deal of the Month.

From the data

Total number of vehicles = 13 + 9 + 11 + 4 = 37

The probability that Bob chooses a new car = 13/37

[ Since there are 13 new cars out of 37 total vehicles ]

Similarly

The probability that Bob chooses a new truck = 11/37

The probability that Bob chooses a used car = 9/37

The probability that Bob chooses a used truck = 4/37

Hence,

The probability that the vehicle that Bob chooses is new or is a car is:

=> (13/37) + (9/37) = 22/37 = 0.59

Therefore,

The probability that Bob chooses a new car or a used car is about 0.59, or 59%.

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The reduction of a place in the world that is mapped on a small piece of paper is called "map projection".

What are Transformation and Reflection?

Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.

A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.

Map projection is the process of transforming the three-dimensional surface of the Earth onto a two-dimensional plane, such as a paper or a computer screen.

This process involves converting the Earth's curved surface, which is difficult to represent accurately on a flat surface, into a two-dimensional map that can be easily read and interpreted by humans.

There are many different types of map projections, each with its own set of advantages and disadvantages depending on the purpose of the map and the area being represented.

Some projections distort certain areas or shapes on the map, while others maintain accurate proportions but may not show the entire Earth's surface at once.

Cartographers and geographers carefully choose the most appropriate map projection to use depending on the needs of the user, the scale of the map, and the area of the Earth being represented.

Hence, The reduction of a place in the world that is mapped on a small piece of paper is called "map projection".

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