In each part, find exact values for the first four partial sums, find a closed form for the nth partial sum, and determine whether the series converges by calculating the limit of the nth partial sum. If the series converges, then state its sum. 3 - 14 Determine whether the series converges, and if so find its sum.

Answer:

C. V15

Step-by-step explanation:

Each step we go back a letter in the alphabet and up 3 numbers.

Hope this helps! :)

Answer:

C. V15

Step-by-step explanation:

I got the answer correct.

==========================================================

Work Shown:

x = Ali's share

4x = Pip's share, because it is four times bigger due to the ratio 4:1

x+4x = 5x = total amount of money = 785

5x = 785

x = 785/5

x = 157 dollars is Ali's share

4x = 4*157 = 628 dollars is Pip's share

Note that 157+628 = 785 to help confirm the answer.

To solve the integral of 1/sqrt(x^2 - a^2) dx, we can use the substitution method. Let u = x^2 - a^2, then du/dx = 2x, and dx = du/2x.
Substituting into the integral, we get:

∫ 1/sqrt(x^2 - a^2) dx = ∫ 1/sqrt(u) * du/2x
= (1/2) ∫ 1/sqrt(u) du  

= (1/2) * 2sqrt(u) + C
= sqrt(x^2 - a^2) + C

Therefore, the answer to the integral of 1/sqrt(x^2 - a^2) dx is sqrt(x^2 - a^2) + C, where C is the constant of integration.

In summary, the integral of 1/sqrt(x^2 - a^2) dx can be solved using the substitution method, where u = x^2 - a^2. The final answer is sqrt(x^2 - a^2) + C, where C is the constant of integration.

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The integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

What is intergration?

Integration is a fundamental concept in calculus that involves finding the antiderivative or integral of a function. It is the reverse process of differentiation, which is concerned with finding the derivative of a function.

To find the integral of \(1/\sqrt(x^2 - a^2) dx\), we can use a trigonometric substitution. Let's substitute \(x = a sec(\theta)\), where \(sec(\theta)\) is the reciprocal of the cosine function.

By making this substitution, we can express dx in terms of \(d(\theta)\) as follows:

\(dx = a sec(\theta) tan(\theta) d(\theta)\)

Now, let's substitute these values into the integral:

\(\int \frac{1}{\sqrt{x^2 - a^2}} dx\\\\= \int \frac{1}{\sqrt{(a \sec(theta))^2 - a^2}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\sec^2(theta) - 1)}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\tan^2(theta))}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{a \tan(theta)} (a \sec(\theta) \tan(\theta)) d(\theta)\)

Simplifying the expression, we have:

\(= \int \sec(\theta) d(\theta)\)

The integral of \(sec(\theta)\) can be evaluated as the natural logarithm of the absolute value of \(sec(\theta)\) plus the tangent\((\theta)\):

\(= \ln|\sec(\theta) + \tan(\theta)| + C\)

Finally, substituting back \(x = a sec(\theta)\), we get:

\(= \ln|\sec(\theta) + \tan(\theta)| + C\\\\= \ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\)

Therefore, the integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

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The teacher asks her students to bring all the plasticine they have a total of 19 4/9 plasticine jars.

we can convert all the mixed numbers to improper fractions:

Daniela: 8 5/9 = 77/9

Antonio: 3 4/9 = 31/9

Francisco: 1 2/9 = 11/9

Mariana: 5 7/9 = 56/9

Now we can add them up:

77/9 + 31/9 + 11/9 + 56/9 = 175/9

So the total amount of plasticine is 175/9 jars. We can simplify this fraction to a mixed number if desired:

175/9 = 19 4/9

An improper fraction is a type of fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). It is called "improper" because it does not represent a proper or mixed number.

For example, 7/4 is an improper fraction because the numerator (7) is greater than the denominator (4). This can also be written as a mixed number, 1 3/4, where the whole number is the result of dividing 7 by 4 and the remainder (3) is placed over the denominator.

Improper fractions can be converted to mixed numbers, and vice versa, by dividing the numerator by the denominator to get the whole number, and using the remainder as the numerator of the fraction. For example, to convert 11/3 to a mixed number, divide 11 by 3 to get 3 with a remainder of 2, so the mixed number is 3 2/3.

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Complete Question:

For the art class, the teacher asks her students to bring all the plasticine they can.  Daniela has 8 5/9 plasticine jars, Antonio 3 4/9, Francisco 1 2/9 and Mariana 5 7/9

Answer:

Answer:

= 1.044

Step-by-step explanation:

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

Answer:

0.36 x 2.9 = 1.044

Step-by-step explanation:

The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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Answer:

-k

Step-by-step explanation:

Cos(140)=cos(180-40)=-cos(40)=-k

Answer:

Step-by-step explanation:

Sin (90 - A)  = Cos A

Cos (90 + A) =   -Sin A

Sin 50 = Sin (90 - 40)

          = Cos 40

         = k

Cos 140 = Cos (90 + 50)

             = - Sin 50

            = (- k)

The correct order is to first calculate the actual distance, then determine the number of standard errors, and finally assess the percentage probability or p-value.

The correct order with regard to a claim about a population mean is d. actual distance, number of standard errors, percentage probability.

The first step in assessing a claim about a population mean is to determine the actual distance between the sample mean and the claimed population mean. This involves calculating the difference between the sample mean and the claimed population mean.

The second step is to determine the number of standard errors. This is done by dividing the actual distance by the standard error, which measures the variability of the sample mean.

Finally, the percentage probability is assessed. This involves determining the probability of obtaining a sample mean as extreme as or more extreme than the observed sample mean, assuming the null hypothesis is true. This probability is often referred to as the p-value.

In summary, the correct order is to first calculate the actual distance, then determine the number of standard errors, and finally assess the percentage probability or p-value.

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a) The volume of the composite figure is represented by the cubic equation V = x³ + 16 · x.

b) The measure of the missing side x in the composite figure is 3 inches.

a) In the first part of the question we need to derive the volume formula of the composite figure, which is the sum of the volumes of the cube and the rectangular prism:

V = V' + V''

V = x³ + 16 · x, where x is in inches.

The volume is represented by V = x³ + 16 · x.

b) If we know that V = 25 · x, then the measure of the missing side is:

First, set the volume formula found in section a):

V = x³ + 16 · x

Second, replace the volume:

25 · x = x³ + 16 · x

Third, simplify the expression and clear x within the resulting equation by algebra properties:

25 = x² + 16

x² - 9 = 0

x² = 9

x = 3

The measure of the missing side x is 3 inches.

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Triangle ABC is similar to triangle CDE by the Angle-Side-Angle congruence theorem.

The Angle-Side-Angle (ASA) congruence theorem states that if any of the two angles on a triangle are the same, along with the side between them, then the two triangles are congruent.

For this problem, the triangles were reflected over vertex C, hence:

Additionally, the side length between these two angles is equal, hence the ASA theorem is used to prove the similarity of the two triangles.

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Answer:

x = 5 cm.

Step-by-step explanation:

Since this is a right triangle, we can just use Pythagorean Theorem to find the hypotenuse:

a² + b² = c²

3² + 4² = x²

9 + 16 = x²

25 = x²

5 = x

Therefore, x is 5 cm.

Answer:

Step-by-step explanation:

solution is w = 6.6

The forces in each member of the truss are as follows: a) F_AB = 0 N (compression) b) F_BC = F_CD = 150 N (tension) c)F_BD = 150 N (tension)

Free Body Diagram (FBD)

We start by drawing the FBD of the truss. We need to identify the external forces acting on the truss and label the reactions at the supports.

```

            A               E

            |               |

            |               |

     ----300 N----300 N----

            |               |

            B               C

```

Equilibrium Equations

Next, we apply the equilibrium equations to determine the forces in each member.

Vertical Equilibrium:

At joint B:

-ΣFy = 0

300 N - F_BC - F_BD = 0

F_BC + F_BD = 300 N          (Equation 1)

Horizontal Equilibrium:

At joint B:

-ΣFx = 0

-F_AB - F_BD + F_BC = 0

F_AB + F_BD - F_BC = 0      (Equation 2)

At joint C:

-ΣFx = 0

-F_BC + F_CD = 0

F_BC = F_CD                  (Equation 3)

Solving Equations

We have three equations (Equations 1, 2, and 3) with three unknowns (F_AB, F_BC, and F_BD). Solving these equations will give us the forces in each member.

From Equation 3, we can see that F_BC = F_CD. Let's denote F_BC = F_CD = F.

Substituting F_BC = F_CD = F in Equations 1 and 2:

Equation 1: F + F_BD = 300 N

Equation 2: F_AB + F_BD - F = 0

Combining both equations, we have:

F_AB = 2F - 300 N

Calculation

Substituting F_AB = 2F - 300 N in Equation 2:

2F - 300 N + F_BD - F = 0

3F - F_BD = 300 N

F_BD = 3F - 300 N

Substituting F_BD = 3F - 300 N in Equation 1:

F + (3F - 300 N) = 300 N

4F = 600 N

F = 150 N

Therefore, F_AB = 2F - 300 N = 2(150 N) - 300 N = 0 N (compression)

F_BC = F_CD = F = 150 N (tension)

F_BD = 3F - 300 N = 3(150 N) - 300 N = 150 N (tension)

Hence, the forces in each member of the truss are as follows:

F_AB = 0 N (compression)

F_BC = F_CD = 150 N (tension)

F_BD = 150 N (tension)

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Answer: No, the triangles are not similar. They aren't even triangles.

Step-by-step explanation: A is a diamond, which cannot be considered a triangle until it is split in half. 8 and 9 would be a triangle if the diamond wouldn't have been there. B and C is a parallelogram.

(C) Intriguing best accomplishes this goal.

A choice that best accomplishes this goal is:

Therefore, (C) intriguing best accomplishes this goal.

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There is sufficient evidence to conclude that the average Calculus exam score is higher than 72%.

Hence, option (2) is correct.

As per the given data,

we have to select the correct answer for  the correct conclusion for this hypothesis test.

According to the stated question,

we have to  choose the correct conclusion for this hypothesis test from the options given below:

Now, according to the above given information:

P value <a,

Therefore, reject the null hypothesis.

Also,

\(H_{0}\) :μ = 72

and

\(H_{a} :\) μ >72

Thus, we can say that there is sufficient evidence to conclude that the average Calculus exam score is higher than 72%.

Hence, option (2) is correct.

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Answer: 10

The arc length of the semicircle is

a+(a+1)+(a+2)+(a+3)+(a+4)=5a+10

As x = 42, this means a+4 is 42/180 of the arc length of the circle, 5a+10.

So,

(42/180)(5a+10)=a+4

42(5a+10)=180(a+4) [multiply both sides by 180]

210a+420=180a+720 [distributive property]

30a+420=720 [subtract 180a from both sides]

30a=300 [subtract 420 from both sides]

a=10 [divide both sides by 30]

The number 3600 at the end of solving the problem represents the final result.

In order to understand where the number 3600 came from at the end of solving the problem, we need to examine the steps taken during the solution process.

Let's assume we were solving a mathematical problem and arrived at the equation 120 + 3600 = 3720. The equation implies that by adding 120 and 3600 together, we obtain the sum of 3720. However, in this context, we are specifically interested in the origin of the number 3600.

To determine where this number came from, we would need to review the specific calculations or operations conducted before arriving at the final equation.

It could be the result of performing a series of mathematical operations such as multiplication, division, or exponentiation. The detailed calculations leading up to the addition of 120 and 3600 would provide the necessary context to understand the origin of the number 3600.

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Answer: The arrow is pointing to 76.5.

Step-by-step explanation: It's pointing to 76.5 because there are 10 spaces between 75 and 80 so in that case, each line is .5, and since it's on the third line that means it is 1.5 more than 75 so 76.5.

Answer:

C) The arrow points to 76.5.

Step-by-step explanation:

The number line is divided into 10 parts equally.

We can find out the distance between each point by taking the difference between the largest and smallest number on the number line and dividing the difference by 10.

80 - 75 = 5

5/10 = .5

So, the distance between each number/mark on the line is .5

Now, we can label each point by adding .5 to each mark as we go. Then, we'd get this.

*see attachment below

Since the number line constructed here has all the values, we can now tell which value the arrow is pointing to.

The answer is therefore 76.5.

Answer:

b)  \(4x^2-12x+9=0\)

Step-by-step explanation:

We can use the discriminant \(b^2-4ac\) to determine how many real solutions a quadratic equation in the form \(ax^2+bx+c=0\) has.

\(5x^2+9x-4=0\)

\(b^2-4ac=9^2-4(5)(-4)=161 > 0\implies \textsf{2 solutions}\)

\(4x^2-12x+9=0\)

\(b^2-4ac=(-12)^2-4(4)(9)=0 \implies \textsf{1 solution}\)

\(-9x^2+6x+1=0\)

\(b^2-4ac=6^2-4(-9)(1)=72 > 0 \implies \textsf{2 solutions}\)

\(-2x^2-7=0\)

\(b^2-4ac=0^2-4(-2)(-7)=-56 < 0 \implies \textsf{no solutions}\)

If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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Step-by-step explanation:

7y = 7

y = 1

2(1) + 4x = 14

4x = 12

x = 3

Answer:

2x-1=3×+8

Step-by-step explanation:

2×-3x=8+1

-x=9

x=-9

Answer:

  50 lb

Step-by-step explanation:

Before drying, the cranberries have ...

  (100% -99%)(100 lb) = 1 lb

of "meat."

After drying, that represents (100% -98%) = 2% of the total weight. Then the total weight is ...

  1 lb = 2%·x

  x = (1 lb)/0.02 = 50 lb

The dried cranberries will weigh 50 lb.

The equation of a line is y=mx+b

m is the slope

b is the y intercept

Looking at the graph, the y intercept is 10 because the line crosses the y-axis at 10

Since they said the slope is 10, the equation of the line is:

y=10x+10

Answer: 153.94

Step-by-step explanation: Formula for area of a circle: pi * r^2

First find the radius by dividing the diameter by 2: 14/2 = 7

Then plug the radius, 7, and pi, 3.14, into the formula:

(3.14) * (7^2) = 153.94 inches squared

Answer:

A- 7 is the answer

Step-by-step explanation:

Sanyo  option (b) would be chosen using the elimination-by-aspects decision rule.

In the elimination-by-aspects decision rule, you compare the options based on specific aspects and eliminate those that do not meet a certain cutoff point for each aspect.

Here's how the comparison unfolds based on the given information:

1. Performance: The cutoff point is ranked 1. Sanyo and Sony meet the cutoff, but Pioneer does not.

  Eliminated: Pioneer

2. Price: The cutoff point is ranked 4. Sanyo and Pioneer meet the cutoff, but Sony does not.

  Eliminated: Sony

3. Quality: The cutoff point is ranked 4. All three options (Sanyo, Sony, Pioneer) meet the cutoff.

4. Style: The cutoff point is ranked 3. Sanyo meets the cutoff, but Sony and Pioneer do not.

  Eliminated: Sony and Pioneer

Based on the elimination process, the remaining option is Sanyo. Therefore, (b) Sanyo would be chosen using the elimination-by-aspects decision rule.

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Answer:

12 = -15

Step-by-step explanation:

Remember PEMDAS

Parenthesis

Exponents

Multiplication and Division (Left to Right)

Addition and Subtraction (Left to right)

4+ [8 = (8 - 7) + 6 - 12] - 10

4+ [8 = (8 - 7) + 6 - 12] - 10

4+ [8 = 1 + 6 - 12] - 10

4+ [8 = 1 + 6 - 12] - 10

4+ [8 = -5] - 10

4 + 8 = -5 - 10

4 + 8 = -15

12 = -15

Hope this helped!

x+1 - x-8

x-1. x-l

x+1 - x-8

x-1

x-x-8+1

x-1

= -7

x-1

the answer is -7

x-1