Determine whether the series is convergent or divergent by expressing the nth partial sum sn as a telescoping sum. If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) 2 n2 -

In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.

The number VCX is incorrect in Roman Numerals because V (5) cannot be subtracted from X (10) to make 5, and C (100) cannot be subtracted from X (10) to make 90.

In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.

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Noah's estimate of 7.5 hours is closest to the actual mean number of hours of sleep reported by the ten sixth-grade students.

We have,

Compare the estimates given by Lin, Noah, and Diego.

Lin's estimate is 8.5 hours.

Noah's estimate is 7.5 hours.

Diego's estimate is 6.5 hours.

The average of these three estimates:

(8.5 + 7.5 + 6.5) / 3

= 22.5 / 3

= 7.5

It appears that Noah's estimate of 7.5 hours is the closest.

Therefore,

Noah's estimate of 7.5 hours is closest to the actual mean number of hours of sleep reported by the ten sixth-grade students.

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The complete question:

Which estimate of the mean number of hours of sleep reported by the ten sixth-grade students is closest to the actual mean: Lin's estimate of 8.5 hours, Noah's estimate of 7.5 hours, or Diego's estimate of 6.5 hours?

The vertical distance the Mars Rover Curiosity has traveled is approximately 84.954 meters.

An absolute value equation is an equation that contains an absolute value expression, which is defined as the distance of a number from zero on the number line. The equation |x-b|=c represents the distance between x and b is c units. To write the absolute value equations in the form |x-b|=c, we need to determine the values of b and c based on the given solution sets.

For the solution set "All numbers such that x ≤ -14", we know that the distance between x and -14 is always a non-negative value. Therefore, the absolute value of (x-(-14)) or (x+14) is equal to the distance between x and -14. Since we want x to be less than or equal to -14, we can set the absolute value expression to be equal to -c, where c is a positive number. Hence, the absolute value equation is |x+14|=-c.

Similarly, for the solution set "All numbers such that x ≥ -1.3", the distance between x and -1.3 is always a non-negative value. Therefore, the absolute value of (x-(-1.3)) or (x+1.3) is equal to the distance between x and -1.3. Since we want x to be greater than or equal to -1.3, we can set the absolute value expression to be equal to c, where c is a positive number. Hence, the absolute value equation is |x+1.3|=c.

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The volume of the large diamond is approximately 3.51 cm³.

To find the volume of the large diamond with a mass of 481.3 grams and a density of (g/3.51 cm), you can use the formula:

Volume = Mass / Density

The volume of the large diamond, we can use the formula Volume = Mass / Density. Given that the mass is 481.3 grams and the density is (g/3.51 cm), we can substitute these values into the formula.

Simplifying the equation, we find that the volume is equal to 3.51 cm³. This means that the large diamond occupies a space of approximately 3.51 cubic centimeters.

1. First, rewrite the density as a fraction: g/3.51 cm = 481.3 g / 3.51 cm³
2. Next, solve for the volume by dividing the mass by the density: Volume = 481.3 g / (481.3 g / 3.51 cm³)
3. Simplify the equation: Volume = 481.3 g * (3.51 cm³ / 481.3 g)
4. Cancel out the grams (g): Volume = 3.51 cm³

So, the volume of the large diamond is approximately 3.51 cm³, rounded to the nearest hundredth.

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Answer:

Step-by-step explanation:

Density = mass

               volume  

We have density (3.51 cm) and we have mass (481.3)

We need to solve for V (volume)

3.51 =     481.3

               V

Multiply both sides by V to clear the fraction:

3.51 V = 481.3

Divide both side by 3.51

3.51 V = 481.3

3.51         3.51

V = 137.122cm³

rounded to 137.12 cm³

Answer:

B

Step-by-step explanation:

Since the graph is facing down, there will be a negative sign.

In parenthesis it says (x + 1) which means you move one unit left

On the outside it says +2 which means you move the graph 2 units up

Answer:

2/5

Step-by-step explanation:

To convert a percentage to a fraction, we divide the percentage by 100 and simplify the resulting fraction. For example, to convert 40% to a fraction, we divide 40 by 100 to get 0.4 and then simplify the fraction 2/5. Therefore, 40% is equal to 2/5.

Answer:

The triangular prism has two triangular bases and three rectangular lateral faces.

First, we need to find the area of each triangular base. Using the formula for the area of a triangle:

base x height / 2

We can calculate the area of one triangular base as:

(10 x 12) / 2 = 60 units²

Now we need to find the area of each rectangular lateral face. All three faces have the same dimensions of 10 units by 14 units, so the area of each face is:

10 x 14 = 140 units²

To find the total surface area of the prism, we add up the areas of both triangular bases and all three rectangular faces:

Total surface area = 2 x (area of triangular base) + 3 x (area of rectangular face)

Total surface area = 2 x 60 units² + 3 x 140 units²

Total surface area = 120 units² + 420 units²

Total surface area = 540 units²

Therefore, the surface area of the triangular prism is 540 square units.

Answer:

Step-by-step explanation:

git

8. Patricia uses 600 milliliters of water each time she waters her vegetable garden. The correct option is A © 600 mL.

9. 4-5 =-1

For first question:

8. A watering can holds 3 liters of water, and Patricia waters her vegetable garden 5 times a day using one full can in total. To find out how many milliliters of water she uses each time, you need to first convert the 3 liters to milliliters (1 liter = 1,000 milliliters) and then divide by 5.

3 liters × 1,000 milliliters/liter = 3,000 milliliters
3,000 milliliters ÷ 5 = 600 milliliters

So, Patricia uses 600 milliliters of water each time she waters her vegetable garden. The correct answer is 600 mL.

9. For second question, the calculation is as follows:

4 - 5 = -1

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The perimeter of the equilateral triangle whose area is 16root3/4 is 15.9[tex]\sqrt{3/4} cm[/tex]

You should understand that a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted

An equilateral triangle is a special case of an isosceles triangle in which all three sides have the same length

Let the sides of the triangle be a

a + a + a = 16root3/4

3a = 16[tex]\sqrt{3/4}[/tex]

a = 5.3[tex]\sqrt{3/4}[/tex]

Therefore the perimeter of the equilateral triangle is

5.3[tex]\sqrt{3/4} + 5.3\sqrt{3/4} +5.3\sqrt{3/4}[/tex]

Therefore, the  perimeter is 15.9[tex]\sqrt{3/4} cm[/tex]

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The percent discount on the phone because of a sale is 45%.

To find the percent discount, we need to calculate the difference between the original price and the discounted price, and then express that difference as a percentage of the original price.

First, let's find the difference between the two prices: $28 - $15.40 = $12.60. This means that Benjamin saved $12.60 on the phone.

Now, let's find the percent discount. We can do this by dividing the savings by the original price, and then multiplying the result by 100: ($12.60 / $28) * 100 = 45%.

So, Benjamin received a 45% discount on the phone before tax. This calculation shows that the sale allowed him to save a significant amount on his purchase. It's important to compare original and discounted prices to determine if a sale provides good value.

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Answer:

Function A: f(x) = -8^x

Function B: f(x) = 2^x

Function A has a greater horizontal asymptote. As x approaches negative infinity, Function A approaches y = 0 faster than Function B.

To solve this differential equation using separation of variables, we can rearrange it as:

dx/(x^2 + 36) = (t^2 + 4)/dt

Now we can integrate both sides:

∫ dx/(x^2 + 36) = ∫ (t^2 + 4)/dt

To integrate the left side, we can use the substitution u = x/6, du/dx = 1/6 dx, and dx = 6 du:

∫ dx/(x^2 + 36) = ∫ du/u^2 + 1

= arctan(x/6) + C1

To integrate the right side, we can use the power rule:

∫ (t^2 + 4)/dt = (1/3)t^3 + 4t + C2

Putting these together, we have:

arctan(x/6) = (1/3)t^3 + 4t + C

Where C = C2 - C1 is the constant of integration.

Now we can solve for x:

x/6 = 6 tan((1/3)t^3 + 4t + C)

x = 36 tan((1/3)t^3 + 4t + C)

Using the initial condition 2(0) = 6, we have:

x(0) = 36 tan(C) = 6

tan(C) = 1/6

C = arctan(1/6)

Therefore, the solution to the differential equation with the given initial condition is:

x = 36 tan((1/3)t^3 + 4t + arctan(1/6))

First, let's rewrite the equation using the given terms and separating the variables:

(t^2 + 4) dx/dt = (x^2 + 36)

Now, separate the variables:

dx/x^2 + 36 = dt/t^2 + 4

Next, we'll integrate both sides:

∫(1/(x^2 + 36)) dx = ∫(1/(t^2 + 4)) dt

Using the substitution method, we find:

(1/6) arctan(x/6) = (1/2) arctan(t/2) + C

Now, we'll use the initial condition 2(0) = 6 to find the value of C. Since 2(0) = 0, we have:

(1/6) arctan(6/6) = (1/2) arctan(0/2) + C

This simplifies to:

(1/6) arctan(1) = C

Therefore, the solution to the differential equation is:

(1/6) arctan(x/6) = (1/2) arctan(t/2) + (1/6) arctan(1)

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Answer: The transformation is up one and to the left 5

(-5, 1)

Step-by-step explanation:

Please Give brainliest, have a great night!

Answer:   h(x) = g(x+5)+1

Step-by-step explanation:

h(x) = g(x+5)+1

You went 5 in the negative direction x direction; take the opposite sign

Also went up 1 in the y direction so add 1 to equation

Answer:

Step-by-step explanation:

(a) The total payment for a student who registers for m language subjects and n other subjects can be expressed as:

Total payment = Administrative fee + Tuition fee for language subjects + Tuition fee for other subjects

Total payment = RM30 + RM45m + RM40n

Total payment = RM30 + 45m + 40n

(b) For Zaleha who registers for 3 language subjects and 2 other subjects, the total payment can be calculated as:

Total payment = RM30 + (3 x RM45) + (2 x RM40)

Total payment = RM30 + RM135 + RM80

Total payment = RM245

(c) Chan pays RM280 when she registers for 2 language subjects and p other subjects. We can use the formula derived in part (a) to find the value of p:

Total payment = RM30 + (2 x RM45) + (p x RM40)

RM280 = RM30 + RM90 + RM40p

RM280 - RM120 = RM40p

RM160 = RM40p

p = 4

Therefore, Chan registers for 2 language subjects and 4 other subjects.

(a) The surface area of a right pyramid with a square base can be calculated as:

L = base area + 1/2 x perimeter of base x slant height

The base of the pyramid is a square, so its area can be expressed as:

Base area = a^2

The perimeter of the base can be calculated as:

Perimeter of base = 4a

The slant height can be calculated using the Pythagorean theorem:

slant height = sqrt(h^2 + (a/2)^2)

where h is the height of the pyramid.

Substituting these values in the surface area formula, we get:

L = a^2 + 1/2 x 4a x sqrt(h^2 + (a/2)^2)

L = a^2 + 2a x sqrt(h^2 + (a/2)^2)

(b) If a = 10 and b = 12, then the surface area of the pyramid can be calculated as:

L = 10^2 + 2 x 10 x sqrt(h^2 + (10/2)^2)

L = 100 + 20sqrt(h^2 + 25)

Given that L = 192, we can solve for h:

192 - 100 = 20sqrt(h^2 + 25)

92 = 20sqrt(h^2 + 25)

4.6 = sqrt(h^2 + 25)

4.6^2 - 25 = h^2

h^2 = 2.76

h = sqrt(2.76)

h ≈ 1.66

Substituting these values in the surface area formula, we get:

L = 10^2 + 2 x 10 x sqrt(1.66^2 + (10/2)^2)

L ≈ 314.9

Therefore, the surface area of the pyramid is approximately 314.9 square units.

(c) If L = 192 and a = b, then the surface area formula can be simplified as:

L = a^2 + 2a x sqrt(h^2 + (a/2)^2)

192 = a^2 + 2a x sqrt(h^2 + (a/2)^2)

We also know that the height of the pyramid is equal to the side length of the triangular faces. Since the pyramid is a right pyramid, the height and slant height are related by the Pythagorean theorem:

h^2 + (a/2)^

To find the probability of Sarah cleaning her room or doing her homework, we can use the addition rule for probabilities. However, we need to be careful not to count the probability of Sarah cleaning her room and doing her homework twice. Therefore, we need to subtract the probability of Sarah cleaning her room and doing her homework from the sum of the probabilities of Sarah cleaning her room and doing her homework separately.

Let C be the event that Sarah cleans her room, and let H be the event that Sarah does her homework. Then we know:

P(C) = 0.40 (the probability that Sarah cleans her room)

P(H) = 0.70 (the probability that Sarah does her homework)

P(C and H) = 0.24 (the probability that Sarah cleans her room and does her homework)

Using the addition rule, we can find the probability of Sarah cleaning her room or doing her homework as follows:

P(C or H) = P(C) + P(H) - P(C and H)

          = 0.40 + 0.70 - 0.24

          = 0.86

Therefore, the probability of Sarah cleaning her room or doing her homework is 0.86, or 86%.

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All real numbers will be the function's domain. D is the right answer in this case.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set(x).

A function's range is the collection of values it can take as input.

After we enter an x value, the function outputs this sequence of values.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

Let a be the leading coefficient and the parabola's vertex be the point (h, k).

The parabola's equation will then be provided as,

y = a(x - h)² + k

The graph shows where the vertex of the parabola will be. (-1.5, -4.5). The equation is then presented as:

y = a(x + 1.5)² - 4.5

Therefore, all real numbers will be the function's domain. D is the right answer in the case.

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Correct question:

The graph of the quadratic function f is shown in the grid. Which of these best represents the domain of f?

A: y>=4.5

B: All real numbers less than -4 or greater than 1

C: -4<=x<=1

D: All real numbers ​

PJ's design is best described as a randomized controlled trial (RCT), which is a type of experimental study that randomly assigns participants to a control group or an intervention group.

In this case, the control group did not receive the soft music during high stakes science testing, while the intervention group did. By administering both a pretest and a posttest, PJ was able to measure any differences in performance between the two groups. The use of randomization helps to ensure that any differences observed between the groups can be attributed to the intervention (soft music) rather than to other factors that may have influenced the results. Overall, PJ's RCT design is a rigorous way to test the effects of a specific intervention on a particular outcome.

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The value of A, B and C from the given equation are 0, 0 and 6 respectively.

The given equation is y=x²+x.

Here, the table is

X   -2 -1   0  1  2

Y    2  A  B  2 C

When x=-1

y=(-1)²-1

y=0

So, A=0

When x=0

y=(0)²+0

y=0

So, B=0

When x=2

y=(2)²+2

y=6

So, C=6

Therefore, the value of A, B and C are 0, 0 and 6 respectively.

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According to the model, each additional year of education adds $1200 to a person's yearly income in their first job after completing schooling.

We're given the equation y = 1200x + 7000, where x represents the number of years of education, and y represents the yearly income.

To find how much 1 year of education adds to a person's yearly income, we need to look at the coefficient of the variable x, which is 1200.

So according to the model, 1 year of education adds $1,200 to a person's yearly income.

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We use the fundamental property of proportions where:

[tex] \space [/tex]

[tex] \bf \frac{4x + 2}{39} = \frac{5x - 2}{42} \\ \\ \bf 39 \cdot (5x - 2) = 42 \cdot (4x + 2) \\ \\ \bf 195x - 78 = 168x + 84 \\ \\ \bf 195x - 168x = 84 + 78 \\ \\ \bf 27x = 162 \\ \\ \bf x = \frac{162}{27} \implies \bf \red{ \boxed{ \bf x = 6} } [/tex]

The number is 6.

Hope that helps! Good luck! :)

The correct interpretation of the 95% confidence level is that if we were to repeat this sampling process multiple times and construct confidence intervals in the same way, about 95% of the intervals would contain the true mean number of suitable apples produced per tree.

In other words, we are 95% confident that the true mean number of suitable apples produced per tree is between 375 and 520 based on this particular sample of 40 trees. However, we cannot say with certainty that the true mean falls within this interval, nor can we say that it falls outside of this interval with 95% confidence.

It's important to note that the confidence level refers to the long-run behavior of the method of constructing confidence intervals, rather than the probability that the true mean falls within the specific interval calculated from this one sample.

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The total or actual time he needs to practice is 140 min whereas he practiced for 98 min during the school week.

We need to find the total time he must practice for a week. To find the total time we assume that the total time is x min.

Given Data:

Dmitri practices time during the school week = 98 min

Dmitri practices amount of time = 70% of his total time

Total time = x

Then the equation is given as

70% × (x) = 98

0.70 × (x) = 98

x = 98 / 0.70

x = 140

Therefore, The total time of the practices is 140 min

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Cathy served 32 more people on Tuesday than on Monday.

Given, on Monday, Cathy served 9 tables with 6 people at each table. On Tuesday, Cathy served 86 people. We have to find the number of people she served more on Tuesday than on Monday.

So, on Monday she served = 9 tables x 6 people per table

= 54 people.

To find out how many more people Cathy served on Tuesday than on Monday, we can subtract the number of people served on Monday from the number served on Tuesday.

i.e. 86 - 54 = 32.

Therefore, Cathy served 32 more people on Tuesday than on Monday.

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First, we need to convert the mixed number 2 3/8 to an improper fraction:

2 3/8 = (2 x 8 + 3) / 8 = 19/8

To find out how many times Craig needs to fill a 1/3 cup measuring cup, we can divide 19/8 by 1/3:

(19/8) / (1/3) = (19/8) x (3/1) = 57/8

Therefore, Craig needs to fill a 1/3 cup measuring cup 57/8 times to measure 2 3/8 cups.

The student should receive $5.69 in change.

The price of the shirt after the coupon is applied is 0.75 times the regular price, so:

Price of the shirt = 0.75x

If x = $18, then the price of the shirt is:

Price of the shirt = 0.75($18) = $13.50

The clerk adds 6% sales tax to the price of the shirt:

Sales tax = 6% of $13.50 = 0.06($13.50) = $0.81

So the total cost of the shirt is:

Total cost = $13.50 + $0.81 = $14.31

If the student pays with a $20 bill, the change the student should receive is:

Change = $20 - $14.31 = $5.69

Therefore, the student should receive $5.69 in change.

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Answer:

(x-6)²+(y+3)²=17²

Step-by-step explanation:

The equation of a circle with center (a,b) and radius r is given by the formula:

(x - a)² + (y - b)² = r²

In this case, the center of the circle is (6,-3), and it passes through the point (-9,5). To find the radius of the circle, we need to calculate the distance between the center and the point on the circle. Using the distance formula, we get:

r = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-9 - 6)² + (5 - (-3))²]

= √[225 + 64]

= √289

= 17

So, the radius of the circle is 17. Now we can plug in the values for the center and radius into the equation of a circle:

(x - 6)² + (y + 3)² = 17²

Ginny's family traveled 3/10 of the total distance to her aunt's house on Sunday.

Let's say the total distance to Ginny's aunt's house is represented by the fraction 1.

On Saturday, Ginny's family traveled 3/10 of the distance, leaving 7/10 of the distance remaining.

Then, on Sunday, they traveled 3/7 of the remaining distance.

To find out what fraction of the total distance was traveled on Sunday, we need to multiply the distance traveled on Saturday and Sunday and divide by the total distance:

So, we have

Fraction = 3/7 * 7/10

Evaluate

Fraction = 3/10

Therefore, Ginny's family traveled 3/10 of the total distance to her aunt's house on Sunday.

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