Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive. n8n n=1 L = lim Vam = — (Enter 'inf' for .) n-> is: non n=1 A. convergent B. divergent C. The Root Test is inconclusive Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive. Š(+) n + 3 4n + 14 n=1 L liman = (Enter 'inf' for o.) — n->00 n n+3 is: n=1 A. convergent OB. divergent C. The Root Test is inconclusive Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive. -n2 1+ 6n n=1 L lim van! = inf (Enter 'inf' for o.) n->00 Em 4 (1+ on) -" is: A. convergent B. divergent C. The Root Test is inconclusive

The balance after 3 years is $552.50.

We have,

To find the interest earned, we can use the simple interest formula:

I = Prt

where I is the interest earned, P is the principal (starting amount), r is the interest rate (as a decimal), and t is the time (in years).

Substituting the given values, we get:

I = 500 x 0.035 x 3

I = $52.50

Therefore, the interest earned is $52.50.

To find the balance, we need to add the interest earned to the principal:

Balance = Principal + Interest

Balance = $500 + $52.50

Balance = $552.50

Therefore,

The balance after 3 years is $552.50.

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Step-by-step explanation:

Let the increase in the size of the length and breath be 'x'.

The area of the rectangle = 12in × 8in

=96 in²

From the question,

(12+x)(8+x)=96×2 in²

or, 96+12x+8x+x²= 192

or, x²+20x+96-192=0

or, x²+20x-96=0

or, x²+24x-4x-96=0

or, x(x+24)-4(x+24)=0

or, (x-4)(x+24)=0

Either, Or,

x-4=0 x+24=0

Therefore, or, x= –24 (Which is impossible)

x=4

So the new dimensions are 12+4=16 inch and 8+4=12 inch.

Answer:

2.224,700

3.543,000

4.28,665

5.757,770

6.240,000

7.17,500

8.57,684

9.4,139.254

Step-by-step explanation:

Hope this helps!!! :))

please look at the attached image.

Answer:

60

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The probability that the marble is large or white is 0.5714.

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

Probability of an event is

P(A) = Number of favorable outcomes/ Total Number of outcomes      

       = n(A)/n(S)

where

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space.

We have,

Number of large marbles = 14

Number of small marbles = 10

Number of large green marbles = 8 which implies

Number of large white marbles = 14 - 8 = 6

Number of small white marbles = 4 which implies

Number of small green marbles = 10 - 4 = 6.

Now, let

Let X be the event of drawing large marble.

Let Y be the event of drawing small marble.

Let M be the event of drawing white marbles.

Let N be the event of drawing green marbles.

Since only one marble is drawn at a time ,

so P(X) =  14/24

    P(Y) = 10/24

    P(M) = 10/24

    P(N) = 14/24

We have to find the probability that a marble is large or white i.e. P(X∪M).

P(X∪M) = P(X) + P(Y) - P(X∩M)

P(X∩M) = In 14 large marbles 6 are white marbles = 6/14.

P(X∪M) = P(X) + P(Y) - P(X∩M) = 14/24 + 10/24 - 6/14 = 0.5833+0.4167-0.4286 = 0.5714.

Therefore, the probability of drawing large or white marble is 0.5714.

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The blue ribbon is 2.2 times longer than the orange ribbon

From the information given, we have that;

Now, lets convert the mixed fractions to improper fractions;

Length of orange ribbon = 95/12

Length of blue ribbon = 209/12

The ratio is expressed as;

Length of blue ribbon/length of orange ribbon

Substitute the values, we have;

= 209/12 ÷ 95/12

Take the inverse of the divisor and multiply

= 209/ 12 × 12/95

= 2. 2 times

Hence, it is 2.2 times longer.

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Answer:

161 cm

Step-by-step explanation:

Since 115 cm is 5 boxes, we take 115 and divide it by 5. This will get us the cm of 1 box. 115/5=23

Now we take 23 and multiply it by 7 to get the final height. 23x7=161

Answer:

5 boxes have 115 cm height

Then 1 box height is 115 / 5 = 23 cm

7 boxes will have height of 23 * 7 = 161 cm

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The solution to the inequality, -2(8x – 4) < 2x + 5, is: B. x > 1/6.

To find the solution to an inequality, solve the inequality to isolate the variable.

Given the inequality, -2(8x – 4) < 2x + 5, open the bracket:

-16x + 8 < 2x + 5

Combine like terms

-16x - 2x < -8 + 5

-18x < -3

Divide both sides by -18 then reverse < to >

-18x/-18 > -3/-18

x > 1/6

The solution is: B. x > 1/6

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This tells us that the product of two multiples of two numbers is also a multiple of those two numbers. Matrices help to illustrate this relationship visually.

Suppose a, b is a multiple of c, d, and abcd = 0. This means that there are some integers n1 and n2 such that a = n1c and b = n2d. We can represent this using matrices as follows:

a = n1c = [n1 0] [c 0] = [n1c 0]

b = n2d = [0 n2] [0 d] = [0 n2d]

Now, we can take the product of these two matrices to find the product of a and b:

ab = [n1c 0] [0 n2d] = [0 0] [n1c n2d] = [0 n1c n2d 0]

This result is a multiple of both c and d, since the product of two multiples of two numbers is also a multiple of those two numbers. This shows that a, c is a multiple of pb, d. Matrices help to illustrate this relationship visually by showing that the product of two matrices is also a multiple of both of the original matrices.

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The expression  \(\frac{5}{2} \times \frac{3}{10}\) in the simplest form can be written as \(\frac{3}{4}\).

Mathematically, an expression is a collection of numbers, variables, mathematical operations, functions, and often symbols combined according to peculiar rules to represent a mathematical calculation or association. It can be supposed to as a mathematical idiom or formula.

By combining numbers, variables, operators, and functions, mathematical expressions can represent a wide range of calculations and associations.

The given expression is \(\frac{5}{2} \times \frac{3}{10}\).

\(\frac{5}{2} \times \frac{3}{10} = \frac{1}{2} \times \frac{3}{2}\)

          \(= \frac{3}{4}\).

Hence, the fraction is \(\frac{3}{4}\).

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The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Answer:151

Step-by-step explanation:

Answer:

151

Step-by-step explanation:

Answer:

B is the answer

Step-by-step explanation:

(√(1.5³ * 1.5⁷))/1.5²

√ 1.5 ^(3+7) ÷ 1.5²

√1.5^10 ÷ 1.5²

1.5⁵ ÷ 1.5²

1.5^(5-2)

1.5³

Answer:

I think it is c I hope it helps have a good day

the margin of error for this confidence interval is 0.85. This means that we can be 98% confident that the true difference in mean scores between nontraditional math classes and traditional math classes is between 1.798 and 4.198, with a margin of error of 0.85.

To find the margin of error for a confidence interval, we can use the formula:

Margin of error = (Upper bound of interval - Lower bound of interval) / 2

In this case, the upper bound of the confidence interval is 4.198 and the lower bound is 1.798. So, we have:

Margin of error = (4.198 - 1.798) / 2

= 1.7 / 2

= 0.85

what is margin?

Margin can have different meanings depending on the context, but in general, it refers to the amount by which one quantity or value differs from another quantity or value.

In finance, margin refers to the amount of money or collateral required to trade in a particular market or asset, such as stocks or futures. It also refers to the difference between the current market value of an asset and the amount of money borrowed to buy that asset.

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Answer:

0.4476

Step-by-step explanation:

Answer:

Step-by-step explanation:

The signs of both intercepts are negative, so the segment connecting them will form a triangle with the axes in the 3rd quadrant. The line will have negative slope. The points and line are shown in red in the attachment.

__

The equation produces a line with x-intercept -2 and y-intercept 6. The sign of the y-intercept is wrong, and the slope of the line is positive. The equation cannot be the equation of the line through the given points. This line is shown in blue in the attachment.

Answer:

Since she started with $80 and ended with with $35,24, we can find the total amount she spent by subtracting these amounts:

$80 - $35.24 = $44.76

This means that she spent $44.76 on coffee. If each pound cost $7.46, we can divide $44.76 by $7.46 to see how many pounds she bought (ignoring tax):

44.76 / 7.46 = 6 pounds of coffee purchased

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The number of pheasants in 2012 was 1832. The number of pheasants in 2016 was 422. The minimum viable density is 100 pheasants per hectare.

So, we need to find out the year in which the population will fall below 100 pheasants per hectare.

First, we need to find out the rate of decline per year which can be calculated as follows: Rate of decline per year = (1832 - 422) / (2016 - 2012)= 1410 / 4= 352.5 per yearNow, let the number of pheasants per hectare be y after t years from 2012.

Then, y = 1832 - 352.5t (as we know the rate of decline per year)We need to find the year in which the population will fall below 100 pheasants per hectare. So, we need to solve the equation:1832 - 352.5t = 100⇒ 352.5t = 1732⇒ t = 1732 / 352.5⇒ t = 4.91 Therefore, the population will fall below the minimum viable density of 100 pheasants per hectare after 4.91 years from 2012, which is around 2017 or 2018.

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The integral θ(r)=∫⎝⎛±2μ(E−U−2μr2l2)l/r2dr⎞⎠⎟+constant gives the change in the angle θ of a body undergoing orbital motion as a function of the radius r.

The integral θ(r)=∫⎝⎛±2μ(E−U−2μr2l2)l/r2dr⎞⎠⎟+constant is a result of the conservation of angular momentum. The angular momentum of a body is defined as the product of its mass, its velocity, and the distance from the center of rotation.

In the case of orbital motion, the velocity of the body is given by v=rω, where ω is the angular velocity. The angular momentum is then l=mrv=mr2ω.

The conservation of angular momentum states that the angular momentum of a body remains constant unless an external torque is applied. In the case of orbital motion, the only external torque is the gravitational force.

The gravitational force is always perpendicular to the velocity, so it does not change the magnitude of the angular momentum. However, it does change the direction of the angular momentum, which is why the body undergoes orbital motion.

The integral θ(r)=∫⎝⎛±2μ(E−U−2μr2l2)l/r2dr⎞⎠⎟+constant can be derived by using the conservation of angular momentum and the equation for the gravitational force. The integral gives the change in the angle θ of the body as a function of the radius r. The ± sign in the integral represents the two possible directions of rotation.

The integral θ(r)=∫⎝⎛±2μ(E−U−2μr2l2)l/r2dr⎞⎠⎟+constant is a powerful tool for studying orbital motion. It can be used to calculate the change in the angle of the body as it moves along its orbit, and it can also be used to calculate the total energy of the body.

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Answer:

300 to 1.

Step-by-step explanation:

A centimeter is one hundredth of a meter (hence the "centi" part) So by changing the meters value into that of the hundreds, you'll get your scale factor, the same applies things like millimeters and kilometers, with the only exception being that you'd have to adjust the numbers, for higher or lower.

Answer:

B

Step-by-step explanation:

It's a closed dot, so the sign will be less than or equal to 5.

Answer:

A

Step-by-step explanation:

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

(a) Limitations: Assumes reversible process, constant heat capacity.

(b) Limitations: Assumes constant T and P, and independent DH and DS with temperature.

(c) Limitation: Assumes non-expansion conditions, may not account for volume changes in real scenarios.

The surface area of the triangular prism is 5166 square inches.

We need to find the area of the triangular face. The area of a triangle is given by the formula:

Area = (1/2) × base × height

Area = (1/2) × 42 × 28

= 588 square inches

The total surface area of those two faces is 2 times the area we just calculated:

Total area of the two triangular faces = 2 × 588

= 1176 square inches

Area of each rectangular face = length× width

= 38 × 35

= 1330 square inches

There are 3 rectangular faces

The total area of those three faces is 3 times the area

Total area of the three rectangular faces = 3 × 1330

= 3990 square inches

Total surface area of the triangular prism by adding together the areas of the two triangular faces and the three rectangular faces:

Total surface area = Total area of the two triangular faces + Total area of the three rectangular faces

Total surface area = 1176 + 3990 = 5166 square inches

Therefore, the surface area of the triangular prism is 5166 square inches.

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Answer:

70degrees

Explanation:

The diagrammatical representation of the statement is as shown;

Since the sum of angles on a straight line is 180degrees, then;

m8x+2 + 5x = 180

13x + 2 = 180

13x = 180 + 2

13x = 182

x = 182/13

x = 14

Get mmmmHence the measure of m

Answer: 26

Step-by-step explanation:

42+10= 52 , 52-3=49

75-49= 26

Therefore, the sales tax rate on the washer and dryer set was 5.25%.

Sales tax rates vary depending on the country, state, and even city or municipality where the sale is taking place. Therefore, it's difficult to provide a single answer without more information about the specific location you're asking about.

For example, in the United States, the sales tax rate can range from 0% in some states to as high as 10.25% in certain cities or counties. In Canada, the federal sales tax is 5%, but provinces and territories may also have their own sales tax rates.

To find the sales tax rate, we need to divide the sales tax by the total cost of the washer and dryer set:

Sales tax rate = sales tax / total cost

Total cost = $2900 (cost of washer and dryer set)

Sales tax = $152.25\2900

Sales tax rate = 152.25 / 2900

Sales tax rate = 0.0525 or 5.25%

Therefore, the sales tax rate on the washer and dryer set was 5.25%.

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No, the three lines 2x1 − 4x2 = 8, 4x1 + 6x2 = −40, and −2x1 − 10x2 = 48 do not have a common point of intersection. They form a system of linear equations that is inconsistent.

To determine if the three lines have a common point of intersection, we need to check if there is a solution to the system of linear equations. We can rewrite the system of equations in matrix form as:

| 2  -4 |   | x1 |   |  8 |

| 4   6 | * | x2 | = | -40 |

|-2 -10 |   | x3 |   |  48 |

If we attempt to solve this system using Gaussian elimination or any other method, we will find that it leads to an inconsistent system, meaning there is no solution that satisfies all three equations simultaneously.

This can be seen by examining the matrix formed by the coefficients of the variables. The second row is a linear combination of the first row, and the third row is a multiple of the first row. Inconsistent systems occur when the rows of the coefficient matrix are linearly dependent or when one row is a multiple of another.

Therefore, the given system of equations does not have a common point of intersection.

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