a. Write the first four terms of the series.

b. Does the series diverge or converge?

c. If the series has a sum, find the sum. Show your work.

Answer:

A Mudslinger tire weighs 20.71 pounds and a Roadripper tire weighs 19.52 pounds

Step-by-step explanation:

Let the weight of a Mudslinger tire=m

Let the weight of a Roadripper tire=r

4 Mudslinger tires and 6 Roadripper tires weigh 200 pounds

4m+6r=200.....(i)

7 Mudslinger tires and 2 Roadripper tires weigh 184 pounds

7m+2r=184....(ii)

To find the values of m and r, we solve the two derived equations simultaneously.

4m+6r=200.....(i)

7m+2r=184....(ii)

Multiply (ii) by 3 to get (iii)

21m+6r=552....(iii)

4m+6r=200.....(i)

SUbtract (i) from (iii)

17m=352

m=352/17=20.71 pounds

Substitute m=20.71 in (i)

4(20.71)+6r=200

6r=200-82.84=117.16

r=117.16/6=19.52 pounds

Answer: The answer is 3, I just finished doing the assignment.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

The answer is standardization.

Step-by-step explanation:

Achievement tests are used in describing students’ learning abilities and academic accomplishments.

Since standardized achievement tests can give a better indication of students’ weaknesses, the test results will corroborate what can be seen on a daily basis, and the results can give insight into how a student's achievement compares to the average national student.

So, Brandon's concern was directly related to the issue of standardization because he wanted to make sure the test fulfilled the requirements of a standardized test ( i.e the questions, conditions for administering, scoring procedures, and interpretations) were consistent, and if so his score would not deviate greatly from the average test taker, and he wouldn't be an exception in obtaining such a high score.

Answer:

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=2,\:y=-1[/tex]

Step-by-step explanation:

Considering the system of the equation

[tex]\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}[/tex]

[tex]\mathrm{Subsititute\:}y=-2x+3[/tex]

[tex]\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}[/tex]

[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11[/tex]

[tex]4x-3\left(-2x+3\right)=11[/tex]

[tex]4x+6x-9=11[/tex]

[tex]10x-9=11[/tex]

[tex]10x-9+9=11+9[/tex]

[tex]10x=20[/tex]

[tex]x=2[/tex]

[tex]\mathrm{For\:}y=-2x+3[/tex]

[tex]\mathrm{Subsititute\:}x=2[/tex]

[tex]y=-2\cdot \:2+3[/tex]

[tex]y=-1[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=2,\:y=-1[/tex]

Answer:

The solution (x, y) = (-5, 3)

Step-by-step explanation:

-x - 8 = -y .... (1)

9y - 12 + 3x = 0 .... (2)

from equation (1)

-x = - y + 8 ... (3)

multiply equation (3) by -1

x = y - 8 ..... (4)

substituting equation (4) in equation (2)

9y - 12 + 3 ( y - 8) = 0

9y - 12 + 3y - 24 = 0

12y - 36 = 0

12y = 36

y = 36 /12

y = 3

Substitute y = 3 in equation (4)

x = y - 8

x = 3 - 8

x = -5

Final answer:

Using the Pythagorean theorem, the length of the parcel of land was calculated to be 240 feet, given that its width is 100 feet and the diagonal is 20 feet longer than the length.

Explanation:

To solve for the length of the parcel of land, given that it has a width of 100 feet and a diagonal that is 20 feet longer than the length, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this situation, let's denote the length of the parcel as 'L' and the diagonal as 'D'. We then have the relationship:

D = L + 20 feet

We can establish the equation L2 + 1002 = (L + 20)2.

Expanding the right side of the equation gives us L2 + 10,000 = L2 + 40L + 400. Simplifying the equation by subtracting L2 from both sides, we get  10,000 = 40L + 400. Subtracting 400 from both sides gives us 9,600 = 40L, which simplifies to L = 240 feet when we divide both sides by 40.

Therefore, the length of the parcel is 240 feet.

Answer:

?

Step-by-step explanation:

Convert 4/10 into 40/100(so you can have same denominator as other fraction) and then add 40/100 and 37/100 and you will get the answer!

Final answer:

The volume of the cone is approximately 860.6 cm³.

Explanation:

To find the volume of a right circular cone, we can use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. In this case, the diameter of the base is 18.6 cm, so the radius is half of that, which is 9.3 cm. The height of the cone is 8.8 cm. Plugging these values into the formula, we get V = (1/3)π(9.3 cm)²(8.8 cm). Calculating this, we find that the volume of the cone is approximately 860.6 cm³.

Answer:

$600

Step-by-step explanation:

Divide 240 by 2/5

Answer:

FALSE

Step-by-step explanation:

The mode is a measure of the number with the highest frequency in a group of data. In the set of values (32, 21, 68, 21), the number that appears most is 21 and this is the mode.

If a set of data has two modes, it is bi-modal. If it has several modes, it is multi-modal

Consider the set of data below

2,2,3,3,5,7,8

The numbers 2 and 3 appears with the same frequency, therefore this set of data is bi-modal.

Answer:       y= 16/x

Step-by-step explanation:

Answer:

B) Observing how probability works with real items

Step-by-step explanation:

Just took the quiz

Answer:

A Series is always a periodic sum of terms, so only A and D will apply to that definition

(where A= 1/2 + 1/4 + 1/6 + 1/16 + 3.14159 and B=25 - 5 - 10 - 15 - - 125

Answer:

The exact work required to pump all the gasoline to the surface of the ground is π × 5.094 × 10⁶ j

Step-by-step explanation:

Here, we note that volume of a slice is given by

Length × Width × Height

Length of slice = Length of cylinder = 15 ft

Since the slice height is Δy ft thick and located y ft above the center of the cylinder, then

Width of slice = 2 × √(r² - y²)

Where:

r = Radius of the cylinder =5 ft

∴ Width of slice = 2 × √(25 - y²)

∴Volume of slice = 15 ×2 × √(25 - y²)×Δy

Mass of slice then = 42 × 15 ×2 × √(25 - y²)×Δy = 1260 × √(25 - y²)×Δy

The force required to lift the slice is the weight of the slice, which is given by

32.2 × 1260 × √(25 - y²)×Δy = 40572 × √(25 - y²)×Δy N (Newtons)

The work done by the force is the product of the force and the distsnce through which the force acts.

Work done = 40752×(10-y) × √(25 - y²)×Δy

Therefore total work done is given by

[tex]W = \int\limits^5_{-5} {40752\times (10-y) \times \sqrt{ (25 - y^{2} )} } \, dy[/tex]

= 5094000·π J = π × 5.094 × 10⁶ j

The exact work required to pump all the gasoline to the surface of the ground = π × 5.094 × 10⁶ j

The calculation requires determining the volume and displacement of each slice of gasoline in the tank and then integrating over these from the bottom to the top of the tank (from -5 to 5 feet).

To calculate the exact work required to pump all the gasoline to the surface, we need to first determine the displacement of each slice of gasoline and then integrate over the total volume. The displacement of a slice at height y is the distance it needs to be moved to the surface, which is (10 - y) feet. The volume of a cylindrical slice of thickness delta y is given by the area of the cylinder's cross section times the slice's thickness, i.e., volume = pi * r^2 * delta y. Here, r = 5ft and delta y is the thickness of the slice. Therefore, the volume of the slice is 25*pi*delta y ft3. The endpoints of the integral are defined by the top and bottom of the tank relative to the center, which in this case are -5 and 5 feet. Therefore, the lower endpoint is -5 and the upper endpoint is 5.

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Answer:

a c

Step-by-step explanation:

Final answer:

All three calculated numbers are positive, and therefore, the product of any two of them will also be positive. Option B is correct, which states that at least two numbers must be positive, making the resulting product nonnegative.

Explanation:

The statement that the product of two of the numbers 651000 - 82001 + 3177, 791212 - 92399 + 22001, and 244493 - 58192 + 71777 is nonnegative relies on the principles of arithmetic involving the addition and multiplication of numbers with different signs. Calculating the given numbers:

651000 - 82001 + 3177 = 573176 (positive)

791212 - 92399 + 22001 = 710814 (positive)

244493 - 58192 + 71777 = 255078 (positive)

All three numbers are positive, so the product of any two would also be positive, according to the multiplication rules that state the product of two positive numbers is always positive.

Therefore, the correct answer to the statement is:

B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative.

The rate of change for company A is $8 an hour and it would cost $42 to rent a canoe for four hours from company A.

The rate of change for company B is $15 an hour and it would cost $60 to rent a canoe for four hours from company B.

Step-by-step explanation:

Step 1:

For company A, [tex]c = 8h + 10,[/tex] where c is the cost after h hours.

When [tex]h=1,[/tex] [tex]c = 8(1) + 10 = 18.[/tex]

When [tex]h=2,[/tex] [tex]c = 8(2) + 10 = 26.[/tex]

The rate of change for company A [tex]= 26 - 18 = 8.[/tex]

The rate of change for company A is $8 an hour.

When [tex]h=4,[/tex] [tex]c = 8(4) + 10 = 42.[/tex]

So it would cost $42 to rent a canoe for four hours from company A.

Step 2:

For company A, the cost is $15 per hour so [tex]c = 15h,[/tex] where c is the cost after h hours.

When [tex]h=1,[/tex] [tex]c =1(15) =15.[/tex]

When [tex]h=2,[/tex] [tex]c = 2(15)= 30.[/tex]

The rate of change for company B [tex]= 30 - 15 = 15.[/tex]

The rate of change for company B is $15 an hour.

When [tex]h=4,[/tex] [tex]c = 4(15) = 60.[/tex]

So it would cost $60 to rent a canoe for four hours from company B.

Answer:

The Alan's average for course is 72.65.

Step-by-step explanation:

Given that,

Each test counts as 15% of the course grade. 20% of course grade is counted term test paper. Alan has test scores of 79, 95, 89, and 81. Alan got 81 score on his term paper . Alan's final examination score = 85.

[tex]\sum w=1[/tex]

Let n number x₁,x₂,.......,[tex]x_n[/tex] with respect to assigned weight[tex]w_1[/tex],[tex]w_2[/tex],.......,[tex]w_n[/tex] is

[tex]{\textrm{weighted mean}}= \frac{\sum w.x}{\sum w}[/tex]

Where [tex]\sum w.x[/tex] is the sum of the products the number with the relevant weight.

weighted mean  [tex]=\frac{79\times 15\%+95 \times 15\%+89\times 15\%+81\times 20\%+85\times20\%}{1}[/tex]

                           =72.65

The Alan's average for course is 72.65.

Answer:

0.31 yr

Step-by-step explanation:

The formula for interest compounded continuously is

[tex]FV = PVe^{rt}[/tex]

FV = future value, and

PV = present value

If FV is twice the PV, we can calculate the doubling time, t

[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]

1. Brianna's doubling time

[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.065}\\\\& = & \textbf{10.663 yr}\\\end{array}[/tex]

2. Adam's doubling time

The formula for interest compounded periodically is

[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]

where

n = the number of payments per year

If FV is twice the PV, we can calculate the doubling time.

[tex]\begin{array}{rcl}2 & = & \left (1 + \dfrac{0.0675}{4} \right )^{4t}\\\\&= & (1 + 0.016875 )^{4t}\\& = & 1.016875^{4t}\\\ln 2& = & 4 (\ln 1.01688)\times t \\& = & 0.066937t\\t& = & \dfrac{\ln 2}{0.066937}\\\\& = & \textbf{10.355 yr}\\\end{array}[/tex]

3. Brianna's doubling time vs Adam's

10.663 - 10.355 = 0.31 yr

It would take 0.31 yr longer for Brianna's money to double than Adam's.

Answer:

a=6 b=4

Step-by-step explanation:

they can't both equal 5 so you need to find 2 numbers that add up to equal 10 but when you subtract one from the other it equals 2

Answer:

Therefore the required number is 0.25.

Step-by-step explanation:

Given that, the number is less than 1 has two decimal place.

The digit is the hundredths place has value of [tex]\frac{5}{100}[/tex]

                                                                           =0.05

If a number divides with 100, then the point of the number shifts precede of two digits.

The digit in tenth place has a value of [tex]\frac2 {10}[/tex]

                                                              =0.2

The number is = tenth place value + hundredths place value

                        = 0.2+0.05

                        =0.25

Therefore the required number is 0.25.

Specifically looking at a number less than one with two decimal places: 2/10 in the tenths place and 5/100 in the hundredths place, resulting in the number 0.25.

The tenths place value, 2/10, means that there is a 2 in the tenths place. The hundredths place value, 5/100, means there is a 5 in the hundredths place. Therefore, combining these values, we get the number 0.25.

This demonstrates how decimal place values work, with each position to the right of the decimal point representing a fraction of ten (tenths, hundredths, etc.). The given values fit precisely into the decimal system, illustrating the concept of decimal place values clearly.

Answer:

For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]

And the average is calculated with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

Where n represent the sample size

N represent the population size, and X the observations for this case the annual income.

This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]

After calculate the average they got:

[tex] \bar X= 35031[/tex]

And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data

Step-by-step explanation:

For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]

And the average is calculated with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

Where n represent the sample size

N represent the population size, and X the observations for this case the annual income.

This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]

After calculate the average they got:

[tex] \bar X= 35031[/tex]

And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data

Let f = fish

If f < 12, let the fish go.

We cannot catch a fish measuring 11.99 inches.

If f = fish, then f < 11.99. It must be released.

two equations which can model this situation is :  [tex]y=2x[/tex]  and  [tex]x+y=1250[/tex]  

Step-by-step explanation:

Here we have , Bronson is an action and horror movie junkie. He started a movie review vlog and needs to keep up with his movie viewing at a high pace. It has been a total of 50 weeks since he has stated his vlog and he has watched 1250 movies. He has watched twice as many horror movies a action movies. We need to Write two equations that can model this situation.​ Let's find out:

Let Bronson watched x action movies and y horror movies , than according to question horror movies he watched is twice that of action movies i.e.

⇒ [tex]y=2x[/tex]       ........(1)

Now ,  he has watched 1250 movies i.e.

⇒ [tex]x+y=1250[/tex]            .......(2)

⇒ [tex]x+2x=1250[/tex]

⇒ [tex]3x=1250[/tex]

Therefore , two equations which can model this situation is :  [tex]y=2x[/tex]  and  [tex]x+y=1250[/tex]  .

Answer: $187.5

Step-by-step explanation:

The interest = 5000× ( 7.5/100 )÷2

=5000 × 0.075 ÷2

= 5000 ×0.0375

= 187.5 has interest semiannually

Hence, he gets 187.5

Answer:

C and E

Step-by-step explanation:

A parameter is a percentage of a population.

A, B, and D are percentages from surveys (samples).

C and E are percentages from populations.

Answer: It’s either 6, or 2, though the answer is most likely 6, because of the way the table is created.

Step-by-step explanation:

Period is 12.

We can see the pattern 50, 33, 50, 67 that keeps repeating every m=12 points.

Answer:

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Answer:

The test statistic value is 15.3.

Step-by-step explanation:

The hypothesis for this test is:

H₀: The average number of homeless people is not increasing, i.e. μ = 42.3.

Hₐ: The average number of homeless people is increasing, i.e. μ > 42.3.

Given:

[tex]\bar x=45.3\\\sigma=6.2\\n=1000[/tex]

As the population standard deviation is provided use a single mean z-test for the hypothesis testing.

The test statistic is:

[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3[/tex]

Thus, the test statistic value is 15.3.

Using the z-distribution, it is found that the test statistic is of z = 15.3.

At the null hypothesis, it is tested if the mean number has not increased, that is, it still is of 42.3, hence:

[tex]H_0: \mu = 42.3[/tex]

At the alternative hypothesis, it is tested if it has increased, that is, the mean is greater than 42.3, hence:

[tex]H_1: \mu > 42.3[/tex]

We have the standard deviation for the population, hence, the z-distribution is used.

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The parameters are:

For this problem, the values of the parameters are:

[tex]\overline{x} = 45.3, \mu = 42.3, \sigma = 6.2, n = 1000[/tex]

Hence:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{45.3 - 42.3}{\frac{6.2}{\sqrt{1000}}}[/tex]

[tex]z = 15.3[/tex]

The test statistic is of z = 15.3.

To learn more about the z-distribution, you can take a look at https://brainly.com/question/16313918