determine the number of terms required to approximate the sum of the series with an error of less than 0.001.

The quartic function with only two real zeros of x=0 and x=4 is x² - 4x = 0

A quartic function is a quartic polynomial, that is, a polynomial with integer coefficients whose highest degree is four. The coefficient of the variable to the fourth degree cannot be zero. Examples of quartic functions include

From the roots;

a = 0 ; b = 4

From the polynomial expressions

x² - (a +b)x + ab = 0

x² - (0 +4 )x + 0*4 = 0

x² - 4x = 0

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The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.

Let the amount of money loaned at 9% be x

the amount of money loaned at 11% be y

According to the question,

Total money loaned = 20,500

Thus the equation formed is,

x + y = 20,500 ------ (i)

Simple interest is calculated by

I = P * r * t

where I is the simple interest

r is the rate of interest

t is the time

Thus, the interest on x = 0.09x

the interest on y = 0.11y

Total interest gained = 2,225

Thus the equation formed is,

0.09x + 0.11y = 2225 -------(ii)

Multiply (i) by 0.09

0.09x + 0.09y = 1845

Subtract the above from (ii)

0.02y = 380

y = 19000

x = 1500

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Answer:

The slope is undefined

Step-by-step explanation:

as - 4-2/-8-(-8)

Is - 6/0

Answer:

Step-by-step explanation:

The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm

This means that the required length of computer chips is between 1.1cm - 1.3cm

Where 1.1cm = [1.2 - 0.1]

1.3cm = [1.2 + 0.1]

Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.

The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:

- The length of the chips.

The length of the chips his production team produces should be tailored to meet the length specification of his client.

Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.

One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.

Using a calculator, we can find the sine of 98 degrees as follows:

sin 98° ≈ 0.9848

Rounding this to four decimal places, we get:

sin 98° ≈ 0.9848

Therefore, sin 98° is approximately equal to 0.9848.

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Answer:

divide by 2 equals 30.5 minus 7 equals to 23,5

Step-by-step explanation:

smaller is 23,5

B is 37.5

The total hours you study on Friday and Saturday is ; 3 hours

It is easy to calculate the Mean of a data table and we do this by Adding up all the numbers, then divide by how many numbers there are.

From the table, we are given number of hours spent for 5 days as;

Sunday = 0.75 hours

Monday = 1.5 hours

Tuesday = 0 hours

Wednesday = 2.5 hours

Thursday = 1 hour

Thus, if average for the week of 7 days is 1.25 and total for Friday and Saturday is x, then we have;

(0.75 + 1.5 + 0 + 2.5 + 1 + x)/7 = 1.25

x + 5.75 = 8.75

x = 8.75 - 5.75

x = 3 hours

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Answer:

20.22 miles

Step-by-step explanation:

If 10 laps is 6.74 then 30 laps is 3*6.74 which is 20.22

Answer:

A, B, C, and D

Step-by-step explanation:

all answer choices are the same

Blocking has reduced the estimate of experimental error from MS = 37.75 to MS = 2.65, a reduction of approximately 93%.

What is statistics ?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, summarize, and analyze data in order to make inferences and draw conclusions about populations based on samples. Statistics is widely used in fields such as science, medicine, business, engineering, social sciences, and many other areas where data are collected and analyzed. The goal of statistics is to provide insights and knowledge that can be used to make informed decisions and solve problems.

a. The sum of squares for the factor is 14.18

b. The number of degrees of freedom for the single factor in the experiment is DF = 1

c. The number of degrees of freedom for error is DF = 22

d. The mean square for error is MS = 37.75

e. The value of the test statistic is F = 0.376

f. If the significance level is 0.05, your conclusions are not to reject the null hypothesis. Yes

g. An upper bound on the P-value for the test statistic is p ≤ 0.05

h. A lower bound on the P-value for the test statistic is p > 0.01

i. Laura used 2 levels of the factor in this experiment

j. Laura replicated this experiment 12 times

k. Reconstructed ANOVA display:

Source DF SS MS F

Factor 1 14.18 14.18 15.97

Blocks 11 12.00 1.09 -

Error 12 31.75 2.65 -

Total 23 58.93 - -

Therefore, blocking has reduced the estimate of experimental error from MS = 37.75 to MS = 2.65, a reduction of approximately 93%.

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Answer:

8.5

Step-by-step explanation:

18=2x+1

-1        -1

_______

17=2x

_    _

2     2

8.5=x

Answer: 21.15 ft²

Step-by-step explanation:

We can use the formula for the area of a triangle:

(b×h)/2

In this case, the base is 9 and the height is 4.7.

So, we substitute the variables with the numbers in this problem.

(9 × 4.7)/2

9 × 4.7 = 42.3

42.3/2 = 21.15

So, our final answer is 21.15 ft²

Step-by-step explanation:

b)

\( {x}^{2} + x - 156 = 0 \\ (x + 13)(x - 12) = 0 \\ x = - 13 \\ or \\ x = 12\)

Step 1

State the formula for the expected value

Step 2

Find the probabilities

Step 3

Draw up the table

Hence, the expected value = 6.4

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

i did it on edge

The first five terms of the given sequence are:

C: 18, 30, 42, 54, 66

The formula for the nth term of an arithmetic sequence is expressed as:

aₙ = a + (n - 1)d

where:

a is first term

d is common difference

n is number of term

The formula for the sequence is 12x + 6. Thus:

First term = 12(1) + 6 = 18

Second term = 12(2) + 6 = 30

Third term = 12(3) + 6 = 42

Fourth term = 12(4) + 6 = 54

Fifth term = 12(5) + 6 = 66

Thus, the sequence is : 18, 30, 42, 54, 66

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Answer:

The degrees of freedom are:

\(df=n-1=10-1=9\)

The confidence level is 0.95 or 95%, the significance would be \(\alpha=0.05\) and \(\alpha/2 =0.025\), the critical value for this case would be \(t_{\alpha/2}=2.262\)

And replacing we got:

\(54.7-2.262\frac{9.956}{\sqrt{10}}=47.58\)    

\(54.7+2.262\frac{9.956}{\sqrt{10}}=61.82\)    

Step-by-step explanation:

Information given

In order to calculate the mean and the sample deviation we can use the following formulas:  

\(\bar X= \sum_{i=1}^n \frac{x_i}{n}\) (2)  

\(s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}\) (3)  

\(\bar X= 54.7\) represent the sample mean

\(\mu\) population mean  

s=9.956 represent the sample standard deviation

n=10 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

The degrees of freedom are:

\(df=n-1=10-1=9\)

The confidence level is 0.95 or 95%, the significance would be \(\alpha=0.05\) and \(\alpha/2 =0.025\), the critical value for this case would be \(t_{\alpha/2}=2.262\)

And replacing we got:

\(54.7-2.262\frac{9.956}{\sqrt{10}}=47.58\)    

\(54.7+2.262\frac{9.956}{\sqrt{10}}=61.82\)    

Answer:

15 ways

Step-by-step explanation:

girl 1 and boy 1

girl 2 and boy 1

girl 3 and boy1

girl 1 and boy 2

girl2 and boy 2

girl 3 and boy 2

girl 1 and boy 3

girl 2 and boy 3

girl 3 and boy 3

girl 1 and boy 4

girl 2 and boy 4

girl 3 and boy 4

girl 1 and boy 5

girl 2 and boy 5

girl 3 and boy 5

Given:

A taxi company has 10 taxis.

On a certain day, only eight taxi drivers show up for work.

So, 8 taxis can be driven.

How many taxis can be used to pick up passengers?

So, the answer will be 8 taxis

on another day, 10 taxi drivers show up for work, but five taxis are in the repair shop.

So, the remaining taxis that can be driven = 10 - 5 = 5 taxis

So, the answer to part 2: 5 taxis

Answer:

the answer is down below there are several of them.

Step-by-step explanation:

the exact form is- 22/3

decimal form is- 7.3

mixed number form is- 7 1/3

mark me brainliest if i am correct

Answer:

Step-by-step explanation:

There are two minus signs in front of the 5. Anytime you have an even number of minus signs in front of a number, the sign goes positive.

So - - - (-4) would become 4 because there are 4 minus signs in front of the 4.

- - - -  - (-9) would give just 9.

In this case, the question becomes 2 1/3 + 5 = 7 1/3

I don't know how you are to enter the answer. The alternate answer is 7.333

Answer:

To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.

Step-by-step explanation:

The acceleration of the collar at point A is 5 ft/s^2.

A) To determine the normal force on the collar at point A, we need to consider the forces acting on the collar. The only force acting on the collar in the vertical direction is the weight of the collar (5 lb), which is balanced by the normal force exerted by the rod. Therefore, we can write:

N - 5 = 0

where N is the normal force. Solving for N, we get:

N = 5 lb

B) To determine the acceleration of the collar at point A, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force on the collar is given by the force exerted by the spring, which is equal to the spring constant times the displacement of the collar from its unstretched length. At point A, the displacement of the collar is:

x = L - y = 3 - 0 = 3 ft

where L is the length of the rod and y is the position of the collar on the rod. Therefore, the force exerted by the spring is:

F = kx = 10 lb/ft × 3 ft = 30 lb

The weight of the collar is:

W = mg = 5 lb

where g is the acceleration due to gravity. The net force on the collar is therefore:

Fnet = F - W = 30 - 5 = 25 lb

Using Newton's second law, we can write:

Fnet = ma

where a is the acceleration of the collar. Solving for a, we get:

a = Fnet / m = 25 lb / 5 lb = 5 ft/s^2

Therefore, the acceleration of the collar at point A is 5 ft/s^2.

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Answer:

it's cut in half. the rest of the numbers are 20, 10, 5, 2.5

Step-by-step explanation:

divide all that is shown by 2 that's my proof

Answer:

a)  $497.70

b)  392.4 square feet

c)  $1,200

Step-by-step explanation:

A regular octagon has 8 sides of equal length.

Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:

\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)

If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:

\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)

Therefore, the cost of the railing is $497.70.

\(\hrulefill\)

To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:

\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)

Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:

\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)

Therefore, the area of the gazebo is 392.4 square feet.

\(\hrulefill\)

To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:

\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)

Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.

a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:

P = 8s = 8(9) = 72 feet

Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:

Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20

Therefore, the cost of the railing is $4,939.20.

b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:

A = (1/2)(10.9)(72) = 394.56 square feet

Therefore, the area of the gazebo is 394.56 square feet.

c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:

Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68

Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.

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Answer:

A student needs to take 10 dance classes to learn it

Step-by-step explanation:

Answer:

D is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

20 for both

Step-by-step explanation:

hope this helps

Answer:

1606588.92

Step-by-step explanation:

Answer:

1. 84 2. 360

Step-by-step explanation:

Use multiplication l*w*h