what is the answer to the second question and third question

Answer:

slope = 1

y-intercept = 5

Step-by-step explanation:

change in y-values = 1

change in x-values = 1

slope = 1/1 or 1

to find the y-intercept ('b'), select an ordered pair:  (1, 6)

use the slope-intercept formula and solve for 'b':

6 = 1(1) + b

6 = 1 + b

5 = b

slope = 1

y-intercept = 5

a. To find the Maclaurin series for f(x) = 5e^-2x, we first need to find the derivatives of the function.

f(x) = 5e^-2x

f'(x) = -10e^-2x

f''(x) = 20e^-2x

f'''(x) = -40e^-2x

The Maclaurin series for f(x) can be written as:

f(x) = Σ (n=0 to infinity) [f^(n)(0)/n!] x^n

The first four nonzero terms of the Maclaurin series for f(x) are:

f(0) = 5

f'(0) = -10

f''(0) = 20

f'''(0) = -40

So the Maclaurin series for f(x) is:

f(x) = 5 - 10x + 20x^2/2! - 40x^3/3! + ...

b. The power series using summation notation can be written as:

f(x) = Σ (n=0 to infinity) [f^(n)(0)/n!] x^n

f(x) = Σ (n=0 to infinity) [(-1)^n * 10^n * x^n] / n!

c. To determine the interval of convergence of the series, we can use the ratio test.

lim |(-1)^(n+1) * 10^(n+1) * x^(n+1) / (n+1)!| / |(-1)^n * 10^n * x^n / n!|

= lim |10x / (n+1)|

As n approaches infinity, the limit approaches 0 for all values of x. Therefore, the series converges for all values of x.

The interval of convergence is (-infinity, infinity).

Learn more about Maclaurin series here:

https://brainly.com/question/31745715

#SPJ11

The correct answer is option C, when the distribution of the data is approximately symmetric and bell-shaped.

According to the Empirical Rule, also referred to as the 68-95-99.7 Rule, for a normal distribution, roughly 68% of the data will lie within one standard deviation of the mean, 95% of the data will lie within two standard deviations of the mean, and 99.7% of the data will lie within three standard deviations of the mean.

Only when the distribution of the data is symmetric and bell-shaped does this rule hold.

The Empirical Rule cannot be used to estimate percentages if the data is skewed to the left or right.

The Empirical Rule can be used to predict the population from which the data were taken, making it a useful tool when examining data with a normal distribution.

It's crucial to remember that this rule is merely an estimation and may not be correct depending on whether the data follows a normal distribution.

Complete Question:

The empirical rule can be used to estimate some specific percentages _______.

Select one:

A. when the distribution of the data is skewed to the right.

B . when the distribution of the data is skewed to the left.

C. when the distribution of the data is approximately symmetric and bell-shaped.

D. when the distribution of the data has any shape.

To learn more about distribution visit:

https://brainly.com/question/27820465

#SPJ4

Answer:

Min = 1 4/6

Max = 3

Sum = min + max

=> sum = 1 4/6 + 3

=> sum = 4 /4/6

Answer:

4 4/6

Step-by-step explanation:

Answer:

The last one

Step-by-step explanation:

Answer:

f(4) = 17

Step-by-step explanation:

f(n) = 8+3(n-1)

f(4) = 8+3(4-1)

f(4) = 8+3(3)

f(4) = 8+9

f(4) = 17

Answer:

see below

Step-by-step explanation:

sqrt(24)  = sqrt( 4*6)

sqrt( 4) sqrt(6)  

2 sqrt(6)

Answer:

Yes,

Common ratio = 5.

Step-by-step explanation:

If its geometric it will have a common ratio.

5/1 = 5

25/5 = 5

125/25 = 5

So its geometric with commo ratio 5.

$2100 was invested at 2% and $2900 ($5000 - $2100) was invested at 3%.

Let x be the amount invested at 2% and y be the amount invested at 3%. We know that x + y = $5000 and the interest earned is $129. We can use the formula for simple interest, I = Prt, where I is the interest earned, P is the principal (or initial amount invested), r is the interest rate, and t is the time period.

Thus, we have:

0.02x + 0.03y = $129 (1)

x + y = $5000 (2)

We can solve for one of the variables in terms of the other from equation (2), such as y = $5000 - x. Substituting this into equation (1), we get:

0.02x + 0.03($5000 - x) = $129

Simplifying and solving for x, we get:

0.02x + $150 - 0.03x = $129

-0.01x = -$21

x = $2100

Therefore, $2100 was invested at 2% and $2900 ($5000 - $2100) was invested at 3%.

Know more about simple interest here:

https://brainly.com/question/30964674

#SPJ11

Answer:

(8.3, 3.15 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

Here (x₁, y₁ ) = (4.6, 2.3) and (x₂, y₂ ) = (12, 4) , then

midpoint = ( \(\frac{4.6+12}{2}\) , \(\frac{2.3+4}{2}\) ) = ( \(\frac{16.6}{2}\) , \(\frac{6.3}{2}\) ) = ( 8.3, 3.15 )

Answer:

\(mid \: point \: for \: x = \frac{x1 + x2}{2} \\ = \frac{4.6 + 12}{2} \\ x = \frac{16.6}{2} \\ x = 8.3 \\ mid \: point \: of \: y = \frac{y1 + y2}{2} \\ y = \frac{2.3 + 4}{2} \\ \frac{6.3}{2} = 3.15 \\ then(x \: y) = (8.3 \: 3.15) \\ thank \: you\)

Answer:

Rounding up numbers means to make a number with many numerical values or digits into a more simpler way.

Step-by-step explanation:

In order to round up a number you have to look to the digit next to it and if its greater then five it rounds up, if it's less then five it stays the same. If the number only has one digit then you have to look at that number and round up by seeing if its greater than or less than five.

Examples:

\(7\)

\(7>5\)

\(7=10\)

7 rounded up equals 10 because 7 is more near 10 then it is to one.

Round the number 12,371 to the nearest thousand.

This means to find the thousands place value (two) check the number next to the thousands place value (hundreds or three) and check to see if that number is greater then five or not.

\(12,371\)

\(3 <5\)

\(=12,000\)

Therefore the 12,371 rounded to the nearest thousand is "twelve-thousand" and that's because three is not greater then or equal to five.

Hope this helps.

To solve the equation sec(2x) + tan(2x) = 11 over the interval [0, 2π), we can use the identity sec^2(θ) - tan^2(θ) = 1:

1. Rewrite the given equation as sec(2x) = 11 - tan(2x).

2. Square both sides of the equation:
(sec(2x))^2 = (11 - tan(2x))^2.

3. Use the identity sec^2(θ) - tan^2(θ) = 1 to replace sec^2(2x):
1 + tan^2(2x) = (11 - tan(2x))^2.

4. Expand the right side of the equation:
1 + tan^2(2x) = 121 - 22*tan(2x) + tan^2(2x).

5. Subtract tan^2(2x) from both sides and simplify:
1 = 121 - 22*tan(2x).

6. Solve for tan(2x):
tan(2x) = (121 - 1) / 22 = 120 / 22 = 60 / 11.

7. Find 2x using the inverse tangent function:
2x = arctan(60 / 11).

8. Divide by 2 to find x:
x = (1/2) * arctan(60 / 11).

Since the interval is [0, 2π), we need to find all the solutions within that range. Since the tangent function has a period of π, we should also check the solution x = (1/2) * (arctan(60 / 11) + π). Calculate the two x values and check if they are within the given interval. If they are, they are the solutions to the original equation.

Visit here to learn more about  tangent function : https://brainly.com/question/30910929
#SPJ11

Answer:

1. True

2. HGK

3. 17⁰

Step-by-step explanation:

1. All angles in a triangle need to add up to 180. The right angle is a given 90⁰ so the other two angles need to add up to 90⁰ to equal 180⁰. Angle C corresponds to Angle K so Angle H corresponds to Angle E. So add Angle C and H together and it sums up to 90⁰ so it is true.

2. HGK; you match it up with the markings inside the triangle

3. Same logic with number 1 but you subtract 90 from 73 to find Angle K.

I hope this helps!!!

Answer:

i have made it in above picture

hope it helps

The question is incomplete. The complete question is :

One of the products produced by Branco Food Company is All-Bran Cereal, which competes with three other brands of similar all-bran cereals. The company's research office wants to investigate if the percentage of people who consume all-bran cereal is the same for each of these four brands. Let us denote the four brands of cereal by A B C and D. A sample of 900 persons who consume all-bran cereal was taken, and they were asked which brand they most often consume. Of the respondents, 201 said they usually consume Brand A, 224 consume Brand B, 299 consume Brand C, and 176 consume Brand D. Does the sample provide enough evidence to reject the null hypothesis that the percentage of people who consume all-bran cereal is the same for all four brands? Use alpha = 0.025. Find the value of the test statistic x^2. x^2 = the tolerance is +/-2% Using alpha = 0.025, can you conclude that the current percentage distribution is different from the hypothesized one? We conclude that the current percentage distribution from the hypothesized one.

Solution :

          A      B      C      D               Total

\($o_i$\)      201   224   299  176            900

\($e_i$\)      225  225    225  225

\($X^2 =\sum \frac{(o_i-e_i)^2}{e_i} = 37.5733$\)

\($X^2 = 9.3484$\)

We reject \($H_0$\)

\($\alpha = 0.025$\) level

\($H_0: A = B=C=D\ \ \ (1/4)$\)

\($H_a: A,B,C,D $\)  are not equal.

The distribution is multinomial hypothetical distribution.

Answer:

I believe the value is equal to 8

Answer:

87 mins

Step-by-step explanation:

The percentage of pages she read = 100-53= 47%

47%------------41 mins

53% ------------- x

x= (41×53)/47

x= 46.23 mins

nearest minute = 46 mins

Total reading assignments is 41+46= 87 mins

Answer:

87 minutes.

Step-by-step explanation:

to get the percentage of the read part, do 100% - 53% = 47%

41min = 47%

  ?        = 100%

cross multiply;

41 × 100 ÷ 47 = 87.2340...

round off to get 87 min

Answer:

y=50x

Step-by-step explanation:

The dots rise up by 50 and go right by one. rise/run=slope

There is no y-intercept because the line intersects at the origin, (0,0)

So, the answer is y=50x.

Answer$550.32

Step-by-step explanation: 7day = $320

commission = 8% of 2879

=230.32

 total earnings = 320 + 230.32

= 550.32

Answer:

B

Step-by-step explanation:

for every given input there is a unique output in B, there are two times in which 5 is the output. So it is not a function

Answer:

-8,-6,-3,7,9,10

Answer:

The cashier is wrong

\(Amount = 64.99\)

Step-by-step explanation:

Given

\(Jeans=34.95\)

\(Shirt = 24.95\)

\(Sales\ Tax = 8.5\%\)

Solving (a): Is the Cashier's step correct?

The cashier is wrong at step 2 because instead of calculating the sales tax, the cashier add the sales tax percentage to the total cost.

Solving (b):

First, calculate the total cost by adding the cost of jeans and shirt respectively:

\(Total = 34.95 + 24.95\)

\(Total = 59.90\)

Next, multiply the sales tax percentage to the total cost to get the sales tax amount.

\(Sales\ Tax = 8.50\% * 59.90\)

\(Sales\ Tax = 5.0915\)

Add the sales tax to the total, this gives the total payable amount.

\(Amount = 59.90 + 5.0915\)

\(Amount = 64.9915\)

\(Amount = 64.99\) approximated

Answer: 10x + 7

Step-by-step explanation:

multiply everything

2x + 7x + x + 7

combine like terms

10x + 7

Answer: A. Let's use x to represent the number of hours Opal works for the photographer, and y to represent the number of hours she coaches soccer. Then we can create the following system of inequalities to represent the situation:

12x + 7y ≥ 150 (Opal needs to earn at least $150 per week)

x + y ≤ 20 (Opal cannot work more than 20 hours per week)

B. There are different ways Opal can meet her goals, but here are two possible solutions:

Solution 1: Opal works for the photographer for 10 hours and coaches soccer for 10 hours. Then her total earnings for the week would be:

12(10) + 7(10) = 120 + 70 = $190

This meets her goal of earning at least $150 per week, and it also satisfies the constraint that she cannot work more than 20 hours per week.

Solution 2: Opal works for the photographer for 15 hours and coaches soccer for 5 hours. Then her total earnings for the week would be:

12(15) + 7(5) = 180 + 35 = $215

This also meets her goal of earning at least $150 per week, and it satisfies the constraint that she cannot work more than 20 hours per week.

C. To check if (10,6) is a solution to the system of inequalities, we need to substitute x = 10 and y = 6 into both inequalities and see if they are true:

12(10) + 7(6) ≥ 150

120 + 42 ≥ 150

162 ≥ 150 (true)

10 + 6 ≤ 20 (true)

Since both inequalities are true, (10,6) is a solution to the system. However, this solution does not meet Opal's goal of earning at least $150 per week, as her total earnings would be:

12(10) + 7(6) = 120 + 42 = $162

So, while (10,6) satisfies the constraints of the system, it is not a valid solution to the problem.

Step-by-step explanation:

Answer:

Have a good day people

Step-by-step explanation:

Answer:

fishing + camping = 15

not fishing + camping = 10

Becca needs approximately 5 bottles of engine oil to completely fill her car engine.

Since Becca's car engine has a capacity of 3.6 quarts and contains 1.2 quarts of engine oil, the remaining space left in her car engine is given by:

Space = 3.6 - 1.2

Space = 2.4 quarts.

By applying direct proportion, we have:

1 bottle = 0.5 quart.

x bottles = 2.4 quarts.

Cross-multiplying, we have:

0.5x = 2.4

x = 2.4/0.5

x = 4.8 ≈ 5 bottles.

Read more on direct proportion here: brainly.com/question/1266676

#SPJ1

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

Simple the area is 88

Step-by-step explanation:

Answer:

KM

KL

LM

Step-by-step explanation:

Answer:

y = -1/2x + 4

Step-by-step explanation:

y=mx+b

3 = m* 2 + b   .. pass (2,3)

y = 0       x = - b/m  .. x intercept

-b/m = 2b .... divide b both side

-1/m = 2           m= -1/2

b = 3 - 2m = 3 - (2*-1/2) = 4

equation:  y = -1/2x + 4