Find the value of x to the nearest tenth

Answer:

[tex]\sum^\infty_{n=0} -5 (\frac{x+2}{2})^n[/tex]

Step-by-step explanation:

Rn(x) →0

f(x) = 10/x

a = -2

Taylor series for the function f at the number a is:

[tex]f(x) = \sum^\infty_{n=0} \frac{f^{(n)}(a)}{n!} (x - a)^n[/tex]

[tex]f(x) = f(a) + \frac{f'(a)}{1!}(x-a)+\frac{f"(a)}{2!} (x-a)^2 + ...[/tex] ............ equation (1)

Now we will find the function f and all derivatives of the function f at a = -2

f(x) = 10/x            f(-2) = 10/-2

f'(x) = -10/x²         f'(-2) = -10/(-2)²

f"(x) = -10.2/x³      f"(-2) = -10.2/(-2)³

f"'(x) = -10.2.3/x⁴     f'"(-2) = -10.2.3/(-2)⁴

f""(x) = -10.2.3.4/x⁵    f""(-2) = -10.2.3.4/(-2)⁵

∴ The Taylor series for the function f at a = -4 means that we substitute the value of each function into equation (1)

So, we get [tex]\sum^\infty_{n=0} - \frac{10(x+2)^n}{2^{n+1}}[/tex] Or [tex]\sum^\infty_{n=0} -5 (\frac{x+2}{2})^n[/tex]

Taylor series  is a power series that gives the expansion of a function f (x) in the neighborhood of a point.

Taylor series is,   [tex]f(x)=f(a)+\frac{f'(a)}{1!}(x-a)+\frac{f''(a)}{2!}(x-a)^{2}+........[/tex]

[tex]f(x)=\sum_{n=0}^{\infty }-\frac{10(x+2)^{n}}{2^{n+1}}[/tex]

Here,  f(x) = 1/x  and a = -2

Now find derivative,

 f(x) = 10/x            f(-2) = 10/-2

f'(x) = -10/x²         f'(-2) = -10/(-2)²

f"(x) = 10.2/x³      f"(-2) = 10.2/(-2)³

f"'(x) = -10.2.3/x⁴     f'"(-2) = -10.2.3/(-2)⁴

Substituting above values in Taylor series expansion.

We get,   [tex]f(x)=\sum_{n=0}^{\infty }-\frac{10(x+2)^{n}}{2^{n+1}}[/tex]

Learn more:

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Answer:

The answer is option D.

Hope this helps you

Answer:

(x + 2) ^2 (x - 2) ^ 2 so A is the answer.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

A) 95% confidence interval for the population mean PEF for children in biomass households = (3.214, 3.386)

95% confidence interval for the population mean PEF for children in LPG households

= (4.125, 4.375)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.

C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.375)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Step-by-step explanation:

A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.

Finding the critical value from the z-tables,

Significance level for 95% confidence interval

= (100% - 95%)/2 = 2.5% = 0.025

z (0.025) = 1.960 (from the z-tables)

For the children in the biomass households

Sample mean = 3.30

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.20

N = sample size = 755

σₓ = (1.20/√755) = 0.0436724715 = 0.04367

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 3.30 ± (1.960 × 0.04367)

CI = 3.30 ± 0.085598

95% CI = (3.214402, 3.385598)

95% Confidence interval = (3.214, 3.386)

For the children in the LPG households

Sample mean = 4.25

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.75

N = sample size = 750

σₓ = (1.75/√750) = 0.063900965 = 0.063901

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 4.25 ± (1.960 × 0.063901)

CI = 4.25 ± 0.125246

95% CI = (4.12475404, 4.37524596)

95% Confidence interval = (4.125, 4.375)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.

The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.

Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂

The null hypothesis is

H₀: μ ≥ 0 or μ₁ ≥ μ₂

The alternative hypothesis is

Hₐ: μ < 0 or μ₁ < μ₂

Test statistic for 2 sample mean data is given as

Test statistic = (μ₂ - μ₁)/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = 3.30

n₁ = 755

s₁ = 1.20

μ₂ = 4.25

n₂ = 750

s₂ = 1.75

σ = √[(1.20²/755) + (1.75²/750)] = 0.07740

z = (3.30 - 4.25) ÷ 0.07740 = -12.27

checking the tables for the p-value of this z-statistic

Significance level = 0.01

The hypothesis test uses a one-tailed condition because we're testing in only one direction.

p-value (for z = -12.27, at 0.01 significance level, with a one tailed condition) = < 0.000000001

The interpretation of p-values is that

When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.

Significance level = 0.01

p-value = 0.000000001

0.000000001 < 0.01

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.

C) For FEY for biomass households,

Sample mean = 2.3 L/s

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation = 0.5

N = sample size = 755

σₓ = (0.5/√755) = 0.0182

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 2.30 ± (1.960 × 0.0182)

CI = 2.30 ± 0.03567

95% CI = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.375)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Hope this Helps!!!

Answer:

0.1/4-3/20=1/40-6/40=-1/8 200% of this is -1/4

Step-by-step explanation:

This shows that  200 percent of (0.020(5/4) + 3 ((1/5) - (1/4))) is -2.75

Given the expression as shown in the question:

[tex]200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{1}{5}- \frac{1}{4} )][/tex]

Expand the expression in the square bracket using the distribution law as shown:

[tex]=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{4-5}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{-1}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )-(\frac{3}{20} )]\\=200\% \ of \ [0.020(1.25 )-\frac{3}{20}]\\=\frac{200}{100} \times [0.025-0.15]\\=2 \times [-0.125]\\=-2.75[/tex]

Hence the correct answer to the expression is -2.75.

Learn more here: https://brainly.com/question/19383460.

Answer:

P(Chase) > P(Ava)

700 > 587

Therefore, Ava's claim is wrong!

On day 14, Chase's bacteria population will be greater than Ava's bacteria population.

Step-by-step explanation:

Please refer to the attached image.

Ava's bacteria population is modeled by the following equation.

[tex]$ b(t) = 200(1+0.08)^t $[/tex]

Where t is time in days and b(t) is the population of the bacteria after t days.

The graph represents the population of Chase's bacteria.

Ava claims that on day 14, she will have more bacteria than Chase.

Let us compare the population of both bacteria.

Chase bacteria population when t = 14 days:

From the graph, the population is approximately 700 at t = 14 days

P(Chase) ≈ 700

Ava bacteria population when t = 14 days:

at t = 14 days

[tex]b(t) = 200(1+0.08)^t \\\\ b(14) = 200(1.08)^{14} \\\\ b(14) = 200 (2.93719)\\\\ b(14) = 587.44[/tex]

So, the population is approximately 587 at t = 14 days

P(Ava) ≈ 587

P(Chase) > P(Ava)

700 > 587

Therefore, Ava's claim is wrong!

On day 14, Chase's bacteria population will be greater than Ava's bacteria population.

Answer:

D

Step-by-step explanation:

Trust

Using the Pythagorean theorem

Hypotenuse = sqrt( 11^2 + 7^2)

= sqrt( 121 + 39)

= sqrt( 160)

= 12.694

Answer:

B) (x^2-2x)/(2x+6)

Step-by-step explanation:

When dividing fractions, it's just like multiplying the reciprocal of the second fraction : x/y divided by z/w = x/y * w/z.

We use that and we get (x-2)/(x+3) * x/2. we simplify and get x(x-2)/2(x+3). So Our answer is B

it's 15, since it is divisible by both 15 (15 x 1) and 3 (3 x 5)

Answer:

15

Step-by-step explanation:

Well to find the least common denominator of [tex]\frac{1}{3}[/tex] and [tex]\frac{11}{15}[/tex].

We have to see if 11/15 can be reduced, and by looking at the fraction it can’t be reduced.

So we just have to make 1/3 fraction have the same demimitator as 11/15.

So we just multiply it by 3 to get 15 go the LCD is 15.

Answer:

0

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

  and the given points

m = ( 2-2)/ ( 3-4)

    = 0/ -1

    = 0

The slope is zero

Answer:

Step-by-step explanation:

Given the function f(x,y) = [tex]\frac{4xy^{2} }{7x^{2} + y^{4} }[/tex], we are to show that lim (x, y)→(0, 0) f(x, y) exist. To show that, the following steps must be followed.

[tex]\lim_{(x,y) \to (0,0)} \frac{4xy^{2} }{7x^{2} + y^{4} }\\[/tex]

substituting the limit x = 0 and y = 0 into the function we have;

[tex]\frac{4(0)^{2} }{7(0)^{2} + (0)^{4} }\\= \frac{0}{0} (indeterminate)[/tex]

Since we got an indeterminate function, we will then substitute y = mx into the function as shown;

[tex]\lim_{(x,mx) \to (0,0)} \frac{4x(mx)^{2} }{7x^{2} + (mx)^{4} }\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2} x^{3} }{7x^{2} + m^{4}x^{4} }\\\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2} x^{3} }{x^{2}(7 + m^{4} x^{2}) }\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2}x }{7 + m^{4} x^{2} }[/tex]

Substituting x = 0 , the limit of the function becomes;

[tex]\frac{4m^{2}(0) }{7 + m^{4} (0)^{2} }\\= \frac{0}{7}\\ = 0[/tex]

Since the limit of the function gives a finite value of 0 (the limit tends to 0). This shows that the limit exists.

Answer:

the slope is 8

Step-by-step explanation:

The coefficient of x,  "m"  is the slope in the slope-intercept form:

y = mx + b

Answer:

49.8 nautical miles

Step-by-step explanation:

Recall that speed = distance/time

Time = 2hours

Speed = 12knots and 16 knots respectively

D = speed×time

D1 = 12×2 = 24

D2 = 16×2 = 32

Using the 'cosine rule' we have:

a^2 = b^2+c^2-2bc cos Θ

Where a =?

b =24

c = 32

Θ = 125°

a² = 24² + 32² - 2(24)(32)cos125°

a^2 = 576+1024 - 1536cos125°

a² = 1600 - 1536(-0.57357)

a² = 1600+881.0134

a² = 2481.0134

Then, a² = 2481.013406

a =√2481.013406

Hence, a = 49.8 nautical miles

In this exercise we must use the knowledge about triangles to calculate the distance that a ship will travel, in this way we find that:

49.8 nautical miles

First, remember the formula for distance, which is:

[tex]Speed = distance/time[/tex]

And knowing that the data reported in the exercise are:

So putting the values ​​informed in the distance formula, we have:

[tex]D = speed*time\\D_1 = 12*2 = 24\\D_2 = 16*2 = 32[/tex]

Using the 'cosine rule' we have:

[tex]a^2 = b^2+c^2-2bc cos \theta[/tex]

Find the a, will have:

[tex]b =24 \ \ \ c = 32 \ \ \ \theta = 125\\a^2 = 24^2 + 32^2 - 2(24)(32)cos125\\a^2 = 576+1024 - 1536cos125\\a^2 = 1600 - 1536(-0.57357)\\a^2 = 1600+881.0134\\a^2 = 2481.0134\\a=49.8[/tex]

See more about triangles at brainly.com/question/25813512

Answer:

[tex]\boxed{\sf \ \ x=6 \ \ }[/tex]

Step-by-step explanation:

Hello,

BMN and NPC are two similar triangles so

[tex]\dfrac{BM}{MN}=\dfrac{NP}{PC}\\\\ \dfrac{10-x}{x}=\dfrac{x}{15-x}\\\\<=>(15-x)(10-x)=x^2\\\\<=>150-25x+x^2=x^2\\\\<=>25x=150\\\\<=>x=6[/tex]

espero que esto ayude

Answer:

2.26 repeating

Step-by-step explanation:

Convert the fraction to a decimal by dividing the numerator by the denominator.

hope this helpes

be sure to give brainliest

Answer:

Step-by-step explanation:

The vertex can be located most easily by completing the square of

f(x) = -X^2 - 2x - 1 (which is equivalent to -(x^2 + 2x + 1).  The latter expression can be rewritten as -(x + 1)^2, which indicates that the x-coordinate of the vertex is -1.  The corresponding y-value is 0.  Vertex is at (-1, 0).

The function is increasing for x < -1 and decreasing for x > -1.

The domain of the function is "all real numbers."

The range is (-infinity, 0)

Answer:

Step-by-step explanation:

We would apply the future value which is expressed as

FV = C × [{(1 + r)^n - 1}/r]

Where

C represents the yearly payments of the young professional.

FV represents the amount of money

in your account at the end of 40 years.

r represents the annual rate.

n represents number of years or period.

From the information given,

r = 4% = 4/100 = 0.04

C = $76000

n = 40 years

Therefore,

FV = 76000 × [{(1 + 0.04)^40 - 1}/0.04]

FV = 76000 × [{4.8 - 1}/0.04]

FV = 76000 × 95

FV = P7220000

Answer:

Yeah, you got the answer right.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

To begin with notice that  

        [tex]\displaymode{ \tan(x) = \frac{30}{10 + 30\cot(y)} }[/tex]

From that equation you get that

10 tan(x)  +  30tan(x) cot(x) = 30

therefore

tan(x) + 3 tan(x) cot(x) = 3

Answer:

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

2¹³

13 x 13

Step-by-step explanation:

We simply find numbers that can multiply to 26 and write out the multiplication to get our answer.

Answer: option D on edge 2020

Step-by-step explanation:

if you reverse the formula for mean, then you just insert the numbers and you have your answer

Hey there! :)

Answer:

Point V.

Step-by-step explanation:

Given the coordinates of T at (-6.5, 1), U represents T before any reflections. (Helps to visualize this better)

Reflecting across the x-axis results in the sign of the y-coordinate changed. Point T after this reflection becomes (-6.5, -1).

Finally, reflecting across the y-axis will change the sign for the x-coordinate.

(-6.5, -1) becomes (6.5, 1). This is represented by point V.

Answer:

a1- 2 terms

a2- 6x, 9y

a3- 6,9

b1-2 terms

b2- 7x, 12x

b3- 7,12

c1- 3 terms

c2- 5x^2, 2y, 3

c3- 5,2,3

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

The null hypothesis for a chi-square goodness of fit test states that the data are consistent with a specified distribution.

While the alternative hypothesis states that the data are not consistent with a specified distribution.

In this case study, the test is for a nose distribution. Thus the null hypothesis would be that the population has a normal distribution.

Answer:

620 comic books

2480 / 4 is 620.

620 x 3 is 1860.

1860 + 620 is 2480.

Done!

Answer:

30x - 18

Step-by-step explanation:

6(5x - 3)

Apply the distributive property.

6(5x) + 6(-3)

30x + - 18

Answer:

30x - 18 is your final answer

Answer:

113

Step-by-step explanation:

Let the number of adult tickets sold =a

Let the number of student tickets sold =s

A total of 259 tickets were sold, therefore:

a+s=259

Adult tickets were sold for $24 each and student tickets were sold for $16 each.

Total Revenue = $5,312

Therefore:

24a+16s=5,312

We solve the two derived equations simultaneously.

From the first equation

a=259-s

Substitute a=259-s into 24a+16s=5,312

24(259-s)+16s=5,312

6216-24s+16s=5,312

-8s=5,312-6216

-8s=-904

Divide both sides by -8

s=113

Therefore, 113 student tickets were sold.

Answer:

Yup P is the right one having 62.26%

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

We can set it up as

P = 33/53

Q = 20/48

R = 54/90

S = 44/83

This is because we are calculating the percent of yellow birds in the total amt. of birds in a specified park.

Now we calculate =>

P = 33/53 = around 0.62

Q = 20/48 = around 0.416

R = 54/90 = 0.6

S = 44/83 = around 0.53

We find that Park P has the greatest percentage and -->

Thus, Park P is our answer and yes, you are correct.