What is the area of a sector with a central angle of 5pi over 6 radians and a radius of 5.6ft

Answer:

Seventeen billion, eight hundred fifty-seven million and twelve.

Step-by-step explanation:

Answer:

17,857,000,012 = 17 billion 857 million 12

Step-by-step explanation:

Bye lad!

What is your question?

Answer:

yeah what's your question?

Answer:

The taylor's series for f(x) = ln x centered at c = 1 is:

[tex]ln (x) = \sum\limits^{\infty}_{n = 1} {\frac{(-1)^{n+1}(x-1)^n}{n} }[/tex]

Step-by-step explanation:

The calculations are handwritten for clarity and easiness of expression.

However, the following steps were taken in arriving at the result:

1) Write the general formula for Taylor series expansion

2) Since the function is centered at c = 1, find f(1)

3) Get up to four derivatives of f(x) (i.e. f'(x), f''(x), f'''(x), [tex]f^{iv}(x)[/tex])

4) Find the values of these derivatives at x =1

5) Substitute all these values into the general Taylor series formula

6) The resulting equation is the Taylor series

[tex]ln (x) = \sum\limits^{\infty}_{n = 1} {\frac{(-1)^{n+1}(x-1)^n}{n} }[/tex]

Answer:

9 mile trip

Step-by-step explanation:

$15 + $15 = $30

$15 + $9 = $24

$15 + $25 = $40

$15 + $12 = $27

$30 > $25

$24 < $25

$40 > $25

$27 > $25

Answer:

c) H0: µ = 7 hours (null hypothesis)

H1: µ < 7 hours (alternative hypothesis and original claim)

Step-by-step explanation:

The hypothesis test is performed in order to see if a sample outcome gives evidence to reject a null hypothesis and support the researchers claim.

In this case, the claim is that the mean amount of sleep for adults is less than 7 hours.

For this claim, the alternative hypothesis will state the researcher's claim: the mean amount of sleep for adults is significantly less than 7 hours.

The null hypothesis will state the opposite: the mean amount of sleep for adults is not significantly less than 7 hours. In this case, it is the same to claim that the mean amount is 7 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=7\\\\H_a:\mu< 7[/tex]

Answer:

A = 166.66

Step-by-step explanation:

You have the following functions:

[tex]y_1=x^2-24\\\\y_2=1[/tex]

In order to calculate the area of the given region, you first calculate the points at which the function y = x^2-24 intersects the line y=1:

[tex]1=x^2-24\\\\0=x^2-25\\\\x=\sqrt{25}=\pm 5[/tex]

Next, you take into account that the area between the two function is given by:

Where you have used the fact that y2 is above the y1 function.

Next, you calculate the following integral:

[tex]A=\int_{-5}^{5}(1-(x^2-24))dx=\int_{-5}^{5}(25-x^2)dx\\\\A=(25x-\frac{1}{3}x^3)|_{-5}^{5}\\\\A=(25(5)-\frac{1}{3}(125))-(25(-5)-\frac{1}{3}(-125))\\\\A=166.66[/tex]

Then, the area of the bounded region is 166.66

Answer:

Step-by-step explanation:

y>3/2 x-1

y<3/2 x-1

graphs do not intersect any point.

so no solution.

Answer:

D

Step-by-step explanation:

no solution

Answer:

The probability of getting even 7 times out of 8 is 1/256. Hope this helps!!

Step-by-step explanation:

21/7 = 3 is the answer of your question

Answer:

2nd Option

Step-by-step explanation:

Standard Form: ax² + bx + c

This can be modified to fit any degree polynomial, as long as the highest degree is first, and then decreasing. So our answer is B.

Answer:

[tex]\boxed{\sf \ \ \ 8^5 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]8*8*8*8*8 =8^5[/tex]

because we use five time 8 in the multiplication

hope this helps

Answer: True

Step-by-step explanation: Taking the triangle from the left and moving it to the right creates a rectangle. From there just do 12.8×4.5.

Answer:

0.015 radians per second.

Step-by-step explanation:

They tell us that at the moment the speed would be 6 ft / s, that is, dx / dt = 6 and those who ask us is dθ / dt.

Which we can calculate in the following way:

θ = arc sin 100/200 = pi / 6

Then we have the following equation of the attached image:

x / 100 = cot θ

we derive and we are left:

(1/100) * dx / dt = - (csc ^ 2) * θ * dθ / dt

dθ / dt = 0.01 * dx / dt / (- csc ^ 2 θ)

dθ / dt = 0.01 * 6 / (- csc ^ 2 pi / 6)

dθ / dt = 0.06 / (-2) ^ 2

dθ / dt = -0.015

So there is a decreasing at 0.015 radians per second.

The horizontal distance and the height of the kite are illustration of rates.

The angle is decreasing at a rate of 0.24 radian per second

The given parameters are:

[tex]\mathbf{Height =y= 100ft}[/tex]

[tex]\mathbf{Speed =\frac{dx}{dt}= 6fts^{-1}}[/tex]

[tex]\mathbf{Length = 200}[/tex]

See attachment for illustration

Calculate the angle using the following sine ratio

[tex]\mathbf{sin(\theta) = \frac{100}{200}}[/tex]

[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]

The horizontal displacement (x) is calculated using the following tangent ratio:

[tex]\mathbf{tan(\theta) = \frac{100}{x}}[/tex]

Take inverse of both sides

[tex]\mathbf{cot(\theta) = \frac{x}{100}}[/tex]

[tex]\mathbf{cot(\theta) = \frac{1}{100}x}[/tex]

Differentiate both sides with respect to time (t)

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dx}{dt}}[/tex]

Substitute known values

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 6}[/tex]

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

Recall that:

[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]

Take inverse of both sides

[tex]\mathbf{csc(\theta) = 2}[/tex]

Square both sides

[tex]\mathbf{csc^2(\theta) = 4}[/tex]

Substitute [tex]\mathbf{csc^2(\theta) = 4}[/tex] in [tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

[tex]\mathbf{-4 \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

Divide both sides by -4

[tex]\mathbf{\frac{d\theta}{dt} = -\frac{24}{100}}[/tex]

[tex]\mathbf{\frac{d\theta}{dt} = -0.24}[/tex]

Hence, the angle is decreasing at a rate of 0.24 radian per second

Read more about rates at:

https://brainly.com/question/6672465

Answer:

C. Approaches 35

Step-by-step explanation:

If we graph the expression, we see that we have an asymptote at y = 35.

Answer:

The answer is below

Step-by-step explanation:

What must be applied to know if the result is true or reliable is a  test statistic, since due to it we can calculate how true or rather what is the probability that this data will occur. There are many types of  test statistic, use the one that best fits the data.

The veracity of the medium where the information comes from is also important, whether they took a representative sample or not, among other parameters.

Answer:

She forgot to combine the 2 negative signs and turn it into a positive.

Step-by-step explanation:

When you subtract a negative, you are adding the number. So if we have 3.5 - (-4.1), it would equal 3.5 + 4.1, which is 7.6

Answer:

She subtracted a negative incorrectly by simply subtracting a positive when subtracting a negative means to add a positive.

Step-by-step explanation:

She subtracted 3.5 - 4.1 which is -0.6

The problem is subtracting -4.1 which means to add 4.1

3.5 - (-4.1) = 3.5 + 4.1 = 7.6

She did: 3.5 - (-4.1) = 3.5 - 4.1 = -0.6 which is incorrect.

Each line between 0 and 1 is 1/10 ( there are 10 lines)

First arrow is on the 3rd line so would be 3/10

The next arrow is 3 away from that so would be 3/10

The 3rd arrow is 2 away from the 2nd so would be 2/10

3/10 + 3/10 + 2/10 = 8/10

The answer is b

Answer:

Step-by-step explanation:

Given That:

Let A = {the first board is green} and B = {the second board is green}.

A lumber company has just taken delivery on a shipment of 10,000 2×4 boards.

Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other.

We are to compute the following probabilities :

P(A)

P(B)

P(A ∩ B)

To start with the probability P(A)

[tex]P(A) = \dfrac{1000}{10000}[/tex]

P(A) = 0.1

[tex]P(B) = P(B|A)*P(A)+P(B|A')*P(A')[/tex]

where;

[tex]P(B|A) = \dfrac{N(B|A)}{N-1}[/tex]

[tex]P(B|A) = \dfrac{999}{9999}[/tex]

[tex]P(B|A) =0.0999[/tex]

[tex]P(B|A') = \dfrac{N(B|A')}{N-1}[/tex]

[tex]P(B|A') = \dfrac{1000}{999}[/tex]

[tex]P(B|A') = 0.10[/tex]

Recall that :

[tex]P(B) = P(B|A)*P(A)+P(B|A')*P(A')[/tex]

[tex]P(B) = 0.0999*0.1+0.10*(1-0.1)[/tex]

[tex]P(B) = 0.00999+0.10*(0.9)[/tex]

[tex]P(B) = 0.00999+0.09[/tex]

[tex]P(B) = 0.0999[/tex]

P(A ∩ B) = P(B|A)B

P(A ∩ B) = 0.0999 × 0.10

P(A ∩ B) = 0.00999

(b)

Given that A and B are independent; Then:

P(A ∩ B) = P(A) × P(B)

0.00999 = 0.1 × 0.09999

0.00999 =  0.00999

As such A and B are independent

However; when P(A ∩ B) = P(A) = P(B) = 0.1

P(A ∩ B) = P(A) × P(B)

P(A ∩ B) = 0.1 × 0.1

P(A ∩ B) =  0.01

Answer:

A ∪ B = {1,3,6,9,12,15,18,24}

Step-by-step explanation:

Let A = {3,6,9,12,15}

B = {1,6,12,18,24}

So,

A ∪ B = {3,6,9,12,15} ∪ {1,6,12,18,24}

A ∪ B = {1,3,6,9,12,15,18,24}

Answer:

{1,3,6,9,12,15,18,24}

Step-by-step explanation:

The union is joining of the elements of the sets

{3, 6, 9, 12, 15}U {1, 6, 12, 18, 24}

= {1,3,6,9,12,15,18,24}

Answer:

C. Critical values: r = +0.396

Step-by-step explanation:

Hello!

A linear correlation for two variables X₁ and X₂ was calculated.

For a sample n= 25 the sample correlation coefficient is r= 0.767.

Be the hypotheses:

H₀: ρ = 0

H₁: ρ ≠ 0

α: 0.05

For this hypothesis test, the rejection region is two-tailed, and the degrees of freedom are Df= n-2= 25-2= 23

So using the Pearson product-moment correlation coefficient table of critical values, under the entry for "two tailed tests" you have to cross the level of significance and the degrees of freedom to find the corresponding critical value:

[tex]r_{n-2;\alpha }= r_{23;0.05}= 0.396[/tex]

Since the calculated correlation coefficient is greater than the critical value, you can reject the null hypothesis, this means that the correlation is significant at level 5%

I hope this helps!

Answer:

Increase: 1.7

Decrease: 0.3

Step-by-step explanation:

Increase:

100% + 70% = 117%

117/ 100 = 1.7 (multiplier)

Decrease:

100% - 70%= 30%

30/ 100 = 0.3 (multiplier)

Answer:1.P(exactly 2 kids are girls)=3/8

2. P(at least 1 is boy)=7/8

Step-by-step explanation:

1.P(exactly 2 kids are girls)=N(outcomes with 2 girls) /Total number of outcomes.

All possible outcomes are ggb,gbg, bgg, gbb, bgb, bbg, ggg, bbb - total 8

Outcomes where are exactly 2 girls are:

ggb,gbg, bgg - total 3 outcomes

So P(exactly 2 are girls)=3/8

2. P(at least 1 is boy)=Number of outcomes , where are at least 1 boy (1,2 or all 3 kids are boys)/ Total number of outcomes

All possible outcomes are ggb,gbg, bgg, gbb, bgb, bbg, ggg, bbb - total 8

Outcomes, where at least 1 kid is boy: ggb,gbg, bgg, gbb, bgb, bbg, bbb - total  7

P(at least 1 is boy)=7/8

Answer:

The answer is option D.

Step-by-step explanation:

To find LJ we use the sine rule

From the picture

LK / sin J = LJ / sin K

LK = 9

J = 89°

K = 23°

So now LJ is

9 / sin 89° = LJ / sin 23°

Make LJ the subject

That's

LJ = 9 sin 23° / sin 89°

LJ = 3.51

The final answer is

Hope this helps you.

Answer:

17.1 meters

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse.

6 and 16 are the legs, because they form the right angle. c is the hypotenuse because it is opposite the right angle.

[tex]6^2+16^2=c^2[/tex]

Evaluate the exponents.

6^2= 6*6= 36

16^2= 16*16= 256

[tex]36+256=c^2[/tex]

Add 36 and 256.

[tex]292=c^2[/tex]

Since c is being squared, take the square root of both sides of the equation. The exponent and square root will cancel and leave c by itself

[tex]\sqrt{292} =\sqrt{c^2}[/tex]

[tex]\sqrt{292}=c[/tex]

[tex]17.0880075=c[/tex]

Round to the nearest tenth. The 8 in the hundredeth place tells us to roung the 0 in the tenth place up to a 1.

[tex]17.1=c[/tex]

c= 17.1 m

The missing length, or the hyptenuse is 17.1 meters.

Answer:

A

Step-by-step explanation:

Given the equality y > -½, it means the values of y is greater than -½.

The values of y would range from 0 upwards. I.e. 0, ½, 1, 1½, 2. . .

Thus, when graphed on a number line, the circle that appears like "o" would start from -½, and the "o" would not be full or shaded to indicate that -½ is not included in the values of y, which are greater than -½. Since the values of y are greater than -½ the direction of the arrow that indicates values of y would point towards our far right, to indicate the values included as y.

Therefore, the graph that indicates the inequality y > ½ is A

Answer:

A

Step-by-step explanation:

Hey there! :)

Answer:

x > 9/5.

Step-by-step explanation:

Given:

2/3x - 1/5 > 1

Start by adding 1/5 to both sides:

2/3x > 1 + 1/5

2/3x > 6/5

Divide 2/3 from both sides by multiplying by the reciprocal:

2/3x × 3/2 > 6/5 × 3/2

x > 18/10

Simplify:

x > 9/5.

Answer:

[tex]x=38.5^\circ[/tex]

Step-by-step explanation:

Given that the left angle = [tex](3x-3)^\circ[/tex]

The right angle across from it [tex]= 6(x-10)^\circ[/tex]

The other two angles are x and x.

We know that the sum of angles at a point equals 360 degrees.

Therefore,

[tex](3x-3)^\circ+6(x-10)^\circ+x+x=360^\circ\\3x-3+6x-60+2x=360\\11x-63=360\\11x=360+63\\11x=423\\x=38.5^\circ[/tex]

The value of x is approximately 38.5 degrees.

Answer:

[tex]\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C[/tex]

Step-by-step explanation:

Given the function: [tex]f(x)=\dfrac{8x^3}{5}+3x-\dfrac{4}{5}[/tex]

To take the antiderivative (or integral) of a function, we follow the format below.

[tex]f(x)=x^n\\$Then its antiderivative\\Antiderivative of f(x)$=\dfrac{x^{n+1}}{n+1}[/tex]

Therefore, the antiderivative of f(x) is:

[tex]=\dfrac{8x^{3+1}}{5(3+1)}+\dfrac{3x^{1+1}}{2}-\dfrac{4}{5}x+C\\=\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C[/tex]

We want to check our result by differentiation.

[tex]\dfrac{d}{dx}\left(\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C\right)\\=\dfrac{d}{dx}\left(\dfrac{8x^{4}}{20}\right)+\dfrac{d}{dx}\left(\dfrac{3x^{2}}{2}\right)-\dfrac{d}{dx}\left(\dfrac{4}{5}x\right)+\dfrac{d}{dx}\left(C\right)\\\\=\dfrac{32x^{3}}{20}+\dfrac{6x}{2}-\dfrac{4}{5}+0\\\\=\dfrac{8x^{3}}{5}+3x-\dfrac{4}{5}[/tex]

Answer:

Step-by-step explanation:

Using the proportion test

Null hypothesis: p <= 0.22

Alternative hypothesis: p > 0.22

Using the formula

z score = p - P /√ (P(1-P)/n)

Where p is 74/200= 0.37, P = 0.22, n = 200.

0.37-0.22 / √(0.22(1-0.22)/200)

0.15 / √(0.22(0.78)/200)

0.15 / √(0.1716/200)

0.15/ √0.000858

0.15 / 0.02929

= 5.1212

To help arrive at a conclusion, we have to find the p value, using a p value calculator at the 0.05 level of significant, the p value is less than 0.00001... Thus we would reject the null as there is sufficient statistical evidence to prove that the proportion is higher than that reported by the polling ​organization.

Answer:

d. i and iii

Step-by-step explanation:

Notice that the definition provided states that the outcome needs to be numerical in order for a variable to be deemed a random variable:

i. The amount of rain is described in inches (i.e. 1.5 in; 2.0 in) and thus may be considered a random variable

ii. The major of a student is not quantitative as it is a descriptive variable (i.e. Arts; Psychology) and thus is not a random variable

iii. The number of books purchased is a numeric quantity (i.e. 15 books) and may be considered a random variable

Therefore, the answer is d. i and iii

Answer:

Step-by-step explanation:

i and iii

Answer:

THE CURVED ONE

Step-by-step explanation:

THE OTHER ONES R STRAIGHT LINES

THE ONE ON THE TOP  RIGHT CORNER IS A PARABOLA

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

                    ✌ -ZYLYNN JADE ARDENNE