Need help, Will mark brainlest!

Answer:

Dy/Dx=-4x/(1+x²)²

Step-by-step explanation:

The differential of 1_x² over 1+x²​

First of all

1_x² over 1+x²​ = (1_x²) / (1+x²​)

Let (1_x²) = u

Let (1+x²​) = v

Differential = Dy/Dx

Dy/Dx of (1_x²) / (1+x²​)

= (VDu/Dx -UDv/Dx)V²

u = (1-x²)

Du/Dx = -2x

(VDu/Dx) =(1+x²)(-2x)

V = 1+x²

Dv/Dx = 2x

UDv/Dx= (1-x²)(2x)

v² = (1+x²)²

Dy/Dx = ((1+x²)(-2x) - (1-x²)(2x))/(1+x²)²

Dy/Dx= ((-2x -2x³)-(2x-2x³))/(1+x²)²

Dy/Dx=( -2x -2x - 2x³ +2x³)/(1+x²)²

Dy/Dx=-4x/(1+x²)²

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

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 range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Step-by-step explanation:

The complete question is:

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Solution:

As the sample size is large, i.e. n = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.

So,[tex]\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})[/tex]

The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.

The critical value of z for 98% confidence level is,

z = 2.33

Compute the 98% confidence interval as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)[/tex]

Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Answer:

The decision is to not reject the null hypothesis.

At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50% (P-value = 0.1443).

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion of all those using the drug that experience relief is significantly higher than 50%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

The significance level is 0.01.

The sample has a size n=200.

The sample proportion is p=0.54.

[tex]p=X/n=108/200=0.54[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.54-0.5-0.5/200}{0.035}=\dfrac{0.038}{0.035}=1.061[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>1.061)=0.1443[/tex]

As the P-value (0.1443) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50%.

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:

Answer:

Step-by-step explanation:

Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]

To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;

[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]

As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;

[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]

Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]

Since the limit of the sequence gave a finite number , the sequence converges.

Note that the only case when the sequence diverges id when the limit of the sequence is infinite

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

Answer:

8 is in the hundreds place as well as in the tens place.

Step-by-step explanation:

We use the base 10 system. 880 would represent eight hundred and eighty. So our 0 would be the ones place, 8 in the tens place, and 8 also in the hundreds place.

Answer:

a. [tex]N(1)=2600[/tex]

b. [tex]N'(a) = 470/a[/tex]

c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)

d. lim a→[infinity] N′(a) = 0

Step-by-step explanation:

a.

the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:

[tex]N(1)=2600 + 470ln(1)[/tex]

[tex]N(1)=2600 + 470*0[/tex]

[tex]N(1)=2600[/tex]

b.

To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:

[tex]N'(a) = 2600' + (470ln(a))'[/tex]

[tex]N'(a) = 0 + 470*(1/a)[/tex]

[tex]N'(a) = 470/a[/tex]

c.

The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).

The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.

d.

When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.

Answer:

[tex]\$45[/tex]

Step-by-step explanation:

[tex]20+(2.5*20)=45[/tex]

Marking up means that the new value is added onto the original value.

As we are increasing the original price by 250% of the price, we need to multiply it by 2.5, as that is equal to 250%

Answer:

20*2.5 = $50 Gross margin $70 Selling price

Step-by-step explanation:

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:

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 ∪ 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:

B.

Step-by-step explanation:

According to SohCahToa, when using Sin to find a side value, you must use opposite over hypotenuse.

So in this case to find x, you would do the Sin(L)=x/y

Answer:

B.  Sin(L)=x/y  indeed!

Step-by-step explanation:

Answer:

0.15 or 15%

Step-by-step explanation:

If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.

To calculate how much the price went up each day on average, we will create exponential equation.

x = price of the stock

y = average daily change

[tex]x*y^{4} =1.75x[/tex]  divide by x

[tex]y^{4} = 1.75[/tex]

We will calculate it using logarithms.

y = 1.15016, rounded to 1.15

We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%

A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.

Given that are two events P(A) = 1/3, P(B) = 1/3, and P(A ∩ B) = 2/9.

We need to determine if the events are independent or not.

The chance of occurrences A and B intersecting (P(A B)) must be compared to the sum of both events' individual probabilities (P(A) × P(B)) in order to assess if events A and B are independent.

Two events A and B are independent if and only if:

P(A ∩ B) = P(A) × P(B)

Let's check if this condition holds for the given probabilities:

P(A) = 1/3

P(B) = 1/3

P(A ∩ B) = 2/9

Next, add up the odds of each separately:

P(A) × P(B) = (1/3) × (1/3) = 1/9

We can infer that A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.

In other words, the likelihood that one event (A) occurs influences the likelihood that another event (B) occurs, and vice versa.

The probability of both events happening at once (P(A B)) would be equal to the product of their individual probabilities (P(A) × P(B)) if A and B were independent, but this is not the case in this situation.

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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:

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

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Answer:

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

All outcoms of the dices:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

36 in all

Total outcomes:

In this question, we want all with no repetition.

There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.

Desired outcomes:

One landing on six:

(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).

10 desired outcomes.

Probability:

10/30 = 0.3333

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Answer: The width of the garden is 6 Meters

Step-by-step explanation:

3x + x = 24

The length is 3x and the width is x

24 / 4 = 6

x= 6

The width of the garden is 6 Meters

Answer:

x = 6

Step-by-step explanation:

3x + x = 24

24 / 4 = 6

x = 6

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:

a. 125.0714; 11.1835.

b. 109.4375; 10.4612.

Step-by-step explanation:

Given the following data;

70, 65, 71, 78, 89, 68, 50, 75.

Mean = 70.75

The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.

We would then find the square of this deviation;

[tex]=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2[/tex]

[tex]=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625[/tex]

= 875.5

Next is to find the population variance;

[tex]V = \frac{875.5}{8}[/tex]

Variance, V = 109.4375

The population standard deviation is the square root of the population variance;

[tex]Sd = \sqrt{109.4375}[/tex]

Standard deviation, Sd = 10.4612

To find the sample variance;

[tex]V = \frac{875.5}{8-1}[/tex]

[tex]V = \frac{875.5}{7}[/tex]

Variance, V = 125.0714

The sample variance is;

[tex]Sd = \sqrt{125.0714}[/tex]

Standard deviation, Sd = 11.1835

Therefore,

a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.

b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.

Answer:

C. 20.67

Step-by-step explanation:

I got it right on edge :)

Answer:

8 and 4/9 i think... i am sorry if i am wrong

Step-by-step explanation:

Step-by-step explanation:

firstly firstly we have to suppose f(X) as y and then solve it by interchanging X and y.

hope this is helpful

Answer:

B

Step-by-step explanation:

To find inverse you switch f(x) and x use y for f(x) then solve for y.

1. x = 2y - 8

2. x + 8 = 2y

3. (x + 8) / 2 = y

4. 1/2x + 4 = y

Answer:D

Step-by-step explanation:

Answer:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Step-by-step explanation:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Answer:

13/20<--->65%

21/25<--->84%

3/4<--->75%

2/5<--->40%

3/5<--->60%

To find the matching pairs, divide the fraction and move the decimal point to your answer 2 places to the right to then get a percentage.

Ex:  1/2=   .50->5.0->50.->50%

The image did not show the rest of the answers, but I worked with what information I received from the current image, producing 5 sets of answers. If there are more than 5 sets, please send a second image with your question so we can help you with the rest.

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%

Fractions are written as a ratio of two integers. In order to convert fractions to percentage, we will simply multiply the fraction given  by 100.

For the fraction 13/20

13/20 * 100 = 13 * 5

13/20 = 65%

For the fraction 21/25

21/25 * 100 = 21 * 4

21/25 = 84%

For the fraction 3/4

3/4 * 100 = 3 * 25

3/4 = 75%

For the fraction 2/5

2/5 * 100 = 2 * 20

2/5 = 40%

For the fraction 3/5

3/5 * 100 = 3* 20

3/5 = 60%

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%
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Answer:

ADB = Major Arc

arc measure = 310

Step-by-step explanation:

major arc measure = 360 - 50 = 310