What is the value of the expression below?
(-8)^4/3

Answer:

125/6(In(x-25)) - 5/6(In(x+5))+C

Step-by-step explanation:

∫x2/x1−20x2−125dx

Should be

∫x²/(x²−20x−125)dx

First of all let's factorize the denominator.

x²−20x−125= x²+5x-25x-125

x²−20x−125= x(x+5) -25(x+5)

x²−20x−125= (x-25)(x+5)

∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx

x²/(x²−20x−125) =x²/((x-25)(x+5))

x²/((x-25)(x+5))= a/(x-25) +b/(x+5)

x²/= a(x+5) + b(x-25)

Let x=25

625 = a30

a= 625/30

a= 125/6

Let x= -5

25 = -30b

b= 25/-30

b= -5/6

x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)

∫x²/(x²−20x−125)dx

=∫125/6(x-25) -∫5/6(x+5) Dx

= 125/6(In(x-25)) - 5/6(In(x+5))+C

Answer:

43 mountain climbers have not climbed either mountain.

Step-by-step explanation:

Total number of mountain climbers, i.e. n(U) = 60

Number of mountain climbers who have climbed Mt. Everest, n(E) = 10

Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15

Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15

Using the formula to find number of climbers who have climbed either of the mountains:

[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]

[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]

To find, who have not climbed either mountain:

[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]

So, the answer is:

43 mountain climbers have not climbed either mountain.

13 since  i think it's when a single didget number has a 1 at the beginning. i might be wrong thoough

Answer:

y= 4.25x + $10

Step-by-step explanation:

A tool rental shop charges a flat fee of $10.00 to rent out their chain saw

An amount of $4.25 is charged for each of the days

Let x represent the amount that is charged for each day

Let y represent the total cost of the chain saw

Since the rental fee for each day is given as $4.25 and the flat fee is given as $10 then, the equation can be expressed as

y= $4.25x + $10

Hence the equation that expresses the cost y of renting this saw if it is rented for x days is y= $4.25x + $10

Answer:

50 meters

Step-by-step explanation:

The area of a circle is [tex]\pi r^2[/tex], so assuming that [tex]\pi[/tex] is 3.14, we can make the equation [tex]3.14 \cdot r^2[/tex].

Assuming the radius is r, which is 4, we can substitute the values into the equation.

[tex]3.14 \cdot 4^2\\3.14\cdot16\\50.24[/tex]

This question is asking for the area to the nearest square meter so rounding 50.24 to the nearest square meter results in 50.

Hope this helped!

Answer:

A ) i) X control chart : upper limit = 50.475, lower limit = 49.825

    ii) R control chart : upper limit =  1.191, lower limit = 0

Step-by-step explanation:

A) Finding the control limits

grand sample mean = 1253.75 / 25 = 50.15

mean range = 14.08 / 25 = 0.5632

Based on  X control CHART

The upper control limit ( UCL ) =

grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475

The lower control limit (LCL)=

grand sample mean - A2 *  mean range = 50.15 - 0.577(0.5632) = 49.825

Based on  R control charts

The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191

The lower control limit = D3 * mean range = 0 * 0.5632 = 0  

B) estimate the process mean and standard deviation

estimated process mean = 50.15 = grand sample mean

standard deviation = mean range / d2  = 0.5632 / 2.326 = 0.2421

note d2 is obtained from control table

Answer:

x^2 + 2x - 20 = 0

x^2 + 2x - 20 + 20 = 0 + 20  ( add 20 to both sides)

x^2 + 2x = 20

x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)

( x + 1 )^2 = 21

x = [tex]\sqrt{21}-1[/tex]

x = [tex]-\sqrt{21}-1[/tex]

Answer:

A)  x = –1 ± square root 21

is the answer:)

Answer:

Option C

Step-by-step explanation:

The whole numbers a,b and c such that [tex]a^2+b^2 = c^2[/tex] are Pythagorean triples satisfying the Pythagorean theorem.

Answer:

C

Step-by-step explanation:

a, b, and c are side lengths of the triangle.

The three side lengths that make up a right triangle are most commonly known as Pythagorean triples.

Answer:

(A) 15 centimeters

Step-by-step explanation:

A midsegment of a triangle is always 2 things:

Half the size of the bottom of the triangle (in this case AC)

Parallel to the bottom of the triangle.

Since ABC is an equilateral triangle, we know that EVERY side is 30cm, including AC.

So the midsegment of ABC, LM, must be 15 cm.

Hope this helped!

Answer:

Option d: n = 36, p = 0.97, x = 36.

Step-by-step explanation:

We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.

We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.

Let X = Number of cans that are properly filled

The above situation can be represented through binomial distribution;

[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]

where, n = number of trials (samples) taken = 36 cans

            x = number of success = all cans are properly filled = 36

            p = probabilitiy of success which in our question is probability that

                  can have the correct amount, i.e. p = 97%

So, X ~ Binom (n = 36, p = 0.97)

Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.

Answer:

"If an angle has measure 90°, then it is a right angle" , True

Step-by-step explanation:

We have the following:

"If an angle is a right angle, then it’s measure is 90"

The idea is to write the opposite of the previous conditional statement.

We know that if the statement is "If p, then q", then its inverse will be "If q, then p".

So the opposite of our given statement will be :

"If an angle has measure 90°, then it is a right angle"

And this statement is true since every angle that measures 90 ° is considered a right angle.

Answer:

The standard Deviation would increase

Step-by-step explanation:

Is this advantages?

Answer:

1/30

Step-by-step explanation:

The probability of getting ”E” is 1/6.

There is only 1 “E” out of 6 letters.

There is no replacement.

There are now 5 letters without “E”.

”A”, “B”, “C”, “D”, “F”

The probability of getting ”B” is 1/5.

There is only 1 “B” out of 5 letters.

⇒ 1/6 × 1/5

⇒ 1/30

Answer:

Increase

Step-by-step explanation:

Precision describes the closeness of estimates from different samples, it refers to the width of the confidence interval and can aso be described as the margin of error. While the confidence level describes the accuracy.

Going for a higher confidence level will bring about a wider confidence interval, and thus lead to a less precise estimate.

Answer:

Null hypothesis :

[tex]H_o:p_1-p_2 = 0[/tex]

Alternative hypothesis:

[tex]H_1:p_1-p_2 \neq 0[/tex]

Decision Rule:

To reject the null hypothesis if  z < -1.65 and z > 1.65

Conclusion:

Failed to reject null hypothesis if z > -1.65 or z < 1.65

z -value = 0.33022

P-value = 0.7414

Decision Rule:

Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1

Conclusion:  we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode

Step-by-step explanation:

From the summary of the given statistical data sets.

Let consider to [tex]p_1[/tex] represent percentage of the first group ; &

[tex]p_2[/tex] represent percentage of the second group

The null and the alternative hypothesis can be stated s follows:

Null hypothesis :

[tex]H_o:p_1-p_2 = 0[/tex]

Alternative hypothesis:

[tex]H_1:p_1-p_2 \neq 0[/tex]

At the level of significance ∝ = 0.1; the two tailed critical value from the z-table

[tex]z_{\alpha/2} = 1.65[/tex]

Decision Rule:

To reject the null hypothesis if  z < -1.65 and z > 1.65

Conclusion:

Failed to reject null hypothesis if z > -1.65 or z < 1.65

However; from the question:

There are 55 people in the first group and this group will be administered the new drug.

There are 45 people in the second group and this group will be administered a placebo.

After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.

The test statistic for the for the first group who suffered from the second episode can be denoted as :

[tex]\hat p_1 = \dfrac{\overline x_1}{n_1}=0.11[/tex]

The test statistic for the for the second group who suffered from the second episode can be denoted as :

[tex]\hat p_2 = \dfrac{\overline x_2}{n_2}=0.09[/tex]

where;

[tex]n_1[/tex] = sample size of group 1 = 55

[tex]n_2[/tex] = sample size of group 2 = 45

The total probability of both group is :

[tex]\hat p = \dfrac{n_1 \hat p_1 + n_2 \hat p_2}{n_1 + n_2}[/tex]

[tex]\hat p = \dfrac{55*0.11+ 45 * 0.09}{55+45}[/tex]

[tex]\hat p = \dfrac{6.05+ 4.05}{100}[/tex]

[tex]\hat p = \dfrac{10.1}{100}[/tex]

[tex]\hat p = 0.101[/tex]

The standard error of the statistic [tex]\hat p_1 - \hat p_2[/tex] an be computed as follows:

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{ p_1 (1 - \hat p)( \dfrac{1}{n_1}+\dfrac{1}{n_2})}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101 (1 - 0.101)( \dfrac{1}{55}+\dfrac{1}{45})}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101(0.899)(0.0404)}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.0036682796}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)=0.060566[/tex]

Now; The test statistics is determined to be :

[tex]z = \dfrac{(\hat p_1 - \hat p_2 ) - (p_1-p_2)}{SE(\hat p_1 - \hat p_2)}[/tex]

[tex]z = \dfrac{(0.11-0.09) - 0}{0.060566}[/tex]

z = 0.33022

Hence; the value for the test statistics =  0.33022

the value for the test statistics =  0.33

From the z value; The P-value for the test statistics can be computed as:

P-value = 2P(Z ≥ |z|)

P-value = 2P(Z ≥  0.33022)

P-value = 2 × P (Z ≤ - 0.33022)

From the z table Z ≤ - 0.33022 = 0.3707

P-value = 2 × 0.3707

P-value = 0.7414

Decision Rule:

Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1

Conclusion:  we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode

It's adding 3 and subtracting 2 every time.

This means the next two terms would be +3 and -2 since the last one was -2.

The next term = 4+3=7

The next next term = 7-2=5

Answer:

Please see the attached picture.

Hope it helps...

Best regards!!

Answer:

The Azimuths are 81 degrees, 6 degrees for Grid Azimuths and 269 degrees, 194 degrees for back Azimuths

Step-by-step explanation:

Stream = 89 degrees and Pond = 14 degrees

To Convert to grid Azimuth

G-M Azimuth of 89-8=81 degrees

G-M Azimuth of 14-8=6 degrees

To obtain the back Azimuth for the stream

89+180=269 degrees

To obtain the back Azimuth for the pond

14+180=194 degrees

Answer:

   (-10, -3)

Step-by-step explanation:

Replacing x with x+1 in a function moves its graph 1 unit to the left. The point that is 1 unit to the left of (-9, -3) is (-10, -3).

Answer:

The answer is

Step-by-step explanation:

(x² + 3x + 4)(3x² - 2x + 1)

Expand the terms

We have

3x⁴ - 2x³ + x² + 9x³ - 6x² + 3x + 12x² - 8x + 4

Group like terms

That's

3x⁴ - 2x³ + 9x³ + x² - 6x² + 12x² + 3x - 8x + 4

Simplify

We have the final answer as

Hope this helps you

Answer:

In order for a sample to be considered biased, some members of the total population must have either a larger or lower chance of being included in the sample. In this case, your sample contained 17 reviews. It is biased because it was completely voluntary and customers who have a bad experience with a product or service generally tend to express more their dissatisfaction than satisfied customers show their satisfaction.

In marketing, there is a saying that unsatisfied clients talk bad about our product or service 4 times more than satisfied clients. I'm not sure if this saying is exact or not, but all marketing research point in the same direction.

This means that clients that did not get a good service or got no service at all, are more likely to post a review about the company than clients who got a good service. This is what makes the sample biased.

Answer:

[tex]\huge\boxed{f^{-1}(x)=-\dfrac{1}{8}x+1}[/tex]

Step-by-step explanation:

[tex]f(x)=-8x+8\to y=-8x+8[/tex]

change x with y

[tex]x=-8y+8[/tex]

solve for y

[tex]-8y+8=x[/tex]          subtract 8 from both sides

[tex]-8y+8-8=x-8[/tex]

[tex]-8y=x-8[\tex]        divide both sides by (-8)

[tex]\dfrac{-8y}{-8}=\dfrac{x}{-8}-\dfrac{8}{-8}\\\\y=-\dfrac{1}{8}x+1[/tex]

Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation

[tex]x^2+z^2=16[/tex]

Parameterize this circle by

[tex]\mathbf r(t)=4\cos t\,\mathbf i+4\sin t\,\mathbf k[/tex]

with [tex]0\le t\le2\pi[/tex].

The surface is oriented such that its normal vector points in the positive y direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.

Now compute the line integral of F along C :

[tex]\displaystyle\iint_S\mathrm{curl}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r[/tex]

[tex]=\displaystyle\int_0^{2\pi}\mathbf F(4\cos t,0,4\sin t)\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}(4\sin t\,\mathbf i+4\cos t\,\mathbf j)\cdot(-4\sin t\,\mathbf i+4\cos t\,\mathbf k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}-16\sin^2t\,\mathrm dt[/tex]

[tex]=-8\displaystyle\int_0^{2\pi}(1-\cos(2t))\,\mathrm dt=\boxed{-16\pi}[/tex]

Line integral of F along C is,

[tex]\rm \int \int_S curl F(x,y,z) dS = -16\pi[/tex]

Step-by-step explanation:

Given :

Hemisphere -   [tex]x^2 +y^2+z^2=16[/tex]

Calculation :

Accordind to Stoke's theorem the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation

[tex]x^2+z^2=16[/tex]

then parameterize the circle,

[tex]\rm r(t) = 4 cos(t) \;\hat{i} + 4 sin(t)\;(\hat{k})[/tex]

with , [tex]0\leq t\leq 2\pi[/tex]

Line integral of F along C is,

[tex]\rm \int \int_S curl F(x,y,z) dS = \int_{C}^{} F(x,y,z) \;dr[/tex]

[tex]= \int_{0}^{2\pi} F(4cos(t),0,4sin(t)) \;\dfrac{dr}{dt}.dt[/tex]

[tex]= \int_{0}^{2\pi}(4sin(t)i+4cos(t) j).(-4sin(t)i+4cos(t)k) \;dt[/tex]

[tex]= \int_{0}^{2\pi} -16sin^2tdt[/tex]

[tex]=-8 \int_{0}^{2\pi} (1-cos(2t))dt[/tex]

[tex]= -16\pi[/tex]

For more information, refer the link given below

https://brainly.com/question/8130922?referrer=searchResults

Answer:

B = (A - 6) / 10

Step-by-step explanation:

This problem has 2 variables and 1 equation so it is not trivial to solve with confidence the value of B; however, we can solve for B in terms of A.  With that being said, let's start.

If A divided by B = 10:

A/B = 10

10 remainder of 6

Could also be written as 10 & 6/B since B is the divisor.  Rewrite this, you can get the equation:

A/B = (10B + 6) / B

A = 10B + 6

A - 6 = 10B

B = (A - 6) / 10

Thus, you have solve B in terms of A.

Cheers.

Answer:

$[58543.42; 73456.58]

Step-by-step explanation:

Hello!

For the variable

X: salary of a college graduate that took a statistics course

Out of n= 43 students, the calculated mean is [tex]\frac{}{X}[/tex]= $66000

The population standard deviation is δ= $18908

There is no information about the variable distribution, but since the sample size is big enough (n≥30), you can apply the CLT and approximate the distribution of the sample mean to normal [tex]\frac{}{X}[/tex]≈N(μ;σ²/n)

Then you can apply the approximation of the standard normal distribution to calculate the 99% CI

[tex]\frac{}{X}[/tex] ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{Singma}{\sqrt{n} }[/tex]

[tex]Z_{1-\alpha /2}= Z_{0.995}= 2.586[/tex]

[tex]\frac{Singma}{\sqrt{n} }= \frac{18908}{\sqrt{43} }= 2883.44[/tex]

[66000±2.586*2883.44]

$[58543.42; 73456.58]

With a 99% confidence level you'd expect that the interval $[58543.42; 73456.58] will include the average salary of college graduates that took a course of statistics.

I hope this helps!

Answer:

f^-1(x) = x + 5

Step-by-step explanation:

f(x) = x-5

y = x-5

Exchange x and y

x = y-5

Solve for y

x+5 = y-5+5

x+5 =y

The inverse is x+5

Answer:

5050

Step-by-step explanation:

Place value of a digit is the value of digit based on its position the given number.

to determine the place value of a digit

we multiply the digit by number of 10's which is equal to number of digits in its right.

example

for a number 1234687

the place value of 3 is

we take 3 and

multiply it by number of 10' in its right

number of 10's in the right is 4

thus place value of 3 = 3*10*10*10*10 = 30000

________________________________________________

15954

place value of 5 at thousandth position = 5*10*10*10 = 5000

place value of 5 at tens position = 5*10 = 50

Thus, sum of place value of 5 in 15954 = 5000+50 = 5050

Answer:

The sample size is  [tex]n = 600[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample proportion is  [tex]\r p = 0.48[/tex]

     The  margin of error is  [tex]MOE = 0.04[/tex]

Given that the confidence level is 95%  the level of significance is mathematically represented as

        [tex]\alpha = 100 - 95[/tex]

        [tex]\alpha = 5 \%[/tex]

        [tex]\alpha = 0.05[/tex]

Next  we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is

                   [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because  

[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (  [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error

Generally the margin of error is mathematically represented as

      [tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p(1- \r p )}{n} }[/tex]

substituting values

          [tex]0.04= 1.96* \sqrt{ \frac{0.48(1- 0.48 )}{n} }[/tex]

         [tex]0.02041 = \sqrt{ \frac{0.48(52 )}{n} }[/tex]

         [tex]0.02041 = \sqrt{ \frac{ 0.2496}{n} }[/tex]

          [tex]0.02041^2 = \frac{ 0.2496}{n}[/tex]

           [tex]0.0004166 = \frac{ 0.2496}{n}[/tex]

=>       [tex]n = 600[/tex]

Answer:

z = 1.55

Step-by-step explanation:

The answer is attached.

Answer:

b. [tex]g(x)=f(x)-5[/tex]

Step-by-step explanation:

You have that the function f(x) has its y-intercept for y=3.

Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.

In this case you have that f(x) has been translated vertically downward.

The general way to translate a function vertically in the coordinate system is:

[tex]g(x)=f(x)+a[/tex]      (1)

being a positive or negative.

if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:

a = -2 -3 = -5

Then, the answer is:

b. [tex]g(x)=f(x)-5[/tex]

Answer: g(x) = f(x) - 5

Step-by-step explanation:

just took this