Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001.

Answer:

Step-by-step explanation:

Given the Revenue in dollars modelled by the function R(x) = 60x-0.5x²

Cost in dollars C(x) = 3x+5

Profit function = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = 60x-0.5x²-(3x+5)

P(x) = 60x-0.5x²-3x-5

P(x) = -0.5x²+57x-5

The rate of change of total revenue = dR(x)/dt

dR(x)/dt = dR(x)/dx * dx/dt

dR(x)/dx = 60-2(0.5)x²⁻¹

dR(x)/dx = 60-x

Given x = 40 and dr/dx = 15 units per day

dR(x)/dt = (60-x)dx/dt

dR(x)/dt = (60-40)*15

dR(x)/dt = 20*15

dR(x)/dt = 300dollars

Rate of change of revenue = 300dollars

For the rate of change of cost;

dC(x)/dt = dC(x)/dx * dx/dt

dC(x)/dt = 3dx/dt

dC(x)/dt when dx/dt = 15 will give;

dC(x)/dt = 3*15

dC(x)/dt = 45 dollars.

Rate of change of revenue  = 45dollars

For the profit;

Profit = Rate of change of revenue -  rate of change of cost

Profit made = 300-45

profit made = 255 dollars

Answer:

The interest is

Step-by-step explanation:

Simple interest is given by

[tex]I = \frac{P \times R \times T}{100} [/tex]

where

P is the principal

R is the rate

T is the time given

From the question

The principal / P = $ 5700

The rate / R = 4.5%

The time given / T = 3 years

So the interest is

[tex]I = \frac{5700 \times 4.5 \times 3}{100} [/tex]

[tex]I = \frac{76950}{100} [/tex]

We have the final answer as

I = $ 769.50

Hope this helps you

Answer:

9 years

Step-by-step explanation:

Answer:

0.1875

Step-by-step explanation:

σM=σ/√N

=8/√7500

=8/86.608

=0.092

Z=(x-μ)/σ/√N

=(25.5-36)/8/√7500

=-10.5/0.0092=-1141.304

Z score = -1.3125

=(27-36)/8/√7500 =

=9/0.0092=978.261

Z score= -1.125

-1.125-(-1.3125)=-1.125+1.3125)= 0.1875

The probability that the sample mean will be between 25.5 and 27 years

P(between 25.5 and 27) = 0.1875

Parameterize the square (call it S) by

[tex]\mathbf s(u,v)=2u\,\mathbf x+2v\,\mathbf z[/tex]

with both [tex]u\in[0,1][/tex] and [tex]v\in[0,1][/tex].

Take the normal vector pointing in the positive y direction to be

[tex]\dfrac{\partial\mathbf s}{\partial v}\times\dfrac{\partial\mathbf s}{\partial u}=4\,\mathbf y[/tex]

Then the current is

[tex]\displaystyle\iint_S(y^2+5)\,\mathbf y\cdot4\,\mathbf y\,\mathrm dA=20\int_0^1\int_0^1\mathrm dA=\boxed{20\,\mathrm A}[/tex]

where [tex]y^2+5[/tex] reduces to just 5 because [tex]y=0[/tex] for all points in S.

Answer:

the solution to the system of inequality is C

Answer:

Possible solution 1: -4.5 and -8

Solution 2: 4 and 9.

Step-by-step explanation:

Let the two numbers be a and b.

One of them (let it be b) is 1 more than twice the other one. In other words,

b= 1+ 2a.

Their product is 36. Or:

a(b) = 36.

Substitute b:

a(1+2a) = 36

2a^2 + a = 36

2a^2 + a - 36 = 0

This is now a quadratic. We can factor to solve it. Find two numbers that equals 2(-36)=-72 and add to 1. We can use 9 and -8. Thus:

2a^2 - 8a + 9a - 36 = 0

2a(a - 4) +9(a-4) = (2a+9)(a-4) = 0

So, a = -9/2 = -4.5 or a = 4.

Thus, b can equal 1 + 2(-4.5) = -8 or 1 + 2(4) = 9

Answer:

$25

Step-by-step explanation:

De la pregunta anterior, se nos da la siguiente información

Yo TENÍA $ 5

Mi mamá me dió $ 10

Mi papá me dió $ 30

Mi tío y mi tía me dieron $ 100

Yo TENÍA otros $ 20

Si miras arriba, notarás que la palabra TENÍA está en mayúscula.

Esto se debe a que para resolver esta pregunta correctamente, tenemos que concentrarnos o prestar atención a los tiempos verbales del inglés que se usan al hacer la pregunta.

La pregunta dice: ¿Cuánto tenía?

Esto significa que la pregunta anterior es sobre cuánto tenía en el pasado antes de que sus padres, tío y tía le dieran dinero.

Por lo tanto, la cantidad de dinero que tenía

= $20 + $5

= $ 25

The total amount I have altogether will be $165

In order to get the total amount that you have, we will add all the cash you were given and the ones you have altogether.

Amount initially owned = $5

Amount given by relatives = $10 + $30 + $100

Amount given by relatives = $140

If he has another $20

Total amount I have = $5 +$140 + $20

Hence the total amount I have altogether will be $165

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Answer:

Arrow from 0 to 4.7 and from 4.7 to 2.4

Step-by-step explanation:

4.7 is also 0+4.7

arrow from 0 to 4.7.

-2.3 from 4.7 is 4.7-2.3=2.4

arrow from 4.7 to 2.4.

Answer:

Use the interactive number line to find the difference.

4.7 - 2.3 = 4.7 + (-2.3) =

✔ 2.4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have

[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]

Substitute:

[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]

The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:

[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]

We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:

[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]

[tex]=\dfrac{14}{7}=2[/tex]

The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!

Answer:

The percentage is  [tex]P(x_1 < X < x_2) = 47.7 \%[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = \$ 150000[/tex]

    The standard deviation is  [tex]\sigma = \$ 1200[/tex]

    The prices we are considering is [tex]x_1 = \$150000 \to \ x_2 = \$ 152400[/tex]

Given that the price is normally distributed , the percentage the percentage of buyers who paid between $150,000 and $152,400 is mathematically represented as

      [tex]P(x_1 < X < x_2) = P(\frac{x_1 - \mu}{\sigma } < \frac{X - \mu}{\sigma } < \frac{x_2 - \mu}{\sigma })[/tex]

So   [tex]\frac{X - \mu}{\sigma }[/tex]  is equal to z (the standardized value of  X  )

   So

        [tex]P(x_1 < X < x_2) = P(\frac{x_1 - \mu}{\sigma } <Z < \frac{x_2 - \mu}{\sigma })[/tex]

substituting values

       [tex]P(x_1 < X < x_2) = P(\frac{150000 - 150000}{1200 } <Z < \frac{152400 - 150000}{1200 })[/tex]

      [tex]P(x_1 < X < x_2) = P(0<Z < 2)[/tex]

      [tex]P(x_1 < X < x_2) = P( Z < 2) - P( Z < 0 )[/tex]

From the standardized normal distribution table [tex]P(Z < 2 ) = 0.97725[/tex] and  

   [tex]P(Z < 0) = 0.5[/tex]

So  

     [tex]P(x_1 < X < x_2) = 0.97725 - 0.5[/tex]

    [tex]P(x_1 < X < x_2) = 0.47725[/tex]

The percentage is  [tex]P(x_1 < X < x_2) = 47.7 \%[/tex]

Answer:

see below

Step-by-step explanation:

20x^3+8x^2-30x-12

Factor out the greatest common factor 2

2 (10x^3+4x^2-15x-6)

Then factor by grouping

2 ( 10x^3+4x^2      -15x-6)

Factor out 2 x^2 from the first group and -3 from the second group

2  ( 2x^2( 5x+2)  -3( 5x+2))

Factor out ( 5x+2)

2 ( 5x+2) (2x^2-3)

The 2 can go in either term to get binomials

( 10x +4) (2x^2-3)

or ( 5x+2) ( 4x^2 -6)

Answer:

[tex](10x+4)(2x^2 -3)[/tex]

Step-by-step explanation:

[tex]20x^3+8x^2-30x-12[/tex]

Rewrite expression (grouping them).

[tex]20x^3-30x+8x^2-12[/tex]

Factor the two groups.

[tex]10x(2x^2 -3)+4(2x^2 -3)[/tex]

Take the common factor from both groups.

[tex](10x+4)(2x^2 -3)[/tex]

Answer:

a geometric figure labeled CD would be a segment

Step-by-step explanation: you need to attached the pictures with the question

Answer:

36

Step-by-step explanation:

You did not attach a picture, so I just assumed where the lengths of 15 and 39 were.

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question,

The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__

from the equation of motion given, the constant b is the velocity of the body. For us to get the dimension of b, we have to find the dimension of the velocity .

Since velocity is the rate of change of displacement of a body, then;

VELOCITY = DISPLACEMENT/TIME

displacement is measured in metres while time in seconds.

expressing the formula in terms of its fundamental unit,

v = metre/secs

Since the fundamental quantity of the metre is length (L) and that of seconds is the time (T); the dimensions is expressed as;

V = L/T

V = L * 1/T

V = L * T⁻¹

V = LT⁻¹

Hence the dimension of b is  LT⁻¹.

Note that the dimension of a body is written in terms of its fundamental quantities.

The dimensions of b from the given equation are; B: LT⁻¹

The complete question is;

The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__

Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;

Velocity = Distance/Time

Now, distance is also called Length and represented by L in basic parameters units while Time is represented by T.

Thus, the dimensions of b are; L/T or expressed as LT⁻¹

Read more on dimensional analysis at; https://brainly.com/question/1528136

Answer:

[tex](B) \dfrac12H (B+D)[/tex]

Step-by-step explanation:

[tex]\text{Area of a trapezoid }= \dfrac12 ($Sum of the parallel sides) \times $Height\\Parallel Sides = B and D\\Height =H\\Therefore:\\\text{Area of the trapezoid }= \dfrac12 (B+D) H[/tex]

The correct option is B.

Answer:

You didn't put an attachment to show what solid you wanted rounded

Step-by-step explanation:

Answer:

A sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.

Step-by-step explanation:

We are given that an electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours.

We have to find a sample such that we are 98% confident that our sample mean will be within 4 hours of the true mean.

As we know that the Margin of error formula is given by;

The margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]

where, [tex]\sigma[/tex] = standard deviation = 40 hours

            n = sample size

            [tex]\alpha[/tex] = level of significance = 1 - 0.98 = 0.02 or 2%

Now, the critical value of z at ([tex]\frac{0.02}{2}[/tex] = 1%) level of significance n the z table is given as 2.3263.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]

                 [tex]4=2.3263 \times \frac{40}{\sqrt{n} }[/tex]

                 [tex]\sqrt{n}= \frac{40 \times 2.3263}{ 4}[/tex]

                  [tex]\sqrt{n}=23.26[/tex]

                   n = [tex]23.26^{2}[/tex] = 541.03 ≈ 541

Hence, a sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.

Answer:

The answer c is correct.  

Step-by-step explanation:

When two chords share an endpoint, the inscribed angle has half of the measure of the intercepted arc.   In this example, ADE is the inscribed angle, so its measure is one half of the arc AE's measure. m<ADE= 1/2(mAE)

i hope this helped :)

The relationship between the measure of angle ADE and the measure of arc AE is  m∠ADE  = [tex]\frac{1}{2}[/tex] m (arc AE) .

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent. This is called the Congruent Inscribed Angles Theorem

According to the question

The relationship between the measure of angle ADE and the measure of arc AE .

∠ADE  is a  inscribed angle

arc AE  is a  intercepted arc

According to Inscribed Angle Theorem

∠ADE  = [tex]\frac{1}{2}[/tex] arc AE

Hence, the relationship between the measure of angle ADE and the measure of arc AE is  m∠ADE  = [tex]\frac{1}{2}[/tex] m (arc AE) .

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Answer:

[tex] z =\frac{33.3- 34}{\frac{5}{\sqrt{54}}}= -1.028[/tex]

[tex] z =\frac{34.3- 34}{\frac{5}{\sqrt{54}}}= 0.441[/tex]

An we can use the normal standard table and the following difference and we got this result:

[tex] P(-1.028<z<0.441)= P(z<0.441) -P(z<-1.028) = 0.670 -0.152 =0.518[/tex]

Step-by-step explanation:

Assuming this statement to complete the problem "with a standard deviation 5 mpg"

We have the following info given:

[tex]\mu = 34[/tex] represent the mean

[tex]\sigma= 5[/tex] represent the deviation

We have a sample size of n = 54 and we want to find this probability:

[tex] P(33.3 < \bar X< 34.3)[/tex]

And for this case since the sample size is large enough >30 we can apply the central limit theorem and then we can use this distribution:

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

And we can use the z score formula given by:

[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] z =\frac{33.3- 34}{\frac{5}{\sqrt{54}}}= -1.028[/tex]

[tex] z =\frac{34.3- 34}{\frac{5}{\sqrt{54}}}= 0.441[/tex]

An we can use the normal standard table and the following difference and we got this result:

[tex] P(-1.028<z<0.441)= P(z<0.441) -P(z<-1.028) = 0.670 -0.152 =0.518[/tex]

Answer:

hello :- 9/7 and 3/8

Step-by-step explanation:

y = 6(7x + 9)(8x – 3)

y=0 means :   7x+9=0   or 8x-3=0

7x = -9  or 8x=3

x= - 9/7   or x= 3/8

Answer:

-9/7, 3/8

Step-by-step explanation:

The zeroes can be found in the parenthesis.

You need to set each parenthesis to zero first.

7x+9=0

subtract 9

7x=-9

divide 7

x=-9/7

For 8x-3=0

add the 3

8x=3

divide the 8

x=3/8

Answer:

0.287

Step-by-step explanation:

Use binomial probability:

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

P = ₇C₄ (0.53)⁴ (0.47)³

P ≈ 0.287

Answer:

No solutions.

Step-by-step explanation:

You will only have solutions when the two lines meet. But since the slopes are the same, the two lines are parallel. Since the y-intercepts are different, that means that the two slopes will never intersect, which means that there are no solutions.

Hope this helps!

Answer: no solution

Step-by-step explanation: When lines have the same slope, the graphs of the two lines are parallel which means they never intersect.

Let's look at an example.

Below, you will see two equations.

Both of the lines have a slope of 1.

So, they must be parallel which means they don't cross.

So there is no solution.

Answer:

52 green, 15 orange

Step-by-step explanation:

g + o = 67   g = green, o = orange, x = total

g = 3o + 7

use substitution: (3o + 7) + o = 67

solve for o:

4o + 7 = 67

4o = 60

o = 60/4 = 15

solve for g:

g + 15 = 67

g = 52

Answer:

A

Step-by-step explanation:

A divisor refers to a number by which another number is to be divided.

So what this question is practically asking us is that which of the values in the options to 2 decimal places is the result dividing the population by the number of seats

Thus we have;

140,000/9 = 15,555.55555 which to 2 decimal places is 15,555.56

Answer:

-11xy

Step-by-step explanation:

Subtracting a negative means adding.

-14xy - (-3xy) = -14xy + 3xy = -11xy

Answer:

sorry i am not able to understood

Step-by-step explanation:

The most appropriate statement is the one that correctly reflects the confidence interval obtained from the survey data, as stated above.

The most appropriate statement to make regarding the true average number of days of "not good" mental health in 2010 for US residents, based on the given information, is:

"For these 1,151 residents in 2010, we are 95% confident that the average number of days of 'not good' mental health is between 3.40 and 4.24 days."

The 95% confidence interval of 3.40 to 4.24 days is obtained from the survey data, and it provides an estimate of the range within which the true average number of days of "not good" mental health falls for the entire population of US residents.

Regarding the provided options:

There is not sufficient information to calculate the margin of error of this confidence interval: This statement is not accurate since the margin of error can be calculated using the formula Margin of Error = (Upper Limit - Lower Limit) / 2.

For all US residents in 2010, based on this 95% confidence interval, we would reject a null hypothesis stating that the true average number of days of "not good" mental health is 5 days: This statement is not supported by the given information. The confidence interval provides an estimate of the range within which the true average lies, but it does not involve a comparison to a specific value such as 5 days.

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Based on the provided information and the 95% confidence interval of 3.40 to 4.24 days for "not good" mental health in 2010,

The most appropriate statement to make regarding the true average number of days of "not good" mental health for US residents in 2010 is:

"For these 1,151 residents in 2010, we are 95% confident that the average number of days of 'not good' mental health is between 3.40 and 4.24 days."

This statement accurately represents the confidence interval obtained from the survey data.

It indicates that the true average number of "not good" mental health days for the entire US population in 2010 is likely to fall within this range with a 95% level of confidence.

It's important to note that this statement only applies to the specific sample of 1,151 US residents surveyed in 2010.

To make inferences about the true average number of "not good" mental health days for all US residents in 2010, a different sample with a larger representative size would be required.

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Answer:

( x+2) ^2 = 11

x =1.32,-5.32

Step-by-step explanation:

x^2 + 4x -7 = 0

Add the constant to each side

x^2 + 4x -7+7 = 0+7

x^2 + 4x = 7

Take the coefficient of the x term

4

Divide by 2

4/2 =2

Square it

2^2 = 4

Add this to each side

x^2 + 4x +4 = 7+4

Take the 4/2 as the term inside the parentheses

( x+2) ^2 = 11

Take the square root of each side

sqrt( ( x+2) ^2)  =±sqrt( 11)

x+2 = ±sqrt( 11)

Subtract 2 from each side

x = -2 ±sqrt( 11)

To the nearest hundredth

x =1.32

x=-5.32

Answer:

[tex](x+2)^2=11[/tex]

[tex]x=-2 \pm \sqrt{11}[/tex]

Step-by-step explanation:

[tex]x^2+4x-7=0[/tex]

[tex]x^2+4x=7[/tex]

[tex]x^2+4x+4=7+4[/tex]

[tex](x+2)^2=11[/tex]

[tex]x+2=\pm\sqrt{11}[/tex]

[tex]x=-2 \pm \sqrt{11}[/tex]

Answer:

10/3.

Step-by-step explanation:

To find the slope, we do the rise over the run.

In this case, the rise is 4 - (-6) = 4 + 6 = 10.

The run is -2 - (-5) = -2 + 5 = 3.

So, the slope is 10/3.

Hope this helps!

10/3

Step-by-step explanation:

gradient=y²-y¹

x²-x¹

= -6-4

-5-(-2)

= -10

-5+2

= -10

-3

=10/3