Simplify.
Remove all perfect squares from inside the square roots.
Assume a and b are positive.

Answer:

178.5 actually

Step-by-step explanation:

Answer:

Error in the sphere's surface: 29 [tex]cm^2[/tex]  and relative error in surface measure: 0.011

Error in the sphere's volume: 205 [tex]cm^3[/tex] and relative error in the volume measure: 0.017

Step-by-step explanation:

(a)

The measured length (l) of the circumference is 90 cm with an error of 0.5 cm, that is:

[tex]l=2\,\pi\,R=90\,cm\\R=\frac{90}{2\,\pi} \,cm=\frac{45}{\pi} \,cm=14.3239\,\,cm[/tex]

and with regards to the error:

[tex]dl=0.5 \, cm\\dl=2\,\pi\,dR\\dR=\frac{dl}{2\,\pi} =\frac{1}{4\,\pi} cm = 0.0796\,cm[/tex]

then when we use the formula for the sphere's surface, we get:

[tex]S=4\,\pi\,R^2\\dS=4\,\pi\,2\,R\,(dR)\\dS=8\,\,\pi\.(\frac{45}{\pi} \,\,cm)\,(\frac{1}{4\pi}\,cm) =\frac{90}{\pi} \,\,cm^2\approx \,29\,cm^2[/tex]

Then the relative error in the surface is:

[tex]\frac{dS}{S} =\frac{90/\pi}{4\,\pi\,R^2} =\frac{1}{90} =0.011[/tex]

(b)

Use the formula for the volume of the sphere:

[tex]V=\frac{4\,\pi}{3} R^3\\dV=\frac{4\,\pi}{3}\,3\,R^2\,(dR)=4\,\pi\,R^2\,(\frac{1}{4\pi}) \,cm=(\frac{45}{\pi})^2 \,\,cm^3\approx 205\,\,cm^3[/tex]

Then the relative error in the volume is:

[tex]\frac{dV}{V} =\frac{205}{12310.5} \approx 0.017[/tex]

Answer:

[tex]\boxed{\mathrm{Option \ C}}[/tex]

Step-by-step explanation:

=> [tex]x^2+22x = 31[/tex]

=> [tex](x)^2+2(x)(11) = 31[/tex]

Since b = 11 , So [tex](11)^2[/tex] needs to be added to both sides

Adding [tex](11)^2[/tex]  to both sides

=> [tex](x)^2+2(x)(11)+(11)^2 = 31+(11)^2[/tex]

Completing the square

=> [tex](x+11)^2 = 31+121[/tex]

=> [tex](x+11)^2 = 152[/tex]

Answer:

[tex]g(x) = |x| + 1[/tex]

Step-by-step explanation:

Given

[tex]y = |x|[/tex]

Required

Translate 1 unit up

Start by replacing y with f(x)

[tex]f(x) = |x|[/tex]

To translate an the graph of an absolute function upward, you make use of the formula;

[tex]g(x) = f(x) + k[/tex]

Where k is the number of units

In this case; [tex]k = 1[/tex]

Hence;

[tex]g(x) = f(x) + k[/tex]

Substitute [tex]k = 1[/tex]

[tex]g(x) = f(x) + 1[/tex]

Substitute  [tex]f(x) = |x|[/tex]

[tex]g(x) = |x| + 1[/tex]

Hence, the resulting equation is [tex]g(x) = |x| + 1[/tex]

Step-by-step explanation:

to find the sum of nth term

equation is

n/2 ( 2a + (n-1)d) where a is the 1st term and d is the common difference

5/2 ( 120 +( 4 × 31))

5/2 ( 120 + 124)

5/2 × 244

5 × 122 dividing 244 by 2

610

Answer: 610

Step-by-step explanation:

This sequence starts at 60 and increases by increments of 31.  Thus, to get the last two numbers, do 122+31=153, and 153+31=184.  Then add 60+91+122+153+184 to get 610.

Hope it helps <3

The price that guarantees the maximum revenue is $40.

The maximum revenue possible in this situation is $8000.

Given that the company can sell 225 items at a price of $35, and for every dollar increase in price, the number of items sold decreases by 5, we can set up a relationship between price and quantity sold.

Let's denote the price as "P" and the quantity sold as "Q". We can express this relationship as follows:

Q = 225 - 5(P - 35)

This equation represents the decrease in quantity sold as the price increases.

To find the price that guarantees the maximum revenue, we need to find the price at which the quantity sold multiplied by the price is maximized. This is equivalent to finding the maximum value of the revenue function.

Revenue (R) is calculated as:

R = P × Q

To find the price that guarantees the maximum revenue, we need to maximize the revenue function R(P).

Let's substitute the expression for Q into the revenue function:

R(P) = P × (225 - 5(P - 35))

Now, simplify and expand the equation:

R(P) = P × (225 - 5P + 175)

= P × (400 - 5P)

To find the maximum revenue, we need to find the value of P that maximizes R(P). This can be done by finding the critical points of the function, which are the values of P where the derivative of R(P) equals zero.

Let's take the derivative of R(P) with respect to P:

dR(P)/dP = 400 - 10P

Setting the derivative equal to zero and solving for P:

400 - 10P = 0

10P = 400

P = 40

Therefore, the price that guarantees the maximum revenue is $40.

To find the maximum revenue, substitute P = 40 into the revenue function:

R(40) = 40 × (225 - 5(40 - 35))

= 40 × (225 - 5(5))

= 40 × (225 - 25)

= 40 × 200

= 8000

Hence, the maximum revenue possible in this situation is $8000.

To learn more about the derivative;

https://brainly.com/question/24898810

#SPJ12

Answer:

a = 6, b = 7, c = 8, d = 7 and e = 6

Step-by-step explanation:

Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.

The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.

When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be a = 6 + 0 = 6 ft

When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be b = 6 + 1 = 7 ft

When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.

So the height will be c = 6 + 2= 8 ft

When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be d = 6 + 1 = 7 ft

When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be e = 6 + 0 = 6 ft

So the answers are:

a = 6, b = 7, c = 8, d = 7 and e = 6

Answer:

6, 7, 8, 7, 6

Step-by-step explanation:

Answer:

12a + 3b.

Step-by-step explanation:

3(4a + b)

= 3 * 4a + 3 * b

= 12a + 3b.

Hope this helps!

Answer:

[tex]12a+3b[/tex]

Step-by-step explanation:

[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=3,\:b=4a,\:c=b\\=3\times \:4a+3b\\\mathrm{Multiply\:the\:numbers:}\:3\times \:4=12\\=12a+3b[/tex]

Answer: the intersection point is (2.4, -4.8)

Step-by-step explanation:

A) we have the function:

y = 0.5*x - 6.

First we want to know if this function intersects the line y´ = -1.5*x

Now, first we can recall that two lines are parallel only if the slope is the same for both lines, here we can see that the slopes are different, so the lines are not parallel, which means that the lines must intersect at some point.

Now, to find the intersection point we asumme y = y´ and want to find the value of x.

0.5*x - 6 = -1.5*x

(0.5 + 1.5)*x - 6 = 0

2.5*x = 6

x = 6/2.5 = 2.4

Now, we evaluate one of the functions in this value of x.

y = 0.5*2.4 - 6 = -4.8

So the intersection point is (2.4, -4.8)

Answer:

$42.88

Step-by-step explanation:

We can set up a cross product fraction ratio to find how much 21 pounds of turkey costs.

[tex]\frac{10}{20.42} = \frac{21}{x}[/tex]

Let's apply the cross multiplication property.

[tex]20.42\cdot21=428.82[/tex]

Now we divide this by 10.

[tex]428.82\div10=42.882[/tex]

This simplifies down to [tex]42.88[/tex].

Hope this helped!

Complete Question

A committee has six members. There are three members that currently serve as the​ board's chairman comma vice chairman comma and treasurer . Each member is equally likely to serve in any of the positions. Three members are randomly selected and assigned to be the new chairman comma vice chairman comma and treasurer . What is the probability of randomly selecting the three members who currently hold the positions of chairman comma vice chairman comma and treasurer and reassigning them to their current​ positions?

The probability is ?

Answer:

The probability is [tex]P(3 ) = \frac{ 1 }{20 }[/tex]

Step-by-step explanation:

From the question we are told that

       The total number of members is  n = 6  

       The  number of member to be selected is  r =  3  

Generally the number of ways of selecting 3 members from 6  is mathematically evaluated as

          [tex]\left n } \atop {}} \right. C _r = \frac{n! }{(n-r ) ! r !}[/tex]

=>       [tex]\left 6 } \atop {}} \right. C _ 3 = \frac{6 ! }{(6-3) ! 3 !}[/tex]

=>        [tex]\left n } \atop {}} \right. C _r = \frac{6* 5* 4 * 3! }{3 ! 3*2 * 1}[/tex]

=>       [tex]\left n } \atop {}} \right. C _r = \frac{6* 5* 4 }{3 *2 * 1}[/tex]

=>        [tex]\left n } \atop {}} \right. C _r =20[/tex]

Now the number of ways of selecting the 3 members who currently hold the position is  n  = 1

  So the probability is mathematically represented as

                 [tex]p(k ) = \frac{ n }{\left n } \atop {}} \right. C _r }[/tex]

substituting values

                  [tex]P(3 ) = \frac{ 1 }{20 }[/tex]

Answer:

V = pi 36 units^3

V =113.04 units^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = pi ( 2) ^2 *9

V = pi 36

Letting pi = 3.14

V =113.04

Answer:

[tex]\boxed{Side \ Length \ of \ hot \ tub = 4.8\ ft.}[/tex]

Step-by-step explanation:

Scale Factor = 5

Also,

B'C' = 24 feet

Since both are squares so both have all sides equal.

Sqaure A'B'C'D' is dilated by a scale factor of 5

So,

AB = BC = CD = DA = 24/5 = 4.8 ft.

The length of one side of the hot tub is 4.8 feet and this can be determined by using the concept of dilation.

Given :

The following steps can be used in order to determine the length of one side of the hot tub:

Step 1 - According to the given data, the dilation factor is 5.

Step 2 - So, after the dilation by a factor of 'a' the length of the side be 'b' becomes 'ab'.

Step 3 - So, according to the given data, the length of B prime C prime is 24 feet. Therefore, after the dilation by a factor of 5, the length of the segment BC becomes:

[tex]\rm =\dfrac{24}{5}=4.8\;feet[/tex]

So, the length of one side of the hot tub is 4.8 feet. Therefore, the correct option is b).

For more information, refer to the link given below:

https://brainly.com/question/2856466

Answer:

[tex]\large \boxed{\sf \ \ x=0, \ \ y=-5 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We have two equations:

(1) -2x - 4y = 20

(2) -3x + 5y = -25

5*(1)+4*(2) gives

   -10x - 20y -12x + 20y = 100 - 100 = 0

   -22x = 0

   x = 0

I replace in (1)

   -4y = 20

   y = -20/4 = -5

There is one solution x = 0, y = -5

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The two equations are

-2x-4y=20

-3x+5y=-25

multiply equation 1 by 5 and equation 2 by 4

-10x-20y=100

-12x+20y=-100

-22x=0

x=0

Substitute value in either equation

y=-5

So,option 1 is correct only one solution

Answer:

9 is the answer

Step-by-step explanation:

got a delivery of 60ib...but dont have enough .thats why he or she sells 29..totally he or she have 38ib of carrots ...so when we subtract 38_29

its =9

Answer:

a. (24 ln 2 − 7) / 9

b. x tan x + ln|cos x| + C

Step-by-step explanation:

a. ∫₁² x² ln x dx

Integrate by parts.

If u = ln x, then du = 1/x dx.

If dv = x² dx, then v = ⅓ x³.

∫ u dv = uv − ∫ v du

= (ln x) (⅓ x³) − ∫ (⅓ x³) (1/x dx)

= ⅓ x³ ln x − ∫ ⅓ x² dx

= ⅓ x³ ln x − ¹/₉ x³ + C

= ¹/₉ x³ (3 ln x − 1) + C

Evaluate between x=1 and x=2.

[¹/₉ 2³ (3 ln 2 − 1) + C] − [¹/₉ 1³ (3 ln 1 − 1) + C]

⁸/₉ (3 ln 2 − 1) + C + ¹/₉ − C

⁸/₉ (3 ln 2 − 1) + ¹/₉

⁸/₃ ln 2 − ⁸/₉ + ¹/₉

⁸/₃ ln 2 − ⁷/₉

(24 ln 2 − 7) / 9

b. ∫ x sec² x dx

Integrate by parts.

If u = x, then du = dx.

If dv = sec² x dx, then v = tan x.

∫ u dv = uv − ∫ v du

= x tan x − ∫ tan x dx

= x tan x + ∫ -sin x / cos x dx

= x tan x + ln|cos x| + C

Answer:

  (3/4)a

Step-by-step explanation:

The angle at K is 120°, so the angle at L is its supplement: 60°. That makes triangle FKL an equilateral triangle with a base of FL = a. The vertex at K is centered over the base, so is a/2 from G.

The midsegement length is the average of GK and FL, so is ...

  midsegment = (GK +FL)/2 = (a/2 +a)/2

  midsegment = (3/4)a

Answer:

The minimum svore required to get an A is 85.3.

Step-by-step explanation:

Complete Question

Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 8.

The instructor wants to give an A to the students whose scores were in the top 10% of the class. What is the minimum score needed to get an A?

Solution

Scores in the top 10% of the class will have a minimum greater than the remaining bottom 90% of the class.

If the minimum score for the top 10% of the class is x'

P(X ≤ x') = 90% = 0.90

If the z-score of this minimum score of the top 10%, x', is z'.

P(X ≤ x') = P(z ≤ z') = 0.90

using the z-distribution tables

z' = 1.282

But the z-score of any value is given as the value minus the mean divided by the standard deviation.

z = (x - μ)/σ

So,

z' = (x' - μ)/σ

Mean = 75

Standard deviation = 8

z' = 1.282

1.282 = (x' - 75)/8

x' = (1.282 × 8) + 75 = 85.256

= 85.3 to 3 s.f.

Hope this Helps!!!

Answer:

The required probability for the high temperature which 90% of the August days exceed. is 0.0333

Step-by-step explanation:

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61° F  to 91° F   . Find the high temperature which 90°  F of the August days exceed.

Let assume that X is the random variable

The probability mass function is:

[tex]f(x) = \dfrac{1}{b-a}[/tex]

[tex]f(x) = \dfrac{1}{91-61}[/tex]

[tex]f(x) = \dfrac{1}{30}[/tex]

Thus; The probability density function of X can be illustrated as :

[tex]f(x) = \left \{ {{ \ \ \dfrac{1}{30}} \atop { \limits }}_ \right. _0[/tex]       61 <  x < 91  or otherwise

The required probability for the high temperature at 90°  F can be calculated as follows:

[tex]P(X> 90) = \int\limits^{91}_{90} {f(x)} \, dx[/tex]

[tex]P(X> 90) = \int\limits^{91}_{90} \ {\dfrac{1}{30} \, dx[/tex]

[tex]P(X> 90) = {\dfrac{1}{30} \int\limits^{91}_{90} \ \, dx[/tex]

[tex]P(X> 90) = {\dfrac{1}{30} [x]^{91}_{90}[/tex]

[tex]P(X> 90) = {\dfrac{1}{30} (91-90)[/tex]

[tex]P(X> 90) = {\dfrac{1}{30} \times 1[/tex]

[tex]P(X> 90) = 0.0333[/tex]

The required probability for the high temperature which 90% of the August days exceed. is 0.0333

Answer:

Solution,

∆ ACB = ∆ EFD

finding the value of X,

[tex] \frac{x}{3.8} = \frac{15}{5} [/tex]

Apply cross product property

[tex]x \times 5 = 15 \times 3.8[/tex]

Calculate the product

[tex]5x = 57[/tex]

Divide both sides by 5

[tex] \frac{5x}{5} = \frac{57}{5} [/tex]

Calculate

[tex]x = 11.4[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

D. The linear parent function

Step-by-step explanation:

Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable. The independent variable is commonly depicted as x while the dependent variable is y.

Thus a linear equation is an equation of the type y=ax where a is a constant term. The equation of a straight line graph his y=mx +c, where;

m= gradient of the straight line graph

x= the independent variable

y= the dependent variable

c= the vertical intercept

Answer:

The linear parent function :)

Step-by-step explanation:

Answer:

[tex]x^\frac{8}{3} y^\frac{16}{3}[/tex]

Step-by-step explanation:

Given the expression [tex](x^4y^8)^\frac{2}{3}[/tex], to simplify the expression using the rational exponents;

Applying one of the law of indices to simplify the expression;

[tex](a^m)^n = a^{mn}[/tex]

[tex](x^4y^8)^\frac{2}{3}\\\\= (x^4)^\frac{2}{3} * (y^8)^\frac{2}{3}\\\\= x^{4*\frac{2}{3} } * y^{8*\frac{2}{3} }\\\\= x^\frac{8}{3} * y^\frac{16}{3}\\ \\The \ final \ expression \ will \ be \ x^\frac{8}{3} y^\frac{16}{3}[/tex]

Answer:

x=2 y=4

Step-by-step explanation:

Answer:

$253

Step-by-step explanation:

Margin of error is the critical value times the standard error.

MoE = z × σ/√n

At 99% confidence, z = 2.576.

MoE = 2.576 × 844/√74

MoE = 253

Answer:

7

Step-by-step explanation:

f(x) = 2^(x + 3)

Shifted 10 units to the right:

f(x) = 2^(x + 3 − 10)

f(x) = 2^(x − 7)

Therefore, k = 7.

Answer:

100

Step-by-step explanation:

The population is changing linearly. This means that the population is increasing by a particular value n every year.

From 2009 to 2017, there are 8 increases and so, the population increases by 8n.

The population increased from 1700 to 2500. Therefore, the population increase is:

2500 - 1700 = 800

This implies that:

8n = 800

=> n = 800/8 = 100

The average population growth per year is 100.

Answer:

100

Step-by-step explanation:

aaaaa

Answer:

8(7 + 4) = 88

Step-by-step explanation:

56:

1 x 56

2 x 28

4 x 14

7 x 8

32:

1 x 32

2 x 16

4 x 8

Answer:

8(7+4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

For this particular organism population the growth rate is so that is doubled every 20 years. Using the starting population of 9 billion individuals by year 2000 you have to calculate the expected population values every 20 years.

All you have to do is multiply the original population by 2 to obtain the next value.

Year 2000:

Population: 9*10⁹ or 9 000 000 000 x 2= 18 000 000 000

To express 18 billion in  scientific notation you have to add a "comma" after the first digit and then count the number of digits behind it:

1, 8 000 000 000 there are 10 digits behind the first digit. This notation  summarizes the number in base 10 exponents so 18 billion in scientific notation is:

1.8 * ten "exponent the number of digits behind the comma"

1,8*10¹⁰So the population for year 2020 will be 1,8*10¹⁰

Next for year 2040 you have to multiply the population of year 2020 by 2

1,8*10¹⁰ x 2= 3,6*10¹⁰

And so on:

2060: 3,6*10¹⁰ x 2)= 7.2*10¹⁰

2080: 7.2*10¹⁰ x2= 1.44*10¹¹

2100: 1.44*10¹¹ x2= 2.88*10¹¹

2120: 2.88*10¹¹x2= 5.76*10¹¹

2140: 5.76*10¹¹x2= 1.152*10¹²

2160: 1.152*10¹²x2= 2.304*10¹²

2180: 2.304*10¹²x2= 4.608*10¹²

2200: 4.608*10¹² x2= 9.216*10¹²

2220: 9.216*10¹²x2= 1.8432*10¹³

2240: 1.8432*10¹³x2= 3.6864*10¹³

2260: 3.6864*10¹³x2= 7.3728*10¹³

2280: 7.3728*10¹³x2= 1.47456*10¹⁴

2300: 1.47456*10¹⁴x2= 2.94912*10¹⁴

2320: 2.94912*10¹⁴x2= 5.89824*10¹⁴

2340: 5.89824*10¹⁴x2= 1.179648*10¹⁵

2360: 1.179648*10¹⁵x2= 2.359296*10¹⁵

2380: 2.359296*10¹⁵x2= 4.718592*10¹⁵

2400: 4.718592*10¹⁵x2= 9.437184*10¹⁵

So for year 2400 the expected population will be 9.437184*10¹⁵, writen in common notation that is:

9 437 184 000 000 000 individuals

I hope this helps!

Answer:

1km

Step-by-step explanation:

1000m=1km

Ez Money

Answer:

1000m= 1km

if you convert 1m to km is 0.001km times it by 1000, you get 1km.

Answer:

11/36

Step-by-step explanation:

Find the probability that neither dice shows a 5 (also means the dice can show any number except 5- where there are 5 possible choices out of 6):

= 5/6 x 5/6

=25/36

If we subtract the probability that neither dice shows a 5, we can obtain the probability that at least 1 dice shows a 5- (either one of them is 5, or both of them is 5)

1- 25/36

=11/36