Simply this expression (3 + 2i)^2

Answer:

3/11

Step-by-step explanation:

There are eleven equal parts.

So the denominator is 11.

He copies 8 parts on Sunday.

11-8=3.

He copied 3 parts on Saturday.

Hope this helps ;) ❤❤❤

Answer: 54 mL

Step-by-step explanation:

Simply do 9(number of containers)*6(Syrup per container) to get 54 mL of syrup.

Hope it helps <3

Answer:

4 boys

Step-by-step explanation:

Let x represent boys and y represent girls

Hence, x : y = 3 : 2

x/y = 3/2  

2x = 3y ------ (1)

x/y + 4 = 3/3

3x = 3(y + 4)

3x = 3y + 12 --------- (2)

From (1): x = 3y/2

Substitute x into (2) we have:

9y/2 = 3y + 12

9y = 6y + 24

9y - 6y = 24

3y = 24

∴ y = 8

From (2) : 3x = 24 - 12 = 12

∴ x = 4

Hence there Four boys

Answer:

see explanation

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle then the median is the average of the values either side of the middle.

Given

3   8   14   19   22   29   33   37   43   49

                            ↑ middle is between 22 and 29

median = [tex]\frac{22+29}{2}[/tex] = [tex]\frac{51}{2}[/tex] = 25.5

The upper quartile [tex]Q_{3}[/tex] is the middle value of the data to the right of the median.

29   33   37   43   49

               ↑

[tex]Q_{3}[/tex] = 37

The lower quartile [tex]Q_{1}[/tex] is the middle value of the data to the left of the median.

3   8   14   19   22

           ↑

[tex]Q_{1}[/tex] = 14

The min is the smallest value in the data set, that is 3

The max is the largest value in the data set, that is 49

The 5 number summary is

3,  14,  25.5,  37,  49

Answer:

-3

Step-by-step explanation:

2x + 3 +7x = -24

Add the X together

9x +3 = -24

Bring over the +3. [when you bring over change the sign]

9x = -24 -3

9x = -27

-27 divide by 9 to find X

therefore answer is

x= -3.

Hope this helps

Answer:

x = -3

Step-by-step explanation:

question is

2x + 3 + 7x = -24

First you combine the like terms

2x and 7x you can add them so it will be 9x

so it will then it will be like this:

9x + 3 = -24

now you take the 3 and send it to the other side, and right now the 3 is positive so when it goes to the other side it will turn into -3

so

9x = -24 -3

again now you combine the like terms

-24 -3 = - 27

now you have

9x = -27

now just divide each side by 9

x = -27/9

x = -3

Sorry if this doesnt help

Answer:

False

Step-by-step explanation:

To find <A, we can do 5x - 80 = 3x + 20.

As we simplify, we will get 2x = 100, which is x = 50

Therefore, <A will be 50 degrees and not 45 degrees.

Also, if you need y, you can do:

3y - 7 = y + 7

2y = 14

y = 7

Answer:

23 dimes; 32 nickel

Step-by-step explanation:

Let n = number of nickels.

Let d = number of dimes.

A nickel is worth $0.05; n nickels are worth 0.05n.

A dime is worth $0.10; d dimes are worth 0.1d.

Number of coins:

d + n = 55

Value of the coins:

0.1d + 0.05n = 3.9

Solve d + n = 55 for d:

d = 55 - n

Substitute 55 - n for d in second equation.

0.1(55 - n) + 0.05n = 3.9

5.5 - 0.1n + 0.05n = 3.9

-0.05n = -1.6

n = 32

Substitute 32 for n in d + n = 55 and solve for d.

d + 32 = 55

d = 23

Answer: 23 dimes; 32 nickel

Answer:

(3) x ≥ -3

(4) 2.5 gallons

(4) -12x + 36

Step-by-step explanation:

Hey there!

1)

Well its a solid dot meaning it will be equal to.

So we can cross out 1 and 2.

And it's going to the right meaning x is greater than or equal to -3.

(3) x ≥ -3

2)

Well if each milk container has 1 quart then there is 10 quarts.

And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.

(4) 2.5 gallons

4)

16 - 4(3x - 5)

16 - 12x + 20

-12x + 36

(4) -12x + 36

Hope this helps :)

Answer:

Step-by-step explanation:

Given that:

If C(x) =  the cost of producing x units of a commodity

Then;

then the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

We are to consider a given function:

[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]

And the objectives are to determine the following:

a) the total cost at a production level of 1000 units.

So;

If C(1000) = the cost of producing 1000 units of a commodity

[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]

[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]

[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]

[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]

[tex]C(1000) = $310491.1064[/tex]

[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]

(b) Find the average cost at a production level of 1000 units.

Recall that :

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

SO;

[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]

Using the law of indices

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]

c(1000) =$ 310.49 per unit

(c) Find the marginal cost at a production level of 1000 units.

The marginal cost  is C'(x)

Differentiating  C(x) = 54,000 + 130x + 4x^{3/2} to get  C'(x) ; we Have:

[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]

[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]

[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 319.7366596[/tex]

[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]

(d)  Find the production level that will minimize the average cost.

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

the production level that will minimize the average cost is c'(x)

differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]

Also

[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]

[tex]x^2 = 27000\sqrt{x}[/tex]

[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]

x= 0;  or  [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900

Since  production cost can never be zero; then the production cost = 900 units

(e) What is the minimum average cost?

the minimum average cost of c(900) is

[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]

c(900) = 60 + 130 + 4(30)

c(900) = 60 +130 + 120

c(900) = $310 per unit

Answer:

d - 12.50 = 17

add 12.50 to both sides to get d alone.

d = 12.50 + 17

Answer:

It's B d= 17 + 12.50

Step-by-step explanation:

Got it right on edg

the ancient Greek used the golden ratio

Answer:

An important proportion that the Ancient Greeks used was the Golden Mean, the a0

Step-by-step explanation:

Also known as Golden Ratio, Divine Proportion, or Golden Section

Answer:

0.078

Step-by-step explanation:

The probability P(A) of an event A happening is given by;

P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]

From the question;

There are two events;

(i) Drawing a first card which is a king: Let the event be X. The probability is given by;

P(X) = [tex]\frac{number-of-possible-outcomes-of-event-X}{total-number-of-sample-space}[/tex]

Since there are 4 king cards in the pack, the number of possible outcomes of event X = 4.

Also, the total number of sample space = 52, since there are 52 cards in total.

P(X) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

(ii) Drawing a second card which is a queen: Let the event be Y. The probability is given by;

P(Y) = [tex]\frac{number-of-possible-outcomes-of-event-Y}{total-number-of-sample-space}[/tex]

Since there are 4 queen cards in the pack, the number of possible outcomes of event Y = 4

But then, the total number of sample = 51, since there 52 cards in total and a king card has been removed without replacement.

P(Y) = [tex]\frac{4}{51}[/tex]

Therefore, the probability of selecting a first card as king and a second card as queen is;

P(X and Y) = P(X) x P(Y)

= [tex]\frac{1}{13} * \frac{4}{51}[/tex] = 0.078

Therefore the probability is 0.078

Answer:

36 tickets

Step-by-step explanation:

At a city museum, child tickets are sold for $5.30, and adult tickets are sold for $9.40

The total sales that were made are $1206

Let x represent the number of child tickets that were sold

Let y represent the number of adult tickets that was sold

5.30x +9.40y= 1206

The number of adult tickets sold was three times greater than the child tickets

y= 3x

Substitute 3x for y in the equation

5.30x + 9.40y= 1206

5.30x + 9.40(3x)= 1206

5.30x + 28.2x= 1206

33.5x= 1206

Divide both sides by the coefficient of x which is 33.5

33.5x/33.5= 1206/33.5

x = 36

Hence the number of child tickets that were sold that day is 36 tickets

Answer:

1

Step-by-step explanation:

[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]

Answer:

[tex]\boxed{V=lwh}[/tex]

Step-by-step explanation:

The formula for volume of a cuboid is:

[tex]V=lwh[/tex]

[tex]volume = length \times width \times height[/tex]

Answer:

V = l w h

Step-by-step explanation:

Volume of a Cuboid = Length × Width × Height

Where l = length, w = width and h = height

Answer:

Option (D)

Step-by-step explanation:

In the picture attached,

An obtuse angle triangle ABC has been given.

By applying Sine rule in the triangle,

[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]

Since, m∠A + m∠B + m∠C = 180°

45° + 110° + m∠C = 180°

m∠C = 180°- 155° = 25°

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]

[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]

b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]

b = 15.56

b ≈ 15.56

[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]

a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]

a = 11.712

a = 11.71

Therefore, Option (D) will be the answer.

Answer:

8 and 9

Step-by-step explanation:

If x is the smaller integer, and x + 1 is the larger integer, then:

(x + 1)² + 3x = 105

x² + 2x + 1 + 3x = 105

x² + 5x − 104 = 0

(x + 13) (x − 8) = 0

x = -13 or 8

Since x is positive, x = 8.  So the two integers are 8 and 9.

Answer:

To find the x-intercept, simply plug in the value y = 0 into your equation and then solve for x. To find the y-intercept, plug in x = 0 and solve for y.

Answer:

it took 7 hours for the bread to drop at a constent rate

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{2x+1}{x^2(x+1)} \ \ }[/tex]

Step-by-step explanation:

Hello,

This is the same method as computing for instance:

[tex]\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{2*3}=\dfrac{5}{6}[/tex]

We need to find the same denominator.

Let's do it !

For any x real different from 0, we can write:

[tex]\dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{1}{x^2}+\dfrac{1}{x(x+1)}\\\\=\dfrac{x+1+x}{x^2(x+1)}=\dfrac{2x+1}{x^2(x+1)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: n = 2401

Step-by-step explanation:

Given;

Confidence level = 2% - 99%

n = ? ( which is the sample size is unknown ).

Solution:

Where;

n = [z/E]^2*pq

Since no known value for ( p ) estimate is given, the "least biased" estimate is p = 1/2

Substituting the given data into the formula.

n = [1.96/0.02]^2(1/2)(1/2)

n = 2401

The minimum number of truck drivers the statistician needs to sample for an accurate result is 2401

Answer:

  181.8 yd

Step-by-step explanation:

The law of cosines is good for this. It tells you for triangle sides 'a' and 'b' and included angle C, the length of 'c' is given by ...

  c^2 = a^2 +b^2 -2ab·cos(C)

For the given geometry, this is ...

  c^2 = 400^2 +240^2 -2(400)(240)cos(16°) ≈ 33,037.75

  c ≈ √33037.75 ≈ 181.8 . . . yards

Marsha's ball is about 181.8 yards from the hole.

Answer:

181.8 yds

Step-by-step explanation:

I got it correct on founders edtell

Answer: A, (0, -3)

Step-by-step explanation:

Inequalities, once graphed, take the form of the image you attached:

Linear inequalities are straight lines, sometimes dotted and sometimes solid, with shading on one side of the line.

Any point in the shading is a correct solution to the inequality.

In this case, the line is solid, so any point on the line is a solution to the inequality.

Looking at answer choice A: (0, -3), it lies on the line as the y-intercept.

The correct choice is A.

Answer:

Option (B)

Step-by-step explanation:

If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.

Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]

a + c = 172°

Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.

Therefore, a = c

⇒ a = c = 86°

Therefore, a = 86°

Option (B) will be the answer.

Answer:

[tex]79591.8872 in^3/s[/tex]

Step-by-step explanation:

we know that the volume of a right circular cone is give as

[tex]V(r,h)= \frac{1}{3} \pi r^2h\\\\[/tex]

Therefore differentiating partially  with respect to  r and h we have

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [2rh\frac{dr}{dt} +r^2\frac{dh}{dt}][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [218*198*1.1+109^2*2.4][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [47480.4+28514.4]\\\\\frac{dV}{dt} = \frac{\pi}{3} [75994.8]\\\\ \frac{dV}{dt} = 3.142 [25331.6]\\\\ \frac{dV}{dt} =79591.8872 in^3/s[/tex]

Answer:

70

Step-by-step explanation:

You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.

When the wavelength of a diffraction grating is decreased,  the distance between lines decreases.

The diffraction grating is used to carry out interference experiments. It consists of a  number of small lines that are constructed to be close to each other and produce an interference pattern.

The outcome of decreasing the wavelength of incident light on a diffraction grating is that the distance between lines decreases.

Learn more about diffraction grating:https://brainly.com/question/13902808

#SPJ1

Answer:

The mean for all such groups randomly selected is 0.09*800=72.

Step-by-step explanation:

The value of the standard deviation is 7.

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

The standard deviation is calculated by using the formula,

[tex]\sigma = \sqrt{Npq}[/tex]

N = 600

p = 9%= 0.09

q = 1 - p= 1 - 0.09= 0.91

Put the values in the formulas.

[tex]\sigma = \sqrt{Npq}[/tex]

[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]

[tex]\sigma[/tex] = 7

Therefore, the value of the standard deviation is 7.

To know more about standard deviation follow

https://brainly.com/question/475676

#SPJ2

Answer:

x < -( 8-2b) /a  a > 0

Step-by-step explanation:

−ax + 2b > 8

Subtract 2b from each side

−ax + 2b-2b > 8-2b

-ax > 8 -2b

Divide each side by -a, remembering to flip the inequality ( assuming a>0)

-ax/-a < ( 8-2b) /-a

x < -( 8-2b) /a  a > 0

Answer: [tex]x<\frac{-8+2b}{a}[/tex]

                  [tex]a>0[/tex]

Step-by-step explanation:

[tex]-ax+2b>8[/tex]

[tex]\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}[/tex]

[tex]-ax>8-2b[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]

[tex]\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)[/tex]

[tex]ax<-8+2b[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}a[/tex]

[tex]\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0[/tex]

[tex]x<\frac{-8+2b}{a};\quad \:a>0[/tex]