Calculate the median 5,10,12,4,6,11,13,5

Answer:

A

Step-by-step explanation:

First express [tex]\sqrt{2}[/tex] + i[tex]\sqrt{2}[/tex] in trig form

| z | = [tex]\sqrt{(\sqrt{2})^2+(\sqrt{2})^2  }[/tex] = [tex]\sqrt{4}[/tex] = 2

Θ = [tex]tan^{-1}[/tex]( [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]) = [tex]tan^{-1}[/tex]( 1) = [tex]\frac{\pi }{4}[/tex]

Thus

[tex]\sqrt{2}[/tex] + i[tex]\sqrt{2}[/tex] = 2 [ cos[tex]\frac{\pi }{4}[/tex] + isin[tex]\frac{\pi }{4}[/tex] ]

Hence

([tex]\sqrt{2}[/tex] + i[tex]\sqrt{2}[/tex] )³

= 2³ [ cos ([tex]\frac{\pi }{4}[/tex] × 3) + isin([tex]\frac{\pi }{4}[/tex] × 3 ) ]

= 8 [ cos([tex]\frac{3\pi }{4}[/tex] ) + isin([tex]\frac{3\pi }{4}[/tex]) ] → A

The standard form of the give complex number is

8 [ cos(\frac{3\pi }{4} ) + isin(\frac{3\pi }{4}) ]

We have given that,

First express  [tex]\sqrt{2} + i\sqrt{2}[/tex]  in trig form

[tex]| z | = \sqrt{(\sqrt{2})^2+(\sqrt{2})^2 } = \sqrt{4} = 2[/tex]

[tex]\theta = tan^{-1}( \frac{\sqrt{2} }{\sqrt{2} }) = tan^{-1}( 1) = \frac{\pi }{4}[/tex]

Thus, [tex]\sqrt{2} + i\sqrt{2} = 2 [ cos\frac{\pi }{4} + isin\frac{\pi }{4} ][/tex]

[ r(cos θ + i sin θ) ]^n = r^n(cos nθ + i sin nθ)

Hence, [tex](\sqrt{2} + i\sqrt{2} )^3[/tex]

[tex]= 2^3 [ cos (\frac{\pi }{4} \times 3) + isin(\frac{\pi }{4} \times 3 ) ][/tex]

[tex]= 8 [ cos(\frac{3\pi }{4} ) + isin(\frac{3\pi }{4}) ] \implies A[/tex]

Thererefore the standard form of the give complex number is

8 [ cos(\frac{3\pi }{4} ) + isin(\frac{3\pi }{4}) ].

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Answer:

Step-by-step explanation:

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have r = 10cm and H = 25 cm.

Substitute:

[tex]V=\dfrac{1}{3}\pi(10^2)(25)=\dfrac{1}{3}\pi(100)(25)=\dfrac{250\pi}{3}\ cm^3[/tex]

[tex]\pi\approx3.14\to V\approx\dfrac{(250)(3.14)}{3}\approx261.67\ cm^3[/tex]

Let's solve your inequality step-by-step.

x+11>2

Step 1: Subtract 11 from both sides.

x+11−11>2−11

x>−9

Answer:

x>−9

Answer: 18,000deg

Step-by-step explanation:

(3000rev/min)*(1min/60s)*(360deg/1rev)=18,000deg

Answer:

18,000

Step-by-step explanation:

We know that the electric motor makes 3000 revolutions in a minute/60 sec.

In one second, the motor makes 3000/60 revolutions.

In one second, the motor makes 50 revolutions.

∴ 1 revolution = 360 degrees

50 revolutions = 360 × 50 degrees

50 revolutions = 18,000 degrees

Answer:

498

Step-by-step explanation:

38×12 + 7×6 = 498

don't worry!

Answer: B 498

Step-by-step explanation:12 times 38 because it is 12 eggs in each cartons plus 7 times 6 because she also bought 7 quail eggs equal to 498

Answer:

7/10

Step-by-step explanation:

To make things simple, let's turn 80% into a fraction, 8/10. To get a common denominator let's turn 8/10 into 4/5. Since they are both of equal size, the first group would have 2/5 left-handed people and the second 1/5 left-handed people. Let's imagine that each group has 5 people in it. There would be 10 people in total. There is 1 person for each fifth so we can add now. 4 + 3 = 7 right handed people. To check, 2 + 1 = 3 and 3 + 7 = 10. so 7/10 of the class is right-handed.

The fraction of the class is right handed is 7/10

We have given that

80% of the second group are right-handed.

let's turn 80% into a fraction,

The fraction form of 80% can be calculated by dividing 80 by 100

So we get,

[tex]=\frac{80}{100} \\\\=\frac{8}{10}[/tex]

=8/10.

To get a common denominator let's turn

8/10 =4/5             .....(divide the numerator and denominator by 2)

Since they are both of equal size,

The first group would have 2/5 left-handed people and

The second 1/5 left-handed people.

Let's imagine that each group has 5 people in it.

There would be 10 people in total.

There is 1 person for each fifth so we can add now.

4 + 3 = 7 .....(1)

right handed people.

we can check it,

2 + 1 = 3 and 3 + 7 = 10. .........(2)

Therefore we get,

7/10 of the class is right-handed.

The fraction of the class is right handed is 7/10

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Answer: [tex]x=56.5\ km[/tex]

Step-by-step explanation:

Given the right triangle in the image, you need to remember the following identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

Observe the triangle. You can identify that:

[tex]\alpha=28\°\\adjacent=x\\hypotenuse=64[/tex]

Then, knowing these values, you can substitute them into  [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]:

[tex]cos(28\°)=\frac{x}{64}[/tex]

Finally, you have to solve for "x".

Therefore, the value of "x" rounded to the nearest tenth is:

[tex]64*cos(28\°)=x\\x=56.5\ km[/tex]

Answer:

A: x= -18, B: y= 10, C: x= 42, D: 14

Step-by-step explanation:

Note: The photo you used was hard to read, so I just assumed what the equations were.

A) x+14=-4

-14      -14

x=-18

B) y-14=-4

+14      +14

y=10

C) z/14=3

times 14         times 14

x=42

D) 2/7x=4

times 7/2      times 7/2

x=14

You would multiply outcomes 3 times to get the total number of elements in the sample space because the experiment has three stages.

4^3 = 64

Note: You can also multiply 4 three times.

Answer: C. 64

Step-by-step explanation:

We know that the number of total elements in the sample space is given by :_

[tex]N^n[/tex], where N is the number of total possible outcomes for an event and n is the number of times event is repeated.

Given: The number of equally likely sample outcomes of a single stage of an experiment = 4

The number of stages in the experiment = 3

Then , the total number of elements in the sample space :-

[tex](4)^3=64[/tex]

Hence, the total number of elements in the sample space = 64.

Answer:

f(x) = x(x + 9)(x − 9)

Step-by-step explanation:

Answer: f(x) = x(x+9)(x-9)

Step-by-step explanation:

[tex]x \div y = 3 \div 5 \\ it \: means = \\ 3y = 5x \\ x - y = 18 \\ [/tex]

To solve we multiply the last equation by 5 and we get the following:

5x-5y=90

But 5x=3y and we replace it in this equation:

3y-5y=90

-2y=90

y=-45

and x-(-45)=18 , x+45=18

x=-27

length* width

12*10= 120

Volume /120

960/120=8

height is 8 inches

Answer:

c

Step-by-step explanation:

PI times radius squared

Statement C describes how to find the area. Area of the circle is obtained by dividing the diameter in half and multiply by π.

Area describes the region or the space of the given figure. If the circle has a radius of 'r' units, the area is calculated as;

A = π r² sq. units.

Because the radius of a circle is half its diameter, if the diameter is 'd', then,

r= d/2,

The area may be represented as;

A = π r² sq. units.

Area of the circle is obtained by dividing the diameter in half and multiply by π.

Hence,statement C describes how to find the area.

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Answer:

The answer is A. Was this a test question or a normal lesson?

Step-by-step explanation:

Answer:

the correct answer is B. 10%

Step-by-step explanation:

From the given question, we recall the following,

The probability of Wayne making a three pointer = 21%

Now, what is the the probability he makes his first three pointer on the fourth shot.

The next step is to find a solution to the question

The probability of not shooting a 3 pointer is  1- 0.79 = 1-p=q

All the throws of wayne are independent of each other

If two or  ore event are independent we have,

P (AnB) = P(A) * P(B)

P (AnBnC) = P(A) *P (B) *P (C)

P (AnBnCnD) = P(A) * P(B)* P(C) *P(D)

Now, let make first 3 pointer on the 4th shot, we have:

q³= p (0.79)³ (0.21) =10% or (1-0.21) x (1-0.21)x (1-0.21) x 0.21=(0.79) x (0.79) x (0.79) x(0.21)=0.1

which is =10%

Answer:

x = 3 and y = 3

Step-by-step explanation:

2 x + 3 y = 15 { Equation 1 }

x + y = 6 { Equation 2 }

( Multiply the x variable by 2 so equation 1 and 2 have the same x variable )

2 x + 3 y = 15 { Equation 1 }

2 x + 2 y = 12 { Equation 2 }

( Minus equation 2 from 1 so we are left with an independent variable )

y = 3

( Substitute y = 3 into equation 1 to solve for x )

2 x + 9 = 15

( Solve )

2 x + 9 = 15

[ Subtract 9 from both sides ]

2 x = 6

[ Divide by 2 from both sides ]

x = 3

Answer: x=3

y=3

Step-by-step explanation:

2x+3y=15

x+y=6

2x+3y=15

x=6-y

2(6-y)+3y=15

y=3

x=6-3

x=3

(3,3)

Answer:

The answer is B. Hope this helped! c;

Step-by-step explanation:

Answer:

B)Out of every 5 trials the desired outcome will occur approximately 2 times

Step-by-step explanation:

The theoretical probability of an event occurring is 2/5. Which best describes the experimental probability associated with this?

The answer is -

Out of every 5 trials, the desired out come will be approximately 2 times.

Theoretical probability is based on reasoning. It is written as a ratio of the number of favorable outcomes to the number of possible outcomes.

Answer:

See diagram below

Step-by-step explanation:

I added the picture but not sure if you can see it?  Hope it helps!

Final answer:

Chantale's motion can be graphically represented on a position-time graph, with walking segments shown by lines with positive slopes, the running back segment by a line with a negative slope, and the stationary segment at school by a horizontal line.

Explanation:

The question pertains to plotting a graph of Chantale's motion as she moves to and from school, which is a concept from kinematics in physics. We can visualize her walk as a position-time graph, where each part of her travel (A to D) corresponds to a different segment of the graph.

A. Walking towards home: This would be represented by a line moving away from the origin (assuming the school is the origin) with a positive slope, showing that distance from school is increasing over time.

B. Running back to school: This segment of the graph will have a negative slope as Chantale moves closer to the origin (school).

C. Spending 2 minutes at school: During this time, her position does not change, so the graph will show a flat, horizontal line indicating no movement.

D. Walking back home: This would again be a line with a positive slope as she moves away from the school to her house.

To encompass the entire journey, you would see a graph with segments that reflect these motions, and each segment would follow the order of actions A to D.

Answer:

[tex]\boxed{\text{Degree = 4; Max. no. of terms = 5}}[/tex]

Step-by-step explanation:

(x² + x + 2)(x² – 2x + 3)

1. Degree of product

The degree of the product of two polynomials is the sum of their degrees.

Each polynomial is of degree 2, so the degree of the product is 4.

That is, the term of highest degree must come from x² × x² = x⁴.

2. Maximum number of terms

The maximum number of terms is one more than the degree of the product.

Thus, there is a maximum of five terms in the product: one for each power of x plus a constant term.

P = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅

Answer:

Step-by-step explanation:

the graph of f(x)=3x becomes the graph of g(x)=3x-2 if the entire graph of f(x) = 3x is translated down by 2 units.

4 desserts

The number of meals can be expressed by c * s * d = m, where c is main courses, s is salads, d is desserts, and m is meals.

Fill in the variables.

6 * 2 * d = 48

Simplify.

12 * d = 48

Divide both sides by 12.

d = 4

So, there are 4 desserts.

Answer:

2.

Step-by-step explanation:

The reason I say this one is because that equation say p is greater than 48 that is why,

Answer: Option number 3!

Answer:

5 hr.

Step-by-step explanation:

this is because one car is moving at 30 miles an hour and the other at 30+20 miles an hour = 50mph. so after 1 hour one car would have gone 30 miles and the other 50 = 80 altogether not 400 yet. After 2 hours one car would have gone 60 miles and the other 100 = 160 not 400 yet. ECT... After five hours one car has gone 150 mile (30mph*5hr = 150miles) and the other 250miles (59mph*50hr = 250miles) = 400, since 150+250=400. Therefore it would take 5hr for the cars to meet. and crash ._.

Final answer:

The two cars traveling towards each other, one at 30 mph and the other at 50 mph, will meet after 5 hours, since their combined speed is 80 mph and they are 400 miles apart.

Explanation:

To solve the problem of when two cars moving towards each other will meet, we can use the concept of relative speed. The first car travels at 30 mph, and the second car travels at the faster speed of 50 mph (since it is 20 mph faster than the first car). The combined speed at which the two cars are moving towards each other is the sum of their individual speeds.

The formula for time is:

Time = Distance / Speed

Given that the two cars are 400 miles apart, and the combined speed is 30 mph + 50 mph = 80 mph, the time it takes for the two cars to meet is:

Time = 400 miles / 80 mph = 5 hours

Therefore, the cars will meet after 5 hours of travel.

Answer:

60 students were in each bus.

Step-by-step explanation:

248-8=240

240 students rode on busses.

240/4= 60

60 students per bus.

248-8= 240 (taking away 8 because 8 of the students are not taking the bus)

240/4=60 (dividing the number we got by 4 because there are 4 busses)

i hope i helped :)

See the attached picture.

The Y values would remain the same, the X values become the negative of the original values.

Answer:

14 and 16

Step-by-step explanation:

absolute value of a negative is the positive

Answer:

Answer is 14 and 16.

Step-by-step explanation:

Absolute value is never negative.

Hope my answer has helped you!

Answer:

The cost is less than $1.30

Step-by-step explanation:

Let

y-----> the total cost of a mobile phone call

x----> the time in minutes

we know that

if time were x=5 minutes

the cost would be

y=0.30+0.20(5)=$1.30

but

the time is less than 5 minutes

therefore

the cost would be

y< $1.30

Answer:

The possible cost of a call if it is shorter than 5 minutes ranges between 30 cents and maximum 130 cents

Step-by-step explanation:

Define a function as

Y: Cost of a call in cents

X: Number of minutes of call

So using the statement we can find that

Y=30+20X

because the cost of the call has a fix cost of 30 cents plus 20 cents per minute used. If the calls is shorter than 5 minutes for x = 5

Y=30+20X = 30 + (20*5) = 30 + 100 = 130 which is the cost of a call of max 5 minutes

Because you pay a fixed cost of 30 even if you spend very little time. X= 0 then the possible cost of a call if it is shorter than 5 minutes ranges between 30 cents and maximum 130 cents

Answer:

I believe it is 1/6 for the pencil and 1/3 for the pen. Altogether, 2/9.

Step-by-step explanation:

There is 1 purple pencil out of 6 and 1 black pen out of 3.

Using probability of independent events, it is found that there is a [tex]\frac{1}{15}[/tex] probability  that she will select a purple pencil and a black pen in that order.

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

If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this question:

The probability is:

[tex]P(A \cap B) = P(A)P(B) = \frac{1}{5} \times \frac{1}{3} = \frac{1}{15}[/tex]

[tex]\frac{1}{15}[/tex] probability  that she will select a purple pencil and a black pen in that order.

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Answer:

Step-by-step explanation:

xy = 300

x + y = 50                       Solve for y

y = 50 - x                        substitute into xy = 300

x(50 - x) = 300               Remove the brackets.

50x - x^2 = 300             Bring the left to the right.

0 = x^2 - 50x + 300

This is a quadratic. It will have 2 solutions.

a=1

b = - 50

c = 300

Put these into the quadratic equation.

It turns out that x has two values -- both plus

x1 = 42.03

x2 = 6.97

x1 + y1 = 50

42.03 + y = 50

y = 50 - 42.03

y = 7,97

(42.03 , 7.97)

====================

x2 + y2 = 50

6.97 + y2 = 50

y2 = 50 - 6.97

y2 = 43.03

(6.97 , 43.03)

Answer:

x ≈ 6.97, y ≈ 43.03; x ≈ 43.03, y ≈ 6.97

Step-by-step explanation:

System: x + y = 50, xy = 300

Alter 1st equation: y = 50 - x

Substitute: x(50 - x) = 300

Distribute: -x² + 50x = 300

Subtract: -x² + 50x - 300 = 0

Quadratic formula: x = (-50 ± √(2500 - 4 * -1 * -300))/(-2)

Simplify: x = (-50 ± √1300)/-2

Distribute: x = 25 ± (10√13)/-2

Simplify: x = 25 - 5√13 --> x ≈ 6.97, x = 25 + 5√13 --> x ≈ 43.03

Substitute: 6.97 + y = 50 --> y ≈ 43.03, 43.04 + y = 50 --> y ≈ 6.97

Answer:

34n

Step-by-step explanation:

The product of 34 and the number of pounds

The product means multiply

So the product of 34 and the number of pounds = 34 × n = 34n

The question involves mathematical conversion of units from pounds to ounces and calculating percent composition. Multiplying by 16 converts pounds to ounces, while percent composition is found by dividing the mass of the component by the total mass and then multiplying by 100. Exact numbers, like the number of bags, do not affect significant figures.

The student appears to be dealing with a conversion problem within a mathematics context, specifically involving the units of pounds and ounces. When converting from a larger unit (pounds) to a smaller unit (ounces), the correct operation is multiplication since there are 16 ounces in one pound. A clear example of this is provided where 4.5 pounds, written as 4(1/2) pounds, is converted to ounces resulting in 72 ounces.

Furthermore, the problem addresses the percent composition of a substance by mass, which is a concept commonly encountered in chemistry but framed here within a mathematical question. Using the provided formula and mass values, we calculate the percent composition by dividing the mass of the desired product by the total mass of the product and then multiplying by 100 to get a percentage. The percentages indicate the fraction of the total mass that is made up of a specific component. The key information given in the example is that the mass of the desired product is 73.0, and the total mass of the product is 215, therefore, the percent composition is 34.0%.

Lastly, the question states that because the number of bags is an exact value, it is not considered in the significant figures. This means we are not to worry about the precision of measurement when it comes to counting items, which is a principle applied to exact numbers in significant figure rules.