Which pair of complex numbers has a real-number product? (1 3i)(6i) (1 3i)(2 – 3i) (1 3i)(1 – 3i) (1 3i)(3i)

Question:

A teacher puts students' names in a hat and chooses without looking to get a sample of 3 students. What type of sample is this?

Answer:

Simple random

Answer:

36 total students in the class

Step-by-step explanation:

There are 24 boys in the class.

Since they sit in pairs, and exactly 1/4 of the boys sit with a girl, then one-quarter of the 24 boys sits with a girl.

1/4 * 24 = 6, so 6 of the boys sit with a girl.  Reflexively, 6 girls sit with a boy.

Since the problem states that exactly half of the girls sit with a boy, then half of the total number of girls is 6 (since we know that exactly 6 girls were sitting with a boy).

1/2 * x = 6

Multiplying both sides by 2...

x=12

So there are 12 girls total in the class, half (6) of whom sit with a boy.  

There are 24 boys total in the class, one-quarter (6) of whom sit with a girl.  The rest of the boys (18) sit in pairs with another boy (9 pairs), and the rest of the girls (6) sit with another girl (3 pairs).

Since there are 12 girls total and 24 boys total in the class, the total number of students is the sum of 12 and 24

12+24 =36 total students in the class

The figures have corresponding sides that are proportional, therefore, they are similar figures.

When two figures are similar to each other, the corresponding sides are proportional to each other.

The two figures given have two opposite sides that are parallel and congruent to each other. Therefore:

DA/VS = 21/7 = 3

AB/ST = 15/5 = 3

Thus, we can conclude that since their corresponding sides are proportional, therefore, they are similar to each other.

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Answer:

58%

Step-by-step explanation:

29 / 50  * 100% = 58 %    ( rather pathetic score, huh?)

Answer:

58%

Step-by-step explanation:

the boy gets 29 marks out of 50

Then

He gets 29 × 2 marks out of 50 × 2

Then

He gets 58 marks out of 100

Therefore

He scored 58%

Equations b,c, and e accurately represent this statement.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

The three equation accurately represents this statement is;

4.9 x-(-3) = 12.8

3+ 4.9 x = 12.8

12.8 = 4.9 x +3

Hence, equations b,c, and e accurately represent this statement.

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Answer:

D

Step-by-step explanation:

this is because when multipled you get 0.3204 so u round and it becomes 0.320

Answer:

D

Step-by-step explanation:

0.04 x 8.01 = [tex]\dfrac{4}{100} . \dfrac{801}{100}[/tex]

[tex]=\dfrac{3204}{10000}\\\\\\0.3204[/tex]

[tex]R_{x-axis}[/tex] means [tex]P(x,y) \longrightarrow P'(x,-y)[/tex].

[tex]R_{y-axis}[/tex] means [tex]P(x,y) \longrightarrow P'(x,-y)[/tex]

The equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1) is y = x + 8

The equation of a line in slope intercept form is expressed as;

y = mx + b

The equation of the perpendicular bisector will be given as y = -1/m x+ b

where

m is the slope

b is the y-intercept

Determine the slope

Slope = -1-5/9-3

Slope = -6/6

Slope = -1

For the y-intercept

-1 = -1(9) + b

-1 = -9 + b

b = 8

Determine the equation

y = -1/m x + b

y = -1/(-1) x + 8

y = x + 8

Hence the equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1) is y = x + 8

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⊰________________________________________________________⊱

Answer:

x=5

Step-by-step explanation:

Apply the distributive property,

2(x+6)-10=12

2x+12-10=12

Collect a few like terms

2x+2=12

Subtract 2 from both sides

2x=10

Divide the equation by 2.

x=5

Done!!

⊱______________________________________________________⊰

2(x+6) - 10 = 12
2(x+6) = 22
x+6 = 11
x = 11 - 6 = 5

x = 5

Answer:

12 and 14

Step-by-step explanation:

The first number can be assigned x, the second will be assigned x+2 so that it will be even.

3(x)+5(x+2) = 106

3x+5x+10 = 106

8x = 96

x = 12

x+2 = 14

The two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.

We are given two consecutive even numbers, thus the larger number will be two more than the smaller one, as consecutive even numbers differ by two.

We assume the smaller number to be x.

Thus, the larger number = x + 2.

We have been given that three times the smaller number summed with five times the larger number results in 106.

This can be shown by the linear equation in one variable:

3x + 5(x + 2) = 106.

To find the numbers, we need to solve this linear equation in one variable as follows:

3x + 5(x + 2) = 106,

or 3x + 5x + 10 = 106 {Simplifying},

or, 8x + 10 = 106 {Simplifying},

or, 8x + 10 - 10 = 106 - 10 {Subtracting 10 from both sides of the equation},

or, 8x = 96 {Simplifying},

or, 8x/8 = 96/8 {Dividing both sides of the equation by 8},

or, x = 12 {Simplifying}.

Thus the smaller number, x = 12.

The larger number, x + 2 = 12 + 2 = 14.

Thus, the two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.

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The orthocentre for the triangle ABC is (1.85, 5.88).

Triangle ABC has vertices at A(2, 8), B(6, 2) and C(-3, 2).

We need to use analytical geometry to determine the coordinates of the orthocentre.

Steps to find the orthocentre:

Step 1: First, we will find the slopes of any two sides of the triangle (say AC and AB).

Step 2: Next, we can find the slopes of the corresponding altitudes. Remember that if two lines are perpendicular to each other, they satisfy the following equation.

Step 3: Next, we will use the slope-point form of the equation of a straight line to find the equations of the lines that are coincident with the altitudes BE and AD.

Step 4: Next, we can solve the equations of BE and CF simultaneously to find their solution, which gives us the coordinates of the orthocentre H.

Now, the slope of AC=2-8/-3-2=6/5 and the slope of BE=5/6.

The slope of AB=2-8/6-2=-6/4=-3/2 and the slope of CF=-2/3

The slope of BE=y-2/x-6=5/6

⇒6x-5y-26=0----(1)

The slope of CF=y-2/x+3=-2/3

⇒-2x-3y=0----(2)

By solving (1) and(2), we get

y=26/14=13/7=1.85 and x=5.88

Therefore, the orthocentre for the triangle ABC is (1.85, 5.88).

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Answer:

54 possibles

Step-by-step explanation:

Digit ONE    3 choices

Digit two      3 choices

digit three    3 choices

digit  four      2 choices    

        3  x  3   x  3  x  2   = 54 choices meet all of the conditions

Answer:

Angle Q is acute.

Step-by-step explanation:

In an obtuse triangle, there is one obtuse angle and the other two angles are acute.

The probability that the sample will be rejected if five items from 1 lot is selected is 26/15504.

Given Industrial product is product in lots of 20. If sample contains more than one defective then the lot will be rejected.

Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula of calculating probability is as under:

Probability= number of items/ total items.

Sample from 1 lot =5

Samples in 1 lot=20

Lot will be rejected when 1 sample, 2 sample , 3 sample, 4 sample or all the samples are defective.

Probability that the lot will be rejected=[tex](5C_{2} +5C_{3} +5C_{4} +5C_{5})/20C_{5}[/tex]

=(10+10+5+1)/15504

=26/15504

Hence the probability that lot will be rejected if the lot is rejected if more than one defective is observed is 26/15504.

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The length of extra cable that is required to connect the two pieces of existing cable is equal to 182 meters.

In order to determine the length of extra cable that is required to connect the two pieces of existing cable, we would apply the law of cosine as follows:

B² = A² + C² - 2(A)(C)cosB

Substituting the given parameters into the formula, we have;

B² = 325.0² + 430.0² - 2(325.0)(430.0)cos23

B² = 105,625 + 184,900 - 279,500(0.9205)

B² = 290,525 - 257,279.75

B² = 33,245.25

B = √33,245.25

B = 182.33 ≈ 182 meters.

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It will take 29.4 years for the population of Africa to be two times what it is today. This reflects: doubling time.

Doubling time is the time it takes for a particular amount of size or value to double at a given growth rate. By applying the 70 rules, we can find the doubling time of the exponentially increasing population. To do this, divide 70 by the growth rate (r).

Rule of 70 is a simplified way to determine the doubling time using the equation doubling time = 70 / r. Where r is the percentage growth rate of the population. For example, if the population of 10 species increases by 2 individuals per year, the r value will be 20%.

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[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex] is the equation of the ellipse.

The equation of an ellipse is given by

[tex]\rm \dfrac{ (x-h)^2 }{a^2} + \dfrac{ (y-k)^2}{b^2} = 1[/tex]

here

(h,k) is the center

c = is the distance between center to focus

c = [tex]\rm \sqrt{a ^2 - b^2}[/tex]

as the a = 10 , component length

and c = 8

8 = [tex]\rm \sqrt{10 ^2 - b^2}[/tex]

8² = 10² -b²

b² = 36

b = 6

h = 0 ,k = 0

Substituting the values given

[tex]\rm \dfrac{ (x-0)^2 }{10^2} + \dfrac{ (y-0)^2}{6^2} = 1[/tex]

[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex]

Therefore the equation of the ellipse has been determined.

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Answer:

Its 31.0 as the the two triangles are similar and the scale factor is 2

The probability of getting 3 or more who were involved in a car accident last year is 0.126.

Given 9% of the drivers were involved in a car accident last year.

We have to find the probability of getting 3 or more who were involved in a car accident last year if 14 were selected randomly.

We have to use binomial theorem which is as under:

n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex]

where p is the probability an r is the number of trials.

Probability that 3 or more involved in a car accident last year if 14 are randomly selected=1-[P(X=0)+P(X=1)+P(X=2)]

=1-{[tex]14C_{0}0.9^{0} (0.1)^{14} +14C_{1} (0.9)^{1} (0.1)^{13} +14C_{2} (0.9)^{2} (0.1)^{12}[/tex]}

=1-{1*0.2670+14!/13!*0.9*0.29+14!/2!12!*0.0081*0.2358}

=1-{0.2670+0.3654+0.2358}

=1-0.8682

=0.1318

Among the options given the nearest is 0.126.

Hence the probability that 3 or more are involved in the accident is 0.126.

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Answer:

Step-by-step explanation:

Answer:

SSS similarity

Step-by-step explanation:

From the smaller triangle to the larger triangle, the ratio of each pair of corresponding sides is 2.

The total number of lemon candies is 1, solved using the linear equation in one variable 3l + 12 = 15, where l is the number of lemon candies.

We assume the number of chocolate candies to be c.

We assume the number of vanilla candies to be v.

We assume the number of peppermint candies to be p.

We assume the number of lemon candies to be l.

The total number of candies is given as 15.

This can be represented by the linear equation: c + v + p + l = 15 ... (i).

The number of peppermint candies and lemon candies together is given to be twice the number of chocolate and vanilla candies together.

This can be represented by the linear equation: p + l = 2(c + v) ... (ii).

There are eight more peppermint candies than lemon candies.

This can be represented by the linear equation: p = l + 8.

Substituting p = l + 8 in (ii), we get,

l + 8 + l = 2(c + v),

or, 2(l + 4) = 2(c + v),

or, c + v = l + 4.

Substituting c + v = l + 4, and p = l + 8, in (i), we get:

l + 4 + l + 8 + l = 15,

or, 3l + 12 = 15,

or, 3l = 15 - 12 = 3,

or, l = 3/3 = 1.

Therefore, the total number of lemon candies is 1, solved using the linear equation in one variable 3l + 12 = 15, where l is the number of lemon candies.

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There were 15 blue marbles in the bag before removing some

Let B=blue marbles and Y= yellow marbles

The ratio of B to Y is

[tex]\frac{B}{Y} =\frac{8}{5}[/tex]

If we remove 12 blue marbles and add 12 yellow marbles,

the ratio will be

[tex]\frac{B-12}{Y+21} =\frac{1}{3}[/tex]

[tex]3(B-12)=1(Y+21)[/tex]

[tex]3B-36=Y+21\\[/tex]

[tex]3(\frac{8}{5}Y)-36=Y+21[/tex]

[tex]\frac{24}{5}Y-Y=21+36[/tex]

[tex]\frac{19}{5}Y=57[/tex]

[tex]Y=\frac{57*5}{19}\\[/tex]

[tex]Y=15[/tex]

[tex]B=\frac{8}{5} (15)\\B=24[/tex]

Hence, there were 15 blue marbles in the bag before removing some

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Answer:

Step-by-step explanation:

Discussion.

Not directly. But the quadratic formula can do it. But that's not your question.

the factors you get must contain the factors for 1 which are 1 and - 1

These factors must add to - 5. There's no way that will happen with 1 and - 1 and you would be creative math if you tried to say that you could make one of the factors (x -1-1-1-1-1-1). That creates a whole new question.

The Solution set 1 , 2 , 3, 4 matches with equations 4 , 1 , 2 , 3

The system of equations are the set of equations that have common solution.

The set of equations given are

y+5 = x² - 3x

2x +y = 1

On subtracting equation 1 from 2

5 - 2x = x² -3x -1

x² -x -6 = 0

(x-3)(x +2) = 0

x = 3 , -2

At x = 3 , -2; y = -5 , 5

The set of equation are

y -17 = x²-9x

-x +y =1

-17 +x = x² -9x -1

x²-10x +16 = 0

x² - 8x -2x +16 = 0

(x -8) (x-2) = 0

at x = 2 ,8 ; y = 3 ,9

The set of equation is

y +12 = x²+x

x +y =3

12 - x = x²+x -3

x²+2x -15=0

x² +5x -3x -15 = 0

x(x+5) -3(x+5) = 0

(x-3)(x+5) = 0

x = 3 ,-5

At x = 3 , -5 , y = 0,8

The set of equation is

y-15 = -x² +4x

x +y = 1

-15 -x = -x²+4x -1

x²-5x -14 = 0

x² -7x +2x -14 = 0

x(x-7) +2(x-7) = 0

(x +2) (x-7) = 0

x = -2 , 7

at x = -2 , 7 ; y = 3 ,-6

Therefore the Solution set 1 , 2 , 3, 4 matches with equations 4 , 1 , 2 , 3

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Answer:

See below

Step-by-step explanation:

Diameter  of the semi circles = 15 - 3-3 = 9mm

   radius = 4.5 mm

area of rectangle tha goes through the semicircles = 5 x 15 = 75 mm^2

area of two semicircles =

                 area of circle with radius 4.5 = pi r^2 = 63.62 mm^2

    total area = 75 + 63.62 = `38.62 mm^2

Perimeter   Two small side rectangles = 2   * (3+5+3) =26 mm

   perimeter of cicle with diameter 9   =  pi * d = 9pi = 28.27 mm

           total perimeter = 54.27 mm

(check my math !)

Step-by-step explanation:

36 eggs in 3 cartons.

now we double the cartons, so, we need to double the eggs too, because there is a direct relationship between cartons and the number of eggs.

so. in 2×3 cartons are then 2×36 = 72 eggs.

Answer:

43

Step-by-step explanation:

sequence: +5

∴ninth term of sequence = 38+5

                                          = 43