Multiply each pair of factors. type the product in the space provided. (6 3i)(6 − 3i) = (4 − 5i)(4 5i) = (−3 8i)(−3 − 8i) =

Answer:

1759400

I like that a lot actually !!

Step-by-step explanation:

Have A Wonderful Day !!

Answer:

D

Step-by-step explanation:

1200=30%

1200/x=30%

1200*.3=400

400=x

Answer:

143 oil changes

Step-by-step explanation:

We first find the unit rate.

(91 oil changes)/(7 days) = 13 oil changes/day

Since we want to know the number of oil changes in 11 days, we multiply the unit rate by 11 days.

13 oil changes/day * 11 days = 143 oil changes

In a linear equation, 9.14 does he save by paying off the loan when the next payment is due .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Jan  293  18  311  1,507 16.25%

Feb  296  15  311  1,212 32.67%

Mar 298           12  311   913 49.25%

Apr  301            9  311   612 66.00%

May  304    6  311  308 82.92%

Jun  308    3  311    0        100.00%

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Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

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With employees ranging in age from 40 to 30, 36 to 22, there is a 46-year age difference between them. The average difference between each age and the population's mean age is measured.

We employ the following formula to determine the variance of a population:

σ² = Σ(x - μ)² / N

σ² = Σ(x - μ)² / N

where:

σ² =  the population variance

Σ = the sum of

x = the value of each element in the population

μ = the population mean

N = the population size

First, we need to find the population mean:

μ = (40 + 30 + 36 + 22) / 4 = 32

Next, we calculate the sum of the squared deviations from the mean:

(40 - 32)² + (30 - 32)² + (36 - 32)² + (22 - 32)² = 64 + 4 + 16 + 100 = 184

Then, we divide the sum of squared deviations by the population size:

σ² = Σ(x - μ)² / N = 184 / 4 = 46

Therefore, the population variance is 46.

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The  following points are inside, outside or on the circle.

Point (5,-2) is outside the circle.

Point (-2,8) is on the circle.

Point (0,10) is outside the circle.

Point (0,0) is inside the circle.

What is circle ?

A circle is a geometric shape consisting of all the points in a plane that are a given distance from a given point, called the center. It can also be defined as the locus of points at a fixed distance from a given point. A circle is a two-dimensional figure and is perfectly round. It has no corners or edges. The distance from the center of the circle to any point on its circumference is called the radius.

According to the question:
We need to determine whether each point lies inside, outside, or on the circle with equation \((x+2)^2+(y-3)^2=36.\)

Point (5,-2): To check if this point is inside, outside, or on the circle, we can substitute x=5 and y=-2 into the equation and see if we get a true statement. \((5+2)^2+(-2-3)^2\) = 49+25 = 74, which is greater than 36. Therefore, the point (5,-2) is outside the circle.

Point (-2,8): Similarly, substituting x=-2 and y=8 into the equation, we get \((-2+2)^2+(8-3)^2 = 25\), which is equal to 36. Therefore, the point (-2,8) lies on the circle.

Point (0,10): Substituting x=0 and y=10 into the equation, we get\((0+2)^2+(10-3)^2 = 49\), which is greater than 36. Therefore, the point (0,10) is outside the circle.

Point (0,0): Substituting x=0 and y=0 into the equation, we get \((0+2)^2+(0-3)^2 = 13\), which is less than 36. Therefore, the point (0,0) is inside the circle.

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Answers : A and D

Step - by - step explanation :

tip : when finding constant of proportionality it's always Y divided by X

A = what is 22.5 divided by 3 ?  7.5 ( now multiply 7.5 by the next X [ 4 ] )

what is 7.5 x 4 ?  30 ( and since on the graph it also says 30 then you can assume this one has a proportional relationship )

B = what is 12 divided by 3 ?  4 ( now multiply 4 by the next X [ 5 ] )

what is 4 x 5 ?  20 ( and because the graph says 25 then you know it's NOT a proportional relationship )

C = what is 8.5 divided by 2 ?  4.25 ( now multiply 4.25 by the next X [ 5 ] )

what is 4.25 x 5 ?  21.25 ( and because the graph says 22.5 then you know it's NOT a proportional relationship )

D = what is 10 divided by 2 ?  5 ( now multiply 5 by the next X [ 3 ] )

what is 5 x 3 ?  15 ( and since on the graph it also says 15 then you can assume this one has a proportional relationship )

( sorry it took me so long to write this )

Answer:

71° F

Step-by-step explanation:

Consider the rational part of f(t)

\(\frac{40t^3}{t^3+100}\)  ( divide numerator and denominator by t³

= \(\frac{40}{1+\frac{100}{t^3} }\)

As t → infinity then \(\frac{100}{t^3}\) → 0 , the expression simplifies to

\(\frac{40}{1+0}\) = \(\frac{40}{1}\) = 40

Thus after driving for a long time

f(t) = 31 + 40 = 71° F

Answer:

The area and the perimeter of the square barn which has each side 9 meters long is 81 m² and 36 m.

Step-by-step explanation:

Answer:

Mean = 30516.67

Standard deviation, s = 3996.55

P(x < 27000) = 0.0011518

Step-by-step explanation:

Given the data:

28500 35500 32600 36000 34000 25700 27500 29000 24600 31500 34500 26800

Mean, xbar = Σx / n = 366200 /12 = 30516.67

Standard deviation, s = [√Σ(x - xbar) / n-1]

Using calculator, s = 3996.55

The ZSCORE = (x - mean) / s/√n

Zscore = (27000 - 30516.67) / (3996.55/√12)

Zscore = - 3516.67 / 1153.7046

Zscore = - 3.048

P(x < 27000) = P(Z < - 3.049) = 0.0011518

Answer:

√89

Step-by-step explanation:

√(4+4)2+(0-5)2

√(8)2+(-5)2

√64+25

√89

The center of the circle is (h, k) = (-g, -f) = (h, k), and the radius of the circle is

r = \(\sqrt{-2h^2 - 2k^2 + r^2}\).

Given that an equation of a circle can be written in the form

\(\( (x-h)^{2}+(y-k)^{2}=r^{2} \)\)

where \( (h, k) \) is the center and \( r \) is the radius.

Expanding terms, the equation can also be written as:

\(x^{2} - 2hx + h^{2} + y^{2} - 2ky + k^{2} = r^{2}\)

The general equation of a circle is given by

x^2 + y^2 + 2gx + 2fy + c = 0

where (−g, −f) is the center and r is the radius, and the formula for the radius r is given as follows:

r = \(\sqrt{g^2 + f^2 - c\)}

Let's now write the given equation in the general form of the circle equation.

Consider the given equation.

x^2 - 2hx + h^2 + y^2 - 2ky + k^2 = r^2

Rearranging this equation, we obtain:

x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0

Compare this equation with the general equation of a circle, we have

\(2g = -2h \Rightarrow g = -h\)

\(2f = -2k \Rightarrow f = -k\)

c = h^2 + k^2 - r^2

\begin{aligned}r &=\(\sqrt{g^2 + f^2 - c} \\\) &

= \(\sqrt{(-h)^2 + (-k)^2 - (h^2 + k^2 - r^2)} \\\) &

= \(\sqrt{-2h^2 - 2k^2 + r^2}\\)end{aligned}

Therefore, the center of the circle is (h, k) = (-g, -f) = (h, k), and the radius of the circle is

r = \(\sqrt{-2h^2 - 2k^2 + r^2}\).

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Answer:

24/6= 4

4 words per minute

Step-by-step explanation:

Answer:

4 words per minute

Step-by-step explanation:

Rafael can type 24 words in 6 minutes, so we divide 24 and 6 to get 4 words per minute.

Answer:  there are 30,240 possible passwords that can be created by picking five tickets without returning them to the bag.

Step-by-step explanation: If you pick five tickets without returning them to the bag, the number of possible passwords you can create is determined by the number of choices for each position.

For the first ticket, you have 10 options (0-9).

For the second ticket, you have 9 options remaining (as you've already chosen one ticket).

For the third ticket, you have 8 options remaining.

For the fourth ticket, you have 7 options remaining.

For the fifth ticket, you have 6 options remaining.

To find the total number of possible passwords, you multiply the number of options for each position together:

Total number of possible passwords = 10 * 9 * 8 * 7 * 6 = 30,240.

Therefore, there are 30,240 possible passwords that can be created by picking five tickets without returning them to the bag.

The number of permutations for a 'password' drawn from five tickets in a set of ten numbered 0-9 (without replacing the tickets) is 30,240.

This question is about calculating the number of combinations in a given set. Here, the set is 10 tickets numbered 0-9, and you're creating a 'password' by drawing five tickets without replacement. This scenario can be solved using the concept of permutations in mathematics.

The number of possible passwords can be represented as the product of 10 (number of options for the first ticket), 9 (remaining options for the second ticket), 8 (for the third ticket), 7 (for the fourth), and 6 for the last ticket. Therefore, the number of passwords is 10*9*8*7*6 = 30,240 different possible passwords.

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Answer:

9/10

Step-by-step explanation:

answer is 9/10 i think

Answer:

.90 as a repeating fraction is .90909090

Step-by-step explanation:

hope this helps

Step-by-step explanation:

Perimeter = 5.2cm + 7.8 cm + 4cm = 17 cm

Answer:

the equation would look like x = 2x + 3

Step-by-step explanation:

Answer:

y=2x=3

Step-by-step explanation:

The values of the expressions are P 9, 3 = 504, C 9, 3 = 84, P 8, 8 = 40320 and C 9, 9 = 1

From the question, we have the following parameters that can be used in our computation:

(A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9.

The above expressions are permutation and combination expressions

Using the above as a guide, we have

Expression (A) P9, 3

Apply the permutation formula

P n, r = n!/(n - r)!r!

So, we have

P 9, 3 = 9!/6!

Evaluate

P 9, 3 = 504

Expression (B) C 9, 3

Apply the combination formula

C n, r = n!/(n - r)!r!

So, we have

C 9, 3 = 9!/(6! * 3!)

Evaluate

C 9, 3 = 84

Expression (C) P8, 8

Apply the permutation formula

P n, r = n!/(n - r)!r!

So, we have

P 8, 8 = 8!/0!

Evaluate

P 8, 8 = 40320

Expression (D) C 9, 9

Apply the combination formula

C n, r = n!/(n - r)!r!

So, we have

C 9, 9 = 9!/(9! * 0!)

Evaluate

C 9, 9 = 1

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Answer:

225/4 sqrt(3) in ^3

Step-by-step explanation:

The volume is found by

V = Bh

The B is the triangle

B = s^2 sqrt(3)/4

  = 5^2 sqrt(3)/4

  25/4  sqrt(3)

We know the height is 9

V =  25/4  sqrt(3) *9

V = 225/4 sqrt(3)

this is approximately 97.42785793 in^3

The sum of 8 of the interior angles of a regular dodecagon is equal to a total of 1200°.

A dodecagon is a 12-sided polygon. A regular dodecagon is a regular polygon with vertices evenly distributed around a circle and all sides the same length. Regular dodecagons have all of their internal angles and sides the same size. They can also be uneven, having various angles and sides of varying lengths. You will almost likely end up with an uneven dodecagon if you try to draw one freehand.

The sum of all the interior angles of a regular dodecagon is equal to:

Sum = (12-2)x180° = 1800°

Now, for the sum of 8 of the interior angles of a regular dodecagon is equal to:

⇒1800°÷12=150°

⇒150°×8=1200°

Therefore, the sum of 8 of the interior angles of a regular dodecagon is equal to a total of 1200°.

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The volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.


To find the volume of the solid, we can use the method of cylindrical shells. The region bounded by y = x^2 and y = 6 in the first quadrant is a parabolic shape above the x-axis.
To set up the integral for the volume, we consider an infinitesimally small vertical strip of thickness Δx at a distance x from the line x = -3. The height of the strip is given by the difference between the two curves: h = 6 – x^2. The circumference of the cylindrical shell is given by the formula 2πr, where r is the distance between x and the line x = -3, which is r = x + 3.

The volume of the infinitesimal shell is then given by dV = 2π(x + 3)(6 – x^2)Δx. Integrating this expression from x = 0 to x = 3, we obtain the volume V = ∫[0,3] 2π(x + 3)(6 – x^2)dx. Evaluating this integral, we find V ≈ 481.39 cubic units.
In summary, the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.

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At asymptote, pigeons make the correct choice on nearly 100% of the matching to sample trials exists true about matching to sample.

A random experiment has a result known as a sample. One particular value is chosen at random from a set of potential values when we sample a random variable. A sample is that specific value. The probability distribution of the random variable specifies the possible values and their probabilities.

An easier-to-manage portion of a larger group is referred to as a sample. A larger population's traits are contained in this subset. When populations are too big for a statistical test to include every potential participant or observation, samples are used.

Therefore, the correct answer is option a) at asymptote, pigeons make the correct choice on nearly 100% of the matching to sample trials

The complete question is:

Which is TRUE about matching to sample?

a) at asymptote, pigeons make the correct choice on nearly 100% of the matching to sample trials

b) it is a very difficult task for pigeons

c) the training procedure for organisms such as pigeons is complex and extensive

d) all of the above are true

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Answer:The correct answer is 75.6

Step-by-step explanation:

because i took the quiz myself

Sonny get 240=240 because  the cross products of the proportion are equal.

Proportion : Two ratios are said to be in proportion when the two ratios are equal.

For Example , If Smith walks 5 km in 1 hour then he will walk 25 km in 5 hours. denoted by

\(\frac{5}{1} =\frac{25}{5} \\ \\ 5=5\).

According to the given question the equation can be written as

\(\frac{16}{x} =\frac{48}{15}\)

Sonny substituted 5 for x in the proportion , the equation can be written as

\(\frac{16}{5} =\frac{48}{15} \\ \\ Doing .the .cross.product\\ \\ 16*15=48*5\\ \\ 240=240\)

Therefore , Sonny get 240=240 because  the cross products of the proportion are equal.

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"The speeds in race a are likely to be near 145 mph and the speeds in race b are likely to be near to 153 mph" correctly describes the consistency of the speeds of the cars in the two races.

Based on the given information, the box plot for race A has a larger range of speeds (from 120 to 170 mph) compared to the range of speeds in race B (from 125 to 165 mph). The box plot for race A also has a larger interquartile range (from 143 to 165 mph) compared to the interquartile range in race B (from 140 to 150 mph). However, the median speed in race A (153 mph) is lower than the median speed in race B (145 mph).

Therefore, it is not accurate to say that the speeds in race A are likely to be near 170 mph and the speeds in race B are likely to be near 165 mph. Likewise, it is not accurate to say that the speeds in race A are likely to be near 120 mph and the speeds in race B are likely to be near 125 mph.

The correct answer is that the speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near 153 mph. This is because the medians of the two box plots are relatively close to each other, and the box plot for race B has a smaller range and interquartile range, indicating greater consistency in the speeds of the cars in that race compared to race A.

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The population of the city will be approximately 408,022 after 5 years with a 3% annual growth rate.

To find the population of the city after a certain number of years with a 3% annual growth rate, we can use the formula:

P = P₀(1 + r)ⁿ

where:

P₀ = initial population

r = annual growth rate (as a decimal)

n = number of years

P = population after n years

In this case, we have:

P₀ = 350,000

r = 0.03 (since the annual growth rate is 3 percent, or 0.03 as a decimal)

n = the number of years we want to find the population for

Substituting these values into the formula, we get:

P = 350,000(1 + 0.03)ⁿ

Simplifying:

P = 350,000(1.03)ⁿ

If we want to find the population after, say, 5 years, we can substitute n = 5 into the formula:

P = 350,000(1.03)⁵

P ≈ 408,022

Therefore, the population of the city will be approximately 408,022 after 5 years with a 3% annual growth rate.

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Answer:

70°

Step-by-step explanation:

In the context it says that Franklin St. is parallel to Washington St.

The 110° formed by Franklin St. and Mulberry St. is a supplementary angle to Angle x.

Supplementary angles are angles that add up to each other to make 180°

So lets subtract:

180 - 110 = 70°

Angle x = 70°

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

60

Step-by-step explanation: