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All imaginary numbers can be written as complex numbers in the form a + bi.
For the number 5i, what is the value of a and b?
1) A =5 and B=1
2) A=1 and B=5
3) A= 0 and B = 5
4) a= 5 and b = 0

Answer:

$16.50

Step-by-step explanation:

Total cost: $70.40

Per CD w/ tax: $70.40 ÷ 4 = $17.60

Price of CD w/out tax: $17.60 - $1.10 = $16.50

The probability that a student chosen at random is study Spanish but not French as required is; 92 / 195.

It follows from the task content that the probability that a randomly selected student is studying Spanish but not French is to be determined.

Since there are 104 students studying Spanish; 12 of which study both Spanish and French.

Hence, the number of students studying Spanish but not French is; 104 - 12 = 92.

Ultimately, since there are 195 students in total;

The probability that the randomly selected students studies Spanish but not French is;

= 92 / 195.

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Answer: Inequality that describes the number of people P that she can invite if Janelle has No more than $95 dollars to spend on the party bags: 7P  ≤  95  

Step-by-step explanation:

Given: The cost of the party bag is $7 per person.

P represents the number of people that she can invite.

Total cost for P people = ( cost per person) x (P)

=$ 7P   (i)

If  Janelle has No more than $95 dollars to spend on the party bags.

That means , Total cost ≤ $ 95

From (i)

7P  ≤  95   , which is the required inequality.

The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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The length of one side of the box is 10 inches.

Suppose that: The side length of the considered cube is L units.

Then, we get the Volume of that cube = L³ cubic units.

The volume of a cube is of the form V =  L³, where L is the side length.

Given that the shipping box has a volume of 1,000 cubic inches.

Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:

1000 =  L³

Cube root both sides:

L = \(\sqrt[3]{1000}\)

Therefore, each side is 10 inches.

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506.433 minutes elapse before the minute hand next points in the same direction as the hour hand.

Conversion of hours to minute:

As we all know, an hour is made up of sixty minutes, therefore

1 hour=60minutes

Thus, all you need to do to convert time from hours to minutes is to multiply the time in hours by 60 to get the time in minutes.

If you want to convert minute to hours divide the given time in minutes by 60.

The hands line up 11 times every 12 hours, or roughly every 1:05.5 hours; the precise number is 1:05.4545 repeating.

The repetition time is 8:43.6363. When expressed in seconds, the result is 8:43:38.1818 repeating, or 8:43:38 and 2/11.

This is 261 and \(\frac{9}{11}\) degrees, or 261.818 repeated.

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Answer: m<A = 35

Step-by-step explanation: The sum of the measures

of the interior angles of a triangle is 180°.

So we can setup the equation 3x + 5 + 8x + 65 = 180.

Combining our numbers and variables on the left, we have 11x + 70 = 180.

Now subtract 70 from both sides to get 11x = 110.

Dividing both sides by 11, we find that x = 10.

In the diagram, the m<A is represented as 3x + 5.

Plugging a 10 in for x, we have 3(10) + 5 or 30 + 5 which is 35.

So the m<A = 35.

Answer:

(-3, -3)

Step-by-step explanation:

1.) Rewrite the second equation so 3y is on one side of the equation:

3y=6+5x

2.) Substitute the given value of 3y (replacing 3y with 6+5x, since we know they equal each other) into the equation 17x=-60-3y

Should end up with this:

17x=-60-(6+5x)

3.) Solve 17x=-60-(6+5x)

Calculate Difference: 17x=-66-5x

Combine Like Terms: 22x = -66

Divided both sides by 22 to isolate and solve for x: -3

So We know x=-3, now we got to find the y value. We can use either the first or second equation to find y value, so lets use the second.

3y=6+5x

1.) We know that x=-3, so we can simply substitute x in the equation

3y=6+5x with -3

3y=6+5(-3)

2.) Solve 3y=6+5(-3)

Combine Like Term: 3y=6+-15

Combine Like Term Even More: 3y= -9

Divide by 3 on both sides to isolate and solve for y: y=-3

So now we know y=-3 and once again we know x=-3, so if we format that

(-3,-3)

^  ^

x  y

Answer:

50°

Step-by-step explanation:

65 + 65 +C = 180

130+C = 180

C = 180 - 130 = 50

Hi there!

\(\large\boxed{C = 50^o}\)

A line contains an angle of 180°, so:

∠C = 180° - 65° - 65°

∠C = 180° - 130°

∠C = 50°

Answer: 0.0114

Step-by-step explanation:

Since we are given the information that the quality control manager samples 700 LED bulbs and finds out that 8 bulbs have defects in them.

The probability that a bulb selected at random will have a defect will be calculated as follows:

= Number of defected bulbs / Total number of bulbs sampled

= 8/700

= 0.0114

Therefore, the probability is 0.0114.

The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

Let the random variable & parameters be;

x1 : Number of successes from group 1

x2 : Number of successes from group 2

p1: Proportion of successes in group 1

p2: Proportion of successes in group 2

n1 : number of trial in group 1

n2: number of trial in group 2

We are given;

x1 = 260

n1 =985

x2 = 194

n2 = 842

Thus;

p1 = 260/985

p1 =0.2640

p2 = 194/842

p2 = 0.2304

Constructing a (1 - α)100% confidence interval for proportion from the formula;

(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]

plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;

(-0.0184631, 0.0855743)

Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

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Answer:

23/39

Step-by-step explanation:

Step 1:

12/13 + ( - 1/3 )

Step 2:

36/39 - 13/39

Answer:

23/39

Hope This Helps :)

Answer:

1503

Step-by-step explanation:

1803 - 300

The required distance between points B and A is 5 / 10.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Location of the point A = -7 / 10

Location of the point b = -2 /10

The distance between the point = location of point B - Location of point A
                                                        = -2/10 - (-7/10)
                                                        = -2/10 + 7 / 10
                                                        = 5 / 10

Thus, the required distance between points B and A is 5 / 10.

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Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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The unit rate for the given case is 8 shirts per hour.

The ratio of two numbers a and b can be written as a : b = a/b. The ratio of two quantities is the unit rate of one quantity with respect to the other.

The total number of shirts are 32.

And, the time for sale is 4 hours.

Now, the unit rate can be calculated by taking the ratio of shirts and time as below,

Unit rate = Number of shirts ÷ Time

⇒ 32 ÷ 4 = 8

Hence, the unit rate of the sale is 8 shirts per hour.

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Answer: X = 121

Step-by-step explanation:

Because 180 degrees is a flat line, you subtract 59 from 180 to get the remaining angle values

Answer:

Use Simple Interest Formula=PrT/100

SI=$1800×5×6/12÷100

=4500/100

=$45

Step-by-step explanation:

$45 is the interest that's gonna be owed after 6months so therefore the total $ she owed after 6 months would be: $45 + $1,800=$1,845.

Answer:

m = -18

Step-by-step explanation:

6 + m/2 = -3

Subtract 6 from each side

6 + m/2 -6 = -3-6

m/2 = -9

Multiply each side by 2

m/2 * 2 = -9*2

m = -18

\(\huge\text{Hey there!}\)

\(\huge\boxed{\mathsf{6+ \dfrac{m}{2}=-3}}}\\\huge\boxed{\rightarrow\mathsf{6 + \dfrac{1}{2}m = -3}}\)

\(\huge\boxed{\rightarrow \mathsf{\dfrac{1}{2}m+ 6 = -3}}\\\\\huge\boxed{\text{SUBTRACT 6 to BOTH SIDES}}\\\huge\boxed{\mathsf{\dfrac{1}{2}m + 6 - 6 = -3 + 3}}\)

\(\huge\boxed{\mathsf{\dfrac{1}{2}m = -9}}\)

\(\huge\boxed{\text{MULTIPLY 2 to BOTH SIDES}}\)

\(\huge\boxed{\mathsf{\dfrac{1}{2}m \times 2 = 2 \times -9}}\)

\(\huge\boxed{\mathsf{m = 2\times-9}}\\\huge\boxed{\mathsf{2\times-9 = m}}\\\huge\boxed{\mathsf{2\times-9 = \bf -18}}\\\\\huge\boxed{\textsf{Therefore, your answer: \bf -18}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\huge\boxed{\frak{Amphitrite1040:)}}\)

Since both conditions are satisfied, we can conclude that the series converges by the Alternating Series Test.

The given series is: `∑(n=1 to infinity) ((-1)^(n+1) / n^2(n^3 + 8))`.

To test for convergence or divergence, let us use the alternating series test.

The alternating series test states that if the alternating series `∑(-1)^(n-1) * b_n` satisfies the following conditions:the terms `b_n` are positive and decreasing as n increases,and `b_n` approaches zero as n approaches infinity,then the series converges.

It is to be noted that the series converges slowly if `b_n` approaches zero very slowly or if the terms are initially quite large.

To apply the alternating series test to the given series, we must first determine if `b_n` is positive, decreasing, and approaches zero as n approaches infinity.

In this case, `b_n = 1/(n^2(n^3 + 8))`.

Clearly, `b_n` is positive since the denominator is always positive.

Moreover, `b_n` is decreasing since increasing n will make both the numerator and denominator larger.

Finally, `b_n` approaches zero as n approaches infinity since the denominator grows much faster than the numerator. Therefore, the alternating series test applies to the given series.Hence, the given series is convergent.

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To derive a formula for P(A ∪ B ∪ C), we can use the inclusion-exclusion principle, which states that:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

We know P(A), P(B), P(A ∪ B), and P(C), but we need to find P(A ∩ B), P(A ∩ C), P(B ∩ C), and P(A ∩ B ∩ C).

We can use the following formulas to find these probabilities:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

P(A ∩ C) = P(A) + P(C) - P(A ∪ C)

P(B ∩ C) = P(B) + P(C) - P(B ∪ C)

P(A ∩ B ∩ C) = P(A) + P(B) + P(C) - P(A ∪ B) - P(A ∪ C) - P(B ∪ C) + P(A ∪ B ∪ C)

Substituting these formulas in the inclusion-exclusion principle, we get:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A) - P(B) - P(A ∪ B) - P(A) - P(C) + P(A ∪ C) - P(B) - P(C) + P(B ∪ C) + P(A) + P(B) + P(C)  - P(A ∪ B) - P(A ∪ C) - P(B ∪ C) + P(A ∪ B ∪ C)

Simplifying this expression, we get:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∪ B) - P(A ∪ C) - P(B ∪ C) + P(A ∩ B ∩ C)

Therefore, the formula for P(A ∪ B ∪ C) is:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∪ B) - P(A ∪ C) - P(B ∪ C) + P(A ∩ B ∩ C)

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Answer:

630 cubic inches of 630 in³

Step-by-step explanation:

The formula for the volume of a triangular prism = (Area of the base) × Height of the triangular prism

Area of the base = 1/2 × base × height

= 1/2 × 5 inches × 12 inches

= 30 square inches

Volume of the Triangular prism = Area of the base × Height of the Triangular Prism =

Height of the triangular prism = 21 inches

Volume of the Triangular Prism = 30 Square inches × 21 inches

= 630 cubic inches of 630 in³

The equation of the circle will be -

(x - 4)² + (y - 13)² = 64

The general equation of a circle with (h, k) representing the circle's center, and {r} represents the length of its radius is

(x – h)² + (y – k)² = r²

We can write the equation of the circle as -

(x – h)² + (y – k)² = r²

(x - 4)² + (y - 13)² = r²

(x - 4)² + (y - 13)² = r²

(x - 4)² + (y - 13)² = r²

Also -

2πr = 16π

r = 8

So. the equation of the circle will be -

(x - 4)² + (y - 13)² = 64

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Answer:

184

Step-by-step explanation:

SA = 2LW + 2LH + 2WH

SA = 2(5 × 4) + 2(5 × 8) + 2(4 × 8)

SA = 2(20) + 2(40) + 2(32)

SA = 40 + 80 + 64

SA = 184

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YW

Answer:

If the distribution is symmetric then the mean can be used to find the center. When it is skewed right or left with high or low outliers then the median is better to use to find the center. The best measure of spread when the median is the center is the IQR.

Step-by-step explanation:

Hope this helps :)