(-55 +94i) + (13 – 12i) =

Express your answer in the form (a + bi).

Answer:

8

Step-by-step explanation:

Combine like terms, -4 and 8, 2x and 3x.

After combining the terms, you get x+4=12.

Subtract 4 from both sides and get x=8

Answer:

D

Step-by-step explanation:

It's D because 60 +70 +(180-130)=180

= 60+70+50=180

To find the sum and carry for this function on a truth table, we must first complete the truth table by computing the function's values for all possible inputs.

The given function is\(Q = (X*2) + (Y/2) + Z\)

Here's the truth table:X Y Z Q0 0 0 00 0 1 10 1 0 20 1 1 31 0 0.5 1.51 0 1 21 1 0.5 3.5 1 1 3

From the truth table above, we can see that the sum of Q for all eight input combinations is 12.

To find the carry, we will need to determine the maximum output value for the given function.

We can observe that the highest output value is 3.5.

Therefore, there is no carry for this function since the highest output value is less than four.

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a). We have proved all the given conditions.

b). It is true that condition 3 holds for all regular languages L1 and L2.

(a) Regular languages L1 and L2 can be suggested as follows:

Let \(L_1={0^{(n+1)} | n\geq 0}\)

and

\(L_2={1^{(n+1)} | n\geq 0}\)

We have to prove three conditions:1. L1 ⊈ L2:

The given languages L1 and L2 both are regular but L1 does not contain any string that starts with 1.

Therefore, L1 and L2 are distinct.2. L2  L1:

The given languages L1 and L2 both are regular but L2 does not contain any string that starts with 0.

Therefore, L2 and L1 are distinct.3. (L1 ∪ L2)* = L1* ∪ L2*:

For proving this condition, we need to prove two things:

First, we need to prove that (L1 ∪ L2)* ⊆ L1* ∪ L2*.

It is clear that every string in L1* or L2* belongs to (L1 ∪ L2)*.

Thus, we have L1* ⊆ (L1 ∪ L2)* and L2* ⊆ (L1 ∪ L2)*.

Therefore, L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Second, we need to prove that L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Every string that belongs to L1* or L2* also belongs to (L1 ∪ L2)*.

Thus, we have L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Therefore, (L1 ∪ L2)* = L1* ∪ L2*.

Therefore, we have proved all the given conditions.

(b)It is true that condition 3 holds for all regular languages L1 and L2.

This can be proved by using the fact that the union of regular languages is also a regular language and the Kleene star of a regular language is also a regular language.

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The no. of ways in which the doctor visits her patients during morning rounds = 5!

That means we can only find the number of ways if we n+1 factorial the number of rounds. In this case, the factorial is 1x2x3x4x5= 120

The product of all positive integers less than or equal to n in mathematics is known as the factorial of a non-negative integer, indicated by the symbol n! Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1.

In addition to highlighting the connections between variables, it also enables the isolation and individual analysis of the impacts of changing a single variable. The primary drawback is how challenging it is to explore with more than two parameters or several levels.

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Answer:

Step-by-step explanation:

45

When the determinant of matrix B is also 2.

When a scalar multiple of a row is multiplied by a matrix, the determinant of the resulting matrix is also multiplied by that scalar.

Given that the determinant of matrix A is det(A) = 2, and matrix B is obtained from A by multiplying the third row by 4, we can determine the determinant of B.

Let's denote the original matrix A as A₀ and the modified matrix B as B.

Multiplying the third row of A₀ by 4 yields matrix B. However, this operation does not affect the determinant of A₀, so det(B) = det(A₀).

Therefore, det(B) = det(A₀) = 2.

Hence, the determinant of matrix B is also 2.

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Answer:

y = 9/13

Step-by-step explanation:

x = -4 + y

5(-4 + y) + 4y = 7

-20 + 9y = 7

9y = -13

Answer:

5x + 4y = 7 × -2

-2x - 2y = 8 × 5

-10x - 8y = -14

-10x - 10y = 40

Step-by-step explanation:

2y = -54 ÷2

y = -27

Now substitute the value of y into equation (1)

5x + 4y = 7

5x + 4(-27) = 7

5x = 7 + 108

5x = 115

X = 23

Answer:

25

Step-by-step explanation:

you would root 125 by 3 and then square (because of the 2) to get 25

125^2/3

125=5x5x5

125=5^3

125^2/3=5^3(2/3)

And 5^3(2/3) is 25

Answer:

$35

Step-by-step explanation:

take $250- $75. That tells you how much you need to still make. which is $175. now you need to figure out per month for the next 5 months. Divide 175 by 5 = 35

$35 per month you will need to save.

The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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Divide total distance by total liters used.

448 km / 112 liters = 4 km per liter.

Using 1 liter of gas the boat can travel 4 km.

Answer:

1 litre = 4 km

Step-by-step explanation:

448/112 = 4/1

Cross multiplication, 448 x 1 divided by 112 = 4

When the full moon is at position 3, positions 9 and 12 experience low tide.

The correct option is 9 and 12.

The positions of the moon and the sun have an impact on the tides of the Earth's oceans.

What is a tide?

Tides are the regular rise and fall of the sea level due to the gravitational influence of the Moon and the Sun on the Earth. The gravitational pull of the Moon on the Earth produces two tidal bulges, one on the side of the Earth facing the Moon and one on the side opposite the Moon. The Moon's gravitational pull causes high tides in the area of the bulge and low tides elsewhere on the Earth. The tides are affected by the location of the Sun and the Moon as they orbit the Earth.

In order to determine which two positions experience low tide, the Moon's position must be considered.

When the Moon is directly overhead or opposite to the Earth, its gravitational pull has the greatest effect, causing the greatest difference between high and low tides, also known as spring tides.

When the Moon is at a 90-degree angle to the Earth, its gravitational pull is less, causing a smaller difference between high and low tides, also known as neap tides.

In the given case, when the full moon is at position 3, positions 9 and 12 experience low tide.

Thus, the correct option is 9 and 12.

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The substitution method works by solving one of the equations for one of the variables (you choose the equation and the variable) and then plugging this back into the other equation, substituying for the chosen variable and solving for the other.

For instance, lets solve problem 10. We have the following system:

We can see that the "easiest" way to solve them is by substituting the value of y given in the second equation into the first one. It gives

because y=-3x. Now, we must move -3x to the left hand side as +3x. It yields,

since 6x+3x=9x, we have

Now, if we move -9 to the left hand side as +9, we obtain

then, x=1. Until now, we solved for x. Now. we must subsitute this value into the second equation. It yields,

which gives y=-3. Finally, the answer is x=1 and y=-3.

We can check that this is the correct solution by substituting these values into both equations:

Now, in the second one, we have

Then our answer is corrrect!

Answer:

Total paper required = 165 cm²

Step-by-step explanation:

Paper required to cover the entire block = (Surface area of the prism at the base - area of the top of the prism) + Lateral surface area of the pyramid

Surface area of the rectangular prism = 2(lb + bh + hl)

(here l, b, h are the length, width and height respectively)

                                                               = 2(5×5 + 5×4 + 4×5)

                                                               = 2(25 + 20 + 20)

                                                               = 2×65

                                                               = 130 cm²

Area of the top of the prism = (side)²

                                              = 5²

                                              = 25 cm²

Lateral area of the square pyramid = 4 × Area of one lateral side

                                                          = 4 × \([\frac{1}{2}(\text{Base})(\text{Height})]\)

                                                          = 4 × \([\frac{1}{2}(5)(6)]\)

                                                          = 60 cm²

Total paper required = (130 - 25) + 60

                                   = 105 + 60

                                   = 165 cm²

Answer: Angle BEC is also 45 degrees.

Step-by-step explanation: This is because the opposite and congruent angle of BEC is 45 degrees. Congruent means the same. Therefore, Angle BEC is 45 degrees.

The multiplication chart shows the square numbers located diagonally. If you needed to find the next square number, 11 x 11 problem i solved.

A table that displays the result of two numbers is known as a multiplication chart. The left column typically has one set of numbers, and the top row typically contains another set of numbers. Calculation time and effort are greatly reduced when using a multiplication chart.

A grid including all the times tables is plainly displayed on a multiplication chart. It's a useful tool for remembering multiplication facts. You can memorize it with the aid of this.

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d) Rolling an even number that is less than 2 is not a valid outcome when rolling a die.therefore, option d) is correct.

The outcome that is not possible is (d) rolling an even number that is less than 2 on a die.

A standard die has six sides numbered from 1 to 6, and all the even numbers on a standard die are 2, 4, and 6.

The statement "rolling an even number that is less than 2" contradicts the fact that the lowest even number on a die is 2.

Thus, it is not possible to roll an even number that is less than 2 on a standard die, making it an invalid outcome.

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4.0 mL of marcaine will be needed to draw up to equal the 1%.

Marcaine is a brand name for the medication bupivacaine, which is a local anesthetic used to numb a specific area of the body during a surgical or medical procedure.

To determine the amount of marcaine that is needed to be drawn up to equal the 1% lidocaine, we can use the following formula:

(Concentration of Lidocaine) / (Concentration of Marcaine) = (Volume of Lidocaine) / (Volume of Marcaine)

In this case, we know that the concentration of lidocaine is 1% and the concentration of marcaine is 0.25%. So we can plug these values into the formula:

1 / 0.25 = (Volume of Lidocaine) / (Volume of Marcaine)

To solve for the volume of marcaine, we can multiply both sides of the equation by the volume of lidocaine:

(Volume of Lidocaine) / (Volume of Marcaine) = 4

Therefore, 4.0 mL of marcaine will be needed to draw up to equal the 1%.

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where

p = principal

r = rate

t = time

Principal is the amount of money invested for a period of t years with an interest rate r

Answer:

6.93768377668

Step-by-step explanation:

confusion

Answer:

The answer to that is A ...

1.The universal set is defined as {Sarah, Allen, Kara, Todd, Joseph, Lydia, Matt, Caleb, Britney, Ethan}.

2.Caleb and Britney are included in both subsets since they like both football and basketball.

1. The universal set (U) consists of all the students in Mrs. Austin's class. In this case, U = {Sarah, Allen, Kara, Todd, Joseph, Lydia, Matt, Caleb, Britney, Ethan}.

2. The two subsets are:
 a) The set of students who like football (F) = {Sarah, Allen, Kara, Todd, Caleb, Britney}
 b) The set of students who like basketball (B) = {Joseph, Lydia, Matt, Caleb, Britney}

Caleb and Britney are included in both subsets since they like both football and basketball.

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

95 times

Step-by-step explanation:

Probability of rolling a 5 =1/6

So no. of times 5 is expected when the number cube is rolled out 570 times = 570*1/6 = 95 times

1)First determine the probability of rolling a 5

2)Since you can only roll a 5 once in a 6-sided cube the probability is ⅙ or about 0.1667

3)Multiply the probability and the total number of rolls

.1667 * 570= 95

Answer : 95 times

Answer:

Step-by-step explanation:

4 x 10 = 40

2 x 5 = 10

4 x 3 = 12

total area = 62cm^2

The area of the figure is 62 square centimeters.

To find the area of the figure, we need to calculate the sum of the areas of the three rectangles.

The dimensions of each rectangle:

1st rectangle: Length (l) = 4 cm, Breadth (b) = 10 cm

2nd rectangle: Length (l) = 5 cm, Breadth (b) = 2 cm

3rd rectangle: Length (l) = 4 cm, Breadth (b) = 3 cm

The formula to calculate the area of a rectangle is:

Area = Length * Breadth

Calculating the area of each rectangle:

1st rectangle: Area = 4 cm * 10 cm = 40 cm²

2nd rectangle: Area = 5 cm * 2 cm = 10 cm²

3rd rectangle: Area = 4 cm * 3 cm = 12 cm²

Now, we add up the areas of all three rectangles to find the total area of the figure:

Total area = 40 cm² + 10 cm² + 12 cm² = 62 cm²

Therefore, the area of the figure is 62 square centimeters.

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Answer:

3n + 2

Step-by-step explanation:

\(−n+(−4)−(−4n)+6\)

Open the parentheses

\( - n - 4 + 4n + 6 \\ \)

Add similar elements

\( - n + 4n - 4 + 6 \\ 3n + 2 \\ \)

Answer:

\( - n + 6\)

Step-by-step explanation:

\( - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6\)

The expression of the confidence interval $64.4 \% < p < 82.4 \%$ in the frequency distribution  form of ˆ$p±ME$ is given below.

.The data have a mean (M) of 1150 and a standard deviation (SD) of 150, which correspond to a normal distribution.

The midpoint is given by, ˆ$p=\frac{64.4+82.4}{2}=73.4\%$.Now, subtracting the lower limit from the midpoint gives,$73.4\%-64.4\%=9.0\%$Similarly, subtracting the midpoint from the upper limit gives, $82.4\% -73.4\% =9.0\%$ Therefore, the margin of error is given by $ME=9.0\%$Hence, the confidence interval in the form of ˆ$p±ME$ is $\boxed{73.4\%±9.0\%}$.

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