13 + 2i is (7 + 3i) + (6 − i) in standard form.
What are mathematical operations?
The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
To add two complex numbers in standard form, we simply add the real parts and the imaginary parts separately.
(7 + 3i) + (6 − i) = (7 + 6) + (3i − i) = 13 + 2i
Therefore, (7 + 3i) + (6 − i) in standard form is 13 + 2i.
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Two circles are concentric if they have the same center.
Mark draws one card from a standard deck of 52. he receives $ 0.45 for a club, $ 0.55 for an ace and $ 0.75 for the ace of clubs. how much should he pay for one draw?
Mark should pay $0.1692 for one draw.
To calculate how much Mark should pay for one draw, we need to find the expected value, which is the sum of the products of each outcome's probability and its associated value.
Calculate the probabilities:
Probability of drawing a club: [tex]\( \frac{13}{52} = \frac{1}{4} \)[/tex]
Probability of drawing an ace: [tex]\( \frac{4}{52} = \frac{1}{13} \)[/tex]
Probability of drawing the ace of clubs: [tex]\( \frac{1}{52} \)[/tex]
Calculate the expected values:
Club: [tex]\( 0.45 \times \frac{1}{4} = 0.1125 \)[/tex]
Ace: [tex]\( 0.55 \times \frac{1}{13} = 0.0423 \)[/tex]
Ace of clubs: [tex]\( 0.75 \times \frac{1}{52} = 0.0144 \)[/tex]
Sum the expected values:
[tex]\( 0.1125 + 0.0423 + 0.0144 = 0.1692 \)[/tex]
Thus, Mark should pay $0.1692 for one draw.
A local theater has floor seating, balcony seating, and box seating. if the theater contains 2,500 seats with 425 seats in the balcony and 215 box seats, how many seats are on the floor?
How much is 5lbs to kg?
1 pound = 0.453592 kg
5 x 0.453592 = 2.26796 kg
round to 2.27 kg
Kate is constructing an equilateral triangle. She has already used her straightedge to construct the line segment shown.
A line segment with endpoints labeled as A and B.
What should Kate do for her next step?
Use the straightedge to draw a line that passes through point A.
Place the point of the compass on point A and draw an arc, using AB as the width for the opening of the compass.
Use the straightedge to draw another line segment that does not intersect AB¯¯¯¯¯.
Place the point of the compass on point A and draw an arc, using a width for the opening of the compass that is less than 12AB.
The next step that Kate should take in construction of an equilateral triangle after using a straight edge to construct the given line segment is;
Option B; Place the point of the compass on point A and draw an arc, using AB as the width for the opening of the compass.
This is about steps involved in constructing an equilateral triangle which means 3 equal sides.
First step; This first step entails drawing a line with the given measurement of the side of the equilateral triangle and label it ABSecond step; This step entails placing the point of the compass at point A and opening the leg to touch point B which means length AB will be the width to be used to draw an arc.Step 3; The same process in step 2 is carried out but this time the point of the compass will be placed at point B and opening the second leg to touch point A which means length AB will be the width to be used to draw an arc to intersect the other one drawn.Step 4; The point of intersection is now joined by a straight line to points A & B respectively.Thus, option B is the correct next step.
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Which ordered pairs in the form (x, y)(x, y) are solutions to the equation
7x−5y=287x−5y=28 ?
Select each correct answer.
(4, 10)(4, 10)
(−1, −7)(−1, −7)
(7, 9)(7, 9)
(−6, −14)
Membership for the alpine rock-climbing gym costs $25 per month plus a $125 sign-up fee. Membership for Rocco’s rock-climbing gym costs $30 per month plus a $50 sign-up fee. A. After how many months will the memberships cost the same? B. If you only wanted a one-year membership, which gym would you join to pay the least amount of money?
After [tex]15[/tex] months memberships will cost the same.
What is membership ?Memberships means that you are the member of any specific group.
We have,
Cost of Membership of Alpine Rock-Climbing gym [tex]=\$25[/tex] per month
And, Cost of sign-up fee of Alpine Rock-Climbing gym [tex]=\$125[/tex]
And,
Cost of Membership of Rocco’s Rock-Climbing gym [tex]=\$30[/tex] per month
And, Cost of sign-up fee of Rocco’s Rock-Climbing gym [tex]=\$50[/tex]
Now,
Let number of months [tex]=m[/tex]
So,
According to the question;
[tex]125+25m=50+30m[/tex]
⇒ [tex]5m=75[/tex]
[tex]m=15[/tex]
So, After [tex]15[/tex] months memberships will cost the same.
B.You should join Rocco’s Rock-Climbing gym to pay the least amount of money in a year.
We have,
One year = [tex]12 months[/tex]
So,
Total cost of one year of Alpine Rock-Climbing gym [tex]=125+25m[/tex]
[tex]=125+25*12[/tex]
[tex]=\$425[/tex]
Total cost of one year of Rocco’s Rock-Climbing gym[tex]=50+30m[/tex]
[tex]=50+30*12[/tex]
[tex]=\$410[/tex]
So, Rocco’s Rock-Climbing gym is cheaper than Alpine Rock-Climbing gym.
Hence, we can say that you should join Rocco’s Rock-Climbing gym to pay the least amount of money in a year.
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A theorem is a statement that can be easily prove using a corollary
⇒A theorem is a statement that can be easily prove using a corollary
False Statement
Corollary Means , a Theorem written in another way , when it has been proved.
For Example:The Sum of Angles of Triangle is 180°.-----Theorem
Corollary→If three distinct rays intersect at three points , and sum of interior Angles formed at their point of Intersection is 180°, then it is a Triangle.
Correct Statement will be:
A theorem is a statement that can be easily proved using an Axiom or Postulate.
From a normally distributed population, a simple random sample of size 30 is taken. The mean of the sample is 144 and the standard deviation of the sample is 12.
Which interval is the 90% confidence interval for the population mean?
(139.7, 148.3)
142.4, 145.6)
143.3, 144.7)
140.4, 147.6)
The 90% confidence interval for the population mean is (140.4, 147.6), derived from a sample with a mean of 144 and a standard deviation of 12.
Let's break down the steps used to calculate the 90% confidence interval for the population mean:
- Sample mean ([tex]\bar{x}[/tex]): 144
- Sample standard deviation (s): 12
- Sample size (n): 30
- Critical value at 90% confidence (z): 1.645
The formula for the confidence interval is:
[tex]\[ (\bar{x} - z \cdot \frac{s}{\sqrt{n}}, \ \bar{x} + z \cdot \frac{s}{\sqrt{n}}) \][/tex]
Calculate the standard error (SE):
SE = s / sqrt(n)
SE = 12 / sqrt(30)
SE ≈ 2.188
Calculate the margin of error (ME):
ME = z * SE
ME = 1.645 * 2.188
ME ≈ 3.594
Calculate the lower limit (L):
L = [tex]\bar{x}[/tex] - ME
L = 144 - 3.594
L ≈ 140.406
Calculate the upper limit (U):
U = [tex]\bar{x}[/tex] + ME
U = 144 + 3.594
U ≈ 147.594
So, the 90% confidence interval for the population mean is approximately (140.406, 147.594), which rounds to (140.4, 147.6) when considering the appropriate level of precision. Therefore, the correct answer is (D) (140.4, 147.6).
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A person boards the loading station of a Ferris wheel 21 feet off the ground. The wheel is always rotating at a constant rate. He wants to ride all day. Forty minutes after the wheel opened , he is at the highest point on the wheel, 443 feet high. He is at the exact same location 28 minutes later. The question is the generate 5 points which represent elapsed time and height? X elapsed time(minutes) Y height(feet)
Rita's company reimburses her expenses on food, lodging, and conveyance during business trips. the company pays $55 a day for food and lodging and $0.45 for each mile traveled. rita drove 300 miles and was reimbursed $2,335. part
a.create an equation that will determine the number of days x on the trip part
b.solve this equation justifying each step with an algebraic property of equality. part
c.how many days did rita spend on this trip? (1 point)
Which shows the reflection of the figure over the line
Answer:
The answer appears to be A
Step-by-step explanation:If you redrew the answer backwards, the reflection would match the first one
Answer:
Step-by-step explanation:
What is 8.61×10−88.61×10−8 in decimal form? 0.000000861 0.0000000861 8,610,000 861,000,000?
multiply each equation by a number that produces opposite coefficients for x or y
1x-1y=100
3/8x + 7/8y= 2000
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}1x-1y=100&\text{multiply both sides by (-3)}\\\dfrac{3}{8}x+\dfrac{7}{8}y=2000&\text{multiply both sides by 8}\end{array}\right\\\\\left\{\begin{array}{ccc}-3x+3y=-300\\3x+7y=1600\end{array}\right\\\\\text{or}\\\\\left\{\begin{array}{ccc}1x-1y=100&\text{multiply both sides by 7}\\\dfrac{3}{8}x+\dfrac{7}{8}y=2000&\text{multiply both sides by 8}\end{array}\right\\\\\left\{\begin{array}{ccc}7x-7y=700\\3x+7y=1600\end{array}\right[/tex]
Answer:
1st option is: -3
2nd option is: 8
Step-by-step explanation: I just did the assessment on edge
help me solve this???
3p - 1 = 5(p - 1) - 2(7 - 2p)
PleAse help and show how you got it if you don’t mind
A rectangular garden measures 38m by 20m, to the nearest metre. Calculate the maximum possible area of the garden.
if 120 marks is 60% what is full marks
Can someone check this for me? Thanks.
(b) Suppose it is also known that AD ≅ CD. Which postulate or theorem can be used to prove that ΔABD ≅ ΔCBD?
I'm guessing it's the SAS congruence postulate but I'm not very good at this so I'm not sure.
What are the next two numbers in this pattern? 5, â30, 180, â1080, . . ?
Calculate the volume of the following shapes. Use the approximation of pi.
1) A sphere with a radius of 4.5 cm
2) A cylinder with a radius of 2.1 cm and a height of 8.0 cm
3) A cone with a radius of 8.0 cm and a height of 2.0 cm
Please explain your work!
Find all real and imaginary zeros for a polynomial function
A polynomial function is an algebraic expression with one or more terms. The real zeros can be found by setting the function equal to zero and solving for x. The imaginary zeros can be found using the complex conjugate theorem.
Explanation:A polynomial function is an algebraic expression that consists of one or more terms. The real zeros of a polynomial function are the values of x that make the function equal to zero. To find the real zeros, set the polynomial function equal to zero and solve for x using methods such as factoring, synthetic division, or the quadratic formula.
The imaginary zeros of a polynomial function are the values of x that make the function equal to a complex number. These can be found by using the complex conjugate theorem. If a + bi is a zero, then a - bi is also a zero, where a and b are real numbers and i is the imaginary unit, sqrt(-1).
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Four balls of wool will make 8 kintte caps.how many balls of wool will ola need if she wants to make 6 caps
A line passes through (−1,−6) and (7,2) .Find the slope-intercept form of the equation of the line. Then fill in the value of the slope, m, and the value of the y-intercept, b, below.
The equation of the line passing through the points (- 1, -6) and (7, 2) will be → y = x - 5. The slope will be [m] = 1 and the y - intercept will be -5.
What is the slope intercept form of a straight line?The slope intercept of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a straight line passing through the points (- 1, -6) and (7, 2)
We have a straight line that passes through the coordinates as follows -
(- 1, -6)
(7, 2)
The slope of the line can be calculated using the formula -
m = (y₂ - y₁)/(x₂ - x₁)
m = (2 + 6)/(8)
m = 8/8
m = 1
The line is passing through the point (7, 2). We can write -
y = mx + c
y = x + c [m = 1]
2 = 7 + c
c = 2 - 7
c = -5
The equation of the straight line will be -
y = x - 5
Now, the slope of the line will be [m] = 1 and the y - intercept will be -5.
Therefore, the equation of the line passing through the points (- 1, -6) and (7, 2) will be → y = x - 5. The slope will be [m] = 1 and the y - intercept will be -5.
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multiply each equation by a number that produces opposite coefficient for x or y 4x +5y =7
3x-2y=-12
Final answer:
To produce opposite coefficients for x and y in the given equations, we can multiply the first equation by -3 and the second equation by 4. This allows us to eliminate the x variable and solve for y. The solution to the system of equations is x = -2 and y = 3.
Explanation:
To multiply each equation by a number that produces opposite coefficients for x or y, you need to find a number that, when multiplied by the coefficient, results in a value with the opposite sign. For example, if the coefficient is positive, you need to multiply by a negative number, and if the coefficient is negative, you need to multiply by a positive number.
In the given equations, we have:
4x + 5y = 7
3x - 2y = -12
To produce opposite coefficients for x, we can multiply the first equation by -3 and the second equation by 4. This gives us:
-12x - 15y = -21
12x - 8y = -48
Now, we can add these two new equations to eliminate the x variable:
-12x - 15y + 12x - 8y = -21 + (-48)
-23y = -69
To solve for y, we divide both sides of the equation by -23:
y = -69 / -23
y = 3
Now, we can substitute this value of y back into one of the original equations (let's use the first equation) to solve for x:
4x + 5(3) = 7
4x + 15 = 7
4x = 7 - 15
4x = -8
x = -8 / 4
x = -2
Therefore, the solution to the system of equations is x = -2 and y = 3.
If only one number in a fraction is negative,does that mean the whole fraction is negative
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 +9x - 14 =0
Beliefs to the left of center emphasize the need for
A die is rolled twice. what is the probability of showing a 3 on both rolls?
In six years, Clem Kadiddlehopper will be five times as old as he was 26 years ago. How old is he now?