22i + 13 - (7i + 3+ 12i) + 16i - 25
Answers
22i - 7i - 12i + 16i + 13 - 3 - 25
19i - 15 (Answer)
Answer:
-15 + 19i
Step-by-step explanation:
For this equation, it is just a matter of simplifying.
So, first, distribute the - (negative) to the numbers in the parenthesis.
22i + 13 -7i - 3 - 12i + 16i - 25
Now simplify all like terms and write in standard form (a + bi).
-15 + 19i
This is your answer.
Related Questions
The names of the automobile manufacturer of the car that you drive is what type of variables ( scales of measurement)
Answers
The type of variable that represents the names of the automobile manufacturers would be the categorical variable.
What are variables in research work?A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.
There are various types of variables that include the following:
categorical variables.Nominal variables. Ordinal variables. Numeric variables. Continuous variables. Discrete variables.Learn more about variables here:
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Stephen and Lauren bought a home to flip
for a profit. After budgeting a total of
$23,150 for improvements, they started by
spending $10,350 on subbing out some of
the work. They would like to replace all
thirty-two of the windows in the home.
What is the maxium amount they can
afford to spend on each window?
Answers
Answer:
400 dollars
Step-by-step explanation:
A machine produce 98 parts in 1 hour how many it produce in 72 hours
Answers
98 times 72 = 7,056
Answer:
Hope this helps
Step-by-step explanation:
the answer would be 7056
98*72=7056
Brainliest is appreciated
Ruby has saved $4072.24 towards her retirement by the time she is 26 years old. She initially invested $2500 in an account that earned interest compounded annually. If Ruby made the investment on her sixteenth birthday at what rate has the account been earning interest?
Answers
At 5% rate the account been earning interest.
Given that Ruby has saved $4072.24, and she initially invested $2500, we can plug in these values into the formula:
4072.24 = 2500(1 + r/1\()^{(1 )(10)\)
Simplifying the equation, we get:
(1 + r)¹⁰ = 4072.24/2500
Taking the 10th root of both sides, we have:
1 + r = (4072.24/2500\()^{(1/10)\)
Subtracting 1 from both sides, we find:
r = (4072.24/2500\()^{(1/10)\)- 1
r = 1.05000008852 - 1
r = 0.05000008852
r = 5%
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Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of a bluefish is 284 mm (millimeters) with a standard deviation of 39 mm. For pompano, the mean is 123 mm with a standard deviation of 34 mm. Stewart caught a bluefish that was 322 mm long, and Gina caught a pompano that was 176 mm long. Who caught the longer fish, relative to fish of the same species
Answers
This comparison is based on the standard deviations and mean lengths provided for each species. Other factors such as the variability of fish lengths within each species and the specific size distribution of fish in the area may also influence the comparison.
To determine who caught the longer fish relative to fish of the same species, we need to compare the lengths of the individual fish to the mean lengths of their respective species.
For Stewart's bluefish, the mean length of a bluefish is given as 284 mm with a standard deviation of 39 mm. Stewart's bluefish measured 322 mm in length. To assess whether Stewart's bluefish is longer than average for bluefish, we can calculate its z-score using the formula:
z = (x - μ) / σ
where x is the measured length of the fish, μ is the mean length of the species, and σ is the standard deviation.
For Stewart's bluefish:
z = (322 - 284) / 39 ≈ 0.974
A z-score of 0.974 indicates that Stewart's bluefish is approximately 0.974 standard deviations above the mean length for bluefish.
Similarly, for Gina's pompano, the mean length of a pompano is given as 123 mm with a standard deviation of 34 mm. Gina's pompano measured 176 mm in length. We can calculate the z-score for Gina's pompano:
z = (176 - 123) / 34 ≈ 1.559
A z-score of 1.559 indicates that Gina's pompano is approximately 1.559 standard deviations above the mean length for pompano.
Comparing the z-scores, we can conclude that Gina's pompano (with a z-score of 1.559) is longer relative to fish of the same species than Stewart's bluefish (with a z-score of 0.974). Therefore, Gina caught the longer fish relative to fish of the same species.
It's important to note that this comparison is based on the standard deviations and mean lengths provided for each species. Other factors such as the variability of fish lengths within each species and the specific size distribution of fish in the area may also influence the comparison.
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Help please i need it thanks.
Answers
Answer:
x is less than or equal to 7
Step-by-step explanation:
pls help, it is due now. Thank You so much to whoever helps!
Answers
Answer:
(7, -1)
Step-by-step explanation:
3x + 7y = 14
y = x - 8
3x + 7(x - 8) = 14
3x + 7x - 56 = 14
10x - 56 = 14
Add 56 to both sides.
10x = 70
Divide both sides by 10.
x = 7
3(7) + 7y = 14
21 + 7y = 14
Subtract 21 from both sides.
7y = -7
Divide both sides by 7.
y = -1
(7, -1)
which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
Answers
Answer:
it's b :)
Step-by-step explanation:
negate the following statements.
Answers
The earth is not the center of the solar system
Angle A and angle B are not congruent
The money you gave me was not enough
She is enjoying her time
I did bring the key
I hope this helps.
Help explain how to solve
Answers
The value of the angle U in the triangle is 92.10 degrees.
How to find the angle in a triangle?The angle U in the triangle can be found using cosine rule as follows:
Let's use cosine formula to find the angle U
c² = a² + b² - 2ab cos C
Hence,
Therefore,
a = 58.8
b = 38.4
c = 71.4
Hence,
71.4² = 58.8² + 38.4² - 2(58.8)(38.4) cos U
5097.96 = 3457.44 + 1474.56 - 4515.84 cos U
5097.96 - 4932 = - 4515.84 cos U
165.96 = - 4515.84 cos U
divide both sides by - 4515.84
cos U = 165.96 / - 4515.84
cos U = - 0.03675063775
U = cos⁻¹ - 0.03675063775
U = 92.1032274244
Therefore,
U = 92.10 degrees
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there are 10 marbels in a bag, 4 are multi colored and 6 are solid. what is the probability of picking a solid marble and then another solid marble without replacing the first marble?
Answers
Answer:
(2/5) * (3/4) = 3/10 = 0.3
simplify this 2x - 1 = 8
Answers
Answer is below. Look at the steps to clearly understand my answer.
Now, the first time to simplifying this to add both sides by 1.
2x - 1 = 8 → 2x - 1 + 1 = 8 + 1
Since we added both sides, we'll now simplify the problem.
Add both numbers.
2x - 1 + 1 = 2x8 + 1 = 92x = 9Lastly, we'll divide both sides of the equation by the same term.
2x = 9\(\frac{2x}{2} =\frac{9}{2}\)Now, cancel both terms that are in both the numerator and denominator.
If you look back at the fraction, 2 is in the numerator and denominator, so we'll cancel those terms.
When you cancelled the terms, you should get x = 9/2.
Any questions? Comment below.
Answer:
Hi, there the answer is \(x=\frac{9}{2}\)
Step-by-step explanation:
Step 1: Add 1 to both sides.
2x−1+1=8+1
2x=9
Step 2: Divide both sides by 2.
2x /2 = 9 /2
x= 9 /2
Hope This Helps :)
Which word is associated with multiplication when computing probabilities? Choose the correct answer below Disjoint O And O Not
Answers
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .
According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.
The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.
Therefore,
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
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What is the number of sides in a regular polygon when the measure of each interior angle is 162?
Answers
Answer:
20
Step-by-step explanation:
interior angle + exterior angle = 180°
162° + exterior angle = 180° ( subtract 162° from both sides )
exterior angle = 18°
the sum of the exterior angles of a polygon = 360° , then
number of sides = 360° ÷ 18° = 20
Read the questions and choose the best answer.
Answers
How can you determine the equation of a line in y =mx + b form from its graph?
Answers
Answer:
I'm gonna go a little out of order.
To determine b, find where the line crosses the y-axis. If it's positive, put it as " + " and if it's negative, put it as " - ".
To determine m, find two points on the line that are directly on the number. Example, choose (4, 1) instead of (4.1, 5.2). Go up/down and left/right (while making sure to count) until you reach the second number. going up and right will be considered positive while down and left are considered negative.
Using rise/run, put your number for up/down as a numerator over your left/right, which will be a denominator.
Insert m and b and you're good to go!
Which statement correctly compares the function on this graph with the function y=2x-5?
Answers
The statement that correctly compares the function of the given graph with the function y = 2x - 5 is; Option C: The function shown on the graph has a greater rate of change and a higher starting point.
What is the rate of change of the function?The rate of change of function is defined as the change in the value of the function with respect to x value.
Rate of change of function f(x) is;
f'(x) = df(x)/dx
The given function is; y = 2x - 5
Thus;
Rate of change of function = f'(x) = df(x)/dx = dy/dx = d(2x - 5)/dx = 2
The starting point of the function f is the y-intercept of the function.
The y-intercept of the function is the point where the function touches the y-axis which can be calculated by putting x value is equals to 0.
Thus; y = 2*0 - 5
y= -5
The starting point of function is -5.
Slope = (y intercept)/(x - intercept)
Slope = 4/1 =4
Thus, the rate of change of the graph = slope of the graph= 4
The y-intercept of the graph is equal to the starting point of the graph which is -5
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Someone please help hurry I need to turn this in
Answers
Answer:
option a is right cz both have same value itz 1/root 2 hope it may help u
The diameter of a table tennis ball is 20 millimeters.
What is the approximate area of the table tennis ball?
Answers
Answer:
2512
Step-by-step explanation:
The surface area of the table tennis ball will be around 1256.64 mm².
What is the sphere?A sphere is a 3D geometrical object which has a radius and becomes a point that revolves around a fixed point called the center.
A sphere has surface area and volume based upon the radius of the sphere.
For example, if you have a sphere of radius r then its surface area will be 4πr² and volume will be (4/3)πr³.
The table tennis ball is the form of a sphere.
Given that,
The diameter of a table tennis ball is 20
Radius(r) = 20/2 = 10 mm
Surface area of an sphere = 4πr²
So,
Area = 4π(10)² = 1256.64 mm².
Hence "The surface area of the table tennis ball will be around 1256.64 mm²".
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What is the slope for the function with the greater slope? Mark all that apply
Answers
On a piece of paper, graph this system of equations. y=x-2. y= x2 - 6x + 8
Then determine which answer choice matches the graph you drew and identify the solutions to the system.
A. Solutions: (2,0) and (5, 3)
B. Solutions: (2,0) and (4,2)
C.Solutions: (-2,0) and (2,0)
D.Solutions: (2,0) and (3,-1)
Answers
The correct answer for the equation is: solutions (2,0) and (5,3).
According to the question, the expression can be simplified by substituting the values in the expression:
Therefore the required expression can be written as:
(x = 2; y = 0) and (x = 5; y = 3)
\(y = x-2 = 2-2 =0\)
\(y = x-2 = 5-2 =3\)
Both the solutions satisfied the given expression.
(x = 2; y = 0) and (x = 5; y = 3)
\(y=x^{2} -6x+ 8 = 4 -12+8=0\)
\(y=x^{2} -6x+ 8 = 25 -30+8=3\)
Both the solutions satisfied the given expression.
Hence, the correct answer for the equation is: solutions (2,0) and (5,3).
What is simplification?
The word simplification is the procedure in which complicated expression can be written in a simpler form to make the calculation easy. This method is used to calculated the answers for the unknown quantity.
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Each side of an equilateral triangle measures 30cm. Find the length of an altitude, a , of the triangle?
Answers
Answer:
\(X=25.98cm\)
Step-by-step explanation:
From the question we are told that:
Length of each side \(l=30cm\)
Let the triangle be divide by two form a right angle triangle with base angles as \(90 \textdegree\)(angle of perpendicularity) and \(60 \textdegree\) (angle on each vertices of an equilateral triangle)
Generally the equation for the Altitude X is mathematically given by
Trigonometric Rule
\(X=30sin60\)
\(X=15\sqrt{3}\)
\(X=25.98cm\)
Find the Maclaurin series of the function: (4x^2)*e^(-5x) and its coefficients C0 toC4
Answers
Answer:
C0 = 1, C1 = -20x^2, C2 = 100x^4, C3 = -666.67x^6, C4 = 6666.67x^8.
Step-by-step explanation:
We can use the Maclaurin series formula for the exponential function and then multiply the resulting series by 4x^2 to obtain the series for (4x^2)*e^(-5x):e^(-5x) = ∑(n=0 to ∞) (-5x)^n / n!
Multiplying by 4x^2, we get:
(4x^2)*e^(-5x) = ∑(n=0 to ∞) (-20x^(n+2)) / n!
To get the coefficients C0 to C4, we substitute n = 0 to 4 into the above series and simplify:
C0 = (-20x^2)^0 / 0! = 1
C1 = (-20x^2)^1 / 1! = -20x^2
C2 = (-20x^2)^2 / 2! = 200x^4 / 2 = 100x^4
C3 = (-20x^2)^3 / 3! = -4000x^6 / 6 = -666.67x^6
C4 = (-20x^2)^4 / 4! = 160000x^8 / 24 = 6666.67x^8
Therefore, the Maclaurin series for (4x^2)*e^(-5x) and its coefficients C0 to C4 are:
(4x^2)*e^(-5x) = 1 - 20x^2 + 100x^4 - 666.67x^6 + 6666.67x^8 + O(x^9)
C0 = 1, C1 = -20x^2, C2 = 100x^4, C3 = -666.67x^6, C4 = 6666.67x^8.
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You are heading to a picnic with a cooler filled with 10 small juice boxes (5 red, 3 purple, 2 green) and 5 large juice boxes (3 red, 1 purple, and 1 green). You mix the contents of the cooler well so there is no pattern by color or size. Note For all the problems in this assignment you must enter your answers as a fraction or a sum or a product of fractions. For example, if your answer is 4/15 + 6/15, leave it in that form or you could write it as 10/15 or 2/3 but don't write it as a decimal. Use to indicate multiplication and to indicate raising a number to a certain power. (eg. (4/15)^2 means 4/15*4/15) 1. Suppose you randomly selected one juice box from the cooler. What is the chance that the juice box is either red or green?
Answers
The probability of selecting a juice box that is either red or green is 7/15 or about 0.47.
There are a total of 15 juice boxes in the cooler, 5 of which are red and 2 of which are green. Therefore, the probability of selecting a red juice box is 5/15, or 1/3, and the probability of selecting a green juice box is 2/15.
To find the probability of selecting either a red or a green juice box, we can add the individual probabilities of selecting a red juice box and a green juice box.
P(selecting a red or a green juice box) = P(selecting a red juice box) + P(selecting a green juice box)
= 5/15 + 2/15
= 7/15
This means that out of every 15 juice boxes selected at random, approximately 7 will be either red or green.
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!!PLEASE HELPP!! (check if I’m right pls)
Answers
Answer: It's correct
Step-by-step explanation:
These cones are similar find the volume of the smaller cone round to the nearest 10th 2 is the radius
Answers
Answer:
4.2 units^3
Step-by-step explanation:
Volume of a cone 1/3(nr^2h)
n = 22/7
r = radius
h = height
1/3 x (22/7) x (2^2) = 4.2
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
The Earth is 1.496 × 108 km from the Sun. Express this number in standard form.
Answers
Answer:
161.568
Step-by-step explanation:
use a calculator just multiply
Answer:
Step-by-step explanation:
the standard form is
1.496 × 10^8=149,600,000 km
help me pls asap!!!!!
Answers
The 9 pack, 1 pack = 0.52
The 4 pack is better because it's cheaper
Find the missing value. Hint: Use the number line to find the missing value. − 7 = −7=minus, 7, equals − ( − 2 ) −(−2)minus, left parenthesis, minus, 2, right parenthesis
Answers
Answer:
The missing value is -9
Step-by-step explanation:
Given
\(-7 = _ -(-2)\)
Required
Determine the missing value
Represent _ with a variable
\(-7 = x -(-2)\)
Open the bracket
\(-7 = x -1*-2\)
\(-7 = x + 2\)
Subtract 2 from both sides
\(-7 - 2 = x + 2 - 2\)
\(-9 = x\)
Reorder
\(x = -9\)
Hence, the missing value is -9
Answer:
The answer is 4=−2+6
Step-by-step explanation:
I checked on khan
Out of the 60 students on a school trip, 70 percent brought there lunch, and the rest brought money to buy lunch. How many students were buying lunch
Answers
Answer:
18 were buying lunch:)
Answer: 42/This should be the right answer since 42 should be 70 percent of 60.