Answer:
14+22i
Step-by-step explanation:
We multiply and simplify (3-5i)(-2+4i) to get:
14 + 22i
How to multiply and simplify (3-5i)(-2+4i)?A complex number is a number of the form a + bi, where a and b are real numbers, and i is an imaginary unit satisfying i² = -1. For example, 2 + 3i is a complex number.
Complex numbers can be multiplied using the following rules:
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
Thus, the two complex numbers can be multiplied and simplified as follow:
(3-5i)(-2+4i) = 3(-2+4i) -5i(-2+4i)
= 3(-2) + 3(4i) -5i(-2) -5i(4i)
= -6 + 12i + 10i -20i²
= -6 + 22i + 20 (Note: i² = -1)
= -6 + 20 + 22i
= 14 + 22i
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Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us? 14 75 31 23 77 63 88 40 68 11 60 Range=nothing (Round to one decimal place as needed.)
Answer:
The range is 77.
The variance is 739.8.
The standard deviation is 27.2.
Step-by-step explanation:
The data provided, in ascending order is as follows:
S = {11 , 14 , 23 , 31 , 40 , 60 , 63 , 68 , 75 , 77 , 88}
The range of a data set is the difference between the maximum and minimum values.
From the above data set we know,
Maximum = 88
Minimum = 11
Compute the range as follows:
Range = Maximum - Minimum
= 88 - 11
= 77
The range is 77.
Compute the mean of the data as follows:
[tex]\bar x=\frac{1}{n}\sum x_{i}=\frac{1}{11}\times [11+14+23+...+88]=50[/tex]
Compute the variance as follows:
[tex]\sigma^{2}=\frac{1}{n-1}\sum (x_{i}-\bar x})^{2}[/tex]
[tex]=\frac{1}{11-1}\times [(11-50)^{2}+(14-50)^{2}+...+(88-50)^{2}]\\\\=\frac{1}{10}\times 7398\\\\=739.8[/tex]
The variance is 739.8.
Compute the standard deviation as follows:
[tex]\sigma=\sqrt{\frac{1}{n-1}\sum (x_{i}-\bar x})^{2}}=\sqrt{739.8}=27.199265\approx 27.2[/tex]
The standard deviation is 27.2.
A recreation park measures 560 m long by 700 m wide. A 250-m by 150-m area of the park is used for soccer and baseball fields. How much of the area remains?
Answer:
354,500 square m
Step-by-step explanation:
Remaining area = Area of park - Area used for soccer and baseball field
= 560 * 700 - 250* 150
= 392,000 - 37,500
= 354,500 square m
The formula for the size of a file that was downloaded over time t and at an average rate r is r.t.
Siena downloaded a file at a rate of 800 kilobytes per second for about 110 seconds.
What calculation will give us the estimated size of the file Siena downloaded, in megabytes?
Answer:
The size of file downloaded is 88 megabytes.
Step-by-step explanation:
Given that:
Average rate of downloading the file = [tex]r[/tex]
Time taken to download = [tex]t[/tex]
Formula for the size of file downloaded = [tex]r.t[/tex]
Rate of downloading, [tex]r = 800\ kilobytes/sec[/tex]
Time taken, [tex]t[/tex] = 110 seconds
To find:
Size of file downloaded in megabytes = ?
Solution:
First of all, let us apply the given formula to find the size of file downloaded:
Size of file downloaded = [tex]r.t[/tex]
Size of file downloaded = 800 kilobytes seconds [tex]\times[/tex] 110 seconds =
88000 kilobytes.
Now, let us convert the unit kilobytes to megabytes to find the answer.
Conversion formula:
1000 kilobytes = 1 megabyte
Let us use unitary method to find the number of megabytes in 88000 kilobytes.
1 kilobytes = [tex]\frac{1}{1000}[/tex] megabytes
88000 kilobytes = [tex]\frac{1}{1000} \times[/tex] 88000 megabytes
[tex]\Rightarrow[/tex] 88 megabytes.
Therefore, the size of file downloaded is 88 megabytes.
Answer:
800/1000*110
Step-by-step explanation:
Write an inequality to represent the graph. a dashed line passing through points 0 comma negative 3 and 2 comma 2 with shading above it
A.y is greater than two fifths times x minus 3 B. y is less than two fifths times x minus 3 C. y is greater than five halves times x minus 3 D. y is less than five halves times x minus 3
Answer: y > (5/2)*x - 3
Step-by-step explanation:
Ok, the thins we should notice.
The line is shaded, so the values of the line are not solutions of the inequality, then we should use < or >.
The shaded part is above the line, so we have:
y > a*x + b.
A linear relationship can be written as:
f(x) = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now, we know that our line passes through the points (0, -3) and (2, 2)
Then the slope is:
a = (2 -(-3))/(2 - 0) = 5/2.
f(x) = (5/2)*x + b.
To find the value of b, we can replace the values of one of the points in the equation, let's use the point (0, -3)
f(0) = -3 = (5/2)*0 + b
-3 = b
Then the line is:
f(x) = (5/2)*x - 3
Then the inequality is:
y > (5/2)*x - 3
I don't know how to commit on these posts but the guy above is wrong.
Give an expression for the answer using permutation notation, combination notation, factorial notation, or other operations. Then evaluate. Of the first questions on a test, a student must answer . Of the second questions, the student must answer . In how many ways can this be done?
Answer:
This question is not complete. Let me explain the concept of combination and permutation.
Step-by-step explanation:
The general formula for factorial is n! = n×(n - 1)×(n - 2)×...×2×1
0! = 1
Example 1:
How many different words can we make using the letters D, S, K and Z?
Solution:
We have 4 letters here.
Therefore, to get the possibility of the numbers, we will use:
4! = 4 x 3 x 2 x 1 = 24. We have 24 different words that can be made with the letters.
Permutation
The general formula for permutation is n P r = n! / (n - r)!
Example 2:
Find 5 [tex]P_{3}[/tex]
Solution: This will give 5!/(5-3)! = (5 x 4 x 3 x 2 x 1) / 2!
= 120 / 2 x 1 = 120 / 2 = 60
Combinations
The general formula for combination is n C r = n! / [ (n - r)! r! ]
Example 3:
Find 4[tex]C_{3}[/tex]
Solution: 4[tex]C_{3}[/tex] will give 4!/(4-3)!3! = (4 x 3 x 2 x 1) / 1!3!
= 24 / 1(3 x 2 x 1) = 24 / 6 = 4
Example 4: In Nigeria, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet. How many number plates will be formed if neither the digits nor the letters are repeated?
Solution: Note that we have 26 letters in the alphabet chart.
(9 P 4) × (26 P 3) = 9!/(9-4)! x 26!/(26-3)! = 47,174,400
Student work
TRY IT #1
Write each of the following as a rational number.
b. 3
c-4
Answer:
b. 3 = 3/1
c. -4 = -4/1
Step-by-step explanation:
An integer can be written as a rational number with a denominator of 1. The denominator can be anything else, too, in which case the numerator must be multiplied by that same value.
__
b. 3 = 3/1 = 6/2 = 27/9
__
c. -4 = -4/1 = 8/-2 = -12/3
Evaluate |3 - 5 + 7|.
-5
5
-15
15
Answer:
B. 5
Step-by-step explanation:
|3 - 5 + 7|=|- 2 + 7 | =| 5 | =5Answer is: B. 5
Order these numbers from least to greatest.
5.09, 5.7, 5.7081, 5.009
Answer:
5.009, 5.09, 5.7, 5.7081
Answer:
5.009, 5.09, 5.7, 5.7081
Let (-3, 7) be a point on the terminal side of 0.
Find the exact values of sin 0, sec 0, and tan 0.
Answer:
[tex]\sin O \approx 0.919[/tex], [tex]\sec O \approx -2.539[/tex] and [tex]\tan O = -\frac{7}{3}[/tex].
Step-by-step explanation:
Given a point (x, y) with respect to origin and in rectangular coordinates, the exact value of sine, secant and tangent functions are, respectively:
[tex]\sin O = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\sec O = \frac{1}{\cos O} = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex]
[tex]\tan O = \frac{\sin O}{\cos O} = \frac{y}{x}[/tex]
Given that [tex]x = -3[/tex] and [tex]y = 7[/tex], the exact values of sine, secant and tangent are:
[tex]\sin O = \frac{7}{\sqrt{(-3)^{2}+7^{2}}}[/tex]
[tex]\sin O \approx 0.919[/tex]
[tex]\sec O = \frac{\sqrt{(-3)^{2}+7^{2}}}{-3}[/tex]
[tex]\sec O \approx -2.539[/tex]
[tex]\tan O = \frac{7}{-3}[/tex]
[tex]\tan O = -\frac{7}{3}[/tex]
Hermione went to a pet store and bought a fish tank that cost $62.00 plus 5% sales tax. She
gave the clerk $100.00. How much change should she receive?
A $43.00
B $38.00
C $34.90
D $33.00
The number 430,290,100 in expenden form
Answer:
400,000,000+30,000,000+200,000+90,000+100
What's the length of an arc with a central angle of 100° and a radius of 2 inches?
Answer:
the answer is 4) 10π/9 inches
Step-by-step explanation:
all answers have π on the nominator but i could not insert it for some reason
[tex]Question 7 options:\\1) \frac{40}{3}inches \\2) \frac{5}{3} inches\\3) \frac{100}{3} inches \\4) \frac{10}{9} inches[/tex]
A circle is a curve sketched out by a point moving in a plane. The length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Given that the radius of the circle is 2 inches, while the angle made by the arc at the centre of the circle is 100°. Therefore, the length of the arc can be written as,
Length of the arc = 2 × π × R × (θ/360°)
= 2 × π × 2 inches × (100°/360°)
= 10π / 9 inches
= 3.49 inches
Hence, the length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.
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What is corrrectly plotted points for y=-x+3
Answer:
Here. I have graphed this for you. The points are at +3 and +3
Step-by-step explanation:
Using cross multiplication, which of the following is the solution to 7/3x = 2/(x+5)?
Step-by-step explanation:
Hey, there!!
[tex] \frac{7}{3x} = \frac{2}{x + 5} [/tex]
By cross multiplication,
[tex]7.(x + 5) = 2 \times 3x[/tex]
[tex]7x + 35 = 6x[/tex]
[tex]7x - 6x = -35[/tex]
Therefore, x= -35.
Hope it helps...
Find the product:
(x+9)(x-9)
a 18
b. -81
C. - 18
d. x-64
Answer:
x^2 -81
Step-by-step explanation:
(x+9)(x-9)
FOIL
first x*x = x^2
outer -9x
inner 9x
last -9*9 = -81
Add them together
x^2 -9x+9x -81
Combine like terms
x^2 -81
Answer: B
Step-by-step explanation:
Simply using (a-b)(a+b)=a^2-b^2.
Evaluate the power (9^2).
x^2 - 81
What is the radius of a circle whose equation is (X +5 )2+(Y -3 )2=four squared
Answer: 4
Step-by-step explanation:
The standard equation of a circle is (x−h)^2 + (y−k)^2 = r^2, with (h,k) being the center and r being the radius. In the equation you provided, r = 4.
Answer:
Step-by-step explanation:
(x-h)²+(y-k)²=r²
radius=r
p(n,6)=3p(n,5) what is the value of n.
Answer:
n = 10
Step-by-step explanation:
3n1!/(n-4)! = (n-1)!/( n-1-5)
3n(n-1)(n-2)(n-3)(n-4) / N-4 -------- case1 ( cancel ( n-4) from top and bottom)
= (n-1)(n-2)(n-3)(n-4)(n-5)(n-6) / n-6 --------- case 2 ( Cancel n-6 from top and
bottom and also cancel n-1,
n-2, n-3 with case 1)
3n = ( n-4)(n-5)
3n = n² - 5n - 4n + 20
3n = n² - 9n + 20
0 = n² - 9n - 3n + 20
0 = n² - 12n + 20
0 = (n-2)(n-10)
n = 2 ( not valid) n = 10
Therefore n = 10
Which of these questions is most likely to result in response bias? A. "What do you think of this TV show?" B. "What is your opinion of this TV show?" C. "How do you like this great new TV show?" D. "How do you feel about this TV show?"
Answer: C. "How do you like this great new TV show?"
The term "great" put in there skews the question to make people think the show is great, when it may not be. So people may have a tendency to say they really like the show when they may not.
Or perhaps they may like the show (somewhat) but the fact that they can sense the bias built into the question makes them decide to say opposite and say they don't like the show. Maybe this sort of scenario would have them rebel in a way.
Either way, the use of "great" is likely to alter the opinion of people answering the question.
part 5 please assist me with this problems
Answer: 14) 44° 15) 6.5
Step-by-step explanation:
Law of Cosines: a² = b² + c² - 2bc · cos A
Note: The letters can be swapped
14) Given: a = 7, b = 6, c = 10, A = ???
7² = 6² + 10² - 2(6)(10) · cos A
49 = 36 + 100 - 120 cos A
49 = 136 - 120 cos A
-87 = - 120 cos A
0.725 = cos A
43.5° = A
15) Given: A = 21°, b = 18, c = 16
a² = 18² + 16² - 2(18)(16) · cos 21°
= 324 + 256 - 576 cos 21°
= 580 - 576 cos 21°
= 42.26
[tex]a=\sqrt{42.26}[/tex]
= 6.5
Find the sum of (x + 5) and (2x + 3) *
A) 9x + 1
B) 5x + 2
C) 8x + 3
D) 3x + 8
Answer:
D
Step-by-step explanation:
We know that we are adding the two expressions because the question says "sum" which means that we need to add. Let's combine like terms. We know that x + 2x = 3x and 5 + 3 = 8 so the answer is 3x + 8.
Answer:
D. 3x+8
Step-by-step explanation:
We want to find the sum of (x+5) and (2x+3). Sum means addition, so we must add the 2 expressions.
(x+5)+(2x+3)
Now, we must simplify by combining like terms.
First, combine the terms with variables.
(x+2x) + (5+3)
3x + (5+3)
Next, add the constants, or terms without variables.
3x+ 8
The sum of (x+5) and (2x+3) is 3x+8. This makes choice D the correct answer.
You have a lead ball with a mass of 420 g. The density of lead is 10.5 g/cm square. What is the volume of the ball?
Answer: Volume = 40 cm3
Step-by-step explanation:
The similarities and differences between correlation and regression Correlation and regression are two closely related topics in statistics. For each of the following statements, indicate whether the statement is true of correlation, true of regression, true of both correlation and regression, or true of neither correlation nor regression. Regression Correlation Both Correlation and Regression Neither Correlation nor Regression Can tell you whether one variable (such as smoking) causes another (such as cancer) Can be influenced by extreme values on one or both variables Can tell you the degree to which a linear relationship exists between two variables?
Answer:
Both variables Can tell you the degree to which a linear relationship exists between two variables.
Step-by-step explanation:
Correlation and regression are two statistical concepts that are closely related and complement each other. They are powerful tools used in modern-day machine learning and artificial intelligence.
Correlation evaluates the linear relationship between two variables, using regression as a tool to assess the degree at which a dependant variable changes ( either increasing or decreasing ) based on the value of an independent variable.
The correlation coefficient is the degree of the linear relationship between two variables, ranging from zero ( for non-linear) to one ( for highly linear).
which pairs of angles in the figure below are vertical angles? Check all that apply
Calculate. (3 1/3 −1 5/6 ) ÷ 2 1/7 −1 1/3 · 2.4
Find the area of the shape shown below.
6
2.
units2
Answer:
12 [tex]units^{2}[/tex]
Step-by-step explanation:
square: 2 x 2 = 4 units sq
small triangle: 2 x 2 = 4, 4 / 2 = 2 units sq
big triangle: 2 x 6 = 12, 12 / 2 = 6 units sq
4 + 2 + 6 = 12 units sq
Answer:
12 units²
Step-by-step explanation:
we need to notice that the shape has two right triangles and a rectangle
the area of right triangles is b*h/2 and of the rectangle side*length
area of first triangle
Base=2
Height=2
[tex]A=\frac{2*2}{2} =2[/tex]
Area of the square
Side=2
Length=2
[tex]A_2=2*2=4[/tex]
Area of the second triangle
Base=2
Height=6
[tex]A_3=\frac{2*6}{2} =6[/tex]
so we need to add all three areas
[tex]A_T=A_1+A_2+A_3\\\\A_T=2+4+6=12\\\\A_T=12[/tex]
So the area is 12 units²
Increasing the value of m increases the line’s intersection with the y-axis. intersection with the x-axis. steepness.
The increasing the value of m increases the line’s intersection with the y-axis. intersection with the x-axis which is stepness
What is stepness of line?The slope of a line is a measure of its steepness. In mathematics, the stepness or gradient of a line is a number that describes both the direction and the steepness of the line. The stepness of a line is defined as the change in y-values divided by the change in x-values.How to solve this problem?The steps are as follow:
Decreasing the value b decreases the line’s intersection with the y-axisSo the answer is stepnessTherefore the increasing the value of m increases the line’s intersection with the y-axis. intersection with the x-axis which is stepness
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Answer: C
Step-by-step explanation:
What is the value of the expression
(
43
+
7
2
)
2
2
2
2
(43+7
2
)
?
Answer:
The question is not clear
Find the area of the figure. (Sides meet at right angles.)
5 m
4 m
4 m
3 m
3 m
3 m
þ m
Answer:
53 m^2
Step-by-step explanation:
53 m^2 is the area of the figure given!
So as given in the question that the sides meet at right angles.
we take the bottom of the upper rectangle as 5m, then the upper side of the lower rectangle will be 3+5+3= 11.
Now, by using the formula of the area of a rectangle that is Area = Height x width, we areas of the two rectangles. Then add both the areas.
Finally we get the area of the given figure!
Hope it helps you!
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Answer:
A = 53 m²
Step-by-step explanation:
A = A1 + A2
= 4m×5m + 3m×(3m + 5m + 3m)
= 20m² + 3m×11m
= 20m² + 33m²
= 53 m²
walk block.
a)sentence
b)fragment
Answer is fragment because is fragment walk block
Write two related division statements for : -3 x 8 = -24
Answer:
8/-24=-3
-3/-24=8
I hope this is the answer