Answer:
The sum of the expression (8 - 4i) + (-2 +7i) is (6 + 3i)
Step-by-step explanation:
In the complex numbers (a + bi) and (c + di), we can add the real parts together and the imaginary parts together, so their sum is
(a + bi) + (c + di) = (a + c) + (b + d)i
Let us use this fact to solve our question
∵ The complex numbers are (8 - 4i) and (-2 + 7i)
∴ Their sum = (8 - 4i) + (-2 + 7i)
∵ The real parts are 8 and -2
∵ 8 + -2 = 8 - 2 = 6
∴ The sum of the real parts is 6
∵ The imaginary parts are -4i and 7i
∵ -4i + 7i = 3i
∴ The sum of the the imaginary parts is 3i
∵ (8 - 4i) + (-2 + 7i) = (8 - 2) + (-4 + 7)i
∴ (8 - 4i) + (-2 + 7i) = 6 + 3i
∴ The sum of the expression (8 - 4i) + (-2 +7i) is (6 + 3i)
Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1 52 probability.
Required:
a. List the sample points in the event a jack is selected.
b. List the sample points in the event a club is selected.
c. List the sample points in the event a face card ( jack, queen, or king) is selected.
d. Find the probabilities associated with each of the events in parts (a), (b), and (c).
Answer:
Kindly check explanation
Step-by-step explanation:
A deck of card:
Number of hearts = 13
Diamond = 13
Spade = 13
Club = 13
Each of heart, club diamond and spade has is numbered from (2,3,4,5,6,7,8,9,10,Ace, queen, Jack, king)
Hence, a club, diamond, spade and heart has one of each of the above numbers.
a. List the sample points in the event a jack is selected.
Jack : ( heart, club, diamond, spade)
B.) club is selected :
Cub : (Ace, 2, 3,4,5,6,7,8,9,10,king,queen,jack)
C)
Jack : ( heart, club, diamond, spade)
Queen : (heart, club, diamond, spade)
King : (heart, club, diamond, spade)
D) probability = required outcome / Total possible outcomes
P(jack selected) = 4 /52 = 1/13
P(club selected). = 13/52 = 1/4
P(face card selected) = 12 / 52 = 3/13
A bowl of fruit contains seven pieces of fruit, including two bananas and five apples. Three pieces of fruit are chosen. What is the probability that one banana and two apples are chosen?
Answer:
[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
A combination refers to the selection of objects such that order does not matter. A permutation refers to the arrangement of objects such that order do matter.
Number of bananas = 2
Number of apples = 5
One banana and two apples are chosen.
So,
probability that one banana and two apples are chosen = [tex]\frac{C(2,1)\,C(5,2)}{C(7,3)}[/tex]
[tex]C(2,1)=\frac{2!}{1!(2-1)!}=2[/tex]
[tex]C(5,2)=\frac{5!}{2!(5-2)!}=\frac{5!}{2!31} =10[/tex]
[tex]C(7,3)=\frac{7!}{3!(7-3)!} =\frac{7!}{3!4!}=35[/tex]
So,
Probability that one banana and two apples are chosen = [tex]\frac{2(10)}{35}=\frac{4}{7}[/tex]
Answer:
Or 57.14%
Step-by-step explanation:
On a family road trip, Mr. Peters travels 130
miles in 2 hours. At this rate, how many miles
will he travel in 7 hours?
An integer divided by an integer is an integer
Answer:
an integer divided by an integer will always result in a fraction- therefore, the resultant number will not be an irrational number and there will always be either a repeated pattern or a single set of decimal points. Take for example 3/4= 0.75. As you can see the number is a rational number that is real.
Step-by-step explanation:
An integer divided by an integer is sometimes not an integer.
1/5t+2- =17
1/5t
.1/5t
T=
Answer:
poop i forgot my ramen noodles are in the microwave
Step-by-step explanation:
Lauren can wash a
car in 20 minutes.
How long will it take,
in hours, for her to
wash 60 cars?
Answer:
The answer is 20 hours
Step-by-step explanation:
20x60=1200
1200÷60=20
=========================================
One way to solve
1 car = 20 minutes
3*(1 car) = 3*(20 minutes) multiply both sides by 3
3 cars = 60 minutes
3 cars = 1 hour
20*(3 cars) = 20*(1 hour) ... multiply both sides by 20
60 cars = 20 hours
-------------------
Another way to solve
(1 car)/(20 minutes) = (60 cars)/(x minutes)
1/20 = 60/x
1*x = 20*60 ... cross multiply
x = 1200 minutes
x = (1200 min)*( (1 hr)/(60 min) )
x = (1200/60) hr
x = 20 hours
The SAT is required of most students applying for college admission in the United States. This standardized test has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (The Washington Post, August 30, 2006). Consider the following scores on the writing component of the test of eight male and eight female students.
Males Females
620 660
570 590
540 540
580 560
590 610
580 590
480 610
620 650
570 600
610 620
590 630
570 640
610 590
590 640
570 580
550 560
530 570
560 560
620 600
520 600
560 590
620 590
580 590
610 630
530 560
480 600
590 560
620 560
590 560
580 560
Required:
a. Construct the null and the alternative hypotheses to test if females outscore males on writing tests.
b. Assuming the difference in scores is normally distributed, calculate the value of the test statistic. Do not assume that the population variances are equal.
c. Implement the test at α=0.01 and interpret your results.
Answer:\
a
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex]
b
[tex]t = -0.39[/tex]
c
The conclusion
There is sufficient evidence to conclude that the female outscores the male.
Step-by-step explanation:
From the question we are told that
The sample size for male is [tex]n_1 = 30[/tex]
The sample size for female is [tex]n_2 = 30[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex]
Generally the sample mean for male is
[tex]\= x_1 = \frac{\sum x_i}{n_1}[/tex]
=> [tex]\= x_1 = \frac{620 + 570 +540 + \cdots + 580 }{30}[/tex]
=> [tex]\= x_1 = 574.33 [/tex]
Generally the standard deviation of male is
[tex]s_1 = \sqrt{\frac{\sum (x_1 - \= x)^2}{n_1} }[/tex]
=> [tex]s_1 = \sqrt{\frac{ (620 - 574.33)^2 + (570 - 574.33)^2 + (540 - 574.33)^2 + \cdots +(580 - 574.33)^2 }{30} }[/tex]
=> [tex]s_1 =206.24 [/tex]
Generally the sample mean for female is
[tex]\= x_2 = \frac{\sum x_i}{n_2}[/tex]
=> [tex]\= x_2 = \frac{660 + 590 +560 + \cdots + 560 }{30}[/tex]
=> [tex]\= x_2 = 593.33 [/tex]
Generally the standard deviation of male is
[tex]s_2 = \sqrt{\frac{\sum (x_1 - \= x)^2}{n_2} }[/tex]
=> [tex]\sigma_1 = \sqrt{\frac{ (660 - 593.33)^2 + (590 - 593.33)^2 + (560 - 593.33 )^2 + \cdots +(560 - 593.33)^2 }{30} }[/tex]
=> [tex]s_2 =169.31 [/tex]
Generally the degree of freedom for unequal variance is mathematically represented as
[tex]df = \frac{[\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2} ]^2}{ \frac{[\frac{s_1^2}{n_1}]^2}{n_1 -1} +\frac{[\frac{s_2^2}{n_2}]^2}{n_2 -1} }[/tex]
=> [tex]df = \frac{[\frac{206.24^2}{30} +\frac{169.31^2}{30} ]^2}{ \frac{\frac{206.24^2}{30}}{30 -1} +\frac{\frac{169.31^2}{30}}{30 -1} }[/tex]
=>[tex]df = 56[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x _1- \= x_2 }{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} }[/tex]
=> [tex]t = \frac{574.33- 593.33 }{\sqrt{\frac{206.24^2}{30} + \frac{169.31^2}{30}} }[/tex]
=> [tex]t = -0.39[/tex]
From the t distribution table the value of [tex]P(t < -0.39)[/tex] at a degree of freedom of [tex]df = 56[/tex] is
[tex]P(t < -0.39) = 0.3490080[/tex]
Hence the p-value is [tex]p-value = 0.3490080[/tex]
From the values obtained we see that the p-value is >[tex]\alpha[/tex]
Hence we fail to reject the null hypothesis.
The conclusion is
There is sufficient evidence to conclude that the female outscores the male
What is the sum of 16.5 x 10 exponent 4
Find the standard deviation of the following data. Round your answer to one decimal place. x 00 11 22 33 44 55 P(X
Complete question :
Find the standard deviation of the following data. Round your answer to one decimal place.
X: 0 1 2 3 4 5
P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2
Answer:
1.833
Step-by-step explanation:
Given the data :
X: 0 1 2 3 4 5
P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2
Standard deviation (s) = Sqrt[Σx²*f(x) - E(x)²]
E(x) = (0*0.2) + (1*0.3)+(2*0.1)+(3*0.1) + (4*0.1) + (5 * 0.2) = 2.2
Sqrt[Σx²*f(x) - E(x)²]: [(0^2 * 0.2)+(1^2 * 0.3)+(2^2 * 0.1)+(3^2 * 0.1) + (4^2 * 0.1) + (5^2 * 0.2)] - 2.2²
Sqrt(8.2 - 4.84) = 1.833
To determine whether they have a certain disease, 100 people are to have their blood tested.However, rather than testing each individual separately, it has been decided first to place the peopleinto groups of 10. The blood samples of the 10 people in each group will be pooled and analyzedtogether. If the test is negative, one test will suffice for the 10 people, whereas if the test is positive,each of the 10 people will also be individually tested and, in all, 11 tests will be made on this group.Assume that the probability that a person has the disease is .1 for all people, independently of eachother, and compute the expected number of tests necessary for each group. (Note that we areassuming that the pooled test will be positive if at least one person in the pool has the disease.)
Answer:
The expected number of tests necessary for each group is 7.51.
Step-by-step explanation:
The probability of a person having the disease is, P (X) = 0.10.
Then the probability of a person not having the disease is P (X') = 0.90.
It is provided that if the test is negative, one test will suffice for the 10 people.
Bur if the test is positive, each of the 10 people will also be individually tested and, in all, 11 tests will be made on this group.
Compute the expected number of tests necessary for each group as follows:
Expected number of tests = Negative Result × P (X') + Positive Result × P (X)
[tex]=(1\times (0.90)^{10})+(11\times [1-(0.90)^{10}])\\=0.3486784401+7.1645371589\\=7.513215599\\\approx 7.51[/tex]
Thus, the expected number of tests necessary for each group is 7.51.
Pattie's Produce charges $2.29 for a package of strawberries. On average, Pattie's Produce sells 95 packages of strawberries daily. They estimate that for each 20-cent increase in the cost of a package of strawberries, 9 less packages will be sold each day. Let x represent the number of 20-cent increases in the cost of a package of strawberries. Which inequality represents the values of x that would allow Pattie's Produce to have a daily revenue of at least $255 from selling the packages of strawberries? A. B. -1.872 – 1.615 + 217.55 > 255 -1.812 + 21.61r + 217.55 > 255 -1.8r2 – 21.611 + 217.55 < 255 C. D. -1.812 + 1.61x + 217.55 < 255
Answer:
A. -1.8x² – 1.61x + 217.55 > 255
Step-by-step explanation:
Since Pattie's Produce charges $2.29 for a package of strawberries and 95 packages can be produced daily. The money gotten daily = $2.29 × 95 packages = $217 Since 20 cent increase leads to 9 less package.
The number of 20-cent increases in the cost of a package of strawberries can be gotten from:
(2.29 + 0.2x)(95 - 9x) > 255
217.55 - 20.61x + 19x - 1.8x² > 255
-1.8x² - 1.61x + 217.55 > 255
Answer:
A. -1.8x² – 1.61x + 217.55 > 255
Step-by-step explanation:
EDMENTUM
lines A and B are parallel lines find the measures of angle 1
Answer:
33Step-by-step explanation:
alternate angles are equal
see attached
The measure of ∠1 is 33° .
What is alternate interior angles?When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.
According to the question
As given , lines A and B are parallel lines
therefore ,
∠1 = 33°
∠3 = 57°
they are between parallel line and opposite of transversal line
So, they are alternate interior angles and are equal .
Hence, The measure of ∠1 is 33° .
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Find the distance between the points (2, -9) and (-1, 4).
A.13.34
B.5.10
C.13.04
D.5.83
Answer:
A. 13.34
Step-by-step explanation:
This is the formula d=√((x_2-x_1)²+(y_2-y_1)²)
Plug in
d=√(-1-2)² + (4+9)²
d= √9 + 169
d= √178
d= 13.34
A junior basketball player has a goal of scoring at least 1,000 points in his high-school career. His team plays twenty games per year, and after two years he has 320 points
what is the value of the expression if m=2 and n-6?
Answer:
where is the expression
Step-by-step explanation:
（＾_＾）（＾_＾）（＾_＾）
If P(E)=0,40,P(E or F)=0.55, and P/E and F)=0.20, find P(F).
P(F)-(Simplify your answer.)
Answer:
screeeeeeeeeeredc vbggrewdsc
Step-by-step explanation:cdscx de2wqsax
wewdsnswercwdsx
==================================
Work Shown:
P(E or F) = P(E) + P(F) - P(E and F)
0.55 = 0.40 + P(F) - 0.20
0.55 = P(F) + 0.20
P(F) + 0.20 = 0.55
P(F) = 0.55 - 0.20
P(F) = 0.35
---------
note: Sometimes you may see the formula as
P(E and F) = P(E) + P(F) - P(E or F)
but it's an equivalent form to the first equation above.
What is the sum of 3x2+5x-6 and -x2+3x+9
Answer:
2x2+8x+3
Step-by-step explanation:
=3x2+5x+−6+−x2+3x+9
=(3x2+−x2)+(5x+3x)+(−6+9)
=2x2+8x+3
A ballon is released from the top of a building. The graph shows the height of the balloon over time. What does the slope and y-intercept reveal about the situation?
The grid shows the number of hours four people worked and the total amount they each earned in dollars.
Total Amount Earned (dollars)
55
Yves
45+
40+
35+
Mia
30
25+
Sam
20+
Carlos
15+
10+
5+
+++++
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Hours Worked
5
Which statement is true?
O A. Sam worked 20 hours and earned $5.
O C. Mia worked 35 hours and earned $7 an hour.
O D. Yves worked 5 hours and earned $50 an hour.
O B. Carlos worked 2 hours and earned $20.
Ok
Answer:
The correct statement are D and B.
Step-by-step explanation:
There are 4 data points on the grid labeled with names: Carlos at point (2, 20). Sam at point (5, 25). Yves at point (5, 50). Mia at point (7, 35).
The data can be represented in tabular form as follows:
Employees Number of hours Amount earned
Carlos 2 $20
Sam 5 $25
Yves 5 $50
Mia 7 $35
The provided data can be written in statement form as follows:
Carlos worked 2 hours and earned $20 an hour.Sam worked 5 hours and earned $25 an hour.Yves worked 5 hours and earned $50 an hour.Mia worked 7 hours and earned $35 an hour.Thus, the correct statement are D and B.
I need help please help me out
Answer:
2821
Step-by-step explanation:
Uhm.. sorry if its wrong i'm not completely sure about it :/
HELP, ILL GIVE BRAINLIEST BUT HELP ASAP WITH THIS!!
Answer:
proportional
Step-by-step explanation:
10. Which of the following does not represent an
arithmetic sequence?
A. -7, -3, 1, 5, 9...
B. -64, -16, -4, -1...
C. 0, 2, 4, 6...
D. 3,-2, -7, -12...
Answer:B
Step-by-step explanation:because an arithmetic sequence would be either adding or subtracting and B is dividing or if it’s easier from right to left it’s multiplying
Jackson has 429 matchbox cars in his collection. If 4 out of 9 are blue cards, how many are not blue
The m 3 +m 5 =180 true false will mark brainest
Answer:
true I'm positive that the correct answer
Answer:
TrueStep-by-step explanation:
∠3 and ∠5 are supplementary internal angles that adds up to 180
so ∠3 + ∠5 = 180
Little Bo Peep needs to buy 10 new sheep.
Farm M: one sheep costs $20
Farm Q: Set of 5 sheep costs $75.
How much will it cost Little Bo Peep to buy 10 sheep from Farm M?
Answer:
200$
Step-by-step explanation:
10 TIMES 20 IS 200
Find the balance in the account after the given period. $4000 principle earning 3% compounded annually 6 years
Answer: it would be 3000 that’s what it is
Step-by-step explanation:
Lucy, charlie, and Michael have a total of $95 in their wallet. Charlie has $10 more than lucy. Michael has 3 times what Lucy has. How much does each have?
What is the equation for calculating portion size?
Answer:
How to Easily Calculate the Serving Size in Recipes
Weigh the Food. Before you can accurately divide your recipe into servings, you need to know how much it weighs in total. ...
Divide the Recipe into Servings. ...
Calculate Calories. ...
Save the Information.
Step-by-step explanation:
Write a pair of numbers whose greatest common factor is 10 will give brainlist
Answer:
20 and 10
Step-by-step explanation:
Answer:
20 ,10
Step-by-step explanation:
hope it helps
Which expressions are equivalent to the given expression? sqrt40
4sqrt10
160 1/2
40 1/2
2sqrt10
5sqrt8
Answer:
[tex]2 \: sqrt \: 10.[/tex]
Step-by-step explanation:
[tex]sqrt \: 40 = \sqrt{40} = \sqrt{4 \times 10} = \\ \sqrt{4} \times \sqrt{10} = 2 \times \sqrt{10} = \\ 2 \sqrt{10} = \\2 \: sqrt \: 10[/tex]
♨Rage♨
[tex]2\sqrt{10}[/tex] expression is equivalent to the given expression [tex]\sqrt{40}[/tex].
What is expression?An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.
Given expression
[tex]\sqrt{40}[/tex]
We can write it into [tex]\sqrt{4 .(10)}[/tex]
= [tex]\sqrt{4}.\sqrt{10}[/tex]
= [tex]2\sqrt{10}[/tex]
Hence, [tex]2\sqrt{10}[/tex] expression is equivalent to the given expression [tex]\sqrt{40}[/tex].
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