Explanation:
Complex numbers are numbers that have both imaginary and real number parts. Imaginary numbers occur when you take the square root of negative numbers. Here are some examples of imaginary numbers:
[tex]\sqrt{-1} = i[/tex] and [tex]\sqrt{-16} = 4i[/tex]
Real numbers are just normal numbers.
Complex numbers can be expressed generally in the form:
[tex]a+bi[/tex]
PLEASE SOLVE ASAP!
The sum of the measures of two complementary angles is equal to ____.
Answer: Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
Step-by-step explanation:
Answer:
90°
Step-by-step explanation:
A box contains 3 green marbles, 5 blue marbles, and 7 red marbles. Three marbles are selected at random from the box, one at a time, without replacement. Find the probability that the first two marbles selected are not red, and the last marble is red. Round your answer to four decimal places.A box contains 3 green marbles, 5 blue marbles, and 7 red marbles. Three marbles are selected at random from the box, one at a time, without replacement. Find the probability that the first two marbles selected are not red, and the last marble is red. Round your answer to four decimal places.
Answer:
The probability is [tex]P(K) = \frac{ 28 }{195} [/tex]
Step-by-step explanation:
From the question we are told that
The number of green marbles is [tex]n_g = 3[/tex]
The number of red marbles is [tex]n_b = 5[/tex]
The number of red marbles is [tex]n_r = 7[/tex]
Generally the total number of marbles is mathematically represented as
[tex]n_t = n_r + n_g + n_ b[/tex]
[tex]n_t = 7 + 3 + 5[/tex]
[tex]n_t = 5 [/tex]
Generally total number of marbles that are not red is
[tex]n_k = n_g + n_ b[/tex]
=> [tex]n_k = 3 + 5[/tex]
=> [tex]n_k = 8[/tex]
The probability of the first ball not being red is mathematically represented as
[tex]P(r') = \frac{n_k}{n_t}[/tex]
=> [tex]P(r') = \frac{ 8}{15}[/tex]
The probability of the second ball not being red is mathematically represented as
[tex]P(r'') = \frac{n_k - 1}{n_t -1}[/tex]
=> [tex]P(r'') = \frac{ 8 -1 }{15-1}[/tex] (the subtraction is because the marbles where selected without replacement )
=> [tex]P(r'') = \frac{ 7 }{14}[/tex]
The probability that the first two balls is not red is mathematically represented as
[tex]P(R) = P(r') * P(r'')[/tex]
=> [tex]P(R) = \frac{ 8}{15} * \frac{ 7 }{14}[/tex]
=> [tex]P(R) = \frac{ 8 }{30}[/tex]
The probability of the third ball being red is mathematically represented as
[tex]P(r) = \frac{n_r}{ n_t -2}[/tex] (the subtraction is because the marbles where selected without replacement )
[tex]P(r) = \frac{7}{ 15 -2}[/tex]
=> [tex]P(r) = \frac{7}{ 13}[/tex]
Generally the probability of the first two marble not being red and the third marble being red is mathematically represented as
[tex]P(K) = P(R) * P(r)[/tex]
[tex]P(K) = \frac{ 8 }{30} * \frac{7}{ 13}[/tex]
=> [tex]P(K) = \frac{ 28 }{195} [/tex]
Write 37/3 as a mixed number
Answer:
12 1/3
Step-by-step explanation:
Answer:
12 1/3
Step-by-step explanation:
1. Divide the numerator by the denominator.
Divide 37 by 3, which equals 12 with a remainder of 1.
37 ÷ 3 = 12 r1
2. Find the whole number.
The whole number is the number of times the denominator divides into the numerator.
3 (the denominator) divides into 37 (the numerator) 12 times, so 12 is the whole number.
Make the remainder the new numerator.
Because the remainder (the leftover value) of dividing 37 by 3 is 12, 1 is the new numerator. The denominator is still 3. So, the mixed fraction is:
12 1/3
Hope it helps...
write the following numbers in words 560 451 2008
Answer: five billion six hundred four million five hundred twelve thousand eight
Step-by-step explanation:
A rectangle is inscribed in a circle
17 in.
18 in.
15 in.
Part A
Calculate the exact area of the cirde. Use the key on the calculator. Round answer to the nearest hundredth if necessary
square inches
Part B
Calculate the area of the rectangle. Round answer to the nearest hundredth if necessary
A=
square inches
Part
Calculate the area of the shaded region
Area of the shaded region
square inches
9514 1404 393
Answer:
A) 226.98 in^2
B) 120 in^2
C) 106.98 in^2
Step-by-step explanation:
A) The diagonal of the rectangle is the diameter of the circle. The area can be found using the formula ...
A = (π/4)d^2
A = (π/4)(17 in)^2 = 72.25π in^2 ≈ 226.98 in^2
__
B) The area of the rectangle is the product of its length and width:
A = LW
A = (15 in)(8 in) = 120 in^2
__
C) The shaded area is the difference between the circle area and the rectangle area:
shaded area = (226.98 in^2) -(120 in^2) = 106.98 in^2
Find the unit rate. 3/8 mile in 3/4 hour
We are required to find the unit rate, that is, miles per hour
The unit rate is 1/2 miles per hourNumber of miles = 3/8 mileNumber of hours = 3/4 hourTherefore, unit rate = = 3 / 8 ÷ 3/4= 3 / 8 × 4/3= 12/24= 1/2Read more:
https://brainly.com/question/8406966
f(x) = 4x + 5
g(x) = -10x² + 8x – 7
Find: f(x) · g(x)
Answer:
G(x) =0.4/0.7
F(x)= 6.6/14
Step-by-step explanation:
G(x)= 0.4/0.7
F(x)= 4(0.4)+5
=6.6
4(0.7)+5
=14.
Dm me if I'm wrong. If not, please mark as brainliest
Heeeeeeeeeeeeeeeeeelpppppppppppp
Answer:
As both these angles form a linear pair, they together will form 180°
So,
(2x + 45)° + x = 180°
=> 2x + 45 + x = 180°
If my answer helped, kindly mark me as the brainliest!
Thank You!!
Hydrogen peroxide decomposes back to water and oxygen when exposed to air and light. When bought at a pharmacy for home use, hydrogen peroxide is sold in dark bottles that are labeled as a concentration of 3% by weight. A chemistry student wants to test the concentration of hydrogen peroxide that has been decanted to light and dark bottles, and exposed to air for 10, 20 and 30 hours. The concentration is tested by titration with potassium permanganate, and each sample is tested twice.answer choices are: color/hours, 2, 6, 12, dark/light, 10/20/30 hours, and concentrationquestions: Response variable (s):Factor(s):Experimental Unit (s):Replication(s):Treatment(s):
Answer:Response variable (s)-concentration, (s): Treatment- 2,6,12 hours,Replication(s)-10/20/30 hours
Experimental Unit- dark/light
Factors-color/hours
Step-by-step explanation:
Factors refer to explanatory variables tat are being studied in an experiment. They are manipulated in order to obtain a response (dependent) variable.
Treatments refer to a combination of factor levels in the experiment. Each factor has two or more levels
The experimental unit refers to the physical entities assigned at random to treatments during the experiment.
Replication refers to the number of times the same experiment is carried out. It enhances the reliability of the result of an experiment.
The concentration is tested by titration with potassium permanganate, and each sample is tested twice Replication-10/20/30 hours.
We have to determine
The concentration is tested by titration with potassium permanganate, and each sample is tested twice.
What is hydrogen peroxide?Hydrogen peroxide is a chemical compound that is gaseous in nature. Its viscosity is greater than that of water.
Since it is unstable it slowly decomposes in the presence of light to form water and oxygen.
The control experiment is necessary for the determination of reliability and statistical significance of results obtained.
Replication helps to ensure accuracy and randomization aids us in making quality generalizations from experimental data.
Testing the concentration of hydrogen peroxide decanted to dark bottles is the control experiment.
Testing the concentration of the species after exposure to air for 10,20 and 30 hours is randomization.
Replication refers to the number of times the same experiment is carried out. It enhances the reliability of the result of an experiment.
Testing each sample twice is replication.
To know more about Hydrogen peroxide click the link given below.
https://brainly.com/question/18709693
A 28-story hotel building has 18,000 square feet of space for rooms per floor. The average room is 16 ft x 28 ft. How many rooms do you have available?
Answer:
1,120 rooms
Step-by-step explanation:
You need to find out how many hotel rooms are on one floor, and then multiply that by 28. So each room is 16ft x 28ft, which comes out to be 448ft^2. Then to find how many of these rooms go onto one floor, you must divide 18,000 by 448. This equals about 40. So 40 rooms per floor, times 28 floors is: 1,120. And that's your answer! Make sure you understand how we got that. If you have any questions I can help! :)
use the model to solve 4 friends equally split in one half of a pound of candy how much will each friend get
Answer:
.25 pounds
Step-by-step explanation:
Unfortunately, the type of model that is supposed to be used is not given so I will just solve what I can. So each friend gets and equal amount. If we have 1 pound in the beginning, and 4 friends, then we have to divide the candy by 4. So we do 1 pound/4=.25 pounds. If you want to go above and beyond, we can always convert the pounds into ounces and make it so each friend gets 4 ounces of candy.
What is the slope of the line passing through the points (-2, 6) and (1, -3)
Answer:
slope is -3
Step-by-step explanation:
use slope equation, shown in picture hope this helps
what is the answer to this simultaneous equation
2x+3y=13
4x-y=-2
How to find the volume using the formula V=l•w•h to solve for the formula of W
A farmer sold 53.2 pounds of carrots and 29.4 pounds of green beans to a restaurant. How many pounds of these two vegetables did the restaurant buy? Explain your thinking. *
Answer:
just add up the 2 numbers pretty simple
Step-by-step explanation:
53.2 plus 29.4
Answer: 82.6 lb
Step-by-step explanation:
Since the restaurant is buying the pounds given from the farmer, add the pounds together.
Add
53.2 + 29.4 = 82.6
Hence, the restaurant bought 82.6 pounds of vegetables.
Division using place value step by step
2,440 / 8 I know answer. I just need shown steps please & thank you!
Answer:
see attached
Step-by-step explanation:
The usual methods of long division use place value. Each quotient digit is aligned over the appropriate dividend digit to give it the proper place value.
!!!!Translate the sentence into an equation!!
The sum of 7 times a number and 3 is 6.
Answer:
7x + 3=6 that is the equation
Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she
sold 6 fewer books than she did on Tuesday. During the three days Rachel sold 19 books. Create an equation that can
be used to find m, the number of books Rachel sold on Monday.
Equation:
Step-by-step explanation:
1. Let the number of books sold on Monday be x.
2. And, The no. of Books sold on Tuesday be 2x , which is twice as the books sold on monday.
3. Now, The no. of books sold on Wednesday be 2x-6 ,
which is fewer than the books sold on Tuesday.
Where Total no. of books sold on 3 days is 19.
so, The equation be like: x+2x+2x-6 = 19
Answer:
m = 5
Step-by-step explanation:
On Tuesday, she sold twice as many books as she did on Monday. An equation is now formed from this:
I Tu = Mo * 2
On Wednesday, she sold 6 fewer books than she did on Tuesday. An equation is now formed from this:
II We = Tu - 6
During the three days Rachel sold 19 books. An equation is now formed from this:
III Mo + Tu + We = 19
The task says that you should just use one equation to find out how many books were sold on Monday. So take the last equation and replace Tu and We with terms in which Mo occurs.
Substitute equation I into equation III:
IIIa Mo + Mo*2 + We = 19
Replace Tu in Equation II with Equation I:
II a We = Mo * 2 - 6
Substitute equation IIa into equation IIIa:
IIIb Mo + Mo * 2 + Mo * 2 - 6 = 19
Now the equation is converted to Mo (Mo = m):
m + m * 2 + m * 2 - 6 = 19 | + 6
m + 2 m + 2 m = 25
5 m = 25 | : 5
m = 5
Which is larger, 3.2 x 10^4 or 3.2 x 10^5
Answer:
3.2 x 10^5
Step-by-step explanation:
Answer:
3.2 x 10^5
Step-by-step explanation:
it had a bigger exponent.
A psychology professor wants to know whether verbal ability is related to memory quality in current first-year students at her small college. Participants in the study (first-year students at her college) complete an online memory task. The students are first shown a list of 60 words. Next they are shown a list of 10 words that were on the original list. Then they are asked to identify the words on the second list that appeared on the original list. She uses the percentage of words that were correctly recognized on the original list as her measure of memory quality. She also asks the students to report several characteristics such as their age, gender, and verbal SAT score. Each of the 750 first-year students (338 males and 412 females) at her school volunteers to participate. The professor chose 75 students at random to complete the memory task and answer the questions. The average percentage of words that were correctly recognized on the original list was 68%. The professor infers that if all 750 first-year students had completed the study, the results would show that an average of 68% (plus or minus sampling error) of the words were correctly recognized as being on the original list. Which of the following are variables in the study? Check all that apply.
A. The students' verbal SAT scores
B. The students' percentage of words that were correctly recognized on the original list
C. The 75 students
D. The 750 students
Answer:
The variable are
A and B
Step-by-step explanation:
Generally we can define a variable as a name of a placeholder representing a value now considering the option to be selected from we see that
The students' verbal SAT scores is a variable because it is a phrase or a place holder that represent a value (in the is case a numerical value) which the score its self
The second option The students' percentage of words that were correctly recognized on the original list is also a variable because it is a placeholder of a name (in this case a phrase ) that represented the actual value itself
The third option The 75 students is not a variable because it is not representing any value but itself is the value
The third option The 750 students is not a variable because it is not representing any value but itself is the value
An animal shelter has a ratio of dogs to cats that's 3:2. If there are 45 animals at the shelter, how many
dogs are there?
A. 15
B. 90
C. 20
D. 45
Which number is divisible by both 5 and 6?
O A) 132,359
OB) 142,645
OC) 164,780
OD) 193,560
Answer: D/193,560
Step-by-step explanation: 193,560 divided by 5 = 38712
193,560 divided by 6 = 32260
Answer:
D
Step-by-step explanation:
GIVING EXTRA POINTS AND BRAINLIEST
Answer:
1. d<=200
2. f>=35
Step-by-step explanation:
Answer:
d ≤ 200
f ≥ 35
Step-by-step explanation:
"no more than 200 " means it can be equal to or less than 200. Therefore, we would use the "less than or equal to" sign, or "≤". We would put 200 at the end as it is no more than 200 feet, so 200 is the max.
"at least 35" means it is equal to or more than 35. Therefore, we would use the "greater than or equal to sign" or "≥". Since it is talking about 35 miles, we put the 35 at the end with the sign pointing away from it since 35 is the lesser number.
Remember, the "mouth" or opening of the equality sign always points to the greater or bigger number. You can think of it as an alligator wanting to eat the bigger number.
Hope this helps! :)
Coffee beans sell for $8.00 per pound. How much would 5 1 Over 4
pounds of coffee beans cost?
In Belmont it snowed 1 inch in the morning and 1/5 of an inch in the afternoon. What was the total amount of snowfall ?
Answer:
11/5 or 1 and 2/10
Step-by-step explanation:
9514 1404 393
Answer:
1 1/5 inches
Step-by-step explanation:
It should come as no surprise that the sum of 1 and 1/5 can be written as the mixed number 1 1/5.
Recognizing that 1 = 5/5, the sum of 1 and 1/5 can also be written as the improper fraction ...
1 1/5 = 5/5 +1/5 = (5+1)/5 = 6/5
The total snowfall was 1 1/5 or 6/5 inches.
what is the slope of the line that goes through the points (-3,8) and (0,23)?
Answer:
m=5 or the slope is 5
Step-by-step explanation:
This is because you use the expression y2-y1/x2-x1
While vacationing, Rosalie sees a mountain and its reflection on the still water of a lake. She draws the mountain and its reflection as a projection on the coordinate grid, treating the x-axis as the line of reflection. In her drawings, she represents the summit of the mountain using the coordinates (-6,8) .
What are the coordinates of the summit in her projection?
will mark brainlest
Answer:
I would say (2,-9) is her projection
Answer:
ok bet my niqgqa
Step-by-step explanation:
Andy saved $80 over the summer from his part-time job. He withdrew 30% of the money to buy new clothes. How much money does Andy have left in
the account after withdrawing the money?
Answer:
$56 I think
Step-by-step explanation:
because 30% of 80 is 24 and 80-24=56
Weights of different sandwiches in two lengths are shown in the table.
Weight of Sandwiches by Length of Roll
6-inch Roll 12-Inch Roll
3
Cheese sandwich
e
Chicken salad sandwich
3
Ib
4
1
Egg salad sandwich
Ib
Vegetable sandwich
Which sandwich's weight is proportional to its length?
O cheese sandwich
O
chicken salad sandwich
o egg salad sandwich
o vegetable sandwich
Answer:
Egg salad sandwich is proportional to its length
Step-by-step explanation:
Weight of Sandwiches by Length of Roll
6-inch Roll 12-Inch Roll
Cheese sandwich [tex]\frac{1}{4}[/tex] [tex]\frac{3}{4}[/tex]
Chicken salad sandwich [tex]\frac{3}{4}[/tex] [tex]1\frac{3}{4}[/tex]
Egg salad sandwich [tex]\frac{2}{3}[/tex] [tex]1\frac{1}{3}[/tex]
For cheese sandwich proportion
[tex]\frac{6}{\frac{1}{4}}=\frac{12}{\frac{3}{4}}\\24 \neq 16[/tex]
So, Cheese sandwich weight is not proportional to its length
For Chicken salad sandwich proportion
[tex]\frac{6}{\frac{3}{4}}=\frac{12}{\frac{7}{4}}\\8 \neq \frac{48}{7}[/tex]
So, chicken salad sandwich is not proportional to its length
For Egg salad sandwich proportion
[tex]\frac{6}{\frac{2}{3}}=\frac{12}{\frac{4}{3}}\\9=9[/tex]
So, egg salad sandwich is proportional to its length
Consider the functions f(x) = 5x – 2, g(x) = 5x² + 2 and r(x) = –2x + 4.
Evaluate f(g(5)).
10 points!
Answer:
f(-2x+4) = -10x+18
Step-by-step explanation:
Answer:
733 I hope that helps! Sorry if its incorrect