An elementary school is offering 3 language classes: one in Spanish, one inFrench, and one in German. The classes are open to any of the 100 students inthe school. There are 28 students in the Spanish class, 26 in the French class,and 16 in the German class. There are 12 students that are in both Spanish andFrench, 4 that are in both Spanish and German, and 6 that are in both Frenchand German. In addition, there are 2 students taking all 3 classes.(a) If a student is chosen randomly, what is the probability that he or she isnot in any of the language classes
Answer:
0.5 = 50% probability that he or she is not in any of the language classes.
Step-by-step explanation:
We treat the number of students in each class as Venn sets.
I am going to say that:
Set A: Spanish class
Set B: French class
Set C: German class
We start building these sets from the intersection of the three.
In addition, there are 2 students taking all 3 classes.
This means that:
[tex](A \cap B \cap C) = 2[/tex]
6 that are in both French and German
This means that:
[tex](B \cap C) + (A \cap B \cap C) = 6[/tex]
So
[tex](B \cap C) = 4[/tex]
4 French and German, but not Spanish.
4 that are in both Spanish and German
This means that:
[tex](A \cap C) + (A \cap B \cap C) = 4[/tex]
So
[tex](A \cap C) = 2[/tex]
2 Spanish and German, but not French
12 students that are in both Spanish and French
This means that:
[tex](A \cap B) + (A \cap B \cap C) = 12[/tex]
So
[tex](A \cap B) = 10[/tex]
10 Spanish and French, but not German
16 in the German class.
This means that:
[tex](C - B - A) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 16[/tex]
[tex](C - B - A) + 2 + 4 + 2 = 16[/tex]
[tex](C - B - A) = 8[/tex]
8 in only German.
26 in the French class
[tex](B - C - A) + (A \cap B) + (B \cap C) + (A \cap B \cap C) = 26[/tex]
[tex](B - C - A) + 10 + 4 + 2 = 26[/tex]
[tex](B - C - A) = 10[/tex]
10 only French
28 students in the Spanish class
[tex](A - B - C) + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 16[/tex]
[tex](A - B - C) + 10 + 2 + 2 = 28[/tex]
[tex](A - B - C) = 14[/tex]
14 only Spanish
At least one of them:
The sum of all the above values. So
[tex](A \cup B \cup B) = 14 + 10 + 8 + 10 + 2 + 4 + 2 = 50[/tex]
None of them:
100 total students, so:
[tex]100 - (A \cup B \cup B) = 100 - 50 = 50[/tex]
(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?
50 out of 100. So
50/100 = 0.5 = 50% probability that he or she is not in any of the language classes.
Consider the function graphed below.
What is the average rate of change of the function over the interval [1, 3] ?
A.36
B. 48
C.72
D.96
Answer:
A. 96
Step-by-step explanation:
By using slope formula we got that average rate of change of the function over the interval [1, 3] is 48 .
What is the average rate of change?the rate at which one variable of a function changes in relationship to another variable is called average rate of change.
Here we can see in graph that
when x =1 y=12
and when x= 3 ,y=108
Now we know that rate of change is same as slope of straight line passing through that points
So average rate of change can be calculated as
[tex]=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]=\frac{108-12}{3-1}\\\\[/tex]
[tex]\frac{96}{2}[/tex]
=48
By using slope formula we got that average rate of change of the function over the interval [1, 3] is 48 .
To learn more about rate of change visit :https://brainly.com/question/8728504
Which of the following are true statements? Select two that apply.
Answer:
Options A and C are correct answers
Step-by-step explanation:
A) [tex] \angle 5\: and \:\angle 1[/tex] are complementary.
C) [tex] \angle 3\: and \:\angle 4[/tex] form a linear pair.
Hope it helps you in your learning process.
At the Demarest Mountain ski slope lounge, they serve hot cocoa. A serving of
hot cocoa uses 1 and a half tablespoons of cocoa. The large jar holds 90
tablespoons of cocoa mix, but the jar is half empty. How many more servings of
Hot Cocoa can they give out?
First one to answer gets BRAINLIEST no cap look at the picture.
Answer:
your answer will be 56 square millimeters
Step-by-step explanation:
hope it helps
Answer:
34 square meaters.
Step-by-step explanation:
Look at picture below!
There are three numbers for the combination to the store's safe. The first number is 17. The two numbers can be multiplied together to give a product of 28. What are all of the possibilities for the other two numbers? IT IS MULTIPLICATION BTW
Answer:
1 28
2 14
4 7
Step-by-step explanation:
7 4
14 7
28 1
...........
5th grade math. correct answer will be marked brainliest.
Answer:
1
12 ------
3
Find each product mentally, using the distributive property, 4x51/8. (giving brainliest)
Answer:
25.5
Step-by-step explanation:
4 x 51 / 8
204/8
25.5
Answer:
Step-by-step explanation:
4×15/8 = 4×(1+⅞) = 4×1 + 4×⅞ = 4 + 7/2 = 4 + 3.5 = 7.5
Please help
A 136
B 208
C 352
D 576
Answer im not in grade
Step-by-step explanation:
4) Let a represent "x is a multiple of 3".
Let b represent "x is odd".
When x is 36, which of the following is true?
Step-by-step explanation:
When x=36, only the first statement is true (x is a multiple of 3). this is because 12×3= 36
36 is not odd, making the other statement false
The total weight of 9 bags of potatoes is 36 kilograms each bag weights the same amount what is the weight in grams of each bag of potatoes
Answer:
4000
Step-by-step explanation:
36kg = 36000g
36000g/9 bags = 4000g
The weight of one bag of potatoes is 4 Kg,
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The total weight of 9 bags of potatoes is 36 kilograms.
Then, weight of one bag of Potato is
= 36/9
= 4 Kg
Thus, One bag weigh 4 Kg.
Learn more about Unitary Method here:
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Pls help me show work too:(
Use the distance formula to find the distance between (2,1) and (6,8). Round to the tenths place. thats the question there isn't any picture or graph
please help!:(
Answer this correctly I’ll give brainalist + 10 points
The number of that grow sugar beet =12
Answer:
I think question is not proper
you should check it again
hope your day will fine
Answer:
Whatttt
Step-by-step explanation:
an electronics store is having a 20%-off on all cell phones. the original price of a cell phone is x dollars. which expression represents the sale price of a cell phone?
a. x - 0.2
b. x - 0.8
c. 0.2*x
d. 0.8*x
Answer: x*.2
Step-by-step explanation:
When you are trying to find the sale price you want to multiply the origanal price of the cellphone to the percentage you are getting off. Hope this helped!
The sum of 6 times a number and 4 is 9
Sally earns graduated commission on her sales each month. She earns 6% commission on the first $45,000 in sales and 8% on anything over that. If Sally had $51,000 in sales this month, how much commission did she earn?
a.
$4,080
b.
$3,180
c.
$3,060
d.
$2,820
Answer:
Sally earns graduated commission on her sales each month. She earns 6% commission on the first $45,000 in sales and 8% on anything over that. If Sally had $51,000 in sales this month, how much commission did she earn?
a. ) $4,080 b. ) $3,180 <<<CORRECT c. ) $3,060 d. ) $2,820
Step-by-step explanation:
Edge 2021
Rashads teacher buys paperback books for her classroom library. Each book costs $6, and she spends a total of $150. Which equation models the number of books, n, she buys? A. 6n=150 B. n/6=150 C.150-n=6 D. 6•150=n
Answer:
A
Step-by-step explanation:
6n=150
5x + 4 = 3x + 10 how would you solve for the value of x? How would you prove your solution is correct? How would you prove another value is incorrect? Explain in as much detail as possible.
5x+3=3x+10 the first thing we're going to do it to subtract 3 from both sides which would look like this
5x+3-3x=10 (the minus because it changed place)
from 5x and 3x we get 2x so the next step is 2x=10-3 which is 7
so now we have
2x=7
x=7/2
Answer:
x=3
Step-by-step explanation:
5x+4 = 3x+10
2x = 6
therefore, x = 3
Verification:
5 * 3 + 4 = 3 * 3 + 10
15+4 = 9+10
19=19
Therefore, LHS= RHS
Hence Proved!
A rectangle has a length of (x+3) feet and a width of 1/2x feet.
If the perimeter is 21 feet, what is the length of the rectangle?
Allison had 310 rocks in the rock collection after three months, her collection increases by 40% how many rocks does she have now?
Answer:
434
Step-by-step explanation:
310 times .4 (percentage) = 124 which is how much she gained, then you add that onto the original amount to find how many she has now, which is 434
WILL MARK BRAINLEIST HELPP PLEASEEEE
Answer:
15
Step-by-step explanation:
9x + 25 + x + 5 = 180
Add numbers = (25 + 5 = 30)
9x + 30 + x = 180
Combine like terms = (9x + x = 10x)
10x + 30 = 180
Subtract 30 from each side (10x + 30 - 30 = 180 - 30)
10x = 150
Divide 10 from each side (10x/10 = 150/10)
x = 15
A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members use each facility. A survey of the membership indicates that 75% use the golf course, 50% use the tennis courts, and 5% use neither of these facilities. One club member is chosen at random. What is the probability that the member uses the golf course but not the tennis courts
Answer:
0.45 = 45% probability that the member uses the golf course but not the tennis courts
Step-by-step explanation:
I am going to solve this question using the events as Venn sets.
I am going to say that:
Event A: Uses the golf courses.
Event B: Uses the tennis courts.
5% use neither of these facilities.
This means that [tex]P(A \cup B) = 1 - 0.05 = 0.95[/tex]
75% use the golf course, 50% use the tennis courts
This means, respectively, by:
[tex]P(A) = 0.75, P(B) = 0.5[/tex]
Probability that a member uses both:
This is [tex]P(A \cap B)[/tex]. We have that:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
So
[tex]P(A \cap B) = 0.75 + 0.5 - 0.95 = 0.3[/tex]
What is the probability that the member uses the golf course but not the tennis courts?
This is [tex]P(A - B)[/tex], which is given by:
[tex]P(A - B) = P(A) - P(A \cap B)[/tex]
So
[tex]P(A - B) = 0.75 - 0.3 = 0.45[/tex]
0.45 = 45% probability that the member uses the golf course but not the tennis courts
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
B) one solutionStep-by-step explanation:
to understand thisyou need to know about:linear equationPEMDAStips and formulas:[tex]\sf\text{a system of linear equation has only one solution if $\frac{a_1}{a_2}\neq \frac{b_1}{b_2}$}[/tex]given:[tex] \begin{cases}2x - 4y = - 1 \\ 8x - 11y = - 19 \end{cases}[/tex]let's solve:[tex] \sf substitute \: the \: value \: of \: a \: b : \\ \frac{2}{8} \ne \frac{ - 4}{ - 11} \\ [/tex][tex]\text{$\therefore$ the system of linear equation has only one solution}[/tex]
16. On a yachting trip in the South Pacific, you discover a previously unknown island. You notice that there is a population of especially fluffy and particularly cute long-eared rabbits living there. These rabbits seem to have no predators at all on the island, and their mating habits seem to be perfectly random. When they are first surveyed, they have an average ear length of about 18 cm. When they are sampled again in five years, what will likely be true of their ear length
Answer: Their ear length will be thesame because there's no force of evolution.
Step-by-step explanation:
Based on the information given in the question as we are informed that the rabbits have no predators and that their mating habits seem to be perfectly random.
We should note that when they are sampled again in five years, due to the fact that there's no source of evolution, their ear length will be thesame. Also, their offspring number will be thesame as well.
what are prime factors
Answer:
Prime Factors is a factor of a given integer which is also a prime number.
7x10+2x1+6x1/10+3x1/1000
Answer:72.603
Step-by-step :
70 + 2 + 6 ÷ 10 + 3 ÷ 1000
=72.603
Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800; SSTR = 4560.
Set up the ANOVA table for this problem (to 2 decimals, if necessary).
Source of Variation Sum of Squares Degrees of Freedom Mean Square F
Treatments
Error
Total
Use {Exercise 13.07} Three different methods for assem = .05 to test for any significant difference in the means for the three assembly methods.
Calculate the value of the test statistic (to 2 decimals).
The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 11
What is your conclusion?
SelectConclude not all means of the three assembly methods are equalCannot reject the assumption that the means of all three assembly methods are equal
Item 12are my calculations correct?
Given :
Number of methods, k = 3
Number of the observations, n = 30
Degrees of freedom Treatment = k - 1
= 3 - 1 = 2
Degrees of freedom for error = n - k
= 30 - 3 = 27
[tex]$SSTR = 4560, \ SST = 10800$[/tex]
[tex]$SSE = SST - SSTR$[/tex]
= 10800 - 4560
= 6240
[tex]$SSE_{treatment} = MS_{treatment } \times DF_{treatment}$[/tex]
[tex]$MS_{treatment} = \frac{4560}{2}=2280$[/tex]
[tex]$MS_{error}=\frac{SSE_{error}}{DF_{error}}$[/tex]
[tex]$=\frac{6240}{27}=231.1$[/tex]
[tex]$F=\frac{MS_{treatment}}{MS_{error}}$[/tex]
[tex]$=\frac{2280}{231.1}=9.865$[/tex]
Source variation Sum of square Degrees of freedom Mean square F
Treatment 4560 2 2280 9.8653
Error 6240 27 231.11111111
Total 10800
The critical value of F for the 0.05 sig level and df (227) is 3.354
Since the test stat > critical value of F, so we reject null hypothesis and state that there is a significant difference in the means of the three assembly methods.
Type the answer in the box.
d = 6 y = 10 g = 8
Step-by-step explanation:
[tex](6) + \frac{1}{2} (10 + 8)[/tex]
[tex]6 + \frac{1}{2} (18)[/tex]
[tex]6 + \frac{18}{2} [/tex]
[tex]6 + 9[/tex]
[tex]15[/tex]
Answer:
15
Step-by-step explanation: