Treating the amounts as Venn sets, we have that 161 students signed up for only Math, considering that 40 did not sign for any.
What are the Venn sets?For this problem, we consider the following sets:
Set A: Students that have signed up for Arts.Set B: Students that have signed up for Humanities.Set C: Students that have signed up for Math.4 students had signed up for all three courses students, hence:
(A ∩ B ∩ C) = 4.
8 students had signed up for both a Math and Humanities, hence:
(B ∩ C) + (A ∩ B ∩ C) = 8
(B ∩ C) = 8.
18 students had signed up for both a Math and Language Arts, hence:
(A ∩ C) + (A ∩ B ∩ C) = 18
(A ∩ C) = 14.
9 students had signed up for both a Language Arts and Humanities, hence:
(A ∩ B) + (A ∩ B ∩ C) = 9
(A ∩ B) = 5.
36 students had signed up for a Humanities course, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 36
B + 5 + 8 + 4 = 36
B = 19.
51 students had signed up for a Language Arts course, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 36
A + 5 + 14 + 4 = 51
A = 28.
Considering that there are 279 students, and supposing 40 did not sign for any course, we have that:
A + B + C + (A ∩ B) + (B ∩ C) + (A ∩ C) + (A ∩ B ∩ C) + 40 = 279.
28 + 19 + C + 5 + 8 + 14 + 4 + 40 = 279
118 + C = 279
C = 161
161 students signed up for only Math, considering that 40 did not sign for any.
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Decide what values of the variable cannot possibly be solutions for the equation. Do not solve.
By inspecting the denominator, the values of x cannot be solutions of the rational equation are x₁ = - 3 and x₂ = 2.
What values does lead to an indetermination in a rational equation?
A rational equation is an expression of the P(x) / Q(x), where P(x) and Q(x) are the equations of the numerator and the denominator functions. The rational equation becomes undefined for all x-values such that Q(x) = 0. Then, we must look up for all values of x such that:
x² + x - 6 = 0
x² + [3 + (- 2)] · x - 6 = 0
x² - 2 · x + 3 · x - 6 = 0
x · (x - 2) + 3 · (x - 2) = 0
(x + 3) · (x - 2) = 0
x₁ = - 3 ∨ x₂ = 2
The values of x cannot be solutions of the rational equation are x₁ = - 3 and x₂ = 2.
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Eli runs a distance of 3 miles in 2/5 of an hour. jess runs a distance of 4/5 mile in 1/10 of an hour. who had the faster speed
Jess had a faster speed of 8 miles/hour
Given:
3 miles in 2/5 hour
4/5 miles in 1/10 hour
To find the quotient, we must switch to the inverse approach,
where 2/5 becomes 5/2 and 1/10 becomes 10/1.
For Eli:
A distance of 3 miles is covered in 2/5 of an hour.
3 miles equals 2/5*1
3 miles equals 2/5 hour
The inverse amount is multiplied as
3*5/2 miles = 1 hour.
7.5 miles
Eli moves at a 7.5 mph speed.
For Jess:
1/10 of a mile is covered in 4/5miles.
1/10 * 1 hour times 4/5 miles
1/10 hour equals 4/5 miles.
The inverse number is multiplied as follows: 4/5 * 10/1 = 1 hour.
40 miles at a speed of 5 miles per hour.
1 hour Equals 8 miles
Jess's speed is 8 miles per hour.
Hence, Jess had a faster speed of 8 miles per hour
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Simplify the expressions:
−8y³ x 5y8
Hi! Your answer is 11. When multiplying terms with exponents, the exponents add up.
Step-by-step explanation:
You want to multiply the terms with the exponents. You should get 3 and 8, add those up and you will get 11.
Hope this helps! Have a good day :)
IF YOUR GOOD AT MATH PLEASE HELP ME PLEASE!
Here are the inequalities:
x ≥ 8
x < 3
x ≤ 3
x ≤ 8
x < 8
x ≥ 3
What are the inequalities?Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
for example :
2 < 3 means 2 is less than 3
3 >2 means 3 is greater than 2
Steps to interpret an inequality graph :
If the circle above the number is colored, the inequality sign to use is either ≥ or ≤.
If the circle above the number is not colored, the inequality sign to use is either < or >.
If the arrow is pointing to the left, the inequality sign would either be ≤. or <.
If the arrow is pointing to the right, the inequality sign would either be ≥ or >.
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How many different 10-letter words (real or imaginary) can be formed from the following letters? E, T, A, R, N, I, T, C, F, R Question content area bottom Part 1 enter your response here ten-letter words (real or imaginary) can be formed with the given letters.
Answer:
10! or 3628800 words=============================
Given 10 letters and we are looking for the number of 10-letter words.
This is about the permutation of 10:
[tex]_{10}P_{10} = 10! = 3628800[/tex]What is the solution to the system of equations?
7x-y=6
-7x+y=-6
Answer:
x= 7/ y+6
Step-by-step explanation:
Add y to both sides.
7x=6+y
The equation is in standard form.
7x=y+6
Divide both sides by 7.
7
7x = 7/y+6
Dividing by 7 undoes the multiplication by 7.
Step-by-step explanation:
that's what I think it isx=7/y+6
NEED OF IMMEDIATE HELP
Answer:
There are no sampling errors, as all numbers add up to 100, however, there is a bias, as the highest number is 52 for movies, and the person who conducted the survey was a movie theater manager to his own customers.
7th- grade question
7. Billy cut the grass for 3/5 of an hour on Monday and 3/10 of an hour on
Tuesday. What fraction of an hour did he spend cutting grass for the two
days?
A. 1/5
B. 2/5
C. 5/10
D. 9/10
Answer:
The answer is c because if you multiply 3/5 and 3/10 by doing butterfligt
A 75% antifreeze solution is to be mixed with a 90% antifreeze solution to get 360 liters of a 85% solution. How many liters
of the 75% and how many liters of the 90% solutions will be used?
In linear equation , 240 liters of 90% solutions will be used.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Let x be the quantity of 75% antifreeze solution and y be the quantity of 90% antifreeze solution,
Since, the total quantity of the mixture = 360,
⇒ x + y = 360 ----- (1),
Also, the resultant solution is of 85% antifreeze solution,
⇒ 75 % of x + 90% of y = 85% of 360
0.75x + 0.90y = 0.85 × 360
0.75x + 0.90y = 306
75x + 90y = 30600 -----(2),
Equation (2) - 75 × equation (1),
We get,
15y = 3600
⇒ y = 240
Hence, 240 liters of 90% solutions will be used.
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The sum of a daughter and mother's age is 55. The age of the daughter is the
mother's age reversed. Find the age of the daughter if the age of the mother is
greater than 40 years.
{x€N | 25 ≤ x² < 50}
Answer:
x = { 5; 6; 7}
Step-by-step explanation:
25 ≤ 25 < 36 < 49 < 50
=> x² = {25; 36; 49}
Because x€N => x = {5; 6; 7}
Add (4) and (−15) if right i will give brainliest
−11
−19
19
11
-11 is the answer to this question
Answer:-11
Step-by-step explanation:
-15 + 4 = -11
help me out please!!!!
Answer:
I believe the Answer is C.
Step-by-step explanation:
Kiara and Donovon attend different middle schools. They both went to their schools’ winter carnivals. Kiara paid a $5 entrance fee and bought several tickets costing $0.75 each for games and rides. Donovon paid a $7 entrance fee and bought several tickets costing $0.50 each for games and rides. How many tickets, , must Kiara and Donovan each buy in order for the cost of attending their school carnivals to be the same?
Using linear functions, it is found that they have to buy 8 tickets for the costs to be the same.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we consider that:
The entrance fee is the intercept.The cost for carnivals(games/rides) is the slope.Hence the cost functions for Kiara and Donovon are given, respectively, by:
K(x) = 5 + 0.75x.D(x) = 7 + 0.5x.The costs will be the same when:
K(x) = D(x)
5 + 0.75x = 7 + 0.5x.
0.25x = 2
x = 2/0.25
x = 8.
They have to buy 8 tickets for the costs to be the same.
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can I get help with this Problem
PLEASE ANSWERING THIS QUESTION QUICKLY!
When f(x)=9x^2-x-2, evaluate f(-3)
f(-3)= (blank)
Explain your answer!
Show your work!
Do not spam answers!
No nonsense answers!
No incorrect answers!
Thanks!
Answer:
f(-3)= 9(-3)^2+3-2= 9(9)+3-2= 81+1 = 82
4x = y + 3
8x - 3= 2y
Graph the system
At the movie theatre, child admission is 5.50 and adult admission is 9.20. On Monday, three times as many adult tickets as child tickets were sold, for a total sales of 662.00 . How many child tickets were sold that day?
A cube-shaped box has a side length of 6n³ centimeters. Amelia has several cube-shaped blocks with a side length of 2n centimeters that she needs to store in the box. what is the volume of one block? what is the volume of the box
The volume of blocks is 8n³ cm³ and volume of box is 216 n⁹ cm³.
According to the question we have been given that the
side length of the cube shaped box = 6n³ cm
side length of the cube shaped blocks = 2n cm
We need to find the volume of the box and the blocks.
The formula for the volume of cube is
V = (s)³ cubic units.
where, s = side length of the cube
Now putting the required values in the above formula we get
volume of box = (6n³)³ cm³
= 216 n⁹ cm³
volume of the blocks = (2n)³ cm³
= 8n³ cm³
Hence the volume of blocks is 8n³ cm³ and volume of box is
216 n⁹ cm³.
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Express 60 as the product of its prime factors
Write the factors in as ascending order and give your answer in index form
Answer:
2^2 × 3 × 5
Step-by-step explanation:
hope this works :)
Multiply.
9/4 ⋅ 14
A. 23/4
B. 28
C. 63/2
D. I don't know.
Answer:
C. 63/2
Step-by-step explanation:
[tex] \frac{9}{4} \times 14 \\ = \frac{9}{4} \times \frac{14}{1} \\ = \frac{9 \times 7}{2} = \frac{63}{2} \\ please \: if \: found \: helpful \: rate \: brainliest.[/tex]
The answer is 63/2
I got 100% on the test
I hope this helps!
Proof that this answer is correct and not fake
find values for x so that the perimeter of the figure is less than 100 meters
Answer:
x=21
Step-by-step explanation:
21*2+25*2=92
Answer:
x < 23
Explanation:
perimeter of a rectangle = 2(length + width)
Here given:
Length = x + 4Width = xSetting equation:
[tex]\sf \rightarrow 2(x + 4 + x) < 100[/tex]
[tex]\sf \rightarrow 2(2x + 4) < 100[/tex]
[tex]\sf \rightarrow 4x + 8 < 100[/tex]
[tex]\rightarrow \sf 4x < 100 - 8[/tex]
[tex]\sf \rightarrow4x < 92[/tex]
[tex]\sf \rightarrow x < 23[/tex]
Please Help Me! Will be brainlest
E=-7g^4+3g^2h^2-11h^4
F=6g^4-13g^2h^2+8h^4
E+F=
The addition of the given expression "E = - 7g⁴ + 3g²h² - 11g⁴" and "F = 6g⁴ - 13g²h² + 8h⁴" is "- g⁴ - 10g²h² - 3g⁴"
ExponentE = - 7g⁴ + 3g²h² - 11g⁴
F = 6g⁴ - 13g²h² + 8h⁴
E + F = (- 7g⁴ + 3g²h² - 11g⁴) + (6g⁴ - 13g²h² + 8h⁴)
= - 7g⁴ + 3g²h² - 11g⁴ + 6g⁴ - 13g²h² + 8h⁴
collect like terms= -7g⁴ + 6g⁴ + 3g²h² - 13g²h² - 11g⁴ + 8h⁴
evaluate= - g⁴ - 10g²h² - 3g⁴
Therefore, the addition of the given expression "E = - 7g⁴ + 3g²h² - 11g⁴" and "F = 6g⁴ - 13g²h² + 8h⁴" is "- g⁴ - 10g²h² - 3g⁴"
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You get hired for a job through ACME Employment Agency. You signed a contract that requires you to pay 20% of your first 6 weeks pay. The job pays you $42,700 per year. How much must you pay ACME for their services?
if DF = 9x-39 find EF
DE = 47
EF = 3X+10
The length of the line segment EF is 106.
The distance between the end points of DF is equal to 9x-39.The distance between the end points of DE is equal to 47.The distance between the end points of EF is 3x + 10.Applying the logic that the line segments are a part of the same straight line, we can conclude thatThe length of the line segment DF is equal to the sum of the lengths of the line segments DE and EF.DF = DE + EF.9x - 39 = 47 + (3x + 10)9x - 6x = 47 + 10 + 393x = 96x = 32The length of the line segment EF is 3*32 + 10.The length of the line segment EF is 96 + 10.Thus, the length of the line segment EF is 106.To learn more about distance, visit :
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7 grade
1. Andrea walked 1/2 miles in 1/3 of an hour at a constant speed. What was that speed?
A. 1 miles per hour
B.1.25 miles per hour
C.1.5 miles per hour
D.2.5 miles per hour
Answer:
C
Step-by-step explanation:
0.5 of a mile in 20 minutes
60/20=3
0.5*3=1.5
Correct answer is C
center at (2, -2) and twice the area of the circle (x, -7)² + (y, -7)² =7
Answer:
[tex](x-2)^2+(y+2)^2=14[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the center of the circle.r is the radius of the circle.Given equation:
[tex](x-7)^2+(y-7)^2=7[/tex]
Therefore:
center = (7, 7)radius = √7Area of a circle
[tex]\sf A=\pi r^2[/tex]
where:
r is the radius.Therefore, the area of a circle with radius √7 is:
[tex]\implies \sf Area=\pi \left(\sqrt{7}\right)^2=7 \pi\:\:square\:units[/tex]
Therefore, a circle with twice the area would be:
[tex]\implies \sf Area = 2 \cdot 7 \pi = 14 \pi \:\: square\:units[/tex]
Therefore, its radius would be:
[tex]\begin{aligned}\implies \sf \pi r^2 & = \sf14 \pi\\\sf r^2 & = \sf 14\\\sf r & = \sf \sqrt{14}\end{aligned}[/tex]
So the equation of a circle with a center at (2, -2) and a radius of √14 is:
[tex]\implies (x-2)^2+(y-(-2))^2=\left(\sqrt{14}\right)^2[/tex]
[tex]\implies (x-2)^2+(y+2)^2=14[/tex]
Enter the value of 3/4(8.8)=
Answer:
6.6 is the answer
Step-by-step explanation:
Hope it helps you
Evaluate-nx + x when x = 2.
Answer:
-2n + 2
Step-by-step explanation:
They give you the X value which is 2
All you do is substitute
-2n + 2
Hope this helped
HELPPPOOOOMEEEEEEW PLEASE
Answer: 124 degrees
Step-by-step explanation:
JKL=YKL+JKY
10x+14=6x-6+64
10x+14=6x+58
4x+14=58
4x=44
x=11
JKL=10x+14
JKL=10(11)+14
JKL=110+14
JKL=124 degrees