In a school of 685 students, there are 385 students involved in sports teams, and there are
450 involved with the music program. There are 87 students that are not involved in either
program. There are some students involved in both programs.
a) Draw a Venn diagram to represent this situation.
b) Use the additive principle of non-mutually exclusive sets to determine the number of
students that are involved in both team sports and music
C) use the addictive principle for the probability of non-mutually exclusive events to determine the probability of a student being involved in team sports or involved in music
Answers
Answer:
A) check attached picture
B) 272
C) 0.4478
Step-by-step explanation:
From the information given ;
A) The Venn diagram of the information can be found in the attached picture.
B) Number of students involved in both team sports and music.
n(student in sports team) = 385
n(students involved in music) = 450
Number of students involved in both music and team sport = y
Number of students not involved in either team sport or music = 87
Total number of students = 650
Therefore,
n(music alone) = 450 - y
n(team sport alone) = 385 - y
Adding the following:
n(music alone) + n(team sport alone) + n( both music and team sport) + n(neither music nor team sport) = Total number of students
450 - y + 385 - y + y + 87 = 650
922 - y = 650
922 - 650 = y
y = 272
Therefore, number of students involved in both music and team sport = 272
C) probability of being involved in team sport or in music.
P(being involved in music) = (450 - 272) / 650 = 0.2738
P(being involved in team sport) = (385 - 272) / 650 = 0.1738
P(involved in both) = 272 / 650 = 0.4184
P(involved in neither) = 87 / 650 = 0.1338
P(being involved in team sport) or p(being involved in music)
P(being involved in team sport) + p(being involved in music)
0.1738 + 0.2738 = 0.4478
Related Questions
(-3)(-)-4+ (-2)(09-11)
Slove the problem
Answers
Answer:
The answer is -8
Step-by-step explanation:
(3)(-4)=-12 (-2)(-2)=4
Multiple the polynomials (3x^2+4x+4) (2x-4)
Answers
Answer:
6x³ - 4x² - 8x - 16
Step-by-step explanation:
Step 1: Distribute the 2x
6x³ + 8x² + 8x
Step 2: Distribute the -4
-12x² - 16x - 16
Step 3: Combine the 2 distributions
6x³ + 8x² + 8x - 12x² - 16x - 16
Step 4: Combine like terms
6x³
8x² - 12x² = -4x²
8x - 16x = -8x
-16
Step 5: Rewrite
6x³ - 4x² - 8x - 16
━━━━━━━☆☆━━━━━━━
▹ Answer
6x³ - 4x² - 8x - 16
▹ Step-by-Step Explanation
(3x² + 4x + 4) (2x - 4)
Distribute
3x²(2x - 4) + 4x(2x - 4) + 4(2x - 4)
Remove parentheses
6x³ - 12x² + 4x(2x - 4) + 4(2x - 4)
Collect like terms
6x³ - 12x² + 8x² - 16x + 8x - 16
6x³ - 4x² - 16x + 8x - 16
Solve
6x³ - 4x² - 8x - 16
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Please help!! Tamar is measuring the sides and angles of Triangle TUV to determine whether it is congruent to the triangle below.
Answers
Answer:
Measure of angle T = 25 degrees and TU = 12
Step-by-step explanation:
Tamar is measuring the sides and angles of Triangle T U V to determine whether it is congruent to the triangle below. For triangle K L M, side K M is 27 millimeters, side L M is 20 millimeters, and side K L is 12 millimeters. Angle K is 45 degrees, angle M is 25 degrees, angle L is 110 degrees. Which pair of measurements would eliminate the possibility that the triangles are congruent? Measure of angle T = 25 degrees and Measure of angle U = 45 degrees Measure of angle T = 110 degrees and Measure of angle V = 25 degrees Measure of angle T = 25 degrees and TU = 12 Measure of angle T = 110 degrees and UV = 27
Answer: Two triangles are congruent to each other if they have the same shape and size (i.e the same sides and angles).
The ways used to find congruence are:
1) Angle-side-angle: If two angles and an included side of a triangle is equal to the two angles and corresponding side of another triangle, then they are equal.
2) Side-side-side: If all three sides of a triangle is equal to the three sides of another triangle, then the two triangles are congruent.
3) Side angle side: If two sides and an included angle of a triangle is equal to the two sides and corresponding angle of another triangle, then they are equal.
4) Hypotenuse - leg: If the hypotenuse and one leg of a triangle is equal to the hypotenuse and leg of another triangle then they are equal.
5) Angle angle side: If two angles and an non included side of a triangle is equal to the two angles and corresponding side of another triangle, then they are equal.
Measure of angle T = 25 degrees and TU = 12 would eliminate the possibility that the triangles are congruent because if T = 25°, then the side opposite angle T (UV) is suppose to be 12
Answer:
the answer is C
Step-by-step explanation:
I got it right on my final exam on edge
Which of the following choices must be true in order for ΔABC ≅ ΔEDC by the AAS congruency theorem? ∠B ≅ ∠D ∠A ≅ ∠E AC ≅ EC AB ≅ DE
Answers
Answer:
∠A ≅ ∠E
Step-by-step explanation:
The AAS (Angle-Angle -Side) congruence theorem implies that triangles ABC and EDC are congruent if both have equal two angles and a non included side.
In the given figures,
<ACB ≅ <ECD (vertical opposite angles)
BC ≅ DC (congruence property)
<ABC ≅ <EDC (alternate angles property)
∠A ≅ ∠E (alternate angle property)
With respect to AAS congruence theorem, ∠A ≅ ∠E is the correct option.
PLEASE HELP ME! can someone explain this to me pls?
Answers
(5)^2 + b2 = (6)^2
25 + b2 = 36
-25. -25
b2 = 11
square root both sides to cancel out
and then label the missing side on the triangle = √11
and then point to the theta symbol and find sin, cos, tan, csc, sec, and cot
for example: sin (opposite/hypotenuse) = √11 /6
SOHCAHTOH
Factor 2x4 - 20x2 - 78.
Answers
Answer:
2x⁴ - 20x² - 78
To factor the expression look for the LCM of the numbers
LCM of the numbers is 2
Factorize that one out
That's
2( x⁴ - 10x² - 39)
Hope this helps
Answer:
2(x² + 3)(x² - 13)
Step-by-step explanation:
2x⁴ - 20x² - 78
Factor out 2.
2(x⁴ - 10x² - 39)
Find 2 numbers that multiply to get -39 and add to get -10. Those numbers are -13 and 3.
2(x⁴ - 13x² + 3x² - 39)
2(x² + 3)(x² - 13)
Question is down below
Answers
Answer:
a ) [tex]2 / n[/tex],
b ) [tex]15[/tex]
Step-by-step explanation:
This is a nice and short question we have here.
Given that a bag has n counters, and that one counter is blue, respectively the rest is red, if two counters are taken at random there isn't a definite percentage that one of the counters chosen is red or blue, but there is a fractional representation of this.
We could express n ( number of counters ) to form a probability of 2 / n. As you can see, two counters are taken at random over n counters, and thus we derived this fraction.
a ) [tex]2 / n[/tex]
____
Now we have this second part -
[tex]2 / n = 2 / 16,\\16 - 1 = 15[/tex]
Therefore, there are 15 red counters. Hope that helps!
Mario writes the equation (x+y ) 2 = z 2 +4( 1 2 xy) (x+y)2=z2+4(12xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
Answers
Answer:
For the drop down menu:
i) x + y
ii) z²
iii) ½ xy
The complete question related to this found on brainly (ID:16485977) is stated below:
Mario writes the equation (x+y)² = z² +4( 1/2 xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
_____finds the area of the outer square by squaring its side length.
_____finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
Find attached the diagram of the question.
Step-by-step explanation:
Pythagoras theorem is a formula that shows the relationship between the sides of a right angled triangle.
Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
From the diagram of the question.
Hypotenuse = z
Opposite = y
Adjacent = x
z² = x² + y²
Area of outer square = area of inner square + 4(area of triangles)
area of inner square = length² = (x+y)²
Expanding area of the outer square:
(x+y)² = (x+y)(x+y) = x²+xy+xy+y²
(x+y)² = x²+y²+2xy
= z² + 2xy
Area of inner square = length² = z²
Area of triangle = ½ base × height
= ½ × x × y = ½ xy
Area of outer square = area of inner square + 4(area of triangles)
(x + y)² = z² + 4(½xy )
Therefore, it is a true equation.
( x + y )² finds the area of the outer square by squaring its side length.
z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
So for the drop down menu:
i) x + y
ii) z²
iii) ½ xy
CAN SOMEONE TUTOR ME PLSSSSS ????
Answers
Answer:
[tex] \frac{105}{4} [/tex]
please see the attached picture for full solution..
hope it helps...
Good luck on your assignment..
what is -5c plus 2 less than or equal to 27. I need this for very difficult homework if anyone can help :)
Answers
Answer:
c ≥ -5
Step-by-step explanation:
-5c +2 ≤ 27
Subtract 2 from each side
-5c +2-2 ≤ 27-2
-5c ≤25
Divide by -5, remembering to flip the inequality
-5c/-5 ≥25/-5
c ≥ -5
Answer: [tex]x\geq 5[/tex]
Step-by-step explanation:
[tex]-5x+2\leq 27\\Subtract\\-5x\leq 25\\Divide\\x\geq 5[/tex]
It's important to remember that when you divide both sides of an inequality by a negative number to flip the sign.
Hope it helps <3
identify the variable expression that is not a polynomial.
A. y+23
B. 3\sqrt(x)-2
C. x^3
D. 13
Answers
Answer:
B. 3\sqrt(x)-2
Step-by-step explanation:
A polynomial cannot have a variable in the denominator
A constant is a polynomial
3\sqrt(x)-2 and this cannot be simplified to get rid of the variable in the denominator so it is not a polynomial
if y varies inversely as x and y=6 when x=8 find y when x=7
Answers
Answer:
y = 5 1/4
Step-by-step explanation:
For direct or inverse variation relation
relation between two variable and y can be expresses in form of
y = kx where k is constant of proportionality .
Only thing happens in inverse relation is that when x increases then y decreases and vice versa. That is care by constant of proportionality
__________________________________
Thus, let the inverse relation be
y = kx
given
when y = 6 then x = 8
we will plug this value in y = kx
6 = k*8
=>k = 6/8 = 3/4
Thus,
relation is
y = 3/4 x
we have to find y when x = 7 ,
lets put x = 7 in y = 3/4 x
y = 3/4 *7 = 21/4 = 5 1/4
Thus, when x = 7 then y = 5 1/4
Bottle A contains more soda than Bottle B. Pour from Bottle A into Bottle B as much soda as B already contains. Now pour from B into A as much soda as A now contains. Then pour from A into B as much soda as B now contains. Each bottle now contains 64 ounces. How many more ounces of soda were in Bottle A than Bottle B at the beginning?
Answers
Answer:
Bottle A started with 88 and bottle B started with 40
Step-by-step explanation:
To find out what they started with I got the ounces they finished with an the equation they did to get there.
Ended in 64 oz.
To get there:
A => B
B => A
A => B
Every time a pour is made the bottle to the right is doubled so I got 64 and divided it by 2 to see what B had before the pour of bottle A.
B had 32 oz. and A had 96 oz. before the last pour. I got 96 oz. because for them to end up with 64 oz. A has to have 32 oz. + 64 oz. since you are pouring 32 oz. into bottle B.
Now you have this equation:
A => B
B => A
96 oz. => 32 oz.
64 oz.
I then do the same thing I did to find 96 and 32. Since B is giving to A now it has to have more then A but it has to end up with 34 oz. for this is got 96 oz. and I divided it by 2 which got me 48. So on the second pour A started with 48 and B had to have given A 48 plus have 32 so it could end up with 34 therefore making it have 80 oz.
Now you have this equation:
A => B
80 oz. => 48 oz.
96 oz. => 32 oz.
64 oz.
For the last part to get the first ounces to answer the question you will do the same steps. Get half of 80 to see what B had before the 2nd pour which will be 40 and then you have to get 48 + 40 sine bottle A has to have the same amount of soda as B plus 48 oz. that it ends up with. This will have bottle A as 88 oz.
The Answer:
88 oz. => 40 oz.
80 oz. => 48 oz.
96 oz. => 32 oz.
Both will end up with 64 oz.
Factor completely.
a 2 + 28 a + 27
Answers
Hey there! :)
Answer:
(x + 27)(x + 1)
Step-by-step explanation:
Given:
a² + 28a + 27
Find numbers that add up to 28 and multiply to 27:
We can find that the numbers 27 and 1 add up to 28 and multiply to form 27. Therefore, the equation in factored form is:
(x + 27)(x + 1)
Answer:
(a+27)(a+1)Solution,
[tex] {a}^{2} + 28a + 27 \\ = {a}^{2} + (27 + 1)a + 27 \\ = {a}^{2} + 27a + a + 27 \\ = a(a + 27) + 1(a + 27) \\ = (a + 27)(a + 1)[/tex]
Hope this helps..
Good luck on your assignment..
Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can get at least 25% of the student population to sign a petition. So far, 82 students have signed the petition. Jose used the following steps to write an inequality that can be used to determine the number of student signatures still needed: Step 1. Declare the variable: Let x = the number of student signatures still needed. Step 2. Create a ratio equivalent to StartFraction total number of signatures needed over total number of students in the school EndFraction : StartFraction x + 82 over 426 EndFraction. Step 3. Convert 25% to a decimal: 25% = 0.25. Step 4. Write the inequality: StartFraction x + 82 over 426 EndFraction less-than-or-equal-to 0.25. What is Jose’s error? In Step 1, x should be equal to the total number of students in the school. In Step 2, the ratio should be StartFraction x over 426 EndFraction. In Step 3, the decimal should be 0.025. In Step 4, the inequality should
Answers
Answer: Step 4
Step-by-step explanation:
1. Define variable x as student signatures still needed (Correct)
[tex]2)\ \dfrac{x+82}{426}[/tex] (Correct)
3. 25% = 0.25 (Correct)
[tex]4)\ \dfrac{x+82}{426}\leq 0.25[/tex] (Error)!
The inequality symbol should be GREATER THAN or equal to (≥) because Jose needs 25% or more (not less).
Answer:
In Step 4, the inequality should be StartFraction x + 82 over 426 EndFraction greater-than-or-equal-to 0.25.
¯\_ _/¯
( ﾉ ﾟｰﾟ)ﾉ ＼(ﾟｰﾟ＼)
USE THE IMAGE ATTACHED BELOW please help me with my work answer it correctly I HAVE SO MUCH WORK DURING QUARANTINE
Answers
Answer:
Question 1:
a. The answer is B because the graph inclined really quickly and then it inclined at a much slower pace, suggesting that the person was running and then walking.
b. The answer is C because you can see on the graph that after a while, the distance from the starting point goes back to 0, indicating that the person forgot something at home.
Question 2:
a. The dashed line reaches the bottom at 15:30 so the answer is C.
b. Siobhan travels 8 km to go from home to school so the answer is 2 * 8 = 16 which is option D.
Question 3:
The answer is C because after the distance from the starting point increased, it then decreased and came back to the original point suggesting that he walked, turned around and walked back to the starting point.
Answer:
first page : a) A because it is the shortest time with no stop
b) C the graph goes up and return to the start point after a while
second page : it is at 3:30 0r 15:30
b): 8 km going to schools and 8 coming back is 16
third page it is C because he walk up a certain distance and come back to the starting point
write a function that represents the situation: A population of 210,000 increases by 12.5% each year
Answers
Answer
y= 12.5x + 210,000
Step-by-step explanation:
This is a linear function because it is increasing constantly by 12.5 percent so it will me written as y=mx+b
The value of function that represents the situation is,
⇒ P = 210,000 (1.125)ⁿ
Where, n is number of years.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The situation is,
⇒ A population of 210,000 increases by 12.5% each year.
Now, Let number of years = n
Hence, The value of function that represents the situation is,
⇒ P = 210,000 (1 + 12.5%)ⁿ
⇒ P = 210,000 (1 + 0.125)ⁿ
⇒ P = 210,000 (1.125)ⁿ
Learn more about the mathematical expression visit:
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Robert want to buy a sports cap that is on sale for 25% off if the original price is 35$ and the sales tax is 6% how much will robert need to pay for the cap
Answers
Answer: $27.825
Step-by-step explanation:
From the question, we are informed that Robert want to buy a sports cap that is on sale for 25% off and the original price is 35$. This means the price of the sports car will be:
= Original price - Discount
= $35 - (25% × $35)
= $35 - (0.25 × $35)
= $35 - $8.75
= $26.25
We are further told that there is a sales tax of 6%. The amount that Robert will need to pay for the cap will be:
= $26.25 + (6% × $26.25)
= $26.25 + (0.06 × $26.25)
= $26.25 + $1.575
= $27.825
Answer:
27.83
Step-by-step explanation:
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then she glued the pyramids' bases together to form the gemstone. The surface area of the gemstone is 520 square inches. What is the value of x? Explain.
Answers
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
25. En cada par de triangulos, las marcas iguales indican elementos congruentes. ¿Que par de triangulos es congruentre segun el criterio LAL? justifica 26.indica cual criterio se debe usar para determinar la congruencia de cada pareja de triangulos.
Answers
Answer:
i cant read spanish. sorry
Step-by-step explanation:
Round
7.8652
to 2 decimal places.
Answers
Answer:
7.87?
Step-by-step explanation:
Examine the diagram of circle C. Points Q, V, and W lie on circle C. Given that m∠VCW=97∘, what is the length of VW⌢?
Answers
Answer:
[tex] \frac{97pi}{18} m [/tex]
Step-by-step Explanation:
==>Given:
radius (r) = 10 m
m<VCW = 97°
==>Required:
Length of arc VW
==>Solution:
Formula for length VW is given as 2πr(θ/360)
Using the formula, Arc length = 2πr(θ/360), find the arc length VW in the given circle
Where,
θ = 97°
r = radius of the circle = 10 m
Thus,
Arc length VW = 2*π*10(97/360)
Arc length VW = 20π(97/360)
Arc length VW = π(97/18)
Arc length VW = 97π/18 m
Our answer is,
[tex] \frac{97pi}{18} m [/tex]
Graph the system of equations on the coordinate plane and determine the solution to
the system
y=-1/2x+5
y=2x-10
Answers
Answer:
(6,2)
Step-by-step explanation:
y=-1/2x+5
y=2x-10
-1/2 x+5 =2x-10 to find the solution y=y ( point of intersection of two lines)
-1/2 x-2x = -10-5 solve for x
-5/2 x=-15
x=-30/-5=6
y=2x- 10 substitute x in the equation to get y
y=2(6)-10
y=2
(2,3)
Dont put the other answer, it’s wrong I
did the math.
Solve: 3/x-4 >0 A.x -4 C.x>4 D.x<-4
Answers
Answer:
C. x>4
Step-by-step explanation:
3/(x-4) > 0
3>0, so
x-4 >0
x > 4
PLEASE HELP ME I WILL MAKE YOU THE FAMOUS
Which description matches the graph of the inequality y<-1/2x+5 A.a shaded region above a dashed boundary line B.a shaded region below a dashed boundary line C.a shaded region below a solid boundary line D.a shaded region above a solid boundary line
Answers
Answer:
B
Step-by-step explanation:
dashed line above the shaded area, shaded area below dashed boundary line
The equation of a line is y = 4x + 15. what is the y-intercept of the line.
Answers
Answer:
15
Step-by-step explanation:
[tex]y = 4x + 15 \\ equating \: it \: with \\ y = mx + b \\ we \: find \\ b = 15 \\ \implies \: y - intercept = 15[/tex]
Answer:
Y intercept = 15
Step-by-step explanation:
Formula we use,
→ y = mx + b
→ b = y intercept
Then the y intercept will be,
→ y = mx + b
→ y = 4x + 15
→ [ b = 15 ]
Thus, required answer is 15.
Amad was curious if triangles \triangle ABC△ABCtriangle, A, B, C, and \triangle EDF△EDFtriangle, E, D, F were congruent. He was able to map one figure onto the other using a reflection and a rotation. Amad concluded: "I was able to map \triangle ABC△ABCtriangle, A, B, C onto \triangle EDF△EDFtriangle, E, D, F using a sequence of rigid transformations, so the figures are congruent."
Answers
Answer:
There is no error, Amad is correct.
Step-by-step explanation:
Khan Academy Checked.
Amad had done no error. His conclusion is true.
What is Congruency?Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.
For example,
In the figure given above, Δ ABC and Δ PQR are congruent triangles. This means that the corresponding angles and corresponding sides in both the triangles are equal.
Sides: AB = PQ, BC = QR and AC = PR;
Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.
Therefore, Δ ABC ≅ Δ PQR
The following are the congruence theorems or the triangle congruence criteria that help to prove the congruence of triangles.
SSS (Side, Side, Side)SAS (side, angle, side)ASA (angle, side, angle)AAS (angle, angle, side)RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)As, from the given cases the prediction of congruency of two triangles is correct. There is no error he made.
Hence, Amad had not made any error.
Learn more about congruency here:
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how to solve: f(-1)=(1/4)^x
Answers
Answer:
f(-1) = (1/4)^x = 4
Step-by-step explanation:
When solving a f(x) equation, the x represents the number that will be used to replace x in the equation. So, from the equation, the value of x is -1. You would plug in -1 for x.
f(-1) = (1/4)^-1
Solve the exponent.
f(-1) = 4
So, the value of f(-1) is 4.
SOMEONE HELPPP PLEASEEEE
Answers
Answer:
a. Domain = All real numbers
Range = y ≥ 2
b. Domain = -4 < x ≤ 4
Range = 0 ≤ y < 4
Please help me with this question (Will get brainlist)
Answers
Answer:
169=169
Step-by-step explanation:
The pythagoras theorem states that if
[tex] {a}^{2} + {b}^{2} = {c }^{2} [/tex]
Then the triangle is a right triangle
So
[tex]{5}^{2} + {12}^{2} = {13}^{2} [/tex]
[tex]25 + 144 = 169[/tex]
[tex]169 = 169[/tex]
Therefore A is a right triangle
Answer:
Step-by-step explanation:
The pythagorian theorem :now the longest edge is 13 cm so : 13²must be equal to 5²+12²
5²+12²= 169[tex]\sqrt{169}[/tex]= 13so this triangle must be right angled