[tex]\dfrac{10} 7 + \dfrac 2{20} +7 - 4\\\\\\=\dfrac{20(10)+7(2)}{140}+3\\\\\\=\dfrac{200+14+140(3)}{140}\\\\\\=\dfrac{634}{140}\\\\\\=\dfrac{317}{70}[/tex]
Please help ASAP!
George believes the Art Club students at his school have an unfair advantage in being assigned to the art class they request. He asked 500 students at his school the following questions: "Are you in the Art Club?" and "Did you get the art class you requested?" The results are shown in the table below:
Art Club Not in Art Club Total
Received art class requested 100 265 365
Did not get art class requested 65 70 135
Total 165 335 500
Help George determine if all students at his school have an equal opportunity to get into the art class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
165 total students in art club. 100 of those got the requested class.
100/165 = 0.6061
335 total students not in art club. 265 got the requested class.
265/335 = 0.7910
the probability was higher for kids not in art club, so all students had an equal opportunity.
If 5 cars are selected from 8 and arranged side-by-side in a parking lot, how many permutations are
possible?
==========================================================
Explanation:
We have five slots which we can label A,B,C,D,E
There are 8 choices for slot AThen 7 choices for B6 for C5 for D4 for EWe start at 8 and count down by 1 each time until all slots are accounted for. Then multiply out those items: 8*7*6*5*4 = 6720
--------------
Another approach is to use the nPr permutation formula.
Plug in n = 8 and r = 5.
[tex]n P r = \frac{n!}{ (n-r)! }\\\\8 P 5 = \frac{8!}{ (8-5)! }\\\\8 P 5 = \frac{8!}{ 3! }\\\\8 P 5 = \frac{8*7*6*5*4*3!}{ 3! }\\\\8 P 5 = 8*7*6*5*4\\\\8 P 5 = 6720\\\\[/tex]
In the second to last line, the "3!" factorial terms cancel out.
We have the string 8*7*6*5*4 show up again to help reinforce the previous section.
Can someone please answer my trigonometry problem? I've been trying to get answers all day for something so minimal.
Find each measurement indicated. Round your answers to the nearest tenth.
Answer:
∠B ≈ 30.0°
Step-by-step explanation:
The law of sines can be used to solve a triangle when two sides and an angle opposite one of them are given.
__
sin(B)/b = sin(C)/c
sin(B) = (b/c)sin(C) . . . . solve for sin(B)
sin(B) = (14/28)sin(91°) ≈ 0.49992385
The angle is found using the inverse sine function:
B = arcsin(0.49992384) ≈ 29.99496°
Rounded to tenths, the angle is ...
m∠B ≈ 30.0°
_____
Additional comments
Many triangle solver apps and web sites are available if all you want is an answer.
When using your calculator, be sure the angle mode is set to "degrees."
The Law of Sines can also be used to solve a triangle when two angles and one side are known.
In ΔRST, = 93 inches, ∠S=123° and ∠T=28°. Find the length of r, to the nearest 10th of an inch
Answer:
<r=29
Step-by-step explanation:
Joaquin is constructing the perpendicular bisector of ab. What should be his first step?
(100 points cuz why not)
Answer:
D. Open the compass so that the distance from the two points of the compass is wider than half the length of [tex]\over{AB}[/tex].
Step-by-step explanation:
To construct a perpendicular for [tex]\over{AB}[/tex], we must first take a compass & take the distance of its arms wider than half the length of [tex]\over{AB}[/tex].
This is done in order to get two intersecting arcs in the top & bottom of [tex]\over{AB}[/tex] so that a perpendicular bisector can be drawn through it.
After two intersecting lines are drawn below & above [tex]\over{AB}[/tex], draw a line joining these 2 points through their points of intersection. The point where it intersects [tex]\over{AB}[/tex] is the middle-most point of [tex]\over{AB}[/tex] & now a perpendicular bisector of [tex]\over{AB}[/tex] is constructed.
[tex]\rule{150pt}{2pt}[/tex]
Answer:
D
Step-by-step explanation:
factor by grouping
NEED HELP ASAP
# after letters are the exponent
1: 28v+16v2-21v-12
2: 49x3-35x2+56x-40
3: 24r3-64r2-21r+56
Answer and step-by-step explanation:
[tex]28v^3 +16v^2-21v-12 =[/tex] collecting [tex]4v^2[/tex] in the first two terms and [tex]-3[/tex] in the last two:
[tex]4v^2(7v+4)-3(7v+4) =[/tex] collecting the bracket
[tex](7v+4)(4v^2-3)[/tex]
Bonus stage: if you are factoring over the real numbers and not over the rational, the second brackets is a difference of squares. Else, you stop here.
[tex](7v+4)(2v+\sqrt3)(2v-\sqrt3)[/tex]
NEXT!
[tex]49x^3-35x^2+56x-40=[/tex]As before, [tex]7x^2[/tex]in the first two, and [tex]8[/tex] in the last two:
[tex]7x^2(7x-5)-8(7x-5)[/tex] collecting the bracket again
[tex](7x-5)(7x^2-8) =[/tex]again, bonus step
[tex](7x-5)(\sqrt7 x +2\sqrt2) (\sqrt7x-2\sqrt2)[/tex]
FINALLY!
[tex]24r^3-64r^2-21r+56 =\\8r^2(3r-8) -7(3r-8)=\\(3r-8)(8r^2-7) =[/tex]Again, bonus step
[tex](3r-8)(2\sqrt2r+\sqrt7)(2\sqrt2r-\sqrt7)[/tex]
Since usually most courses talk about factorization of polynomials BEFORE talking about real numbers, I would stop at the third stage, skipping the fourth.
ANSWER ASAP FOR BRAINLIEST
Dimitar puts only dimes and quarters into his piggy bank. Right now, it contains five more dimes than quarters, and their total value is exactly $74. How many quarters and how many dimes are in Dimitar's piggy bank?
0.35x=73.85, comgining moving terms
divide both sides by 0.35
x=211 quarters, which is $52.75 ANSWER
x+5=216 dimes, which is $21.60 ANSWER
That total is $74.35
Answer:
the answer is 210 quarters and 215 dimes
Step-by-step explanation:
helppppp ....Simpson Office Furniture pays Sam Hughes a $840 monthly salary plus a 7% commission on merchandise he sells each month. Assume Sam's sales were $18,600 for last month. Calculate the following amounts:
Answer:
$2,142
Step-by-step explanation:
7% of 18,600 is 1,302
Add this to 840 and you get a total of $2,142
Commission is $1,302
Gross pay is $840
Please help!!!! Find the value of x.
Answer: 84
Step-by-step explanation:
A rectangular swimming pool has a length of 50 meters, a width of 25 meters, and a depth of 2 meters. How much paint would be needed to cover the sides and bottom of the pool?
Answer:
2500m³
Step-by-step explanation:
A = length x width x height
50m x 25m x 2 m
=2500m³
From 1984 to 1995 the winning scores for a golf tournament were 275,279,279,276,278,277,280,282,284and 270 Find the mean of the data is
Answer: The mean of the data is 278.
Step-by-step explanation:
To the the mean of the data, we’ll have to add all the numbers up and divide it by the amount of data.
275+279+279+276+278+277+280+282+284+270=2780
2780/10=278
6*10^-2 is how many times as large as 2*10^-8?
Choose 1 answer:
A
3*10^-10
B
3*10^-6
C
3*10^6
D
3*10^10
Answer:
C) [tex]3\cdot10^{-6}[/tex]
Step-by-step explanation:
Divide the two numbers:
[tex]\displaystyle \frac{6\cdot10^{-2}}{2\cdot10^{-8}}=\frac{6}{2}*\frac{10^{-2}}{10^{-8}}=3\cdot10^{-2-(-8)}=3\cdot10^{-2+8}=3\cdot10^{6}[/tex]
Thus, C is the correct choice.
Answer:
is A
Step-by-step explanation:
Calculate volume of hemisphere with radius 3.2 cm
The volume, V, of a sphere with radius r is V = [4/3 pi r^3]
Answer:
V ≈ 68.63 cm³
Step-by-step explanation:
the volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex]πr³
the volume of a hemisphere is half the volume of a sphere, so
V = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³ , then
V = [tex]\frac{2}{3}[/tex] π × 3.2³
= [tex]\frac{2}{3}[/tex] π × 32.768
≈ 68.63 cm³ ( to 2 dec. places )
Which of the following correctly uses the Pythagorean Theorem to find the missing side ?
A. 8² + (10)² = 2²
B. X + 8=10
C. x² +8² = (10)²
D. x² + (10)² = 8²
Answer:
C
Step-by-step explanation:
hyp² = opp² + adj²
10² = 8² + x²
I need help!! I don’t know which one it is.
Which point is closest to point A?
Point__
Answer:
Point D
Step-by-step explanation:
The length from Point A to Point D is 6 units, while the length from point A to Point C is 7 units, and the length from Point A to Point B is also 7 units. Because to reach Point C, you have to make one turn, adding one more unit. Same with Point B.
============================================================
Explanation:
Point A is at (-3,3) while point B is at (2,5)
Let's use the distance formula to find the distance between these points.
[tex]A = (x_1,y_1) = (-3,3) \text{ and } B = (x_2, y_2) = (2,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-2)^2 + (3-5)^2}\\\\d = \sqrt{(-5)^2 + (-2)^2}\\\\d = \sqrt{25 + 4}\\\\d = \sqrt{29}\\\\d \approx 5.3852\\\\[/tex]
The distance from A to B is approximately 5.3852 units.
-------------
Point C is at (-2,-2)
Let's find the distance from A to C
[tex]A = (x_1,y_1) = (-3,3) \text{ and } C = (x_2, y_2) = (-2,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-(-2))^2 + (3-(-2))^2}\\\\d = \sqrt{(-3+2)^2 + (3+2)^2}\\\\d = \sqrt{(-1)^2 + (5)^2}\\\\d = \sqrt{1 + 25}\\\\d = \sqrt{26}\\\\d \approx 5.099\\\\[/tex]
The distance from A to C is approximately 5.099 units.
So far, point C is the closest to point A.
-------------
Point D is at (3,3)
We could use the distance formula to find the distance from A to D, but we can simply subtract the x coordinates and make the result positive if needed. This works because points A and D have the same y coordinate.
D - A = 3 - (-3) = 3+3 = 6
The distance from A to D is 6 units.
Or you could count out the horizontal spaces between the points and you should count 6 spaces.
----------------
Summary:
Distance from A to B = 5.3852 (approximate)Distance from A to C = 5.099 (approximate)Distance from A to D = 6 (exact)The smallest distance value is the 5.099, which is from A to C.
Therefore, point C is closest to point A.
A triangle has sides of lengths 16,14 and 50 .is the triangle right angle triangle?
Answer:
no
Step-by-step explanation:
using the converse of Pythagoras' identity
If the square on the longest side is equal to the sum of the squares of the other 2 sides, then the triangle is right.
longest side = 50 ⇒ 50² = 2500
16² + 14² = 256 + 196 = 452
since 452 ≠ 2500 then the triangle is not right
A triangle has sides of lengths 16,14 and 50. Is the triangle right angle triangle?
❒ Explanation -:We will solve this question using Pythagoras theorem.
We know,
[tex] \small \boxed{\rm{ c² = a² + b²}}[/tex]
[tex] \small\rm{Where,} [/tex] [tex]\small\sf{ c > a \: and \: c > b}[/tex]
[tex] \small\sf{ 50² = 16² + 14²}[/tex]
[tex]2500 = 256+ 196[/tex]
[tex]2500≠452[/tex]
[tex] \small\bf{ c² ≠ a² + b²}[/tex]
Hence, the triangle is not a right-angled triangle.
jeff can solve 16 math problems in 25 minutes. How many problems can he solve in 42 minutes?
Answer:
27
step by step explanationfrom the explanation,
let the number of maths that can be solved in 42 minutes = X
16 maths--------------25minutes
x maths --------------42 minutes
cross multiplying
X×25= 16×42
dividing bothsides by 25
25X/25 = 16×42/25
X = 672/25
X = 26.88 = 27 (approximately)
therefore 27 problems can be solved in 42 minutes
Find the midpoint M of the line segment joining the points A = (7, - 8) and B = (- 3, - 4)
Answer:
The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
Use this calculator to calculate the midpoint, the distance between 2 points, or find an endpoint given the midpoint and the other endpoint.
Step-by-step explanation:
Step-by-step explanation:
(7+(-3))/2 , (-8+(-4))/2(7-3)/2 , (-8-4)/24/2 , -12/2midpoint = (2,-6)Find the surface area of the prism.
10 ft length
1 ft height
5 ft width
Answer:
Surface Area = 130 sq ft
Step-by-step explanation:
If you don't have a picture, draw a picture so you can see what's up. See image. Surface area is the area of all the faces of a 3d shape (a solid) all added up. This solid is a box. It has six faces. Each face is a rectangle. The top and bottom are the same. The front and back are the same. The left and right sides are the same. See image.
Area of a rectangle is:
A = l × w
Area of the top:
5 × 10 = 50
Area of the bottom also 50.
Area of the left side:
1 × 5 = 5
Area of the right side is also 5.
Area of the front:
1 × 10 =10
Area of the back is also 10.
ADD up all 6 areas:
50+50+5+5+10+10
Surface area = 130
Area has square units.
SA = 130 square ft
3. Find the probability of rolling a prime number when a 14-sided die is rolled.
Answer:
3/7
Step-by-step explanation:
Probability = number of favorable outcomes/total number of possible outcomes
We know the total number of possible outcomes is 14 since there are 14 sides to the dice.
Let's find how many of those numbers are prime numbers.
2, 3, 5, 7, 11, and 13 are all the prime numbers between 1 and 14, so there are 6 favorable outcomes.
Now create the fraction then reduce.
6/14 reduce by 2/2
3/7
What is the average rate of change of the function over the interval x = 0 to x = 4? f(x)=2x−13x 5 enter your answer, as a fraction, in the box.
The average rate of change of the function over the interval x = 0 to x = 4 is: 61/400.
What is the Average Rate of Change of a Function?Average rate of change = f(b) - f(a) / b - a
Given the function, f(x) = 2x - 1 / 3x + 5.
a = 0, f(a) = 2x - 1 / 3x + 5 = 2(0) - 1 / 3(0) + 5 = -1/5
b = 4, f(b) = 2x - 1 / 3x + 5 = 2(4) - 1 / 3(4) + 5 = 7/17
Average rate of change = 7/17 - (-1/5) / 4 - 0 = 61/400
Learn more about average rate of change on:
https://brainly.com/question/11627203
#SPJ4
What percentage of canadians live within 100 miles of the u. S. Border?.
Answer:
90%
Step-by-step explanation:
what shape always has four congruent sides
Answer:
A rhombus
Step-by-step explanation:
A rhombus is a parallelogram with 4 congruent sides and it always has four congruent sides. It also has two pairs of equal angles.
Answer: rhombus
Step-by-step explanation: Correct answer is a rhombus! A rhombus is a parallelogram with 4 congruent sides and it always has four congruent lines . a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST .THANKS .
Which of the following figures uses the SSS theorem to prove that AEFG SAHIJ?
Answer:
W.
Step-by-step explanation:
SSS, or Side-Side-Side is used to prove two triangles similar
Figure W. is the only one that uses three side marks, all of the others use at least one angle to prove them similar.
Solve the equation by factoring. 2x^2 + 6x = -4
Answer:
x=-2 x=-1
Step-by-step explanation:
2x^2 + 6x = -4
Add 4 to each side
2x^2 + 6x +4= -4+4
2x^2 + 6x +4=0
Factor out 2
2( x^2 +3x+2) = 0
Divide by 2
x^2 +3x +2 =0
( x+2)(x+1) =0
Using the zero product property
x+2 =0 x+1 =0
x=-2 x=-1
Answer:
x = -1, -2
Step-by-step explanation:
Bring the constant term to the left hand side :
2x² + 6x = -42x² + 6x + 4 = 0Divide throughout by 2 :
(2x² + 6x + 4)/2 = 0/2x² + 3x + 2 = 0Splitting the middle term :
x² + x + 2x + 2 = 0x(x + 1) + 2(x + 1) = 0Factors obtained :
(x + 1)(x + 2)Finding the zeros :
x + 1 = 0 ⇒ x = -1x + 2 = 0 ⇒ x = -2Solve simultaneously:
x-4y=1
6y=x-2
Answer:
separate : x-4y=1
= x-2y = 10
the other one: x = 6y + 2
togetehr : x = -1 , y = -1/2
step-by-step explanation:
i don't know if they're together so ima give you the answer for them if they are and just separte answers
Need help please answer ASAP!
#10
x²-9x²-3²(x+3)(x-3)Option A and B
#11
√9a²+16a²√a²(9+16)√a²(25)√5²a²5aOption C
Answer:
10. (2) x - 3
11. (3) 5a
Step-by-step explanation:
Question 10
x² - 9 = (x + 3)(x - 3)x² - 5x + 6 = (x - 3)(x + 2)x - 3 is a common factor(2) x - 3Question 11
Simplifying
√9a² + 16a²√a² (9 + 16)a√25(3) 5aplease tell me the answer of the question please.
Answer:
total price = 100*80 = 8000
donated = 10 *80 = 800
sold = 90*88 = 7290
pofit = cp - sp
cp = 8000 sp = 7290
= 710
Step-by-step explanation:
The cost of a taxi fare is $5 plus $1.50 per kilometre travelled. a) Derive a formula for calculating the cost, $P, of travelling n km. b) Use your formula to calculate the cost of travelling 25 km. please help me
Answer:
Step-by-step explanation:
Formula
P = 5 + 1.50n
P is the total Cost
n is the number of Km travelled.
Solution
Substitute n = 25 into the formula
P = 5 + 1.5 * 25
P = 5 + 37.5
P = 42.50
Answer
42.50 dollars for 25 km.
Simplify these four questions
Answer:
a. 5a + 3b-5
b. 4e^2 + f^2 + f
c. 42xy(z)^2
d. 7x(y)^2
Step-by-step explanation:
I added/subtracted/multiplied/divided like terms.
