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Complete Question
An arts academy requires there to be 5 teachers for every 90 students and 3 tutors for every 30 students.
How many students does the academy have per teacher?Per tutor?
How many tutors does the academy need if it has 80 students
Answer:
a) 18 students per teacher
b) 10 students per tutor
c) 8 tutors
Step-by-step explanation:
a) How many students does the academy have per teacher?
5 teachers for every 90 students
Hence,
5 teachers = 90 students
1 teacher = x students
Cross Multiply
5 × x = 1 × 90
5x= 90
x = 90/5
x = 18 students
We have 18 students per teacher
b) How many students Per tutor?
3 tutors = 30 students.
1 tutor = x students
3 × x = 30 × 1
x = 30/3
x = 10 students
We have 10 students per tutor
c) How many tutors does the academy need if it has 80 students
3 tutors = 30 students.
30 students = 3 tutors
80 students = x tutors
Cross Multiply
30 × x = 80 × 3
x = 80 × 3/30
x = 8 tutors
The school needs 8 tutors for 80 students.
A ball is dropped from a height of 8 feet. If every time it bounces, it bounces 60% of its previous height, what is the total distance traveled by the ball?
Answer:
20feetStep-by-step explanation:
Initial height of the ball = 8feet
If it bounces 60% of its previous height, its new height will be;
60% of 8
= 60/100 * 8
= 480/100
= 4.8 ft
If it bounces 60% of its current distance, new height will be expressed as;
60% of 4.8
= 0.6 * 4.8
= 2.88
The height of the ball will keep reducing and form a geometric progression of the form 8, 4.8, 2.88...
In order to get the total distance traveled by the ball, we need to calculate the sum to infinity of the sequence;
S∞ = a/1-r where;
a is the first term = 8
r is the common ratio
[tex]r = \frac{4.8}{8} = \frac{2.88}{4.8}\\r = 0.6[/tex]
Substitute into the formula;
S∞ = a/1-r
S∞ = 8/1-0.6
S∞ = 8/0.4
S∞ = 20feet
Hence the total distance traveled by the ball is 20feet
Nolan uses 3 yards of string. He cuts the string into pieces that are 1/6 yard long. How many pieces does Nolan have?
Answer:
18
Step-by-step explanation:
6×3=18
Answer:
18
Step-by-step explanation:
if cost $25 per day to rent a tux plus a $50 cleaning fee. if samuel paid $200, how many days did he have the tux?
Answer:
6 days
Step-by-step explanation:
Answer:
he had the tux for 6 days because he paid the cleaning fee
Step-by-step explanation:
SOMEONE HELP ME PLS
Answer:
1/5^15
Step-by-step explanation: when ever you want to convert the number becomes a fraction to sibstitute for the sighn change and the exponent stays positive.
How can you solve one-variable equations using inverse operations?
Answer:
you can't, im sorry I don't knowbit but I do need points
The x-axis is the ? Axis
The y-axis is the ? Axis
Another name for the point 0,0 is the ?
Answer:
The x-axis is the HORIZONTAL axis (left to right)
The y-axis the VERTICAL axis ( up and down)
Another name for the point (0 , 0) is the ORIGIN
HELP ME PLEASE: I WILL GIVE BRAINLIEST AND IT IS 20 POINTS
Answer:
0
Step-by-step explanation:
any log with a base of one and it becomes logv5 (1) after logv5(logV3 (3) because log3(3) equal one so then logv5 (1) is 0
Albert claims that −6 is the greatest integer solution of the inequality 3x−1≤35+9x. Solve the inequality to show if Albert is correct or not.
Answer:
albert einstein
Step-by-step explanation:
A neon sign blinks every 6 minutes, and another sign blinks every 8 minutes. How often do they blink at the same time?A.Every 14 minutesb.Every 24 minutesc.Every 48 minutesd.Every 2 minutes
Answer:
b. Every 24 minutes
Step-by-step explanation:
A neon sign blinks every 6 minutes, and another sign blinks every 8 minutes.
The first step is to:
Find and list multiples of each time each neon sign blinks.
This means, we find the Multiples of 6 and 8
Multiples of 6:
6, 12, 18, 24, 30, 36
Multiples of 8:
8, 16, 24, 32, 40
The first and common multiple of 6 and 8.
Therefore, the Least common multiple [LCM(6, 8) ] = 24
Hence, they often blink at the same time every 24 minutes.
Therefore, option b.Every 24 minutes is correct.
I NEED THE ANSWER NOW
Answer:
The last one
Step-by-step explanation:
68/5 - 22/5 = 46/5 = 9 1/5
Answer:
Option d
Explanation:
[tex]\frac{68}{5} - \frac{22}{5} = \frac{46}{5}[/tex]
46/5 in mixed fraction is [tex]9\frac{1}{5}[/tex]
rules of a formal debate
Answer:
Step-by-step explanation:
be formal and dont yell
Answer:
Each of the six speakers (three affirmative and three negative) speak in succession to each other, beginning with the Affirmative Team. The speaking order is as follows: First Affirmative, First Negative, Second Affirmative, Second Negative, Third Affirmative, and finally Third Negative.
Step-by-step explanation:
What are the solutions to the equation w/2w-3= 4/w
Answer:
w=2 , w=6 are the zeroes of the expression
Explanation:
We have been given the expression
after cross multiplication of the given expression so as to simplify it we will get
Solution to the given equation is w=2,w=6
Therefore these are the solutions of the given expression.
Jack bought 500 shares in Glastonbury Goods at $17.85 per share on January 18, 2015. On January 25, 2017, he sold 300 shares after its price had dropped to $15.25 per share. He bought 250 more shares on January 31, 2017 when the price had fallen to $11.90 a share. He sold all of his stock at $18.00 per share on February 5, 2017. How much of a profit/loss did Jack make over the course of his investment? ____________________ profit or loss
Answer:
$775 profit
Step-by-step explanation:
Here, we want to know how much profit or loss Jack made;
he sold 300 shares at $15.25
Amount lost on this will be;
(17.85-15.25) * 300 = -$780
The number of shares he sold at $18 will be the 250 he bought now, and the 200 left unsold before
So profit now will be;
200(18-17.85) + 250(18-11.9)
= $30 + $1525 = $1555
So he made $1555 and lost $780
The amount of profit made is $1555-$780 = $775
I really really need the answer to this NOW
Answer:
185 and 1/3
Step by step explanation
What is the remainder when 3x2−7x+5 is divided by x+5?
Answer: 2
Step-by-step explanation:
Find the slope of the line that goes through the points (9,-13) and (7,3).
hi
You have two points A ( X;Y) and B ( X ; Y)
slope is : ( Yb -Ya) / (Xb -Xa )
(3 - (-13) ) / ( 7 - 9) = (3 +13) / -2 = 16/-2 = - 16/2 = -8
slope is -8
Answer:
-8
Step-by-step explanation:
The slope formula is as follows:
m = y2 - y1 / x2 - x2
You would first plug in the points into the formula, and this is what you would get:
m = 3 - (-13) / 7 - 9
From there, because of additive inverse, the negative signs would become + signs.
m = 3 + 13 / 7 - 9
You would now add/subtract.
m = 16 / -2
And lastly, you would simplify.
m = 8/-1
8/-1 is the same thing as a slope of -8.
Geometry 9th grade will give brainliest
Step-by-step explanation:
7.90.
PLEASE HURRY ILL GIVE BRAINLEST AND 50 POINTS FOR THE CORRECT ANSWER ASAP
Answer:
m∠W is 28°
m∠X is 24°
Step-by-step explanation:
In any triangle, the measure of an exterior angle at one vertex of a triangle equals the sum of the measures of the two interior angles opposite to this vertex
In the given figure
∵ ∠WYZ is an exterior angle of Δ XYW at vertex Y
∵ ∠W and ∠X are the interior angles of Δ XYW opposite to the vertex Y
→ Use the fact above
∴ m∠WYZ = m∠X + m∠W
∵ m∠WYZ = 52°
∵ m∠X = 3y°
∵ m∠W = (4y - 4)°
→ Substitute them in the equation above
∵ 52 = 3y + 4y - 4
→ Add the like terms
∴ 52 = 7y - 4
→ Add 4 to both sides
∵ 52 + 4 = 7y - 4 + 4
∴ 56 = 7y
→ Divide both sides by 7
∵ [tex]\frac{56}{7}[/tex] = [tex]\frac{7y}{y}[/tex]
∴ 8 = y
→ Substitute y in the measures of ∠X and ∠W
∵ m∠X = 3(8)
∴ m∠X = 24°
∵ m∠W = 4(8) - 4 = 32 - 4
∴ m∠W = 28°
Evaluate: f(2) if f(x) = 4 - 2x
f(2) = 0
f(2)= 2
f(2)= 4
f(2) = 8
Answer:
f(2) = 0
Step-by-step explanation:
Evaluate: f(2) if f(x) = 4 - 2x; plug in 2 for x
f(2) = 4 - 2(2) = 4 - 4 = 0
Answer:
f(2) = 0
Step-by-step explanation:
Put 2 in the place of x,
f(2) = 4 - 2(2)
f(2) = 4 - 4
f(2) = 0
5x + 2y = 7
Solve for y
The correct answer is attached below:
Answer:
y= 7/2-5x/2
Step-by-step explanation:
what is the akis of symmetry
y=2x^2-8x+1
Answer:
2
Step-by-step explanation:
Brian bought a jacket that cost d dollars. He paid the clerk $60,00 He received $7.39
in change. How much did Brian pay for the jacket?
Answer:
52.61 is what Brian payed for the Jacket.
Step-by-step explanation:
52.61 + 7.39 = 60$ in total.
Answer:
ok so a jacket would never cost 60,00 i think you meant 60.00 so it would be $52.61 for the jacket
Step-by-step explanation:
Subtract 7.39 from 60
if you really did mean 60000 the answer would be 5992.61
lines A and B are parallel what is the measurement of angle b?
Answer:
79
Step-by-step explanation:
Since the two lines are parralel, then the angles should be the same.
Answer:
79 degrees for sure
Step-by-step explanation:
this is because im pretty sure its right.
both angles look same to me trust me
pls mark braineslt if im right
When two angles are supplementary their sum is equal to 180 degrees. Let x equal one of two supplementary angles. If the other angle is equal to 67 degrees, write
an equation in terms of x for the sum of the two angles.
since we know supplementary angles equal 180 degrees, we know that 67 plus x must equal 180 degrees, so the equation for this problem would be
67+x=180, and x is equal to 113
what is the answer to this?
Answer:
AA
Step-by-step explanation:
The smaller triangle and the bigger triangle have the same angle of 60 on one side.
They also have a common point at the top, which is also called a common angle.
You only need two angles to show that two triangles are similar, because the other angle has to be the same because all angles in a triangle add up to 180.
Find tan-1 1.4281 to the nearest degree.
a. 10°
b. 55°
C. 5°
d. 35°
Answer:
[tex]\:x=55^{\circ \:\:}[/tex]
Therefore, option 'b' is correct.
Step-by-step explanation:
Let x be the angle
tan x = 1.4281determining the [tex]\tan ^{-1}\left(1.4281\:\right)[/tex]
[tex]\:\tan \:x\:=1.4281\:[/tex]
[tex]x=\tan ^{-1}\left(1.4281\:\right)[/tex]
[tex]\:x=55^{\circ \:\:}[/tex]
Therefore, option 'b' is correct.
What is m? 45º 90º 180º 270º
need help asap
Answer:
90
Step-by-step explanation:
it looks like it's a right angle
Answer:
The answer is 90 degrees
Step-by-step explanation:
Using the Triangle Sum Theorem, find x and the missing angles (2x +1) (5x +5) x= Angle (2x+1) = Angle (5x+5) =
Answer:
x = 12
(2x + 1)° = 25°
(5x + 5)° = 65°
Step-by-step explanation:
By the property of a triangle,
Sum of all angles of a triangle is 180°
In the given right triangle,
(2x + 1)° + 90° + (5x + 5)°= 180°
7x + 96 = 180
7x = 180 - 96
x = [tex]\frac{84}{7}[/tex]
x = 12
Angle (2x + 1)° = 2(12) + 1 = 25°
Angle (5x + 5)° = 5(12) + 5 = 65°
Therefore, all three angles of the right triangle are 25°, 90° and 65°.
Name a ray with an endpoint of A.
A rectangle of side 48cm by 60cm is divided into squares of side X cm. Find the greatest value of X
and find the area of the square.
Answer:
greatest value of X = 12
Area of square = 144 cm²
Step-by-step explanation:
The greatest value of X will be the highest common factor of 48 and 60 since we are told that the rectangle is divided into squares.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The highest common factor between both factors of 48 and 60 is 12.
Thus,
greatest value of X = 12
Area of square = 12 × 12
Area of square = 144 cm²