Answer: There are 48 students in the class.
Step-by-step explanation:
Let the number of students = S
Let the number of benches = B
If 4 students sit on each bench, 3 benches are left vacant.
S = 4(B - 3)
S = 4·B - 12 } Equation 1
If 3 students sit on each bench, 3 students still standing.
S = 3·B + 3 } Equation 2
We can match the two equations because they both indicate the same number of students.
4B - 12 = 3·B + 3
on solving this
4·B - 3·B = 3 + 12
B = 15 → number of benches
That is the number of benches, therefore substituting the value for B in equation 1
S = 4·B - 12 Equation 1
S = 4·15 -12
S = 60 - 12 = 48 → number of students
Answer: There are 48 students in the class.
VerificationThere are 48 students and 15 benches.
If 4 students sit on each bench, 3 benches are left vacant.
48students ÷ 4students/bench = 12 benches are occupied and left 3 vacant benches.
If 3 students sit on each bench, 3 students still standing.
15benches * 3 students/bench = 45 students are sitting and 3 students remain standing.
Checked!![tex]\textit{\textbf{Spymore}}[/tex]
Final answer:
By creating a system of equations from the given conditions, the number of students in the class is calculated to be 48.
Explanation:
To find the number of students in the class based on the provided scenario, we can set up a system of equations based on the given conditions:
If 4 students sit on each bench, 3 benches remain empty.
If 3 students sit on each bench, 3 students remain standing.
Let's use B to represent the total number of benches and S to represent the total number of students. The first condition tells us that when 4 students sit on each bench, there are B - 3 benches filled, which means 4(B - 3) students are seated. The second condition implies that if 3 students sit on each bench, all the benches are filled, and 3 more students are still standing, which can be represented by 3B + 3.
Therefore, we can write two equations as follows:
4(B - 3) = S
3B + 3 = S
Since both expressions equal S, we can set them equal to each other:
4(B - 3) = 3B + 3
Simplifying this equation, we can find the number of benches (B), and then substitute back to find the number of students (S).
4B - 12 = 3B + 3
B = 3 + 12 = 15 benches
Now we substitute B into one of our original equations to find S:
S = 4(B - 3)
S = 4(15 - 3)
S = 4 × 12
S = 48 students
Therefore, there are 48 students in the class.
Select the correct answer from the drop down menu
[tex](\frac{f}{g})(x)=\frac{x^{2} +2x-3}{x^2-9}[/tex] since x = 4, you plug in 4 into the x's in the equation
[tex](\frac{f}{g} )(4)=\frac{(4)^2+2(4)-3}{(4)^2-9} = \frac{16 + 8 - 3}{16 - 9}[/tex] Simplify
[tex]\frac{21}{7} =3[/tex]
so [tex](\frac{f}{g})(4)=3[/tex]
(f + g)(x) = (x² + 2x - 3) + (x² - 9) Plug in 4 for x
(f + g)(4) = 4² + 2(4) - 3 + (4)² - 9
(f + g)(4) = 16 + 8 - 3 + 16 - 9 = 28
moira scores 78 marks out of a possible 120 marks. What's Moira 's score as a percentage?
to figure out the percentage, you’ll have to do 78 divided by 120 (because it’s 78/120) which is 0.65. now, you’ll have to multiply by 100, so her percentage is 65%.
Type the correct answer in the box. If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is °.
Answer:
x = 35 degrees.
Step-by-step explanation:
cos x = sin(20 + x)
Using the identity cos x = sin(90 - x):
20 + x = 90 - x
2x = 70
x = 35 degrees (answer).
Answer:
Value of x is 35°.
Step-by-step explanation:
Given:
cos x = sin ( 20 + x )
To find: Value of the x.
We know that [tex]sin\,(90-\theta)=cos\,\theta[/tex]
Consider,
cos x = sin ( 20 + x )
sin ( 90 - x ) = sin ( 20 + x )
Comparing both sides,
90 - x = 20 + x
-x - x = 20 - 90
-2x = -70
x = 35°
Therefore, Value of x is 35°.
find the commission on a $750 sale if the commission is 24%
Answer:
The commission is $180
Step-by-step explanation:
To find the commission take the total (750) and multiply it by the percentage of commission (.24).
When you do this, you will get $180.
Hope this helps! :)
Answer:
its 180
Step-by-step explanation:
which of the following is circumference of a circle whose equation is x2+y2=100
Answer:
C = [tex]200\pi[/tex]
Step-by-step explanation:
C = [tex]2 \pi r[/tex], where r - radius
Since the equation of the circle is:
[tex]x^2 + y^2 = 100[/tex]
The radius is 100.
C = [tex]200\pi[/tex]
Find the area and perimeter of the triangle below if a = 164 feet, b=221 feet, c=352 feet, and h=76 feet
Answer:
Perimeter=737 feets
Area=13542.6 ft²
Step-by-step explanation:
Well assuming that a,b,c are the three sides of the triangle and h is the height then;
Perimeter=distance around the figure
P=164+221+352= 737 feet
Area of a triangle given three sides is calculated using the formulae;
Area=√s (s-a) (s-b) (s-c) where s=(a+b+c)/2
Finding s;
s=(164+221+352)/2 =368.5 feet
Finding the area
A= √ 368.5 (368.5-164) (368.5-221) (368.5-352)
A=√368.5 (204.5) (147.5) (16.5)
A= 13542.6 ft²
Can someone check over this? And explain if it's wrong?
Answer:
You are correct!
:D
A 4-digit number ends in 3. If you put the number 3 in the first position, the number will decrease by 738. Find the original 4-digit number?
Answer:
4153
Step-by-step explanation:
(x-3)/10 + 3000 = x-73
(x-3)/10 = x - 3738
x-3 = 10x - 37380
x = 10x - 37377
-9x = -37377
x = 4153
: P
Answer:
4153
Step-by-step explanation:
Let the original number be x
First, you subtract 3 from the original number. This removes 3 from the last digit, but leaves a zero there.
Now to remove the zero, you divide by 10.
Finally, to put the 3 at the first position, you add 3000.
Now Moving the last digit, 3, to the first position the number becomes :[tex]\frac{x-3}{10}+3000[/tex]
We are given that the number will decrease by 738.
A.T.Q
[tex]\frac{x-3}{10} + 3000 = x-738[/tex]
[tex]\frac{x-3}{10}= x - 3738[/tex]
[tex]x-3 = 10x - 37380[/tex]
[tex]x = 10x - 37377[/tex]
[tex]-9x = -37377[/tex]
[tex]x = 4153[/tex]
Hence the original 4-digit number is 4153.
tx²+3x-7=0 has two real solution. what can be the deducted about the value of t?
Answer:
value of t is greater than equal to -9 / 28.
Step-by-step explanation:
Given Quadratic Polynomial : tx² + 3x - 7 = 0
Also, It has real solutions.
Standard Quadratic equation, is ax² + bx + c = 0
here, Determinant, D = b² - 4ac
decides nature of the roots.
if D < 0 , roots / solutions are complex
if D = 0 , roots are real and equal.
if D > 0 , roots are real and different.
As given roots are real solutions.
Means Dis either equal to 0 or greater than 0
when D = 0
we have, 3² - 4 × t × (-7) = 0
9 + 28t = 0
t = -9 / 28
when D > 0
we have, 3² - 4 × t × (-7) > 0
9 + 28t > 0
t > -9 / 28
Therefore, value of t is greater than equal to -9 / 28.
Quadratic relations help needed! Thank you
For this case we have that the distance between two points is:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2 (y_ {2} -y_ {1}) ^ 2}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}) :( 3 \sqrt {7}, 2 \sqrt {5})\\(x_ {2}, y_ {2}) :( 5 \sqrt {7}, 5 \sqrt {5})[/tex]
Substituting:
[tex]d = \sqrt {(5 \sqrt {7} -3 \sqrt {7}) ^ 2+ (5 \sqrt {5} -2 \sqrt {5}) ^ 2}\\d = \sqrt {(2 \sqrt {7}) ^ 2+ (3 \sqrt {5}) ^ 2}\\d = \sqrt {4 (7) + 9 * (5)}\\d = \sqrt {28 + 45}\\d = \sqrt {73}\\d = 8.5440[/tex]
Answer:
[tex]d = 8.54[/tex]
Find the product. Write your answer in exponential form. 2^-8*2
Answer:18446744073709600000
Step-by-step explanation:
2^-8*2=2^64=
h=64t-32t^2 find the maximum height attained by the obiect
Check the picture below.
so if we just find its vertex, we know how many feet it went up by its y-coordinate.
[tex]\bf h=64t-32t^2\implies h=-32t^2+64t+0 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h=\stackrel{\stackrel{a}{\downarrow }}{-32}t^2\stackrel{\stackrel{b}{\downarrow }}{+64}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{64}{2(-32)}~~,~~0-\cfrac{64^2}{4(-32)} \right)\implies \left( \stackrel{\stackrel{\textit{how many}}{\textit{seconds}}}{1}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{it went up}}}{32} \right)[/tex]
What are the solutions of the quadratic equation (x – 8)2 – 13(x – 8) + 30 = 0? Use u substitution to solve. x = –11 and x = –18 x = –2 and x = 5 x = 2 and x = –5 x = 11 and x = 18
Answer:
x=11 and x=18
Step-by-step explanation:
The given quadratic equation is;
[tex](x-8)^2-13(x-8)+30=0[/tex]
Let u=(x-8)
[tex]u^2-13u+30=0[/tex]
Split the middle term;
[tex]u^2-10u-3u+30=0[/tex]
Factor by grouping
[tex]u(u-10)-3(u-10)=0[/tex]
[tex](u-10)(u-3)=0[/tex]
We have either u=10 or u=3
This implies that;
x-8=10 or x-8=3
x=10+8 or x=3+8
x=18 or x=11
Answer:
The answer is D on EDGE 2020
Step-by-step explanation:
Nine is 50% of what number
Answer:
15.
Step-by-step explanation:
Divide each side by .15 9/.15 = .15/.15x
The .15 on the right side of the equation cancels to 1, so once you divide 9 by .15, you get the answer.
60 = x
18. ..................
identify which segment is the hypotenuse
1)lm
2)mn
3)ln
4) none of the above
the hypotenuse is always the line directly in front of the right angle.
so the answer is 2) mn
geckos and iguanas are both lizards. The length of the average gecko is about two fifths of the length of average iguana. Geckos are about 10 in. long. What is the lenth of an average iguana.
Answer:
25 in.
Step-by-step explanation:
Since we know geckos are 2/5 of an Iguana's length, we need to find the length of 1/5.
So if 10 in. is 2/5, 5 in, is 1/5.
Now, since the denominator is 5, we multiply 5 in. by 5.
5x5=25 in.
25 in. is the length of an average Iguana.
if 8g=96, then g equals
Answer:
g = 12Step-by-step explanation:
[tex]8g=96\qquad\text{divide both sides by 8}\\\\\dfrac{8g}{8}=\dfrac{96}{8}\\\\g=12[/tex]
The Empire State Building is 1250 feet tall. At 3:00 pm, Pablo stands next to the building and has an 8-foot shadow. If he is 6 feet tall, how long is the Empire State Building's shadow at 3:00 pm?
1666.67 feet
1.67 feet
166.67 feet
16.67 feet
Answer:
1666.67
Step-by-step explanation:
6ft.......................................8ft
1250ft................................xft
1250/6 = x/8
x = 1250/6*8
If mike only has 100 dollars to spend on games, how many $20 games can he afford to buy?
Answer: 5
Step-by-step explanation: If Mike Only has $100 To Spend On Games, He Can Buy 5 Games Because We Multiply 20 By 5 To Get A Product Of 100.
Therefore, Mike Can Afford 5 Games With No Money Left.
Have A Fantastic Day!
Be Safe,
Eric
Mike can afford to buy 5 $20 games.
To determine how many $20 games Mike can afford to buy with $100, we divide the total amount of money he has by the cost of one game.
Total money Mike has = $100
Cost of one game = $20
Number of games Mike can afford = Total money / Cost of one game
Number of games Mike can afford = $100 / $20
Number of games Mike can afford = 5
Therefore, Mike can buy 5 games with $100.
Which data set is represented by the modified box plot? 116, 118, 114, 117, 151, 126, 122, 114, 124 100, 104, 114, 116, 117, 118, 122, 126, 151 116, 118, 104, 117, 151, 136, 142, 104, 124 106, 108, 104, 107, 151, 126, 132, 104, 124
100, 104, 114, 116, 117, 118, 122, 126, 151
That was the correct answer for the test I took
The probability for success of an event is P(A), and the probability of success of a second event is P(B). What is the
probability of both events occurring, in that order?
A.) P(A + B)
B.) P(A) . P(B)
C.) P(A) + P(B)
D.) P(A x B)
Answer:
b I am sure because to x the number to the the probability and we don't know which ]h one so there is a 50% 50% chance for both.
Step-by-step explanation:
Answer:
Option B - [tex]P(A)\cdot P(B)[/tex]
Step-by-step explanation:
Given : The probability for success of an event is P(A), and the probability of success of a second event is P(B).
To find : What is the probability of both events occurring, in that order?
Solution :
The probability for success of an event is P(A).
The probability of success of a second event is P(B).
As the events are independent so the probability of both events occurring, in that order is [tex]P(A)\cdot P(B)[/tex]
Therefore, Option C is correct.
The probability of both events occurring, in that order is [tex]P(A)\cdot P(B)[/tex]
X^2=26 in the simplest radical form
Answer:
5^2
Step-by-step explanation:
Answer:
x = ±sqrt(26)
Step-by-step explanation:
x^2 = 26
Take the square root of each side
sqrt(x^2) = sqrt(26)
x = ±sqrt(26)
This cannot be simplified any further
consider these four points: A(4,3) B(1/2,1/5) C(0.6,0.7) D(3/4,root 7/4). which point lies on the circumference of the unit circle? point blank
Answer:
Point D lies on the circumference of the unit circle
Step-by-step explanation:
Use the unit circle formula x^2 + y^2 = 1 plug the possible answer choices into this formula and determine which one is true.
D(3/4,root 7/4) lies on the circumference of the unit circle , Option D is the correct answer.
What is a Unit Circle ?A unit circle is a circle with 1 unit radius and the center is at origin .
The equation of a unit circle is x ² + y² =1
The points given are
A(4,3) B(1/2,1/5) C(0.6,0.7) D(3/4,root 7/4).
To check if they lie on the circumference of a unit circle , They have to be substituted in the equation of unit circle.
Point A
4 ² + 3² =1
16+ 9 ≠ 1
Point B
(1/2) ² + (1/5)² =1
(1/4) + (1/25) = 1
29/100 ≠ 1
Point C
(0.6) ² + (0.7)² =1
0.85 ≠ 1
Point D
(3/4)² + (√7/4)² =1
(9/16) + (7/16) = 1
1 = 1
Therefore , Option D, D(3/4,root 7/4) lies on the circumference of the unit circle.
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Please help me with this and thank you
Answer:
The answer is D
Step-by-step explanation:
(12 + 6) x (11 - 7) = 72
18 x 4 = 72
72 = 72
The answer is D
What is angle E and what is the process finding it?
Answer: 39 degrees
Step-by-step explanation: The angle sum of a triangle is 180 degrees so we take 102 from 180.
180-102=78
Since the two angles are the same then we just divide 78 by 2
78/2=39
Answer:
∠E ≈ 37°
Step-by-step explanation:
Using the Sine Rule in ΔEFG, that is
[tex]\frac{26}{sinE}[/tex] = [tex]\frac{42}{sin102}[/tex] ( cross- multiply )
42 × sinE = 26 × sin102° ( divide both sides by 42 )
sinE = [tex]\frac{26(sin102)}{42}[/tex] ≈ 0.6055..
E = [tex]sin^{-1}[/tex] (0.6055 ) ≈ 37°
WHAT IS 6 x 6 x 6 x 6 x 6 is exponet form
Answer:
Exponent of 5
Step-by-step explanation:
Because there are 5 6s it would be 6 to the exponent of 5.
Given, 6×6×6×6×6
Have to write in Exponent form
So....Its given that there are 5 six so..we can write is as
[tex] = {6}^{5} [/tex]
Hope itz help!!✌☑️Write the relation as a set of ordered pairs. WILL MARK BRANLIEST!! PLEASE HELP ASAP!!!!
Answer:
Option a.
Step-by-step explanation:
An ordered pair is written in the following form: (x, y). It means, first the independent variable and secondly the dependent variable.
In the diagram, the first circle represents the independent variable, and the second circle represents the dependent variable.
Then, the set of ordered pairs is (From left to right)
(-3, 3) ; (0, 0) ; (2, -2).
So the correct option is option a.
Answer:
The correct answer is option a
(-3, 3), (0, 0) and (2, -2)
Step-by-step explanation:
From the figure we can see three points are marked.
Each points can be written as ordered pair (x, y)
From left to right we can write,
the three pots are,
(-3, 3), (0, 0) and (2, -2)
Therefore the correct answer is option a
17 out of 20 teens say they eat or drink something before school. if 3,000 students attend that highschool, predict the number of teenagers that eat or drink something before school PLZ HURRRRRRRRRRRYYYYYYYYYYYYY
Answer:
2,550
Step-by-step explanation:
3,000 divided by 20 equals 150.
17 multiplied by 150 equals 2,550.
the answer is 2,550 I agree
what is 25 1/2 × 5 –3 = 5 x
Answer:
25 1/2 × 5 - 3 = 5x
51/2 × 5 - 3 = 5x
255/2 - 3 = 5x
255/2 - 6/2 = 10x/2
255 - 6 = 10x
249 = 10x
x = 249/10 = 24.9
The value of x in the equation [tex]25\frac{1}{2} * 5 -3 = 5x[/tex] is x=24.9
What is the value of x in the equation [tex]25\frac{1}{2} * 5 -3 = 5x[/tex]?Given:
An equation is given as [tex]25\frac{1}{2} * 5 -3 = 5x[/tex].Find:
The value of x.Solution:
The given equation is [tex]25\frac{1}{2} * 5 -3 = 5x[/tex]
Now, solving the equation, we get;
[tex]25\frac{1}{2} * 5 -3 = 5x[/tex]
[tex]\frac{51}{2} *5 - 3 =5x[/tex]
Now, multiplying the 51/2 with 5, we get;
[tex]\frac{255}{2} - 3 = 5x[/tex]
Now, we will take lcm and we get;
[tex]\frac{255-6}{2} = 5x[/tex]
[tex]\frac{249}{2} = 5x[/tex]
Now, multiplying with 2 on both sides of the equation, we get;
249 = 10x
Now, dividing by 10 into both sides of the equation, we get;
x = 24.9
Hence, the value of x in the equation [tex]25\frac{1}{2} * 5 -3 = 5x[/tex] is x=24.9
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HD, JD, and KD are perpendicular bisectors of EFG find each length
Answer:
Part 1) [tex]HD=\sqrt{105}\ units[/tex]
Part 2) [tex]JD=2\sqrt{34}\ units[/tex]
Part 3) [tex]KD=6\sqrt{2}\ units[/tex]
Step-by-step explanation:
step 1
Find the length HD
In the right triangle HDF
Applying the Pythagoras Theorem
[tex]FD^{2} =HF^{2} +HD^{2}[/tex]
substitute the values and solve for HD
[tex]19^{2} =16^{2} +HD^{2}[/tex]
[tex]HD^{2}=19^{2}-16^{2}[/tex]
[tex]HD^{2}=105[/tex]
[tex]HD=\sqrt{105}\ units[/tex]
step 2
Find the length JD
In the right triangle JDF
Applying the Pythagoras Theorem
[tex]FD^{2} =JD^{2} +FJ^{2}[/tex]
we have
[tex]FD=19\ units[/tex]
[tex]FJ=JG=15\ units[/tex] ----> because JD is a perpendicular bisector
substitute the values and solve for JD
[tex]19^{2} =JD^{2} +15^{2}[/tex]
[tex]JD^{2}=19^{2}-15^{2}[/tex]
[tex]JD^{2}=136[/tex]
[tex]JD=\sqrt{136}\ units[/tex]
[tex]JD=2\sqrt{34}\ units[/tex]
step 3
Find the length KD
In the right triangle KDG
Applying the Pythagoras Theorem
[tex]GD^{2} =KD^{2} +GK^{2}[/tex]
we have
[tex]GD=FD=19\ units[/tex]
[tex]GK=17\ units[/tex]
substitute the values and solve for KD
[tex]19^{2} =KD^{2} +17^{2}[/tex]
[tex]KD^{2}=19^{2}-17^{2}[/tex]
[tex]KD^{2}=72[/tex]
[tex]KD=\sqrt{72}\ units[/tex]
[tex]KD=6\sqrt{2}\ units[/tex]