Select the correct answer.
A school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second grade travel in the bus. How
many ways can the students be seated if all of the second-grade students occupy the first row?
OA 25P20
OB. SPs * 20P15
OC5C525C14
OD. SPs *15P15
OE PSX25C5
Answer:
B. [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]
Step-by-step explanation:
No. of students from first grade = 15
No. of students from second grade = 5
There are 5 rows of seats
Each row contains 5 seats
Total seats = 25
No. of ways for second-grade students to occupy the first row (i.e first 5 seats) = [tex]^{5} P_{5}[/tex]
Remaining seats = 20
So, now we are left with 15 first grade students
So, No. of ways for first-grade students occupy remaining seats = [tex]^{20} P_{15}[/tex]
Using the counting rule principle,
No. of ways for the students can be seated if all of the second-grade students occupy the first row = [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]
So, Option B is the correct answer
Hence, no. of ways for the students can be seated if all of the second-grade students occupy the first row is ×
There are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.
What is permutation?A permutation in math is the number of ways in which a set of data or objects can be ordered or arranged, where the order matters.
Given that, a school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second-grade travel in the bus.
Since you have to place all first-grade students in the first three rows,
Therefore,
For the 15 first-graders of the first three rows (15 seats), we have ¹⁵P₁₅ since all 15 places have to be occupied by all 15 first-graders.
Then we have 10 remaining seats left to be assigned to the 5 second-graders = ¹⁰P₅
We then multiply the permutation numbers of those two arrangements to get the total ways:
¹⁵P₁₅ x ¹⁰P₅
Hence there are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.
Learn more about permutation click;
https://brainly.com/question/30649574
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PLease help me :( You will get 20 pionts! And i will mark Brainliest!
picture is also included
Question:
Which term describes how the two sides of this figure are related ?
A. Induction
B. Symmetry
C. Scientific method
D. Deduction
Answer:
B. Symmetry
Step-by-step explanation:
They are symmetrical, meaning they are mirrored or both look the same.
Hope this helps! :)
How can you solve for X in the proportion of7/8 equals X/24
Answer and Step-by-step explanation:
The last answer choice is correct.
Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x
The process being used in the last answer choice is called Cross multiplication, and is used to find the unknown value in fractions.
[tex]\frac{7}{8}[/tex] × [tex]\frac{x}{24}[/tex]
7 × 24 = 8x
168 = 8x
21 = x
#teamtrees #PAW (Plant And Water)
what is the meaning of the quadratic formula. write it down?
Answer:
Quadratic formula is the tool for solving for an unknown number (usually x)
Step-by-step explanation:
The formula is below
Answer:
Below.
Step-by-step explanation:
The formula, which gives the solutions of the equation, is
x = [-b ±√(b^2-4ac)]/2a.
- a, b and c are the coefficients of the quadratic equation
ax^2 + bx + c = 0.
Help me with this!!!
Answer:
4th answer
Step-by-step explanation:
g(h(x)) means to put the formula for h(x) into the formula for g( ).
[tex]g(h(x))=g(2x-2)=-3(2x-2)^3-2(2x-2)^2\\=-3(8x^3-24x^2+24x-8)-2(4x^2-8x+4)\\=-24x^3+72x^2-72x+24-8x^2+16x-8\\=-24x^3+64x^2-56x+16[/tex]
Cubing the binomial 2x - 2 can take some time!
what is the value of x?
Answer:
6 sqrt(3) = x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 60 = x/12
12 sin 60 =x
12 ( sqrt(3)/2) =x
6 sqrt(3) = x
Answer:
x=6[tex]\sqrt{3}[/tex]
Step-by-step explanation:
take 60 degree as reference angle
using sin rule
sin 60=opposite/hypotenuse
[tex]\sqrt{3[/tex]/2=x/12
do cross multiplication
2*x=12*[tex]\sqrt{3}[/tex]
x=12[tex]\sqrt{3}[/tex] /2
x=6[tex]\sqrt{3}[/tex]
What is the value of x?
Answer:
Solution given:
sin 47=opposite/hypotenuse
Sin 47=x/18
x=sin47*18
x=13.16ft
Answer:
ammaamakamamMN8181(18736
Step-by-step explanation:
88271(1(1+1+382(2(#!#
A basketball team wants to paint half of free-throw circle grey. If the circumference of the free-throw is 30.77, what is the area that will be painted grey. Use 3.14 or pie.
Answer:
3.14
Step-by-step explanation:
Because you know it's the right answer.
a ball is shot out of a homemade air cannon. It flies through the air such that its height, as a function of time, is given by: h= -16t^2 + 64t + 10. where h is the height of the ball in feet and t is the time since it was fired in seconds. Max estimates that it takes 4 seconds for the ball to hit the ground and Cole estimates it takes 5 second. Algebraically determine who is closer and support your answer.
Answer:
Max
Step-by-step explanation:
the function given that h = -16t³+64t+10
the general function Equation:
h = at²+bt+c
=> t at the highest point is defined by t = -b/2a
= -64/2(-16) = -64/-32 = 2 second
the total times that the ball hits the ground
= 2× 2 seconds = 4 seconds.
so, Max is right
Answer:
Solution given:
Let h=0=when the ball hit the ground,the height=0.
h= -16t^2 + 64t + 10.
0=16t²-64t-10
8t²-32t-5=0
∆=[tex] \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}[/tex]
taking positive
t1=[tex] \frac{8+\sqrt{74}}{4}=4.15seconds[/tex]
t2=[tex] \frac{8-\sqrt{74}}{4}(t2<O)(neglected)[/tex]
So
t=4.15seconds closer to 4seconds.So
Max is closer.
Using the graph, determine the value of the slope.
v
CO 3
What is the slope?
4
2
What is true about the graph?
4
-2
-2
Intro
Done
Answer:
gradient of horizontal slope is 0
SUPER URGENT: Complete the general form of the equation of a sinusoidal function having an amplitude of 6, a period of 2pi/3, and a phase shift to the left 1 unit.
y =
Answer:
y = 6·sin(3·(x - 1)) + c
Step-by-step explanation:
The general form of an equation for a sinusoidal function is presented ad follows;
y = a·sin(b·(x - h) + c
Where;
a = The amplitude of the equation
T = The period = 2·π/b
h = The phase shift
c = The vertical shift
From the question, we have;
a = 6,
2·π/3 = 2·π/b
∴ b = 3
h = 1
We get;
y = 6·sin(3·(x - 1)) + c.
Use the Pythagorean theorem and the following diagram to help you find the area and perimeter of the following triangle. Please show your work and steps, so partial credit may be given:
Answer:
Perimeter = 30
Area = 30
Step-by-step explanation:
[tex](x+8)^2 -x^2 = 12^2[/tex]
[tex]x^2 +16x +64 - x^2 = 144[/tex]
[tex]16x+64=144[/tex]
[tex]16x = 80[/tex]
[tex]x = 5[/tex]
Double check:
[tex]\sqrt{12^2 + 5^2} = (5+8)\\\sqrt{12^2 + 5^2} = 13\\13 = 13[/tex]
Perimeter:
[tex]12+5+13=30[/tex]
Area([tex]\frac{1}{2}bh[/tex]):
[tex]\frac{1}{2}[/tex] × 12 × 5 = 30
According to Pythagorean theorem,
Δ (Hypotenuse)² = (1st Leg)² + (2nd Leg)²
⇒ (x + 8)² = x² + 12²
⇒ x² + 64 + 16x = x² + 144
⇒ 16x = 80
⇒ x = 5
Hypotenuse = (x + 8) = (5 + 8) = 13
1st Leg = 5
2nd Leg = 12
We know that : Perimeter is the Sum of all sides of the Triangle
⇒ Perimeter = Hypotenuse + 1st Leg + 2nd Leg
⇒ Perimeter = 13 + 5 + 12
⇒ Perimeter = 30
We know that :
[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]
Base = 1st Leg
Height = 2nd Leg
[tex]\implies \sf{\textsf{Area of the Triangle} = \dfrac{1}{2} \times 5 \times 12}[/tex]
[tex]\implies \sf{\textsf{Area of the Triangle} = 30}[/tex]
Part A
Find the formula for the corresponding inverse function g(x).
Part B
Select all of the points that would appear on the graph of y = g(x).
1. A
2. B
3. C
4. D
5. E
6. F
What is constant of proportionality? I'm still having trouble understanding it. Can someone please give me a give problems and tell me how to find the COP (constant of proportionality) <3 thamks.
Answer:
See Explanation
Step-by-step explanation:
Given two variables (say x and y); the constant of proportionality is the ratio between these to variables.
Illustration; y is directly proportional to x
The above statement can be represented as:
[tex]y\ \alpha\ x[/tex]
When converted to an equation, you get
[tex]y\ =k x[/tex]
k, in the above equation, represents the constant of proportionality
Divide both sides by x to solve for k
[tex]k = \frac{y}{x}[/tex]
Take for instance: [tex]y = 3x[/tex]
Divide both sides by x
[tex]\frac{y}{x} = 3[/tex] --- 3 is the constant of proportionality
what is the length of the missing leg?
Answer:
[tex]a=\sqrt{609}\\\\a\approx 24.67793[/tex]
Step-by-step explanation:
To solve for the leg of the missing right triangle, one must use the Pythagorean theorem. The Pythagorean theorem states the following,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the sides adjacent to or next to the right angle. (c) is the side opposite the right angle. Substitute in the given values and solve for the unknown,
[tex]a^2+b^2=c^2\\[/tex]
Substitute,
[tex]a^2+40^2=47^2\\[/tex]
Simplify,
[tex]a^2+1600=2209\\[/tex]
Inverse operations,
[tex]a^2=609[/tex]
[tex]a=\sqrt{609}\\\\a\approx 24.67793[/tex]
Answer:
b = 9 mm
Step-by-step explanation:
Using Pythagoras; identity in the right triangle
b² + 40² = 41²
b² + 1600 = 1681 ( subtract 1600 from both sides )
b² = 81 ( take the square root of both sides )
b = [tex]\sqrt{81}[/tex] = 9 mm
Can y’all help me ASAP please?
Step-by-step explanation:
[tex]8 log_{5}( {x}^{5} ) = 8 \times 5 log_{5}(x) \\ = 40 log_{5}(x) [/tex]
The original price of a skateboard, not including tax, was $96. Charlie bought the skateboard on sale, and he saved 30% off of the original price.
What was the sale price of the skateboard?
find the equation of a circle with a point at ( 10 , - 4 ) and a point at ( -2 , - 4 )
Answer:
Solution given:
letA=(10,-4)
B=(-2,-4)
centre[C](h,k)=[tex]\frac{10-2}{2},\frac{-4-4}{2}=(+4,-4)[/tex]
radius=[tex]\sqrt{(4-10)²+(-4+4)²}=6[/tex]units
we have
Equation of a circle is;
(x-h)²+(y-k)²=r²
(x-4)²+(y+4)²=36
or.
x²-8x+16+y²+8y+16=36
x²-8x+8y+y²=36-32
x²-8x+8y+y²=4
The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.
Answer:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]
Step-by-step explanation:
the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter
since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle
remember midpoint formula,
[tex] \displaystyle M = \left( \frac{x _{1} + x_{2} }{2} , \frac{ y_{2} + y_{2}}{2} \right)[/tex]
let,
[tex] \displaystyle x _{1} = 10[/tex][tex] \displaystyle x _{2} = - 2[/tex][tex] \displaystyle y _{1} = - 4[/tex][tex] \displaystyle y _{2} = -4[/tex]thus substitute:
[tex] \rm\displaystyle M = \left( \frac{10 + ( - 2)}{2} , \frac{ - 4 + ( - 4)}{2} \right)[/tex]
simplify addition:
[tex] \rm\displaystyle M = \left( \frac{8}{2} , \frac{ - 8}{2} \right)[/tex]
simplify division:
[tex] \rm\displaystyle M = \left( 4, - 4 \right)[/tex]
so the centre of the circle is (4,-4)
since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is
[tex] \displaystyle r = 4 - ( - 2)[/tex]
simplify which yields:
[tex] \displaystyle\boxed{ r =6}[/tex]
recall the equation of circle
[tex] \displaystyle (x - h) ^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
we acquire that,
h=4k=-4r=6therefore substitute:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y - ( - 4))}^{2} = {6}^{2} [/tex]
simplify:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]
and we are done!
also refer the attachment
(the graph is web resource of desmos)
Find the 23rd term of the arithmetic sequence whose common difference is d=4 and whose first term is a^1 = 3.
Answer: the 23rd term of the arithmetic sequence=91
Step-by-step explanation:
The nth term of an arithmetic sequence is given as
an=a+ (n-1) d
Given common difference , d=4 and
first term is a^1 = 3.
We have that
a₂₃=3+ (23-1) 4
a₂₃=3+ (22) 4
a₂₃=3+ 88
a₂₃=91
the 23rd term of the arithmetic sequence=91
If triangle ABC is similar to triangle PQR, which equation is true?
AB/PO = 1
AB = PO
AB/PO = BC/QR
AB /PO = QR/BC
Answer:
AB/ PQ = BC/QR
Step-by-step explanation:
In similar triangles, ratio of corresponding sides are equal.
So, [tex]\frac{AB}{PQ}= \frac{BC}{QR}=\frac{AC}{PR}[/tex]
Name the labelled points between A and C B and D B and E E and A
6x - y= 16 and 3x + 2y + -12 Answer.
Answer:
x= 4/3
y= -8
if you ment 3x + 2y = -12 in the second problem
Step-by-step explanation:
|- 3x| >= - 7
CAN SOMEONE PLEASE GIVE ME THE SOLUTION SET TO THIS INEQUALITY( WORTH 100 POINTS)
Answer:
x < [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
Have a great summer :)
Answer:
someone answered this and its correct
Step-by-step explanation:
:D
se cumple que: A^2 + B = 486 y el M.C.D. de A y B es 9. ¿Cuál es el valor de B
Answer:
i dont know spanish
Step-by-step explanation:
can u helpppp me????
Answer:
XY=6
Step-by-step explanation:
13-7=6
Answer:
XY = 6
Step-by-step explanation:
We know that the whole line (XZ) is equal to 13, and we know that YZ + XY is equal to XZ.
XZ = XY + YZ
13 = XY + 7
6 = XY
Hope this helped :)
Given the similar triangles at the left, write a similarity statement.
HELP IS NEEDED!!!!! PLEASE HELP ME ASAPPP!!!
Answer:
∆ABC~=∆PQR
Angle BAC=QPR
What is a two-column proof
Answer:
A two-column proof uses a table to present a logical argument and assigns each column to do one job, and then the two columns work in lock-step to take a reader from premise to conclusion.
Step-by-step explanation:
Basically in simple terms, one side is the statements, and the otherside is the reasoning
A rectangular tank measures 30 cm by 20 cm by 40 cm. How many milliliters of water are in the tank when it is full? How many liters is that?
Answer:
24000ml or 24L
Step-by-step explanation:
wxhxl = volume
20cm x 30cm x 40cm = volume
volume = 24000cm3
1cm3 = 1ml
24000cm3 = 24000ml
1000ml = 1L
24000ml = 24L
Can you explain it if you could I don’t get it
Step-by-step explanation:
The Triangle Sum Theorem states that the interior angles of a triangle add up to 180 degrees. A square for an angle symbolizes that the angle is 90 °, as is the case with angle ∠ACB.
Therefore, as ∠CAB = 2x and ∠ABC = 3x, and angles ∠ACB, ∠CAB, and ∠ABC make up the interior angles of the triangle, we can say that ∠ACB + ∠CAB + ∠ABC = 180, so 90 + 2x + 3x = 180
90 + 2x + 3x = 180
90 + 5x = 180
subtract 90 from both sides to separate the x and its coefficient
5x = 90
divide both sides by 5 to separate the x
x = 18
(a) ∠CAB = 2x = 18(2) = 36
(b) ∠ABC = 3x = 18(3) = 54
(c) Any triangle with a 90° angle is called a right triangle. This has a 90° triangle, and is therefore a right triangle. Similarly, a 90° angle in a triangle is called a right angle.
in circle O, the measure of ABC is 68. what is the measure of AC?