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.
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I need help on number 1
Answer:
V =960 in ^3
Step-by-step explanation:
V = l*w*h
V = 12*8*10
V =960 in ^3
What is the product?
Answer:
Step-by-step explanation:
In exponent multiplication, if base are same just add the powers.
[tex](-6a^{3}b+2ab^{2})(5a^{2}-2ab^{2}-b)=(-6a^{3}b)*(5a^{2}-2ab^{2}-b)+2ab^{2}*(5a^{2}-2ab^{2}-b)\\\\[/tex]
[tex]=(-6a^{3}b)*5a^{2}-(-6a^{3}b)*2ab^{2}-(-6a^{3}b)*b+ 2ab^{2}*5a^{2}-2ab^{2}*2ab^{2}-2ab^{2}*b\\\\=-30a^{3+2}b+12a^{3+1}b^{1+2}+6a^{3}b^{1+1}+10a^{1+2}b^{2}-4a^{1+1}b^{2+2}-2ab^{2+1}\\\\=-30a^{5}b+12a^{4}b^{3}+6a^{3}b^{2}+10a^{3}b^{2}-4a^{2}b^{4}-2ab^{3}\\[/tex]
Asia is the largest of the world’s seven continents with an area of approximately 1.7 times 10 Superscript 7 square miles. Australia, the smallest continent, has an area of approximately 3.1 times 10 Superscript 6 square miles.
How much larger is Asia than Australia? Express the answer in scientific notation.
1.40 times 10 Superscript 6 square miles
2.93 times 10 Superscript 6 square miles
1.39 times 10 Superscript 7 square miles
2.01 times 10 Superscript 7 square miles
The amount of area larger is Asia than Australia will be 1.39 × 10⁷. Then the correct option is C.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
Asia is the largest of the world’s seven continents, with an area of approximately 1.7 times 10⁷ square miles.
Australia, the smallest continent, has an area of approximately 3.1 times 10⁶ square miles.
Then the amount of area larger is Asia than Australia will be
⇒ 1.7 × 10⁷ – 3.1 × 10⁶
⇒ 1.7 × 10⁷ – 0.31 × 10⁷
⇒ 1.39 × 10⁷
Then the correct option is C.
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Given the function f(x) = 3x + 1 what is f(-2)?
Answer:
-5
Step-by-step explanation:
f(-2) means that -2 is going to be our input in this function.
To solve this, simply substitute -2 for x in the expression given.
If f(x) = 3x+1, then f(-2) = 3(-2) + 1
3(-2)+1 = -6+1 = -5
Hope this helped!
Answer:
f(-2) = 3(-2) + 1
f(-2) = 6 + 7
Therefore: f(-2) = 7
I need help please and urgent!
Answer:
the answer is blurry for me take a picture again
Step-by-step explanation:
Which angles in the picture are NOT supplementary?
Answer:
2nd option
1 and 3 ; 2 and 4
Step-by-step explanation:
supplementary angles are those whose sum equal to 180°.
How to solve this? I have no clue and also teach me on how to solve this! Thank you!!! thank you for your time!!!!
The answer you have is the correct answer. When reflecting across the x-axis, the x-coordinate will always remain the same, but the y-coordinate value will be the opposite (in this case -5 will become 5)
Find a round to the nearest tenth 12 22 75 x x=?
Answer:
By law of Sines[tex]\frac{Sin75^o}{22} =\frac{Sinx}{12}[/tex][tex]\frac{Sin75}{22}(12)=\frac{Sinx}{12} (12)[/tex][tex]0.5268=Sinx[/tex][tex]Sin^(0.5268)=x[/tex][tex]x=31.789[/tex][tex]x=31.79^o[/tex]-----------------------hope it helps..have a great day!!The square of a number 60 greater than half of the number. Form a
quadratic equation and solve to determine the possible values of the
number.
Answer:
Sorry Baby i don't know
Step-by-step explanation:
Bye
You have a hospital bill of $14,000. You have an insurance plan that has a $2,000 deductible and a 20% coinsurance clause. How much do you pay towards the total bill?
Answer:
4400
Step-by-step explanation:
First take off your deductible
14000-2000
12000
Now find 20 % of this amount
12000*20%
12000 * .20
2400
You have to pay the deductible and the 20%
2000+2400
The cost to mail a letter is a base charge of $0.42 plus $0.17 for each ounce. Write an expression to represent the cost for mailing a letter that is w ounces. Then find the cost for mailing a letter that is four ounces.
Answer:
$0.42 + $0.17w = x
$0.42 + $0.17 x 4 = $1.10
Step-by-step explanation:
for building the equation, we were given the variable for ounces so just multiply the amount of ounces by .17 and for solving for four ounces just input 4 into W and boom equation solved
Answer:
$0.42 + $0.17 x 4 = $1.10
Step-by-step explanation:
If f(x) = 2x²+2 and g(x) = x² - 1 ,find (f- g)(x).
A. 3x² +3
B. 3x² +1
C. x² +1
D. x² +3
Step-by-step explanation:
(F-g) (X)
= f(x) - g(x)
(2x² + 2 )-(x²-1) =
3x²+3
PLEASE HELP AND ASAP!!!!
Find the mean of the given set of numbers. 1, 4, 2, 2, 6, 9
Answer:
4
Step-by-step explanation:
Answer:
There are several different means:
Arithmetic: 4 (This is most likely your answer.)
Geometric: 3.0862
Harmonic: 2.3736
Hope that this helps!
Geraldo orders a private jet for a party that has a flat rate of 175,000
dollars plus an addition 65,000$ for each additional passenger. He as AT
MOST 1 million dollars to spend ($1,000,000) how many people can he
take with him? (Round down to the nearest human and WRITE YOUR
ANSWER AS A SENTENCE)*
Answer:
im not really sure but try 600,0
Step-by-step explanation:
Which linear inequality is represented by the graph?
A.y<2/3x+3
B.y>3/2x+3
C. y>2/3 x + 3
D.y<3/2x + 3
PLEASE HELP THIS IS SUPER IMPORTANT!!!! A culture of bacteria has an initial population of 860 bacteria and doubles every 9
hours. Using the formula Pt= P0x2t/d, where Pt is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 4 hours, to the nearest whole number?
Answer:
1170Step-by-step explanation:
Substitute values into given equation and solve for P(t):
P(t) = P₀*2^(t/d)P(4) = 860*2^(4/9) = 1170 (rounded)The triangle is isosceles find the length h of side x in simplest radical form with a rational denominator
Answer:
x = √3
Step-by-step explanation:
Find the diagram attached
Given
Opposite = √3
Adjacent = x
Acute angle theta = 45degrees
According to SOH CAH TOA;
tan theta = opp/adj
tan 45 = √3/x
x = √3/tan45
x = 1
x = √3
Hence the value of x in its simplest radical form is √3
If the graph of y=x squared +6x-12 is symmetrical about x=K, what is the value of K?
pls help me on this i don't know what to do
Answer:
A.
Step-by-step explanation:
Factor out x^2-3x-40. Know that the zeroes of a function multiply to be equal to the constant (-40) and add up to the coefficient of the x term (-3). The two numbers that do that are -5 and 8. Recall that to be zeroes, at least one of the x-values must make the equation equal 0. So if x=-5, (x+5) is the term that would be 0.
You could also multiply the factored forms that are given to find the correct one.
In circle P, BC = 24 ft. What is the length of arc AC?
A)π
B)2π
C)4π
D)8 π
Answer:
b
Step-by-step explanation:
Jewel is 7 years old and John is 16 years younger than Dave. One year ago, Dvae's age was twice the sum of Jewel's and John's ages. Fine the current age of each of them.
Answer:
Jewel is 7 years old
John is 1 year old
Dave is 17 years old
Step-by-step explanation:
From the question we are told that:
Jewel age is [tex]J=7 years[/tex]
John age [tex]J'=(D-16)years[/tex]
Dave's age a Year ago
[tex]D-1=2(J-1+J'-1)[/tex]
So that Dave.s age this Year could be
[tex]D=2((J-1)+(J'-1))+1[/tex]
Simplifying Equation for Dave's age we have
[tex]D=2((7)-1+(D-16)-1)+1[/tex]
[tex]D=2(6+D-15)+1[/tex]
[tex]D=2(D-9)+1[/tex]
[tex]D=2D-18+1[/tex]
[tex]D=17 Years[/tex]
Dave is 17 years old
Therefore
Johns age is
[tex]J'=(D-16)[/tex]
[tex]J'=17-16[/tex]
[tex]J'=1year old[/tex]
John is 1 year old
factorise using suitable identities
x^2 - 2x + 1
Answer:
(x - 1)^2
Step-by-step explanation:
using middle term break method
x^2 - 2x + 1
here, we need to numbers which gives 1 when multiplied and 2 when add .
=x^2 - (1 + 1)x + 1
=x^2 - x - x + 1
=x(x - 1) -1(x - 1)
=(x -1)(x - 1)
=(x - 1)^2
Step-by-step explanation:
by middle term factorisation method
x^2 -2x + 1
= x^2 -( 1+1)x + 1
= x^2 -x -x + 1
= x(x-1) -1( x -1)
= (x-1)(x-1)
OR
we know above polynomial ( quadratic ) equation is in form
(a - b )^2 = a^2 -2ab + b^2
so it's factories form is
( a- b)( a- b)
Consider the equation y = -2x + b. Find the value of b if the line passes through (-5, 4).
Select one:
a. b = -3
b. b = 4
c. b = 2
d. b = -6
Answer:
b = -6 (Answer d)
Step-by-step explanation:
The slope-intercept equation is y = -2x + b, and we know that the line passes through (-5, 4). Substitute -5 for x and 4 for y, to obtain:
4 = -2(-5) + b, or
4 = 10 + b, or
b = -6 (Answer d)
Amira is trying to find the height of a radio antenna on the roof of a local
building. She stands at a horizontal distance of 26 meters from the building.
The angle of elevation from her eyes to the roof (point A) is 23°, and the
angle of elevation from her eyes to the top of the antenna (point B) is 33°. If
her eyes are 1.54 meters from the ground, find the height of the antenna (the
distance from point A to point B). Round your answer to the nearest meter if
necessary.
Answer:Using the formula for the area of the composite shape, Area of composite shape = Area of rectangle + area of the square. ⇒ Area of composite shape = 14+9 = 23 square inches.
Step-by-step explanation:
Which of the following systems of inequalities has solutions represented by the graph shown below?
Answer:
y ≤ 1/2x - 1
y ≤ -2x + 4
ZA=
Round your answer to the nearest hundredth.
С
A
?
5
8
B
Answer:
∠A = 38.68°
Step-by-step explanation:
[tex]sinA=\frac{5}{8}\\A=sin^{-1}(\frac{5}{8})\\A=38.68[/tex]
The measure of the ∠A in this right-angled triangle is, 38.68°.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
From the given figure, With reference to ∠A, the Opposite is 5 units and the hypotenuse is 8 units.
We know, sin = opposite/hypotenuse.
Therefore, sinФ = 5/8.
Ф = sin⁻¹(5/8).
Ф = 38.68°.
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can someone pls help for brainlest
Answer:
144
Step-by-step explanation:
Determine wether the lines given are parallel, perpendicular or neither
Answer:
Neither
Step-by-step explanation:
We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect. So if the slopes have reciprocals, they are perpendicular. Otherwise, they are neither.
The road leading to the top of a hill has an angle of elevation of 23 degrees. The hill is 120 feet high. What is the length of the road to the top of the hill?
Answer:
2760
Step-by-step explanation:
23 multiply by 120
=2760
Question is due soon I need help
Answer:
looks like C is best guess