[tex]\begin{aligned}&9P(n,5)=P(n,3)\cdot P(9,3)\\&9\cdot\dfrac{n!}{(n-5)!}=\dfrac{n!}{(n-3)!}\cdot\dfrac{9!}{6!}\\&\dfrac{n!}{(n-5)!}=\dfrac{n!}{(n-3)!}\cdot7\cdot8\\&\dfrac{1}{(n-5)!}=\dfrac{56}{(n-3)!}\\&(n-4)(n-3)=56\\&n^2-3n-4n+12-56=0\\&n^2-7n-44=0\\&n^2-11n+4n-44=0\\&n(n-11)+4(n-11)=0\\&(n+4)(n-11)=0\\&n=-4 \vee n=11\end[/tex]
[tex]n[/tex] can't be negative, therefore [tex]n=11[/tex]
Answer:
Step-by-step explanation:
9P(n,5)=P(n,3).P(9,3)
9n(n-1)(n-2)(n-3)(n-4)=n(n-1)(n-2)×9×8×7
(n-3)(n-4)=8×7
(n²-4n-3n+12)=56
(n²-7n+12)=56
n²-7n+12-56=0
n²-7n-44=0
n²-11n+4n-44=0
n(n-11)+4(n-11)=0
(n-11)(n+4)=0
n=11,-4
n=-4(rejected as n is a natural number.)
Hence n=11
Please help!!! In 2000, the median household income was $41,990. In 2010, it was $49,445. What is the average rate of change in the median household income over this time period?
Answer: 745.50
Step-by-step explanation:
49445-41990=7455
7455/10=745.50
Lila’s dog Mollie had 8 puppies. 6 of them were male and 2 were female. What percent of Mollie’s puppies were female?
A scale drawing of a new pool is shown above.All the corners are right angles.What is the perimeter of the actual pool?
The lengths are 6in 2 in 5 in and 3 in
A.550 ft
B.800ft
C. 1100 ft
D.1500 ft
PLS EXPLAIN
The perimeter of the actual pool will be option C. 1100 ft.
What is the perimeter?It's the sum of the length of the sides used to make the given figure.
A scale drawing of a new pool is shown. All the corners are at right angles.
The lengths are 6 in, 2 in, 5 in and 3 in.
Perimeter = 6 + 2 + 5 + 3 + 2 + 4
= 22 in
We have given a scale;
1/2 in = 25 ft
So, 1 in = 50 ft
26 in will be
22 x 50 = 1100 ft
Hence, the perimeter of the actual pool will be option C. 1100 ft.
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6) Which statement about the ladder is true?
A. The ladder has parallel line
segments only.
B. The ladder has perpendicular line segments only.
C. The ladder has parallel line
segments and perpendicular line
segments.
D. The ladder has neither parallel line segments nor perpendicular line segments.
The true statement about a ladder is; the ladder has parallel line segments and perpendicular line segments.
Parallel lineParallel lines are lines that never meet on the same plane which have equal distance apart from each other.
Perpendicular lineThey are lines that intersect each other to form a right angle.
Therefore, the ladder has parallel line segments and perpendicular line segments.
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(02.04 LC)
Choose the equation of the horizontal line that passes through the point (2, 4).
Oy=2
Ox=2
Oy = 4
Ox=4
Answer:
You're correct
Step-by-step explanation:
Which graph represents a reflection across the x-axis of g(x) = (3)x?
The graph we need is [tex]y=-3^x[/tex], which is shown in the attached image.
Mr Ade's monthly salary is #460 after paying #50 for his house, giving #2 to each 5 children and setting aside #290 for food, how much has he left?
The amount of money left for Mr Ade after deducting his house payment, children allowance and food is #110
Total balanceMr Ade's total salary = #460Amount paid for his house = #50Amount given to each child = #2
Number of children = 5
Total given to his children = #2 × 5= #10
Amount for food = #290Balance left = 460 - (50 + 10 + 290)
= 460 - (350)
= #110
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Suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.
Determine the iterative rule for each sequence. Show your work.
Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show two calculations to convince your friend that both your rules work.
my table is below (it is correct, I checked with my math teacher, it is ten percent added to the previous week for all you doubters)
The iterative rule for each sequence in the table will be to use the slope-intercept form of the equation of a line y=mx+b.
How to depict the information?In this situation, x is the week, and y is the amount paid. Basically, you need to find the slope, represented by m, which is the amount the amount paid increases by each week, and the y-intercept, b, which is the "amount paid" at week 0.
The x-coordinate is the week, and the y coordinate is the amount paid. Because the weeks are incrementing by 1, x2-x1=1.
After that, to complete the rule, you need to find the y-intercept. If the amount paid is 200 on week 1, and the amount paid increases by 50 each week.
Another way to think about it is by plugging your points into the incomplete rule. Let b represent the y-intercept. Plug in the values for week 1 and solve for b.
The calculations to convince your friend that both your rules work are:
m=(y2-y1)/(x2-x1)
(x1,y1)=(1,200)
(x2,y2)=(2,250)
m=(250-200)/(2-1)
=50/1 =50
y=50x+b
200=50(1)+b
200=50+b
b=200-50
b=150
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describe how you can use similar triangles to explain that the slope
Similar triangles can be used to explain the slope through the right angle.
What is a triangle?It should be noted that a triangle refers to a shape that has three sides and angles.
In this case, similar triangles can be used to explain the slope through the right angle. The slope of the hypotenuse is what we are concerned about.
The legs of the triangle will be the horizontal change and the vertical change of the endpoints.
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Graph the image of the figure given the transformation
This transformation requires us to shift 1 unit left and 4 units down.
QUESTION IS DOWN BELOW 15 POINTS EACH
Answer:
a)
density = mass/volume
density = 320/128
density = 2.5 g/cm3
b)
mass = density x volume
mass = 65 x 26
mass = 1690g
Answer:
a) d = 2.5g/cm3
b) m = 1690g
Step-by-step explanation:
density equals mass between volume
a) [tex]d=320g/128cm^{3} =2.5g/cm^{3}[/tex]
mass equals density by volumen
b)[tex]m=(26g/cm^{3} )(65cm^{3} )=1690g[/tex]
Hope this helps
If the coordinates of one endpoint of a
line segment are (2, 3) and the midpoint
of the segment is (5,3), what are the
coordinates of the other endpoint of the
segment?
Answer: (8,3)
Step-by-step explanation:
The distance from (2,3) to (5,3) is 3. The only other point that is 3 units away from (5,3) where y=3 is (8,3).
Use the function below to find F(2).
Answer:
Step-by-step explanation:
[tex]F(2)=\frac{1}[3} \cdot 4^{2}=\frac{16}{3}[/tex]
Question 14 of 49
Which of the following objects is best described by the term line segment?
A. The point where two sides of a triangle meet
B. The perimeter of a triangle
C. The angle formed by two sides of a triangle
D. One side of a triangle
SUBMIT
Option (A) one side of a triangle is the object that best describes the term line segment is the correct answer.
What is a line segment?
A line segment is a part of line that is bounded by two distinct end-points. A line segment has a fixed length. Figures such as a triangle, polygon, hexagon, square are made of different numbers of line segments.
For the given situation,
A line segment is a portion or piece of a line that allows you to build polygons, determine slopes, and make calculations.
From the definition of line segment we know that the object that best describes the term line segment is one side of a triangle.
Hence we can conclude that option (A) one side of a triangle is the object that best describes the term line segment is the correct answer.
Match the type of insurance to the coverage it provides.
1. Insurance that covers the insured only for a specific, stated term, such as ten years
endowment
2. Insurance that covers the insured for life, and for which premiums are paid by the insured until his death
ordinary whole life
3. Insurance that covers the insured for life, for which he only has to pay a certain number of years
limited-payment life
4. Insurance that provides both insurance and savings
term
The answers include the following:
Insurance that covers the insured only for a specific, stated term, such as ten years endowment - Term life insurance Insurance that covers the insured for life, and for which premiums are paid by the insured until his death ordinary whole life - Whole life insurance.Insurance that covers the insured for life, for which he only has to pay a certain number of years - Limited-payment life insurance.Insurance that provides both insurance and savings term- Universal life insurance.What is Insurance?
This is a form of risk management which protects individuals from any form of loss or damage.
Life insurance has different types which are appropriately mentioned and matched above.
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Write out the form of the partial fraction decomposition of the fraction. Do not determine the numerical values of the coefficients.
[tex]\frac{x^4}{(x^3+x)(x^2-x+7)}[/tex]
Factorizing the denominator gives
[tex]\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{x^4}{x(x^2+1)(x^2-x+7)} = \dfrac{x^3}{(x^2+1)(x^2-x+7)}[/tex]
Then the partial fraction decomposition would take the form
[tex]\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{a_0x + b_0}{x^2+1} + \dfrac{a_1x + b_1}{x^2-x+7}[/tex]
Please help! Need to pass!
The height of the ramp of Raúl is calculated as; 8ft
How to use the principle of similar triangles?Both big and small triangles are similar triangles because all three of their corresponding angles are congruent.
Now, to get the height we will use the concept of similar triangles to get;
h/2 = 12/3
Cross multiply to get;
h = 24/3
h = 8 ft
Thus, the height of the ramp of Raúl is 8ft.
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twelve bottles of water cost $9. How many bottles can you buy for $3?
What is the cost per bottle of water? How much would 7 bottles of water cost?
That is the answer for the 3 questions
The B737-400 aircraft costs $2948 dollars per hour to operate. The algebraic expression 2948t gives the total cost to operate the aircraft for t hours. Find the total cost to operate the B737-400 for 3.6 hours.
Answer:
The required cost is $10,612.8
Step-by-step explanation:
Find the value at t = 3.6:
2948t, t=3,6
Substitute t=3,6
Multiply 2948x3,6
Solution = 10612,8
Giving brainliest :)
Answer:
Your answer should be D. $48,856.11
Step-by-step explanation:
This formula is for Compound Continuously.
[tex]A=P*e^{rt}[/tex]
P = 40,000
e = 2.71...
r = 2.5% = 0.025
t = 8 years
Plug in our variables and solve for the money of the account within 8 years.
A = 40,000*e^(0.025*8)
A = 40,000*e^(0.2)
A = 48,856.11033
A = $48,856.11
epresents a function?
{(2, 3), (3, 4), (5, 6), (2, 9)}
{(4, 2), (5,2), (6, 2), (9, 2)}
{(1, 2), (1, 3), (1, 4), (1, 5)}
{(-4, 9), (-8, -12), (-4, -15), (-8, -21)}
Answer:
No, it does not represent a function
Step-by-step explanation:
A function can be described as a set of points where each x coordinate has 1 corresponding Y coordinate
1 has multiple different Y coordinates
2 has multiple different Y coordinates
-4 has multiple different Y coordinates
Answer:
Only the second one
Step-by-step explanation:
All of the others have multiple values for 'x'
a function can only have one value for each value of x
Example: the first one when x = 2 it has two 'y' values 3 and 9
Multiply (-3) by (+1,4
The product (-3) * (1, 4) is (-3, -12)
How to multiply the numbers?The expression is given as:
(-3) * (1, 4)
Rewrite the expression as
(-3 * 1, -3 * 4)
Evaluate the product
(-3, -12)
Hence, the product (-3) * (1, 4) is (-3, -12)
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Find the equation for the line that passes through the point (2, -3), and that is parallel to the line with the equation x - 3y = 3
Step-by-step explanation:
the slope of a line is the factor of x, when the equating looks like
y = ...
so,
x - 3y = 3
x = 3y + 3
3y = x - 3
y = 1/3 x - 1
so, the original slope is 1/3.
a parallel line has the same slope.
having a specific point we can use the point-slope form as equation :
y - y1 = m(x - x1)
with m being the slope, and (x1, y1) being a point on the line.
y - -3 = 1/3(x - 2)
y + 3 = 1/3(x - 2)
simplified that is
y + 3 = 1/3 x - 2/3
y = 1/3 x - 2/3 - 3 = 1/3 x - 2/3 - 9/3 = 1/3 x - 11/3 =
= 1/3 × (x - 11)
Answer:
[tex]y=\frac{1}{3}x - \frac{11}{3}[/tex]
Step-by-step explanation:
We are given the line x-3y=3.
We want to write the equation of the line that is parallel to this line, and that passes through (2, -3).
Parallel lines have the same slope.
Therefore, let's find the slope of x-3y=3.
The line is currently written in standard form, which is ax+by=c, where a, b, and c are free integer coefficients.
In order to find the slope of this line, we can convert it into slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.
To do that, we need to isolate y on one side; this is the same as solving the equation for y.
x - 3y = 3
Start by subtracting x from both sides
-3y = -x + 3
Now divide both sides by -3
[tex]y = \frac{1}{3} x - 1[/tex]
The slope of the line is 1/3, as 1/3 is the coefficient in front of x.
It is also the slope of our new line.
Since the question doesn't specify which format for the equation of the line, we can use any form. However, let's put the equation of the new line into slope-intercept form.
So, substitute 1/3 as m in y=mx+b.
[tex]y = \frac{1}{3} x + b[/tex]
Now we need to find b.
As the equation passes through the point (2, -3), we can use its values to help solve for b.
Substitute 2 as x and -3 as y.
[tex]-3 = \frac{1}{3} (2) + b[/tex]
Multiply.
[tex]-3 = \frac{2}{3} + b[/tex]
Subtract 2/3 from both sides (we can write this as an improper fraction).
[tex]-\frac{11}{3} = b[/tex]
Substitute -11/3 as b in the equation.
[tex]y=\frac{1}{3}x - \frac{11}{3}[/tex]
Solve this trig identity step by step
The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
How to solve the trigonometric identity?
Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
Using the identity a² - b² = (a + b)(a - b), we have
(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =
= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)
Also, Using the identity a² - b² = (a + b)(a - b), we have
(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]
= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]
= 1 × cos⁴θ
= cos⁴θ
So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
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Which pair of expressions is equivalent using the Associative Property of Multiplication?
4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
4(2a ⋅ 5) = 8a ⋅ 20
4(2a ⋅ 5) = (2a ⋅ 5) ⋅ 4
4(2a ⋅ 5) = 4 ⋅ 2a ⋅ 5
Answer:
out of 700 full marks dolma obtained 525 marks in an examination express her marks in percent
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
All the roles have now been cast, and the lead actors playing the following parts are gathered around a large circular table for their first read: Jean Valjean, Inspector Javert, Thénardier, Enjolras, Marius, Fantine, adult Cosette, adult Éponine, and Madame Thénardier. It is your job to seat these 9 actors, the 3 producers, and the director around the table.
In Les Misérables, Monsieur Thénardier and Madame Thénardier are married, and during Act 2, Cosette and Marius become married. If the Thénardiers must next to one another, and Cosette and Marius must sit next to one another, but there are no restrictions on how the others can sit, how many different ways can you seat the 13 people around the circular table?
4
17,160
14,515,200
6,227,020,800
There are 14,515,200 ways to arrange the people around the table
How to determine the number of ways?The given parameters are:
People = 13
Thénardiers = 2 actors
Cosette and Marius = 2 actors
If the married actors must seat together, then the actors must be grouped as 1.
The 2 actors can be arranged in 2! ways each
Now, there are 9 individuals remaining
The 9 people can be arranged in 9! ways
So, the number of ways is
Ways= 2! * 2!* 9!
Evaluate
Ways =14,515,200
Hence, there are 14,515,200 ways to arrange the people around the table
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Which list shows all the factors of 16?
A. 1, 2, 4, 8
B. 1, 2, 3, 8, 16
C. 1, 2, 4, 8, 16
D. 16, 32, 48, 64
Answer:
C
Step-by-step explanation:
To be a factor of 16 they need to be numbers that divide into it without remainders.
Answer:
Step-by-step explanation:
its C
Find the critical value z alpha/2 that corresponds to the given confidence level. 81%
Critical values are basically cut-off values that indicate regions where the test statistic is unlikely to lie. The required critical value is 1.31.
What are critical Values?Critical values are basically cut-off values that indicate regions where the test statistic is unlikely to lie; for example, if the null hypothesis is true, the critical value is surpassed with probability alpha.
The value of α can be written as,
α = 1 - 0.81 = 0.19
[tex]z_{\frac{\alpha}{2}} = \dfrac{0.19}{2}= 0.095[/tex]
Now, using the z-table the value of z will be,
z = 1.31
Hence, the required critical value is 1.31.
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Help me with this please!! :)
Answer: 26 cards
Step-by-step explanation: Just divide 52 by 2 and you get 26 cards :)
I need help because Im losing it
The fraction of the colored part is 10/12 or 5/6. None of the option is correct
Fractions and proportionsFractions are written as a ratio of two integers. From the given question;
3 square divided into4 equal parts will have a total of 12 parts. If Kelly colors 10 parts, the fraction of the colored part will be:
Fraction. = 10/12
Fraction = 5/6
Hence the fraction of the colored part is 10/12 or 5/6
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