The value of n in the permutation equation P(n, 5) = 2520 is 7
How to evaluate the permutation expression?The expression is given as:
P(n, 5) = 2520
The above expression is a permutation expression.
The permutation expression is different from the combination expression, and the permutation expression is calculated using the following permutation formula
P(n,r) = n!/(n - r)!
Substitute 5 for r in the above equation
P(n,5) = n!/(n - 5)!
Substitute the given values in the above equation
n!/(n - 5)! = 2520
Expand the above equation
n(n-1)(n - 2)(n - 3)(n - 4)(n - 5)!/(n - 5)! = 2520
Evaluate the quotient in the above equation
n(n-1)(n - 2)(n - 3)(n - 4) = 2520
Express 2520 as 7 * 6 * 5 * 4 * 3
n(n-1)(n - 2)(n - 3)(n - 4) = 7 * 6 * 5 * 4 * 3
By comparing the equation, we have
n = 7
Hence, the value of n in the permutation equation P(n, 5) = 2520 is 7
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NO LINKS!! Please help me with this problem
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given vertex and Focus are of a vertical parabola having an opening downward as the focus is in downward direction as the vertex.
Focus of the parabola can be written as :
[tex]\qquad \sf \dashrightarrow \: (h ,k+ a )[/tex]
where, h and k are coordinates of vertex
so,
k + a = -2 -1 + a = -2a = -1So, the equation of parabola can be written as :
[tex]\qquad \sf \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)[/tex]
plug in the values ~
[tex]\qquad \sf \dashrightarrow \: (x - 1) {}^{2} = 4(- 1)(y + 1) {}^{} [/tex]
[tex]\qquad \sf \dashrightarrow \: (x - 1) {}^{2} = - 4(y + 1)[/tex]
Answer:
[tex](x-1)^2=-4(y+1)[/tex]
Step-by-step explanation:
Standard form of a parabola with a vertical axis of symmetry:
[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]
Vertex = (h, k)Focus = (h, k+p)Directrix: y = (k-p)Axis of symmetry: h = kIf p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.Given:
vertex = (1, -1)focus = (1, -2)Comparing with the formulas:
⇒ h = 1
⇒ k = -1
⇒ k + p = -2 ⇒ -1 + p = -2 ⇒ p = -1
Substituting the values into the formula:
[tex]\implies (x-1)^2=4(-1)(y-(-1))[/tex]
[tex]\implies (x-1)^2=-4(y+1)[/tex]
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 316 people entered the park, and the admission fees collected totaled 924.00 dollars. How many children and how many adults were admitted
Answer: pretty sure
There were 108 children and 175 adults.
Question 3(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following tables shows the correct steps to transform x2 + 6x +8=0 into the form (x-p)² =q?
[p and q are integers]
The correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;
x^2 + 6x +8 +1 = 0 + 1
x^2 + 6x +8 +1 = 1
x^2 + 6x + 9 = 1
(x+3)² = 1
Vertex form of a quadratic equationThe vertex form of a quadratic equation is expressed as:
a(x-h)² + k
Given the quadratic equation
x^2 + 6x +8=0
Subtract 8 from both sides
x^2 + 6x +8 - 8 = 0 - 8
x^2 + 6x = -8
Complete the square
(x^2+6x+3^2) = -8 + 9
(x+3)² = -8 + 9
(x+3)² = 1
Hence the correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;
x^2 + 6x +8 +1 = 0 + 1
x^2 + 6x +8 +1 = 1
x^2 + 6x + 9 = 1
(x+3)² = 1
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evaluate f(x)=4|x|+3 for x=-5
(02.03 MC)
Choose the equation that represents the graph.
graph of a line passing through points negative 2 comma 0 and 0 comma negative 4
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
y = - 2x - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, - 4) ← 2 points on the line
m = [tex]\frac{-4-0}{0-(-2)}[/tex] = [tex]\frac{-4}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4
y = - 2x - 4 ← equation of line
convert this into a standard number
[tex]10^{6}[/tex]
Answer:
1,000,000
Step-by-step explanation:
The attached place value chart shows the power of ten associated with each number place in a decimal number.
ApplicationYou have ...
1 × 10⁶ = 1,000,000
(Put the multiplier digit in the appropriate number place, and fill the remaining spaces with zeros. The digits 32,465 on the chart can be ignored.)
__
Additional comment
For powers of 10, the exponent (6 in this case) tells you the number of zeros to the right of the digit 1. That is, 10^6 is 1 followed by 6 zeros:
1,000,000
x+11=35 solve on algebraic equation
Answer:
x = 24
Step-by-step explanation:
x + 11 = 35
x = 35 - 11
x = 24
x+11=35
Subtract 11 on both sides.
x=35−11Subtract 11 from 35 to get 24.
x=24 === AnswerRepresent each expression as a power of a, a cannot be equal to 0
Answer:
a^-27
Step-by-step explanation:
(a^3)^-3)^3)
(a^-9)^3)
a^-27
When we represent the expression ((a³)⁻³)³ as a power of a, the result obtained is a⁻²⁷
How to represent the expression as a power of a?The following data were obtained from the question:
Expression: ((a³)⁻³)³Representation as power of a =?We can represent the expression ((a³)⁻³)³ as a power of a by using the power law of indices as illustrated below:
((a³)⁻³)³
Recall
(Bᵐ)ⁿ = Bᵐⁿ (i.e multiply the power)
Thus,
((a³)⁻³)³ = (a⁻⁹)³
= a⁻²⁷
Thus, we can conclude from the above calculation that the representation of the expression ((a³)⁻³)³ as a power of a is a⁻²⁷
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Simplify the following expression.x-[tex]\frac{2}{3}[/tex] x[tex]\frac{6}{7}[/tex]
Keeping the bases and adding the exponents, the simplified expression is:
[tex]x^{\frac{4}{21}}[/tex]
How to solve a product of two terms with the same base and different exponents?We keep the bases and add the exponents.
Hence:
[tex]x^{-\frac{2}{3}} \times x^{\frac{6}{7}} = x^{-\frac{2}{3} + \frac{6}{7}} = x^{\frac{-14 + 18}{21}} = x^{\frac{4}{21}}[/tex]
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If a diameter of a circle has endpoints (-3,5) and
(5, 7), then the center of the circle is
Answer:
(1 , 6)
Step-by-step explanation:
the center of the circle is the midpoint of the diameter
Which is the point of coordinates:
[tex](\frac{-3+5}{2} ,\frac{5+7}{2} )[/tex]
Then the center is the point :
[tex](1 , 6)[/tex]
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:
[tex]\longrightarrow\bold{(-3,5)}[/tex]
[tex]\longrightarrow\bold{(5, 7)}[/tex]
Calculate the average value between the x-coordinates of the diameter and do the same for the y-coordinates:
[tex]\longrightarrow\sf{C_x=\dfrac{-3+5}{2} = \dfrac{2}{2} =1}[/tex]
[tex]\longrightarrow\sf{C_y= \dfrac{5+7}{2} = \dfrac{12}{2} = 6 }[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\longrightarrow\sf{=(1,6)}[/tex]
What are the domain and range of g(x)=√x+4?
OD: [4, ∞) and R: [0, ∞)
OD: (-4, ∞) and R: (-∞, 0)
OD: [-4, ) and R: [0, ∞)
OD: (4,) and R: (-∞, 0)
Answer:
Domain [-4 , +∞)
Range [0 , +∞)
Step-by-step explanation:
the function g such that g(x)=√(x+4) ,is defined
for the values of x that verify :
x + 4 ≥ 0
⇔ x ≥ -4
Then
The domain of g is [-4 , +∞)
………………………………………………
Let x ∈ [-4 , +∞)
then x ≥ -4
then x + 4 ≥ 0
then g(x) = √(x+4) ≥ 0
Therefore, we can affirm that the range of g is [0 , +∞)
Gene is tossing a normal quarter. He tosses the quarter 12 times and it lands on heads 9 times. If Gene tosses the quarter again, what is the probability that it lands on tails? Input your answer in fraction form.
Answer:
1/2
Step-by-step explanation:
This is an independent event. It does not matter what happened before the chances of getting a tail on one toss will always be what I want/all outcomes. There are only 2 outcomes: heads or tails. I am only looking for one of those outcomes, so 1/2.
Sharon is planting tulip
bulbs in her garden. In the
catalog she sees a disclaimer that there is a 1/15 probability that a bulb will not flower. If Sharon plants 90 bulbs, how many tulips can she expect to see in her garden?
Answer:
84 flowers.
Step-by-step explanation:
We must multiply 90 by 1/15 to get 6 bulbs that will not flower. 90-6 is 84.
You are building a ramp for your grandparent’s house. The ramp will replace the steps that go to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the front door. How long will the ramp need to be?
Answer:
10.4403 or the square root of 109
Step-by-step explanation:
We do this by finding the height (3) and squaring it then the base (10) and squaring that, this sets up the Pythagorean theorem which is A^2+B^2=C^2 then you square C to find it's value
Find the indicated real nth root(s) of a.
n=3, a = - 216
Answer:
-6
Step-by-step explanation:
A suitable calculator can find this for you directly.
Odd root of a negative number-1 raised to an odd power is -1. That means an odd-index root of a negative number will be the opposite of the corresponding root of its absolute value:
∛(-216) = -∛216 = -6
__
Additional comment
Many calculators and spreadsheets do not respond well to requests for roots of negative numbers. A calculator with built-in support for complex numbers is the best choice for this sort of problem.
The second attachment shows a calculator capable of finding the complex roots as well as the real one.
Simplify the following fractions.
Answer:
The solution for the above fraction is
[tex] \frac{146}{167} [/tex]
Step-by-step explanation:
Greetings!
look at the attachment above for the explanation.
Please look at the attachment and answer my question :(
Answer:
AB / BC = 2 / 3
A equals 9 and C = 13
AC = 13 - 9 = 4
AB + BC = 13
A) AB + BC = 4
B) AB / BC = 2/3 Therefore BC = AB / (2/3)
B) BC = 1.5 AB
A) BC = 4 - A/B
Multiplying equation A) by -1
A) -BC = -4 + AB then we add equation B)
B) BC = 1.5 AB then adding both equations
0 = 2.5 AB -4
2.5 AB = 4
AB = 1.6
Since A = 9 then the number at B is 9 + 1.6
equals 10.6
Step-by-step explanation:
Answer:
The number at B is 10.6
Step-by-step explanation:
Let the number at B be x.
We know that distance between two points on the number line is the absolute value of the difference of numbers at those points.
Then distances representing the lengths of segments AB and BC are:
AB = x - 9BC = 13 - xWe are given the ratio of segments:
AB/BC = 2/3Substitute and solve for x:
(x - 9)/(13 - x) = 2/33(x - 9) = 2(13 - x)3x - 27 = 26 - 2x3x + 2x = 26 + 275x = 53x = 53/5x = 10.6What is the radian measure of central angle AOB in the circles? Write down the answer in the lowest terms
5pi/12 radians
The arc measure is 75, so theta must also be the same. if theta is 75, and 75 in radians is 5pi/12 radians, then the answer is that.
Which of the following is the most accurate statement about Spatial Relations?
A- Children understand the spatial world watching movies about animals all over the world.
B- Children Need to know, use and be able to read spatial terms before they can demonstrate spatial awareness.
C-Spatial terms such as above, below, behind, and under are used to describe objects in space from different perspectives and are important for children to understand and express as they understand spatial relations.
Option C. The correct statement about spatial relationshipo is that Spatial terms such as above, below, behind, and under are used to describe objects in space.
What are spatial relationship?These are the types of relationships that are used to relate objects to the location of somethings else. It makes use of words like under, above etc.
It is one of the knowledge that children need in the preoperational stage to learn how to use logical operations.
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Solve the proportion
12
8
=
7.5
x
Answer:
9.8 is the final anwser
Step-by-step explanation so easy
A text message plan costs $9 per month plus $0.39 per text. Find the monthly cost for x text message The monthly cost of x messages is dollars. (Use integers or decimals for any numbers in the expression.) *
Answer:
The monthly cost = $9 + $0.39x
Step-by-step explanation:
Two friends, Jamie and Devin, are working together at the Sparrowtown Cafe today. Jamie works every 2 days, and Devin works every 7 days. How many days do they have to wait until they next get to work together?
Answer:
14 days
Step-by-step explanation:
let assume they both work on Monday (today)
devin works every 7 days,that is devin works every Monday.
jamie has to work for 14 days inorder to work with devin again
1. Which one of the following statements expresses a true proportion? A. 3:49:12 OB. 2:1 1:2 OC. 54:9 = 6:3 OD. 7:98:9
Answer:
3:4 9:12
Step-by-step explanation:
Rewrite the ratios as fractions. 3:4 becomes 3/4, and 9:12 becomes 9/12, which simplifies to 3:4. Therefore A is a true proportion.
Assignment
Slide the green dot from 0 to plot the number at the correct
location.
Plot-1.
-6 -5 4 -3 -2 -1 0 1
2
3 4
5
+
6
Use the interactive number line to find each sum to
complete the table.
A
1
-1
-4
-6
B
2
-2
1
-3
A + B
3
R
S
T
From the number line, the values which completes the sum in the table are:
R = -3.S = -3.T = -9.What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
How to find each sum?From the table of values (see attachment), the values on the number line are represented as follows:
a + b = a + b
R = -1 - 2
R = -3.
a + b = a + b
S = -4 + 1
S = -3.
a + b = a + b
T = -6 - 3
T = -9.
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What is DC to the nearest tenth? I need help, thank you:)
The measure of the length DC to nearest tenth is 24.1 units
Pythagoras theoremIn order to determine the measure of DC from the figure shown, we will use the pythagoras theorem
Determine the measure of BC
BC² = 22² - 15²
BC² = 259
BC = 16.09
Determine the measure of DC
DC² = 259 + 28²
DC = √583
DC = 24.1 units
Hence the measure of the length DC to nearest tenth is 24.1 units
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write the expression 5x(x+9) -7(x+9) in complete factored form.
(5x-7)(x-9)
Step-by-step explanation:Factoring is the inverse of the distributive property. This means that we want to find the factors, not the product.
Partial Factoring
The expression we are given has already been factored to an extent. Both terms are split into 2 different factors. This was done by factoring out the greatest common factor (GCF) from both terms. In the first term, the GCF was 5x, and in the second, the GCF was -7.
Complete Factoring
Even though it was partially factored, we can factor it more. When given the situation:
a(x + y) - b(x + y)The expression can be factored into:
(a - b)(x + y)You can add (subtract in this case because 7 is negative) the values from outside the parentheses together. This term can then be multiplied by the value within the parentheses.
Thus, 5x(x+9) -7(x+9) can be factored into:
(5x-7)(x-9)Remember this trick only works when both terms share a factor like (x-9).
A sience teacher uses an overhead projector to display a diagram of a pulley sytem. the actual diagram is 6'' by 7.2''. The image projected onto the wall is 4' 2'' by 5'' what is the scale factor of the projection
Answer:
25/36, or .694444
Step-by-step explanation:
First, let's convert 6" to inches.
That gives us 72. After we convert 4'2" into inches, we get 50.
This means that the diagram goes from 72 inches wide to 50. Put this into a proportion to find the scale factor:
50/72 = 25/36 = .6944444
Use the table to the right to answer the following question.
Compare the energy released by fission of 1 kilogram of element B to that released by burning 1 kilogram of element A.
The energy is compared based on the information given below.
How to illustrate the energy?Energy released by burning 1 kilogram of element A = EA = 5.1 * (10)8
Energy released by fission of hydrogen in 1 kilogram of element B = EB = 1.3 * (10)10
Therefore,
Ratio = EB / EA = 1.3 * (10)10 / 5.1 * (10)8 = 25
Thus, the fission of 1 kg of element B releases 25 times as much energy as burning 1 kilogram of element A.
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The other part of the question:
Energy released by burning 1 kilogram of element A = 5.1 times 10 Superscript 8
Energy released by the fission of hydrogen in 1 kilogram of element B = 1.3 times 10 Superscript 10
Solutions greatest to smallest for function
=2+5−7
The greatest or maximum value for the given function = -8.25
The minimum or smallest value for the given function =-4
Calculation of greatest and smallest functionsThe maximum value of a function is the highest value of that function. To calculate the greatest function, the following equation is used,
Formula max = c - (b2 / 4a)
Where,
a = 2
b = 5
C = -7
Therefore maximum function
= -7 -(5*2/4*2)
= -7-(10/8)
= -7 - 1.25
= -8.25
The minimum value of a function is the least value of that function.
Formula for the minimum = c - b^2/4a.
= -7-5^2/4*2
= -32/8
= -4
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How do i convert the follwing Powers Of Ten into standard numbers?
[tex]10^{7}[/tex]
[tex]10^{5}[/tex]
[tex]10^{8}[/tex]
[tex]10^{12}[/tex]
[tex]10^{6}[/tex]
The standard numbers are obtained from the given numbers as follows;
10⁷ → 1000000010⁵ → 10000010⁸ → 10000000010¹² → 100000000000010⁶ → 1000000Which method can be used to express the numbers in standard form?The standard form of numbers is obtained by expressing the number completely and not using powers of 10
The given numbers in powers of 10 can be expressed in standard form by writing the specified number of zeros next to 1 given by the power of 10 as follows;
Number → Standard form
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