Answer: 120 different ways. It is a permutation.
Step-by-step explanation:
Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).
The number of ways to award the medals in 120 different ways.
What is permutation?When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
Given
Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has a first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).
To know more about permutation refer to :
https://brainly.com/question/1216161
#SPJ2
Answer I need help this question because I don’t know what it is and I need help
Answer:
17
Step-by-step explanation:
QS and RS equal the same
5x - 8 = 3x + 2
-3x +8 -3x +8
2x = 10
x = 5 you would then plug x into QS
5(5) - 8
25 - 8
17
Answer:
17
YA
Step-by-step explanation:
Which is equivalent
Answer:
D
Step-by-step explanation:
Using the rules of exponents
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
• [tex]a^{\frac{1}{2} }[/tex] ⇔ [tex]\sqrt{a}[/tex]
Hence
[tex]36^{-\frac{1}{2} }[/tex] = [tex]\frac{1}{36^{\frac{1}{2} } }[/tex] = [tex]\frac{1}{\sqrt{36} }[/tex] = [tex]\frac{1}{6}[/tex]
For this case we must find an expression equivalent to:
[tex]36 ^ {- \frac {1} {2}}[/tex]
By definition of power properties we have to:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
So, rewriting the expression we have:
[tex]\frac {1} {36 ^ {\frac {1} {2}}}=[/tex]
By definition of power properties we have to:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]\frac {1} {\sqrt {36}} =\\\frac {1} {\sqrt {6 ^ 2}} =\\\frac {1} {6}[/tex]
Answer:
Option D
If 80% of M is equal to 50% of N and N≠0, what is N M equal to?
Answer:
0.625N
Step-by-step explanation:
0.50N
0.80M = 0.50N, so M = ------------
0.80
and so:
0.50N
N*M = N*------------ = (5/8)N, or 0.625N
0.80
«
In simplified form, V18 is _
Answer:
3V2
Step-by-step explanation:
V18
V9 times 2 equals 18
V3 to the second power because 3 times 3=9 so we get 3V2
Shining Star Preschool purchased a van for $38,000. Suppose MACRS allows vans to be depreciated fully in 6 years according to six fixed percents: 20% the first year, 32% the second year, 19.2% the third year, 11.52% the fourth and fifth years, and 5.76% the sixth year. What is the book value for the van at the end of the first year?
Answer:
The book value for the van at the end of first year will be $30400
Step-by-step explanation:
Cost of van = $38,000
Amount of depreciation after one year = 20%
Finding 20% of 38,000
=38,000 *(20/100)
= 7600
so, amount of van after 1 year = 38,000 - 7600
= 30400
So, the book value for the van at the end of first year will be $30400
The book value of the Shining Star Preschool's van at the end of the first year is $30,400, after depreciating 20% of its original cost of $38,000 using the MACRS method.
Using the Modified Accelerated Cost Recovery System (MACRS), the van is depreciated over 6 years with fixed percentages assigned to each year. The first year's depreciation is 20% of the purchase price.
To calculate the depreciation expense for the first year, we multiply the purchase price by the first year's depreciation rate:
Depreciation Expense (Year 1) = Purchase Price imes Depreciation Rate
Depreciation Expense (Year 1) = $38,000 imes 20%
Depreciation Expense (Year 1) = $7,600
Now, we subtract this depreciation expense from the purchase price to find the book value at the end of the first year:
Book Value (End of Year 1) = Purchase Price - Depreciation Expense (Year 1)
Book Value (End of Year 1) = $38,000 - $7,600
Book Value (End of Year 1) = $30,400
Therefore, the book value of the van at the end of the first year is $30,400.
the graph of an equation with a negative discriminant always has what characteristic
Answer:
See below.
Step-by-step explanation:
The zeroes of the equation will not be real so the graph will not pass through the x-axis.
How many solutions does this system have?
Answer:
One Solution
(2, 1)
Step-by-step explanation:
We have the following system of equations
[tex]x+4y = 6\\y=2x-3[/tex]
To solve the system, substitute the second equation in the first equation and solve for the variable x
[tex]x+4(2x-3) = 6[/tex]
[tex]x+8x-12 = 6[/tex]
[tex]9x = 6+12[/tex]
[tex]9x = 18[/tex]
[tex]x = \frac{18}{9}[/tex]
[tex]x = 2[/tex]
Now substitute the value of x into any of the two equations and solve for the variable y.
[tex]y=2(2)-3[/tex]
[tex]y=4-3[/tex]
[tex]y=1[/tex]
Finally the system of equations has one solution
(2, 1)
1/6 + 2/3 tell me wat it is pls
Answer: 5/6
Step-by-step explanation:
2/3=4/6
1/6 + 4/6 = 5/6
Answer:
5/6
Step-by-step explanation:
you can rewrite 2/3 plus 1/6 as:
2/3+1/6
To add fractions you need to have a common denominator (the bottom half of the fraction). In this case 6 is a common denominator. To convert 2/3 we need to multiply it by the appropriate form of 1. We can multiply by 1 because 1 times anything does not change the value:
(2/2⋅2/3)+1/6⇒2/2⋅2/3+1/6⇒4/6+1/6⇒5/6
Jonathan bought a new computer for $2,016, using the electronics store's finance
plan. He will pay $112 a month for 18 months. Which equation can Jonathan use to
find out how much money he still owes after each month of the plan?
Select one:
a. y = 2,016 - 112x
b. y = 2,016 + 112x
C. y = 112r
d. y = 1126 – 2,016
Answer:
a. 2016-112x
Step-by-step explanation:
because each month he need to pay $112 so it have to be multiplied to the number of month and then answer should be subtracted from 2016
What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
For this case we must find the value of the variable "x" of the following expression:
[tex]2 (3x-1) \geq4x-6[/tex]
We apply distributive property to the terms within parentheses: [tex]6x-2 \geq4x-6[/tex]
We subtract 4x on both sides:
[tex]6x-4x-2 \geq-6\\2x-2 \geq-6[/tex]
We add 2 to both sides:
[tex]2x \geq-6 + 2\\2x \geq-4[/tex]
We divide between 2 on both sides:
[tex]x \geq \frac {-4} {2}\\x \geq-2[/tex]
Answer:
[tex]x \geq-2[/tex]
Answer: [tex]x\geq -2[/tex]
Step-by-step explanation:
Given the inequality [tex]2(3x - 1) \geq 4x -6[/tex] you need to solve for "x".
Apply Distributive property on the left side of the equation:
[tex]6x - 2 \geq 4x -6[/tex]
Now add 2 to both sides:
[tex]6x - 2+(2) \geq 4x -6+(2)[/tex]
[tex]6x \geq 4x -4[/tex]
The next step is to subtrac [tex]4x[/tex] from both sides:
[tex]6x-(4x) \geq 4x -4-(4x)[/tex]
[tex]2x \geq -4[/tex]
And finally, divide both sides by 2:
[tex]\frac{2x}{2}\geq \frac{-4}{2}\\\\x\geq -2[/tex]
Which choice shows a function with a domain of {-4, -2, 2, 4}?
Answer:
Option C.
Step-by-step explanation:
Domain of any function is always represented by x - values when graphed.
Option A.
it has only one x value that is x = 2
Not correct.
Option B.
In this graph straight line doesn't intersect x - axis at x = -2 and -4.
So Not correct.
Option C.
If we see the x- values of the given set of coordinates, we find domain of the given function is { -4, -2, 2, 4}
Therefore, it's correct option.
Option D.
Given set with the coordinates shows domain set as {1, 0, 2, 6}
So it's not the answer.
Therefore, option C is correct.
The ratio (m-2c) : (m+c) is equivalent to 1 : k show that m= c(2k+1)/k-1
[tex]\bf m-2c~:~m+c~~=~~1:k\qquad \implies \cfrac{m-2c}{m+c}=\cfrac{1}{k}\implies k(m-2c)=m+c \\\\\\ mk-2kc=m+c\implies mk-m-2kc=c\implies mk-m=2kc+c \\\\\\ \stackrel{\textit{common factor}}{m(k-1)=c(2k+1)}\implies m=\cfrac{c(2k+1)}{k-1}[/tex]
The coordinates of s are (5,4). What are the coordinates of s after the figure is rotated 90 about the origin
A point is written as ( h, k) when a point is rotated 90 degrees about the origin the new point becomes (-k,h)
s is located at (5,4) where h = 5 and k = 4
The rotated point would be located at (-4,5 )
What is the tangent ratio for angle F?
HF (hypotenuse) = 13
FG (leg a) = 5
HG (leg b) = 12
Answer:
12/5
Step-by-step explanation:
tan(F) =opposite side to angle F over (Fraction Bar) adjacent side to angle F
[tex] \tan(F)=\frac{\text{ opposite side to angle F } }{ \text{ adjacent side to angle F} } [/tex]
The side that is opposite is the side that doesn't include F.
The side the is adjacent will include F (this is not the hypotenuse which is opposite the 90 degree angle).
So
[tex]\tan(F)=\frac{12}{5}[/tex]
5. What is the length of an arc that subtends a central angle of 75° in a circle whose radius is 5 inches?
Round off your answer to the nearest whole number.
A. 7
B. 4
C. 16
D. 21
Answer:
[tex]\boxed{\text{A. 7 in}}[/tex]
Step-by-step explanation:
The formula for the arc (s) of a circle is
[tex]s = r\theta \times \dfrac{\pi}{180^{^{\circ}}}[/tex]
where θ is measured in degrees.
Data:
r = 5 in
θ = 75°
Calculation:
[tex]s = \text{5 in} \times 75^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{7 in}\\\\\text{The length of the arc is }\boxed{\textbf{7 in}}[/tex]
The center of a circle is at (−5, 2) and its radius is 7. What is the equation of the circle? (x−5)2+(y+2)2=14 (x+5)2+(y−2)2=49 (x+5)2+(y−2)2=14 (x−5)2+(y+2)2=49
The standard equation of a circle is in the form:
(x-a)^2 + (y-b)^2 = r^2
where; a is the x coordinate of the center, b is the y coordinate of the center, and r is the radius of the center.
In this case, a is -5, b is 2, and r is 7.
Therefore, the equation of this circle would be
(x+5)^2 + (y-2)^2 = 49
Answer:
Second option: [tex](x +5)^2 + (y -2)^2 =49[/tex]
Step-by-step explanation:
The center-radius form of the circle equation is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where "r" is the radius and the center is at the point [tex](h,k)[/tex]
Since the center of this circle is at the point [tex](-5, 2)[/tex], we can identify that:
[tex]h=-5\\k=2[/tex]
We know that the radius is 7, then:
[tex]r=7[/tex]
Now we must substitute these values into the equation [tex](x - h)^2 + (y - k)^2 = r^2[/tex] to find the equation of this circle.
This is:
[tex](x - (-5))^2 + (y - 2)^2 = (7)^2[/tex]
[tex](x +5)^2 + (y -2)^2 =49[/tex]
What is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]?
x f(x)
-6 2.5
-
22.5
02
20
A. 5
B. 25
c. 1
D.
0.5
What is the complex number V-36 + 10?
Answer:
Step-by-step explanation:
Answer:
= 5.099 i
Step-by-step explanation:
The problem tells us to find the square root of -36 +10
√(-36 + 10)
= √(-26)
Which is an imaginary number
Lets remember that, √(-1) = i
= i*√(26)
= 5.099 i
Please see attached images for more information
Tom bought a soft drink for two dollars and five candy bars. He spent a total of $22. How much did each candy bar class?
Answer:
c = $5.00
Step-by-step explanation:
Let c = the cost of each candy bar
3 + 8c = 43
8c = 40
The length of a rectangle is
3
yd
more than twice the width
x
. The area is
230
yd
2
.
Area of a rectangle is Length times width.
The Width is given as X and the length is 2x+3
Now you have x * 2x+3 = 230
Multiplying x to 2x+3 = 2x^2 +3x
2x^2 +3x = 230
Subtract 230 from both sides:
2x^2+3x-230 = 0
Factor the polynomial:
(x-10) (2x+23) = 0
Solve for each x:
x = 10 and X = -11.5
Since a side of a rectangle can't be a negative number x = 10.
The width = x = 10 yards.
The length = 2(10) +3 = 23 yards.
kurt is buying a new cell phone. he knows that the more features the cell phone has, the more expensive it will be
Answer:the cost of the cell phone is a function of the number of features
Step-by-step explanation:
Because the cost depends on the features
What is the range of the function f(x) = -(x + 3)2 + 7?
all real numbers less than or equal to 7
all real numbers greater than or equal to 7
all real numbers less than or equal to -3
all real numbers greater than or equal to -3
Answer:
It's A-all real numbers less than or equal to 7
Step-by-step explanation:
I just took the unit test and got a 100 on it!
The range of the function f(x) = -(x + 3)² + 7 is {y: y ∈ R, y ≤ 7}. So, option A is correct.
How to find the range of a function?Consider the given function as y = f(x)Solve for x ( isolate x from the equation)The domain of the obtained function is the range of the function f(x).Finding the range:Given that,
f(x) = -(x + 3)² + 7
⇒ y = -(x + 3)² + 7
⇒ (x + 3)² = 7 - y
⇒ (x + 3) = √(7 - y)
⇒ x = (√(7-y)) - 3
Thus, all the real values less than or equal to 7 for y define the function. So, the domain for the obtained function is {y: y ∈ R, y ≤ 7}.
Therefore, the range of the given function is {y: y ∈ R, y ≤ 7}.
Learn more about the range of a function here:
https://brainly.com/question/2264373
#SPJ2
Helppp please I’ll give 28 points
Answer:
54 cm^2
Step-by-step explanation:
The area of a right triangle is the easiest triangle for which you can find the area.
The area of any triangle is Base * height / 2
The base and height of a right triangle are always the two sides that are not the hypotenuse. In this case
base = 9
height = 12
Area = 9 * 12/2
Area = 54 square cm.
Answer: A
A circle has a circumference of 28.36 units what is the diameter of the circle
Answer:
The diameter of circle d is 9.03
Step-by-step explanation:
Circumference of Circle = 28.36
We need to find the diameter of circle.
The formula used to find the circumference of circle is:
C = 2πr
we know that radius is half of diameter
so r = d/2
Putting value of r in above equation
C = 2π(d/2)
C = πd
The value of π is 3.14. finding value of d
28.36 = 3.14 * d
=> d = 28.36 / 3.14
d = 9.03
So, the diameter of circle d is 9.03
Answer:
The diameter is approximately 9 units
Step-by-step explanation:
Circumference is given by
C = pi *d
28.36 = pi *d
Let use 3.14 for pi
28.36 = 3.14 *d
Divide each side by 3.14
28.36 /3.14 = 3.14 d/3.14
9.031847134 = d
The diameter is approximately 9 units
Angles whose terminal sides lie on the x-or y-axis are _____.
a)reference angles
b)quadratic angles
c)quadrantal angles
d) terminal angles
Angles whose terminal sides lie on the x and y axis are Quadrantal angels.
Hope it helps.
Answer:
The correct answer option is c) quadrantal angles.
Step-by-step explanation:
When the terminal sides lie on the x axis or the y axis in the standard position, the angles are called as quadrantal angles.
For example when one of the sides lie on the x axis and one lies on the y axis, it makes an angle of 90 degrees which is a quadrantal angle (as shown in the picture attached).
I need help on this question
Answer:
6e^2f (3f^2-2e)
Step-by-step explanation:
18 e^2 f^3 - 12 e^3 f
18 e^2 f^3 = 2*3*3 ee fff
12 e^3 f = 2*2*3 eee f
The common terms are 2 *3*eef
Factor that out
2*3*eef (3ff - 2e)
Combine like terms
6e^2f (3f^2-2e)
Rationalize the denominator and simplify 15sqaure root 6 over 3sqaure root 5
[tex]\bf \cfrac{15\sqrt{6}}{3\sqrt{5}}\implies \cfrac{15\sqrt{6}}{3\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{15\sqrt{6}\cdot \sqrt{5}}{3(\sqrt{5})^2}\implies \cfrac{15\sqrt{6\cdot 5}}{3(5)} \\\\\\ \cfrac{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\sqrt{30}}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \sqrt{30}[/tex]
Fernando has $10 to buy snacks for his friends at the baseball game. A
package of peanuts costs $0.99 and a box of Cracker Jacks costs $1.79. This
relationship can be represented by the inequality 99p+179€ 10. Two of
Fernando's friends want Cracker Jacks. Which inequality represents how
many packages of peanuts he can buy?
Answer:
6
Step-by-step explanation:
I added 2 cracker jacks to get how much money he had left the kept subtracting. 99 from the money he had left
If my friend and i went to get ice cream, I have $30 and each ice cream is $5. What equation would help me solve this? I need an equation...
Your question asks to make an equation with the information that was given.
Answer: y = -5x + 30In order to make an equation for your question. We would be making an equation with the formula: y = mx + b.
Formula: y = mx + b
m = change
x = amount of ice cream
b = starting value
We would need to gather the key information from the question.
Key information:
You have $30
Each ice cream cost $5
With the information above, we can make an equation for the question.
What we know is that you started with $30, so that means that 30 would be your b value (starting value).
Your equation should look like this:
y = mx + 30
Now, we know that each ice cream cost $5, but since we're paying for the ice cream, we would subtract that from our starting value. This means that our change would be -5, since we are taking away $5 each time we buy ice cream.
Your equation should look like this:
y = -5x + 30
The equation above would be the equation for your question.
We would do nothing to x but just leave it as is, since we don't know how many ice creams you're going to buy.
y = -5x + 30 should be your FINAL answer.
I hope this helps!Best regards, MasterInvestorSuppose U={1,2} is the universal set and T={2}. Then what is the complement of T
Answer:
T'={1}
Step-by-step explanation:
Definition:
Given a set T, the complement of T is the set of all elements in the universal set U, but not in T.
We can write T^c
You can also say complement of T in U
Complement of T( T')= U-T
where U={1,2} and T={2}
Now put the sets of U and T in the formula:
T'=U-T
T'={1,2}-{2}
T'{1}
Thus the Complement of T(T')={1}....
The complement of a set T in a universal set U is all the elements in U that are not in T. If U={1,2} and T={2}, the all the elements in U that are not in T corresponds to {1}. So, the complement of T is {1}.
Explanation:In the field of Mathematics, specifically in set theory, the complement of a set T in a universal set U is the set of all elements in U that are not in T. When we say complement of T, we are referring to the set of all outcomes in the universal set U that are NOT in T.
In this case, the universal set U={1,2}, and the event T={2}. Therefore, the complement of the set T in relation to U would be the set of all elements in U that are not in T. Hence, since 2 is in T, the only number left in U that is not in T is 1. So, the complement of T is {1}.
Learn more about Complement of a Set here:https://brainly.com/question/30913259
#SPJ3