Answer:
me
Step-by-step explanation:
A group of 20 people are going to run a race. The top three runners earn gold, silver, and bronze medals. How many outcomes are possible for these awards?
Answer:
There are 6,840 possible outcomes for these awards.
Step-by-step explanation:
Given that a group of 20 people are going to run a race, and the top three runners earn gold, silver, and bronze medals, to determine how many outcomes are possible for these awards, the following calculation must be performed:
20 x 19 x 18 = X
380 x 18 = X
6.840 = X
Therefore, there are 6,840 possible outcomes for these awards.
Total outcomes that are possible for these awards are 6840 outcomes, calculated using permutation.
Total number of people=20
what is the difference between permutation and combination?permutation means the arrangement of items while the combination is all about the selection of some out of many.
let us say start with the gold medal
no of ways a gold medal can be given = ²⁰C₁ = 20
Now, the number of people left is 19
no of ways a silver medal can be given = ¹⁹C₁ = 19
Now, the number of people left is 18
no of ways a bronze medal can be given = ¹⁸C₁ = 18
possibility of total outcomes=20*19*18 = 6840ways
Therefore, total outcomes that are possible for these awards=6840
to get more about permutations and combinations refer to the link,
https://brainly.com/question/4658834
The curve
[tex]y = \sqrt{x - 3} [/tex]
has a tangent with gradient
[tex] \frac{1}{2} [/tex]
at point N.
Find the coordinates of N.
Answer:
Point N(4, 1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)FunctionsFunction NotationTerms/CoefficientsAnything to the 0th power is 1Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \sqrt{x - 3}[/tex]
[tex]\displaystyle y' = \frac{1}{2}[/tex]
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y = (x - 3)^{\frac{1}{2}}[/tex]Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)[/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1[/tex]Multiply: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}[/tex][Derivative] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x - 3}}[/tex]Step 3: Solve
Find coordinates
x-coordinate
Substitute in y' [Derivative]: [tex]\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply 2 on both sides: [tex]\displaystyle 1 = \frac{1}{\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply √(x - 3) on both sides: [tex]\displaystyle \sqrt{x - 3} = 1[/tex][Equality Property] Square both sides: [tex]\displaystyle x - 3 = 1[/tex][Addition Property of Equality] Add 3 on both sides: [tex]\displaystyle x = 4[/tex]y-coordinate
Substitute in x [Function]: [tex]\displaystyle y = \sqrt{4 - 3}[/tex][√Radical] Subtract: [tex]\displaystyle y = \sqrt{1}[/tex][√Radical] Evaluate: [tex]\displaystyle y = 1[/tex]∴ Coordinates of Point N is (4, 1).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Find the measure of angle 1
HELP
Answer:
75°
Step-by-step explanation:
The chord- chord angle is half the sum of of the arcs intercepted by the angle and its vertical angle, then
∠ 1 = [tex]\frac{1}{2}[/tex] (110 + 40)° = 0.5 × 150° = 75°
A spaceship traveled 81 billion miles. In scientific notation that is _____ miles.
8.1 × 10 10
8.1 × 10 -9
8.1 × 10 9
8.1 × 10 -10
plz help it's being timed
Answer:
A (8.1 x 10^10)
Step-by-step explanation:
1. 1 billion is 1,000,000,000 or 10^9
2. 81 Billion should be 81 x 10^9, but the correct notation should always show a single digit number, so you need to also divide 81 per 10
3. Thus, the answer is 8.1 x 10^10
Answer:
8.1 × 10^10
:)
Which trigonometric ratio is correct?
1 point
125 cm
105 cm
d
Sin(d) = 105/125
Cos(d) = 105/125
Tan(d) = 105/125
Option 4
Tan(d)=105/125 is trigonometric ratio corect
is -7 less the -8
is -8 less then or equal to -8
I need with the volume!!!
Answer:
Tim read 81 pages.
Step-by-step explanation:
If he read 3 pages on Monday and tripled the amount of pages he red based of off the amount of pages he read the previous day, he would have read 3 pages on Monday, 9 pages on Tuesday, 27 pages on Wednesday, and 81 pages on Thursday.
Monday: 3
Tuesday: 3 x 3 = 9
Wednesday: 9 x 3 = 27
Thursday: 27 x 3 = 81
I hope this helps you! :D
A quilt is made of 15 red squares and 35 blue squares. Find the ratio, in lowest terms of:
Someone help pls :D
The ratio of red squares to blue squares is 3 : 7
The ratio of blue squares to total squares is 7 : 10
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
The number of red squares = 15
The number of blue squares = 35
Now , the total number of squares is N = 50 squares
a)
The ratio of red squares to blue squares is = number of red squares / number of blue squares
The ratio of red squares to blue squares is = 15 / 35
The ratio of red squares to blue squares is = 3 : 7
b)
The ratio of blue squares to total squares is = number of blue squares / total number of squares
The ratio of blue squares to total squares is = 7 : 10
Hence , the proportion is solved
To learn more about proportion click :
https://brainly.com/question/7096655
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The complete question is :
A quilt is made of 15 red squares and 35 blue squares. Find the ratio, in lowest terms of:
a) The ratio of red squares to blue squares
b) The ratio of blue squares to total squares
Someone help me please with this ? Like right now please
Answer: 6472
Step-by-step explanation:
You have to multiply and add
Is 8 a solution to 48 < 4x?
plz need answers quickly
Answer:
No
Step-by-step explanation:
We need to tell that whether 8 satisfies the given inequality. The inequality is ,
[tex]:\implies[/tex] 48 < 4x
now substitute x 12 is equal to 8 and check whether if it satisfies the given inequality.Putting x = 8
[tex]:\implies[/tex] 48 < 4x
[tex]:\implies[/tex] 48 < 4 * 8
[tex]:\implies[/tex] 48 < 32
this is not possible as 48 is greater than 32. x is equal to 8 is not a solution of the given inequality .No it is not a solution .[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{48 < 4x}[/tex]
[tex]\large\textsf{TURN the given EQUATION}[/tex]
[tex]\mathsf{4x > 48}[/tex]
[tex]\large\textsf{DIVIDE 4 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{4x}{4}>\dfrac{48}{4}}[/tex]
[tex]\large\textsf{CANCEL out: }\mathsf{\dfrac{4}{4}}\large\textsf{ because that gives you 1}[/tex]
[tex]\large\textsf{KEEP: }\mathsf{\dfrac{48}{4}}\large\textsf{ because it helps us compare to the x value.}[/tex]
[tex]\mathsf{x >\dfrac{48}{4}}[/tex]
[tex]\mathsf{\dfrac{48}{4}}\\\\\mathsf{= 48\div4}\\\\\mathsf{\boxed{\bf = 12}}[/tex]
[tex]\boxed{\mathsf{x > 12}}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \bf NO, because }\mathsf{\bf x < 12}\large\text{ \bf \& it is an O.P.E.N. circle shaded}}}\\\boxed{\boxed{\large\text{\bf the right}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Triangle PQR is similar to triangle DEF as shown.*
A.
B.
D.
C.
A rectangular red sticker has a perimeter of 26 millimeters and an area of 30 square millimeters. What are the dimensions of the sticker? (blank) millimeters by (blank) millimeters
Answer:
3 millimeters by 10 millimeters
Step-by-step explanation:
What which is equivalent to√x10?
Answer:
E) x^5
Step-by-step explanation:
example, [tex]\sqrt{3}[/tex] = 3^1/2 where '1' is the coefficient of 3
[tex]\sqrt{3}[/tex] is the same as [tex]\sqrt[2]{3}[/tex] (it's assumed to be 2 unless another number is there)
so, √x^10 is the same as x^(10/2) which is x^5
(4x2 - X - 5) + (6x2 + x)
Answer:
10x2 - 5 (the 2 has to be small too.)
help pleaseee! dont guess
Answer:
1: True, 2: False
Step-by-step explanation:
With the first one, probability by defintion is the odds of if an event will happen or not, so it is true.
With the second one, it is false as if something is for sure going to happen, it will have a 100% or "1" chance of occurring. If it has a 1% chance of occuring, it would be 0.01.
!!!!NEED HELP ASAP!!!! NO LINKS OR REPORT
Answer:
x = -11 5/17
Step-by-step explanation:
3x + 2y = 12
2x - 3y = -57
5x + y = -45
y = -5x - 45
2x - 3 (-5x - 45) = -57
2x + 15x + 135 = -57
17x + 135 = -57
17x = -192
x = -11 5/17
Type the missing number that makes these fractions equal: 4/?=8/14
Answer:
4/7 = 8/14
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
[tex]\frac{4}{x} =\frac{8}{14} \\[/tex]
cross multiply
8x = 14 x 4
8x = 56
x = 7
Mike has 2 bank accounts. In his checking he has $136.89 and in his savings account he has $653.23.
Answer:
Whats the question and if its adding the answer is 790.12
Step-by-step explanation:
Also, if you could answer my question that'dd be great!
Ms. Benton drew a right angle and split it into 2 angles. one of the labels inside was labeled 5x and the other angle was labeled 4x. what does x equal?
Answer choices:
5°
10°
15°
20°
please help
Answer:
B-10⁰
Step-by-step explanation:
5 x 10 is 50, 4 x 10 is 40, add those and you get 90⁰
I will give brainiest
Answer:
there should be 4 points below the trend line
Step-by-step explanation:
4
HELP ME IM STUCK PLEASE QUICK
Answer:
C) 24>x
Step-by-step explanation:
The inequality is just turned around. 24>x is thw same thing as x<24.
Hope this helped :)
Answer:
D
Step-by-step explanation:
x+3≥12
<=> x≥8
so 8 is less than x
x is less than 24 means 24>8 but in this case we must follow a model so x is less than 24 can be write 24≥x (read x is less than 24 or is equal to 24)
For her birthday, Patty's parents gave her $5,000.00 which they put into a savings account that earns 10% interest compounded continuously. When Patty started college, she withdrew the entire balance of $5,789.00 and used it to pay for tuition. How long was the money in the account?
Answer:
1.465 years
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 per year,
Then, to solve for time t, when compound interest is compounded continuously, the formula is given as:
t = ln(A/P) / r
Where
A = Amount after time t = $5,789.00
P = Principal = Initial amount = $5,00
r = 0.1
Hence,
t = ln(5,789.00/5,000.00) / 0.1
t = 1.465 years
Therefore, the money was in the account for 1.465 years
Samantha has chocolate bars and lollipops in the the ratio 4:5. If she has 12 chocolate bars,how many lollipops does she have?
What expression is equivalent to -8 (1/2 + 1/4)
Answer:
(-4 - 2)
Step-by-step explanation:
-8 (1/2 + 1/4) = -6/1 = -6
-4 - 2 = -6
Which triangle makes this statement true?
Answer:
A.
Step-by-step explanation:
i pretty sure
hii! please help asap. i’ll give brainliest
Answer:
4
Step-by-step explanation:
Answer:
last one
Step-by-step explanation:
it has 15.95 and only 1 16.00 :D
A life guard in a tower 20 ft above sea level spots a struggling surfer at an angle of depression of 15 . How far is the surfer from the base of the tower?
Answer: [tex]19.31\ ft[/tex]
Step-by-step explanation:
Given
The tower is at a height of [tex]h=20\ ft[/tex]
the angle of depression is [tex]15^{\circ}[/tex]
Suppose the surfer is x ft away from the base of the tower
[tex]\therefore \text{From the figure, we can write}\\\\\Rightarrow \cos 15^{\circ}=\dfrac{x}{h}\\\\\Rightarrow x=h\cos 15^{\circ}\\\Rightarrow x=20\cos 15^{\circ}\\\Rightarrow x=19.31\ ft[/tex]
Therefore, the surfer is at a distance of 19.31 ft from the base of the tower.
Write the recursive formula for the sequence
37, 67, 97, 127, 157
Answer:
The recursive formula for this arithmetic sequence would be [tex]a_{1} = 37[/tex], [tex]a_{i} = a_{i-1} + 30[/tex].
Step-by-step explanation:
A recursive formula is a formula that defines each term of a sequence using the preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence, as well as an equation defining [tex]a_{i}[/tex] in terms of preceding terms. Since the first term of this sequence is 37, that means [tex]a_{1} = 37[/tex]. The pattern in this arithmetic sequence between each term in ascending order would be 30 more than the previous term, so you can create the function [tex]a_{i} = a_{i-1} + 30[/tex]. So the recursive formula for this arithmetic sequence would be [tex]a_{1} = 37[/tex] and [tex]a_{i} = a_{i-1} + 30[/tex].
1/5 - 2x ≥ -4
Solve for X.
Answer:
x≤21/10
Step-by-step explanation:
[tex] \frac{1}{5} - 2x \geqslant - 4 \\ - 2x \geqslant - 4 - \frac{1}{5 } \\ 2x \leqslant 4 + \frac{1}{5} \\ 2x \leqslant \frac{21}{5} \\ x \leqslant \frac{21}{10} [/tex]
PLEASE HELP!!!!!!!!!!
[tex]115 = l \times 2.5 \times 5.75[/tex]
[tex] \huge \mathrm{Answer࿐}[/tex]
given :
[tex]\longmapsto[/tex] volume = 115 yd³
Dimensions are :
[tex] 2\frac{1}{2} yd [/tex][tex] 5\frac{3}{4} yd [/tex]LWe know,
[tex] \large \boxed{ \mathrm{volume = l \times b \times h}}[/tex]
[tex]115 = 2\frac{1}{2} \times 5\frac{3}{4} \times l[/tex][tex]l \times \dfrac{5}{2} \times \dfrac{23}{4} = 115[/tex][tex]l \times \dfrac{115}{8} = 115[/tex][tex]l = 115 \times \dfrac{8}{115} [/tex][tex]l = 8 \: yd[/tex]Therefore Length of the prism is 8 yards.
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[tex]\mathrm{ \#TeeNForeveR}[/tex]