39,916,800 ternary strings are there with exactly 3 zeros, 5 ones and 3 twos.
What is permutation?The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.
Given that, A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For example, the ternary string 2122010 consists of exactly 2 zeros, 2 ones and 3 twos
This is just the number of permutations of the set {0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2}. There are 11 elements in the set, so there are 11! = 39,916,880 possible ternary strings with exactly 3 zeros, 5 ones and 3 twos
Hence, 39,916,800 ternary strings are there with exactly 3 zeros, 5 ones and 3 twos.
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P(H)=
P(T)=
let me know if you know how to do this
After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.
As given in the question,
After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails ,
Number of total outcomes = { H , T }
Total number of outcomes = 2
Number of favourable outcomes to represent heads = 1
Number of favourable outcomes to represent tails = 1
Probability =(Number of favourable outcomes)/ (Total number of outcomes)
Probability of getting heads from the total outcomes is equal to
P(H) = 1 / 2
Probability of getting tails from the total outcomes is equal to
P(T) = 1/2
Therefore, after flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.
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1.
In Triangle QRS, A is the midpoint of QR, B is the midpoint of RS, and C is the
Rubric midpoint of SQ.
Also, QA = 10, BR = 15, and SQ = 28.
What is the perimeter of triangle ABC?
Use words, number, and/or pictures to show all of your work.
The perimeter of the triangle ABC with respect to the given information is 78.
What is meant by perimeter?Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it. A circle's or an ellipse's circumference is its furthest boundary. Numerous real-world uses exist for calculating perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.
Given,
In triangle QRS,
A is the midpoint of QR, B is the midpoint of RS, and C is the midpoint of SQ.
And also given that QA=10, BR=15, SQ=28
Let p represent the triangle ABC's perimeter.
QR + RS +SQ = p
2(QA) + 2(BR) + SQ = p
2(10) + 2(15)+ 28 = p
20 + 30+ 28 = p
78=p
Therefore, the perimeter of triangle ABC is 78
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The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 65% pure fruit juice?
PLEASE HELP
24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
According to the question,
We have the following information:
The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice.
Now, let's take x pints of 55% pure fruit juice and y pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
So, we have:
x+y = 40
x = 40-y ...(1)
55x/100+80y/100 = 40*65/100
55x+80y = 40*65
Putting the value of x from equation 1:
55(40-y)+80y = 2600
2200-55y+80y = 2600
2200+25y = 2600
25y = 2600-2200
25y = 400
y = 400/25
y = 16 pints
Putting this value in equation 1:
x = 40-y
x = 40-16
x = 24 pints
Hence, 24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
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You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $36, otherwise you lose $30. What is your expected value for the game?
The expected value for the game is -12.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
The probability of rolling a 2 or 5:
= P(2 or 5)
= 1/6 + 1/6 = 1/3
The probability of not rolling a 2 or 5:
= 1 - 1/3
= 2/3
The expected return:
= (1/3)(36) + (2/3)(-36)
= 12 - 24
= -12
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The graph of a quadratic function with vertex (-3, 1)
Find the range and the domain.
Write the range and domain using Interval notation.
Answer:
Domain: (negative infinity, positive infinity)
Range: (negative infinity, 1]
Step-by-step explanation:
the sum of a number with the square of its following algebraic language
Answer:
a + (a+1)²
Step-by-step explanation:
The following of the number "a" is:
a+1
Then:
The sum of a number with the square of its following algebraic language is:
a + (a+1)²
The algebraic expression for the sum of a number with the square of its following number can be written as:
x + ( x + 1)²Where x is the given number and (x + 1 )² represents the square of the following number.
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Marcus is on an Olympic training programme.
As part of the programme, he has to have a
blood test and a fitness test at regular
intervals.
Marcus has a blood test every 42 days and a
fitness test every 44 days.
On the day before the training programme
started, Marcus had a blood test and a fitness
test.
After how many days will he next have a blood
test and fitness test on the same day?
Answer:
Step-by-step explanation:
so if it takes 42 days and 44 days just add them up
42 plus 42 = 82 plus 42=124 plus 42= 166plus 42= 208 plus 42 = 250 plus 42 = 292 plus 42= 334 plus 42= 376 plus 42=418
44 plus 44= 88 plus 44=132 plus 44=176 plus 44 = 220 plus 44= 274 plus 44= 318 plus 44= 362 plus 44=406 plus 44= 450 plus
just keep going
A florist makes centerpieces.
18 roses in each centerpiece.
best way to use compatible numbers to
estimate the number of roses the florist
needs for 24 centerpieces?
A 10 x 25 = 250
B 20 x 25 = 500
D
25 X 30 = 750
30 × 30 = 900
The best compatible number to use for 24 x 18 = 432.
24 can be written as 25
18 can be written as 20.
So,
20 x 25 = 500
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The number of roses in one centerpiece = 18 roses.
The number of roses in 24 centerpieces.
= 24 x 18
= 432
The best compatible number to use for 24 x 18 = 432.
24 can be written as 25
18 can be written as 20.
So,
20 x 25 = 500
Thus,
The best compatible number to use for 24 x 18 = 432.
24 can be written as 25
18 can be written as 20.
So,
20 x 25 = 500
Option B is the correct answer.
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If 3 oranges cost $1.75,how much would 20 oranges cost?
Answer:$12
Step-by-step explanation:
1.75/3= 0.6 (1dp)
0.6 x 20 = 12
Answer:
$11.67
Step-by-step explanation:
3 oranges = 1.75
1 orange = 0.58333333333
20*0.58333333333 = 11.6666667
PEMDAS Simplify using order of operations.
7 + 3 x 5
Answer: 22
Step-by-step explanation:
3 times 5 then add 7
5. Find x, y, and z. Round to the nearest thousandth.
The unknown side and angle of the triangle is as follows:
x = 63°y = 31.19 unitsz = 15.89 unitsHow to find the side and angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
Hence, let's find x, y and z.
The sum of angles in a triangle is 180 degrees.
Hence,
180 - 27 - 90 = x
x = 63 degrees.
sin 63° = opposite / hypotenuse
sin 63 = y / 35
cross multiply
y = 35 sin 63
y = 31.1852283466
y = 31.19 units
sin 27 = z / 35
z = 35 sin 27
z = 15.8896674909
z = 15.89 units
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Write the equation of the line that passes through
the points (-6,-3) and (2, 0). Put your answer in
fully simplified point-slope form, unless it is a
vertical or horizontal line.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-6)}}} \implies \cfrac{0 +3}{2 +6} \implies \cfrac{ 3 }{ 8 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{3 }{ 8 }}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +3 = \cfrac{3 }{ 8 } ( x +6) \end{array}}[/tex]
My answer and step by step explanation is provided as an attachment.
which solution for the value of x in the figure below is incorrect? explain
50 POINTS PLEASE HELP The graph represents a quadratic function. Write an equation of the function in standard form.
The equation of the graph is y = 2[tex]x^{2}[/tex] + 9x + 4
What is a quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x
a[tex]x^{2}[/tex]+bx +c=0
with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
From the graph the roots of the equation are -4 and -1/2
so if x = -4, them x + 4 = 0 is a factor,
Also, if x = -1/2, then x + 1/2 = 0 is a factor
Multiply and expand the two factors
(x + 4)(x + 1/2) = 0
[tex]x^{2}[/tex] + x/2 +4x + 2 = 0
multiply through by 2
2[tex]x^{2}[/tex] + x +8x + 4 = 0
2[tex]x^{2}[/tex] +9x +4 = 0
In conclusion, the equation of the function in standard form is 2[tex]x^{2}[/tex] +9x +4 = 0
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Willis borrowed $1400 at 9% simple interest to be paid back in 2 years. How much interest will he pay?
If he borrowed $1400 at 9% simple interest to be paid back in 2 years. The interest he will pay is $1,663.34.
How to find the interest?Using this formula
Interest = Principal ( 1+ Interest rate)^ time
Where:
Interest =?
Principal = $1400
Interest rate = 9% or 0.09
Time = 2 years
Let plug in the formula
Interest = $1,400 ( 1+ 0.09) ^ 2
Interest = $1,400 ( 1.09) ^2
Interest = $1,400 ( 1.1881)
Interest = $1,663.34
Therefore he will pay the amount of $1,663.34 as interest.
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During a building project, a brick is
dropped from a height of 1,936 ft. If the
equation for height as a function of time is
h(t) = -16t2 initial height where t is time
in seconds and h(t) is height in feet, how
many seconds will it take for the brick to
hit the ground?
Answer:
11 seconds
Step-by-step explanation:
[tex] - 16 {t}^{2} + 1936 = 0[/tex]
[tex] - 16 {t}^{2} = - 1936[/tex]
[tex] {t}^{2} = 121[/tex]
[tex]t = 11[/tex]
2. Katie is planting a garden for her science fair project. She needs of a cup of soil to go in 8 different pots. How many cups of soil does she need in total?
Answer:
She needs 8 cups of soil
one cup per pot
Step-by-step explanation:
The height of a triangle is 8 centimeters greater than the base. The area of the triangle is 356.5 square centimeters. Find the length of the base and the height of the triangle.
Answer: base = 23 height = 31
Step-by-step explanation:
Area of triangle = (bh)/2
A = 356.5 cm2
h = b+8
356.5 = (b(b+8)) / 2
2(356.5) = b2 + 8b
0 = b2 + 8b - 713
Use quadratic equation to solve for b (there are on-line quadratic equation solvers, or you can do it manually)
b = -31 , 23
23 is the base 23 + 8 = 31 = height
Select the values that make the inequality -2h ≤ -40 true. Then write an equivalent inequality, in terms of h. (Numbers written in order from least to greatest going across.) The answers are
10,15,17,
19,20,21,
23,25,30.
The values that make the inequality -2h ≤ -40 true are
23,25,30Equivalent form of the inequality is written as
h ≥ 20How to find the values of the unequallyInequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using only "equal to"
solving the inequality
-2h ≤ -40
dividing through by a negative number changes the inequality
diving through by -2 gives
h ≥ 20
Therefore, h are values greater than 20 and 23, 25, and 30 are all greater than or equal to 20
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x = 15.3568 - (1+x)^25
The value of x in the algebraic equation x = 15.3568 - 1(1+x)^25 is 0.115
Mathematical OperationArithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.
In this case, we have to solve for x in the algebraic equation using mathematical operation.
x = 15.3568 - (1 + x)^25
Collect like terms
x + (1+x)^25 = 15.3568
Solving for x
x = 0.115
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Unit form 3 tens 8 ones x 1000
The expression 3 tens 8 ones × 1000 can be evaluated and the value is; 38,000.
What is the value of the word phrase as given?It follows from the task content that the value of the expression represented by the word phrase as given is to be determined.
On this note, it follows that we have;
First, 3 tens and 8 ones can be written as;
(3 × 10) + (8 × 1)
= 30 + 8
= 38.
Therefore, the result of the evaluation is; 38 × 1000 = 38, 000.
Ultimately, the result of the expression is; 38,000.
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Can someone please help me with this??
Answer:
3 * (8 + (n - 1)*x*1/3 ) = 3 * ( 0 )
..
the third term of the sequence is 165 find the 1st term subtract 2 and multiply by 3
Answer:
Step-by-step explanation:
Formula for geometric sequence is:
[tex]a_{n} =a_{1} (r)^{n-1}[/tex]
Now we substitute the values in:
[tex]165=a_{1} (3)^{3-1}[/tex]
165=a1(-2x3)^2
165=a1x9
Answer is 23
Equation of the line that passes through the points given (0,2) and (-2,0)
In the football club, 36 footballers are Latvians, while there are 4 times less footballers of other nationalities. How many total athletes does the football club have?
Answer:
45
Step-by-step explanation:
Number of Latvian footballers(n¹) = 36
Numer of footballers of other nationalities(n²)=36/4=9
Now total number of footballers= n¹+n²= 36+9 =45
Z
E
140⁰
180
D120°
40
mZAOC
60
135⁰
80
C
90°
80⁰
What is the measure for the following <?
m
40
60
80
Answer:
Question 1:
The angle m∠DOX is greater than 90 degrees, but less than 135 degrees.
Looking at the diagram we see that:
m∠DOX = 120 degrees.
Question 2:
The angle m∠COX is the sum of two angles that in total are 80 degrees.
Therefore, the equation is:
m∠COX = m∠AOX + m∠COA
Question 3:
The BOA angle measurement is given by:
BOA = 60 - 40
BOA = 20 degrees
Therefore, an angle that measures 20 degrees is:
BOA.
Question 4:
From the previous question we have:
m∠BOA = 60 - 40
m∠BOA = 20
The measure of m∠BOA is 20 degrees
Question 5:
The measure of the angle EOD is given by:
m∠EOD = 140 - 120
m∠EOD = 20 degrees
THANKS
50
4.8
(41 votes)
Step-by-step explanation:
Copy and complete the workings below to
calculate the value of c.
c² = 9² + 40²
C² =...
c=...
Answer:
41
Step-by-step explanation:
9² + 40² = 1681
the s.r of 1681 is 41
We s.r the answer because we need the singular of C, not C²
Hope this helps
The Bloomington Times had 8,050 subscribers last year. This year, after the paper was bought out, it had 70% more. How many subscribers were there this year?
due tomorrow pleaseeeeeee help
Answer:
13685
Step-by-step explanation:
8050 x 0.70 = 5635
8050 + 5635 = 13685
Which of the following uses set builder notation to denote the set of all real numbers that are greater than or equal to 3 and less or equal to 9?
The given set written on set builder notation is:
{x| x ∈ R, 3 ≤ x ≤ 9}
How to write the set?We want to write the given set using set builder notation, the set is the set of all real numbers that are greater than or equal to 3 and less or equal to 9.
So the set can be written as an inequality as:
3 ≤ x ≤ 9
To define the set using the set builder notation, we also need to clarify that x belongs to the real number set, this is x ∈ R.
Then the set that we need to write is:
{x| x ∈ R, 3 ≤ x ≤ 9}
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-
1) The difference quotient for f(x)=√x at the point (16, 4) is
a) 16 + h 16
h
b) √4 + h - √16
h
c) √4 + h - 16
h
d) √16 + h - 4
h
Difference quotient for f(x) = √x at (16,4) is √16+h - 4 / h
Difference quotient is mathematical operation used to solve derivation of function by using following formula :
difference quotient = [tex]\frac{f(x+ h) - f(x) }{h}[/tex]
For the function f(x) = √x at point (16,4)
f(x +h) = [tex]\sqrt{x+h}[/tex]
putting value in formula
difference quotient = [tex]\frac{\sqrt{x+h} -\sqrt{x} }{h}[/tex]
now , putting x = 16 ,
difference quotient = √16+h - √16 / h
taking square root of 16 ,
= √16+h - 4 / h
So, the required Difference quotient for the function at (16,4) is √16+h - 4 / h
option (d) is correct
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