Answer:
The answers to the question are as follows
a). Please see the examples of bit strings of length 5 and 6 that are palindromes in the following explanation.
b). The number of even length palindromes is [tex]26^{\frac{n}{2} }[/tex]
The number of odd length palindromes is [tex]26^{\frac{n+1}{2} }[/tex]
c). The number of ternary string palindromes of length n is 702.
Step-by-step explanation:
a). Examples of bit strings of length 5 and 6 that are palindromes are
Bit strings of length 5 Bit strings of length 6
Kayak Hannah
Level Redder
Civic Terret
Madam Kakkak
Solos degged
Tenet
Rotor
Minim
Radar
Refer
Terret
b). When n is even, we have a choice of any of the 26 characters for the first letter, similarly, we can choose any character for the second, and so on up till the n/2 th position after which subsequent letters depend on the letter chosen before the half point following the definition of a palindrome.
Therefore we have n/2 independent choices with repetition therefore we have [tex]26^{\frac{n}{2} }[/tex] palindromes of even length with or without meaning in the alphabet
On the other hand, when n is odd, we are free to chose any letter up to the middle letter as before this means we have [tex]\frac{n-1}{2} +1 = \frac{n+1}{2}[/tex] free choices
Therefore the number of odd length palindromes are [tex]26^{\frac{n+1}{2} }[/tex]
c). For a ternary string palindrome, we have 26 letters for the first position, and also 26 for the second, while the third is the same as the first which is one option.
Where n = 2 we have 26 ways of selecting the first and second letters which are equal
Therefore the number of ternary string palindromes of length n are 26×26 + 26 = 702
Bit string palindromes of length 5 and 6 are strings that are the same forward and backward, like '10101' or '100001'. The number of palindromic bit strings of length n is 2 raised to the floor of n/2, and the number of ternary string palindromes of length n is 3 raised to the floor of n/2.
Explanation:A palindrome is a string that remains the same when reversed. Examples of bit string palindromes of length 5 include '10001', '01110', '10101', '01010'. For length 6, examples could be '100001', '011110', '101101', '010010'.
In general, to calculate the number of palindromic bit strings for any given length, the first half of the string can be anything (2 ⌊n/2⌋ possibilities), and the second half must mirror the first. Thus there are 2 ⌊n/2⌋ bit string palindromes of length n.
For ternary palindromes (strings composed of the digits 0, 1, and 2), use the same logic but switch the base to 3. Thus there are 3 ⌊n/2⌋ ternary string palindromes of length n.
Learn more about palindromes here:https://brainly.com/question/14076732
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A jewelry designer is making a pendant. The pendant will be a circular dis (center O) with a circular hold cut out of it, as shown. The radius of the disc is 35 millimeters. Find the area of the pendant. Use 3.14 for π and round to the nearest tenth
Answer:
2884.8 millimeters squared
Step-by-step explanation:
Given:
The radius of the disc is 35 millimeters, so the area of it is:
π[tex]r^{2}[/tex] = 3.14*[tex]35^{2}[/tex] = 3846.5
Then, we find out the area of the circular hold cut out of the bigger one, its radius is a haft of the radius of the bigger circle = 35/2 = 17.5
π[tex]r^{2}[/tex] = 3.14*[tex]17.5^{2}[/tex] =961.6
=> the area of the pendant = 3846.5 - 961.6 =2884.8 millimeters squared
The final result is the area of the pendant is 2887.1 mm².
To find the area of the pendant:
Calculate the area of the circular disc: A = πr² = 3.14 x (35 mm)² = 3.14 x 1225 = 3848.5 mm²Calculate the area of the circular hole: A_hole = πr_hole². Since the hole is at the center, the radius of the hole is half the radius of the disc, so r_hole = 35/2 = 17.5 mm. A_hole = 3.14 x (17.5 mm)² = 3.14 x 306.25 = 961.4375 mm²Find the area of the pendant by subtracting the area of the hole from the area of the disc: A_pendant = A - A_hole = 3848.5 mm² - 961.4375 mm² = 2887.0625 mm²Therefore, the area of the pendant is 2887.1 mm².
Very urgent... I need it right now.. please help me with explanation!
Answer:
a) Water height, H(g) = 8g^2 + 3g -4 - [9g^2 -2g -5] = 8g^2 + 3g -4 -9g^2 + 2g +5 = -g^2 +5g +1
b) g = 1
H(g) = -(1)^2 + 5(1) + 1 = -1 + 5 + 1 = 5
g=2
H(g) = -(2)^2 + 5(2) + 1 = -4 + 10 + 1 = 7
g=3
H(g) = -(3)^2 + 5(3) + 1 = -9 +15 +1 = 5
c) Greatest height
Find the vertex of the parabole
The vertex is at the mid point between the two roots.
To find the roots you can use the quadratic equation
The result is g = 5/2 + [√29]/2 and g = 5/2 - [√29]/2
The middle poin is 5/2 = 2.5
Now find H(2.5) = -(2.5)^2 + 5(2.5) + 1 = 7.5 ≈ 7.3
hope this helps
Please assist me with this problem.
Answer:
r = 1.20w +2.50$12.58$9.00Step-by-step explanation:
a) The retail price (r) is the wholesale price (w) plus 20% of that price plus $2.50:
r = w + 0.20w + 2.50
r = 1.20w + 2.50
__
b) Substituting w=8.40, we have ...
r = 1.20·8.40 +2.50 = 12.58
The retail price of the chair is $12.58.
__
c) Substituting r=13.30, we have ...
13.30 = 1.20w +2.50
10.80 = 1.20w . . . . . . . subtract 2.50
9.00 = w . . . . . . . . . . . . divide by 1.20
The wholesale price of the chair is $9.00.
PLEASE HELP
A student says that the function f(x)=3x4+5x2+1 is an even function. Is the student's statement true or not true, and why?
1) The student's claim is not true, because for any input of x, f(x)=−f(x).
2) The student's claim is not true, because for any input of x, f(x)=f(−x).
3) The student's claim is true, because for any input of x, .f(x)=−f(x).
4) The student's claim is true, because for any input of x, f(x)=f(−x).
Answer:
It's D.
Step-by-step explanation:
Final answer:
The function f(x) = 3x⁴+5x²+1 is an even function because f(-x) equals f(x) for any value of x, confirming the student's statement as true.
Explanation:
The function f(x) = 3x4+5x2+1 is indeed an even function. This can be determined by checking if f(-x) = f(x) for any value of x. An even function is symmetrical about the y-axis and does not change when x is replaced with -x. Applying this to the given function:
f(-x) = 3(-x)4+5(-x)2+1 = 3x4+5x2+1
f(x) = 3x4+5x2+1
Since f(-x) and f(x) are indeed equal, the function is even. Therefore, the correct answer to the student's statement that the function is even is: 4) The student's claim is true, because for any input of x, f(x) = f(-x).
Jane must select three different items for each dinner she will serve. The items are to be chosen from among five different vegetarian and four different meat selections. If at least one of the selections must be vegetarian, how many different dinners could Jane create?
A. 30
B. 40
C. 60
D. 70
E. 80
Answer:
Therefore, Jane can create 80 different dinners.
Step-by-step explanation:
We know that Jane must select three different items for each dinner she will serve. If at least one of the selections must be vegetarian.
The items are to be chosen from among five different vegetarian and four different meat selections.
First we count the number of combinations for one vegetarian dinner and 2 meat dinners.
[tex]C_1^5\cdot C_2^4=5\cdot \frac{4!}{2!(4-2)!}=5\cdot 6=30[/tex]
Now we count the number of combinations for 2 vegetarian dinner and 1 meat dinners.
[tex]C_2^5\cdot C_1^4=10\cdot 4=40\\[/tex]
Now we count the number of combinations for 3 vegetarian dinner.
[tex]C_3^5=\frac{5!}{3!(5-3)!}=10\\[/tex]
We get 30+40+10=80.
Therefore, Jane can create 80 different dinners.
By selling a laptop at $1,000 for which consumers are willing to pay up to $1,200, a consumer electronics firm makes a profit of $400 per unit. In this scenario, the amount $600, that is ($1200 – $1000) + $400, is the
Answer:
600
Step-by-step explanation:
The area of the dining room at Thomas Jefferson so I'm in Monticello is about 342 ft.² is the approximate length of one side is a prime number less than 25 what are the approximate dimensions of the room?
Answer:
Yes, the approximate length of one side is a prime number less than 25.
The approximate dimensions of the room are 19 ft by 18 ft.
Step-by-step explanation:
Assuming the dining room is rectangular in shape
Approximate area of the dining room = 342 ft^2
The area of a rectangle is calculated by multiplying the length of the rectangle by the width.
Assuming the approximate length is a prime number less than 25
The closest prime number to 25 is 19
Approximate length = 19 ft
Approximate width = approximate area ÷ approximate length = 342 ft^2 ÷ 19 ft = 18 ft
Approximate dimensions of the room = 19 ft by 18 ft
The measure of the seven angles in a nonagon measure 138, 154, 145, 132, 128, 147, and 130. If the two remaning angles are equal in measure, what is the measure of each angle
Answer:
The measure of each angle is 143 degrees.
Step-by-step explanation:
We are given the following in the question:
A nonagon in which measure of seven angles are:
138, 154, 145, 132, 128, 147, 130.
Angle sum property of a nonagon:
The sum of interior angles if a nonagon are 1260 degrees.Let the two equal angle of nonagon be x degrees. Thus, we can write:
[tex]138+154+ 145+132+ 128+ 147+ 130+2x = 1260\\\Rightarrow 974 + 2x = 1260\\\Rightarrow 2x = 1260 - 974\\\Rightarrow 2x = 286\\\Rightarrow x = 143[/tex]
Thus, the measure of two equal angles is 143 degrees.
Final answer:
Using the formula for the sum of interior angles of a polygon and subtracting the sum of the seven given angles from the total, we find that the remaining two equal angles in a nonagon each measure 111 degrees.
Explanation:
The measure of the seven angles in a nonagon are given as 138, 154, 145, 132, 128, 147, and 130 degrees. To find the measure of each of the remaining two equal angles, we first need to calculate the sum of the angles in a nonagon. Using the formula for the sum of interior angles (S = (n-2) × 180 degrees, where n is the number of sides), we find that a nonagon has interior angles that add up to 1260 degrees. We then sum the seven given angles and subtract this total from 1260 to find the total measure of the remaining two angles. Finally, we divide this result by 2 to get the measure of each of the two equal angles. This allows us to determine that the measure of each of the two equal angles in the nonagon is 111 degrees.
My teacher is making us do online and my problems is to find 62×1000 annex Then there's a blank zeros to Then another blank to form the product So can you help
Answer:
Step-by-step explanation:
We are to find 62×1000
We can write in standard form
62×10³
6.2×10×10³
Using indices
a^m × a^n = a^(m+n)
Therefore,
6.2×10¹+³
6.2×10⁴
Using the normal multiplication
................1000
...............×. .62
...…......-------------
....., ... ..2 0 0 0
.......+.6 0 0 0
-------------------
..........6 2 0 0 0
----------------------
In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply.
a. We take repeated random samples of size 10 from a population of unknown shape.
b. We take repeated random samples of size 15 from a population that is normally distributed.
c. We take repeated random samples of size 50 from a population of unknown shape.
d. We take repeated random samples of size 25 from a population that of unknown shape.
Answer:
is d
Step-by-step explanation:
What is the radius of the circle with an equation of x2 - 12x + y2 + 4y = -4?
Answer:
radius = 6
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² - 12x + y² + 4y = - 4
Using the method of completing the square on the x and y terms
add (half the coefficient of the x/y term )² to both sides
x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = - 4 + 36 + 4, that is
(x - 6)² + (y + 2)² = 36 ← in standard form
with r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6
Answer:
6
Step-by-step explanation:
h = -12/-2 = 6
k = 4/-2 = -2
h² + k² - r² = 4
6² + (-2)² - 4 = r²
r² = 36
r = sqrt(36) = 6
An 18-slice pizza was made with only pepperoni and mushroom toppings, and every slice has at least one topping. Exactly ten slices have pepperoni, and exactly ten slices have mushrooms. How many slices have both pepperoni and mushrooms
Answer:
2
Step-by-step explanation:do it on a piese of parer them it will make more sence
- Two consecutive integers are 5 and 6. Write a quadratic equation that
could be used to determine these two integers.
Answer:
x^2 -11x +30 = 0
Step-by-step explanation:
If these two integers are solutions of the quadratic, then its factors are ...
(x -5)(x -6) = 0
Multiplying this out, we get ...
x^2 -11x +30 = 0
A rotating object makes 5/6 of a revolution in 7/10 second. Find the approximate speed in revolutions per second. Write your answer as a decimal to the nearest hundreth.
Answer:
1.19 revolutions per second.
Step-by-step explanation:
Given:
A rotating object makes 5/6 of a revolution in 7/10 second.
To find:
Find the approximate speed in revolutions per second ?
Solution:
As here given that a rotating object makes 5/6 of a revolution in 7/10 second,
we will have to find that in one second how many revolution does this object make:
By unitary method:
In [tex]\frac{7}{10}[/tex] second, a rotating object makes = [tex]\frac{5}{6}[/tex] revolution
In 1 second, a rotating object makes = [tex]\frac{5}{6}\div\frac{7}{10}[/tex]
[tex]=\frac{5}{6}\times\frac{10}{7} = \frac{50}{42}=1.190\ revolution[/tex]
Therefore, the approximate speed of object is 1.19 revolution per second.
We can also find by, [tex]speed = \frac{distance}{time}[/tex]
[tex]=\frac{5}{6} \div\frac{7}{10} \\=\frac{5}{6} \times\frac{10}{7} =\frac{50}{42} = 1.19[/tex]
We can use any one to solve this type of question:
Finally, the approximate speed is 1.19 revolutions per second.
Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches
Carl has [tex]\( \frac{163}{36} \)[/tex] inches of string left out of the 20 inches he started with after tying the parcel and the box.
To find out how much string Carl has left after tying the parcel and the box, we'll subtract the lengths of string used from the total length he started with.
1. Convert the mixed numbers to improper fractions:
-[tex]\(10 \frac{2}{9}\) inches = \(10 + \frac{2}{9} = \frac{90}{9} + \frac{2}{9} = \frac{92}{9}\)[/tex] inches
- [tex]\(5 \frac{1}{4}\) inches = \(5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4}\)[/tex] inches
2. Add the lengths of string used:
[tex]\[\text{Total length used} = \frac{92}{9} + \frac{21}{4}\][/tex]
3. Find a common denominator to add the fractions:
The common denominator for 9 and 4 is 36.
[tex]\[\frac{92}{9} = \frac{92 \times 4}{9 \times 4} = \frac{368}{36}\] \[\frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36}\][/tex]
4. Add the fractions:
[tex]\[\frac{368}{36} + \frac{189}{36} = \frac{368 + 189}{36} = \frac{557}{36}\][/tex] inches
5. Subtract the total length used from the total length Carl started with:
[tex]\[20 - \frac{557}{36}\][/tex]
6. Convert the mixed number result to an improper fraction:
\[20 = \frac{720}{36}\]
7. Subtract the fractions:
[tex]\[\frac{720}{36} - \frac{557}{36} = \frac{720 - 557}{36} = \frac{163}{36}\][/tex] inches
Now, Carl has [tex]\(\frac{163}{36}\)[/tex] inches of string left.
We can convert this to a mixed number if necessary.
The correct question is:
Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches?
Ans:
Carl has [tex]\( {4 \frac{19}{36}} \)[/tex] inches of string left after tying both the parcel and the box.
1. Convert the mixed numbers to improper fractions:
- 10 2/9 inches = [tex]\( \frac{92}{9} \) inches[/tex]
- 5 1/4 inches = [tex]\( \frac{21}{4} \) inches[/tex]
2. Add the lengths of string used:
[tex]\( \frac{92}{9} \) inches (parcel) + \( \frac{21}{4} \) inches (box)[/tex]
To add these fractions, find a common denominator:
The least common multiple of 9 and 4 is 36.
[tex]\( \frac{92}{9} = \frac{92 \times 4}{9 \times 4} = \frac{368}{36} \)\\ \( \frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36} \)\\ \( \frac{368}{36} + \frac{189}{36} = \frac{368 + 189}{36} = \frac{557}{36} \) inches[/tex]
3. Subtract the total used from the initial length of string:
Initial length of string = 20 inches
Total used = [tex]\( \frac{557}{36} \) inches[/tex]
To subtract, convert 20 inches to a fraction with the common denominator of 36:
[tex]\( 20 = \frac{720}{36} \)[/tex]
Now, subtract:
[tex]\( \frac{720}{36} - \frac{557}{36} = \frac{720 - 557}{36} = \frac{163}{36} \) inches[/tex]
4. Convert the fraction to a mixed number (if necessary):
[tex]\( \frac{163}{36} \)[/tex] inches is already in its simplest form. To convert to a mixed number:
[tex]\( 163 \div 36 = 4 \) remainder \( 19 \)[/tex]
So, [tex]\( \frac{163}{36} = 4 \frac{19}{36} \) inches[/tex]
The correct question is:
Carl used 10 2/9 an inch of string to tie a parcel and another 5 1/4 of an inch of string to tie a box, how much string is left he started with 20 inches?
Ans:_______
Let p and q be the propositions. p : I bought a lottery ticket this week. q : I won the million dollar jackpot. Express each of these propositions as an English sentence. a) ¬p b) p ∨ q c) p → q d) p ∧ q e) p ↔ q f ) ¬p → ¬q g) ¬p ∧ ¬q h) ¬p ∨ (p ∧ q)
Answer:
a) ¬p : I didn't buy a lottery ticket this week.
b) p ∨ q: I bought a lottery ticket this week or I won the million dollar jackpot.
c) p → q: If I didn't buy a lottery ticket this week, then I won the million dollar jackpot.
d) p ∧ q: I bought a lottery ticket this week and I won the million dollar jackpot.
e) p ↔ q: I bought a lottery ticket this week if and only if I won the million dollar jackpot.
f ) ¬p → ¬q: If I didn't buy a lottery ticket this week, then I didn't win the million dollar jackpot.
g) ¬p ∧ ¬q: I didn't buy a lottery ticket this week and I didn't win the million dollar jackpot.
h) ¬p ∨ (p ∧ q): I didn't buy a lottery ticket this week or I bought a lottery ticket this week and I won the million dollar jackpot.
Step-by-step explanation:
In logic, a word or group of words that joins two or more propositions together to form a connective proposition it's called connective, also called sentential connective, or propositional connective
1. Negation: the symbol is ¬, or ~. It is use for saying that the proposition is false. This connective proposition only affects one statement.
2. Disjunction ("or"): the symbol is ∨. It is use for saying that at least one of the propositions are true.
3. Conjunction ("and"): the symbol is ∧. It is use for saying that both of the propositions, at the same time are true.
4. Conditional (“if . . . then”): the symbor is →. In this structure the first proposition it's called antecedent and the second one consecuent. For this connective the only case when it's not true is when the antecendent is true and the consecuent is false.
5. Biconditional ("if and only if"): the symbol is ↔. This structure is a double conditional. And the proposition is true when antecent and consecuent are both true or both false.
Final answer:
The student's question involves translating logical propositions into English sentences. These include negation, disjunction, conjunction, conditional, and bi-conditional statements based on the scenarios presented.
Explanation:
The student wants to express each proposition as an English sentence. The propositions include notations for negation (¬), disjunction (∨), conjunction (∧), and implication (→), as well as bi-conditional (↔).
a) ¬p: 'I did not buy a lottery ticket this week.'b) p ∨ q: 'I bought a lottery ticket this week or I won the million dollar jackpot (or both).'c) p → q: 'If I bought a lottery ticket this week, then I won the million dollar jackpot.'d) p ∧ q: 'I bought a lottery ticket this week and I won the million dollar jackpot.'e) p ↔ q: 'I bought a lottery ticket this week if and only if I won the million dollar jackpot.'f) ¬p → ¬q: 'If I did not buy a lottery ticket this week, then I did not win the million dollar jackpot.'g) ¬p ∧ ¬q: 'I did not buy a lottery ticket this week and I did not win the million dollar jackpot.'h) ¬p ∨ (p ∧ q): 'I did not buy a lottery ticket this week or I both bought a ticket and won the million dollar jackpot.'Each sentence corresponds to different logical statements found in propositional logic.
A 24.6 g marble sliding to the right at 62.0 cm/s overtakes and collides elastically with a 12.3 g marble moving in the same direction at 15.5 cm/s. After the collision, the 12.3 g marble moves to the right at 77.5 cm/s. Find the velocity of the 24.6 g marble after the collision. cm/s
Answer:
Velocity of the 24.6 g marble is 31 cm/s.
Step-by-step explanation:
Given:
Marble 1:
Mass of the marble [tex](m_1)[/tex] = 12.3 gm
Velocity of [tex]m_1[/tex] before collision [tex]v_1_i[/tex] = 15.5 cm/s
Velocity of [tex]m_1[/tex] after collision [tex]v_1_f[/tex] = 77.5 cm/s
Marble 2:
Mass of the marble [tex](m_2)[/tex] = 24.6 gm
Velocity of [tex]m_2[/tex] before collision [tex]v_2_i[/tex] = 62 cm/s
Velocity of [tex]m_2[/tex] after collision [tex]v_2_f[/tex] = ?
From the law of conservation of momentum, we know that momentum before equals the momentum after :
So,
⇒ [tex]P(i)=P(f)[/tex]
⇒ [tex](m_1\times v_1_i )+(m_2\times v_2_i) =(m_1\times v_1_f)+(m_2\times v_2_f)[/tex]
⇒ Plugging the values.
⇒ [tex](12.3\times 15.5) +(24.6\times 62)=(12.3\times 77.5)+(24.6\times v_2_f)[/tex]
⇒ [tex]190.65+1525.2=953.25+24.6\times v_2_f[/tex]
⇒ [tex]1715.85=953.25+24.6\times v_2_f[/tex]
⇒ [tex]1715.85-953.25=24.6\times v_2_f[/tex] ...subtracting both sides 953.25
⇒ [tex]762.6=24.6\times v_2_f[/tex]
⇒ [tex]\frac{762.6}{24.6}\ =v_2_f[/tex] ...dividing both sides with 24.6
⇒ [tex]31=v_2_f[/tex]
⇒ [tex]v_2_f =31[/tex] cm/s
The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.
A company's revenue can be modeled by r=2t^2-23t+77, where r is the revenue (in millions of dollars) for the year that is t years since 2005. Predict when the revenue was or will be at 14 million
Answer:
t=2652
Step-by-step explanation:
I need helpp please help me!!!
Answer:
SAS
Step-by-step explanation:
Constructing arithmetic sequences Learn Recursive formulas for arithmetic sequences(Opens a modal)Recursive formulas for arithmetic sequences(Opens a modal)Explicit formulas for arithmetic sequences(Opens a modal)Explicit formulas for arithmetic sequences(Opens a modal)Arithmetic sequence problem(Opens a modal)Converting recursive
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is an = a1 + (n-1)d, and the explicit formula is an = a1 + (n-1)d.
Explanation:An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is given by: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. The explicit formula for an arithmetic sequence is given by: an = a1 + (n-1)d. The explicit formula allows you to directly find any term in the sequence without having to find the previous terms.
If a farmer can trade four chickens for a pig, three pigs for two sheep, and five sheep for two cows, what is the minimum number of cows he needs to trade for $20$ chickens?
Answer:
The minimum of cows he needs are: 2
Step-by-step explanation:
There's a relation between each animal:
5 chickens equals 1 pig
3 pigs equals 2 sheep
5 sheep equals 2 cows
You can understand it as the following three abstractions:
5c = 1p (1)
3p = 2s (2)
5s = 2o (3)
Where:
c is for chickens
p is for pigs
s is for sheep
o is for cows
So now you have three equations with 4 variables. The next step is to obtain an equation that relates directly the variable c (chickens) with the variable o (cows). In order to do that from the equation 2 we obtain s in terms of p, as follow:
[tex]3p =2s\\s=\frac{3p}{2} \\[/tex]
Then we replace s in the equation 3 and we obtain v in terms of p:
[tex]5(\frac{3p}{2} )=2v\\\\2v=\frac{15}{2} p\\\\[/tex]
[tex]v=\frac{15}{2*2} p \\\\v=\frac{15}{4} p[/tex]
Now we replace v in the equation 1:
[tex]4c = \frac{4}{15} v[/tex]
[tex]c=\frac{1}{15} v[/tex] (4)
The equation 4 means that 1 chicken equals the fifteenth part of a cow. For this case the farmer needs 20 chikens, so we multiply per 20 each part of the equation 4:
[tex]20c = 20 * \frac{1}{15} v\\ \\\ 20c = \frac{20}{15}v = \frac{4}{3}v \\\\20c = 1.3333v[/tex]
As it is impossible to have 1.3333 cows, the answer is 2 cows approximately.
Answer:
2
Step-by-step explanation:
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 42 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 48 births.
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
c. Is the result of 42 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
Answer:
a) [tex]\mu = 24,\sigma = 3.46[/tex]
b) Significantly low:
[tex]x < 17.08[/tex]
Significantly high:
[tex]x > 30.92[/tex]
c) 42 girls are significantly high.
Step-by-step explanation:
We are given the following in the question:
[tex]p = 0.5[/tex]
a) mean and the standard deviation for the numbers of girls in groups of 48 births
[tex]\mu = np = 48(0.5) = 24\\\sigma = \sqrt{np(1-p)} = \sqrt{48(0.5)(1-0.5)} = 3.46[/tex]
b) Range rule of thumb
Significantly low: According to this rule the observations lying below two standard deviation of mean is considered significantly low.
[tex]x = \mu - 2\sigma\\x = 24 - 2(3.46) = 17.08[/tex]
Significantly high: According to this rule the observations lying above two standard deviation of mean is considered significantly high.
[tex]x = \mu + 2\sigma\\x = 24 + 2(3.46) = 30.92[/tex]
c) Significance of 42 girls
[tex]42 > \mu + 2\sigma[/tex]
Since 42 is greater than 30.92, 42 girls are significantly high. Thus, the method is not significant.
PLEASE HELP ME IDK HOW TO DO THIS
The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months since January 2001. (m = 0 represents January 2001.) *see attached table*
A sine function is written to represent the data.
What is the amplitude, period, and vertical shift of this equation?
Answer:
Amplitude is 17
Period = 12
Vertical shift of 50
Step-by-step explanation:
One complete cycle in 12 months
Mean line is at y = 50, so vertical shift of 50
Amplitude = 67-50 = 17
Or , 50 - 33 = 17
The vertical shift, amplitude, and period of the given equation would be as follows:
Amplitude [tex]= 17[/tex]
Period [tex]= 12[/tex]
Vertical Shift [tex]= 50[/tex]
What is Temperature?Given that,
Duration of the cycle [tex]= 12[/tex] months
∵ Period [tex]= 12 months[/tex]
The Mean line lies at [tex]y = 50[/tex]
So,
The vertical shift [tex]= 50[/tex]
Now,
Amplitude [tex]= 67-50[/tex]
[tex]or[/tex]
[tex]50 - 33[/tex]
[tex]= 17[/tex]
Learn more about "Amplitude" here:
brainly.com/question/9351212
The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle
Answer: the area of the original rectangle is 300 square meters.
Step-by-step explanation:
Let L represent the original length of the rectangle.
Let W represent the original width of the rectangle.
The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. This means that the length of the new rectangle is 2L and the width of the new rectangle is 3W
If the area of the new rectangle is equal to 1800 square meters, it means that
2L × 3W = 1800
6LW = 1800
LW = 1800/6
LW = 300 square meters
In a lilac paint mixture, 40% of the mixture is white paint, 20% is blue, and the rest is he rest is red. There are 4 cups of blue paint used in a batchof lilac paint. How many cups of white paint are used
Answer:
8
Step-by-step explanation:
The ratio of white paint to blue paint in the mix is ...
40% : 20% = 2 : 1
We can multiply this ratio by 4 cups to find ...
white : blue = 8 cups : 4 cups
There are 8 cups of white paint in the mixture.
Answer: the number of cups of white paint are used is 8
Step-by-step explanation:
Let x represent the total number of cups of paint used in the mixture.
40% of the mixture is white paint, this means that the number of cups of white paint used is 0.4x
20% of the mixture is blue paint, this means that the number of cups of blue paint used is 0.2x
If the rest is red, it means that the number of red cups used is
x - (0.2x + 0.4x) = 0.4x
There are 4 cups of blue paint used in a batch of lilac paint. This means that
0.2x = 4
x = 4/0.2 = 20
Therefore, the number of cups of white paint are used is
0.4 × 20 = 8
A ship departs from Port miami with 5678 tons of cargo the ship docks at the Bahamas and the uploads some cargo the crew also loads three times the quantity of cargo that was unloaded of the ship holds 8588 tons now how many tons of cargo did the ship unload at the bahamas
Answer: the ship unloaded 1455 tons of cargo at the bahamas.
Step-by-step explanation:
Let x represent number of tons of cargo that the ship unloaded at the bahamas.
The initial number of tons of cargo in the ship is 5678 tons. If it unloads x tons of cargo, the number of tons of cargo left would be
5678 - x
The crew also loads three times the quantity of cargo that was unloaded. This means that the number of tons of cargo that it loaded is 3x. The total number of tons of cargo in the ship would be
5678 - x + 3x
= 5678 + 2x
If the ship holds 8588 tons now, it means that
5678 + 2x = 8588
2x = 8588 - 5678
2x = 2910
x = 2910/2
x = 1455 tons of cargo
Ten year old Chi learned a lot of math from his older brother, Shing. One day, Shing told him that when you multiply a number by 10, you just add zero?
Answer:
This is true
Step-by-step explanation:
10x1 is 10. 10x10 is 100. but if u did 100x10 you would add the amount of zeros total. which would be 1000. so 400x10 is 4000
5/12 of the pupils in a school are left-handed and the rest are right-handed. There are 276 more pupils who are right-handed than left-handed. What is the total number of pupils in the school?
Answer:
There are a total number of 1656 students in the school.
Step-by-step explanation:
Let's set up this word problem in mathematical terms.
We can call the number of Left Handed Students as X,
and we can call the number of Right Handed Students as Y.
Since there are 276 more right handed pupils than left handed, we have the following equation:
X + 276 = Y -Equation 1
Also, since there are 5/12 ratio of left handed students and 7/12 right handed students, we get:
Total Students = T
(5/12) T = X -Equation 2
(7/12) T = Y -Equation 3
Substituting equations 2 and 3 into equation 1 we get:
[tex]\frac{5}{12} T+276=\frac{7}{12} T[/tex]
Solving for Total number of students (T) we get:
T = 1656
What is an equation of the line that passes through the points (−5,−7) and (5,1)?
Answer:
y = 4/5x -3
Step-by-step explanation:
in order to do this :
firstly , find the midpoint of the points.use the formula :
[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]
= [tex]\frac{-5 + 5}{2} , \frac{-7 + 1}{2}[/tex]
midpoint =(0 , -3)
secondly , get the gradientuse the formula :
[tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{1-(-7)}{5-(-5)}[/tex]
=[tex]\frac{8}{10}[/tex]
simplified to 4/5
gradient = 4/5
Thirdly , create the equationformula for the equation of a line
(Y-y1) = m( X-x1)
now use the values of the midpoint and the gradient(m)
y +7 = 4/5 (x + 5)
y = 4/5x + 4-7
y = 4/5x -3Answer:
y = 0.8x - 3
Step-by-step explanation:
Slope = (-7-1)/(-5-5) = -8/-10 = 0.8
When x = 5, y = 1
1 = 0.8(5) + c
1 = 4 + c
c = -3
y = 0.8x - 3
Find AB. (Brainly says it is too short this is why this is here)
The length of AB is 31 yd.
Solution:
Given data:
The side opposite to angle A is "a" = 22 yd
The side opposite to angle B is "b" = 26 yd
The side opposite to angle C is "c" = AB
Angle C = 80°
To find the length of AB:
Using cosine formula,
[tex]c^2=a^2+b^2-2ab \cdot \cos C[/tex]
Substitute the given values in the formula, we get
[tex]c^2=22^2+26^2-2(22)(26)\cdot \cos 80^\circ[/tex]
[tex]c^2=484+676-1144\cdot \cos 80^\circ[/tex]
[tex]c^2=1160-1144\cdot (0.1736)[/tex]
[tex]c^2=1160-198.5984[/tex]
[tex]c^2=961.4016[/tex]
Taking square root on both sides, we get
c = 31
AB = 31 yd
The length of AB is 31 yd.