Answer:
4/12
Step-by-step explanation:
1/3=x/12
using the butterfly method you see that
12=3x
and when solved you get
x=4
giving you
4/12
Also multiply 1/3 by 4 on each side
One third is equivalent to 4 over 12.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Let the unknown number be x.
Here, 1/3 = x/12
Multiply both the numerator and denominator of 1/3 by 4, we get
4/12
So, 4/12 = x/12
x=12
Therefore, the unknown number is 12.
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A survey was given to people who own a certain type of car. What percent of the people surveyed were completely satisfied with the car?
A cryptographer uses a combination of two functions to develop the initial "key” in a sequence of coded numbers. The functions are:
f(x) = log5(x) – 8
g(x) = x3 + 3
Which is h(x) = f(x) – g(x)?
h(x) = log5(x) – x3 – 5
h(x) = log5(x3) – 3
h(x) = log5(x) – x3 + 11
h(x) = log5(x) – x3 – 11
The value of the function h(x) = f(x) – g(x) will be h(x) = log5(x) – x³ – 11. The correct option is D.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a cryptographer uses a combination of two functions to develop the initial "key” in a sequence of coded numbers. The functions are:
f(x) = log5(x) – 8
g(x) = x³ + 3
The value of the function h(x) = f(x) - g(x) is,
h(x) = f(x) - g(x)
h(x) = log5(x) – 8 - x³ - 3
h(x) = log5(x) – 8 - x³ - 11
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Answer:
D. h(x) = log5(x) – x3 – 11
Step-by-step explanation:
Let X and Y be independent and identically distributed exponential random variables with rate λ.
Let U = X/Y and let V = XY . Find the joint desnity for (U, V ). Also find the marginal densities fU (u)
and fV (v).
The joint density for (U, V) is given by:
f(u,v) = fX/Y,XY(u,v) = fX(v/u) * fY(v/u) * |(v/u)|= λ^2 * v * e^(-λv/u) * |(v/u)|
The marginal density for U is given by:
fU(u) = ∫f(u,v)dv
= ∫λ^2 * v * e^(-λv/u) * |(v/u)|dv
= λ^2 * u * ∫ve^(-λv/u)dv
= λ^2 * u * (-(u/λ)^2 * e^(-λv/u))|v=0 to v=∞
= λ^2 * u * (-(u/λ)^2)
= λ^3 * u^2
The marginal density for V is given by:
fV(v) = ∫f(u,v)du
= ∫λ^2 * v * e^(-λv/u) * |(v/u)|du
= λ * v * ∫e^(-λv/u) * |(v/u)|du
= λ * v * (∫e^(-λv/u)du)|v=0 to v=∞
= λ * v * (-(u/λ) * e^(-λv/u))|u=0 to u=∞
= λ * v * (-1)
= λ * v
Therefore, the joint density for (U, V) is
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4. Suppose y varies directly with x. If y = 6 when x = -2, find x when y = 15.
Answer:
x is -7.5 or -14/2 or -7½
Step-by-step explanation:
- Supposing y varies directly with x
[tex] { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} [/tex]
[k is a constant of proportionality (k ≠ 0)]
- When y is 6, x is -2
[tex] \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}[/tex]
- Therefore, the equation is;
[tex]{ \boxed{ \tt{y = - 2x}}}[/tex]
- What is x when y is 15
[tex]{ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}[/tex]
The value of x is -5
The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:
k = y/x
k = 6/-2
k = -3
Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation
15 = -3x
Then solve x,
x = [tex]\frac{-15}{3}[/tex]
x = -5
Therefore, when y = 15, x = -5.
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Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same?
The number of visits Jim must make to make Plan A the cheaper option is 6 and 5 visits will cost the same.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Suppose n number of visits will make plan A cheaper than B.
The total cost of A < total cost of B
50 + 10n < 25 + 15n
15n - 10n > 50 - 25
5n > 25
n > 5
n = 6
At n = 5
Total cost of A = 50 + 10 x 5 = $100
Total cost of B = 25 + 15 x 5 = $100
Hence "Jim needs to visit 6 times, and 5 visits will cost the same, for Plan A to be more affordable".
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Differentiate the function with respect to x. Answer is B. I need the step. Thank you
Answer:
y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.
Step-by-step explanation:
Rewrite the equation to -((6 c^2 - 20 x^3) dx)/(3 + 5 x^2) + dy = 0 and solve
Solve (dy(x))/(dx) = (6 c^2 - 20 x^3)/(5 x^2 + 3):
Integrate both sides with respect to x:
Answer: y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.
What is the missing number, what property did you use? 0=–––×3×4
Answer:
0, zero product property
Step-by-step explanation:
A bag contains 1 gold marbles, 6 silver marbles, and
28 black marbles. Someone offers to play this game:
You randomly select one marble from the bag. If it
is gold, you win $3. If it is silver, you win $2. If it is
black, you lose $1.
What is your expected value if you play this game?
Step-by-step explanation:
the expected value is the sum of all values multiplied by their corresponding probabilities.
and a probability is always
desired cases / totally possible cases.
in the bag are
28 + 6 + 1 = 35 marbles
the probability to pull the gold is
1/35
the probability to pull a silver is
6/35
the probability to pull a black is
28/35 = 4/5
the expected value = $3×1/35 + $2×6/35 - $1×28/35 =
= 3/35 + 12/35 - 28/35 =
= -13/35 = -0.371428571... ≈
≈ -$0.37
that means (like with all games of that kind like all casino games) the bank will win in the long run.
your only chance to win is to play very few times and get a winner by pure chance. the longer you play you might actually hit a winner somewhere in between, but the surer you still lose in total.
Write the tangent equation to solve for angle f
Answer:
Tan(f) = 24/7
Step-by-step explanation:
Tan is opposite over adjacent.
The opposite of angle F is 24 and the adjacent is 7.
PLEASEEEEEEEEEEE HURRY WILL GIVE BRAINLYEST
The proportion to calculate triangle side LM in the given triangle is 3/2
How to calculate the side LMThe side LM is calculated using the idea of similar triangle, in this case the triangles are equal in proportion to each other
To find the proportion we take the ratio of the sides this is done as follows
LM / HJ = MN / JK = LN / HK
substituting the values
MN / JK = 9 / 6 = 3 / 2
the proportion is = 3/2
to find LM
4.5 * 3/2
= 6.75 cm
Using proportion of 3/2 the length of side LM is solved to be 6.75 cm
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Analyze the data with a nonparametric test and comment on the results and write a conclusion.
Rank in Weight Rank in Dominance Hierarchy
1 3
2 4
3 1
4 8
5 7
6 2
7 5
8 6
9 9
OR
7C
Here are some data based on a study by St. Leger, et al. (1978 and described in Howell, 1995). The data come from 10 countries. One variable is the number of physicians per 10,000 population. The other variable is an infant mortality rate that is adjusted so that the wealth of the country is not being measured. Analyze the data with a nonparametric test and comment on the results and write a conclusion.
Physicians Rank Mortality Rank
1 2
2 1
3 4
4 3
5 6
6 5
7 9
8 8
9 10
10 7
On solving the provided question, we can say that - correlation coefficient , r= .95
What is correlation coefficient ?The Pearson's correlation coefficient, also known as the Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a statistical indicator of the linear relationship between two sets of data.
[tex]S_{xx}[/tex] = ∑[tex]x^2[/tex] + [tex]nx^2[/tex] = 60
[tex]S_{yy} = 60[/tex]
r = .95
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Which inequality matches the graph? X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Dotted line on graph has positive slope and runs through negative 3, negative 8 and 1, negative 2 and 9, 10. Above line is shaded. a −2x + 3y > 7 b 2x + 3y < 7 c −3x + 2y > 7 d 3x − 2y < 7
The inequality equation of the given description of the inequality graph is; 3x - 2y < 7
What is the inequality of the graph?Given :
X range is negative 10 to 10, and Y range is negative 10 to 10.
Dotted line on graph has positive slope and runs through points: (-3,-8), (1,-2), and (9,10).
Now, since we know the coordinates through which the graph runs, we can pick two coordinates and use it to find the slope through the formula;
m = (y₂ - y₁)/(x₂ - x₁)
If we pick (-3,-8), (1,-2), we have;
m = (-2 - (-8))/(1 - (-3)
m = 6/4
m = 3/2
We will use formula for equation of a line in point slope form to get;
y - y₁ = m(x - x₁)
y - 10 = (3/2)(x - 9)
2y - 20 = 3x - 27
3x - 2y = 7
Because, above the line is shaded, therefore, the correct inequality matching the graph is 3x - 2y < 7
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the high temperature for the week were 50, 52, 71, 54, and 51. what is the mean of the temperatures without the outlier?
Answer: 55.6 or 55.60
Step-by-step explanation: Okay, so we have to add up all the numbers and divide by how many numbers there are, so we would add 50 + 52 + 71 (Including this outlier) + 54 + 51, to get 278. Now, since there are 5 numbers in the data set, we would divide 278 by 6, and you should get 55.6 or 55.60 (They are the same thing)
What is the length of X Y? 5 units 4 units 3 units 2 units
The length of XY in the given figure is 3 units.
What does congruent mean?same in size and form
Congruent refers to things that are exactly the same size and form. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
What is an example of congruent?Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.
In the above question,
According to the congruency criteria
HI=XY
Hence, Value of XY is 3 units.
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Choose Yes or No to tell whether the fraction and percent are equivalent.
40/1000 and 40%
6/5 and 120%
50/33 and 117%
1/8 and 12.5%
m/JHI =(2x+7)° and m/GHI = (8x - 2)° and m/JHG= 65°. Find m/JHI and m/GHI
The value of m/JHI and m/GHI is angle 19 and 46.
What is angle ?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
[tex]\begin{aligned}2 x+7+8 x-2 & =65 \\10 x+5 & =65 \\10 x & =60 \\x & =6\end{aligned}[/tex]
m/JHI =(2x+7) = (2* 6+7)=12+7=19.
m/GHI = (8x - 2)° = (8*6-2)=48-2=46
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PLEASE HELP ILL DO ANYTHING
20. A triathlon is about 51 kilometers. One participant completed
two of the three legs of the race and traveled 42 kilometers.
Solve the equation 42+ d = 51 for the distance, d, of the
third leg of the race.
21. Analyze and Persevere w
Answer:
d=9
Step-by-step explanation:
42 km is 2 of the 3 legs
51 is the total triathlon
51 - 42 = 9
6. How much will you pay for 14.8 gallons of diesel fuel at $1.39 per gallon?
Round to the nearest cent
Answer:
$20.5
Step-by-step explanation:
If f(x) = 3x + 1
Find f(-4)
the top of an electric pole is s supported by a wire of 26 ft long on the ground level. how far is tightened spot from the foot of the pole if its height is 24 ft?
Answer:
The tightened spot is 10 feet away from the foot of the pole.
Step-by-step explanation:
1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.
2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.
⭐What is the Pythagoras' Theorem?
[tex](C)^2 = (A)^2 + (B)^2[/tex]An equation to find a 3rd side lengthC = hypotenuseA = one legB = another leg3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.
Let B= the distance from the tightened spot to the foot of the pole.
[tex](C)^2 = (A)^2 + (B)^2[/tex]
[tex]26^2 = 24^2 + B^2[/tex]
[tex]676 = 576 + B^2[/tex]
[tex]100 = B^2[/tex]
[tex]\sqrt{100} = \sqrt{(B)^2}[/tex]
[tex]10 = B[/tex]
∴ The tightened spot is 10 feet away from the foot of the pole.
Diagram:
How do fractions 1/4 and 1/8 compare
The product of x and 10 is greater then or equal to 23
Answer:
x ≥ 2.3
Step-by-step explanation:
Product means multiplication
10x ≥ 23 Divide both sides by 10
x ≥ 2.3
An airplane covers 50 miles in 1 hour. How many miles can the airplane cover in 1/2 an hour
Consider the polynomial g(x) = 4x³ - x2 - 24x+6
a. List all possible rational zeros of the polynomial. (Assume all numbers shown are both + and -).
O1, 2, 4, 1/2, 1/3, 2/3, 4/3, 1/6
1, 2, 3, 4, 6, 1/2, 3/2, 1/3, 2/3, 4/3, 1/4, 3/4, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/4, 3/4
O1, 2, 3, 6, 1/2, 3/2, 1/4, 3/4
b. List all actual zeros of the polynomial (rational, irrational, real, and complex).
Give exact answers, separated by commas as necessary.
Zeros:
Answer:
a. x = 1/4
b. x = [tex]+\sqrt{6}[/tex], [tex]-\sqrt{6}[/tex], 1/4
Step-by-step explanation:
a. I factorised the polynomial.
[tex]g(x) = 4x^3 - x^2 -24x +6 = 0[/tex]
[tex]-x^2 (-4x + 1) +6 (-4x +1)[/tex]
[tex](-4x+1)(-x^2+6)[/tex]
Solved for the roots.
[tex]-4x + 1 = 0[/tex]
[tex]-4x = -1[/tex]
[tex]x = \frac{1}{4}[/tex]
[tex]-x^2+6 = 0[/tex]
[tex]-x^2 = -6[/tex]
[tex]x^2 = 6[/tex]
[tex]x = +\sqrt{6}[/tex]
[tex]x=-\sqrt{6}[/tex]
A rational number is a real number that's digits terminate and/or repeat. Therefore, 1/4 is the only rational zero.
b. All of the zeros we found in part A. are [tex]+\sqrt{6}, -\sqrt{6}, and \frac{1}{4}[/tex]
Sybush
5 Resuelve como en el ejemplo.
TH
.-6+8-10 + 13 = +2 -10 + 13 = -8 + 13 = +5
b) 5-9+7-6
d) -8 + 12-9-2
a) 10-3-5 + 11
c) −2+2+7+8
The Answers for the four parts are
a) 5-9+7-6=-3
b) -8 + 12-9-2=-7
c) 10-3-5 + 11 =13
d) −2+2+7+8= 15
What are Integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
a) 5-9+7-6
= -4 +7-6
= 3-6
=-3
So, the value of 5-9+7-6 is (-3).
b) -8 + 12-9-2
= 4-9-2
= -5-2
=-7
So, the value of -8 + 12-9-2 is (-7).
c) 10-3-5 + 11
= 7-5+11
= 2+11
=13
So, the value of 10-3-5 + 11 is (13).
d) −2+2+7+8
= 0+7+8
= 7+8
= 15
So, the value of −2+2+7+8 is (15).
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The Translation of the Attached Question:
Solve as in the example
A table of values of a linear function is shown below. Find the output when the input is n . Type your answer in the space provided.
Input 1 2 3 4 n
output -1 3 7 11
PLEASE ANYONE I NEED HELP ASAP THANK YOU!!
Answer:
input: n
output: 15
Step-by-step explanation:
⭐What is a linear function?
A linear function is an equation that increases by a constant, additive amount.A linear function looks like a straight line when graphed.⭐To find the output that corresponds to n, we can:
make a table of values to find the constant, additive amount of this linear functionuse said constant, additive amount to find the output that corresponds to n⭐Remember:
"input" = x-values"output" = y-values
Consider the problem of computing (xy)for given integers x and y: we want the whole answer.We know two algorithms for doing this: the iterative algorithm which performs (y - 1) multiplications by x; and the recursive algorithm based on the binary expansion of y.Compare the time requirements of these two algorithms, assuming that the time to multiply an n-bit number by an m-bit number is O(mn).
The recursion tree is log2m and has log2m nodes .
A recursive algorithm calls itself with smaller input values and returns the result for the current input by carrying out basic operations on the returned value for the smaller input.
A iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for recurrence relations of types that occur in the analysis of many divide and conquer algorithms.
Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.
Iterative: The pseudocode for this algorithm is as follows.
product = x;
for i = 2 to y do
product = product * x
The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .
The resulting number after the multiplication is i.n bits long. Thus
adding up all the multiplication cost we get
n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in
the input length of y which is m = log2 y.
Recursive: The pseudocode for this algorithm is as follows:
function recursive (x ,y)
if y is even then return (x(by2c))2
if y is odd then return x ∗ (x(by2)c)2.
Computing (x(by2c))2
requires a multiplication involving two y2
n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this
recursive routine is
T(y) = O(n) when y is 1-bit long.
T(y) = T(y2) + O(y2n2) otherwise.
Applying the Master Theorem we can conclude that T(y) ∈ O(y2n2). The height
of the recursion tree is log2m and has log2m nodes.
Thus both the algorithms have the same worst case complexity.
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Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.
product = x;
for i = 2 to y do
product = product * x
The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .
n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in
the input length of y which is m = log2 y.
function recursive (x ,y)
if y is even then return (x(by2c))2
if y is odd then return x ∗ (x(by2)c)2.
Computing (x(by2c))2
requires a multiplication involving two y2
n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this
recursive routine is
T(y) = O(n) when y is 1-bit long.
T(y) = T(y2) + O(y2n2) otherwise.
Thus both the algorithms have the same worst case complexity.
A. Find m
B. Using the answer above, Find m
Answer:
∠ b = 108° , ∠ d = 72°
Step-by-step explanation:
(a)
the sum of the 3 angles in a triangle = 180° , that is
∠ a + ∠ b + ∠ c = 180°
25° + ∠ b + 47° = 180°
∠ b + 72° = 180° ( subtract 72° from both sides )
∠ b = 108°
(b)
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then
∠ d = ∠ a + ∠ c = 25° + 47° = 72°
A school bought 105 boxes of chocolate cookies and 22 boxes of vanilla cookies
for a fundraiser. Each box contained 12 cookies.
The school then repacked the cookies into smaller packs of 8 to sell.
How many small packs were there? How many cookies were left over?
Answer:190 small packs and 4 cookies left over
Step-by-step explanation:
Add the boxes of cookies together 105+22=127
Multiply each box by 12
127 x 12=1524
Because we need to put them into smaller packs of 8 cookies
we need to divide by 8
1524÷8=190 small boxes
This is a total of 190 x 8=1520 cookies there are 4 cookies left over
In 2003, the price of a certain automobile was approximately $30,600 with a depreciation of $1,440 per year. After how many years will the car's value be $19,080?
a) Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.
Answer:
b)Solve the equation to find the answer to the question above. (Note: Include the units, in this case years.)
Answer:
Answer:
a) v(t) = 30600 -1440t
b) 8 years
Step-by-step explanation:
You want an equation that models the value of a car that is initially $30,600 and falls at the rate of $1440 per year. Then you want the number of years it takes for the value to fall to $19,080.
a) EquationSince the rate at which the value falls is a constant, we can use a linear equation for the model. Its form will be ...
value = initial value - (depreciation per year) × years
v(t) = 30,600 -1440t
b) TimeThe time it takes for the value to fall to 19080 can be found by solving for t:
19080 = 30600 -1440t
1440t = 30600 -19080 = 11520
t = 11520/1440 = 8
After 8 years the car's value will be $19,080.