g(x)=-x^2 is the reflection of your function f(x) over the x-axis.
What is function?
The function f(x)=x2 is a parabola facing upward with its vertex at (0,0), and including the points (1,1), (2,4), (-1,1), and (-2,4).
A function that is a reflection across the x-axis compared to f(x) would be the mirror image of f(x). It would have the opposite y-values for each x-value. It would also have its vertex at the same place as f(x).
Therefore, it would be a parabola pointing downward, with the points (1, -1), (2,-4), (-1,-1), and (-2,-4).
To get the opposite values for y, you simply need to place a negative in front of the x2. So the function would be g(x) = - x2.
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How many permutations of the letters ABCDEFGH contain (no letters are repeated) (12 pts)? a. The string ED? b. The string CDE? c. The strings BA and FGH? d. The strings AB, DE, and GH? e. The strings CAB and BED? f. The strings BCA and ABF?
The total number of permutations satisfying the given conditions is 720 + 120 + 30 + 30 + 48 + 48 = 996.
a. The string ED can be treated as a single object. We can arrange the remaining 6 letters in 6! ways. So, the total number of permutations with ED is 6! = 720.
b. Similar to part (a), the string CDE can be treated as a single object. We can arrange the remaining 5 letters in 5! ways. So, the total number of permutations with CDE is 5! = 120.
c. The strings BA and FGH can be placed in the remaining 6 positions in 6 × 5 = 30 ways.
d. The strings AB, DE, and GH can be placed in the remaining 5 positions in 5! / (2! × 2! × 2!) = 30 ways, using the formula for permutations with repeated objects.
e. The strings CAB and BED can be placed in the remaining 4 positions in 4! ways. So, the total number of permutations with CAB and BED is 2 × 4! = 48.
f. The strings BCA and ABF can be placed in the remaining 4 positions in 4! ways. So, the total number of permutations with BCA and ABF is 2 × 4! = 48.
Therefore, the total number of permutations satisfying the given conditions is 720 + 120 + 30 + 30 + 48 + 48 = 996.
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Determine the simple interest earned on a $6000 investment at 5.5% for 12 years
Answer:
369,000
Step-by-step explanation:
$6000x5.5x12
the issue of corporate tax reform has been cause for much debate in the united states. among those in the legislature, 28% are republicans, 50% are democrats and 22% are independents. it is reported that 34% of the republicans, 35% of the democrats and 31% of independents favor some type of corporate tax reform. suppose a member of congress is randomly selected and he/she is found to favor some type of corporate tax reform. what is the probability that this person is a democrat? round your answer to four decimal places. do not round intermediate value(s).
The probability that a randomly selected member of Congress who favours corporate tax reform is a Democrat is 0.4444, rounded to four decimal places.
To solve this problem, we can use Bayes' theorem. Let D represent the event that the selected member is a Democrat, and R represent the event that the selected member is a Republican, and I represent the event that the selected member is an Independent. Let F represent the event that the selected member favors some type of corporate tax reform. We are given the following probabilities:
P(R) = 0.28, P(D) = 0.50, P(I) = 0.22
P(F|R) = 0.34, P(F|D) = 0.35, P(F|I) = 0.31
We want to find P(D|F), the probability that the selected member is a Democrat given that they favor corporate tax reform. We can use Bayes' theorem:
P(D|F) = P(F|D)P(D) / [P(F|D)P(D) + P(F|R)P(R) + P(F|I)P(I)]
Plugging in the values we know, we get:
P(D|F) = 0.35 * 0.50 / [0.35 * 0.50 + 0.34 * 0.28 + 0.31 * 0.22]
P(D|F) = 0.4444 (rounded to four decimal places)
Therefore, the probability that the selected member is a Democrat given that they favour corporate tax reform is 0.4444.
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explain how to find a recurrence relation for the num- ber of bit strings of length n not containing two con- secutive 1s
To find a recurrence relation for the number of bit strings of length n not containing two consecutive 1s, we simply add the possibilities from cases when the last bit is a 0 and the last bit is a 1.
We are required to find a recurrence relation for the number of bit strings of length n that do not contain two consecutive 1s. To do this, we will consider two cases:
1. The last bit is a 0
2. The last bit is a 1
Case 1: If the last bit is a 0, the bit string of length n can end in any bit string of length n-1 (since adding a 0 at the end does not create consecutive 1s). Let's call the number of such bit strings with no consecutive 1s A_n. So, in this case, there are A_(n-1) possibilities.
Case 2: If the last bit is a 1, the bit string of length n must end in a bit string of length n-2 (since adding a 1 after a 0 does not create consecutive 1s). In this case, there are A_(n-2) possibilities.
To find the total number of bit strings of length n with no consecutive 1s, we simply add the possibilities from both cases. Therefore, the recurrence relation can be defined as:
A_n = A_(n-1) + A_(n-2)
This is the recurrence relation you need to determine the number of bit strings of length n that do not contain two consecutive 1s.
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Why can the sine ratio never be greater than 1?
Because the sine and cosine ratios involve dividing a leg (one of the shorter two sides) by the hypotenuse (the longest side), the ratio values will never be greater than one, because (some number) / (a larger number) is always less than one.
What is sine and cosine?Sine & cosine are trigonometric functions of an angle in mathematics. In the context of a right triangle, the sine and cosine of an acute angle are defined as follows: for the specified angle, the sine is the ratio of the length of the side opposite that angle to the length of the triangle's longest side (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.
The sine and cosine functions for an angle θ are simply denoted as sin θ and cos θ. In general, the definitions of sine and cosine can be extended to any real value expressed in terms of the lengths of specific line segments in a unit circle.
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a marine aquarium has a small tank and a large tank, each containing only red and blue fish. in each tank, the ratio of red fish to blue fish is 333 to 444. the ratio of fish in the large tank to fish in the small tank is 464646 to 555. what is the ratio of blue fish in the small tank to red fish in the large tank?
The ratio of the blue fish in the small tank to red fish in the large tank is 10 to 69.
Ratio is the relationship between two quantities.
Let x : y = ratio of the blue fish in the small tank to red fish in the large tank
Hence, there are x blue fish in the small tank for every y red fish in the large tank.
If in each tank, the ratio of red fish to blue fish is 3 to 4, then in each tank, in terms of x and y, the ratio is:
small tank :
red : blue = 3 : 4 = (3/4)x : x
large tank :
red : blue = 3 : 4 = y : (4/3)y
If the ratio of fish in the large tank to fish in the small tank is 46 to 5, then
(y + (4/3)y) : ((3/4)x + x) = 46 : 5
Simplifying the proportion,
(y + (4/3)y) : ((3/4)x + x) = 46 : 5
(7/3)y : (7/4)x = 46 : 5
(161/2)x = (35/3)y
x/y = (35/3) / (161/2)
x/y = x : y = 10 : 69
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given the if/else statement: if (a < 5) b = 12; else d = 30; which of the following performs the same operation?
The equivalent operation is: b = (a < 5) ? 12 : (d = 30);
The original if/else statement is:
if (a < 5)
b = 12;
else
d = 30;
In this statement, the condition (a < 5) is evaluated. If the condition is true (i.e., if the value of a is less than 5), then the statement b = 12; is executed. Otherwise, if the condition is false (i.e., if the value of a is greater than or equal to 5), then the statement d = 30; is executed.
The equivalent operation using the conditional (ternary) operator is:
b = (a < 5) ? 12 : d = 30;
In this statement, the condition (a < 5) is evaluated. If the condition is true, the value 12 is assigned to b. This is indicated by ? in the statement. The : separates the true and false cases.
If the condition is false (i.e., if the value of a is greater than or equal to 5), the value 30 is assigned to d. This is the value assigned after the : in the statement.
The ternary operator statement (a < 5) ? 12 : d = 30; achieves the same outcome as the original if/else statement, providing an alternative way to write the logic based on the condition a < 5.
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Which is the most accurate way to describe a vector field F on R3? (a) A function F from R to R3 (b) A function F from R3 to R. (c) A function F from R3 to R3 (d) None of the other choices
The most accurate way to describe a vector field F on R3 is (c) a function F from R3 to R3
A vector field is best described as a function F from R3 to R3. In other words, at each point (x, y, z) in 3D space, the vector field assigns a vector (F1(x, y, z), F2(x, y, z), F3(x, y, z)). The vector field can be visualized by drawing arrows or streamlines to represent the direction and magnitude of the vector at each point in space. A vector field assigns a vector to each point in space, so it requires a function that maps from R3 (a point in space) to another vector in R3.
The vector field is useful in physics, engineering, and mathematics for modeling various physical phenomena, such as fluid flow, electromagnetic fields, and gravitational fields.
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Review: Angle Bisectors
A
Directions: Label the diagram with the
proper congruence markings and known
measurements.
Answer:
m∠AOC = 15°m∠BOC = 15°Step-by-step explanation:
Given the angle ∠AOB
It is stated that CO is the angle bisector of ∠AOB.
Given that ∠AOB = 30°
As we know that the angle bisector bisects the angle into two equal angles.
Thus, the angle bisector CO bisects the angle ∠AOB into two equal angles, which are:
m∠AOCm∠BOCas
∠AOB = 30°
Thus, the two formed angles i.e m∠AOC and m∠BOC by the angle bisector would be half of the angle bisector as the angle bisector bisects the angle ∠AOB into two equal angles.
Therefore,
m∠AOC = 15°m∠BOC = 15°help please please please please please please please please
Question 1= $7,620
Question 2 (a) $3,211
Question 2 (b) $9,828
What is 39.2÷2? equal to?
Answer:
19.6 is the correct answer
Answer:
19.6
Step-by-step explanation:
39.2/2
19.6
Which function represents the graph below?
Answer:
b
Step-by-step explanation:
Since it intercepts y at 4, and x at 2, we use y=ax+b and rearrange to get the equation from y=2x+4 to 2x-y=-4
Answer:
b) 2x - y = -4
Step-by-step explanation:
The y-intercept is the y-coordinate of the point (0, b) where the graph crosses the y-axis. It is also the value of y when x = 0.
The crosses the y-axis at point (0, 4). Therefore, the y-intercept, b = 4.
Next, we need to determine which of the given options matches the graph. It helps to transform each of them into their slope-intercept form, y = mx +b:
a) 2x + y = 42x - 2x + y = - 2x + 4
y = -2x + 4 (This is not the correct answer because the slope, m = -2. The given graph has a positive slope).
b) 2x - y = - 42x - 2x - y = - 2x - 4
-y = -2x - 4
Divide both sides by -1:
\(\frac{-y}{-1} = \frac{-2x - 4}{-1}\)
y = 2x + 4 This is the correct answer because it matches the y-intercept (0, 4), and has a positive slope of 2.
We could easily disregard the last two options because both of their y-intercept is 0.
Therefore, the correct answer is Option b) 2x - y = - 4
0.03249 in standard form to 4 significant figures is
Answer:
3.349 • 10²
I moved the decimal over 2 spots to the left.
14% out of 100% equals how many people out of 10?
Answer:
1.4 people out of 10
Step-by-step explanation:
Just divide it by 10
Answer:
only 4 people
What is the length, in units, of segment CD?
Answer:
The answet is C.
Step-by-step explanation:
First, you have to find the angle of ACB using Sine Rule, sinθ = opposite/hypotenuse :
\( \sin(θ ) = \frac{oppo.}{hypo.} \)
\(let \: oppo. = 4 \\ let \: hypo. = 5\)
\( \sin(θ) = \frac{4}{5} \)
\(θ = {\sin( \frac{4}{5} ) }^{ - 1} \)
\(θ = 53.1 \: (1d.p)\)
Given that line AB is parallel to line CD so ∠C = 90°. Next, you have to find the angle of ACD :
\(ACD = 90 - 53.1 = 36.9\)
Lastly, you can find the length of CD using Cosine rule, cosθ = adjacent/hypotenuse :
\( \cos(θ) = \frac{adj.}{hypo.} \)
\(let \: θ = 36.9 \\ let \: adj. = 5 \\ let \: hypo. = CD\)
\( \cos(36.9 ) = \frac{5}{CD} \)
\(CD \cos(36.9) = 5\)
\(CD = \frac{5}{ \cos(36.9) } \)
\(CD = 6.25 units\: (3s.f)\)
Which transformation can NOT be used to prove that ABC is congruent to DEF?
Answer: it is dilation
Step-by-step explanation: i took the exam
Answer:dialation
Step-by-step explanation:
Solve each inequality (show work)
Answer:
5 less than or equal to x
Step-by-step explanation:
make x subject
AJSKASJASJJAJSKJSAKSJAJKS What is x
PLEASE HELP ME ASAP! IT'S DUE TODAY
The constant ratio in each representation include the following: r = 3.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Next, we would determine the common ratio in each representation as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -6/-2 = -18/-6
Common ratio, r = 3.
Based on comparison with the exponential equation, the common ratio is given by;
Common ratio, r = 3.
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Help plz !!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
275
need help ASAPP and show your work ( will rate 5 starts )
The cosine model is y = - 7 + 10 · cos (π · x/30 - π).
The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).
How to find sinusoidal functions from a given graph
Sinusoidal functions are periodic trascendent expressions which involves trigonometric functions. There are two kinds of sinusoidal functions:
\(y = A \cdot \cos (B\cdot x + C) + D\) (1)
\(y = A\cdot \sin (B\cdot x + C) + D\) (2)
Where:
A - AmplitudeB - Angular frecuencyC - Angular phaseD - MidpointFirst, we find the amplitude and the midpoint:
A = [3 - (- 17)]/2
A = 10
D = [3 + (- 17)]/2
D = - 7
Now we find the angular phase and the angular frequency for each model:
Cosine model (x, y) = (0, - 17), (x, y) = (30, 3)
- 17 = 10 · cos C - 7 (3)
3 = 10 · cos (30 · B + C) - 7 (4)
By (3):
- 10 = 10 · cos C
cos C = - 1
C = acos(- 1)
C = - π
And by (4):
3 = 10 · cos (30 · B - π) - 7
10 = 10 · cos (30 · B - π)
cos (30 · B - π) = 1
30 · B - π = acos 1
30 · B - π = 0
30 · B = π
B = π/30
The cosine model is y = - 7 + 10 · cos (π · x/30 - π).
Sine model
Obtain the sine model by using trigonometric expressions:
cos θ = sin (θ + π/2) (5)
By (5):
y = - 7 + 10 · sin (π · x/30 - π + π/2)
y = - 7 + 10 · sin (π · x/30 - π/2)
The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).
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The sum of two numbers is 2715. The bigger number is 4 times as much as the smaller number. What is twice of the smaller number?
Answer:
1086
Step-by-step explanation:
let 4x=bigger number x=smaller number
4x+x=2715
5x=2715
5x/5=2715/5
x=543 (smaller number)
4x=4(543)=2172 (bigger number)
so
2172+543=2715
then
What is TWICE of the smaller number?
543*2=1086
20 is what percent of 52? Round your answer to the nearest tenth.
20 is about
5
% of 52.
The number x percent of 52 gives 20. Thus, the number x would be equal to 38.5.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
We need to find the number x percent of 52 which gives 20.
x% of 52 = 20
x/100 × 52 = 20
x = 20 × 100/ 52
x = 0.384615
convert it to a percentage by multiplying by 100
38.4615
round to the nearest tenth
38.5
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Question content area left
Part 1
Complete the table to find the value of a nonzero number raised to the power of 0.
Your question was incomplete. Please refer below to find the table in the image.
We need to know about powers and indices to solve the problem. The value of nonzero number raised to the power of 0 is 1.
When a number is raised to a certain power, it can be simplified as the number is multiplied to itself the number of times as the power. For example if we write \(2^{3}\) we mean 2x2x2 which is 8. Similarly in this question we have to find the various powers of 9, the answer to \(9^{4}\) is given, we need to find for the powers 3,2,1, and finally 0.
\(9^{3}\)=9x9x9=729
\(9^{2}\)=9x9=81
\(9^{1}\)=9
\(9^{0}\)=1
When any nonzero number is raised to the power of zero the result is one.
Therefore we found out using the concept of powers and indices that the value of a nonzero number raised to the power of 0 is 1.
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Evaluate the integralI=∫cxydx+(x−y)dywhen C consists of line segments from (0,0) to (3,0) and from (3,0) to (4,2)
The value of the given line integral ∫cxydx+(x−y)dywhen C consists of line segments from (0,0) to (3,0) and from (3,0) to (4,2) is 23/2.
We can evaluate the line integral by breaking it up into two parts along the two line segments of the curve:
∫cxydx+(x−y)dy = ∫C1xydx+(x−y)dy + ∫C2xydx+(x−y)dy
where C1 is the line segment from (0,0) to (3,0) and C2 is the line segment from (3,0) to (4,2).
Along C1, y = 0, so the integral reduces to:
∫C1xydx+(x−y)dy = ∫₀³ x(0)dx + (x - 0)dy = ∫₀³ xdx = [x²/2]₀³ = 9/2
Along C2, we can parameterize the curve as x = 3t, y = 2t for 0 ≤ t ≤ 1, so dx = 3dt and dy = 2dt. Substituting these into the integral, we get:
∫C2xydx+(x−y)dy = ∫0¹ (3t)(2t)(3dt) + (3t - 2t)(2dt)
= ∫₀¹ (18t² + 2t)dt = [6t³ + t²]₀¹ = 7
Thus, the line integral over the entire curve C is:
I = ∫C1xydx+(x−y)dy + ∫C2xydx+(x−y)dy = 9/2 + 7 = 23/2.
Therefore, the value of the given line integral is 23/2.
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During a basketball pratice, Dakota attempted 40 free throws and was successful on 25% of them. How many successful free throws did he make?
What is the answer? Don’t give me 4.
Answer:
what?
Step-by-step explanation:
........................................................................
Consider the following function f(x)=x4+3, x>=0.Find an explicit formula for f^-1
The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.
To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Which equation represents a proportional relationship?
y=x+1
y=3x+3
y=4x
y=8+x
Answer:
y=4x
Step-by-step explanation:
All other equations have a y-intercept. When graphed, the y-value will not start at zero; in a proportional relationship, the y-value starts at zero and increases at a rate proportional to the x-value. :)
Seis restado de c es mayor que 24
The given statement in the form of inequality is given as -
c - 6 > 24.
What is an inequality? What are algebraic expressions?An inequality is used to make unequal comparisons between two or more expressions. For example → ax + b > c
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the statement as -
"Six subtracted from c is greater than 24"
We can write the inequality as -
c - 6 > 24
Therefore, the given statement in the form of inequality is given as -
c - 6 > 24.
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{Question in english -
Six subtracted from c is greater than 24}