x = {x | x ≠ 0, x ≠ ±7} is the domain of the given function h(x) = 9x/x(x²-49). So, Option B is the correct option.
What is a function's domain?Functions are used to assign outputs to inputs. A function's domain is the collection of all potential inputs to the function. The domain of f(x)=x2 is all real numbers, for example, whereas the domain of g(x)=1/x is all real numbers except x=0.
How do we determine a function's domain?Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a technique to successfully create a single value y using a value for x, that chosen x-value is said to belong to f's domain.
The given function is h(x) = 9x/x(x²-49)
We need to determine the domain of this function.
Let us equate the denominator of the function to zero to find x value.
x(x²-49) = 0
x = 0
x²-49 = 0
x = ± 7
Thus, x = 0,-7,+7
So, domain can be intervals between the x values obtained but cannot be equal to the x values.
Therefore, x = {x | x ≠ 0, x ≠ ±7} is the domain of the given function h(x) = 9x/x(x²-49). So, Option B is the correct option.
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Qwq I’m starting to regret getting math class-
Answer:
B the number that is 6 to the right of 1 on the number line
Step-by-step explanation:
you only have a few months left, keep fighting~
What is the value of y in the equation y = 3 x − 2 , y = 3 x − 2 , given that x = 5 ?
Answer:
13 (Answer B)
Step-by-step explanation:
In the expression 3v - 8, what is the variable a= V b= - c= 3 d= 8
Answer:
a. v
Step-by-step explanation:
Given
\(3v - 8\)
Required
Identify the variable
Literary, variable means things that change in values;
Going by this definition, we have that:
3 -> This is not a variable because its value will always be 3
v -> This is a variable because its value can change once its value changes, the result of the expression will also change
- -> This is not a variable; it is an arithmetic operator to subtract
8 -> This is not a variable because its value will always be 8
Take for instance
\(v = 2\)
\(3v - 8 = 3 * 2 - 8 = 6 - 8 = -2\)
When \(v =5\)
\(3v - 8 = 3 * 5 - 8 = 15 - 8 = 7\)
Notice that there's a difference in both results;
This is as a result of v being a variable
how many different spanning trees does each of these simple graphs have? a) k3 b) k4 c) k2,2 d) c5
The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.
a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.
b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.
c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.
d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.
Therefore, the number of different spanning trees for each graph is:
a) K3: 1
b) K4: 4
c) K2,2: 2
d) C5: 5
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If Test 1 was administered to community Y, whose diabetes prevalence is equal to the diabetes prevalence in community X, then the PPV would:A. Decrease B. Not change C. Increase D. Cannot be determined with the given information
As long as the prevalence of diabetes is the same in both communities, the PPV of Test 1 would not change. The answer is B. Not change.
If Test 1 was administered to community Y, whose diabetes prevalence is equal to the diabetes prevalence in community X, then the PPV would not change. This is because the PPV is dependent on the prevalence of the disease in the population being tested, not on the population itself. Therefore, as long as the prevalence of diabetes is the same in both communities, the PPV of Test 1 would not change. The answer is B. Not change.
If Test 1 was administered to community Y, whose diabetes prevalence is equal to the diabetes prevalence in community X, then the Positive Predictive Value (PPV) would B. Not change. This is because the PPV is influenced by the prevalence of the condition in the population being tested, and since the prevalence is equal in both communities, the PPV would remain the same.
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What is the sum of 15 and it's addictive inverse
Answer:
zero
Step-by-step explanation:
the additive inverse of 15 is -15 so the sum is zero
Answer: The sum Is zero, explanation below
Step-by-step explanation:
The Addictive inverse of a number is its opposite so for example the addictive inverse of 12 is -12 or x is -x so the equation would be
15 + -15
making your answer zero :D
SHEEEESSSHHHH
A fair 20-sided die is rolled repeatedly, until a gambler decides to stop. The gambler pays $1 per roll, and receives the amount shown on the die when the gambler stops (e.g., if the die is rolled 7 times and the gambler decides to stop then, with an 18 as the value of the last roll, then the net payo↵ is $18 $7 = $11). Suppose the gambler uses the following strategy: keep rolling until a value of m or greater is obtained, and then stop (where m is a fixed integer between 1 and 20). (a) What is the expected net payoff? (b) Use R or other software to find the optimal value of m.
The expected net payoff E(m) is equal to m + 10.5 and the optimal value of m is 20.
To calculate the expected net payoff, we need to determine the probabilities of stopping at each value from 1 to 20 and calculate the corresponding payoff for each case.
Let's denote the expected net payoff as E(m), where m is the threshold value at which the gambler decides to stop.
(a) To calculate the expected net payoff E(m), we sum the probabilities of stopping at each value multiplied by the payoff for that value.
E(m) = (1/20) * m + (1/20) * (m + 1) + (1/20) * (m + 2) + ... + (1/20) * 20
Simplifying the equation:
E(m) = (1/20) * (m + (m + 1) + (m + 2) + ... + 20)
E(m) = (1/20) * (20 * m + (1 + 2 + ... + 20))
E(m) = (1/20) * (20 * m + (20 * (20 + 1)) / 2)
E(m) = (1/20) * (20 * m + 210)
E(m) = m + 10.5
Therefore, the expected net payoff E(m) is equal to m + 10.5.
(b) To find the optimal value of m, we need to maximize the expected net payoff E(m).
Since E(m) = m + 10.5, we can see that the expected net payoff is linearly increasing with m.
Therefore, the optimal value of m would be the maximum possible value, which is 20.
Hence, the optimal value of m is 20.
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Find the volume V of the solid obtained by rotating the region bounded by the curves about the specified line. y=x, y=0, x=5, x=7; rotated about x=1.
The volume value for the solid is obtained as 381.33 unit³.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The equations of the lines in terms of y-axis are, y = x and y = 0.
The equations of the lines in terms of x-axis are, x = 5 and x = 7.
The solid is rotated about the line, x = 1.
Now, the solid is rotated about the line crossing the x-axis at the point x =1.
The height of the solid in the bounded will be, h = 1 - x.
The radius of the solid in the bounded will be r = 0 - x = -x.
The volume of the solid in a small region can be given as -
dV = 2πrh dx ....(1)
Here, dx is the width of the small element.
The above equation can be integrated by taking the limits according to the lines bounding the solid, which are given as -
5 ≤ x ≤ 7
The limits for the volume of the small element are from 0 to V.
Integrating the equation (1), we get -
\(\int\limits^V_0 {dV} =\int\limits^7_5 {2 \pi rh} \, dx\)
Substitute the values in the above equation, and we get -
\(\int\limits^V_0 {dV} =\int\limits^7_5 {2 \pi(-x)(1-x)} \, dx\)
\([V]_0^V=2\pi\int\limits^7_5 {(-x+x^2)} \, dx\)
\([V]-0=2\pi\int\limits^7_5 {-x\, dx}+2\pi\int\limits^7_5 {x^2} \, dx\)
\(V=2\pi\bigg[-\frac{x^2}{2}\bigg]_5^7+2\pi\bigg[\frac{x^3}{3}\bigg]_5^7\)
\(V=2\pi\bigg[-\bigg(\frac{7^2}{2}-\frac{5^2}{2}\bigg)\bigg+\bigg(\frac{7^3}{3}-\frac{5^3}{3}\bigg)\bigg]\)
Solving further, we get -
\(V=2\pi\bigg[-\frac{49}{2}+\frac{25}{2}+\frac{343}{3}-\frac{125}{3}\bigg]\)
\(V=2\pi\bigg[-\frac{24}{2}+\frac{218}{3}\bigg]\)
\(V=2\times\frac{22}{7}\times\frac{364}{6}\)
V = 381.33 unit³
Therefore, the volume of the solid is 381.33 unit³.
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Rhind Rhind Papyrus Problem 27
A quantity ,and its ⅕ added together becomes 21. What is the quantity
which means : x + x ⅕ = 21
Answer:x=35/2 or 17.5
Step-by-step explanation:
x + .2x = 21
1.2x = 21
1.2x/1.2 = 21/1.2
x = 17.5
answer a i just did it
Step-by-step explanation:
If f(x) = 3 – x2, find f(-2).
Answer:
f(- 2) = - 1
Step-by-step explanation:
To evaluate f(- 2) substitute x = - 2 into f(x) , that is
f(- 2) = 3 - (- 2)² = 3 - 4 = - 1
Is y=1/2x-1 proportional
Answer: No
Step-by-step explanation: Since y=2x+1 does not pass through the origin (i.e. there exists the constant term of 1 ), the variables y and x are not directly proportional - though, they do have a linear relationship.
Simplify the expression.
one half cubed − 2 ÷ square root of 64
negative fifteen sixty fourths
fifteen sixty fourths
negative one eighth
one eighth
The expression (1/2)^3 - 2 ÷ \(\sqrt{64}\) - 1564 - 18 is -1582.125
Given,
(1/2)^3 - 2 ÷ \(\sqrt{64}\) - 1564 - 18
What is PEMDAS rule?The order of solving an equation
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
Simplify (1/2)^3 - 2 ÷ \(\sqrt{64}\) - 1564 - 18.
(1/2)^3 - 2 ÷ (64)^1/2 - 1564 - 18.
Exponents first.
1/8 - 2 ÷ 8 - 1564 - 18 [2^3 = 8]
Division
1/8 - 2/8 - 1564 - 18
1/8 - 1/4 - 1564 - 18
Subtraction
0.125 - 0.25 - 1564 - 18
0.125 - 1582.25
-1582.125
The answer is -1582.125
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a car is driving at 55 kilometers per hour. how far, in meters, does it travel in 3 seconds? myopenmath
The car travels 45.84 meters in 3 seconds.
To solve this problem, we need to convert the speed of the car from kilometers per hour to meters per second since the time given is in seconds.
To do this, we can use the conversion factor that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds.
So, 55 kilometers per hour is equal to (55 x 1000) / 3600 = 15.28 meters per second.
Now, we can use the formula: distance = speed x time
Plugging in the values, we get distance = 15.28 meters per second x 3 seconds = 45.84 meters.
Therefore, the car travels 45.84 meters in 3 seconds.
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Identify the equation for the line of the graph below.
the polygons in each pair are similiar. help find the missing side length???
Answer:
\(x=12\)
Step-by-step explanation:
Since the polygons are similar, we can use the formula: \(\frac{x}{15}=\frac{32}{40}\). Using cross-multiplication , we obtain: \(40x=15*32\\x=\frac{15*32}{40}= 12\).
washing powder cost 12.87 for 9 kg. hwo much does 1 kg cost to the nearst cent
Answer:
hard
Step-by-step explanation:
I don't know because I have never learnt these things
Answer:
\(1.43\)
Step-by-step explanation:
9kg -------> 12.87
1kg ---------> x
let the unknown number be x
\(9 = 12.87 \\ 1 = x \\ use \: \: cross \: \: multipication \\ 9x = 12.87 \\ \frac{9x}{9} = \frac{12.87}{9} \\ x = 1.43\)
If (x > 5) y = 1; else if (x < 5) { if (x < 3) y = 2; else y = 3; } else y = 4; what is the value of y if x = 4?
The value of y when x = 4 is 3.
In this given condition statement, if x is greater than 5, the value of y is 1. If x is less than 5, there is an additional condition.
If x is less than 3, the value of y is 2.
Otherwise, if x is not less than 3, the value of y is 3. Lastly, if x is equal to 5, the value of y is 4.
In the case of x = 4, x is less than 5 but not less than 3.
Therefore, the condition statement within the else condition is satisfied, resulting in the value of y being 3.
This means that when x is equal to 4, the value of y equals 3 as per the given conditions.
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Plz help due tomorrow
Answer:
C) B>A
Step-by-step explanation:
if it doesn't make sense think of it like the number in between A and B is .5. You can visibly see that A is less than or below .5 and B is above or greater than .5, so B is greater than A.
5 5/9 - 2 4/9?? Help!
Answer:
The answer would be 3 1/9
Step-by-step explanation:
5-2= 3 5/9-4/9 = 1/9
Answer:
3 1/9
Step-by-step explanation:
(5 x 9 + 5)/9 - 2 4/9
(45 + 5)/9 - 2 4/9
50/9 - 2 4/9
50/9 - (2 x 9 + 4)/9
50/9 - (18 + 4)/9
50/9 - 22/9
(50 - 22)/9
28/9
3 1/9
worth 30 points. i really need help.
Answer: a) w = -26, -2
b) x = -4, -1
c) k = 17, -1
d) z = 65, 935
Multiple choice: D)
Step-by-step explanation:
a) (w+26)(w+2) = 0
w = -26, w = -2
b) (x+4)(x+1) = 0
x = -4, x = -1
c) (k-17)(k+1) = 0
k = 17, k = -1
d) (z-65)(z-935) = 0
z = 65, x z 935
Multiple Choice
D)
Multiply all terms by 2.
PLEASE MARK AS BRAINLIEST!Hillary earns $60 per week at her job, plus $2 for each item she sells. She wants to
earn at least $300 per week. Write an inequality to represent how many items, x, Hilary
must sell.
Answer:
60+2x≥300
Step-by-step explanation:
So we know that she makes a base of $60 a week and gets $2 extra for every item she sells. First, we set up an equation for how many items she would have to sell to make exactly $300 in a week. 60+2x=300. Now, all we do is replace the equal sign with a ≥ sign because it says at least which means more than or equal to.
Answer:
120 items
Step-by-step explanation:
60+2x=300
-60. -60
2x=240
2. 2
x=120
Solve for x. Leave your answer in simplest radical form.
There are two Right angled triangles in the given figure, with two missing sides, let's name the other missing side be " y "
According to Pythagoras theorem,
\( \boxed{ \large \boxed{h {}^{2} = {b}^{2} + p{}^{2} }}\)
note :
p = perpendicular / opposite sideb = base / adjacent sideh = hypotenuselet's solve for " y² " first ( square of other missing side )
\(➢ \: \: {y}^{2} = {8}^{2} + 3 {}^{2} \)
\(➢ \: \: {y}^{2} = 64 + 9\)
\(➢ \: \: {y}^{2} = 73\)
now let's solve for " x " , by using pythagorous theorem
\(➢ \: \: {x}^{2} = {y}^{2} + {6}^{2} \)
\(➢ \: \: {x}^{2} = 73 + 36\)
\(➢ \: \:x {}^{2} = 109\)
\(➢ \: \: x = \sqrt{109} \)
Approximate :
\(➢ \: \: 10.44 \: \: units\)
\( \mathrm{✌TeeNForeveR✌}\)
Express x^2-8+5 in the form (x-a)^2-b where a and b are integers
Answer:
(x-4)^2-9 where a=4 and b=9
Step-by-step explanation:
x^2-8x+5
x^2-8x+16-16+5
(x-4)^2-9, a=4 and b=9
The distributive property can be applied to which expression to factor 12x3 – 9x2 + 4x – 3?
Answer:
3x2(4x – 3) + 1(4x – 3)
Step-by-step explanation:
find the inverse of function of a function g=((a,1),(b,2),(2,3),(d,4))
Answer:
g inverse = (1,a),(2,b),(c,3),(4,d)
Step-by-step explanation:
I think the third part of the question should be (c,3) not (2,3)
if it's (2,3) then the inverse becomes (3,2)
Answer:
Inverse of function g = {(1,a),(2,b),(3,2),(4,d)}
Step-by-step explanation:
Hey there! :)
Please see an explanation below for better understanding to the answer - also let me know if you have any questions!
What is Inverse Function?Inverse Function is a function that swaps domain and range.
What are domain and range?Domain is the set of all x-values while Range is the set of all y-values, can be defined in coordinate point as (x,y).
StepsIf (x,y) is an original function then (y,x) will be an inverse function of original.
We are given the function g = {(a,1),(b,2),(2,3),(d,4)} - swap the domain and range.
Therefore, the inverse of function g is \(\displaystyle \large{g^{-1}}\) = {(1,a),(2,b),(3,2),(4,d)}
(x-7y=62) (3x+2y=2) substitution
The solution to the system of equations is (x, y) = (6, -8).
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this system of equations using substitution, we need to solve one of the equations for one of the variables in terms of the other variable and then substitute that expression into the other equation.
Let's solve the first equation for x in terms of y:
x - 7y = 62
x = 7y + 62
Now we can substitute this expression for x into the second equation:
3x + 2y = 2
3(7y + 62) + 2y = 2
Simplifying:
21y + 186 + 2y = 2
23y = -184
y = -8
Now we can substitute this value for y into either equation to find x:
x - 7(-8) = 62
x + 56 = 62
x = 6
Therefore, the solution to the system of equations is (x, y) = (6, -8).
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NEED HELP PLZ ANSWER IMMEDIATELY IM GOING TO GET IN TROUBLE A jacket usually sells for $61.00. If the jacket is 40% off, and sales tax is 8%, what is the total price of the jacket, including tax?
Answer:
$39.528
Step-by-step explanation:
61*0.6 = 36.6
36.6*1.08 = $39.528
Answer:
39.53
Step-by-step explanation:
Multiply 61 by .4. The answer is 24.4. Subtract 24.4 from 61. This is the sale price after the discount but before the sales tax. The answer to that is 36.6. Multiply 36.6 by .08, the answer is 2.928. Round to the nearest hundreths. Add this to 36.6. You're final answer is 39.53.
FIRST TO GET RIGHT GETS BRAINLIEST.
Answer:
770
Step-by-step explanation:
So start by adding 140 + 70 and then you get 210 and then so you muliply 70*11 and you get 770. :D
A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x Overbar, while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question. Confidence Level 90% 95% 99% z*-score 1. 645 1. 96 2. 58.
Using the z-distribution, as we have the standard deviation for the population, it is found that the 99% confidence interval for the population mean is given by:
\(\overline{x} \pm 2.58\frac{s}{\sqrt{n}}\)
What is a t-distribution confidence interval?The confidence interval is:
\(\overline{x} \pm z\frac{s}{\sqrt{n}}\)
In which:
\(\overline{x}\) is the sample mean.z is the critical value.n is the sample size.s is the standard deviation for the population.99% confidence level, hence\(\alpha = 0.99\), z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so \(z = 2.58\).
The other parameters are symbolic, hence the interval is given by:
\(\overline{x} \pm 2.58\frac{s}{\sqrt{n}}\)
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10. (1 point) Suppose after the shock, the economy temporarily stays at the short-run equilibrium, then the output gap Y
2
−Y
1
is 0.
A>
B<
C=
D incomparable with 11. ( 1 point) The inflation gap π
2
−π
1
is 0.
A>
B<
C=
D incomparable with
12. (1 point) Suppose there is no government intervention, the economy will adjust itself from short-run equilibrium to long-run equilibrium, at such long long-run equilibrium, output gap Y
3
−Y
1
0.
A>
B<
C=
D incomparable with 13. (1 point) The inflation gap π
3
−π
1
is 0.
A>
B<
C=
D incomparable with
14. (1 point) Suppose the Fed takes price stability as their primary mandates, then which of the following should be done to address the shock. A monetary easing B monetary tightening C raise the
r
ˉ
D lower the
r
ˉ
15. (1 point) After the Fed achieve its goal, the output gap Y
3
−Y
1
is 0. A > B< C= D incomparable with
Suppose after the shock, the economy temporarily stays at the short-run equilibrium, then the output gap Y2−Y1 is: B< (less than)As the output gap measures the difference between the actual output (Y2) and potential output (Y1), when the output gap is less than zero, that is, the actual output is below potential output.
The inflation gap π2−π1 is 0. C= (equal)When the inflation gap is zero, it means that the current inflation rate is equal to the expected inflation rate.12. Suppose there is no government intervention, the economy will adjust itself from short-run equilibrium to long-run equilibrium, at such long-run equilibrium, output gap Y3−Y1 is 0. C= (equal). As the long run equilibrium represents the potential output of the economy, when the actual output is equal to the potential output, the output gap is zero.13.
The inflation gap π3−π1 is 0. C= (equal) Again, when the inflation gap is zero, it means that the current inflation rate is equal to the expected inflation rate.14. (1 point) Suppose the Fed takes price stability as their primary mandates, then which of the following should be done to address the shock. B monetary tightening When the central bank takes price stability as its primary mandate, it aims to keep the inflation rate low and stable. In the case of a positive shock, which can lead to higher inflation rates, the central bank may implement a monetary tightening policy to control the inflation.
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