Answer: 96
Step-by-step explanation:
A palindrome is a number that is the same when reading in both ways (right to left, and left to right), for example, 121
Then, we have 9 digits, and all the digits need to be even.
the options are: 0, 2, 4, 6, 8.
Now, we can think of a 9-digit number as 9 empty slots, and in each slot, we can put a number.
But because this is a palindrome, the first digit must be equal to the ninth, and the second digit must be equal to the eight, and so on.
So, we can think it as actually only 5 slots, where in each slot, we can put an even number, now let's count the options that we have in each selection.
For the first digit we have 4 options: 2, 4, 6 and 8 (0 is not counted here because if the first digit was a 0, then this would not be a 9-digit number).
for the second digit, we have also 4 options (because we already toked one, but now the 0 can be chosen)
for the third digit, we have 3 options
for the fourth digit, we have 2 options
for the fifth digit, we have only one option.
The total number of combinations is equal to the product of the number of options for each selection:
C = 4*4*3*2*1 = 96
Please help me solve!
Answer:
Step-by-step explanation:
Comment
There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2
The graph shows that there is a peak at x = 2. That is where the maximum volume is,
Answer
x = 2
cosa/2-tana +sina/1-cota=cosa+sina
Answer:
Cosa/2-tana+sina
Step-by-step explanation:
Cosatana
Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b to complete the solutions.
The roots of the given polynomials exists
[tex]$x=8+\sqrt{10},[/tex] and [tex]$ x=8-\sqrt{10}[/tex]
What is the formula of the quadratic equation?For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are
[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Therefore by using the formula we have
[tex]$x^{2}-16 x+54=0[/tex]
Let, a = 1, b = -16 and c = 54
Substitute the values in the above equation, and we get
[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]
simplifying the equation, we get
[tex]$x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1}[/tex]
[tex]$x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1}$[/tex]
[tex]$x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]
Therefore, the roots of the given polynomials are
[tex]$x=8+\sqrt{10},[/tex] and [tex]$ x=8-\sqrt{10}[/tex].
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HELP ASAP!!!! PLEASEEE!!!
Answer:
2
-2
Step-by-step explanation:
Use the second equation for x = -4.
f(-4) = 2
Use the third equation for x = 3.
f(x) = -x + 1 = -3 + 1 = -2
No links, provide full answer
The value of M is:
M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.
What are the family of solutions behind an equation of the form p · q = k?
In this question we have a product of two nonzero real numbers equal to 5, whose mathematical form is:
p · q = 5, where p = 2 · x + √(4 · x² + 5) = k and q = 2 · y + √(4 · y² + 5) = 5 / k
Then, we proceed to find the solutions for x and y in terms of k:
2 · x + √(4 · x² + 5) = k
2 · x = k - √(4 · x² + 5)
4 · x² = k² - 2 · k · √(4 · x² + 5) + 4 · x² + 5
2 · k · √(4 · x² + 5) = k² + 5
4 · k² · (4 · x² + 5) = (k² + 5)²
4 · x² + 5 = (k² + 5)² /(4 · k²)
4 · x² = (k² + 5)² /(4 · k²) - 5
x = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5], for k ≠ 0.
2 · y = 5 / k - √(4 · y² + 5)
4 · y² = 25 / k² - (10 / k) · √(4 · y² + 5) + 4 · y² + 5
(10 / k) · √(4 · y² + 5) = 25 / k² + 5
(100 / k²) · (4 · y² + 5) = (25 / k² + 5)²
4 · y² + 5 = (k² / 100) · (25 / k² + 5)²
4 · y² = (k² / 100) · (25 / k² + 5)² - 5
y = ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5], for k ≠ 0.
Therefore, the value of M is:
M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.
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PLEASE HELP IM STUCK
Answer:
If I'm not mistaken that is the answer
A meson when at rest decays 2 μs after it is created. If moving in the laboratory at 0. 99C. Its lifetime according to laboratory clocks would be?
The lifetime of meson according to laboratory clocks would be 14 μs.
In this question,
Meson decay, Δt = 2μs
Velocity, y = 0.99C, where C is the speed of the light
Time measurement depends on the reference frame of clock.
Time dilation, Δt' = y Δt
⇒ [tex]\frac{\Delta t }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-\frac{(0.99c)^{2} }{c^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.99^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.9801 } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{0.0199} } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{0.1410} } }[/tex]
⇒ 14.18 × 10⁻⁶ ≈ 14 μs
Hence we can conclude that the lifetime of meson according to laboratory clocks would be 14 μs.
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What type of function is f(x) = 2 log5(3x)? exponential logarithmic polynomial rational
The type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)
What kind of function is a given expression?
In this problem we must check the characteristics of an expression and conclude what kind of function is. First, we need to find if any trascendent operator, it not, then the function may be either polynomial or rational. If the function has a trascendent operator, then we must check if it is logarithmic or exponential.
At first glance, we see that the function includes only one trascendent operator, a "log" operator that creates a function of the form f(x) = A · ㏒ₙ (B · x). Therefore, the type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)
RemarkThe statement is poorly formatted, correct form is shown below:
What type of function is f(x) = 2 · ㏒₅ (3 · x)? a) Exponential, b) Logarithmic, c) Polynomial, d) Rational.
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Answer: Logarithmic
Step-by-step explanation: Got the question right on test.
67 is the difference of Gail’s height and 16.
Point M is on line segment \overline{LN}
LN
. Given LN=2x-5,LN=2x−5, MN=x-1,MN=x−1, and LM=3,LM=3, determine the numerical length of \overline{LN}.
LN
.
Considering the relation built the presence of point M on line LN, the numerical length of LN is of 9 units.
What is the relation from the presence of point M on the line LN?Point M splits line LN into two parts, LM and MN, hence the total length is given by:
LN = LM + MN.
From the given data, we have that:
LN = 2x - 5.LM = 3.MN = x - 1.Hence we first solve for x.
LN = LM + MN.
2x - 5 = 3 + x - 1
x = 7.
Hence the total length is:
LN = 2x - 5 = 2 x 7 - 5 = 14 - 5 = 9 units.
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What is the end behavior of the function f(x)=12x2?
dis i know functiin of fx is ♾
Answer:
4th option
Step-by-step explanation:
the end behaviour is what happens when x gets larger and positive (right- hand end )or larger and negative ( left- hand end )
f(x) = [tex]\frac{1}{2}[/tex] x² ← is of even degree (2) and has a positive leading coefficient , then
• even degree and positive leading coefficient
f(x) → +∞ as x → + ∞ and
f(x) → + ∞ as x → - ∞
Which graph represents (y-3)^2/25 + (x+1)^2/4 > 1 and y <= square root{x+5}+2
Answer:
B. the second graph.
Step-by-step explanation:
Literally the photo is on the question.
Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2. Therefore, the correct option is option B.
What is graph?The study of graphs, that are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this sense, a network consists of vertices, also known as nodes or points, linked by edges, also known as links or lines.
Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics that are investigated in discrete mathematics is graphs. Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2.
Therefore, the correct option is option B.
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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
I'll assume the ODE is
[tex]y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}[/tex]
Solve the homogeneous ODE,
[tex]y'' - 3y' + 2y = 0[/tex]
The characteristic equation
[tex]r^2 - 3r + 2 = (r - 1) (r - 2) = 0[/tex]
has roots at [tex]r=1[/tex] and [tex]r=2[/tex]. Then the characteristic solution is
[tex]y = C_1 e^x + C_2 e^{2x}[/tex]
For nonhomogeneous ODE (1),
[tex]y'' - 3y' + 2y = e^x[/tex]
consider the ansatz particular solution
[tex]y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x[/tex]
Substituting this into (1) gives
[tex]a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1[/tex]
For the nonhomogeneous ODE (2),
[tex]y'' - 3y' + 2y = e^{2x}[/tex]
take the ansatz
[tex]y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}[/tex]
Substitute (2) into the ODE to get
[tex]b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1[/tex]
Lastly, for the nonhomogeneous ODE (3)
[tex]y'' - 3y' + 2y = e^{-x}[/tex]
take the ansatz
[tex]y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}[/tex]
and solve for [tex]c[/tex].
[tex]ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16[/tex]
Then the general solution to the ODE is
[tex]\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}[/tex]
(08.01 mc) sue wants to know how many families in her small neighborhood of 50 homes would volunteer to help at a neighborhood animal shelter. she put all the addresses in a bag and drew a random sample of 25 addresses. she then asked those families if they would volunteer to help at the shelter. she found that 18% of the families would volunteer to help at the shelter. she claims that 18% of the neighborhood families would be expected to help at the animal shelter. is this a valid inference?
Answer:
Yes, this is a valid inference because she took a random sample of the neighborhood.
Step-by-step explanation:
As we can see, Sue's survey was perfectly random and without any prejudice.
18% of the families, according to her research, would volunteer at the shelter. According to her, 18% of the local households should be required to volunteer at the animal shelter.
Therefore, given that she chose a representative sample of the area, her conclusion is valid.
What is the range of the function f(x) = |x + 4| + 2?
R: {f(x) ∈ ℝ | f(x) ≤ 2}
R: {f(x) ∈ ℝ | f(x) ≥ 2}
R: {f(x) ∈ ℝ | f(x) > 6}
R: {f(x) ∈ ℝ | f(x) < 6}
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]
You need to remember that the form of an Absolute Value Function is:
• For the vertex:
[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]
[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]
• For the definition:
If "a" is positive (+) , then the range of the function is:
[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]
If "a" is negative (-), the range of the function is:
[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]
In this case we can identify that:
[tex]\small\longrightarrow \sf{a = 1}[/tex]
[tex] \small\longrightarrow\sf{a = 2}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]
determine the rate of change for the right side of…
Answer:
Decreasing at an increasing rate
Step-by-step explanation:
graph looks like an arch
right side is going down
right side is going down as x increases
If a function has a positive average rate of change over
an interval, does that mean that the function must be increasing over that
interval? Explain.
Step-by-step explanation:
Yes, an positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval. By definition, a function, f is increasing over an interval [a,b], if f(b)> f(a)
Yes, a positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval.
What is the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Yes, a positive average rate of change indicates that the endpoint of our period is higher than the interval's starting point. A function f is rising over the range [a,b] by definition if f(b)> f. (a)
Therefore, the positive average rate of change over an interval must be increasing over that interval.
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What is the tenth term in the sequence 9, 13, 17, 21, 25…?
Step-by-step explanation:
its 29 9x4=29 9+4=13 13+4=17
Help me in thisssssss
Answer:
34
Step-by-step explanation:
(a + [tex]\frac{1}{a}[/tex] ) = 6← square both sides
(a + [tex]\frac{1}{a}[/tex] )² = 6² ← expand left side using FOIL
a² + 1 + 1 + [tex]\frac{1}{a^2}[/tex] = 36
a² + 2 + [tex]\frac{1}{a^2}[/tex] = 36 ( subtract 2 from both sides )
a² + [tex]\frac{1}{a^2}[/tex] = 34
This design is made from 1 blue circle, 4 orange circles and 16 green circles. The circles touch each othe Given that the radius of each green circle is I unit, find the exact radius of a the orange circles, b the blue circle.
The radius of the orange circle is 1.5 unit and the radius of the blue circle is 2.25 units
How to determine the radii of the circles?The figure that completes the question is added as an attachment
The orange circle
The radius of the green circle is given as:
r = 1
One and half green circle make up the radius of the orange circle.
So, the radius of the orange circle is
R = 1.5 * r
This gives
R = 1.5 * 1
R = 1.5
Hence, the radius of the orange circle is 1.5 unit
The blue circle
The radius of the orange circle is given as:
r = 1.5
One and half orange circle make up the radius of the blue circle.
So, the radius of the blue circle is
R = 1.5 * r
This gives
R = 1.5 * 1.5
R = 2.25
Hence, the radius of the blue circle is 2.25 units
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A necklace calls for red, blue and white beads in the ratio of 5: 8:12. Ming has used
350 beads, how many of them are white in colour?
Answer:
168Step-by-step explanation:
find unity
350 : (5 + 8 + 12) =
350 : 25 = 14
multiply the units by the white ratio14 * 12 = 168
To the nearest foot what is the length of a pendulum that makes one full swing in 1.9s
A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.
What is the length of a pendulum?A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.
Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".
Given the equation:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
where L is the length in feet and T is the time in seconds.
Given that T = 1.9sec,
Hence:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
L = 2.93 feet
A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.
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4.
Find the perimeter of the triangle.
A. 294 m
B. 119 m
C. 84 m
D. 168 m
Answer:
84m
Step-by-step explanation:
The perimeter of a triangle is the sum of the length of the external sides.
Therefore, the perimeter of the triangle = 21m + 28m + 35m = 84m.
Hey there!
What is the formula for finding the perimeter of a triangle?
a + b + c = perimeter
What does the labels mean?
a = side 1
b = base
c = side 2
What should the equation look like?
21m + 28m + 35m = perimeter
How do should it be solve?
21m + 28m + 35m = perimeter
49m + 35m = perimeter
84m = perimeter
What is the answer to the question?
84m
Good luck on your assignment and enjoy your day!
~Amphitrite1040
Find the mean and standard deviation for the set of data. {16,22,8,5,20,18,14,17,24}
The mean of the set is : 16
The Slandered deviation of set : 5.8689389538863
What is mean?Moderation is the quality of falling at or close to a medium point, whether it is in terms of location, period of time, quantity, or rate. 2 is the arithmetic mean. 3 denotes a plural noun: a tool for achieving one's goals. Attempt to locate it using all available techniques.
The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.
What is Standard Deviation?An indicator of how much a group of numbers vary or are dispersed is the standard deviation. When the standard deviation is low, the values tend to fall within a narrow range of the set's mean, but when it is large, the values tend to deviate from that mean more.
Calculating average:Average x = 16
Count n = 9
Sum Sum =144
Average = Sum / Count
= 144 / 9
= 16
Standard Deviation, σ: 5.8689389538863
Count, N = 9
Sum, Σx: = 144
Mean, μ: = 16
Variance, σ²: = 34.444444444444
Calculating slandered devotion:
[tex]\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}[/tex]
[tex]\sigma^{2}=\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}[/tex]
[tex]=\frac{(16-16)^{2}+\ldots+(24-16)^{2}}{9}[/tex]
= 310/9
= 34.444444444444
σ = √34.444444444444
σ = 5.8689389538863
The mean of the set is : 16
The Standard deviation of set : 5.8689389538863
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Given the functions f(x) = x3 x2 – 2x 3 and g(x) = log(x) 2, what type of functions are f(x) and g(x)? justify your answer. what key feature(s) do f(x) and g(x) have in common? (consider domain, range, x-intercepts, and y-intercepts.)
The functions f(x) and g(x) are different functions
The function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common feature in both functions is their range
According to the statement
we have given that the some functions and we have to justify these functions.
The functions are given as:
f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2
This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common key features of the functions
To do this, we plot the graphs of both functions
From the attached graph, we have the following features:
Function f(x)
Domain: -∞ < x < ∞
Range: -∞ < y < ∞
y - intercept = 3
x - intercepts = -2.37
Function g(x)
Domain: x > 0
Range: -∞ < y < ∞
y - intercept = None
x - intercepts = 0.01
By comparing the key features above, we can conclude that the common features in both functions is their range.
The functions f(x) and g(x) are different functions
The function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common feature in both functions is their range
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A circle is described by the equation x2 y2 14x 2y 14 = 0. what are the coordinates for the center of the circle and the length of the radius?
Answer:
length is (-7,-1) and radius is 6
Step-by-step explanation:
We are given the expression of the equation of a circle that is
x2 + y2 + 14x + 2y + 14 = 0.
Using completing the squares:
x2 + y2 + 14x + 2y + 14 = 0(x+7)^2 + (y+1) ^2 = -14 + 49 + 1(x+7)^2 + (y+1) ^2 = 36 center thus is at (-7,-1) and the radius is equal to square root of 36 equal to 6.
The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. on the bottom shelf are 3 fiction and 5 nonfiction books. choosing which 2 books describes a pair of dependent events?
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change. Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance. Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is. Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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Alonso brings \$21$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost \$2.50$2.50dollar sign, 2, point, 50. Then, he notices that the store only sells avocados in bags of 333 for \$5$5dollar sign, 5. He wants to buy as many avocados as he can with his remaining money.
How do u get 3 bags of avacodes or 9 avacadoes ??
Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
EquationAmount Alonso brings to the market = $21Cost of an egg = $2.50Cost of avocados in bags of 3 = $5Number of avocados bought = x21 = 2.50 + 5x
21 - 2.50 = 5x
18.50 = 5x
x = 18.50 / 5
x = 3.7 bags of avocados
To get 3 bags of avocados or 9 avocados
= $5 × 3
= $15
Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
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Four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. What is the measure of the final interior angle?
108°
127°
150°
487°
Answer:
127
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Round 4709.94107458 to the nearest whole number
4710
Explanation:4709.94107458
The nearest whole number for 4709.94107458 is 4710 since the number 9 after the decimal is greater than 5. Therefore, if you add 1 to 9 before the decimal, you get 10.
Hope this helps :)