Answer:
whats the question? please explain
A polynomial function whose degree is 5 has at most how many turning points.
A is the set of integers greater than or equal to -9 and less than or equal -2
B = {-30, -27, 20, 24, 28}
a) Find the cardinalities of A and B.
n(A)=
n(B) =
Answer:
The cardinality Of Set A= 8, Set B = 5
SET :an organized collection of objects
Cardinality : It is defined as how many elements make in a set or other grouping.
Step1: Integers greater than or equal to -9 and less than or equal to -2 are
= -9,-8,-7,-6,-5,-4,-3,-2
Step 2: Form a set using given elements, we have
Set A = {-9,-8,-7,-6,-5,-4,-3,-2}
Step 3: Count the no. of elements
we have, no. of elements is 8.
For given Set B = {-30, -27, 20, 24, 28}
we have, no. of elements is 5.
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Please help! Will give the brainliest!
The answer is J. [tex](x+4)(x-2)=x\cdot x[/tex]
Consider the two regression lines 3x+2y=26 and 6x+y=31, the regression coefficient of y on x is
The regression lines 3x+2y=26 and 6x+y=31 are linear regressions
The mean values are 4 and 7 and the correlation coefficient between x and y is 0.25
The standard deviation of x is 2/13
The mean value and the correlation
We have the equations to be:
3x+2y=26 and 6x+y=31
Make y the subject in the second equation
y = 31 - 6x
Substitute y = 31 - 6x in the first equation
3x+2[31 - 6x] = 26
Expand
3x+ 62 - 12x = 26
Collect like terms
3x - 12x = 26 - 62
Evaluate
-9x = -36
Divide by - 9
x = 4
Substitute x = 4 in y = 31 - 6x
y = 31 - 6 * 4
y = 7
This means that the mean values are 4 and 7
To determine the correlation coefficient, we make y the subject in 3x+2y=26 and x the subject in 6x+y=31.
So, we have:
y = 13 - 3x/2 and x = 31/6 - 1/6y
The above means that:
Bxy = -1/6 and Byx = -3/2
The correlation coefficient is then calculated as:
r^2 = Bxy * Byx
r = -1/6 * -3/2
r = 0.25
Hence, the correlation coefficient between x and y is 0.25
The standard deviation of x
We have:
Var(y) = 4
In (a), we have:
y = 13 - 3x/2
To solve further, we make use of:
Var(y) = Var(ax + b) = a^2Var(x)
This gives
Var(y) = Var(13 - 3x/2) = 13^2 * Var(x)
So, we have:
Var(y) = 13^2 * Var(x)
Substitute 4 for Var(y)
4 = 13^2 * Var(x)
Divide both sides by 13^2
4/13^2 = Var(x)
Express 4 as 2^2
(2/13)^2 = Var(x)
So, we have:
Var(x) = (2/13)^2
Take the square root of both sides
SD(x) = 2/13
Hence, the standard deviation of x is 2/13
Trigonometry problem
Answer:
Hi! So, I'm pretty sure the answer is 1 (rounded).
However, I'm not sure if you're trying to find the answer to COS pi/10 or "the function in terms of cofunction of a complementary angle" which I'm not too sure about. I've given you the answer to the first part if this was not the right way to read the problem I deeply apologize.
Step-by-step explanation:
Using any calculator with the Cos, Sin, and Tan function, you can input
COS (pi / 10) which equals .9999849678 (which you can round as needed)
Find the equation of a line that is perpendicular to Y= 4X +5 that passes through (2,-5)
Answer:
4y +x =18
Step-by-step explanation:
y - (-5) -1
----------- = ------
x - 2 4
4y +20 = -x+2
4y +x =18
solve the equation 7m^2-4m+1=0. fully simplify all answers, including non-real solutions
m=
Answer:
m is not an element of real number
Helppppppoppppoppppppppppppppp
If $5000 is invested at a rate of 3% interest
compounded quarterly, what is the value of
the investment in 5 years? (Use the formula
A = P (1 + =)",
, where A is the amount accrued, P
is the principal, r is the interest rate, n is
the number of times per year the money is
compounded, and t is the length of time, in years.)
The value of the investment in 5 years is $5805.9
What is Interest ?Interest is the amount earned over years for the amount invested.
It is given that
Principal = $5000
Rate = 3%
Compounded Quarterly
Time = 5 years
Amount = ?
The Amount is given by the formula
Amount = P( 1 + (r/n))ⁿˣ
Here n = t = time period for which the investment has been done.
Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵
Amount = 5000 (1.16)
Amount = $ 5805.9
Therefore , The value of the investment in 5 years is $5805.9
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Which equation represents an exponential function with the initial value of 500?
Answer:
A exponential equation is usually of the form f(x)=a (1±r)ˣ.
Our limitation: Initial Vale is 500.
Let's look at our options:
#1- Initial Value of 1000 --- WRONG!
#2- Initial Value of 1000 --- WRONG!
#3- Initial Value of 500 ---- Maybe
#4- Initial Value of 500 ---- Maybe
Let's look at 3 and 4:
#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!
#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!
Hence, #3 Is correct!
Step-by-step explanation:
Well, I hope you understood, and I'd gladly explain anything that didn't make sense. A brainliest would be appreciated, thank you!
-Zylynn Jade Ardenne
Which expression is equivalent to 2x² - x + ?
O A
O
B
C
D
²(x - 2)²
2
IN
2 X-
16
Answer: [tex]2\left(x-\frac{1}{4} \right)^{2}[/tex]
Step-by-step explanation:
[tex]2x^{2}-x+\frac{1}{8}\\\\=2\left(x^{2}-\frac{1}{2}x \right)+\frac{1}{8}\\\\=2\left(\left(x-\frac{1}{4} \right)^{2}-\frac{1}{16} \right)+\frac{1}{8}\\\\=2\left(x-\frac{1}{4} \right)^{2}-\frac{1}{8}+\frac{1}{8}\\\\=\boxed{2\left(x-\frac{1}{4} \right)^{2}}[/tex]
from a survey involving 1000 University students market research company found that 780 students on laptops 460 on cars and 380 owned cars and laptops if a university student is selected at random what is each empirical probability. (A) the student owns either a car or laptop. (B) the student owns neither a car nor a laptop is.
Considering the definition of probability:
the probability that the student owns either a car or laptop is 86%.the probability that the student owns neither a car nor a laptop is 14%.Definition of ProbabitityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
The probability of any event A is defined as the quotient between the number of favorable cases (that is, the number of times that event A may or may not occur) and the total number of possible cases:
[tex]Probability=\frac{number of favorable cases}{total number of possible cases}[/tex]
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Events and probability in this caseIn first place, let's define the following events:
A: The event that a student owned a laptop.
B: The event that a student owned a car.
Then you know:
P(A)= [tex]\frac{780}{1000}[/tex]= 0.78P(B)= [tex]\frac{460}{1000}[/tex]= 0.46P(F and R)= P(F∩R)= [tex]\frac{380}{1000}[/tex]= 0.38 [The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.]In this case, considering the definition of union of events, the probability that the student owns either a car or laptop is calculated as:
P(A∪B)= P(A) + P(B) -P(A∩B)
P(A∪B)= 0.78 + 0.46 -0.38
P(A∪B)= 0.86= 86%
Then, the probability that the student owns either a car or laptop is 86%.
On the other hand, considering the definition of the complementary event and its probability, the probability that the student owns neither a car nor a laptop is calculated as:
P [(A∪B)']= 1- P(A∪B)
P [(A∪B)']= 1 - 0.86
P [(A∪B)']= 0.14= 14%
Finally, the probability that the student owns neither a car nor a laptop is 14%.
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which relation describes the graph?
Answer:
A.
Step-by-step explanation:
The other graphs answers have a point at (3, 1) which is not on the graph.
solve the following inequality
The solution set of the inequality is:
w ∈ (-∞, -1] U [3, ∞)
How to solve the given inequality?
The graphed parabola is f(w), and we have the inequality:
f(w) ≤ 0.
So we need to identify the intervals such that the parabola is below the horizontal axis. By looking at the graph, we can see that the two intervals are:
Left side:
(-∞, -1]
Right side:
[3, ∞)
Where the brackets are used because points x = -1 and x = 3 are solutions.
Then the solution set of the inequality is:
w ∈ (-∞, -1] U [3, ∞)
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Choose the correct range , mean and standard deviation for participant age written in correct APA format . A. Participants ranged in age from 4 to 90 ( M = 26.24 , SD = 23.00 ) . B. Participants ranged in age from 18 to 54 ( M = 26.24 , SD = 8.04 ) . C. Participants ranged in age from 18 to 54 ( M = 23.00 , SD = 26.24 ) . D. Participants ranged in age from 4 to 26.24 ( M = 26.24 , SD = 8.04 ) . E. Participants ranged in age from 18 to 58 ( M = 23.00 , SD = 8.04 ) .
The range, the mean, and standard deviation are mathematically given as
Participants ranged in age from 4 to 26.24 ( M = 26.24 , SD = 8.04 ). Option D.
What are the range, the mean, and standard deviation?Given the data presented below the given
A look at the result shows that the lowest and highest values are between 1s and 58, with a mean and standard deviation of 26.10 and 8.90, respectively.
Participants' ages varied from 18 to 58 (m-26.14, std dev = 8.01), hence option (d) is accurate.
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The Pythagorean Identity states that: (sin x)^2 + (cos x)^2 = 1
Given cos 0 = 5/3, find sin 0
sin 0 = ?/?
Simplify the fraction.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:sin(\theta) = \cfrac{2}{3} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cos {}^{2} ( \theta) + \sin {}^{2} ( \theta) = 1[/tex]
[tex]\qquad \tt \rightarrow \: {\bigg( \cfrac{ \sqrt{5}}{3} \bigg) }^{2} + \sin {}^{2} ( \theta) = 1[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{5}{9} + \sin {}^{2} ( \theta) = 1[/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = 1 - \cfrac{5}{9} [/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = \cfrac{9 - 5}{9} [/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = \cfrac{4}{9} [/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \sqrt \cfrac{4}{9} [/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \pm \cfrac{2}{3} [/tex]
Generally, only positive value is taken :
[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \cfrac{2}{3} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Prove that C(50,3) + C(50,4) = C(51,4)
By definition of the binomial coefficient,
[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]
so we have
[tex]C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)[/tex]
as required.
yo
24
yx
SECTION B
(a) Identity element;
(b) Inverse of 3 and -5 under *
Range y
[30 marks]
Answer all the questions in this section. All questions carry equal marks.
1. A binary operation is defined on the set of real numbers, R, by x + y = x + y + 10.
Find the:
The inverse of 3 and _ 5
Answer:
Sorry I don't know the answer
I have a quick geometry question! Thank you!
Answer:
e4fodor8rsidididi2f2
Answer:
9
Step-by-step explanation:
3:4
AB:12
cross multiply giving
3×12:4AB
36: 4AB
divide both sides by 4,thus
AB=9
Which relation below is NOT a function?
A. {(-2, 4), (1,3), (0,4)}
B. {(5,5), (4,4), (3,3) }
C. {(-4,0), (-7,0), (11, 0)}
D. {(1,4), (2,5) (1,7)}
The relation {(1,4), (2,5) (1,7)} is not a function because there is two mirror image of y for a single value of x option (D) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we know for every single value of x there should be only one image in y set.
If there are multiple images are there for a single value of x then the relation is not a function.
In a set of relations:
D. {(1,4), (2,5) (1,7)}
There is two mirror image of y for a single value of x:
Thus, the relation {(1,4), (2,5) (1,7)} is not a function because there is two mirror image of y for a single value of x option (D) is correct.
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f(x) = 3x² + 5x - 2
g(x) = 5x³-4x² + 4
Find (f + g)(x)
Answer: [tex]5x^3 - x^2 + 5x+2[/tex]
Step-by-step explanation:
[tex](f+g)(x)=(3x^2 + 5x-2)+(5x^3 - 4x^2 +4)=3x^2 + 5x-2+5x^3 - 4x^2 +4=\boxed{5x^3 - x^2 + 5x+2}[/tex]
help me pls i dont understand it
Answer:
Step-by-step explanation:
x×4=2x²(x-1)
2x³-2x²-4x=0
2x(x²-x-2)=0
x≠0
x²-x-2=0
x²-2x+x-2=0
x(x-2)+1(x-2)=0
(x-2)(x+1)=0
x=2
or
x=-1 (rejected)
Answer:
Step-by-step explanation:
Formula
The following relationship exists between the parts of each chord.
(x - 1)(2x^2) = 4*x
Solution
The easiest way to start is to divide both sides of the equation by x.
(x - 1)(2x^2)/x = 4x / x Divide by x
( x-1)(2x) = 4 Remove the brackets
2x^2 - 2x = 4 Subtract 4 from both sides
2x^2 - 2x - 4 = 4 - 4 Combine
2x^2 - 2x - 4 = 0 Pull out the common factor
2(x^2 - x - 2) = 0 Divide by 2
x^2 - x - 2 = 0 Factor
(x - 2)(x + 1)
Answer:
x can be 2 or x can be - 1 on paper. The x on the upper right prohibits that. A line can't have a length of - 1. So - 1 is called an extraneous solution.
The answer is x = 2
The depth of a certain part of the Earth's seabed is 36,024 feet. How deep is it in (a) fathoms? (b) leagues (marine)?
The depth of the sea bed is 5104 fathom and 1.986 league
What is a Seabed ?The bottom of an ocean , the ocean floor is called Seabed .
It is given that
The depth of a certain part of the Earth's seabed is 36,024 feet
The depth in fathom is given by = depth in feet / 6
The depth in fathom is = 36024 / 6
= 5104 fathom
1 league = 6046.1 * 3 feet = 18138.1 feet
The depth in League (marine) = Depth in feet / 18138.1
The depth in League (marine) = 36024/18138.1
= 1.986 league
Therefore the depth of the sea bed is 5104 fathom and 1.986 league.
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Find the distance between the parallel lines y=x-5 and y=x+6
Answer:
11
Step-by-step explanation:
i don't know
Question 1(Multiple Choice Worth 4 points)
Which set of line segments could create a right triangle?
O24, 30, 35
O 12, 18, 30.
O 18, 24, 30
O 18, 24, 35
Answer: 18, 24, 30
Step-by-step explanation:
For the segments to create a right triangle, they must satisfy the Pythagorean theorem.
The only set which satisfies the Pythagorean theorem, is 18, 24, 30, since [tex]18^{2}+24^{2}=30^{2}[/tex]
To find the possible roots of the polynomial 4x3 + x4 – 7x2 – 8x - 8
divide factors of ± __ by factors of ± __ .
The complete statement is divide factors of ± 8 by factors of ± 1
How to complete the statement?The polynomial is given as:
4x^3 + x^4 - 7x^2 - 8x - 8
Rewrite properly as:
x^4 + 4x^3 - 7x^2 - 8x - 8
The first term in the above equation is 1 i.e. 1x^4, while the last term is 8
To determine the possible rational roots, we divide the factors of the last term i.e. 8 by the factors of the first term i.e. 1
Hence, the complete statement is divide factors of ± 8 by factors of ± 1
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The number of measles cases has increased by 5.3% since 2000.
Express your answer rounded correctly to the nearest hundredth.
Stated another way, the number of measles cases is
times what it was in 2000.
Express your answer rounded correctly to the nearest tenth of a percent.
Stated another way, the number of measles cases was
% of what it is now.
The expressions for the number of measles are y = a(1.05)^x and y = a(1.1)^x
How to express the number of measles?Let the initial number of measles in 2000 be represented as:
Initial = a
The rate of increase is given as:
Rate, r = 5.3%
The number of measles in x years after 2000 is represented as:
y = a * (1 +r)^x
Substitute r = 5.3%
y = a * (1 + 5.3%)^x
So, we have:
y = a * (1 + 0.053)^x
Evaluate the sum
y = a * (1.053)^x
To express to the nearest hundredth, we approximate to 2 decimal places
y = a(1.05)^x
To express to the nearest tenth, we approximate to 1 decimal place
y = a(1.1)^x
Hence, the expressions for the number of measles are y = a * (1.05)^x and y = a * (1.1)^x
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Jakub wants to build a new shed.
The area of the shed is 37 m².
The width of the shed is 5 m.
What is the length of the shed?
3
Answer:
74 mStep-by-step explanation:
Jakub wants to build a new shed.
The area of the shed is 37 m².
The width of the shed is 5 m.
What is the length of the shed?
to find the side, having the area, you need to use the inverse formula Area = W * L
so
L = A: W
L = 37 : 5 = 7.4 m
If the area of the shed is 37 m²,width of the shed is 5 m as a result the length of the shed will be 7.4 m.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that, the area of the shed is 37 m². The width of the shed is 5 m.
Since the shed is rectangular. The length of width is found as,
Area = length × width
A = l × w
l=A/w
l=37/5
l=7.4 m
Thus, if the area of the shed is 37 m², the width of the shed is 5 m as a result the length of the shed will be 7.4 m.
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You invest $1000
in an account at 2.5% per year simple interest. How much
will you have in the account at the beginning of the 4th year? Round your
answer to the nearest whole dollar.
A. $1075
B. $1163
C. $3250
• D. $1088
i dont speak English 3456
What is the distance in units between the points (-1, 5) and (-1,
-3)?
Answer:
8 [units].
Step-by-step explanation:
if to see the given coordinates, then it is clear the x-coordinates are equal. It means, the required distance can be calculated:
d=5+3=8 [units].