The value of card(B) is card(B) = 4954
How to determine the card(B)?The set is given as:
B={1,3,5,7,9,….9907}
The above set is the set of odd numbers from 1 to 9907.
The number of elements is the cardinality
And it can be calculated using
L = a + (n - 1)d
Where
L = 9907
a = 1
d = 2
So, we have:
9907 = 1 + (n - 1)2
Subtract 1 from both sides
9906 = (n - 1)2
Divide by 2
n - 1 = 4953
Add 1 to both sides
n = 4954
This means that
card(B) = 4954
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use the Pythagorean identity with X=8 and Y=5 to generate a Pythagorean triple
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming the formula:}[/tex]
[tex]\mathbf{a^2 + b^2 = c^2}[/tex]
[tex]\huge\textbf{If so:}[/tex]
[tex]\mathbf{x^2 + y^2 = c^2}[/tex]
[tex]\mathbf{8^2 + 5^2 = c^2}[/tex]
[tex]\mathbf{8\times 8 + 5 \times 5 = c^2}[/tex]
[tex]\mathbf{64 + 25 = c^2}[/tex]
[tex]\mathbf{89 = c^2}[/tex]
[tex]\huge\textbf{Subtract \boxed{\rm{\bf c^2}} to both sides:}[/tex]
[tex]\mathbf{89 - c^2 = c^2 - c^2}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathbf{-c^2 + 89 = 0}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf 89} to both sides:}[/tex]
[tex]\mathbf{-c^2 + 89 - 89 = 0 - 89}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{-c^2 = -89}[/tex]
[tex]\huge\textbf{Divide \boxed{\bf{-1}} to both sides:}[/tex]
[tex]\mathbf{\dfrac{-c^2}{-1} = \dfrac{-89}{-1}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{-c^2 = -89}[/tex]
[tex]\huge\textbf{Take the square root of the number:}[/tex]
[tex]\mathbf{c = \pm \sqrt{89}}[/tex]
[tex]\huge\textbf{Thus, this possibly means:}[/tex]
[tex]\mathbf{c = \sqrt{89} \ or\ c = -\sqrt{89}}[/tex]
[tex]\huge\textbf{Thus, your answer possibly is:}[/tex]
[tex]\huge\boxed{\mathsf{c = \sqrt{89} \ or\ c = -\sqrt{89}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A store is currently offering a 60% discount on all items purchased. Your cashier is trying to convince you to open a store credit card and says to you, "In addition to the 60% discount you are receiving for purchasing these items on sale today, you will get an additional 20% off for opening a credit card account. That means you are getting 80% off!"
a. What is the mistaken assumption here?
b. Why is that assumption incorrect?
c. If you did truly have 80% discount, explain what should happen when you go to the counter to buy $500 worth of items?
d. If you got your 60% discount and opened the card for an additional 20%, what is the actual % discount you would receive?
e. Is it better to apply the 60% discount first or the 20% discount first?
Answer:
a the assumption is that after the 60% discount, the 20% will contribute to the old price, not the adjusted price
b this is incorrect because the 20% discount will be added on after the 60% discount has been used
c the 500 dollars would turn to 100 dollars
d 40
e it would be best to first apply the 60% coupon first over the 20% coupon
Un constructor tiene un predio, por lo que está considerando que los terrenos sean rectangulares con un perímetro de 64 metros.
Based on the perimeter of the rectangle, and the adjustments to make the plot a square, the sides are 13m and 19m.
What are the sides of the plot?The perimeter is:
2(L + W) = 64
L + W = 32
The adjustment to make the plot a square would mean that both sides can be equal:
L + 3 = W - 3
L = W - 6
Substituting in the original formula gives:
L + W = 32
W - 6 + W = 32
2W = 38
W = 19 m
L would be:
L + W = 32
L + 19 = 32
L = 13m
The rest of the question is:
No obstante, para que los terrenos puedan ser cuadrados, se tendría que aumentar el ancho en 3 m y disminuir 3 m de largo. Entonces, ¿cuánto mediría el ancho y el largo del terreno rectangular?
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Last answers 5
Let me know the answer fast
I’m super confused please help me
Answer:
See below
Step-by-step explanation:
Look at it from the front and the side as shown in the diagram and draw what you would see:
Review the four points shown on the polar coordinate
system.
5ad6
B
C
76
27/3
4/3
2
3/2
N
4
50/3
A
6
D
11/6
Which point represents (-6.II) ?
Opoint A
Opoint B
Opoint C
Opoint D
The answer is Point B.
Need help with the question
Answer:
x = 0 or x = 1
Step-by-step explanation:
f(x) = |x| - 4
g(x) = x³ - 4
f(x) = g(x)
|x| - 4 = x³ - 4
Add 4 to both sides.
|x| = x³
x = x³ or -x = x³
x³ - x = 0 or x³ + x = 0
x(x² - 1) = or x(x² + 1) = 0
x = 0 or x + 1 = 0 or x - 1 = 0
x = 0 or x = -1 or x = 1
x = -1 does not work, so we discard that solution.
Answer: x = 0 or x = 1
Answer:
values of x: x = 1 and x = 0
Step-by-step explanation:
Given:
f(x)= |x| - 4g(x) = x³ - 4Want: x - values when f(x) = g(x)
f(x) = g(x) → |x| - 4 = x³ - 4positive interval x ≥ 0negative interval x < 0|x| - 4 = x³ - 4, the 4 cancel out on both sides
|x| = x³
|x| - x³ = x³ - x³
|x| - x³ = 0, x ≥ 0
-x - x³ = 0, x < 0
x = 0
x = -1, x ≥ 0
x = 1
x = 0, x < 0
The intersections are x = 0 and x = 1 and no solution
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5q²-2/3(6q²-6q-3)+3q
Answer:
[tex]q^2+7q+2[/tex]
Step-by-step explanation:
Check the attachment I added, hope it helps!
A real estate agent is showing homes to a prospective buyer. There are 10 homes in the desired price range listed in the area. The buyer wants to visit only 3 of them. a. In how many ways could the 3 homes be chosen if the order of visiting is considered? b. In how many ways could the 3 homes be chosen if the order of visiting is not important?
There are 720 ways that the 3 homes could be chosen if the order of visiting is considered. There are 120 ways that the 3 homes could be chosen if the order of visiting is not important.
What is permutation?A permutation is the arrangement or ordering of a finite set of an element.
From the information given:
If there are 10 homes in the desired price range listed in the area:
Then:
n = 10 and r = 3So, the number of ways of choosing 3 out of 10 (without replacement) and arranging is:
[tex]\mathbf{^nP_r= \dfrac{n!}{(n-r)!}}[/tex]
[tex]\mathbf{^nP_r= \dfrac{10!}{(10-3)!}}[/tex]
[tex]\mathbf{^nP_r= \dfrac{10\times 9\times 8 \times 7!}{(7)!}}[/tex]
= 720 ways
Now, the number of ways of choosing 3 out of 10 if the order of visiting is not important is the combination of the elements and it can be computed as:
[tex]\mathbf{^nC_r= \dfrac{n!}{(n-r)!r!}}[/tex]
[tex]\mathbf{^{10}C_3= \dfrac{10!}{(10-3)!3!}}[/tex]
[tex]\mathbf{\implies \dfrac{10\times 8\times 9 \times 7!}{(7)! \times 3\times 2}}[/tex]
[tex]\mathbf{\implies \dfrac{10\times 8\times 9}{6}}[/tex]
= 120 ways
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These points are linear.
Find the slope.
x-3-2-10/1/2
y-8 0 8 162432
slope = [?]
Enter
The slope of the given line according to the table is -8
How to calculate the slope of a functionThe slope of a function is also defined as the rate of change of the function.
Using the coordinate points (-3, 8) and (-2, 0) from the table
Slope = 0-8/-2-(-3)
Slope = -8/-2+3
Slope = -8/1
Slope = -8
Hence the slope of the given line according to the table is -8
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The model for the height of the balloon captured from the ground with a balloon launcher can be represented by the function… how long will it take for the balloon to hit the ground after it’s launched?
Answer:
2 seconds
Step-by-step explanation:
To find the time it takes for the balloon to reach the ground, you need to set the equation equal to 0. This is because the ground technically has a height of 0.
h(t) = -16² + 128t <----- Original expression
0 = -16² + 128t <----- Plug 0 in for h(t)
16² = 128t <----- Add 16² to both sides
256 = 128t <----- Solve 16²
2 = t <----- Divide both sides by 128
Therefore, if t = 2, it will take the balloon 2 seconds to reach the ground.
==========================================================
Explanation:
The balloon is on the ground when the height is zero.
Replace h with 0 and solve for t.
[tex]h(t) = -16t^2 + 128t\\\\0 = -16t^2 + 128t\\\\-16t^2 + 128t = 0\\\\-16t(t - 8) = 0\\\\-16t = 0 \ \text{ or } \ t-8 = 0\\\\t = 0/(-16) \ \text{ or } \ t = 0+8\\\\t = 0 \ \text{ or } \ t = 8\\\\[/tex]
Ignore t = 0 because this is when the balloon is initially on the ground. In other words, the balloon starts on the ground, so it makes sense that t = 0 leads to h = 0.
The other solution t = 8 is what we're after. The balloon touches the ground again at the 8 second mark. This is the length of time the balloon is in the air.
A quick way to determine and confirm the answer is to use graphing software. Check out the diagram below. We have a parabola with x intercepts of 0 and 8.
What is the solution to the system of equations?
O (5, 0)
O (0,5)
O (0-5)
O (-5, 0)
Answer: (0, -5) which is choice C
Explanation:
The solution is where the lines cross or intersect. This point is on both lines at the same time to make both equations true.
an a horizontal number line, positive numbers are____
On a vertical number line, negative numbers are_____
The number 0 is
Answer:
Positive number are located above 0 and negative numbers are located below 0 on a vertical number line
Answer:
On a horizontal number line, positive numbers are down from ANS= 0 to the left of 0✔ to the right of 0X up from 0.On a vertical number line, negative numbers are ✔ ANS=down from 0 to the left of 0to the right of 0up from 0.The number 0 is a negative numbera positive number✔Ans= neither positive nor negative.
Step-by-step explanation:
yw
Q(3x)=12x+2 then what is Q(x-2)
Answer:
it's ax+b form answer is Q(x-2)=4x-6
Step-by-step explanation:
ax+b=Q(x),Q(x-2)=a(x-2)+2
Q(3x)=a(3x)+b=12x+2, 3a=12 =>a=4,b=2
the original q of x is 4x+2
Q of x-2 =4(x-2)+2=4x-8+2=4x-6
brainliest!!!!!!
Question 4(Multiple Choice Worth 1 points)
(06.05 MC)
Given the functions k(x) = 2x² - 5 and p(x) = x - 3, find (k. p)(x).
(kop)(x) = 2x² - 6x + 4
(kop)(x) = 2x² - 12x + 13
(kop)(x) = 2x² - 12x + 18
(kop)(x) = 2x² - 8
Answer:
2x² - 12x + 13
Step-by-step explanation:
Given following:
k(x) = 2x² - 5p(x) = x - 3Start solving from right to left across the function.
Steps:
k[p(x)]k[x - 3]2(x - 3)² - 52(x² - 6x + 9) - 52x² - 12x + 18 - 52x² - 12x + 13Answer:
2x² - 12x + 13
Step-by-step explanation:
Steps:
k[p(x)]
k[x - 3]
2(x - 3)² - 5
2(x² - 6x + 9) - 5
2x² - 12x + 18 - 5
2x² - 12x + 13 pls brainlest
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.
R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
Triangle RST was transformed by using the rule (x,y) → (-x,-y) and the transformation is described by the transformation of 180° rotation about the origin.
Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Here we have transformed the triangle using the rotation method.
Rotation is the geometric transformation that revolves each point in a shape a predetermined number of degrees around that point. When the number of degrees is positive, the shape spins counterclockwise; when the number of degrees is negative, it rotates clockwise. The following is a broad description of how rotation about the origin can be transformed.
(X,Y) to rotate 90° (-y, x)180° rotation (x, y) (-x,-y)To rotate (x,y) 270° (y, -x)Here the points change to R'(-1,-1) , S'(-3,-1) and T'(-1,-6).
A 180° rotation about the origin will be the transformation.
The triangles RST and R'S'T' are first plotted on a graph. The graph is provided for your reference below.
The original triangle RST, which was in quadrant 1, has changed to triangle R'S'T', which is in quadrant 3, as shown in the graph. The rotation around the origin is 180° from quadrant 1 to quadrant 3.
Your question was incomplete. Please check below for full content.
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.
R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
Which describes the transformation?
The transformation was a 90° rotation about origin.
The transformation was a 180° rotation about origin.
The transformation was a 270° rotation about origin.
The transformation was a 360° rotation about origin.
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6.62607004081818181818181 X 10^-34
The solution to this is 6.62607e-34.
How to solve for exponentialsWe have the value is raised to the power of -34
We have to solve this using a calculator
This is similar to
[tex]6.62607004081818181818181*\frac{1}{10000000000000000000000000000000000}[/tex]
The number of zeros are 34
We would have 6.62607e-34 as the final solution.
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PLEASE FIGURE THIS OUT!
Figure M and it’s congruent image, figure N, are graphed on the coordinate plane below.
Describe a sequence of transformations that will take figure M onto its congruent image, figure N.
Answer:
Vertical shift up 2, horizontal shift left 2 reflection over x-axis then reflection over the y-axis.
Step-by-step explanation:
36 is what percent of 48?
The base and height of a right triangle are 20 inches and 15 inches. Find the length of the hypotenuse.
Answer:
25
Step-by-step explanation:
its both numbers squared and added, then square root the result
You enter an elevator on the ground floor, which is labeled 0. You get off on the floor labeled +4. What is your location?
A four floors above the ground floor
B. four floors below the ground floor
C. four floors near the ground floor
D. four floors around the ground floor
Answer:
A. four floors above the ground floor
Step-by-step explanation:
if you start at 0 which is the ground floor and go up 4, that would be +4, since, in theory, going up would be considered positive. So the answer is A.
five people arrived at the check _ out counter of a hotel at the same time, in how many different ways can the people line up?
There are 120 different ways the people can line up
How to determine the number of ways?The number of people that arrived is:
n = 5
Take the factorial to calculate the number of ways they can line up
n! = 5!
Expand
n! = 5* 4 * 3 * 2 * 1
Evaluate
n! = 120
Hence, there are 120 different ways the people can line up
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Julián just retired, and has $800,000 to invest. A very safe Certificate of Deposit (CD) account pays 2.5%, while a riskier bond fund pays 5% in interest. Julián figures he needs $36,000 a year in interest to live on. How much should he invest in each account to make enough interest while minimizing his risk?
An equation is formed of two equal expressions. Julian should invest $160,000 in CD and $640,000 in Bond.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount invested in CD be represented by x, while the amount invested in bond be represented by y. The total amount that Julian had is,
x + y = 800,000
x = 800,000 - y
The interest that Julian needs in a year is $36,000. Therefore, the total interest should be,
0.025x + 0.05y = 36000
0.025(800,000 - y) + 0.05y = 36000
20,000 - 0.025y + 0.05y =36,000
0.025y = 16,000
y = $640,000
Substitute the value of y
x + y = 800,000
x = $160,000
Hence, Julian should invest $160,000 in CD and $640,000 in Bond.
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given the function f(x) shown, sketch the graph of f(x-2)
Step-by-step explanation:
substitute different values of x inorder to get values of y. so since the value of y will have 2 units substracted from the original function leaving us with shifting. but the graph would be parabolic or slightly curved than my graph.
GIVE EXAMPLE OF ACTION PLAN THAT SHOWS A CONTEXTUALIZED LEARNING PROGRAM
An example of contextualization in teaching is when writing skills are taught with reference to topics.
How to illustrate the information?It should be noted that the contextualization of basic skills is the instructional approach that gives connections in teaching.
In this case, an example of contextualization in teaching is when writing skills are taught with reference to topics.
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if f(x)=4x-x^2 find f(x+h)-f(x+h)/2h
Answer:
0
Step-by-step explanation:
numerator are the same the difference between same number or variable will be zero
Identify the graph and describe the solution set of this system of inequalities.
y<-x-10
y>-x-2
Answer:
-x-2<y<-x-10
Step-by-step explanation:
A bag of tokens contains
8
8 red,
7
7 green, and
9
9 blue tokens. What is the probability that a randomly selected token is purple? Enter your answer as a fraction.
Answer:
As the bag doesnt conatain any purple token;
purple token = 0
number of total tokens in bag = 24
therefore, the probability of choosing a purple token = 0/24
Hope it helps
A line passes through the point (-2,7) and has a slope of -5. What is the value of a if the point (a,2) is also on the line?
Answer:
a = -1
Step-by-step explanation:
The slope, m from point -2,7 to a,2 has to be -5
m = (y1-y2)/(x1-x2)
-5 = ( 7-2)/(-2 -a) solve for 'a'......cross multiply
10+ 5a = 5
5a = -5
a = -1
Find the equation of the line tangent to the graph of f(x)=(lnx)^(4)at x=10
Hello,
Step-by-step explanation:
[tex]f(x) = ln(x) {}^{4} [/tex]
[tex](ln(u)') = \frac{u'}{u} [/tex]
[tex]f'(x) = \frac{4ln {}^{} (x) {}^{3} }{x} [/tex]
[tex]f'(10) = \frac{4ln {}^{} (10) {}^{3} }{10} = \frac{12ln(x)}{x} [/tex]
[tex]f(10) = ln(10) {}^{4} [/tex]
[tex]y = \frac{12ln(x)}{x} (x - 10) + 4ln(10)[/tex]
[tex]y = f'(a)(x - a) + f(a)[/tex]