9514 1404 393
Answer:
55
Step-by-step explanation:
Here's one way to count them.
12 consecutive integers will have 3 each of the integers whose value is 0, 1, 2, or 3 mod 4. To make a total that is 0 mod 4, any of these combinations of mod 4 values may be used:
000 -- 1 combination
013 -- 27 combinations, 3 each of mod 0, mod 1, and mod 3
022 -- 9 combinations, 3 of mod 0, and 3 ways to choose 2 of mod 2
112 -- 9 combinations, 3 of mod 2, and 3 ways to choose 2 of mod 1
233 -- 9 combinations, 3 of mod 2, and 3 ways to choose 2 of mod 3
__
Consider the set of 12 consecutive integers 1 .. 12. Then here are the 9 "233" combinations. Mod 2 integers are 2, 6, 10, and mod 3 integers are 3, 7, 11.
(2, 3, 7), (2, 3, 11), (2, 7, 11),
(3, 6, 7), (3, 6, 11), (6, 7, 11),
(3, 7, 10), (3, 10, 11), (7, 10, 11)
The total number of combinations that will be divisible by 4 is ...
1 + 27 + 9 + 9 + 9 = 55 . . . . combinations with a sum divisible by 4
__
Additional comment
The number of ways that 3 can be chosen from 12 is 220, so this is 1/4 of that total. It is perhaps not surprising that the remainders from division by 4 are uniformly distributed among the possibilities.
A computer program to list the 220 subsets and the mod 4 remainders of their totals confirms this is the correct number.
There are [tex]55[/tex] ways of these integers be selected to give a sum.
Given that:
It has consecutive integers .
Now,
Address the formula for [tex]C(n,r)[/tex],
[tex]C(n,r)=\frac{n!}{(n-r)!n!}[/tex]
Here,
[tex]n=12,r=3[/tex]
[tex]C(12,3)=\frac{12!}{(12-3)!3!} \\\\C(12,3)=\frac{12!}{9!3!} \\\\C(12,3)=\frac{12*11*10*9*8*7*6*5*4*3*2*1}{9*8*6*7*5*4*3*2*1*3*2*1} \\\\C(12,3)=\frac{12*11*10}{3*2*1} \\\\C(12,3)=4*5*11\\\\C(12,3)=220[/tex]
The sum [tex]mod 4[/tex] of any given subset increases by [tex]1[/tex] when the set is “slid” to the left.
Every subset gives rise to all four values [tex]mod 4[/tex] by sliding each of four places.
Since, The sum of the integer is divides by [tex]4[/tex].
Thus,
[tex]220\div 4=55[/tex]
Hence, it has [tex]55[/tex] ways .
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Help me with this question
Answer:
D. The graph of g(x) is the graph of f(x) compressed vertically and then reflected over the x axis.
Step-by-step explanation:
A function shows the relationship between two or more variables.
If a function y = f(x) is reflected over the x axis, the x coordinate remain unchanged, but the y coordinate is negated. Hence the function y = f(x) becomes y = -f(x).
A function y = f(x) is compressed or stretched vertically by a factor k to give y = kf(x). If 0 < k < 1, the function is vertically compressed whereas if k > 1, the function is vertically stretched.
Given the function f(x) = x², the function is vertically compressed by a factor of 2/3 to form a function f(x)' = (2/3)x². The function is then reflected over the x axis to produce a function g(x) = (-2/3)x²
Can anyone help me please ????
Hey there! The topic for this problem is Limit of Function!
As for the question, we are given the quadratic function and we have to find the limit, the value that approaches to a.
[tex] \large \boxed{lim_{x \longrightarrow a} f(x)}[/tex]
We call this, "The limit of f(x) when x approaches a."
Then you may ask, "How do we find the limit of function?". That is a very nice question! The answer to your problem is just substitute x-value in. Although this substitution method only applies when the approaching value doesn't make the denominator to 0. I believe that in the beginning of Limit topic, we learn how to find or evaluate the basic limit that only requires substitution.
So from the question, we receive:
[tex] \large{lim_{x \longrightarrow 2} ( {x}^{2} - 3x - 1)}[/tex]
Next step is to substitute x = 2 in the function.
[tex] \large{lim_{x \longrightarrow 2} ( {2}^{2} - 3(2) - 1)}[/tex]
Evaluate the value.
[tex] \large{lim_{x \longrightarrow 2} ( 4 - 6 - 1)} \\ \large{lim_{x \longrightarrow 2} ( - 3)}[/tex]
Cancel the limit out and there you have it!
[tex] \large \boxed{ - 3}[/tex]
Answer
The limit of quadratic function when x approaches 2 is -3.Now whenever you learn limit, you must know that limit is when we substitute the approaching value. That means x —> 2 is not x = 2 but x approaches 2.
Regarding the limit, any questions and doubts can be asked through comment and I will get back to you soon!
Thank you for using Brainly and I hope you have a fantastic day! Good luck on the assignment.
Find the volume of a rectangular solid with the given dimensions: length 8 feet, width 17 feet, height 10 feet. What is the volume?
Answer: 1360 cubic meter
Step-by-step explanation:
Volume of solid= Length*width*height
=8*17*10
=1360 cubic meter
Ricardo earned $52,000 last year. He just received a 3% salary increase. What is his new yearly salary?
=======================================================
Explanation:
Having the salary increase by 3% means we can use the multiplier 1.03
Think of it like 100% + 3% = 1 + 0.03 = 1.03
The new salary is 52,000*1.03 = 53,560 dollars
----------------
The slightly longer way to do this is to first figure out how much 3% of 52,000 is
3% of 52,000 = 0.03*52,000 = 1560
Ricardo earns $1560 more dollars on top of the salary of $52,000
So overall his new salary is $1,560 + $52,000 = $53,560
----------------
Personally, I prefer the first method because it's quicker and it allows for multiple percentage increases to chain together. It also could be used to chain in percentage decreases as well.
Six consecutive numbers add up to a total of 69.what is the highest of these numbers?
Answer:
14
Step-by-step explanation:
9+10+11+12+13+14=69
The [tex]HIGHEST[/tex] of these numbers is [tex]14[/tex]
Let the [tex]CONSECUTIVE[/tex] numbers be : [tex]a, a+1, a +2,a+3,a+4,a+5[/tex]
Taking the sum :
[tex]a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 = 69\\6a + 15 = 69\\6a = 69 - 15\\6a = 54\\a = 54 / 6\\a = 9[/tex]
[tex]HIGHEST[/tex] value = [tex]a + 5 = 9 + 5 = 14[/tex]
Hence, [tex]HIGHEST[/tex] value = [tex]14[/tex]
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Find the 3rd term in the expansion of (a + b)^7 in simplest form.
9514 1404 393Answer:
21·a^5·b^2
Step-by-step explanation:
The k-th term is ...
C(7, k)·a^(7-k)·b^k . . . . . where k counts from 0 to n
Then k=2 for the third term. The coefficient of it is ...
C(7, 2) = 7!/(2!(7-2)!) = 7·6/(2·1) = 21
The third term is ...
21·a^5·b^2
......................
Answer:
the distance between the 2 points is 6.4 units.
Step-by-step explanation:
point 1 has the coordinates (-4, -2).
point 2 has the coordinates (1, 2).
the distance between both points is the Hypotenuse of the right- angled triangle of the coordinate difference lines in parallel to x- and y-axis.
so, how long is the difference in x dimension ?
and his long is the difference in y dimension ?
these are the sides of the triangle.
the difference in x dimension :
1 - -4 = 1 + 4 = 5
the difference in y dimension :
2 - -2 = 2 + 2 = 4
P1P2² = 4² + 5² = 16 + 25 = 41
P1P2 = sqrt(41) = 6.4
What is the surface area of a rectangular prism with length 12 mm, width 3mm and height 5 mm
Answer:
The surface area of the rectangular prism is of 22 square millimeters.
Step-by-step explanation:
Surface area of rectangular prism:
The surface area of a rectangular prism with length l, width w and height h is given by:
[tex]S = 2(lw + lh + wh)[/tex]
Length 12 mm, width 3mm and height 5 mm
This means that [tex]l = 12, w = 3, h = 5[/tex]
Surface area:
[tex]S = 2(lw + lh + wh) = 2(12(3) + 12(5) + 3(5)) = 2(36 + 60 + 15) = 2(111) = 222[/tex]
The surface area of the rectangular prism is of 22 square millimeters.
O, R and S are points in the same horizontal plane. /OR/ = 20m and /OS/= 32m.The bearing of R and S from O are 030° and 135° respectively. How Far East of R is S
The more accurate value is 12.6274169979696, though it's not fully exact.
Round this however you need to.
The exact distance 32*sin(45) - 10 meters.
===========================================================
Explanation:
Refer to the diagram below.
I'll use point A in place of point O since the letter 'oh' is very similar looking to the number zero.
Plot point A at the origin (0,0). While at point A, look directly north. Then turn 30 degrees eastward to look at the bearing 030°. Next, move 20 meters along that bearing direction to arrive at point R. Segment AR is 20 meters long.
In the diagram, note how angle RAB is 30 degrees. The side opposite this is BR = m.
We can use the sine ratio to say that
sin(angle) = opposite/hypotenuse
sin(A) = BR/AR
sin(30) = m/20
m = 20*sin(30)
m = 10
-----------------------------------
While still at point A, look directly north and turn 135 degrees clockwise (ie toward the east) and move 32 meters along that bearing. You'll arrive at point S as the diagram shows.
Notice how
angle RAB + angle RAC + angle CAS = 30+60+45 = 135
The remaining angle DAS is 180-135 = 45 degrees.
When focusing on triangle DAS, we can say
sin(A) = DS/AS
sin(45) = n/32
n = 32*sin(45)
n = 22.6274169979696
This value is approximate.
----------------------------------
Subtract the values of m and n
n - m = 32*sin(45) - 10 = exact distance
n - m = 22.6274169979696 - 10
n - m = 12.6274169979696
n - m = 12.6274 = approximate distance
Round it however you need to. I'm choosing to round to four decimal places.
So we see that point S is roughly 12.6274 meters east of point R.
If your teacher wants the exact distance, then stick with 32*sin(45)-10.
given f(x) = 2x³+3x²-12x+7 = (x-1)² (2x+7), differentiate to find f¹(x)
Step-by-step explanation:
We use the symbol f − 1 to denote an inverse function. For example, if f (x) and g (x) are inverses of each other, then we can symbolically represent this statement as:
g(x) = f − 1(x) or f(x) = g−1(x)
One thing to note about the inverse function is that the inverse of a function is not the same as its reciprocal, i.e., f – 1 (x) ≠ 1/ f(x). This article will discuss how to find the inverse of a function.
Since not all functions have an inverse, it is therefore important to check whether a function has an inverse before embarking on determining its inverse.
We check whether or not a function has an inverse in order to avoid wasting time trying to find something that does not exist.
Write an equation of the line that has a slope of -3 and y-intercept 7 in slope-intercept form.
Answer:
Step-by-step explanation:
No. 1 “The printing of more
currency notes will increase inflation.”
One hundred forty-eight ten thousandth is
Solve the inequality: 13 + 2 v − 8 + 6 > − 7 − v
Answer:
V< 6
Step-by-step explanation:
11+2v > -7-v
3v> -18
v<6
Planes A and B intersect.
Which describes the intersection of line m and line n?
P
m
2
O point w
O point X
Opoint Y
point Z
.
n2
X
Y
W
k
.
V
2
-
Answer:
I think about point Y ......
If planes A and B intersect, point w describes the intersection of line m and line n.
What is Coordinate system?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements.
In the given figure, the planes A and B intersected.
We have to find the point where the line l and line m intersects.
The intersection of a line and a line can be the empty set, a point, or another line.
Two straight lines will intersect at a point if they are not parallel.
The point of intersection is the meeting point of two straight lines.
The lines m and line n are intersected at the point w.
Hence, if planes A and B intersect, point w describes the intersection of line m and line n.
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A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.
Calculate the cyclist's average speed in mph.
Answer:
15 mph
Step-by-step explanation
i used a calculator but correct me if im wrong pls
9.
Write the equation of a line through points (5, 5) and (1, 0) in point-slope form.
9514 1404 393
Answer:
y = 5/4(x -1)
Step-by-step explanation:
The slope formula can be used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (0 -5)/(1 -5) = -5/-4 = 5/4
The point-slope form is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Using the point (1, 0), we can write the equation as ...
y = 5/4(x -1)
Write .125 as a fraction reduced to lowest terms.
Answer:
1/8
Step-by-step explanation:
Hope this helps you! <33
Answer:
1/8
Step-by-step explanation:
We all know 1/2 is 0.5, right?
If you split that in half again, you get 0.25 as 1/4.
If you divide that again by two, you get 1/8 as 0.125
The area of a circle is 42.29m2.
Find the length of the diameter rounded to 1 DP.
Step-by-step explanation:
area of a circle=πr²
=42.29m²
42.29m²=πr²
then find for r, multiply it by two to obtain the diameter of the circle
5. A car travels 40 kilometers at an average speed of 80 km/h and then travels 40
kilometers at an average speed of 40 km/h. The average speed of the car for this 80 km
trip is:
A) 40 km/h
B) 45 km/h
48 km/h
D) 53 km/h
E) 80 km/h
Answer:
D
Step-by-step explanation:
Total distance traveled is 80KM.
Total time taken is 1.5 hrs(0.5+1)
Average Speed = 80/1.5
=53, 3
100 Brainly points!!!!
In the figure, polygon ABCD is dilated by a factor of 2 to produce A’B’C’D’ with the origin as the center of dilation.
Point A’ is at _ options > •(2,1), (-2,-2), (1,2), (-2,2)•
& point D is at _ options > (-2,2), (4,-2), (4,2), (-2,-2).
Answer:
Point A’ is at (-2,-2)
& point D' is at (4,-2)
Step-by-step explanation:
Point A’ => (-1×2, -1×2) => (-2 , -2)
Point D' => (2×2 , -1×2) => (4 , -2)
A is at (-1,-1)
So A' is at
2(-1,-1)(-2,-2)D is at
(2,-1)D' is at.
2(2,-1)(4,-2)Suppose a sample of 1390 suspected criminals is drawn. Of these people, 514 were captured. Using the data, estimate the proportion of people who were caught after being on the 10 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The estimate for the proportion of people who were caught after being on the 10 Most Wanted list is of 0.37.
Step-by-step explanation:
Estimate of the proportion of people who were caught after being on the 10 Most Wanted list.
Number of people captured divided by the size of the sample.
We have that:
514 of 1390 people were captured. So
514/1390 = 0.37
The estimate for the proportion of people who were caught after being on the 10 Most Wanted list is of 0.37.
ASAP!!! Use the relationships in the diagrams below to calculate the the values of the variables if possible part. B
Answer: y = 57°;
Angle Values: 66° and 114°.
Step-by-step explanation:
The sum of the corresponding angles is 180°.
y + 9 + 2y = 180
3y = 180 - 9
3y = 171
y = 57
Angle Values:
57° + 9° = 66°
57° · 2 = 114°
Solve:
n = 8
4
O n = 2
0 n = 12
Ô n = 24
0 n = 32
Answer:
1/4 n = 8
n = 8 * 4
n = 32
so option 4 i.e.
n = 32. is the ans
Answer:
n=32
Step-by-step explanation:
Given :
[tex]\frac{1}{4} n=8[/tex]
Now,
Value of n can be calculated as :
[tex]\frac{1}{4} n=8[/tex]
n=8×4
n=32
Therefore, option (D) is correct.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
6y - 3x = 30
Answer:
y=(x/2)+5
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept form. To get that, we need y by itself so we have to add 3x to both sides: 6y=30+3x. Now we divide by 6 and rearrange the right side: y=(3x+30)/6.
y = (3x/6)+(30/6) => y = (x/2)+5. We also know that the slope is 1/2 and the y-intercept is 5 because of the slope-intercept equation.
Larry is paid 8.5% of all sales plus 4.25% of sales over $6800. Find Larry's gross pay from total sales of $12,200.
Answer:
$1266.50Step-by-step explanation:
Larry's gross pay is:
12200*8.5/100 + (12200 - 6800)*4.25/100 = 1037 + 229.50 = 1266.50We can find Larry's gross pay,
→ 12200×8.5/100+(12200-6800)×4.25/100
→ 1037 +229.50
→ 1266.50
Hence, $ 1266.50 is the solution.
What is the square root of 13?
Answer:
3.605551275
Step-by-step explanation:
Find the equation of the straight line that passes through the points (1, 10) and (3, 2)
ANSWER ASAP
Answer:
y = -4x+14
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
m = (2-10)/(3-1)
=-8/2
= -4
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -4x+b
Substitute a point into the equation
10 = -4(1)+b
Add 4 to each side
14 = b
y = -4x+14
Answer:
y=-4x+14
Step-by-step explanation:
m=y1-y2/(x1-x2) and m= y-y1/x-x1
10-2/1-3=-4
m=-4 so -4=y-10/x-1
-4x+4=y-10
-4x+14=y
Chet has $1200 invested in a bank account modeled by the function P(n) = 1200(1.002)
Answer:
Answer: 3) R(n) = 1200(1.002)n - 100n
Step-by-step explanation:
After n months, which function represents Chet’s net worth, R(n)?
(1) R(n) = 1200(1.002)n + 100n
(2) R(n) = 1200(1.002)12n + 100n
(3) R(n) = 1200(1.002)n - 100n
(4) R(n) = 1200(1.002)12n - 100n
Answer: 3) R(n) = 1200(1.002)n - 100n
Net worth is the amount of his savings minus his debt,
Everything in the problem is in terms of months, so there is no need to multiply the exponent by 12, which would convert n years into months.
The diagram shows a right-angled triangle.
xo
26 cm
17 cm
Find the size of angle x.
Give your answer correct to 1 decimal place.
Answer:
Diagram? I don't see a diagram.
Where is the diagram?
Step-by-step explanation:
cách hiếp dâm công an ko bắt
Answer:
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Step-by-step explanation:
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