The function B is defined any positive whole number N as being the product BN=(N-1)(N-2)(N-3) what is the sum of B1,B2,B3 and B4?
Answers
The calculated sum of B1,B2,B3 and B4 is 6
How to determine the sum of B1,B2,B3 and B4?From the question, we have the following parameters that can be used in our computation:
BN=(N-1)(N-2)(N-3)
Express properly
So, we have
B(N) = (N-1)(N-2)(N-3)
using the above as a guide, we have the following equations
B(1) = (1-1)(1-2)(1-3) = 0
B(2) = (2-1)(2-2)(2-3) = 0
B(3) = (3-1)(3-2)(3-3) = 0
B(4) = (4-1)(4-2)(4-3) = 6
When the above functions are added, we have
Sum = 0 + 0 + 0 + 6
Evaluate the sum
Sum = 6
Hence, the sum of B1,B2,B3 and B4 is 6
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Related Questions
Mr. Ledford is concerned about the amount of sleep the students in his district are getting. He selects a random sample of 14 seniors in his district and asks them how many hours of sleep they get on a typical school night. He then uses school records to determine the most recent grade-point average (GPA) for each student. His regression output along with a residual plot and a histogram of the residuals are given below.
Sleep (hrs) 9 8.5 9 7 7.56 7 5.5 6 8.5 6.5 8
GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7
Required:
Do these data provide convincing evidence of a linear relationship between the hours of sleep students typically get and their academic performance, as measured by their GPA?
Answers
Answer:
Hence, the data provides convincing evidence that a linear relationship exists between hours of sleep observed and academic performance as measured by GPA.
Step-by-step explanation:
Given the data:
Sleep (hrs) 9 8.5 9 7 7.56 7 5.5 6 8.5 6.5 8
GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7
The scatter plot shows a positive linear trend. With the correlation Coefficient depicting a R value of 0.56. The residual plot also depicts a a randomly scattered values of the residual values. Similarly, a plot of the normal values of residuals
The data provided has a linear correlation between the hours of sleep observed and academic performance as measured by GPA.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
We have given data of the 14 seniors shown in the table.
To solve this question we will calculate the correlation coefficient 'r'
The formula for correlation coefficient :
[tex]\rm r =\frac{n\sum xy-\sum x \sum y}{\sqrt{[n\sum x^2-(\sum x)^2]}[n\sum y^2-(\sum y)^2]} }[/tex]
From the table the value of n = 14
[tex]\rm \sum x = 104.5[/tex] , [tex]\rm \sum y =47.7[/tex] , [tex]\rm \sum xy =357.8[/tex] , [tex]\rm \sum x^2 =797.25[/tex] , [tex]\rm \sum y^2 =163.09[/tex]
Put all the values in the above formula we get:
[tex]\rm r =\frac{14\times357.8-104.5 \times47.7}{\sqrt{[14\times 797.25-104.5^2][14\times163.09-47.7^2]} }[/tex]
[tex]\rm r = \frac{5009.2-4984.65}{\sqrt{(241.25)(7.97)} }[/tex]
[tex]\rm r = \frac{24.55}{43.849}[/tex]
r = 0.559 ≈ 0.56
The value of the correlation coefficient is 0.56 which is between the values 0.5 to 0.7 shows that the variables are moderately correlated.
Thus, the data provided has a linear correlation between the hours of sleep observed and academic performance as measured by GPA.
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●10 Kate is reading a 500-page book. The graph below represents the relationship between the
number of hours Kate has spent reading and the number of pages she has read.
Kate’s
rate
0 1
50
2
100
3
150
200
4 5
250
6
300
350
400
450
x
y
Reading Rate
Number of Pa
ges Read
Time (in hours)
(5, 200)
On the grid in your Student Answer Booklet, copy the x-axis, the y-axis, and the line
representing Kate’s reading rate exactly as shown. Be sure to label the line “Kate’s rate.”
Answers
"200" (and any subsequent words) was ignored because we limit queries to 32 words
Kate is reading 40 pages per hour.
The whole book takes 12.5 hour to complete.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
From the data we have (5, 200) and (5,0)
then slope= (200-0) / 5
= 40
So, Kate is reading 40 pages per hour.
Now, to read the whole book i.e., 500 pages it takes
= 500/40
= 12.5 hours
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PLEASE ANSWER ASAP FOR BRANILEST!!!!!!!!!!!!!!!!!!!!
Answers
Answer: 60
Step-by-step explanation: Plug in 8 for x and either use the linear supplements theorem to solve or the vertical angles congruence theorem.
I don't know what to do I'm very confused
Answers
Answer:
x = 33.8°
Step-by-step explanation:
The resulting diagram we have is a right triangle. To find x, apply trigonometric function.
Reference angle = x
Opposite = 116
Adjacent = 173
Apply TOA:
Tan x = Opp/Adj
[tex] tan (x) = \frac{116}{173} [/tex]
[tex] x = tan^{-1}(\frac{116}{173}) [/tex]
[tex] x = tan^{-1}(\frac{116}{173}) [/tex]
x = 33.8° (nearest tenth)
Find the area of each figure
Answers
a = 20, b = 9, h = 21/-16
20+9/2 * (21-16) = 29/2 * 5 = 72.5
The area of the trapezoid = 72.5 in^2
Area of the rectangle = l * w
l = 16, w = 20
16 * 20 = 320
The area of the rectangle: 320 in^2
Andrew wrote the number 186,425 on the board. In which number is the value of the digit 4
exactly 100 times the value of the digit in the number Andrew wrote?
A 681,452
B 462,017
C 246,412
D 124,655
Answers
Answer:
C
Step-by-step explanation:
The four is in the hundreds so times one hundred it'd be in the 10,000 so it is C.
Factor 16a + 10.
(Please help)
Answers
Answer:
2(8a+5)
Step-by-step explanation:
To factor means to find a number that can divide all the terms in the expression and leave whole number quotients. The factor is written outside the bracket while the quotients are written inside the bracket. In the question, 2 can divide both 16a and 10 giving 8a and 5. This is how the answer was obtained.
= 2(8a+5)
hope it helps
Solve the formula S=43.14r^2 for r.
Answers
Explanation:
Sid has £5 to buy apples and bananas.
He uses his money like this:
He buys 18 apples.
Then he buys as many bananas as possible.
With his change, he buys more apples.
How many apples and bananas does he buy?
(Apples=6p Each)
(Bananas= 40p Each)
(pls add working out)
Answers
He can buy 9 bananas
Answer:
Apples: 23 , bananas = 9
Step-by-step explanation:
Apples = 18 x 6 = 108p = 1,08£
5-1,08 = 3,92£
£3,92 = 392p
Bananas = 392 : 40 = 9,8= 9
40x9 = 360p = 3,60£
change = 3,92 -3,60 = 32p
apples = 32 : 6 = 5,33 = 5
total apples = 23
Please help me with this ASAP ASAP please
Answers
Answer:
r = 16 cm ; l = 34 cm ; LA = 544π cm^2 ; SA = 800π cm^2
Step-by-step explanation:
The volume of the cone can be find with this formula
V = (base area x height)/3
thanks to this formula we can find the base surface
base surface = (V x 3)/height
base surface = (2560π x 3)/30 = 256π cm^2
the formula of the base surface is
base surface = radius^2 x π
so we can find the radius in this way:
radius = √base surface/π
radius = √256π/π = 16 cm
slant height = [tex]\sqrt{radius^2 + height^2}[/tex]
[tex]\sqrt{16^2 + 30^2} =\sqrt{256 + 900} = \sqrt{1156} = 34[/tex] cm
lateral surface = radius x slant height x π = 16 x 34 x π = 544π cm^2
surface area = base area + lateral surface = 256π + 544π =800π cm^2
+b4+c4 = 20² (b²+c²), prove
that A:45° or 135°
Answers
A is either 45° or 135°.
To prove the given statement, let's assume that the points B and C lie on a coordinate plane, with the origin (0, 0) as the common vertex of the right angles at points B, C, and A. Let the coordinates of points B and C be (x₁, y₁) and (x₂, y₂) respectively.
Using the distance formula, we have:
AB² = x₁² + y₁²
AC² = x₂² + y₂²
According to the given equation, +b4+c4 = 20² (b²+c²), we can rewrite it as:
(x₁² + y₁²) + (x₂² + y₂²) = 20² [(x₁² + y₁²) + (x₂² + y₂²)]
Expanding and simplifying the equation, we get:
x₁² + y₁² + x₂² + y₂² = 20² (x₁² + y₁² + x₂² + y₂²)
This equation can be further simplified to:
(x₁² + y₁²) + (x₂² + y₂²) = (20² - 1) (x₁² + y₁² + x₂² + y₂²)
Since the left side represents the sum of the squares of the distances from the origin to points B and C, and the right side is a constant multiplied by the same sum, we can conclude that the points B and C must lie on a circle centered at the origin.
In a circle, the sum of angles subtended by two perpendicular chords at the center is either 180° or 360°. Since the given problem involves right angles, we consider the sum of angles to be 180°.
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To exercise, Ana goes up and down a ladder. She starts at the sixth step and walks as follows: up 3 steps, down 4 steps, up 2 steps, down 3 steps. On what step does she end up?
Answers
Answer:
step 4
Step-by-step explanation:
she's at 6 then goes up 3 which would mean she's at step 9. then she goes does 4 so subtract 9-4=5. She would be on step 5 but she decides to go up 2 so add. 5+2=7. then she goes down 3 steps so subtract. 7-3=4. she ends up at step 4.
Help pls fast ....................
Answers
Answer:
its A. 5
Step-by-step explanation:
5/10 is also known as 1/2 so 5/10 is equal to 1/2
What is an equation of the line that passes through the points
(3,-3) and (-3,-3)?
(1) y = 3
(3) y=-3
(2) x =-3
(4) x=y
Please help asap
Answers
Answer:
(3) [tex]y=-3[/tex]
Step-by-step explanation:
The two points have the same y coordinates so the slope is zero and because both points have an y of -3 the y coordinate will always be -3.
The circumference of a circle is like the ________ of a figure.
A. shape
B. perimeter
C. area
Answers
Answer:
The answer would be 'B. perimeter'.
What is the image of the point (4,1) after a rotation of 270° counterclockwise about
the origin?
Will give brainliest
Answers
Answer:
1,-4
Step-by-step explanation:
formula for rotation of 270 is (x,y) to (y,-x)
What is the value of 6(x + 15) - 12 when x = 12?
provided on your answer document.
Answers
Answer: 162
Step-by-step explanation:
6(12+15) Following the order of operations, (P.E.M.D.A.S), you should do parentheses first. So you add 12 and 15 to get 27. Were left with 6(27). So we multiply 6 and 27. The final answer is 162.
4
27
x 6
--------
162
Plzzzzzz helpppp me
Answers
Answer:
15
Step-by-step explanation:
Just substitute x in the equation
so x=3
so
3^2=9, 5x3=15, -9
equals 15
start by replacing x with 3
so your equation now would look like
f(3)= (3)^2+5(3)-9
next start by doing exponents
f(3)= 9+5(3)-9
now you can do multiplication
f(3)= 9 + 15 - 9
add everything together
9 + 15 -9
your answer is 15. hope this helps
given the circumference of circle b is 85 ft . what is the arc lenght of arc ADC?and the lenght of arc Ac
Answers
Answer:
Length of arc AC = 10.6 ft
Length of arc ADC = 73.4 ft
Step-by-step explanation:
θ = 45°
Circumference = 85 ft
✔️First, find the radius:
Circumference of a circle = 2πr
Thus:
85 = 2πr
Solve for r
Use 3.14 as π
Divide both sides by 2π
85/2π = r
85/2*3.14 = r
85/6.28 = r
r = 13.5350318 ≈ 13.5 ft (nearest tenth)
✔️Find length of arc ADC:
Length of arc = θ/360 × Circumference of the circle
θ = 360 - 45° = 315°
Circumference = 85 ft
Plug in the values
Length of arc ADC = 315/360 × 85
= 74.375 ≈ 73.4 ft (nearest tenth)
✔️Find length of arc AD:
Length of arc = θ/360 × Circumference of the circle
θ = 45°
Circumference = 85 ft
Plug in the values
Length of arc AC = 45/360 × 85
= 10.625 ≈ 10.6 ft (nearest tenth)
Solve to find the height of a triangle with the base of 10 feet in the area of 21 feet
Answers
Answer: 4.2
Step-by-step explanation:
hb=2A
b=2·21
10=4.2ft
A consumer group surveyed the prices for white cotton extra-long twin sheet sets in five different department stores and reported the average price as $16 with standard deviation $3.81. Assume that the population is normal and has a standard deviation equal to $3.81. 9. Provide a 95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets. z* is 1.96
Answers
Answer:
95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.
(12.6604 ,19.3396)
Step-by-step explanation:
Step(i):-
Given that mean of the sample = 16
Given that the standard deviation of the sample = 3.81
The standard deviation of the Population = 3.81
Level of significance = 0.05
Step(ii):-
95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.
[tex](x^{-} - Z_{0.05} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.05} \frac{S.D}{\sqrt{n} } )[/tex]
([tex](16 - 1.96 (\frac{3.81)}{\sqrt{5} } , 16 +1.96 (\frac{3.81)}{\sqrt{5} })[/tex]
( 16 - 3.3396 , 16 + 3.3396)
(12.6604 ,19.3396)
Final answer:-
95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.
(12.6604 ,19.3396)
Draw a square that has (-2,4) and (3,-1) as two of its vertices
Answers
Answer:
square with (-2,4) and (3,-1) vertices
Which are undefined terms that can be used to define other terms?
O point, segment, ray
O point, line, plane
O line, plane, cube
O line, ray, angle
Answers
Answer:
Point, Line, Plane
Step-by-step explanation: They are undefined terms because its is easier to define them using examples rather than word for word
Helpppppppppppppppppppppppppppppppppp
Easyyy
Answers
Answer:
duuuuuuude if its easy then why do you need help huh answer me
Step-by-step explanation:
PLEASE HELP ME!! My grades are bad and I need the answer before Friday. Somebody PLEASE help!!! I rlly need to get this done!!
Answers
Step-by-step explanation:
Just telling you, if your grades are bad,
you should listen to the teacher more in class time,
take notes, and more.
Btw, the equation is...
I hope this will help you.
I cannot give answers for everything.
I hope this helps!
Select all numbers that have an absolute value of 4.
Answers
You didnt give us the numbers but it should be 4 and -4
HELP................!!!!!!!!
Answers
Answer:
a
Step-by-step explanation:
Identity the coterminal angle between 360° and 360° for the angle - 120°
No
Answers
Jimmy has 317 of feet of chord for his science experiment. James has 3/5
feet of chord for his science experiment as well. (a) How many feet of
chord do they have altogether? (b) Who has more chord, Jimmy or
James? Help please
Answers
Answer:
(a)317 and 3/5 (b) jimmy
Step-by-step explanation:
(a) 317 and 3/5 because i plus there chord both (b) no explanation cause jimmy has mire chord than james
Answer:
A.317 3/5
B.jimmy
Step-by-step explanation:
sana Po makatulong
need help ASAP plssssssssssssssssss
3,945 ÷ 45 = (?)
R (?)