==============================================
Explanation:
The recursive rule
f(n+1)=f(n)-3
can be rearranged to
f(n) = f(n+1)+3
after adding 3 to both sides
----------------
Now let's say we plug in n = 3
f(n) = f(n+1)+3
f(3) = f(3+1)+3
f(3) = f(4)+3
f(3) = 22+3
f(3) = 25
Repeat for n = 2
f(n) = f(n+1)+3
f(2) = f(2+1)+3
f(2) = f(3)+3
f(2) = 25+3
f(2) = 28
Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).
Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.
2. A bag contains one red, one blue and one white marble. One marble is chosen at random
from the bag, and then replaced into the bag. A second marble is chosen.
a) Draw a probability tree and find the sample space.
(3 marks)
Answer:
Step-by-step explanation:
Which of the following is not an example of a parent function?
y=x
y=2x^3
y=1/2
y=2^x
9514 1404 393
Answer:
(b) y=2x^3
Step-by-step explanation:
The function y=2x^3 is an example of the parent function y=x^3 being vertically scaled by a factor of 2. As such, it is not the parent function.
_____
Additional comment
A parent function is one that has not been translated or scaled in any way. One could argue that the parent function of the form y=constant is y=1, so that the function y=1/2 has been scaled by a factor of 1/2. In this problem, we recognize the parent function y=x^3 has clearly been scaled to get y=2x^3, so the latter is not an example of a parent function.
If this is a "check all that apply" question, then y=1/2 is another reasonable answer.
Answer:(b) y=2x^3
Step-by-step explanation:
What is 34% plus 29% times 60
Answer:
34%+29%=63% 63%x60=37.8
Step-by-step explanation:
because math
Answer:
[tex] { \tt({34\% + 29\%) \times 60}} \\ = 63\% \times 60 \\ = \frac{63}{100} \times 60 \\ = 37.8[/tex]
How many numbers lie between the squares of 39 and 40
Answer:
i guess its 1...
Step-by-step explanation:
Answer:
79 numbers
Step-by-step explanation:
39 x 39 = 1521 ( Find the square of 39)
40 x 40 = 1600 (Find the square of 40)
1600 - 1521 = 79 ( Finding the difference of the two squares)
Can someone help me with this question please.
Answer:
The rule is to divide the weight of the bag by 4 to find the number of marbles.
Step-by-step explanation:
The rule is to divide the weight of the bag by 4 to find the number of marbles.
Three-fourths (one-fourth x + 8) minus (one-half x + 2) = StartFraction 3 Over 8 EndFraction (4 minus x) minus one-fourth?
Answer:
if I am understood your question correctly, X would be 84/29
Step-by-step explanation:
A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.
Clothes Food Toys
43 30 52
24 38 58
42 46 43
35 54 49
28 47 63
31 42 53
17 34 48
31 43 58
Required:
a. Find the values of mean and standard deviation.
b. Is there a difference in the mean attention span Of the children for the various commercials?
Answer:
(a)
Mean
[tex]\bar x_1 = 31.375[/tex]
[tex]\bar x_2 = 41.75[/tex]
[tex]\bar x_3 = 53.00[/tex]
Standard deviation
[tex]\sigma_1 = 8.73[/tex]
[tex]\sigma_2 = 7.65[/tex]
[tex]\sigma_3 = 6.04[/tex]
(b) Yes, there is a difference in the mean
Step-by-step explanation:
Solving (a): The mean and standard deviation of each commercial
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
For clothes:
[tex]\bar x_1 = \frac{43+24+42+35+28+31+17+31}{8}[/tex]
[tex]\bar x_1 = \frac{251}{8}[/tex]
[tex]\bar x_1 = 31.375[/tex]
For food:
[tex]\bar x_2 = \frac{30+38+46+54+47+42+34+43}{8}[/tex]
[tex]\bar x_2 = \frac{334}{8}[/tex]
[tex]\bar x_2 = 41.75[/tex]
For toys:
[tex]\bar x_3 = \frac{52+58+43+49+63+53+48+58}{8}[/tex]
[tex]\bar x_3 = \frac{424}{8}[/tex]
[tex]\bar x_3 = 53.00[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
For clothes:
[tex]\sigma_1 = \sqrt{\frac{(43 - 31.375)^2 +.............+(31 - 31.375)^2}{8-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{533.875}{7}[/tex]
[tex]\sigma_1 = \sqrt{76.2678571429}[/tex]
[tex]\sigma_1 = 8.73[/tex]
For food:
[tex]\sigma_2 = \sqrt{\frac{(30 - 41.75)^2 +............+(43 - 41.75)^2}{8-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{409.5}{7}}[/tex]
[tex]\sigma_2 = \sqrt{58.5}[/tex]
[tex]\sigma_2 = 7.65[/tex]
For toys:
[tex]\sigma_3 = \sqrt{\frac{(52-53.00)^2+...................+(58-53.00)^2}{8}}[/tex]
[tex]\sigma_3 = \sqrt{\frac{292}{8}}[/tex]
[tex]\sigma_3 = \sqrt{36.5}[/tex]
[tex]\sigma_3 = 6.04[/tex]
Solving (b): Difference in mean in the commercials;
In (a), we have:
[tex]\bar x_1 = 31.375[/tex]
[tex]\bar x_2 = 41.75[/tex]
[tex]\bar x_3 = 53.00[/tex]
[tex]\bar x_1 \ne \bar x_2 \ne \bar x_3[/tex]
Hence, there is a difference in their means
A system of equations is shown below:
y = 3x − 7
y = 2x + 1
What is the solution to the system of equations?
(8, 17)
(−8, 17)
(−8, −17)
(8, −17)
Answer:
(8, 17)
Step-by-step explanation:
y= 3x -7 -----(1)
y= 2x +1 -----(2)
Substitute (1) into (2):
3x -7= 2x +1
Being x terms to one side, constant to the other:
3x -2x= 7 +1
x= 8
Substitute x= 8 into (2):
y= 2(8) +1
y= 16 +1
y= 17
∴ The solution is (8, 17).
PLEASE ANSWER MAKE SURE YOU ARE RIGHT PLEASE I WILL MARK AS BRAINIEST
FIND THE VOLUME OF THE CYLINDER
Answer:
Find the volume of the cone, the answer i got was 37.68 but it asked to round so it should be 37.7
Hope this helps :)
Answer:
If we want to find volume of cone we must use this formule: πr²*high/3.
Step-by-step explanation:
let's solve step by step
firstly you know the radius is 3 and high is 4
if we accept π to 3. the answer is must be (3*3*4)/3 and finally the answer is 12 units³
How many exterior walls does the building have?
Answer:
18
Step-by-step explanation:
360÷20=18
twentycharactersignorethis
the building has 16 exterior walls
The time to complete an exam is approximately Normal with a mean of 48 minutes and a standard deviation of 3 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes.
Answer:
This means the average amount of time is 48 minutes but many people will do it in 45 to 51
Hope This Helps!!!
1. The curved surface area of a cylinder of height 21cm is
660cm", find its radius. please help me .....
I will give brainliest.
Answer:
21 times 660 and then you will get the answer
Please help me understand
Answer:
A is is correct since the interquatile or a is 15 since 15 plus 15 equals 30 and 20 plus 20 equals 40
B is incorrect since the interquare are not both 30
C is incorrect since both interquatiles are wrong
D is incorrect since the standrard devations are off
four times a certain number decreased by twice the same number gives 17. the number is
Answer:
8.5
Step-by-step explanation:
[tex]\int _{2.2}^{+\infty \:}\frac{10.648}{x^2}[/tex]
Step-by-step explanation:
[tex]\int _{2.2}^{+\infty \:}\frac{10.648}{x^2}dx = 10.648 \int _{2.2}^{\infty \:}\frac{dx}{x^2}[/tex]
[tex] = - \frac{10.648}{x} | _{2.2}^{ \infty} = 4.84[/tex]
Defined the total variation distance to be a distance TV(P,Q) between two probability measures P and Q. However, we will also refer to the total variation distance between two random variables or between two pdfs or two pmfs, as in the following.
Compute TV(X,X+a) for any a∈(0,1), where X∼Ber(0.5).
TV(X,X+a) = ?
Answer:
1
Step-by-step explanation:
Computing Tv(X, X + a ) for any a∈(0,1)
Given that : X∼Ber(0.5)
∴ The probability mass function
P(X = 1 ) = 0.5
P(X = 0) = ( 1 - 0.5 )
and expectation E[X] = 0.5
hence ; TV ( X, X + a ) = 1
Complete the table of inputs and outputs for the given function. g(x) = 3 - 8x g() 0 -5 3 Reset
Answer:
Step-by-step explanation:
characteristics of the median
Answer:
Median: The median is the middle value of the data set when the data is arranged in ranking order. It always lies at the center of the data set and not affected by the extreme values or outliers. For the calculation of median, the variable should be measured at least at the ordinal level.
Can someone please help me?
Find the midpoint of the line segment.
Answer:
-2,-3
Step-by-step explanation:
PLEASEEEE HELP QUICKKKK
Given:
Line A goes through (0,y) and (-2,0).
Line B goes through (1,2) and (3,10).
To find:
The value of y for which the system of given linear equation (equation of line A and line B) has no solutions.
Solution:
Two linear equation has no solutions if they are parallel line.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We know that the slopes of two parallel lines are the same.
So, the given system of given linear equation has no solutions if
Slope of line A = Slope of line B
[tex]\dfrac{0-y}{-2-0}=\dfrac{10-2}{3-1}[/tex]
[tex]\dfrac{-y}{-2}=\dfrac{8}{2}[/tex]
[tex]\dfrac{y}{2}=4[/tex]
Multiply both sides by 2.
[tex]\dfrac{y}{2}\times 2=4\times 2[/tex]
[tex]y=8[/tex]
Therefore, the required value of y is 8.
If f(x)=x^2−8x and g(x)=−12x^2 what is g(f(−4))?
Answer:
-27648
Step-by-step explanation:
In this problem, we are looking for the function of g in terms of the function f. Simply put, we just replace the variable x in the function g with f(-4).
Step 1, writing g(f(-4)):
[tex]g(f(-4))=-12(f(x))^2[/tex]
Great! Let us substitute f(x) with the given expression.
Step 2, substituting and simplifying:
[tex]\\g(f(-4))=-12(x^2-8x)^2\\g(f(-4))=-12((-4)^2-8*(-4))^2\\g(f(-4))=-12(16+32)^2\\g(f(-4))=-12*2304\\g(f(-4))=-27648[/tex]
g(f(-4) is [tex]\fbox{-27648}[/tex].
I hope this helps! Let me know if you have any questions :)
The weight, in pounds , of Mike's five pet dogs are listed below.What is the mean absolute deviation (MAD) of the weights?
16 , 23 , 27 , 41 , 53
Type the answer in the box.
______ pounds
Answer:
it would be 32
Step-by-step explanation:
you would add them all up then divide it by five
Answer: The answer is 32
You work no more than 12 hours a week at your two jobs. The first job pays you $8 an hour, and the second job pays you $10 an hour. You must earn at least $100 each week. Which graph represents this situation (let x represent hours at job 1 and y represent hours at job 2)?
Answer:
10 hours at job (1)
2 hours at job (2)
Step-by-step explanation:
As per the given information, one earns ($8) dollars at one of their jobs, and ($10) hours at the other. One must earn a total of ($100) dollars, and can work no more than (12) hours. Let (x) be the hours worked at job 1 and (y) be the hours worked at job two.
Since one can work no more than (12) hours, the sum of (x) and (y) must be (12), therefore the following equation can be formed;
[tex]x+y=12[/tex]
One earns ($8) dollars at one of their jobs and ($10) at the other, but one earns a total of (100) one can form an equation to represent this situation. Multiply the hours worked by the money earn per hour for each job, add up the result and set it equal to (100).
[tex]8x+10y=100[/tex]
Now set up these equations in a system;
[tex]\left \{ {{x+y=12} \atop {8x+10y=100}} \right.[/tex]
Use the process of elimination to solve this system. The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations in the system such that one of the variable coefficients is the additive inverse of the other. That way, when one adds the equation, the variable cancels, one can solve for the other variable then back solve to find the value of the first variable,
[tex]\left \{ {{x+y=12} \atop {8x+10y=100}} \right.[/tex]
Manipulate,
[tex]= \left \{ {{(*-8)(x+y=12)} \atop {8x+10y=100}} \right.\\\\[/tex]
Simplify,
[tex]= \left \{ {{-8x-8y=-96} \atop {8x+10y=100}} \right.\\[/tex]
Add,
[tex]=2y=4[/tex]
Inverse operations,
[tex]y=2[/tex]
Backsolve for (x), use equation one to achieve this,
[tex]x+y=12\\[/tex]
Substitute,
[tex]x+2=12[/tex]
Inverse operations,
[tex]x=10[/tex]
Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each notebook coats $3. Which of the following graph represents the possible combinations of pens and notebooks that she may purchase?
Answer:
3p + 8n, 12p + 2n, 9p+4n, 6p+6n
8 columns bar graph.
Step-by-step explanation:
$2 = pen
$3 = notebook
This could be written as a bar graph in multiples of $6.00 along y axes.
3 pens + 8 notebooks. Then 12 pens + 2 notebooks.
Then 9 pens + 4 notebooks . Then 6 pens + 6 notebooks
3p + 8n, 12p + 2n, 9p+4n, 6p + 6n
3p = $6
8n = $24
12p = $24
2n = $6
9p = $18
4n = $12
6p = $12
6n = $18
and so on...
How do I solve this and do the explanation of it
Answer:
180-66
114
hope it helps mark as brainlist
Write the formulae of area and volume of different solid shapes. Find out the variables and constants in them.
Answer:
Step-by-step explanation:
1 . Sphere :
[tex]Surface \ Area = 4\pi r^2\\\\ Volume = \frac{4}{3} \pi r^3[/tex]
Variable is ' r '
Others Constants.
2. Cone :
[tex]Surface \ Area = \p r^2 + \pi rs[/tex] [tex][ \ s = \sqrt { r^2 + h^2 } \ , r = base \ radius, h = height \ ][/tex]
[tex]Volume = \frac{1}{3} \pi r^2 h[/tex]
Variables are ' r ' and ' h '
Others constants.
3. Cuboid ( Rectangular Prism )
[tex]Surface \ Area = 2 ((l\times b) + ( b \times h) + ( l \times h)) \\\\Volume = l \times \ b \times \ h[/tex]
Variables : l , b , h
Constant is 2
4. Cylinder
[tex]Surface \ Area = 2 \pi r h + 2 \pi r^2 \\\\Volume = \pi r^2 h[/tex]
Variables : ' r ' and ' h '
Others constants..
Answer:
shapes. cuboid. cube. cylinder. prism. sphere. pyramid. rightcircularcone. volumeformula. l×w×h. v=a . 3. v=πr . 2. h. v=b×h. v=( 3. 4)πr . 3. v=( 3. 1)×h×b. v=( 3. 1)πr . 2. h. variables. l=length,w=width,h=height. a=side. r=radius,h=height. b=base,h=height. r=radiusofthesphere. b=areaofthebase,h=heightofthepyramid. r=radiusofthecircularbase,h=height
Step-by-step explanation:
Write the equation of the line in Point-Slope Form given the information below. Slope =−1/5 Y-Intercept =−3 Point-Slope Form:
Answer:
[tex]y - 0= \frac{ - 1}{5}( x + 15)[/tex]
Given the system of equations, what is the solution? 2x+y = -1 х- у = -5
Answer:
x=-2, y=3
Step-by-step explanation:
make it easy first, solve for x in the second equation: x= -5+y.
then sub that in for the other x: 2(-5+y)+y= -1
now combine like terms: -10+3y= -1
solve for y: 3y=9, y= 3
then replace y for your second equation: x-3= -5
solve for x= -5+3.... so then its -2
check by replacing all variables with your new solutions:
2(-2), which is -4+3 does equal -1
(-2) -3 does equal -5.
your answers are x=-2, y=3
Select the correct answer.
What is this expression in simplified form?
5v2.9v6
OA. 45v3
OB. 90
O C. 90v3
OD. 45V2
Answer:
C. 90√3
Step-by-step explanation:
5√2 . 9√6 = 45√12 = 45×2√3
= 90√3
The simplified form is 90√3.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Given expression is, 5√2×9√6
=5×9×√(2×6)
=45×√12
=45×2√3
=90√3
Hence, the simplified form is 90√3 .
To learn more on multiplication click:
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