==============================================
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.
Which system of equations is represented by the matrix below?
54 5-167
7 -4 23
O A. x+ 5y = -16
x - 4y = 23
OB. 4x + 5y = -16
7x - 4y = 23
C. 4x + 5y = -16
7x + 4y = 23
9514 1404 393
Answer:
B
Step-by-step explanation:
In order for the matrix to represent the equations, the coefficients in the equations need to match the terms in the matrix. That is only the case for choice B.
__
Details are important in math.
The slope of a line is -, and the y-intercept is 10/3. What is the equation of the line written in general form?
Consider random samples of size 86 drawn from population A with proportion 0.43 and random samples of size 60 drawn from population B with proportion 0.15
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
(b) Are the sample sizes large enough for the Central Limit Theorem toa
Yes or No?
Answer:
a) The standard error is s = 0.071.
b) Yes, as both sample sizes are above 30.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Samples of size 86 drawn from population A with proportion 0.43
This means that [tex]n = 86, p = 0.43[/tex]. So:
[tex]s_A = \sqrt{\frac{0.43*0.57}{86}} = 0.0534[/tex]
Samples of size 60 drawn from population B with proportion 0.15:
This means that [tex]n = 60, p = 0.15[/tex]. So:
[tex]s_B = \sqrt{\frac{0.15*0.85}{60}} = 0.0461[/tex]
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
This is:
[tex]s = \sqrt{s_A^2 + s_B^2}[/tex]
[tex]s = \sqrt{(0.0534)^2 + (0.0461)^2}[/tex]
[tex]s = 0.071[/tex]
The standard error is s = 0.071.
(b) Are the sample sizes large enough for the Central Limit Theorem. Yes or No?
Yes, as both sample sizes are above 30.
eople
Find the perimeter and area of the figure pictured below.
odules
fice 365
3.7 m
om
11.4 m
ades
2.3 m
9.2 m
Q
Perimeter
m
Area -
m2
Answer:
Perimeter: 41.2 m
Area: 54.83 m^2
Step-by-step explanation:
REFER TO THE IMAGE ATTACHED AS A
GUIDE.
PERIMETER:
(ADD UP ALL THE LENGTHS OF EACH SIDE)
Must be all 6 sides (see image, I solved for the two missing lengths)
3.7 + 9.1 + 11.4 + 9.2 + 2.3 + 5.5 = 41.2
perimeter is 41.2 m
AREA:
(See image again)
Shape is divided into two rectangles:
Top rectangle area: 11.4 x 3.7 = 42.18 m^2
Bottom triangle area: 5.5 x 2.3 = 12.65 m^2
ADD:
42.18 m^2 + 12.65 m^2 = 54.83 m^2
The area of the whole figure is 54.83 m^2
HOPE THIS HELPS
Which statement proves the given triangles are similar?
Answer:
it's the second one
Step-by-step explanation:
Identify the domain of the function shown in the graph. Need heal ASAP
Answer:
D
Step-by-step explanation:
the domain of the function is the boundaries in the X condition. using the graph we see X starts at 2 and ends at 7 so the domain is
[tex]2 \leqslant x \leqslant 7[/tex]
Which of the following phrases would represent this expression?
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3
Answer:
the quotient of x and 3
Step-by-step explanation:
x divided by 3
division answers are called quotients
Answer:
Step-by-step explanation:
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3 is correct. We are dividing x into 3, not 3 into x.
How do you find the amplitude, period, and shift for f(x)=−4cos(3x−π)+1?
Answer:
(a) Amplitude = 4
(b) [tex]T = \frac{2\pi}{3}[/tex] --- Period
(c)
[tex]C = \frac{\pi}{3}[/tex] --- phase shift
[tex]D =1[/tex] --- vertical shift
Step-by-step explanation:
Given
[tex]f(x) = -4\cos(3x - \pi) + 1[/tex]
Rewrite the function as:
[tex]f(x) = -4\cos(3(x - \frac{\pi}{3}) + 1[/tex]
Solving (a): The amplitude
A cosine function is represented as:
[tex]f(x) = A\cos[B(x - C)] + D[/tex]
Where:
[tex]|A| \to Amplitude[/tex]
So, in this equation (by comparison):
[tex]|A| = |-4|[/tex]
[tex]|A| = 4[/tex]
The amplitude is 4
Solving (b): The period (T)
This is calculated as:
[tex]T = \frac{2\pi}{B}[/tex]
By comparison:
[tex]B =3[/tex]
So:
[tex]T = \frac{2\pi}{3}[/tex]
Solving (c): The shift
The phase shift is C
The vertical shift is D
By comparison:
[tex]C = \frac{\pi}{3}[/tex] --- phase shift
[tex]D =1[/tex] --- vertical shift
ASAP PLEASE!!The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed. Find the probability P(T=1). write your answer as a fraction.
Answer:
[tex]P(T = 1) = \frac{3}{8}[/tex]
Step-by-step explanation:
The table, along with the relative frequency chart, state that the probabilities are:
[tex]P(T = 0) = \frac{1}{8}[/tex]
[tex]P(T = 1) = \frac{3}{8}[/tex]
[tex]P(T = 2) = \frac{3}{8}[/tex]
[tex]P(T = 3) = \frac{1}{8}[/tex]
Find the probability P(T=1)
As given by the table, and by the relative frequency chart, [tex]P(T = 1) = \frac{3}{8}[/tex]
PLEASE HELP
If the absolute value represents the distance from zero, can we have a negative distance?
Answer:
No, you cannot have a negative distance.
Step-by-step explanation:
No, you cannot have a negative distance.
Let's say you were asked for the absolute value of -4. How many units is -4 away from 0? The answer would be 4. There is no negative distance from 0.
Hope this helps, please mark brainliest! :)
Quick !
The perimeter of the rectangle below is 118 units. Find the length of side AD.
Answer:
24
Step-by-step explanation:
the perimeter is all sides added up
therefore to solve for "z"
3z + 3z + 4z + 3 + 4z + 3 = 118
simplify
14z + 6 = 118
isolate z by first subtracting 6 from both sides and then dividing by 14 for both sides
z=8
plug z into side CB as AD and CB are congruent
3(8)
=24
emma can read 4 pages of a book in 8 minutes how many pages can she read per minute if she still had it 24 pages how many pages are there in the book
Answer:
Emma can read 30 pages per minute
Number of book pages 28
Step-by-step explanation:
Use the distributive property to write the next step in simplifying th
numerical expression
7(2 + 7)
A. 7• 2+7•7
B. 7• 2+7
C. (7+2) • (7 + 7)
D. 7+2 • 7+ 7
Answer:
A)
Step-by-step explanation:
PLEASE HELP ME
WITH STEPS
Answer:
,(i) answer is 203,918
(ii)answer is227,306.36
What is the HFC of the following: 4 (x2-x+1) and 28 (x3+1)?
Your Answer is in the above image.
Plz help 1+1 PLZ SEND ANSWER
Answer:
2
Step-by-step explanation:
Find the value of each shape so that they will add up to give you the specified sums in each row and each column.
How does this solving problem relate to system of equations?
Answer:
Step-by-step explanation:
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)
Which expression is equivalent to -6(-⅔+2x)?
O-4-12x
O-4+ 2x
O 4-12x
O 4+ 12x
Answer:
4-12x
Step-by-step explanation:
opening the brackets;
(-6×-2/3)- 12x
-2×-2 -12x
4-12x
Answer:
4 - 12x
Step-by-step explanation:
We can find an equivalent expression by distributing
-6(-⅔+2x)
Distribute by multiplying -6 times what's inside of the parenthesis ( -2/3 and 2x )
-6 * -⅔ = 4
-6 * 2x = -12x
We would be left with 4 - 12x
a binomial distribution
has 30% rate of SUCCESS.
there are 6 triats. what
is probability that there
will be exactly 2 Successes
Answer:
0.324
Step-by-step explanation:
Given that :
Success rate = 30%
p = 30% = 0.3
q = 1 - p = 1 - 0.3 = 0.7
Number of trials, n = 6
Probability of having exactly 2 successes ; x = 2
P(x = 2)
Usibgbtge binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 2) = 6C2 * 0.3^2 * 0.7^4
P(x = 2) = 15 * 0.3^2 * 0.7^4
P(x = 2). = 0.324135
P(x = 2) = 0.324
Question attached below
Answer:
s(8) = 1162
Step-by-step explanation:
We are told that the acceleration is;
a(t) = 18t + 16
Now, acceleration is the first derivative of velocity. Thus, we will integrate the acceleration function to get the velocity function.
v(t) = ∫a(t) = ∫(18t + 16)
v(t) = 9t² + 16t + c
We are told that at t = 0, v(0) = 16
Thus;
9(0)² + 16(0) + c = 16
c = 16
Thus;
v(t) = 9t² + 16t + 16
Also, the velocity is the first derivative of distance. Thus;
S = ∫v(t) = ∫9t² + 16t + 16
S = 3t³ + 8t² + 16t + c
At t = 0, s(t) = 10. Thus;
10 = 3(0³) + 8(0²) + 16(0) + c
c = 10
Thus;
s(t) = 3t³ + 8t² + 16t + 10
At t = 8;
s(8) = 3(8³) + 8(8²) + 16(8) + 10
s(8) = 1162
which elements in the following set are integers -8,3/4,-0.18,0,0.16,5,-2/7,6
Answer:
345
Step-by-step explanation:
plzzzzzzzzzzzzzzzzz help meeeeeeeeeeeeeeeeeee
i do anything just help
1.) Create a table of x and y values that represents a proportional relationship.
a) Explain how you know the relationship is proportional.
b) What equation models the values in the table?
2) Create a table of x and y values that represents a linear, non-proportional relationship.
a) Explain how you know the relationship is non-proportional.
b) What equation models the values in the table?
Answer:
Table could be first x = 2, y = 4, then x = 4, y = 8. It is proportional because both (x,y) values equal 1/2. The equation is x = 1/2y. Last, the table could be the same, or you could do first, x = 6, y = 12, then x = 12, y = 24, because they still equal 1/2.
Step-by-step explanation:
The area of a triangular sign is 6x² + 24x What is the measure of the base? (View attachment)
Answer:
[tex]2x + 8[/tex]
Step-by-step explanation:
Area of triangle equal
[tex] \frac{b \times h}{2} = a[/tex]
where b is the base and h is the height.
Plug in what we know.
[tex] \frac{b \times 6x}{2} = 6 {x}^{2} + 24x[/tex]
Multiply 2 by both sides.
[tex]b \times 6x = 2(6 {x}^{2} + 24x)[/tex]
Divide 6x by both sides.
[tex]b = \frac{12 {x}^{2} + 48x }{6x} = 2x + 8[/tex]
A gardener wants to plant 875 roses in the garden. Can he plant them in rows having 7 plants each without any plants left? Justify your answer. *
Answer:
Yes
Step-by-step explanation:
875 roses / 7 plants per row
875 / 7 = 125 rows, which is a whole number, meaning nothing is left over
9. Use the Distributive Property to simplify (-5 - c)(-1).
a 5 - C
b C
c-5 + c
d 5 + C
Answer:
D. 5 + c
Step-by-step explanation:
( - 5 - c ) ( - 1 )
use distributive property ; to multiply -5 and - c by -1.
= -1 × - 5 - ( +1 ) × - c= 5 + cFind all derivatives of y^n of the function y=√x+5
Hello,
As somebody has distroyed my question, (may be he have not understood ?)
i will reply to y=(√x)+5
[tex]\displaystyle \boxed{\dfrac{d^n y}{dx^n} =(-1)^n*n!! *\dfrac{1}{2^n} *x^{-\frac{2n+1}{2} }\\}\\y'=\dfrac{1}{2} *x^{-\frac{1}{2}} \\\\y''=-\dfrac{1}{4} *x^{-\frac{3}{2}} \\...\\[/tex]
help me please if you can't don't touch it
Answer:
option B : 31.4 cm
Step-by-step explanation:
Given radius , r = 5cm
Circumference = [tex]2 \pi r[/tex]
= 2 x 3.14 x 5
=10 x 3.14
= 31.4 cm
Answer:
b. 31.4
Step-by-step explanation:
The radius of the circle can be plugged into C=(pi)2r. So 5x2= 10 and 10x(pi)= 31.4
Given m n, find the value of X.
Answer:
x = 62
Step-by-step explanation:
62 and x are alternate exterior angles and alternate exterior angles are equal when the lines are parallel
Which of the following phrases are expressions?
Answer:
C ,D , E just follow it . thank me later if its right
Answer:
E
Step-by-step explanation:
(10+7)(50+1)
=17×51
=867