Which of the following sequences is an arithmetic sequence? Select all correct answers.
Select all that apply:
1,2,3,4,5,6,…
5,0,−5,−10,−5,0,…
−4,−6,−8,−10,−8,−6,…
3,0,−3,−6,−9,−12,…
6,5,4,3,2,1,…
Answer:
1st, 4th and 5th are in arithmetic sequence.
Answer:
a) 1,2,3,4,5,6............
d) 3,0, -3 ,-6,-9,-12.............
e) 6,5,4,3,2,1...........
are arithmetic sequence
Step-by-step explanation:
Arithmetic sequence is series of numbers that the difference of consecutive terms is constant
a) 1, 2 , 3 , 4 , 5 , 6...........
Common difference = 1
d) 3,0, -3 ,-6,-9,-12.............
Common difference = second term - first term
= 0 - 3 = -3
e) 6,5,4,3,2,1...........
Common difference = 5 - 6 = - 1
If you buy a motorcycle for $12,500 in 2015 and it depreciates (shrinks) in value by 15.5% every year, how much will it be worth in 2020?
A) $10,562.50
B) $1718.33
C) $6732.90
D) $5385.10
Answer:
D) $5385.10
Step-by-step explanation:
Exponential equation of decay:
The exponential equation for the decay of an amount after t years is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
If you buy a motorcycle for $12,500 in 2015 and it depreciates (shrinks) in value by 15.5% every year
This means that [tex]A(0) = 12500, r = 0.155[/tex]
So
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]A(t) = 12500(1-0.155)^t[/tex]
[tex]A(t) = 12500(0.845)^t[/tex]
How much will it be worth in 2020?
2020 is 2020 - 2015 = 5 years after 2015, so this is A(5). So
[tex]A(5) = 12500(0.845)^5 = 5385.10[/tex]
The correct answer is given by option D.
On the day of a child's birth, a parent deposits $30,000 in a trust fund that pays 3% interest, compounded continuously. Determine the balance in this account on the child's 24th birthday.
Answer:
3/100 × 30000 is the answer to your question.
Can you help thanks!
Answer:
y = 3x + 41
Step-by-step explanation:
First, lets set up the slope-intercept form equation, that is...
y = mx + b
m = slope
b = y-intercept
because the y-intercept is a positive value, it cannot be y=-3x-41 or y= 3x-41
now, we know that b = 41, but what is the slope?
Well, here are tips for doing slope
if the line is gradually increasing upwards, then it is a positive slope
if the line is gradually decreasing downwards, then it is a negative slope
because the line in the picture is positive, this proves y=-3x+41 wrong, therefore making y = 3x + 41 the only correct answer
Therefore, your correct answer is y = 3x + 41
You deposit
$
6500
into an account paying
8
%
annual interest compounded monthly. How much money will be in the account after
7
years?
Use the formula A = p(1 + r/n)^(nt).
Here is the set up:
A = 6500[1 + (0.08/4)]^(4•7)
Solve for A.
You purchase a new car for $24,000. If you obtain a 5 year bank loan at 2.75% compounded monthly, what is your monthly loan payment?
Answer:
The monthly loan payment is of $458.88.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Amount owed after 5 years:
Loan of 24000 means that [tex]P = 24000[/tex]
5 years means that [tex]t = 5[/tex]
Interest rate of 2.75% means that [tex]r = 0.0275[/tex]
Compounded monthly means that [tex]n = 12[/tex]
The amount is A(5). So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(5) = 24000(1 + \frac{0.0275}{12})^{12*5}[/tex]
[tex]A(5) = 27533[/tex]
What is your monthly loan payment?
$27,533 in 5 years = 5*12 = 60 months. So
27533/60 = 458.88
The monthly loan payment is of $458.88.
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
-8x+8=-6x+20 and x= -6
Step-by-step explanation:
Reason to equation:
This image shows alternative interior angles.
Alternative interior angles are congruent to each other.
How to find x:
-8x+8=-6x+20
We subtract 8 from both sides
-8x=-6x+12
We add 6x to both sides
-2x=12
We divided -2 from both sides
-2x/-2x = 12/2
Leaving us with x=-6
the landscaper uses 4 bags of topsoil to cover 3/8 of the garden. how many bags of topsoil will he need to buy to cover the whole garden
What value of n makes the equation true ? Show your work.
Answer:
n = 6
Step-by-step explanation:
Given the expression
[tex](\frac{19^8}{7^n})^4 = (\frac{19^4}{7^3})^8 \\\frac{19^{32}}{7^{4n}} = \frac{19^{32}}{7^{24}}\\\frac{1}{7^{4n}} = \frac{1}{7^{24}} \\Reciprocate \ both \ sides\\7^{4n} = 7^{24}\\4n = 24\\n = \frac{24}{4}\\n = 6[/tex]
Hence the value of n is 6
Transformations of Functions (A1)
The graph of y=f(x) is the solid black graph below. Which function represents the dotted graph?
A: y=−f(x+1)
B: y=−f(x−1)
C: y=−f(x)+1
D: y=−f(x)−1
Answer:
i think the answer is B, good luck
Answer:
c i do believe good luck with the answer
Sue needs 1/3 of a cup of flour for 1/4 of a batch of cookies. How much flour does she need for a whole batch of cookies?
***WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER***
Answer:
1 1/3 cups of flour
Step-by-step explanation:
1/3 x 4 = 4/3 = 1 1/3
Hope that helps! :)
-Aphrodite
I'll try to give Brainlyest please help!!
Answer:
D. 2r = 16
Step-by-step explanation:
r/2 = 16, r=32
8= r/8, r=64
4r=16, r=4
2r=16
/2 /2
r=8
Given z, find lzl.
Z = 10i
IzI = [?]
Answer: it's 10, not 210.
please help me i will mark brainliest! :D
Answer:
19.50
Step-by-step explanation:
If the scarf is 25% off, you have to pay 100% -25% = 75%
26 *75%
26 *.75
19.5
Julie had 3 1/3 cups of flour. A brownie recipe called for 2 2/3 cups of flour. If Julie made one batch of brownies, how much flour did she have left over?
Answer:
2/3
Step-by-step explanation:
3 1/3-2 2/3= 2/3
Please tell me please
Answer:
C
Step-by-step explanation:
It is one whole shaded diagram (100%) and half of the diagram (50%), making 150%
Answer:
a or c
Step-by-step explanation:
Igor, whose eye height is 4.5 ft., wishes to find the height of an oak tree out in front of his castle. He places a mirror on the ground between himself and the tree. He is now 5.5 feet away from the center of the mirror and the mirrors is 70 feet from the tree. What is the height of the oak tree in front of Igor´s castle?
Please this is due in 15 minutes
Please help will give brainliest!
Answer:
Yes, Yes, No, Yes.
Step-by-step explanation:
2/5 as a decimal = 0.4
4 ÷ 0.4 = 10
1 is correct.
2 x 10 = 20
2 is correct.
6 x 10 = 60
3 is incorrect.
10 ÷ 2 = 5
4 is correct.
Solve for x and y:
Ty– 5x = 45
x = 8 - 2y
O x = 5, y = 10
O x = 5, y = -2
x = -2, y = 5
O x = 4, y = 2
Answer:
x = -2
y = 5
Step-by-step explanation:
7y - 5x = 45 -------------------(I)
x = 8 - 2y -----------------------(II)
Substitute x = 8 - 2y in equation (II)
7y - 5(8-2y) = 45
7y + 8 *(-5) - 2y*(-5) = 45
7y - 40 + 10y = 45
17y - 40 = 45
17y = 45 + 40
17y = 85
y = 85/17
y = 5
Plugin y = 5 in equation (II)
x = 8 - 2*5
x = 8 - 10
x = -2
Need help only on 9 and11 thank you don’t know really how to do
غف8ىرف4-
ف8غ4ى0ض8رص90
If you know the area of a circle, how can you find its radius? Use the drop-down menus to explain your answer. Choose.. the area by n, and then take the Choose... of the answer. Choose
1 choose: multiply or Divide
2 Choose: square or square not
Answer:
This is the answer!!!
Step-by-step explanation:
The sum of −7 times a number and 8 times the sum of the number and 1 is the same as the number minus 7.
Answer:
n has no value.
There is no solution to this equation
Step-by-step explanation:
let n be the number
In pieces:
sum of the number and 1: (n + 1)
8 times the sum: 8(n + 1)
-7 times a number: -7n
sum of -7 times and...: -7n + 8(n + 1)
number minus 7: n - 7
the same as: =
All together:
-7n + 8(n + 1) = n - 7
-7n + 8(n+1)=n-7
-7n + 8n+8=n-7
0=-15
What is the difference/ ratio of the numbers 6.25, 25, 100, 400,
The function f is defined by f(x) = 5x2 + 2x + 5. What is the value of f(2)?
Answer:
[tex]f(x) = 5 {x}^{2} + 2x + 5 \\ when \: x = 2 \\ f(2) = 5( {2})^{2} + 2(2) + 5 \\f(2) = 29[/tex]
The following 5 questions are based on this information: An economist claims that average weekly food expenditure of households in City 1 is more than that of households in City 2. She surveys 35 households in City 1 and obtains an average weekly food expenditure of $164. A sample of 30 households in City 2 yields an average weekly expenditure of $159. Historical data reveals that the population standard deviation for City 1 and City 2 are $12.50 and $9.25, respectively.
Required:
At the 5% significance level, is the economist claim supported by the data?
Answer:
>> Null hypothesis; H0: μ1 - μ2 ≥ 0
Null hypothesis; Ha: μ1 - μ2 < 0
>> z = 1.85
>> p-value = 0.03
>> there is evidence sufficient to reject the claim that average weekly food expenditure of households in City 1 is more than that of households in City 2.
The economist claim is not supported by data.
Step-by-step explanation:
We are given;
Sample mean of city 1; x1¯ = 164
Sample mean of city 2; x2¯ = 159
Sample size of city 1; n1 = 35
Sample size of city 2; n2 = 30
Standard deviation of city 1; σ1 = 12.5
Standard deviation of city 2; σ2 = 9.25
Let's define the hypotheses;
Null hypothesis; H0: μ1 - μ2 ≥ 0
Null hypothesis; Ha: μ1 - μ2 < 0
Test statistic which is the z-score Formula between 2 mean is;
z = ((x1¯ - x2¯) - 0)/√((σ1)²/n1) + ((σ2)²/n2))
z = (164 - 159 - 0)/√((12.5²/35) + (9.25²/30))
z = 5/2.705
z = 1.85
From online p-value from z-score calculator attached, using z = 1.85, one tailed, significance value of 0.05, we have;
p-value = 0.03
The p-value is less than the significance value, and so we will reject the null hypothesis and conclude that there is evidence sufficient to reject the claim that average weekly food expenditure of households in City 1 is more than that of households in City 2.
Let f(x)=3(12)x+1. Which is equal to f(1)?
Answer:
just substitute the value of x as 1
f(x)=3(12)x+1
f(1)=3(12)(1)+1
f(1)=3(12)(1)+1
f(1)=36+1
f(1)=37
Hw
EXERCISE solve the following problems
? Rhonda had to draw the lines of symmetry in the parallelogram below
She drew this:
Was she correct?
Yes No
shape
Explain your answer
How many lines of symmetry are
in the 5-pointed star to the right?
raw the lines of symmetry
what is 20 x 3-4 + 80 / 988 + 444444 x 343
7-3 Multiplying Binomials
Write a polynomial in standard form for the volume of the rectangular prism shown.
5x+1
3x - 4
X+2
Answer:
Step-by-step explanation:
Use FOIL method.First multiply (5x + 1) and (3x - 4). Then multiply (15x² - 17x - 4) by (x +2)
Volume of the rectangular prism = length *width * height
= (5x + 1) (3x -4)(x +2)
= [ 5x*3x + 5x*(-4) + 1*3x + 1*(-4) ] (x + 2)
= [15x² - 20x + 3x - 4] (x +2) {Combine like terms}
= [15x² - 17x - 4] (x + 2)
=[15x² -17x - 4]*(x) + [15x² - 17x -4]*2
= [15x²*x - 17x*x - 4*x ]+ 15x²*2 - 17x *2 - 4*2
= 15x³ - 17x² - 4x + 30x² - 34x - 8
= 15x³ - 17x² + 30x² - 4x - 34x - 8 {Combine like terms}
= 15x³ + 13x² - 38x - 8
Ken flips a coin and draws a card. Is this a independent or dependent event?