Answer:
Please check the explanation.
Step-by-step explanation:
Given the sequence
[tex]40,\:10,\:\frac{5}{2},\:\frac{5}{8}[/tex]
A geometric sequence has a constant ratio 'r' and is defined by
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
Computing the ratios of all the adjacent terms
[tex]\frac{10}{40}=\frac{1}{4},\:\quad \frac{\frac{5}{2}}{10}=\frac{1}{4},\:\quad \frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}[/tex]
The ratio of all the adjacent terms is the same and equal to
[tex]r=\frac{1}{4}[/tex]
Thus, the given sequence is a geometric sequence.
As the first element of the sequence is
[tex]a_1=40[/tex]
Therefore, the nth term is calculated as
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
[tex]a_n=40\left(\frac{1}{4}\right)^{n-1}[/tex]
Put n = 5 to find the next term
[tex]a_5=40\left(\frac{1}{4}\right)^{5-1}[/tex]
[tex]a_5=40\cdot \frac{1}{4^4}[/tex]
[tex]a_5=\frac{40}{4^4}[/tex]
[tex]=\frac{2^3\cdot \:5}{2^8}[/tex]
[tex]a_5=\frac{5}{2^5}[/tex]
[tex]a_5=\frac{5}{32}[/tex]
now, Put n = 6 to find the 6th term
[tex]a_6=40\left(\frac{1}{4}\right)^{6-1}[/tex]
[tex]a_6=40\cdot \frac{1}{4^5}[/tex]
[tex]a_6=\frac{40}{4^5}[/tex]
[tex]=\frac{2^3\cdot \:5}{2^{10}}[/tex]
[tex]a_6=\frac{5}{2^7}[/tex]
[tex]a_6=\frac{5}{128}[/tex]
Thus, the next two terms of the sequence 40, 10, 5/2, 5/8... is:
[tex]a_5=\frac{5}{32}[/tex][tex]a_6=\frac{5}{128}[/tex]Question 3
What is the smallest solution to the equation 14-5x| = 1?
0.6
0-1.0
o 1.0
O 1.6
Answer:
0.06
Step-by-step explanation:
0x x it expand almost done ✅✅✅
What is the slope of the tangent line for the function f(x)=2x^2-5x+1 at the point (1,-2)
A. -1
B.-9
C. 1
D. 0
E.9
This is given by the limit
[tex]\displaystyle \lim_{x\to1} \frac{f(x) - f(1)}{x - 1} = \lim_{x\to1} \frac{(2x^2 - 5x+1) - (-2)}{x - 1} = \lim_{x\to1} \frac{2x^2 - 5x + 3}{x - 1}[/tex]
Observe that [tex]2x^2-5x+3=0[/tex] when [tex]x=1[/tex], and factorizing gives
[tex]2x^2 - 5x + 3 = (x - 1) (2x - 3)[/tex]
so that
[tex]\displaystyle \lim_{x\to1} \frac{f(x) - f(1)}{x - 1} = \lim_{x\to1} (2x-3) = 2\cdot1 - 3 = \boxed{-1}[/tex]
(A)
a number z is divided by four added to one in mathematical translate?
[tex]\displaystyle\\Answer:\ \frac{z}{4} +1[/tex]
Complete the equation.
(8 x 3) x 3 =
× (3 x 3)
Answer:
x=0
Step-by-step explanation:
Mr. Arcos is opening a new restaurant. His restaurant has 8 tables with places for 4 people at each table. It also has 4 tables with places for 6 people at each table.
Today he is buying plates for the restaurant. The plates he is buying come in sets of 6 plates. How many sets of plates does he need to buy?
In the given case, we can conclude Mr. Arcos needs to buy 10 sets of plates for his restaurant.
To find out how many sets of plates Mr. Arcos needs to buy, we first need to determine the total number of people his restaurant can accommodate.
There are 8 tables with places for 4 people each, so these tables can seat a total of 8 x 4 = 32 people.
Additionally, there are 4 tables with places for 6 people each, which can seat a total of 4 x 6 = 24 people.
Therefore, the restaurant can accommodate a total of 32 + 24 = 56 people.
Since the plates come in sets of 6, we divide the total number of people (56) by the number of people served by each set (6) to find out how many sets of plates Mr. Arcos needs to buy: 56 / 6 = 9.33 sets. Since plates cannot be bought in fractions, he will need to round up to the nearest whole number. Therefore, he will need to buy at least 10 sets of plates for his restaurant.
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Im struggling on finding the arewa on this and how to give my answer as one decimal can somebody help me please
Answer:
5.8
Step-by-step explanation:
Area = (h x b)/2
A = (2.5 x 4.6)/2 = 5.75 = 5.8
The figure above is the aerial view of a parking lot
where the rectangles represent the entrances and
the circles represent the exits. What is the total 401
number of ways a driver can enter and exit this
parking lot?
A. 4
B. 7
C. 10
D. 12
Answer:
12
Step-by-step explanation:
There are 4 entrances and 3 exits, and thus 4(3)=12.
The principal interest formula I = Prt can be used to find the interest earned on an initial amount of money, called the
principal, P, given an interest rate, r, and an amount of time over which interest is accrued, t. Solve I = Prt for P when
I = $5,480, r = .04 annual interest, and t 7 years. Round your answer to the nearest hundredth.
PLEASE HELP GUYS
Answer:
1885.714
Step-by-step explanation:
I = ptr
5280 = 7×0.4×p
p = 5280/2.8
p = 1885.7
Find the probability of a point chosen at random being in the shaded area of the diagram at the right
Answer:
1/2
Step-by-step explanation: because it is shaded or not
Absolute value of -3 is
Answer:
Step-by-step explanation:
The absolute value of -3 is 3.
Answer: 3
Step-by-step explanation:
In 2017, U.S. exports to Canada were $39.4 billion more than exports to Mexico. Together,
exports to these two countries totaled $525.4 billion. How much were exports to each
country.
The exports to each country are:
Exports to Mexico are $243 billion.Exports to Canada are $282.4What are equations?The equation is described as the state of being equal and is often represented as a math expression with equal values on either side, or it refers to a problem in which many factors must be considered. 2+2 = 3+1 is an example of an equation.So,
let the exports to Mexico be 'x'.
Exports to Canada will be x + 39.4.
Given:
U.S. exports to Canada were $39.4 billion more than exports to Mexico. Together,Exports to these two countries totaled $525.4 billion.So, the equation becomes:
x + x + 39.4 = 525.42x + 39.4 = 525.42x = 525.4 - 39.42x = 486x = 243So, exports to Mexico are 243 billion.
Exports to Canada are 243 + 39.4 = 282.4
Therefore, the exports to each country are:
Exports to Mexico are $243 billion.Exports to Canada are $282.4Know more about equations here:
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Write the equation of the quadratic function given vertex V and
point P, which lies on the function. Write the equation in standard
form f(x) = ax2+bx+c.
V (1,-9)
P (0,-8)
The quadratic equation that passes through points (1, - 9) and (0, - 8) is y = x² - 2 · x - 8.
What is the quadratic equation that passes through two points?
Graphically speaking, quadratic equations are parabolas. The quadratic equation in vertex form is described by this formula:
y - k = C · (x - h)²
Where:
(h, k) - Vertex of the parabola.C - Vertex constant.If we know that (x, y) = (0, - 8) and (h, k) = (1, - 9), then the vertex constant is:
- 8 + 9 = C · (0 - 1)²
1 = C · (- 1)²
1 = C
C = 1
Then, the quadratic equation in vertex form is:
y + 9 = (x - 1)²
Whose standard form is:
y + 9 = x² - 2 · x + 1
y = x² - 2 · x - 8
The quadratic equation that passes through points (1, - 9) and (0, - 8) is y = x² - 2 · x - 8.
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A 24 oz bottle of a new soda costs $3.33. What is the unit rate, rounded to the nearest tenth of a cent?
Which of the following is the graph of y = |x-3l?
Answer:
You only show one answer A. Lucky for you it's the correct one.
Step-by-step explanation:
use the graph of the following function f(x) to find f(1)
From the graph of the function y = x - 1, it is found that f(1) = 0.
What is the missing information?This problem is incomplete, but researching it on a search engine, it gives us the graph of the function y = x - 1.
How to find the numeric value of a function given a graph?To find the numeric value of a function at x = a, we have to check the value of the horizontal axis when the vertical axis is of a.
For this problem, we want the numeric value at x = 1, hence, when the horizontal axis is of 1, the vertical axis is of 0, hence f(1) = 0.
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still trying to find help solving. Today is the last day, can someone help?
Answer:wow we have the same homework
Step-by-step explanation:
4²×3³×(-1)¹²² please solve this question tomorrow my exam of maths
The value of 4²×3³×(-1)¹²² is 432.
How to find the value of 4²×3³×(-1)¹²²?When a number is repeatedly multiplied by itself, the result is a power of that number.
A power of the original number would be produced if you multiplied a number by itself any number of times.
When a single number is added up several times, it is said to be multiplied.
given that 4²×3³×(-1)¹²²
now find the value of 4²×3³×(-1)¹²².
4² = 4 × 4
3³ = 3 × 3 × 3
(-1)¹²² = 1
then, multiply these numbers.16 X 27 X 1 = 432
Hence, the value of 4²×3³×(-1)¹²² is 432.
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help plsssssssssssssssssssssssssssssss
Answer:
The answer is D
28/48 simplified how do you simplify????????????????????
Answer: 14/24 or 7/12
Step-by-step explanation: keep on dividing 2 or just divide by 4
The table shows ordered pairs of the function y=8-2x. What is the value of y when x=8
Answer:
y = - 8
Step-by-step explanation:
substitute x = 8 into the equation
y = 8 - 2(8) = 8 - 16 = - 8
last question is How many people carried a tablet but not a cell
phone?
Answer:
No.1 is 89 No.2 is 11 No.3 is 60 and the last one is 29
solve for x 3x + 6y = 9
A certain plant grows 1 1/6 inches every week. How long will it take the plant to grow 6 1/6 inches?
It will take 6.14 weeks for the plant to grow the required length
The growth rate of the plant each week = 1 1/6 inches
Converting the mixed fraction into an improper fraction we multiply the whole number by the denominator and add the numerator to get the improper fraction, therefore
The growth rate of a plant in improper form = 7/6 inches
Required growth rate = 6 1/6 inches
The required growth rate in improper fraction = 43/6 inches
Number of weeks it will take the plant to grow the required length = Required length/Growth rate each week = (43/6)/(7/6)
= 43/7 weeks or 6.14 weeks
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21 The average person at rest takes approximately 16 breaths per minute. Approxir many breaths do they take in 70 years of 365 days each? Use a calculator. Write in exponential notation using powers of 10.
A person will take 5.88672 × [tex]10^{8}[/tex] breaths in 70 years.
Here, we are given that on average a person at rest takes approximately 16 breaths per minute.
1 hour = 60 minutes
Thus, in 1 hour a person will take-
60 × 16
= 960 breaths
Now, 1 day = 24 hours
Thus, in 1 day, a person will take-
24 × 960
= 23,040 breaths
Further, 1 year = 365 days
Thus, in 1 year, a person will take-
23,040 × 365
= 8,409,600 breaths
In 70 years, a person will take-
8,409,600 × 70
= 588,672,000 breaths
We can express this in exponential notation as-
5.88672 × [tex]10^{8}[/tex]
Thus, a person will take 5.88672 × [tex]10^{8}[/tex] breaths in 70 years.
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Elizabeth has 4 boxes of 100 toys and 3 toys that aren't in boxes. How many toys does she
have?
Answer:
Elizabeth has 403 toys.
Step-by-step explanation:
The main goal is to figure out how many toys Elizabeth has. So she has 4 boxes and each box has 100 toys. If she has 4 boxes of 100 it mean she have 400 toys but that's not the final answer. she also has 3 toys not in the boxes so we have to add that as well. So if we add 3 toys to the 400 toys we'd get a total of 403. Therefore Elizabeth has 403 toys and that would be our final answer.
I hope this helps, have a blessed day! :D
5(g + 8) - 7 = 117 - g
Answer: g=14
Step-by-step explanation:
5(g + 8) - 7 = 117 - g
5g+40-7=117-g
5g+33=117-g
6g+33=117
6g=84
g=14
[tex]5(g + 8) - 7 = 117 - g[/tex]
[tex]5g + 5 \cdot 8 -7 = 117 -g\\[/tex]
[tex]5g + 40 -7 = 117 -g[/tex]
[tex]6g = 117 - 40 + 7[/tex]
[tex]6g = 84[/tex]
[tex]g = 94 : 6[/tex]
[tex]g = 14[/tex]
Suppose you are heading to the
beach with a friend. The beach is 80
miles from your house and the drive
takes about 1 hour and 30 minutes.
Your friend's house is 64 miles from
the beach. Use direct variation to
determine how long it will take to
drive to the beach if you leave from
your friend's house.
The time it would take to drive to the beach if you leave from the friend's house is 1 hour 12 minutes
Calculating timeFrom the question, we are to calculate how long it would take to drive to the beach if you leave from your friend's house
From the given information,
The beach is 80 miles from your house and the drive takes about 1 hour 30 minutes
Distance, d, varies directly with time, t.
d ∝ t
d = vt
Where v is the proportionality constant.
Now, we will find v
d = 80 miles
t = 1.5 hours = 3/2 hours
Thus,
80 = (3/2)v
v = (2 × 80)/3
v = 160/3 miles/hour
Now, we will determine t when d is 64 miles
d = vt
64 = 160/3 × t
t = (64 × 3)/160
t = 192/160 hours
t = 6/5 hours
t = 1 hour 12 minutes
Hence, the time it would take to drive to the beach if you leave from the friend's house is 1 hour 12 minutes
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branlyueer099799893
3 minutes ago
Mathematics
College
ANSWER RIGHT AWAY PLEASE!
question one: simply the exponents. (show your work)
- 21^0 = ?
- (2/3)^-2 = ?
question two: Solve the problem. (leave your answer as a base number with an exponent and show your work)
- 4^6 / 4^2 = ?
question three: Convert the number into numerical form. (show your work)
- 8.723 x 10^-10 = ?
question four: Solve the problem. (leave your answer in scientific notion and show your work)
- 5.1 x 10^8 - 2.3 x 10^3 = ?
- 6 x 10^5 x 1.1 x 10^7 = ?
PLEASE ANSWER I WILL GIVE 100 POINTS TO ANYONE WHO ANSWERS AND MARK BRAINLIEST AT LEAST ANSWER THE ONES YOU KNOW
Determine the equation for the given line in slope-intercept form.
y=-5/3x-1
y=5/3x+1
y=3/5x+1
y=-3/5x-1
Answer:
The last answer is correct
y = [tex]\frac{-3}{5 }[/tex] x - 1
Step-by-step explanation:
You can see that the graph crosses the y axis at (0,-1). So, the graph crosses the y axis at -1. Count how much you go down and the to right from the point on the left to the point on the right. You go down 3 and left 5. This is a negative slope of [tex]\frac{-3}{5}[/tex].
y = mx + b Put in the slope for m and the y-intercept by b
y = [tex]\frac{-3}{5}[/tex]x = 1
Which of the following statements models deductive reasoning?
I own a mean cat. My friend Lisa owns a mean cat. Therefore, all cats are mean.
People who follow a vegan diet do not eat steak. Mindy follows a vegan diet. Therefore, Mindy does not eat steak.
There has been a hurricane in Florida every August for the past two years. Therefore, there will be a hurricane in Florida in August this year.
Every test in Mr. Johnson’s class this year has been easy. Therefore the test in Mr. Johnson’s class today will be easy.
Answer:
B.
Step-by-step explanation:
Vegans by definition do not eat any products containing the meat of an animal. Therefore if Mindy truly follows a vegan diet, she would not eat steak.
Answer:People who follow a vegan diet do not eat steak. Mindy follows a vegan diet. Therefore, Mindy does not eat steak.
Step-by-step explanation:
Because deductive reasoning is when you make an inference about something. In option 2 they are making an inference that if Mindy does not eat steak she is a vegetarian. They have come to that conclusion by inferring she is a vegetarian because she does not eat steak.