Answer:
1. Add 3
2. Multiply 4
Step-by-step explanation:
Given
[tex](1)\ 1, 4, 7, 10, 13[/tex]
[tex](2)\ 2, 8, 32, 128, 512[/tex]
Required
The rule
[tex](1)\ 1, 4, 7, 10, 13[/tex]
This is a linear function because successive terms have a common difference
The common difference between each term is:
[tex]d = 4 - 1 = 3[/tex]
[tex]d = 7 - 4 = 3[/tex]
[tex]d = 10 - 7 = 3[/tex]
[tex]d = 13 - 10 = 3[/tex]
The above shows that 3 is [tex]added\ to\ each\ term[/tex] to get the next term.
Hence, the rule is: Add 3
[tex](2)\ 2, 8, 32, 128, 512[/tex]
This is a geometric function because successive terms have a common ratio
The common ratio between each term is:
[tex]r = 8/2 = 4[/tex]
[tex]r = 32/8 = 4[/tex]
[tex]r = 128/32 = 4[/tex]
[tex]r = 512/128 = 4[/tex]
The above shows that 4 [tex]is\ multiplied\ to\ each\ term[/tex] to get the next term.
Hence, the rule is: Multiply 4
find the nth term of the sequence 7,25,51,85,127
Let a (n) denote the n-th term of the given sequence.
Check the forward differences, and denote the n-th difference by b (n). That is,
b (n) = a (n + 1) - a (n)
These so-called first differences are
b (1) = a (2) - a (1) = 25 - 7 = 18
b (2) = a (3) - a (2) = 51 - 25 = 26
b (3) = a (4) - a (3) = 85 - 51 = 34
b (4) = a (5) - a (4) = 127 - 85 = 42
Now consider this sequence of differences,
18, 26, 34, 42, …
and notice that the difference between consecutive terms in this sequence b is 8:
26 - 18 = 8
34 - 26 = 8
42 - 34 = 8
and so on. This means b is an arithmetic sequence, and in particular follows the rule
b (n) = 18 + 8 (n - 1) = 8n + 10
for n ≥ 1.
So we have
a (n + 1) - a (n) = 8n + 10
or, replacing n + 1 with n,
a (n) = a (n - 1) + 8 (n - 1) + 10
a (n) = a (n - 1) + 8n + 2
We can solve for a (n) by iteratively substituting:
a (n) = [a (n - 2) + 8 (n - 1) + 2] + 8n + 2
a (n) = a (n - 2) + 8 (n + (n - 1)) + 2×2
a (n) = [a (n - 3) + 8 (n - 2) + 2] + 8 (n + (n - 1)) + 2×2
a (n) = a (n - 3) + 8 (n + (n - 1) + (n - 2)) + 3×2
and so on. The pattern should be clear; we end up with
a (n) = a (1) + 8 (n + (n - 1) + … + 3 + 2) + (n - 1)×2
The middle group is the sum,
[tex]\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8[/tex]
so that
a (n) = a (1) + (4n ² + 4n - 8) + 2 (n - 1)
a (n) = 4n ² + 6n - 3
Please help: What is the area of this shape?
In a survey, 18 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a sample mean of $47 and sample standard deviation of $3. Construct a confidence interval at a 90% confidence level.
Answer:
The 90% confidence interval for the mean amount spent on the children's birthday gift is between $45.77 and $48.23.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7396
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.7396\frac{3}{\sqrt{18}} = 1.23[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 47 - 1.23 = $45.77
The upper end of the interval is the sample mean added to M. So it is 47 + 1.23 = $48.23
The 90% confidence interval for the mean amount spent on the children's birthday gift is between $45.77 and $48.23.
Help please?
I’m struggling on this the teacher didn’t teach us this
Answer:
58°
Step-by-step explanation:
A flat angle equals 180°, so we can simply subtract the given angle from the total, 180.
180 - 122 = 58
So, ∠CDE = 58°.
Good luck n.n
Answer:
58°
Step-by-step explanation:
∠AEC =∠AED+∠CED
So,
∠AEC=180°
∠AED=122°
∠CED=?
∠AEC =∠AED+∠CED
180°=122°+∠CED
∠CED=180°-122°
∠CED=58°
What is the answer please help me no links I will report you
Answer:
Step-by-step explanation:
36 - 4
Step-by-step explanation:
(6x - 2)(6x + 2)
= (6x)(6x) + (6x)(-2) + (2)(6x) + (-2)(2)
= 36 - 12x + 12x - 4
= 36 - 4
what is the conjugation ending of er verb
Answer:
je -parle
tu - parles
il/elle/on - parle
nous - parlons
vous - parlez
ils/elles - parlent
Answer:
Verbs with infinitives ending in -er form a second group of regular verbs in Spanish, often called second conjugation verbs.
Step-by-step explanation:
To conjugate these verbs in the present tense, drop the -er from the infinitive and add the second conjugation present tense endings: -o, -es, -e, -emos, -en.
Which of these describes two thirds?
Answer:
2/3
two thirds
0.666666666
Step-by-step explanation:
please mark this answer as brainliest
The Spanish club wants to raise $325.00 to attend a special program at
the Museum. The club decides to sell tacos at basketball games. The
tacos will sell for $1.50 for a small and $2.50 for a large. Write an
equation to relate the number of small and large tacos you must sell
to raise $325.00.
The value V (in dollars) of a milling machine depends on the number of hours x it is operated as
given by the formula V = 750,000 - 120x. After one year, the value of the milling machine is
between $450,000 and $480,000.
Which range for the hours the machine is operated does this correspond to?
Basically, you have to understand the logic of a function.
V = 750,000 - 120xIf I plug in a value into V that represents the value of a milling machine, if I simplify the equation, I will be able to find x, the corresponding time to the value of the milling machine.
Knowing this logic, we can plug in $450,000 and $480,000, and then we will have two x-values. Then we can just find the range of the x-values to find our answer! :)
Let's go.
V = 750,000 - 120x
Plugged in 450,000 for V so now we can simplify the equation and find out what is the corresponding x-value for this value at this certain time.
450,000 = 750,000 - 120x
-450,000 -450,000
0 = 750,000 - 120x
+120x on both sides to isolate x
120x = 300,000
x = 2500
So, our first x-value in the range is 6250 hours. Now, let's plug in the larger value to find out the other x-value in the range.
V = 750,000 - 120x
480,000 = 750,000 - 120x
-480,000 -480,000
0 = 270,000 - 120x
Add 120x on both sides to isolate x
120x = 270,000
x = 2250
So, we found 2250 and 2500. So, the range of hours it corresponds to is 2250-2500.
How did waterways provide Detroit with such a vital military position?
Answer:
Your source water comes from the Detroit River, situated within the Lake St. Clair, Clinton River, Detroit River, Rouge River and Ecorse River watersheds in the U.S., and parts of the Thames River, Little River, Turkey Creek and Sydenham watersheds in Canada.
Step-by-step explanation:
please mark this answer as brainliest
Arlie is on an airplane that has traveled 420 miles in 3/4 of an hour. At this rate, how far will the airplane travel in the next 1/2 hour?
[tex]16 \: 3 \: by \: 4[/tex]
evaluate the answer according to the law of exponents
Answer:
16 3/4=[16×4+3]/4=67/4 is your answer
You used 15.6 kWh to recharge an EV at a cost of 11.6 cents per kWh. How
much did you spend to recharge the car?
$180.96
$18.00
$1.36
$1.81
Answer:
1.81
Step-by-step explanation:
the reason is because many may think by using a calculator, and make a mistake by putting 15.6 x 11.6, and think "Oh its 180.96" but they forget that they are multiplying cents, but with money you round the nearest decimal to a cent, so they get 1.81
15.6 x 11.6 = 180.96
flip it and jump the 1 a single spot to the left. (1 80.96)
Now jump the decimal between the 1, and the 8. (1.8096)
Now round the thousandth and ten thousandth to remove the zero and make it one. (1.8096= 1.81)
And that's how you get 1.81
if i'm wrong I need to go back to 5th grade and learn my money and decimals semester.
Mrs. Galicia is creating a bunny farm. The farm starts with 300 bunnies and is growing at a rate of 15.25% per month. How many months will it take for the farm to double in size? *must solve using log/ln method* * DO NOT round/estimate during calculation steps* * Round your final answer, t, to 4-decimal places*
6.55 months? i dont know for sure but i tried
Essentials of University Mathematics
Example 3.
Find the length of the vector PQ from the point P(3.-5. 2) to the
point QC-5.4.9)
Find a unit vector with the direction of PQ
Answer:
The length of the vector is of [tex]\sqrt{194}[/tex]
The unit vector with the direction of PQ is [tex](\frac{8}{\sqrt{194}}, \frac{9}{\sqrt{194}}, \frac{7}{\sqrt{194}}[/tex]
Step-by-step explanation:
Vector from point P(3,-5,2) to Q(-5,4,9)
The vector is:
[tex]PQ = Q - P = (-5-3, 4-(-5), 9-2) = (8,9,7)[/tex]
The length is:
[tex]\sqrt{8^2+9^2+7^2} = \sqrt{194}[/tex]
The length of the vector is of [tex]\sqrt{194}[/tex]
Find a unit vector with the direction of PQ
We divide each component of vector PQ by its length. So
[tex](\frac{8}{\sqrt{194}}, \frac{9}{\sqrt{194}}, \frac{7}{\sqrt{194}}[/tex]
The unit vector with the direction of PQ is [tex](\frac{8}{\sqrt{194}}, \frac{9}{\sqrt{194}}, \frac{7}{\sqrt{194}}[/tex]
A machine produces metal pieces that are cylindrical in shape. A sample of pieces is taken, and the diameters are found to be 1.01, .97, 1.03, 1.04, .99, .98, .99, 1.01, and 1.03 centimeters. Find a 99% confidence interval for the mean diameter of pieces from this machine, assuming an approximate normal distribution. Interpret the interval carefully in the context of the problem
10 people ate pie and 1 person ate cake. How many more people at the pie than the cake?
Answer:
9
Step-by-step explanation:
10 subtract 1 is 9.
Given:
10 people ate pie
1 person ate cake
No of people who ate the pie than the cake
10-1 =9
the original piece of a book is $25. the book is on sale for 30% off. what percent are we paying? what is the price you will pay for the book
show work please and thank you :)
Answer:
$17.50
Step-by-step explanation:
multiply 25 and 30, the divide the answer by 100, the deduct that result from the original price
7.
12
6
a
a.
х
Above are two similar triangles. Which of the following could be the values of x and y?
x=6, y=10
b. x=6, y=8
C. x=8, y=9
d. x=9, y=8
Answer:
x = 9
y = 8
Step-by-step explanation:
We can find the value of x and y using similarity ratio because the triangles are similar
6/4 = x/6 cross multiply expressions
4x = 36 divide both sides by 4
x = 9
same goes with y
6/4 = 12/y cross multiply expressions
6y = 48 divide both sides by 6
y = 8
Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1725.
What was the rate charged per hour by each mechanic if the sum of the two rates was $195 per hour?
Note that the ALEKS graphing calculator can be used to make computations easier.
х
5
?
First mechanic: $ [per hour
Second mechanic: $ per hour
Answer:
75
120
Step-by-step explanation:
Let the first mechanic's hourly rate = x
Let the second mechanic's hourly rate = y
x + y = 195
15x + 5y = 1725 Divide this equation by 5
3x + y = 345 Write the first equation below this one. Subtract
x + y = 195
2x = 150 Divide by 2
x = 150/2
x = 75
====================
x + y = 195
75 + y = 195
y = 195 - 75
y = 120
Suppose a student typically spends 5/2 hours each week doing research on the Internet. How much research time does a student spend each device in 1 week?
Answer:
Step-by-step explanation:
5/2 hours = 2 1/2 hours
2 1/2 hours = 120 minutes + 30 minutes = 150 minutes.
I don't know if he has more than 1 device or not. But if he does, then this time is the base and you just multiply by 2 1/2 for each device.
Answer:
Solution given:
a student typically spends 5/2 hours each week
research time does a student spend each device in 1 week=5/2=2hours and 30min=150minutes
What is the area?
4.6 yd
7.7 yd
Answer:
A = 35.42 yd²
Step-by-step explanation:
We need to find the area if the dimensions are given as 4.6 yd and 7.7 yd.
The area of a rectangle shaped figure is given by :
A = lb
Where
l is length and b is the breadth
So, put all the values,
A = (4.6)(7.7)
= 35.42 yd²
So, the area of the figure is equal to 35.42 yd².
Neeed help plz urgent need to turn in this assignment
Answer:
The area of the shaded region of the figure in the exercise is:
27.98 [tex]in^{2}[/tex]Step-by-step explanation:
To obtain the area of irregular shapes, you can divide that shape in figure you know and you can obtain the area, first, we're gonna calculate the area of the right side and the left side with the formula below:
Area of a rectangle = base * height.Area of right rectangle = 1.6 in * 5.2 inArea of right rectangle = 8.32 [tex]in^{2}[/tex]How the left rectangle and the right rectangle have the same measurements, we can say:
Area of left rectangle = 8.32 [tex]in^{2}[/tex]You can see in the center there is a rectangle too, but you need just a half formed by a triangle, you can use two form for this: calculating the area of the triangle or calculating the area of the whole rectangle and next to divide in 2, we're gonna use the first:
Area of triangle = (base * height) / 2In the exercise, the base of the shaded triangle is 2.7 inches, and the height you must add the measurements in the right side:
Height of the triangle = 1.6 in + 5.2 in + 1.6 inHeight of the triangle = 8.4 inNow we replace in the formula:
Area of triangle = (2.7 in * 8.4 in) / 2Area of triangle = 22.68 [tex]in^{2}[/tex] / 2Area of triangle = 11.34 [tex]in^{2}[/tex]By last, you must add all the calculated areas from the shaded regions:
Area of the shaded region = 8.32 [tex]in^{2}[/tex] + 8.32 [tex]in^{2}[/tex] + 11.34 [tex]in^{2}[/tex]Area of the shaded region = 27.98 [tex]in^{2}[/tex]In triangle ABC, m∠A=(6x+9)∘, m∠B=(x−8)∘, and the exterior angle at C is 141∘.
What is the measure of angle B?
12∘
20∘
141∘
129∘
Answer:
12°
Step-by-step explanation:
Let's start with the easy first.
We know that m∠C is 39° because together ∠C and the exterior angle equal 180°. And 180 - 141 = 39.
Now, we can use this to find the remaining two angles.
180° - 39° = 141°
So, this means that we can set up m∠A + m∠B = 141°.
6x + 9 + x - 8 = 141
7x + 1 = 141
7x = 140
x = 20
Finally, we can plug in for our x value and find m∠B.
m∠B = x - 8
m∠B = 20 - 8
m∠B = 12°
Answer:
12
Step-by-step explanation:
John went to his baseball game. His mom dropped him off at 4:40 pm and he left his game at 7:50 pm. How long was John at his game?
Answer:
I got 3 hours and 10 minutes
Step-by-step explanation:
If you continuously add numbers in decimal form you will find the answer also.
But also another way in order to find a time answer you could also subtract
7.50-4.40= 3.10
or just 3.1 in this case.
But in a time frame always add the 0 to it.
So 3 hours and 10 minutes!
I think so indeed.
If there were five times as many children as adults at the picnic and there were at least 120 people at the picnic, how many adults and children were at the picnic?
Answer:
20 adults
100 Children
Step-by-step explanation:
Answer: 20 adults and 100 children
Step-by-step explanation:
a = adults, c = children
120 = a + c
c = 5a
120 = a + 5a
120 = 6a
20 = a
20 times 5 is 100 so 100 children
Consider a component that fails according to the Exponential distribution with rate 2. Failures can be of three severities 1, 2, and 3, and the failure of severity i occurs with probability Oli. The repair time for failure of severity i is exponentially distributed with rate ui. Failures of severity 1 are show stoppers, that is, the system fails completely when a failure of severity 1 occurs. On the other hand, failures of severities 2 and 3 do not completely knock out the system, and it continues to operate in a degraded mode.
a) Draw a state transition diagram that represents the failure and repair processes of the component.
b) Derive an expression for the system to be completely available.
c) Derive an expression for the system to be operating in a degraded mode.
Answer:
attached below
Step-by-step explanation:
a) Diagram of state transition representing failure and repair process of component
attached below
b) expression for the system to be completely available
attached below
c) Expression for system to be operating in a degraded mode
attached below
What is the area=???
Answer:
5x^2 + 2
Step-by-step explanation:
pretty sure
Answer:
6.25
Step-by-step explanation:
x+2=5x
2= -x+5x
2=4x
2/4=4x/4
1/2=x
Plug into formla of rectangel: L*W
L= 5(0.5)= 2.5
W= 0.5+2 = 2.5
L*W= 2.5*2.5 = 6.25
What is another way to look at the circumference of a circle?
a. perimeter
C. diameter
b. area
d. radius
Please select the best answer from the choices provided
Answer:
d radias
Step-by-step explanation:
The another way to look at the circumference of a circle is the perimeter of the circle. Option A is correct.
What is the circumference of the circle?The circumference of the circle is the length of its boundary. It can found out using the following formula,
[tex]P=2\pi r[/tex]
Here, (r) is the radius of the circle.
The overall length of the straight sided figure is called its perimeter.The overall length of the circle boundary which is curved is called the circumference.Thus, the another way to look at the circumference of a circle is the perimeter of the circle. Option A is correct.
Learn more about the circumference of the circle here;
https://brainly.com/question/402655
What is the simplified form for 4 to the 3rd power .4 to the 8th power ?
Answer:
64 and 65536
Step-by-step explanation:
you just multiply everything