Answers
Answer:
The correct answer option is: [tex]a_n=\frac{5}{2} n-\frac{11}{2}, 37[/tex].
Step-by-step explanation:
We are given the following arithmetic sequence and we are to write an explicit formula for it and the find the 17th term of the sequence:
{[tex]a_n[/tex]}={[tex]-3, -\frac{1}{2} ,2,\frac{9}{2} ,7[/tex]}
From the given options, we can put in the values of n and check if it proves to be true.
For [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex], put values of [tex]n[/tex] from 1 to 5 which the number of the term.
[tex]a_1=\frac{5}{2} (1)-\frac{11}{2}\\\\a_1=-3[/tex]
[tex]a_2=\frac{5}{2} (2)-\frac{11}{2}\\\\a_2=-\frac{1}{2}[/tex]
[tex]a_3=\frac{5}{2} (3)-\frac{11}{2}\\\\a_3=2[/tex]
[tex]a_4=\frac{5}{2} (4)-\frac{11}{2}\\\\a_4=\frac{9}{2}[/tex]
[tex]a_5=\frac{5}{2} (5)-\frac{11}{2}\\\\a_5=7[/tex]
Therefore, the formula for the given sequence is [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex].
Also, [tex]a_{17}=\frac{5}{2} (17)-\frac{11}{2}=37[/tex]
Answer: The correct one is an=5/2n-11/2,37 so A :)
Related Questions
If Sue rides 10 miles per hour on her bike, and this relationship is graphed, which ordered pair would not be on the graph?
(2, 20)
(5, 50)
(6, 60)
(8, 85)
Answers
Answer:
(8, 85) Would make this relationship not a function because every time you count up 1 it goes up 10 and 8 would match to 80 not 85 making 8, 85 the ordered pair would not be on the graph.
Given Sue's speed of 10 miles per hour, we're looking for an ordered pair that does not fit the relationship y = 10x. While (2,20), (5,50), and (6,60) all fit this relationship, the pair (8,85) does not, hence it won't be on the graph.
Explanation:Sue's speed on her bike is 10 miles per hour. This relationship can be graphed as a straight line in a coordinate plane because the speed remains constant - the distance covered increases uniformly over time. So, for each hour (x), she covers a distance of 10x miles (y). Therefore, we can identify the ordered pair that does not belong on the graph by determining which one does not fit the relationship y = 10x.
(2,20): y=10*2=20, so the pair (2,20) fits the relationship.(5,50): y=10*5=50, therefore the pair (5,50) fits the relationship.(6,60): y=10*6=60, hence the pair (6,60) fits the relationship.(8,85): y=10*8=80, but the given y-value is 85, therefore the ordered pair (8,85) does not fit the relationship and would not be on the graph.Learn more about Linear Relationships here:https://brainly.com/question/31693063
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Tossing coins imagine tossing a fair coin 3 times. (a) what is the sample space for this chance process? (b) what is the assignment of probabilities to outcomes in this sample space?
Answers
Answer:
(a) what is the sample space for this chance process?
If we toss a coin three times then there are total [tex]2^{3}=8[/tex] outcomes
The sample space associated with the given chance process is:
[tex]S= \left \{ HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\right \}[/tex]
(b) what is the assignment of probabilities to outcomes in this sample space?
Since the given sample space has eight outcomes and we know that a fair coin is tosses three times. Therefore, the probability of all the events mentioned in the given sample space is same. Hence we have:
[tex]Probability = \frac{1}{8}[/tex]
When tossing a fair coin three times, the sample space includes all combinations of heads (H) and tails (T). With a fair coin, the probability of each possible outcome (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT) is equal, at 0.125.
Explanation:When we're discussing the tossing of a fair coin three times, we're delving into the area of probability. (a) The sample space in this scenario is all the possible outcomes we could have. Those outcomes are: TTT, TTH, THT, THH, HTT, HTH, HHT, and HHH (Remember: H represents a head and T represents a tail).
(b) When we talk about the assignment of probabilities, we mean the likelihood of each potential outcome occurring. With a fair coin, it's equally likely to land on heads or tails - a 0.5 chance for each. Therefore, each of the eight possible outcomes has a 1/8 or 0.125 probability of occurring, granted that all outcomes are equally likely. So, for for instance, the probability of getting one head and two tails (HHT, HTH, THH) is 3/8 or 0.375, and similarly for all other cases.
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Help me with these math questions......
Answers
Answer: y = 0
Step-by-step explanation:
[tex]\frac{x^{0}}{x^{2}}[/tex]
exponent of denominator > exponent of numerator so, y = 0
*****************************************************************************
Answer: [tex]y=\frac{x^{2}+8}{3}[/tex]
Step-by-step explanation:
y = [tex]\sqrt{3x-8}[/tex]
To find the inverse, swap the x's and y's and solve for "y":
x = [tex]\sqrt{3y-8}[/tex]
x² = 3y - 8
x² + 8 = 3y
[tex]\frac{x^{2}+8}{3}=y[/tex]
*****************************************************************************
Answer: -6x - 3h
Step-by-step explanation:
f(x + h) = 7 - 3(x + h)²
= 7 - 3(x² + 2xh + h²)
= 7 - 3x² - 6xh - 3h²
-f(x) = -(7 - 3x²)
= -7 + 3x²
f(x + h) - f(x) = 7 - 3x² - 6xh - 3h² -7 + 3x²
= -6xh - 3h²
= h(-6x - 3h)
[tex]\frac{f(x+h)-f(x)}{h}=\frac{h(-6x-3h)}{h}[/tex]
= -6x - 3h
Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?
Answers
Martha in 1 hour = 1/2 room.
As like the Martha,
Jamie in 1 hour = 1/6 room.
Both together,
[tex] \frac{1}{2} + \frac{1}{6} \\ \frac{3 + 1}{6} = \frac{4}{6} = \frac{2}{3} \\ = 0.6666...[/tex]
= 0.67 hours to paint a room.
!! Hope It Helps !!
In the formula for the volume of a cylinder, how is the area of the base determined?
Answers
Answer:
area of base = [tex]\pi r^2[/tex]
where 'r' is the radius
Step-by-step explanation:
Volume of the cylinder formula = [tex]\pi r^2h[/tex]
volume of cylinder = area of base * height
The base of a cylinder is a circle. so we use the area of circle for the base of cylinder while finding volume
We know area of the circle is [tex]\pi r^2[/tex]
So area of the base of cylinder is [tex]\pi r^2[/tex]
To find volume of the cylinder , we multiply the base of the cylinder with height
To determine the base of the cylinder we need radius of the cylinder
area of base = [tex]\pi r^2[/tex]
where 'r' is the radius
Answer: c
Step-by-step explanation: teehee
Type the correct answer in the box.
An airplane takes off from point A in a straight line, as shown in the diagram.
The distance from A to E is ____ feet.
Answers
Answer:
11700
Step-by-step explanation:
The triangles are similar (presumably) because their ratios are the same for all three corresponding sides.
Equation
Set up the proportionAB/AC = AD /AEGivens
AB = 5600 feetAD = 5200 feetAC = 5600 + 7000 = 12600 feetAD = ?Solution
5600 / 12600 = 5200 / x Cross multiply5600x = 12600 * 5200 Simplify the right.5600x = 65,520,000 Divide by 5600x = 65,520,000/5600 Do the divisionx = 11,700Answer:
11700
Step-by-step explanation:
The cost of a car rental is thirty dollars a day plus fifteen cents a mile. If the total cost to rent the car was one hundred and eighty dollars, how many miles was the car driven if it was rented for four days?
Answers
Answer:
Step-by-step explanation:
Alright, lets get started.
Suppose car was driven x miles in its 4 days trip.
Cost of a car rental is thirty dollar per day.
So, for 4 days, the car rental will be = [tex]30*4=120[/tex] $
For 1 mile, it adds fifteen cents,
So, for x miles, the cost will be = [tex]0.15 x[/tex] $
As per question, total rent is 180 $
Total rent will be = [tex]120 + 0.15 x = 180[/tex]
Subtracting 120 in both sides
[tex]0.15 x = 180-120=60[/tex]
[tex]x=\frac{60}{0.15}[/tex]
[tex]x=400[/tex]
It means car was driven 400 miles. : Answer
Hope it will help :)
15(x+2000)=3300 is my question on common core. I don't know how to solve this correctly.
Answers
15x + 30000 = 3300
subtract 30000 from both sides
15x = -26700
divide 15 from both sides so you get x alone
x =-1780
If the arc length of a sector in the unit circle is 3 radians, what is the measure of the angle of the sector?
A) 1.5 radians
B) 3 radians
C) 6 radians
D) 9 radians
Answers
Answer:
B) 3 radians
Step-by-step explanation:
The arc length is the product of the radius and angle. You have ...
... 3 radians = 1 × angle
so
... 3 radians = angle
_____
Comment on units
The formula is
... s = rθ . . . . . where s is the arc length, r is the radius, and θ is the central angle in radians.
The units of both s and r are units of length, so the units of angle are ...
... (length units)/(length units) = <no units>
That is, "radians" are fully equivalent to "no units."
The trouble with this problem statement is that it expresses "arc length" in units of "radians." This only works if the units of the radius of the unit circle are "no units". Ordinarily, that would not be the case. The length of the radius of the unit circle is usually "one length unit." If the central angle is 3 radians, then the arc length is "3 length units," not "3 radians."
The following ordered pairs are solutions to a linear equation: (-20, 11.5), (-21, 12), and (-22, 12.5).
Which of the following graphs shows all of the ordered pairs in the solution set of this linear equation?
Answers
Answer:
option A
Step-by-step explanation:
The following ordered pairs are solutions to a linear equation: (-20, 11.5), (-21, 12), and (-22, 12.5).
Frame the equation of line y=mx+b using ordered pairs
(-20, 11.5), (-21, 12)
[tex]slope m = \frac{y_2-y_1}{x_2-x_1} =\frac{12-11.5}{-21+20}=-0.5[/tex]
m= -0.5
Now plug in (-21,12) and find out b
y=mx+b
12= -0.5(-21) + b
12= 10.5 +b
Subtract 10.5 on both sides
So b= 1.5
Equation of line is y=-0.5x + 1.5
Slope is negative so graph will be decreasing
Option A and option C graphs are decreasing
y intercept is the b values = 1.5
y intercept is (0,1.5)
Lets find x intercept
Plug in 0 for y in the equation y=-0.5x+1.5
0 = -0.5x+1.5
subtract 1.5 on both sides
1.5 = -0.5x
Divide by -0.5
so x= 3
So x intercept is (3,0)
Option A graph has x intercept (3,0) and y intercept (0,1.5)
What is the surface area of a rectangular prism that has a length of 9 feet, a width of 5 feet, and a height of 7.5 feet?
A. 300 ft2
B. 150 ft2
C. 337.5 ft2
D. 43 ft2
Answers
Hello.
The Answer: A. 300 ft^2
Step-by-step explanation: Find the area of two sides (Length*Height)*2 sides.
Find the area of adjacent sides (Width*Height)*2 sides.
Find the area of ends (Length*Width)*2 ends.
Add the three areas together to find the surface area.
Formula: A= 2( W l + H L + H W)
Have a nice day.
Answer:
A 300 ft2
Hope this help's!
Someone help please!
Answers
Order the numbers from least to greatest: –13, 16, 3, –20, 15, –10.
Answers
Answer:
-20,-15,-13,-10,3,15,16
Step-by-step explanation:
negative to positive
The amount of water in a bottle is reduced by 85% to 20 milliliters. How much water was originally in the bottle?
Answers
To find the original quantity when given the percent it was reduced and the amount left, divide the amount left by the percentage that is left:
The bottle was reduced by 85%, which means there is 15% left left in the bottle ( 100% - 85% = 15%)
Now divide the amount left by the percentage left:
20 / 0.15 = 133.33
The original amount was 133.33 milliliters ( Round answer as needed)
m x 5 = 30
m = ?
A) 3
B) 4
C) 5
D) 6 what the answer
Answers
Answer:
M= D) 6
Step-by-step explanation:
just do 30 divided by 5=M
Answer:
D) 6 is your answer
Step-by-step explanation: You have to substitute the #'s in for m then multiply it by 5, and if it equals 30, it's your answer... But it has to be a true statement...
A) 3:
m x 5 = 30
3 x 5 = 30
15 = 30
FALSE
B) 4:
m x 5 = 30
4 x 5 = 30
20 = 30
FALSE
C) 5:
m x 5 = 30
5 x 5 = 30
25 = 30
FALSE
D) 6:
m x 5 = 30
6 x 5 = 30
30 = 30
TRUE
Three of the angles of quadrilateral are 100 degrees, 104 degrees and 44 degrees. What is the size of the 4th angle
Answers
Which real numbers are zeroes of the function f(x)=2x^3-x^2-8x+4
Answers
Answer:
2, -2 and 1/2
Step-by-step explanation:
As the the first coefficient is 2 and the last number is 4 1/2, 2, -2 seem likely zeros ( By the rational roots theorem).
f(2) = 2*8 - 4 -16 + 4 = 0 so 2 is a zero.
f(-2) = -16 - 4 +16 + 4 = 0 so -2 is a zero
f(1/2) = 2*1/8 - 1/4 - 4 + 4 = 0 so 1/2 is the other zero.
Since the highest degree is 3 the maximum number of zeroes is 3.
Answer:
Try math
way if you need help on apex
Step-by-step explanation:
45 trucks, each with 3.5-ton payload, are needed to unload a freight train. How many trucks with a 2.5-ton payload would be needed to do the same job?
Answers
Answer:
The answer is 63 trucks.
Step-by-step explanation:
If we need 45 trucks with 3.5 ton each to do the job; then we have a 157.5 ton payload. So if we divide the 157.5 ton into 2.5 ton trucks we get a total of 63 trucks.
3.5 x 45 = 157.5
2.5 x 63 = 157.5
The number of trucks required with 2.5 payloads will be 32.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 45 trucks, each with a 3.5-ton payload, are needed to unload a freight train.
The number of trucks for 2.5 tons of payloads will be calculated as,
3.5 Tons of payload = 45 Trucks
2.5 Ton = ( 45 x 2.5 ) / 3.5
2.5 Ton = 32 Trucks
Therefore, the number of trucks required with 2.5 payloads will be 32.
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How many rows are needed to seat all students. When there are 846 students and each row holds 18 people
Answers
846/18
Kelly saved $150. That is 50% of the money she earned this summer. How much did Kelly earn this summer?
Answers
Question
Kelly saved $150. That is 50% of the money she earned this summer. How much did Kelly earn this summer?
Answer:
300$Step-by-step explanation:
50% = 1/2 = 0.5
150 is the 50% of the money she earned this summer.
Solution
150 * 2 = 300$
Answer:
$300
Step-by-step explanation:
If 150 is 50% you multiply 150 by 2 to get 300 and that would make it 100% of what she got that summer.
A person ate 2400 calories in a day. Of these, 36% came from fat. How many calories came from fat?
Answers
Answer:
864 calories came from fat. What I did was just subtract 2400 from 36% and got it.
Step-by-step explanation:
The calories that come out from fat will be 864 calories.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
A person ate 2400 calories in a day. Of these, 36% came from fat.
36% of 2400 = (36/100)2400
⇒ 864 calories.
Hence "The calories that come out from fat will be 864 calories".
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A store Is having a 20% off sale on all merchandise if my buyers one item and save $13 what was the original price of their of her precio is having a 20% off sale on all merchandise if my buyers one item and save $13 what was the original price of her purchase
Answers
PLEASE HELP ME!!! (LINK) find the missing value in the solution to the equation. thank you!!
Answers
Answer:
4
Step-by-step explanation:
x = - 3
y - 4 = - 2.(x + 3)
y - 4 = - 2.(- 3 + 3)
y - 4 = - 2.0
y - 4 = 0
y = 4
I hope I helped you.
(-3, ?)
To find the missing value, which is "y", since you know x = -3, you can plug it into the equation to find "y"
y - 4 = -2(x + 3)
y - 4 = -2(-3 + 3)
y - 4 = -2(0)
y - 4 = 0 Add 4 on both sides
y = 4
For vectors t, u, v, and w defined as shown, select the TRUE equation.
Answers
i dont really unserstand what this is?
Answer:
t= u+v+w
Step-by-step explanation:
i did the test and got it right
Sherman goes golfing every 6^\text{th}6 th day and Brad goes golfing every 7^\text{th}7 th day. If Sherman and Brad both went golfing today, how many days until they will go golfing on the same day again? Days
Answers
Answer:
42 days.
Step-by-step explanation:
We have been given that Sherman goes golfing every 6th day and Brad goes golfing every 7th day.
To find the number of days after that both will go golfing on the same day we will find LCM of 6 and 7.
Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48,..
Multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56,...
We can see that least common multiple of 6 and 7 is 42, therefore, both will go golfing on the same day again on 42nd day.
The formula for the lateral surface area of a cylinder is S=2πrh , where r is the radius of the bases and h is the height. Solve for r. r=2hπ/S r=S/2πh r=2Sπh r=h/2πS
Answers
Answer:
Option B is correct.
[tex]r = \frac{S}{2\pi h}[/tex]
Step-by-step explanation:
It is given that :
The formula for the lateral surface area of a cylinder is [tex]S = 2\pi rh[/tex]
where
S represents the lateral surface area of cylinder,
r represents the radius of the bases and
h represents the height of the cylinder.
Solve for r;
Given: [tex]S = 2\pi rh[/tex]
Divide both sides by [tex]2 \pi h[/tex],
[tex]\frac{S}{2\pi h} =\frac{2\pi rh}{2\pi h}[/tex]
Simplify:
[tex]r = \frac{S}{2\pi h}[/tex]
Therefore, the radius of the bases of the cylinder is, [tex]r = \frac{S}{2\pi h}[/tex]
Final answer:
The radius of the base of a cylinder, denoted as 'r', can be solved from the lateral surface area formula 'S=2πrh' by rearranging the formula to 'r = S / (2πh)'.
Explanation:
The question requires solving for r (the radius of the bases) from the formula for the lateral surface area of a cylinder, which is S=2πrh. To solve for r, we start by isolating r on one side of the equation. Here's how we can do it step by step:
Start with the formula for lateral surface area: S=2πrh.Divide both sides of the equation by 2πh to isolate r: S / (2πh) = r.Thus, the formula for r is r = S / (2πh).This equation shows that the radius can be found by dividing the lateral surface area by twice the product of π and the height of the cylinder.
BRAINLIEST GOES TO FIRST CORRECT ANSWER, NO STEPS NEEDED
If the roots of a quadratic equation are 1±√5, then the product of the roots is:
a) -24
b) -4
c) 26
Answers
Answer:
Its option B -4
Step-by-step explanation:
Answer:
b) -4
Step-by-step explanation:
The roots are (1-sqrt5) and (1+sqrt(5)
FOIL
first:1*1 =1
outer: 1 * sqrt(5) = sqrt(5)
inner -1*sqrt(5) = -sqrt(5)
last sqrt(5) * - sqrt(5) = -5
Add them together: 1+sqrt(5) - sqrt(5) -5 = -4
ABCD is a parallelogram. if side AB=6x-10, side BC=4x-5, and side CD =3x+5, find the value of x
x=
Answers
Answer:
x=5
Step-by-step explanation:
If ABCD is a parallelogram, then AB = CD
AB=CD
6x-10 = 3x+5
Subtract 3x from each side
6x-3x -10 = 3x-3x+5
3x-10 = 5
Add 10 to each side
3x-10+10 = 5+10
3x = 15
Divide by 3 on each side
3x/3 =15/3
x=5
Answer:
6
i just did the test rn
Step-by-step explanation:
A rectangular garden has a total area of 48 square yards.Draw and label2 possiblerectangular garden with different side lengths that have the same area.
Answers
Two possible rectangular gardens with different side lengths and an area of 48 square yards are:
Square garden: 6 yards by 6 yards
Long and narrow garden: 8 yards by 6 yards
Explanation:Given:
Total area of the garden = 48 square yards
Objective:
Find possible combinations of side lengths for rectangular gardens with the same area.
Step 1: Square Garden
Let the side length of the square garden be x.
Area of the square garden = x^2
Set the area equation: x^2 = 48
Solve for x:
Take the square root of both sides: x = √48
Approximate the value: x ≈ 6.928 yards
Therefore, a square garden with sides of approximately 6.93 yards will have an area of 48 square yards.
Step 2: Long and Narrow Garden
We know the total area is 48 square yards.
Try different values for the width (w) and calculate the corresponding length (l) using the area formula: l * w = 48
For example, if w = 6 yards:
Calculate the length: l = 48 / w = 48 / 6 = 8 yards
Verify that the area matches: l * w = 8 * 6 = 48 square yards
Therefore, a long and narrow garden with a length of 8 yards and a width of 6 yards will also have an area of 48 square yards.
A store is having a sale where school supplies are 30% off theirr original price. A backpack is on sale for 11.20. What was the original price of the backpack?
Answers
Answer:
$16
Step-by-step explanation:
x*0.7=11.20
11.20/0.7=16