Answer:
a = 4
Step-by-step explanation:
You are given an arithmetic sequence with second term 5.5 and fifth term 10. You want to know the first term.
Common differenceThe 2nd term will have 3 times the common difference added to it to make the 5th term. Then that difference can be found from ...
5.5 +3d = 10 . . . . using 'd' for the common difference
3d = 4.5
d = 1.5
First termThe second term (a2) is obtained by adding the common difference (d) to the first term (a1):
a2 = a1 +d
5.5 = a1 + 1.5
4.0 = a1
The value of 'a' is 4.
__
Additional comment
The 'd' we're using here to represent the common difference is not to be confused with the 'd' in the problem statement that represents the fourth term of the list.
The fact that adjacent list members have the same difference is what tells you this is an arithmetic sequence. In terms of the problem statement, you have ...
{a, b, c, d, e} = {4, 5.5, 7, 8.5, 10}
Here, we have used the more common notation for elements of an arithmetic sequence.
Consider a data set with at least three data values suppose the highest value is increased by 10 and the lowest is decreased by five
plss give your self a answer
I'm really confused about this equation. I'm trying to figure it out, but I'm lost and think I'm overthinking it
Jet A Travels at 417 mph and gets halfway to its destination in two hours. Jet B makes the same journey but makes it to the destination in 5 minutes. How fast is Jet B in MPH, or how much faster is Jet B than Jet A As A Multiplier?
Example: 417 * 48 = 20016 Or Jet B = X MPH
I think the answer is 417 * 48 = 20016 and Jet B= 20016
But I just need reassurance, or a definitive answer
Answer:
Jet B speed: 20,016 mphspeed multiplier: 48Step-by-step explanation:
You want the speed and speed multiplier for Jet B given that it makes a journey in 5 minutes that takes Jet A 2 hours for half the journey.
Speed multiplierFor the same distance, speed is inversely proportional to time.
speed multiplier = (speed B)/(speed A) = (time A)/(time B)
speed multiplier = ((2 h)/(1/2))/(5 min)
speed multiplier = (240 min)/(5 min) = 48
SpeedThe speed of Jet B is 48 times that of Jet A:
48(417 mph) = 20016 mph . . . . speed of Jet B
__
Additional comment
The time for the full trip by Jet A can be found using the proportion ...
partial time/partial distance = total time/total distance
If the total distance is "1 unit", then this proportion is ...
(2 h)/(1/2) = t/1 . . . . . where t/1 = t is the time for the full trip by Jet A
You will recognize the value (2 h)/(1/2) as the time value we used for Jet A in the above solution.
please im failing math and this is an extra credit problem.
Answer:
1:30 pm
Step-by-step explanation:
You want the time when Sahil catches up to Joaquin, who left at 8 am riding 50 mph when Sahil left at 8:30 am, riding at 55 mph.
Time, Speed, DistanceThe relation between time, speed, and distance is ...
distance = speed × time
time = distance / speed
Joaquin has a head start of 0.5 hours (30 minutes), during which time he traveled ...
head start distance = (50 mi/h) × (0.5 h) = 25 mi
Sahil is traveling 55 - 50 = 5 mph faster than Joaquin, so closes that gap at the rate of 5 mi/h. The time it takes to close the gap entirely is ...
time = distance / speed = 25 mi / (5 mi/h) = 5 h
So, 5 hours after Sahil starts at 8:30, the two riders will be at the same place.
Sahil catches Joaquin at 1:30 pm.
__
Additional comment
By the time the gap is closed at 1:30 pm, both riders will have traveled a distance of ...
distance = speed × time = 50 mi/h × 5.5 h = 55 mi/h × 5 h = 275 mi
In the attached graph, we have written equations for the total distance traveled by each motorcycle. The x-value used is the clock time on a 24-hour clock. That is, their meeting time of 13.5 hours corresponds to 13:30 hours or 1:30 p.m. on a 12-hour clock.
Only answer if you are 100% sure!
Answer:
$29.865
Step-by-step explanation:
Because 3.75/2 =1.875 so $1.875 plus $15 Plus the flat $12.99
Using a linear function, it is found that he spent $29.865 for the 4.5 hours he was on the river.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The intercept is the flat rate of $12.99.The slope is the cost per hour of $3.75.Hence the cost of x hours is given by:
C(x) = 12.99 + 3.75x.
For 4.5 hours, the cost is given as follows:
C(4.5) = 12.99 + 3.75(4.5) = $29.865.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
What of the following is not a vertical asymptote of the function
f(x)= tan(pi x/4) / x^2-8x+15?
2
3
4
5
6
Rewrite the function as
[tex]f(x) = \dfrac{\tan(\left(\frac{\pi x}4\right)}{x^2 - 8x + 15} = \dfrac{\sin\left(\frac{\pi x}4\right)}{\cos\left(\frac{\pi x}4\right) (x-3) (x-5)}[/tex]
Vertical asymptotes occur wherever the denominator is zero (but not necessarily when the numerator is also zero).
We have
[tex]\cos\left(\dfrac{\pi x}4\right) (x-3) (x-5) = 0[/tex]
[tex]\implies \cos\left(\dfrac{\pi x}4\right) = 0 \text{ or } x - 3 = 0 \text{ or } x - 5 = 0[/tex]
In the first case, we have
[tex]\cos\left(\dfrac{\pi x}4\right) = 0 \implies \dfrac{\pi x}4 = \pm\dfrac\pi2 + 2n\pi \implies x = \pm 2 + 8n[/tex]
where [tex]n[/tex] is an integer. That is, any of [tex]x\in\{\ldots,-10,-2,\boxed{6},14,\ldots\}[/tex] and [tex]x\in\{\ldots,-6,\boxed{2},10,18,\ldots\}[/tex] are asymptotes.
In the latter two cases, we get [tex]x=\boxed{3}[/tex] or [tex]x=\boxed{5}[/tex]. The numerator is finite at these values [tex]\left(\sin\left(\frac{3\pi}4\right)=\frac1{\sqrt2}\text{ and } \sin\left(\frac{5\pi}4\right)=-\frac1{\sqrt2}\right)[/tex].
This means [tex]x=4[/tex] is not an asymptote. (C)
The term containing b^6 in the expansion of (a + b2)10
The term containing b^6 is -210 a^6 b^6
The given expansion can be solved by using the Binomial expansion
The binomial expansion for two terms (a + b) raised to the power n is given by
(a+b)^n = Σ[tex]a^{n-k} * b^k[/tex] * n!/k!(n-k)!
To find term contain b^6 we use the formula
Use the formula T r+1 =(−1) ⁿCr [tex]a^{n-r} * b^r[/tex]
Putting n=10,
we get 10-r=6
r=4
Therefore,
it is the fourth term ,
T = (-1)^3 10!/4!6! [tex]a^{10-6} * (b^2)^4[/tex]
= -1 x 10x9x8x7/4x3x2=-210 [tex]a^6 b^6[/tex]
Hence the term containing b^6 is -210 a^6 b^6
For further reference:
https://brainly.com/question/2165968?referrer=searchResults
#SPJ9
Write three different expressions that equivalent to 8 to the power 2 x 4 to the power of 2
Answer:
One could be: 8*8 times 4*4
Another could be: 8 to the second power times 4 to the second power
A third way to write this could also be: 8*4*8*4
Step-by-step explanation:
Hope its helpful
Elroy's Balloon Emporium sells boxes of balloons. There are 500 balloons in a box. In January, they sell 3 boxes.In February they sell 6 boxes .If they started with 10 boxes, how many balloons do they have left to sell?
Answer:
500
Step-by-step explanation:
3+6=9
10-9=1
They sell 9 out of the 10 boxes. if each box has 500 balloons, then they have 500 left
Answer: 500 balloons
Step-by-step explanation: if you do 500 x 10 you get 5000 and then you do 3 x 500 + 6 x 500 then you get 4500 then subtract that from 5000
A company that manufactures bicycles has costs given by the equation below in which x is the number of bicycles manufactured and C is the cost to manufacture each bicycle. Complete parts a. through c.
a) cost C of manufacturing 1000 bicycle is $170
b) cost C of manufacturing 7000 bicycle is $110
c) As more bicycle is manufactured the cost of manufacturing decreases
What is an mathematical expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
given expression of cost of bicycle C in terms of number of number of bicycles x is :
C = (100x + 70,000)/ x
a) Now, to get the cost C of manufacturing 1000 bicycle substitute x as 1000 in above expression :
C = (100x + 70,000)/ x
C = 100 + (70,000/ x)
C = 100 + 70,000/1000
C = 100 + 70
C = 170 bicycle's
b) Now, to get the cost C for 7000 bicycle substitute x as 7000 in above expression :
C = (100x + 70,000)/ x
C = 100 + (70,000/ x)
C = 100 + 70,000/7000
C = 100 + 10
C = 110 bicycle's
c) As it is observed from the above analysis as more bicycle is manufactured the cost of manufacturing decreases.
Read more about cost of manufacturing at:
https://brainly.com/question/15282742
#SPJ1
She begins at sea level, which is an elevation of o feet.
She travels down 27.2 feet.
She then ascends 2.1 feet.
Next, she descends a second time, 19.6 feet.
How many feet must she now rise to get back to sea level?
Answer:
She will need to rise 55.4 feet.
Step-by-step explanation:
-27.2 feet + 2.1 feet = -25.1
-25.1 + -19.6 = 44.6
100- 44.6 = 55.4 feet
6. Find the product: 6.45 x 19.3
Showing each step... use the product rule to simplify the following monomial.
INCLUDE ANY STEP THAT SHOWS HOW EXPONENTS ARE CHANGING (for example,
exponents adding, subtracting, multiplying, etc.).
Show Your Work
3a4 . 5a³
-7=
n-10
3
2 step eq
3(n-10)=-7
Solve the equation in 2 step equation.
n=18.5
Given that 3(n-10)=7
step1: multiplication
Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.
3n-30=7
step2: adding 30 on both sides of the equation.
When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.
2n-30+30=7+30
2n=37
step3: divide the equation by 2.
Basically, dividing is the act of dividing anything into equal sections or groups.
[tex]\frac{2n}{2} =\frac{37}{2}\\ n=\frac{37}{2} or 18.5[/tex]
Therefore, n=18.5
To learn more about equation visit: https://brainly.com/question/10413253
#SPJ9
9x7/9-6+13 order of Operations
((9×7)÷9−6)+13
(63÷9−6)+13
(7−6)+13
1+13
14
Answer:
9 X 7 / 9 - 6 + 13
we can cut 9
=7-6 + 13
=1+13
=14
A 55-inch is cut into two pieces. One piece is 4 times the length of the other. Find the length of the shorter piece.
The shorter section is x inches length, or 44.
What constitutes a length?
A line segment can be drawn on paper and has a set length. the measurement of the separation between the longest or longer side of an object's ends. 2: an exact distance The three miles of the road. 3: How much time something requires The movie lasts for two hours. 4: a lengthy fragment of something She purchased a length of pipe in
accordance with the instruction;
the shorter portion should be x.
It is 4x because the longer portion is 4 times as long as the other.
4x + x = 55
5x = 55
4x = 44
x = 11
The length of the shorter piece is x, which is 44
TO KNOW MORE ABOUT LENGTH VISIT;
https://brainly.com/question/14759249
#SPJ9
Find an equation of the line that satisfies the given conditions. Through (4, 9); parallel to the line passing through (5, 7) and (1, 3)
Answer:
y = 1x + 5
Step-by-step explanation:
First, lets calculate the equation of the line passing through (5, 7) and (1, 3) in slope-intercept form
The general equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept is rise over run =
[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x₁, y₁) and (x₂, y₂) are any two points on the line
For the line passing through (5, 7) and (1, 3) , the slope
[tex]m = \dfrac{3 - 7}{1 - 5}[/tex]
[tex]m = \dfrac{-4}{-4}[/tex]
[tex]m = 1[/tex]
To compute the y-intercept, plug in any of the two points x and y values and solve for b
Take point 5, 7 ==> when x = 5, y must be 7
We get
7 = 1 x 5 + b
7 = 5 + b
2 = b (subtract 5 from both sides)
b = 2
So the equation of the line is
y = 1x + 2
A line parallel to another line will have the same slope and a different y-intercept
Therefore a parallel line will also have slope 1 and its equation will be of the form
y = 1x + b
To calculate this b, plug in the point (4, 9) into the equation and solve for b
9 = 1 x 4 + b
9 = 4 + b
b = 5
So the equation is
y = 1x + 5
Graph attached shows the real picture
Grayson bought snacks for his teams practice. He bought a bag of popcorn for $3.50 and a five pack of juice bottles. The total cost before tax was $11.05. Right and solve an equation which can be used to determine J, how much each bottle of juice cost.
The each bottle of juice cost $ 7.55 before tax .
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Grayson bought bag of popcorn (P)= $3.50
Five pack of juice bottles.
The total cost before tax was $11.05.
According to given question we have
Let the cost of the juice bottles be x.
P+ x= $11.05.
$3.50+x=$11.05
x=$11.05-$3.50
x=$ 7.55
Therefore, the each bottle of juice cost $ 7.55 before tax .
Learn more details about arithmetic here:
https://brainly.com/question/11559160
#SPJ1
b. The cardinal number of (2, 4, 6, ..., 106) is
The cardinal number of (2, 4, 6, ..., 106) is 53.
The cardinal number of a set is the number of elements in the particular set.
We are given the set (2, 4, 6, ..., 106). As we can can clearly see, it is forming an Arithmetic Progression (AP).
Hence, let the number of elements or the cardinal number of the set be n.
Hence, according to the formula of AP, we can write,
2 + (n-1)(2) = 106
2(n-1) = 106 - 2
2(n-1) = 104
n - 1 = 104/2
n - 1 = 52
n = 52 + 1
n = 53
Hence, the cardinal number of the set is 53.
To learn more about cardinal number, here:-
https://brainly.com/question/13095210
#SPJ1
PLS HELP! LAST QUESTION! The scatter plot shows prize money, in thousands of dollars, for a contest over eight consecutive years.
Predict the amount of prize money in year 10 of the contest.
$11,790
$20,340
$35,200
$45,900
From the given scatter plot, finding a line of best fit, the estimate of the amount of prize money in year 10 of the contest is of $11,790.
How to find the equation of the line of best fit using a calculator?To find the equation of the line of best fit, we need to insert the points (x,y) from the scatter plot in the calculator.
From the scatter plot, the points are given as follows:
(1, 9.5), (2,9), (3,7), (4,10), (5,11), (6, 10), (7, 10.5).
Inserting these points into a calculator, the line of best fit for the prize in year x is given as follows:
P(x) = 0.32143x + 8.28571
For year 10, we have that x = 10, hence:
P(10) = 0.32143(10) + 8.28571 = $11,500.
The closest option is $11,790, and the difference is due to rounding of coefficients or points in the table.
More can be learned about a line of best fit at https://brainly.com/question/22992800
#SPJ1
A person is putting oranges into a box. The dimensions of the box
are 13 inches by 16 inches by 13 inches. Assuming oranges are
spherical with a 2.8-inch diameter, how many oranges should fit in
the box? (Hint: Packing spheres in a rectangular prism usually takes
up 190% of the volume of the spheres using random packaging.)
Answer:
oranges
The number of oranges that will fit in the box is 235 oranges.
How to find the number of oranges that will fit in the box using volume?The dimensions of the box are 13 inches by 16 inches by 13 inches.
Therefore,
volume of the box = lwh
where
l = lengthw = widthh = heightHence,
volume of the box = 13 × 16 × 13
volume of the box = 2704 inches³
volume of the spherical orange = 4 / 3 πr³
where
r = radius of the sphere = 2.8 / 2 = 1.4 inchesvolume of the spherical orange = 4 / 3 × 3.14 × 1.4³
volume of the spherical orange = 34.46464 / 3
volume of the spherical orange = 11.4882133333 inches cube = 11.5 inches³
number of oranges in the box = 2704 / 11.5
number of oranges in the box = 235.130434783
number of oranges in the box = 235 oranges
Therefore, the number of oranges that will fit in the box is 235 oranges.
learn more on volume here: https://brainly.com/question/481704
#SPJ1
NEED ANSWER PLS HURRY !!
Answer:it's the second option
Step-by-step explanation:
-x is already -1 so why would factoring it make it -1 again
Lily's book has 468 pages. Joe's book is 2 2/3 as long as Lily's book. How many pages is Joe's book?
Answer: Joe's book has 1248 Pages.
Step-by-step explanation:
468 * 2 2/3
Multiply 2 and 3 to get 6.
468×( 6+2/3)
Add 6 and 2 to get 8.
468x(8/3)
Express 468×(8/3) as a single fraction
468x8/3
Multiply 468 and 8 to get 3744.
3722/3
Divide 3744 by 3 to get 1248.
1248
So Joe's Book has 1248 pages
The length of a rectangle is 5 times the width. If the perimeter of the rectangle is 108 feet, find the length
and the width.
Answers:
Length = 45 feet
Width = 9 feet
=========================================================
Work Shown:
x = width
5x = five times the width = length
P = perimeter of the rectangle
P = 2*(length + width)
P = 2*(5x+x)
P = 2*(6x)
P = 12x
Set this equal to the stated perimeter (108) and solve for x.
12x = 108
x = 108/12
x = 9 feet is the width
5x = 5*9 = 45 feet is the length
-------------
Check:
P = 2*(9+45) = 108
or you could add up the four sides like this
P = 9+45+9+45 = 108
Either way the answers are confirmed.
Karen worked her 40 regular hours last week, plus 6 hours at the time-and-a-half rate. Her gross pay was $650. What was her hourly rate?
As Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).
As given,
Regular working hours =40 hours
Overtime at the rate of (1.5 of regular hours) = 6 hours
Gross pay =$650
Let 'h' be the hourly rate
Required equation
40h + 6(1.5h) =650
⇒ 40h +9h=650
⇒49h=650
⇒h=$13.27(approximately)
Therefore, as Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).
Learn more about hourly rate here
brainly.com/question/25951023
#SPJ1
a pebble dropped into a calm pond causing ripples in the form of concentric
Answer:
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by r ( t ) = 0.6 t r(t) = 0.6t r(t)=0.6t, where t is the time in seconds after the pebble strikes the water.
Step-by-step explanation:
Answer:
well dude it's because of the law of gravity
1. What information can be seen most easily in the dot plot?
a dot plot can easily show all the data.
Step-by-step explanation:
In this example, a dot plot can easily show all the data. If the data set is very large (more than 100 values, for example) or if there are many different values that are not exactly the same, it may be hard to see all of the dots on a dot plot.
A store has clearance items that have been marked down by 25%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?
we end up paying 41.25 % of the original price after the addition sale on the clearance.
Let the original price of the good be x
Now, there is a sale of 25 %.
So the price will become
Price = x - 25 % of x
Price = x - 25 / 100 x
Price = x - 0.25 x
Price = 0.75 x
Now, there is an addition 45 % sale on the price.
so the price become:
New price = P = 0.75 x - 45 % of 0.75 x
P = 0.75 x - 45 / 100 (0.75 x)
P = 0.75 x - 0.45( 0.75 x)
P = 0.75 x - 0.3375 x
P = 0.4125 x
percentage of original price is:
P = 41.25 % of x
Therefore, we get that, we end up paying 41.25 % of the original price after the addition sale on the clearance.
Learn more about percentage here:
https://brainly.com/question/843074
#SPJ9
Identify the Property of Operation that is being used.
3(a – 2) = 3a – 6
Question 1 options:
Distributive Property
Commutative Property
Identity Property
Associative Property
-------------------------------
(5 x 4) x 2 = 5 x (4 x 2)
Question 2 options:
Commutative Property
Distributive Property
Associative Property
Identity Property
-------------------------------
Simplify the expression.
9y + 6 – 7y - 3
Question 3 options:
-2y - 3
2y + 3
2y + 9
-2y + 9
-------------------------------
9y + 6 – 7y - 3
Question 3 options:
-2y - 3
2y + 3
2y + 9
-2y + 9
-------------------------------
a + b + 2a + 2b + 5 − b
Question 5 options:
3a + 2b + 5
3a + 4b + 5
2a + 4b + 5
2a + 2b + 5
Answer:
3×a-3×2=3a-6
3a-6=3a-6 proved
Find the slope of the line.
Completing the square first gets brainliest maths Question plus 30 points.
Answer:
Hello,
Step-by-step explanation:
a)
[tex]x^2-2x-6=x^2-2x+1-1-6\\\\=(x-1)^2-7\\[/tex]
b)
[tex]x^2-2x-6=(x-1)^2-7\\\\=(x-1-\sqrt{7} )(x-1+\sqrt{7} )\\\\\\\boxed{x=1-\sqrt{7} \ or\ x=1+\sqrt{7} }\\[/tex]