Question:
Consider the sequence of numbers: [tex]\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}[/tex]
Which statement is a description of the sequence?
(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.
(B) The sequence is recursive and can be represented by the function
f(n + 1) = f(n) + 3/8 .
(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .
(D) The sequence is arithmetic and can be represented by the function
f(n + 1) = f(n)3/8.
Answer:
Option B:
The sequence is recursive and can be represented by the function
[tex]f(n + 1) = f(n) + \frac{3}{8} .[/tex]
Explanation:
A sequence of numbers are
[tex]\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}[/tex]
Let us first change mixed fraction into improper fraction.
[tex]\frac{3}{8}, \frac{3}{4}, \frac{9}{8}, \frac{3}{2}, \frac{15}{8}[/tex]
To find the pattern of the sequence.
To find the common difference between the sequence of numbers.
[tex]\frac{3}{4}-\frac{3}{8}=\frac{6}{8}-\frac{3}{8}= \frac{3}{8}[/tex]
[tex]\frac{9}{8}-\frac{3}{4}=\frac{9}{8}-\frac{6}{8}= \frac{3}{8}[/tex]
[tex]\frac{3}{2}-\frac{9}{8}=\frac{12}{8}-\frac{9}{8}= \frac{3}{8}[/tex]
[tex]\frac{15}{8}-\frac{3}{2}=\frac{15}{8}-\frac{12}{8}= \frac{3}{8}[/tex]
Therefore, the common difference of the sequence is 3.
That means each term is obtained by adding [tex]\frac{3}{8}[/tex] to the previous term.
Hence, the sequence is recursive and can be represented by the function [tex]f(n + 1) = f(n) + \frac{3}{8} .[/tex]
Every seat that is sold in the auditorium costs 8 dollars. In addition to that, the auditorium makes 300 dollars as a flat rate. If the auditorium made $2772.00 dollars, how many seats were sold?
Answer:
309
Step-by-step explanation:
8x + 300 = 2772
subtract 300 from both sides of the equal sign
8x = 2472
divide 8 from both sides of the equal sign
x = 309
The total no. of seats that have been sold is 309
What are linear equalities in one variable?
The linear equation in one variable is an equation that is expressed within the form of ax+b = zero, where a and b are integers, and x is a variable and has only one answer.
Conclusion: For example, 2x+3=8 is a linear equation having a single variable in it. therefore, this equation has only one solution, which is x = 5/2.
let the auditorium sell x seats for 8 dollars per seat.
In addition to that auditorium made 300 dollars.
The total money earned by the auditorium by selling x seats and the addition of 300 dollars is 2772 dollars.
8x + 300 = 2772
8x = 2772 - 300
8x = 2472
x = 2472/ 8
x = 309
The above question is an example of linear equalities in one variable.
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1. 0.07 = 10m
2. 10.1 = t + 7.2
how would you solve these equations?
Answer: 0.007 and 2.9
Step-by-step explanation:
1) 0.07 = 10m
divide by 10 on both sides
= 0.007
2) 10.1 = t + 7.2
subtract 7.2 from both sides
2.9 = t
The values are;
1. m = 0. 007
2. t = 2.9
How to simply the expressionsFirst, we need to know that algebraic expressions are defined as expressions that are made up of constants, factors, variables and coefficients.
From the information given, we have that;
1. 0.07 = 10m
First, divide both sides by the coefficient of m, we get;
m = 0.07/10
Divide the values
m = 0. 007
2. 10.1 = t + 7.2
collect like terms
't = 10. 1 - 7. 2
subtract the values
t = 2.9
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Subtract the fraction 7/8-1/4 Write the difference in simplest form A:3/8 B:5/8 C:7/8 or D:11/8
Answer:
5/8
Step-by-step explanation:
First, you need to find a common denominator. In this case, the common denominator is 8. To change the second fraction into a fraction that you can easily subtract, you have to multiply the second fraction by 2/2 (which simplifies to one, so you're not changing the value of the fraction at all). Now, the equation reads, 7/8 - 2/8. From here, you just need to subtract the numerators, which ends up being 5/8.
Answer:
B. 5/8
Step-by-step explanation:
Between 7/8 and 1/4, the common denominator is 2. By multiplying 1/4 by 2, you'll get 5/8 after subtracting 2/8 from 7/8.
John is selling tickets to an event. Attendees can either buy a general admission ticket or a VIP ticket. The general admission tickets are $70 and the VIP tickets are $105. If she knows he sold a total of 33 tickets and made $2730, how many of each type did she sell?
Answer:
The number of general admission tickets sold was 21 and the number of VIP tickets sold was 12
Step-by-step explanation:
Let
x ----> the number of general admission tickets sold
y ----> the number of VIP tickets sold
we know that
[tex]x+y=33[/tex] ---> equation A
[tex]70x+105y=2,730[/tex] ----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both lines
using a graphing tool
The solution is the point (21,12)
see the attached figure
therefore
The number of general admission tickets sold was 21 and the number of VIP tickets sold was 12
Final answer:
To solve how many general admission and VIP tickets John sold, a system of equations is formed and solved, revealing that John sold 21 general admission tickets and 12 VIP tickets.
Explanation:
John is selling tickets to an event with two different pricing options, general admission tickets at $70 and VIP tickets at $105. He sold a total of 33 tickets resulting in revenue of $2730. To determine how many of each type of ticket he sold, we will use a system of equations.
Let x represent the number of general admission tickets sold and y represent the number of VIP tickets sold. We can then form the following two equations based on the information provided:
x + y = 33 (equation 1: total number of tickets sold)
70x + 105y = 2730 (equation 2: total revenue from ticket sales)
To solve this system, we can use the method of substitution or elimination. Here, we'll use substitution for simplicity. First, solve equation 1 for x:
x = 33 - y
Substitute this expression for x in equation 2:
70(33 - y) + 105y = 2730
Simplify and solve for y:
2310 - 70y + 105y = 2730
35y = 420
y = 12
Since y = 12, substitute y back into equation 1 to find x:
x = 33 - 12 = 21
Therefore, John sold 21 general admission tickets and 12 VIP tickets.
The best answers gets the branliest and 20 points
Answer:
b and c
Step-by-step explanation:
When x=8 and y=20. Find y when x=68
Answer:
[tex]8(68) + 20[/tex]
[tex]8 \times 68 + 20[/tex]
[tex]544 + 20[/tex]
[tex]x = 564[/tex]
Answer:
170
Step-by-step explanation:
8/20=x/y
simplify. 2/5
2/5=68/y
68*5/2=y
68*5=340
340/2=170
y=170
The player who received the most votes, by percentage, for the Heisman Trophy in a year was Reggie Bush in 2005. Though his trophy was vacated, he received 784 first place votes, 89 second place votes and 11 third place votes. How many total points did he receive that year? First place votes are worth 3 points, second place votes are worth 2 points, and third place votes are worth 1 point.
A) 995
B) 1541
C) 2415
D) 2541
E) 2733
D) 2541
Step-by-step explanation:
The question is on multiplication,where you multiply the votes by the number of points and then add to find the total.
Given that the player got;
784 votes @ 3 points
89 votes @ 2 points
11 votes @1 point
Total number of points will be;
(784*3)+(89*2)+(11*1)=2541 points
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Keywords : player, votes, percentage,trophy,points
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There are 3x-2 trees planted in each room of a rectangular parecl of land. If there are a total 24x-16 trees planted in the parcel, how many rows of trees are there in the parcel?
Answer:
8 rows of trees are there in the parcel.
Step-by-step explanation:
The number of trees planted in each row = (3 x -2) trees
The total number of trees planted on the land = (24 x - 16)
Let us assume the total number of rows planted = m
Now,as we know:
The plants in each row x The number of rows = Total trees Planted
⇒ (3 x -2) x (m) = (24 x - 16)
[tex]\implies m = \frac{24x-16}{3x-2}[/tex]
Simplifying for the value of m, we get:
[tex]m = \frac{24x - 16}{3x-2} = \frac{8(3x-2)}{3x-2} = 8\\\implies m = 8[/tex]
Hence, the total number of rows planted = 8
the width of a box is one third of its length. the height of the box is one third of its width. if the length of the box is 27cm, what is the volume of the box?
a. 81cm³
b. 162cm³
c. 243cm³
d. 729cm³
Answer:
d) 729cm^3
Step-by-step explanation:
Length =27cm
Width = 1/3 of length
= 1/3 of 27cm = 1/3 × 27cm = 9cm
Height = 1/3 of width
= 1/3 of 9cm = 1/3 × 9cm = 3cm
Thus, length = 27cm; width = 9cm; height = 3cm
Hence, volume = length × width × height
= 27cm × 9cm × 3cm
= 729cm^3
Volume is a three-dimensional scalar quantity. The volume of the box is 729 cm³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a room or box that is the shape of a rectangular prism is calculated by multiplying the length, width, and height of the prism.
Volume = Length × Width × Height
Given that length of the box is 27 cm. Also, it is mentioned that the width of a box is one third of its length. Therefore, the width of the box is,
Width of the box = (1/3) × 27cm = 9cm
Further, the height of the box is one third of its width. Therefore, the height of the box is,
Height of the box = (1/3) × 9cm = 3 cm
Furthermore, the volume of the box can be written as,
Volume of the box = Length × Width × Height
= 27cm × 9cm × 3cm
= 729 cm³
Hence, the volume of the box is 729 cm³.
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Burt’s parents allow him to watch 10 hours of television per week. This week Burt is planning to watch several two-hour movies and four hours of sports. Solve to find the number of movies Burt is planning to watch this week.
After setting aside 4 hours for sports, Burt has 6 hours left for television. Since each movie is 2 hours, Burt can watch 3 two-hour movies in the remaining time.
Burt's parents allow him a total of 10 hours of television per week. Since he is planning to watch four hours of sports, we subtract this amount from the total to find the time remaining for watching movies. Here's how we solve for the number of movies Burt can watch:
Total TV time allowed: 10 hours per week
Time planned for watching sports: 4 hours
Time remaining for movies: 10 hours - 4 hours = 6 hours
Since each movie is two hours long, we then divide the remaining time by the length of one movie:
6 hours divided by 2 hours/movie = 3 movies
Therefore, Burt is planning to watch three two-hour movies this week.
A six sided die is tossed and a coin is flipped. What is the fractional probability that the die lands on an even number and the coin is heads?
Answer:
3/12
Step-by-step explanation:
{1, 2, 3, 4 ,5 ,6}
There are 3 even numbers and the coin would be 1/2.
3/6*1/2=3/12
Liana saves $25 every month in her savings account. She took out $100 one
time to Christmas shop. She now has $450 in her account. Write and solve an equation to determine how many months Liana has been saving money. Let m
represent the number of months.
Answer:
Step-by-step explanation:
25m - 100 = 450
25m = 450 + 100
25m = 550
m = 550/25
m = 22 <==== 22 months
What is the slope of the line that passes through the points (-3,3) and (1,-5)
The slope of the line that passes through (–3, 3) and (1, –5) is –2
Solution:
Given slope of the line passes through two points (–3, 3) and (1, –5).
Formula for the slope of the line passes through two points is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex]x_1=-3, x_2=1, y_1=3,y_2=-5[/tex]
Substitute these in the slope formula, we get
⇒ [tex]m=\frac{(-5)-3}{1-(-3)}[/tex]
⇒ [tex]m=\frac{-5-3}{1+3}[/tex]
⇒ [tex]m=\frac{-8}{4}[/tex]
⇒ [tex]m=-2[/tex]
Hence, the slope of the line that passes through (–3, 3) and (1, –5) is –2.
Which grades are middle school in, I'm from Australia so I don't know
Step-by-step explanation:
I think up to grade8 are middle school.
but I am not sure about my answer.
Answer:
6th, 7th, and 8th
Step-by-step explanation:
In America this is the standard middle school grades, however some schools diverge and also include 5th, or sometimes 9th. This, however, is VERY uncommon.
Could someone please help me with these systems. I have to use substitution.
-7x+2y=18
6x+6y=0
Please show your steps so I can learn too. Thank you.
Final answer:
Using substitution, we solve the equation 6x + 6y = 0 for y, yielding y = -x. Substituting into -7x + 2y = 18 and solving for x gives x = -2. Substituting x back into y = -x, we find y = 2.
Explanation:
To solve the system of equations using substitution, we can isolate one variable in one equation and then substitute it into the other equation. In this case, we've been given the system:
-7x + 2y = 18
6x + 6y = 0
From the second equation, we can isolate y:
6x + 6y = 0
x + y = 0
y = -x
Now, substitute y = -x into the first equation:
-7x + 2(-x) = 18
-7x - 2x = 18
-9x = 18
x = -2
Now that we have the value for x, we can substitute it back into y = -x to find y:
y = -(-2)
y = 2
The solution to the system is x = -2 and y = 2.
Can you help me make a Word problem
Answer:hey
Step-by-step explanation:
PLEASE HELP ME PLEASE AND THANK
Answer: OPTION C.
Step-by-step explanation:
You can observe in the picture given in the exercise that [tex]\angle E[/tex] is formed by two secants intersecting outside the circle.
It is necessary to remember that, by definition:
[tex]Angle\ formed\ by\ two\ Secants=\frac{1}{2}(Difference\ of\ Intercepted\ Arcs)[/tex]
You can also identify that the Intercepted Arcs are the following:
[tex]CD=110\°\\\\AB=30\°[/tex]
Then, knowing the measures of the Intercepted Arcs, you can substitute them into the equation shown before and then evaluate, in order to calculate the measure of [tex]\angle E[/tex] , which is the angle formed by the intersection of the secants.
Therefore, you get:
[tex]m\angle E=\frac{1}{2}(110\°-30\°)\\\\m\angle E=40\°[/tex]
Outcome
A
B
C
D
Probability
.25
.33
.37
.05
What is the probability of either outcome B or D?
a.
.28
c.
.19
b.
.38
d.
.33
Answer b
Answer:
the answer is b
Step-by-step explanation:
Answer:
B. 0.38
Step-by-step explanation:
There are 453.592 grams in one pound. A semi-slick, Kevlar tire weighs about 520 grams. What is the tire’s weight in pounds?
Answer:
The tire's weight in 1.146 pounds.
Step-by-step explanation:
Given:
There are 453.592 grams in one pound.
A semi-slick, Kevlar tire weighs about 520 grams.
Now, to find the tire's weight in pounds.
As, given 1 pound is 453.592 grams.
The weight of tire = 520 grams.
So, to get the tire's weight in pounds by using conversion factor:
1 pound = 453.592 grams.
Thus, 520 grams is:
[tex]\frac{520}{453.592}[/tex]
[tex]=1.146\ pounds.[/tex]
Therefore, the tire's weight in 1.146 pounds.
Chanita wants to swim the 21-mile English Channel in 48 hours. On the first day she swam 9 miles and then was picked up by a ferry to spend the night. The next day, she has 12 hours of daylight to complete the remaining distance. What inequality represents the minimum rate she has to swim on the second day to complete the distance? the inequality is 9 +
The inequality 12x+9 ≥ 21 represents the minimum rate Chanita have to swim on second day to complete the distance.
Step-by-step explanation:
Given,
Length of English Channel = 21 miles
Distance covered on first day = 9 miles
Time to complete remaining distance on second day = 12 hours
Let,
x be the distance covered per hour on second day.
Time to cover distance * Distance covered per hour + Distance on first day ≥ Total distance
12x+9 ≥ 21
The inequality 12x+9 ≥ 21 represents the minimum rate Chanita have to swim on second day to complete the distance.
Keywords: addition, inequality
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Answer:
The answer is in the picture below. :)
Step-by-step explanation:
7• blank=1 Answer is a fraction
Answer:
1/7
Step-by-step explanation:
if 7 × (?) = 1, just take 1 and divide by 7. Thus, your answer is 1/7
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = x^−3.141
A.) This is not an exponential function because the variable is in the base position.
B.) The base is x.
C.) This is a polynomial.
D.) The base is −3.141.
Answer:
A.
Step-by-step explanation:
The variable x is in the base position so it is not exponential..
An exponential function is where the exponent is the variable , like for example 2^x.
The function f(x) = x^-3.141 is not an exponential function because in an exponential function, the base must be constant, and here x is the exponent, not the base.
Explanation:The function f(x) = x−3.141 is not an exponential function. In an exponential function, the base is a constant and the exponent is the variable. Since the variable x is in the exponent here and the base is not a constant, we do not have an exponential function according to the definition.
Therefore, the correct answer is A: This is not an exponential function because the variable is in the base position and not in the exponent where we typically find the variable in exponential functions.
HELP!! If over A few weeks Carla saw 15 mayflies how many flying insects did she see
Step-by-step explanation:
Given expression
Number of insect Number of mayflies
x [tex]\frac{3}{14}x[/tex]
According to problem
[tex]\frac{3}{14}x[/tex][tex]=15[/tex]
⇔[tex]x = \frac{15 \times 14}{3}[/tex]
⇔[tex]x = 70[/tex]
Number of insect = 70
Julie spend $5.62 at the store. Micah spends 5 times as much as Julie. Jeremy spends $6.72 more that Micah. How much money does each person spend?
Answer:
Julie Spends $5.62, Micah spends $28.10 and Jeremy Spends $34.82
Step-by-step explanation:
If Micah spends 5 times as much as Julie, that is $28.10 because 5.62 x 28.10 = 28.10. If Jeremy spends 6.72 more than Micah, you would do 28.10 + 6.72, which is 34.82
I think I did the math correct but I may be wrong
Answer:
reeeeee
Step-by-step explanation:
ererrrrrrrrrrrrrrrr
The function f is defined by f(x)=2.1x−1.7. Use this formula to find the following values of f. f(x+2)
The value of [tex]f(x+2)=2.1x+2.5[/tex]
Step-by-step explanation:
Given: The function [tex]f(x)=2.1x-1.7[/tex]
Using this formula, we need to find the value of [tex]f(x+2)[/tex]
Hence, we need to substitute [tex]x[/tex] by [tex]x+2[/tex] to find the value of [tex]f(x+2)[/tex]
[tex]f(x+2)=2.1(x+2)-1.7[/tex]
Multiplying the term [tex](x+2)[/tex] by [tex]2.1[/tex], we get,
[tex]f(x+2)=2.1x+4.2-1.7[/tex]
Adding the constant term,
[tex]f(x+2)=2.1x+2.5[/tex]
Thus, the value of [tex]f(x+2)[/tex] is [tex]f(x+2)=2.1x+2.5[/tex]
Melinda is thinking of two numbers. Each number is greater than 5. If she multiplies one of the numbers by 3 it will be equal to the other number. What could Melindas numbers be?
Can someone please help me?
Answer:
15.5 seconds.
Step-by-step explanation:
From the time the driver activated the brakes until he stopped, he travelled 76 - 14 = 62 meters.
During this time the car slowed down from 8 m/s to 0 m/s.
Assuming the deceleration was constant during this time we can apply one of the equations of motion for constant acceleration:
s = (u + v)t / 2 where u = initial velocity, v = final velocity, s = distance and t = the time, so:-
62 = (8 + 0)t/ 2
62 = 8t/2
4t = 62
t = 15.5 seconds.
a pentgon has angle of 104,102,115.111 what the angle of the fifth angle
The fifth angle is 108 degrees
Solution:
Given that a pentagon has angle of 104, 102, 115 and 111 We have to find the angle of fifth angle
A pentagon is a five sided polygon
The sum of all the interior angles of a pentagon is 540 degrees
Given that,
Angle 1 = 104
Angle 2 = 102
Angle 3 = 115
Angle 4 = 111
Angle 5 = ?
Let the angle be "x"
So to find the fifth angle, add all the angles and equate to 540 degrees
Angle 1 + Angle 2 + Angle 3 + Angle 4 + Angle 5 = 540
104 + 102 + 115 + 111 + x = 540
432 + x = 540
x = 540 - 432
x = 108
Thus the fifth angle is 108 degrees
What is the distance ?
Distance between 2 points formula: √(x2 − x1)² + (y2 − y1)²
= √(7 - (-3))² + (-1 - 5)²
= √10² + -6²
= √100 + 36
= √136
≈ 11.662 (Note that this number is rounded because its a a non-terminating decimal).
Best of Luck!
Use these photos separately and PLEASE don’t use a calculator and show your work. I’m desperate.
Answer:
16
Step-by-step explanation:
swtich tk it be 10/160
10 into 160 is 0
subtract 160-0=1
move the 2nd digt down
16-10=6
bring down 3rd digit
=60
60 into 60 is 0
Answer:
Step-by-step explanation:
I think I've already solved this question.