Answer:
The relationship between the number of months and the total amount paid is proportional for both Hank's and Lynn's loans.
Step-by-step explanation:
Hank and Lynn are both paying off car loans
Hank paid $2,000 upfront when he bought his car, and he pays $200 each month.
Therefore, the total amount paid (C(h)) after x months by given by
C(h) = 2000 + 200x ......... (1)
So, this relation is proportional but not directly proportional.
Lynn did not pay any money upfront when she bought her car, and she pays $275 each month.
Therefore, the total amount paid (C(l)) after x months by given by
C(l) = 275x ......... (2)
So, this is a directly proportional relation which is also proportional.
hope it helps mark me as brainliest.
write down in terms of n, an expression for the nth term of the following sequences 2 5 8 11 14
Answer:
[tex]a_{n}[/tex] = 3n - 1
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 5 - 2 = 8 - 5 = 11 - 8 = 14 - 11 = 3
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 3 , thus
[tex]a_{n}[/tex] = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1
The expression for the nth term of the series is [tex]a_n = 3n-1[/tex].
Given that,
Sequence; 2, 5, 8, 11, 14.
We have to find, the expression in terms of n for the nth term of the following given sequences?
According to the question,
The nth of the arithmetic sequence is,
[tex]\rm a_n = a+ d(n-1)[/tex]
Where a is the first term of the sequence,
d is the common difference between the terms,
n is the number of terms.
Then,
The given sequence is 2, 5, 8, 11, 14.
Here, the common difference between the terms is 3.
And the first term of the sequence is 2.
Substitute all the values in the formula,
Therefore,
The nth term of the given terms is,
[tex]\rm a_n = a+ d(n-1)\\\\a_n = 2+ 3(n-1)\\\\a_n + 2+3n-1\\\\a_n = 3n-1[/tex]
Hence, The required expression for the nth term of the series is [tex]a_n = 3n-1[/tex].
For more details refer to the link given below.
https://brainly.com/question/17043393
Allan built a doghouse and he wanted the house to have an area of 24 square feet. He also wanted the width to be 2/3 the length. What are the dimensions of the doghouse?
Answer:
Dimension of doghouse is 4ft by 6ft
Step-by-step explanation:
Here, we are interested in calculating the dimensions of the doghouse.
Let the length of the doghouse be x, this means that the width would be 2/3 of x which equals 2x/3
Now, the area of rectangle is L * B
x * 2x/3 = 24
2x^2 = 3 * 24
2x^2 = 72
diverse both sides by 2
x^2 = 36
hence x = 6ft
The width would be 2/3 * 6 = 12/3 = 4 ft
Which complex number has a distance of V17 from the origin on the complex plane?
O 2 + 151
O 17 +7
O 20 – 3i
O 4-7
Answer:
[tex]4-i[/tex]
Step-by-step explanation:
Use the formula for the distance of a complex number from the origin on the complex plane.
[tex]\sqrt{a^2+b^2}[/tex]
[tex]a+bi[/tex]
[tex]4-i[/tex]
[tex]\sqrt{4^2-i^2}[/tex]
[tex]\sqrt{4^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}[/tex]
The complex number that has a distance of [tex]\sqrt{17}[/tex] is [tex]4-i[/tex].
By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)
How to determine the distance of a complex numberComplex numbers are a generalization from real numbers, whose expression are of the form a + i b, where a and b are the components of the real and imaginary components, respectively. The magnitude of complex numbers is determined by Pythagorean theorem, this is, the distance from the origin to the location of the number on the complex plane:
[tex]r = \sqrt{a^{2}+b^{2}}[/tex]
If we know that a = 4 and b = -1, then the magnitude of the complex number is:
[tex]r = \sqrt{4^{2}+(-1)^{2}}[/tex]
[tex]r = \sqrt{17}[/tex]
By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)
RemarkThe statement presents several typing mistakes, correct form is shown below:
Which complex number has a distance of [tex]\sqrt{17}[/tex] from the origin on the complex plane?
A. 2 + i 15
B. 17 + i
C. 20 - i 3
D. 4 - i
To learn more on complex numbers, we kindly invite to check this verified question: https://brainly.com/question/10251853 #SPJ5
0.9a+4.96=3.6+1.4a what is the answer simplfy
Answer:
2.72
Step-by-step explanation:
the other one copied my answer from another website.
Explanation:
Move all the terms containing a to the left side of the equation
-0.5a+4.96=3.6
Subtract 4.96 from right side
-0.5a=3.6-4.96
Would be
-0.5a=-1.36
Divide each term by -0.5 and simplify
a= 2.72
Find the value of [2-3(2-3)-1]-1 .
Answer:
the answer to this is 3
Step-by-step explanation:
hope this helps
Answer:
your answer to this question is 3
Step-by-step explanation:
What is the value of 3-(-2)
Answer:
5
Step-by-step explanation:
3-(-2)=5
Answer:
5
Step-by-step explanation:
It becomes 3+2 because the negatives cancel out.
What are the answers? No hurry; I just have other things to do.
Answer:
what u need help with
Step-by-step explanation:
Who can solve for Y ? 2y < -4
Answer:
y < -2
Step-by-step explanation:
2y < -4
Divide both sides by 2.
y < -2
Answer:
y <-2. :::::::::::::::::::::::
Step-by-step explanation:
2y< -4 ==> y<-2
A psychologist has designed a questionnaire to measure individuals' aggressiveness. suppose that the scores on the questionnaire are normally distributed with a standard deviation of . suppose also that exactly of the scores exceed . find the mean of the distribution of scores. carry your intermediate computations to at least four decimal places. round your answer to at least one decimal place.
Answer: μ = 647.4
Step-by-step explanation:
The question says
"A psychologist has designed a questionnaire to measure individuals' aggressiveness. suppose that the scores on the questionnaire are normally distributed with a standard deviation of . suppose also that exactly of the scores exceed"
And we are told to find the mean of the distribution scores.
Given mean μ = ?
we have from standard normal table that
P(Z > 1.282) = 0.1
Therefore the given Z score of a score of 750 is given thus 1.282.
the z score is given:
x - μ / α = 1.282
750 - μ / 80 = 1.282
Therefore μ = (750 - 80)*1.282 = 647.4
So we have that μ = 647.4
cheers i hope this helped !!!
Simplify
8c^3d^2
4cd^2
Answer:
[tex]2c^{2}[/tex]
Step-by-step explanation:
[tex]\frac{8c^33d^2}{4cd^2}[/tex]
[tex]\frac{2c^2d^0}{1}[/tex]
Answer:
[tex]2 {c}^{2} [/tex]
Step-by-step explanation:
[tex] \frac{8 {c}^{3} {d}^{2} }{4 {c}^{1} {d}^{2} } \\ = 2 {c}^{3 - 1} {d}^{2 - 2} \\ = 2 {c}^{2} {d}^{0} [/tex]
we know that,
[tex] {d}^{0} = 1[/tex]
so,
[tex] = 2 {c}^{2} {d}^{0} \\ = 2 \times {c}^{2} \times 1 \\ = 2 {c}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What are the solutions to the nonlinear system of equations below? Check all that apply x ^ 2 + y ^ 2 = 4 (x ^ 2)/(2 ^ 2) - (y ^ 2)/(2 ^ 2) = 1
Answer:
hey did you happen to get the answer for this?
Step-by-step explanation:
The answer is -2.0 and 2.0
Solve -3(x-2)<8 or -3(x-2) > 12
Answer:
x = (14/3,6)
Step-by-step explanation:
-3(x-2) < 8
taking negative sign to opposite side relational operator changes.
3(x-2) >8
Similarly
3(x-2)<12
Now
8< 3(x-2) < 12
dividing by 3
8/3 < x-2 < 4
adding 2
8/3 +2 < x < 6
Therefore x = (14/3, 6)
Hope it helps ...
There are 80 picnic tables at the park. During the first weekend of the summer, there were 40 available tables. During the second weekend of the summer, there were 20 available tables. During the third weekend of the summer, there were 10 available tables. Based on the pattern, how many picnic tables will be available during the fourth weekend of the summer?
will mark brainliest
Answer:
5
Step-by-step explanation:
We can see a pattern of 1/2 as the week progresses. 1/2 of 80 is 40, 1/2 of 40 is 20, 1/2 of 20 is 10, so for the fourth week 1/2 of 10 is 5.
if one song is $50 and i have $17000 how many songs can i buy
Answer:
340 songs, 17000/50 = 340 lol
Answer:
340
Step-by-step explanation:
17000÷50=340.
hope this helps
The domain of the function is given. Find the range.
f(x) = 2x - 1
Domain: (-2, 0, 2, 4)
Range: (5,1, -3,7)
Range: (-5, 1, -3,7)
Range: (-5, -1,3,7)
Range: [5, 1, +3, +7)
Answer:
Range={ -5,-1,3,7). [ option C]
Please see the attached picture for full solution..
Hope it helps..
Good luck on your assignment..
which two of the following is continuous data?
Answer:
B. Age of student
D. Time taken to run 1 mile
Step-by-step explanation:
From the list of given options, only B and D satisfy the required condition.
One unique determinant of continuous data is that; they are measured and not counted.
Now, let's categorize option A to D into two
1. Counted data
2. Measured data
Options that fall into the category of measured data are said to be continuous data.
A. Concert attendance; The number of people in a concert is counted
B. The age of a student is measured (in years)
C. Number of pens in a box is counted
D. Time taken to run 1 mile is measured (in units like seconds, minutes, hours, etc...)
In summary; we have
Counted
A. Concert Attendance
C. Number of pens in a box
Measured
B. Age of a student
D. Time taken to run 1 mile
Hence, the continuous data are Age of a student and Time taken to run 1 mile
Using the following image, solve for UW
answer:15x
Step-by-step explanation:
because 2x +3 is 5x 5x+10 is 15x
The length of a rectangle is 15 meters more than the width. The perimeter is 50 meters. The width is:
Answer:
5 meters
Step-by-step explanation:
The perimeter of a rectangle can be expressed as 2l+2w.
2l+2w=50
l=w+15
Substitute:
2(w+15)+2w=50
2w+30+2w=50
4w+30=50
4w=20
w=5
Hope this helps!
Ghani is going to use these instructions to make a fizzy drink instruction: mix 5 parts of lime juice with 3 parts of lemonade ghani thinks thats he has 300ml of lime juice and 200ml of lemonade if he is correct what is the greatest amount of fizzy drink can he make?
Answer: 480 ml
The greatest amount of fizzy drink can he make is 480 ml
Step-by-step explanation:
Given;
Mixing ratio = 5 : 3
Volume of lime juice = 300ml
Volume of lemonade = 200ml
From the given ratio;
5 ml of lemon juice needs 3 ml of lemonade to make 8 ml of fizzy drink.
Assuming all the lemon juice were used;
For 300ml of lemon juice,
It'll require 300/5 × 3 ml of lemonade.
Volume of lemonade needed V2= 300/5 × 3 = 180 ml
Volume of fizzy drink = volume of lemon juice + volume of lemonade
Volume of fizzy drink = 300ml + 180ml = 480ml
The greatest amount of fizzy drink can he make is 480 ml
2x^2+14x-36 factored. please and thanks
Answer:
2 (x - 2) (x + 9)
Step-by-step explanation:
Mark brainliest please
The area of a circle is 18pi square inches. If the area of a sector of this circle is 6pi square inches, then which of the following must be the sector's central angle?
Please help I’ll give you brainliest promise !
Answer:
240 degrees
Step-by-step explanation:
Mathematically, the area of a circle is
A = 2 * pi * r^2
we need to calculate the radius of the circle first
18pi = 2pi * r^2
divide both sides by 2pi
r^2 = 9
r = 3 inches
Area of sector = angle/360 * pi * r^2
6pi = angle/360 * pi * 3^2
6pi = angle/360 * 9pi
(360 * 6pi)/9pi = angle
40 * 6 = 240 degrees
Help me im just too lazy to figure it out :)
Answer:
m=-16
Step-by-step explanation:
To solve the equation, we want to find out what m is. In order to do this, we have to get m by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
-35=m-19
19 is being subtract from m (-19). The opposite of subtraction is addition. Add 19 to both sides (+19) The -19 and +19 equal 0, and therefore cancel each other out.
-35+19=m-19+19
-35+19=m
-16=m
Let's check our solution. Plug -16 back in for m in the original equation.
-35=m-19
-35=-16-19
-35=-35
Both sides of the equation are the same, so we know that m is equal to -16.
electricity has two different rates off peak is 10pm to 6am and charged at 8p per hour. peak is 6am to 10pm and is charged at 12p per hour. alison turns uses electricity from 8pm to 11:30 pm. what is the dost of her electricity for that period
Answer:
32p
Step-by-step explanation:
the times between 8pm and 11.30pm are:
8pm,9pm,10pm,11pm,11.30pm.
so, find the cost associated with each of them:
8pm: 12p
9pm: 12p
10pm: 12p
11pm:8p
11.30pm: 4p
sum:12+12+12+8+4 = 12 x 4 = 32p
find the second derivative of the function P(t) =(2t+4)/(t+1)
use the quotient rule then after using it the first time use it again on your resulting equation, since you are looking for the second derivative
Use the law of sines to find the value of y. Round to the nearest tenth.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
1.4 units
1.6 units
2.5 units
2.6 units
Answer:
b) 1.6 units
y = 1.586 ≅ 1.6 units
Step-by-step explanation:
Explanation:-
step(i):-
The sine rule
[tex]\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]
Given a = 2 and b = y
∠A = 75° and ∠ B = 50°
Step(ii):-
by sine rule
[tex]\frac{a}{Sin A} = \frac{b}{Sin B}[/tex]
[tex]\frac{2}{Sin 75} = \frac{y}{Sin 50}[/tex]
Cross multiplication , we get
2 × sin 50° = y sin 75°
2 × 0.766 = y × 0.9659
[tex]y = \frac{ 2 X 0.766}{0.9659} = 1. 586[/tex]
y = 1.586 ≅ 1.6 units
Answer:
Step-by-step explanation:
Which measurements could be the length of the third
side? Select all that apply.
A student is constructing a triangle with the following
dimensions:
side length of 10 inches
side length of 30 inches
19 inches
0 21 inches
D 35 inches
45 inches
in ohon
Answer:
35 and 21
Step-by-step explanation:
the sum of the two lengths of two sides must be greater than the length of the third side.
10+30=40
45 doesn't work: 40<45.
10+19=29
29<30
19 doesn't work
10+21=31
31>30
21 works
35+10=45
45>30
35 also works
Answer:
35 and 21, good luck!! sorry I'm late
What is the probability that you’re on mars right now?
The probability of you being on Mars right now is very slim, because no one that we know of currently lives on Mars.
What is: 6x^2-4x-10?
[tex]answer \\ (3x - 5)(2x + 2) \\ solution \\ {6x}^{2} - 4x - 10 \\ = {6x}^{2} - (10 - 6)x - 10 \\ = {6x}^{2} - 10x + 6x - 10 \\ = 2x(3x - 5) + 2(3x - 5) \\ = (3x - 5)(2x + 2) \\ hope \: it \: helps[/tex]
Answer:
x = 1⅔ or -1
Step-by-step explanation:
6x² -4x - 10
a=6, b=-4, c=-10, ac= -60
factors -10 & 6
6x² + 6x - 10x -10 =0
(6x² + 6x) - (10x - 10) =0
6x(x +1) - 10(x+1) =0
(6x-10)(x+1)=0
6x-10=0 or. x+1=0
6x= 10 or x= -1
x= 10/6 or. x= -1
x=1⅔ or x= -1
another EASY question for y’all mathy people, easy points! Question in photo.
Answer:
the answer is c
Step-by-step explanation:
What is the equation of the translated function, g(x), if
f(x) = x??
Answer:
There is not enough information to solve. We need some more information to solve this question. The best we can do is
g(x) = g(f(x))
