Suppose that 18 inches of wire costs 90 cents. At the same rate, how much (in cents) will 15 inches of wire cost?
Answers
18 inches cost 90 cents
The porportion is inches / cents = 18/90
For 15 inches of wire: 15/x, where x is the cost of 15 inches of wires in cents.
So, equal both:
18/90 =15/x
Solve for x:
x = 15 / (18/90)
x= 75 cents
Related Questions
Determine whether the sequence converges or diverges. If it converges, find the limit. [Hint:
consider limit laws, the Squeeze Theorem, behavior of related real-valued functions, etc.]
(a) an = 2 + (0.86)^n
(b) an =(4^n)/(1+9^n)
(c) an = arctan(ln n)
Answers
(a) converges; consider the function f(x) = a ˣ, which converges to 0 as x gets large for |a | < 1. Then the limit is 2.
(b) converges; we have
4ⁿ / (1 + 9ⁿ) = (4ⁿ/9ⁿ) / (1/9ⁿ + 9ⁿ/9ⁿ) = (4/9)ⁿ × 1/(1/9ⁿ + 1)
As n gets large, the exponential terms vanish; both (4/9)ⁿ → 0 and 1/9ⁿ → 0, so the limit is 1.
(c) converges; we know ln(n ) → ∞ and arctan(n ) → π/2 as n → ∞. So the limit is π/2.
For the given data, construct a frequency distribution and frequency histogram of the data using five classes. Describe the shape of the histogram as symmetric, uniform, skewed left, or skewed right. Data set: ages of 20 cars randomly selected in a student parking lot 12 6 4 9 11 1 7 8 98 9 13 5 15 7 6 8 8 21 A. skewed right B. uniform C. symmetric D. skewed left
Answers
To construct a frequency distribution and frequency histogram of the data using five classes, we first need to determine the range of the data and the class interval.
The range is the difference between the highest and lowest values in the data set, in this case, 98 - 1 = 97.
We can divide the range by the number of classes to determine the class interval. In this case, 97/5 = 19.4.
We will round up to 20 to have easily divisible numbers.
The class intervals with the frequency would be:
1-20: 3
21-40: 2
41-60: 0
61-80: 3
81-100: 2
Next, we need to create a frequency histogram by plotting the class intervals on the x-axis and the frequencies on the y-axis, and then drawing a bar for each class interval representing the frequency.
The histogram will be skewed right. A histogram is skewed right when the tail of the histogram extends farther to the right than the left. In this case, the majority of the data falls in the lower class intervals, but there are a few outliers on the higher end, which extends the histogram to the right.
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The basketball team raised a total of $154,694 in September and $29,987 more in October than in September. How much money did they raise in October?
Answers
Answer:
$184,681
Step-by-step explanation:
154,694+29,987= 184,681
Just add the two numbers up. Hope this helps
Unas deportivas cuestan $600 he visto que hay una rebaja del 20% cuánto dinero rebajado las reporteras
Answers
Answer:
600/100*20=6*20=120
600-120=480$
Question 14 (Essay Worth 12 points)
(Comparing Data HC)
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School
9, 7, 2,0
8, 7, 6, 5, 5, 5, 4, 3, 1, 0
0
1
South Lake School
5,8
0, 1, 2, 6, 6, 8
2
0 3
Key: 2|1|0 means 12 for Sky View and 10 for South Lake
5, 5, 6, 7, 8
0,6
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (2 points)
7
Answers
To find the measures of center, we need to determine the median for each school.
For Sky View School:
Arrange the data in order: 0, 0, 1, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9
The median is the middle value, which is 5.
For South Lake School:
Arrange the data in order: 0, 0, 1, 2, 2, 5, 6, 6, 8
The median is the middle value, which is also 5.
Therefore, the median class size for both schools is 5.
Part B: Measures of variability
To find the measures of variability, we need to determine the range and interquartile range (IQR) for each school.
For Sky View School:
The smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 1 + 2 + 3 + 4)/5 = 2. The third quartile is the median of the upper half, which is (6 + 7 + 8 +9)/4 = 7.25 (rounded to two decimal places).
Therefore, the IQR is 7.25 - 2 = 5.25.
For South Lake School:
The smallest value is 0 and the largest value is 8, so the range is 8 - 0 = 8.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 0 + 1 + 2)/4 = 0.75 (rounded to two decimal places). The third quartile is the median of the upper half, which is (6 + 6 + 8)/3 = 6.67 (rounded to two decimal places).
Therefore, the IQR is 6.67 - 0.75 = 5.92 (rounded to two decimal places).
Part C: Choosing a school based on class size
If you are interested in a smaller class size, South Lake School is the better choice. This is because the range and IQR for South Lake School are smaller than those for Sky View School, indicating that the class sizes at South Lake School are more consistent and less variable. Additionally, the largest class size at South Lake School is 8, while the largest class size at Sky View School is 9, further indicating that South Lake School may have smaller class sizes overall.
Measures of center for Sky View School:
Mean = (0+1+2+3+4+5+5+5+6+7+7+8+9)/13
Mean = 4.8
Median = 5
Measures of center for South Lake School:
Mean = (0+1+2+2+3+5+6+6+8+8)/10
Mean = 4.1
Median = 5
Part B:
Measures of variability for Sky View School:
Range = 9 - 0 = 9
Interquartile Range (IQR) = Q3 - Q1 = 7 - 2 = 5
Variance = [(0-4.8)^2 + (1-4.8)^2 + (2-4.8)^2 + (3-4.8)^2 + (4-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (6-4.8)^2 + (7-4.8)^2 + (7-4.8)^2 + (8-4.8)^2 + (9-4.8)^2]/12
Variance = 7.6
Standard Deviation = √7.6
Standard Deviation = 2.76
Measures of variability for South Lake School:
Range = 8 - 0 = 8
Interquartile Range (IQR) = Q3 - Q1 = 6 - 1 = 5
Variance = [(0-4.1)^2 + (1-4.1)^2 + (2-4.1)^2 + (2-4.1)^2 + (3-4.1)^2 + (5-4.1)^2 + (6-4.1)^2 + (6-4.1)^2 + (8-4.1)^2 + (8-4.1)^2]/9
Variance = 6.45
Standard Deviation = √6.45
Standard Deviation = 2.54
Part C:
If you are interested in a smaller class size, South Lake School is a better choice for you. This is because the measures of center and variability for South Lake School are both smaller than those for Sky View School.
Name:
11. Find the measure of each acute angle.
(2x + 6°
(5x + 14°
Answers
Answer:
A
Step-by-step explanation:
Dc is a little bit more than a few other things but I think it’s Going and the kids have to be in a different room yet I think it’s going on for me and my kids are in my car so I’m going to go get my car off at my moms and I can go pick it out I have a lot to go
Question 1 of 5 Which number line shows the solutions to x < 5? OA. -3 -6 -4 -2 0 2 4 6 8 OB. O C. -8 -6 -4 -2 0 2 4 6 8 -8-6-4-2 0 2 4 6 8 OD. 864 2 0 2 4 6 8
Answers
The number line that shows the solutions of x < 5
B. O What is number line?A number line is a visual representation of the real numbers, ordered from left to right, with zero in the middle. It is typically a straight line that extends infinitely in both directions, with evenly spaced markings that represent specific points along the line.
The solution of x < 5 should consist of number less than 5
The inequality used is less than and hence should have values saying less than
Other options has numbers more than 5 such as 6 except option B
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What way does f(x) shift for log (DWX) ?
Left, right, down, up?
Answers
The function f(x) can shift for log (w ± dx) in any of the four directions
How to determine the direction of shiftFrom the question, we have the following parameters that can be used in our computation:
log(DWX)
Express properly
log(w ± dx)
Where w and d are constants and x is the variable
The above function is a logarithmic function, and the parent function is
log(x)
The direction the function shifts is dependent on the values of w and d i.e.
w ± dx > 1 will shift the function right0 < w ± dx < 1 will shift the function leftAlso, the vertical shift depends on the w ± dxRead more about transformation at
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I have another riddle.
If you buy one rabbit and a rabbit can produce 5 per year, then how many rabbits will you have in 9 years?
Answers
Total number of rabbits produced in 9 years will be 45.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a rabbit can produce 5 new rabbits per year
Total number of rabbits produced in 9 years will be -
n = 5y = 5 x 9 = 45 new rabbits
Therefore, total number of rabbits produced in 9 years will be 45.
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I will award brainless to the person that actually explains how they got their answer other then “It’s right on edge”
Points D, E, and F are on circle C and EF ≅ DF.
Circle C is shown. Line segments D C and E C are radii. Point F is on the opposite side. Lines are drawn from points D and E to point F. Tangents D G and E G intersect at point G. Angle D G E is 76 degrees and angles G D C and G E C are 90 degrees. D F and E F are congruent.
What is the measure of ∠CDF?
14°
19°
26°
38°
Answers
Answer:
14°
Step-by-step explanation:
Angle DCE is congruent to Angle GDF
To find the measure of Angle CDF, you need to find the measure of Angle DCE first.
360° = 76° + 90° + Angle DCE + 90°
360° = 256° + Angle DCE
Angle DCE = 104°
Then you subtract 90° from 104° (Angle DCE) to get the measure of Angle CDF
104° - 90° = 14°
Angle CDF = 14°
Answer:
C. 26 degrees
Step-by-step explanation:
Just did the review on Edg (2021)!!
Given the ordered pair (12,5), find cot θ
Answers
Answer:
12 left and 5 down
Step-by-step
On the X Axis, you need to move 12 points left.
On the Y Axis, you need to move 5 points down.
This will bring you to (0, 0)
Can someone help me with the equation in the picture below.
Answers
Answer:
x=3
Step-by-step explanation:
First, you would distribute the 4 to the (x-3), giving you 2x-6+4x-12
From there combine like terms, 2x+4x=6x, -6+-12=-18
6x+-18=0
6x=18
divide both side by 6, and you get 3=x!
I hope that all makes sense :)
The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answers
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
Suppose that ƒ is a function given as f(x) = 4x² + 5x + 3.
Simplify the expression f(x + h).
f(x + h)
Simplify the difference quotient,
ƒ(x + h) − ƒ(x)
h
=
Submit Question
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f(x+h)-f(x)
f'(x) =lim
h→0
h
ƒ(x + h) − f(x)
h
=
Answers
Answer:
f(x +h) = 4x² +4h² +8xh +5x +5h +3
(f(x+h) -f(x))/h = 4h +8x +5
f'(x) = 8x +5
Step-by-step explanation:
For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.
F(x+h)Put (x+h) where h is in the function, and simplify:
f(x+h) = 4(x+h)² +5(x+h) +3
= 4(x² +2xh +h²) +5x +5h +3
f(x +h) = 4x² +4h² +8xh +5x +5h +3
Difference quotientThe difference quotient is ...
(f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h
= (4h² +8xh +5h)/h
(f(x+h) -f(x))/h = 4h +8x +5
LimitWhen h=0, the value of this is ...
f'(x) = 4·0 +8x +5
f'(x) = 8x +5
__
Additional comment
Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.
<95141404393>
Lisa, Felipe, and Justin have a total of $120 in their wallets. Lisa has $6 more than Justin. Felipe has 4 times what Justin has. How much does each have?
Answers
Let
x -----> Lisa's amount
y -----> Felipe's amount
z -----> Justin's amount
we have that
x+y+z=120 --------> equation A
x=z+6 ------> equation B
y=4z -----> equation C
substitute equation B and equation C in equation A
so
(z+6)+4z+z=120
solve for z
6z+6=120
6z=120-6
6z=114
z=$19
Find the value of x
substitute the value of z in equation B
so
x=19+6
x=$25
Find the value of y
substitute the value of z in equation C
y=4(19)
y=$76
therefore
Lisa's amount is $25
Felipe's amount is $76
Justin's amount is $19
Christina’s savings account grows at a rate of 2% compounded quarterly. If her initial deposit is $750, write a function A(t)
that models the balance of the savings account after t years.
Answers
Answer:
Step-by-step explanation:
A = P * (1 + r/n)^(n*t
The function that gives the amount of money in dollars, J(t), in Jamie's account t years after the initial deposit is A = 750(1.0002)^4t. (in dollars)
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
For this case, we're given that:
Initial amount Christina deposits = P = $750
Rate of interest = 2% compounding quarterly
Time = t years
Rate of interest is compounding quarterly.
Each year has 4 quarters.
Quarterly interest rate compounding quarterly = 2%.
t years has 4t quarters = T
Thus, we get the final amount in Christina’s account as
A = P * (1 + r/n)^(n*t)
A = 750(1 + 0.02/100)^4t
A = 750(1.0002)^4t
Thus, the function that gives the amount of money in dollars, J(t), in Christina’s account t years after the initial deposit is A = 750(1.0002)^4t (in dollars)
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Hi! Can you plz answer this for me I am bad at math plz
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation:
base = 21 / 8 mm
height = 10 mm
area = 1/2 × base × height
= 1/2 × 21/8 × 10
= 13 1/8
when somebody says why you like me what should i say
Answers
Answer:
Not even related to math. But say no.... Unless you really like them then say yes
Step-by-step explanation:
The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100
Answers
answer: the range is 41.
to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.
then we subtract the minimum from the maximum.
59 - 100 = 41.
Which is NOT true?
7 + 7 = 19 - 5
9 + 9 = 11 + 7
19 = 13 + 5
20 - 12 = 4 + 4
Answers
Answer:
c.19 = 13 + 5
Step-by-step explanation:
Please help me I have no clue what this is steps would be great I have a exam and I have no clue what I'm doing anyways... HELP MEEEEEE if you have time to help me with this that would be amazing.
Answers
Answer:
D. Infinitely Many Answers
Step-by-step explanation:
Simply the function -x+4(x-2)
-x+4x-8
3x-8
Notice it is the same with the the first function
Thus, they are the same function, so they intersect each other infinitely many.
What is the product of 1.2 and 0.6
Answers
Answer:
.72
Step-by-step explanation:
simple multiplication
Ryan went to see a baseball game. The game started at 10:39 AM and ended at 2:12 PM. How long was the game?
Answers
Answer: The game was 3 hours and 55 minutes.
Step-by-step explanation: As the game started at nearly 11, if you carefully add up and write down every answer, you'll get to that conclusion as since it started at almost 11, the game was almost 4 hours.
In total, the game was 3 hours and 55 minutes. (I hope this helps and my explanation wasn't to confusing!)
40% of 30 equals what percent of 48?
Answers
Solution: 30 is what percent of 48 is equal to (30 / 48) x 100 = 62.50%. So if you buy an item at $48 with $30 discounts, you will pay $18 and get 62.50% discount cashback rewards. So 30 out of 48 as a percentage is 62.50%
40 percent of 30 is equal to 25 percent of 48.
We have to find first 40% of the number 30.
40% of 30 = 40% × 30
= (40 / 100) 30
= 0.4 × 30
= 12
Now we have to find what percent of 48 is 12.
Let the required percentage be x.
x% of 48 = 12
(x/100) 48 = 12
x/100 = 12/48
x/100 = 0.25
x = 0.25 × 100
x = 25%
Thus, 40% of 30 equals 25% of 48.
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What is the solution of 6(3 − 2x) = 54?
Answers
Step-by-step explanation:
6(3-2x)=54
18-12x=54
-12x=54-18
-12x=36
x=36 /-12
x=-3
he entire graph of the function is shown in the figure below.
Write the domain and range of using interval notation.
Someone please help me. I really nee help. this question is due tonight before 8 and im stuck.
Answers
The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].
The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).
In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.
So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.
In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].
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estimate the solution.
y=x+4
y=3x−1
Answers
9514 1404 393
Answer:
(x, y) = (2.5, 6.5)
Step-by-step explanation:
I find it easier just to solve the system of equations:
x + 4 = 3x - 1
5 = 2x
x = 5/2 = 2.5
y = x+4 = 6.5
(x, y) = (2.5, 6.5)
__
Additional comments
The first equation has a positive y-intercept and a positive slope, so makes a triangle with the axes in the 2nd quadrant.
The second equation has a negative y-intercept and a (more) positive slope, so makes a triangle with the axes in the 4th quadrant. The slope is greater for this line, so the lines will intersect in the 1st quadrant. Without more effort, the best estimate at this point is that x and y are both positive and y > 4.
Sphenathi and other matriculants plan to pass Bloemfontein at 07.25 to travel the above stated distance to Uptington. Determine (to the nearest km/h) the average speed at which they must travel to be in Uptington by 09:45.
Answers
Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.
To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.
The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:
2 hours + 20 minutes / 60 = 2.33 hours
Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.
We can use the formula for average speed: average speed = distance / time
In this case, the average speed should be such that the distance divided by the time is equal to the average speed.
d / 2.33 = average speed
Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:
250 / 2.33 = average speed
To find the average speed to the nearest km/h, we'll calculate the result:
average speed ≈ 107.3 km/h
Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.
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2x+5=10
someone help me
Answers
Answer:
2x=5 x=2.5
Step-by-step explanation:
2x+5=10
2x=10-5
2x=5
x=2.5
Answer:
yes the answer is 10
Step-by-step explanation:
find the third, fourth, and fifth terms of the sequence defined by
a1 = 1, a2 = 3,
and
an = (−1)nan − 1 + an − 2
for
n ≥ 3.
Answers
The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.
The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.
Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.
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