The perimeter of a rectangular house is 122 ft. the width is 5 ft less than the length. find the length and the width.
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Jodie uses her college printer to print pages at the rate of $0.06 per page. She decides to rent a printer for $80 a year. The cost of printing using the rented printer is $0.02 per page.
Part A: Write an inequality that can be used to calculate the number of pages that Jodie should print in a year so that the amount she pays for the rented printer is less than the college printer. Define the variable used. (5 points)
Part B: How many pages should Jodie print in a year to justify renting the printer? Show your work.
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Jodie uses her college printer to print pages at the rate of $0.06 per page.
=> cost of college printer = 0.06x
She decides to rent a printer for $80 a year. The cost of printing using the rented printer is $0.02 per page.
cost of rented printer = 80 + 0.02x
Part A: Write an inequality that can be used to calculate the number of pages that Jodie should print in a year so that the amount she pays for the rented printer is less than the college printer.
cost of rented printer < cost of college printer
=> 80 + 0.02x < 0.06x <-------- inequality
Part B: How many pages should Jodie print in a year to justify renting the printer? Show your work.
=> 80 < 0.06x - 0.02x
=> 80 < 0.04x
=> 0.04 x > 80
=> x > 80 / 0.04
=> x > 2000
Answer: Jody should print at least 2000 pages to justify the rent of the printer.
6-1. let x have a poisson distribution with a mean of 4. find (a) p(2≤x≤5). (b) p(x≥3). (c) p(x≤3).
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[tex]f_X(x)=\dfrac{e^{-4}4^x}{x!}[/tex]
So,
a. [tex]\mathbb P(2\le X\le5)=\dfrac{e^{-4}4^2}{2!}+\cdots+\dfrac{e^{-4}4^5}{5!}\approx0.6936[/tex]
b. [tex]\mathbb P(X\ge3)=\dfrac{e^{-4}4^3}{3!}+\dfrac{e^{-4}4^4}{4!}+\cdots\approx0.7619[/tex]
c. [tex]\mathbb P(X\le3)=\dfrac{e^{-4}4^0}{0!}+\cdots+\dfrac{e^{-4}4^3}{3!}\approx0.4335[/tex]
Find the missing number of each unit rate
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6/2 = 3/1
12/4 = 3/1
if the last on is negative it would -24/8 = -3/1 if positive 3/1 hope this helps remember you would reduce your fraction
12/4 reduces to 3/1
Can you do the remaining problems?
Suppose e(x) = 3 and e[x(x − 1)] = 27.5. (a) what is e(x2)? [hint: first verify that e[x(x − 1)] = e[x2 − x] = e(x2) − e(x).]
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The formula for the volume of a sphere is Upper V equals four thirds pi r cubedV=
4/3πr3, where r is the radius of the sphere. The steel ball to the right is in the shape of a sphere and has a diameter of 3030 millimeters.
a. Find the exact volume of the sphere.
b. Find a 2-decimal-place approximation for the volume.
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now, that rounded to 2 decimals is just 523.60
After calculating, the volume of the sphere obtained will be equal to V = 1.45 × 10¹⁰ mm³.
What is Volume?Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.
As per the given data in the question,
The formula for the volume of the sphere is given as,
V = 4/3 π r³
Diameter = 3030 mm
r = D/2
r = 3030/2
r = 1515 mm
So, the volume will be,
V = 4/3 π (1515³)
V = 1.45 × 10¹⁰ mm³
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You've got 60 homework problems to do and it took you 10 minutes to do eight of them. At that rate, how long will it take?
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x minutes : 60 problems
10 * 60/8 = 150/2 = 75 minutes for 60 problems
You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over. What fractional portion of the original bowl of salad does each friend receive?
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Answer:
[tex]\frac{2}{3x}[/tex]
Where, x = total friends
Step-by-step explanation:
Given,
The part of the salad has eaten = [tex]\frac{1}{3}[/tex]
Total part of the salad = 1,
Thus, the remaining part of the salad = original part - part has eaten
[tex]=1-\frac{1}{3}[/tex]
[tex]=\frac{3-1}{3}[/tex]
[tex]=\frac{2}{3}[/tex]
If there are x friends,
Then the portion of the original bowl of salad received by each friend
[tex]=\frac{\text{Remaining part}}{\text{Total friends}}[/tex] [tex]=\frac{2}{3x}[/tex]
6578 divided 34
20\5
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Answer:
263.56 :)
Step-by-step explanation:
Plz help 35 points!!! The floor of a rectangular banquet has an area of 1,600 m2.The length is 80 m.What is the width?
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your problem looks like:
80x=1600 and then just solve so x =20
Mr. and Mrs. Zeller close on a 20 year home loan for $150,000. The monthly payment with no points is $1,160, but if they buy a point it is $1,150. What might you infer if Mr.and Mrs. Zeller choose not to buy a point? a. They plan to sell the house at the end of 5 years. b. They plan to sell the house at the end of 15 years. c. They plan to sell the house at the end of 20 years. d. They plan to sell the house at the end of 25 years.
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Answer:
the answer is A they plan to sell it in 5 years
Step-by-step explanation:
what is r^m divided by r^m equal to.
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What is the common difference for the arithmetic sequence?
4.7, 6, 7.3, 8.6, 9.9,...
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if 2 pounds of strawberries cost 4.50 how much would 3 pounds cost
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An object's position is given by x(t) = 5 + 10 t 2. what is its acceleration after 5 s
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The acceleration after 5 seconds is 20 m/s^2.
Explanation:To find the acceleration, we need to take the second derivative of the position function.
x(t) = 5 + 10t^2
Taking the derivative with respect to time, we get:
v(t) = 20t
Taking the derivative again, we get the acceleration:
a(t) = 20
Therefore, the acceleration after 5 seconds is 20 m/s^2.
The cost of 5 cds and a $ 12 DVD
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The cost of 5 CDs and a $12 DVD is $62.
Explanation:The subject of this question is Mathematics. The question asks for the cost of 5 CDs and a $12 DVD. To find the total cost, we need to know the price of each CD and the price of the DVD.
Let's say the price of each CD is $10. The total cost of 5 CDs would be 5 multiplied by $10, which is $50.Adding the cost of the DVD, which is $12, to the cost of the CDs, we get a total cost of $50 + $12 = $62.Therefore, the cost of 5 CDs and a $12 DVD is $62.
Given f(x) = x^2 - 10x + 22, what is the range of f?
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For a parabola that opens up, it is everything greater than the vertex.
If the vertex is (h,k) then the range is y >= k.
Vertex can be found using completing the square:
[tex]x^2 -10x +22 \\ \\ (x^2 -10x + (\frac{-10}{2})^2) +22 - (\frac{-10}{2})^2 \\ \\ (x^2 -10x+25) +22-25 \\ \\ (x-5)^2 - 3[/tex]
(h,k) = (5,-3) ------> Range is y >= -3
Vertex may also be found using formula [tex]h = \frac{-b}{2a} [/tex]
a = 1, b = -10, c = 22
[tex]h = \frac{10}{2} = 5[/tex]
[tex]k = 5^2 - 10(5) +22 \\ \\ k = 25 -50+22 \\ \\ k = -3[/tex]
------> Range is y >= -3
f(x)=x2-10x+22 domain of f
Answer: all real numbers
Range of F
Answer: y> -3
the circle with center (3,5) and radius 2 has a equation?
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Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found. Find the slope and y-intercept of the line.
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Answer:
m=-63 b=825
Step-by-step explanation:
The slope of the line would be - [m] = - 63 and the [y] intercept is - [c] = 835.
What is the general equation of straight line? What is a mathematical function, equation and expression?straight line : The general equation of a straight line is -[y] = mx + c
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods.
It is given that a graph has number of days on the x - axis and number of canned goods on the y-axis. The line goes through points (2, 699) and (8, 321). The slope of the line can be written as -
[m] = (321 - 699)/(8 - 2)
[m] = -378/6
[m] = - 63
For the point (2, 699), we can write -
y = - 63x + c
699 = - 63 x 2 + c
699 = -126 + c
c = 699 + 126
c = 835
Therefore, the slope of the line would be - [m] = - 63 and the [y] intercept is - [c] = 835.
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{Complete question -
A graph has number of days on the x-axis and number of canned goods on the y-axis. A line goes through points (2, 699) and (8, 321).
Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found.
Find the slope and y-intercept of the line.}
Which three statements would produce the truth value F when p is true and q is false?
A. p -> q
B. ~p/\~q
C. p->~q
D. q\/~p
C. p/\~q
please help
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Answer with Step-by-step explanation:
p is true then ~p is false.
q is false then ~q is true.
A. p -> q
if p is true and q is false then this gives false truth value.
Hence, here truth value is F
B. ~p/\~q
if any one of them is false then it gives false truth value.
Hence, here truth value is F(since,~p is false)
C. p->~q
true statement implies a true statement hence, truth value will be true
Hence, here truth value is T(p true implies ~q true)
D. q\/~p
if any one of them is true then compound statement is true.
Hence, here truth value is F(since, ~p and q both are false)
E. p/\~q
if both true then compound statement is also true.
Hence, here truth value is T(since p and ~q both are true)
the sum of two numbers is 18 . the difference of the two numbers is -2 find the numbers
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a + b = 18
a - b = -2
2a = 16
a = 8
8 + b = 18
b = 10
Ryan uses 3 bars of clay for a sculpture. The first bar is 1.15 centimeters long. The second bar is 3.92 centimeters long. What is the total length of 2 bars?
Enter your answer in the box.
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there are 1,525 pages in a book. Julia and Kim round the number of pages to the nearest hundred
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In the case of rounding up, the number beside the must be above 5
But, in the case of rounding down, the number beside must be below 5.
The hundred place is the number 5.
The number before the 5 is the number 2
Since 2 is lower than 5, we round it down..
Thus the answer is 1,500
Hope this helps :))
Julia and Kim round the number of pages to the nearest hundred as 1500.
Given that, there are 1,525 pages in a book.
What is the rounding off numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
In the given number, digit in the tens place is 2, so the number rounded to nearest hundred as 1500.
Therefore, Julia and Kim round the number of pages to the nearest hundred as 1500.
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whats the nearest tenth to -61 square root
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that is, i=√-1
so we can write
[tex]\sqrt{-61}=(\sqrt{-1})(\sqrt{61})=(i)(\sqrt{61})[/tex] [tex] \sim (i)(7.81) \sim 7.8i[/tex]
the √(-61) is a complex number √61i
But if you wish to find the value of an irrational and imaginary number, I will give you the approximate answer.
[tex] \sqrt{-61} \to \sqrt{-1*61} \to \sqrt{-1} * \sqrt{61} \to i* \sqrt{61} \to i*7,81024...\: \boxed{\approx 7.8i}[/tex]
A geologist have two rocks on a scale that weighs 2 1/2 lbs together rock a was 1/7 of a the total weight how much did rock a weight
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By using the given fraction of rock 'a' against the total weight of two rocks, we can find that rock 'a' weighs approximately 0.357 lbs.
Explanation:The student's question involves calculating the weight of a rock, given as a fraction of a total weight. In this case, they are talking about a scenario where a geologist uses a scale to weigh two rocks together, with a total weight of 2 1/2 lbs, and rock 'a' is specified to be 1/7 of this total weight. To determine the weight of rock 'a', we simply divide the total weight by 7.
So, 2 1/2 lbs is equivalent to 2.5 lbs (since 1/2 is the same as 0.5). To find the weight of rock 'a', we take this total weight and perform the operation: 2.5 ÷ 7 = 0.357 lbs.
Therefore, rock 'a' weighs approximately 0.357 lbs. Remember, this is an estimation because the weight of the rock is being given as a fraction of the total weight, and actual weights can vary based on factors such as density and volume.
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Amanda can jog 18 miles in 5 hours. At this rate, how many miles can Amanda jog in 4 hours?
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__ __
5 4
x = 18•4 / 5
72/5 = 14.4 final answer
we know that
Amanda can jog [tex]18[/tex] miles in [tex]5[/tex] hours
so
by proportion
Find the number of miles that Amanda can jog in [tex]4[/tex] hours
[tex]\frac{18}{5} \frac{miles}{hours} =\frac{x}{4} \frac{miles}{hours} \\ \\5*x=18*4 \\ \\x=72/5 \\ \\ x=14.4\ miles[/tex]
therefore
the answer is
[tex]14.4\ miles[/tex]
Factor out the coefficient of the variable. The expression 2.2x +4.4 factored is
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Nick is driving to a town 30 miles away. He is averaging about 45 miles per hour. If he makes no stops, how long will the trip take (in minutes)?
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45 miles per hour
= 45 miles per 60 minutes
= 3/4 mile per minute
Now, use a ratio to solve.
30 miles : x minutes = 3/4 mile : 1 minute
30=3/4x
x=40
Nick will take 40 minutes to get to the town.
Hope this helps!
8 = 4x + 12 what does x equal
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-4 = 4x
-1 = x
1) subtract 12 from both sides.
-4 = 4x
2) divide each side by 4
-1 = x
A red candle is 8 inches tall and burns at a rate of 7/10 inch per hour. A blue candle is 6 inches tall and burns at a rate of 1/5 inch per hour. After how many hours will both candles be the same height?
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Answer:
4 hours
Step-by-step explanation:
The height of the red candle in inches can be modeled by ...
h = 8 - (7/10)t
where t is the number of hours it burns.
Likewise, the height of the blue candle can be modeled by ...
h = 6 - (1/5)t
The heights of the two candles will be the same when one expression for height is equal to the other.
8 - (7/10)t = 6 - (1/5)t
2 = t(7/10 - 1/5) . . . . . . . . . add (7/10)t -6
2/(5/10) = t = 4 . . . . . . . . . divide by the coefficient of t
The measure of arc XZ is 28° what is the measure of XYZ
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Angle XYZ is marked in blue
It turns out that angle XYZ is exactly half the measure of arc XZ. This is due to the inscribed angle theorem. Angle XYZ is an inscribed angle that cuts off, or subtends, arc XZ.
measure of arc XZ = 28 degrees
measure of angle XYZ = (1/2)*(measure of arc XZ)
measure of angle XYZ = (1/2)*(28 degrees)
measure of angle XYZ = 14 degrees
Answer: D) 14 degrees