The number of gallons of coffee a mathematician drinks on any given day is inversely proportional to how much sleep he gets the night before. On Monday, he got 9 hours of sleep and drank 2 gallons of coffee. On Tuesday, he got 6 hours of sleep. How many gallons of coffee did he drink?
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Related Questions
In the year 2001, a total of 7.2 million passengers took a cruise vacation. The global cruise industry has been growing at 9% per year for the last decade. Assume that this growth rate continues.
How many cruise passengers (in millions) are predicted in the year 2002?
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To predict the number of cruise passengers in 2002, multiply the growth rate by the previous year's number of passengers and add that to the previous year's total.
Explanation:To predict the number of cruise passengers in the year 2002, we need to apply the growth rate of 9% to the number of passengers in the previous year (2001).
Therefore, the predicted number of cruise passengers in the year 2002 is
7.848 million
.
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Write an equation of four lines that intersect to form the sides of a parallelogram
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To write equations for four lines forming a parallelogram, we use the slope-intercept form ensuring two sets of parallel lines. Opposite lines have equal slopes and by manipulating the y-intercepts, we ensure they intersect appropriately to form a parallelogram.
Writing an equation for four lines that intersect to form the sides of a parallelogram involves ensuring that opposite sides are parallel and equal in length. One straightforward approach is to use the slope-intercept form of a line, y = mx + b, to define the lines.
Let's start by defining two lines with slopes 'm' and 'm' (since opposite sides of a parallelogram are parallel) and two lines with slopes '-1/m' to ensure they are also parallel to each other but perpendicular to the first set of lines. If we assume lines have y-intercepts at 'b' and '-b' respectively (to ensure symmetry and simplify calculations), our equations would be:
y = mx + b (Line 1)y = mx - b (Line 2) - Parallel to Line 1y = (-1/m)x + k (Line 3) - Perpendicular to Line 1y = (-1/m)x + l (Line 4) - Parallel to Line 3Here, m represents the slope of the first set of parallel lines, b represents the y-intercept of line 1, -b represents the y-intercept of line 2, and k and l are the y-intercepts of lines 3 and 4. By adjusting 'b', 'k', and 'l' we ensure the lines intersect to form a parallelogram.
These lines will form a parallelogram as long as 'k' and 'l' are chosen such that the distances between the y-intercepts of lines 1 and 2, and lines 3 and 4, are equal, satisfying the condition for parallel lines in a parallelogram. This way, we can visually imagine or draw a parallelogram with these four lines as its sides.
Cereal costs $2.79 for 16.4 ounces. At this rate how much does 25 ounces of cereal cost?
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what is the cost of painting the walls and ceiling of a room with walls 30 foot by 25 foot by 1st foot with paint that covers at $9.50 per square yard, allowing for 1275 square feet for doors, windows, and baseboards?
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therefore, the surface area of that room is
2 10x25 rectangles, front and back
2 30x10 rectangles, left and right
and 2 25x30 rectangles, top and bottom
so the area will be (2*10*25) + (2*30*10) + (2*25*30), which gives us 2600 square feet though, not yards.
let's add the doors, windows and others which is 1275, so 2600 + 1275, that gives us 3875 square feet.
now, the paint is 9.5 for square yard, no feet, so let's do some conversion then,
[tex]\bf \begin{array}{ll} yards&feet\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1yd&3ft\\ (1yd)^2&(3ft)^2\\ yd^2&3^2ft^2\\ &9ft^2 \end{array}[/tex]
so, if there are 9 square feet in one square yard, how many square yards are there in 3875 square feet?
[tex]\bf \begin{array}{ccll} yd^2&ft^2\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&9\\ x&3875 \end{array}\implies \cfrac{1}{x}=\cfrac{9}{3875}\implies \cfrac{3875}{9}=x[/tex]
that's how many yd² are there in 3875 ft².
now, we know for every yd², is $9.50, so then the cost will be
[tex]\bf 9.5\cdot \cfrac{3875}{9}\implies \cfrac{95}{10}\cdot \cfrac{3875}{9}\implies \cfrac{73625}{18}~~\approx~~ \stackrel{\$}{4090.2778}[/tex]
If a truck hauls 5 loads per week how many loads would it haul in a 1 year period
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1 year = 52 weeks
52 * 5 = 260 loads
What is a 6% increase to $62,900
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6% = 0.06
multiply:
62900*0.06 = 3,774 ( Would be the amount of increase)
add:
62900 + 3774 = 66,674 (would be the new total)
Find the standard matrix of the linear transformation t(x, y, z) = (x − 2y + z, y − 2z, x + 3z).
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What is the reciprocal of 6 4/5?
A.) 5/34
B.) 29/5
C.) 34/5
D.) 15/5
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Answer:
A
Step-by-step explanation:
The denominator in the original question is 5.
Therefore the answer must have 5 in the numerator. The answer can only be A.
6 4/5 = (30 + 4) / 5 = 34/5 This is the original fraction. The upside down of the original fraction is the reciprocal. Upside down of 34/5 is 5/34. You can come to this conclusion by doing this.
The formal definition of a reciprocal is 1/a where a is a fraction.
In this case a = 34/5. The reciprocal is 1/a = 1 // 34/5. You don't change anything by making it 1/1 // 34/5
1/1 // (34/5) Invert and multiply the bottom.
1/1 * 5/34 = 5/34
The perimeter of a college athletic field is 104104 meters and the length is 1414 m more than the width. find the length and width.
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A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is π/3 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
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notice, the "x" distance, whilst the balloons are moving up up and up, is not changing, thus, is a constant.
[tex]\bf tan(\theta )=\cfrac{y}{x}\implies tan(\theta )=\cfrac{y}{3}\implies tan(\theta )=\cfrac{1}{3}y \\\\\\ \stackrel{chain~rule}{sec^2(\theta )\cfrac{d\theta }{dt}}=\cfrac{1}{3}\cdot \cfrac{dy}{dt}\implies \cfrac{1}{cos^2(\theta )}\cdot \cfrac{d\theta }{dt}=\cfrac{1}{3}\cdot \cfrac{dy}{dt}[/tex]
[tex]\bf \cfrac{3\cdot \frac{d\theta }{dt}}{cos^2(\theta )}=\cfrac{dy}{dt}\quad \begin{cases} \frac{d\theta }{dt}=0.1\\\\ \theta =\frac{\pi }{3} \end{cases}\implies \cfrac{3\cdot 0.1}{cos^2\left( \frac{\pi }{3} \right)}=\cfrac{dy}{dt}\implies \cfrac{0.3}{\left( \frac{1}{2} \right)^2}=\cfrac{dy}{dt} \\\\\\ \cfrac{0.3}{\frac{1}{4}}=\cfrac{dy}{dt}\implies \stackrel{rad/min}{1.2}=\cfrac{dy}{dt}[/tex]
The observer and the balloon form a right triangle (see attachment).
The balloon is rising at 1.2 rad per min
Using tangent rule, we have:
[tex]\mathbf{tan(\theta) = \frac{y}{x}}[/tex]
Substitute 3 for x
[tex]\mathbf{tan(\theta) = \frac{y}{3}}[/tex]
Differentiate both sides with respect to time (t)
[tex]\mathbf{sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{3} \cdot \frac{dy}{dt}}[/tex]
Make dy/dt, the subject
[tex]\mathbf{\frac{dy}{dt} = 3 \cdot sec^2(\theta) \cdot \frac{d\theta}{dt} }[/tex]
Substitute [tex]\mathbf{\theta = \frac{\pi}{3}\ and\ \frac{d\theta}{dt} = 0.1}[/tex]
So, we have:
[tex]\mathbf{\frac{dy}{dt} = 3 \cdot sec^2(\pi/3) \cdot 0.1 }[/tex]
Using a calculator, we have:
[tex]\mathbf{\frac{dy}{dt} = 3 \cdot 2^2 \cdot 0.1 }[/tex]
Multiply
[tex]\mathbf{\frac{dy}{dt} = 1.2}[/tex]
Hence, the balloon is rising at 1.2 rad per min
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A dentist orders 15 boxes of floss and 20 boxes of toothbrushes each month. Floss is sold 79 to a box, how many items does the dentist order each month
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complete question:
A dentist orders 15 boxes of floss and 20 boxes of toothbrushes each month. Floss is sold 70 to a box and toothbrushes are sold 50 to a box . how many items does the dentist order each month.
Answer:
The dentist orders 1050 number of floss and 1000 number of toothbrushes. The items are 2 different items namely floss and toothbrushes.
Step-by-step explanation:
The dentist orders 15 boxes of floss and 20 boxes of toothbrushes each month.
The floss is sold 70 to a box, this means about 70 numbers of floss occupies each box of floss. To get the total number of floss items in the 15 boxes of floss, we have to multiply the number of boxes of floss by the number of floss present in each box. Mathematically,
70 × 15 = 1050 items of floss
The boxes of toothbrushes is 20 . For each box the number of toothbrushes is 50 . To get the total number of tooth brushes we multiply the number of boxes by the total number of toothbrushes in each box.
50 × 20 = 1000 items of toothbrushes.
The dentist orders 1050 number of floss and 1000 number of toothbrushes. The items are 2 different items namely floss and toothbrushes.
solve this equation
h(t)= -16t+175t+500
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if f(x)= -6x+6 then f^-1(x)=
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[tex]\bf \stackrel{f(x)}{y}=-6x+6\qquad inverse\implies \boxed{x}=-6\boxed{y}+6 \\\\\\ x-6=-6y\implies \cfrac{x-6}{-6}=y\implies -\cfrac{x}{6}+1=\stackrel{f^{-1}(x)}{y}[/tex]
To find the inverse of f(x) = -6x + 6, swap the variables and solve for y, yielding the inverse function f^-1(x) = 1 - (x/6).
To find the inverse function, f-1(x), of the given function f(x) = -6x + 6, you need to follow a series of steps. First, swap the 'x' and 'y', so it becomes x = -6y + 6. Next, solve this equation for 'y' to find the inverse function. Add 6x to both sides to get x + 6y = 6, then subtract x from both sides to have 6y = 6 - x. Dividing both sides by 6 results in y = 1 - (x/6). Therefore, the inverse function is f-1(x) = 1 - (x/6).
solve this system of linear equations. separate the x- and y- values with a coma. -x=29-14y
-9x=-19+14y
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We are given the two equations:
(1) -x=29-14y
(2) -9x=-19+14y
Multiply (1) by 9:
-9x = 261 – 126y
Subtract the two equations:
-9x = 261 – 126y
-
-9x=-19 + 14y
0 = 280 – 140y
140y = 280
y = 2
From (1):
-x = 29 – 14 (2)
x = -1
Answers:
x = -1
y = 2
the value of a particular investment follows a pattern of exponential growth. in the year 2000 you invested money in a money market account. the value of your investment t years after 2000 is given by the exponential growth model A=2600e^0.052t. how much did u initially invest in the account? please show work
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the 2600 is the constant so you initially invested $2600
Round $8.0443 to the nearest cent
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I hope this helps.
To round $8.0443 to the nearest cent, we leave the second decimal at 4, since the third decimal is also a 4, resulting in $8.04
To round $8.0443 to the nearest cent, you need to look at the third decimal place, which is a '4'. Since we are rounding to the nearest cent, we only keep two decimal places. If the third decimal place is 5 or more, we would round up the second decimal place. However, because it is 4, we do not round up. Therefore, $8.0443 rounded to the nearest cent is $8.04
In Ms. Hendricks class, there are 10 boys and 12 girls. What is the ratio of boys to girls? Express your answer as a fraction in simplest form.
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complete the calculation how to find partial products
1 2 4
× 2
----------
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This is:
- 124 = 100 + 20 + 4
- 2 = 2
Now muliply 2 times each term of the terms 100, 20 and 4
=> 2 * 100 = 200
2 * 20 = 40
2 * 4 = 8
Then,
(100 + 20 + 4 )
x 2
-----------------------
8
40
200
------------------------
248
Which of the following statements describes the process for solving 4 x ≥ -24?
Divide both sides of the inequality by -24 and flip the symbol.
Divide both sides of the inequality by -24 but don't flip the symbol.
Divide both sides of the inequality by 4 and flip the symbol.
Divide both sides of the inequality by 4 but don't flip the symbol.
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First, you have to isolate the x, and so you divide by 4
However, because you are not dividing by a negative number, you will keep the sign the way it is
hope this helps :D
The correct answer is option D
Divide both sides of the inequality by 4 but don't flip the symbol.
------------------------
Note: The only time you flip the symbol is when we divide by negative sign.
I hope this helps!
Give the numerical value of n corresponding to 5d.
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Final answer:
The numerical value of n for the 5d orbitals is 5, which indicates that the d subshell in question is located in the fifth principal energy level of an atom.
Explanation:
The numerical value of n corresponding to the 5d orbitals is 5. In the context of atomic and quantum physics, the principal quantum number, denoted as n, signifies the principal electronic shell of an atom. Since the question refers to 5d, it means we are discussing the d subshell in the fifth principal energy level (n=5).
For a d subshell, which is represented by the azimuthal quantum number (l) having a value of 2, the first principal shell where a d subshell appears is when n=3. Therefore, the 5d subshell is present in the fifth principal energy level. As for the ml values of the d orbitals, which represent the magnetic quantum number, they can be -2, -1, 0, +1, or +2 for any d subshell.
Bottles of water sell for $1.50 each. Graph the relationship between the number of bottles of water sold and the total cost.
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draw a graph with number of bottles on the x axis ( and number it 1 through 10 )
put price on the y axis and label it in increments of $1.50 ( 1.50, 3.00 , 4.50, 6.00, etc.
Then put dots on the intersection of price with the number of bottles and then draw a straight line through the dots.
for every 1 bottle of water sold the price increases by 1.50
so at x 1 y = 1.50
at x 2 y = 3.00
at x 3 y = 4.50
and so on
In a classroom of 32 students 14 are male. What percentage in the class is female
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18+14= 32
Mikayla withdraws $20 on 4 different days during a week. Find the total change in her account balance after the withdrawals.
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20 times 4 = 80
so the change in her account would be negative 80 dollars
The change in her account after 4 withdrawals of $20 the change in her account will be $(D - 80)
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given that Mikayla withdraws $20 on 4 different days during a week.
Assuming she had $D before she had made any withdrawals.
∴ The situation can be represented numerically as,
(D - 20 - 20 - 20 - 20) dollars.
= (D - 80) dollars.
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can someone help with my homework
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With conversion fractions, the denominator unit is always what you want to cancel out. In this case, we want to cancel out "seconds" because we want to effectively replace "seconds" with "minutes" (which is what conversions are really). The numerator is the unit we want to convert to. Take care to note that sometimes you'll need multiple conversions, and sometimes it's not going to involve one conversion fraction only.
Have a look at the attached image to get a better sense of what is going on. Note the red slash marks to indicate cancellations.
write 60,000+9,000+400+90+8 in standard form
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Chad has 6 fewer sandwiches than Sarah.chad had 7 sandwiches. how many sandwiches did Sarah made?
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Sarah made total 13 sandwiches.
What is an algebraic expression?
An algebraic expression is consists of variables, numbers with various mathematical operations.
Given that,
The number of sandwiches chad have = 7
Also, Chad has 6 fewer sandwiches than Sarah,
Let the number of sandwiches Sarah have = x,
According to condition,
Sarah has 6 more sandwiches than Chad,
⇒x = 7 + 6
⇒x = 13
The number of sandwiches that Sarah made is 13.
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A seamstress has one-fourth of a foot of thread. Then she uses one-fifth of a foot of thread to sew a hole. How much of the thread is left?
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first make a common denominator
5/20 - 4/20 = 1/20
Debbie's city took a survey about a plan for a new park. The city surveyed 600 people. 60% of the people surveyed liked the plan for the park. How many people liked the plan?
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All we have to do to find out how many people like the plan is multiplication.
We multiply the total number of people by 60% - in decimal form.
600 · 0.6 = 360
360 people liked the plan.
Hopefully that answer it
the sum of 5 consecutive integers is 110. what is the fourth number in the sequence
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20+21+22+23+24= 110.
So, the 4th number is 23.
Justin is going on a 2000 kilometer road trip with two friends. The car consumes 6 liters of gas for every 100 kilometers and gas costs $1.20 per liter. If Justin and his two friends want to spilt it evenly, how much should each pay and how many liters of gas do they need
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2000 / 100 = 20
20 * 6 = 120 liters total gas
120 * 1.20 = $144 total for gas
144 / 3 = $48 each