Answer:
50 cats would take 6 hours to catch 75 rats.
Step-by-step explanation:
After reading the statement we noticed the existence of two relationships:
1) The amount of cats is directly proportional to the quantity of caught rats.
2) The amount of cats is inversely proportional to time taken to catch rats.
That is to say:
[tex]n \propto \frac{x}{y}[/tex]
[tex]n = k\cdot \frac{x}{y}[/tex] (Eq. 1)
Where:
[tex]n[/tex] - Amount of cats, dimensionless.
[tex]x[/tex] - Amount of caught rats, dimensionless.
[tex]y[/tex] - Time, measured in hours.
[tex]k[/tex] - Proportionality ratio, measured in hours.
Then, we obtain the following relationship by eliminating the proportionality ratio in (Eq. 1):
[tex]\frac{n_{1}\cdot y_{1}}{x_{1}} = \frac{n_{2}\cdot y_{2}}{x_{2}}[/tex] (Eq. 2)
Where:
[tex]n_{1}[/tex], [tex]n_{2}[/tex] - Initial and final amounts of cats, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final amounts of caught rats, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final times, measured in hours.
Now we clear final time in (Eq. 2):
[tex]y_{2} = y_{1}\cdot \left(\frac{n_{1}}{n_{2}} \right)\cdot \left(\frac{x_{2}}{x_{1}} \right)[/tex]
By knowing that [tex]y_{1} = 2\,h[/tex], [tex]n_{1} = 12[/tex], [tex]x_{1} = 6[/tex], [tex]n_{2} = 50[/tex], [tex]x_{2} = 75[/tex], then we get that time taken by 50 cats to catch 75 rats is:
[tex]y_{2} = (2\,h)\cdot \left(\frac{12}{50} \right)\cdot \left(\frac{75}{6}\right)[/tex]
[tex]y_{2} = 6\,h[/tex]
50 cats would take 6 hours to catch 75 rats.
If a person walks 1/3 mile in 15 minutes, how far will that person walk in one hour? (ik im dumb dont need to say it.)
Answer:
1 and 1/3 miles in an hour
Step-by-step explanation:
thats slow, ive walked a mile in ten minutes, lol
I DONT UNDERSTAND HELLPPP
Answer:
choice answer choice f
Suppose y varies directly with x. If y = 6 when x = 18, find the value of y when
x= 8.
Answer:
y = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition
y = 6 when x = 18 , then
6 = 18k ( divide both sides by 18 )
k = [tex]\frac{6}{18}[/tex] = [tex]\frac{1}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x ← equation of variation
When x = 8, then
y = [tex]\frac{1}{3}[/tex] × 8 = [tex]\frac{8}{3}[/tex]
NEED HELP ASAP PLEASE
Answer:
[See Below]
Step-by-step explanation:
[tex]Hey~There![/tex]
_______________________
➜ First let's turn each number into a decimal:
[tex]14\frac{2}{5}=14.4[/tex] [tex]4\sqrt{13} =14.42220510[/tex]➜ Now we order then from Least to Greatest:
[tex]14.33[/tex], [tex]4\sqrt{13}[/tex], [tex]14\frac{2}{5}[/tex]_______________________
So your answer would be [tex]\bold~B[/tex].
_______________________
[tex]Hope~this~helps~Mate!~\\-Your~Friendly~Answerer,~Shane[/tex] ヅ
I need help with this math task, I don't know if you can do it with a photo or not, but I need the result, thanks!!
Answer:
under 1: 225
under 2: 450
under 3: 765
under 4:1020
Step-by-step explanation:
it multiplies each day
will mark brainles if answered quickly
Answer:
A {-3, -2, -1, 0, 1, 2, 3}
Answer:
A
Step-by-step explanation:
Rational numbers are whole numbers
can you tell who is the fastest animal In the world
Answer:
Cheetah
Step-by-step explanation:
please please help me!!
Answer:
k=1
Step-by-step explanation:
because the intercept form, y=mx plus b the y intercept changes where the graph is positioned. the line has been translated down to the y intercept 1, therefore that is what k equals
The √28 is between which two whole numbers?
Answer:
between 5 and 6
Step-by-step explanation:
Choose 2 perfect squares either side of 28, that is
25 < 28 < 36, then
[tex]\sqrt{25}[/tex] < [tex]\sqrt{28}[/tex] < [tex]\sqrt{36}[/tex] , thus
5 < [tex]\sqrt{28}[/tex] < 6
You fill your car with gasoline at a service station for $2.75 per gallon. You pay with a $50 bill.
How much change will you receive if you buy g gallons of gasoline? How much change will you
receive if you buy 14 gallons?
TEEHEE HELPP ME PLS PLS PLS PLS???
Answer:
That is true not false dont get confused
Custom steel products also makes staircase frames like those shown here. How would the pattern you described be shown in a table? Graph? Equation?
Answer:
Graph would be the most reasonable.
Step-by-step explanation:
Hope I helped, good luck!<3!!
\Mrs. Sing invests $12,876 for her business at an annual interest rate of 7 percent for 3 years. Which number will Mrs. Sing substitute for r in the simple interest formula?
I = p r t
0.007
0.07
0.7
7
Answer:
0.07
Step-by-step explanation:its becuase 7% outta 100% =0.07. so I=Prt
We have to solve for r
r=r/100
7%/100
0.07 per year
Hope this helps mark as brainliest plz
Answer:
0.07
Step-by-step explanation:
give brainlest pls
-1/2 = m -7/4
solve for m
Answer:
[tex]\boxed {m = \frac{5}{4}}[/tex]
Step-by-step explanation:
Solve for the value of [tex]m[/tex]:
[tex]-\frac{1}{2} = m - \frac{7}{4}[/tex]
-Switch sides:
[tex]m - \frac{7}{4} = -\frac{1}{2}[/tex]
-Add both sides by [tex]\frac{7}{4}[/tex] and the least common multiple of both [tex]2[/tex] and [tex]4[/tex] is [tex]4[/tex]. So, convert [tex]-\frac{1}{2}[/tex] to a fraction with denominator [tex]4[/tex]:
[tex]m - \frac{7}{4} + \frac{7}{4} = -\frac{1}{2} + \frac{7}{4}[/tex]
[tex]m = -\frac{2}{4} + \frac{7}{4}[/tex]
-Since both [tex]-\frac{2}{4}[/tex] and [tex]\frac{7}{4}[/tex] have the same denominator, then you would add the numerators:
[tex]m = \frac{-2 + 7}{4}[/tex]
[tex]\boxed {m = \frac{5}{4}}[/tex]
Therefore, the value of [tex]m[/tex] is [tex]\frac{5}{4}[/tex].
Danica is buying a teal Jansport backpack at Kohl's for $45. The backpack is on sale for 15% off. What is the sale price of the backpack?
The backpack price is $38.25
The points (5,-2) and (7,r) lie on a line with slope 4. Find the missing coordinate r.
Answer:
A slope of four means that it moves up four and over 1. Since 7-5 is 2, you must half the 1. (7, 2.5)
Expand & simplify
(x+2)(x−3)(x+4)
ALGEBRA NATION!!! NEED HELP :(
PLEASE HELP GOTTA GO TO CROSS COUNTRY PRACTICE PLEASE AND THANKS MARK YOU BRAINLIEST
Answer:
1. $13.78
2. 5.3lbs
3. $4.56
4. 30.44lbs
5. $32.07
Step-by-step explanation:
Simple addition and subtraction.
IIIlas' car usses 65 L of petrol to travel 728 km, while Hanis car uses 48 L in 552 km
how much petrol would each car use to travel 830 km ?
Answer:
65l-728km
x-830km
65×830/728=53950÷728=74,107
48L-552
x-830
48×830/552=39840/552=72.173
f(x)=2x+1,g(x)=X2-2x-4
A contractor bought 12.6 ft2 of sheet metal. He has used 3.7 ft2 so far and has $160.20 worth of sheet metal remaining. The equation 12.6x−3.7x=160.2 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:$18 per square foot
Step-by-step explanation:
12.6x-3.7x=160.2
8.9x=160.2
x=18
$18 per square foot
The function T = 25 - sin ( – 4)) +5
+55 gives the average monthly temperature, T, in a city, where m represents the
month. In which month is the average temperature the same as in m = 3?
Om = 5
Om = 7
Om = 9
O. m = 11
Answer:
the third one ithink
Step-by-step explanation:
Which expression is equivalent to 6(2x-8) *
A : 12x+48
B: 12x-8
C: 12x-48
D: 2x-48
Answer:
C.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
6(2x-8)
6 * 2x = 12x
6 * -8 = -48
12x - 48
please someone help ... ( i’ll mark brainiest , hehe :) )
the expression 9.78(4.3x + 5.15) simplifies to
Answer: 42.097x+50.4185
Step-by-step explanation:
Triangle XYZ is a right triangle with the right angle at vertex Y.
Angle X must be
.
Angle Z must be
.
The sum of angles X and Z must be
90°.
The sum of angles X and Z is 90°.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle XYZ.
∠Y = 90°
Now,
The sum of the three angles must be 180°.
So,
∠X + ∠Y + ∠Z = 180
∠X + ∠Z = 180 - 90
∠X + ∠Z = 90
Thus,
∠X + ∠Z = 90
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ2
Determining Angle Relationships in Right Triangles
Acute
Acute
Equal to
Step-by-step explanation:
see picture
Lola purchased two pairs of shoes that each cost $20.00. She then purchased a pair of jeans for $14.50 and a shirt for $8.25. What is the total amount of money she spent, before tax?
Answer: $62.75
Step-by-step explanation:
1.)$20.00 x2= $40.00
2.)$14.50 +$8.25= $22.75
3.)$40.00 +$22.75= $62.75
Hope this helps
Given the equation y = -3x + 6, the slope is
Answer:
-3 I think...
Step-by-step explanation:
y=mx+b. where m is the slope, since -3 is the value for m, it is the slope
In a traffic jam, it once took me 2.5 hours to drive 30 miles across Atlanta. What was my speed in miles per hour on this trip?
speed = distance ÷ time = 30 ÷ 2.5 = 12 mph