Given that the radius of the puddle expands, originally, at a rate of 1/4 unit/second instead of 1/2 unit/second.
The current rate of expension of the radius,
\frac {r(t)}{t}=frac 1 4 unit/second ...(i)
The resultant composite function is area, A(r(t)).
The area of a circular region having radius r is,
[tex]A(r)=\pi r^2[/tex]
If the radius is the function of time, then the composite function is
[tex]A(r(t))=\pi \(r(t))^2[/tex]
To determine the rate of change of area with respect to time, differentiate the composite function A(r(t)) once with respect to time, we have
[tex]\frac {d\{A(r(t))\}}{dt}=\pi \left(2\frac {d\{r(t)\}}{dt}\right)[/tex]
So, the composite function is changing twice of the rate of change of the radius.
By using equation (i), if r(i) is changing with R= 1/4 unit / second.
Then, A(r(t)) will change 2 x 1/4 = 1/2 square unit/second.
WILL GIVE BRAINLIEST
Mickey Mouse was finally buying a pair of shoes that fit! The shoes he chose cost $120. The store was offering a 25% discount. How much did Mickey save with the discount?
(PLEASE SHOW WORK!)
Adele swam the length of the pool in 32.56 seconds. Alexandria swam the length of the pool in 29.4 seconds. How many seconds faster was Alexandria's time than Adele's time?
Answer:
3.16
Step-by-step explanation:
Answer:
Adele was 3.14 seconds faster than Alexanderia
Step-by-step explanation:
Alexamdria - Adele
Can someone help me with my geometry hw?...
Answer:
sure, i'll try my best!
Step-by-step explanation:
❤️✨
Answer:
ftftftftftfjhgrew
Step-by-step explanation:
4weyye45y5e4
How much interest is earned on an initial investment
of $700 with a 5% annual rate for 2 years?
Select one:
$350
$700
$70
$35
Answer:
$70
Step-by-step explanation:
700*0.05=35
35*2=70
Someone give me a reminder on converting factored form into standard form, per say
(x - 9)(x + 3)
1.
Tadashi had a veggie pizza that was cut into 8 equal pieces. He
ate 2 pieces and left the other 6 in the box. What fraction of the
pizza did he eat?
2.
Mrs. Selleck baked a cake and cut it into 10 equal pieces.
Her
family ate 6 pieces and she took the rest to her next-door
neighbor. What fraction of the cake was given to her neighbor?
3.
Dr. Tinibu has 10 t-shirts. 2 of them are clean and 8 are dirty.
What fraction of Dr. Tinibu's shirts are clean?
4.
Peppa has a carton with a dozen eggs in it. 6 eggs are brown.
The rest are white. What fraction of her eggs are white?
Answer:
1/4, 2/5, 1/5, 1/2
Step-by-step explanation:
1. He ate 2/8's of the pizza, which is simplified to 1/4.
2.She gave 4/10's of the cake to her neighbor, which simplifies to 2/5.
3.2/10 t-shirts are clean. Divide that by the GCF of 2, simplifies to 1/5.
4.6/12 eggs are white, which is equivalent to 1/2.
Therefore, the answers are:
[tex]\frac{1}{4}[/tex][tex]\frac{2}{5}[/tex][tex]\frac{1}{5}[/tex][tex]\frac{1}{2}[/tex]Know more about Pizza here:
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GIVING BRAINLIST!!!
Column A
the volume of a cube with
side x, where x > 1
Column B
the volume of a rectangular solid with
sides x, x + 1, and x - 1, where x > 1
A) the quantity in column A is larger
B) the quantity in column B is larger
C) the two quantities are equal
D) relationship cannot be determined with the given information
Answer:
its b
Step-by-step explanation:
I just got it right
Help me solve this problem please 12 please
Which of the following linear equations when graphed on a
coordinate grid has the steepest slope?
Y=5/2x-1
Y=3x+1/4
Y=4x+3/5
Y=1/3x-2
Answer:
y = 4x + 3/5
Step-by-step explanation:
The slopes are 5/2, 3, 4, 1/3.
The larger the absolute value of the slope is, the steeper the graph is.
The largest slope is 4, so that equation has the graph with the steepest slope.
Answer: y = 4x + 3/5
hich equation represents a line that passes through (-2, 4) and has a slope of ?
y-4 = {(x + 2)
y+4 =}(x - 2)
y+2 = (x-4)
y-2-3(x +4)
Answer:y+2 = (x-4)
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Michael makes 16/5 pounds of pumpkin pie filling per minute. How many pounds of pie filling will he make in half an hour?
A.13/10
B.96
C.13/5
D.8/10
Answer:
the answer would be c
Step-by-step explanation:
The amount of pounds of pumpkin made in 30minutes is 96 pounds
Ratio and proportionsFractions are written as a ratio of two integers.
If Michael makes 16/5 pounds of pumpkin pie filling per minute, then;
16/5 pounds of pumpkin = 1 minutes
In order to determine the amount made in half an hour (30 mins)
x = 30mins
Take the ratios
16/5x = 1/30
5x = 480
x = 480/5
x = 96
Hence the amount of pounds of pumpkin made in 30minutes is 96 pounds
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Which equation and solution represents the answer to the following question: Mr. McGuire buys a bottle of water for $1.99 and the sales tax is 7%. What was the total amount he paid for the bottle of water? *
3 points
A. 7 ÷ 1.99 = 3.52
B. 1.99 ÷ 0.07 = 2.06
C. 1.99 x 0.07 = 0.14
D. 1.99 x 1.07 = 2.13
To rent a certain meeting room, a college charges a reservation fee of $41 and an additional fee of $8.30 per hour. The history club wants to spend at most $99.10 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality fort.
Answer:
7hours maxStep-by-step explanation:
let the total charges be y
and the number of hours be t
the total cost can be modelled linearly as
y=mt+c
given that
c=$41
m=$8.30
Therefore for y=99.10, we want to solve for t
99.1=8.3t+41
solve for t
99.1-41=8.3t
58.1=8.3t
t=58.1/8.3
t=7
therefore the time is 7hours max
Look at the number line. From the point shown on the number line, you move one more unit to the right. What should you do next from the new point to model that the sum of opposites is zero? A. Draw an arrow that points 1 unit to the right. B. Draw an arrow that points 2 units to the left. C. Draw an arrow that points 2 units to the right. D. Draw an arrow that points 3 units to the left.
Answer:
b
Step-by-step explanation: mark brainliest
Answer:
The Answer is B I just did the test!!
Step-by-step explanation:
A car that travels 20 miles in \frac{1}{2} 2 1 hour at constant speed is traveling at the same speed as a car that travels 30 miles in \frac{3}{4} 4 3 hour at a constant speed.
Step-by-step explanation:
If distance is 20 miles and time is (1/2) h. Its speed is given by :
[tex]v=\dfrac{d}{t}\\\\v=\dfrac{20\ miles}{1/2\ h}\\\\v=40\ mph[/tex]
If the distance is 30 miles and the time is (3/4) hours. Its speed is given by :
[tex]v=\dfrac{d}{t}\\\\v=\dfrac{30\ miles}{3/4\ h}\\\\v=40\ mph[/tex]
So, the rate or the speed ib both the case is constant.
AT&T charges $70.00 a month plus $10 per gig of data. Sprunt charges $80.00 a month plus $5 per gig of data. Which equation could be used to determine when the two cell phone plans will be equal?
Answer:
AT&T charges $70.00 a month plus $10 per gig of data. Sprunt charges $80.00 a month plus $5 per gig of data. Which equation could be used to determine when the two cell phone plans will be equal?
Step-by-step explanation:
AT&T's plan would be less expensive than the Sprunts because they have different charges a month
Hope this helps
help me pls !!!! i’m dumb
Answer:
212 is correct answer
Step-by-step explanation:
Answer the following question. G(2)
Answer:
12
Step-by-step explanation:
g(x)=5x-4
g(2)=5(2)-4
g(2)=10-4
g(2)=6
6x2=12
g=12
Caffeine in the body decays by a factor of every 2 hours.
Answer:
Exponential, because the function grows by a common factor.
What are the perimeter and the area of the square?
Answer:
The perimeter is 16√5
The area is 80
Step-by-step explanation:
Just add 4√5, 4 times, or multiply 4√5 by 4 which still ends up 16√5
Multiply 4√5 by itself which is 80
Hope this helps!
help me please 9x+184=7x+156
x=?
Answer:
I believe x = -14.
I might be wrong
Step-by-step explanation:
30 POINTS!!! HELP ME PLZZ I NEED HELP WITH THIS!!!
Answer:
Step-by-step explanation:
3/12 x 2/9 = 24/27
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ok.............
.....
Answer:
nice question bro.....
Which choice shows a true conditional, with the hypothesis and conclusion identified correctly?
A:
If two lines intersect at right angles, then the two lines are perpendicular.
Hypothesis: Two lines are perpendicular.
Conclusion: Two lines intersect at right angles.
B:
If two lines intersect at right angles, then the two lines are perpendicular.
Hypothesis: Two lines are perpendicular.
Conclusion: Two lines do not intersect at right angles.
C:
Two lines are parallel if the lines intersect at right angles.
Hypothesis: Two lines intersect at right angles.
Conclusion: Two lines are parallel.
D:
Two lines are perpendicular if the lines intersect at right angles.
Hypothesis: Two lines intersect at right angles.
Conclusion: Two lines are perpendicular.
Answer:A:
If two lines intersect at right angles, then the two lines are perpendicular.
Hypothesis: Two lines are perpendicular.
Conclusion: Two lines intersect at right angles.
Step-by-step explanation:
I NEED THE ANSWER SOOOOO BAD I WILL GIVE BRAINLIEST TO THE FIRST TO ANSWER!!
30% of $14,00
Answer:
If it's 30% of 1400 then its 420, if its 30% of 14000, then it's 4200
Step-by-step explanation:
An urn contains 5 white and 3 black balls. Two balls are drawn at random without replacement. If X denotes the number of white balls, then find the probability distribution of X.
Answer:
Generally the probability distribution of the number of white balls (X) is
X 0 1 2
P(X) 0.35714 0.5357 0.10714
Step-by-step explanation:
From the question we are told that
The number of white balls is [tex]N_w = 5[/tex]
The number of black balls is [tex]N_b = 3[/tex]
Generally the total number of balls the urn contains is
[tex]N_t = N_w + N_b = 5 + 3 = 8 \ balls[/tex]
Generally the probability that of the two balls drawn that the balls are 2 white balls and 0 black balls is
[tex]P( 2_w \ , 0_b) = \frac{ ^{N_w} C _2 * ^{N_b} C _0 }{^{N_t} C_2}[/tex]
Here C stands for combination hence we would be making use of the combination feature in our calculator
=> [tex]P( 2_w \ , 0_b) = \frac{ ^5 C _2 * ^3 C _0 }{^{8} C_2}[/tex]
=> [tex]P( 2_w \ , 0_b) = 0.10714[/tex]
Generally the probability that of the two balls drawn that the balls are 1 white balls and 1 black balls is
[tex]P( 1_w \ , 1_b) = \frac{ ^{N_w} C _1 * ^{N_b} C _1 }{^{N_t} C_2}[/tex]
=> [tex]P( 1_w \ , 1_b) = \frac{ ^5 C _1 * ^3 C _1 }{^{8} C_2}[/tex]
=> [tex]P( 1_w \ , 1_b) = 0.5357[/tex]
Generally the probability that of the two balls drawn that the balls are 0 white balls and 2 black balls is
[tex]P( 0_w \ , 2_b) = \frac{ ^{N_w} C _0 * ^{N_b} C _2}{^{N_t} C_2}[/tex]
=> [tex]P( 0_w \ , 2_b) = \frac{ ^5 C _0 * ^3 C _2 }{^{8} C_2}[/tex]
=> [tex]P( 0_w \ , 2_b) = 0.35714[/tex]
Generally the probability distribution of the number of white balls (X) is
X 0 1 2
P(X) 0.35714 0.5357 0.10714
The sun produces 3.9 x 10(33) ergs of radiant energy per second. How many ergs of radiant energy does the Sun produce in 2.45 x 10(5) seconds? Please help!
Answer:
3.9
Step-by-step explanation:
Answer:
157657.5 ergs of radiant energy
brainliest plz
An open box is formed from a rectangular piece of cardboard that is 5 in longer than it is wide, by removing squares of side 4 in from each corner and folding up the sides. If the volume of the carton is then 336 in what were the dimensions of the original piece of cardboard?
This question is incomplete
Complete Question
An open box is formed from a rectangular piece of cardboard that is 5 in. longer than it is wide, by removing squares of side 4 in. from each corner and folding up the sides. If the volume of the carton is then 336 in³, what were the dimensions of the original piece of cardboard?
Select one:
a. 15 in. by 20 in.
b. 7 in. by 12 in.
c. 11 in. by 16 in.
d. 19 in. by 24 in.
Answer:
a. 15 in. by 20 in.
Step-by-step explanation:
We are told that:
An open box is formed from a rectangular piece of cardboard that is 5 in longer than it is wide, by removing squares of side 4 in from each corner and folding up the sides.
Volume of the carton = 336 in³
Step 1
We find the area of the new piece of the cardboard
Volume of the carton/side of the square removed
= 336 in³/4 in
= 84 in²
Step 2
An open box is formed from a rectangular piece of cardboard that is 5 in longer than it is width.
Length = 5 + Width
Hence, we find the factors of 84 in² that has a difference of 5 in
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
Hence, the Factors with a difference of 5 inches = 7 and 12
The Length = 12 inches
Width is 7 inches.
The dimensions of the new piece of cardboard is 7 inches by 12 inches
Step 3
What were the dimensions of the original piece of cardboard?
Remember in the question, we are told that squares of sides 4 inches were removed from both corners
Hence,
4 inches + 4 inches = 8 inches was removed.
The dimensions of the original piece of cardboard =
Original Width = Width of the new cardboard + 8 inches
= 7 inches + 8 inches
= 15 inches.
Original length = Length of the the new cardboard + 8 inches
= 12 inches + 8 inches
= 20 inches.
Therefore, the dimensions of the original piece of cardboard is 15 inches by 20 inches
Which tablo represents a linear function that has a slope of 5 and a y-intercept of 20
0
y
0
20
40
60
8
4
0
4
8
y
0
-20
-40
60
Х
0
20
40
60
y у
4
0
4
8
Answer:
Table (1)
Step-by-step explanation:
We have to find the table representing a linear function with slope = 5 and y-intercept = 20.
We know y-intercept means value of the function at x = 0,
From all the tables given in picture,
Table (1) shows the value of the function is 20 at x = 0,
So the table (1) should be the answer.
Now we will recheck the answer for the slope = 5
Since slope of a line passing through the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is calculated by the formula,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through (-4, 0) and (0, 20) will be,
m = [tex]\frac{20-0}{0-(-4)}[/tex]
= 5
Now we are sure that Table (1) is the answer.
Can someone work out this for me :)
Answers:
a) First statement. Same as 1/2 x 6/11.
b) Second statement. Smaller than 6/11.
c) First statement. Same as 6/11 divided by 2.
================================================
Explanation:
Part (a)
The "of" means "multiply". So we simply replace "of" with the multiplication symbol and that's all we need to do.
---------------
Part (b)
Taking half of something will make it smaller. For example, if you have 100 cookies and you took half of them, then you'll be taking 50 cookies. The value 50 is smaller than 100.
The same idea applies to 1/2 x 6/11.
---------------
Part (c)
Multiplying by 1/2 is the same as dividing by 2.
So [tex]\frac{6}{11} \times \frac{1}{2} = \frac{6}{11} \div 2[/tex]
Note that [tex]\frac{1}{2} \times \frac{6}{11}[/tex] and [tex]\frac{6}{11}\times \frac{1}{2}[/tex] are the same thing because we can multiply two numbers in any order we want.
Answer:
a) First statement. Same as 1/2 x 6/11.
b) Second statement. Smaller than 6/11.
c) First statement. Same as 6/11 divided by 2.
Step-by-step explanation:
