Answer: 8.5
Step-by-step explanation: (42.50 - 17) ÷ (5 - 2)
= 25.50 ÷ 3
= 8.5
Thank me later
The second side of a triangular deck is 4 feet longer than the shortest side, and the third side is 4 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 52 feet, what are the lengths of the three sides?
Answer:
13 ft, 17 ft, 22 ft
Step-by-step explanation:
let x be the shortest side, then second side is x + 4 and the third side is
2x - 4
sum the 3 sides and equate to 52
x + x + 4 + 2x - 4 = 52 , simplify
4x = 52 ( divide both sides by 4 )
x = 13
x + 4 = 13 + 4 = 17
2x - 4 = 2(13) - 4 = 26 - 4 = 22
lengths of 3 sides are 13 ft, 17 ft and 22 ft
As a bowl of soup cools, the temperature of the soup is given by the twice-differentiable function H for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where H(t) is measured in degrees Celsius (C), and time t is measured in minutes. Values of H(t) at selected values of time t are shown in the table above.
a) Use the data in the table to approximate H'(5). Show the computations that led to your answer. Using correct units, explain the meaning of H'(5) in the context of the problem.
b) Is there a time t for 0[tex]\leq[/tex]t[tex]\leq[/tex]12 at which the temperature of the soup is 60C? Justify your answer.
c) The temperature of the soup is also modeled by the twice-differentiable function C for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where C(t) is measured in degrees Celsius (C), and time tis measured in minutes. It is known C(3)= 80 and the derivative of C is given by C'(t)= -3.6e-0.05t. Write an equation for the line tangent to the graph at t=3 and use it to approximate C(5).
d) Based on the model given in part c, at what rate, in degrees Celsius per minute minute, is the rate of change of the temperature of the soup changing at t=3 minutes?
The rate of change of temperature with time at a point in time is given by
the derivative of the function for the temperature of the soup.
The correct responses are;
a) H'(5) is approximately -2.6 degrees Celsius per minute.b) Yesc) The equation for the line tangent is y = -3.6·t + 90.8The approximate value of C(5) is 72.8 °Cd) The rate of change of the temperature of the soup at t = 3 minutes is -3.6 degrees Celsius per minute.Reasons:
a) From the data in the table, we have;
The approximate value of H'(5) is given by the average value of the rate of
change of the temperature with time between points, t = 3, and t = 8
Therefore;
[tex]\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}[/tex]
Which gives;
[tex]\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}[/tex]
Therefore, H'(5) = -2.6°C per minute
b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12
At t = 0, H(0) = 90 °C
At t = 12, H(12) = 58 °C
58 °C < 60 < 90 °CTherefore, there exist a temperature, of 60 °C between 90° C and 58 °C
c) The given derivative of C is, [tex]C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}[/tex]
At t = 3, we have;
[tex]The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1[/tex]
Therefore, we have;
y - 80 ≈ -3.1 × (x - 3)
The equation for the tangent is; y = -3.6 × (x - 3) + 80
y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8
The equation for the tangent is; y = -3.6·x + 90.8The value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8
C(5) ≈ 72.8°d) Based on the the model above, the rate at which the temperature of the
soup is changing at t = 3 minutes is -3.6 degrees per minute.
Learn more about calculus and concepts here:
https://brainly.com/question/20336420
Which of the following is the figure most likely the graph of?
A) f(x) = (2/3)x
B)f(x) = –2x
C)f(x) = (3/2)x
D)f(x) = 2x
The accurate line represented by line b because during such experiment ( osmosis or mass transfer) there would be a time where the system be in equilibrium meaning that that the net movement will be zero. In line B at time starting 15 min equilibrium is reached no further movement is attained beyond it.
Multiply:
5m^3 n^5 (25m^6 n)
A. 125m^18n^10
B. 30m^9 n^5
C. 30m^9 n^6
D. 125m^9 n^6
Answer:
D
Step-by-step explanation:
5m^3 n^5 (25m^6 n)
-->5m^3*25n^6m^6
-->125m^9 n^6
How do you multiply fractions? And do we have to simplify them by any chance or no?
To multiply a fraction, imagine it this way. Start with 1/4. Then if you multiply 1/4 by 2 it would be 1/2.
If you have a quarter, and you times that quarter by 2, you have half a dollar.
It only needs to be simplified if you can simplify the fraction.
Answer:
Ok say your doing 1/4 * 2/4 you move the /4 over to the side and multiply 1 and 2 that would be 2 so then you put the the 2 on top of the /4 and you have 2/4… Now if you have odd numbers like 1/4 * 1/6 you would simplied the 6 and 4 what can go into (divide by the same number) 6 AND 4 both… 2 because so you change the 1/4 and 1/6 to a 1/2 * 1/2 those multiplied together equal 1/2
Step-by-step explanation: pls give brainleist and dont for get to leave a rating and heart
you walk 3/4 miles to a grocery store. Then you walk another 1/5 miles to a shoe store. How many miles have you walked in all?
Answer:
19/20 miles
Step-by-step explanation:
3/4 + 1/5
3/4 = 0.75
1/5 = 0.2
3/4 + 1/5
= 0.75 + 0.2
= 0.95
= 95/100
= 19/20
Therefore,
the miles you have walked in all is 19/20.
Help please , need answer ASAP
Answer:
(fg)(9) = 948
Step-by-step explanation:
(fg)(9) = f(9)×g(9) = (9 +3)(9^2 -2) = (12)(79)
(fg)(9) = 948
plz help me to answer
Answer:
if you can only pick one it's e
Step-by-step explanation:
Im 90% sure a and c are both true answers while 70% sure that b and d are both true answers so unless someone says otherwise e is your best bet
When using a ruler, where is the unit?
- The tick marks on the ruler.
- The space between the tick marks on the ruler.
-The numbers on the ruler.
Answer:
Is it The numbers on the ruler?
Step-by-step explanation:
Listen
ol
Figure B is a scale image of Figure A, as shown.
2.5
Figure A
Figure B
Enter the scale factor applied to Figure A to produce Figure B.
Enter your answer as a fraction, like this. 42/53
Answer:
scale factor = [tex]\frac{14}{5}[/tex]
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original.
scale factor = [tex]\frac{7}{2.5}[/tex] = [tex]\frac{7(2)}{2.5(2)}[/tex] = [tex]\frac{14}{5}[/tex]
3 2/3 + 2 3/5 + x = 8
Answer: x= [tex]-\frac {109}{15}[/tex]
Choose all the numbers that make the comparison true.
42 > __
A, 22
B, 64
C, 41
D,40
E, 40
Answer:
22, 40, 40, and 41
Step-by-step explanation:
happy to help have a nice day
A recipe requires 1/3 cup of water for every 2/5 cups of sugar. How much
sugar would you need for a full cup of water?
Answer:
1 1/5
Step-by-step explanation:
Given ABCD, solve for x.
A. 11
B. 13
C. 14
D. 12
Answer:
Step-by-step explanation:
Because you have a parallelogram, the two angles shown are "same side interior angles" which means they add up to 180°.
We would say that they are supplementary (they add up to 180°)
So add them together and set them equal to 180°
(4x+18) + (8x+30) = 180°
This is all adding, so we dont really need any of these parenthesis.
4x+18+8x+30=180
Add the x terms together and add the constants (plain numbers) together.
12x + 48 = 180
Subtract 48 from both sides of the equation.
12x = 132
Divide both sides by 12
x = 11
Which list of angle measures could be the angle measures of a triangle?
find the greatest common factor GCF and the least common multiple LCM of these Numbers. 8and 9
Answer:
LCM is [tex]72[/tex]
GCF is [tex]1[/tex]
Step-by-step explanation:
LCM is least common multiplier
LCM of
[tex]8,9=8\times 9\\\\=72[/tex]
GCF is greatest common factor
Factors of [tex]8=1,2,4,8[/tex]
Factors of [tex]9=1,3,9[/tex]
Greatest common factor is [tex]1[/tex]
GCF is [tex]1[/tex]
can some1 please help:(
A) -2/5hope it helps ....❤
Need an answer right away for many points! I will report if it is not applicable.
Answer:
I don't know
Step-by-step explanation:
plus all of them = Answer
Answer:
Step-by-step explanation:
False Line of symmetry is x = -1
False The maximum of f(x) = 3
we can find the maximum of f(x) by putting it in vertex form (y - 3) = - 1(x + 7)² which tells us that the vertex is at (-7, 3)
True -7 < -1
HELP ANSWER PART A AND B
Answer:
part A: median is 12
part B: interquartile rage is 10
Step-by-step explanation:
Part A: to find your median on a box and whisker plot, you just need to look at your middle line in your box. In this case it's 12.
Part B: to find your interquartile range on a box and whisker plot, you subtract your Q1 and Q3. Your Q1 and Q3 will be the two outside lines that make up the rest of your box, in this case would be 6 and 16. To find your Q1 if you don't already have your plot set up, you separate the numbers that are given to you in half and find the median of each side. The first half will be your Q1 and the second half your Q3.
The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one of the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.) You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left on the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one?
Answer:
I'd swap with one on the table (the left one) but with my luck it would be a sword made of rubber
Desmond has 169 square bricks that he is arranging in a row to make a patio. Every row must have to have the same number of bricks. How many bricks are in each row? Describe the shape of the patio
Martina's fish tank has 15 liters of water in it. She plans to add 5 liters per minute until the tank has at least 60 liters. What are the possible numbers of minutes
. :
Martina could add water?
Use t for the number of minutes
Write your answer as an incqua ty solved fort
Answer:
9 minutes
Step-by-step explanation:
60=15+5t
45=5t : subtract 15 from both sides
9=t : divide by 5 for both side
Company A makes 20 notebooks in 4 hours. Company B make 28 notebooks in
3 hours. Write a statement comparing the number of notebooks made per
hour.
Please look for the question in the picture.
Which of the following is the graph of y = |x - 3|
Answer:
y = | x - 3 | is graphed on the attachment below ↓
Step-by-step explanation:
If you ever need an equation graphed, here's a useful site called Desmos that can do that really well and for free.
Melissa has 120 kilograms of rice. Her mother sold 105 kilograms. What percent of the rice was sold? with solution :D please
Answer:
225
Step-by-step explanation:
po ang answer ko
please comment if I'm wrong
im stuck step bro #im a guy
Answer:
Well then...
Step-by-step explanation:
HELP!!
is {(-3,-6),(-2,-1),(-1,-0),(0,3),(1,15)} a function??
It's a function because we don't have any repeated x coordinates. Any given x input value leads to exactly one y output value.
The domain is {-3,-2,-1,0,1} which is the set of all x inputs.
The range is {-6, -1, 0, 3, 15} which is the set of y outputs.
Jasmine is scuba diving at an elevation of −68.4 feet when her friend signals to come higher. Jasmine makes three ascents, each an equal distance, to reach an elevation of −15.6 feet, where her friend is located. What was Jasmine's elevation after her first ascent? Enter your answer as a decimal in the box.
Answer:
-35.2
Step-by-step explanation:
-68.4-(-15.6)= (-52.8)
-52.8÷3=(-17.6)
-52.8-(-17.6)=-35.2
Answer:-35.2
Step-by-step explanation:
Use the long division method to find the result when 12x3 - 27x2 + 13x + 30 is
divided by 4x + 3.

Answer:
your answer will become 69.