b = 14
Step-by-step explanation:
3b/7 - 1 = 5
+1
3b/7. = 6
x7
3b. = 42
÷3
b = 14
Hope this helps!
This exercise uses Newton's Law of Cooling.
Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to
cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k - 0.1947, assuming time is measured in hours. Suppose that the
temperature of the surroundings is 60°F.
(a) Find a function TCC) that models the temperature t hours after death.
TL)
х
(6) If the temperature of the body is now 78°F, how long ago was the time of death? (Round your answer to the nearest whole number.)
Xhr
By applying the Newton's law of cooling and performing the neccessary calculations, the time of death of the body is about 4 hours ago.
Newton's law of coolingAccording to the Newton's law of cooling;
T(t) = T(s) + (To - Ts)e^-kt
T(t) = temperature at time t
T(s) = temperature of the surroundings
To = Initial temperature
k = cooling constant
t = time taken
Substituting the values;
T(t) = 60 + (98.6 - 60)e^- 0.1947t
To find the time taken to attian a temperature of 78°F;
78 = 60 + (98.6 - 60)e^- 0.1947t
78= 60 + 38.6e^- 0.1947t
78 - 60 = 38.6e^- 0.1947t
18/38.6 = e^- 0.1947t
0.466 = e^- 0.1947t
ln0.466 = lne^- 0.1947t
ln0.466 =- 0.1947t
t = ln0.466 /- 0.1947
t = 4 hours
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The graph shows the vertical position of a ball attached to a spring oscillating between a low point and a high point as a function of time.
Select all statements that describe the graph.
The amplitude is 24 cm.
The ball travels 24 cm in 1 s.
It takes the ball 2 s to complete a cycle.
The midline is at f(x)=0.
Step-by-step explanation:
The statements that describe the graph are,
The ball travels 24 cm in 1s.
It takes the ball 2s to complete a cycle
The midline is at f(x)=0
I hope it helped you
An investment of $1,000 earns an annual interest rate of 2%. How much more interest is earned in Year 5 with compound interest than with simple interest?
An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method.
How to determine money gain by simple interest
Simple interest (C) is the amount of money gained and solely related to the initial capital ([tex]C_{o}[/tex]), in monetary units. The money earned by simple interest is determined by the following formula:
[tex]C = \frac{C_{o}\cdot r\cdot t}{100}[/tex] (1)
Where:
r - Interest rate, in percentaget - Time, in yearsCompound interest (C) takes into account the capital throughout time and its formula is presented below:
[tex]C = C_{o}\cdot \left[\left(1+\frac{r}{100} \right)^{t}-1\right][/tex]
Now we proceed to determine the simple and compound interest: ([tex]C_{o} = 1000[/tex], r = 2, t = 5)
Simple interestC = [(1000) · (2) · (5)]/100
C = $ 100
Compound interestC = (1000) · {[1+(2/100)]⁵-1}
C = $ 104.08
An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method. [tex]\blacksquare[/tex]
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Work out the this sheet
Answer:
A -- She saves 200₤.
B -- She will have 28₤ after buying presents.
Step-by-step explanation:
If two boxes = 20 then one box will be 10. Now we count all boxes. There are 20 boxes... 20 x 10 = 200, so she saves 200₤. If she spends 172₤ on Christmas presents she will have 28₤. (200 - 172 = 28).
X + 10 <14
thank you!
Answer:
x < 4
Step-by-step explanation:
Subtract 10 from both sides.
x + 10 - 10 < 14 - 10
Simplify the arithmetic:
x < 14 - 10
Simplify again..
and then u get x < 4
hope this helps <33
Which is the BEST description of the data in the scatterplot?
Answer:
2. linear with a negative correlation
What is the vertex of angle 1
Answer:
b
Step-by-step explanation:
Answer:
i believe it be
Step-by-step explanation:
correct me if its wrong
For the pair of functions, find the quotient (f/g)
You are training your dog to catch a frisbee. You are playing in a large field, and you are standing next to your dog when you throw the frisbee. If the path of the frisbee is y = –x2 + 8x + 7 and the path of the dog is modeled by y = 2x + 7, will the dog catch the frisbee? If so, what are the coordinates of the point or points where they meet?
Yes, they intersect at the coordinates (0, 7) and (3, 13)
Yes, they intersect at the coordinates (0, 7) and (6, 19)
Yes, they intersect at the coordinates (0, 7) and (7, 21)
No, the paths do not cross
Answer:
Yes, they intersect at the coordinates (0, 7) and (6, 19)
Step-by-step explanation:
[tex]y = -x^2 + 8x + 7\\y = 2x + 7\\y = y\\-x^2 + 8x + 7 = 2x + 7\\-x^2+ 6x = 0\\x^2 - 6x = 0\\x(x - 6) = 0\\x = 0\ \ \text{or}\ \ x = 6\\[/tex]
[tex]\text{if}\ x = 0\\y = 2x + 7\\y = 2(0) + 7 = 7\\\text{coordinate is:}\ (0, 7)[/tex]
[tex]\text{if}\ x = 6\\y = 2x + 7\\y = 2(6) + 7 = 12 + 7 = 19\\\text{coordinate is:}\ (6, 19)[/tex]
Answer:
B. Yes, they intersect at the coordinates (0, 7) and (6, 19)
Step-by-step explanation:
I took the Algebra exam
Allie has a round tablecloth with a radius of 2 meters. What is the tablecloth's circumference?
100 POINTS
What is the best name of the solid that can be formed by this net?
A. cube
B. cylinder
C. rectangular prism
D. square prism
Answer: rectangular prism
Step-by-step explanation:
Answer:
rectangular prism
Step-by-step explanation:
Louise measured the perimeter of her rectangular scrapbook to be 154 cm. If the scrapbook is 37 cm wide, how long is the scrapbook?
Answer: 40 cm.
Step-by-step explanation: Perimeter involves adding all the sides of a shape to get the perimeter. So far, two sides of the scrapbook have been given, which are both 37 cm. 37 x 2 = 74, so that leaves us with two sides left, which are the lengths of the scrapbook. The total perimeter is 154, so if we subtract 74 from 154, we get 80. However, we have to split the 80 in half because we have two sides left. Therefore, the scrapbook's length is 40 cm for one side. I hope this isn't too confusing.
Have a great day! :)
please help!!!!!!!!!!!!!!!
Answer:
There are 8 oz of soup per can : True
In 8 cans, there are 21 oz of soup : False
There are 2 oz of soup in 16 cans : False
In 1/8 of a can, there is 1 oz of soup : True
Step-by-step explanation:
To start, we know we have 168 oz of soup and 21 cans that are all the same size. To find how much is each can, (We know that they will all have the same amount since it says equally sized cans.) we can simply divide the amount we have of soup in oz by the amount of cans we have.
168 / 21 = 8.
This means that all the cans will be filled with 8 oz of soup. Making the first statement true.
Since there are 8 oz in each can, we can do 8 cans * 8 oz to find how many oz are in 8 cans of soup.
8 * 8 = 64 oz.
There are 64 oz of soup in 8 cans. Making the second statement false.
Now again, since there are 8 oz in each can, we can do 16 cans * 8 oz to find how many oz are in 16 cans of soup.
16 * 8 = 128 oz.
There are 128 oz of soup in 16 cans. Making the third statement false.
For the last question, to find 1/8 of a can of soup, we can take 8 oz (8 oz in one can) and divide it by 8.
8/8 = 1
Meaning 1/8 of a can of soup is 1 oz of soup. Making the fourth statement true.
Willie runs 4 miles in 44 minutes. If Willie runs at the same rate, how many miles can he run in 66 minutes?
Answer:
6 miles in 66 mins
Step-by-step explanation:
4 miles = 44 mins
simplify to the lowest point
1 mile = 11 mins
? = 66 mins
? = 1 x 6
you can run 6 miles in 66 mins
Answer:
Step-by-step explanation:
4/44= 0.0909090909...*66=6
find the propotunate value by dividing each initial value and multiply it by the listed secondary value
HELPPPPPPPPPPPPPPPPP AGIANNNNNNNNNNNNNNN
Two binomials that have a product of y^2 - 1
Answer:
(y-1) x (y+1)
Step-by-step explanation:
Write the number in the exponential
form with an exponent of 2
Use a² - b² = (a - b)(a +b) to factor the expression
1. [15 points] An electric company makes motors for a variety of applications. Its two plants ship their production to three dealers. The production hours available in the plants for the second quarter vary because of downtime for scheduled maintenance on equipment: Plant April May June A 400 360 360 B 425 350 375 Plant A requires 20 hours to produce a motor. Plant B requires 25. Because B is older and less efficient, production costs are $100 more per motor in B than in A. Shipping costs from the plants to the dealers and orders for the quarter are show below Monthly Shipping orders costs from Dealer April May June A B 1 12 9 11 45 60 2 10 12 8 50 70 3 8 11 12 75 40 Building ahead and stockpiling of motors is possible with a cost of $55 per month. Orders that are not shipped in the month requested are subject to a contractual penalty of $80 per month. At the end of June all orders need to be satisfied. Formulate an LP problem that can determine a production schedule to meet the demands for the motors with the minimum total of shipping, storage, penalty and production differential costs.
For each of the following expressions, identify the base and the exponent. 2× ,10² , x×
Answer:
2 is the base, 10 is the base, and x is the base. X is the exponent of 2, x is the exponent of 10, and x is the exponent of x.
Step-by-step explanation:
What is the greatest common factor of 36 and 90 ?
A 6
B 18
C 36
D 180
Answer:
B
Step-by-step explanation:
It's 18! Obviously it's not 180 because it's too big. It can't be 36 because 36 doesn't go evenly into 90. 6 is too small, so the answer is 18.
A plane travels at a speed of 205mph in still air. Flying with a tailwind, the plane is clocked over a distance of 550 miles. Flying against a headwind, it takes 1
hour longer to complete the return trip. What was the wind velocity? (Round your answer to the nearest tenth.)
Answer:
55.5 mph
Step-by-step explanation:
Time period of flight
Distance travelled / Speed of plane550 miles / 205 mph2.68 hoursReturn trip flight speed
Distance travelled / Time taken550 miles / 2.68 + 1 hours550 miles / 3.68 hours149.46 mphWind velocity
Original speed - Speed on return trip205 - 149.4655.5455.5 mphGiven vectors, a= (-2 -3) and b= ( 1 -1 ) find 2a-3b
Answer:
(-10,0)
Step-by-step explanation:
2a =[2(-2) , 2(-3)] = (-4 -6) <--- add them
-3b = [-3(1) . -3(-1)] = (-3 +3) <--- add them
2a - 3b =
[(-4 -6), (-3 +3)] =
(-10,0)
The distance between the Earth and the Moon is approximately 1,260,000,000 feet, and a rocket can travel there at a speed of about 1,540,000 ft/min. How long will it take the rocket ship to travel to the moon and back, in minutes? Express your final answer in minutes and round to the nearest minute. Be sure to convert each number to scientific notation first, before performing any operations. show your work.
It will take approximately 169 minutes for a the rocket to travel a distance of 1,260,000,000 feet at 1,540,000 ft/min
Speed, Distance and TimeGiven Data
Distance = 260,000,000 feetSpeed = 1,540,000 ft/minApplying the relationship between speed, distance and time we have
Speed = Distance/Time
Substituting our given data into the expression we have
1,540,000 = 260,000,000/time
Making time subject of formula
time = 260,000,000/1,540,000
time = 169 miniutes
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The ratio of Wei Ling's age to Wei Xuan's age 5 years ago was 2: 5. In 9 years
time, the ratio of Welling's age to Wel Xuan's age will be 3:4 How old is Wei
Xuan now?
Answer:
15 years old
Step-by-step explanation:
Start by defining the variables that we are going to use throughout our working:
Let the current age of Wei Ling and Wei Xuan be L and X years old respectively.
Next, form equations using the given information.
5 years ago
Wei Ling: (L -5) years old
Wei Xuan: (X -5) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan's is 2: 5,
[tex] \frac{ L - 5}{X - 5} = \frac{2}{5} [/tex]
Cross multiply:
2(X -5)= 5(L -5)
Expand:
2X -10= 5L -25
2X= 5L -25 +10
2X= 5L -15 -----(1)
9 years time
Wei Ling: (L +9) years old
Wei Xuan: (X +9) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan is 3: 4,
[tex] \frac{L + 9}{X + 9} = \frac{3}{4} [/tex]
Cross multiply:
3(X +9)= 4(L +9)
Expand:
3X +27= 4L +36
3X= 4L +36 -27
3X= 4L +9 -----(2)
Let's solve using the elimination method.
(1) ×3:
6X= 15L -45 -----(3)
(2) ×2:
6X= 8L +18 -----(4)
(3) -(4):
6X -6X= 15L -45 -(8L +18)
0= 15L -45 -8L -18
0= 7L -63
7L= 63
L= 63 ÷7
L= 9
Substitute L= 9 into (1):
2X= 5(9) -15
2X= 45 -15
2X= 30
X= 30 ÷2
X= 15
Thus, Wei Xuan is 15 years old now.
Select the correct answer from each drop-down menu.
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0.
The equation of this circle in standard form is
. The center of the circle is at the point
, and its radius is
units.
Step-by-step explanation:
[tex](x - 2) {?}^{2} + (y + 3) { = 18} [/tex]
SOLVE FOR X IN THE FOLLOWING EQUATION :-- -3(2X+3)+4X=4/3X+11
Answer:
-6
Step-by-step explanation:
-2x - 9 = 4/3x+11
-
-6x-27=4x+33
-
-6x-27-4x=33
-
=6x-4x=33+27
-
10x=33+27
-
-10x=60
-
x= -6
What is the quotient?
-3/8 ÷ -1/4
-1 1/2
-3/32
3/32
1 1/2
Answer:
1 1/2
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Please help me understand the question
Answer:
a and c
Step-by-step explanation:
Help help help help math
Answer:
x = 6
Step-by-step explanation:
(4x - 3) × 2 = 3(x + 8)
8x - 6 = 3x + 24
8x - 3x = 24 + 6
5x = 30
x = 6
PLEASE HELP PLEASE PLEASE
Answer:
4 degrees is the closest thing i could think of while looking at this.
find the value of angle BAC
Answer:
The value of angle BAC = 75°
Step-by-step explanation:
=> Angle BAC + 105° = 180°
=> Angle BAC = 180° - 105°
=> Angle BAC = 75°