We have to find the time required for an object to cool from 300°F to 260°F by evaluating the following where t is time in minutes:t = 10/ln 2 ∫260300 (1/T - 100) dT.
To find the time t, let's first evaluate the integral using integration by substitution: Let u = T, then du/dT = 1 dT= du
Now we have,[tex]t = 10/ln 2 ∫260300 (1/T - 100) dT= 10/ln 2 ∫260300 (1/u - 100) du= 10/ln 2 ln|u| - 100u |_260^300= 10/ln 2 [ ln|300| - ln|260| - 100(300) + 100(260) ]= 10/ln 2 [ 5.7038 - 3000 + 2600 ]= 10/ln 2 ( - 94.6913 ) ≈ 133.4775[/tex]
minutes.
Therefore, the time required for the object to cool from 300°F to 260°F is approximately 133.4775 minutes.
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A school’s Spanish club is selling printed caps to raise money for a trip. The printer charges $150 in advance plus $3 for every cap ordered. If the club sells caps for $12.50 each, a least how many caps do they need to sell to make a profit?
Answer:
at least 16 caps
Step-by-step explanation:
150-3c=12.5c
subtract 3c from each side
150=9.5c
divide each side by 9.5
≈15.8
up to 16
The least number of caps that need to be sold to make a profit is 16 caps.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
The total cost of ordering x caps.
= 150 + 3x
Now,
Cost of selling one cap = $12.50
Number of x caps to sell to make a profit.
12.50x > 150 + 3x
12.50 - 3x > 150
9.50x > 150
x > 150/9.50
x > 15.78
We can cross-check.
The total cost of ordering 16 caps.
= 150 + 3 x 16 = 150 + 48 = $198
Amount after selling 16 caps.
= 12.50 x 16
= $200
Thus,
16 caps need to be sold to make a profit.
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Write the equation of the line that passes through the points (-1, -6) and (4,5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer: y + 6 = 11/5( x + 1)
Step-by-step explanation:
To write the equation in point-slope form we need to first find the slope of the line.
The slope is the difference between the y coordinates divided by the difference between the x coordinates.
-6 - 5= -11
-1 - 4 = -5
-11/-5 = 11/5
The slope is 11/5 .
The point-slope formula says that y - b = m(x - a) where m is the slope and
b is the y coordinate of one of the point and a is the x coordinate of the same point.
We will use the point (-1,-6)
The x coordinate is -1 and the y coordinate is -6.
b will be -6 and a will be -1 while m will be 11/5.
y -(-6) = 11/5(x-(-1)
Reduce it to lowest terms.
y + 6 = 11/5( x + 1)
your savings grow by $126 per week and by week 43 you have $5763 how much money did you have by week 0
Answer:
345(I think)
Step-by-step explanation:
8 less than the product of 2 and a number is 16. What is the number?
The answer is 24 when using like terms and the order of operations.
The number would be -4 which is 8 less than the product of 2 and a number is equal to 16.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Let the number would be n
Given that 8 is less than the product of 2 and a number is equal to 16.
According to the statement of the question,
⇒ 8 - (n*2) = 16
⇒ -(n*2) = 16 - 8
Apply the subtraction operation,
⇒ -2n = 8
⇒ n = -8/2
Apply the division operation,
⇒ n = -4
Hence, the number would be -4 which is 8 less than the product of 2 and a number is equal to 16.
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A $40,000 was bought in 2010. The value is depreciating at a rate of 4.5%. How much is the car worth in 2020?
approximately 38,200..... i think ?
Law of Syllogism.
If a natural number ends in 0, then it is divisible by 10. If a natural number is divisible by 10, then it is divisible by 5.
Answer:
true
Step-by-step explanation:
if it is 10,20,30,40etc...
10÷5=2
20÷5=10
30÷5=15
40÷5=20
If a natural number ends in 0, then it is divisible by 10. If a natural number is divisible by 10, then it is divisible by 5 is a correct statement.
What is Law of Syllogism ?Law of Syllogism says if a then b and if b then c implies if a then c this transition property can hold true to many of mathematical operations.
According to the given question If a natural number ends in 0, then it is divisible by 10. If a natural number is divisible by 10, then it is divisible by 5 then if a natural number ends with 0 it is divisible by 5.
This is law of Syllogism it states that (according to this question frame )
If a is divisible by b and b is divisible by c then a is also divisible by c called transitivity.
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A + B/ C = D, Solve for B
Answer:
B = DC - A
Step-by-step explanation:
A + B / C = D Multiply C
A + B = CD Subtract A
B = CD - B
25 POINTS
What is the value of f(4) + g(3)? Two functions are shown. f(x) = 64(0.5) * Enter your response here: g(x) = 20x + 12 Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, .,-, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or a decimal.
Answer:
[tex]\displaystyle f(4) + g(3) = 76[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = 64\left(\frac{1}{2}\right)^x\text{ and } g(x)=20x+12[/tex]
And we want to find the value of:
[tex]f(4)+g(3)[/tex]
We can find the value of each function individually.
Find f(4):
[tex]\displaystyle \begin{aligned} f(4) & = 64\left(\frac{1}{2}\right)^{(4)} \\ \\ & = 64\left(\frac{1^4}{2^4}\right) \\ \\ & = 64\left(\frac{1}{16}\right) \\ \\ & = 4\end{aligned}[/tex]
Find g(3):
[tex]\displaystyle \begin{aligned} g(3) & = 20(3) + 12 \\ \\ & = (60) + 12 \\ \\ & = 72\end{aligned}[/tex]
Therefore, substitute:
[tex]\displaystyle \begin{aligned} f(4) + g(3) & = (4) + (72) \\ \\ & = 76\end{aligned}[/tex]
Therefore, in conclusion:
[tex]\displaystyle f(4) + g(3) = 76[/tex]
Can anyone send me the answer for this
answer :
is equals to 2 Kama Q is equals to 3 Kama P is equal to minus Q is equals to 9 Pharma fees equals to minus 25 Q is equals to 6 = 2 - 61
step by step explainaion:2 by 3 Kama minus 5 by 9 Kama minus 25 by 6 - 61 by to all rational
can someone plz answer this asap
PLEASE HELP I DONT WANNA FAIL, THIS IS TOO HARD AND STRESSFUL
Answer:
That is hard. What grade are you in.
Step-by-step explanation:
In a certain town 65% of homeowners watch cable TV, 40% watch Netflix, and 20% watch both.
Draw a Venn Diagram. Choose a homeowner at random. If homeowner watches cable TV, what is
the probability they watch Netflix?
Answer:
.31
Step-by-step explanation:
a. b. c. or .d
please help me . ASAP
Answer: Choice A
The second fraction should not have been multiplied by 9
This is because 1/9 already has the LCD in the denominator. LCD stands for lowest common denominator.
The first fraction 2/3 does not have 9 in the denominator, which is why they multiplied top and bottom by 3
2/3 = (2*3)/(3*3) = 6/9
After each fraction has the same denominator (9), you can add the numerators to place over the LCD like so
6/9 + 1/9 = (6+1)/9 = 7/9
This means,
2/3 + 1/9 = 6/9+1/9 = 7/9
GONZALEZ
Problem 3.3
In order to scale figure F back to figure E, what scale
factor should you use?
20
Submit and Explain
21
20
Answer:
Step-by-step explanation:
The Thompson Family are filling in their circular garden with new soil for the spring. The garden has a diameter of 24 cm. The cost of the soil is $5.50 per square centimeter. How much money are they going to spend to fill their garden with new soil?
Answer:
$2488.46Step-by-step explanation:
This problem is on the mensuration of flat shapes.
firstly, we need to solve for the area of the garden.
given that the diameter d=24cm
the radius is d/2= 12cm
Therefore the area is expressed as
A= πr^2
A=3.142*12^2
A=3.142*144
A=452.448 cm^2
We are given that a square cm cost $5.50 to sandfill
therefore the entire garden will cost $5.50*452.448
$2488.46
E is the midpoint of AB. If
AE = 4x +6 and EB = 10x - 12,
what is AB?
Answer:
36
Step-by-step explanation:
Since E is the midpoint, AE and EB are equal. We can write this as such,
4x+6=10x-12 if we solve from here we get 6x=18. Simplify to get x=3. sub in three for x in the AE equation, 4(3)+6 and solve. You'd get 18 as your answer. Double that to get the solution since AE= 1/2AB. 18*2= 36
AB=36
two numbers are in ratio s:t .if the first is a,find the second
Answer:
The second number is a*t/s
Step-by-step explanation:
s/t = a / x Let x be the second number.
sx = at divide by s
x = at/s
4 (32 - 139)
Simplify
Answer:
-428
Step-by-step explanation:
32-139=(-107)
4*(-107)=(-428)
Can someone help with these problems?
Answer:
First, you have to substitue 3 into x
20 - 5(3)
20 - 15
= 5
so the first one is 5
the next one we will do the same but with 4
20 - 5(4)
20 - 20
= 0
Step-by-step explanation:
Answer:
20-5(3)
20-15
=5
than
20-5(4)
20-20
=0
and there is your answer
Step-by-step explanation:
Help me solve this problem please
what is 62.3 times .34
Answer: 21.182
Step-by-step explanation:
What is, 3 to the power of 2, times, 3 to the power of 5.
A. 3 to the power of 7
B. 3 to the power of 10
C. 9 to the power of 7
D. 9 to the power of 10
Answer:
3^7
Step-by-step explanation:
3^2 * 3^5
a^b * a^c, since the bases are the same, we can add the exponents
a^ ( b+c)
3^(2+5)
3^7
Answer:
ha
Step-by-step explanation:
please
someone please help fast first correct will be marked as brainiest
Answer:
A
CAB
BAC
Step-by-step explanation:
The angle can be named by the vertex
A
or by using the three points starting from one side through the vertex and ending at the other side
CAB
or BAC
Answer:
ABC,CAB,BAC,CBA,A
Step-by-step explanation:
HOPE THIS HELPED PLZ GIVE ME BRAINLIEST
Katherine drove 13 miles in 1/5 hour. On average, how fast did she drive, in miles
per hour?
Answer:
65 miles per hour
Step-by-step explanation:
r = d/t
1 : 5 = 0.2
r = 13 : 0.2 = 65
Ms. Aikins is saving money for a vacation. Her goal is to save $250.00 a month. She has made 11 deposits or $18.00 so far. How much more money does Ms. Aikins need to meet her goal?
Answer:
if 1 deposit = $18, she´ll need $52
If she just has $18, she´ll need $232
which expression is equal (x+4)(-3x^2-4x+2)
Answer:
-3x^3-16x^2-14x+8
Step-by-step explanation:
[tex](x+4)(-3x^2-4x+2)\\\\Distribute\:parentheses\\\\=x\left(-3x^2\right)+x\left(-4x\right)+x\times\:2+4\left(-3x^2\right)+4\left(-4x\right)+4\times \:2\\\\Apply\:minus-plus\:rules\\+\left(-a\right)=-a\\\\=-3x^2x-4xx+2x-4\times\:3x^2-4\times\:4x+4\times\:2\\\\Simplify\\-3x^2x-4xx+2x-4\times\:3x^2-4\times\:4x+4\times\:2:\\\\\quad -3x^3-16x^2-14x+8\\\\=-3x^3-16x^2-14x+8[/tex]
Solve for v.
-V + 1 = 3
round 0.0625 to the nearest thousandth
Answer:
0.0630
Step-by-step explanation:
hope this helps
Solve to the nearest tenth
[tex] \sqrt{18} [/tex]
Complete the statement.
3 1/4÷ ? =1
Answer:
3 1/4
Step-by-step explanation:
The general rule of thumb is that if the solution is 1 and the operation is division, the the dividend (in this case 3 1/4) should be equal to the divisor (represented with the question mark; ?).
Answer:
3 1/4
Step-by-step explanation:
3 1/4
3 1/4 = 1 :)
will this answer count?
