Answer:
The object's temperature after 18 minutes is of 426ºC.
Step-by-step explanation:
The temperature after t minutes is modeled by an exponential function, which has the following format:
[tex]T(t) = T(0)(1-r)^{t}[/tex]
In which T(0) is the initial temperature, and r is the cooling rate, as a decimal.
Its initial temperature is 730°C and it cools at a rate of 2.95% per minute
This means that [tex]T(0) = 730, r = 0.0295[/tex]. So
[tex]T(t) = T(0)(1-r)^{t}[/tex]
[tex]T(t) = 730(1-0.0295)^{t}[/tex]
[tex]T(t) = 730(0.9705)^{t}[/tex]
Find the object's temperature after 18.0 minutes.
This is [tex]T(18)[/tex]. So
[tex]T(t) = 730(0.9705)^{t}[/tex]
[tex]T(18) = 730(0.9705)^{18} = 426[/tex]
The object's temperature after 18 minutes is of 426ºC.
The required value of the object's temperature after 18.0 minutes is 425.83.
Given that,
An object's temperature cools exponentially after it is removed from a furnace (hot oven).
If its initial temperature is 730°C and it cools at a rate of 2.95% per minute,
We have to determine,
Find the object's temperature after 18.0 minutes.
According to the question,
The initial temperature is 730°C and it cools at a rate of 2.95% per minute,
The temperature after t minutes is modeled by an exponential function, which has the following format is,
[tex]= T(t) = T(0).(1-r)^t[/tex]
Where T(0) is the initial temperature, and r is the cooling rate, as a decimal.
Then,
T(0) = 730°c and r = 2.95% = 0.0295
Substitute all the values in the equation,
[tex]= T(t) = T(0).(1-r)^t\\\\= T(t) = 730 \times (1-0.0295)^t[/tex]
Therefore,
The object's temperature after 18.0 minutes is,
[tex]= T(t) = T(0).(1-r)^t\\\\= T(18) = 730 \times (1-0.0295)^{18}\\\\= T(18) = 730 \times 0.5833\\\\ = T(18) = 425.8361[/tex]
Hence, The required value of the object's temperature after 18.0 minutes is 425.83.
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Simplify the following expression.
-6 + 5 x 2 + 10 x (-2)
Answer:
= -16
Step-by-step explanation:
You will use the Please Excuse My Dear Aunt Salley method (Paranthesis, mutiplication, division, addition, and subtraction)
-6 +5 x 2 +10 x (-2)
-6 +10 -20 (a positive times a negative equals a negative)
= -16
Step-by-step explanation:
-6 + 5 x 2 + 10 x ( -2 ) PEMDAS
-6 + 10 + -20 Parensthesis, Exponents, Multiplication & Division
4 - 20 left to right, Addition & Subtraction left to right.
-16.
what is the probability
Answer:
2:12
Step-by-step explanation:
any genius student ????
can anyone teach me about how to do graph of linear inequalities ....??
please give me the proper answer ;( !!!!!
Step-by-step explanation:
To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line. If the inequality is strict ( < or > ), graph a dashed line.
Solve the following system by elimination. Show work and explain each step.
3x + 2y=16
2x +5y=21
The value of x and y using the elimination approach on the equations will be 3.45 and 2.81 respectively.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
Given the set of equations,
3x + 2y=16
2x +5y=21
Multiply by 2 to the first equation and by 3 to the second equation.
Fist becomes ⇒
6x + 4y = 32
Second become ⇒
6x + 15y = 63
By subtracting second - first
11y = 31
y = 2.818181...
By substitution,
6x + 4(2.81) = 32
x = 3.454545..
Hence "The value of x and y using the elimination approach on the equations will be 3.45 and 2.81 respectively".
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Debra deposits $800 into an account that pays simple interest at a rate of 5% per year. How much interest will she be paid in the first 5 years?
Answer:
200$ in first year
Step-by-step explanation:
HELP ASAP
Solve the system of equations
X + 3y = -20 and -4x - 4y=0 by combining the equations
Answer:
x=10 and y=-10
Step-by-step explanation:
first pick for what you want to solve for first, in this case I picked y
so I put them for subtraction and i hade to multiply the first equation by 4 so I could cancel my X's and I just solved for y
then I plugged in my answer to the first equation, you can pick any of the 2 equations, and I solved for x
With distances in feet, use the see saw principle to find the number of feet represented by N in the balanced seesaw shown.
Answer:
The answer is 4
Step-by-step explanation:
Im sorry if im wrong im not that good at math
What is the greatest common factor of 24, 18, and 36?
Answer:
most likely 6
Step-by-step explanation:
because factors of 36 is 4,2,6 etc factors of 18 is 6 and 24 and it the gcf
Answer:
The greatest common factor is 6
Step-by-step explanation:
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
#3 i don’t even understand what the question is asking for
What is 1/3 divided by 2 in fraction form
Answer:
1/6
Step-by-step
When 1/3 divided by 2 gives 1/6.
What is fraction?fraction, In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.
In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
If we divide 1/3 by 2, which is not possible
Fraction also multiplication only.
To make the division into multiplication we have to reciprocal the number on the right side of the division
So,
1/3÷2
=1/3*1/2
= 1/6
Hence, 1/3 divided by 2 in fraction form gives 1/6.
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Help ASAP !!!
If Leah drove 1,200 miles and used 60 gallons of gas , her average miles per gallon is how much?
Answer:
20
Step-by-step explanation:
We will start by writing the following ratio
miles:gas
1200:60
This means that we have
x:1
divide 1200 by 60 to get x
I get
x=20
Answer:
20 miles per gallon.
Step-by-step explanation:
You have to divide 1,200 by 60. Then you will be left with 20 miles/gallon
Write the equation of the line that passes through (9,3) and (7,3)
Answer:
y=3
Step-by-step explanation:
First, let's find the slope (m) of the line, which we do with the equation (y2-y1)/(x2-x1)
the given points are (9,3) and (7,3)
we can label the points:
x1=9
y1=3
x2=7
y2=3
now substitute into the equation
m=(3-3)/(7-9)
m=0/-2
m=0
the slope is 0.
Now, use slope-point form, which is y-y1=m(x-x1)
substitute using the given numbers
y-3=0(x-9)
multiply
y-3=0
add 3 to both sides
y=3
the equation is y=3
hope this helps :)
True or false:a. If the proportion of defectives in the sample is less than 12%, it is reasonable to conclude that the new process is better.b. If the proportion of defectives in the sample is only slightly less than 12%, the difference could well be due entirely to sampling variation, and it is not reasonable to conclude that the new process is better.c. If the proportion of defectives in the sample is a lot less than 12%, it is very unlikely that the difference is due entirely to sampling variation, so it is reasonable to conclude that the new process is better.
Answer:
false
Step-by-step explanation:
In a population, the percentage or fraction which is not conforming to (defeating) is defined as a ratio of the population's figures of non-conforming goods to the sum of goods in the inhabitants, and the further discussion can be defined as follows:
In option A, it is wrong because the proportion of both the sample is simply an approximation. The real percentage could be more than 12%. Furthermore, the conclusion also that the new procedure is better cannot be reasonably concluded.In options (b and c) both are correct because it is based on the explanation of whether, if the fraction of defective differences is bigger, we can only determine that its new procedure is better or not as a minor difference may occur from the variance of samples.Learn more:
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Brianna buys a $3200 refrigerator using an installment plan that requires 20% down
and a 4.1% interest rate. How much is her down payment?
Answer:
the down payment is 22.0 percent
Step-by-step explanation:
Answer:
Step-by-step explanation:
3260
Convert the
following 35 minutes to seconds
Answer:
2,100 sec
Step-by-step explanation:
Answer:
2100seconds
Step-by-step explanation:
♪＼(*＾▽＾*)／＼(*＾▽＾*)／
Plz I will give brainliest
Answer:
1/16 or 0.0625 as a decimal
Pleaseeeeeee help me with this ASAP
Answer:
736
Step-by-step explanation:
25*32=800
16*4=64
800-64
I WILL GIVE BRAINLIEST Which of the following tables of x– and y–values represents a function? Select all that apply.
Answer:
A and C
Step-by-step explanation:
For a table of x and y variables to be a function, each x-value must not have two different y-values assigned or related to it. However, different x-values can have the same y-value.
Therefore, the table in option A and option C are functions because every of their x-value has exactly one y-value that corresponds it.
How much was Ray's paycheck for working 46 hours? Show your work.
Would Ray make more money working 40 hours a week for two weeks or working 32 hours one week and 46 hours but the next? Justify your solution.
Answer:
Part C Would Ray make more money working 40 hours a week for two consecutive weeks, or working 32 hours one week and then 46 hours the next?
Step-by-step explanation:
Tami spins a spinner with seven sections. The sections are
numbered 1 through 7, and all sections are the same size.
What is the probability that the spinner lands on 4?
please help me
Answer:
B
Step-by-step explanation:
if all sides are equal and there are 7 sides than each side has and equal opportunity to be landed on.
Answer:
B
Step-by-step explanation:
I got right:)
Switch row 2 and row 3:
4−1−4
8−46
−231
−7
30
−2
4−1−4
−7
Answer:
-2 3 1 -2
8 -4 6 30
Step-by-step explanation:
the second part is
-4 6 2 -4
(3m – 9) -- (-10m – 9)
Answer:
-13m - 18
Step-by-step explanation:
(3m - 9) -- (-10m - 9 )
Subtract the 3m to the -10m, and add the 9's together.
Answer:
the answer is 13m
Step-by-step explanation:
remove parenthesis : 3m – 9 + 10m – 9
simplify : 3m - 9 +10 +9 = 13m
Write the quadratic function in standard form
Answer:
B. f(x) = x² + 10x + 17
Step-by-step explanation:
Given:
f(x) = (x + 5)² - 8
Required:
Write in standard form
SOLUTION:
f(x) = (x + 5)² - 8
Expand (x + 5)²
f(x) = (x + 5)(x + 5) - 8
f(x) = x(x + 5) +5(x + 5) - 8
f(x) = x² + 5x + 5x + 25 - 8
Add like terms
f(x) = x² + 10x + 17
To find the total after an i tease or 5% , you could multiply the original amount by 105%.
A. True
B. False
what is 1 over 2 x 6 what is 1 over 2 x 7 and what is 3 over 4 x 12 and what is 2 over 5 x 30
exampel of 1 over 2
1/2
A local water storage facility is currently empty. The city
water workers begin filling it at a rate
of 500 gallons per minute. It immediately begins
sending some of its water into the city's water
pipes at a rate of 150 gallons per minute.
a) How much-water will be in the water storage facility
in 25 minutes?
B.) write an equation to find the number of gallons,y,in the storage facility after x minutes.
Answer: See explanation
Step-by-step explanation:
a) How much-water will be in the water storage facility in 25 minutes?
Since the city water workers begin filling it at a rate of 500 gallons per minute, in 25 minutes they'll have filled:
= 500 × 25
= 12500 gallons
It immediately begins sending some of its water into the city's water pipes at a rate of 150 gallons per minutes. In 25 minutes, they'll have sent:
= 150 × 25
= 3750 gallons
Amount that'll be left in the tank will be:
= 12500 - 3750
= 8750 gallons
b. Write an equation to find the number of gallons,y,in the storage facility after x minutes. This will be:
y = (500 × x ) - (150 × x)
y = 500x - 150x
y = 350x
The heights in inches, of some small trees for sale at a garden store are 62, 62, 59, 61, 59, 70, 59, and 62. What is the median height? What is the mode? What is the mean height?
Answer:
Step-by-step explanation:
the mean height, remember is the average
62+62+59+61+59+70+59+62=494/8=61.75
median is the middle value, so we will write the numbers in order
59,59,59,61,62,62,62,70
we have an even number so we add the middle numbers and divide by 2,
the median=61+62=123/2=61.50
mode is the number that occurs most often : 62 and 59
Triangle ABC has side length of 14, 8 and 10.4 what are the possible side lengths of a triangle DEF if ABC is similar to DEF
Answer:
DEF can have possible side lengths of 28, 16, 20.8
Step-by-step explanation:
Triangle Similarity
If the three sides of two triangles have the same proportion, the triangles are similar (SSS theorem).
Triangle ABC has side lengths of 14, 8, and 10.4.
Any other triangle whose side lengths are the same lengths of ABC multiplied by a constant scale factor is similar to ABC.
For example, select scale factor 2. Thus, the triangle of side lengths 2*14=28, 2*8=16, and 2*10.4=20.8 is similar:
DEF can have possible side lengths of 28, 16, 20.8
Any other scale factor will do.
What is the solution to
f(x) = g(x)?
Select each correct answer.
Answer:
f(x)=g(x) is the only answer
Step-by-step explanation:
Find the series:0,2,6,12,20and.......?
Answer:
The series is represented by sum [tex]f(n) = 2 \cdot \Sigma\limits_{i=0}^{n} n[/tex], [tex]n \in\mathbb{N }[/tex]. The remaining element of the series is 30.
Step-by-step explanation:
This exercise consist in deriving the function which contains every element of the given series. The sum that contains all elements of the series { 0, 2, 6, 12, 20,...} is represented by the following formula:
[tex]f(n) = 2 \cdot \Sigma\limits_{i=0}^{n} n[/tex], [tex]n \in\mathbb{N }[/tex] (1)
Where [tex]n[/tex] is the cardinal associated with the element of the series.
Lastly, we proceed to evaluate the sum for the first five elements:
n = 0
[tex]f(0) = 0[/tex]
n = 1
[tex]f(1) = 0 +2[/tex]
[tex]f(1) = 2[/tex]
n = 2
[tex]f(2) = 0 + 2 + 4[/tex]
[tex]f(2) = 6[/tex]
n = 3
[tex]f(3) = 0 + 2 + 4 + 6[/tex]
[tex]f(3) = 12[/tex]
n = 4
[tex]f(4) = 0+2+4+6+8[/tex]
[tex]f(4) = 20[/tex]
The series is represented by sum [tex]f(n) = 2 \cdot \Sigma\limits_{i=0}^{n} n[/tex], [tex]n \in\mathbb{N }[/tex].
Lastly, the missing element is found by evaluating the function at [tex]n = 5[/tex], that is:
n = 5
[tex]f(5) = 0 + 2 + 4 + 6 + 8 + 10[/tex]
[tex]f(5) = 30[/tex]
The remaining element of the series is 30.
