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The temperature of the body after 60 minutes is  60.5° F.

Using the Newton's law of cooling;

T(t) =[tex]Ts + (To - Ts)e^-kt[/tex]

T(t) = temperature at time t

Ts = temperature of the surrounding

To = Temperature of object

t = time taken

k = cooling constant

Now;

[tex]T(t) -Ts=(To - Ts)e^-kt\\45 - 67 = (34 - 67)e^-15k\\-22 = -33e^-15k\\-22/-33 = e^-15k\\0.667 = e^-15k\\ln(0.667) = ln( e^-15k)\\-0.405 = -15k\\k = -0.405/ -15\\k = 0.027[/tex]

At t = 60 min

[tex]T(t) = Ts + (To - Ts)e^-ktT(60) = 67 + (34 - 67)e^-( 0.027*60)\\T(60) = \\67 + (-33)e^-( 0.027 * 60)\\T(60) = \\60.5 F[/tex]

T(60) = 60.5° F

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Answer:

T≈169

Step-by-step explanation:

Enter only the final temperature into the input box.

T_a = 67\hspace{50px}T_0=210

T  

a

​

=67T  

0

​

=210

\text{Write Formula:}

Write Formula:

T=67+(210-67)e^{-kt}

T=67+(210−67)e  

−kt

Plug in givens

\color{blue}{T}=67+143e^{-k\color{green}{t}}

T=67+143e  

−kt

Simplify

\text{Plug in given time and temperature:}

Plug in given time and temperature:

\color{blue}{193}=67+143e^{-k(\color{green}{1.5})}

193=67+143e  

−k(1.5)

Simplify

\text{Solve for }k\text{:}

Solve for k:

193=

193=

\,\,67+143e^{-1.5k}

67+143e  

−1.5k

-67\phantom{=}

−67=

\,\,-67

−67

126=

126=

\,\,143e^{-1.5k}

143e  

−1.5k

\frac{126}{143}=

143

126

​

=

\,\,\frac{143e^{-1.5k}}{143}

143

143e  

−1.5k

​

Divide by 143

0.8811189=

0.8811189=

\,\,e^{-1.5k}

e  

−1.5k

\ln\left(0.8811189\right)=

ln(0.8811189)=

\,\,\ln\left(e^{-1.5k}\right)

ln(e  

−1.5k

)

Take ln of both sides

\ln\left(0.8811189\right)=

ln(0.8811189)=

\,\,-1.5k

−1.5k

\frac{\ln\left(0.8811189\right)}{-1.5}=

−1.5

ln(0.8811189)

​

=

\,\,\frac{-1.5k}{-1.5}

−1.5

−1.5k

​

Divide by -1.5

0.0843751=

0.0843751=

\,\,k

k

k\approx

k≈

\,\,\color{blue}{0.084}

0.084

Round k to nearest thousandth

\text{Complete Formula:}

Complete Formula:

T=67+143e^{-\color{blue}{0.084}t}

T=67+143e  

−0.084t

Plug in k

\text{Find temperature after }\color{green}{4}\text{ minutes:}

Find temperature after 4 minutes:

T=67+143e^{-0.084(\color{green}{4})}

T=67+143e  

−0.084(4)

Plug in time

T=67+143e^{-0.336}

T=67+143e  

−0.336

Multiply

T=169.1911041

T=169.1911041

Plug into the calculator

T\approx 169

T≈169

Answer:

6311000

Step-by-step explanation:

The first thing we do is calculate the total amount of people in both states. 6.89 x10 raised to the 6th power is equal to 6890000. Then we multiply 5.79 by 10 to the fifth power, which equals to 579000. Then we subtract the numbers, and get 6311000. They want you to answer in standard notation, which is the regular way of writing numbers such as 10, instead of 10^1.

The difference in population

[tex] = (6.89 \times {10}^{6} ) - (5.79 \times {10}^{5} ) \\ = (6.89 \times 10 \times {10}^{5} ) - (5.79 \times {10}^{5} ) \\ = (68.9 \times {10}^{5} ) - (5.79 \times {10}^{5} ) \\ = (68.9 - 5.79) \times {10}^{5} \\ = 63.11 \times {10}^{5} [/tex]

Answer:

[tex]63.11 \times {10}^{5} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Number 1.

[tex]5^x=2[/tex], first we will take the [tex]log[/tex] of both of these numbers getting us,

[tex]x=\frac{log(2)}{log(5)}[/tex], which then gives us that [tex]x=0.4306777777....[/tex]

Number 2

[tex]e^x=10[/tex], solve for our exponent, [tex]2.718282^x=10[/tex], use the logarithmic formula, and we get,

[tex]x=\frac{log(10)}{log(2.718282)}[/tex], which then we get that [tex]x=2.302585[/tex]

Answer:

32+24=8(4+3)

20+8=4(5+2)

100+75=25(3+4)

49+28=7(7+4)

32+24=12(3+2) I don't know if this is right because 12 times 3 is 36 but that was the last option

Step-by-step explanation:

it's distributive property you multiply the numbers on the inside by the numbers on the outside.

274.32 is the answer. Tell me if I need to be more precise.

Answer:

b = 13.5

Step-by-step explanation:

2 -b/3 = -5/2

im assuming we want to find b. therefore we want b = something. so because b is on top of a fraction right now, I will multiply both sides by 3 so -b is not on top of a fraction anymore.

6 -b = -15/2

we should get rid of the divided by 2 on the other side too, to make it easier. we can do this by multiplying 2 on both sides.

12 - 2b = -15

remember, we want to isolate b. so first we should get rid of the 12 next to the 2b. we can do this by subtracting 12 on both sides!

-2b = -27  

finally, we can divide both sides by -2 and b will be isolated!

b = 13.5

Step-by-step explanation:

The graph has a slope of 0.5 and a y-intercept of 5

The equation is given as:

A linear equation is represented as:

Where m represents the slope, and c represents the y-intercept

So, by comparison:

m = 0.5

c = 5

This means that:

The slope is 0.5, and the y-intercept is 5

Hence, the graph of  has a slope of 0.5, and a y-intercept of 5

See attachment for the graph of

A

i know its a because the other kids'answer is wrong.

Answer:

no solutions exist

Step-by-step explanation:

We can solve this by using system of equations and using substitution.

2(8-3y)+6y=2      Substitute x=8-3y into the first equation.

16-6y+6y=2         Distribute.

16=2                     Simplify.

16 does not equal 2, so there are no solutions.

Answer:

142.25 miles

Step-by-step explanation:

239- 96.75

142.25

Answer:

Step-by-step explanation:

Answer:

the answer would be 7/5

Step-by-step explanation:

2 of them would already make a whole, and if you add another one, it's going to be more than just one pitcher of lemonade.

Answer:

0.2 inches

Step-by-step explanation:

12.5 weeks = 2.5 inches

1 week = p inches

Cross multiply

12.5p = 2.5

Divide both sides by 12.5

p = 2.5 / 12.5

p = 0.2 inches

Hence, the length grown in 1 week is 0.2 inches

Hope I Helped You:)

Answer:

17

Step-by-step explanation:

Let the smaller number = x

Let the larger number = y

y = 2x + 8

y - x = 25                Add x to both sides

y = x + 25               Substitute this into the first equation

x + 25 = 2x + 8       Subtract 8 from both sides

x + 25 - 8 = 2x        Combine

x + 17 = 2x               Subtract x from both sides.

17 = 2x - x                Combine

17 = x

Answer:

B

Step-by-step explanation:

The Width of the Rectangle (read Polygon) is 8 units and the Length of the Rectangle is 12 units.

The area of the polygon is 96 square units. Therefore, the correct answer is option C.

From the given graph, we have polygon ABCD.

From the graph, we have AB=DC=12 units and BC=AD=8 units.

Here, the given polygon is rectangle.

Area of a rectangle = Length×Breadth

Now, area of a rectangle = 12×8

= 96 square units

Perimeter of a rectangle = 2(Length+Breadth)

= 2(12+8)

= 2(20)

= 40 units

Therefore, the correct answer is option C.

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Answer:

solution

Step-by-step explanation: total=209.75

Answer:

a₈ = 2

Step-by-step explanation:

Substitute n = 8 into the nth term rule

A(8) = - 12 + 2(8 - 1) = - 12 + 2(7) = - 12 + 14 = 2

Answer:

Step-by-step explanation:

This relation (this group of points) is NOT a function. In order to be a function, every x-value (the first number in the pair) can only be paired up with one y-value (only one partner for the x)

In this relation, -6 is paired up with four different y-values (four different partners!)

If you plotted these points on a graph, you would see they are all lined up in a vertical line. If you have learned about the vertical line test, you will see that a vertical line goes through all four points. This set of points fails the vertical line test. To be a function, a vertical line can only touch the points one at a time.

To be a function, every x can only have one y partner.

Answer:

Happy holidays to everyone!

Step-by-step explanation:

Answer:

p=36

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:

p/18+7-(9)=0

Simplify p/18

(p/18+7)-9=0

7= 7/1= 7*18/18

p+7*18/18=p+126/18

(p+126)/18-9=0

9=9/1=9*18/18

(p+126)-(9*18)/18=p-36/18

p-36/18=0

p-36=0

p=36

Hope this helped :)

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{3})~\hspace{10em} \stackrel{slope}{m}\implies 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{7}(x-\stackrel{x_1}{6}) \\\\\\ y-3=7x-42\implies y = 7x-39[/tex]

Answer:

[tex]y-3=7(x-6)[/tex]

Step-by-step explanation:

We are given that a line has a slope (m) of 7 and passes through the point (6,3).

We want to write the equation of this line.

There are three ways to do it:

As the question doesn't specify, either form should work, but let's write the equation in point-slope form as that's the easiest to do.

As we are already given both the point and the slope, we can plug them both into the equation.

Starting with the slope, substitute 7 for m.

[tex]y-y_1=7(x-x_1)[/tex]

Now, substitute 6 as [tex]x_1[/tex] and 3 as [tex]y_1[/tex].

[tex]y-3=7(x-6)[/tex]

Answer: The equation of the line is y = 3/2 x + 1

Step-by-step explanation:

Slope 3/2; The Equation of the line passing through (-4, -5) having a slope of 3/2 is y + 5 = 3/2 (x + 4) or y = 3/2 times X + 6 - 5 or y = 3/2 times X + 1[Ans] graph {3/2*x+1[-10, 10, -5, 5]}

I hope this makes sense to you :)

Answer:

1 3/8   D

Step-by-step explanation:

The first and most obvious part of the answer is that the paper clip is at least 1 inch long. The question is how much longer?

It is between 1/4 of an inch and 1/2 of an inch. In fact it is exactly half way between them.

So that resembles an average.

(1/4 + 1/2)/2 = (1/4 + 2/4) / 2 = (3/4)/2

[tex]\frac{\frac{3}{4} }{2} = \frac{\frac{3}{4} }{\frac{2}{1} }[/tex]

Now the trick is to invert the denominator (make it 1/2) and multiply

3/4 * 1/2 = 3/8

Answer:8.15

Step-by-step explanation: 8.15

Answer:

Marsha has driven 252 miles

Step-by-step explanation:

In order to figure out the problem, you take the total distance and multiply it by the fraction she has gone. This would be 630*(2/5) which would equal 252. Thus, Masha has driven 252 total miles.

Hope this helps!

Answer: 252 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

The tenure of an FD can vary from 7, 15 or 45 days to 1.5 years and can be as high as 10 years. These investments are safer than Post Office Schemes as they are covered by the Deposit Insurance and Credit Guarantee Corporation (DICGC).

The length of FD in a right-angled triangle with EC as 18 units and CF as 26 units is 20.2 units.

The length of FD can be found using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is FD, and the other two sides are EC and CF.

EC = 18 units

CF = 26 units

Plugging these values into the Pythagorean Theorem, we get:

[tex]FD^2[/tex] = [tex]EC^2[/tex] + [tex]CF^2[/tex]

[tex]FD^2[/tex] = [tex]18^2[/tex] + [tex]26^2[/tex]

[tex]FD^2[/tex] = 324 + 676

[tex]FD^2[/tex] = 1000

FD = [tex]\sqrt{[/tex](1000)

FD = 10 * [tex]\sqrt{[/tex](10)

FD = 20.2 units

Therefore, the length of FD is 20.2 units.

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Correct Question:

In a right-angled triangle with EC as 18 units and CF as 26 units, what is the length of FD.

Answer:

3

Step-by-step explanation:

75÷5-[(9-7)×3]×2

do innermost inclusion symbols first, which would be 9-7

75÷5-[2×3]×2

now multiply 2 and 3

75÷5-(6)×2

now divide 75 by 5

15-6×2

now multiply

15-12

3

The required simplified value of the given expression is 13.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 75÷5−[(9−7)×3]×2

Following the PEMDAS rule,
= 25 - [2×3]×2
= 25 -[6]×2
= 25 - 12
= 13

Thus, the required simplified value of the given expression is 13.

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Answer:

the 2nd choice

Step-by-step explanation:

hope this helps

may i get braineist pls

Answer:

A. or y=-1/3x-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

8 adult tickets cost 8($9.50) = $76

21 kids tickets cost 21($3) = $63

The total cost of these tickets is $76 +63 = $139.

__

aa adult tickets cost 9.50aa

kk kids tickets cost 3.00kk

The total cost of these tickets is 9.50aa +3.00kk.

_____

Additional comment

We ordinarily expect a variable to be a single letter. This problem statement defines each variable using a double letter, so that is what we have used. (Sometimes Brainly doubles up variable content in copied text, so we suspect that may have happened here.)