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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:

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 probability would be 30% but as a fraction it would be 3/10

Step-by-step explanation:

Answer:

7/15

Step-by-step explanation:

The probability of the first one is 7/10 and the second one is 6/9. Multiply them together and you get 42/90, which simplifies to 7/15.

Answer:8.15

Step-by-step explanation: 8.15

Answer:

5

Step-by-step explanation:

If sheila has $46 to buy pads with, and each pad costs $8, then:

8 · 5 = 40

8 · 6 = 48

48 > 46,

So maximum amounts of pads she could is 5, and have remaining $6

Answer:

46÷8=5.75 so the answer is 5

Explanation :

________________________________

Factorizes:

⇒ a² + 8a + 16 = 0.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ a² + 4a + 4a + 16 = 0.

⇒ a(a + 4) + 4(a + 4) = 0.

⇒ (a + 4)(a + 4) = 0.

⇒ (a + 4)² = 0.

⇒a=-4.

Hence a=-4.

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:

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:

Hope this image helps you. (sorry if it's tiny writing.)

Step-by-step explanation:

Answer:

5,5

Step-by-step explanation:

Answer:

Happy holidays to everyone!

Step-by-step explanation:

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:

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:d=18FT

Step-by-step explanation:

YOUR WELCOM :)

Answer:

x<-3

Step-by-step explanation:

Step-by-step explanation:

1 _21:00_ , _22:10_, 1:10

2. 1:20

3. 18:00

4. 21:35

1. 21:00, 22:10, 1 hr and 10 minutes

2. 20 minutes

3. 18:40

4. 21:35

Answers:

[tex]I(-2,-1) \to I \ ' \ (-5,-2.5)\\\\J(-1,2) \to J \ ' \ (-2.5,5)\\\\K(2,-1) \to K \ ' \ (5,-2.5)\\\\[/tex]

===============================================

Explanation:

Since the center of dilation is the origin, we multiply each preimage coordinate by 2.5 (which is the scale factor).

For example, the preimage point J(-1, 2) moves to J ' (-2.5, 5)

This will cause the image triangle I'J'K' to be larger than the preimage IJK. Specifically, each side of the image is 2.5 times longer compared to the preimage.

Answer:

i' (-5, -2.5) J' (-2.5, 5) K' (5, -2.5)

Step-by-step explanation:

you just take the original coordinates and multiply them by 2.5

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:

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.

[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:

B

Step-by-step explanation:

Answer:

brain less or i hack ur acc to ban

Step-by-step explanation:

u cant report me because im hacker

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:

142.25 miles

Step-by-step explanation:

239- 96.75

142.25

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

A good option available to you as a financial expert is to request a part payment from the customer while the remaining part is to be made on the next pay day.

For a good financial management, the best decision to make profit or avoid loss is paramount.

The most difficult challenge faced today by loan companies is the non complaisance of the customers to pay back when the period given expires.

The best option that may be available for the loan manager must be a request  for the customer to pay part of the loan and complete the payment in the next  pay day.

Thus, a good option available to you as a financial expert is to request a part payment from the customer while the remaining part is to be made on the next pay day.

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Step-by-step explanation:

you have to be careful what you are typing.

the way you wrote the numbers Asia would be a tiny place with very few people.

but I think you meant to say :

area is 4.46 × 10⁷ km²

with 3.70 × 10⁹ people.

people / km² = 3.70/4.46 × 10⁹/10⁷ =

= 0.829596413... × 10² = 82.9596413... =

= 82.96 people/km²

The population density will be equal to 82.96 people/km2. The correct option is B.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the area is 4.46 × 10⁷ km² with 3.70 × 10⁹ people. The population density will be calculated as below:-

Density = people / km² = ( 3.70 × 10⁹ ) / ( 4.46 x 10⁷ )

Density = 0.829596413... × 10² = 82.9596413

Density = 82.96 people/km²

Therefore, the population density will be equal to 82.96 people/km2. The correct option is B.

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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:

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