Mathematics High School

The temperature of a cup of coffee t minutes after it has been poured is described by the function
C(t) = 20 + 60(0.95)^t .
a. How many minutes does it take for the coffee to cool to a temperature of d degrees?
b. About how fast is the temperature dropping when t = 1?

Answers

Answer 1
a) You want to find t such that
.. C(t) = d
.. d = 20 +60*0.95^t
.. (d -20)/60 = 0.95^t
.. log((d -20)/60) = t*log(0.95)
.. t = log((d -20)/60)/log(0.95) . . . . . . time to cool to d degrees (d > 20)

b) C'(t) = 60*0.95^t*ln(0.95)
.. C'(1) = 60*0.95*ln(0.95) ≈ -2.924 °C/min

Related Questions

Use the angle sum identity to find the exact value of cos 105

Answers

so use the angle sum identity which we know to be cos(105) =cos(45+60)=cos45 cos 60 - sin 45 sin 60 

Find the complement of an angle whose measure is 74 degrees. Show all work.

Answers

Answer:
angle = 16°

Explanation:
Complementary angles are angles that add up to 90°
Assume that the angle that we are looking for is x.
Based on the definition of the complementary angles, the equation will be as follows:
x + 74 = 90
Now, we will simply solve for x as follows:
x = 90 - 74
x = 16°

Hope this helps :)

Answer:

16⁰

Step-by-step explanation:

Angle = 74⁰

Complement = 90 - 74 = 16⁰

A trapezoid has bases that measure 10 centimeters and 14 centimeters and a height that measures 8 centimeters. What is the area?

Answers

the answer is 96 cm using the formula (a+b)h/2.

Hope this helped!

Brainliest Plz?

What is true about the solutions of a quadratic equation when the radicand in the quadratic formula is negative? No real solutions Two identical rational solutions Two different rational solutions Two irrational solutions

Answers

The answer is 
no real solutions. <<<<  answer.

To confirm this, the question is saying what is the square root of (say) - 5?
There is no answer in the real number system.

Answer:

If the radicand in the quadratic formula is negative then no real solutions possible.

Step-by-step explanation:

Given that when the radicand in the quadratic formula is negative then we have to find the true statement about the solution of quadratic equation.

Radicand of quadratic formula i.e the discriminant of quadratic formula.

[tex]D=b^2-4ac[/tex]

which comes in the solution under the root.

The solution of general quadratic equation is

[tex]x=\frac{-b\pm \sqrt D}{2a}[/tex]

As discriminant is negative then we can not find any real root for the given equation.

Hence, option 1 is correct.

No real solutions possible.

Suppose you buy a CD for $300 that earns 3% APR and is compounded quarterly. The CD matures in 3 years. How much will this CD be worth at maturity?

A. $328.14
B. $309.12
C. $309.10
D. $303.01
help?,

Answers

Amount spent at start C = $300 Rate = 3% = 0.03 Number of periods = 3 years Future Value at the maturity FV = 300 x (1 + 0.03) ^3= 300 x 1.0927 = 328 The correct answer would be 328.14

What is the value of x?


Answers

There two things you need to remember with regards to your figure. 
Firstly, the sum of all angles in a triangle is equal to 180.

Secondly, supplementary angles are two angles that form a straight line. In other words, the two lines sum up to 180 degrees. 

Looking at your figure and the rules written above, you can then assume that the measure of angle x is equal to the sum of the two angles given inside the triangle.

53 + 45 = 98

Angle x is 98 degrees

 


Sue can sew a precut dress in 3 hours. helen can sew the same dress in 2 hours. if they work​ together, how long will it take them to complete sewing that​ dress? round to one decimal place.

Answers

1/3 + 1/2 = 1/t


The LCD is 2*3*t. 

If you multiply everything by the LCD, you can clear your fractions.


6t (1/3) + 6t (1/2) = 6t (1/t)

2t + 3t = 6

5t = 6

5t/5 = 6/5


Answer: 
Which is: t = 1.2 hrs. 

Final answer:

Sue and Helen can sew a dress in 1.2 hours when working together.

Explanation:

Calculating Time to Sew a Dress Together

Sue and Helen are working together to sew a dress and we need to calculate the total time it will take them to complete the sewing when working simultaneously. Sue can sew a precut dress in 3 hours, which means Sue's rate is 1 dress per 3 hours, or
1/3 dress per hour. Helen can sew the same dress in 2 hours, which means Helen's rate is 1 dress per 2 hours, or
1/2 dress per hour. Working together, their combined rate is the sum of their individual rates:

Total rate = 1/3 + 1/2

This results in a combined rate of 5/6 dresses per hour when we find a common denominator and add the fractions. To find the time it takes them to sew one dress together, we take the reciprocal of their combined rate:

Time = 1 / (5/6) hours

This simplifies to 6/5 hours.

Therefore, Sue and Helen will take 1.2 hours to complete the dress when working together.

If sound travels approximately 1 km in 3 s, and the lightning is striking 10 km from your house, how much time passes between a flash of lightning and the sound of thunder?

Answers

If the lightning is 10 km and the sound takes 3 seconds to travel 1 km, then the sound takes 30 seconds to travel 10 km.

3 seconds * 10 kilometers = 30 seconds

please help i have 2 questions thank you

Answers

Hello,

Here is your answer:

Since the second question is already solved ill solve the first on:

The proper answer to this question is option D "17.2".

Here is how:

Formula for area:

b*w*h

3*7=21

21-3.7=17.2

Your answer is D.

If you need anymore help feel free to ask me!

Hope this helps!

How the bloody hell do I answer these? Please explain how you did it.

1. In the xy plane, line m passes through the points (a,0) and (0,2a), where a>1. What is the slope of line m?
a)-2 b)-1/2 c)2 d)-2a e)2a

2. First, 3 is subtracted from x and the square root of the difference is taken. Then, 5 is added to the result, giving a final result of 9. What is the value of x?
a)3 b)4 c)5 d)16 e)19

3. If S is the set of positive that are multiples of 7, and if T is the set of positive integers that are multiples of 13, how many integers are in the intersection of S and T?
a)none b)one c)seven d)thirteen e)more than thirteen

4. A florist buys roses at $0.50 each and sells them for $1.00 each. If there are no other expenses, how many roses must be sold in order to make a profit of $3.00?
a)100 b)150 c)200 d)300 e)600

Answers

1. the formula for the slope is
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
where (a,0) is x1, y1 and (0,2a) is x2, y2. try to see if you can do it now (:

2. take a number x, then step by step do whatever the question asks for example "First, 3 is subtracted from x" so you know the first thing you need to do is x-3, then go on and you'll get an equation which you can use to solve for x, try it!

3. make a set, S, which has multiples of 7. then make a set, T, which has multiples of 13.
now the intersection of S and T is a set having all elements of S, also found in T (basically the numbers that are common to both). try doing it now!

for fourth, this requires a profit formula(that I do not know), must be explained in your book, try going over it, I'm sure you'll find it there!

The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of the area when r = 5 inches and r = 21 inches. (a) r = 5 inches

Answers

A=πr²
dA/dt=dA/dr×dr/dt
dA/dr=2πr
dA/dt=2πr dr/dt
we are told that the radius is increasing at the rate 3 in/min
dr/dt=3 in/min

we are required to find:
a] (dA/dt) when radius is r=5 inch
dA/dt=2πr dr/dt
dA/dt=2π(5)×3
dA/dt=30π in²/ min

b] (dA/dt) when radius is r=21 in
dA/dt=2πr dr/dt
dA/dt=2π(21)×3
dA/dt=126π in²/min

Final answer:

The rate of change of the area of a circle with a radius increasing at a constant rate can be calculated using the derivative of the area formula. For r = 5 inches, the rate is 30π square inches per minute and for r = 21 inches, the rate is 126π square inches per minute.

Explanation:

The student is asking about the rate of change of the area of a circle when its radius is increasing at a constant rate. This is a calculus problem that involves derivatives and can be solved using the formula for the area of a circle, A = πr² where A is the area and r is the radius. The rate of change of the radius, ℓr/ℓt, is given as 3 inches per minute.

To find the rate of change of the area, denoted as ℓA/ℓt, we take the derivative of A with respect to t, using the chain rule, which gives us ℓA/ℓt = 2πr(ℓr/ℓt). When r = 5 inches, substituting the values, we obtain ℓA/ℓt = 2π(5)(3) = 30π square inches per minute. Similarly, when r = 21 inches, ℓA/ℓt = 2π(21)(3) = 126π square inches per minute.

PLEASE HELP ASAP!!! 51 PTS

Answers

Answer is the first one, no doubt
The answer to this question is the first choice

y-1=-1/4(x+5)
x+5=-4y+4
x+5-5=-4y+4-5
x=-4y-1

I hope this helps!!!!!!!!!!

Which of the following numbers is irrational?



negative 15 over 4, negative 7 over 9, square root of 4, π






negative 15 over 4
negative 7 over 9
square root of 4
π,

Answers

An irrational number is one that can’t be expressed as a simple fraction.

For instance, the first few digits of the square root of two is written as 1.414213562373095... The digits keep going and cannot be expressed as a fraction. But think of 0.33333... That can easily be written as one-third. The distinguishing feature is that there’s no pattern in the digits for the square root of two.

The first two options are integer fractions. We rule those out immediately. The square root of four is tempting, but realize that it is just equal to two. We come to π (pi).

Arguably the most famous irrational number is π, which starts off as 3.14159265358979... Here, there is again no pattern and the digits extend forever. This meets our definition of our irrational.

The rational numbers are -15/4, -7/9, and √4, the irrational number is π.

What is an irrational number?

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

It is given that:

It is given that the numbers are:

-15/4

-7/9

√4

π

As we know, the number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

The rational number can be written in the form of p/q

Where q cannot be zero.

-15/4 - It is a rational number.

-7/9 - It is a rational number.

√4 = 2 - It is a rational number.

π - Pi is an irrational number.

Thus, the rational numbers are -15/4, -7/9, and √4, the irrational number is π.

Learn more about the irrational number here:

brainly.com/question/17450097

#SPJ2

What is measure of angle C? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

Answers

The answer is tan-1(3/4)= 36.87

A car travels at an average speed of 40 miles per hour for the first 100 miles of a 200-mile trip, and at an average speed of 50 miles per hour for the final 100 miles. what is the car's average speed for the entire 200-mile trip?

Answers

Total distance = 200 miles

Time needed for the first 100 miles
= 100 ÷ 40 = 2.5 hours

Time needed for the second 100 miles
= 100 ÷ 50 = 2 hours

Total time = 2.5 + 2 = 4.5 hours

Average speed = 200 ÷ 4.5 hours = 44.4 miles per hour

What is the y intercept of the line given by the equation y= 8x + 75

Answers

The y intercept is (0,75)


 

Answer: (0,8)

Step-by-step explanation:

here you go

What is the value of x?

Answers

32 / 4 = 8
40/8 =5
x = 5
x = 5 
hope this helps

2. Rhianna is buying a car for $14,390. She has a $1000 trade-in allowance and will make a $1500 down payment. She will finance the rest with a 4-year auto loan at 2.6% APR.

Answers

Answer: Her payment will be $261

To find this value, you just need to start with the numbers that you know.

First, find the cost of the loan. 14390 - 1000 - 1500 = 11890
We have to subtract her down payment and trade in allowance.

Then, we need the rate of 2.6%

Finally, the term of the loan is 4 years or 48 months.

Simply plug these values into your equation or use an online calculator. There are numerous ones you can find online.

Answer:

$261.08

Step-by-step explanation:

Worth of Car=$14,390

Trade-in allowance=$1000

Down Payment= $1500

Value of Loan=14390-(1000+1500)

=$11890

The Monthly Payment for a loan P, taken at a Monthly interest rate, r for a number of m months, is gotten using the formula:

[TeX] Monthly\:Payment=\frac{rP}{1-(1+r)^{-m}} [/TeX]

P=$11890

Monthly Interest Rate,r=0.026/12=0.002167

Number of Months, m=4*12=48 Months

[TeX] Monthly\:Payment=\frac{0.002167*11890}{1-(1+0.002167)^{-48}} [/TeX]

=$261.08

The Monthly Payment on the car loan is $261.08.

helpppppppppppppppppppppp

Answers

For this case what you should do is evaluate the function at a point where you can find the value of and without problems.
 So we have to:
 y = sin (x + 90)
 We evaluate x = 0
 y = sin (0 + 90)
 y = 1
 Answer:
 y = sin (x + 90)
 Option A

the point (0,0) is a solution to which of these inequalities?
a.y+7< 2x + 6
b.y- 7< 2x - 6
c.y -6< 2x - 7
d.y + 7< 2x -6

Answers

the apex answer to it D. y – 7 < 2x – 6

Answer:  The correct option is (B) [tex]y-7<2x-6.[/tex]

Step-by-step explanation:  We are given to select the inequalities that has the point (0, 0) as a solution.

Option (A):

The given inequality is

[tex]y+7<2x+6.[/tex]

At the point (0, 0), we have

[tex]L.H.S.=y+7=0+7=7,\\\\R.H.S.=2x+6=2\times0+6=6.[/tex]

Since 7 > 6, so the point (0, 0) is not a solution to this inequality.

This option is NOT correct.

Option (B):

The given inequality is

[tex]y-7<2x-6.[/tex]

At the point (0, 0), we have

[tex]L.H.S.=y-7=0-7=-7,\\\\R.H.S.=2x-6=2\times0-6=-6.[/tex]

Since -7 < - 6, so the point (0, 0) is a solution to this inequality.

This option is correct.

Option (C):

The given inequality is

[tex]y-6<2x-7.[/tex]

At the point (0, 0), we have

[tex]L.H.S.=y-6=0-6=-6,\\\\R.H.S.=2x-7=2\times0-7=-7.[/tex]

Since -6 > - 7, so the point (0, 0) is not a solution to this inequality.

This option is NOT correct.

Option (D):

The given inequality is

[tex]y+7<2x-6.[/tex]

At the point (0, 0), we have

[tex]L.H.S.=y+7=0+7=7,\\\\R.H.S.=2x-6=2\times0-6=-6.[/tex]

Since 7 > - 6, so the point (0, 0) is not a solution to this inequality.

This option is NOT correct.

Thus, the point (0, 0) is a solution to the inequality [tex]y-7<2x-6.[/tex]

Option (B) is correct.

The cost of 16 notebooks at store J is $24. The notebooks at store J are all the same price. The cost of notebooks at store J are all the same price. The cost of store K is shown on the graph below.
Which store has the least expensive cost per notebook and how much?

Answers

now, we know that at Store J, for 16 books is 24 bucks...hmmm how much is it for 10 books anyway?

[tex]\bf \stackrel{Store~J}{\begin{array}{ccll} books&cost\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 16&24\\ 10&x \end{array}}\implies \cfrac{16}{10}=\cfrac{24}{x}\implies x=\cfrac{10\cdot 24}{16}\implies x=15[/tex]

so, that much at Store J.

now, look at the graph, notice the point when x = 10, y = 8, so at Store K, is 8 bucks for 10 books.

which is cheaper?  well, surely you'd know that.

find the simplified form of (-7.4)^0?

A.-1

B.-7.4

C.0

D.1

Answers

The answer to this is d.) 1. This is because any number that is raised to the zero power is 1. 

Final answer:

Any non-zero number raised to the power of 0 is 1, so the simplified form of (-7.4)⁰ is 1 that is option D is correct.

Explanation:

The simplified form of (-7.4)⁰ is determined by one of the fundamental rules of exponents, which states that any non-zero number raised to the power of 0 is 1. This means that regardless of what the base number is, as long as it is not zero, if the exponent is 0, the result will always be 1. It is important to note that 0^0 is an indeterminate form and is not covered by this rule. Therefore, the simplified form of (-7.4)⁰ is:

D. 1

A number cube is rolled 450 times. The number 3 comes up 67 times. What is the theoretical probability of rolling a three,

Answers

The answer to this is 67 / 450

We know that:
Experimental probability = number of positive results / number of experiments

So the Experimental probability = 67 / 450

Find the vertex of y = x2 + 14x − 40 by completing the square.

Answers

 x = 10 x = 4 Two real solutions:

x =(14+√36)/2=7+3= 10.000 

or:

x =(14-√36)/2=7-3= 4.000 

Express 1.21212121.... as a fraction

Answers

that would be 1 21/99  or  120/99 as an improper fraction.

To solve such questions we will have to observe the fact that this is a repeating decimal number with the repeating figures being 2 and 1 as 21.

Thus, we can represent 1.21212121... as [tex] 1.\overline{21} [/tex]

Let us represent the original number 1.21212121... by the letter "a". Thus,

a=1.21212121...=[tex] 1.\overline{21} [/tex]

Therefore,[tex] a=1.\overline{21} [/tex]..................(equation 1)

Let us now multiply (equation 1) by 100 to get:

[tex] 100a=100\times 1.212121...=121.\overline{21} [/tex].....(equation 2)

Now, when we subtract (equation 2) from (equation 1), we will get:

[tex] 100a-a=121.\overline{21}-1.\overline{21} [/tex]

[tex] 99a=120 [/tex]

[tex] \therefore a=\frac{120}{99} [/tex]

Thus the given number 1.21212121... can be represented as a fraction as [tex] \frac{120}{9} [/tex].



For which pair of function is (g*f)(a)=|a|-2

1. f(a)=a^2-4 and g(a)= sqaureroot a
2. f(a)= 1/2a-1 and g(a)=2a-2
3. f(a)=5+a^2 and g(a) = sqaureroot (a-5)-2
4.f(a) =3 -3a and g(a)=4a-5

Answers

None of the pairs will deliver (g×f)(a). If you intend (g∘f)(a), then ...

... selection 3 is appropriate.

Answer:

The correct pair is 3

Step-by-step explanation:

1.

[tex]f(a)=a^{2}-4 , g(a)=\sqrt{a} \\gof(a)=g(a^{2} -4)\\=\sqrt{a^{2}-4 } \neq |a|-2[/tex]

2.

[tex]f(a)=\frac{1}{2\cdot a-1}, g(a)=2\cdot a -2\\gof(a)=g(\frac{1}{2\cdot a-1} )\\=\frac{2}{2\cdot a-1}-2\\=\frac{4-2\cdot a}{2\cdot a-1}\neq|a|-2[/tex]

3.

[tex]f(a)=5+a^{2} , g(a)=\sqrt{a-5} -2\\gof(a)=g(5+a^{2} )\\=\sqrt{5+a^{2}-5 } -2\\=\sqrt{a^{2} } -2\\=|a|-2[/tex]

4.

[tex]f(a)=3-3\cdot a , g(a)=4\cdot a-5\\gof(a)=g(3-3\cdot a )\\=4(3-3\cdot a)-5\\=7-12\cdot a\neq|a|-2[/tex]

Hence, the Option 3 is correct


The Truth About Antibacterial Soap
According to Discovery Fit & Health, about 75 percent of liquid soaps claim to be antibacterial. While this kind of soap sounds like a good idea, it is really not more effective than regular soap. Soap in general works by binding with dirt and grime and bacteria. This binding action allows the particles to be washed away easily. Antibacterial soap really does no more than regular soap. In fact, to be more effective than regular soap, antibacterial soap should stay on your skin for about two minutes to do what it claims it can do. Most people do not wash their hands that long. In addition, antibacterial soap may do harm. First it kills both beneficial and harmful bacteria. Second, scientists believe bacteria may become resistant to antibacterial agents over time, especially if they are not used correctly. Finally, antibacterial soap does nothing to viruses. Most of the time, we get sick from viruses, not bacteria. In sum, antibacterial soap does not live up to the hype. You are better off just using regular soap.
Works Cited
Is Antibacterial Soap Any Better than Regular Soap?

http://health.howstuffworks.com/skin-care/cleansing/myths/question692.htm


How is "The Truth About Antibacterial Soap" organized?

Fact by fact
Cause and effect
Chronological order
Problem-solution

its actually language arts not math sorry

Answers

it is organized in chronological order

Answer:

chronlogical order

the other answer for the other question is they dont wash their hand long enough

I WILL GIVE BRAINLIEST!!! I BEG SOMEBODY TO HELP ME PLS!!!

What is the slope of this line?

A) -1/4
B) 1/4
C) -4
D) 4

Answers

Since the grid is square and the angle is steep, you know the magnitude of the slope is greater than 1.

Since the line slopes downward (to the right), you know the sign of the slope is negative.

Only selection C is a viable choice. (It also happens to be right, since the line drops 4 units for each horizontal unit.)

If, triangle MNO congruent triangle PQR which of the following can you NOT conclude as being true?
A. ray MN congruent ray PR
B. angle M congruent angle P
C. ray NO congruent ray QR
D. angle N congruent angle Q,

Answers

A. ray MN congruent ray PR Since the two triangles are congruent, you can assume that those elements in the same relative position are also congruent. So ray MN congruent to ray PQ ray NO congruent to ray QR ray MO congruent to ray PR angle M congruent to angle P angle N congruent to angle Q angle O congruent to angle R Now with the above 6 items, look at the available options and see what isn't in the above list and the statement "A. ray MN congruent ray PR" pops out as something that's not true, so that is the answer.

Heyo! ;D

So, we can conclude that based on the information given above, the only one we cannot conclude on being true would be Option A) Ray MN ≅ Ray PR

Please help asap! Match the graph with the correct equation.

Answers

The answer to this is A. y+2=-(x-4)
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