Answer:
16.033 min
Step-by-step explanation:
We can write Newton's Law of Cooling as
T = Tₐ + (T₀ - Tₐ)e^(-kt), where
Tₐ = ambient temperature of the surroundings
T₀ = initial temperature of the object
k = the cooling constant
t = the time
(1) Calculate the cooling constant
Data:
T = 110 °F
T₀ = 180 °F
Tₐ = 70 °F
t = 20 min
Calculation:
110 = 70 + (180 - 70)e^(-k×20)
40 = 110e^(-20k)
0.363 64 = e^(-20k)
-1.0116 = -20k
k = 0.050 580 min⁻¹
(2)After adding cream
(a) Calculate T₀
2 oz × 40 °F + 12 oz × 180 °F = 14 oz × T₀
80 °F + 2160°F = 14T₀
2240 °F = 14T₀
T₀ = 160 °F
(b) Calculate the time to cool to drinking temperature
110 = 70 + (160 - 70)e^(-0.050 580t)
40 = 90e^(-0.050 580t)
0.444 44 = e^(-0.050 580t)
-0.810 93 = -0.050580t
t = 16.033 min
It will take 16.033 min for the mixture to reach drinking temperature
To determine the time it takes for the mixture to reach drinking temperature, we first calculate the initial temperature of the mixture after adding 2 ounces of 40°F cream to the 180°F coffee, which turns out to be 165°F. Then, according to Newton's Law of Cooling, the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F would be the same as the time it took for the original coffee to cool from 235°F to 180°F, given the cooling constant doesn't change when we add the cream. Therefore, the mixture will take approximately 20 minutes to reach drinking temperature.
Explanation:To determine the time it takes for the mixture to reach drinking temperature, we first need to calculate the initial temperature of the mixture. When you add 2 ounces of 40°F cream to the 180°F coffee, the temperature of the mixture instantly becomes the weighted average of the temperature of the coffee and of the cream. Thus, we have:
(12 * 180 + 2 * 40) / (12 + 2) = 165°F.
Now we need to calculate the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F. According to Newton's Law of Cooling, the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. If we assume that the proportionality constant (or the cooling constant) doesn't change when we add the cream, then the time it takes for the mixture to cool from 165°F to 110°F will be the same as the time it took for the original coffee to cool from 235°F (165 + 70) to 180°F (110 + 70), which is 20 minutes. We can conclude that the mixture will take approximately 20 minutes to reach drinking temperature.
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6x^2-66x+144=0 solving quadratic equation
Factor out the common term 6
6(x^2 - 11x + 24) = 0
Factor x^2 - 11x + 24
6(x - 8)(x - 3) = 0
Solve for x;
x = 8,3
Consider the infinite geometric series ∑∞ n=1 -4(1/3)^n-1
a. Write the first four terms of the series.
b. Does the series diverge or converge.
c. If the series has a sum, find the sum.
a. The series is
[tex]\displaystyle\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-4-\frac43-\frac4{3^2}-\frac4{3^3}-\cdots[/tex]
(first four terms are listed)
b. The series converges because this is a geometric series with [tex]r=\dfrac13<1[/tex].
c. Let [tex]S_N[/tex] be the [tex]N[/tex]-th partial sum of the series:
[tex]S_N=\displaystyle\sum_{n=1}^N-4\left(\frac13\right)^{n-1}[/tex]
[tex]S_N=-4-\dfrac43-\dfrac4{3^2}-\cdots-\dfrac4{3^{N-1}}[/tex]
Multiplying both sides by [tex]\dfrac13[/tex] gives
[tex]\dfrac13S_N=-\dfrac43-\dfrac4{3^2}-\dfrac4{3^3}-\cdots-\dfrac4{3^N}[/tex]
Subtracting this from [tex]S_N[/tex] gives
[tex]S_N-\dfrac13S_N=\dfrac23S_N=-4+\dfrac4{3^N}[/tex]
[tex]\implies S_N=-6+\dfrac6{3^N}[/tex]
As [tex]N[/tex] gets larger and larger [tex](N\to\infty)[/tex] the rational term converges to 0 and we're left with
[tex]\displaystyle\lim_{N\to\infty}S_N=\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-6[/tex]
Is the data set approximately periodic? If so, what are the period and amplitude?
The tables show the value of a stock, in dollars, each week for 20 weeks.
Identify whether the data set is approximately periodic and, if so, determine the period and amplitude.
Question 2 options:
The data set is not approximately periodic.
The data set is approximately periodic with a period of 5 and an amplitude of about 3.
The data set is approximately periodic with a period of 10 and an amplitude of about 6.
The data set is approximately periodic with a period of 10 and an amplitude of about 11.
➷ The data set is not approximately periodic
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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Answer:
The data set is not approximately periodic.Step-by-step explanation:
The given data doesn't show any periodic pattern, the change is not constant, and it doesn't simulate any simple pattern because the increase is like random, the first increase is for 1.35, the second is for 0.13, the third one is for 0.65, it doesn't show any periodic behaviour.
In addition, the variables involved aren't periodic, because it's about stocks, which it changes randomly.
Therefore, the right answer is the first option.
A recipe for 4 ounces of frosting calls for 2 teaspoons of sugar. How much sugar would you need to make 12 ounces of frosting?
Answer: 6 teaspoons of sugar
Step-by-step explanation: Create a proportion
4 ounces of frosting = 2 teaspoons of sugar
8 ounces of frosting = 4 teaspoons of sugar
12 ounces of frosting = 6 teaspoons of sugar
To make 12 ounces of frosting, you would need 6 teaspoons of sugar.
Explanation:To find out how much sugar is needed to make 12 ounces of frosting, we can set up a proportion using the given information. The recipe calls for 2 teaspoons of sugar for 4 ounces of frosting. We can set up the proportion: 2 teaspoons / 4 ounces = x teaspoons / 12 ounces.
To solve the proportion, we can cross multiply and divide. So, (2 teaspoons)(12 ounces) = (4 ounces)(x teaspoons). This simplifies to 24 = 4x. Dividing both sides by 4, we find that x = 6 teaspoons.
Therefore, you would need 6 teaspoons of sugar to make 12 ounces of frosting.
Write an equation for the nth term of the geometric sequence 3584, 896, 224... Find the sixth term of this sequence
Answer:
Step-by-step explanation:
r = [tex]\frac{a_n}{a_{n-1}} = \frac{896}{3584} = \frac{1}{4}[/tex]
Using the geometric series formula for the nth term:
[tex]S_n = a \cdot \frac{1-r^n}{1-r} => S_{6} = 3584 \cdot \frac{1 - (\frac{1}{4})^{6} }{1 - \frac{1}{4} } = 4777\frac{1}{2}[/tex]
Final answer:
The equation for the nth term of the geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. The sixth term of the sequence is 14.
Explanation:
The given sequence is a geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a common ratio. To find the equation for the nth term of the geometric sequence, we need to find the common ratio. We can do this by dividing any term in the sequence by the previous term.
For example, dividing the second term 896 by the first term 3584 gives us a common ratio of 1/4.
So, the equation for the nth term of the sequence is:
an = a1 × r(n-1)
where a1 is the first term and r is the common ratio.
To find the sixth term, we can substitute n = 6 into the equation:
a6 = 3584 × (1/4)(6-1)
a6 = 3584 × (1/4)5
a6 = 14
WHAT IS 11/6 simplified I CANT DO THIS MATH IT IS TOOOOO HARDDDDD JK IM JUST TO LAZY >:( thanks
Answer:
It can't be simplified.
x^2-18x+67=0
form:
(x+?)^2 = ?
(x-?)^2 = ?
Answer: form by math and can multiply two numbers or divide your choice
Step-by-step explanation:
A figure is translated using the rule (x, y) → (x – 3, y + 6). Which describes how the figure is moved?
A. left 3 units and down 6 units right
B. 3 units and down 6 units left
C. 6 units and down 3 units left
D. 3 units and up 6 units
Answer:
3 units to the right and 6 units upStep-by-step explanation:
f(x) + n - shift the graph of f(x) n units up → (x, y + n)
f(x) - n - shift the graph of f(x) n units down → (x, y - n)
f(x - n) - shift the graph of f(x) n units to the right → (x - n, y)
f(x + n) - shift the graph of f(x) n units to the left → (x + n, y)
===================================
(x, y) → (x - 3, y + 6)
x - 3 → shift the graph 3 units to the right
y + 6 → shift the graph 6 units up
Answer:
the right answer is left 3 units and up 6 units
Step-by-step explanation:
Which of the following is true about a function that is constant?
It is a horizontal line.
It moves in an upward direction.
It moves in a downward direction.
It is a curve.
HELP ME PLZZZZZZZZZZZZZZZZZZZZZ
Graph of constant function is a horizontal line
It’s a horizontal line because all of the x’s must be different
Find sin and tan (Picture provided)
Answer:
Option C. [tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] , [tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]
Step-by-step explanation:
we know that
If cosine of angle theta is positive then angle theta belong to the I or IV quadrant
and
If co secant of angle theta is negative then angle theta belong to the III or IV quadrant
therefore
angle theta belong to the IV quadrant (common solution)
Part 1) Find [tex]sin(\theta)[/tex]
we know that
[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]
we have
[tex]cos(\theta)=4/7[/tex]
substitute the value
[tex]sin^{2}(\theta)=1-(4/7)^{2}[/tex]
[tex]sin^{2}(\theta)=1-(16/49)[/tex]
[tex]sin^{2}(\theta)=(33/49)[/tex]
[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] ----> is negative because the angle belong to the IV quadrant
Part 2) Find [tex]tan(\theta)[/tex]
we know that
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
we have
[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex]
[tex]cos(\theta)=4/7[/tex]
substitute the values
[tex]tan(\theta)=\frac{-\frac{\sqrt{33}}{7}}{4/7}[/tex]
[tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]
If I got 12 baseball cards on monday 24 on tuesday and gave some to my brother and had 13 baseball cards left, how many did I give to my brother?
Answer:
23 Cards were given to your brother.
Step-by-step explanation:
12 + 24 = 36
36 - 13 = 23
Answer:
you gave him 23 cards
Step-by-step explanation:
12+24=36, 36-13=23
Peter has hockey cards. He knows that he has less than 100. When he puts the in piles of 3 he has 2 cards left. When in 4 piles he has 1 card left and when in 5 piles he has 3 cards left to the side. How many cards does Peter have in total?
he has 84 hockey cards total
Determine the slope of the line that has the following coordinates: (0, 2) (4,3)
Slope = (y2-y1)/(x2-x1)
Slope = (3-2)/(4-0)
Slope = 1/4
Answer:
[tex]\large\boxed{the\ slope=\dfrac{1}{4}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have (0, 2) and (4, 3). Substitute:
[tex]m=\dfrac{3-2}{4-0}=\dfrac{1}{4}[/tex]
Point M is located between X and Y on this number line.
<-----x-------------y----->
-4 -2 0 2 4 6 8
( -2 is X and 6 is Y )
Which number could not be the coordinate of point M?
a- √48
b- √18
c- √35
d- √27
Answer:
√48 could not be M.
Step-by-step explanation:
M must be between - 2 and 6, so:
a. √48 = 6.93 so this can't be M.
b. √18 = 4.24 so this could be M.
c and d could also be M.
The coordinate of point M can be any of the given options.
Explanation:To determine the possible coordinates of point M, we need to find the values between X (-2) and Y (6) on the number line provided. Starting from X (-2) and moving towards Y (6), the numbers that lie between them are -2, 0, 2, 4, and 6. We can see that all the given options for the coordinate of point M can be found on the number line. Therefore, none of the given numbers could not be the coordinate of point M.
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Use synthetic division to perform the indicate division. Write the poly nominal in the form p(x) = d(x)q(x) + r(x)
[tex](3x^{2} -2x+1)[/tex] ÷ [tex](x-1)[/tex]
Linda saves $1.55 every day. Tyron saves $3.90 every day. Linda started saving 3 days earlier than Tyron. On which day will Tyron's savings be more than Linda's savings?
To determine when Tyron's savings will surpass Linda's, we can set up an inequality using their daily saving rates and the fact that Linda started 3 days earlier. Solving for the number of days Tyron needs to save, we find that Tyron will surpass Linda's savings after saving for 2 full days.
Linda and Tyron are saving money on a daily basis, but Linda started saving 3 days earlier than Tyron. To find out on which day Tyron's savings will be more than Linda's, we need to set up an equation.
Let's define x as the number of days after which Tyron starts saving. Since Linda starts 3 days earlier, she has been saving for x + 3 days by the time Tyron starts saving.
Linda's daily savings: $1.55
Tyron's daily savings: $3.90
Linda's total savings after x + 3 days: $1.55(x + 3)
Tyron's total savings after x days: $3.90x
We want to find the value of x at which Tyron's total savings exceed Linda's, so we set up the inequality:
$3.90x > $1.55(x + 3)
Now, solve for x:
$3.90x > $1.55x + $4.65
$3.90x - $1.55x > $4.65
$2.35x > $4.65
x > $4.65 / $2.35
x > 1.978
Since x represents the number of days and we cannot have a fraction of a day in this context, x must be at least 2 days. Therefore, Tyron's savings will be more than Linda's after he has saved for 2 days.
The explicit rule for a sequence is given.
an=3n+1
What is the recursive rule for the sequence?
a1=3; an=an−1+1
a1=4; an=an−1+3
a1=1; an=an−1+3
a1=4; an=an−1+1
The second one should be it
I’m not sure bc I’m going off of my head
The ratio of boys to girls in Ella's grade is 3/4 the ratio of boys to girls in minhs grade is 4 to 5 each grade has a total of 20 girls how many boys are in each grade
Answer:
Ella's Grade: 15
Minh's Grade: 16
Step-by-step explanation:
If each grade has 20 girls in the grade, then that implies effectively that the ratios would apply via fractions, which are 3:4 and 4:5. As such, take both Fractions and increase them both to 20: 15:20 and 16:20.
The number of boys in Ella's grade is 15 and Minh's grade is 16
Given that,
The ratio of boys to girls in Ella's grade is 3:4
And the ratio of boys to girls in Minh's grade is 4:5
The total number of girls is 20
Computation:
Let the number of boys be [tex]x[/tex]
So in the case of Ella's,
[tex]\frac{3}{4}=\frac{x}{20}\\x=\frac{20\times3}{4}\\x=15[/tex]
And in case of Minh's,
[tex]\frac{4}{5}=\frac{x}{20}\\x=\frac{20\times4}{5}\\x=16[/tex]
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Our solar system is 1.18 × 1013 meters in diameter, and the Milky Way galaxy is 7.8 × 1020 meters in diameter. How many times wider is the Milky Way galaxy than our solar system? Write your answer in scientific notation, and round the coefficient to the nearest tenth.
Divide 7.8 by 1.18:
7.8 / 1.18 = 6.61 = 6.6 rounded to the nearest tenth.
When you divide scientific notation, subtract the exponents: 20 - 13 =7
The answer becomes 6.6 x 10^7
Division is one of the four fundamental arithmetic operations. The number of times the milk way is wider than the solar system is 6.61 × 10⁷.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that our solar system is 1.18 × 1013 meters in diameter, and the Milky Way galaxy is 7.8 × 1020 meters in diameter. Therefore, the number of times the milk way is wider than the solar system is,
Number of times = (Diameter of MIlky way)/(Diameter of Solar System)
= 7.8 × 10²⁰ meters/ 1.18 × 10¹³ meters
= 6.61 × 10⁷
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Explain how the number of edges for the rectangular prison compares to the number of edges for the unit cube
Answer:
Step-by-step explanation:
A rectangular prism has 12 edges. In geometry, a prism is a solid figure with parallel ends or bases that are the same size and shape, with each side representing a parallelogram. The parallelograms in a rectangular prism are all rectangles.
The rectangular prism also has six faces, or flat sides. The surface area of a rectangular prism is determined by multiplying the length by the width of each of the six rectangles and by then adding the products together.
Find three solutions of the equation.
y = –8x
(0, 0), (–3, 22), (–2, 16)
(3, –24), (0, 0), (–1, 9)
(–2, 16), (3, –24), (–4, 32)
(–2, 16), (3, –24), (2, –17)
Answer:
3rd group of possible answers is the correct set
Step-by-step explanation:
Each of the three points in the 3rd line of possible answers is a solution of the given equation, as can be verified by substitution:
If x = -2, y = -8(-2) = +16
If x = 3, y = -8(3) = -24
If x = -4, y = -8(-4) = +32
Answer:
c
Step-by-step explanation:
I need help with this. This is hard.
h = 12.
See the attached picture:
Find the area of a triangle when
Answer:
The area of the triangle = 31.5 feet² ⇒ answer (c)
Step-by-step explanation:
∵ Area of any Δ = 1/2 (side 1)(side 2)(sin the angle between them)
∴ The area of the Δ = 1/2 (b)(c) sin(∠A)
∵ b = 11 feet
∵ c = 10 feet
∵ m∠A = 35°
∴ Area of the Δ = 1/2 (11)(10) (sin(35)) = 31.547 feet²
∴ The area of the triangle = 31.5 feet²
∴ The answer is (c)
Using he equation 12(x-3.20)=54 , carolyn determines that she will make a profit of $7.70 on each necklace. Which error did carolyn make?
Answer:
This is correct, Carolyn will make $7.70 for each necklace but she loses $3.20 most likely for the suplices for the making of the necklace so she really earns $4.50.
Step-by-step explanation:
There are two large pieces of construction paper. The red piece has an area of 90 inches squared , while the blue piece is 12 inches wide. Which paper is larger?
Answer:
You cant solve this without one more number.
Step-by-step explanation:
You need the length of the blue piece because it could be smaller or larger at this point. I may be wrong but unless I am missing something, and I totally might be if this is a kind of math I've never done, then please feel free to ignore me :) and have a lovely day!
There are 888 employees on The Game Shop's sales team. Last month, they sold a total of ggg games. One of the sales team members, Chris, sold 171717 fewer games than what the team averaged per employee. How many games did Chris sell?
Answer:
[tex]\frac{g}{8}-17[/tex] games
Step-by-step explanation:
Employees: 8
Sales last month: g
Average: [tex]\frac{totalGames}{Employees}[/tex]
To find out how many games Chris sold, we have to take the average and subtract 17.
[tex]\frac{g}{8}-17[/tex]
Since there are no more values we can use, this is as simple as we can get it. If we knew how many games they sold last month, we could get an exact answer for Chris using this expression.
Answer:
g over 8 -17
Step-by-step explanation:
Identify the range of the function shown in the graph.
Answer:
The correct option is D) All real numbers.
Step-by-step explanation:
Consider the provided function.
Range: Range is the set of output value produce by the function, or the range is the set of all possible y values.
Now consider the provided graph of the function.
The graph of the function is a straight line and function produces the positive and negative value of y.
By interpreting the graph it can be concluded the the range of the function is all real numbers.
Thus, the correct option is D) All real numbers.
Please help me out!!!!!
Answer:
x = 22°Step-by-step explanation:
A diameter of a rhombus is an angle bisector. Therefore we have the equation:
[tex]3x-11^o=x+23^o[/tex] add 11° to both sides
[tex]3x=x+44^o[/tex] subtract x from both sides
[tex]2x=44^o[/tex] divide both sides by 2
[tex]x=22^o[/tex]
What is the slope?
x = -4
Answer:
The slope is undefined
Step-by-step explanation:
x = -4 is a vertical line. Slope is defines as the change in y divided by the change in x.
(change in y)/(change in x)
All the points on this line have the same x value, so the change in x is zero. This means we have
(change in y)/0, which is undefined.
Answer:
UNDEFINED
Step-by-step explanation:
Any initial value set to equal x is considered an undefined rate of change [slope], which is a vertical line.
I am joyous to assist you anytime.
Kim kept track of how much cereal she ate for 2 months and found that she ate 256 ounces of cereal in that time. How many pounds is that? (16 ounces = 1 pound)
Answer:
16 pounds
Step-by-step explanation:
Total cereal she ate = 256 ounces
How many pounds she ate = ?
Given that (16 ounces = 1 pound)
Therefore, we have to divide the total ounces by 16 to calculate the cereal she ate in pounds = 256/16 = 16 pounds
Answer:
A. 16
Step-by-step explanation: