A thermometer reading 96°F is placed inside a cold storage room with a constant temperature of 37°F. If the thermometer reads 88°F in 5 minutes, how long before it reaches 58°F? Assume the cooling follows Newton's Law of Cooling: U = T+ (U. - T)ekt (Round your answer to the nearest whole minute.) 45 minutes 0 1 minutes 0 16 minutes 14 minutes

Answer:

Step-by-step explanation:

- 4x^3 / (- 4) = 32 / (- 4)

x should and cannot be negative or it shouldn't be for example (- x) = 90

cubic root (x^3) = cubic root (- 8)

x = cubic root (- 8)

x = 2i

what is "i"?

It is an imaginary number as you cannot square, cubic, or whatever root with a negative in it. so instead you must add "i" to remove the negative as a replacement and indicator that it was a negative number.

Answer:

y = 35x - 517.

Step-by-step explanation:

y=35x−7

This line has a slope of 35so we can write a line parallel to it as

y - y1 = 35(x - x1) where (x1, y1) is a point on the line.

We are given this point (15, 8), so:

y - 8 = 35(x - 15)

y = 35x - 525 + 8

y = 35x - 517  is the required equation.

Yes, that is correct. The sides of an equilateral triangle inscribed in a circle are closer to the center of the circle than the sides of a square inscribed in the same circle.

This is because an equilateral triangle has all its vertices on the circumference of the circle, whereas a square has only four of its vertices on the circumference. As a result, the sides of the equilateral triangle are closer to the center of the circle than the sides of the square. This property of inscribed shapes is important in geometry and has many practical applications in fields such as architecture and engineering.

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If an object that has a volume of 30 cubic inches weighs 24 ouncess then the constant of variation is 0.8.

If the weight of an object varies directly with its volume, then we can write the following proportion

Weight / volume = constant of variation

Let's use w to represent the weight of the object and v to represent its volume. We are given that an object with a volume of 30 cubic inches weighs 24 ounces, so we can write

w / v = k

Where k is the constant of variation. We can solve for k by substituting the given values

24 / 30 = k

Simplifying this expression, we get

0.8 = k

Therefore, the constant of variation is 0.8.

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Answer:

y = -9/5x + 9/5

Step-by-step explanation:

From this points, we can determine the slope and the y-intercept.

First, we do:   y/x  -  y1/x1

=> 0/3 - (3 - 2)

=> 0-3/ 3 + 2

=> -3/5

So the slope of the equation is -3/5.

The equation is: y = mx + b

In this equation "m" = slope.

=>  b = constant

Now we take the x and y points from the above numbers.

=> Let's take 3 as x and 0 as y.

=> 0 = -3/5 *3 + b

=> 0 = -9/5 + b

=> Take the -9/5 to the other side

=> 9/5 = b

So, the constant number which is not multiplied by the x is 9/5

Now, our equation looks like:

y = -9/5x + 9/5

If you have any doubts about this question, ask me the comments and I will answer it as soon as possible.

The integral test states that if a series is a sum of terms that are positive and decreasing, and if the terms of the series can be expressed as the values of a continuous and decreasing function, then the series converges if and only if the corresponding improper integral converges.

Let's apply the integral test to the given series. We need to find a continuous, positive, and decreasing function f(x) such that the series is the sum of the values of f(x) for x ranging from 2 to infinity.

For the first series, we have:

∑n=2∞n(lnn)p

Let f(x) = x(lnx)p. Then f(x) is continuous, positive, and decreasing for x ≥ 2. Moreover, we have:

f'(x) = (lnx)p + px(lnx)p-1

f''(x) = (lnx)p-1 + p(lnx)p-2 + p(lnx)p-1

Since f''(x) is positive for x ≥ 2 and p > 0, f(x) is concave up and the trapezoidal approximation underestimates the integral. Therefore, we have:

∫2∞f(x)dx = ∫2∞x(lnx)pdx

Using integration by substitution, let u = lnx, then du = 1/x dx. Therefore:

∫2∞x(lnx)pdx = ∫ln2∞u^pe^udu

Since the exponential function grows faster than any power of u, the integral converges if and only if p < -1.

For the second series, we have:

∑n=2∞1/n(ln⁡n)²

Let f(x) = 1/(x(lnx)²). Then f(x) is continuous, positive, and decreasing for x ≥ 2. Moreover, we have:

f'(x) = -(lnx-2)/(x(lnx)³)

f''(x) = (lnx-2)²/(x²(lnx)⁴) - 3(lnx-2)/(x²(lnx)⁴)

Since f''(x) is negative for x ≥ 2, f(x) is concave down and the trapezoidal approximation overestimates the integral. Therefore, we have:

∫2∞f(x)dx ≤ ∑n=2∞f(n) ≤ f(2) + ∫2∞f(x)dx

where the inequality follows from the fact that the series is the sum of the values of f(x) for x ranging from 2 to infinity.

Using the comparison test, we have:

∫2∞f(x)dx = ∫ln2∞(1/u²)du = 1/ln2

Therefore, the series converges if and only if p > 1.

In summary, the series ∑n=2∞n(lnn)p converges if and only if p < -1, and the series ∑n=2∞1/n(ln⁡n)² converges if and only if p > 1. For values of p such that -1 ≤ p ≤ 1, the series diverges.
To find the values of p for which the series converges or diverges using the integral test, we will first write the series and then perform the integral test.

The given series is:

∑(n=2 to infinity) [1/n(ln(n))^p]

Now, let's consider the function f(x) = 1/x(ln(x))^p for x ≥ 2. The function is continuous, positive, and decreasing for x ≥ 2 when p > 0.

We will now perform the integral test:

∫(2 to infinity) [1/x(ln(x))^p] dx

To evaluate this integral, we will use the substitution method:

Let u = ln(x), so du = (1/x) dx.

When x = 2, u = ln(2).
When x approaches infinity, u approaches infinity.

Now the integral becomes:

∫(ln(2) to infinity) [1/u^p] du

This is now an integral of the form ∫(a to infinity) [1/u^p] du, which converges when p > 1 and diverges when p ≤ 1.

So, for the given series:

- It converges when p > 1.
- It diverges when p ≤ 1.

In conclusion, using the integral test, the series ∑(n=2 to infinity) [1/n(ln(n))^p] converges for values of p > 1 and diverges for values of p ≤ 1.

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Answer:

12 answer

Step-by-step explanation:

(8x-34)=(5x+2) (correspounding angle)

8x-5x=34+2

3x=36

x=36/3

x=13

Answer:

2500000000

Step-by-step explanation:

→ Multiply 1 by 25000

1 × 25000 = 25000

→ Convert into metres

2500000

→ Convert into centimetres

2500000000

Answer:

2.00 cm

1 km on the ground = 2.00 cm on the map.

This means that 1 cm on the map is 25000 cm in real life, which is 250 m or 0.25 km. It is also useful to note that if 1 cm is 0.25 km, then 4 cm will represent 1 km in real life.

It will cost $375 to hire the doctor for 45 minutes

The doctor charges $500 for an hour

60 minutes makes 1 hour

60 minutes= $500

Therefore the amount that will be charged for 45 minutes can be calculated as follows

60 minutes= $500

45 minutes= x

Cross multiply both sides

60x= 500×45

60x= 22500

x= 22500/60

x= 375

Hence it will cost $375 to hire the doctor for 45 minutes

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Answer:

x=5 and x=-8

Step-by-step explanation:

take f(x)=g(x)

2x+30 = x2 +5x-10

you get above values of x

I began my job as a student on 08/21/2019 and worked for a total of 905 days until my graduation on 05/20/2022. This is calculated by taking the total number of days between the start and end date - 3 years - which is 1095, and then subtracting the weekends and holidays - 190 days - during that period. This demonstrates my commitment to my job as a student.

08/21/2019 - 05/20/2022

= 3 years

= 1095 days

- 190 days (weekends and holidays)

= 905 days

Starting on 08/21/2019, I have been working at my job as a student for 905 days as of 05/20/2022. This is determined by taking the total number of days - 3 years - between the start date and end date, which is 1095 days, and then subtracting 190 days for the weekends and holidays during that period. This leaves me with 905 days of work as a student.

I began my job as a student on 08/21/2019, and my graduation was on 05/20/2022. After calculating the total number of days between the two dates - 3 years - which is 1095, and then subtracting the weekends and holidays during that period - 190 days - I have worked as a student for 905 days up until my graduation date. This demonstrates the commitment and dedication I had to my job as a student.

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To express a percent as a decimal number, divide it by 100. To express a percent as a fraction, write it as a numerator over 100.

a) Kyle scored 95.5% on his last test. To express this as a decimal, divide 95.5 by 100, which equals 0.955. To express this as a fraction, write \(\frac{95.5}{100}\), which can be simplified to \(\frac{191}{200}\)

b) The store's sales increased by 140%. To express this as a decimal, divide 140 by 100, which equals 1.4. To express this as a fraction, write \(\frac{140}{100}\), which can be simplified to \(\frac{7}{5}\).

c) By getting a car tuned up, you can reduce its emissions by 0.9%. To express this as a decimal, divide 0.9 by 100, which equals 0.009. To express this as a fraction, write \(\frac{0.9}{100}\), which can be simplified to \(\frac{9}{1000}\).

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Answer:

D is the correct answer.........

Answer:

D) there are 30 grams of protein in 6 tablespoons.

Step-by-step explanation:

Answer: The student got the wrong answer. ✅

Step-by-step explanation: When you add 364 and 728 together, you get 1092. To make it easier to understand, it is like having 3 piles of 100, 6 piles of 10, and 4 ones on one side, and 7 piles of 100, 2 piles of 10, and 8 ones on the other side, when you put them together you get 10 piles of 100, 8 piles of 10 and 12 ones.

To find the biggest number they have in common, you can divide both numbers by 2 and you get 182 and 364.

So the correct way to rewrite 364 + 728 is 364 * (3+2) ✅

Consequently, the room has a 7 meter width. The room's length is

\(= 7 * 3 meters = 21 meters\)

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Given that the length of the rectangular space is three times its breadth

The chamber has a 56-meter perimeter.

Assume that the room's width is x.

As a result, the room is three times as long.

The room's perimeter is now equal to 2(3x + x).

\(Here, 2(3x + x) = 56\\ 2 * 4x = 56\\ 8x = 56\\ x = 7.\)

Consequently, the room has a 7 meter width.

The room's length is

\(= 7 * 3 meters\\= 21 meters\)

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The required equation of the line is y = -(1/2)x + 1/2 which passes through the points (-9,5), (17,-8).

The slope of a line is expressed as the gradient of the line.

Given that line passes through the points (-9,5), (17,-8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = -9, y₁ = 5

x₂ = 17, y₂ = -8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 5 = (-8- 5)/(17-(-9))[x -(-9)]

⇒ y - 5 = (-13)/(26)[x +9]

⇒ y - 5 = -1/2(x +9)

⇒ y = -(1/2)x - 9/2 + 5

⇒ y = -(1/2)x + 1/2

Therefore, the equation of the line is y = -(1/2)x + 1/2 which passes through the points (-9,5), (17,-8).

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Answer:

50 packages

Step-by-step explanation:

Area of the box: A= (l)(w)(h)

                              =(20)(5)(10)

                              =1000cm^3

Area of the package: A= (5)(1)(4)

                                      =20cm^3

1000/20=50 packages

50 number of packages that she can put in the box without it overflowing

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that Kiara has a box that is 20 centimeters long, 5 centimeters wide, and 10 centimeters deep.

Length=20

Width=5

Height=10

Area of cube=Length×width×height

=20×5×10

=1000 cm³

The other packages is 5 centimeters long, 1 centimeter wide, and 4 centimeters deep.

Area=5×1×4

=20 cm³

We need to find the greatest number of packages that she can put in the box without it overflowing

To find this we have to divide 1000 by 20

1000/20=50

Hence, 50 number of packages that she can put in the box without it overflowing

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The curve x = t^2 − 3t, y = t intersects the y-axis when x = 0, which occurs when t = 0 and t=3. is 8root2/5

When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. Here, lines P and Q intersect at point O, which is the point of intersection.

In general, an intersection curve consists of the common points of two transversally intersecting surfaces, meaning that at any common point the surface normals are not parallel. This restriction excludes cases where the surfaces are touching or have surface parts in common.

A=∫ ​( t)(2t−2)dt

=∫ 2t ^(3/2) −2t ^(1/2)dt

=8root(2)/15

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Answer:

28 tomatoes

Step by step explanation:

She used 7 tomatoes 4 times therefore 7×4=28

Answer:

90%

Step-by-step explanation:

The ice cream is 1 part cashew, 3 parts marshmallow, and 36 parts chocolate ice cream.  That's a total of 40 parts.  So the fraction that is chocolate ice cream is:

36/40 = 0.9

So 90% of Heavenly Hash ice cream is chocolate ice cream.

Answer:

Inequality Form:

X ≥ 7

Interval Notation:

[ 7 , ∞ )

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

X ≥ 7

Interval Notation:

[ 7 , ∞ )

i think its this

The perimeter of the triangle will be 37.5 units. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The sum of all the sides of the triangle will be known as the perimeter of the triangle.

From the graph, the coordinate of a triangle will be (-8, 7), (6, 3), and (2, -4).

Then the perimeter of the triangle will be given as,

\(\rm P = \sqrt{(6 + 8)^2+(3 - 7)^2} + \sqrt{(2 - 6)^2+(-4 - 3)^2} + \sqrt{(2 + 8)^2+(-4-7)^2}\\\\P = \sqrt{212} + \sqrt{65} + \sqrt{221}\)

Simplify the equation, then we have

P = 14.56 + 8.06 + 14.87

P = 37.49 ≈ 37.5 units

The perimeter of the triangle will be 37.5 units. Then the correct option is C.

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Answer:

c =

Step-by-step explanation:

Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

Angle relationships, where we're given a diagram containing 2+ parallel lines and a transversal, can tell us a lot about the angles.

The two angles indicated in the diagram measure 4x + 19 degrees and 6x + 7 degrees.

These two angles form a "Z" pattern, meaning they are on opposite sides of the transversal and opposite sides of the two parallel lines. They are alternate angles.

Alternate angles are always equal. Therefore, we can set up the following equation and solve for x:

\(4x + 19 = 6x + 7\\19 = 2x + 7\\12 = 2x\\x = 6\)

x = 6

Represents the vector f + g.  C.

The sum of two vectors, we simply add their corresponding components.

In this case,
f + g = (4 - 1, 3 + 0, 7 + 2) = (3, 3, 9)
So the resulting vector has components (3, 3, 9).
Now we need to find the graph that represents this vector.

Graphing a vector in three dimensions can be challenging, but we can use the following method:
Start at the origin (0, 0, 0) of the 3D coordinate system.
Move 3 units in the x-direction, 3 units in the y-direction, and 9 units in the z-direction.
Mark the endpoint of this displacement as the tip of the vector.

Option A has a similar direction, but it is longer than f + g.

Option B has the correct length, but it is pointing in the wrong direction.

Option D is pointing in the correct direction, but it is too short.

We only add the respective components of the two vectors to get their sum.

Thus, f + g = (4 - 1, 3 + 0, 7 + 2) = (3, 3, 9) in this situation.

The resultant vector has three (3), three (3), and nine (9).

We now need to identify the graph that this vector is represented by.

It might be difficult to graph a vector in three dimensions, however we can try the following approach:

Start at the 3D coordinate system's origin (0, 0, 0).

Move three units in the x, three units in the y, and nine units in the z directions.

Make a note of the vector's tip being the terminus of this displacement.

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The line parallel to line  y = 7x - 6 and passing through points  (5, 8)  is

Given data

y = 7x - 6

(5, 8) and is parallel

From the line,  y = 7x - 6, the slope is 7. Since slope of parallel lines are equal, the new line will have same slope and pass through points  (5, 8).

y - 8 = 7 ( x - 5 )

y - 8 = 7x - 35

y = 7x - 35 + 8

y = 7x - 27

Hence we can say that the line parallel to line  y = 7x - 6 and passing through points  (5, 8)  is y = 7x - 27

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The equation of the line parallel to y = 7x - 6 passing through (5, 8) is y = 7x - 27

The equation of the line is parallel to the equation y = 7x - 6.

Parallel line have the same slope.

Therefore, let's represent the equation as follows:

y = mx + b

where

Therefore, the slope of the graph y = 7x - 6 is 7.

The equation of the line that contains (5, 8) and parallel to the graph can be computed as follows

y = 7x + b

let's find the y-intercept

8 = 7(5) + b

8 - 35 = b

b = - 27

Therefore, the equation of the line parallel to y = 7x - 6 passing through (5, 8) is y = 7x - 27

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