The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 5.8% per hour. How many hours does it take for the size of the sample to double?

Answer:

The width of the living room is 10 feet.

Step-by-step explanation:

Let the width of the living room is w.

And the length of the room is 2w - 8 ft.

Given,

The area of the room is 192  feet^2, by using the formula of area of a rectangle we get,

A = l × w

192 = (2w - 8) × w

Now,

192 = 2w^2 - 8w                              ( By expanding)

200 = 2w^2                                     (By adding 8w to both sides)

100 = w^2                                        (Dividing both sides by 2)      

If we take square root on both sides,

w = 10

So,

The width of the living room is 10 feet.

The function of the number of hours of operation of the assembly line will be 2772 + 110[17t - 1/2t²].

The cost of the first 2 hours of operation will be $6292

From the information, A(t) = 17t - 1/2t² power lawn mowers, 10 and we suppose that the factory's cost of manufacturing units is C(x) after hours of operation, an assembly line has assembled C(x) = 2772 + 110x.

Therefore, the (composite) function of the number of hours of operation of the assembly line will be:

= 2772 + 110[17t - 1/2t²]

The cost of the first 2 hours of operation will be:

2772 + 110[17t - 1/2t²]

= 2772 + 110[17 × 2 - 1/2 × 2²

= 2772 + 110(34 - 2)

= $6292

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According to the diagram, angle JKL is

Adjacent angles are angles that share a common vertex and a common side, but do not overlap. In a trapezoid, adjacent angles can be any pair of angles that share a common vertex and a common side.

angle JKL and angle MKL are adjacent angels having same vertex at k

angle JKM = angle JKL  angle MKL

94 = angle JKL + 47

angle JKL = 94 - 47

angle JKL = 47

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The substraction of 50 3/5 ft and 48 1/3 can be expressed as34/15.

The concept that will be used here is substraction. One of the four operations used in mathematics, along with addition, multiplication, and division, is substraction. Removal of items from a collection is represented by the operation of subtraction. For instance, the adjacent image shows 5 2 peaches, which are 5 peaches with 2 peaches subtracted, for a total of 3 peaches.

50 3/5 ft - 48 1/3 =

this mixed numbers can be converted to fractions as

253/5 - 145/3

= 34/15

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The answer to the question on the value of x in a triangle is x = 60 degrees.

The fact that all the angles are labeled as x means that this is an equilateral triangle which is a triangle where all the angles are equal.

Should this be the case, the value of x would be:

= Sum of interior angles of triangles / Number of sides in triangle

Sum of interior angles of triangles = 180 degrees

Number of sides = 3 sides

The value of x is:

= 180 / 3

= 60 degrees

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Two other points on this line are (1, 1.5) and (2, 3)

From the question, we have the following parameters that can be used in our computation:

This means that the slope (m) of the line is

m = 6/4

Evaluate

m = 1.5

For the other points, we have

f(2) = 2 * 1.5 = 3

f(1) = 1 * 1.5 = 1.5

So, we have (1, 1.5) and (2, 3)

Hence, the points are (1, 1.5) and (2, 3)

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Answer:

N-27 = 9n + 5

Step-by-step explanation:

write equation to the word sentence 9.5 less than a number n equals 27 the answer n-27 = 9n + 5 that is posted to this question on your website is wrong according to my homework check.

The value of n for the given condition "9.5 less than a number n equals 27" is, 36.5

Given that,

A statement,

"9.5 less than a number n equals 27"

To solve for the value of "n",

we can start by subtracting 9.5 from both sides of the equation,

9.5 less than a number n = 27

So, it can be written as,

n - 9.5 = 27

n = 36.5

Therefore, 9.5 less than a number n equals 27 the answer n-27 = 9n + 5

Answer:

c = 8

Step-by-step explanation:

4x³ + cx² + x + 2 ÷ x + 2 = ...

first we divide

4x³ + cx² by x + 2

and that is by doing 4x³/x = 4x².

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

now we need to find the remainder, as with regular number divisions :

4x² × (x + 2) = 4x³ + 8x²

which we need to subtract from the left side

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

- 4x³ + 8x²

----------------

0 cx² - 8x²

now we pull down the next position (x) and divide that by x + 2

4x³ + cx² + x + 2 ÷ x + 2 = 4x² + 1

- 4x³ + 8x²

----------------

0 cx² - 8x² + x

and the same again, to find the remainder, we have to subtract 1×(x + 2) = x + 2 from the left side

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

- 4x³ + 8x²

----------------

0 cx² - 8x² + x

- x + 2

-----------------------------

cx² - 8x² 0 0

the polynomial is divisible by x + 2, if the remainder is 0.

so,

cx² - 8x² = 0

cx² = 8x²

c = 8

Answer:

The equation of the line that is perpendicular to y= 3/2x - 4 and goes through the point (2,-2) is y = -2/3x + 4.

Step-by-step explanation:

14. The mean of  the Zoo-venir Stand sales is of 23.9, representing the quotient between the sum of all the amounts and the number of observations.

15. The range of the Zoo-venir Stand sales is of 30, representing the difference between the highest number and the lowest number.

Considering the key format of the stem-and-leaf plot, the observations are given as follows:

12, 13, 13, 13, 14, 15, 15, 16, 17, 20, 21, 21, 22, 22, 23, 24, 25, 25, 25, 26, 27, 27, 28, 29, 29, 32, 34, 34, 37, 41, 42.

The mean is given by the sum of all observations divided by the number of observations, hence it's value is of: 23.9.

The range is the difference between the highest observation and the lowest observation, hence it is of:

42 - 12 = 30.

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The volume of the solid obtained by rotating about the x-axis the region enclosed by the curves is 32π/5 cubic units.

In this problem, we are asked to find the volume of a solid obtained by rotating a region enclosed by curves about the x-axis. We will use integration to calculate the volume.

First, let's sketch the region and the solid we need to find the volume of.

The region is enclosed by the curves

=> y = 16 /(x² + 16), y = 0, x = 0, and x = 4.

When we rotate this region about the x-axis, we get a solid with a hole in the center, shaped like a donut.

To find the volume of this solid, we can use the method of cylindrical shells.

We start by taking a thin strip of the region, parallel to the y-axis, and of width dy. This strip has height y, and we rotate it about the x-axis to get a cylindrical shell of thickness dy and radius x.

The volume of this cylindrical shell is given by the formula V = 2πxy dy, where x is the distance from the y-axis to the edge of the shell.

To express x in terms of y, we can solve for x in the equation

y = 16 /(x² + 16).

y(x² + 16) = 16

x² = 16/y - 16

x = √(16/y - 16)

Now we can substitute x into the formula for V to get:

V = 2πx(16/(x² + 16)) dy

[tex]= 2\pi(16/y - 16)^{1/2}(16/y) dy \\\\= 32\pi(y - y^{3/2}) dy[/tex]

To find the total volume, we integrate this expression from y = 0 to y = 1 (since the maximum value of y is 16/16 = 1):

[tex]\int_0^1 32\pi(y - y{(3/2)}) dy = 32\pi/5[/tex]

Therefore, the volume of the solid obtained by rotating the region about the x-axis is 32π/5 cubic units.

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a) The average rate of change is -0.6333.

b) For $500 after the inflation rate from 1917 to 1920 the worth will be 242.20631771406.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given:

a) The average rate of change

= (15.9- 17.8)/ (1920 - 1917)

= -1.9 / 3

= -0.6333

So, the equation can be

y = -0.6333x + b

and, 17.8 = -0.63333(1917)+ b

b= 1231.79

So, y= -0.6333x + 1231.79

b) For $500 after the inflation rate from 1917 to 1920 the worth will be 242.20631771406.

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Answer:

350

Step-by-step explanation:

∑ (xy) means the sum of the products of x and y , that is

∑ (xy)

= (7 × 2) + (2 × 5) + (5 × 7) + (9 × 4) + (6 × 2) + (10 × 9) + (9 × 9) + (8 × 4) + (4 × 10)

= 14 + 10 + 35 + 36 + 12 + 90 + 81 + 32 + 40

= 350

As per the question Sales revenue is $198,000 (from the sale of inventory)

Sales revenue, which is sometimes referred to as revenue from sales or just sales, is the entire sum of money that a business makes from the selling of goods or services to clients. It is one of the main revenue streams for the majority of businesses and is frequently used as a key performance indicator (KPI) to gauge a business's success.

Calculating sales income involves multiplying the quantity sold by the cost per unit. As an illustration, if a business sells 1,000 pieces of a product at $100 each, its sales revenue would be $100,000 ($100 x 1,000).

Sales revenue is a crucial indicator for businesses to monitor since it indicates how much demand there is for a company's goods or services.

According to question:

Cost of goods sold = $110,000 (the cost of the inventory that was sold)

Gross margin = Sales revenue - Cost of goods sold = $198,000 - $110,000 = $88,000

Expenses = Cost of goods sold + Operating expenses = $110,000 + $36,000 = $146,000

Operating income = Gross margin - Operating expenses = $88,000 - $36,000 = $52,000

Non-Operating Items = Gain on sale of land = $80,000 (the difference between the selling price and the original cost of the land)

Net income = Operating income + Non-Operating Items = $52,000 + $80,000 = $132,000

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Answer:

approximately 0.567088608.

Step-by-step explanation:

The division of 1.28 by 2.26 can be done as follows:

The value of the segment in the geometry of the triangle is 17.5.

A triangle is a sort of polygon with three sides, as was said in the introduction. The vertex of a triangle is where two of its sides meet at an angle. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

If a line is parallel to one side of the triangle and intersects the other two sides, then it divides the side into segments of proportional length.

Thus,

12 / (12 + 14) = 15 / (15 + x)

12(15 + x) = 15(26)

180 + 12x = 390

12x = 210

x = 17.5

Hence, the value of the segment in the geometry of the triangle is 17.5.

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The support vector of the input dsolve('Dy = -3*y') is "dsolve(diff(y,t) == -3*y)".

A symbol is a mathematical object that represents a mathematical entity, such as a number, a variable, or a function. In mathematical software, symbols are used to represent variables, which can be used in mathematical expressions to perform computations.

In the past, character vectors or strings were used to represent symbols in certain mathematical software programs.

In the future release of this software, support for character vectors or strings will be removed. Instead, the program will require users to use the "syms" function to declare variables as symbols.

As an example of how this might be used in practice, consider the differential equation

=> "dy/dt = -3y".

In the past, this equation might have been entered into a mathematical software program using a character vector or string to represent the variable "y".

However, in the future release of this software, the user will need to use the "syms" function to declare "y" as a symbol. The equation would then be entered using the "diff" function, like this:

=> "dsolve(diff(y,t) == -3*y)".

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On solving the provided question, we can say that  the linear equation are 3y - 2x = -9 and y = -2x +5 => 3(-2x +5) - 2x = -9 => x = 3

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

the linear equation are

3y - 2x = -9 and y = -2x +5

3(-2x +5) - 2x = -9

-6x + 15 -2x = -9

-8x = -24

x = 3

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The length of the segment QV is  9.2 units

What is a square?

Regular quadrilaterals, such as a square, have four equal sides and four equal angles (right angles, 90-degree angles, or angles of /2 radian). It is also known as a rectangle with two neighbouring sides of identical length. It is the only regular polygon whose internal angle, central angle, external angle, and diagonal length are all equal (90°).

diagonal length, d=a√2 , where,  d--> diagonal length ,  a= side length

So, d= 13* 1.4142 = 18.3847 units

Diagonals bisect each other

QV = d/2 = 18.3847/2  = 9.1923

Rounding to 1 decimal place

QV = 9.2 units

The length of the segment QV is  9.2 units

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Answer:

1.) M=9,100(1 + 0.05)^6

Step-by-step explanation:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

In this formula the "P" represents the principle amount, or the original amount. The "r" represents the interest rate in decimal form, while the "n" represents the number of compounds in the time unit (usually years), and the "t" represents the amount of time that has passed (usually years)

In this case it says annual interest rate of 5% and nothing of compound monthly, etc... so n=1, and r=0.05. We're also given the principle amount of 9,100 and the time passed is just 6 years, so t=6. Plugging all this information into the equation we get:

[tex]A=9,100(1+0.05)^6[/tex]

which makes the first option correct.

[tex]\cfrac{6}{4+\sqrt{2}}\implies \cfrac{6}{4+\sqrt{2}}\cdot \cfrac{4-\sqrt{2}}{4-\sqrt{2}}\implies \cfrac{6(4-\sqrt{2})}{\underset{\textit{difference of squares}}{(4+\sqrt{2})(4-\sqrt{2})}} \implies \cfrac{6(4-\sqrt{2})}{(4)^2 - (\sqrt{2})^2} \\\\\\ \cfrac{6(4-\sqrt{2})}{16 - 2}\implies \cfrac{6(4-\sqrt{2})}{14}\implies \cfrac{3(4-\sqrt{2})}{7}\implies \cfrac{12-3\sqrt{2}}{7}[/tex]

Answer:

Step-by-step explanation:

To calculate the depreciation expense for each year of the equipment's life using the diminishing-balance method, we need to first find the straight-line rate, and then find the diminishing-balance rate by doubling the straight-line rate.

Step 1: Calculate the straight-line rate

The straight-line rate can be calculated as follows:

SLR = (Cost - Residual Value) / Useful Life

SLR = (32900 - 4700) / 4

SLR = $27,600 / 4

SLR = $6,900 per year

Step 2: Calculate the diminishing-balance rate

The diminishing-balance rate can be calculated as follows:

DBR = 2 * SLR

DBR = 2 * $6,900

DBR = $13,800

Step 3: Calculate the depreciation expense for each year

The depreciation expense for each year can be calculated as follows:

Year 1: Depreciation Expense = Cost * (DBR / 2)

Year 1: Depreciation Expense = $32,900 * ($13,800 / 2)

Year 1: Depreciation Expense = $32,900 * $6,900

Year 1: Depreciation Expense = $227,621

Year 2: Depreciation Expense = (Cost - Year 1 Depreciation) * (DBR / 2)

Year 2: Depreciation Expense = ($32,900 - $22,761) * ($13,800 / 2)

Year 2: Depreciation Expense = $10,139 * $6,900

Year 2: Depreciation Expense = $70,223

Year 3: Depreciation Expense = (Cost - Year 1 Depreciation - Year 2 Depreciation) * (DBR / 2)

Year 3: Depreciation Expense = ($32,900 - $22,761 - $70,223) * ($13,800 / 2)

Year 3: Depreciation Expense = $10,016 * $6,900

Year 3: Depreciation Expense = $68,609

Year 4: Depreciation Expense = (Cost - Year 1 Depreciation - Year 2 Depreciation - Year 3 Depreciation) * (DBR / 2)

Year 4: Depreciation Expense = ($32,900 - $22,761 - $70,223 - $68,609) * ($13,800 / 2)

Year 4: Depreciation Expense = $21,307 * $6,900

Year 4: Depreciation Expense = $146,763

So, the depreciation expenses for each year of the equipment's life are:

Year 1: $22,761

Year 2: $70,223

Year 3: $68,609

Year 4: $146,763

This is how you can calculate the depreciation expense for each year of the equipment's life using the diminishing-balance method.

After solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.

What is meant by the system of equations?

A set of equations with a finite number of solutions is referred to as a system of equations. A system of equations in algebra consists of two or more equations and looks for common answers to the equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.

Given,

  Cost of material for small chair = $10

Cost of material for large chair = $15

The selling price for a small chair = $22

The selling price for a large chair = $51

The total money spent on materials = $305

Designer makes 8 more small chairs than large chairs.

If the number of large chairs = t  and the number of small chairs =  s

Using the given equations, we can write the following system of equations.

10s + 15t = 305

s - t = 8

Now we make the coefficient of s in both equations the same.

Multiply 10 in the second equation.

10s + 15t = 305

10s - 10t = 80

Subtracting,

5t = 225

t = 45

s = 8 + t = 45 + 8 = 53

Therefore after solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.

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The volume of the irregular figure is solved to be

The volume of the irregular figure is solved by the formula

= area of the figure * thickness

The area of the figure is solved by dividing the firue into regular shapes and this will result to two rectangles

Area of the first rectangle

= length x width

= 4 * (12 - 5)

= 4 * 7

= 28 square centimeters

Area of the second rectangle

= 10 * 5

= 50 square centimeters

Total area = 50 + 28 = 78

volume = 78 * 1 = 78 cubic centimeters

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Using trigonometric functions and Pythagoras' theorem, the x value of different right-angled triangles is found.

What is a right-angled triangle?

A right triangle, also known as a right-angled triangle, is a triangle with one right angle, or two perpendicular sides. The sum of the other two angles is 90 degrees.

In all of these figures, one of the angles is 90°. So we can use Pythagoras' theorem and trigonometric relations, to solve the questions.

1) Opposite side = 5

sin 27° = Opposite side/ hypotenuse

0.45 = 5/x

x = 11.11

2) Hypotenuse = 16

   cos 63 = adjacent side/hypotensue

    0.45 = x / 16

    x = 7.2

3) Hypotenuse = 29

    sin 67 = opposite side/hypotensue

    0.92 = x/29

      x =  26.68

4) Opposite side = 27

  tan 39° = opposite side/ adjacent side = 27/x

0.81 = 27/x

x = 33.33

5) sin Q = opposite side / hypotensue = 14/50 = 7/25

   sin R = opposite side / hypotensue = [tex]\sqrt{50^2 - 14^2}[/tex]/50 = 48/50 = 24/25

  cos Q = PQ/ 50 = 48/50 = 24/25

   cos R = PR/50 = 14/50 = 7/25

tan Q = sin Q/cos Q = 7/24

tan R = sin R/cos R = 24/7

Therefore using trigonometric functions and Pythagoras' theorem, the x value of different right-angled triangles is found.

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The Total Surface Area for given prism will be 166 [tex]cm^2[/tex].

The entire surface area of a rectangular prism may be computed by adding the areas of its six sides. A rectangular prism's surface area may be determined using the following formula:

[tex]Surface Area = 2(l*w) + 2(l*h) + 2(w*h)[/tex]

where:

l = length of the rectangular prism

w = width of the rectangular prism

h = height of the rectangular prism

Using this formula for given problem,

Given,

l=5cm

w=4cm

h=7cm

[tex]\text{Total Surface area}=2.(5.7)+2.(4.5)+2.(4.7)\\\\=70+40+56\\\\=166\;cm^2[/tex]

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The equation in slope-intercept form is y = 10x + 41.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (-3, -4).

Points on y-axis = (11, 1).

At point (-3, 11), a linear equation of this line can be calculated in slope-intercept form as follows:

y - 11 = (1 - 11)/(-4 + 3)(x + 3)

Y - 11 = 10(x + 3)

y = 10x + 30 + 11

y = 10x + 41.

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Answer: $31.20

Step-by-step explanation:

0.6% = 0.006

.: fee = 0.006 x 5200 = $31.20

The area of rhombus ABCD is 98.28 cm². Therefore, option C is the correct answer.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, in rhombus ABCD, AD=10 cm and OC=7.8 cm.

Here, BC²=OC²+OB²

10²=7.8²+OB²

OB²=100-60.84

OB²=39.16

OB=√39.16

OB=6.3 cm

AC=2×7.8

AC=15.6 cm

BD=2×6.3 =12.6 cm

We know that, area of rhombus is 1/2 ×(Product of diagonals)

Now, area= 1/2 ×15.6×12.6

= 98.28 cm²

Therefore, option C is the correct answer.

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