A side of the triangle below has been extended to form an exterior angle of 66°. Find the value of x.

(a) The solution of the seasonal-growth model is

P(t) = P0[tex]e^{(k/r sin(rt))}[/tex]

(b) After solving we get [tex]\lim_{t \to \infty} P(t)[/tex] = NONE . As, t approaches to infinity

(a) To solve the differential equation DP/dt = kPcos(rt-[tex]\theta[/tex]),

The variables can be split apart and integrat:

∫(1/P) dP = ∫k cos(rt-[tex]\theta[/tex] ) dt

ln|P| = (k/r)sin(rt- [tex]\theta[/tex] ) + C

where

C is the constant of integration.

By solving for P, we get:

P(t) = [tex]e^{(k/r sin(rt- \theta ) + C)}[/tex]

We can determine the value of C by using the initial condition P(0) = P0:

P(0) = [tex]e^{(k/r sin(- \theta) + C)}[/tex]= P0

C = ln(P0) - (k/r)sin(-[tex]\theta[/tex] )

C = ln(P0) + (k/r)sin([tex]\theta[/tex] )

By substituting this into the expression for P(t), we get:

P(t) = [tex]e^{(k/r sin(rt-\theta) + ln(P0) + (k/r)sin(\theta))}[/tex]

By simplifying, we get:

P(t) = P0[tex]e^{(k/r sin(rt-\theta) + k/r sin(\theta))}[/tex]

P(t) = P0[tex]e^{(k/r sin(rt))}[/tex]

(b) We must take into account the behavior of sin(rt) as t approaches infinity in order to determine the limit of P(t) as t approaches infinity. Sin(rt) will fluctuate between -1 and 1 as t grows because the sine function oscillates between -1 and 1.

As a result, the term [tex]e^{(k/r sin(rt))}[/tex] will bounce between [tex]e^{(-k/r)}[/tex] and [tex]e^{(k/r)}[/tex] as t approaches infinity, but it won't converge to a single value.

As a result, there is no P(t) limit as t approaches infinity.

Hence, the answer is:

[tex]\lim_{t \to \infty} P(t)[/tex] = NONE.

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a) Sample size 13:(43.614, 44.386)

b) Sample size 1300:(43.9663, 44.0337)

The weight of the screws is normally distributed and has a variance of 0.64g^2. In a sample, the mean of the screws was 44g. The following are the two-sided (symmetrical) confidence intervals with a 95 percent confidence level for the expected value of the weight:Option a) Sample size 13:For a sample size of 13, the standard error of the mean is calculated as follows:SE = σ/√nwhere SE is the standard error, σ is the variance, and n is the sample size.In this case, SE = √(0.64)/√(13) = 0.1772.The t-distribution should be used to calculate the confidence interval since the population's standard deviation is unknown.The t-value corresponding to the 95% confidence interval with 12 degrees of freedom (df = n – 1) is 2.179. Therefore, the confidence interval can be calculated as follows:44 ± 2.179(0.1772)= 44 ± 0.386= (43.614, 44.386)The expected weight of the screws in the population is estimated to be between 43.614 g and 44.386 g.Option b) Sample size 1300:For a sample size of 1300, the standard error of the mean is calculated as follows:SE = σ/√nwhere SE is the standard error, σ is the variance, and n is the sample size.In this case, SE = √(0.64)/√(1300) = 0.0172.The z-distribution should be used to calculate the confidence interval since the sample size is large enough to assume that the sample mean is approximately normally distributed.The z-value corresponding to the 95% confidence interval is 1.96. Therefore, the confidence interval can be calculated as follows:44 ± 1.96(0.0172)= 44 ± 0.0337= (43.9663, 44.0337)The expected weight of the screws in the population is estimated to be between 43.9663 g and 44.0337 g.

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5??????????????????????

Answer:

x = y = 4.24

Step-by-step explanation:

sin45 = x/6

x = 6(sin45) = 4.24

y = 6(cos45) = 4.24

Because this is a 45-45-90 isosceles triangle, x=y

Answer: To solve the inequality x − (5 − 3x) ≤ 2x − 1, we need to simplify it by first distributing the negative sign in front of the parentheses, and then combining like terms. This gives us:

x - 5 + 3x ≤ 2x - 1

4x - 5 ≤ 2x - 1

Next, we can isolate the variable on one side of the inequality by subtracting 2x from both sides:

4x - 2x - 5 ≤ -1

2x - 5 ≤ -1

Finally, we can isolate x by adding 5 to both sides and dividing by 2:

2x ≤ 4

x ≤ 2

So the solution to the inequality is x ≤ 2.

To graph this solution on a number line, we can put a closed dot at 2 and shade to the left of it, since all values less than or equal to 2 satisfy the inequality. Therefore, the correct graph is A, a number line with a closed dot at 2 shaded to the left.

Step-by-step explanation:

The surface area of the prism is 210.4 in².

The surface area of a prism is the sum of the areas of all of its faces.

For a right prism (a prism with rectangular bases), the formula for the surface area is:

Surface Area = 2(length x width) + (height x perimeter of base)

where;

The surface area of the prism is calculated as;

S.A = 2 (9 in x 5 in) + ( 4.3)(2 (9 in + 5 in )

S.A = 90 in²  +  120.4 in²

S.A = 210.4 in²

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The figures converted from fraction to decimal to percent (Questions 9-14) are given as follows:

       Percent                             Decimal                              Fraction

9)      316.2%.                            3.162                                   3 4861/30000

10)    6.94%.                              0.0694                                347/5000.
11)     15.27%.                             0.1527                                 1527/10000

12)    217 2761/3367%              2.178                                    1089/500

13)    723 12/21%                       7.236                                  1809/250
14)    87%                                  0.87                                     87/100

9) Given the compound fraction:   3 4861/30000

To convert 3 4861/30000 to a decimal, we first need to convert the mixed number to an improper fraction:

3 4861/30000 = (30000*3 + 4861)/30000

= 94861/30000

To convert this fraction to a decimal, we divide the numerator by the denominator:

94861/30000 ≈ 3.162

To convert 3 4861/30000 to a percentage, we multiply the decimal by 100:

3.162 x 100 ≈ 316.2%

So, 3 4861/30000 as a percentage is approximately 316.2%

10)  Given the decimal 0.0694
To convert 0.0694 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.0694 = 694/10000

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

694/10000 = (3472)/(50002) = 347/5000

So, 0.0694 as a fraction is 347/5000.


To convert 0.0694 to a percentage, we multiply the decimal by 100:

0.0694 x 100 = 6.94%

So, 0.0694 as a percentage is 6.94%.


11) Given the decimal - 0.1527

To convert 0.1527 to a percentage, we multiply the decimal by 100:

0.1527 x 100 = 15.27%

So, 0.1527 as a percentage is 15.27%.

To convert 0.1527 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.1527 = 1527/10000

12) Given the compound percentage - 217 2761/3367%

To convert 217 2761/3367% to a decimal, we first need to convert the mixed number to an improper fraction:

217 2761/3367% = (3367*217 + 2761)/3367% = 733400/3367%

743032/3367% = 217.82001782%
217.82001782% = 2.1782001782
220.680724681% [tex]\approx[/tex] 2.178

Thus, in fraction:

2.178 = 2.178/1

Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000

= 2.178/1 x 1000/1000

= 2178/1000

= 1089/500


13) Given the compound fraction - 723 12/21%


To convert 723 12/21% to a decimal, we first need to convert the mixed number to an improper fraction:

723 12/21% = (21*723 + 12)/21% = (15195/21)%

(15315/21)% = 7.23571428571
15315/21%  [tex]\approx[/tex] 7.236


Converting 7.236 to fraction:

7.236 = 7.236/1


Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000


= 7.236/1 x 1000/1000

= 7236/1000: Divide numerator and denominator by 4

= (7236÷ 4)/(1000÷4)

= 1809/250


14) Given 0.87:

To convert 0.87 to a percentage, we multiply the decimal by 100:

0.87 x 100 = 87%

So, 0.87 as a percentage is 87%.

To convert 0.87 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.87 = 87/100

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the perimeter of D'E'F is 5 times larger than the perimeter of DEF.

If the scale from DEF to D'E'F is 5:1, then the corresponding side lengths are multiplied by a factor of 5 when going from DEF to D'E'F. This means that if the perimeter of DEF is P, then the perimeter of D'E'F is 5P.

To see why this is true, consider the perimeter of DEF:

P = DE + EF + FD

When we scale up by a factor of 5, we get:

D'E' + E'F' + F'D' = 5DE + 5EF + 5FD

= 5(DE + EF + FD)

= 5P

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The y-intercept of the graph is located at (0, 0). So, the value of c is 0.

What is graph?

A graph is a visual representation of data that displays the relationship between two or more variables. It consists of a set of points, called vertices or nodes, which are connected by lines or curves, called edges or arcs. The vertices represent the variables, while the edges represent the relationship between them.

To find the y-intercept of the graph of y = -7x + 140y, we need to substitute x = 0 into the equation and solve for y. This will give us the y-coordinate of the point where the graph intersects the y-axis.

Substituting x = 0, we get:

y = -7(0) + 140y

y = 140y

Simplifying the equation, we get:

139y = 0

Dividing both sides by 139, we get:

y = 0

Therefore, the y-intercept of the graph is located at (0, 0). So, the value of c is 0.

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Based on the angles, a triangle can be classified as either acute, right, or obtuse and based on the sides, a triangle can be classified as either equilateral, isosceles, or scalene.

To classify a triangle, we need to consider both its angles and sides. Based on the angles, a triangle can be classified as either acute, right, or obtuse.

An acute triangle has all three angles measuring less than 90 degrees. A right triangle has one angle measuring exactly 90 degrees. An obtuse triangle has one angle measuring greater than 90 degrees.

Based on the sides, a triangle can be classified as either equilateral, isosceles, or scalene.

An equilateral triangle has all three sides equal in length. An isosceles triangle has two sides of equal length. A scalene triangle has all three sides of different lengths.

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To calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.

What is rate ?

In mathematics, a rate is a ratio that compares two quantities with different units. It is typically expressed as the amount of change of one quantity with respect to another quantity. Rates are often used in the context of describing how quickly or slowly something changes over time or space.

To calculate a rate, we need to divide two quantities that have different units. For example, if we want to find the rate of a car's speed, we divide the distance traveled (in miles) by the time taken to travel that distance (in hours).

The formula for rate is:

rate = quantity / time

To calculate a unit rate, we need to divide a rate by the quantity being measured. For example, if the rate is the number of miles traveled per hour, the unit rate would be the number of miles traveled in one hour. To find the unit rate, we divide the rate by 1 hour.

The formula for unit rate is:

unit rate = rate / 1

When calculating rates or unit rates, it is important to make sure that the units of the quantities being divided are consistent. If the units are not the same, we need to convert them to the same unit before performing the division.

Therefore, to calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.

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Therefore , the solution of the given problem of cardinality comes out to be A×B×C is 3 .

A's cardinality is equivalent to its element count if A has a finite amount of elements. Say |A|=5 if A=2, 4, 6, 8, 10. The outcome of a numbering process is referred to as "cardinality". A set's cardinality is determined by the number of components in it. For illustration, the group 1, 2, 3, 4, and 5 has a greater cardinality of five than the set 1, 2, 3, and 5, each of which has an attributes of three.

Here,

a)

I "Chinese New Year of 2023" has one cardinal element, making it one-dimensional.

ii) Since there are three elements in S and each element can either be included in a subset or not, the power set P(S) of S=1,,apple has 23 = 8 elements.

iii) xRx2=3 has two components because the squares of two real numbers, 3 and -3, are both 3.

iv) Since "0" is regarded as one element and there are five other distinct elements in the collection,  {{0,1,2},3,4,5,∅,{{0}}}  has six elements.

b)

=> A={0,1,2}, B={apple}, and C={apple}

The set difference between C and A is only the element 0, which is absent from C, so A=apple0,1,2=apple.

Consequently, A, B, and C include the following components:

=> {(0,apple,apple), (1,apple,apple), (2,apple,apple)}

=>  A×B×C is 3 .

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The value of distance between city B to city C given by 'x' is found as: 41 miles.

Distance in air miles from city A to each city B and city C are-

City A to City B= 11

City A to city C= 29

City B to City C= X

Then,

Distance between city B to city C = distance between city A to city B +  between city A to city C

x = 29 + 11

Solving the linear equation:

x = 41

Thus, the value of distance between city B to city C given by 'x' is found as: 41 miles.

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225 hamburgers were sοld οn Saturday

A linear equatiοn is an equatiοn οf a straight line in twο variables, usually written in the fοrm y = mx + b, where m is the slοpe and b is the y-intercept. It represents a relatiοnship between twο variables that is linear, meaning that as οne variable changes, the οther changes at a cοnstant rate.

Let's use algebra tο sοlve the prοblem.

Let x be the number οf hamburgers sοld οn Saturday.

Then, accοrding tο the prοblem, the number οf cheeseburgers sοld οn Saturday is 73 mοre than the number οf hamburgers sοld, sο the number οf cheeseburgers sοld is x + 73.

The prοblem alsο tells us that the tοtal number οf hamburgers and cheeseburgers sοld is 523. Sο we can set up an equatiοn:

x + (x + 73) = 523

Simplifying the left side οf the equatiοn:

2x + 73 = 523

Subtracting 73 frοm bοth sides:

2x = 450

Dividing bοth sides by 2:

x = 225

Therefοre, 225 hamburgers were sοld οn Saturday.

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The area of one slice of a large pizza with a diameter of 24 inches is 56.52 square inches.

The formula for calculating the area of a circle is A = πr^2, where A is the area of the circle, π is the constant pi (3.1415) and r is the radius of the circle. To calculate the area of a slice, we must first calculate the radius of the pizza. To do this, we divide the diameter of the pizza (24 inches) by 2, which yields a radius of 12 inches.

Now that we have the radius, we can calculate the area of one slice. Plugging the radius of 12 inches into the equation, we get A = 3.1415*12^2 = 452.16 square inches. Since each pizza is cut into 8 equal slices, each slice would have an area of 452.16/8 = 56.52 square inches.

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we can deduct that the angle on the L vertex is 25°, because that way all three angles will result in 180°.

We know that JKLM is a parallelogram, which means that its opposite sides are parallels, such that: JK // ML and JM // KL.

So, we know that the angle MLJ equals 25°, and JK // ML, from this we can say that angles LJK and MLJ are equal, because they are ''internal alternate angles'', since that they are inside the parallels.

So, angle LJK is 25, and JKL is a triangle, which has the angle at K vertex equal to 130°. We know that internal angles in a triangle must sum 180°.

Since that, two angles, in the triangle JKL, measure 130° + 25° = 155°; we can deduct that the angle on the L vertex is 25°, because that way all three angles will result in 180°.

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Answer:

A

Step-by-step explanation:

we know that

tan x=sin x/cos x

if  

then

x belongs to the II quadrant or IV quadrant

sin 30°=

cos 30°=

therefore

tan 30°=

the angle theta has a 30-degree reference angle and is located in Quadrant II or IV

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

So first you would combine like terms which in this case are 9x, -6x, y, and y

So: 9x+y-6x+y

(9x-6x)+(y+y)

3x+2y is the final answer

hope this helped

Answer:

Step-by-step explanation:

Answer:

Total profit after 10 years = [tex]\$5,277,064[/tex]

Step-by-step explanation:

Let [tex]a_n[/tex]  represent the profit in the nth year

Then [tex]a_{n+1}[/tex]  represents the profit in year  [tex]n+[/tex]1

[tex]\text{Common ratio } r = \dfrac{a_{n+1}}{a_n}[/tex]

The sum of a geometric sequence is given by
[tex]S_n = a_1 \cdot \dfrac{1 - r^n}{1-r}[/tex]

where
[tex]a_1 =[/tex] first term
[tex]r =[/tex] common ratio
[tex]n =[/tex] number of terms

Calculation of r

To calculate r we see that the profit increases by 16% every year

16% = 16/100 = 0.16

If profit increases by 0.16, then next year's profit
= this year's profit(1 + 0.16)

= this year's profit x 1.16

r = 1.16 the ratio of a term to the previous term

In this problem we are given the first term as
[tex]a_1 = 247,500[/tex] [tex]\text{ = profit in first year}[/tex]
[tex]n = 10 =[/tex] number of years

[tex]r = 1.16[/tex]

Plugging these values into equation [1] for the sum we get
[tex]\begin{aligned}S_n &= a_1 \cdot \dfrac{1 - r^n}{1-r}\\\\&= 247500 \cdot \dfrac{1-1.16^{10}}{1-1.16}\\\\& = 247500 \cdot \dfrac{-3.41143}{-0.16}\\& = 247500 \cdot 21.3215\\& = 5277064\end{aligned}[/tex]

Therefore the total profit after 10 years
= $5,277,064

Answer:

18x + 22y

Step-by-step explanation:

4x (3) + 5y (3) + 2x (3) + 7y

Multiply the coefficients of the variables x and y with the constants, so that:

4x (3) + 5y (3) + 2x (3) + 7y

= 12x + 15y + 6x + 7y

Then just add up the coefficients with the same variable:

12x + 6x = 18x

15y + 7y = 22y

So the final answer is:
18x + 22y

[tex]\huge\text{Hey there!}}[/tex]

[tex]\mathsf{4x^3 + 5y^3 + 2x^3 + 7y}[/tex]

[tex]\large\textsf{COMBINE the LIKE TERMS (if you have any):}[/tex]

[tex]\mathsf{= (4x^3 + 2x^3) + (5y^3) + (7y)}[/tex]

[tex]\mathsf{= 4x^3 + 2x^3 + 5y^3 + 7y}[/tex]

[tex]\mathsf{= 6x^3 + 5y^3 + 7y}[/tex]

[tex]\large\textsf{Therefore your ANSWER should be:}[/tex]

[tex]\huge\boxed{\mathsf{6x^3 + 5y^3 + 7y}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

блина я сама не

Step-by-step explanation:

The slope of the line that passes through the points (6,10) and (6,−2) is undefined.

The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical terms, the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

Now, let's apply this formula to the given points (6, 10) and (6, -2). Here, x₁ = 6, y₁ = 10, x₂ = 6, and y₂ = -2. Substituting these values in the formula, we get:

slope = (-2 - 10) / (6 - 6)

Notice that the denominator is zero, which means that the line is a vertical line. In this case, the slope is undefined.

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The Answer should be 4:1 it's the half of the 8 to 2

There are four numbers: 8, 15, 100 and 123.

Number is a mathematical object used to count, measure, and label. It is used in many different contexts, from everyday life to scientific research. Numbers can be represented in various forms, such as symbols, digits, and words. They are used to represent quantities, distances, time, and other concepts. Numbers can also be used to represent relationships, such as equations, which are statements that describe how two or more things are related.

To solve this problem, it is best to line the numbers up on the y axis or x axis. To multiply the numbers, start by multiplying the numbers on the y axis first. So, 8 x 15 = 120. Then, multiply the result by the number on the x axis which is 100. 120 x 100 = 12,000. Finally, multiply 12,000 by the last number on the x axis which is 123. 12,000 x 123 = 1,476,000. Therefore, the answer to the problem is 1,476,000.

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i have no idea what that is

The price per unit that yields maximum revenue is $400.

We can start by finding the demand function for the product. Since the demand is assumed to be linear, we can use two data points to find the equation of the line:

(40, 300) and (45, 275)

Using the point-slope form of a line, we get:

(275 - 300) / (45 - 40) = -5/25 = -1/5

y - 300 = (-1/5)(x - 40)

y = (-1/5)x + 320

where y is the number of units sold per week and x is the price per unit.

The revenue function is simply the product of the price and the number of units sold:

R = xy

Substituting the demand function, we get:

R = x(-1/5)x + 320x

Simplifying, we get:

R = -1/5x^2 + 320x

To find the price per unit that yields maximum revenue, we need to take the derivative of the revenue function with respect to x and set it equal to zero:

dR/dx = -2/5x + 320 = 0

Solving for x, we get:

x = 800/2 = $400

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Answer: 32

Step-by-step explanation:

the min is 54 while the max is 86

86-54 is the range which is 32

The gross earning per week is = $ 495.56.

The salary to hourly wage calculator allows you to view your earnings over several time frames. It is a versatile tool that enables you to change your annual salary into an hourly payout, compute your monthly salary into an hourly rate, change your weekly rate into an annual salary, etc. You will save time and effort by using our salary converter, which completes all tasks fast and easily.

Joseph works 5 hours on Monday

10 hours on Tuesday,

9. 5 hours on Wednesday

8. 25 hours on Thursday

6 hours on Friday

7. 5 hours on Saturday

He is paid $9. 85 per hour and time and a half for all hours over 40 per week.

Total working hour= 5+10+9.5+8.25+6+7.5=46.25

Earning per hour is = 9.85

total earning= 46.25*9.85=$455.56

total gross earning= $ 455.56+40=495.56

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97 bielorrusias hacen falta para comprarte un perro

The system of equations y = x + 3 and y = x² - 2x + 3 when solved for x and y is x = 0 and y = 3 & x = 3 and y = 6

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

y = x² - 2x + 3

Using the graph to solve the equations

y = x + 3

y = x² - 2x + 3

We simply write out the point of intersection of y = x + 3 and y = x² - 2x + 3

When y = x + 3 is plotted, we have the intersection to be

(0, 3) and (3, 6)

Hence, the solutions are (0, 3) and (3, 6)

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