X
%
60°
4
Z
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Y
Given right triangle XYZ, what is the value of tan(Y)?
02/0
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A fraction of the rectangle is shaded = 1/4

Consider following diagram.

The rectangle below consists of 8 unit squares.

To find: fraction of the rectangle is shaded

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part is denominator.

consider a fraction 1/8.

Here, numerator is 1, denominator is 8

When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8

Here, a rectangle consists of 8 unit squares. Out of 8 unit squares, 2 squares are shaded.

So, the fraction would be 2/8

We simplify above fraction 2/8 = 1/4

So, 1/4 of the rectangle is shaded.

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The angles converted to degrees are: 615°, 165°, 112.5° with their respective quadrants of their terminal side as: 3rd, 2nd, and 2nd.

We simplify each angles of the angle in the radian to a single fraction and then convert them to degree by multiplying by 180°/π as follows:

11π/4 + 2π/3 = (33π + 8π)/12 {12 is the LCM of the denominators}

11π/4 + 2π/3 = 41π/12

11π/4 + 2π/3 = 41π/12 × 180°/π

11π/4 + 2π/3 = 615°

The terminal side of 615° is in the 3rd quadrant

π/6 - 5π/4 = (2π - 15π)/12 {12 is the LCM of the denominators}

π/6 - 5π/4 = -13π/12

π/6 - 5π/4 = -13π/12 × 180°/π

π/6 - 5π/4 = -195°

π/6 - 5π/4 = 165° {changing -195° to positive angle by adding 360°}

The terminal side of 165° is in the 2nd quadrant.

9π/8 - π/2 = (9π - 4π)/8 {8 is the LCM of the denominators}

9π/8 - π/2 = 5π/8

9π/8 - π/2 = 5π/8 × 180°/π

9π/8 - π/2 = 225°/2

9π/8 - π/2 = 112.5°

The terminal side of 112.5° is in the 2nd quadrant.

Therefore, the angles converted to degrees are: 615°, 165°, 112.5° with their respective quadrants of their terminal side as: 3rd, 2nd, and 2nd.

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The figures cone Z and cylinder Y have the same volume.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic metre (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.

The formula for volume of the cone Z is given by

Volume = 1/3* pi * radius *radius *height

The formula for volume of the cylinder Y is given by

Volume =  pi * radius *radius *height

Since, it is given that Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.

Thus, substituting  in the formula of volume of the cone Z, we get,

Volume = 1/3* pi * radius *radius *3*height

Simplifying, we have,

Volume =  pi * radius *radius *height

Hence, the volume of the cone Z = volume of the cylinder Y

Thus, the figures cone Z and cylinder Y have the same volume.

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The cost of the one baseball card will be $45

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the cost of one dozen baseball cards is $540. The cost of one baseball card will be calculated by dividing the total cost by 12.

Cost = 540 / 12

Cost = $45

Hence, the cost of one card will be $45.

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The sum of interior angles of the given 22 sided convex polygon is; 3600°

When it comes to finding the sum of the interior angles of a a convex polygon that has n sides, we can say that its interior angle sum is given by the following equation:

S = ( n − 2) × 180°.

where;

n is the number of sides of the convex polygon

Thus, for a 22 sided convex polygon;

S = (22 - 2) × 180°

S = 20 × 180°

S = 3600°

That represents the sum of interior angles of the given polygon.

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 (√7)^3  is equal to 7^(3/2)

The Power of a Power Property

The Power of a Power Property states that when you have a base raised to an exponent, and that base is also raised to an exponent, you can simplify the expression by multiplying the exponents.

For example, (a^x)^y = a^(xy)

In the case of square root of 7^3, the expression (√7)^3 can be written in the form of base and exponent, where the base is √7 and the exponent is 3.

Now, we can use the Power of a Power Property to simplify the expression, by multiplying the exponents.

So, (√7)^3 = (7^(1/2))^3 = 7^(1/2 * 3) = 7^(3/2)

This means that the square root of 7^3 is equal to 7^(3/2) because the Power of a Power Property allows us to simplify the expression by multiplying the exponents.

It's worth noting that the square root of 7^3 is the same as taking the cube root of 7^3, which is 7^(3/3) = 7^1 = 7.

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Answer:

2) Acute triangle, isosceles

3) Both are 65 degrees

4) (diagram)

5) a) both 25 degrees

b) midpoint

Step-by-step explanation:

2) If you're struggling search up "draw a triangle" and you'll find a website that will draw it for you. It will help you get an idea of it looks like and its nature.

3) We know that sides AB and AC are 5cm. So this triangle is an isosceles which makes the 2 remaining angles equal (if you draw a diagram it will be clear)

So:

180-50/2 = 65

ABC and ACB = 65 degrees each

4) Construct the line AH down the middle like in the diagram I drew.

5) a) Since AH is a straight line, we know that the angle AHB will be 90 degrees. After question 3 we also know that angle ABH is 65 degrees.

BAH = 180-90-65

BAH = 25 degrees

CAH = 50 - 25

CAH = 25 degrees

b) AH is the midpoint for BAC because the 2 segments formed are both 25 degrees.

The end behavior for f(x)=x^5 is as x approaches infinity, f(x) approaches infinity and as x approaches negative infinity, f(x) approaches negative infinity

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

f(x) = x^5

Calculate f(oo) and f(-oo) i.e the function at infinity and negative infiniyt

So , we have

f(x) = (oo)^5 = +oo

f(x) = (-oo)^5 = -oo

This means that x increases with f(x)

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Answer: The current ratio is a measure of a company's ability to meet its short-term obligations, it is calculated by dividing the current assets by current liabilities. If Hill Sports paid $10 million of its accounts payable on June 30, 2019, it would have reduced its current liabilities by $10 million.

To find out the current ratio after the payment, we need to know the current assets and current liabilities as of June 30, 2019.

If we assume that the current assets were $40 million and the current liabilities were $20 million as of June 30, 2019,

The current ratio = current assets / current liabilities = 40/20 = 2

After the company paid $10 million of its accounts payable, the current liabilities would be reduced by $10 million to $10 million.

So the new current ratio would be:

current assets / current liabilities = 40/10 = 4

So, Hill Sports' current ratio would have been 4 on June 30, 2019, if the company were to have paid $10 million of its accounts payable.

Step-by-step explanation:

The current ratio of a company, a liquidity ratio, would increase if a company pays part of its accounts payable thus reducing its current liabilities. However, the exact current ratio cannot be determined without specific financial figures for Hill Sports' current assets and liabilities.

The current ratio of a company is a liquidity ratio that measures a company's ability to pay short-term obligations or those due within one year. It is calculated by dividing a company's Current Assets by its Current Liabilities. Accounts payable is generally counted as a current liability.

So, if Hill Sports was to pay $10 million of its accounts payable, this would decrease its current liabilities by $10 million. Assuming the current assets remains the same, this would result in an increase in the current ratio because the denominator (current liabilities) is decreasing.

Without specific numbers for Hill Sports' current assets and liabilities, we cannot calculate the exact current ratio. However, the change in the ratio can be estimated if the original figures are known.

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The volume of a tank can be calculated by multiplying its length, width, and height.

Therefore, the expression to calculate the total amount of water a tank can hold in gallons can be represented by V = lwh, where V is the volume, l is the length, w is the width, and h is the height of the tank.

To find out how many -gallon buckets of water it takes to fill the tank, we can divide the total amount of water the tank can hold by the size of each bucket. This can be represented by the expression: n = V/g, where n is the number of buckets, V is the total amount of water the tank can hold, and g is the size of each bucket.

For example, if the tank is 8 feet long, 4 feet wide, and 2 feet tall and each bucket holds 1 gallon of water, the total amount of water the tank can hold is V = (8)(4)(2) = 64 gallons. Thus, the volume of a tank buckets of water needed to fill the tank would be n = 64/1 = 64 buckets.

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Complete question : Raul has a tank with a capacity of 200 gallons and wants to use buckets that hold 5 gallons each. How many buckets does he need to fill the tank?

The series for this problem is absolutely convergent, as the limit assumes a value lower than 1.

The infinite series for this problem is defined as follows:

[tex]\sum_{i = 1}^{\infty} \frac{1}{n!}[/tex]

Hence the general term is given as follows:

[tex]a_n = \frac{1}{n!}[/tex]

The limit is given as follows:

[tex]L = \lim_{n \rightarrow \infty} \left|\frac{a_{n + 1}}{a_n}\right|[/tex]

The (n + 1)th term is given as follows:

[tex]a_{n + 1} = \frac{1}{(n + 1)!}[/tex]

The factorial can be simplified as follows:

(n + 1)! = (n + 1) x n!.

Hence the limit will be calculated of:

1/[(n + 1) x n!] x n! = 1/(n + 1).

The result of the limit is given as follows:

[tex]L = \lim_{n \rightarrow \infty} \frac{1}{n + 1} = 0[/tex]

As the limit assumes a value of zero, the series is absolutely convergent.

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A linear function is a function that represents a straight line on the coordinate plane. So the pairs 3x-y=4 and 6x-2y=8 make each system of linear equations with the correct number of solutions.

What is meant by linear?

3x - y = 4                                      6x-2y = 8

3x=4+y                                          6x = 8 + 2y

3x/3 = 4/3 + y/3                             6x/6 = 8/6 + 2y/6

x = 4 + y/3                                    x = 4 + y/3

-3+y=7                                            -2x-4y = -8

y = 7 + 3                                           -2x = -8 +4y

y = 10                                               -2x/-2 = -8/-2 + 4/-2

                                                        x = -2(y-2)

y=-4x-5                                                     y=-4x+1

Axis interception points of -4x-5:           Axis interception pointsof -4x+1:

X Intercepts (-5/4,0),                               X Intercepts (1/4,0),

Y Intercepts (0,-5).                                  Y Intercepts (0,1).

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Mathematically, Aaliyah needs to read 8.75 hours (or 8 hours, 45 minutes) to fulfill her promise of reading 50 more pages than Yohance.

The mathematical operations used to determine the hours that Aaliyah needs to read this weekend to meet her target include multiplication, addition, and division.

In the first instance, we must determine the total pages read by Yohance this weekend using multiplication as follows: 300 (7.5 x 40).

Secondly, the additional pages Aaliyah will read are added to Yohance's to show the total pages read by Aaliyah.

Lastly, the total pages are divided by Aaliyah's reading speed or rate to determine the hours she requires.

                                           Aaliyah    Yohance

Average pages per hour       40             40

Additional page                     50

Yohance weekend reading time = 7.5 hours

Total pages read by Yohance this weekend = 300 (7.5 x 40)

The total pages to be read by Aaliyah this weekend = 350 (300 + 50)

Aaliyah's total weekend reading time 8.75 hours (350/40)

Thus, for Aaliyah to read 50 more pages than Yohance, she needs 8.75 hours to fulfill her promise.

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The equation used to model the amount of money that Jada would have in the account after x years is [tex]y= 200(1 + {0.03})^{x}[/tex].

Jada would have in her account $218 after 36 months. The solution has been obtained by using the concept of compound interest.

What is compound interest?

When interest is calculated, it is done so using both the principal and the interest that has accumulated over the preceding period. Unlike simple interest, which does not take the principal into account when computing the interest for the following month, compound interest takes the principal into account. Compound interest is commonly represented by the letter C.I. in mathematics.

We know that formula for compound interest is

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

So, here A= y, P = $200 , n=1 and t=x and r = 0.03

Thus, we get

[tex]y= 200(1 + \frac{0.03}{1} )^{x}[/tex]

[tex]y= 200(1 + {0.03})^{x}[/tex]

So, the second equation is the correct one.

The amount of money Jada would have after 36 months means the amount after 3 years.

So, x=3

Putting this in the equation, we get

[tex]y= 200(1 + {0.03})^{3}[/tex]

y = 200 (1.09)

y = $218

Hence, the equation used to model the amount of money that Jada would have in the account after x years is [tex]y= 200(1 + {0.03})^{x}[/tex] and Jada would have in her account $218 after 36 months.

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Answer:  In the month of October, the animal shelter saved 92 animals.

Step-by-step explanation: In the month of October, the animal shelter saw an increase of 15% of animals being saved from the previous month. To calculate this increase, we can use the formula:

increase = (original number) x (percent increase)

In this case, the original number is 80 (the number of animals saved in September) and the percent increase is 15%. So:

increase = 80 x 0.15 = 12

This means that in October, the animal shelter saved an additional 12 animals beyond the 80 animals that were saved in September. To find the total number of animals saved in October, we add this increase to the original number:

animals saved in October = 80 + 12 = 92

So, in the month of October, the animal shelter saved 92 animals.

Answer:

97.4

Step-by-step explanation:

Answer:

20.80 kg

Step-by-step explanation:

45 lb + 12 oz = 45 lb + 12/16 lb = 45.75 lb

45.75 lb × (1 kg)/(2.2 lb) = 20.80 kg

The function would be [tex]f(x)=\frac{1}{2}x + 1 \ and\ f(x)=\frac{1}{2}x - \frac{1}{2}[/tex]

What is linear function?

A linear function is one with one or two variables that does not have exponents. It is a function that has a straight line graph.

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. To find the equation of the linear function given the values of x and f(x), we can use two points and use the slope-intercept form of the equation.

A way to find the equation of the linear function is to use the point-slope form: f(x) = m(x-x1) + f(x1), where (x1,f(x1)) is a point on the line.

If we use the points (-4,-2) and (0,0) we can find the slope:

m = (0 - (-2)) / (0 - (-4)) = 2/4 = 1/2

then using point-slope form:

f(x) = 1/2(x - (-4)) + (-2)

f(x) = 1/2x + 1

so the equation of the linear function is f(x) = 1/2x + 1

Alternatively, we can use the two points (-2,-1) and (0,0) we can find the slope:

m = (0 - (-1)) / (0 - (-2)) = 1/2

then using point-slope form:

f(x) = 1/2(x - (-2)) + (-1)

f(x) = 1/2x - 1/2

so the equation of the linear function is f(x) = 1/2x - 1/2.

Therefore, equation f(x) = 1/2x+1 and f(x) = 1/2x - 1/2 represents the given values of x and f(x)

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The most clearly violated principle of ethical research in this scenario is individual information should be kept private, only summary results should be made public.

Ethical research requires that the privacy and confidentiality of study participants be protected. This is because the information collected from participants is often sensitive and personal, and the participants may have trusted the researcher to keep their information private.

In this scenario, the researcher has published the raw data, including personal information such as each participant's name, residence, and medical history, which could potentially compromise the privacy of the participants.

This is a clear violation of the principle of confidentiality, as the participants may not have agreed to have their personal information made publicly available.

It is important for researchers to be transparent and honest in their reporting of results, but they also have a responsibility to protect the privacy of their participants.

The publication of raw data, including personal information, should only be done with the explicit consent of the participants or under special circumstances where it is necessary for scientific advancement or the public good.

In conclusion, while the researcher's intention of being transparent in their reporting of results is commendable, the publication of the raw data, including personal information, is a clear violation of the principle of ethical research and could have serious consequences for the privacy and confidentiality of the study participants.

Hence, the correct answer is D.

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--The given question is incomplete; the complete question is

"A researcher collects various pieces of information from volunteers for a study into the health effects of drinking and smoking. The information collected includes each volunteer's name, residence, age, height, weight, medical history and their history of smoking cigarettes and drinking alcohol. All participants agreed to provide their information after the researcher explained how it would be used.

When publishing their results, the researcher feels that it would be unethical not to include the raw data which they have used to support their findings. So the researcher publishes the findings of the study, including all the supporting data on all the study participants, in a well-known journal.

The principle of ethical research most clearly violated (if any) is:

A. the researcher has falsified results

B. the researcher has failed to report negative results

C. no ethical principles have been violated; there was no informed consent

D. individual information should be kept private, only summary results should be made public"--

At x =6 the function has a positive slope.

A function is a mathematical expression, rule, or law that describes the relationship between an independent variable and a dependent variable. At x = 2 and x = 6, the function y(x) is zero, and it has a value of 1 for all other values of x. the dependent variable. Functions are essential for building physical relationships in both math and science.

A function, which generates one output from a single input, is an illustration of a rule. origin of the image. An illustration of this is Y=X2.

But

At x = 2, the function starts to decline and has a negative slope. negative derivative

while

At x = 6, the function increases with a positive slope, producing a positive derivative.

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The perimeter of the plane figure which is a quadrilateral with four straight sides is equal to 16 inches.

To know the perimeter of a plane figure, we add up all the length of its sides or boundaries together. That is the sum total of the length of a plane figure is called its perimeter.

The plene figure has for sides who two of it is 5 inches each and the other two is 3 inches each.

thus we calculate for the perimeter as follows:

perimeter of the plane figure = 5 in + 5 in + 3 in + 3 in

perimeter of the plane figure = 16 inches

Therefore, the perimeter of the plane figure which is a quadrilateral with four straight sides is equal to 16 inches.

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Based on given polynomial, The complete equation is = x² - 6x - 3.

A polynomial can be multiplied in just three steps.

The first step is to multiply each term in one polynomial by each term in the other polynomial using the distributive law.

Use the exponent rule to sum powers of related variables.

Then, to simplify the resulting polynomial, add or eliminate like elements.

The fact that multiplying two polynomials always yields a degree higher than the degree of the original polynomials should not be overlooked.

If a variable has the same exponent but various exponents for the provided polynomials, we must use the exponent law.

Given,

                a______________

x²       (b) __         -6x³             (c)__

9x      9x³              (d)___        -27x

We know that (a) is some polynomial in the form Ax² + Bx + c

Based on the above table,

It is clear that

on multiplying x² ×  1 term = (b)

x² × 2 term = -6x³

⇒ 2 term = -6x³ / x² = -6x                             (1)

x² × 3 term = (c)

Now,

9x × 1 term = 9x³

⇒ 1 term = x²                                                  (2)

9x × -6x = (d)

⇒ d = -54x²                                                     (3)

9x × 3 term =  -27x

3 term = -3                                                      (4)

From (1), (2) and (4),

The complete equation is = x² - 6x - 3

Value of (b) =  x² ×  1 term = (b)= x² × x² = x⁴

Value of (c) = x² × 3 term = (c) = x² ₓ -3 = -3x²

Value of (d) =  -54x²    [From (3)]

So the complete table is -

                (a) x² - 6x - 3

x²       (b) -6x         -6x³           (c) -3

9x      9x³           (d) -54x²     -27x

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Answer: all of the above

Step-by-step explanation:

Answer: square,Rectangle,Rhombus and trapezoid

Step-by-step explanation:

they all have pairs of parallel sides

Please mark me brainllest

Answer:

10, 8

Step-by-step explanation:

Let x be the number of salads and y be the number of burgers.

We know that:

x + y = 28 (the total number of people)

8x + 4y = 152 (the total cost in dollars)

We can use the first equation to solve for one variable in terms of the other.

x = 28 - y

Now we can substitute this expression into the second equation:

8(28 - y) + 4y = 152

224 - 8y + 4y = 152

224 = 12y

y = 18 (burgers)

We can then use this value to find the number of salads

x = 28 - y = 28 - 18 = 10 (salads)

So the manager bought 10 salads and 18 burgers

Answer: To rewrite the given expressions as equivalent rational expressions with the denominator (5a+2)(a−4)(a+2), we need to factor the denominators of the given expressions and cancel out any common factors between the numerator and denominator.

2/5a^2-18a-8

We can factor the denominator: 5a^2-18a-8 = (5a+8)(a-1)

Now we can cancel out the common factor of (a-1) from the numerator and denominator

2/(5a+8)

8a/5a^2+12a+4

We can factor the denominator: 5a^2+12a+4 = (5a+4)(a+1)

Now we can cancel out the common factor of (a+1) from the numerator and denominator

8a/(5a+4)

Now we can multiply the numerators and denominators of both expressions with (5a+2)(a−4)(a+2)

(2*(5a+2)(a−4)(a+2)) / (5a+8)(a-1)(5a+2)(a−4)(a+2) = 2(a−4)(a+2) / (5a+8)(a-1)

(8a*(5a+2)(a−4)(a+2)) / (5a^2+12a+4)(5a+2)(a−4)(a+2) = 8a(5a+2) / (5

Step-by-step explanation:

Answer: Fall Out Boy's service is cheaper than Five Seconds of Summer's service.

Step-by-step explanation: The cost of Five Seconds of Summer's tutoring service can be represented by the equation:

C = 5 + 5h

where C is the total cost and h is the number of hours.

The cost of Fall Out Boy's tutoring service can be represented by the equation:

C = 9 + 3h

To compare the cost of the two services, we can use the substitution method. We can set the number of hours (h) equal to a variable and substitute that variable into the equation for both services.

For example, if we set h = 4 (4 hours of tutoring), we get:

C(Five Seconds of Summer) = 5 + 5(4) = 25

C(Fall Out Boy) = 9 + 3(4) = 21

The cost of Fall Out Boy's service is $21 and the cost of Five Seconds of Summer's service is $25. Therefore, Fall Out Boy's service is cheaper for 4 hours of tutoring.

We can also graph the cost of the two services on a coordinate plane. The x-axis represents the number of hours and the y-axis represents the cost. The equation for Five Seconds of Summer's service would be y = 5 + 5x and the equation for Fall Out Boy's service would be y = 9 + 3x

Service | Equation

Five Seconds of Summer y = 5 + 5x

Fall Out Boy |                        y = 9 + 3x

Las pesas de menor masa son listadas como sigue:

En esta pregunta tenemos seis casos de tres pesas, entre las cuales debemos determinar cuál tiene la menor masa. Esto implica el uso de la conversión entre unidades de masa a una única unica, tal que la pesa de menor capacidad será la de menor cantidad. El procedimiento se resume a continuación:

Caso 1

32 hectogramos - 3200 gramos

4 kilogramos - 4000 gramos

500 decagramos - 5000 gramos

La pesa de 32 hectogramos reporta la menor masa.

Caso 2

35 gramos

4500 miligramos - 4.5 gramos

80 decigramos - 8 gramos

La pesa de 80 decigramos reporta la menor masa.

Caso 3

9500 decigramos - 950 gramos

6 kilogramos - 6000 gramos

70 hectogramos - 7000 gramos

La pesa de 9500 decigramos reporta la menor masa.

Caso 4

365 decigramos - 3650 gramos

90 gramos

30 decagramos - 300 gramos

La pesa de 90 gramos reporta la menor masa.

Case 5

75 hectogramos - 7500 gramos

5 kilogramos - 5000 gramos

6200 gramos

La pesa de 5 kilogramos reporta la menor masa.

Case 6

8500 hectogramos - 850000 gramos

30 kilogramos - 30000 gramos

900 decagramos - 9000 gramos

La pesa de 8500 hectogramos reporta la menor masa.

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By applying Trigonometry functions it can be concluded that cos θ = -√2/2 will be met if θ = 135° or 225° (option D)

Trigonometry is a branch of mathematics that studies the relationship between side lengths and angles of triangles.

Trigonometry functions can be defined by means of a right triangle, where ABC is a right triangle, a and b are the sides of the triangle and c is the hypotenuse of the triangle.

sin A = opposite side (a) / hypotenuse (c)

cos B = adjacent side (b) / hypotenuse (c)

tan C = opposite side (a) / adjacent side (b)

There are some special angles whose sin, cos, and tan values are frequently used:

          0°     30°       45°       60°     90°    

sin      0      1/2      √2/2     √3/2      1

cos     1     √3/2    √2/2       1/2       0

tan      0    √3/3        1          √3       ~

These values change over the interval:

We have to find all values in the interval [0,360°) that have the given function value cos θ = -√2/2.

cos θ = √2/2

      θ = 45°

Since cos will have a negative value in the interval [90°,270°], then we get the value of θ is 135° and 225°.

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30 is the fast surface area of the balloon expanding when the radius of the balloon is 4 inches

Now, According to the question:

A spherical balloon is expanding at the rate of 60 pie cubic inches /sec.

The radius of the balloon is 4 inches.

Now, Solving the problem:

By using formula:

The formula for the volume of a sphere is V = 4/3 π r³,

where V = volume and r = radius.

Volume = [tex]\frac{4}{3}\pi r^3[/tex]

We have that:

Differentiate the formula:

[tex]\frac{dV}{dt}=4\pi r^2.\frac{dr}{dt}= 60[/tex]

=> [tex]\frac{dr}{dt}=\frac{60}{4\pi r^2}[/tex]

We know that [tex]A=4\pi r^2,[/tex] and so we also have

[tex]\frac{dA}{dt}=8\pi r.\frac{dr}{dt}[/tex]

Plug in what we found for dr/dt and plug in r=4 to get:

[tex]\frac{dA}{dt}=8\pi r.\frac{60}{4\pi r^2}[/tex]

[tex]\frac{dA}{dt}=\frac{120}{r}=\frac{120}{4}[/tex]

[tex]\frac{dA}{dt}=30[/tex]

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