A Small Monster collector is visiting the Knightrola region, bringing 30 Small Monster Containment Devices with them. The devices are highly reliable and can effectively be assumed to always work. How many different types of Small Monsters can the collector capture under the following conditions? a. The collector has access to Grass, Space Electric Scooter, Mask, Citrus, and Rubber Duck type Small Monsters 7 types b. The above, and intends to capture at least one of each of those types c. Both of the above, and intends to capture at least five Space types d. All of the above and intends to capture at most four Electric Scooter types e. All of the above, and intends to capture at most three Rubber Duck type

Answer:$163.68

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = final amount ($600,000)

P = initial amount (unknown)

r = interest rate (8%)

n = number of times interest is compounded per year (12 for monthly)

t = time in years (25)

Substituting in the values, we get:

$600,000 = P(1 + 0.08/12)^(12*25)

Simplifying:

$600,000 = P(1.00666666666667)^300

Dividing both sides by (1.00666666666667)^300:

P = $600,000 / (1.00666666666667)^300

Using a calculator, we get:

P = $163.68

Therefore, we would need to invest $163.68 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.

A sample size that would give the standard deviation of [tex]\bar{x}[/tex] equal to 0.8 years is 1,227.

In Mathematics and Statistics, a sample size that would result in a standard deviation of 0.8 years can be calculated by using the mathematical equation (formula):

Sample size, n = (zσ/ME)²

Where:

By assuming a confidence level of 95% with a z-score of 1.96, we would substitute the given parameters into the formula for sample size as follows;

Sample size, n = (zσ/E)²

Sample size, n = (1.96 × 14.3/0.8)²

Sample size, n = (28.028/0.8)²

Sample size, n = (35.035)²

Sample size, n = 1,227.45 ≈ 1,227.

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Complete Question:

Suppose the standard deviation of the ages of all Florida panthers is 14.3 years. Let [tex]\bar{x}[/tex] be the mean age for a sample of a certain number of Florida panthers. What sample size will give the standard deviation of [tex]\bar{x}[/tex] equal to 0.8 years?

Round the solution up to the nearest whole number, if necessary.

Answer:

Step-by-step explanation:

P(x)=x³+6x²+3x-10=0

x³+2x²+4x²+8x-5x-10=0

x²(x+2)+x(x+2)-5(x+2)=0

(x+2)(x²+x-5)=0

either x+2=0,x=-2

or

x²+x-5=0

[tex]x=\frac{-1 \pm \sqrt{1^2-4 \times 1 \times(-5)} }{2 \times 1} \\=\frac{-1 \pm \sqrt{21} }{2} \\Hence ~x=\frac{-1+\sqrt{21} }{2} \\or\\x=\frac{-1 -\sqrt{21} }{2}[/tex]

Answer:

6 1/40

Step-by-step explanation:

21/8 + 17/5

105/40 + 136/40 = 241/40

241/40= 6 1/40

Answer:

a) 30 × .5 = 15 days

b) .2 + .1 = .3

The deli needs to sell the tuna salad at a price of R2.33 per kg to achieve a profit of 40% of the selling price after 5kg spoilage.

A desired profit also known as target profit means expected amount of profit that the managers of a business expect to achieve by the end of a designated accounting period.

First, let's calculate the cost of the tuna salad the deli purchased:

= 45kg x R1.48/kg

= R66.60

How much tuna salad the deli has left after spoilage:

= 45kg - 5kg

= 40kg

To achieve a profit of 40% of the selling price, the selling price should be 140% of the cost price: which is:

= 140% of cost price

= 1.4 x R66.60

= R93.24

To find the price per kilogram, we divide the selling price by the remaining amount of tuna salad:

= Selling price / Remaining amount of tuna salad

= R93.24 / 40kg

= R2.33/kg

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Answer: 6 dolla per kg

Step-by-step explanation:

Therefore, each drink would have approximately 18.67 grams of sugar if the amount of sugar was redistributed evenly.

In statistics, distribution refers to the pattern of values that a variable can take and how frequently those values occur. It is a mathematical function that describes the probability of occurrence of each possible outcome in a set of events.

There are various types of distributions such as normal distribution, binomial distribution, Poisson distribution, and exponential distribution. Each distribution has a specific shape and characteristics, which can be described by its mean, variance, skewness, and kurtosis.

by the question.

Let's say the amounts of sugar in the six drinks are:

Drink 1: 10 grams

Drink 2: 20 grams

Drink 3: 15 grams

Drink 4: 25 grams

Drink 5: 30 grams

Drink 6: 12 grams

To redistribute the sugar evenly, you would need to add up the total amount of sugar and divide it by the number of drinks. In this case:

Total amount of sugar = 10 + 20 + 15 + 25 + 30 + 12 = 112 grams

Number of drinks = 6

Redistributed amount of sugar = Total amount of sugar / Number of drinks

Redistributed amount of sugar = 112 / 6

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The maximum profit is $2492.08.

What is the selling price?

The cost a consumer pays to purchase a good or a commodity is known as the selling price. It is a price that is higher than the cost price and includes a profit margin. The cost of an item when acquired is referred to as its selling price (S.P.).

Here, we have

Given: A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation.

y = -3x² + 239x - 2268

At a maximum profit, dy/dx = 0, hence:

dy/dx = -6x + 239

0 = -6x + 239

x = 239/6

x = 39.8

The maximum profit is gotten when the selling price of each widget is 39.8. Hence:

y = -3(39.8)² + 239(39.8) - 2268

y = 2492.08

Hence,  the maximum profit is $2492.08.

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Answer:

Para decidir si es mejor rentar o comprar la máquina excavadora, se debe calcular el costo anual de cada opción y compararlos.

Costo anual de renta = Costo de renta mensual x 12 meses + (Costo diario x Días de uso)

Costo anual de renta = 3000 x 12 + (180 x Días de uso)

Costo anual de renta = 36000 + 180D

Costo anual de compra = Costo fijo anual + (Costo diario x Días de uso)

Costo anual de compra = 20000 + (230 x Días de uso)

Para encontrar el número mínimo de días de uso que justificarían la renta en lugar de la compra, se debe igualar ambos costos anuales:

36000 + 180D = 20000 + 230D

50D = 16000

D = 320

Por lo tanto, el constructor tendría que utilizar la máquina excavadora al menos 320 días al año para justificar la renta en lugar de la compra.

Answer:

y = [tex]\frac{1}{3}[/tex] x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x - 10 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (9, - 2 ) into the partial equation

- 2 = [tex]\frac{1}{3}[/tex] (9) + c = 3 + c ( subtract 3 from both sides )

- 5 = c

y = [tex]\frac{1}{3}[/tex] x - 5 ← equation of perpendicular line

The distance between the two towns on the map was found to be 30.67 centimeters by setting up and solving a proportion between the distances on the map and the actual distances.

The problem provides us with a scale on the map of 3 cm to 45 km, which means that every 3 centimeters on the map represents 45 kilometers in the actual world. Let x be the distance between the two towns on the map in centimeters. Using the proportion, we can set up the relationship between the distances on the map and the actual distances as follows:

3 cm / 45 km = x cm / 460 km

Here, we set up a ratio between the distance on the map and the actual distance, where the distance on the map is x centimeters and the actual distance between the towns is 460 kilometers. We can then cross-multiply to solve for x:

45 km * x cm = 3 cm * 460 km

This gives us:

45x = 1380

x = 1380 / 45

x = 30.67 cm

Therefore, the distance between the two towns on the map is 30.67 centimeters.

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John deposits $5025 into a savings account that has an interest rate of 9.5%. The account is compounded monthly for the next 18 years. So in the account the amount will be $27596.60. Option c is correct.

Cοmpοund interest, alsο knοwn as interest οn principle and interest, is the practise οf adding interest tο the initial amοunt οf a lοan οr depοsit. It οccurs when interest is reinvested, οr added tο the bοrrοwed capital rather than paid οut, οr when the bοrrοwer is required tο pay it, sο that interest is made the fοllοwing periοd οn the initial amοunt + any accumulated interest. In business and ecοnοmy, cοmpοund interest is cοmmοn.

We can use the Cοmpοund interest below-

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

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Given,

Time periods (t)= 18years

n = 12 months

Interest in a year (r)= 9.5% or 0.095

Principial amount (P)= $5025

Lets solve for final amount :

[tex]\rm A = 5025(1 + \frac{0.095}{12})^{12 \times 18}[/tex]

A ≈ 27596.59

That is nearby $27596.60.

In the account the amount will be $27596.60. Thus, option c is correct.

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Answer: it is  c. 27596.60

The correct answer of the folowing question is option B and d in context to the circle and triangle

How to solve the problem?

Triangles and circles have a close relationship in geometry, and several interesting properties and theorems connect them.

One triangle inscribed in circle: This statement is true, and it refers to the property of a circle that can be inscribed in a triangle. In other words, if we draw a circle that passes through all three vertices of a triangle, then the triangle is said to be inscribed in the circle. The center of the circle is called the circumcenter of the triangle, and it is the intersection point of the perpendicular bisectors of the sides.

Many triangles inscribed in circle: This statement is also true, as there are many different triangles that can be inscribed in the same circle. For example, if we draw a circle and pick any three points on its circumference, then we can connect these points to form a triangle that is inscribed in the circle.

One circle inscribed in triangle: This statement is true, and it refers to the property of a triangle that can be inscribed in a circle. In other words, if we draw a circle that is tangent to all three sides of a triangle, then the circle is said to be inscribed in the triangle. The center of the circle is called the incenter of the triangle, and it is the intersection point of the angle bisectors.

Many circles inscribed in triangle: This statement is false, as there can only be one circle that is inscribed in a given triangle. However, there are other circles that can be associated with a triangle, such as the circumcircle and the excircles. The circumcircle is the circle that passes through all three vertices of the triangle, while the excircles are the circles that are tangent to one side of the triangle and the extensions of the other two sides.

In summary, triangles and circles are closely related in geometry, and their properties and theorems are important in various areas of mathematics and science.

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According to the solving time will they take together to wax the same car 16 minutes

The minute is a unit of time usually equal to 160 (the first sexagesimal fraction) of an hour, or 60 seconds.

Let's assume that Andrea takes x minutes to wax the car. Then Mathew takes x/2 minutes to wax the same car since he waxes twice as fast as Andrea.

We know that Andrea takes 24 minutes to wax the car. So we can substitute this value in the equation and solve for x.

x = 24 * 2 = 48

So Andrea takes 48 minutes to wax the car alone.

Now we can use the formula:

1/x + 1/(x/2) = 1/t

where t is the time taken by both of them together to wax the same car.

Substituting x = 48, we get:

1/48 + 1/24 = 1/t

Solving for t, we get:

t = 16minutes

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This transformation of figure 1  has been transformed to produce figure 2, can be described by (x' , y') = (x' -y')

Transformation describes how an item moves, particularly as they are shown on a coordinate plane.

There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or position. The four methods comprise

Pre-Image refers to the item's shape before transformation, whereas Image refers to the object's ultimate location and shape.

The linked image's preimage and image may be examined to determine that reflection is the involved translation.

The transformation rule for reflection over the y-axis is as follows:

(x, y) → (x, -y)

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I think it is A... if the original is Red. It is reflected across the x-axis.

I hope this helps !

The best line that represents the relation between the lines that passes through the points (8, 2) and (3, 5) and the line (-3, -7) and (0, -12) is a perpendicular line.

What are perpendicular lines?

In geometry, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90 ∘). The term ‘perpendicular’ originated from the Latin word ‘perpendicularis,’ meaning a plumb line. If two lines AB and CD are perpendicular, then we can write them as AB ⊥ CD.

To determine the relationship between the two lines, we can first find the slope of each line using the two-point formula:

Slope of the line passing through (8, 2) and (3, 5):

m1 = (5 - 2) / (3 - 8) = -3/5

Slope of the line passing through (–3, –7) and (0, –12):

m2 = (-12 - (-7)) / (0 - (-3)) = -5/-3 = 5/3

If the two lines are parallel, their slopes will be equal. However, -3/5 is not equal to 5/3. If the two lines are perpendicular, their slopes will be negative reciprocals of each other. That is,

m1 x m2 = -1

But, (-3/5) x (5/3) = -1, which means that the two lines are perpendicular.

Therefore, the correct answer is C. perpendicular.

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It should be noted that the function that can model the data is a linear function since there's a constant difference or -5.The linear function is y = -5x - 9.

In this case, to determine whether the data is best modeled by a linear, quadratic, or exponential function, we can first plot the data points and see what type of curve they form. However, since we are only given five data points, it can be difficult to make a definitive determination.

One way to estimate the type of function is to look at the differences between the y values. For example, if the differences between the y values increase by a constant amount, then the data may be best modeled by a linear function. If the differences increase by a constant squared amount, then the data may be best modeled by a quadratic function.

Here, the constant difference will be:

= -29 - (-24)

= -5

This depicts a linear function.

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Hypothesis Testing ,Sample data  , Categorical  ,one variable ,one sample and sample z test for a proportion are the  responses to the question were used to learn about the population of adult Americans who self identify as an entrepreneur.

(a) The question type in this study is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.

(b) The study type is sample data, as a sample of adult Americans was surveyed to learn about the population of adults who self-identify as entrepreneurs.

(c) The data is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.

(d) There is one variable in this study, as the responses to the question about self-identification as an entrepreneur are the only data collected.

(e) There is one sample in this study, as only one group of adult Americans was surveyed.

(f) The appropriate method for analyzing the data in this study is the one-sample z test for a proportion. This method is used when we have one categorical variable and want to test whether the proportion of a certain response differs significantly from a hypothesized proportion. In this case, the hypothesized proportion would be the proportion of adult Americans who self-identify as entrepreneurs. We would use the z-test to determine if the proportion of respondents who self-identify as entrepreneurs is significantly different from the hypothesized proportion. If the difference is significant, we can conclude that there is a difference between the sample and population proportions, and if the difference is not significant, we cannot reject the null hypothesis that the sample proportion is the same as the population proportion.

Overall, this study is using categorical data to learn about the proportion of adult Americans who self-identify as entrepreneurs. The appropriate method for analyzing this type of data is the one-sample z test for a proportion, which allows us to test whether the sample proportion is significantly different from the hypothesized population proportion.

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Answer:

[tex]\frac{x^{7} }{y^{10} }[/tex]

Answer:

To find the percentage decrease, we need to find the difference between the original price and the new price, divide that difference by the original price, and then multiply by 100 to express the result as a percentage.

The difference between the original price and the new price is:

990 - 765 = 225

Dividing the difference by the original price gives:

225 ÷ 990 ≈ 0.227

Multiplying by 100 gives:

0.227 x 100 ≈ 22.7

Therefore, the percentage decrease in the monthly price of the contract is approximately 22.7%.

Step-by-step explanation:

Answer:

The answer is 7d < -6

Step-by-step explanation:

3d-8<4d+2

3d+4d<-8+2

7d<-6

Tim's score range would be between 20.2 - 56.25 and 20.2 + 56.25, or between -36.05 and 76.45. To find the percentage of games

a. To find the percentage of candy wrappers that would have between 3.4 and 3.6 ounces, we need to calculate the z-scores for each of the values:

[tex]z-score for 3.4 ounces = (3.4 - 3.5) / 0.16 = -0.625[/tex]

[tex]z-score for 3.6 ounces = (3.6 - 3.5) / 0.16 = 0.625[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers between these two values is approximately 47.70%.

b. To find the percentage of candy wrappers that would have less than 3.3 ounces, we need to calculate the z-score for this value:

[tex]z-score for 3.3 ounces = (3.3 - 3.5) / 0.16 = -1.25[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with less than 3.3 ounces is approximately 10.92%.

To find the percentage of candy wrappers with more than 3.62 ounces, we need to calculate the z-score for this value:

[tex]z-score for 3.62 ounces = (3.62 - 3.5) / 0.16 = 0.75[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with more than 3.62 ounces is approximately 22.77%.

c. To find how many of the 1358 packets made that day have between 3.35 and 3.65 ounces, we need to convert these values to z-scores:

[tex]z-score for 3.35 ounces = (3.35 - 3.5) / 0.16 = -0.9375[/tex]

[tex]z-score for 3.65 ounces = (3.65 - 3.5) / 0.16 = 0.9375[/tex]

Using a z-table or a calculator with a normal distribution function, we can find the percentage of candy wrappers between these two values, which is approximately 62.97%. To find how many packets this represents, we can multiply this percentage by the total number of packets made:

[tex]0.6297 * 1358 = 856 packets[/tex]

Therefore, approximately 856 packets made that day have between 3.35 and 3.65 ounces.

d. To find how many games Tim would have scored 22 points or more if he plays 32 games, we first need to calculate the z-score for this value:

[tex]z-score for 22 points = (22 - 20.2) / 25 = 0.072[/tex]

Using a z-table or a calculator with a normal distribution function, we can find the percentage of games with a z-score greater than or equal to 0.072, which is approximately 53.10%. To find how many games this represents, we can multiply this percentage by the total number of games:

[tex]0.5310 x 32 = 17 games[/tex]

Therefore, Tim would have scored 22 points or more in approximately 17 games out of 32.

e. To find how many games Tim would have scored within 2.25 standard deviations from his average if he plays 32 games, we first need to calculate 2.25 standard deviations:

[tex]2.25 x 25 = 56.25[/tex]

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Answer:

Step-by-step explanation:

Answer:

Thank you for the statement. Is there a question or additional information you would like me to respond to?

Step-by-step explanation:

After answering the provided question, we can conclude that So the total  equation amount of time Sarah spent on these three activities is determined by how much time she spent reading.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x^2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Let's call Sarah's reading time "r" in minutes.

We can deduce from the problem:

Sarah painted for 5 minutes.

Because she spent twice as much time reading as she did painting,[tex]r = 2*5 = 10.[/tex]

She hiked for 35 minutes longer than she read, so [tex]h = r + 35.[/tex]

To calculate Sarah's total time spent on these three activities, simply add the times:

Time spent painting + time spent reading + time spent hiking = total time

Time total =[tex]5 + 10 + (r + 35)[/tex]

Time total = [tex]50 + r[/tex]

So the total amount of time Sarah spent on these three activities is determined by how much time she spent reading.

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The statement which is correct is: If {α, β} is independent, then {w₁, w₂, w₁+ w₂} is in dependent.

In vector space theory, a set of vectors is said to be linearly independent if there is no non-trivial linear combination of vectors equal to vector zero. If such a linear combination exists, the vectors are said to be linearly dependent. These concepts are central to dimension definitions.

The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space are linearly dependent is essential to determining the dimensionality of a vector space.

According to the Question, we know that:

{w₁, w₂, w₃} are linearly independent.

Let, α₁, α₂, α₃ such that

α₁w₁ + α₂w₂+ α₃w₃ = 0

and, α₁ = α₂ = α₃ = 0

Again considering the following, we can say that:

{w₁, w₁+ w₂, w₁+w₂+w₃} such that:

β₁(w₁) + β₂(w₁+ w₂) + β₃(w₁+ w₂+ w₃) = 0

Here, the dependent variable is {α,β} and { w₁+ w₂+ w₃}

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For fau/cet filter:

For pitcher-filter:

Let's start with the fau/cet model:

Contribution margin per unit = selling price - variable cost

Contribution margin per unit = $90 - $25

Contribution margin per unit = $65

Contribution margin ratio = contribution margin per unit / selling price

Contribution margin ratio = $65 / $90

Contribution margin ratio = 0.722

The sales mix is 2 faucet models for every 3 pitcher filters sold, so the contribution margin weighted average is:

= (2/5)($65) + (3/5)($90-$20)

= $42

Now we can calculate the break-even point in units for the faucet model:

= Total fixed costs / contribution margin per unit

= $1,200,000 / $42

= 28,571 units

For pitcher filter:

Contribution margin per unit = selling price - variable cost

Contribution margin per unit = $110 - $20

Contribution margin per unit = $90

Contribution margin ratio = contribution margin per unit / selling price

= $90 / $110

Contribution margin ratio = 0.818

Contribution margin weighted average:

= (2/5)($25) + (3/5)($90-$20)

= $54

Break-even point in units for pitc/her filter:

= Total fixed costs / contribution margin per unit

= $1,200,000 / $54

= 22,222 units

Break-even point in dollars for fau/cet model:

= 28,571 units x $90 per unit

= $2,571,390

Break-even point in dollars for pitc/her-filter:

= 22,222 units x $110 per unit

= $2,444,420

Full question "Multiproduct CVP and decision making. Crystal Clear Products produces two types of water filters. One attaches to the faucet and cleans all water that passes through the faucet. The other is a pitcherfilter that only purifies water meant for drinking. The unit that attaches to the faucet is sold for $90 and has variable costs of $25. The pitcherfilter sells for $110 and has variable costs of $20. Crystal Clear sells two faucet models for every three pitchers sold. Fixed costs equal $1,200,000.

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Value of base and hypotenuse of triangle are 9√3 and 18 respectively.

A right triangle is a triangle with one interior angle measuring 90 degrees, known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are known as the legs of the right triangle. The length of the hypotenuse can be found using the Pythagorean theorem,  that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Height of triangle=9

Base of triangle=y

Hypotenuse of triangle=x

Using trigonometric ratio

Sin30°=Height/Hypotenuse

½=9/x

x=18

Cos30°=Base/hypotenuse

√3/2=y/18

y=9√3

Hence, value of base and hypotenuse of triangle are 9√3 and 18 respectively.

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Any percentage can be written as that number divided by 100. As a decimal, you find that quotient. You can quickly divide any number by 10 by moving the decimal place to the left for every 0 in that multiple of 10. 100 has 2 zeros, so all you need to do to divide by 100 is to move the decimal place 2 places to the left. Therefore, 60% is .6 as a decimal.

Let's say the number we want to find is x. In word problems, "of" indicates multiplication, so 60% of our number would be 6x.

We then add our number to that, giving us .6x + x

We know the result is 160, so

.6x + x = 160

Since any number multiplied by 1 is itself, that x can be written as 1x.

.6x + 1x = 160

Now, we combine our like terms; we add the numbers in front of the x's (aka coefficients).

(.6 + 1)x = 160

1.6x = 160

We want x by itself. 1.6 is multiplied by our number, so to undo multiplication, we do division. This leaves us with

x = 160/1.6

x=100