please help!! performance task: vector operations

Draw u - v + w.

The cone’s radius r in terms of x is x + 7

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

Volume, V = 3πx^2 + 42πx + 147π

Height, h = 9

The volume of a cone is

V = 1/3πr^2h

Substitute the known values in the above equation, so, we have the following representation

1/3πr^2 * 9 = 3πx^2 + 42πx + 147π

So, we have

3πr^2 = 3πx^2 + 42πx + 147π

Divide by 3π

r^2 = x^2 + 14x + 49

So, we have

r = √(x² + 14x + 49)

Take the square roots of both sides

r = x + 7

Hence, the value of r is x + 7

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We need to add approximately 14.86 mL of water to 14 mL of 14% alcohol solution to reduce the concentration to 7%.

First, let's figure out how much alcohol is in the first 14 mL of the 14% alcohol solution.

Alcohol is equal to 0.14 x 14 (14%) times 14%, or 1.96 mL.

We need to add water so that the amount of alcohol stays the same while the overall volume grows in order to lower the concentration to 7%.

Assume that x mL of water needs to be added.

The volume of the solution will be (14 + x) mL with the addition of x mL of water, while the amount of alcohol will remain at 1.96 mL.

The equation for the ultimate concentration can be written as follows:

1.96 mL / (14 + x) mL = 0.07

When we find x and simplify, we get:

x = (1.96 mL / 0.07) - 14 mL

x ≈ 14.86mL

In order to lower the concentration to 7%, we must therefore add around 14.86 mL of water to 14 mL of 14% alcohol solution.

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Answer: You only need to write the formula then rewrite it then multiply then add and then you divive by 2

Step-by-step explanation: it is the top of the shape which is 10cm2

Answer: 3.93701

Step-by-step explanation:

The selling price of the motorcycle is Rs 1,19,400. To calculate this, we can use the formula Selling Price = Original Price - (Original Price × Loss Percentage).

In this case,

To calculate the selling price of an item when a loss percentage is given, we first need to calculate the amount of the loss. This can be done by multiplying the original price by the loss percentage. Then, we subtract the loss amount from the original price to get the selling price.

In this example, the original price of the motorcycle was Rs 135000, and the loss percentage was 12%. Multiplying 135000 by 0.12 gives us a loss amount of 16200, and subtracting this from 135000 gives us a selling price of 119400. This calculation can be used to quickly and accurately determine the selling price of an item when a loss percentage is given.

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For given Step function also known as piecewise function, The range of g(x)  is {-3,2,5} i.e. C.

What exactly is a piecewise function?

A piecewise function has several definitions in various x intervals. The graph of a piecewise function is split into sections that correspond to each of its definitions. The absolute value function is an outstanding example of a piecewise function. Let us look at why it was given that name. We know that an absolute value function is defined as f(x) = |x|.

f(x)=(x if x x≥0)

-x if x<0)

This piecewise function should be interpreted as

When x is higher than or equal to 0, f(x) equals x.

When x is less than zero, f(x) equals -x.

Now,

As range of a given function is given by its y values, here it will be given by values of g(x) and as we can see from question for values of x, g(x) is always equal to -3,2,5.

Hence,

           The range of g(x) is {-3,2,5}.

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Answer:

Step-by-step explanation:

Find the sum: 9/10 9/100

A: 18/100

B: 90/100

C: 18/10

D; 99/100

9/10 = 90/100

so

90/100 + 9/100 = 99/100

Answer: D 99/100 I hope this helps

Step-by-step explanation:

9/10+9/100

Write all numerators above the least common denominator 100

90+9/100

Add the numbers 90+9 which would will give you your answer

99/100

The sum of the measures of the interior angles of a polygon with n sides can be found using the formula (n-2) * 180 degrees.

For a 10-sided figure, we have (10-2) * 180 = 8 * 180 = 1,440 degrees.

Therefore, the sum of the measures of the interior angles of a 10-sided figure is 1,440°.

The answer is A.

"6x - 5" is the expressions that can be subtracted from 9x to give the result in expression 3x+5.

To find the expression that can be subtracted from 9x to result in the expression 3x+5.

Let the expression be (a - b = c),

Here a = 9x

and the result, c = 3x + 5

We have to find out b = ?

Substitute the values of a and b in the above equation then we get;

9x - b = 3x + 5

9x - (3x + 5) = b

b = 6x - 5

Hence the expressions that can be subtracted from 9x to result in the expression 3x+5 is 6x - 5

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Anaiah is currently spending $150 on eggplants and kiwis.

Anaiah is behaving irrationally, because

1) He is not spending his entire income

2) He is spending too much on kiwis

3) He is not balancing what he spends on each good

4) His marginal utility per dollar spent is not the same for both goods.

Currently, Anaiah is spending:

On eggplants: 20 x $3 = $60

On kiwis: 30 x $3 = $90

Total spending: $60 + $90 = $150

Therefore, Anaiah is currently spending $150 on these goods.

The reasons that Anaiah is behaving irrationally are:

He is not spending his entire income: Anaiah has $180 to spend but he is only spending $150, which means he is not maximizing his utility by fully utilizing his budget.

He is spending too much on kiwis: Anaiah's marginal utility per dollar spent on kiwis is lower than his marginal utility per dollar spent on eggplants. Therefore, he should be spending more on eggplants and less on kiwis to maximize his utility.

He is not balancing what he spends on each good: Anaiah is consuming 20 eggplants and 30 kiwis, which means he is not allocating his budget efficiently to maximize his total utility. He should be consuming a combination of eggplants and kiwis that gives him the highest total utility within his budget constraint.

His marginal utility per dollar spent is not the same for both goods: Anaiah's marginal utility per dollar spent on eggplants is 160 utils while his marginal utility per dollar spent on kiwis is 190 utils. Therefore, he should be consuming more eggplants and fewer kiwis to maximize his total utility within his budget constraint.

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The total of a hexagon's internal angles is 720 degrees.

The internal angles of a hexagon may be calculated using the formula "180 - (360/n)," where n is the number of sides. When you enter 6 for a hexagon, the response is 120 degrees.

We might begin by imagining a hexagon to better comprehend the notion. It is a basic design made up of six distinct straight lines that join to form a closed shape. The internal angles are the angles on the inside of the form.

The above-mentioned formula may be used to compute the internal angles of a hexagon. For each inner angle of a hexagon, the computation yields a value of 120 degrees. Hence the total of a hexagon's internal angles is 720 degrees.

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By using the long division method, the result of 19 divided by 20 is 0.95

Long division is a method of dividing two numbers using a step-by-step process of repeatedly dividing the dividend (the number being divided) by the divisor (the number you are dividing by), writing down the results of each step, and subtracting the remainder from the next dividend.

Here, 19 divided by 20

The picture shows the division process

To divide 19 by 20 using long division, you start by dividing 20 into the first digit of 19, which is 1. The result is 0 with a remainder of 1.

Then bring down the next digit, which is 9, and place it next to the remainder to make 19. You then divide 20 into 19, which gives you 0 with a remainder of 19.

Therefore, 19 divided by 20 is 0.95

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Answer: Impossible to answer/ 12 chickens 8 rabbits

Step-by-step explanation: The question asks how many hens there are, or female chickens. We do not know if the chickens are female or male, so we cannot answer. If you meant how many chickens there were, then we start with 20 chickens and 0 rabbits. Doing so, we have 40 legs. When we switch a chicken for a rabbit, we have 19 chickens and 1 rabbit, and 42 legs. So, we can subtract 56-40 giving us 16 extra legs we need, so we divide 16/2 giving us 12 chickens and 8 rabbits.

The expression 350 ml is equivalent to approximately 11.83 fluid ounces (fl oz).

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

350 ml = x oz

To convert milliliters to fluid ounces

We can use the conversion factor of 1 milliliter = 0.033814 fluid ounces.

So, to convert 350 ml to fluid ounces, we can multiply 350 by 0.033814, which gives us:

350 ml x 0.033814 fl oz/ml = 11.83 fl

So, 350 ml is approximately equal to 11.83 fluid ounces.

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The two equations that are true for x = –2 and x = 2 are:

x2 – 4 = 0 (true for x = –2) and 4x2 = 16 (true for x = –2 and x = 2)

Quadratic equation can be defined as equation in which it is in the form of[tex]ax^2+bx+c = 0[/tex]

The options are:

x2 – 4 = 0

x2 = –4

3x2 + 12 = 0

4x2 = 16

2(x – 2)2 = 0

To check which equations are true for x = –2 and x = 2, we can substitute these values into each equation and see if it results in a true statement or not.

Substituting x = –2:

(-2)2 – 4 = 0 --> True

(-2)2 = –4 --> False

3(-2)2 + 12 = 0 --> True

4(-2)2 = 16 --> True

2((-2) – 2)2 = 0 --> False

Substituting x = 2:

22 – 4 = 0 --> False

22 = –4 --> False

3(2)2 + 12 = 0 --> False

4(2)2 = 16 --> True

2((2) – 2)2 = 0 --> True

Therefore, the two equations that are true for x = –2 and x = 2 are:

x2 – 4 = 0 (true for x = –2) and 4x2 = 16 (true for x = –2 and x = 2)

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Answer:

Step-by-step explanation:

1 yard = 1/2in shadow

Then 8ft = 192 * 1/2in

Then the radio tower is 192 yards (1 yard = 3 feet)

The radio tower = 576 feet

Answer:

Step-by-step explanation:

576

The BSA or Body surface area can be calculated by the formula is as follows: Body Surface Area= 0.007184 x (Height(m)^0.725) x (Weight(kg)^0.425)

Body surface area was developed as a metric to be used as such in the modulation of many various pharmaceutical treatments and as a standard index to various physiological measurements like glomerular filtration rate and cardiac output.

The Du Bois and its formula is one of the most widely used methods to determine a person's body surface area, in despite the fact that there are actually numerous variations on this concept. In the measurement of physiological and pharmacological data, the body surface area metric is much highly valued. The most typical reference point for chemotherapeutic drug dosing is body surface area.

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The volume of the solid generated when the region bounded by y = 9x and y = 27x/x is revolved around the x-axis is given by V = 27lnx - 9x + c

To calculate this volume, we need to calculate the area of the cross-section of a shell at x.

The cross-section is found by taking the difference of the two curves, y = 9x and y = 27x/x, at that particular x in the form of a rectangle.

The height of the rectangle is y₂ - y₁ and the width is the interval dx. Therefore, the area of the cross-section is given by

A(x) = (y₂ - y₁)dx = [(27x/x - 9x)dx].

The volume of the solid is then given by the formula

=> V = ∫A(x)dx.

Substituting in the expression for A(x), we have

=>  V = ∫(27x/x - 9x)dx.

Integrating this expression, we get V = 27lnx - 9x + c, where c is an arbitrary constant.

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Answer: 52.64

Step-by-step explanation: add 18.9 and 33.74

The Rational Roots Theorem identifies possible rational roots of a polynomial equation in terms of factors of its coefficients.

The Rational Roots Hypothesis, otherwise called the Judicious Zeros Hypothesis, is a numerical hypothesis that assists with recognizing conceivable objective foundations of a polynomial condition. In particular, that's what it expresses on the off chance that a polynomial condition with number coefficients has a sane root, that root should be of the structure p/q, where p is a variable of the consistent term and q is an element of the main coefficient.

For instance, in the event that a polynomial condition has the structure ax^3 + bx^2 + cx + d = 0, and the main coefficient an and the consistent term d are numbers, then, at that point, the conceivable sane foundations of the situation are the quantities of the structure p/q, where p is a component of d and q is a variable of a.

The Normal Roots Hypothesis is valuable in tackling polynomial conditions and deciding if they have reasonable roots.

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(a) To find the probability that a randomly selected adult who visited a therapist during the past year also used antidepressants, we use the formula:

P(A|B) = P(A and B) / P(B)

where A is the event that an adult used antidepressants, and B is the event that an adult visited a therapist. We are given:

P(A) = 0.43

P(B) = 0.27

P(A and B) = 0.20

Plugging these values into the formula, we get:

P(A|B) = 0.20 / 0.27 ≈ 0.74

Therefore, the probability that a randomly selected adult who visited a therapist during the past year also used antidepressants is approximately 0.74.

(b) To find the probability that an adult visited a therapist during the past year, given that he or she used antidepressants, we use Bayes' theorem:

P(B|A) = P(A|B) * P(B) / P(A)

where A and B are defined as before. We have already calculated P(A|B) and P(B), and we know:

P(A) = 0.43

Plugging these values into Bayes' theorem, we get:

P(B|A) = (0.74 * 0.27) / 0.43 ≈ 0.47

Therefore, the probability that an adult visited a therapist during the past year, given that he or she used antidepressants, is approximately 0.47.

A two-sample t-test is a statistical test used to determine if there is a significant difference between the means of two independent groups or populations.

In research and experimental investigations, the two-sample t-test is frequently used to assess if there is a statistically significant difference between the mean values of two samples or groups.

The average test results of two separate student groups, for instance, may be compared by a researcher to see if one group performs noticeably better than the other.

The two-sample t-test makes the assumption that the two samples are independent, have nearly normal distributions, and have identical variances.

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Using the theorem of angle around a point, the value of GHJ is 237 degrees

When we talk about the "angle around a point," we are usually referring to the total angle formed by two or more lines or line segments that intersect at a common point, known as the vertex.

Specifically, the "angle around a point" is equal to 360 degrees or 2π radians. This is because, when two or more lines intersect at a point, they form multiple angles, and the sum of these angles is always equal to 360 degrees or 2π radians.

Since we know that FPJ and JPI are congruent, this implies that they're equal to one another. We can find the value by setting them as x

x + x + 51 + 66 + 99 = 360

Reason: The sum of angles around a point is equal to 360 degrees

2x + 216 = 360

2x = 360 - 216

2x = 144

x = 72

The value of FPJ and JPI is 72.

The value of GHJ is is equal to 66 + 99 + 72 = 237°

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Answer:

-10 - 4i

Step-by-step explanation:

We can rewrite the equation as (by getting rid of parentheses):

-8 + 3i - 2 - 7i

Now, we can add/subtract the values:

(-8-2) + (-7i+3i)

= -10 - 4i

You are 1 meter behind the fixed point.

The total path length covered by the moving body is called distance covered.

Given is that you move on a rectilinear track and move from a fixed point 12 meters to the right, advance in the same direction 5 meters and then return in the opposite direction 18 meters.

Total displacement = 12 + 5 - 18 = - 1

So, you are 1 meter behind the fixed point.

Therefore, you are 1 meter behind the fixed point.

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{Question in english -

Suppose you move on a rectilinear track and move from a fixed point 12 meters to the right, advance in the same direction 5 meters and then return in the opposite direction 18 meters, the distance between the fixed point and you is}

Refer to the images attached.

Answer:

Step-by-step explanation:

The function to represent the population of bacteria after t days can be written as:

P(t) = P0 * (1 + r)^t

where P0 is the initial population (7500), r is the daily growth rate (14% = 0.14), and t is the number of days.

Substituting the values, we get:

P(t) = 7500 * (1 + 0.14)^t

Simplifying, we get:

P(t) = 7500 * 1.14^t

To find the percentage rate of change per hour, we need to convert the daily growth rate to an hourly growth rate. Since there are 24 hours in a day, the hourly growth rate, denoted by h, is given by:

h = (1 + r)^(1/24) - 1

Substituting the value of r, we get:

h = (1 + 0.14)^(1/24) - 1

= 0.005521

So, the percentage rate of change per hour is:

h * 100% = 0.5521%

Rounding to the nearest hundredth of a percent, we get:

h * 100% ≈ 0.55%

8)

The indicated 3th root of 125 is 5.

9)

The indicated 4th root of 81 is 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

8)

∛125

5 x 5 x 5 = 125

And,

5³ = 125

So,

= ∛5³

= 5

9)

[tex]\sqrt[4]{81}[/tex]

3 x 3 x 3 x 3 = 81

And,

[tex]3^4[/tex] = 81

So,

= [tex]\sqrt[4]{3^4}[/tex]

= 3

Thus,

8)

∛125 is 5.

9)

[tex]\sqrt[4]{81}[/tex] is 3.

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Answer:

yeah sure, what you need?