what was the first standard metric unit of mass?

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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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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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

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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Refer to the images attached.

Answer:

yeah sure, what you need?

(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.

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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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.

Answer:

u < 11

Step-by-step explanation:

u + 7 < 18

u < 11

To solve the inequality:

u + 7 < 18

We need to isolate the variable u on one side of the inequality symbol.

Subtracting 7 from both sides, we get:

u < 18 - 7

Simplifying the right-hand side, we get:

u < 11

Therefore, the solution to the inequality is:

u < 11

In interval notation, the solution is:

(-∞, 11)

Answer: 3.93701

Step-by-step explanation:

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

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

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%

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.

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}

Anil borrowed the sum of money $12,300 on rate of 10% per annum, for a period of 5 years.

We can use the simple interest formula to solve this problem:

Simple Interest = (Principal x Rate x Time) / 100

Where,

Principal = 12,300

Rate = 10% per annum

Simple Interest = 18,450 - 12,300 = 6,150

Substituting the given values in the formula, we get:

6,150 = (12,300 x 10 x Time) / 100

Simplifying the equation, we get:

Time = (6,150 x 100) / (12,300 x 10)

Time = 5 years

Therefore, Anil borrowed the money for a period of 5 years. Simple interest is a type of interest calculation where the interest is calculated only on the principal amount borrowed or invested. It is calculated as a percentage of the principal amount, multiplied by the time period of the loan or investment. Simple interest does not take into account any interest earned on interest, unlike compound interest. It is a straightforward method used to determine the total amount to be repaid on a loan or the interest earned on an investment. Simple interest is commonly used in personal loans, small business loans, and short-term investments.

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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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Yes, 0.5 - 3(-2x - 1 over 3 + 4 + 8x) and -1.5(12x + 7) are equivalent expressions.


To prove this, we can use the distributive property:

0.5 - 3(-2x - 1 over 3 + 4 + 8x)

= 0.5 - 3(-2x/3 - 1/3 + 4/3 + 8x/3)

= 0.5 - (-6x - 1 + 4 + 24x)/3

= (0.5*3 + 6x + 1 - 4 - 24x)/3

= (-1.5*12x - 1.5*7)/3

= -1.5(12x + 7)
No, 0.5 - 3(-2x -1 over 3 +4 + 8x) and -1.5(12x +7) are not equivalent expressions.

To determine if two expressions are equivalent, we can simplify both expressions and compare them.

For the first expression, 0.5 - 3(-2x -1 over 3 +4 + 8x), we can distribute the -3 and combine like terms:

0.5 - 3(-2x) - 3(-1) - 3(3) - 3(4) - 3(8x)
= 0.5 + 6x + 3 - 9 - 12 - 24x
= -18x - 7.5

For the second expression, -1.5(12x +7), we can distribute the -1.5:

-1.5(12x) - 1.5(7)
= -18x - 10.5

As we can see, the simplified expressions are not the same, so they are not equivalent expressions.

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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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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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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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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: 52.64

Step-by-step explanation: add 18.9 and 33.74

The least common denominator is [tex](x^2-3x-4)/(x-4)(x+1) + (x^2-6x+8)/(x-4)(x-2) = 2/(x-4)(x+1)(x-2)[/tex]

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.

Reasonable expressions resemble fractions with variable denominators (and often numerators too).

For rational expressions, any value can be entered with the exception of those that set the denominator to 0 (because division by 0 is an undefinable operation).

In other words, all real numbers other than those that make a rational expression's denominator zero are included in the domain of a rational expression.

[tex]x^2-3x-4 = (x-4)(x+1)\\x^2-6x+8 = (x-4)(x-2)[/tex]

The least common denominator is: [tex](x-4)(x+1)(x-2)[/tex]

To add these two rational expressions, we need to rewrite each of them with the LCD as the denominator:

[tex](x^2-3x-4)/(x-4)(x+1) = [(x-4)(x+1)]/(x-4)(x+1)(x-2) = 1/(x-2)\\(x^2-6x+8)/(x-4)(x-2) = [(x-4)(x-2)]/(x-4)(x+1)(x-2) = 1/(x+1)[/tex]

So the sum of the numerators is 1 + 1 = 2.

Therefore,[tex](x^2-3x-4)/(x-4)(x+1) + (x^2-6x+8)/(x-4)(x-2) = 2/(x-4)(x+1)(x-2)[/tex]

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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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Answer:

$18.27 an hour

Step-by-step explanation:

To figure out how much $38,000 a year is as an hourly wage, divide $38,000 by 40 hours and 52 weeks. So if you were to work full-time, 40 hours a week, making $38,000 a year, you would earn $18.27 an hour.