Rewrite the expression with a rational exponent as a radical expression.
(3 2/3)1/6

Answer:

a) 0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.

b) 0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.

c) 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 7.7 grams per mililiter.

This means that \(\mu = 65, \sigma = 7.7\)

a. What is the probability that the amount of collagen is greater than 60 grams per.

This is 1 subtracted by the pvalue of Z when X = 60. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{60 - 65}{7.7}\)

\(Z = -0.65\)

\(Z = -0.65\) has a pvalue of 0.2578

0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.

b. What is the probability that the amount of collagen is less than 90 grams per.

This is the pvalue of Z when X = 90.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{90 - 65}{7.7}\)

\(Z = 3.25\)

\(Z = 3.25\) has a pvalue of 0.9994

0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.

c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?

Between Z = 1 and Z = -1, so the proportion is the pvalue of Z = 1 subtracted by the pvalue of Z = -1

Z = 1 has a pvalue of 0.8413

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826*100% = 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean

Answer:

Each student receives $70 dollars each.

Step-by-step explanation:

Answer:

I think the answer is 16 cupcakes are not vanilla

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

First is you divide 24 by 6 then you get 4 so 1/6 is equal to 4 cupcakes. That means 2/6 is 8 cupcakes. Last you do 24-8 and you get 16.

9514 1404 393

Answer:

  18 units

Step-by-step explanation:

The distance formula is used to find the distance between two points:

  d = √((x2 -x1)² +(y2 -y1)²)

For AB, the distance is ...

  d = √((0 -(-4))² +(-2 -1)²) = √(16 +9) = √25 = 5

The distances between the other pairs of points can be found the same way. We have elected to let a spreadsheet do the math. It tells us the perimeter of triangle ABC is 18 units.

Answer: 18 units

Step-by-step explanation:

Answer:

The answer is 49

Step-by-step explanation:

We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.

We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:

14/42 = 0.3333

We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:

0.3333 * 147 = 49

Therefore, the best estimate for the number of dogs that suffer from the disease is 49.

Answer:

use sin to find the angle x

Answer:

We can use the triginotemtric ratio inverse cos to solve this problem.

Cos=adjacent side/hypotenuse

cos(h)=21/69

\(cos^-1(21/69)=x\\cos^-1(0.30434782608) \\x=72\)

Step-by-step explanation:

Answer:

3 and 23 Over 32

Step-by-step explanation:

Done

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.

.

.

.

.

Answer:

Stephanie

Step-by-step explanation:

Answer:

steaphanie im pretty sure

Step-by-step explanation:

Answer:

it is 20

Step-by-step explanation:

well the angles looks the same

Answer:

x=20[vertically opposite angle are equal]

Answer:

the explanatory variable is "the amount of practice every year" while the response variable is "the improvement in his game"

Step-by-step explanation:

In simple terms, the difference between explanatory and random variable is that the response variable is usually the focus of a question in a study/experiment while an explanatory variable is a variable that explains changes in the response variable. Which means that the explanatory variable is simply any variable that may affect the response variable.

Now, in this question, the golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.

This means that the amount of practice every year explains how much he improves every year.

Thus, the explanatory variable is "the amount of practice every year" while the response variable is "improvement in his game"

Answer:

Angle ABC,

Step-by-step explanation:

Please give more detail to your question, this doesn't help at all...

The value of u is 2 in the given right-angled triangle.

The given figure is a right-angled triangle with hypotenuse 'u' and the other two sides as \(\sqrt{2}\) and v.

We have to find the value of 'u' using Pythagoras theorem or trigonometric identities.

It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In a right-angled triangle ABC, if

BC = hypotenuse

AC and AB are the other two sides then,

\(BC^2 = AC^2 + AB^2\).

For this problem, we can find the value of u by using trigonometric identities.

From the figure, we have an angle of 45°.

Consider Cos 45°.

Cos Ф = base / hypotenuse

Cos 45° = \(\sqrt{2}\) / u ...........(1)

From trigonometric identities of cosine.

We have,

Cos 45° = 1 / \(\sqrt{2}\)............(2)

From (1) and (2)

We get,

1 / \(\sqrt{2}\) = \(\sqrt{2}\) / u

u = 2.

Thus the value of u is 2 in the given right-angled triangle.

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Answer:

19531250

Step-by-step explanation:

I hope it helps

Answer: Let's start by defining some variables:

Let x be the average yearly salary of an individual with a bachelor's degree.

Let y be the average yearly salary of an individual with a master's degree.

We are told that the average yearly salary of an individual with a master's degree is $35 thousand less than twice that of an individual with a bachelor's degree. This can be expressed mathematically as:

y = 2x - 35000

We are also told that two people with each of these educational attainments earn $115 thousand in total. Since we don't know how many people there are with each degree, let's call the number of individuals with a bachelor's degree "b" and the number of individuals with a master's degree "m". Then we can write:

bx + my = 115000

We can use this equation to solve for one of the variables in terms of the other. Let's solve for b:

b = (115000 - my) / x

Now we can substitute this expression for b into the first equation we wrote:

y = 2x - 35000

and solve for x:

(115000 - my) / x * x + my * (2x - 35000) = 115000

Simplifying this equation, we get:

115000 - my + 2mx - 35000x = 115000

Rearranging and simplifying further, we get:

(2m - 35)x = my

Substituting the expression for b that we found earlier, we get:

(2m - 35)x = (115000 - my) / x * y

Multiplying both sides by x, we get:

(2m - 35)x^2 = (115000 - my) * y

Substituting y = 2x - 35000, we get:

(2m - 35)x^2 = (115000 - my) * (2x - 35000)

Expanding and simplifying this expression, we get:

2mx^2 - 35x^2 = 230000x - myx - 115000y

Substituting y = 2x - 35000 again, we get:

2mx^2 - 35x^2 = 230000x - myx - 115000(2x - 35000)

Expanding and simplifying, we get:

2mx^2 - 35x^2 = 28000x - 115000(35000) + myx

Substituting b = (115000 - my) / x, we get:

2mx^2 - 35x^2 = 28000x - 115000(35000) + x(115000 - bx)

Simplifying further, we get:

2mx^2 - 35x^2 = 28000x - 115000(35000) + x(115000 - (115000 - my) / x)

Multiplying through by x, we get:

2mx^3 - 35x^3 = 28000x^2 - 115000(35000)x + x(115000x - (115000 - my))

Simplifying further, we get:

2mx^3 - 35x^3 = 2x^2my

Now we can substitute y = 2x - 35000 again, and simplify:

2mx^3 - 35x^3 = 2x^2(2x - 35000)

Expanding and simplifying, we get:

2mx^3 - 35x^3 = 4x^3 -

Step-by-step explanation:

The value of x and y will be x =  16° and y = 20°

What is Angles?

In Euclidean geometry, an angle is the shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. The plane that contains the rays contains the angles created by two beams. The meeting of two planes might also result in an angle. Dihedral angles are what these are.

We can write

(6x + y) = (x + 5y)

[By corresponding angles]

6x + y = x + 5y

6x - x = 5y - y

5x = 4y

x = 4y/5

Now by linear pair

4x + (6x + y) = 180

4x + 6x +y = 180

10x + y = 180

By putting the value of x

10(4y/5) + y = 180

8y + y = 180

9y = 180

y = 180/9

y = 20°

Putting the value of y in x we get

x = 4(20) / 5

x = 4(4)

x = 16°

Hence, value of x =  16° and y = 20°

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The probability that a randomly selected item is​ defective is 0.14.

Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.

The likelihood of an occurrence can be determined by dividing the positive outcomes by the entire number of possible outcomes.

Let 'E' be an event the formula for probability is given by

P(E) = [ No of favorable outcomes ]/ [Total No. of outcomes ]

Here we have

Number of digital video recorders​ = 50

Number of defective videos recorder = 7

If we randomly selected a video recorder

Total number of outcomes = 50

The number of outcomes that we get defective video recorder = 7

Using the probability formula,

Probability of selecting defective = 7/50 = 0.14

Therefore,

The probability that a randomly selected item is​ defective is 0.14.

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The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

The graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.

If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.

In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

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a Given data:

Step 1

Jamie did mistake in step 2

2 places to the right

2 zeros

Answer:

A.) 358; 375

B.) 1074 ; 1125

C.) Both the mean and median values in feets could be obtained by just multiplying the values in yards by 3

D.) If we have our median and mean of thee original dataset in inches, we just divide the values by 36 to get our mean and median values in yard.

Step-by-step explanation:

Given the data (in yards)

Rearranged data : x (in yards) :

441, 531, 1008, 1080, 1125, 1179, 1224, 1512, 1566

Mean, m : Σx/n

ΣX = 3222 ; n = sample size, n = 9

m = 3222 / 9

m = 358

Median :

0.5(n +1) th term

0.5(9 + 1)th term

0.5(10) = 5th term = 375

Converting the data to feets :

147, 177, 336, 360, 375, 393, 408, 504, 522

1 yard = 3 feets

In Feets:

441, 531, 1008, 1080, 1125, 1179, 1224, 1512, 1566

Mean, m : Σx/n

ΣX = 9666 ; n = sample size, n = 9

m = 9666 / 9

m = 1074

Median :

0.5(n +1) th term

0.5(9 + 1)th term

0.5(10) = 5th term = 1125

C) Both the mean and median values in feets could be obtained by just multiplying the values in yards by 3

D.) since 1 yard = 36 inches

If we have our median and mean of thee original dataset in inches, we just divide the values by 36 to get our mean and median values in yard.

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

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The "ratio" is used as the scale of measure for this variable.

The ratio scale is the highest level of measurement that includes all the properties of the interval scale (equal intervals) and the true zero point. This means that with ratio data, we can not only compare the values but we can also make meaningful statements about the differences between them, and we can perform mathematical operations, such as addition and multiplication.

In this case, the ages of the respondents are recorded as whole numbers, which represent the number of years they have lived. This type of data has a true zero point, meaning that zero years of age represents an absence of the characteristic being measured. Therefore, this scale is considered a ratio scale.

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--The given question is incorrect; the correct question is

"A researcher asks the following question on a survey:

Data are displayed below: Age of respondents 90 80 70 60 50 40 9 10 20 10 0 What scale of measure is being used for this variable?

ratio

ordinal

interval

nominal"--

Answer:

Letting x be the missing length, we have

\(7 < x < 23\)

Step-by-step explanation:

According to the Triangle Inequality Theorem:

8 + x > 15 -------> x > 7

8 + 15 > x -------> x < 23

x + 15 > 8 -------> x > -7

So we have 7 < x < 23.

By taking a quotient between correspondent side lengths, we will see that the scale factor of the dilation applied to the quadrilateral is S = 4.

The scale factor of the dilation is given by the quotient between the length of one of the sides of the dilated figure and the length of the correspondent side of the original figure.

Here the original figure is the smaller quadrilateral, and the dilated figure is the larger one

If we select the top side, the length on the dilated figure is 72 inches, and the length of that side on the original figure is 18 inches, then the scale factor of the dilation is given by:

S = 72in/18in = 4

The scale factor of the dilation is 4.

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69.7

Step-by-step explanation:

627 ÷ 9

=69.66666666666666

approximately

69.7

\( \sf \leadsto627 \div 9\)

\( \\ \\ \)

\( \sf \leadsto \dfrac{627}{9} \)

\( \\ \\ \)

\( \sf \leadsto \dfrac{627 \div 3}{9 \div 3} \)

\( \\ \\ \)

\( \sf \leadsto \dfrac{209}{3} \)

\( \\ \\ \)

\( \sf \leadsto 69.67\)

The sentence that contains filler is: D. This set also includes heroes like Obi-Wan Kenobi and Anakin Skywalker, both of whom come fully-equipped with their signature lightsabers and Jedi robes. Option D

In this sentence, the phrase "also includes heroes like Obi-Wan Kenobi and Anakin Skywalker" acts as a filler. The main purpose of this phrase is to provide additional information about the set and highlight the inclusion of popular characters from the Star Wars franchise. It doesn't directly contribute to the core information about the set's features or components.

The other sentences (A, B, and C) provide specific details and descriptions about the LEGO set, such as the number of pieces, minifigures, droids, and features like the opening top hatch and cockpit. They directly convey important information about the set itself without any filler or additional unnecessary information.

In marketing or promotional contexts, fillers are often used to enhance the appeal of a product or create excitement by mentioning well-known or desirable elements that may not be directly relevant to the core features. The filler in sentence D serves to attract fans of Obi-Wan Kenobi and Anakin Skywalker by emphasizing their presence in the set and the inclusion of their iconic weapons and attire.

Option D

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Answer:D

Step-by-step explanation:

The hexagon with sides of length 5 inches, 4 inches, 4 inches, 5 inches, 3 inches, and 3 inches has a perimeter of 24 inches.

A hexagon is a regular polygon, meaning all sides and angles are equal in size. It is a symmetrical shape, which means it can be divided into two equal halves.

To calculate the perimeter of this hexagon, we must first identify the length of each side.

All sides of the hexagon have a length of either 5 inches, 4 inches, or 3 inches, as there are two sides of each length.

The perimeter of the hexagon is the sum of the length of all its sides. Adding the length of all the sides, we get

5 + 4 + 4 + 5 + 3 + 3 = 24.

Thus, the perimeter of the hexagon is 24 inches.

Hence, the sum of the length of the sides of a hexagon is always greater than the length of any one of its sides.

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