find the minimum sample size needed to be 95% confident that the sample's variance is within 20% of the population's variance.

We are aware that the researchers estimated that the fatty acid eicosadienoic acid made up 0.07 percent by mass of a 12-gram sample of an orchid plant.

Therefore, the mass of the acid in this sample is 0.0084 grams, or 0.07% of 12 grams.

Therefore, this orchid sample's mass of eicosadienoic acid is 0.0084 grams.

Using the formula 0.07% of 12 grams, we can determine the mass of acid in this orchid sample.

In this orchid sample, eicosadienoic acid has a mass of 0.0084 grams.

It is the most fundamental property of matter and one of the fundamental quantities in physics. Mass can be defined as the amount of material in a body. The kilogram (kg) is the SI unit of mass. Note: A body's mass remains constant over time.

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No, a statistically significant result would not allow the researchers to conclude that receiving treatments at the clinic selected in part (a-ii) causes a higher percentage of successful treatments than at the other clinic.

The study design is a comparison of the success rates of the two clinics without controlling for any other variables that may influence the results. In order to conclude that the clinic you selected causes higher success rates, the researchers would need to control for other variables, such as the types of treatments, the types of patients, the experience of the clinicians, etc.

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A type II error is when you fail to reject a false null hypothesis. This means that you conclude that the null hypothesis is true, even though it is actually false. This error occurs when you do not have sufficient evidence to reject the null hypothesis, and you end up accepting it as true.

Here are the possible options for type II errors:

1.Failing to reject a false null hypothesis (correct answer).

2.Accepting a false alternate hypothesis.

3.Rejecting a false null hypothesis.

4.Rejecting a false alternate hypothesis.

A hypothesis is a tested assertion about the relationship between two or more variables or a theory put up to explain an observed occurrence in a scientific environment.

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We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the hypotenuse c: [1]

a^{2}+b^{2}=c^{2},

So mark the given triangle as ABC in which B is right angled.

AC=24+x

Mark the height of the given triangle as BD and BD=14.

Now using pythagoras theorem,

    (BC)2=(CD)2 + (BD)2

     ⇒(BC)2=(24)2 + (14)2

      ∴(BC)2=772

Now after finding BC we need to find AB using pythagoras theorem.

     (AD)2 +(BD)2 =(AB)2

  ⇒(x)2 + (14)2 =(AB)2 - eq1

  ⇒ (AB)2 + (BC)2 = (24+x)2 - eq2

Substitute eq1 in eq2

⇒(x)2 + (14)2 + (BC)2 =(24+x)2

⇒(x)2 + 576 +772 = 576 + (x)2 + 48x

⇒772=48x

∴x=16.0833

x≈16.

We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.

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64grams of bismuth-214 must be prepared if the shipping time is 120minutes.

What is half cycle?

Time required for a quantity to reduce to half of its initial value is termed as half life. It can help us to know how quickly unstable atoms undergo radioactive decay. This is used generally to characterize any type of exponential decay. It occurs when unstable atomic particles lose energy. Twenty-nine elements are capable of this process.

Rutherford applied the principle of a radioactive element's half-life in the age determination of rocks by calculating the decay period of radium to lead-206.

Given half life of 20min of 1g of Bismuth-214

If the shipping time is 120minutes, then

10min/20min/half life

=6 half life

=1/2^6=1/64

Grams of bismuth-214 that can be prepared in 120 min,

=1gm*64

=64grams.

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The slope intercept form of the equation is y = -1/3 x - 13/3

What is an equation of a line?

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.

Given equation of the line is y = 3x - 5 .

Compare the equation with y = mx + c

m = 3 and c = -5

The slope of the line that perpendicular to the given line is - 1/m = - 1/3

The equation of line that passes through the point (x₁, y₁)  with slope m is y -  y₁ = m (x - x₁).

Given point is (8,-7).

Putting m = - 1/3, x₁ = 8, y₁ = -7 in y -  y₁ = m (x - x₁):

y -  (-7) =  - 1/3 (x - 8)

Rewrite the above equation in the form y = mx + c:

y + 7 = -1/3 m + 8/3

Subtract 7 from both sides:

y  = -1/3 m + 8/3 - 7

y  = -1/3 m - 13/3

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The percentile rank of a core of 71 in the given test is 26.67% and the score of Viktor for the 60th percentile is 85.

The formula for calculating the percentile rank of a set of data is

percentile rank for 'x' = (number of data values below 'x')/total number of data values × 100 i.e., Percentile rank = n/N × 100.

The formula for calculating the percentile is

percentile = rank × total number of data values

Where rank = percentile ÷ 100

A teacher recorded unit 4 test scores from her class.

The scores data is as follows:

58, 64, 68, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

So, the total number of data values N = 15

The percentile rank for a score of 71 on this test is

The number of data values below score 71 is n = 4

Then,

Percentile Rank = n/N × 100 = 4/15 × 100 = 26.67%

Viktor's score, when he is in the 60th percentile is

percentile = rank × 15

Rank = 60 ÷ 100 = 0.6

⇒ percentile = 0.6 × 15 = 9

The data value after 9 positions from the left to right in the data set is 85. So, the score in the 60th percentile is below 85.

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The unit of measure for roll batt insulation is usually in square feet. On the estimate, you should note the type of insulation being used, the type of coverage being provided, the cost of the insulation, and any installation fees.

Roll batt insulation is a type of insulation that is often used to insulate walls, attics, and other areas of the home. The unit of measure for roll batt insulation is usually in square feet. When getting an estimate for the cost of the insulation, it is important to note the type of insulation being used, the type of coverage being provided, the cost of the insulation, and any installation fees that may be involved. This type of information should be noted on the estimate in order to ensure that you are getting the most accurate estimate for the insulation that you need.

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The value of x in the triangle is 140 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Applying the exterior angle theorem,

40 + 100 = x

140 = x

x = 140 degrees.

Therefore, x is 140 degrees.

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Answer:

2.8mm

Step-by-step explanation:

using the sine rule.

Answer:

Step-by-step explanation:

red

Answer:

2

Step-by-step explanation:

4 green balls

5%

would equal 2

Step-by-step explanation:

S=6a^2

294=6a^2

294/6=a^2

a^2=49

a=

[tex] \sqrt{49} [/tex]

a=7

V=a^3

V=7^3

V=343cm3

The accuracy of the given test for meningitis is; 95%

The accuracy of a test is gotten by dividing the number of correct results  by the number of tests.

In this problem, there were 80 volunteers who took the tests, of which the number that had correct results is;

80 - 2 - 2 = 76

Thus, the accuracy is given by:

A = 76/80 = 0.95 = 95%.

That gives us the accuracy of the meningitis test.

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Answer:

-3

Step-by-step explanation:

The formula for the rate of change (slope) between two points is:

[tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]      
So, we plug in the two points:

[tex]\frac{-20-(-5)}{6-1} =\frac{-15}{5} =-3[/tex]
The rate of change is -3

To solve this problem, we can use the Pythagorean theorem to find the height of the balloon. In particular, we can consider the right triangle formed by the stake, the top of the balloon, and the part of the string that is attached to the stake.

[asy]

unitsize(2 cm);

pair A, B, C, D, E;

A = (0,0);

B = (0,8);

C = extension(A,B,A+(1,0),B+(1,0));

D = extension(A,C,A+(0,1),C+(0,1));

E = extension(B,D,B+(0,-1),D+(0,-1));

draw(A--B--C--cycle);

draw(A--D--E--cycle);

draw(rightanglemark(A,D,C,2));

label("$A$", A, S);

label("$B$", B, N);

label("$C$", C, E);

label("$D$", D, E);

label("$E$", E, W);

[/asy]

Let $a$ be the distance from the stake to the top of the balloon, $b$ be the height of the balloon, and $c$ be the length of the string. We know that $a = 8$ feet and $c = 15$ feet, so we can use the Pythagorean theorem to find $b$:

$a^2 + b^2 = c^2$

$8^2 + b^2 = 15^2$

$64 + b^2 = 225$

$b^2 = 161$

$b = \sqrt{161} = \boxed{12.8}$ feet

Therefore, the height of the balloon is approximately 12.8 feet.

The series of transformations that map figure T onto figure U will be first rotated and then translate.

A point, line, or numerical figure can be changed over in one of four ways, and each meaningfully affects the item's construction or potential position. Picture, after interpretation, alludes to the article's definitive association and arrangement. Not long before the alludes to the material's underlying condition.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

The series of transformations that map figure T onto figure U will be first rotated and then translate.

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Ahmed needs 8 cups of yogurt and 4 cups of milk corresponding to the 12 cups of mango,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Ingredient of mango lassi,
3 cups of mango,
2 cups of yogurt,
1 cup of milk,

So,
3 cups of mango = 2 cups of yogurt
1 cup of mango = 2 / 3 cups of yogurt,
12 cups of mango = 12 (2/3) yogurt
                           = 8 cups of yogurt

Now,
3 cups of mango = 1 cup of milk
1 cup of mango = 1/3 cup of milk
12 cup of mango = 12 / 3 cup of milk
12 cup of mango = 4 cups of milk

Thus, Ahmed needs 8 cups of yogurt and 4 cups of milk corresponding to the 12 cups of mango.

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Answer:

1/125

Step-by-step explanation:

Answer:

1\/125 and 1/5^3

Step-by-step explanation:

The statement about the polynomial is an example of deductive reasoning. This is shown by the Option labelled A

We know that the term deductive reasoning has to do with the kind of knowledge that we arrive at by the consideration of the facts of the problem that has been set before us.

In effect, we can be able to define deductive reasoning as a kind of reasoning that moves from the general to the particular. We are looking at the fact that the result that we have in the given instant is obtained after the consideration of a more general proposition.

In this case, we have been told that the remainder would be zero based on the kind of polynomial that we have and this has been induced by looking at the polynomial.

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Answer:

solve each of the following equations in as many ways as you can. Answer that questions that follow y

Answer:

15 more blue bulbs

Step-by-step explanation:

3 : 5 = 45 : b

b = 45 · 5 / 3

b = 15 · 5

b = 75

total bulbs = 45 + 75 = 120

1 : 3 = w : b

(1+3) : 3 = (w + b) : b

4 : 3 = 120 : b

b = 120 · 3 / 4

b = 30 · 3

b = 90

90 - 75 = 15

Answer:

1) a) 0,1

b) 1,2

c) -2,1

d) -3,-2

Step-by-step explanation:

Answer:

The answer is quad 1 and quad 2 are congruent because quad 2 can be created rotating and then translating quad 1

Step-by-step explanation:

The system of equation to show Sebastian's coin is

xx + yy ≥ 15

0.1xx + 0.05yy ≤ $0.65

From the graph, the solution of the system of equation is (-2, 7)

The equation to represent the information is written bearing in mind that

10 dimes  = 1 dollar = 20 nickels

1/10 = 0.1

1/20 = 0.05

let the dimes be xx and the nickels be yy

Sebastian has at least 20 coins worth at most $0.65 combined, is represented as

xx + yy ≥ 15

0.1xx + 0.05yy ≤ $0.65

the graph shows the solution to be the solution is (-2, 7)

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so, she has three boards, 36, 39 and 42 inches, hmmm but she wants the length or longer side to be 3.25 ft, hmmm 36 ÷ 12 is just 3, so that won't do, 42 ÷ 12 is 3.5 ft, nope not that one, 39 ÷ 12 is 3.25, well, that's our board.

so the width has to be smaller than the length, and it has to be a full board, so since we used the 39 incher already, smaller than 39 is 36, so we'll use the 36 incher for the width, that is, the 3 feet one.

From the 3rd board, Mia is going to have to make it match with the 36 incher, that means she needs to saw it off by 6 inches, 42 - 6 = 36, and 6 inches is just 6 ÷ 12 = 0.5 feet.

Check the picture below.

Polynomial function of least degree with integral coefficients that has the given zeros imaginary [tex]\\f(x) & =x^4+5 x^2-6[/tex]

As per the given data:

[tex]\sqrt{6} i$[/tex] is a zero.

Therefore [tex]$-\sqrt{6} i$[/tex] is also a zero.

[tex]$(x+1),(x-1),(x-\sqrt{6} i)$[/tex] and [tex]$(x+\sqrt{6} i)$[/tex] are factors

[tex]$$\begin{aligned}f(x) & =(x+1)(x-1)(x-\sqrt{6} i)(x+\sqrt{6} i) \\& =\left(x^2-1\right)\left(x^2-(\sqrt{6} i)^2\right) \\& =\left(x^2-1\right)\left(x^2-6 i^2\right) \\& =\left(x^2-1\right)\left(x^2+6\right) \\& =x^4+6 x^2-x^2-6 \\f(x) & =x^4+5 x^2-6\end{aligned}$$[/tex]

Therefore the polynomial function is [tex]\\f(x) & =x^4+5 x^2-6[/tex]

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Write a polynomial function of least degree with integral coefficients that have the given zeros of-1, 1, and i times square root of 6.

Answer:

x = 5

Step-by-step explanation:

x + 5 = 10  Subtract 5 from both sides

x + 5 - 5 = 10 - 5

x = 5

check:

x+ 5 = 10

5 + 5 = 10

10 = 10

Value of x is 5. It is a linear equation.

An equation is said to be linear if the greatest power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the standard form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Given equation is

x+5=10

therefore, by shifting the given values

x+5=10

x=10-5

x=5

Therefore, the answer of the given equation is x=5.

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