Which sample is biased?

Answer:

x-2 is a factor of following polynomials:

Step-by-step explanation:

In order to check that which polynomials might have x-2 as a factor, we will put

x-2 = 0 => x = 2 in each polynomial, if the value of polynomial on 2 is zero then x-2 is a factor otherwise not.

So,

a(x) = 6x² - 7x - 5

Putting x = 2

\(a(2) = 6(2)^2-7(2)-5\\= 6(4)-14-5\\=24-14-5\\=24-19\\=5 \neq 0\)

b(x) = 3x² + 15x - 42

\(b(2) = 3(2)^2 + 15(2) - 42\\=3(4)+30-42\\=12+30-42\\=42-42 = 0\)

c(x) = 2x³ + 13x² + 16x + 5

\(c(2) = 2(2)^3 + 13(2)^2 + 16(2) + 5\\=2(8)+13(4)+32+5\\=16+52+32+5\\=105 \neq 0\)

d(x) = 3x³ - 2x² - 15x + 14

\(d(2) = 3(2)^3 - 2(2)^2 - 15(2) + 14\\= 3(8)-2(4)-30+14\\=24-8-30+14\\=38-38 = 0\)

e(x) = 8x⁴ - 41x³ - 18x² + 101x + 70

\(e(2) = 8(2)^4 - 41(2)^3 - 18(2)^2 + 101(2) + 70\\= 8(16)-41(8)-18(4)+202+70\\=128-328-72+202+70\\=0\)

\(f(2) = (2)^4 + 5(2)^3 - 27(2)^2 - 101(2) - 70\\=16+5(8)-27(4)-202-70\\=16+40-108-202-70\\=-324 \neq 0\)

Hence,

x-2 is a factor of following polynomials:

The probability of students chosen have a cat and a dog is:P(cat and dog) = 9/25.

There are 25 students

Those that have cats 15

those that have a dog 16

while, 3 of them have neither

Take x = number of students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

Therefore, the number of students who own a cat and a dog is 9.

The probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

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In a class of 25 students, 15 of them have a cat , 16 of them have a dog and 3 of them have neither. Find the probability that a student chosen at random has a cat and a dog. Find the probability that a student chosen at random has a cat and a dog

There is a probability of 66.5 % chance of it landing on a 5 at least once in 6 dice.

Because there are six faces on a die, you have an even chance of the dice landing on one of these faces each time you roll:

This means that each time that you roll, there is a 5/6 chance that you will not roll a 5.

The probability of not rolling a 6 twice is 5/6 or 69.4%.

Roll the die six times, and the probability of not rolling a 5 is

(5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6)

= (5/6)⁶

= 33.5%

Therefore, the probability of rolling a 5 at least once in 6 dice

= 100%  - 33.5%

= 66.5%

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The value of world exports in 2010 would be worth approximately 1,151 units. To determine the value of world exports in 2010, we need to use the information about the growth rate of world exports from 1965 to 2010.

Using the compound annual growth rate (CAGR) formula, we can find the growth rate: Growth rate = (Final value / Initial value)^(1/number of years). We know that the initial value (world exports in 1965) was 10 units. We can find the final value (world exports in 2010) by multiplying the initial value by the growth rate: Final value = Initial value * (1 + growth rate)^number of years.

We can use data from the World Bank to find the growth rate of world exports from 1965 to 2010. According to the World Bank, the value of world exports in 1965 was $131 billion (in current US dollars) and the value of world exports in 2010 was $16.2 trillion (in current US dollars). The number of years between 1965 and 2010 is 45.Growth rate = ($16.2 trillion / $131 billion)^(1/45) = 1.097

Final value = 10 units * (1 + 1.097)^45 ≈ 1,151 units

Therefore, the value of world exports in 2010 would be worth approximately 1,151 units.

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(1) Every vector space V with dimension n and a generating set S contains a subset that forms a basis for V.

(2) The generating set S for a vector space V must contain at least n vectors.

(1) To prove that there is a subset of S that forms a basis for V, we can use the concept of linear independence. Since S generates V, we can start with S as a potential basis for V. If S is linearly independent, then it already forms a basis for V.

Otherwise, we can remove vectors from S that are linearly dependent on the remaining vectors until we obtain a linearly independent subset. This subset will still generate V and will form a basis for V.

(2) To prove that S must contain at least n vectors, we use the fact that the dimension of a vector space is the minimum number of vectors required to generate it. Since V has dimension n, it implies that at least n vectors are needed to generate V.

Therefore, the generating set S for V must contain at least n vectors.

These proofs highlight the fundamental properties of vector spaces and their generating sets, emphasizing the existence of bases and the relationship between the dimension of the vector space and the number of vectors needed in its generating set.

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Answer:

4

Step-by-step explanation:

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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Answer:

9(6+3) = 54+27

Step-by-step explanation:

dunno how to explain but hope the answer helps

Hey there!

54 + 27 = 81

9(6 + 3)

= 9(6) + 9(3)

= 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9

= 18 + 18 + 18 + 18 + 9

= 36 + 36 + 9

= 72 + 9

= 81

Thus, the equation answwr is: 81

Therefore, the overall answer is:

9(6 + 3)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

The inequality that is true is -5 - 3x > 10.

Step-by-step explanation:

if x = -6

we can subtitution x to every inequality, so :

-5 - 3x > 10

-5 - 3(-6) > 10

-5 - (-18) > 10

-5 + 18 > 10

13 > 10 [true]

-3 - 5x < -14

-3 - 5(-6) < -14

-3 - (-30) < -14

-3 + 30 < -14

27 < -14 [false]

2 - x < -3

2 - (-6) < -3

2 + 6 < -3

8 < -3 [false]

So if x=-6, inequality true is -5 - 3x > 10.

If this was helpful, please mark brainliest. Have a beautiful day.

Answer:

-3

Step-by-step explanation:

(-5) - (-2) = (-3)

hope it helps

Answer:

there is a three degree difference between san Diego and Los Angeles

The value r², called the coefficient of determination, measures the proportion of variability in one variable that can be determined from its relationship with the other variable.

The higher the value of r2, the more of the variation in the dependent variable can be attributed to the independent variable(s), and therefore the better the relationship between the two variables is. Overall, the coefficient of determination is an important statistical measure that is used to evaluate the strength and fit of regression models. It allows researchers to determine how much of the variation seen in the dependent variable can be explained by the independent variable(s), which can help in making predictions and drawing conclusions from the data.

It represents the strength and direction of the correlation between two variables, helping to quantify their linear association. A higher r² value indicates a stronger relationship between the variables, while a value close to zero signifies a weak or no relationship.

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The dimensions of a horizontal cross-section will vary depending on the specific shape or object being considered.

To determine the dimensions of a horizontal cross-section, we need more specific information about the object or shape in question.

A horizontal cross-section refers to a slice or cut made parallel to the horizontal plane.

The dimensions of a horizontal cross-section will depend on the shape or object being sliced. For example, if we have a rectangular prism, a horizontal cross-section would result in a rectangle.

The dimensions of this rectangle would be equal to the dimensions of the corresponding face of the prism.

If we have a cylindrical object, a horizontal cross-section would result in a circle. The dimensions of this circle would be determined by the radius or diameter of the cylinder.

It is essential to provide more information about the shape or object to determine its corresponding horizontal cross-section dimensions.

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Answer:

the answer is c uwU

Step-by-step explanation:

Here, base is the length of the side adjacent to angle   and hypotenuse is the longest side of the right angle triangle.

The length of the side adjacent to angle C is 7.67 inches or 7.7 inches. Option B shows the correct length of the side adjacent to angle C.

A right triangle or right-angled triangle is a triangle in which one angle is a right angle i. e. 90 degrees. The relation between the sides and other angles of the right triangle is the basis for trigonometry.

Given that in a right triangle, angle C measures 40°. The hypotenuse of the triangle is 10 inches long.

The attachment shows the right-angle triangle. In the triangle, hypotenuse AC = 10 inches and angle C = 40 degrees.

We need to find the value of BC.

We know that, in a right-angle triangle,

\(cos C = \dfrac {BC}{AC}\)

\(cos 40^\circ = \dfrac {BC}{10}\)

\(BC = 10 \times cos 40^\circ\)

\(BC = 7.67 \;\rm Inches\)

Hence we can conclude that the length of the side adjacent to angle C is 7.67 inches or 7.7 inches. Option B shows the correct length of the side adjacent to angle C.

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n(t) = 360 * 1.05^t. This formula assumes the growth rate of the student population remains constant at 5% per year. In reality, the growth rate may vary from year to year depending on various factors such as the school's reputation, enrollment policies, and local demographics

The formula for the function n(t) is based on the assumption that the student population grows by 5% per year. To calculate the number of students attending the charter school t years after 1994, we start with the initial number of students in 1994, which is 360, and then multiply it by 1.05 raised to the power of t.

For example, if we want to know how many students are attending the school in 2023 (29 years after 1994), we plug in t=29 into the formula:

n(29) = 360 * 1.05^29

≈ 1,188 students

This formula assumes that the growth rate of the student population remains constant at 5% per year. In reality, the growth rate may vary from year to year depending on various factors such as the school's reputation, enrollment policies, and local demographics. However, the formula provides a useful estimate of the school's enrollment over time based on a simple, consistent assumption.

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It indicates that the test is highly accurate in correctly identifying individuals with hepatitis C (high sensitivity) and accurately ruling out individuals without the disease (high specificity).

Sensitivity and specificity are two important measures of a diagnostic test's performance. Sensitivity refers to the test's ability to correctly identify individuals who have the condition, while specificity refers to its ability to correctly identify individuals who do not have the condition.

In the case of the ELISA test for hepatitis C, a sensitivity of 95% means that the test will correctly identify 95% of individuals who actually have hepatitis C as positive. This indicates a high probability of detecting the disease when it is present.

On the other hand, a specificity of 90% means that the test will correctly identify 90% of individuals who do not have hepatitis C as negative. This suggests that there is a 10% chance of a false positive result, where individuals without the disease are mistakenly identified as positive.

Overall, the high sensitivity and specificity of the ELISA test for hepatitis C make it a valuable tool in the diagnosis and screening of individuals for this infectious disease. However, it is important to consider that no test is 100% accurate, and false results can still occur. Therefore, additional confirmatory tests may be required in certain cases to ensure accurate diagnosis and appropriate medical intervention.

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The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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Answer:

What was it?

Step-by-step explanation:

The change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

To quantify the change in the area of the surface of a cube when its side length triples from s units to 3s units, we can set up an integral.

Let's denote the side length of the cube as "x". The initial side length is "s" and the final side length is "3s". We want to find the change in surface area, which is the difference between the final surface area and the initial surface area.

The surface area of a cube with side length "x" is given by 6x², as each face of the cube has an area of x² and there are 6 faces.

The change in surface area can be calculated as:

ΔA = ∫(6x²) dx,

where the integral is taken from the initial side length "s" to the final side length "3s".

Now let's evaluate the integral:

∫(6x²) dx = 2x³ + C,

where C is the constant of integration.

To find the change in surface area, we substitute the limits of integration:

ΔA = [2x³]s to 3s

= 2(3s)³ - 2s³

= 2(27)s³ - 2s³

= 52s³

Therefore, the change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

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Answer:

Step-by-step explanation:

6. how is twice a number decrease by three is negative seven written as a question A. 2+×_3=7 B. 2×_3=7 C. ×2-3=7 D. (×-3)2=-7​

Answer: 67.27

Step-by-step explanation:

7.1 x 7.1 for the square = 50.41

7.1 divided by 2 = 3.55

3.55 x 4.75= 16.86

Normally here you would divide by 2, but you don’t need two because there is 2 triangles that are the same

Add the 50.41 and the 16.86 and you have your answer!

The trigonometric ratios for the cosine and tangent of the angles can be used to find the sides labeled x in the right triangles with the approximate values presented as follows;

7. 40.9

8. 13

9. 6.9

10. 46.7

11. 23

12. 21.6

Trigonometric ratios are the expression of the relationship between an interior angle and two of the sides of a right triangle.

Whereby the first part is question 7, the trigonometric ratios of the angles indicates that we get;

7. cos(67°) = 16/x

x = 16/(cos(67°)) ≈ 40.9

8. cos(30°) = x/15

x = 15 ×(cos(30°)) = 15×√3/2 ≈ 13

9. tan(60°) = 12/x

tan(60°) = √3

Therefore; √3 = 12/x

x = 12/√3 = 4·√3 ≈ 6.9

10.  tan(70°) = x/17

x = 17 × tan(70°) ≈ 46.7

11.  tan(41°) = 20/x

x = 20/(tan(41°)) ≈ 23

12.  tan(59°) = x/13

x = 13 × tan(59°) ≈ 21.6

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Answer:

the 45th customer.

Step-by-step explanation:

9•1= 9  9•2=18  9•3=27  9•4=36  9•5=45

5 doesn't go into any other number except for 45.

The first customer to receive both a free bagel coupon and a free drink coupon is the 45th customer.

To find the first customer who receives both coupons (a free bagel coupon and a free drink coupon), we need to determine the least common multiple (LCM) of 5 and 9, which represents the point at which both coupon distributions coincide.

The LCM of 5 and 9 is 45.

This means that the first customer to receive both coupons will be the 45th customer. On the 45th customer, both the 5th customer and the 9th customer coincide, so this customer will receive both a free bagel coupon and a free drink coupon.

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Answer:

See below

Step-by-step explanation:

Step 2 and Step 3

Mistake #1: From step 1 to step 2 the 32 randomly changed to 9

Mistake #2: According to PEMDAS multiplication and division comes before addition and subtraction.

During step 3, 8 was added to -6 before 8 was multiplied by 7 which is incorrect as the multiplication should come first.

The real answer should be....

-6 +8(11 - 4)+ 32

Evaluate using PEMDAS

Parenthesis

Exponents

Multiplication and division (left to right)

Addition and Subtraction (left to right)

-6 +8(11 - 4)+ 32

First do the operations inside of the parenthesis. ( Subtract 4 from 11 )

-6 + 8(7) + 32

There are no exponents so we go to the next step.

Next is multiplication.

Multiply 8 and 7

- 6 + 56 + 32

Finally we do the addition and subtraction going left to right.

First add 56 to -6

50 + 32

Then add 50 and 32

= 82

Answer: Step 2 and Step 3.

From step 1 to step 2 the "32" unexpectedly changes into a "9" for no reason.

Step 3 also has a mistake due to misusing PEMDAS, as 6 is removed from the 8(7) to get 2. The 6 should be removed from the 32 instead.

Correct step-by-step explanation:

\(-6 + 8(11-4) + 32\\=-6+8(7)+32\\=-6+8(7)+32\\=8(7)+26=56+26\\=82\)

The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

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Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data is a true statement.

Therefore, it is true that extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that outside the x-range.

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Answer:

g = 5

Step-by-step explanation:

6(g-3)=12

6g-18 = 12

6g = 30

g = 5

Answer:

g = 5

Step-by-step explanation:

→ Expand the bracket

6g - 18 = 12

→ Add 18 to both sides to isolate 6g

6g = 30

→ Divide both sides by 6 to isolate g

g = 5

The new function of T that models the real-world situation in terms of N is T = 560N + 750

The equations of the functions are given as

A = 165N + 750

B = 395N

From the question, we understand that

T = A + B

Substitute the known values in the above equation

So, we have

T = 165N + 750 + 395N

Collect the like terms in the above equation

So, we have

T = 165N + 395N + 750

Evaluate the like terms in the above equation

So, we have

T = 560N + 750

Hence, the new function of T that models the real-world situation in terms of N is T = 560N + 750

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Answer: its 6.9 ft

Step-by-step explanation:

Answer:

it is typically 22 to 7

Step-by-step explanation:

if you divide 22 by 7 you get 3.142857143...

Answer:

  22/7

Step-by-step explanation:

You want to know a ratio commonly used as an alternative to 3.14 for an approximation to pi.

The value 3.14 as an approximation of pi is obtained by simply truncating the value to 2 decimal places. That makes the approximation lower than the actual value by about 0.0507%.

Rational approximations can be found from the expression of pi as a continued fraction. Truncating that fraction at various points gives the approximations ...

  22/7 . . . . high by about 0.0402%

  333/106 . . . . low by about 0.0026%

  355/113 . . . . . high by about 0.0000085%

22/7 is the most commonly used rational approximation of pi instead of 3.14.

__

Additional comment

The continued fraction is non-repeating. It starts ...

  \(3+\cfrac{1}{7+\cfrac{1}{15+\cfrac{1}{1+\cfrac{1}{292+\cfrac{1}{1+\dots}}}}}\)