Give the following definitions and theorems.
What is the span of a set B = (i, , ×n)?
span(B) =

The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.

The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips can be determined by finding the area under the normal distribution curve to the right of the mean.

To find this proportion, we can use the z-score formula:
z = (x - mean) / standard deviation

In this case, we want to find the proportion of bags that contain more than 12 ounces, so x = 12 ounces.

z = (12 - 12.5) / 0.2
z = -2.5 / 0.2
z = -12.5

Next, we need to find the cumulative probability associated with the z-score. We can use a standard normal distribution table or a calculator to find this probability.

Looking up the z-score of -12.5 in the table or using a calculator, we find that the cumulative probability is approximately 0.

Therefore, the proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.

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μ_ȳ = μ

σ_ȳ = σ/√n

Here, we want to find the sample size n such that P(|ത − μ| < 1) ≅ 0.95. Using the CLT, we can write this as:

P(|(ȳ - μ)/(σ/√n)| < 1) ≅ 0.95

We can simplify this expression by multiplying both sides by σ/√n and rearranging:

P(|ȳ - μ| < σ/√n) ≅ 0.95

Now, we can use the fact that the standard deviation σ is known to substitute σ/√n with its value of 5, and we get:

P(|ȳ - μ| < 5/√n) ≅ 0.95

The absolute value of the difference |ȳ - μ| is equivalent to the distance between ȳ and μ, which is a measure of how far the sample mean is from the population mean. We want this distance to be less than 1, so we can rewrite the inequality as:

5/√n < 1

Solving for n, we get:

n > 25

Therefore, the minimum sample size required to ensure that P(|ത − μ| < 1) ≅ 0.95 is n = 26 (rounded up to the nearest integer).

f(x) is continuous for all values of x, as it can be evaluated for any real number, including both rational and irrational numbers.

f(x) is continuous for all values of x. This means that the function can be evaluated for any real number, including both rational and irrational numbers.

For rational numbers, f(x) = 0. This is because rational numbers can be expressed as a fraction, and when a fraction is divided by itself, the result is always 1. We can express this mathematically as f(x) = x/x = 1 * 0 = 0.

For irrational numbers, f(x) = 7. This is because an irrational number cannot be expressed as a fraction, and so when an irrational number is divided by itself, the result is undefined. In this case, we can define f(x) as 7, since it is a constant value that is independent of the value of x. We can express this mathematically as f(x) = x/x = undefined * 7 = 7.

Therefore, f(x) is continuous for all values of x, as it can be evaluated for any real number, including both rational and irrational numbers.

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Answer:

yes

Step-by-step explanation:

The total cost of the vegetable seeds is $18.85

We can multiply the cost per package by the number of packets to get the total cost of the vegetable seeds.

There are 13 packages in this case, each costing $1.45 with VAT.

Cost of seeds overall equals Price per packet * Number of packages

Each box costs $1.45.

There are 13 packages total.

$1.45 * 13 is the total cost of the seeds.

We may multiply the price per package ($1.45) by the quantity of packets (13), which will get the total cost:

Total price of seeds: $1.45 multiplied by 13 equals $18.85

It's vital to remember that, as stated in the problem, tax is already included in the pricing per package. Therefore, there is no need to adjust the estimate to account for additional taxes. Given that there are 13 packets and that the price each box is $1.45, we can calculate the total cost by multiplying the number of packages by the price per package.

In order to buy all 13 packages of vegetable seeds, Kevin would need to spend the whole sum shown. In this instance, the overall expense is $18.85.

Include the appropriate unit in your response, which should be "dollars" ($).

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The greatest common factor of 24, 36 and 72 is 12.

12 is the greatest common factor of 24, 36, and 72

The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.

If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate

This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.

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Since none of the dot products are zero, triangle ΔPQR is not a right triangle. The absence of a right angle is confirmed by the dot product calculations.

To evaluate the side lengths of triangle ΔABC, we can use the distance formula between the given points.

The side lengths are as follows:

AB = √[(0 - (-1))^2 + (-2 - 0)^2 + (3 - 1)^2] = √[1 + 4 + 4] = √9 = 3

BC = √[(-4 - 0)^2 + (4 - (-2))^2 + (1 - 3)^2] = √[16 + 36 + 4] = √56 = 2√14

CA = √[(-4 - (-1))^2 + (4 - 0)^2 + (1 - 1)^2] = √[9 + 16 + 0] = √25 = 5

To determine whether triangle ΔPQR is a right triangle, we can check if any of the three angles are right angles. We can calculate the dot product between the vectors formed by the sides of the triangle and see if the dot product is zero.

Vector PQ = (2 - 3, 0 - 1, 3 - (-1)) = (-1, -1, 4)

Vector PR = (1 - 3, 1 - 1, 1 - (-1)) = (-2, 0, 2)

Vector QR = (1 - 2, 1 - 0, 1 - 3) = (-1, 1, -2)

Now, calculate the dot products:

PQ · PR = (-1)(-2) + (-1)(0) + (4)(2) = 2 + 0 + 8 = 10

PR · QR = (-2)(-1) + (0)(1) + (2)(-2) = 2 + 0 - 4 = -2

QR · PQ = (-1)(-1) + (1)(1) + (-2)(4) = 1 + 1 - 8 = -6

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Russ Krieger, Don Hicks, Pamela Drake, and Stephanie Braun are the four friends who received sports scholarships. Krieger has a full ride as a star in two different sports.

Based on the given clues, we can deduce the full names of the four friends who received sports scholarships.

From clue 1, we know that Hicks and Russ play on the same men's volleyball team. Therefore, one of the friends must be Don Hicks.

From clue 2, we learn that Drake and Braun have both set women's records in swimming. Therefore, one of the friends must be Stephanie Braun.

From clue 3, it is stated that Stephanie and Drake went to the same high school. Combining this information with clue 2, we can conclude that Pamela Drake is the full name of one of the friends.

Lastly, we know that Krieger has a full ride because he is a star in two different sports. Since the other three friends have been assigned their full names, it follows that Russ Krieger is the remaining friend.

In summary, the four friends who received sports scholarships and their full names are: Russ Krieger, Don Hicks, Pamela Drake, and Stephanie Braun.

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The full names of the friends based on the provided clues are Russ Hicks, Pamela Drake, Stephanie Braun, and Don Krieger.

The question involves a puzzle which requires using deduction and logical thinking skills to solve, typically found in mathematics problems.

Based on the clues provided:

Thus, the full names of the friends are Russ Hicks, Pamela Drake, Stephanie Braun, and Don Krieger.

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Rounding to 3 decimal places, the primary root of (4-3i)^(1/5) is approximately:

(4-3i)^(1/5) = 1.380(cos(-0.129) + i sin(-0.129))

To find the primary root of the complex number (4-3i)^(1/5), we can use the polar form of complex numbers.

First, we need to find the modulus (or absolute value) and the argument (or angle) of the complex number (4-3i):

|4-3i| = sqrt(4^2 + (-3)^2) = 5

Arg(4-3i) = arctan(-3/4) = -0.6435 (rounded to 4 decimal places)

Next, we can write the complex number (4-3i) in polar form as:

4-3i = 5(cos(-0.6435) + i sin(-0.6435))

To find the primary root, we need to take the fifth root of the modulus and divide the argument by 5:

|4-3i|^(1/5) = 5^(1/5) = 1.3797 (rounded to 4 decimal places)

Arg(4-3i) / 5 = -0.1287 (rounded to 4 decimal places)

Finally, we can write the primary root in rectangular form by multiplying the modulus by the cosine of the argument divided by 5 for the real part and multiplying the modulus by the sine of the argument divided by 5 for the imaginary part:

(4-3i)^(1/5) = 1.3797(cos(-0.1287) + i sin(-0.1287))

Rounding to 3 decimal places, the primary root of (4-3i)^(1/5) is approximately:

(4-3i)^(1/5) = 1.380(cos(-0.129) + i sin(-0.129))

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Average love of cats is not significantly different from average love of school, but increased love of cats is associated with increased love of school.

If there were zero correlation, the probability of increased love of cats being reliably associated with increased love of school on this 5-point scale would decrease.

The answer to question 1 is: The result of this analysis shows that, on this 5-point scale, the average love of cats is probably not significantly different from the average love of school, but increased love of cats is reliably associated with increased love of school.

The answer to question 2 is: If there were zero correlation between the love of cats and the love of school on this 5-point scale, the average love of cats is probably significantly different from the average love of school, and increased love of cats is probably not reliably associated with increased love of school compared to the observed correlation (R = 0.03) or a larger correlation between the two variables.

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The statisticians evaluate all of the above options: A. The population being measured, B. The method used for the survey, and C. The outcome of the survey.

To measure the quality of a survey, statisticians consider various factors related to the survey process and its outcomes. Evaluating only one aspect may not provide a comprehensive understanding of the survey's quality.

A. The population being measured: The quality of a survey depends on how well the target population is defined and represented.

Statisticians assess whether the chosen population accurately reflects the intended group and if any biases or sampling errors are present.

B. The method used for the survey: The survey methodology plays a crucial role in obtaining reliable and valid data.

Statisticians assess the survey design, sampling techniques, data collection methods, questionnaire quality, and other factors to determine if the chosen method is appropriate and likely to yield accurate results.

C. The outcome of the survey: The survey's outcomes are analyzed to evaluate the quality of the data collected. This includes examining response rates, data completeness, measurement validity, reliability, and other statistical measures.

Statisticians assess the overall quality and integrity of the survey's outcomes to determine if they align with the research objectives and provide meaningful insights.

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Answer:

27 inches

Step-by-step explanation:

1 ft = 12 inches, therefore 2 ft = 24 inches because (12)(2)=24. Then you need to add the other 3 inches to 24, and 24 + 3 = 27 in.

If the power of the polynomial is 1. Then the degree of the polynomial is one.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear polynomial is given below.

⇒ (7/4)x + 3

The power of the polynomial is 1.

Then the degree of the polynomial is 1.

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Answer:

>

Step-by-step explanation:

.4 is bigger than .06. I hope thid helps:D

The size of matrix B is 9×7.

To find the size of matrix B, you need to understand the rules for matrix multiplication. When multiplying two matrices A and B, the number of columns in matrix A must equal the number of rows in matrix B.

In this case, matrix A has 9 rows and 9 columns, so it's a 9×9 matrix. The product AB is given as a 9×7 matrix, meaning it has 9 rows and 7 columns.

Since the number of columns in matrix A (9) must equal the number of rows in matrix B, it tells us that matrix B has 9 rows. To find the number of columns in matrix B, you can use the dimensions of the product AB, which is 9×7. This indicates that matrix B has 7 columns.

Therefore, matrix B is a 9×7 matrix.

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Answer:

0.2083

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The probability of each outcome in the sample space is B. 1/20.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

For given example, the total number of students:n(S) = 5. The probability of selecting one student would be: P(A) = 1/5.

Now, there are 4 students.n(S) = 4

So, probability of selecting second student from remaining 4.P(B) = 1/4

Hence, the probability of each outcome in the sample space would be:

1/5 × 1/4

= 1/20

Therefore, the probability of each outcome in the sample space is 1/20.

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Answer:

The focus (or foci).

Step-by-step explanation:

The focus of a hyperbola are equidistant from the center of the hyperbola. They can be found with the formula c²= a² + b². The points for the foci being

(-c, y) and (c, y).

In this illustration, the foci are the points in blue.

The values of angle J and angle G are 32° and 78° respectively.

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to similar , the corresponding angles must be equal and also the corresponding sides must be equal.

Therefore since triangle HIJ is similar to triangle GEF, then

angle G = angle H

angle I = angle E

angle J = angle F

Therefore;

angle G = angle H = 78°

angle F = angle J = 32°

Therefore the values of angle J and angle G are 32° and 78° respectively.

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Answer:

b

Step-by-step explanation:

The amount of money that Noah needs to invest would be = $ 6,558

An interest rate is defined as the rate at which an individual receives an interest on an invested funds over a stipulated period of time.

The interest rate (R) = 7% = 0.07 (decimal form)

The time for the investment (T) = 10 years.

The present value of the account (A) = $12,900

n compounding frequency = 1

Using the formula;

A = P (1 +r/n) ^nt

12,900 = P ( 1 + 0.07) ^ 10

12,900 = P (1.07) ^10

12,900 =P 1.96715

P = 12,900/1.96715

P =$ 6,558

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The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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Answer:

(1/4)^2

Step-by-step explanation:

Which expression is equivalent to (4^3)^2 ⋅ 4^−8?

(4^3)^2 * 4^-8 =

(4)^6 * (1/4)^-8 =

(1/4)^2 =   your answer

1/4 * 1/4 =

1/16     solved

The expression (4^3)^2 ⋅ 4^−8 simplifies to 4^−2 or 1/16 using the laws of exponents.

The expression (4^3)^2 ⋅ 4^−8 can be simplified by using the laws of exponents. According to these laws, when you raise a power to a power (as in (4^3)^2), you multiply the exponents. Therefore, the equivalent expression for (4^3)^2 is 4^6. For 4^−8, the negative exponent means that this is 'one over' the base raised to the positive of that exponent, which is 1/4^8.

So, the equivalent expression for the whole thing is 4^6 * 1/4^8 or 4^−2, which also equals to 1/4^2 or 1/16.

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The combination has a refractive power of 0.167 diopters.

The refractive power of a lens is given by the formula P = 1/f, where f is the focal length of the lens in meters. The focal length of a lens in diopters (d) is given by f = 1/d.

To find the refractive power of the combination of a 10 d lens and a 15 d lens, we need to find the equivalent focal length of the combination. The equivalent focal length of two lenses in contact can be found using the formula:

1/f = 1/f1 + 1/f2

where f1 and f2 are the focal lengths of the individual lenses.

Substituting the values for the focal lengths of the two lenses, we get:

1/f = 1/10 + 1/15

Simplifying, we get:

1/f = 1/6

Multiplying both sides by 6, we get:

f = 6 meters

Therefore, the refractive power of the combination of the 10 d and 15 d lenses is:

P = 1/f = 1/6 = 0.167 d^-1.

Thus, the combination has a refractive power of 0.167 diopters.

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Answer:

the answer is (B) I used an app to solve it

Answer:

The answer would be "B" because you have to cross multiply, which would give you: -3k = 180. Then, you have to divide 180 by -3, which would give you -60.

The requried fraction of vehicles that are not cars is 7/33.

The fraction of the vehicles that are not cars can be found by deducting the number of cars from the total number of vehicles and then dividing by the total number of vehicles:

Number of vehicles that are not cars = 495 - 390 = 105

Fraction of vehicles that are not cars = (Number of vehicles that are not cars) / (Total number of vehicles) = 105/495

To simplify this fraction, we can divide both the numerator and denominator by the greatest common factor, which is 15:

105/495 = (105 ÷ 15) / (495 ÷ 15) = 7/33

Thus, the fraction of vehicles that are not cars is 7/33.

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