Determine whether the variable given is qualitative-nominal, qualitative-ordinal, quantitative-discrete, or quantitative-continuous.
allergen level (low/medium/high)
qualitative-ordinal since this variable would yield categories with an order
qualitative-nominal since this variable would yield categories with no implied order
quantitative-discrete since this variable would yield numbers that count
quantitative-continuous since this variable would yield numbers that measure

Trish can type 1400 words per minute if she writes 1400 words in 10 minutes, or 1400 per 600 seconds.

The device technique is a method for addressing issues that entails first figuring out the value of a single entity, then increasing that value to figure out the needed value.  For example, 40 pens would cost 400 rupees, which in itself is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, numerical modeling, or math and science of matrices or operators.

given

To calculate the time required, divide the document's length by the word-per-minute rate.

After that, divide the number of minutes by the number of hours.

It takes four hours and ten minutes to complete 250 minutes.

1400 words in 10 minutes

10 minutes = 10 * 60 seconds

= 600 sec

Trish can type 1400 words per minute if she writes 1400 words in 10 minutes, or 1400 per 600 seconds.

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Answer:

81.3181818

Step-by-step explanation:

Also, did you put the comma in the wrong place? did you mean 1,789? if so the answer would be 8.13181818.

An expression is equivalent to 54 if it represents the same numerical value as 54.

The following options are equivalent to 54:

53 + 1

54

54.5 - 0.5

54.57 - 0.07

54.512 - 0.512

The options that are not equivalent to 54 are:

(53)4

0511

516

054.512

Note that a number followed by a trailing zero is not equivalent to the same number without trailing zero as trailing zeroes don't change the value of the number.

Suppose the real number x is greater than 0. Then for any natural number n, the reciprocal of n, 1/n, is less than x if and only if n > 1/x.

Since 1/x is a positive real number, it is always less than a sufficiently large natural number, say N. Hence, 1/N < x.

Therefore, there exists a natural number for which the reciprocal is less than x.

The solution is based on the properties of real numbers and the notion that there is always a natural number greater than any positive real number.

For a given positive real number x, if we take a natural number n that is larger than 1/x, then the reciprocal of n, 1/n, will be less than x. This is because 1/n = n^(-1), which means the value of n^(-1) becomes smaller as n increases.

So, if we choose a sufficiently large natural number, its reciprocal will always be less than any positive real number x. This means that for any positive real number x, there is always a real number greater than 0 (1/n) for which the reciprocal of a natural number (n) is less than it (x).

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the Number will be 35,838.

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

Given A number has 3 ten thousands 2 more thousands than ten thousands, 3 more hundreds than thousands, 2 fewer tens than thousands, and 5 more ones than ten thousands

Fill in a place value chart one step at a time.

3 ten thousands

ten thousands thousands hundreds tens               ones

        3                      ?               ?               ?               ?

2 more thousands than ten thousands(3 + 2 = 5)

ten thousands thousands hundreds tens               ones

       3                       5               ?               ?               ?

3 more hundreds than thousands (= 3 + 5 = 8)

ten thousands thousands hundreds tens               ones

       3                       5                 8               ?               ?

2 fewer tens than thousands(= 5-2 = 3 )

ten thousands thousands hundreds tens               ones

     3                       5               8               3               ?

5 more ones than ten thousands (= 3 + 5 = 8)

ten thousands thousands hundreds tens        ones

      3                            5                8                      3              8

Therefore, the Number will be 35,838.

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In Old English (OE), endian-endode-endod (end/ended/ended in ModE) is an example of a base form of verb inflection.

The base form of the verb "end" in Old English is "endian." This form is used as the root or base form from which other forms of the verb are derived. In this case, "endian" is inflected to "endode" to indicate a past participle form, and to "endod" to indicate a simple past form.

This is an example of a base form of verb inflection, where the base form of a verb is altered to indicate tense, aspect, or voice. This type of inflection is common in older languages like Old English, but has since declined in use in modern English, where auxiliary verbs and word order are used to convey tense and aspect.

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The value of the quadratic equation is A = ( 9x + 10 ) ( x - 2 )

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

A = 9x² - 8x - 20   be equation (1)

On simplifying the equation , we get

A = 9x² - 18x + 10x - 20

On factorizing the equation , we get

A = 9x ( x - 2 ) + 10 ( x - 2 )

Taking the common factors in the equation , we get

A = ( 9x + 10 ) ( x - 2 )

So , when A = 0

( 9x + 10 ) = 0

x = -10/9

And , when ( x - 2 ) = 0

x = 2

Hence , the quadratic equation is A = ( 9x + 10 ) ( x - 2 )

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Step-by-step explanation:

Here is a graph of the given piecewise function:

Graph of f(x)={(1/3 x-1" if " x≤0 -1/2 x+6" if " 0<x≤6

The graph of the given piecewise function is a straight line with two segments. The first segment, which lies between x = 0 and x = 6, has a slope of -1/2 and a y-intercept of 6. The second segment, which lies between x = 0 and x = -∞, has a slope of 1/3 and a y-intercept of -1.

The sampling which represents the format of the morning show where a radio station asks its listeners to call and give their opinion is given by option B. Simple random sampling.

Therefore, the sampling which is used to decide the format of the show is option B . Simple random sampling.

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The answers are: (a) 0.2224, (b) 0.7776, (c) 0.3545, (d) 0.5785

Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a number between 0 and 1 that indicates the likelihood of an event occurring, with 0 meaning that an event is impossible and 1 meaning that an event is certain to occur.

Probability is used to model and make predictions about real-world situations such as the outcome of a coin flip, the results of a survey, or the success of a marketing campaign. It is also used in many fields including statistics, finance, engineering, and sciences to make decisions based on uncertain data.

The problem requires the use of the normal approximation to the binomial distribution to estimate the probabilities. Let X be the number of flights that arrive on time out of 186 flights. Then X follows a binomial distribution with parameters n = 186 and p = 0.88.

We can use the normal approximation to estimate the probability of X taking different values. Let's denote the mean and standard deviation of X as mu and sigma respectively:

mu = np = 186 × 0.88 = 163.68

sigma = √(np(1-p)) = √(186 × 0.88 × 0.12) = 5.55

(a) P(159) = P(X = 159) can be estimated using the normal distribution using the Z-score:

Z = (159 - mu) / sigma = (159 - 163.68) / 5.55 = -0.77

P(159) ≈ P(Z < -0.77) ≈ 0.2224 (using a standard normal table)

(b) P(X ≥ 159) can be estimated using the cumulative distribution function:

Z = (159 - mu) / sigma = (159 - 163.68) / 5.55 = -0.77

P(X ≥ 159) = P(Z ≥ -0.77) = 1 - P(Z < -0.77) = 1 - 0.2224 = 0.7776

(c) P(X < 161) can be estimated using the cumulative distribution function:

Z = (161 - mu) / sigma = (161 - 163.68) / 5.55 = -0.36

P(X < 161) = P(Z < -0.36) = 0.3545 (using a standard normal table)

(d) P(161 ≤ X ≤ 174) can be estimated using the cumulative distribution function:

Z1 = (161 - mu) / sigma = (161 - 163.68) / 5.55 = -0.36

Z2 = (174 - mu) / sigma = (174 - 163.68) / 5.55 = 1.51

P(161 ≤ X ≤ 174) = P(Z1 < Z < Z2) = P(Z < 1.51) - P(Z < -0.36) = 0.9330 - 0.3545 = 0.5785

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The diagonals of a parallelogram are equal in length if and only if the parallelogram is a rectangle. The sum of squares of diagonals is equal to the sum of squares of sides.

We should consider a parallelogram shape that has sides named as and .

a. The corner to corner lines of the parallelogram can be marked as and . These two inclining lines cross each other at the focal point of the parallelogram, isolating each other into halves. This implies that the two inclining lines and have a similar length.

b. Assuming the inclining lines of the parallelogram have similar length, this implies that the parallelogram is really a square shape. This is on the grounds that in a square shape, every one of the sides are equivalent long. Then again, on the off chance that the parallelogram is a square shape, its inclining lines should have a similar length.

c. We can utilize the Pythagorean hypothesis to show that the amount of the squares of the lengths of the slanting lines is equivalent to the amount of the squares of the lengths of the sides. The Pythagorean hypothesis expresses that in a right triangle, the amount of the squares of the two more limited sides is equivalent to the square of the length of the longest side (the hypotenuse). On the off chance that we view at the parallelogram as two nearby right triangles, we can apply the Pythagorean hypothesis to every triangle. This gives us two conditions, and when we add these two conditions, we observe that the amount of the squares of the lengths of the inclining lines is equivalent to the amount of the squares of the lengths of the sides.

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Both the second and the induction hypothesis result from the first inequality.

You established its validity for n=5. Let's now assume that it is true for some number n5. Its validity for n+1 is to be demonstrated. But

2n+1=2×2n>2×n2>(n+1)2.

The first discrepancy is a result of induction, and we are aware of the second (n−1)2≥42>2, since n≥5

We can widen this disparity  (n−1)2>2 as follows:

n2−2n+1>n2−2n−1>2n2−2n−1>2n2>20n2n2+2n+1=(n+1)2,

which is the second inequality claimed in (♠)

2n+1=2n∗2>2n2=n2+n2>n2+2n+1=(n+1)2

2n+1>(n+1)2

Base case: n=5

(the problem states "n

greater than 4

choose the first matching integer, then.

25>52⟹32>25

Now, the Inductive Step:

2n+1>(n+1)2

now expanding

2∗2n>n2+2n+1

now we proved for the n+1 case

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An outcome is any one of the possible results of an action

An outcome is a result of an action, experiment, or random process. In probability, the outcome is a single event or the result of a random experiment.

For example, when you roll a die, the outcome can be any of the numbers from 1 to 6.

In a coin flip, the outcomes are heads or tails.

The set of all possible outcomes of a random experiment is called a sample space.

An outcome can be represented by a single element of the sample space, and the collection of all possible outcomes is called the event.

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The number of peaks, symmetry, tendency to skew, and homogeneity of a distribution are all indicators of its shape.

Explain about the shape of the distribution?

There are two types of data item distributions: symmetric and asymmetric. The "normal distribution" and the "skewed distribution" are two prevalent illustrations of both symmetry and asymmetry. The distribution's two halves are mirror images of one another in a symmetrical distribution.

The number of peaks, the presence of symmetry, the propensity to skew, and the homogeneity of a distribution all help to explain its shape. (Graphs with skewed distributions show a greater number of points on one side than the other.) PEAKS: Graphs frequently show maximums or peaks in a certain area.

Either a normal distribution or a normal curve. When dealing with such a distribution, the mean should be reported.

Simple Frequency Distribution:

A simple frequency distribution is a table that lists each unique score in the data set and the number of times that score appears.

Score Frequency:

1.0 3

1.1 3

1.2 1

1.3 1

1.5 1

2.0 1

2.2 2

2.3 2

2.5 1

3.0 2

3.2 1

3.4 2

3.5 2

3.7 1

3.8 1

4.0 5

Grouped Frequency Distribution:

A grouped frequency distribution is a table that groups the scores into ranges (also known as bins) and lists the number of scores that fall into each range.

Score Range Frequency

1.0-1.9 9

2.0-2.9 7

3.0-3.9 10

4.0-4.9 4

Frequency Polygon:

A frequency polygon is a graph that is created by connecting the midpoints of the top of the bars in a histogram. The x-axis represents the scores and the y-axis represents the frequency.

Histogram:

A histogram is a graph that represents the frequency distribution of a set of continuous data. It is similar to a bar graph, but the bars are adjacent to each other and there are no spaces between the bars.

Shape of the distribution:

The shape of the distribution is right-skewed, which means that the majority of the data is concentrated on the left side of the distribution and there is a long tail of data points on the right side. This is indicated by the fact that the majority of the scores are between 1 and 3, while only a few scores are at 4.0 or above.

Bar Graph:

 __________

Male:  |__|__|__|__|

      10

      ____________________

Female: |__|__|__|__|__|__|

      20

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The distance between A and B is 575.21

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given that, A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 6°, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 13°

tan 6° = 111/base

base = 1056

tan 13°= 111/base-AB

base - AB = 480.79

AB = 575.21

Hence, the distance between A and B is 575.21

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The value of 4 divided by 1/6 is 24

From the question, we have the following parameters that can be used in our computation:

4 divided by 1/6

Next, we represent the statement as an expression

So, we have the following representation

4 / (1/6)

Dividing 4 by 1/6 is the same as multiplying 4 by 6/1, which is:

4 * 6/1

Evaluate the products

So, we have the following representation

24/1

Evaluate the quotient

So, we have the following representation

= 24

The above represents the solution

So 4 divided by 1/6 equals 24.

Hence, the solution is 24

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(1) The Linearity Property for sums states that the sum of two sums is equal to the sum of the individual terms. That is, if a and b are two sums, then a + b = Σ(a + b).

(2) The Telescoping Property for sums states that the sum of a sequence of terms can be expressed as the difference between two terms. That is, if a1, a2, …, an are terms of a sequence, then Σai = a1 - an.

(3) The Geometric Property for sums states that the sum of the first n terms of a geometric sequence is equal to the product of the first term and the sum of the common ratio raised to the nth power. That is, if a is the first term and r is the common ratio, then Σa_i = ar^(n-1).

(4) The Associativity Property for sums states that changing the order of terms in a sum does not affect the result. That is, if a is a sum, then a = Σa = Σ(Σa).

(5) Σk = ∑k = the sum of the first k terms of a sequence.

(6) Σk^-2 = ∑k^-2 = the sum of the inverse of the first k terms of a sequence.

(7) Σk^-3 = ∑k^-3 = the sum of the inverse of the cube of the first k terms of a sequence.

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Answer: D

Step-by-step explanation:

since she must sell at least 40 mugs to meet her goal, y must be greater than or equal to 40

The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

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Answer:

Step-by-step explanation:

The area of square 1 is 13mm*26mm=338mm^2

The area of the second rectangle is 15mm*32mm=480mm^2

The are of both rectangles = 338mm^2+480mm^2=818mm^2

a) The graph of the quadratic function that models this situation is given by the image presented at the end of the answer.

b) The zeros are given as follows: x = 30 and x = 50.

c) The function is defined as follows: y = 0.03x² - 2.4x + 45.

The quadratic function with roots x* and x** is given by the equation presented as follows:

y = a(x - x*)(x - x**)

The roots = zeros are the values of x for which the graph of the function crosses the x-axis, hence:

x* = 30, x* = 50.

Then the function is:

y = a(x - 30)(x - 50)

y = a(x² - 80x + 1500).

When x = 0, y = 45, hence the leading coefficient a is obtained as follows:

1500a = 45

a = 45/1500

a = 0.03.

Hence the definition of the function is given as follows:

y = 0.03(x² - 80x + 1500).

y = 0.03x² - 2.4x + 45.

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[tex](4.8 \times 10^7) + 6,500,500[/tex]

[tex]48,000,000+6,500,500[/tex]

[tex]=\boxed{54,500,500}[/tex]

The length of each piece of yarn in mixed fraction form if total length is 18 feet, is 2(4/7) feet each for 7 pieces.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The number of pieces of yarn Cody has = 3

Length of 1 piece of yarn = 6 feet

The number of pieces Cody needs to cut is = 7

The total length of yarn = Number of pieces of yarn × Length of 1 piece of yarn

Apply the arithmetic operation of multiplication.

Substitute the values into the equation -

The total length of yarn = 3 × 6

The total length of yarn = 18 feet

The length of each yarn piece = Total length of yarn / Number of pieces Cody needs to cut

Apply the arithmetic operation of division.

Substitute the values into the equation -

The length of each yarn piece = 18 / 7

The result is obtained in a fractional form -

The length of each yarn piece = 2(4/7)

Therefore, the length of each piece is 2(4/7) feet.

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The rectangle's length is equal to the circumference of the circle, while the the rectangle's width is equal to radius of the circle. So, the area of the circle is one half of the area of the rectangle.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Note: Radius = diameter/2 = 10/2 = 5 cm.

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circle = πr²

Area of a circle = 25π cm².

Mathematically, the area of a rectangle can be calculated by using this formula:

Area of a rectangle = LW

Where:

Area of a rectangle = 10π × 5

Area of a rectangle = 50π cm².

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"When written in reduced echelon​ form, any m×n matrix will have at least one row of all zeros. When solving Ax=b​, that row will represent an equation with a zero on the left side and a possibly nonzero entry of b on the right side."

Now, According to the question:

"Information available from the question"

Let a be a 3 x 2 matrix. explain why the equation a x b cannot be consistent for all b in.

Since a 3x2 matrix only has 2 columns, matrix A can at most have 2 pivot columns and 2 pivot positions. This cannot fill all 3 rows w/ pivots so Ax=b can't be consistent for all b in R3. If A is an m x n matrix w/ m>n then A can have at most n pivot positions which isn't enough to fill all m rows, so Ax = b can't be consistent for all b in R3.

Hence, The correct option is (A)

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(a) sin(2θ) = 2sin(θ)cos(θ)

(b) cos(2θ) = cos²(θ) - sin²(θ) = 2cos²(θ) - 1 = 1 - 2sin²(θ)

By using the addition and subtraction formulas, we can express 2θ in terms of θ, but we cannot reduce 2θ to θ.

Sin is what?

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.

The sine function for any right triangle with an angle, let's say ABC, will be:

Opposite/hypotenuse = Sin(θ)

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The values that make vector b a linear combination of vectors A1, A2 and A3 are given as follows:

[tex]\alpha_1 = -1.9, \alpha_2 = 1.1, \alpha_3 = 1.5[/tex]

A vector is a linear combination of other vectors when it can be obtained via a system of equations from the other vectors.

Considering the matrices, the system of equations to obtain the values of the variables that make vector b a linear combination of vectors A1, A2 and A3 are given as follows:

Adding the second and the third equation, we have that:

3x + 7y = 2.

Since x = y - 3, the value of y is obtained as follows:

3(y - 3) + 7y = 2

3y - 9 + 7y = 2

10y = 11

y = 1.1.

Then the value of x is of:

3x = 2 - 7(1.1)

x = [2 - 7(1.1)]/3

x = -1.9.

The value of z is obtained as follows:

z = 1 - 2x - 3y

z = 1 - 2(-1.9) - 3(1.1)

z = 1.5.

In the desired notation, these values are given as follows:

[tex]\alpha_1 = -1.9, \alpha_2 = 1.1, \alpha_3 = 1.5[/tex]

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