Question 2
State the probability that a randomly selected, normally
distributed value lies between
a) o below the mean and o above the mean (round to
the nearest hundredths)
b) 20 below the mean and 20 above the mean (round
to the nearest hundredths)

Answer:

a

Step-by-step explanation:

Answer:

Answer: B. Symmetric.

Explanation:

In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.

Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.

Having three straight sides and three angles where they intersect, a triangle is a closed, two-dimensional shape. It is one of the fundamental geometric shapes and has a number of characteristics that can be used to study and resolve issues that pertain to it. The triangle inequality theory states that the sum of a triangle's interior angles is always 180 degrees, and that the longest side is always the side across from the largest angle. Triangles can be used to solve a wide range of mathematical issues in a variety of disciplines and can be categorised based on the length of their sides and the measurement of their angles.

given

We can use the following congruence theories or postulates based on the data in the diagram:

A. ASA

B. AAS

C. LL (corresponding angles hypothesis)

F. SAS

Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.

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If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval  (1, 2)  such that f'(c)>  0.

Applying the  Mean Value Theorem for derivatives, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the interval (a, b) such that:

f'(c) = (f(b) - f(a)) / (b - a)

In the scenario above, we have that f is differentiable, and that f(1) < f(2).

choosing a = 1 and b = 2.

Then applying the Mean Value Theorem, there exists at least one number c in the interval (1, 2) such that:

f'(c) = (f(2) - f(1)) / (2 - 1)

f'(c) = f(2) - f(1)

We have that f(1) < f(2), we have:

f(2) - f(1) > 0

We can conclude by saying that there exists a number c in the interval (1, 2) such that:

f'(c) = f(2) - f(1) > 0

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Descriptive statistics are the most useful in life. Descriptive statistics provide information about a data set and can help to summarize and interpret data. Specifically, I find the mean and median to be the most useful.

Descriptive statistics involves the use of measures such as the mean, median, mode, and range, as well as graphical representations of the data, such as histograms, box plots, and scatter plots.

The mean is the average of a set of data and is useful for summarizing and interpreting data. For example, when I am studying for a test, I often use the mean of my practice test scores to understand my overall performance.

The median is the middle value of a set of data and is useful for understanding the spread of the data. For example, when I am tracking my monthly expenses, I often use the median to understand how much I am spending each month. By taking the median of my monthly expenses, I can get an idea of which expenses are taking up the most of my budget.

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The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.

Two lines intersect at a location, creating an angle.

An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.

Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.

In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.

An angle has two primary components: the arms and the vertex. T

he two rays' shared vertex serves as their common terminal.

Hence, The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.

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The total amount of money Carol originally invested is £22,000 in the bank account.

Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.

This results in exponential growth or accumulation of interest over time.

Let X be the amount that Carol originally invested in the account.

After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).

After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.

After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).

We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:

(X(1.025) - £1000)(1.025) = £23,517.60

Expanding the left-hand side and simplifying, we get:

X(1.025)² - £1000(1.025) = £23,517.60

X(1.025)² = £24,567.63

Dividing both sides by (1.025)², we get:

X = £22,000 (rounded to the nearest pound)

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The complete question is -

On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?

Answer:

Step-by-step explanation:

Using a standard normal table, we can find the area under the curve between -2.11 and -0.85.

P(-2.11 < z < -0.85) = P(z < -0.85) - P(z < -2.11)

Using the table, we find:

P(z < -0.85) = 0.1977

P(z < -2.11) = 0.0174

Therefore,

P(-2.11 < z < -0.85) = 0.1977 - 0.0174 = 0.1803

So the probability that a standard normal random variable falls between -2.11 and -0.85 is 0.1803.

Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:

lwh = 600

For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:

l(3w)h = 3lwh = 3(600) = 1800 cubic feet

Therefore, the volume of the neighbor's pool is 1800 cubic feet.

Step-by-step explanation:

The sample mean is 2.1, the sample variance is 212.5% and the standard deviation is 14.57%

a. The sample mean can be computed as the average of the quarterly percent total returns:

[tex](11.2 - 20.5 + 13.2 + 12.6 + 9.5 - 5.8 - 17.7 + 14.3) / 8 = 2.1[/tex]

So the sample mean is 2.1%, which can be interpreted as the average quarterly percent total return for the stock over the sample period.

b. The sample variance can be computed using the formula:

[tex]s^2 = sum((x - mean)^2) / (n - 1)[/tex]

where x is each quarterly percent total return, mean is the sample mean, and n is the sample size. Plugging in the values, we get:

[tex]s^2 = (11.2 - 2.1)^2 + (-20.5 - 2.1)^2 + (13.2 - 2.1)^2 + (12.6 - 2.1)^2 + (9.5 - 2.1)^2 + (-5.8 - 2.1)^2 + (-17.7 - 2.1)^2 + (14.3 - 2.1)^2 / (8 - 1) = 212.15[/tex]

So the sample variance is 212.15%. The sample standard deviation can be computed as the square root of the sample variance:

[tex]s = \sqrt(s^2) = \sqrt(212.15) = 14.57[/tex]

So the sample standard deviation is 14.57%.

c. To construct a 95% confidence interval for the population variance, we can use the chi-square distribution with degrees of freedom n - 1 = 7. The upper and lower bounds of the confidence interval can be found using the chi-square distribution table or calculator, as follows:

upper bound = (n - 1) * s^2 / chi-square(0.025, n - 1) = 306.05

lower bound = (n - 1) * s^2 / chi-square(0.975, n - 1) = 91.91

So the 95% confidence interval for the population variance is (91.91, 306.05).

d. To construct a 95% confidence interval for the standard deviation (as percent), we can use the formula:

lower bound = s * √((n - 1) / chi-square(0.975, n - 1))

upper bound = s * √((n - 1) / chi-square(0.025, n - 1))

Plugging in the values, we get:

lower bound = 6.4685%

upper bound = 20.1422%

So the 95% confidence interval for the standard deviation (as percent) is (6.4685%, 20.1422%).

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The required probability that a household in Maryland with annual income of ,

$90,000 or more is equal to 0.3377.

$50,000 or less is equal to 0.2218.

Annual household income in Maryland follows a normal distribution ,

Median =  $75,847

Standard deviation = $33,800

Probability of household in Maryland has an annual income of $90,000 or more.

Let X be the random variable representing the annual household income in Maryland.

Then,

find P(X ≥ $90,000).

Standardize the variable X using the formula,

Z = (X - μ) / σ

where μ is the mean (or median, in this case)

And σ is the standard deviation.

Substituting the given values, we get,

Z = (90,000 - 75,847) / 33,800

⇒ Z = 0.4187

Using a standard normal distribution table

greater than 0.4187  as 0.3377.

P(X ≥ $90,000)

= P(Z ≥ 0.4187)

= 0.3377

Probability that a household in Maryland has an annual income of $90,000 or more is 0.3377(rounded to four decimal places).

Probability that a household in Maryland has an annual income of $50,000 or less.

P(X ≤ $50,000).

Standardizing X, we get,

Z = (50,000 - 75,847) / 33,800

⇒ Z = -0.7674

Using a standard normal distribution table

Probability that a standard normal variable is less than -0.7674 as 0.2218. This implies,

P(X ≤ $50,000)

= P(Z ≤ -0.7674)

= 0.2218

Probability that a household in Maryland has an annual income of $50,000 or less is 0.2218.

Therefore, the probability with annual income of $90,000 or more and  $50,000 or less is equal to 0.3377 and 0.2218 respectively.

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Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.

To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.

The formula for finding the number of permutations is:

n! / (n-r)!

where n is the total number of objects and r is the number of objects we choose.

Using this formula, we can calculate the number of permutations as follows:

4! / (4-3)!

= 4! / 1!

= 4 x 3 x 2 x 1 / 1

= 24

Therefore, we can arrange the chosen 3 letters in 24 different ways.

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f(x) = (x+4)^2(x-3) has polynomial function with the following zeros: double zero at -4 simple zero at 3.

If a polynomial has a double zero at -4, it means that it can be factored as (x+4)^2.

If it also has a simple zero at 3, then the factorization must include (x-3).

Therefore, the polynomial function with these zeros is :-

f(x) = (x+4)^2(x-3)

This polynomial has a double zero at -4, because $(x+4)^2$ has a zero of order 2 at -4, and a simple zero at 3, because $(x-3)$ has a zero of order 1 at 3.

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The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.

Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.

The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.

Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:

CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees

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_____The given question is incomplete, the complete question is given below:

Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI

Answer:

1/3

Step-by-step explanation:

using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3

The two cars are approaching each other at a rate of 36 km/hr at the given instant.

We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".

At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem

r^2 = x^2 + y^2

To find the rates of change of x and y, we differentiate both sides of this equation with respect to time

2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)

Simplifying and plugging in the given values

dr/dt = (x(dx/dt) + y(dy/dt)) / r

dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)

dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)

dr/dt = 9 / sqrt(0.0625)

dr/dt ≈ 36 km/hr

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The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.

Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.

The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.

Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.

The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:

6.8x + 4.2(35 - x) (35 - x)

When we simplify, we get:

6.8x + 147 - 4.2x

2.6x + 147

The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:

35(5.31) = 185.85

When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:

2.6x + 147 = 185.85

Subtractiοn οf 147 frοm bοth sides yields:

2.6x = 38.85

When we divide by 2.6, we get:

x ≈ 14.94

Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.

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The process to show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied is shown below.

We prove this using the Pigeonhole Principle, which states that if n items are placed into m containers, and n > m, then at least one container must contain more than one item.

Let us consider the 16 people seated in a row of 20 chairs. Each person occupies one chair, so there are 20 - 16 = 4 empty chairs in the row.

We assume that empty chairs as containers, and people as items that need to be placed into containers.

Since there are more items (people) than containers (empty chairs), there must be at least one group of 2 or more consecutive empty chairs.

Now, let's consider the complement of this statement: Suppose there are no groups of 4 consecutive chairs that are occupied. Then, each group of 4 consecutive chairs contains at most 3 people.

We partition the row of chairs into groups of 4 consecutive chairs.

So, there are 20 - 3 = 17 such groups. By the statement above, each of these groups contains at most 3 people. Therefore, the total number of people seated in the row is at most 17×3 = 51.

But, we know that there are actually 16 people seated in the row. This is a contradiction, since 51 < 16. Therefore, our assumption that there are no groups of 4 consecutive chairs that are occupied must be false, and we have proved that some group of 4 consecutive chairs must be occupied.

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Therefore , the solution of the given problem of unitary method comes out to be  the attraction sold 943 child tickets and 736 adult tickets on that particular day.

It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.

Here,

Assume the attraction sold x tickets for adults and y tickets for kids.

Based on the supplied data, we can construct the following two equations:

=>  x + y = 1679 (equation 1, representing the total number of tickets sold)

=>  35x + 20y = 44620 (equation 2, representing the total revenue generated)

Using the elimination technique, we can find the values of x and y.

When we divide equation 1 by 20, we obtain:

=>  20x + 20y = 33580 (equation 3)

Equation 3 is obtained by subtracting equation 2 to yield:

=>  15x = 11040

=>  x = 736

When we enter x = 736 into equation 1, we obtain:

=>  736 + y = 1679

=> y = 943

As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.

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Roberto needs 4 square yards of fabric to make his costume.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. For instance, the fraction 7/3 is incorrect since 7 is bigger than 3. Mixed numbers, which combine a whole number and a correct fraction, can be created from improper fractions.

Given that, piece of fabric that is 2 2/3 yards long and 1 1/2 yard wide.

Convert the length from a mixed number to an improper fraction:

2 2/3 = (2 x 3 + 2)/3 = 8/3

1 1/2 = 3/2

The area of the rectangle is:

Area = Length x Width

Substituting the values we have:

Area = (8/3) x (3/2) = 4

Hence, Roberto needs 4 square yards of fabric to make his costume.

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From the discriminant of the give quadratic equation, the temperature of the machine will part after 50 minutes of operation.

The given equation that models the temperature of the machine is;

T = -0.005x² + 0.45x + 125

Let check if there's a value that exists for T = 135

Putting T = 135 in the given equation,

135 = -0.005x² + 0.45x + 125

We can simplify this to;

0.005x² - 0.45x + 10 = 0

From the general form of quadratic equation which is ax² + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.

The discriminant of this quadratic equation is given by:

D = b² - 4ac

= (-0.45)² - 4(0.005)(10)

= 0.2025 - 0.2

= 0.0025

The discriminant of the equation is positive which indicates we have two roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.

We can also find the roots of the quadratic equation using the formula:

[tex]x = (-b \± \sqrt(D)) / 2a[/tex]

Substituting the values of a, b, and D, we get:

[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]

Taking the positive value, we get:

x = 50

Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.

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The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.

To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.

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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.

138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.

Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.

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The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a given a right angle triangle in the picture

It is required to find the measure of angle A

Applying cos ratio to find the measure of the angle A:

cosA = 9/14

cosA = 0.642

A = 49.99 ≈ 50 degree

Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

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Random sampling is crucial when surveying as it ensures that the sample selected is representative of the population.

By randomly selecting participants from the population, the sample is likely to be unbiased on average, which means that the results of the study can be generalized to the entire population. Without random sampling, the results of the study may be skewed or biased towards a certain group, which can lead to incorrect conclusions and poor decision-making. Therefore, it is essential to use random sampling when surveying to obtain accurate and reliable results.

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The appropriate 0.5 adjusted formula for normal approximation is option (d) p(x > 8.5)

The appropriate 0.5 adjusted formula for normal approximation to approximate binomial probabilities when n is large is

P(Z > (x + 0.5 - np) / sqrt(np(1-p)))

where Z is the standard normal variable, x is the number of successes, n is the number of trials, and p is the probability of success in each trial.

To approximate binomial probability p(x > 8) when n is large, we need to use the continuity correction and find the appropriate 0.5 adjusted formula for normal approximation. Here, x = 8, n is large, and p is unknown. We first need to find the value of p.

Assuming a binomial distribution, the mean is np and the variance is np(1-p). Since n is large, we can use the following approximation

np = mean = 8, and

np(1-p) = variance = npq

8q = npq

q = 0.875

p = 1 - q = 0.125

Now, using the continuity correction, we adjust the inequality to p(x > 8) = p(x > 8.5 - 0.5)

P(Z > (8.5 - 0.5 - 8∙0.125) / sqrt(8∙0.125∙0.875))

= P(Z > 0.5 / 0.666)

= P(Z > 0.75)

Therefore, the correct option is (d) p(x > 8.5)

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The given question is incomplete, the complete question is:

To approximate binomial probability p(x > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. a) p(x > 7.5) b)  p(x >= 9) c) p(x > 9) d) p(x > 8.5)

Answer:

Relating SSE to Other Statistical Data



(1) 4y-7z is a binomial.

(2) 8-xy² is a binomial.

(3) ab-a-b can be written as ab - (a + b) which is a binomial.

(4) z²-3z+8 is a trinomial.

In algebra, monomials, binomials, and trinomials are expressions that contain one, two, and three terms, respectively.

A monomial is an algebraic expression with only one term. A monomial can be a number, a variable, or a product of numbers and variables.

A binomial is an algebraic expression with two terms that are connected by a plus or minus sign. For example, 2x + 3y and 4a - 5b are both binomials.

A trinomial is an algebraic expression with three terms that are connected by plus or minus signs.

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Classify into monomials, binomials and trinomials.

(1) 4y-7z

(1) 8-xy²

(v) ab-a-b

(ix) z2-3z+8

The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.

Step 1:

The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:

P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38

= (38/38) - (26/38) = 12/38 = 0.316

So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.

Step 2:

The average waiting time can be calculated by finding the expected value of the probability density function:

E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt

= [(t²)/(238)] from 0 to 38

= (38²)/(238) = 19

Therefore, the average waiting time is 19 minutes.

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Answer:

invertible

Step-by-step explanation:

If A is invertible then ∣A∣ =0