yumiko solved |x|>5 by solving x>-5 and x<5. explain the error yumiko made

15

Step-by-step explanation:

I hope you will understand

Area of each plot be 16 square units.

What do you mean by GCD?

The greatest common divisor (gcd) of two or more numbers is the greatest common divisor that divides them exactly. This is also known as the highest common factor (HCF).

If a and b are two numbers, the greatest common divisor of both numbers is given by gcd(a, b). To find the gcd of a number, we need to list all divisors of the number and find the greatest common divisor.

It is given that a farmer has a piece of land measuring 140 m by 936 m he divides it into square plots of equal size.

140 = 2 × 2 × 5 × 7

936 = 2 × 2 × 2 × 3 × 3 × 13

GCD = 2 × 2 = 4

Area = 4 × 4 = 16 square units.

Therefore, area of each plot be 16 square units.

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Answer:

\(K' = 83^o\)

Step-by-step explanation:

Given

\(K = 83^o\)

Reflection: \(y= 2\)

Required

K'

The general rule is that, reflection does alter measurements (angles or lengths).

So, this means that K' will have the same measure as K.

i.e.

\(K' = K\)

\(K' = 83^o\)

When x is a uniformly distributed random variable on [0,1], it divides the interval [0,1] into two subintervals: [0,x] and [x,1]. This division exhibits symmetry, as explained in the following paragraphs.

Consider a uniformly distributed random variable x on the interval [0,1]. The probability density function of x is constant within this interval. When x takes a particular value, it acts as a dividing point that splits [0,1] into two subintervals.

The first subinterval, [0,x], represents all the values less than or equal to x. Since x is randomly distributed, any value within [0,1] is equally likely to be chosen. Therefore, the probability of x falling within the subinterval [0,x] is equal to the length of [0,x] divided by the length of [0,1]. This probability is simply x.

By symmetry, the second subinterval, [x,1], represents all the values greater than x. The probability of x falling within the subinterval [x,1] can be calculated as the length of [x,1] divided by the length of [0,1], which is equal to 1 - x.

The symmetry arises because the probability of x falling within [0,x] is the same as the probability of x falling within [x,1]. This symmetry is a consequence of the uniform distribution of x on the interval [0,1].

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The given statement "The notation "f(x)" (f of x) is another way of representing y-values in a function" is true because it represents the output values.

In Mathematics, a function simply refers to a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.

This ultimately implies that, a function typically shows the relationship between input values (x-values or domain) and output values (y-values or range) of a data set, as well as showing how the elements in a table are uniquely paired (mapped).

Generally speaking, the output values (y-values or range) of a data set (function) are plotted on the y-coordinate of a graph and they are typically denoted by either the notation f(x) or y.

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Complete Question:

The notation "f(x)" (f of x) is another way of representing y-values in a function. True or False?

Answer:

b 17/18

Step-by-step explanation:

Solve the one's in bracket then later solve everything together

The polygon which is as represented in the task content and as required to be named is; Pentagon.

By observation, since the segment lengths of the sides of the polygon seem unequal, the polygon is irregular.

It follows from the task content that the given polygon is a 5 sided polygon whose name is to be determined and classified as a regular or irregular polygon.

For 5 sided polygons, they are called Pentagons.

By further examination, since the side lengths are not equal, the polygon in discuss is an irregular polygon.

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As per the details given, there are 37 dots in the 5th step.

To locate the pattern and decide the range of dots in the 5th step, allow's examine the given records:

Step 1: 6 dots

Step 2: 14 dots

Step 3: 21 dots

Looking on the variations between consecutive steps, we will see that the quantity of additional dots in each step is growing via eight.

In other phrases, the distinction among Step 1 and Step 2 is eight, and the difference between Step 2 and Step 3 is likewise eight.

Thus, we can preserve this sample to decide the quantity of dots within the 4th and 5th steps:

Step 4: 21 + 8 = 29 dots

Step 5: 29 + 8 = 37 dots

Therefore, there are 37 dots in the 5th step.

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There 4,828 adult patrons in the theater

What is simultaneous equations?

Simultaneous equations are two or more equations that are related and are solved together, in essence, the solutions to unknowns in one equation are related to the unknowns in other equations.

In this case, we can assume that the number of adults is A, whereas the number children is C, in essence, the total number of attendees are determined thus:

A+C=5300............(equation 1)

The total revenue earned is determined thus:

$5.50A+$3.50C=$22,906...........(equation 2)

From equation 1, we can solve for C in terms of A

C=5300-A

substitute for C in equation 2

$5.50A+$3.50(5300-A)=$22,906

$5.50A+$13,250-$3.50A=$22,906

$2.00A+$13,250=$22,906

$2.00A=$22,906-$13,250

$2.00A=$9656

A=$9656/$2.00

A=4828 adult patrons

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Answer:

x=99/8

Step-by-step explanation:

Answer:

x=99/8

Step-by-step explanation:

7x+6+9x−24=180

Step 1: Simplify both sides of the equation.

7x+6+9x−24=180

7x+6+9x+−24=180

(7x+9x)+(6+−24)=180(Combine Like Terms)

16x+−18=180

16x−18=180

Step 2: Add 18 to both sides.

16x−18+18=180+18

16x=198

Step 3: Divide both sides by 16.

16x/16 = 198/16

X = 99/8  

Hope it Helps !! :)

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer:  You see this is q trick question meant to get your brain all confused. IT gives you the answer, It states that Tony is 36 years old and Angela is 4 and 1/2 years older than Tony which would make her 40 1/2 years old.

Step-by-step explanation:

\(iii\implies i^3\implies i^2\cdot i\implies (-1)\cdot \sqrt{-1}\implies -\sqrt{-1}\implies -i\)

Answer:

3.99

Step-by-step explanation:

The total sum of central angle of circle is 360 which mean the area of the circle = (12.36 x 360)/89

A=πr^2

=> (12.36 x 360)/89 = 3.14(r^2)

r^2 = 15.92

r = 3.99

Answer:

Step-by-step explanation:

Answer:

500 meters above sea level

Step-by-step explanation:

600-100 = 500

The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers.

The diagram that is best at displaying data dispersion is a box plot. Here's the main answer:When there is a need to compare the distribution of data, a box plot is often the best method.

A box plot is a diagram that shows how a dataset is distributed. It shows how data is spread out and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal (not evenly distributed).

A box plot is a great way to summarize large amounts of data and it is also very easy to read and interpret. It shows a number of statistical values, including the median (the middle value of the data set), the quartiles (the values that divide the data set into four equal parts) and the range (the difference between the maximum and minimum values).

Additionally, it can identify any outliers in the data, which are values that are significantly different from the rest of the data.A box plot is created by drawing a rectangle between the first and third quartiles (the middle 50% of the data) with a line drawn inside it to show the median.

Lines are then drawn from the edges of the rectangle to the minimum and maximum values. Any outliers are marked with a point outside of the rectangle.

The box plot is a great way to compare data sets and to visualize the dispersion of the data

The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal. A box plot is created by drawing a rectangle between the first and third quartiles with a line drawn inside it to show the median.

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The probability that Suspect A is the guilty party is 2/3.

Suppose a crime is committed by one of the two suspects A and B. Initially, there is equal evidence against both of them. Further, in the investigation, it is found that the guilty party had a blood type found in 10% of the population. Suspect A does match this blood type, whereas the blood type of Suspect B is unknown.The probability that A is the guilty party is calculated as follows:

Let P(A) be the probability that A is guilty, and P(B) be the probability that B is guilty.As there is an equal amount of evidence against both suspects, both P(A) and P(B) are equal and can be expressed as P(A) = P(B) = 1/2.Let the probability of the blood type of a guilty party be X.

Since Suspect A's blood type matches the guilty party's blood type, the probability that he is the guilty party is P(X | A) = 1.Since Suspect B's blood type is unknown, we must take into account the possibility of him being the guilty party despite not matching the guilty party's blood type.

As a result, the probability that he is the guilty party is P(X | B) = 0.1.

The probability that the guilty party has blood type X can be expressed as:P(X)

= P(A) P(X | A) + P(B) P(X | B)P(X) = 1/2 × 1 + 1/2 × 0.1P(X) = 0.55

Using Bayes' theorem, we can calculate the probability that Suspect A is the guilty party:

P(A | X) = P(X | A) P(A) / P(X)P(A | X) = 1 × 1/2 / 0.55P(A | X) = 0.9091 ≈ 2/3.

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A percentile is a measure used in statistics to indicate the value below which a given percentage of observations fall. For example, if a data set has a 75th percentile value of 100, then 75% of the observations in the data set fall below the value of 100.

To find the 11th percentile for the given normal distribution with mean μ=58 and standard deviation σ=8, we need to use a standard normal distribution table or a calculator.

We can start by converting the given value to a z-score using the formula:

z = (X - μ) / σ

Where X is the value we want to find the percentile for, μ is the mean, and σ is the standard deviation.

Plugging in the values given, we get:

z = (X - 58) / 8

To find the z-score for the 11th percentile, we can use a standard normal distribution table or calculator to find the z-score associated with a cumulative probability of 0.11.

Using a calculator or table, we find that the z-score associated with a cumulative probability of 0.11 is -1.23.

We can now solve for X using the z-score formula:

z = (X - μ) / σ

-1.23 = (X - 58) / 8

Solving for X, we get:

X = -1.23 * 8 + 58 = 48.16

Therefore, the 11th percentile for this normal distribution is 48.16. This means that 11% of the observations in this distribution fall below the value of 48.16.

A Z-score represents the number of standard deviations an observation is from the mean of the distribution. The formula for calculating a Z-score is:

Z = (X - μ) / σ

In this case, you need to find the Z-score corresponding to the 11th percentile. To do this, you can refer to the Z-table, which provides the area (probability) to the left of a given Z-score. Look for the value closest to 0.11 (representing 11%) in the table. You will find that the Z-score associated with the 11th percentile is approximately -1.23.

Now, you can use the Z-score formula to solve for X:

-1.23 = (X - 58) / 8

To solve for X, perform the following calculations:

X - 58 = -1.23 * 8
X - 58 = -9.84
X = 58 - 9.84
X ≈ 48.16

So, the 11th percentile of the normally distributed random variable X with a mean of 58 and standard deviation of 8 is approximately 48.16.

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Answer:

soln;

given equation is 6x + 5 = 2y

or, 6x -2y + 5 = 0

comparing with ax + by + c = 0

a = 6, b = -2, c = 5

Step-by-step explanation:

27 = x + 3x +5x

27 = 9x

3 = x

Board 1: (3)(1) = 3 inches

Board 2: (3)(3) = 9 inches

Board 3: (3)(5) = 15 inches

Length of the first piece is 3 inches

Length of the second piece is 9 inches

Length of the third piece is 15 inches

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.

According to the problem,

∴ Length of the second piece = 3x inches

∴ Length of the third piece = 5x inches.

Now, all these pieces will add up to 27 inches.

∴ x + 3x + 5x = 27

⇒ 9x = 27

⇒ x = 3

Length of the first piece = 3 inches

Length of the second piece = (3 x 3) inches = 9 inches

Length of the third piece = (5 x 3) inches = 15 inches

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Answer:

7 bananas

Step-by-step explanation:

Using the mean concept, it is found that LeBron scored 10 more points per game on his last two games than on his first two.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For his first two games, he scored 20 + 15 = 35 points, hence the mean is:

35/2 = 17.5 points per game.

For his last two games, he scored 25 + 30 = 55 points, hence the mean is:

55/2 = 27.5 points per game.

The difference is:

27.5 - 17.5 = 10.

On average, LeBron scored 10 more points per game on his last two games than on his first two.

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The possible triples are: (3, 3, 3), (4, 2, 4) as seen by counting theorem.

Now, by the counting principle,

Hence, the possible triples are: (3, 3, 3), (4, 2, 4).

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Answer:

sec θ

Step-by-step explanation:

cos θ + sin θ tan θ

= cos θ + sin θ (sin θ / cos θ)

= cos θ + (sin²θ)/cos θ

= cos θ + (1 - cos²θ) / cosθ

= cos θ + 1/cos θ - cos²θ/cos θ

= cos θ + 1/cos θ - cos θ

= 1/cos θ

= sec θ

The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).

Let's simplify the given expression step by step using the given terms:
Expression:

\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)

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Answer:

trinomial

Step-by-step explanation:

Since this polynomial has 3 different terms, this is, in fact, a trinomial.

Hope this helps :)

Answer:

Not all the means are equal.

Step-by-step explanation:

In an ANOVA table, a sum of squares for the independent variable divided by its respective degrees of freedom.

So if the omnibus null hypothesis is rejected it means that there is sufficient evidence to conclude that not all the means are equal.

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If the omnibus null hypothesis is rejected in a one-factor ANOVA, then, we can conclude that at least one of the population means is different from at least one other population mean.

ANOVA table gives us the total sum of squares ( TSS ), the residual sum of squares ( RSS ) and the estimated sum of squares ( ESS ).

It establishes the relation that:

ESS + RSS = TSS.

If we reject the omnibus null hypothesis, then it means that:

at least one of the population means is different from at least one other population mean.

Therefore, we get that, if the omnibus null hypothesis is rejected in a one-factor ANOVA, then, we can conclude that at least one of the population means is different from at least one other population mean.

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