Solve for x.
60°
(2x+20)°

On solving the provided question we got to know that, the median value won't change if the greatest sample Observation is decreased to 1.3735.

One of three ways to gauge central tendency is the median. The center position of a record is specified when describing it. A measure of central tendency is what this is. The mean, median, and mode are the three most frequently used indicators of central tendency.

The sum of all the values is divided by the total number of values, giving the mean value.

[tex]0.736 + 0.863 + 0.865 + 0.913 + 0.915 + 0.937 + 0.983 + 1.001 + 1.011 + 1.064 + 1.109 + 1.132 + 1.140 + 1.153 + 1.253 + 1.397 = 16.472\\16.472 /16 = 1.0295\\1.0295 is the mean value[/tex]

The number near the middle of the point is the median value. At the halfway point, there are two values.

[tex](1.001 + 1.011) / 2 = 1.006\\ 1.006 is the median value.[/tex]

As a result, the median value, which depicts the middle value of the numbers in the result, is less than the mean value, which depicts the real middle value of the numbers if they were equally distributed.

Their difference is that 1.0295 - 1.006 = 0.0235

1.397 observations make up the biggest sample. It may be made smaller by taking the number and removing the difference between the mean and median.

Consequently, there is a 0.0235-point difference between the mean and median.

Therefore;

[tex]1.397 - 0.0235 = 1.3735[/tex]

The median value won't change if the greatest sample Observation is decreased to 1.3735.

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If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80 then s2 = 18 and C. M = 85

The standard deviation (s2) is a measure of the variability of the sample data, while the mean (M) is a measure of the central tendency. The higher the mean and the higher the standard deviation, the more likely it is that the null hypothesis will be rejected. Therefore, the set of sample characteristics that is most likely to lead to a rejection of the null hypothesis is M = 85 and s2 = 18.

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Answer:

they ran the same speed as each other c

The mass of the heaviest puppy is three times greater than the mass of the lightest puppy.

The number of dots for each input of the dot plot shows the number of times that each measure appears in the data-set.

For example, two dots means that the measure appears twice in the data-set.

From the description of the dot plot, the masses are given as follows:

1/4, 1/2, 1/2, 1/2, 1/2, 3/4, 3/4, 3/4.

Then the masses of the lightest and of the heaviest puppy are given as follows:

The ratio of these masses is given as follows:

3/4/(1/4) = 3/4 x 4 = 3.

(division of fractions, the numerator is multiplied by the inverse of the denominator).

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The percentage of 35 percent of 80 is 28

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

For example, 45% (read as "forty-five per cent") is equal to the fraction

45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.

The percentage of 35 percent of 80 is

= [tex]\frac{35}{100}[/tex]× 80

=28

The percentage of 35 percent of 80 is 28

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The percentage of the hotel rooms in the city which were occupied during the convention is 98%.

What is percentage?

A percentage is a piece of a whole expressed as a number between 0 to 100. Nothing is said to be zero percent; everything is said to be 100 percent; half of something is said to be 50 percent; and nothing is zero percent.

You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

As given in the question,

Number of hotel room occupied = 9,800

Number of hotel room unoccupied = 200

Total number of the rooms in city = 9800 + 200

Total number of the rooms in city = 10,000

To calculate the percentage we proceeds as follow:

(9800/10000)100 = 98%

Therefore, the percentage is 98%.

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Answer:

qwqe

Step-by-step explanation:wqeqwe

4.65 kg the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)

Given that,

A gold statue that is perched on a pedestal with a weight-sensitive alarm is replaced by a thief using a bag of sand. The statue and the bag of sand have the exact same volume, 1.55 L.

We have to calculate the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)

We know that,

Mass of gold = Volume × Density

= 1.55×1000 cc × 19.3

= 29915 grams

= 29.915 Kg

Mass of sand = 1.55×1000×3

= 4650g

= 4.65 Kg

Volume = 1.55 L

= 1.55 × 1000 cc

= 1550 cc

Mass = Volume × Density

Mass of gold = 1550 × 19.3

= 29915 grams

= 29.915 kg

Mass of sand = 1550 × 3

= 4650 grams

= 4.65 kg

Therefore, 4.65 kg the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)

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Answer: A

Step-by-step explanation:

Because Milwaukee's population is smaller than that of Baltimore, the only correct answer would be one that has the population of Baltimore higher than that of Milwaukee, which is only A

The unknown angle measures are 51.5° and 51.5° respectively.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides.

Given, side DE = side EF

Then, ∠D = ∠F

So, the sum of all angles of the triangle = 180°

or, ∠D + ∠E + ∠F = 180°

or, ∠F + 77° + ∠F = 180°

or, 2∠F = 180° - 77°

or, ∠F = 103/2 = 51.5°

And, ∠D = 51.5°

Hence, the unknown angle measures are 51.5° and 51.5° respectively.

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Katie runs fastest among all .

What is the units of conversion ?

Unit of Conversion is a multi-step process involving multiplication or division by a numerical factor.

Given:

Speed of Adam = 13 feet per second

Speed of Stephanie = 199 feet in 17 seconds

Speed of Noah = 1 mile in 592 seconds

Speed of Katie = 878 feet in 1 minute

Now on converting all the units to one single unit,we get  

1 mile = 5280 feet

1 minute = 60 seconds

Speed of Adam = 13 feet per second

Speed of Stephanie = 199 feet in 17 seconds

                                 = [tex]\frac{199}{17}[/tex] feet per second

                                 = 11.705 feet per second

Speed of Noah = 1 mile in 592 seconds

                         = 5280 feet in 592 seconds

                         = [tex]\frac{5280}{592}[/tex] feet per second

                        = 8.919 feet per second

Speed of Katie = 878 feet in 1 minute

                         = 878 feet in 60 seconds

                         = [tex]\frac{878}{60}[/tex] feet per second

                         = 14.6333 feet per second

Hence ,Katie runs fastest among all sice its speed is the highest .

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The standard deviation of X is $2.00.

Probability is the likelihood that a specific occurrence will occur. Probabilities can be written as proportions with a 0 to 1 or 0% to 100% range.

Let X be the amount one wins. If the die is 4 or 5, the amount one wins is $1. If the die is 6, the amount one wins is $4. If the die is 1, 2, or 3, the amount is $0. Then, the probability of winning from 1 to 6 is 1/6.

The value of the expected mean (μ) is,

[tex]\begin{aligned}\mu&=\sum X P(X)\\&=1\times \frac{1}{6}+1\times \frac{1}{6}+4\times \frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}\\&=\frac{6}{6}\\&=1\end{aligned}[/tex]

Therefore, the standard deviation (σ)is [tex]\begin{aligned}\sigma&=\frac{\sum(X-\mu^2)}{n}\\&=\frac{(1-1)^2+(1-1)^2+(4-1)^2+(0-1)^2+(0-1)^2+(0-1)^2}{6}\\&=\frac{12}{6}\\&=2\end{aligned}[/tex]

The answer is $2. The correct option is option E.

The complete question is -

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win. Use Scenario 6-2. Which of the following is the standard deviation of X? A. $1.00 B. $1.35 C. $1.41 D. $1.78 E. $2.00

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Answer:

55

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

Answer:

here this should help you

a) The z-score for a sales associate who makes $36,000 is 1.4

b) The percentage of sales associates with salaries between $26,250 and $38,750 is 84%

c)  The percentage of sales associates with salaries between $27,500 and $37,500 is 95.4%

d) The percentage of sales associates with salaries less than $27,500 is 2.3%

e) Yes, the salary of $42000 should be considered as outlier.

Given,

Mean, [tex]\mu[/tex]=32500

Standard deviation, [tex]\sigma[/tex]=2500

a)

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{36000-32500}{2500}=1.40[/tex]

The sales associate who makes 36000 is 1.4 standard deviation above the mean salary.

b)

As per chebyshev's theorem, [tex](1-\frac{1}{k^2})[/tex] of the observations fall within k standard deviation of the mean, i.e. within [tex]\mu\pm k\sigma[/tex]

[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{26250-32500}{2500}=-2.50\\\\z_2=\frac{x_2-\mu}{\sigma}\\\\z_2=\frac{38750-32500}{2500}=2.50[/tex]

Hence, we need to find proportion of observations within [tex]\mu\pm2.5\sigma[/tex]

k=2.5

[tex](1-\frac{1}{k^2})=1-\frac{1}{2.5^2}=0.84=84\%[/tex]

Hence, 84% of sales associates have salaries between 26250 and 38750.

c)

As per empirical rule for a bell shaped distribution:

[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{27500-32500}{2500}=-2\\\\z_2=\frac{x_2-\mu}{\sigma}\\\\z_2=\frac{37500-32500}{2500}=2[/tex]

Hence, we need to find the proportion of observations within \mu \pm 2\sigma

As per empirical rule, 95.4% of the observations fall within 2 standard deviation of the mean .i.e within [tex]\mu \pm 2\simga[/tex] .Therefore, percentage of sales associates with salaries between 27500 and 37500=95.4%

d)

[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{27500-32500}{2500}=-2[/tex]

Percentage of sales associates with salaries less than 27500 will be equal to the area under the normal curve to the left z=-2

As per empirical rule 95.4% of the observations fall within 2 standard deviation of the mean

Therefore, the percentage of sales associates with salaries less than 27500 : [tex]\frac{100-95.4}{2}=2.3\%[/tex]

e)

[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{42000-32500}{2500}=3.8[/tex]

A z-value greater than 3 is considered as an outlier.

Hence, the salary of 42000 should be considered as outlier.

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The area is:

Explanation:

To find the circle's area, use the formula [tex]\sf{A=\pi r^2}[/tex].

where:

A = area;

π = 3.14 (pi);

r = radius

Diagram:

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 13\ in}\end{picture}[/tex]

Plug in the data:

The numbers are matched to description as follows

-10          This is an integer    

31/π        This is an irrational number

√5          This is an irrational number

-5.6         This is a rational number, but not an integer

An integer are whole numbers both positive and negative

hence -10 is an integer

A rational number is one that has the form p/q, where p and q are both integers and q is not zero

Rational function means that the equation will be a fraction

-5.6 can be written as a fraction and the decimals can be terminated

Irrational numbers are made up of repeating decimals

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Only twice or less, according to 40% of respondents. Suppose the researchers are curious about the percentage of the population that would respond that it was two or less times, in which case the test statistic would be -0.208 and the standard deviation would be 0.048.

H0: The population proportion of women who have experienced two or fewer hangover symptoms in the past year is equal to or greater than 0.5.

Ha: The population proportion of women who have experienced two or fewer hangover symptoms in the past year is less than 0.5.

Set the alpha level

α = 0.05

Calculate the test statistic

n = 618 (women only)

p = 0.4 (from Table 3)

Standard Deviation = sqrt[p*(1-p)/n]

Standard Deviation = sqrt[0.4*(1-0.4)/618]

Standard Deviation = 0.048

Test Statistic = (0.4 - 0.5) / 0.048

Test Statistic = -0.208

Step 4: Make a decision

Since the test statistic (-0.208) is less than the alpha level (0.05), we reject the null hypothesis and conclude that the population proportion of women who have experienced two or fewer hangover symptoms in the past year is less than

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The special segments of a triangle are median, altitude, perpendicular bisector, angle bisector, and mid-segment.

A line segment that establishes a special relationship with the existing segments of a geometrical shape is said to be a special segment.

Using this special segment, we can able to find the other characteristics of the geometry (a triangle or a circle, etc.)

The special segments in a triangle are:

1) Altitude 2) Median 3) Perpendicular bisector and 4) Angle bisector

Altitude: This line segment whose one end starts at one of the vertexes of the triangle and the other end is perpendicular to the opposite side of the triangle.

The point of intersection of three altitudes of a triangle forms an "Orthocenter".

Median: This line segment whose one end starts at one of the vertexes of a triangle and the other end meets at the midpoint of the opposite side.

The point of intersection of three medians of a triangle forms a "Centroid".

Perpendicular bisectors: These line segments whose ends bisect the two sides of the triangle perpendicularly.

The point of intersection of perpendicular bisectors of a triangle form a "Circumcenter".

Angle bisector: This line segment bisects the angle of the triangle and divides the angle into exactly two halves.

The point of intersection of angle bisectors of a triangle form an "Incenter".

We have one more special segment in a triangle i.e., a midsegment. This line connects two midpoints of opposite sides of a triangle and becomes parallel to the third side.

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The value of the function instance, f (-3) as required to be determined according to the graph of f (x) as in the attached image is; -4.

It follows from the task content that the value of the function instance; f (-3) is to be determined according to the attached graph.

By observation; when a vertical line; x = -3 is drawn; it follows that the line passes through and intersects the lines; y = -1 and y = -4.

However, there's an open circle at; y = -1 which indicates that; -1 is not in the range of f (x).

Ultimately, the value of the function instance; f (-3) as required to be determined is; Choice 4; -4.

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Answer: 108

Step-by-step explanation:
8.78x12.356=108.48568 so the estimate would be 108

Answer:

Q1. The sum of your hat size and shoe size is 54.

Q2. The correct answer is 101.

Q3. The correct answer is 6561.

Step-by-step explanation:

Q1. Let's call the size of your hat H and the size of your shoe S. You can set up the following equation based on the given information:

H = 2S

H = S + 18

Substituting the first equation into the second equation, we get:

2S = S + 18

S = 18

Then, substituting this value back into the first equation, we get:

H = 2S

H = 2 * 18

H = 36

The sum of your hat size and shoe size is S + H = 18 + 36 = 54.

Q2. The least 3-digit odd sum of two prime numbers is 101, which can be achieved by adding the two prime numbers 2 and 99. Both 2 and 99 are prime numbers, and their sum is 101, which is a 3-digit odd number.

Q3. The greatest possible product of the ones digits of 4 numbers is 6561, which can be achieved by choosing the numbers 9901, 9911, 9921, and 9931. The ones digits of these numbers are 1, 1, 1, and 1, respectively, and their product is 6561.

The partial fraction decomposition of the function is x⁴ + 2 / x⁵ + 4x³ = -1/8x + 1/2x³ + 9/8x(x²+4)

Partial fraction decomposition function:

In algebra, When an algebraic expression is split into a sum of two or more rational expressions, then each part is called a partial fraction.

Given,

Here we have the expression

x⁴ + 2 / x⁵ + 4x³

Here we need to find the partial fraction decomposition function.

In order to solve this, first we have to factorize the denominator, then we get,

=> x⁴ + 2 / x⁵ + 4x³ = (x⁴ + 2) / x³ (x² + 4)

Now,  Partial fraction for each factors is written as,

=> A/x + B/x² + C/x³ + (Dx + E)/ (x² + 4)

Now, we have to  Multiply through by the common denominator of x³ (x² + 4), then we get,

=>  x⁴+2=A (x²(x²+4)) + B(x(x²+4)) + C (x²+4) + (Dx + E)(x³)

When we simplify this one, then we get,

=> x⁴ + 2 =Ax⁴ + 4Ax² + Bx³ + 4Bx + Cx² + 4C + Dx⁴ + Ex³

Group the x-terms and the constant terms

=> x⁴ + 2 =(A +D)x⁴ + (4A + C) x² + (B + E)x³ + 4Bx + 4C

Coefficients of the two polynomials must be equal, so we get equations

A+D=1

B+E=0

4A+C=0

4B=0

4C=2

After solving these equations, we get

A = -1/8, B = 0, C = 1/2, D=9/8, E = 0

Then when we substitute these values in the original fraction,

=> -1/8x + 1/2x³ + 9/8x(x²+4)

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On solving the question, we got to know that - Due to this, at x=0 there is no vertical asymptote , there is a removable discontinuity at x= -a

Consider a function f(x) that is continuous for all values of a, changes in value as x approaches a while remaining undefined at x = a. increase. The vertical asymptote of f(x) at x = a is now a vertical line that may be drawn.

According to its study, the function's asymptote and discontinuity are found to be as

Due to this, at x=0 there is no vertical asymptote

and, also there is a removable discontinuity at x= -a

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Using Poisson distribution to calculate the probability distribution of the event, the probability is 0.2084

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates an impossibility and 1 indicates a certainty.

A probability distribution is a mathematical function that describes the likelihood of a random variable taking on a particular value or set of values. It is used to describe the behavior of random variables, either discrete (e.g. coin flips) or continuous (e.g. temperatures), and is often used in the field of statistics to predict the behavior of a system or process.

Using Poisson distribution;

P(X ≥ 5) = 1 - P(X ≤ 4)

P= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))

P= 1 - (e^(-4.615) + (4.615*e^(-4.615))/1! + (4.615^2*e^(-4.615))/2! + (4.615^3*e^(-4.615))/3! + (4.615^4*e^(-4.615))/4!)

P = 0.2084

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Answer: They always have one pair of parallel lines.

Step-by-step explanation:

The probability that one of the following numbers is rolled is 0.135.

We are provided a 37 sided dice. Hence, each of the number between 1 to 37 can be rolled. Now, to find the probability of rolling any of these five numbers, we will simply perform the multiplication.

The formula to be used for calculation of probability to roll any one number on the dice -

Probability = number of favourable outcomes ÷ total number of outcomes

Keep the values in formula

Probability = 1/37

Now, for the mentioned five numbers among which any can be rolled, the probability is -

Probability = 5 × (1/37)

Performing multiplication

Probability = 5/37

Performing division

Probability = 0.135

Hence, the probability is 0.135.

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The statement is true for parallelogram is a square is a) All the rhombuses are squares.

In a rhombus, the opposing sides are parallel. In a rhombus, the opposing angles are equal. Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals.

Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals. One of the most significant characteristics of rhombus diagonals is this. Two adjacent angles added together equal 180°.

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Answer:

6418698

-3485835

2932863

Step-by-step explanation: