One of the legs of a right triangle measures 17 cm and its hypotenuse measures 19 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answer:352 square inches

Step-by-step explanation:edge

The point estimate of the population standard deviation is   2.82

Since the  given  simple random sample is   6 8 10 8 10 6. considering  the data of the sample be denoted by X.  the mean of the sample  is

X'=1/n ∑X, where n is the number of data points

 =6+ 8 +10+ 8+ 10+ 6/ 6   =  6

Since  the  formula for The point estimate of the population standard deviation is:

s= [tex]\sqrt{}[/tex](1/(n-1)* ∑(X−X')^2,  where  X' is the sample  mean and n is the

s=[tex]\sqrt{}[/tex]( 1/(6-1)*{(6-6)^2+(8-6)^2+(10-6)^2+(8-6)^2+(10-6)^2)

= [tex]\sqrt{}[/tex](1/5 *(4+16+4+16)

= [tex]\sqrt{}[/tex](1/5 *(40))

=[tex]\sqrt{}[/tex](8)

=1.41*2

=2.82

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The personnel team should not believe that the mean number is ten

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

x = the number of sick days they took for the past year

Also, we have the following representation of the values of x

x = 12; 4; 15; 3; 11; 8; 6; 8

The mean of a set of observations can be calculated using the following equation

Mean = Sum of observations/Count of observations

Substitute the known values in the above equation, so, we have the following representation

Mean = (12 + 4 + 15 + 3 + 11 + 8 + 6 + 8)/8

Evaluate the sum in the above equation

So, we have the following representation

Mean = 67/8

Evaluate the quotient in the above equation

So, we have the following representation

Mean = 8.375

8.375 does not approximate to 10

So, the mean number is not ten

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Answer:


the answer is 3,5 and 7

Step-by-step explanation:

if congruent means identical or technically parallel if you think about it what is on the opposite side of one and that is how you would get the answer of 3,5 and 7 because they are congruent to The Answer 1

Answer:

Step-by-step explanation:

The length of the major arc is (203/18)π.

What is a length of an arc?

The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc.

Here, we have

The circle with center K has an arc with a radius of 7 inches and an angle subtended at the center which measures 70 degrees.

The major arc LNM would have its central angle measured as:

Angle ∅ = 360 - 70 (Sum of angles on a point equals 360)

Angle ∅ = 290

The calculation for the length of an arc is given as;

Length of arc = (∅/360) x 2πr

Where ∅ = 290, and r = 7, the length of the major arc becomes;

Length of arc = (290/360) x 2 x π x 7

Length of arc = (29/36) x 14π

Length of arc = (29 x π x 14)/36

Length of arc = 203π/18

Hence, the length of the major arc is (203/18)π.

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The width of the rectangle is 60 meters

The area A, in square meters, of a rectangle is given by the equation

A = 70w - w²

where w is the width of the rectangle in meters.

70w - w² = 600

70w - w²- 600 = 0

w²-70w+600 = 0

w²-60w-10w+600 = 0

(w-60)(w-10) = 0

w =60

w =10

the width of the rectangle is 60 meters

Subtraction:

The act of removing elements from a collection is represented by subtraction. Subtraction is symbolized by the negative symbol. The stack will now include five oranges rather than nine if, for instance, four of the nine oranges that are stacked together (as in the figure above) are then moved to a basket. As a result, 5 is the difference between 9 and 4, which is the same as 9 less 4. Subtraction can be applied to other types of numbers in addition to natural numbers. Subtraction is represented by the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.

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{4, 5, 6, 7} total 4 values which diagonal can take constraint is it must be an integer.

It is the shape enclosed by 4 line segments. So, it has 4 vertices as well as four angles with the total of 2 diagonals.

It is the shape enclosed by the 3 lines and have 3 vertices with 3 angles and constitute no diagonals.

The triangle inequality applies.

In order for ACD to be a possible triangle, the length of the AC must lie between CD-DA=0 and CD+DA=8.

In order for ABD to be a possible triangle, the length of AC must in range between BC-AB=3 and BC+AB=9.

The values common to both these restrictions are numbers between 3 and 8. Assuming that we don't want the diagonal to be coincident with any of the  sides, its integer length will be one of the ...

{4, 5, 6, 7}

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The  common ratio is 4.

The next 3 terms are 192,768, 3072

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

Here, 48/12 = 12/3 = 4  ( it is a constant ratio )

Hence it is a geometric sequence and common ratio is 4.

Next 3 terms can be found by multiplying the common ratio with the previous term.

48*4=192

192*4=768

768*4=3072

So, the next 3 terms are 192,768, 3072

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When we are writing the steps for solution of this. Then , the first step of solution is simplfy the expression using multiplication of outside bracket terms with inside terms .

We have given that

equation , 3(2x + 6) – 4x = 2(5x – 2) + 6

from expression we eaisly seen it ia an linear equation with one variable "x" .

we will solve it step by step using linear operations like substraction, addition , multiple etc .

first step : simplfy the algebaric expression (multiplication)

=> 3 ×2x + 3× 6 - 4x = 2×5x - 2×2 + 6

=> 6x - 18 - 4x = 10x - 4 + 6

Step 2 : subtraction and addition of similar terms (i.e constant with constant and variable x cofficient with varible cofficient) both sides we get ,

=> 2x - 18 = 10x +2

=> 10x - 2x = 18+ 2

=> 8x = 20

finally , divided by 8 both side to get the value of x .

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The rate at which the water level is rising when the water level is 5 cm is; dh/dt = 1.6 cm/s

We are told that;

length of square side; s = 4 cm

height of pyramid; h = 11 cm

volumetric rate; dV/dt = 35 cm³/s

Since the base is square shaped and we know that area of a square = s², then we can say that;

Volume of pyramid = ¹/₃s²h

The pyramid has a height of 11 cm and length of its' square base side is 11 cm.

Now, regardless of the water height, the surface of the water will always be square shaped. This implies that the ratio of the height to the top side of square will always be the same. Thus, we can say that; s = 4/8 h = h/2

Thus, Volume is;

V = ¹/₃ × (h/2)² × h

V = ¹/₃ × h³/4

V = h³/12

dV/dt = (3h²/4) dh/dt

Plugging in the relevant values gives;

30  = (3 × 5²/4) dh/dt

120 = 75 dh/dt

dh/dt = 120/75

dh/dt = 1.6 cm/s

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Number of ways to form four letters strings formed using a, b, c, d, e with the given conditions is equal to 150ways.

As given in the question,

Given letters are a, b, c, d, e has

Number of vowel = 2

Number of consonant= 3

Number of letter strings to be formed = 4

Condition:

First letter must be vowel

Last letter must be consonant

First place filled in 2 ways

Second and Third place filled in 5ways

Last place filled in 3 ways

Total number of ways to form four letters strings

= 2 × 5 × 5 × 3

= 150

Therefore, number of ways to form four letter string is 150 ways.

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The probability of getting at least one run of 3 heads in a row be

1021/1024.

Given, a simulation is performed to estimate the probability of getting at least one run of 3 heads in a row in 10 flips of a fair coin.

We have to find the probability of getting at least one run of 3 heads in a row.

Required Probability = 1 - P(X = 0) - P(X = 1) - P(X = 2)

P(X = 0) = P(X = 1) = P(X = 2) = (1/2)^10

Required Probability = 1 - (1/2)^10 - (1/2)^10 - (1/2)^10

Required Probability = 1 - 3/1024

So, the probability of the given event be,

1021/1024

Hence, the probability of getting at least one run of 3 heads in a row be

1021/1024.

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We can expand a binomial to the 6th power by simplifying each of the expansion's terms.

An algebraic expression with two non-zero terms is called a binomial. Binomial expression examples: The binomial with two variables, a and b, is a2 + 2b. A binomial in two variables, x and y, is 5x3 - 9y2. A binomial is a polynomial in algebra that is created by adding two terms, each of which is a monomial. After monomials, it is the most basic type of sparse polynomial.

Given,

We can expand a binomial to the 6th power in following steps:

From the nth row of Pascal's triangle, count the number of terms and their coefficients.

Start with the first phrase that has no b terms and only an an.

With each term of the expansion, a loses power.

With each term of the expansion, b's power grows.

Simplify each of the expansion's terms.

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A number is decreased by 8%, the result is 79. So the original number to the nearest tenth is 85.8.

These are the specified parameters:

a number is decreased by 8%, the result is 79.

Suppose, a number = x

a number - 8% a number = 79

x - 8/100 x = 79

100/100 x - 8/100 x = 79

92/100 x = 79

            x = 79 × 100/92

            x = 7900/92

            x = 85.8

So these numbers are 85.8.

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The equation of a line in point slope form is y - y₁ = m(x - x₁) and the equation of a line in slope intercept form is y = mx + b.

The equation of a line can be represented in different form such as point slope form, slope intercept form, general form and standard form.

The equation of a line in point slope form is as follows:

y - y₁ = m(x - x₁)

where

The equation of a line in slope intercept form is as follows:

y = mx + b

where

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The revolution of the gear having 200 teeth was 500 rpm.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Given that the rotational speed of a driven gear is inversely proportional to the number of teeth on a gear.

T1/T2 = R2/R1

As per the question, the required values as

T1 = 200

T2 = 50

R2 = 2,000 rpm

200/50 = 2,000 /R1

R1 = (2,000 × 50)/200

R1 = 500

Therefore, the revolution of the gear having 200 teeth was 500 rpm.

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Using the Central Limit Theorem, the given statements are true or false in following

a) True

b) True

c) True

d)True

e) True

a) From the definition of central limit theorem, by law of large number to sample average converge almost slowly to the population average.

So, based on CLT the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large i.e ., True.

b) Same reason as (a) , based on CLT the usually considers that sample 51Z6 30 is sufficiently large is true

c) If we generate 1000 samples of Binomial (10;0.3)distribution are plot a histogram then it looks like normal distribution.

So, the Central Limit Theorem be applied to both discrete and continols Fandom variables is true.

d) Whatever be the parent distribution , if sample size ,n is large then sample mean means

converges in probability to the population mean.

So, the given option (d) is true .

e) If population size is normally distributed then sample mean is also normally distributed for all sample size.

So, option(e) is also true.

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Complete question:

Problem Central Limit Theorem) _ Are the following statements true or false?

a)Easy. Based the Central Limit Theorem_ the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large.

b)Easy. Then applying the Central Limit Theorem. l usually conziders that sample 51Z6 30 is sufficiently large.

c)Easy. the Central Limit Theorem be applied to both discrete and continols Fandom variables .

d): Assuming that the sample size is sufficiently large the Central Limit Theorem permits draw conclusions about the population based strictly sample data. and without having aIV knowledge about the distribution of the underlying population:

(e) Moderate_ Assuming that the population is normally distributed_ the sampling distribution of the sample mean is normally distributed for samples of all sizes_

The value of c2 is 10

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

1) erode the slope.

2) Decide on the point.

3) In the point-slope form, y y 1 = m (x x 1), substitute the values. y − y 1 = m (x − x 1) .

4) Slope-intercept form should be used to write the equation.

In the above equation, the equation is written in point-slope form

Hence from the above method

m is 4

c2 is 10

Hence the answer is 10

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Answer:

1.70507 x 10^5

Step-by-step explanation:

First, we multiply 1.67 x 1021:

1.67 x 1021 = 1705.07.

So, 1705.07 is for one drop of water. We need to find 100 drops of water. To do this, we can set up this equation:

1705.07 x 100 = 170,507

Now, we have to convert this number into scientific notation. How do we do this? The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number:

1.70507 x 10^5 is our answer.

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The total VA( volt-ampere ) that must be used in a service calculation for 50' show window is 125000VA.

A volt-ampere (SI symbol: VA or V A, abbreviated as VA) is the unit of perceived power in an electrical circuit. The apparent power is equal to the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are commonly used to analyze alternating current (AC) circuits. In direct current (DC) circuits, this product equals the real power in watts. The volt-ampere is dimensionally identical to the watt: 1 VA = 1 W in SI units).

The total VA that must be used in a service calculation for 50' show window is, Therefore, by using VA linear foot method,

200 VA per linear foot×50'=10000VA10000VA×1.25

=125000VA

Hence, the total VA that must be used in a service calculation for 50' shadow is 125000VA.

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When the coffee in the cone is 5 inches high, we need to determine how quickly the level in the pot is rising. deep and how quickly is the cone's level falling? Use the equation for the volume of a cone and a cylinder pot. Make use of it to achieve your goals.

We know that a conical filter with "r" as the radius and "h" as the height will have a volume of V conical 1/3 πr²h (2)

The coffee is draining from a conical filter at a rate of dVdt=10in3/min, and the volume of the cylindrical coffeepot will be Vcylindrical=r2h.

The term "rate of change" (ROC) describes the rate at which something changes over time. Therefore, it is not the magnitude of individual changes but rather the acceleration or deceleration of changes (the rate). Rate of change is used in finance to understand price returns and determine trend momentum.

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Answer:

see explanation

Step-by-step explanation:

(i)

substitute x = g(x) into f(x) , that is

f(g(x))

= f(x² + 5)

= 2(x² + 5) - 1

= 2x² + 10 - 1

= 2x² + 9

--------------------------------------

(ii)

substitute x = f(x) into g(x) , that is

g(f(x))

= g(2x - 1)

= (2x - 1)² + 5 ← expand factor using FOIL

= 4x² - 4x + 1 + 5

= 4x² - 4x + 6

The four types of agile are:
Scrum, Kanban,
Extreme Programming (XP),
Lean Development, and Cryst.

What is the Agile cycle?

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.

Hence,

The four types of agile are:

Scrum, Kanban,

Extreme Programming (XP),

Lean Development, and Cryst.

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The value of x in the similar triangles is 11.4.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore,

ΔACB ~ ΔEFD

Hence,

AC / EF = CB / FD = AB / ED

Therefore, let's find x

x = AB

ED = 3.8

BC = 15

FD = 5

x / 3.8 = 15 / 5

cross multiply

5x = 15 × 3.8

5x = 57

divide both sides of the equation by 5

x = 57 / 5

x = 11.4

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The rate of change of f(x) = 2(4)^x is equal to the rate of change of the function in the graph. Therefore, the correct answer option is: A. equal to.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x for the function in the graph, which represents a line that passes through the points (0, 2) and (1, 6):

Rate of change, m = (6 - 2)/(1 - 0)

Rate of change, m = 4/1

Rate of change, m = 4.

From function 1 [f(x) = 2(4)^x], we can logically deduce that the rate of change is equal to 4.

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The graphs only show the sampling distributions of X and Y, and do not provide any information on whether the estimators are biased or unbiased.

Creating, storing, manipulating, and analyzing graphs and graph data is referred to as "graph management." Graphs are a visual representation of data that are frequently used to highlight correlations between various data points or parameters to depict trends and patterns. Graph handling is the use of specialized software and algorithms to generate and edit graphs, as well as to derive insights from the data they represent. This might involve activities like converting raw data into a graph, utilizing filters to emphasize particular trends, or employing mathematical algorithms to look for patterns in the data. Graph manipulation is an important part of data analysis and visualization, and it is used in a variety of fields such as business, science, and engineering.

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The following statements are TRUE about hypothesis testing ;

hypothesis testing is known as statistical inference type that uses data from a sample to develop inferences about a population parameter or population probability distribution. An educated guess is first made on the parameter or distribution.

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The scale factor of B to A is 1/4

The size by which the shape is enlarged or reduced is called as its scale factor. It is used when we need to increase the size of a 2D shape, such as circle, triangle, square, rectangle, etc.

If A is an image and B is another image, scale factor A to B means figure B was enlarged 4 times the size of A.

So if Figure B is 4 times bigger than A, then figure A is 4 times smaller than B. which means if A is 1/4 times as small as B.

In conclusion, the scale factor of B to A is 1/4

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Answer:

y=2x-5

Step-by-step explanation:

1 u must calculate the slop then the amount of b

by -3=1×2-b

-5=b

so after we find the number if y we will make an equation y=2x-5

115, 540, and 876 are legitimate random samples.

An irregular example is an example that is picked haphazardly. It might be more appropriate to refer to it as a sample chosen at random. In order to avoid bias and other undesirable effects, random samples are used.

Three distinct values between 1 and 1410 will constitute a legitimate random sample. As a result, the first sample cannot be random because 772 are being repeated.

Because 1470 is greater than 1410, the third sample cannot be random.

Because there are four values, the fourth sample cannot be random.

Thus, 115, 540, and 876 are accurate plots.

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