a. Lin is using the diagram to prove the statement, "If a parallelogram has one
right angle, it is a rectangle." Given that EFGH is a parallelogram and angle
HEF is a right angle, write a statement that will help prove angle FGH is also
a right angle.
b. Han then states that the 2 triangles created by diagonal BG must be congruent.
Help Han write a proof that triangle EHG is congruent to triangle GFE.

The year in which the number of both jobs pharmacy technicians and network systems and data communication analysts is equal is 2008.

Considering the set of equations

7.3x - y = -256

12.1x - y = -234

where x represents the period of time since 2003.

y represents the quantity of jobs in thousands.

We have the answer after solving the system:

(x, y) ==> (4.5, 292)

Find the year where the total number of both jobs is equal.

At the solution point, the graphs of the two lines will collide.

The year in which the number from both jobs is equal will be 4.5 years after 2003, since x is the number of years after 2003.

So, here we are:

Year where the sum of the two jobs is equal:

2003 + 4.5 = 2007.5

= 2008 year

As a result, there will be an equal number of both jobs in 2008.

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There are 207 students in the 9 classes at East Middle School. At this rate, how many students are in 6 classes?

1: 54 students

2: 138 students

3: 69 students

4: 250 students

207 / 9 = 23

23 * 6 = 138

Answer:

The letter [tex]r[/tex] in the given formula represents the rate of interest.

Explanation:

Where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).

Hope this helps!

The given expression can be simplified as (x³ + 3x + 5)/(x² - x).

If the fractions have the same denominators then their numerators are added keeping the denominators as the same.

For fractions with different denominators the LCM of the denominators are taken then that is divided by the numerators of each fraction and the number obtained is multiplied to each of them to get the equivalent fraction.

The given expression is as below,

(x² - 5)/x + (x + 8)/(x - 1)

It can be simplified as follows,

(x² - 5)/x + (x + 8)/(x - 1)

= ((x² - 5)(x - 1) + x(x + 8))/(x(x - 1))

= ((x³ - x² - 5x + 5) + x² + 8x)/(x² - x)

= (x³ + 3x + 5)/(x² - x)

Hence, the given expression can be written in the form of single fraction as (x³ + 3x + 5)/(x² - x).

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The equation of circle for both the parts will be as,

(a)  (x-3)² +(y-2)²= 4

(b)   x²+y² = 1

What is circle?

A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.

Main Body:

(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.

Circle centered at (h, k) with radius r:

(x -h)² +(y -k)² = r²

The given circle is ...

(x -2)² +(y -2)² =2²

(x -2)² +(y -2)² = 4

__

(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:

x²+y² = 1

Hence the equation of circle is such.

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The number of tests that it would take for the probability of committing at least one type I error to be at least 0.7 is 118   .

In the question ,

it is given that ,

the probability of committing at least , type I error is = 0.7

we  have to find the number of tests ,

let the number of test be n ,

the above mentioned situation can be written as

1 - P(no type I error is committed) ≥ P(at least type I error is committed)

which is written as ,

1 - (1 - 0.01)ⁿ ≥ 0.7

-(0.99)ⁿ ≥ 0.7 - 1

(0.99)ⁿ ≤ 0.3

On further simplification ,

we get ,

n ≈ 118 .

Therefore , the number of tests are 118 .

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To know the answer check the given file.

Answer:

6, 7, 10

Step-by-step explanation:

7 > x - 4 ( add 4 to both sides )

11 > x , then

x < 11

the values from the table which are solutions are 6, 7, 10

Answer:

Answer is 11

Step-by-step explanation:

7+4>z-4+4

11>z

Answer: Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpoint

Step-by-step explanation: Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointvvIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpoint

Answer:

8

Step-by-step explanation:

23:41

41+23=64

64/8=8

Answer:

You can draw a picture like this:

Step-by-step explanation:

If we are working with fractions, then think of it as a circle.

3 circles divided by 8 people

(Draw 3 circles divided into eighths)

Now, on the first circle, write the number one into one of the slices.

Do the same to the second circle.

Now the third.

How many slices have the number 1 in it?

3 slices have the number 1 in it.

And each whole circle has 8 pieces.

3 (slices) divided by 8 (People) = 3/8

The amount of time it would take for 20% of the water to leak from a full vase is equal to 24.128 minutes.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

From the diagram of the cone (see attachment), we have the following parameters:

Diameter of cone = 4.8 in.

Height of cone = 10 in.

Radius of cone = diameter/2 = 4.8/2 = 2.4 in.

Substituting the given parameters into the formula, we have;

Volume of cone, V = 1/3 × 3.142(2.4² × 10)

Volume of cone, V = 60.32 in³.

For the volume of water that has leaked, we have:

Volume of water leaked = 20/100 × 60.31

Volume of water leaked = 12.062 in³.

For the required amount of time, we have:

Time = Volume/Rate

Time = 12.064/0.5

Time = 24.128 minutes.

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It seems that there is perhaps some missing info here. Could you double check your question to validate the information being asked? Tysm!

Answer:

4 mph

1.5 mph

5 mph

Fastest: Kaliel, slowest: steve

Step-by-step explanation:

The unit for Melissia can be found by finding the slope of the line. The slope is shown to be 4 miles per hour. That is the unit rate, 4 miles per hour.

The unit rate for steve is also shown in the equation y = 1.5x. This equation is the filled in form of y = mx + b where m is equivalent to the slope. Therefore 1.5 is the slope meaning the unit rate is 1.5 miles per hour.

The unit rate for Kaliel is found using the information that he walks 10 miles in two hours. To find how much he goes in 1 hour divide by two getting you 5 miles per hour.

The fastest unit rate is Kalie with 5 miles per hour, and the slowest steve with 1.5 miles per hour.

Answer:

11250

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

hope u new it have fun hsm s

Answer:

no it wont

Step-by-step explanation:

The expressions of the total cost are 1.15t and t * (1 + 0.15)

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

Cost of a ticket = t dollars

Amusement tax on each ticket = 15%

The above parameters mean that the total cost of a ticket can be calculated using the following equation

The total cost of a ticket = Cost of a ticket * (1 + Amusement tax on each ticket)

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

The total cost of a ticket = t * (1 + 15%)

Evaluate the percentage

The total cost of a ticket = t * (1 + 0.15)

So, we have

The total cost of a ticket = t * (1.15)

Evaluate the product

The total cost of a ticket = 1.15t

Hence, the expression is 1.15t

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Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.

One of the common discrete distribution which is used in Statistics is the Binomial distribution. The Binomial distribution often deals with two types of situations, first, the occurring of an event and second, the non-occurring of an event termed respectively as success and failure. The Binomial distribution can be typically characterized by the two parameters namely “n” and “p” where “n” represents the number of trials and “p” represents the fixed probability of occurring of the desired event.

Further, the Binomial distribution can be visualized as an approach to determine the probability of observing a specified number of successes in a specified number of trials. The typical examples of Binomial distribution in our day-to-day life may include the survival of number of cancer patients, from the treatment offered, over a specified period of time;

Winning the number of seats against the number of candidates filed by a certain political party for an election;

Number of people benefiting from a certain house scheme when applied;

Number of covid patients discharged within three days from the hospital after their admission to a hospital for the treatment.

There is another discrete distribution which is equally popular as the Binomial distribution is the Poisson distribution. While the Binomial distribution deals with the number of trials and the probability of a success, Poisson distribution deals with the average number of successes per day or the number of successes observed per unit of time.

Unlike, in the case of a Binomial distribution, for a Poisson distribution, the knowledge of number of trials to get the observed number of successes is not required. The Poisson distribution has only one parameter namely “m” the mean number of successes per given unit of time.

The Poisson distribution is often taken as a limiting case of Binomial distribution, under the following conditions.

The number of trails is indefinitely large i.e., n → ∞

The probability of success, “p” is very small i.e., p → 0

np is finite i.e., np = m where p = m/n and q = 1 – m/n and m > 0.

However, it is not defined if “n” is large means how large and “p” is closed to zero means how small? It is left to the readers to assume how large n should be and how small p should be? As mentioned earlier, the Poisson distribution is often described as a limiting case of Binomial distribution.

Based on the results of the study , published by me clearly proves that even when 10 ≤ n ≤50 and p ≤ 0.2, the Poisson distribution can be a good approximation to Binomial distribution.

Hence the answer is Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.

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lines a and d are neither parallel nor perpendicular.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

The given points of line d is (3,5) and (10,1)

and line an of line a is (5, 8) and (2, 13).

The slope of line d is m 1 = [tex]\frac{1-5}{10-3}[/tex]

m1 = -4/ 7

The slope of line d is m2 = [tex]\frac{13-8}{2-5}[/tex]

m2 = -5/3

if the slope of two lines is equal that is m1 = m2 , then the lines are parallel and the relation m1*m2=−1, then the lines are perpendicular to each other.

Here both condition fails.

Hence, lines a and d are neither parallel nor perpendicular.

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the value for dferror for this analysis is 8.

What is error?

Error is the difference between an actual value and an estimate, or approximate, representation of that value in applied mathematics. The discrepancy between the population's average and the average of a sample taken from that population is a frequent example in statistics. The discrepancy between an irrational number's true value and the values of rational expressions like 22/7, 355/113, 3.14, or 3.14159 serves as an example of round-off error in numerical analysis. A truncation error happens when an infinite series is ignored for all but a small number of terms. For instance, the sum of the infinite series can be used to express the exponential function ex.

df-error = (df-within treatment) - (df-subjects)

df-subjects = n - 1 = 5 - 1 = 4 {n is the no of subjects}

df-within treatment = 12

df-error = 12 - 4 = 8

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Answer:

[tex]\cos(\theta) + \sin(\theta)[/tex]

Step-by-step explanation:

Use the sine angle sum identity.

[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]

[tex]\sin(45\textdegree + \theta)=\sin(45\textdegree)\cos(\theta)+\cos(45\textdegree)\sin(\theta)[/tex]

Now, simplify [tex]\sin(45\textdegree)[/tex] and [tex]\cos(45\textdegree)[/tex] to [tex]\dfrac{\sqrt2}{2}[/tex]:

[tex]\sin(45\textdegree + \theta)=\dfrac{\sqrt2}{2} \cdot \cos(\theta)+\dfrac{\sqrt2}{2} \cdot \sin(\theta)[/tex]

Then, factor out [tex]\dfrac{\sqrt2}{2}[/tex] from each term.

[tex]\sin(45\textdegree + \theta)=\dfrac{\sqrt2}{2} \cdot ( \cos(\theta)+\sin(\theta))[/tex]

Finally, identify what is in the parentheses corresponding to the blank space in the question.

[tex]\cos(\theta) + \sin(\theta)[/tex]

Since , a researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Therefore, the Multiple Regression method will be more appropriate analysis of variance.

Multiple regression analysis is a statistical technique that analyzes the relationship between two or more variables and uses that information to estimate the value of the dependent variable. The goal of multiple regression is to develop a model that describes the dependent variable y with multiple independent variables. Linear regression has only one independent and dependent variable. But for multiple regression, there are many independent variables that help explain or predict the dependent variable y better.

The multiple regression equation is given by

y = a + b 1×1+ b2×2+……+ bk xk

where x1, x2, ….xk are the k independent variables and y is the dependent variable

Advantages of multiple stepwise regression:

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The dimensions of the rectangular swimming pool are 25ft long 10ft wide and 8 feet deep.

A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height. Sometimes the cuboid shape is confused with a cube since it shares some properties of a cube, however, they are different from each other.

Volume of a cuboid  = Length(L) x Width(W) x Depth(d)

but L = 2.5w

2.5w x w x 8 = 2000

20W^2 = 2000

W^2 = 2000/20

W^2 = 100

W = [tex]\sqrt{100}[/tex]

W = 10fft

L = 2.5W, but W = 10ft

L = 2.5 x 10

L = 25ft

In conclusion the length, width and depth are 25ft, 10ft, and 8ft respectively.

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Answer: X is equal to 21

Step-by-step explanation:

Answer:

25 degrees

Step-by-step explanation:

5x - 10 = 115

5x = 115 + 10

5x = 125

5/5 x = 125/5

x = 25

a)The probability that a customer selected will have more than two credit cards is 0.11 ,b)expected value is 1.34 and c)standard deviation is 0.96.

Given, probability distribution table

X p(X)

0 0.18

1 0.44

2 0.27

3 0.08

4 0.03

where,X= number of credit cards people own

Thus, the probability that a customer selected will have more than two credit cards is 0.11 ,expected value is 1.34 and standard deviation is 0.96.

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Your question is incomplete, Here is the complete question.

A bank vice president feels that each savings account customer has, on average, three credit cards. He collected data over a period of time and found the probability distribution given in the following table. The random variable X, represents the number of credit cards people own.

X p(X)

0 0.18

1 0.44

2 0.27

3 0.08

4 0.03

If necessary, use a leading zero and round to 2 decimal places, e.g, 0.25.

(a) Find the probability that a savings account customer selected at random will have more than two credit cards ?

(b) Find the expected value of the number of credit cards a randomly selected customer owns ?

(c) Find the standard deviation of the number of credit cards a randomly selected customer owns ?

The sample size for the given problem is 1499.

What is sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

Given:

An urban economist wishes to estimate the proportion of Americans who own their homes.

p cap = 0.669

1 - p cap = 0.331

margin of error = E = 0.02

 [tex]Z_a_l_p_h_a_/_2[/tex]= 1.645

Sample size = n

[tex]n = (Z_a_l_p_h_a_/_2/E)^2*Pcap*(1 - Pcap)\\= (\frac{1.645}{0.02})^2*0.669*0.331\\ = 1499[/tex]

Hence, the sample size for the given problem is 1499.

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The main difference between experiment and survey is that experiment is laboratory research and survey is field research. Experiments are used to prove theories or hypotheses. Surveys are used to understand the notions of a group of people.

Sum of the 15 two elements subset of $\{1,2,3,4,5,6} = ( N-1) (N)(N+1)/2

Three elements....two at  time  (1,2) (1,3) (2,3)....sum  =   12

Four elements .... two at a time  (1,2) (1,3) (1,4) (2,3) (2,4) (3,4)  .....sum  =  30

Five elements....two at a time  (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5)

Note that for N elements taken 2 at a time....the pattern of sums seems to be

= (N-1)(N)(N+1) / 2

For taking 6 elements taking 2 at a time the sum should be

=(5)(6)(7) /2

=210 /2

=105

Therefore, total sum  of those 15 sums  of the elements of each of the 15 two-element subsets of $\{1,2,3,4,5,6\}$ = 105

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