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The value of the expression given as 10pi is 31.42

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It should be noted that the value of pi is 3.142.

Therefore, the value of 10 pi will be:.

= 10 × 3.142

= 31.42

The value is 31.42.

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The simplified expression is (x-2).

What is expression?

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

We are given a function
(x-1)(x-2)x^2-9x+14/(x-7)(x^2-3x+2)

We have to simplify the above expression

And in order to do so we first simplify the quadratic expression into linear expression or factors Then cancel the common terms from numerator and denominator.

On simplifying the expression we get

(x-1)(x-2)(x-7)(x-2)/(x-7)(x-2)(x-1)

On cancelling the common terms we get

x-2

Which is the required simplified expression.

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Answer:

1. 2,2,3,p

2. 2,2,2,2,a,x,x

If the ratio of jackals to hyenas is 4 to 7 then the number of hyenas will be equal to 294.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.

As per the given information in the question,

The ratio of jackals to hyenas is 4 : 7.

Total number of jackals = 168

Let the total number of hyenas be x.

x = (7 × 168)/4

x = 1176/4

x = 294.

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Answer:

(x-3)^2+(y+2)^2=164

Step-by-step explanation:

radius is

a) The wording for the random variable is given as follows:

n X = the number of 337 randomly selected people who get the vaccine and do not get the flu;

b) The symbol is: n = 337.

c) The symbol is: p = 0.8.

d) P(X = 265) = 0.0426.

e) P(X < 265) = 0.2451.

f) P(X > 265) = 0.7123.

g) P(X = 268) = 0.0545.

h) P(X < 268) = 0.3859.

i) P(X > 268) = 0.5596.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution in this problem are given as follows:

n = 337, p = 0.8.

Hence the mean and the standard deviation for the approximation are given as follows:

Using continuity correction, the probability that exactly 265 people do not get the flu is the p-value of Z when X = 265.5 subtracted by the p-value of Z when X = 264.5.

X = 265.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (265.5 - 269.6)/7.34

Z = -0.56

Z = -0.56 has a p-value of 0.2877.

X = 264.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (264.5 - 269.6)/7.34

Z = -0.69

Z = -0.69 has a p-value of 0.2451.

Hence:

0.2877 - 0.2451 = 0.0426.

Then:

e) P(X < 265) = 0.2451 -> p-value of Z when X = 264.5.

f) P(X > 265) = 1 - 0.2877 = 0.7123 -> one subtracted by the p-value of Z when X = 265.5.

For exactly 268, we have the same logic as follows:

X = 265.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (268.5 - 269.6)/7.34

Z = -0.15

Z = -0.15 has a p-value of 0.4404.

X = 267.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (267.5 - 269.6)/7.34

Z = -0.29

Z = -0.29 has a p-value of 0.3859.

Hence:

0.4404 - 0.3859 = 0.0545.

Then:

h) P(X < 268) = 0.3859 -> p-value of Z when X = 267.5.

i) P(X > 268) = 1 - 0.4404 = 0.5596.

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What Christina did wrong in estimating the percentage is that; She  incorrectly multiplied 90 times 0.9

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

The correct steps should be as follows;

1. (90)(190%)

2. We will break down 190% into 2 sums to get;

(90)(100% + 90%)

3. We will apply distributive property of Algebra to get;

(90)(100%) + (90)(90%)

4. We will convert the percentage to decimal to get;

(90)(1.0) + (90)(0.9)

5. We will multiply out the terms to get;

90 + 8.1

6. We will add up the terms to get; 98.1

Comparing these steps to that of Christina, we can say that what she did wrong was that she incorrectly multiplied 90 times 0.9.

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The p - value is less than the significance level, we conclude that we must reject the null hypothesis .

Given :

think about testing the significance of the regression slope. when the p-value is less than the significance level, we conclude that.

A Hypothesis Test for a Regression Slope :

suppose the p - value less than the significance level we have evidence to reject the null hypothesis.

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A single statement that declares and initializes an array named a that has 10 elements of type int. is as:

int [] denominations = {10,20,30,40,50,60,70,80,90,100};

We know that there are two ways you can declare and initialize as array in Java.

The first with the new keyword, where you have to initialize the values one by one.

The second is by putting he values in curly brackets.

An Array is a collection of data of the same type. Arrays are an important part of the fundamental data structures in Java.

An Array is usually declared so you can have multiple values in the same memory.

The syntax for declaring an array is: datatype[] arrayName;

Datatype means the type of objects that will be stored in the array ed. int, char,etc.

You can declare an array of arrays by following the array declarator with a list of bracketed constant expressions.

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On solving the provided question, we got to know the vertices those are - Q' = (-3, 3), R' = (-5, -3), S' = (-2, -2), T' = (0, 1)

As kids learn about the characteristics of 3D forms, vertices, faces, and edges start to appear often in geometry. Here's what it means and how to figure out how many vertices, faces, and edges each form has. The most popular forms' edge, face, and vertex counts are also included.

[tex]The coordinates of the vertices of the quadrilateral are;[/tex]

[tex]T(-2, 1), Q(1, 3), S(0, -2), R(3, -3)[/tex]

T

The coordinates of the vertices of the quadrilateral are;

[tex]T(2, 0)QRST, gives;\\ T(2, 0)QRST→ T(-2 + 2, 1), Q(1 + 2, 3), S(0 + 2, -2), R(3 + 2, -3)\\ T(2, 0)QRST→ T(0, 1), Q(3, 3), S(2, -2), R(5, -3)\\[/tex]

For the next process R y-axis which is the reflection about the y-axis, the preimage (x, y) becomes the image (-x, y)

Therefore, we have;

[tex]R y-axis(T(0, 1), Q(3, 3), S(2, -2), R(5, -3)) = T'(0, 1), Q'(-3, 3), S'(-2, -2), R'(-5, -3)\\ From which we get (Ry-axis T(2, 0))(QRST = T'(0, 1), Q'(-3, 3), S'(-2, -2), R'(-5, -3).[/tex]

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The RAM of the larger server is 30GB and the RAM of the small server is 20GB.

The first step is to form a system of equations:

2L + 4S = 100 equation 1

L + 3S = 60 equation 2

The elimination method would be used to determine the required values:

In order to determine the value of S, multiply equation 2 by 2

2L + 6S = 120 equation 3

Subtract equation 1 from equation 3 :

2S = 20

Divide both sides of the equation by 2:

S = 20 / 2 = 10

Substitute for s in equation 1 :

2L + 4(10) = 100

2L + 40 = 100

2L = 100 - 40

2L = 60

L = 60 / 2

L = 30

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The set of independent variables of a function called the domain of the function.

Domain is the set of values for which the given function is defined.

The set of all possible values of the dependent variable called the range.

The range of a function refers to all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.

The set of all possible values for the function called the the domain of the function.

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(B) All mathematic teachers who attended the conference.

Option B is the correct option.

The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are the focus of the science of statistics.

A statistic is a numerical representation of a sample property. One example of a statistic is the average number of points students in one math class got at the conclusion of the term if we assume that class to be representative of the population of all math classrooms.

Due to their role in assisting decision-making, statistics are crucial. To track progress, evaluate performance, identify issues, and set priorities, governments, organizations, and corporations all gather statistics.

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The Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is ( -0.0654 , 0.0654 ) .

Given :

Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error.sin x = x − x^3 / 6 ( | error | < 0.01 )

The next nonzero term in the Taylor series for sine is x^5 / 120 .

x^5 / 120 < .00000001

-0.00000001 < x^5 / 120 < .00000001

-0.0000012 < x^5 < .0000012

( -0.0000012 )^1/5 < x < ( .0000012 )^1/5

we have ( .0000012 )^1/5 ≈ .0654

= ( -0.0654 , 0.0654 )

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As the data says , the null and alternate hypothesis will be H0 :p=0.50 and H1:p ≠ 0.50

Let p stand for the true proportion of odds.

To compare the

null hypothesis H0:P = 0.50

alternative hypothesis H1:p 0.50

Let p represent the sample proportion and n represent the sample size.

here,

p = 14/40

= 0.350

n=40, p₀ = 0.500,

= proportional standard error under null 0.50 * (1 -0.50) /40

= 0.079057

The test statistic is as follows:

z = p - p0 / √ p0  ( 1  - p0) / n )

They follow a typical normal distribution under H0

If P-value 0.05 or |Zobs| > 0, we reject H0 t 0.05 threshold of significance. z0.025

Now,

The test statistic value is -1.897367.

1.959964 is the key value.

P-value = 2*P(Z - 1.897367) + P(|z|>Zobs)

= 2 * 0.028890

= 0.057780≈ 0.0578

Because the p-value is greater than 0.05 and |Zobs|  = 1.959964,

As a result, we fail to reject H0 at the 0.05 threshold of significance.

As a result, the population proportion has decreased.

Null and alternate hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always expects no effect or no association between variables, whereas the alternative hypothesis of a test always predicts no effect or no association between variables.

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Answer:

Step-by-step explanation:

Step 1: The sample proportion is pˆ=1440=0.35, the hypothesized proportion is p0=0.5, and the sample size n=40.

Step 2: The test statistic, rounding to two decimal places, is z=0.35−0.50.5(1−0.5)40−−−−−−−−−−√≈−1.897.

Step 3: Since the test is two-tailed and the test statistic is negative, entering the function =2*Norm.S.Dist(−1.90,1) into Excel returns a p-value, rounding to three decimal places, of 0.058.

Answer:

x = 15

Step-by-step explanation:

4(x - 20) = - 20 ( divide both sides by 4 )

x - 20 = - 5 ( add 20 to both sides )

x = 15

Due to the comparison of the responses of drivers at two distinct volume levels, the experiment reported provides an illustration of matched pairs.

For the purpose of comparing the outcomes and coming to a conclusion about this reaction, matched pairs are a sort of experiment that places one or more people in two distinct scenarios.

According to the aforementioned, the scenario described is an example of matched pairs because it calls for the driver to react to obstacles while listening to music at two different volume levels. In this regard, their results are compared to see if the volume affects their performance and reaction time.

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The 95% confidence interval to estimate the proportion of students on financial aid = (0.522, 0.658)

In this question we have been given a university dean is interested in determining the proportion of students who receive some sort of financial aid.

Let p be the population proportion of students who receive some financial aid.

The dean randomly selects 200 students and finds that 118 of them are receiving financial aid.

i.e. n= 200

p{hat} = 118/200 = 0.59

We know that the critical value for 95% confidence interval : z = 1.96

The standard deviation would be,

σ = √[p{hat}(1 - p{hat})/N]

σ = √0.59(1 - 0.59)/200

σ = √(0.0012095)

σ = 0.0348

The 95% confidence interval for population proportion would be,

(0.59 ± (1.96 * 0.0348))

= (0.59 - (1.96 * 0.0348), 0.59 + (1.96 * 0.0348))

= (0.5218, 0.6582)

Therefore, the 95% confidence interval : (0.522, 0.658)

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Based on the given consume reports data, the t value is 2.228.

T - value:

In statistics, t - value measures the size of the difference relative to the variation in your sample data.

Given,

Here we have the tale with  price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports.

Now, we need to find the t test indicate a significant relationship between price and the overall score.

While we looking into the question, the values in this one are,

n = 6

And table of 6 stereo headphone price and overall score are given.

Based on the given details we have calculated the frequency table and the table is attached below.

Based on the resulting table we have identified that the value of t is 2.228.

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Answer:

56°

Step-by-step explanation:

the measurement of angle O is less than 90°, but not 62°, and angle O is larger than angle R, so angle O is not 28°, so the only other option less than 90° is 56°

Answer:

decagon (10-sided polygon)

Step-by-step explanation:

A regular polygon has a minimum rotation of 360/n degrees about its center, where n is the number of sides in the polygon.

Therefore, the regular polygon with a minimum rotation of 36 degrees about its center is a polygon with 360/36 = 10 sides, or a decagon.

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Answer:

b

Step-by-step explanation:

Therefore the point P in the coordinate plane comes out to be (2,10)

and the distance between the points is 50.99 units

equation is another name for a declaration of equality between two expressions that contain variables and/or numbers. From solving equations is essentially solving problems, solving equations has been the central goal of mathematics since its inception. There are many distinct types of equations that range in complexity, from simple algebraic equations that merely need addition or multiplication through differential equations, exponential equations that use exponential expressions, and integral equations.

we know that,

the point p on the line y=5x that is closest to the point (52,0) will be on the line perpendicular to the line y=5x and go through the point (52,0)

step 1

the slope m perpendicular to the line y=5x is

m1=5

if two lines are perpendicular

m1*m2=-1

m2=-1/5

step 2

with m=-1/5 and the point (78,0) find the equation of a line

y-y1=m*(x-x1)-----> y-0=(-1/5)*(x-52)----> y=-0.20x+10.4

step 3

resolve the equation systems

y=5x

y=-0.20x+10.4

Thus substituting the values in y of x

=> 5x=-0.20x+10.4

=> 5.20x=10.4

=> x=2

Therefore the point comes out to be

x=2

y=10

The least distance between P(2,10) &(52,0)= 50.99 units

Therefore the point P in the coordinate plane comes out to be (2,10)

and the distance between the points is 50.99 units

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Answer:

See explanation.

Step-by-step explanation:

Given quadratic:

[tex]x^2+140x-1500[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], first find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

As  a = 1, b = 140 and c = -1500, then:

[tex]\implies a \cdot c=1 \cdot -1500=-1500[/tex]

[tex]\implies b=140[/tex]

Therefore, the two numbers are 150 and -10 as:

[tex]\implies 150 \cdot -10 = -1500[/tex]

[tex]\implies 150+(-10)=140[/tex]

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies x^2+(150-10)x-1500[/tex]

Distribute:

[tex]\implies x^2+150x-10x-1500[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+150)-10(x+150)[/tex]

Factor out the common term  (x + 150):

[tex]\implies (x+150)(x-10)[/tex]

Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.

Given that,

A camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods. The camper's speed while driving was ten times that of the hiker. Three hours were spent driving and hiking together.

We have to determine the camper's hiking speed.

We know that,

Let x represent the increasing rate and 10x represent the driving rate.

Time equation is

80/10x+4/x=3

Simplify

8/x+4/x=3

12/x=3

x=12/3=4

Therefore, Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.

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Answer:

(3 + 8u)(3 - 8u)

Step-by-step explanation:

Conjugated binomials

[tex](9-64u^{2} ) =(3+8u)(3-8u)[/tex]

Hope this helps

The Dialog module prompts the user to select a model, allowing the user to access the database and select data for the decision process or to set criteria for selecting such data .

Given :

prompts the user to select a model, allowing the user to access the database and select data for the decision process or to set criteria for selecting such data.

Dialog module :

The dialog module provides dialog awareness for the Kamailio proxy. It's functionality is to keep track of the current dialog , to offer information about them .

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Answer:

$68.81

Step-by-step explanation:

22% of 56.40 can be found by multiplying

.22 and 56.4, which equals 12.408

therefore, if you add 12.408, or 12.41, to 56.40 you will get 68.81

On solving the provided question, In the case of four numbers, 1 and 3 are odd and 2 and 4 are even. As a result, the numbers are odd in half, so the answer is 1/2.

The proportion of favorable outcomes to all possible outcomes for an event is known as the probability. The quantity of positive outcomes in an experiment with 'n' outcomes is represented by x. The following equation can be used to determine the likelihood of an event:

Probability (event) = positive outcome / overall outcome = x/n

In the case of four numbers, 1 and 3 are odd and 2 and 4 are even. As a result, the numbers are odd in half.

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The hypothesis which motivates the studies which is usually the reason for any data is being collected at first place is called alternative hypothesis.

A hypothesis is an exact clarification that pertains to the set of data that may be examined with the aid of using positive similarly investigations. There are essentially types, namely, null speculation and opportunity speculation. A studies commonly begins offevolved with a hassle. Next, those hypotheses offer the researcher with a few precise restatements and clarifications of the studies hassle.

The standards of the studies hassle withinside the shape of null hypothesis and opportunity hypothesis need to be expressed as a dating among or extra variables. The standards is that the statements need to be the only that expresses the connection among the 2 or extra measurable variables. The null hypothesis and opportunity speculation need to bring clean implications for checking out and mentioning relations.

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Correct Question:

The hypothesis that motivates most studies and is usually the reason the data are being collected in the first place is the __________ hypothesis.