Determine which is the graph of the given function. f(x)= {2x+5 if x <0},f(x) = {5 if 0 <=x<=10}, f(x) = {2x-10 if x >10}

π√π÷√π  is an irrational number. So option (a) is required answer.

A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number 2. Any irrational number, such as p/q, where p and q are integers, q, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.

Examples of irrational number: √3, ∛2, π

π is an irrational because it is neither ending nor recurrent.

Solving each part of options, we get

π√π÷√π = π

√25 = 5

√π÷π = 1

2√2 ÷ √2 = 2

As most of the option give rational number only one option gives irrational number which is π

We get π from option (a)

So, option (a) is correct option.

Learn more about irrational number here:

https://brainly.com/question/43641

#SPJ1

The equation y = 4 has a greater output at x = 4

The graph and the equation have the same output at x = 6

From the question, we have

From the graph, we can see that

When x = 4, the output is 3

The equation y = 4 implies that, the output is always 4 irrespective of the input value

Hence, the equation has a greater output.

Here, we have the same parameters above

From the graph, we can see that

When y = 4, the input is 6

The equation y = 4 implies that, the output is always 4 irrespective of the input value

Hence, they have the same output at x = 6

Read more about linear equations at:

https://brainly.com/question/4074386

#SPJ1

Proving  X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e".

Given :

If I can prove that X is c.e. and ω∖X is c.e. then I can prove that X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e". But I'm not able to proceed on how should I do this.

Take a computable surjection :

f : ω → W.

Defined  G = { f ( x ) ∣ x ∈ ω and ∀y < x ( f ( y ) < f ( x ) ) }.

here clearly, G ⊆ W .

And G is infinite. For if f ( x ) ∈ G, take the smallest y such that f ( y ) > f ( x ); then f ( y ) ∈ V.

Learn more about the theorem here:

https://brainly.com/question/12642646

#SPJ4

Using substitution method, the system of linear equations showed that there 27 and 35 quarters and nickel respectively

System of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

To solve this problem, we have to write a system of linear equations which consist of two linear equations.

Let;

x + y = 62...eq(i)

0.25x + 0.05y = 8.50 ...eq(ii)

Using substitution method

From equation (i)

x + y = 62

x = 62 - y ...eq(iii)

Put equ(iii) into eq(ii)

0.25( 62 - y) + 0.05y = 8.50

y = 35

Put y = 35 in equation (i)

x + 35 = 62

x = 27

The number of quarters and nickels are 27 and 35 respectively

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

Since the initial displacement is made by s0 and body moves with initial velocity and acceleration after that, the final displacement after time t is

[tex]s= \frac {1}{2} at ^{2} + v_{0}t+s_{0}[/tex]

The displacement is only the difference between the locations of the two marks and is unrelated to the route used to get there.

The formula is:

[tex]a= \frac {Velocity}{Time}[/tex] (Acceleration)

[tex]v= \frac {Displacement}{Time}[/tex](Velocity)

Initial Displacement = s0

Displacement from position s0 after time t  = [tex]\frac {1}{2} at ^{2} + v_{0}t[/tex]

Total Final Displacement (s) = [tex]\frac {1}{2} at ^{2} + v_{0}t+s_{0}[/tex]

To learn more about Displacement visit:

https://brainly.com/question/11934397

#SPJ4

The circumcenter of a triangle formed by (4,2), (3,-3) and (2,2) is located at (3, -0.4).

The circumcenter of a triangle is the point of intersection of the three perpendicular bisectors of the sides of a triangle.

Let A = vertex at (4,2)

B = vertex at (3,-3)

C = vertex at (2,2)

Get the midpoint of each side.

midpoint = [(x₂ + x₁)/2 , (y₂ + y₁)/2]

side AB : midpoint = [(3 + 4)/2 , (-3 + 2)/2] = (3.5, -0.5)

side AC : midpoint = [(4 + 2)/2 , (2 + 2)/2] = (3, 2)

side BC : midpoint = [(3 + 2)/2 , (-3 + 2)/2] = (2.5, -0.5)

Get the slope of each side.

slope = (y₂ - y₁) / (x₂ - x₁)

side AB : slope = (-3 - 2) / (3 - 4) = 5

side AC : slope = (2 - 2) / (2 - 4) = 0/-2 = 0

side BC : slope = (2 - -3) / (2 - 3) = -5

Determine the equation of the line of each of the three perpendicular bisectors of the sides of a triangle, that passes through the midpoint and with a slope equal to the negative reciprocal of the slope of the side.

y = mx + b

perpendicular bisector of AB :

-0.5 = -1/5(3.5) + b   ;   b = 0.2   ;   y = -1/5x + 0.2

perpendicular bisector of AC :

since AC is a horizontal line, x = 3

perpendicular bisector of BC :

-0.5 = 1/5(2.5) + b   ;   b = -1   ;   y = 1/5x - 1

Since x is already equal to 3, substitute the value of x in the two other equation and solve for y.

y = -1/5x + 0.2

y = -1/5(3) + 0.2

y = -0.4

y = 1/5x - 1

y = 1/5(3) - 1

y = -0.4

Hence, the circumcenter of the triangle is located at (3, -0.4).

Learn more about circumcenter here: https://brainly.com/question/10508382

#SPJ4

The number of hours to operate the mines to minimize cost are Mine 1 hour = 30 hours and Mine 2 hour = 10 hours

The given parameters can be represented using the following table of values

                             Mine 1 (x)              Mine 2 (y)   Available

Regular grade          5                            20             350

Low grade               17                             10              610

Operating cost      7000                     29000

Time                        54                              27

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 7000x + 29000y

Subject to:

5x + 20y ≥ 350

17x + 10y ≥ 610

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (30, 10)

This means that

Mine 1 hour = 30 hours

Mine 2 hour = 10 hours

Hence, the number of hours are 30 and 10 hours

Read more about minimizing cost at

brainly.com/question/1592715

#SPJ1

Tiles are needed = 90

The number of tiles measuring 40cm by 40cm  that are needed to completely cover a wall 4m by 3.6m is 90.

Squares

Square,  a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).

Number of tiles needed

Convert the Meters to Centimeters

4m = 400cm

3.6m = 360 cm

Then

4m by 3.6m = 400 cm × 360 cm

4m by 3.6m = 144000 cm²

Tiles are needed

Number of needed tiles =  144000 cm² / ( 40 cm × 40 cm)

Number of needed tiles =  144,000 cm² /1600 cm²

Number of needed tiles =  90

Tiles are needed = 90

To learn more about Squares visit:

brainly.com/question/14198272

#SPJ4

The probability that Sophia does not break the piñata on the first hit and does break the piñata on the second hit is of:

0.24 = 24%.

In the context of a problem, a probability is calculated as the division of the number of desired outcomes divided by the number of total outcomes.

In the context of this problem, these probabilities are given by the percentages/proportions stated in the problem.

The probability that Sophia does not break the piñata on the first hit and does break the piñata on the second hit is calculated considering these two outcomes given as follows:

The probability is calculated as the multiplication of these outcomes, as follows:

p = 0.3 x 0.8 = 0.24 = 24%.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The total time for the mass of the element to be 60 grams is 7.5 minutes

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ  for growth rate

x ( t ) = x₀ × ( 1 - r )ⁿ   for decay rate

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units = n

Given data ,

Let the total mass of element be = 520 grams

So , the value of x₀ = 520 grams

Now , the decay rate of element is given by r = 25.1 %

To calculate the time at which the amount of element left is 60 grams = n

where n is the total time = t

So , x ( t ) = 60

The decay rate formula is given by the equation ,

x ( t ) = x₀ × ( 1 - r )ⁿ

Substituting the values in the equation , we get

60 = 520 ( 1 - 25.1/100 )ⁿ

On simplifying the equation , we get

60 = 520 ( 1 - 0.251 )ⁿ

Divide by 520 on both sides of the equation , we get

( 0.749 )ⁿ = 6/52

Taking logarithm on both sides , we get

n × log ( 0.749 ) = log ( 6/52 )

Divide by log ( 0.749 ) on both sides , we get

n = log ( 6/52 ) / log ( 0.749 )

n = -0.9378 / -0.1255

n = 7.47 minutes

Therefore , the value of n time t = 7.5 minutes

Hence ,

The total time for the mass of the element to be 60 grams is 7.5 minutes

To learn more about exponential growth click :

https://brainly.com/question/16528066

#SPJ1

The system of equations is  0.05n+0.10d=1.90  and n=d+2

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The calculation is as follows:

We know that

One nickel = $0.05,

So n nickels are worth 0.05n.

One dime = $0.10,

so dd dimes are worth 0.10d.

Now

The total 0.05n+0.10d =  $1.90

i.e.  

0.05n+0.10d=1.90

And,  

n=d+2

Therefore we can conclude that The system of equations is  0.05n+0.10d=1.90  and n=d+2

To learn more about the equation from the given link

https://brainly.com/question/28218072

#SPJ1

If BCDE is congruent to OPQR, then DE is congruent to QR .

Congruence means the same point on two different shapes , like parallels

so BC is congruent to OP

and

DE is congruent to QR

In plain English, two objects are said to be congruent if they overlap, i.e., have the same size and shape. If two angles have the same measure, they are said to be congruent. They are congruent if the sides' lengths line up.

Two triangles are said to be congruent if their sides and angles are an exact match.

Conditions for Congruence of Triangles:

To learn more about congruence

brainly.com/question/5661105

#SPJ4

Answer:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

the second one

Step-by-step explanation:

The confidence interval limits include 0, which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

The correct option is (a)

"Information available from the question:"

This is incomplete question:

Complete question is this:

A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows.

Women             Men

x1 = 11.7hrs x2 = 14.2hrs

s1 = 3.9hrs s2 = 5.2hrs

n1 = 14         n2 = 17

The following 99% confidence interval was obtained for μ1 − μ2, the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men:

-7.43hrs < μ1 − mμ2 < 2.43hrs

What does the confidence interval suggest about the population means?

a. The confidence interval limits include 0 which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

b. The confidence interval includes only negative values which suggest that the mean amount of time spent watching television for women is smaller than the mean amount of time spent watching television for men.

c. The confidence interval limits include 0 which suggests that the two population means are unlikely to be equal. There appears to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

d. The confidence interval includes only positive values which suggest that the mean amount of time spent watching television for women is larger than the mean amount of time spent watching television for men.

Now, According to the question:

The given confidence interval is:

-7.43hrs < μ1 − mμ2 < 2.43hrs

The interval includes 0 and the populations sampled are small (< 30). Therefore, Option (a) is correct.

Hence, The confidence interval limits include 0, which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

Learn more about Confidence Interval at:

https://brainly.com/question/24131141

#SPJ4

The true statements are they help describe sets of data, they show the data split into four parts and each section of a box plot represents 25% of the data.

A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.

The box plot is also called box-and-whisker plot.

The data is divided into sections by box plots, with each section containing around 25% of the total data.

Box plots are useful as:

They offer a visual overview of the data,

making it simple for researchers to spot skewness,

the dispersion of the data set.

The minimum value, first quartile, median, third quartile, and maximum value are the five values that make up a box plot.

And they don't include mean.

From the above discussion,

we have three statements that are true and those statements are;

they help describe sets of data, they show the data split into four parts and each section of a box plot represents 25% of the data.

Therefore, the correct statements are A, C and E.

To learn more about the box-and-whisker plot;

https://brainly.com/question/2742784

#SPJ1

Answer:

55.13 I'm sure is the answer

There are 714 women out of the total 1295 students:

    [tex]\dfrac{714}{1295}\approx0.551351351351351[/tex]

About 55.14% of the students are women.

The example of the commutative property of addition is option (D) 4 + 3 = 3 + 4

The commutative property of the addition states that changing the order of the numbers or the variable does not affect the result of sum

The commutative property of addition is

A + B = B + A

Here the position of the variable A and B are changed but still the result is same

From the given option

The example that shows the commutative property of  addition is

4 + 3 = 3 + 4

Here the position of the 3 and 4 changed, but the result will be

7 = 7

Therefore, the correct example is option D) 4 + 3 = 3 + 4

Learn more about commutative property  here

brainly.com/question/778086

#SPJ4

The statement which is true about triangle inequalities is that the sum of the lengths of the 2 sides of a triangle is equal than the third side of the triangle.

In Euclidean geometry, triangle inequalities are a theorem which states that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In shorts, the theorem states that the shortest distance between two points is a straight line.

If the length of a side is equal to the sum of the other two sides, then the vertices have to be colinear, meaning that the three sides form a line segment rather than a triangle. This is called the triangle inequality.

Learn more about triangles at: https://brainly.com/question/2773823

#SPJ4

When it come to figuring taxes what you have to do is multiply the amount by what percent the tax is then you add or subtract from the amount. If you don't know how to convert a percentage to a decimal divide the percentage by 100. Always remember to round to the nearest hundredths when dealing with money.

SS: $125 x 0.062 = $7.75    Med: $125 x 0.0145 = $1.81

SS: $432 x 0.062 = $26.78    Med: $432 x 0.0145 = $6.26

SS: $241 x 0.062 = $14.94    Med: $241 x 0.0145 = $3.49

SS: $1,562 x 0.062 = $96.84    Med: $1,562 x 0.0145 = $22.65

The difference of the functions, f(x) = 3x² + 4x - 6 and g(x) = 6x³ - 5x² - 2, is: D. (f - g)(x) = -6x³ + 8x² + 4x - 4.

Finding the difference of two functions involves combining like terms together and then simplify.

Given the functions:

f(x) = 3x² + 4x - 6

g(x) = 6x³ - 5x² - 2

To find (f - g)(x), it implies that we find the difference between f(x) and g(x).

(f - g)(x) = f(x) - g(x)

Substitute

f(x) - g(x) = (3x² + 4x - 6) - (6x³ - 5x² - 2)

Open the parentheses:

f(x) - g(x) = 3x² + 4x - 6 - 6x³ + 5x² + 2

Combine like terms

f(x) - g(x) = - 6x³ + 8x² + 4x - 4

Therefore, the answer is: D. (f - g)(x) = -6x³ + 8x² + 4x - 4

Learn more about the difference of functions on:

https://brainly.com/question/18816629

#SPJ1

Answer: y=[tex]\frac{3x}{2}[/tex]+6

Step-by-step explanation:

isolate y by dividing both sides by 2

y=3x+12/2

y=[tex]\frac{3x+12}{2}[/tex]

y=[tex]\frac{3x}{2}[/tex]+6

The measure of the spread of scores within a set of data is termed as standard deviation. Usually, we are interested in the standard deviation of a population. since, we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation.

When to use the sample or population standard deviation ?

Population standard deviation is of great intrest because our population contains all the values we are interested in. Therefore, we would normally calculate the population standard deviation In two cases first when we have the entire population or second we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize our findings to the population. but, in statistics, a sample is presented from which we wish to estimate (generalize to) a population, and the standard deviation is no exception to this.

Thus it can be concluded that, if we have all is a sample, but we wish to make a statement about the population standard deviation from which the sample is drawn, we need to use the sample standard deviation. There a Confusion can often arise as to which standard deviation to use due to the name "sample" standard deviation incorrectly being interpreted and not the estimate of the population standard deviation based on the sample.

Learn more about Standard deviation at:

https://brainly.com/question/475676

#SPJ4

From a group of 15 randomly selected residents , the probability that at least thirteen of them shop at Walmart is 0.0271  .

6 out of 10 Niceville residents shop at Walmart

So, the probability of shopping at Walmart (p) is = 6/10 = 0.6

The probability of not shopping at Walmart is (q) = 1 - 0.6 = 0.4 .

The number of members in the group is(n) = 15 ;

We have to find the probability that, at least thirteen of them shop at Walmart

By the Binomial Probability Distribution,

we know that ; P(x = a) = ⁿCₐ×pᵃ×qⁿ⁻ᵃ

So , P(x ≥ 13) = P(x=13) + P(x=14) + P(x=15)

Substituting the values of a , n and p and q ,

We get ;

= ¹⁵C₁₃p¹³q² + ¹⁵C₁₄p¹⁴q¹ + ¹⁵C₁₅p¹⁵q⁰

= ¹⁵C₁₃(0.6)¹³(0.4)² + ¹⁵C₁₄(0.6)¹⁴(0.4)¹ + ¹⁵C₁₅(0.6)¹⁵(0.4)⁰

= 0.0219 + 0.0047 + 0.0004

= 0.0271

Therefore, the required probability is 0.0271

Learn more about Binomial Probability Distribution here

https://brainly.com/question/26077592

#SPJ4

Using the t-distribution, the 99% confidence intervals for the given standard deviation are given as follows: (5053.39 , 4126.61)

Given that,

Number of college students = 23

A simple random sample with a mean = $4590

A simple random sample with a standard deviation = $860

The t distributions is wide (has thicker tailed) for smaller sample sizes, reflecting that s can be smaller than σ. The thick tails ensure that the 80%, 95%, 99% confidence intervals are wider than those of a standard normal distribution (so are better for capturing the population mean).

The confidence interval is:

= μ ± [tex]t\frac{s}{\sqrt{n} }[/tex]

In which:

μ is the sample mean.

t is the critical value.

n is the sample size.

s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 23 - 1 = 22 df,

Upon using a t -table or a calculator, we see that the critical t -value for this 99% confidence interval is t0.005=2.581

The parameters are:

μ = $4590

n = 23

Hence, with s = 860, the bounds of the interval are:

= μ ± [tex]t\frac{s}{\sqrt{n} }[/tex]

= 4590 ± 2.581 [tex]\frac{860}{\sqrt{23} }[/tex]

= 4590 ± 2.581 [tex]\frac{860}{4.79}[/tex]

= 4590 ± 2.581 (179.54)

= 4590 ± 463.39

Then,

= 4590 + 463.39   ,      4590 - 463.39

= 5053.39              ,       4126.61

Therefore,

Using the t-distribution, the 99% confidence intervals for the given standard deviation are given as follows: (5053.39 , 4126.61)

To learn more about Standard deviation visit :

brainly.com/question/28306508

#SPJ4