A relation is given below.
{(0, 0), (2, 0.5), (4, 1), (3, 1,5), (4, 2), (5, 1.5), (6, 8)}
Which ordered pair can be removed to make this relation a function?
Why would removing this ordered pair make the relation a function?

True, If the end index for slicing specifies a location after the end of the alphabet, Python will use the list's length instead.

What is slicing?

In Python, there is a concept of string, list and tuples. Sometimes it is required to access part of those string, list and tuples. This is known as slicing.

In case of slicing, suppose the the end index specifies a position beyond the end of the list, Python will return to the default length of the string. So there will be no error if the end index specifies a position beyond the end of the list.

So the above sentence is a true sentence.

To learn more about slicing, refer to the link-

https://brainly.com/question/19660645

#SPJ4

Answer:

D

Step-by-step explanation:

the graph is forever extending to infinity, so there's no definite range

Answer:

12.4

Step-by-step explanation:

Hope this helps :)

\(y = (1/5) x^5 + Ce^ {(-x^5)}\) is the general solution of the given differential equation.

The given differential equation is:

y' + 5x⁴ y = x⁴

To solve this equation, we can use an integrating factor. First, we need to multiply both sides of the equation by the integrating factor, which is \(e^{(int 5x^4 dx)}\):

\(e^{(int 5x^4 dx) }y' + 5x^{4} e^{(int 5x^4 dx)} y = x^4 e^{(int 5x^4 dx)}\)

The integral of 5x⁴ is (5/5)x⁵ = x, so the integrating factor is \(e^{(x^5)}\):

\(e^{(x^5)} y' + 5x^{4} e^{(x^5)} y = x e^(x^5)\)

Now we can recognize the left-hand side as the product of the derivative of the product of \(e^{(x^5)\)and y:

\((d/dx)[e^{(x^5)} y] = x^4 e^{(x^5)}\)

Integrating both sides with respect to x, we get:

\(e^{(x^5)} y = (1/5) x^5 e^{(x^5)} + C\)

where C is the constant of integration. Dividing both sides by \(e^{(x^5)}\), we get the general solution:

\(y = (1/5) x^5 + Ce^(-x^5)\)

where C is an arbitrary constant.

\(y = (1/5) x^5 + Ce^{(-x^5)}\) is the general solution of the given differential equation.

Learn more about Integration:

https://brainly.com/question/30094386

#SPJ1

The value of r is 4 feet, the correct option is A.

The area of a circle is the region occupied by the circle in a two-dimensional plane.

Given

The area of circle Z is 64 ft2.

According to the following formula, we must find the radius of the circle:

\(\rm r =\sqrt{\dfrac{Area}{\pi }}\)

Substitute all the values in the formula

\(\rm r =\sqrt{\dfrac{Area}{\pi }}\\\\\rm r =\sqrt{\dfrac{64}{3.14}}\\\\\rm r =\sqrt{20.38}\\\\r=4.5\)

Hence, the value of r is 4 feet.

To know more about the area of the circle click the link given below.

https://brainly.com/question/19164857

Answer:

The choose (D)

D. Circle

I hope I helped you^_^

The required cross-section for a cone is a circle. Option D is correct.

A conic section is a geometric shape that is obtained by intersecting a cone with a plane. Conic sections include circles, ellipses, parabolas, and hyperbolas.

The type of conic section that is formed depends on the angle of the plane relative to the axis of the cone, as well as the distance of the plane from the vertex of the cone.

Here,
The cross-section of a cone is a circle.

A cross-section is a shape that you get when you slice a 3D object with a plane. If you slice a cone parallel to its base, you get a circle as the cross-section.

Therefore, the correct answer is option D.

Learn more about the conic section here;

https://brainly.com/question/28991363

#SPJ7

Answer:594

Step-by-step explanation: You have to add to find ur answer so it will be 594 ounces

Or just multiply

If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .

In the question ,

it is given that ,

the number of residents in the local apartment complex is = 71

the mean electric bill for the 71 residents = $62 ;

we know that the sample mean is itself called as the best point estimate ;

So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of  local apartment complex which is given as $62 .

Therefore , the best point estimate is $62 .

Learn more about Best Point Estimate here

https://brainly.com/question/19425323

#SPJ4

Answer:

a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

Learn more about probability at https://brainly.com/question/32274851

#SPJ11

The appropriate percentages for the Extremely Patriotic group are 19.42% in 1999 and 32.27% in 2010, corresponding to option d: 193/994 compared to 324/1004.

To calculate the appropriate percentages for the Extremely Patriotic group, we need to compare the counts from the 1999 and 2010 samples.

In 1999:

Number of Extremely Patriotic responses: 193

Total number of respondents: 994

In 2010:

Number of Extremely Patriotic responses: 324

Total number of respondents: 1004

Now we can calculate the percentages:

Percentage for 1999: (193 / 994) × 100 = 19.42%

Percentage for 2010: (324 / 1004) × 100 = 32.27%

Therefore, the appropriate percentages as part of the exploratory data analysis for the Extremely Patriotic group are:

19.42% compared to 32.27% (option d: 193/994 compared to 324/1004).

To know more about appropriate percentages:

https://brainly.com/question/28984529

#SPJ4

Answer:

#1

\({ \tt{ {( \frac{ {2x}^{ - 1} }{ {4x}^{2} } )}^{ - 3} }} \\ \\ = { \tt{ {( \frac{ {x}^{( - 1 - 2)} }{2}) }^{ - 3} }} \\ \\ = { \tt{ ({ \frac{ {x}^{ - 3} }{2}) }^{ - 3} }} \\ \\ = { \tt{( \frac{ {x}^{( - 3 \times - 3)} }{ {2}^{ - 3} } }}) \\ \\ ={ \boxed{ \mathfrak{answer : { \tt{ {b. \: 8 {x}^{9} }}}}}}\)

#2

\({ \tt{ \frac{16 {x}^{3} - {4x}^{2} + 44x - 60 }{4x} }} \\ \\ { \boxed{ \mathfrak{answer : \: { \tt{b. \: 4 {x}^{2} - x + 11 - \frac{15}{x} }}}}}\)

Answer:

to compare them, you have to get the same denominator. So you change the denominator to 24 by multipling 7/12 by 2, and 5/8 by 3. Then you have 14/24 and 15/24. This means that 5/8 is greater than 7/12

Step-by-step explanation:

Hope this helps. If you want, please mark me as brainliest

Answer: Please mark me brainlest 15

24

>

14

24

or

5

8

>

7

12

Step-by-step explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 8 and 12 is 24

For the 1st fraction, since 8 × 3 = 24,

5

8

=

5 × 3

8 × 3

=

15

24

Likewise, for the 2nd fraction, since 12 × 2 = 24,

7

12

=

7 × 2

12 × 2

=

14

24

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

The derivative of the function f(x) = ln(14 - e^(-2x)) is f'(x) = [4xe^(-2x)] / [e^(2x) - 14].

The derivative of the function f(x) = ln(14 - e^(-2x)) is given by:

f'(x) = [1/(14 - e^(-2x))] * [-2e^(-2x)]

To simplify this expression, we can factor out a -2 from the numerator:

f'(x) = [-2/(14 - e^(-2x))] * [e^(-2x)]

Now, we can use the chain rule to differentiate the second factor:

f'(x) = [-2/(14 - e^(-2x))] * [-2x e^(-2x)]

Simplifying further, we get:

f'(x) = [4xe^(-2x)] / [e^(2x) - 14]

Therefore, the derivative of f(x) is f'(x) = [4xe^(-2x)] / [e^(2x) - 14].

For more questions like Function click the link below:

https://brainly.com/question/12431044

#SPJ11

The measure of angle DAB in the given quadrilateral can be calculated as: 109°.

To find the measure of an angle in a quadrilateral, you need to use the fact that the sum of all angles in a quadrilateral is always equal to 360 degrees.

Using the above fact stated, we can add up the three known angles in the given quadrilateral and then subtract it from 360 degrees to find the measure of angle DAB.

Thus, we have:

m<DAB = 360 - (90 + 97 + 64)

m<DAB = 360 - 251

m<DAB = 109°

Learn more about Quadrilateral on:

https://brainly.com/question/30291770

#SPJ1

Answer:

The answer is 98304

Step-by-step explanation:

-Recall that the statement:

The quotient of a and b,

in algebraic notation is:

-Therefore, the expression:

as a statement is:

The quotient of x+3 and x²-4.

Answer: Option A.

The answer to your question is that within 2 standard deviations above and below the mean of the standard normal distribution, approximately 95.44% of the data falls.

The properties of the standard normal distribution. The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. This distribution is important in statistics because it allows us to make comparisons and draw conclusions about different sets of data that have different means and standard deviations.

In the standard normal distribution, we can use the empirical rule, also known as the 68-95-99.7 rule, to estimate the percentage of data that falls within certain intervals of standard deviation from the mean. According to this rule, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% falls within 2 standard deviations, and approximately 99.7% falls within 3 standard deviations.
Therefore, we can conclude that within 2 standard deviations above and below the mean of the standard normal distribution, approximately 95.44% of the data falls. This is because 2 standard deviations above and below the mean cover approximately 95.44% of the total area under the curve.

To know more about standard deviation visit:

https://brainly.com/question/23907081

#SPJ11

Among a group of six students, at least two received the same grade on the final exam.

This problem is a classic example of the Pigeonhole Principle, which states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. In this case, the pigeons are the grades assigned to the six students, and the pigeonholes are the possible grades they could have received (A, B, C, D, or F).

Since there are five possible grades and six students, at least one grade must have been assigned to two or more students. This is because if each student received a different grade, there would be five grades in total, which is one less than the number of students, so at least one grade must be repeated.

learn more about Pigeonhole Principle,

https://brainly.com/question/30322724

#SPJ4

Answer: 2 5/6 I think.

Wait no. I just did the math and it would be 2 1/2

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

We need to identify the function among the given options which is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0,4].What is the Extreme Value Theorem? The extreme value theorem says that a function on a closed interval must have a maximum and a minimum value.

The correct option is-C

In other words, there is an absolute maximum and an absolute minimum value. It is an important theorem in calculus. Let's check the given options for the absolute maximum on the interval [0,4]:a. y=tan⁡x As the function

f(x)=tanx is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4]. Therefore, option a is incorrect .b

. y=tan⁻¹xAs the function

f(x)=tan⁻¹x is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4].

Therefore, option b is incorrect. c.

y=x²−16/x²+x−20 Let's check the critical points of the function

f(x)=x²−16/x²+x−20 by finding its derivative and equating it to zero:

f '(x)= (2x(x² - 20) + (x² - 16)(2x + 1))/ (x² + x - 20)²=0On solving this equation,

we get x=-4, 0, and 4. Now we will check the function values of these critical points as well as at the endpoints of the given interval:[0,4]. We get: f(0) = -4 and

f(4) = 4/3 Since f(4) is greater than all other values, the absolute maximum of f(x) is at

x=4.Therefore, option c is correct .d. y=1/e^x-1As the function f(x)=1/e^x-1 is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4].

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

Answer: y=2/5x+b

Step-by-step explanation:

The tangent vector  → \(r(t)=〈4cos(2t),4sin(2t),5t〉\), normal vector at t=0 is given by →N(0) = 〈-1,0,0〉, and binormal vector at t=0 is given by →\(B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector, normal vector, and binormal vector of the given curve are as follows:

Given curve:

→ \(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0

To find: Tangent vector, the Normal vector, and the Binormal vector (→T, →N and →B) at the point t=0

Tangent vector: To find the tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0,

we need to differentiate the equation of the curve with respect to t.t = 0, we have:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉→r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

Differentiating w.r.t t:→\(r(t) = 〈4cos(2t),4sin(2t),5t〉 → r'(t) = 〈-8sin(2t),8cos(2t),5〉t = 0\),

we have:

→\(r'(0) = 〈-8sin(0),8cos(0),5〉= 〈0,8,5〉\)

Therefore, the tangent vector at t = 0 is given by

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Normal vector:To find the normal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to differentiate the equation of the tangent vector with respect to t.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating w.r.t t:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉t = 0\),

we have:

→\(T'(0) = 〈-16cos(0),-16sin(0),0〉= 〈-16,0,0〉\)

Therefore, the normal vector at t = 0 is given by

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Binormal vector: To find the binormal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to cross-product the equation of the tangent vector and normal vector of the curve.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉\)

The cross product of two vectors:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the binormal vector at t = 0 is given by→B(0) = 〈0, -0.441, -0.898〉

Hence, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are as follows:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The given curve is

→\(r(t)=〈4cos(2t),4sin(2t),5t〉 at the point t=0.\)

We are asked to find the tangent vector, the normal vector, and the binormal vector of the given curve at t=0.

the tangent vector at t=0. To find the tangent vector, we need to differentiate the equation of the curve with respect to t. Then, we can substitute t=0 to find the tangent vector at that point. the equation of the curve Is:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉\)

At t = 0, we have:

→\(r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

We can differentiate this equation with respect to t to get the tangent vector as:

→\(r'(t) = 〈-8sin(2t),8cos(2t),5〉\)

At t=0, the tangent vector is:

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Next, we find the normal vector. To find the normal vector, we need to differentiate the equation of the tangent vector with respect to t. Then, we can substitute t=0 to find the normal vector at that point.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating this equation with respect to t, we get the normal vector as:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉\)

At t=0, the normal vector is:

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Finally, we find the binormal vector. To find the binormal vector, we need to cross-product the equation of the tangent vector and the normal vector of the curve.

At t=0, we can cross product →T(0) and →N(0) to find the binormal vector.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

The normal vector is:

→N(0) = 〈-1,0,0〉Cross product of two vectors →T(0) and →N(0) is given as:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0 is given by →\(T(0) = 〈0.000,0.898,0.441〉.\)

The normal vector at t=0 is given by →N(0) = 〈-1,0,0〉.

The binormal vector at t=0 is given by →B(0) = 〈0, -0.441, -0.898〉.

To know more about binormal vectors visit

brainly.com/question/31673319

#SPJ11

Answer: C is correct

Step-by-step explanation:

-23+18= -5

A) The probability that a randomly chosen child has a height of less than 42.1 inches is 0.036 (rounded to 3 decimal places).B)The probability that a randomly chosen child has a height of more than 41.7 inches is 0.966 (rounded to 3 decimal places).

A) In order to find the probability that a randomly chosen child has a height of less than 42.1 inches, we need to find the z-score and look up the area to the left of the z-score from the z-table.z-score= `(42.1-56.9)/8.2 = -1.8098`P(z < -1.8098) = `0.0359`

Therefore, the probability that a randomly chosen child has a height of less than 42.1 inches is 0.036 (rounded to 3 decimal places).

B) In order to find the probability that a randomly chosen child has a height of more than 41.7 inches, we need to find the z-score and look up the area to the right of the z-score from the z-table.z-score= `(41.7-56.9)/8.2 = -1.849`P(z > -1.849) = `0.9655`.

Therefore, the probability that a randomly chosen child has a height of more than 41.7 inches is 0.966 (rounded to 3 decimal places).

Note: The sum of the probabilities that a randomly chosen child is shorter than 42.1 inches and taller than 41.7 inches should be equal to 1. This is because all the probabilities on the normal distribution curve add up to 1

Learn more about probability here,

https://brainly.com/question/13604758

#SPJ11

Answer:

The answer is number B:34 cm

The bottom is 10, 10 - 3 - 3 (the sides on top) = 4 so we know the middle part is 4.

We know that both of the "small ups" are 2 and the "longer ups" are 5.

Adding this altogether we get:

3 + 3 + 2 + 2 + 4 + 10 + 5 + 5 =

6 + 4 + 4 + 10 + 10 =

10 + 4 + 20 =

14 + 20 =

= 34

So our answer is B. 34 cm

Hope this helps, have a nice day! :D

(I answered in the comments, but one was deleted so I am answering this here too!)