how many rows and columns must a matrix a have in order to define a mapping from r4 into r5 by the rule t .x/ d ax?

Answer:

12. 524 in³ (3 sig. fig.)   13. 2000 cm³ (3 sig. fig.)

Step-by-step explanation:

12. Volume of sphere = (4/3)πr³

= 500/3π

= 524 in³ (3 sig. fig.)

13. Volume of cylinder = πr²h

= 7²π(13)

= 637π

= 2000 cm³ (3 sig. fig.)

The number of different committees with exactly 4 girls is 27720.

Given that there are 12 girls and 8 boys in class council.

The pep rally committee of 7 students is chosen from the class council members. We have to determine the number of different committees with exactly 4 girls.

Total number of committees possible

Let n = number of ways in which a committee of 7 can be chosen from a group of 20 students,

then:

n = 20C7= (20 × 19 × 18 × 17 × 16 × 15 × 14)/(7 × 6 × 5 × 4 × 3 × 2 × 1)= 77520

Therefore, there are 77520 possible committees.

Number of committees with 4 girls

Number of committees with 4 girls and 3 boys = number of ways of selecting 4 girls from 12 and 3 boys from 8

Total number of committees with 4 girls and 3 boys

= (12C4 × 8C3)

= 495 × 56

= 27720

Therefore, the number of different committees with exactly 4 girls is 27720.

There are 27720 different committees with exactly 4 girls.

Learn more about council members from the given link:

https://brainly.com/question/26501694

#SPJ11

The transformation that is used to create this frieze pattern other than translation is glide reflection. A glide reflection involves both a reflection and a translation.

The figure is reflected across a line of reflection and then translated in a specific direction. This creates a pattern that appears to glide along the surface. It is different from a horizontal or vertical reflection, which only involve flipping the figure across a horizontal or vertical line, or a 180° rotation, which involves turning the figure around a point.

Learn more about horizontal here:

https://brainly.com/question/29019854

#SPJ11

For a 90 degrees clockwise rotation,

A' = (y, -x) = (1, -2)

B' = (y, -x) = (3, -3)

C' = (y, -x) = (2, -5)

To plot a triangle onto a coordinate plane, these instructions must be followed:

Begin by drawing x and y axes to establish the necessary framework.

Choose three points upon which to place the vertices of the triangle on the graph.

Then connect the selected points through straight lines, thus resulting in the appearance of three sides; representing each point's distance from one another respectively.

Subsequently attach letter designations such as A, B, and C to each vertex.

Lastly, inspect the measurements of the sides and angles between them to confirm that they correspond with requisites specific to your chosen triangle type (such as an equilateral or Isosceles shape).

Read more about triangles here:

https://brainly.com/question/1058720

#SPJ1

Answer:

yes that is right

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

she put 4 stickers on each car

Answer:

the answer is n=17

Step-by-step explanation:

1/5= 8-5/n-2

Answer:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

Step-by-step explanation:

Swap f(x) and x position of the function, thus:

\(\displaystyle{x=7f(x)+3}\)

Then solve for f(x), subtract 3 both sides and then divide both by 7:

\(\displaystyle{x-3=7f(x)}\\\\\displaystyle{\dfrac{x}{7}-\dfrac{3}{7}=f(x)}\)

Since the function has been inverted, therefore:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

And we can prove the answer by substituting x = 1 in f(x) which results in:

\(\displaystyle{f(1)=7(1)+3 = 10}\)

The output is 10, now invert the process by substituting x = 10 in \(f^{-1}(x)\):

\(\displaystyle{f^{-1}(10)=\dfrac{10}{7}-\dfrac{3}{7}}\\\\\displaystyle{f^{-1}(10)=\dfrac{7}{7}=1}\)

The input is 1. Hence, the solution is true.

To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.

To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:

Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).

To know more about cost visit:

https://brainly.com/question/14566816

#SPJ11

Greetings from Brasil

From radiciation properties:

\(\large{A^{\frac{P}{Q}}=\sqrt[Q]{A^P}}\)

bringing to our problem

\(\large{6^{\frac{1}{3}}=\sqrt[3]{6^1}}\)

The requried radical form of the given expression is ∛6.

Radical form is mathematical expression that represents the value under the nth roots.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

Following the rule \(\sqrt[n]{x} = x^{1/n}\)
Similarly,
\(6^{1/3} = \sqrt[3]{6}\)

Thus, the requried radical form of the given expression is ∛6.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

Answer: The anwser is correct

Step-by-step explanation:

Nadhii has a ratio of 75:25, which is the same as Dylan if you simplify it down. Nadhii's ratio divided down by 25 would be 3:1. Dylan's ratio written out is 3:1. They both have the same ratio.

Step-by-step explanation:

slope intercept form is: y = ax + b

so, 19x - 19y = 18

-19y = -19x +18

\(y = \frac{ - 19x}{ - 19} - \frac{18}{19} \)

\(y = x - \frac{18}{19} \)

i hope that this helps

Two matrices are row equivalent if they can be transformed into each other using elementary row operations.

Elementary row operations are operations such as the addition or subtraction of two rows, the multiplication or division of a row by a non-zero constant, or the interchange of two rows. Row equivalent matrices are equal in terms of row space, meaning any linear combination of the rows of one matrix will yield the same linear combination of the rows of the other matrix. An example of two row equivalent matrices is given below:

Matrix A =

\(\begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \end{bmatrix}\)

Matrix B =

\(\begin{bmatrix} 1 & 2 & 3 \\2 & 3 & 4 \end{bmatrix}\)

These matrices are row equivalent because adding the first row of Matrix A to the second row of Matrix B yields Matrix A. To show this mathematically, let row 1 of Matrix A be represented as r1, and row 2 of Matrix B be represented as r2. We can then say that r2 + r1 =

\(\begin{bmatrix} 1 & 2 & 3 \\6 & 8 & 10 \end{bmatrix}\)

which is equal to Matrix A.

Learn more about Matrices here:

https://brainly.com/question/11367104

#SPJ4

The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

To learn more about the proportional relationship from the given link

https://brainly.com/question/2143065

#SPJ1

Answer:

0.333...

Step-by-step explanation:

since it's forever repeating it still counts as rational

Answer:

hypotenuse = 6.3

Step-by-step explanation:

here 6 and 2 are the legs of the triangle . we are asked to find hypotenuse (longest side)

using pythagoras theorem

a^2 + b^2 = c^2

6^2 + 2^2 = c^2

36 + 4 = c^2

40 = c^2

\(\sqrt{40}\) = c

6.32 = c

6.3 = c

No it is not an irrational number

Athlete would have the best running economy Runner B: VO2 of 42 ml/kg/min at 7.5. Option B

To calculate exercise intensity in METs (metabolic equivalents), we need to know the resting metabolic rate (RMR) of an individual. Without the RMR information, we cannot determine the exercise intensity in METs for the 45-year-old male exercising at 2.26 L/min. Therefore, the exercise intensity in METs cannot be determined, and the correct answer is "Not enough information."

Regarding the question about which athlete has the best running economy, we can compare the VO2 values at the given running speeds.

Runner A: VO2 of 44 ml/kg/min at 8 mph

Runner B: VO2 of 42 ml/kg/min at 7.5 mph

Runner C: VO2 of 46 ml/kg/min at 9 mph

Running economy refers to the energy cost or oxygen consumption required to maintain a given running speed. In this case, a lower VO2 value indicates better running economy.

Comparing the given VO2 values, we can see that Runner B has the lowest VO2 of 42 ml/kg/min at 7.5 mph. This means Runner B has the best running economy among the three athletes. Option B

For more such questions on Athlete visit:

https://brainly.com/question/25631156

#SPJ8

The conditional probabilities in the context of this problem are given as follows:

a. P(A|B) = 2.1%.

b. P(A'|B') = 99.9%.

Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which the probabilities are described as follows:

The probability that a person has tested positive is calculated as follows:

Hence:

P(B) = 0.85 x 0.0025 + 0.1 x 0.9975 = 0.101875.

Hence the conditional probability is:

P(A|B) = 0.85 x 0.0025/0.101875 = 0.021 = 2.1%.

The probability that a person has tested negative is calculated as follows:

Hence:

P(B') = 0.15 x 0.0025 + 0.9 x 0.9975 = 0.898125.

The conditional probability is:

P(A'|B') = 0.9 x 0.9975/0.898125 = 0.999 = 99.9%.

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

#SPJ1

To develop a confidence interval estimate, a critical value is used along with a point estimate and the standard deviation (or sample standard deviation). The confidence interval provides a range of values within which we can estimate the true population parameter.

A. The best point estimate to be used as an estimate of the true mean is $48.08. This is the value that represents the center or average of the data.

B. A critical value is used to develop the confidence interval because it helps determine the range of values that is likely to contain the true population parameter. It takes into account the desired level of confidence and the variability in the data.

E. True. The confidence interval obtained is indeed an estimate of the sample mean amount spent per visit by customers of the restaurant.

F. False. The margin of error will be reported as a value that quantifies the uncertainty in the estimate. It is not necessarily equal to $12.30.

H. False. The statement that the population mean is unknown is true. In practice, the true population mean is usually unknown, which is why we estimate it using a sample.

I. True. If Susanne wants to reduce the width of the confidence interval, she needs to reduce the confidence level. A higher confidence level leads to a wider interval.

J. False. The width of the confidence interval will be reduced if Susanne uses a larger sample size. A larger sample size reduces the standard error and, therefore, the margin of error.

K. False. The statement that the value is $48.84 is not specified in the given information.

L. The sample size needed to estimate the true mean to within $3.40 depends on the desired level of confidence and the variability of the data. Without this information, it is not possible to calculate the exact sample size.

M. False. The information does not specify whether the population standard deviation is known or unknown.

N. False. The value of 36 is not specified in the given information.

O. False. The value of $43.64 is not specified in the given information.

P. False. The value of $47.70 is not specified in the given information.

Q. False. The value of $3.17 is not specified in the given information.

R. False. The value of 180 is not specified in the given information.

Learn more about interval estimate here:

https://brainly.com/question/32393220

#SPJ11

Answer:

Since you didn't list the statements, I'll just list some true statements.

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

There are 17 students in this class.

Majority of students voted for a hamster.

Snake was the least voted for.

9514 1404 393

Answer:

  1.048

Step-by-step explanation:

The generic form of the exponential model is ...

  y = a·b^x

Filling in the given values, we have ...

  100 = a·b^6

  184 = a·b^19

__

Dividing the second equation by the first gives ...

  184/100 = (a·b^19)/(a·b^6)

  1.84 = b^13 . . . . . simplify

  b = 1.84^(1/13) ≈ 1.048022 . . . . find the 13th root

The growth factor is about 1.048.

two polynomials are relatively prime if the greatest common divisor of the two polynomial is 1

How do you prove two polynomials are relatively prime?

Two polynomials from Z[x] are called evaluationally relatively prime if the greatest common divisor of the two polynomials in Z[x] is 1 and gcd(f(t),g(t)) = 1 for all t ∈ Z.

learn more about of polynomial here

https://brainly.com/question/11536910

#SPJ4

The correct answer is (c) The vectors are linearly independent for all real numbers a, excluding a = ±√96.

To determine if the vectors v1 = (a, 1), v2 = (-4, a), and v3 = (4, 6) are linearly independent, we can check the determinant of the matrix formed by these vectors. If the determinant is not equal to zero, the vectors are linearly independent. Otherwise, they are linearly dependent.

The matrix is:
| a, -4, 4 |
| 1,  a, 6 |

The determinant is: a * a * 1 + (-4) * 6 * 4 = a^2 - 96.

Now, we want to find the real number(s) a for which the determinant is not equal to zero:

a^2 - 96 ≠ 0
a^2 ≠ 96

So, the vectors are linearly independent if a^2 is not equal to 96. This occurs for all real numbers a, except for a = ±√96. Therefore, the correct answer is (c) The vectors are linearly independent for all real numbers a, excluding a = ±√96.

learn more about linearly independent

https://brainly.com/question/30720942

#SPJ11

Answer:

30 square feet

Step-by-step explanation:

scale F = 43.744532

Answer:

(0,1)

Step-by-step explanation:

Answer:

The coordinates of the point are (0,1)

Step-by-step explanation:

There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

To know more about types of sampling visit :

https://brainly.com/question/12902833?referrer=searchResults

#SPJ4

Answer:

The correct answer would be D, Right Five Units :)

Step-by-step explanation:

I hope this helps, if it doesn't then just message me and ill be more than happy to help :)

Answer:

D   right 5 units

Step-by-step explanation:

(x-5)   shifts the values 5 units to the right

Answer:

its the 4th one .  The one all the way to the bottom

Step-by-step explanation: