explain in your own words the difference between an implicitly defined function and an explicitly defined function.

Answer:

I think that ans is A.....

Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

Answer:

Step-by-step explanation:

The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe

is 5.75 inches

Determine the volume of metal used to build the pipe.

The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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By using the given flow net with a hydraulic conductivity (k) of 1x10⁻⁵m/s, we can determine various parameters. First, by selecting a datum, we can identify equipotential lines and count the interior lower soil section surface as one.

Additionally, since the system is symmetric, we can analyze the flow net to calculate the required values. To begin, let's establish a datum, which serves as a reference level for potential differences. We can choose any point in the flow net as the datum. By considering the interior lower soil section surface as an equipotential line, we can count it as one of the lines passing through the datum. Next, since the flow net is symmetric, we can mirror the flow pattern to determine the corresponding flow lines and equipotential lines in the remaining half.

Using the given hydraulic conductivity (k) value of  1x10⁻⁵m/s, we can apply Darcy's law to calculate the hydraulic gradient. Darcy's law states that the hydraulic gradient is equal to the difference in hydraulic head divided by the distance between two points. By measuring the distances between equipotential lines and flow lines, we can determine the hydraulic gradient.

Furthermore, by utilizing the hydraulic gradient and the given k value, we can calculate the seepage velocity using the equation v = k * i, where v represents the seepage velocity and i denotes the hydraulic gradient. With the known parameters, we can evaluate the desired values based on the flow net's geometry and symmetry, enabling us to analyze and understand the flow characteristics within the system.

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Answer:

C 60 inches

Step-by-step -

60 x 2 = 120, which is both lengths, and since he width is half the length, then 30 x 2 = 60. So 130 (length) + 60 (width) = 180. So 60 inches would be the maximum length for both sides.

Answer:

C

Step-by-step explanation:

I just took the unit test

There are 4 vertices with degree 3, and 2 vertices with degree 4. So, there are a total of 6 vertices in this graph.

In a simple undirected graph with 10 edges, 2 vertices have a degree of 4 and the rest have a degree of 3. To determine the number of vertices in this graph, use the formula:

Sum of degrees = 2 * number of edges

Let x be the number of vertices with degree 3. Then:

(2 * 4) + (3 * x) = 2 * 10

8 + 3x = 20

3x = 12

x = 4

We also know that two of the vertices have a degree of 4, which means that together they contribute 8 to the sum of all vertex degrees. This leaves us with 20 - 8 = 12 degrees left to distribute among the other vertices. Since the remaining vertices all have a degree of 3, we can set up the equation 3x = 12, where x is the number of remaining vertices. Solving for x, we get x = 4. Therefore, the graph has a total of 6 vertices - two with a degree of 4 and four with a degree of 3.

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Answer:

(4-1)

I think not for sure

Step-by-step explanation:

The number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55

A permutation is an act of putting things or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.

Given that soccer player = 11

We have to find in many ways we can choose a captain and one alternate captain from a team of eleven soccer players

Out of 11 player, we have to pick one captain and one alternate captain

nCr ways

nCr = n!/r!(n-r)!

Here n = 11 and r = 2

= 11C2

= 11!/2!(11-2)!

= 11! / 2!.9!

= ((11x 10 x 9!)/2!.9!)

= (11 x 10)/2

= 110/2

= 55

Therefore the number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55

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Answer: 5/6  

Step-by-step explanation:

25/30(5/5)

5/6(1/1)

(5/1)(6/1)

=5/6

===================================================

Explanation:

Let's solve the first equation for y

4x - 2y = 6

4x-6 = 2y

2y = 4x-6

y = (4x-6)/2

y = (4x/2) - (6/2)

y = 2x - 3

After doing so, we see that 4x-2y = 6 is equivalent to y = 2x-3

Therefore, the original system of equations is effectively listing the same equation twice (one has a different form compared to the other).

Both equations in this system produce the same graph, which leads to infinitely many solutions. All solutions are on the line y = 2x-3.

You can say that all solutions are in the form (x, 2x-3) where x is any real number you want.

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

Here's another approach using substitution

4x - 2y = 6 ... start with the first equation

4x - 2( y ) = 6

4x - 2( 2x-3 ) = 6 .... replace y with 2x-3; ie plug in y = 2x-3

4x - 2(2x) - 2(-3) = 6

4x - 4x + 6 = 6

0x + 6 = 6

0 + 6 = 6

6 = 6

We get a true statement. The last equation is always true regardless of what we plug in for x, so this is another way to see how we get to infinitely many solutions.

Side note: the system is considered dependent since one equation depends on the other. The system is also consistent since it has at least one solution.

Answer:

2 11/12 cups of flour

Step-by-step explanation:

well 2 recipes is 2 1/2 cups of flour

1/3 is 1/3 x 1 1/4= 1/3 + 1/12= 5/12

so 2 11/12 cups of flour

The probability that:

A student has a cat and they do not have a dog = 1/8 or 0.125.

Use the concept of probability defined as:

Probability is the ratio of:

The number of favorable outcomes to the total number of outcomes for an event's taking place.

Given that,

The number of students in the class = 25

\(5\) students have a cat.

\(9\) students have a dog.

\(3\) students have both a cat and a dog.

The objective is to find the probability that given that they don't have a dog, a student has a cat.

To find the probability that one of the pupils has a cat because there isn't a dog in the class:

First, determine the total number of pupils without a dog..

Since there are 25 students in total and 9 have a dog,

Now, 25 - 9 = 16

So the number of students who do not have a dog = 16

Now, determine the number of students who have both a cat and a dog.

According to the question:

There are 3 students who have both,

Subtract this from the percentage of students who own cats.

Therefore,

5 - 3 = 2

So, there are 2 students who have a cat but not a dog.

\(Probability = \frac{\text{(Number of students with only a cat)}}{\text{ (Number of students who do not have a dog)}}\)

Probability = 2 / 16

Probability = 1 / 8

Hence,

The required probability that a student has a cat given that they do not have a dog = 1/8 or 0.125.

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We are asked to simply the following polynomial

Let us find the product of the above polynomial and simplify it

Therefore, the simplified polynomial is

The degree of a polynomial is the highest exponent (power)

For the given case, the highest exponent is 2

Therefore, the degree

The quantity of the street that is being covered by the light would be = 226.87 m². That is option A.

To calculate the area of the circle, the formula that should be used is given as follows;

Area or circle = π r²

where r = Diameter/2

But diameter = 17/2

radius = 8.5

Area of circle = 3.14×8.5×8.5

= 226.87 m²

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a. True. Pivot columns of an echelon form of A form a basis for the column space of A.
b. True. Row operations preserve linear dependence relations among the rows of A.
c. False. The dimension of the null space of A is the number of columns of A minus the number of pivot columns.

18. a. If B is any echelon form of A, then the pivot columns of B form a basis for the column space of A.

This statement is true. An echelon form of a matrix is obtained by performing row operations on the original matrix to transform it into a specific triangular form. In this form, the pivot columns correspond to the columns containing the leading entries in each row. The pivot columns of an echelon form of matrix A will also be pivot columns of matrix A itself.

The column space of a matrix is the span of its column vectors. Since the pivot columns of B are a subset of the column vectors of A, they will also span the column space of A. Therefore, the pivot columns of B form a basis for the column space of A.

b. Row operations preserve the linear dependence relations among the rows of A.

This statement is true. When we perform row operations on a matrix, such as multiplying a row by a scalar, adding rows together, or swapping rows, the resulting matrix will have the same row space as the original matrix. This means that the linear dependence relations among the rows of the original matrix will be preserved in the transformed matrix.

c. The dimension of the null space of A is the number of columns of A that are not pivot columns.

This statement is false. The dimension of the null space of A, also known as the nullity of A, is the number of free variables in the reduced row echelon form of A. It is equal to the number of columns of A minus the number of pivot columns. Therefore, the dimension of the null space of A is the number of columns of A minus the number of pivot columns, rather than the other way around.

To summarize:
a. True. Pivot columns of an echelon form of A form a basis for the column space of A.
b. True. Row operations preserve linear dependence relations among the rows of A.
c. False. The dimension of the null space of A is the number of columns of A minus the number of pivot columns.

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(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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Answer:

The answer is 18 hours

Step-by-step explanation:

3 hours x 6 days

3x6 = 18

The formula that represent the linear relationship between the cost and the sheets is y = 50/3x + 50/3

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Analyzing the coordinates we have:

(35, 600) and (47, 800)

The linear formula is:

Slope (m) = (y2 - y1)  / (x2 - x1)

m = (800 - 600) / (47 - 35)

m = 200 / 12

Simplifying:

m = 100 / 6

m = 50/3

Taking the fist coordinate (35, 600) we get:

y - y1 = m(x - x1)

y - 600 = 50/3 (x - 35)

y - 600 = 50/3x - 1750/3

y = 50/3x - 1750/3 + 600

y = 50/3x + 50/3

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Correctly written question:

A printing firm charges $35 for printing 600 sheets of headed notepaper and $47 for printing 800 sheets. Find the formula assuming the relationship is linear

The formula for the circumference of a circle can be derived from the concept of the circle's diameter and π (pi).

The circumference of a circle is defined as the distance around its outer edge. To derive the formula, we first need to understand that the diameter of a circle is the distance across it, passing through the center. It is equal to twice the radius (the distance from the center to any point on the circle).

Now, if we take the ratio of the circumference to the diameter for any circle, we find that this ratio is always constant, regardless of the size of the circle. This constant ratio is denoted by the Greek letter π (pi), which is approximately equal to 3.14159. Therefore, we can express the circumference of a circle as C = πd, where C represents the circumference and d represents the diameter. Alternatively, we can use the radius (r) and express the formula as C = 2πr. These formulas allow us to calculate the circumference of a circle based on its diameter or radius.

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Answer: when it’s a less than or greater than

Step-by-step explanation:

In the ANOVA procedure, the variance observed in the data set is split into various sum of squares. The number of different sum of squares that an ANOVA usually has is three (option a).

These three sum of squares include:

1. Sum of Squares Total (SST):

This represents the total variance in the dataset. It is the sum of the squared differences between each observation and the overall mean of the dataset.

2. Sum of Squares Between (SSB):

This represents the variance between the group means. It is the sum of the squared differences between each group mean and the overall mean, multiplied by the number of observations in each group.

3. Sum of Squares Within (SSW):

This represents the variance within each group. It is the sum of the squared differences between each observation and its respective group mean.

ANOVA uses these sum of squares to determine if there is a significant difference among the group means by comparing the variance between the groups (SSB) to the variance within the groups (SSW).

If the ratio of SSB to SSW is large enough, it indicates that there is a significant difference among the group means, and the null hypothesis can be rejected.

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The greatest number of shelves Melanie can fill is 15 shelves

Given :

Melanie has 45 horse statues and 60 elephant statues

She wants to put them on shelves so that the same number of each type of statue are on each shelf.

To find greatest number of shelves , we need to take GCF of 45  and 60

Lets find out GCF, greatest common factor

First write the factors for 45  and 60

45 --> 3,3,5

60 --> 2,3,2,5

Common factors are 3,5

GCF is 15

She needs 15 shelves to fill .

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B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

  3200

Step-by-step explanation:

Replace the variables with their values and do the arithmetic.

  (4·5)²·8 = 20²·8 = 400·8 = 3200

Answer:

12a^9b^7

Step-by-step explanation:

Multiply all like terms together.

4 times 3 = 12

a^3(a^6) = a^9

b^2(b^5) = b^7

Combine all together

Answer:2160a2b2

Step-by-step explanation:

Answer:

y = 1/2

Step-by-step explanation:

x = -5y+2

x=3y-2

substitute for x ans solve

3y-2=-5y+2

8y-2=2

8y = 4

y= 4/8

y=1/2

The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

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Answer:

20

Step-by-step explanation:

use ur head

DG, DM, DS, DT GD, GM, GS, GT MD, MG, MS, MT, SD, SG, SM, ST, TD, TG, TM, TS. Those are all the possible combinations using each letter only once in each set.

In short, you can make 20 sets.