WHAT IS THE DIFFERENCE BETWEEN A RELATION AND A FUNCTION?

Answer:

D

Step-by-step explanation:

Answer:

3/8 pound

Step-by-step explanation:

Give that :

Initial pound of gummy drop = 7/8 pound

Amount eaten = 3/8 pound

Amount given to her sister = 1/8

Pound of gummy drop left :

Initial pound of gummy drop - (amount eaten + amount given out)

7/8 - (3/8 + 1/8)

7/8 - (4/8)

7/8 - 4/8

= 3/8 pound

Amount of gummy drop Debby has left = 3/8 pound

The equation of the line r is y = ₋(10/9)x ₊ 7.

Given, parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope intercept form

equation of line q is y = ₋10/9x ₊ 2

it's already in slope intercept form.

hence slope is:

m = (₋10/9) from the above the equation.

we know that the second line will also have a slope of ₋10/9 and we are given the point (9 , ₋3). We can setup an equation in slope intercept form and use these values to solve for the y inetrcept.

y = mx ₊ b

₋3 = ₋10/9 (9) ₊ b

₋3 = ₋10 ₊ b

b = 7

plug the y intercept back into the equation to get our final answer.

y = ₋(10/9)x ₊ 7

hence  we get the equation of the line r as y = ₋(10/9)x ₊ 7.

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To solve this differential equation by making the change of variable u = x + y, we first need to find an expression for y' in terms of u.

Using the chain rule, we have:

du/dx = d/dx (x + y) = 1 + dy/dx

Solving for dy/dx, we get:

dy/dx = du/dx - 1

Substituting into the given differential equation, we have:

5(du/dx - 1) = x + y

Multiplying both sides by dx and rearranging, we get:

5 du/(x + y - 5) = dx

Now we can integrate both sides with respect to their respective variables.

On the left-hand side, we use the substitution u = x + y, which gives:

5 du/u-5 = dx

Integrating both sides yields:

5 ln|u-5| = x+C1

where C1 is a constant of integration.

Substituting back for u = x + y, we have:

5 ln|x+y-5| = x+C1

which can be written as:

ln|x+y-5|^5 = x+C2

where C2 = 5C1.

Exponentiating both sides gives:

|x+y-5|^5 = e^(x+C2) = Ce^x

where C = e^C2.

Taking the fifth root of both sides and using the absolute value notation, we finally arrive at the general solution:

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

or

x + y - 5 = ±(Ce^x)^(1/5)

where the sign of the right-hand side depends on the sign of x + y - 5.

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Least common denominator is the least common multiple of the given denominators.

Find the least common multiple of 3 and 12, this way:

The least common multiple of 3 and 12 is 12, which means that the least common denominator of 1/3 and 7/12 is 12.

The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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a. The x-intercepts of the quadric surface are x = -1 and x = 1.

b. The equations of the xy−,xz− and yz-traces are \(x^2 + y^2/25 = 1, x^2 + z^2/25 = 1 and y^2/25 + z^2/25 = 1.\)

c. The graph of the quadric surface is an elliptical cylinder centered at the origin along the x-axis, with x-intercepts at x = -1 and x = 1.

To find the x-intercepts of the given quadric surface equation, we need to set both y and z equal to zero and solve for x. Let's substitute y = 0 and z = 0 into the equation:

\(x^2 + 0^2/25 + 0^2/25 = 1\\x^2 + 0 + 0 = 1\\x^2 = 1\)

x = ±1

In the given equation, since the coefficients of y^2 and z^2 are positive, the graph represents an elliptical cylinder centered at the origin along the x-axis. The semi-major axis along the x-axis is equal to 1, while the semi-minor axes along the y and z axes are 5 and 5/√25 = 1, respectively. The graph will intersect the x-axis at x = -1 and x = 1, as mentioned earlier.

b. To find the equations of the xy-, xz-, and yz-traces, we fix one coordinate and solve for the remaining two coordinates.

For the xy-trace, we set z = 0. Substituting this into the original equation, we have:

\(x^2 + y^2/25 + 0/25 = 1\\x^2 + y^2/25 = 1\)

This equation represents an ellipse centered at the origin in the xy-plane, with a semi-major axis of 1 and a semi-minor axis of 5.

Similarly, for the xz-trace, we set y = 0:

\(x^2 + 0/25 + z^2/25 = 1\\x^2 + z^2/25 = 1\)

This equation represents an ellipse centered at the origin in the xz-plane, with a semi-major axis of 1 and a semi-minor axis of 5.

Finally, for the yz-trace, we set x = 0:

This equation represents an ellipse centered at the origin in the yz-plane, with a semi-major axis of 5 and a semi-minor axis of 1.

c. The cross-sections in the yz-plane are ellipses, and the cross-sections in the xy- and xz-planes are circles. The yz-trace is an ellipse centered at the origin in the yz-plane, with a semi-major axis of 5 and a semi-minor axis of 1.

The xy- and xz-traces are circles centered at the origin in their respective planes, with a radius of 1. The graph is symmetrical about the x-axis and extends infinitely along the x-axis.

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Answer:

c = 196

Step-by-step explanation:

To obtain a perfect square trinomial

Add ( half the coefficient of the x- term )² to x² + 28x

x² + 2(14)x + (14)², that is

x² + 28x + 196

= (x + 14)² ← a perfect square

Answer:

c = 196

Step-by-step explanation:

28 /2 = 14

14 x 14 = 196

formula =( b/2) x 2

the lower class limit represents the smallest data value that can be included in the classThe statement is true.

The lower class limit is the smallest value that can be included in a class interval.

Therefore, the statement is correct.

The lower class limit represents the smallest data value that can be included in a particular class. In a frequency distribution table, data values are grouped into classes, and each class has a lower and upper class limit. The lower class limit denotes the lowest value within that class, and any data value equal to or greater than the lower limit but less than the upper limit falls into that class.

The statement is true, as the lower-class limit indeed represents the smallest data value that can be included in the class.

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Answer:

it is 0.02

Step-by-step explanation:

According one-way ANOVA, the test is false.

In the given question,

When comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment, a​ one-way ANOVA is appropriate. It is also appropriate in this​ situation, however, to compare two means at a time using multiple independent two sample​ t-tests. We have to check whether this is true or​ false.

We firstly learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the means of two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given method it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Answer:

C. d = C/pi

Step-by-step explanation:

lol nothing really to explain but it's saying diameter equals circumference divided by pi

Hope this helps dude !

Answer:

If he mows 3/20 in 1/6 of an hour he'll mow 18/20 or 9/10 in one hour

which means the ratios are equal

1/6:3/20 = 1:18/20 = 1:9/10

Therefore, Jerry will mow 90% of the lawn in one hour

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may GOd bless you

By geometric formulas, the gray square has an area of 25 square units.

Squares are quadrilaterals with four right angles. In this question we find a geometric system formed by seven squares with distinct dimensions. By geometry, the area of a square (A), in square units, is equal to following formula:

A = l²

Where l is the length of the side of a square, in units.

All the required lengths are represented in the image attached below. First, determine the side length of the gray square:

7 + x = 12

x = 12 - 7

x = 5

The gray square has four sides with a length of 5 units.

Second, determine the area of the gray square by means of square formula:

A = x²

A = 5²

A = 25

According to area formula for squares, the area of the gray square is equal to 25 square units.

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Step-by-step explanation:

All steps are in picture above.

Note:if you need to ask any question please let me know.

here is the answer hope it help you

If the perimeter of the rectangular field is 236, the distance covered by the man is 236* 5 = 1180

Answer:

21 hours

Step-by-step explanation:

After 2 hours the temperature has risen to 7°f

The time taken to rise to an additional 13°f can be calculated as follows

1 hour takes 3.5°f

13°f = 3.5×6

= 21 hours

Hence it would take 21 hours

The function y= 4x -7 belong to the Linear function.

An equation is linear if it contains no powers of x besides x¹ = x and x⁰ = 1.

linear equation is called linear because it's graph form straight lines. we can describe any line by it's average rate of change, or slope, and it's y- intercept.

These aspects of a line is written in slope- intercept form, if equation of line is written in this form y = mx + b.

Here, in this given equation y= 4x -7.  This line has slope 4 and y intercept is point (0, -7).

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Answer: 30 minutes

Step-by-step explanation:

We can solve this problem by first finding how fast Leo bikes. We know that it takes Leo 12 minutes to bike 2 miles. To find how fast he bikes, we can create a proportion where 12/2=60/x, we do this because there are 60 minutes in a hour and we want to find the MPH (Miles Per Hour) he can bike, and the variable x stands for the MPH. To solve the proportion, we have to cross multiply, and then we get 12x=120. When we divide to find x, we find that x=10, which means Leo can bike 10 miles per hour. The park is 5 miles away, and Leo can bike 10 miles an hour, so therefore Leo will be able to bike there in half an hour, which is 30 minutes.

After 2.3167 seconds, the rocket and the ball reach the same height.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

b(t) = -t² - 4t + 22         ...1

p(t) = -2t + 12               ...2

From equations 1 and 2, then we have

-2t + 12 = -t² - 4t + 22

t² + 4t - 2t = 22 - 12

t² + 2t = 10

t² + 2t + 1 = 10 + 1

(t + 1)² = 11

t + 1 = ± 3.3167

t = - 1 ± 3.3167

t = -4.3167, 2.3167

Time is an absolute value. So, it cannot be negative.

After 2.3167 seconds, the rocket and the ball reach the same height.

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A box plot that represents data containing an outlier typically includes a box with a horizontal line inside it representing the median. It also has "whiskers" extending vertically from the box to indicate the range of most of the data. Additionally, there will be one or more individual points or "dots" outside the whiskers, which represent the outliers.

In a box plot, outliers are defined as data points that fall outside the range of the whiskers, which extend from the box. If a box plot displays a data point located beyond the whiskers, it indicates the presence of an outlier in the data set. Outliers are typically represented as individual points or asterisks. These data points are considered to be extreme values that significantly deviate from the rest of the dataset. They can provide valuable insights into the distribution and potential anomalies within the data.

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The number of runs up and runs down for the preceding data is 5.

Runs up refers to the number of observations that are higher than the number of observations before them.

Runs down refers to the number of observations that are lower than the number of observations before them.

As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.

Therefore,

Runs up = 2nd + 4th + 6th observations

             = 3

As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down

Therefore,

Runs down= 3rd +5th observations

                 =2

Therefore,

Runs up + Runs down  =3+2

                                        =5

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the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

The given partial differential equation is:

au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)

a) BCs (Boundary Conditions):

We have u(0, t) = 0 and u(π, t) = 0.

IC (Initial Condition):

We have u(x, 0) = x.

To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.

The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:

X(x) * T'(t) = 4 * X''(x) * T(t) / a

Dividing both sides by X(x) * T(t) gives:

T'(t) / T(t) = 4 * X''(x) / (a * X(x))

Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².

T'(t) / T(t) = -λ²

X''(x) / X(x) = -λ² * (a / 4)

Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.

Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.

Now, applying the boundary conditions:

1) u(0, t) = 0:

Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.

2) u(π, t) = 0:

Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.

Now, let's find the expression for u(x, t) using the initial condition:

u(x, 0) = X(x) * T(0) = x

Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:

C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x

This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.

Therefore, the solution for the initial value problem is:

u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)

where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.

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Answer:

Option c

My logic:

The commutative property of multiplication states that you can multiply a string of numbers in any order and receive the same answer.

Hope this helps!

A parabola is the set of all points in a plane that are equidistant from both a point called the focus and a line called the: directrix

A parabola is a plane curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

A parabola is approximately U-shaped.

It is the graph of a quadratic function.

A fix point is called as the focus and a fixed straight line is the directrix of the parabola.

The fixed point does not lie on the fixed line. (i.e., the focus does not lie on the directrix of the parabola).

Therefore, A parabola is the set of all points in a plane that are equidistant from both a point called the focus and a line called the: directrix

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The required difference quotient is `4x + 2h - 3`.  The given function is f(x) = 2x² - 3x. Now we need to evaluate the difference quotient for each function.

Therefore we have;

Let, `f(x+h)

= 2(x+h)² - 3(x+h)`

So, `f(x+h) = 2(x²+2hx+h²)-3x-3h

Now, `f(x+h) - f(x)

= 2x² + 4hx + 2h² - 3x - 3h - 2x² + 3x`

Simplifying the above expression, we get;

f(x+h) - f(x)

= 4hx + 2h² - 3h`

Therefore, `difference quotient

= (f(x+h) - f(x)) / h`

Substituting the value of `

f(x+h) - f(x)` in the above expression we get;`

(f(x+h) - f(x)) / h

= (4hx + 2h² - 3h) / h

= 4x + 2h - 3`

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The winners of the prizes are distributed throughout the classes as per the percentage of students in the respective group.

The total number of surveyed students is 36.

We calculate the expected number of students for each class is:

Class

Expected Frequency

Freshman

30% of 36 = 10.8

Sophomore

25% of 36 = 9

Junior

25% of 36 = 9

Senior

20% of 36 = 7.2

(b)

We set up:

H0: The number of observed winners is indifferent to the number of expected winners.

H1: The number of observed winners is not indifferent to the number of expected winners.

The Test Statistic Calculation Table:

Class Observed Frequency (fi) Expected Frequency (ei) (fi -ei )² /ei

Freshman 6                                   10.8                                 2.1333

Sophomore 14                                    9                                         2.7778

Junior         9                                    9                                           0

Senior         7                                    7.2                                0.0056

Total =        36                                    36                                    4.9167

The calculated

\(x^{2}\) = 4.9167

The p-value for 4 - 1=3 degree of freedom for the above test score is 0.177999.

(c)

Since p-value (=0.177999) >  α0..05 (standard level of significance),

H0 is failed to be rejected.

The number of observed winners is concluded to be indifferent to the number of expected winners, i.e., the winners of the prizes are distributed throughout the classes as per the percentage of students in the respective group.

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Answer:

2 pie r is the measure of its circumference.

Answer:

you need to know the value of the radius in order to work out the circumfrance. do you have a picture of the math question?