is every relation a function?

Answer:

Given that,

Akeelah’s storage box has a volume of 315 cubic centimeters.

It has a width of 9 cm and a length of 7 cm.

To find the height.

Explanation:

Length (l) = 7 cm

width (w) = 9 cm

Let hight be h,

we know that,

Volume is given by,

Substitute the values we get,

Required height is 5 cm

Answer is: 5 cm

The total area of the quilt is: 112.5 square inches

The six-sided figure is given, and we can deduce the following parameters from the question:

The shape is made of a triangle and a rectangle

The side lengths derived from the question are:

The triangle on top:

base: 5 inches and height: 5.18 inches

The rectangle at the bottom:

Base: 16 inches with a height of 7.5 inches

So, we have the total area of the figure to be

Area of figure = 1/2 * 5 * 6 + 13 * 7.5

Area of figure = 112.5

Based on the parameters, the total area is 112.5 square inches

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For the positive integer n, \(\langle n\rangle\) denote the sum of all the positive divisors of n with the exception of n itself is an option (A). 6.

We start by calculating the value of \(\langle 6 \rangle\), which is the sum of the positive divisors of 6 excluding 6 itself.

Since the divisors of 6 are 1, 2, 3, and 6, we have \(\langle 6 \rangle = 1 + 2 + 3 = 6\).

Next, we need to calculate \(\langle\langle 6 \rangle\rangle\), which is the sum of the positive divisors of 6 excluding 6 itself, and the positive divisors of 6 excluding 6 itself and \(\langle 6 \rangle\).

The divisors of 6 excluding 6 itself are 1, 2, and 3, so \(\langle\langle 6 \rangle\rangle\) is the sum of the positive divisors of 1, 2, and 3.

The divisors of 1 are just 1, the divisors of 2 are 1 and 2, and the divisors of 3 are 1 and 3.

Thus, \(\langle\langle 6 \rangle\rangle = 1 + 2 + 1 + 3 = 7\).

Finally, we need to calculate \(\langle\langle\langle 6\rangle\rangle\rangle\),

which is the sum of the positive divisors of 1, 2, 3, and 7.

The divisors of 1 are just 1, the divisors of 2 are 1 and 2, the divisors of 3 are 1 and 3, and the only divisor of 7 is 1.

Thus, \(\langle\langle\langle 6\rangle\rangle\rangle = 1 + 2 + 1 + 3 + 1 = \boxed{8}\).

For the positive integer n, \(\langle n\rangle\) denote the sum of all the positive divisors of n with the exception of n itself is 6

Hence option A is correct choice.

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Answer:

1232 cm3

Step-by-step explanation:

From a^2 +b^2 = c^2

Height h^2 = 25^2-7^2 cm

h^2 = 576 cm

h = 24 cm

Volume of a cone = (1/3)*h*PI*r^2

=(1/3)*24*(22/7)*7^2

=1232 cm3

The minimum amount of plastic wrap needed to completely wrap 8 containers is  794. 4 in². Option D

The area of each circular end is:

A = πr²

A = 3.14 × (2.75)²

A = 23.68in²

The area of the rectangular side is:

A = h * circumference

circumference = 5.5in * π

circumference = 17.27in

Using the given height of 3 inches, we get:

A = 3in * 17.27

A = 51.81in²

Therefore, the total surface area of each container is:

A = 2 * 23.68 + 51.81

A = 98.17in²

To wrap 8 containers, we need to multiply the surface area of each container by 8:

Total surface area = 8 × 98.17

Total surface area = 794. 4 in²

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Looks like f(x, y) = cot⁻¹(xy), as in the inverse cotangent.

If you're like me and you don't remember the derivative of the inverse trig functions, we can derive it as follows. Let y = cot⁻¹(x), so that for appropriate x we can write cot(y) = x. By the chain rule, differentiating both sides gives

-csc²(y) y' = 1

y' = -sin²(y) = -sin²(cot⁻¹(x)) = - 1 / (x² + 1)

Next, recall that the derivative of a function f(x, y) at a point (a, b) in the direction of a vector v is given by

∇ f(a, b) • v

Compute the gradient ∇ f(x, y) :

∇ f(x, y) = - y / ((xy)² + 1) i - x / ((xy)² + 1) j

At the point P, we have

∇ f(x, y) = - 8/17 i - 8/17 j

So, the derivative of f at P along v = - 4 i + 5 j is

(- 8/17 i - 8/17 j) • (- 4 i + 5 j) = - 8/17

Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").

The members in Jasmine's dance troupe is an illustration equivalent expressions.

The number of members in Jasmine's dance troupe is 62

Assume the number of dancers is n.

One third of the rest is:

\(\mathbf{x = \frac{1}{3}(n - 2)}\)

When she called three more, we have:

\(\mathbf{x = \frac{1}{3}(n - 2) + 3}\)

Expand

\(\mathbf{x = \frac{n}{3} - \frac{2}{3} + 3}\)

\(\mathbf{x = \frac{n}{3} + \frac{-2 + 9}{3}}\)

\(\mathbf{x = \frac{n}{3} + \frac{7}{3}}\)

The remaining dancers (r) are:

\(\mathbf{r = n- \frac{n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{3n - n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{2n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{2n - 7}{3}}\)

When two-fifth of the remaining dancers are added, we have:

\(\mathbf{x = \frac{n}{3} + \frac{7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}\)

\(\mathbf{x = \frac{n+7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}\)

\(\mathbf{x = \frac{n+7}{3} + \frac{4n - 14}{15}}\)

Take LCM

\(\mathbf{x = \frac{5n + 35 + 4n - 14}{15}}\)

\(\mathbf{x = \frac{9n + 21}{15}}\)

\(\mathbf{x = \frac{3n + 7}{5}}\)

When she called one more dancer, we have:

\(\mathbf{x = \frac{3n + 7}{5} + 1}\)

\(\mathbf{x = \frac{3n + 7+5}{5}}\)

\(\mathbf{x = \frac{3n + 12}{5}}\)

The remaining of the dancer is:

\(\mathbf{r = n - \frac{3n + 12}{5}}\)

\(\mathbf{r = \frac{5n - 3n + 12}{5}}\)

\(\mathbf{r = \frac{2n + 12}{5}}\)

When three-fourth are added, we have:

\(\mathbf{x = \frac{3n + 12}{5} +\frac{3}{4} \times \frac{2n + 12}{5}}\)

\(\mathbf{x = \frac{3n + 12}{5} + \frac{6n + 36}{20}}\)

Take LCM

\(\mathbf{x = \frac{12n + 48+6n + 36}{20}}\)

\(\mathbf{x = \frac{18n +84}{20}}\)

When the last two members are added, we have:

\(\mathbf{n = \frac{18n +84}{20} + 2}\)

\(\mathbf{n = \frac{18n +84+40}{20} }\)

\(\mathbf{n = \frac{18n +124}{20} }\)

Multiply through by 20

\(\mathbf{20n = 18n +124}\)

Collect like terms

\(\mathbf{20n - 18n =124}\)

\(\mathbf{2n =124}\\\)

Divide both sides by 2

\(\mathbf{n =62}\)

Hence, the number of members in Jasmine's dance troupe is 62

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Answer: The probability is approximately 20.51%.

Step-by-step explanation:

The correct answer is 21.5 days

Explanation:

We know Marissa has two paid days of vacation plus 1 day for every four months she works. In this context, the first step is to find how much paid days of vacation she will have for working 6.5 years and add this to the 2 paid days of vacation she was given when she began to work. The steps are shown below:

1. Find the number of months in 6.5 by considering each year has 12 months and half year (0.5) is equivalent to 6 months

6 (number of years)  x 12 months =  72 months

0.5 year = 6 months

72 months + 6 months = 78 months (Total of months in 6.5 years)

2. Divide the total of months into 4 considering every 4 months Marissa is given one paid day of vacation.

78 months ÷ 4 = 19.5 days (number of paid days of vacation for working 6.5 years)

Finally, add this result to the two paid days initially given 19.5 days + 2 days = 21.5 days

Step-by-step explanation:

35:12

40:17

45:22

50:27

55:32

Answer:

10,100

Step-by-step explanation:

Rounding off to the Nearest hundred is giving a number which ends as 5600 or 6700 etc. To round a number to its nearest hundred you have to first look at the tenths place ( in this case 53) if a number is 50 or above you round it to the next hundred example - 5678 rounded to the nearest hundred is 5700. If a number is below 50  example - 1348, you round it to the same hundred - 1300.

Hope this helps!

Answer:

When solving a multi step equation, you use PEMDAS (parentheses, exponents, multiplication, division, add, subtract), and you also use PEMDAS when solving a multi step inequality. However, inequalities are tricky in the fact that if you multiply or divide by a negative number, you must flip the sign.

Step-by-step explanation:

Answer:

When solving a multi step equation, you use PEMDAS (parentheses, exponents, multiplication, division, add, subtract), and you also use PEMDAS when solving a multi step inequality. However, inequalities are tricky in the fact that if you multiply or divide by a negative number, you must flip the sign.

Step-by-step explanation:

Answer: A. The average midterm score for those who listen to classical music while studying is higher than the average midterm score for those who don't listen to music while studying.

Step-by-step explanation:

An Alternative Hypothesis is one that disproves the Null Hypothesis in that it believes that indeed there is a change in the dependent variable due to a change in the independent variable.

The Alternative Hypothesis essentially aims to prove the assertion of the Researcher that there is an effect as a result of the introduction of a variable.

Null Hypothesis on the other hand believes that no significant difference exists between a change in a dependant Variable as a result of a change in an independent one.

The correct answer above therefore is that indeed music while studying inspires people to do better in exams than those who do not listen to music while studying. This is the alternative hypothesis because it believes that there was a change in the exam results due to reading while studying.

(a) This study is observational because the consultant is not manipulating any variables or imposing treatments on the machines.

(b) The factors are:

Machine (experimental factor): There are six machines, labeled A through F.

Carton (observational factor): There are 20 cartons selected randomly from each machine.

Deviation from 32 ounces (response variable): This is the weight difference between the actual fill amount and the target fill amount of 32 ounces.

The factor levels are:

Machine: A, B, C, D, E, F

Carton: 1, 2, 3, ..., 20

The factor-level combinations are all possible pairs of machine and carton, such as A-1, A-2, ..., F-20.

(c) This is a nested design because the 20 cartons selected from each machine are not interchangeable between machines.

(d) Here's an example code snippet in R to import the data and display the structure of the dataframe:

data <- read.csv("filling_machine_data.csv")

data$Machine <- factor(data$Machine)

levels(data$Machine)

Assuming the data is stored in a CSV file called "filling_machine_data.csv", the code reads in the data, coerces the Machine variable to a factor, and displays the factor levels of Machine

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Answer:

c = 3

Step-by-step explanation:

the graph of g(x) is the graph of f(x) shifted 3 units down.

the point (4, 1 ) on f(x) shifts to (4, - 2 ) on g(x), a shift of

| 1 - (- 2) | = | 1 + 2 | = | 3 | = 3

g(x) = f(x) - c , with c = 3

Answer:

B—283 cm^2

Step-by-step explanation:

SA=πr^2 + πrl

r=5

l=13

SA=π5^2 + π5*13

SA=π25 + π65

SA=78.5398 + 204.2035

SA=282.7433

SA=283=B

Given:

Radius, r = 7.5 in

Cost of lead = $0.36 per in³

Let's determine how much it will cost to make one ball.

Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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Answer:

2280

Step-by-step explanation:

Multiply 5 times 2325 it ain't that hard g just use google lol

Answer:

hhhhhhhhhhooooooooooooooooooooo

Step-by-step explanation:

Answer: The initial amount of syrup is (total volume of container + 2/5) * 5/5.

Since we don't know the total volume of the container we can not give you the value of S in its simplest form, we only have a relation between the initial amount of syrup and the total volume of the container. call the initial amount of syrup S.

We know that the container was 5/9 filled with syrup, so the initial amount of syrup is 5/9 * the total volume of the container.

We also know that Nick had the same amount of water and syrup left.

And he used 2/5 liter more water than the syrup.

So, if the amount of syrup used is s, and the amount of water used is w, we can set up the following equation:

s + w = S

w = s + 2/5

We also know that the container was filled with water, so the amount of water used is equal to the total volume of the container.

So we can set up another equation:

w = total volume of container

Now we have 2 equations with 2 unknowns, we can substitute the second equation into the first equation.

s + (s + 2/5) = S

Combining like terms and solving for s:

2s + 2/5 = S

2s = 5/5S - 2/5

s = 5/5S - 2/5

Now we can substitute this value of s back into the equation w = s + 2/5 and solve for the initial amount of syrup S.

w = s + 2/5

w = (5/5S - 2/5) + 2/5

w = total volume of container

5/5S - 2/5 + 2/5 = total volume of container

5/5S = total volume of container + 2/5

S = (total volume of container + 2/5) * 5/5

Therefore, the initial amount of syrup is (total volume of container + 2/5) * 5/5.

Step-by-step explanation: If possible, can I please get the brainliest? (:

Answer:

22 feet

Step-by-step explanation:

As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:

Therefore:

Draw a diagram using the given information (see attachment).

From the diagram, we can see that the flagpole and the person are parallel.  Therefore, the two triangles are similar.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, set up a ratio of height to shadow length and solve for h:

\(\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow\)

\(\implies \sf h:168=66:42\)

\(\implies \sf \dfrac{h}{168}=\dfrac{66}{42}\)

\(\implies \sf h=\dfrac{66}{42} \cdot 168\)

\(\implies \sf h=\dfrac{11088}{42}\)

\(\implies \sf h=264\;inches\)

Convert the height into feet by dividing by 12:

\(\implies \sf h=\dfrac{264}{12}=22\;feet\)

Therefore, the height of the flagpole is 22 feet.

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

Answer:

\(\frac{7}{10}\)

Step-by-step explanation:

100\(m^{2}\) -5 = 44  Add 5 to both sides

100\(m^{2}\) = 49  Divide both sides by 100

\(m^{2}\) = \(\frac{49}{100}\)

\(\sqrt{m^{2} }\) = \(\frac{\sqrt{49} }{\sqrt{100} }\)

m = \(\frac{7}{10}\)

Answer:

a.

The growth rate (k) can be calculated using the exponential growth formula: P = P0 * e^(kt), where P0 is the initial population, t is the time in years, and e is the natural logarithm base.

From the information provided, the initial population of elves in 2000 was 23, and in 2003, the population was 34. By substituting the values into the formula and solving for k, we get:

34 = 23 * e^(k * 3)

Taking the natural logarithm of both sides:

ln(34) = ln(23 * e^(k * 3))

Using the logarithmic identity:

ln(34) = ln(23) + ln(e^(k * 3))

Solving for k:

k = (ln(34) - ln(23)) / (3) = 0.175

Therefore, the growth rate (k) for the population of elves is 0.175.

b.

To find the population of elves in 2020, we can use the exponential growth formula:

P = P0 * e^(kt)

Substituting the initial population of elves in 2000, which was 23, and the growth rate (k), which we found to be 0.175, we get:

P = 23 * e^(0.175 * 20)

Calculating the exponential function:

P = 23 * e^3.5

Therefore, there will be approximately 51 elves in 2020.

c.

To find the year when there will be 543 elves, we can use the exponential growth formula and solve for t:

543 = 23 * e^(0.175 * t)

Dividing both sides by 23 and taking the natural logarithm of both sides:

ln(543/23) = 0.175 * t

Solving for t:

t = (ln(543/23)) / 0.175

Therefore, there will be 543 elves in the year 2027.

i am not sure

Answer:

Step-by-step explanation:

(0, 2) (2, 0)

(0-2)/(2-0)= -2/2= -1

y - 2 = -(x - 0)

y - 2 = -x + 0

y = -x + 2