Find the domain and the range of the given relation
{(-6, 0), (-1,5), (9, -3), (-3,9)}

Temperature less than 0° C is -9° C.

To subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.

Given a temperature 9 less than 0,

0° C - 9 = -9° C

Hence, Temperature less than 0° C is -9° C.

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The speed of boat in still water is 15 m per hour.

What is speed?

The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's motion per unit of time, making it a scalar quantity. The instantaneous speed is indeed the upper limit of a average speed as that of the length of the interval approaches zero. The average speed of the object in a period of time is equal to the distance travelled by object divided by duration of the period. Velocity and speed are not the same thing.

The dimensions of speed are time divided by distance.

Given, speed of lazy river current = 5

distance covered = 20 miles downstream

and 10 miles upstream

Let x be the speed in still water
(x+5)T = 20

(X-5)T= 10

2(X-5) = (X+5)

X = 15

Therefore, speed of the boat in still water is 15 m per hour

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Answer:

r = 1

Step-by-step explanation:

  Direct variation describes a relation ship in which two variables are directly proportion and is represented as,

 y = rx or

\(\sf r =\dfrac{y}{x}\)

From the table,

      \(\sf r =\dfrac{5.8}{5.8}\\\\r = 1\)

Answer:

5

Step-by-step explanation:

mean = sum of all values÷number of observation

= 3+7+5+6+4 ÷ 5

= 5

Answer:

Yes, they do form a triangle, So, its true

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

It is false because if we use B as a base which the length of is 15, we need to have at least 15 or more to form a triangle with the other segments. But, segment A and C together is only 13 which is less than 15. So, therefore, the statement is false.

The upper half of the sphere x² + y² + z² = 1 ,the region inside the cylinder x² + y² = 1 and the region inside the cone z = x² + y² are described below:

(a) The upper half of the sphere x² + y² + z² = 1 can be described using different coordinate systems. In rectangular coordinates, it is defined by z ≥ 0. In cylindrical coordinates, the region can be expressed as ρ² + z² ≤ 1 with z ≥ 0, where ρ represents the radial distance from the z-axis. In spherical coordinates, the region can be described as 0 ≤ ρ ≤ 1, 0 ≤ θ ≤ 2π (representing the azimuthal angle), and 0 ≤ φ ≤ π/2 (representing the polar angle).

(b) The region inside the cylinder x² + y² = 1, between the planes z = 0 and z = 5, is bounded by the surfaces x² + y² = 1, z = 0, and z = 5. In rectangular coordinates, it can be described as -1 ≤ x ≤ 1, -1 ≤ y ≤ 1, and 0 ≤ z ≤ 5. In cylindrical coordinates, the region is represented by ρ ≤ 1 (the radial distance from the z-axis) with -1 ≤ z ≤ 5. In spherical coordinates, the region can be described as 0 ≤ ρ ≤ 1, -1 ≤ φ ≤ π/2 (representing the polar angle), and 0 ≤ θ ≤ 2π (representing the azimuthal angle).

(c) The region inside the cone z = x² + y², outside the sphere x² + y² + z² = 1, and below the plane z = 5 is bounded by the surfaces z = x² + y², x² + y² + z² = 1, and z = 5. In cylindrical coordinates, the region can be described as ρ ≤ 1 (the radial distance from the z-axis) with ρ² + z² ≤ 1 and z ≤ 5. In spherical coordinates, the region can be expressed as 0 ≤ ρ ≤ 1, 0 ≤ φ ≤ π/4 (representing the polar angle), and 0 ≤ θ ≤ 2π (representing the azimuthal angle).

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Answer:

Step-by-step explanation:

The expression 36 divided by s = 4 can be solved for s by dividing both sides of the equation by 36:

36/s = 4

Dividing both sides of the equation by 4:

s = 36/4 = 9

So, the value of s that makes the equation true is 9. This means that if you divide 36 by 9, the result will be 4.

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

Step-by-step explanation:

1.  Two people, A and B, are on each end of a 50 foot rope and wish to communicate only with the rope.  They may do so by moving the rope up and down, using the height of the movement to transmit in Morse code.  For A to move B's side of the rope, A must add energy to the rope by moving it up and down on their end.  That energy is transmitted by virtue of the rope movement (up and down) as it moves from A to B.  When that energy reaches B's end of the rope, B can sense the energy by the rope's movement.  But the rope has not changed - it is still the same rope.  The molecules in the rope simply carried the energy in the form of waves along the rope.

2.  Wavelength:  Listening to music illustrates how the wavelength of a sound wave is used to convey meaning in what we call a melody.  

Velocity:  Light travels faster than sound.  Watching a fireworks display, one can easily predict when to cover their ears if a particularly loud firework explodes in the sky.  One can see the explosion well before the sound arrives.

3.  Amplitude:  Amplitude, or the intensity of sound, is evidence by how loud something is.  Hearing a person speak from across the gym is difficult if that person is far away.  But the same voice is easily heard as one approaches, even though it is the same voice.  The amplitude is the height of the sound wave - it carries more energy than a sound wave of the same frequency with a lower amplitude.  Sound energy dissipates the further it travels.

Answer:

I'm confused

Step-by-step explanation:

What am I suposed to do?

The researcher has to divide the volunteers into two groups; the treatment group and the control group at random.

The scientific method must include the tools of observation, experimentation, and, conclusion.

The researcher's ambition is to determine whether using mental imagery can help people remember specific details when given the information provided.

That would need to be done by selecting as many people as possible from the group, and also ensuring that the selection is random by using randomization.

In this case,

The researcher has to divide the volunteers into two groups; the treatment group and the control group at random.

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The candidate key for the relation schema R(A,B,C,D,E): A→B, C→B, D→A, D→B, D→C, C→D, D→E.

Candidate key for the given relation: To find the candidate key for the relation schema R(A,B,C,D,E), we need to follow the below steps:

Here, we have the following functional dependencies: A→B, C→B, D→ABC, AC→D, D→E.

Step 1: To normalize the given dependencies, we have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To check for the minimal dependency, we can eliminate the redundancy by eliminating D→ABC. Therefore, we have the following dependency:

A→B, C→B, D→A, D→B, D→C, D→E.

Step 3: Find the closure on each attribute, which is as follows:

1. A+ = {A,B}

2. B+ = {B}

3. C+ = {B}

4. D+ = {A,B,C,D,E}

5. E+ = {E}

Step 4: The combination of attributes that have all attributes of the relation schema, and it will be a candidate key is AD. Therefore, the candidate key is AD.

Compute the minimal cover of F:

Minimal Cover: The minimal set of dependencies that is equivalent to the given set of dependencies is the minimal cover.

We have the following functional dependencies:

A→B, C→B, D→ABC, AC→D, D→E.

The process to compute the minimal cover of F is as follows:

Step 1: To find the redundant dependencies, we need to split the dependencies. We have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E  becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To eliminate the dependencies with three attributes, we can use the following steps:

If X→YZ, then X→Y and X→Z.

Therefore, we have the following dependency:

D→A, D→B, D→C.

Step 3: To eliminate the dependency with two attributes, we can use the following steps:

If X→Y and Y→Z, then X→Z.

We have the following dependency: AC→D, C→D.

Step 4: Therefore, the minimal cover of F is A→B, C→B, D→A, D→B, D→C, C→D, D→E.

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The surface area of the two solids are listed below:

Case 1 - 232 square centimeters

Case 2 - 240 square centimeters

The surface area of a solid is the sum of the areas of all its faces. There are two cases of solids whose surface areas must be determined. The area formulas for triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Case 1

A = (6 cm) · (8 cm) + 2 · 0.5 · (6 cm) · (12 cm) + 2 · 0.5 · (8 cm) · (14 cm)

A = 232 cm²

Case 2

A = 2 · 0.5 · (8 cm) · (3 cm) + (8 cm) · (12 cm) + 2 · (5 cm) · (12 cm)

A = 24 cm² + 96 cm² + 120 cm²

A = 240 cm²

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Answer:

That

Step-by-step explanation:

Option second, option third, and option fifth are correct in this range 50% of the data lies.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have a box-and-whisker plot.

As we know, the box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale.

From the box plot, we can say:

Between the values 15 and 45, 40 and 50, 45 and 60; 50% of the data lie.

Thus, option second, option third, and option fifth are correct in this range 50% of the data lies.

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93% in decimal form is

On the other hand,

Since 0.93 is greater than 0.875 then 93% is greater than 7/8

Answer:

\(\displaystyle x < 7\)

General Formulas and Concepts:

Algebra I

Equality Properties

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

\(\displaystyle 4x - 4 < 24\)

Step 2: Solve for x

Answer:

x<7

Step-by-step explanation:

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

a. ΔECR and ΔACR have three pairs of congruent sides, both triangles are therefore congruent by the SSS conrguence theorem.

b. ΔTSE and ΔNOH have three pairs of congruent sides, both triangles are therefore congruent by the SSS conrguence theorem.

Congruent triangles are triangles that have the corresponding sides and angles that are congruent to each other and they have the same shape and size.

a. The information given shows that ΔECR and ΔACR have:

three pairs of congruent sides - CR ≅ RC; EC ≅ AC; and ER ≅ AR.

Therefore, both triangles are congruent triangles by the SSS conrguence theorem.

b. The information given shows that ΔTSE and ΔNOH have:

three pairs of congruent sides - TE ≅ NH; SE ≅ OH; and TS ≅ NO.

Therefore, both triangles are congruent triangles by the SSS conrguence theorem.

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

Explanation:

The term "equidistant" means "equally distant".

We want (x,y) to be the same distance to the x axis, the y axis, and the point (3,6).

Let n represent this unknown equal distance. Negative distance doesn't make sense, so we'll have n > 0.

Start at the origin and move n units to the right to arrive at (n,0). We are n units from the y axis.

Now move n units up to arrive at (n,n). This point is guaranteed to be n units away from each axis.

That is one potential point. Other potential points are:

One point for each quadrant.

Let's assume that the answer is in the 1st quadrant since (3,6) is located here.

We need to find an expression that represents the distance from the point (n,n) to (3,6). We'll set that distance expression equal to n so we can solve.

Part 1 of those steps

\(d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\n = \sqrt{(n-3)^2+(n-6)^2}\\\\n^2 = (n-3)^2+(n-6)^2\\\\n^2 = (n^2-6n+9)+(n^2-12n+36)\\\\n^2 = 2n^2-18n+45\\\\\)

Part 2 of those steps

\(0 = 2n^2-18n+45-n^2\\\\0 = n^2-18n+45\\\\n^2-18n+45 = 0\\\\(n-3)(n-15) = 0\\\\n-3 = 0\ \text{ or } \ n-15 = 0\\\\n = 3\ \text{ or } \ n = 15\\\\\)

The quadratic formula could be used as an alternative pathway.

Therefore, the mystery point could be located at (3,3) or at (15,15)

Use the distance formula to verify each answer. I'll let you do this part.

---------

Extra info:

If you were to perform similar steps with the point (-n,n), then you'll find that no real numbered solutions exist. The two solutions would be complex numbers.

The cases (n,-n) and (-n,-n) have no solutions at all.

Therefore, we have confirmed only case (n,n) would work.

The value of fog(x) is 35x - 1.

To find fog(x), we need to substitute g(x) into f(x) wherever we see x in f(x).

So,

fog(x) = f(g(x)) = f(7x + 1)

Now, substitute g(x) = 7x + 1 into f(x) = 5x - 6:

f(g(x)) = 5(7x + 1) - 6

Simplifying:

fog(x) = 35x - 1

Therefore, fog(x) = 35x - 1.

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Complete question:

f(x) = 5x-6, g(x) = 7x + 1 find fog(x).

x/12 + 3 < 7 = x<48 this is the only one i can do because i cant do the others sorry

The linear equation which determines whether we have enough pouches for 120 guests be,

210 = x + 120.

Given, we are a wedding planner who is filling small pouches with biodegradable confetti for a wedding reception.

We want to fill each pouch with of a cup of confetti, and we have a total of 210 fluid ounces of confetti.

We need enough pouches for 120 guests.

Let the number of remaining fluid ounces of confetti be, x

according to the question,

210 = x + 120

So, the linear equation which determines whether we have enough pouches for 120 guests be, 210 = x + 120.

Hence, the linear equation which determines whether we have enough pouches for 120 guests be, 210 = x + 120.

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Answer:

y =  -5/3x+ 4

Step-by-step explanation:

slope is -5/3 and y-intercept is 4

The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

This given test is a test for single sample proportion

The test hypothesis are:

\(H_{o} :p=0.20\), null hypothesis

\(H_{1} :p\neq 0.20\), alternative hypothesis

The test statistic fallows a standard normal distribution and is given by:

\(Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }\)

p=0.20

X=47 plants

Sample size, n=500

x, is the sample mean:

x=X/n=47/500

x=0.094

So, test statistic is calculated as:

\(Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }\)

Z=-5.93

From the z-table, the p-value associated with Z=-5.93 is approximately 0

The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level

In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim

So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

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Juanita will keep $187.50 as profit from her ice cream shop's sales this month.

Juanita will keep 25% of the monthly sales as profit, which is equivalent to $750 x 0.25 = $187.50. This means that out of the total monthly sales of $750, Juanita will keep $187.50 as her profit, while the remaining $562.50 will go towards the expenses of running the ice cream shop.

Profit is the amount of money that a business earns after deducting all its expenses. It is the excess revenue that remains after all the costs of doing business have been taken into account. Profit is essential for businesses as it helps them to sustain their operations, invest in growth opportunities, and generate returns for their owners or shareholders.

In Juanita's case, her profit is 25% of the monthly sales, which is a significant amount that can help her to keep her ice cream shop running smoothly. By keeping a portion of the sales as profit, Juanita can use the money to pay for her expenses, such as rent, utilities, and supplies, while still having enough left over to reinvest in her business or save for her personal use.

Overall, understanding the concept of profit is crucial for entrepreneurs and business owners to ensure that they can generate enough revenue to cover their expenses and make a profit that will help them to grow and succeed in the long run.

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