For each relation, decide whether or not it is a function.

Total amount of water after 18 minutes is 1365 Liters.

Given that

1) Owners of a recreation area are filling a small pond with water.

2)  They are adding water at a rate of 35 liters per minute.

3) There are 700 liters in the pond to start.

4) Let W represent the total amount of water in the pond (in liters),

5) let T represent the total number of minutes that water has been added.

Now we have originally 700 litres i.e. when time =0 W =300

Next is rate of change of water per minutes = Positive 35

Thus the linear relationship between w and T has slope as 35 and y intercept as 300

Hence equation is

y = m x + c

W = 35T + 700

When T=19 minutes

W = 35(19) + 700

W = 1365 litres

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The equation relating W to T is W = 400 + 34T and total amount of water after 18 minutes is 1012 liters.

Equation will be formed by adding the amount of water already present with product of rate of water adding and amount of time in minutes. Representing this as equation -

W = 400 + 34T

Keep the value of T in the equation to find the total amount of water after 18 minutes.

W = 400 + 34×18

Performing multiplication on Right Hand Side of the equation

W = 400 + 612

Performing addition on Right Hand Side of the equation

W = 1012 liters

Therefore, the equation is W = 400 + 34T and amount of water is 1012 liters.

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The intervals in which the submarine is diving with a constant velocity is the intervals in which the graph is linear.

The velocity is given by the change in the position divided by the change in time, as follows:

Velocity = change position/change time.

It means that the velocity is the derivative of the position. Hence, if the velocity is constant, the position is represented by a linear graph, as the derivative of a line is a constant.

Hence, the submarine has a constant speed when the graph is linear, either constant, increasing or decreasing.

This problem is incomplete, hence I cannot give the exact intervals, as I can't see the graph, however you need to just check the graph and verify where it has linear behavior.

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Given:

Trapezoid PQRS is dilated about point P by a scale factor of 3 to form trapezoid P'Q'R'S'.

Required:

We need to find the dilation of Trapezoid PQRS by scale factor 3.

Explanation:

Recall that dilation is a type of transformation that enlarges or reduces a figure (called the preimage) to create a new figure.

Dilations preserve angle measure, betweenness of points and collinearity.

Let P be the perimeter of PQRS.

The dilation P'O'R'S' is enlarged by scale factor 3.

The perimeter of the P'O'R'S' is 3 times the perimeter of PQRS.

The perimeter of PQRS is one-third of the perimeter of P'O'RS is true.

The length of PQ' is 3 times the length of PQ is true since the scale factor is 3.

QR and Q'R' are parallel is true.

The measure of angle P' is 3 times the measure of angle P is not true.

Dilations preserve angle measure.

Final answer:

48 years falls between 40 to 50 on the graph

If you trace from a point close to 50 on the y -axis to meet the slope line

the point of intersection between the trace and the slope line, trace it down to x-axis

The value falls in between 6years and 9 years

-12/5

This is a improper fraction, so lect's corvert it into a mixed fraction

2

5 12

2

Written as a mixed fraction -2 2/5

It's negative

The possible answers are -2 2/5

12/-5

-12/5

Answer:

your a bot  

Step-by-step explanation:

According to the information given in the problem, you know that Alice got got a 13% raise in her salary from last year, therefore, this year she is owning $22,570.

Let be "x" the amount of money in dollars Alice made last year.

Set up the following equation:

So, to solve this equation, you must solve for the variable "x". The procedure for this is shown below:

Rounded to the nearest hundredth:

- Look at the digit in the hundreths place. In this case it is 5.

- Look at the digitt to the right of the digit 5 (In this case is the digit 1, which is located in the thousandths place).

- Since the number in the thousandths place is less than 5, you must round down and just remove all the digits located after the digit 5.

Then:

She made about $19,973.45 last year.

The formula rewritten for b1 is b1 = 2a/h - b2

The unknown base of the trapezoid is 5 inches

A subject of formula is simply described as the variable that is made to stand alone on one side of the equality sign.

It is the variable expressed in terms of other variables in an expression.

Given the formula for the area of a trapezoid as;

a = 1/2h(b1+b2)

Where;

Let's make b1 the subject of formula

cross multiply

(b1+b2)h = 2a

Now, divide both sides by h, we have!

b1 + b2 = 2a/h

Take b2 over the equality sign

b1 = 2a/h - b2

Now, substitute the values into the formula

b1 = 2(78)/12 - 8

Expand the bracket

b1 = 156/12 - 8

Find the quotient

b1 = 13 - 8

find the difference

b1 = 5 inches

Hence, the value is 5 inches

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the current amount of employees today represents an increase of 26% from the previous year, this can be written as:

then,

where x is the number of employees the previous year, then, solve for x

Answer:

there were 35000 employees one year ago.

Graphing the function:

In this case, we are given the value of one angle and told to find the value of angle x. To do so, we will try to relate them based on the position they have in the diagram.

Notice that the two parallel lines split the space into two. One space is in between the lines, and the other space is outside the lines. We can see that both angles are located outside of the parallel lines.

Now, see that the third line splits the space into two. One space is on the left of the third line, and the other one is on the right of the third line. From the diagram, we can tell that each angle is on an opposite side of the third line.

This two relations between these angles (being outside the parallel lines and on opposite sides of third line) gives them the name of alternate outer angles. This angles have the property that they have the same measure.

So, we have the following

so the measure of x, in degrees, is 56°.

The probability that the person has a business major is going to be represented by: p(B | M)

This is the concept that is used in statistical and mathematical analysis to refer to the likelihood and the chances of something happening. That is the likelihood of an event occurring.

We have to define M as the event that the person that has been chosen randomly has a masters degree.

We have to define B as the event that the person that has being chosen randomly has a business major.

Given that the person has a master's degree, the probability that a randomly chosen person was a business major is given as p(B|M)

This would be the conditional probability that is written in the form of

p(B|M) = P(B and M) / P(M)

Where probability P(M) is the probability of having a masters degree, while the prbability P(B) is the probability of having a business degree.

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Answer:

The difference in the depths is equal to 5ft

Step-by-step explanation:

A) snapper (-10 ft) : (b) redfish (-3ft): (c) clam (0 ft) : (d) Hermit Crab (2 ft)

B   The comparison of the depth of hermit crab and redfish,

D = hermit crab - redfish = 2 - (-3) = 5 ft

In order would be 1 snapper) 2 red fish) 3 clam)4 hermit

Answer:

a) Flounder, Bluefish, Clam, Hermit Crab

b) The bluefish is deeper than the hermit crab.

The Solution:

Given:

We are required to find the probability that the second sock is navy blue if the first one was a white sock.

Step 1:

The probability of the first sock being a white is:

Step 2:

The probability of the second sock being a Navy blue is:

Note:

One sock has been taken out without replacement. So, the total number of socks is now 13.

Thus, the probability of the first being White and the second being Navy Blue is:

Therefore, the correct answer is 20/91 or 0.22

1) Gathering the data

Time: 10 yrs ago

Interest rate (r) : 9% (0.09)

Future Value: 300

Initial Deposit:?

2) Since the current balance is given, let's call it Future Value because the amount that made that $300 is what we need to find out. Let's go find the Future Value since it's been 10 yrs ago. Plugging into the formula we have:

Notice that, since this investment was compounded yearly, so n=1.

3) So the initial deposit, 10 years ago was approximately $126.72

To answer this question, we can use the two-point form of the line equation:

Then, we have the points:

(3, 2) --->x1 = 3, y1 = 2

(-2, -18)---> x2 =-2, y2 = -18

Then, we have:

The question in the slope-intercept form is:

First, express all the mixed numbers as decimals:

2 1/2 = (2x2+1)/2 = 5/2 = 2.5

1 2/5 = (5x1+2)/5 = 7/5 = 1.4

1 3/4 = (1x4+3)/4 = 7/4 = 1.75

2 2/3 = (2x3+2)/3 = 8/3 = 2.67

3 1/4 = (3x4+1)/4 = 13/4 = 3.25

Now, we have

1. 2.5

2. 1.4

3. 1.75

4. 2.67

5. 3.25

From least to greatest.

2. 1.4

3. 1.75

1. 2.5

4. 2.67

5. 3.25

The equation for the second line is:

Where m = slope and c = Intercept

Let us rewrite the given equation in that form :

Comparing y = 4x - 1 with y = mx + c:

m = 4 and c = -1

Since line I is parallel to the given line, it means their slopes are equal. Therefore, the slope for line I is also m = 4

Line I contains the Point:

The equation of a line can also be written in the form:

By rearranging the above equation:

The above is the equation for line I

There aren't any SARS-CoV-2 variations listed as Variant Of Interest right now.

A genetic variant with certain genetic markers linked to altered receptor binding, decreased ability of antibodies to neutralise an infection or immunisation, decreased therapy effectiveness, potential impact on diagnosis, or anticipated rise in disease severity.

Potential characteristics of an interesting variant:

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The complete question is-

Labels for SARS-CoV-2 Variants of Interest and Concern.

When he buys the cheapest soap, the amount he save per bar is $0.25.

Money is anything that's used as a medium of exchange.

In this case, three bars of soap cost $3.75. Each bar will bre:

= $3.75 / 3

= $1.25

Also, a package of eight bars of soap for $12. Each bar will be:

= $12 / 8

= $1.5

The amount that will be saved will be the difference between the values above. This'll be:

= $1.5 - $1.25

= $0.25

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We plot and join the given ordered pairs.

The formula of dilation when it is not centred at the origin is:

Then, we can find the coordinates of the image:

Graphing a Quadratic Equation

Let's take as an example the function:

The vertex form of a quadratic function is:

Where a is the leading coefficient and (h,k) is the vertex.

If a is positive, the function is concave up, if negative the function is concave down.

The first step is to obtain the parameters by comparing the given equation with the general equation.

Thus, we have: a = -2. Vertex = (3,5)

Now we locate the vertex in the coordinate plane and draw the parabola opening down.

For more precision, we can substitute some points around the vertex, like for example:

x={1,2,4,5}

We get the y-coordinates:

y={-3,3,3,-3}

Then we plot the graph as follows:

Answer:6_7

Step-by-step explanation:

x = 3, y = -4

The given system of linear equations is:

The graph representing the equations is plotted below:

The point where both lines intersect is the solution to the system of equations.

The lines intersect at the point (3, -4), therefore, (3, -4) is the solution to the system of equations

Answer:

False. It has no solutions.

Step-by-step explanation:

Hope it helps! =D

Answer:If a graph of a quadratic,

f

(

x

)

, does not have an x-intercept

then

f

(

x

)

=

0

has no Real solutions.

Explanation:

The x-axis is composed of all points for which

f

(

x

)

(or, if you prefer,

y

) is equal to

0

If the graph of

f

(

x

)

does not have an x-intercept

then it has no (Real) points for which

f

(

x

)

=

0  

Step-by-step explanation:

No x-intercept means that it does not cross the x-axis. Thus two solutions is definitely ruled out.

However, if you DO NOT INCLUDE a point of coincidence (Vertex coincides with the x-axis) in the phrase "does not have an x-intercept". Then there could be a single value solution if you equate the quadratic to 0. Some people say that it still has two in such a case but they are both the same value. I do not like this way of thinking!

On the other hand, if you DO INCLUDE a point of coincidence in the phrase, then the plot does not cross the x-axis nor does any point on the curve coincide with it. In such an interpretation there is NO SOLUTION THAT IS REAL.  hopes this helps

Answer:

[tex](g \circ h)(-3)[/tex] = 26

Step-by-step explanation:

We are told that:

• [tex]g(n) = -2n - 2[/tex]

• [tex]h(n) = 4n - 2[/tex]

In order to calculate the value of [tex](g \circ h)(-3)[/tex], we need to first define [tex](g \circ h)[/tex].

[tex](g \circ h)[/tex] means that the input for the function [tex]g(n)[/tex] is the function [tex]h(n)[/tex]. Therefore, we have to replace the [tex]n[/tex] in the definition of [tex]g(n)[/tex] with the definition of [tex]h(n)[/tex]:

[tex](g \circ h)[/tex] = [tex]-2(4n - 2) - 2[/tex]

         = [tex]-8n + 4 - 2[/tex]

         = [tex]-8n + 2[/tex]

Now that we know the definition of [tex](g \circ h)[/tex], we can find the value of [tex](g \circ h)(-3)[/tex] by substituting -3 into the definition:

[tex](g \circ h)(-3)[/tex] = [tex]-8(-3) + 2[/tex]

                 = [tex]24 + 2[/tex]

                 = [tex]26[/tex]

A function which models the data in the given table is y = 3848.2x^0.054. Also, an approximate speed of sound when the water temperature is 100°F is equal to 4935 ft/sec.

A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the temperature of water would be plotted on the x-axis of the scatter plot while the speed of sound would be plotted on the y-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that a function for the line of best fit is given by:

y = 3848.2x^0.054

Next, we would determine the speed of sound when the water temperature is 100°F as follows:

y = 3848.2x^0.054

y = 3848.2 × (100)^0.054

y = 3848.2 × 1.2823

y = 4934.55 ≈ 4935 ft/sec.

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Answer: Maybe B

Step-by-step explanation: