A water tank is filled with a hose. The table shows the number of gallions of water in the tank compared to the number of minutes the tank was


being filed The line of best for this data is g = 9m-0. 17


Minutes (m) 13 27 33 60


Gallons (3) 120 241 294 542


Approximately how much water was in the tank after 45 minutes of being filled?


O A 388 gallons


OB 405 gallons


O c 407 gallons


D. $18 gallons

First find Divisor

\(\\ \sf\longmapsto x^2-(-3-2)+(-3)(-2)\)

\(\\ \sf\longmapsto x^2+5x+6\)

Dividend given by

\(\\ \sf\longmapsto x^4-x^3-16x^2+4x+48\)

We know

\(\boxed{\sf Dividend=Divisor\times Quotient +Remainder}\)

\(\\ \sf\longmapsto Dividend=Divisor\times Quotient\)

\(\\ \sf\longmapsto Quotient=\dfrac{Dividend}{Divisor}\)

\(\\ \sf\longmapsto \dfrac{x^4-x^3-16x^2+4x+48}{x^2+5x+6}\)

\(\\ \sf\longmapsto x^2-6x+8\)

Now factor

\(\\ \sf\longmapsto x^2-6x+8=0\)

\(\\ \sf\longmapsto x^2-4x-2x+8=0\)

\(\\ \sf\longmapsto x(x-4)-2(x-4)=0\)

\(\\ \sf\longmapsto (x-4)(x-2)=0\)

\(\\ \sf\longmapsto x-4=0\:or\:x-2=0\)

\(\\ \sf\longmapsto x=4\:or\:x=2\)

Hence all zeros are

In response to the query, Line C traverses Point (10, 10) & (1, 5). Line d and line c are parallel, and line d's slope is 5/9.

Parallel in mathematics refers to the different vectors that should never have cross each other with. Parallel relates directly to complementarity or contemporaneous higher incidence.

A straight line's general equation is: y = mx + c [m] where [m] is the slope of the line and represents the unit change rate of [y] without respect to [x].

The y-intercept, or the place where the graph crosses the [y] axis, is represented by [c].

When (x1, y1) and (x2, y2) are really the coordinates of 2 points on the line, m = (y2 - y1) / (x2 - x1).

adding the values we obtain,

m = (5 - 10) / (1 - 10) = -5 / -9 = 5/9

Therefore, the slope of line [d] would be 5/9.

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If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg according to given standard deviation.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = x- υ/σ

Given that μ = 55, σ = 6;

For x = 49:

z = 49 - 55/6

z = -1

If the dog has a z-score of -1.09, his weight is:

-1.09 = x -55/6

x - 55 = -6.54

x = 48.46

If the dog has a z-score of 1.09, his weight is:

1.09 = x - 55/6

x -55 = 6.54

x = 61.54

Hence ,If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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The vegetable patch has peppers and aubergines in a ratio of 5:3, with a total of 480 vegetables. Increasing the number of peppers by 10% changes the ratio to 11:5 for peppers to aubergines.

The ratio of peppers to aubergines in the vegetable patch is 5:3, and there are 480 vegetables in total. This means that there are 5/8 peppers and 3/8 aubergines. Increasing the number of peppers by

10% gives 5.5/8 peppers and 2.5/8 aubergines.

Simplifying this gives a new ratio of 11:5 for peppers to aubergines.

Therefore, the new ratio of peppers to aubergines in the vegetable patch is 11:5 in its simplest form.

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Answer:

Option 4 is correct

Step-by-step explanation:

Here, we want to select from the options, the dataset that is represented on the histogram

From what we have in the question, there is a range from 60 to 100

Also, there are no terms between 70 and 80

option 1 is wrong as we can see terms between 70 and 80

option 2 is also wrong for this reason

option 3 is incorrect ; looking at the frequency, the numbers between 60 and 70 should be 5 only and we have 6 in that set

Option 4 is the correct answer

Answer:

In this case, the mean is $1400, and the standard deviation is $200.

So, one standard deviation of the mean is 1400+200= $1600 and 1400-200 = $1200.

Therefore, according to the empirical rule, approximately 68% of the farms will have land and building values per acre between $1200 and $1600.

To estimate the number of farms that fall within this range, we can multiply the total number of farms (74) by 0.68.

(74)*(0.68) = 50.32 or about 50 farms

So, according to the empirical rule, approximately 50 farms will have land and building values per acre between $1000 and $1800.

Answer:

B

Step-by-step explanation:

The ratio of water to mix is 1:4.

Answer:

7

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

3 + (5 + 7) = (3 + 5) + 7

3 + (12) = (8) + 7

15 = 15

Answer:

Something does not make sense...

Step-by-step explanation:

The sequence is not geometric or arithmetic because there is no common difference or common ratio between each term.

Not a Geometric or Arithmetic Sequence

Answer:

11

Step-by-step explanation:

5 and a half gallons is 11 half gallons

since 1 half gallon needs 1 salt pckt

11 half gallons will need 11 packets

Answer:

11 salt packets

Step-by-step explanation:

For each half gallon you need one salt packet. So if you have 5 and a half gallons, you need 11 salt packets.

Answer:

Efficency, for getting work done on time, Skill, for able to do what kind of design is requested to her, A listening and patient ear by understanding what the customer needs and taking down details.

Step-by-step explanation:

Answer:

find the area of each side of the shapes and add make sure it's in square centimeters

so here you the answer is 9

Answer:

4.005+(-3.12)

Step-by-step explanation:

Answer:

4.005+(-3.12)

Step-by-step explanation:

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The greatest common factor (divisor) is found in the GCD column of the attached spreadsheet. The GCD is calculated using the spreadsheet function. The least common multiple (LCM) is the product of the numbers, divided by their GCD.

Other multiples shown are 2 times, 3 times, and 4 times the least common multiple.

The rectangular prism is made up of the dimensions

Lenght = 4 cubes

Width = 2 cubes

Height = 4 cubes

The total number of cubes she needs shall be derived as number of cubes along the lenght multiplied by number of cubes along the width, and then multiplied by number of cubes along the height. Therefore, she would have:

\(volume = l \times w \times h \\ volume \: = 4 \times 2 \times 4 \\ volume = 32 \: cubes\)

Therefore, She need 32 cubes to make the prism.

The expression y = α · sin x + β · cos x is a solution of the ordinary differential equations if and only if (α, β) = (0, 0).

According to the statement, we must find in what conditions a given expression may be a solution of an ordinary differential equation. Then, first and second derivatives of the equation are:

y' = α · cos x - β · sin x                 (1)

y'' = - α · sin x - β · cos x              (2)

Then, we substitute on the ordinary differential equation:

(- α · sin x - β · cos x) + (α · cos x - β · sin x) = 0

And by algebraic handling we simplify the resulting expression:

- (α + β) · sin x + (α - β) · cos x = 0

Where each coefficient represents a constant of a linear combination:

α + β = 0

α - β = 0

Then, the solution of the system of linear equations is (α, β) = (0, 0). The expression y = α · sin x + β · cos x is a solution of the ordinary differential equations if and only if (α, β) = (0, 0).

The statement is incomplete and complete form cannot be found, then we decided to create a new statement:

Please prove that y = α · sin x + β · cos x is the solution of the differential equation d²y / dx² + dy /dx = 0 where the following condition is observed, if and only if α = β = 0.

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Answer:

72 cubic feet

Step-by-step explanation:

V=whl

Plug in the numbers and you get your answer!

Have a good day :)

Its speed of Rachel would be 30 meters per second.

Given that,

Stunt driver Rachel is trying to get out of a building that is going to blow up.

Here, the equation is,

\(d = - 38t + 220\)

Where, variable d models Rachel's distance from her exit (in meters) t seconds after the cameras began recording the stunt.

Now, Velocity is the rate at which a distance changes over time.

\(d = - 38t + 220\)

\(\dfrac{d(d)}{dt} = - 38\)

Hence, Speed is the magnitude of velocity.

\(|- 38| = 38\)

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The missing value is 64. The equation can be written as:

log₄(16 · 64) = log₄(16) + log₄(64)

To find the missing value in the equation log₄(16 · 64) = log₄(16) + ?, we can use the logarithmic property you mentioned.

According to the property, the logarithm of a product is equal to the sum of the logarithms of the individual numbers.

Let's solve the equation step by step:

We know that log₄(16 · 64) is equal to the logarithm of the product of 16 and 64.

log₄(16 · 64) = log₄(1024)

We can simplify the right side of the equation by calculating the logarithms individually.

log₄(16) + ? = log₄(16) + log₄(64)

Now, we can substitute the base 4 logarithms of 16 and 64, which are known values:

log₄(1024) = log₄(16) + log₄(64)

The sum of the logarithms of 16 and 64 is the logarithm of their product:

log₄(1024) = log₄(16 · 64)

Therefore, the missing value is 64. The equation can be written as:

log₄(16 · 64) = log₄(16) + log₄(64)

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Answer:

p/2-4

❤❤

Step-by-step explanation:

it's actually like this=

c= p/2-4

The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.

Substitute x = 0 into the function T(x):

T(0) = -19 + 39e^(-0.45*0).

Simplify the expression:

T(0) = -19 + 39e^0.

Since e^0 equals 1, the expression simplifies to:

T(0) = -19 + 39.

Calculate the sum:

T(0) = 20.

Therefore, the initial temperature of the soda is 20 degrees Celsius.

To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):

Substitute x = 20 into the function T(x):

T(20) = -19 + 39e^(-0.45*20).

Simplify the expression:

T(20) = -19 + 39e^(-9).

Use a calculator to evaluate the exponential term:

T(20) = -19 + 39 * 0.00012341.

Calculate the sum:

T(20) ≈ -19 + 0.00480599.

Round the answer to the nearest degree:

T(20) ≈ -19 + 1.

Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.

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INCOMPLETE QUESTION

A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.

Step-by-step explanation:

the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

where the sides and associated angles are always opposite to each other.

and the sum of all angles in a triangle are always 180°.

sin(90) = 1.

4.

there are multiple solutions, as the direction they are going has no relevance to their position to each other right now.

and the angles of depression can be forward or backwards of the plane.

the larger the angle of depression, the closer the ship is.

for the closer ship we get

height/sin(35) = ground distance / sin(180-90-35)

265/sin(35) = ground distance / sin(55)

ground distance (plane to closer ship) =

= 265×sin(55)/sin(35) = 378.4592218... m

for the farther ship we get

height/sin(25) = ground distance / sin(180-90-25)

265/sin(25) = ground distance / sin(65)

ground distance (plane to closer ship) =

= 265×sin(65)/sin(25) = 568.2943339... m

the distance of both ships is

568.2943339... - 378.4592218... = 189.8351121... m

now, this distance applies to the case, where both ships are on the same side of the plane.

if they are on different sides of the plane, then we need to add their individual distances from the plane to get the distance of both ships from each other :

568.2943339... + 378.4592218... = 946.7535557... m

5.

another right-angled triangle.

the string is the Hypotenuse (baseline).

the height and the ground distance are the legs.

so, we get

100/sin(90) = height/sin(52) = 100

= ground distance / sin(180-90-52)

height = 100×sin(52) = 78.80107536... m

ground distance = 100×sin(38) = 61.56614753... m

Answer:

your answer would be 19=x

Answer:

$ 27.6.

Step-by-step explanation:

Let the cost of tea be C.

Let the mass of tea be M

From the question given, we were told that the cost of tea varies directly with the mass. This can be expressed as:

C & M

C = KM

K is called constant of proportionality.

C is the cost of the tea.

M is the mass of tea.

Next, we shall determine the constant of proportionality, K.

Cost (C) = $ 10.35

Mass (M) = 4.5 kg

Constant (K) =..?

C = KM

10.35 = K × 4.5

Divide both side by 4.5

K = 10.35/4.5

K = 2.3

Finally, we shall determine the cost of 12kg of tea as follow:

Mass (M) = 12 kg

Constant (K) = 2.3

Cost (C) =..?

C = KM

C = 2.3 × 12

C = $ 27.6

Therefore, the cost of 12 Kg of tea is $ 27.6

Answer:

$27.6

Step-by-step explanation:

10.35 divided by 4.5 = 2.3

$2.3 for 1 kg

2.3 times 12= 27.6

The optimal solution to the LP relaxation can be either smaller or larger than the optimal IP solution, but it can also provide a lower bound on the optimal IP solution value, and in some cases, it may be very close to the optimal IP solution value.

If both decision variables must be integer, then we are dealing with an Integer Programming (IP) problem. However, we can relax this constraint and solve the Linear Programming (LP) relaxation of the problem. The LP relaxation is solved by allowing the decision variables to take on non-integer values, which often results in a lower objective function value.

In this case, the LP relaxation of the problem will minimize the objective function z = 2x1 + 3x2, but the optimal solution may not be an integer solution. The LP relaxation solution can be either smaller or larger than the optimal IP solution. Therefore, the correct answer is b: "can be either smaller or larger than the optimal IP solution."

However, we can use the LP relaxation solution as a lower bound on the optimal IP solution value. Specifically, we can say that the optimal IP solution value is at least as large as the LP relaxation solution value. In other words, the LP relaxation solution value provides a lower bound on the optimal IP solution value.

Moreover, in some cases, the LP relaxation solution may be very close to the optimal IP solution value. Specifically, the LP relaxation solution may be within 5% of the optimal IP solution value. Therefore, answer choice a: "will be within 5% of the optimal IP solution value" is also a possibility.

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The kind of error where a bank misses an opportunity to make a loan to someone who would have repaid it is known as a Type II error or a false negative.

1. Type II error: When a bank fails to grant a loan to an individual who would have been capable of repaying it, it is considered a Type II error or a false negative. This means that the bank incorrectly rejects a potentially profitable opportunity.

2. Loan evaluation process: Banks assess various factors before approving a loan, such as credit history, income stability, debt-to-income ratio, and collateral. These factors help determine the borrower's creditworthiness and ability to repay the loan.

3. Probability of error: The bank's decision-making process involves setting thresholds or cutoff points for different criteria. If the borrower's profile falls below these thresholds, the loan may be denied. However, these thresholds are not infallible and can lead to errors.

4. Factors contributing to error: There can be several reasons why a bank might miss an opportunity to grant a loan to someone who would have repaid it. Some potential factors include overly strict evaluation criteria, outdated or incomplete data, limited access to information, or human error in the decision-making process.

5. Impact and mitigation: Type II errors can result in missed business opportunities for the bank and potential benefits for the borrower. To minimize these errors, banks can continually refine their loan evaluation processes, adopt advanced data analysis techniques, leverage technology for more accurate assessments, and regularly update their risk models. Additionally, ensuring proper training and supervision of loan officers can also reduce the likelihood of such errors.

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