when hungry, two puppies can eat a bowl of kibble in 9 seconds. how long do they take individually to eat the same bowl if one puppy take 24 seconds longer than the other math problem

The density of the lobster population in the area labeled NBHK is C) 9.02 lobsters/mi^2.

Population density refers to the number of people living in a given area, usually expressed as the number of individuals per square mile or kilometer.

To calculate population density, you can divide the total population of a given area by its land area. For example, if a city has a population of 1 million people and an area of 100 square miles, its population density would be 10,000 people per square mile.

The figure has two trapezoid and the areas are 306 and 756. Total area will be 1062 miles².

Lobster population will be:

= 6817 / 756

= 9

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The probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.

To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means is approximately normal for large sample sizes.

First, we need to calculate the standard error of the mean (SEM) using the formula

SEM = standard deviation / sqrt(sample size)

SEM = 29.5 / sqrt(45) = 4.4

Next, we can standardize the sample mean using the formula

z = (x - μ) / SEM

where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

For the lower limit, we have

z = (185.7 - 193.2) / 4.4 = -1.70

For the upper limit, we have

z = (206.5 - 193.2) / 4.4 = 3.02

We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.

The probability of z being between -1.70 and 3.02 is approximately 0.9429 or 94%. Therefore, the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.

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263 more story artists are there than ​interns.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number

In actual values

Number of story artists = 1620 x 20% = 1620 x 20/100 = 324

Number of interns = 1620 x 5% = 1620 x 5/100 = 81

Difference = 324 - 81 = 263

Hence, 263 more story artists are there than ​interns.

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Complete question:

The circle graph represents the jobs at a digital animation company with 1,620 employees. How many more story artists are there than interns​?

See the image attached.

Note that given the perimeter of the Rhombus above, KN will be 35.03 inches

Since JKLM is a rhombus, all sides have the same length. Let's call this length "x".

Also, since JL and KM are diagonals of the rhombus, they bisect each other at point N. This means that JN = NL and KN = NM.

We know that JN = 16 inches, and we need to find KN. To do this, we need to first find x, the length of the sides.

The perimeter of the rhombus is 72 inches, so we can write:

4x = 72

Dividing both sides by 4, we get:

x = 18

Now we can use the Pythagorean theorem to find NM (which is equal to KN):

(NM)² = (JN)² + (JM)²

We know that JN = 16, and we can find JM using the fact that JL and KM are perpendicular bisectors of each other:

JM = √[(2x)² - x²] = sqrt(3x²) = x √(3)

Substituting x = 18 and simplifying, we get:

(NM)² = 16² + (18 √(3))²

(NM)² = 256 + 972

(NM)² = 1228

NM = √(1228) = 35.03

Therefore, KN is approximately 35.0 inches (to the nearest tenth).

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Solving the given inequality, we get the value of x to be,

x ≥ 16.

In a mathematical equation with an inequality, both sides must be equal. In inequality, we don't use equations but rather compare two values. The signs greater than (or greater than or equal to), less than (or less than or equal to), or not equal to are used in place of the equal sign.

Here in the question, we have the inequality:

x - 4 ≥ 12

Now to simplify this we will add 4 on both sides,

⇒ x - 4 + 4 ≥ 12 + 4

⇒ x ≥ 16

So, this implies that the value of x is greater than or equal to 16.

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Polynomial expressions of [tex]2^{nd}[/tex] degree with one unknown (only [tex]x[/tex]) have [tex]2[/tex] roots. We use the formula below to determine these roots;

This formula is valid for equations of the form [tex]ax^2+bx+c[/tex]. We can convert the equation given in the question into this format to get the result;

Hence, the value of [tex]a[/tex]: [tex]8[/tex],

the value of [tex]b[/tex]: [tex]16[/tex],

the value of [tex]c[/tex]: [tex]3[/tex].

Now, we can find the roots of this equation by using this formula;

We can start by rearranging the equation 5 sin x + 4 cos x = 0 by dividing both sides by cos(x):

5

sin

⁡

�

cos

⁡

�

+

4

=

0

5

cosx

sinx

​

+4=0

Recall that $\frac{\sin x}{\cos x} = \tan x$. So we can substitute this in:

5

tan

⁡

�

+

4

=

0

5tanx+4=0

Now we can solve for $\tan x$:

\begin{align*}

5 \tan x + 4 &= 0 \

5 \tan x &= -4 \

\tan x &= \frac{-4}{5}

\end{align*}

Therefore, the value of $\tan x$ is $\boxed{\frac{-4}{5}}$.

The sampling method described in the question is called "quota sampling."

Quota sampling is a non-probability sampling technique in which researchers select participants based on pre-determined quotas or characteristics, such as age or gender. In this case, the researchers are selecting participants between the ages of 20 and 40.

However, this method may not be representative of the entire population as it does not guarantee that all subgroups within the population have an equal chance of being selected. Therefore, the results may be biased and not accurately reflect the opinions of the entire population.

Therefore, it is important to consider the limitations of quota sampling when interpreting the results

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Rectangle ABCD was translated 8 units left and then 7 units down.

We can see vertex A(2,4) of rectangle ABCD moves to A"(-6,-3), in a way that A translated 8 units left (-8)and 7 units down(-7) to A".

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Vertex is a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet. The plural of a vertex is vertices.

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints.

that is (2-8,4-7)=(-6,-3)

Similarly the other vertices of rectangle ABCD moves to form rectangle A"B"C"D"

B (2,2) → B" (-6,-5)

C (6,2) → C" (-2,-5)

D(6,4) → D" (-2,-3)

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By answering the presented question, we may conclude that As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.

In mathematics, the slope-intercept form of a linear equation is an that the equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point on the line where it intersects the y-axis. Since it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line crosses the y-axis.

Let x denote the number of spelling and y the number of vocabulary questions. Because there are a total of 18 questions, we know:

x + y = 18

5x + 10y = 15 points

We must solve for y 5x + 10y = 100 to put this equation in slope-intercept form.

10y = -5x + 100

y = (-1/2)x + 10

As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.

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a. The probability that the top-selling Red and Voss tire wears out before 60,000 miles can be found by calculating the Z-score and using a standard normal distribution table. The Z-score formula is: Z = (X - μ) / σ, where X is the distance (60,000 miles), μ is the mean (71,000 miles), and σ is the standard deviation (5,000 miles).

Z = (60,000 - 71,000) / 5,000 = -11,000 / 5,000 = -2.2. Using a standard normal distribution table, the probability is approximately 0.0139 or 1.39%.

b. To find the probability that a tire lasts more than 81,000 miles, calculate the Z-score: Z = (81,000 - 71,000) / 5,000 = 10,000 / 5,000 = 2. Using the standard normal distribution table, the probability of a Z-score less than 2 is approximately 0.9772. Since we want the probability of the tire lasting more than 81,000 miles, we need to find the complement: 1 - 0.9772 = 0.0228 or 2.28%.

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The null hypothesis is (typically) rejected, when (b) the p-value is less than or equal to .05.

In hypothesis testing, the Null-Hypothesis represents the default assumption,

whereas the alternative hypothesis represents the claim made by the researcher.

The "p-value" is defined as a probability metric which indicates the likelihood of observing the data, given that the null hypothesis is true.

If the p-value is small (less than or equal to .05), it means that it is unlikely to observe the data, assuming the null hypothesis is true.

Therefore, a p-value less than or equal to .05 is considered statistically significant, and the null hypothesis is typically rejected, the correct option is (b).

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The given question is incomplete, the complete question is

The null hypothesis is (typically) rejected, when select one:

(a) the p-value is less than or equal to .5

(b) the p-value is less than or equal to .05

(c) the p-value exceeds .05

(d) the p-value exceeds .5

A forecast is defined as a(n) prediction of future values of a time series which is option B.

Using past data as inputs, forecasting is a process that produces accurate predictions of the future course of trends. Companies use forecasting to decide how to spend their budgets and make plans for forthcoming costs. Often, this is based on the anticipated demand for the provided goods and services.

Forecasting is a tool used by investors to predict if certain events, such sales projections, would raise or lower the price of a company's stock. For businesses that require a long-term view on operations, forecasting also offers an essential benchmark.

To predict how trends, like as the GDP or unemployment, will change in the upcoming quarter or year, equity analysts utilise forecasting. Lastly, statisticians may examine the probable effects of a change in business operations via forecasting. Data may be gathered, for example, on how altering company hours affects consumer happiness or how changing particular work conditions affects staff productivity.

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Answer: Let's say the total number of students surveyed is "x".

We know that 65% of the students surveyed said their favorite color was red, which means that 325 students said their favorite color was red.

We can set up a proportion to solve for "x":

65/100 = 325/x

To solve for "x", we can cross-multiply:

65x = 32500

Dividing both sides by 65, we get:

x = 500

Therefore, Hakeem surveyed 500 students in total.

Step-by-step explanation:

1) A function to model the cost of C after t years since 2000 is [tex]C = 4,291(1 + 0.0315)^t[/tex]

2)If the trend continues,  a student expect to pay for room and board in 2017 is $7862.35 .

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here we need to use exponential function formula to find the cost function . Then,

=> [tex]f(x)=a(1+r)^t[/tex]

Where a is cost for room in 2000 and r is rate of change.

Then model the cost of room and board C after t years since 2000, we can use the formula:

=> [tex]C = 4,291(1 + 0.0315)^t[/tex]

where 0.0315 represents the annual increase of 3.15% expressed as a decimal.

Now we have to find the cost of room and board in 2017, we need to substitute t = 17 (since 2017 is 17 years after 2000) into the function and round the result to the nearest hundredth.

So,[tex]C = 4,291\times(1 + 0.0315)^{17}[/tex]

=>C = 7,862.35

Therefore, a student would expect to pay approximately $7862.35 for room and board in 2017 if the trend continued.

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The final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

The initial balance of the checking account is $350.

If the customer makes two withdrawals, one $50 more than the other, let's assume the smaller withdrawal amount is x. Then, the larger withdrawal amount will be x + $50.

So, the new balance of the checking account after these two withdrawals would be:

$350 - x - (x + $50) = $350 - 2x - $50 = $300 - 2x

After this, the customer makes a deposit of $75, which would increase the balance of the checking account to:

$300 - 2x + $75 = $375 - 2x

Therefore, the final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.

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Complete question:

Write an expression for the new balance using as few terms as possible. A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.

The minimum score that a student must obtain to be in the top 30% of students taking the national standardized examination for college admission is approximately 658.4.

To find the minimum score that a student must obtain to be in the top 30% of students taking the test, we need to find the score that corresponds to the 70th percentile of the distribution.

Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 70th percentile is approximately 0.52.

We can use the formula for transforming a score from a normal distribution to a standard normal distribution to find the corresponding score in the original distribution:

z = (x - mu) / sigma

where z is the z-score, x is the score in the original distribution, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.

Rearranging this formula, we get:

x = mu + z * sigma

Substituting the values we have, we get:

x = 510 + 0.52 * 270

x = 658.4

Therefore, to be among the top 30% of test-takers and be eligible for admission to the college, a student must score at least 658.4 on the exam.

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Answer:

m = 5

n = 2

c = 7

Step-by-step explanation:

Use the property of degrees (when dividing two same based numbers with different degree indicators, the degree indicators are subtracted)

[tex] \frac{ {9}^{ - 3} }{ {9}^{2} } = \frac{1}{ {9}^{m} } [/tex]

[tex] {9}^{ - 3 - 2} = {9}^{ - 5} [/tex]

[tex] {9}^{ - 5} = \frac{1}{ {9}^{m} } [/tex]

If the degree indicator is negative, the number is written as a fraction (1 in the numerator) and the degree indicator is raised to the denominator with a positive sign:

m = 5

.

[tex] \frac{ {x}^{ - 4} }{ {x}^{ - 6} } = {x}^{n} [/tex]

[tex] {x}^{ - 4 - ( - 6) } = {x}^{ - 4 + 6} = {x}^{2} [/tex]

n = 2

.

[tex] \frac{ ({ - 11})^{7} }{ ( { - 11})^{0} } = ( { - 11})^{c} [/tex]

Raising any number to the zero power makes it one

[tex] \frac{ ({ - 11})^{7} }{1} = ({ - 11})^{c} [/tex]

When dividing by 1, the number does not change

[tex]( { - 11})^{7} = ({ - 11})^{c} [/tex]

c = 7

Answer:

The first box is 4 and the second box is 4

The solution is
([tex]\frac{3}{2}[/tex],1)

Step-by-step explanation:

y = 2x -2  Subtract 2x from both sides

-2x + y = -2  Multiply all the way through by - 2

4x - 2y = 4  You are doing this so that you can add it to the first equation 4x + 2y = 8

     4x + 2y = 8

(+) 4x - 2y = 4

       8x       = 12  Divide both sides by 8

x = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]

To find y substitute [tex]\frac{3}{2}[/tex] for x and solve for y

y = 2x - 2

y = [tex]\frac{2}{1}[/tex] x [tex]\frac{3}{2}[/tex] - 2

y = 3 - 2

y = 1

Helping in the name of Jesus.

Answer:

Part A = 4x - 2y = 4

Part B = (1.5, 1)

Step-by-step explanation:

Part A:

y = 2x - 2

2y = 4x -4

4x - 4 = 2y

4x - 2y = 4

Part B:

4x + 2y = 8

2y = 8 - 4x

y = (8 - 4x)/2

y = 2x -2

(8 - 4x)/2 = 2x -2

8 - 4x = 4x - 4

8x = 12

x = 1.5

4x + 2y = 8

4(1.5) + 2y = 8

6 + 2y = 8

2y = 2

y = 1

(1.5, 1)

The area of the rectangle has a width of 5 1/3 yards long and 2 1/6 yards wide is 104/9 square yards or 11.56 square yards.

When calculating a rectangle's area, we multiply the length by the breadth of the rectangle.

A mixed fraction is one that is expressed by its quotient and remainder.

Area = length * breadth

Given: Length = [tex]5 \frac{1}{3}[/tex] yards

           breadth = [tex]2 \frac{1}{6}[/tex] yards

First, we need to convert a mixed number into the improper fraction

[tex]5 \frac{1}{3}[/tex] = [tex]\frac{(5*3) + 1}{3}[/tex] = [tex]\frac{16}{3}[/tex]

[tex]2 \frac{1}{6} = \frac{(2*6) +1}{6} =\frac{13}{6}[/tex]

Therefore the area of the rectangle = Length * width

= [tex]\frac{16}{3} * \frac{13}{6}[/tex]

=[tex]\frac{104}{9}[/tex]

=[tex]\frac{104}{9} yards^{2}[/tex]

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Complete question:

The rectangle has [tex]5\frac{1}{3}[/tex] yards long and [tex]2 \frac{1}{6} \\[/tex] yards wide. What’s the area

The measure of IJ is 29, when IJ is dilated by a scale factor of 2 to form I' J', and I' J' measures 58. Geometric figures in two or three dimensions can be expanded and contracted using dilation mathematics.

Dilation refers to the change in size without a change in shape of an object. The scale factor may also cause the object's size to either increase or decrease.

Dilation is hence the process of resizing or altering an object. It is a transformation that makes the objects smaller or larger by applying the provided scale factor. It is a transformation that makes the objects smaller or larger by applying the provided scale factor. The pre-image is the original figure, while the image is the new figure created as a result of dilation. Dilation comes in two varieties:

As an object experiences expansion, its size expands.

Contraction is the process of a thing getting smaller.

Given:

I'J' is IJ with the scale factor of 2.

so (IJ) × 2= (I'J)

(IJ) × 2 = 58

58 ÷ 2 = 29

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Answer:

Los dos números naturales son 12 y 58.

Step-by-step explanation:

Llamemos al número más pequeño "x" y al número más grande "y".

Del problema sabemos que:

x + y = 70 (ya que la suma de los dos números naturales es 70)

Cuando el número mayor se divide por el número menor, el cociente es 4 con un resto de 10. Esto se puede escribir como:

y = 4x + 10 (ya que 4 es el cociente y 10 es el resto)

Ahora podemos sustituir la segunda ecuación en la primera ecuación:

x + (4x + 10) = 70

Simplificando esta ecuación, obtenemos:

5x + 10 = 70

Restando 10 de ambos lados, obtenemos:

5x = 60

Dividiendo ambos lados por 5, obtenemos:

x = 12

Ahora que conocemos x, podemos volver a sustituirlo en una de las ecuaciones anteriores para encontrar y:

y = 4x + 10 = 4(12) + 10 = 58

Por lo tanto, los dos números naturales son 12 y 58.

Based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75, thus the correct option is (d). The question is related to hypothesis testing in statistics.

If the p-value is 0.03 and the level of significance is 0.10, we reject the null hypothesis if the p-value is less than 0.10.

Since the null hypothesis is not specified in the question, we assume that it is that the average rating of the fruit drink is no more than 4.75.

Therefore, if the p-value is less than 0.10, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the average rating of the fruit drink is more than 4.75.

Since the p-value, in this case, is 0.03, which is less than the level of significance of 0.10, we would reject the null hypothesis and conclude that based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.

Therefore, the correct answer is (d) based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.

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Answer:Sin and cosine of the acute angle are complementary trigonometric functions. This means that between these trigonometric functions, the rule of complementary acute angles applies: sin64° = cos(90°-64°) = cos26°

So, if we have given cos64° = cosx  and we want to determine the value of the acute angle x, given the complementarity of the angles to 90 degrees, the required value of the angle x is 26°.

The answer is: x = 26°

Step-by-step explanation:

The greatest power of "p" in this situation is 4, which is the coefficient of p4. Consequently, the polynomial has a degree of 4.

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates.

This equation is provided:

1) [tex]$2p^{4}+p^{3}$[/tex]

The greatest power of the polynomial's variable "p" must be identified to categorize this polynomial by degree.

Therefore, the polynomial [tex]$2p^{4}+p^{3}$[/tex] is a polynomial of the fourth degree.

2) [tex]$2x^{2}$[/tex]

The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.

The greatest power of "x" in this situation is 2, which is the coefficient of . Consequently, the polynomial has a degree of 2.

Therefore, the polynomial [tex]2x^2[/tex] is a polynomial of the second degree.

3) [tex]$-5n^{4}+10n-10$[/tex]

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 4, which is the coefficient of . Consequently, the polynomial has a degree of 4.

Therefore, the polynomial [tex]n^4[/tex] is a polynomial of the fourth degree.

4) 6n

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 1, which is the coefficient of [tex]n^1[/tex]. Consequently, the polynomial has a degree of 1.

Therefore, the polynomial [tex]n^1[/tex] is a polynomial of one degree.

5) -6

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The polynomial in this instance doesn't have a component. It has a value of 6 and is a constant word. A constant word is thought to have a degree of zero.

Therefore, equation 6 is a zero-degree polynomial.

6) [tex]$x^{3}-3$[/tex]

The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.

The greatest power of "x" in this situation is 3, which is the coefficient of . Consequently, the polynomial has a degree of 3.

Therefore, the polynomial [tex]x^3[/tex] is a polynomial of the third degree.

7) [tex]$2n^{5}$[/tex]

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 5, which is the coefficient of . Consequently, the polynomial has a degree of 5.

Therefore, the polynomial [tex]n^5[/tex] is a polynomial of the fifth degree.

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Flow rate =[tex]V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex] gallons per hour (rounded to the nearest gallon) will be circulated.

What is meant by rate?

In general, a rate is a measure of how quickly something changes over time or with respect to some other quantity. It is typically expressed as a ratio of two quantities, where the numerator represents the amount of change and the denominator represents the time or other quantity over which the change occurs.

If the new exhibit is 3 1/2 times larger than the old one, then its volume is:

[tex]V_{new} = 3.5 * V_{old[/tex]

We know that in the old exhibit, 576,000 gallons of water circulated over 24 hours. Therefore, the flow rate of water in gallons per hour is:

576,000 gallons / 24 hours = 24,000 gallons per hour

To find the flow rate in the new exhibit, we need to divide the total volume of water by the number of hours. Since we want the flow rate in gallons per hour, we can write:

Flow rate = [tex]V_{new[/tex] / time

Plugging in the values we have:

Flow rate = (3.5 * [tex]V_{old[/tex]) / time

We don't know the time yet, but we do know that the flow rate should be the same as in the old exhibit, which was 24,000 gallons per hour. So we can set up an equation:

24,000 = (3.5 * [tex]V_{old[/tex]) / time

To solve for time, we can multiply both sides by time:

24,000 * time = 3.5 * [tex]V_{old[/tex]

Then we can divide both sides by 24,000:

time = (3.5 * [tex]V_{old[/tex]) / 24,000

Plugging in [tex]V_{old[/tex] = 576,000, we get:

time = (3.5 * 576,000) / 24,000 = 84 hours

Therefore, in the new exhibit, 3.5 times larger than the old one, the flow rate of water in gallons per hour will be:

[tex]Flow rate = V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex]gallons per hour (rounded to the nearest gallon).

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Answer:

To find out how many gallons per hour will be circulated in the new exhibit, we need to first determine the volume of the old exhibit. Given that 576,000 gallons of water circulated through the old tank over 24 hours, we can calculate the amount of water circulated per hour.

To do this, we divide the total gallons by the number of hours:

576,000 gallons / 24 hours = 24,000 gallons per hour

Now, we know that the new exhibit is 3 1/2 times larger than the old one. To find the volume of the new exhibit, we multiply the volume of the old exhibit by 3 1/2.

Let's assume the volume of the old exhibit is x gallons.

The volume of the new exhibit is 3 1/2 times larger than the old one, so the volume of the new exhibit is 3 1/2 * x.

To calculate the new volume, we need to convert the mixed fraction 3 1/2 into an improper fraction. It equals 7/2.

So, the volume of the new exhibit is 7/2 * x.

Now, we can determine the amount of water circulated per hour in the new exhibit.

To find this, we multiply the volume of the new exhibit by the rate of circulation per hour in the old exhibit (24,000 gallons/hour):

(7/2 * x) * 24,000 gallons/hour = (7 * 24,000 * x) / 2 gallons/hour = 168,000x gallons/hour

Therefore, the number of gallons per hour that will be circulated in the new exhibit is 168,000x, where x represents the volume of the old exhibit.

Please note that the actual value of x (the volume of the old exhibit) is not given in the question, so we can't determine the exact number of gallons per hour. However, we can express it as a multiple of the volume of the old exhibit.

Step-by-step explanation:

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The equation Y=8.35x represents a proportional relationship between Y and x.

What is proportion?

In mathematics, two quantities are said to be proportional if they vary in a way that can be expressed as a ratio or fraction. Specifically, if two quantities x and y are proportional, this means that as x increases or decreases, y also increases or decreases by the same factor.

The equation Y=8.35x represents a proportional relationship between Y and x.

In a proportional relationship, when one variable (x) increases or decreases, the other variable (Y) changes by a constant factor. This constant factor is known as the constant of proportionality.

In the given equation, Y and x are directly proportional to each other, with a constant of proportionality of 8.35. This means that if x is multiplied by any factor, Y will also be multiplied by the same factor. For example, if x is doubled, Y will also be doubled (since 2 times 8.35 is 16.7).

Therefore, the equation Y=8.35x represents a proportional relationship between Y and x.

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Therefore, the value of tan N rounded to the nearest hundredth is approximately 0.85.

A triangle is a basic geometrical shape that is formed by connecting three non-collinear points in a plane using straight line segments. The three points are called the vertices of the triangle, and the line segments connecting them are called the sides. The angles formed between the sides of a triangle are also an important characteristic of the triangle. Triangles come in many different shapes and sizes, and they have many interesting properties and applications in mathematics, science, engineering, and other fields.

Since the opposite side of angle N is √67 and the adjacent side is √92, we can use the following formula for tangent:

tan(N) = opposite / adjacent

tan(N) = √67 / √92

We can simplify this expression by rationalizing the denominator:

tan(N) = (√67 / √92) * (√92 / √92)

tan(N) = √(67*92) / 92

tan(N) = √6164 / 92

tan(N) = 78.43 / 92

tan(N) ≈ 0.85 (rounded to the nearest hundredth)

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