The perimeter of your rectangular pool is 130ft. Three time the length is equal to 10 times the width. Find the length and width of the pool. Find the area if the pool.

Answer:

94 ft

Step-by-step explanation:

Answer:

1 hour and 15 minutes

Step-by-step explanation:

For the hours he had slept the last is around 7 hours and 15 minutes and the one where he slept the most is around 8 hours and 30 minutes.  Subtract these two numbers in which your answer is that Tom slept for 1 hour and 15 minutes more than the one where he slept the least.

Answer:

2 hours

Step-by-step explanation:

Answer:

There are 10 choices for each digit, so the probability of not selecting any 1's is (9/10)^4. Therefore, the probability that a randomly chosen number between 0000 and 9999 will contain at least one 1 is

\(1 - {( \frac{9}{10}) }^{4} = .3439 = 34.39\%\)

Out of every 1000 4-digit numbers between 0000 and 9999, we can expect around 474 of them to contain at least one digit that is 1. This probability can also be expressed as a percentage, which is approximately 47.4%.

The probability that a randomly chosen number between 0000 and 9999 contains at least one digit that is 1 can be calculated by finding the complement of the probability that the number does not contain any digit that is 1.
The probability that a number between 0000 and 9999 does not contain any digit that is 1 is equal to the probability of choosing a digit from the set {0, 2, 3, 4, 5, 6, 7, 8, 9} for each of the four digits in the number. Since each digit has 9 possible choices, the total number of possible 4-digit numbers is 9^4 = 6561. Therefore, the probability of choosing a number that does not contain any digit that is 1 is (8/9)^4 = 0.526.
The complement of this probability is the probability of choosing a number that contains at least one digit that is 1, which is equal to 1 - 0.526 = 0.474. Therefore, the probability that a randomly chosen number between 0000 and 9999 contains at least one digit that is 1 is approximately 0.474.
In other words, out of every 1000 4-digit numbers between 0000 and 9999, we can expect around 474 of them to contain at least one digit that is 1. This probability can also be expressed as a percentage, which is approximately 47.4%.

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Answer:

1521

Step-by-step explanation:

ANSWERS

1. Domain: all real values

2. Zeros: 0 (with multiplicity 2) and 3

3. Not periodic. Symmetric about the point (1, 2)

4. Positive for x < 3; negative for x > 3

5. f → ∞ as x → -∞; f → -∞ as x → ∞

6. none

EXPLANATION

1. The domain of a function is the set of all the x-values for which the function exists. In this case, we have a polynomial function and, therefore, the domain is all real values.

2. To find the zeros of the function, we have to solve,

First, factor x² and -1 out. To do so, we have to divide each term by x² and by -1 - or, in other words, divide by -x²,

So, we have,

In this equation, we can see that if x = 0, then the equation is true. Also, if x = 3 the equation is true. So, these are the two zeros, with the particularity that x = 0 has multiplicity 2. This is because the factor related to that zero is x squared.

Hence, the zeros are 0 and 3. 0 has multiplicity 2.

3. As mentioned before, this is a polynomial function, which means that it is not a periodic function. A cubic function is an odd function, and it is symmetric about the origin. However, this function is not the parent function, x³, but it is symmetric about the point (1, 2).

4. We know that the function is zero at x = 0 and at x = 3. For x < 0, the function is positive,

For 0 < x < 3, the function is also positive. This is because x = 0 with multiplicity 2.

Then, since the function crosses the x-axis at x = 3 and that zero has multiplicity 1, we can conclude that the function is negative for x > 3.

Hence, is the function is positive for x < 3 and negative for x > 3.

5. As mentioned in part 4, the function is positive for all values of x less than 3, which means that the function goes to infinity as x goes to negative infinity.

Since for x > 3 the function is always negative, it goes to negative infinity as x goes to infinity.

6. A polynomial function has no restrictions in the domain and, therefore, has no asymptotes.

Rounding to the nearest person, we estimate the city's population in 2025 to be 303,977 based on rate proportional.

When two quantities are directly proportional to one another with regard to time or another variable, this circumstance is referred to as being "rate proportional" in mathematics. For instance, if a population's rate of growth is proportionate to its size, the population will increase in size at an increasingly rapid rate. Similar to this, if an object's speed and applied force are proportionate, then increasing the force will increase an object's speed. Linear equations or differential equations can be used to describe proportional relationships, which are frequently found in many branches of science and mathematics.

To estimate the city's population in 2025, we can use the formula:

\(P(t) = P(0) * e^(kt)\)

where P(0) is the initial population (123,580 in 1990), t is the time elapsed (in years), k is the growth rate (which we need to find), and P(t) is the population at time t.

To find k, we can use the fact that the population is increasing at a rate proportional to the existing population. This means that the growth rate (k) is constant over time. We can use the following formula to find k:

\(k = ln(P(t)/P(0)) / t\)

where ln is the natural logarithm.

Plugging in the given values, we get:

k = ln(152,918/123,580) / 10 = 0.026

This means that the city's population is growing at a rate of 2.6% per year.

Now we can use the formula\(P(t) = P(0) * e^(kt)\) to estimate the population in 2025:

\(P(35) = 123,580 * e^(0.026*35) = 303,977\)

Rounding to the nearest person, we estimate the city's population in 2025 to be 303,977.

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For only one value of t particles have the same velocity, Option (b) is correct.

Velocity is a vector quantity in physics that describes the rate of change of an object's position in space. It is defined as the derivative of an object's position with respect to time, and it has both magnitude and direction.

Velocity is measured in units of length per unit time, such as meters per second (m/s). The magnitude of velocity is the speed of an object, which is the rate at which an object is moving, while the direction of velocity is the direction in which an object is moving.

Velocity is a crucial concept in mechanics and is used to describe the motion of objects and to analyze the interactions between objects. For example, the velocity of an object can be used to calculate its acceleration, which is the rate of change of its velocity. The velocity of an object can also be used to calculate its displacement, which is the change in its position over a certain period of time.

The velocity of the first particle is given by x1'(t) = cos(t), and the velocity of the second particle is given by x2'(t) = \(-2e^{(-2t-1)}\). To find when the two velocities are equal, we set x1'(t) = x2'(t) and solve for t:

cos(t) = \(-2e^{(-2t-1)}\)

\(e^{(2t+1)}\) = -1/2cos(t)

Since cos(t) is positive for 0 <= t <= , we can take the logarithm of both sides to get:

2t + 1 = ln(-1/2cos(t))

We now have an implicit equation that relates t to cos(t). To find how many solutions this equation has, we would need to graph the two functions and find their intersection points, if any.

Therefore, as the question asks for how many values of t the particles have the same velocity, the answer is (B) One.

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The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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The BN structure model with more than 10 nodes can be established. The structure refers to the way the variables are related.

A Bayesian Network (BN) is a probabilistic graphical model that illustrates a set of variables and their probabilistic dependencies. A BN structure is made up of nodes and edges. Nodes represent variables, and edges represent the connections between the variables. The BN structure model can be established by using various algorithms, including structure learning and parameter learning.The BN structure with more than 10 nodes is a complex model with numerous variables and their dependencies. The structure's meaning is how the variables are interrelated, allowing us to estimate the probabilities of certain events or scenarios. The nodes in the structure represent various factors that affect the outcome of an event, and the edges between them demonstrate how these factors are related.The BN structure model is used in many fields, including medical diagnosis, fault diagnosis, and decision making.

The Bayesian Network structure model with more than 10 nodes is a powerful tool for analyzing complex systems. It helps to understand the interrelationships between variables and estimate the probabilities of different events or scenarios. This model is useful in various fields and provides insights into many complex phenomena.

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Answer:

500ml water

400 g flour

2 g salt

5 g yeast

25ml oil

Step-by-step explanation:

Answer:

0.33333333333

Step-by-step explanation:

(3y-1)2=0

6y-2=0

6y=0+2

6y=2

y=2/6

=1/3

square root=0.33333333333

Answer:

y= -2x-8

Step-by-step explanation:

the slope: m= -2

From the given information provided, the approximate volume of the cone is 94.24777 cubic inches.

The volume of a cone can be calculated using the formula V = (1/3) × π × r² × h, where "r" is the radius of the base of the cone, "h" is the height of the cone, and "π" is the mathematical constant approximately equal to 3.14159.

Radius r= 3 inches

Height h= 10 inches

π = 3.14159

Using the formula for the volume of a cone, V = (1/3) × π × r² × h, we can substitute the given values to calculate the volume of the cone:

V = (1/3) × 3.14159 × 3² × 10

V ≈ 94.24777 cubic inches

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The most direct way to measure how dispersed a set of scores is, is by using the range. The range is calculated by subtracting the lowest score from the highest score in the dataset, which gives a quick and easy measure of the spread of the scores.

However, the range can be influenced by extreme scores and may not provide a complete picture of the variability. Other measures of variability, such as the standard deviation and variance, take into account the variability of all scores in the dataset and provide a more robust measure of variability.

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Answer:

1.41

Step-by-step explanation:

Coordinates of point 1 are:

(-2,2)

Coordinates of point 2 are:

(-1,1)

\(Distance \: between \: two \: points \\ = \sqrt{ {(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} } \\ = \sqrt{ { (- 1 - - 2)}^{2} + {(1 - 2)}^{2} } \\ = \sqrt{ { (1)}^{2} + {( - 1)}^{2} } \\ = \sqrt{ 1 + 1 } \\ = \sqrt{2} \\ = 1.41 \)

Answer:

Passes through (0,1) and (1,3).

3-1/1-0=2/1=2

The slope of this line is 2

Step-by-step explanation:

Answer: 8x+55=127

Step-by-step explanation: it would take 9 mins because there’s already 55 gallons of water in the tank so you subtract that from 127 which is 72 then you divide 72 by 8 and get 9

Answer:

For this problem, you could just multiply $5 by 2 OR you could divide $5 by nine to find your Unit Rate and then multiply that number by 18.

For the given,  F, G and H are the midpoints of the sides of ΔJKL, FG = 37, KL = 48, and GH = 30, then measure of FH = 24, measure of JL = 74, measure of KJ = 60 and measure of FJ = 30.

As given in the question,

F, G, and H are the midpoints of the sides of ΔJKL.

F is the midpoint of KJ, G is the midpoint KL, H is the midpoint of JL

Measure of the required sides are as follow:

FH = (KL / 2)                         (by midpoint theorem)

     = (48/2)

     = 24

JL = 2 x FG             (by midpoint theorem)

   = 2 x 37

   = 74  

KJ = 2 x GH             (by midpoint theorem)

    = 2 x 30

    = 60

FJ = GH = 30            (by midpoint theorem)

Therefore, for the given,  F, G and H are the midpoints of the sides of ΔJKL, FG = 37, KL = 48, and GH = 30, then measure of FH = 24, measure of JL = 74, measure of KJ = 60 and measure of FJ = 30.

The complete question is:

If F, G, and H are the midpoints of the sides  KJ, KL, and JL respectively of ΔJKL, FG = 37, KL = 48, and GH = 30, find each of the following measures. FH= JL= KJ= FJ=​

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The cost function, c(x), includes the point (40, 390)

A function is a rule that maps input variables to output variables, with each input producing exactly one output.

The cost functions the chef uses to estimate the cost of the fixed price menu for x guest are ppresented as follows;

The function for the anticipated cost of appetizers, a(x) = 3.25·x

The function for the anticipated cost for the main course, m(x) = 5.25·x

The cost function for the anticipated cost of the desert, d(x) = 1.25·x

The function for the combined function, which is the cost of the fixed price menue is therefore;

c(x) = a(x) + m(x) + d(x)

The po

The point included in the function, c(x) (40, can be found by plugging in the value, x = 40 in the cost function c(x) = a(x) + m(x) + d(x). as follows;

The point on the cost function is; (40, (c(40))

c(40) = a(40) + m(40) + d(40)

c(40) = 3.25 × 40 + 5.25 × 40 + 1.25 × 40 = 390

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The condition of equal variance, also known as homoscedasticity, assumes that the variability of the residuals is constant across all levels of the predictor variable. This means that the spread of the residuals around the regression line should be the same for all values of the predictor.

One way to assess the equal variance assumption is to examine the scatterplot of the residuals against the predicted values. If the plot shows a random pattern with no discernible trend, then the assumption of equal variance is likely met. However, if the plot shows a funnel shape or a pattern where the spread of the residuals increases or decreases as the predicted values increase, then the assumption of equal variance may not be met.

Second, the condition of equal variance (homoscedasticity) is an assumption in regression analysis, where the variability of the response variable remains constant across the range of the predictor variable. When this condition is not met, it is called heteroscedasticity.Lastly, to identify a scatterplot that exhibits heteroscedasticity, look for a plot where the data points exhibit a pattern, such as a widening or narrowing spread, as you move along the x-axis.

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Vector AN = a + ¾ c and  we have shown that vector NM = ¼(2a – 3c) where M is the midpoint of line AB and N divides the line BC in the ratio 1:3 .

(a) To express vector AN in terms of a and c, we need to find the vector from A to N. Since N divides BC in the ratio 1:3, we can write:

BN = 3NC

Since M is the midpoint of AB, we have:

AM = MB

Adding these two equations, we get:

AM + BN = MB + 3NC

Substituting the vectors, we get:

a + BN = ½ (a + b + 2c) + 3c

Simplifying, we get:

BN = ½ (b – a) + 2c

But b = 2a – c (since M is the midpoint of AB)

So, we can write:

BN = ½ (2a – 2a + c) + 2c = ¾ c

Therefore, vector AN = vector AB + vector BN = (b – a) + ¾ c

Substituting b = 2a – c, we get:

Vector AN = a + ¾ c

(b) To show that vector NM = ¼(2a – 3c), we need to find vector NM and simplify it. Since M is the midpoint of AB, we have:

Vector NM = vector NC – vector MC

We know that N divides BC in the ratio 1:3, so we can write:

Vector NC = 3/4 vector BC = 3/4 (vector AB + vector AC)

Since M is the midpoint of AB, we have:

Vector MC = 1/2 vector AB

Substituting these vectors, we get:

Vector NM = 3/4 (vector AB + vector AC) – 1/2 vector AB

Simplifying, we get:

Vector NM = 1/4 vector AB + 3/4 vector AC

But AB = 2a – c (since M is the midpoint of AB)

Substituting, we get:

Vector NM = 1/4 (2a – c) + 3/4 c

Simplifying, we get:

Vector NM = ½ a – 3/4 c

Multiplying by 2, we get:

Vector NM = 2/2 (½ a) – 3/4 c

Simplifying, we get:

Vector NM = ¼ (2a – 3c)

Therefore, we have shown that vector NM = ¼(2a – 3c).

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Answer:

The formula for finding the percentage of something is given as: (No. of items you want to find÷Total no. of items)×100

Percentage of red pins = (21÷70)×100

= 30%

Answer:

Yes, the answer is C {3,5,7}

Domain of a function is the input value and range is the result or output value that we get.

the right answer is c

The required value of the function is 2

In the case of a function from one set to the other, each element of X receives exactly one element of Y.

The given function is of the form :

g(x) = - x² - 7

Now let us find the required values.

g (-3) = - (-3)² - 7 = 2

g (-2) = - (-2)² - 7 = -3

g (1 ) = - ( -1 )² - 7 = -6

Hence the required value of the function is 2 at x = -3 .

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To answer the questions in this problem, the following steps are advised:

Step 1: Compute the probability of obtaining a Red, Yellow, Green, and Blue color on each spin for both Mary and Nyla, as follows:

The probabilty of an outcome is generally defined as:

Now:

- For Mary:

- For Nyla:

Thus:

a) The expected out come for 100 spins are that:

For Mary:

- 22.5 (say, 22) of the total outcomes will be a Red colour

- 30 of the total outcomes will be a Yellow colour

- 22.5 (say, 22) of the total outcomes will be a Green colour

- 25 of the total outcomes will be a Blue colour

For Nyla:

- 27.5 (say, 27) of the total outcomes will be a Red colour

- 25 of the total outcomes will be a Yellow colour

- 27.5 (say, 27) of the total outcomes will be a Green colour

- 20 of the total outcomes will be a Blue colour

b) Mary and Nyla should not expect the same results after 100 spins because the results they each obtained after just 40 spins are markedly different. Also, the process is entirely random and the results cannot be predicted from the onset. Lastly, from the answers obtained in (a) Mary and Nyla should not expect the same outcome.

c) Their results might be different from the expected results based on theoretical probability because the results that are predicted by theoretical probability are for a very large number of spins.

That is, theoretical probability typically estimates what the results will be for a very large number of spins, say 1,000 or so.

Since the number of spins can practically not be that much, the results Mary and Nyla will obtain might be different from the expected results based on theoretical probability.

Answer:

2/3 + 2/3 + 2/3 = 6/3 or 2

Step-by-step explanation:

Repeated addition is the process of adding equal groups of objects together.

To solve 3 × 2/3 using repeated addition, it will look like this:

2/3 + 2/3 + 2/3 = 6/3 or 2

Answer:

To find 3 x 2/3 using repeated addition, we can add 2/3 to itself three times.

2/3 + 2/3 + 2/3 = 6/3

Simplifying the fraction, we get:

6/3 = 2

Therefore, 3 x 2/3 = 2.
________________________________________________________

To multiply a whole number and a fraction, you can first convert the whole number to a fraction by placing it over 1. Then, you can multiply the two fractions using the following formula:

a/b x c/d = ac/bd

Where a and c are the numerators of the fractions, and b and d are the denominators. After multiplying, you can simplify the resulting fraction, if necessary.

For example, to multiply 2 and 3/4, we can convert 2 to 2/1 and then multiply as follows:

2/1 x 3/4 = 6/4

Simplifying the resulting fraction, we get:

6/4 = 3/2

Therefore, 2 x 3/4 = 3/2.

One way to check your answer when multiplying fractions is to simplify both the numerator and denominator of the resulting fraction and compare it to the original fractions. If the simplified resulting fraction is equivalent to the original fractions, then the answer is correct.

Another way to check your answer is to divide the resulting fraction by one of the original fractions and see if the other original fraction is the quotient. For example, to check the answer to 2/3 x 3/4 = 1/2, we can divide 1/2 by 2/3 and see if the resulting quotient is 3/4:

(1/2) / (2/3) = (1/2) x (3/2) = 3/4

Since the resulting quotient is 3/4, which is equal to the other original fraction, 2/3 x 3/4 = 1/2 is correct.

Answer:

13x+4y+27

Step-by-step explanation:

Answer:

13x + 4y + 27

Step-by-step explanation:

6x +12+4y+7x+15

- Rearrange the like terms together.

6x + 7x + 4y + 12 + 15

13x + 4y + 27

Answer:

78 feet

Step-by-step explanation:

6/36=13/x

6×x=13×36

6x=468

6x/6=486/6

x=78