The least common multiple of 3, 5, 6 and 9

The weight of the liquid can be found by multiplying its volume by its density. The volume will be that of a hemisphere, which can be found using the appropriate formula.

The volume of a hemisphere with radius r is given by ...

 [tex]\sf V = \huge \text(\dfrac{2\pi}{3}\huge \text)r^3[/tex]

When the radius is 4 ft, the volume is ...

 [tex]\sf V = \huge \text(\dfrac{2\pi}{3}\huge \text)(4 \ ft)^3 = \dfrac{128\pi }{3} \ ft^3[/tex]

The weight of the liquid in the tank is found using the density.

 [tex]\sf W = \rho V[/tex]

 [tex]\sf W = (75 \ lb/ft^3)\huge \text(\dfrac{128\pi}{3} \ ft^3\huge \text) = 3200\pi \ lb \thickapprox 10,053 \ lb[/tex]

The total weight of the liquid in the tank is about 10,053 pounds.

answer Each person will get 1/8 of a cake.

Step-by-step explanation: 1/2 Divided by 4= 4 = 1 = 1 x 1 = 1 4 2 x 4 = 8

[tex]Q\cap R=\{7\}\\\\Q\cup R=\{0,5,6,7,11\}\\P\cap(Q\cup R)=\{5,6,7\}\\\\P\cap R=\{7\}[/tex]

The scale statement for the photograph is :

"The photograph is magnified by a factor of 200."

A scale statement is described as  a ratio of the length of the drawing or model to the length of the actual object which can be represented in these three way.

If the photograph of a strand of human hair shows the hair magnified by a factor of 200, we can write the statement as  photograph is magnified by a factor of 200.

In order to solve a scale factor, we do the following:

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The expression (7x - 4) - (2 - 1/2x) simplifies to 3/2 is equivalent to 11/2x + 6. A.

To simplify the expression (7x - 4) - (2 - 1/2x), we can remove the parentheses and combine like terms.

(7x - 4) - (2 - 1/2x) = 7x - 4 - 2 + 1/2x

Now, let's combine the like terms:

= 7x + 1/2x - 6

To add the terms with the same variable, we need to have a common denominator.

The common denominator for x and 1/2x is 2x.

= (14x + x) / (2x) - 6

= (15x) / (2x) - 6

= 15/2 - 6

= (15 - 12) / 2

= 3/2

The brackets and merge related words in order to make the statement (7x - 4) - (2 - 1/2x) simpler.

(7x - 4) - (2 - 1/2x) = 7x - 4 - 2 + 1/2x

Let's now mix similar terms:

= 7x + 1/2x - 6

We need a common denominator so that we may sum the words that share the same variable.

2x serves as the common denominator for x and 1/2x.

= (14x + x) / (2x) - 6

= (15x) / (2x) - 6

= 15/2 - 6

= (15 - 12) / 2

= 3/2

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The graph of the function 25x² + 9y² - 108x - 54y - 44  is added as an attachment

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

25x² + 9y² - 108x - 54y - 44

The above function is the equation of an ellipse that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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a) the demand equation in the form of p = f(Q) is p = -10/3Q + 14533.33

b) when the price per unit of calculators is Rs 1650, approximately 3865 calculators are demanded.

c) when 4500 calculators are demanded, the price per unit should be approximately Rs 3010.

To find the demand equation in the form of p = f(Q), we need to determine the relationship between the price per unit (p) and the quantity demanded (Q) based on the given information.

Let's use the two data points provided:

Point 1: Price (p1) = Rs 1200, Quantity (Q1) = 4000

Point 2: Price (p2) = Rs 1500, Quantity (Q2) = 3000

First, we calculate the slope of the demand equation using the formula:

Slope = (Q2 - Q1) / (p2 - p1)

Substituting the values, we get:

Slope = (3000 - 4000) / (1500 - 1200) = -1000 / 300 = -10/3

Next, we use one of the data points and the slope to find the y-intercept (b). Let's use Point 1:

p1 = Rs 1200, Q1 = 4000

Using the equation of a straight line (y = mx + b), we can rearrange it to solve for b:

b = y - mx

b = 1200 - (-10/3)(4000) = 1200 + 40000/3 = 1200 + 13333.33 = 14533.33

Therefore, the demand equation in the form of p = f(Q) is:

p = -10/3Q + 14533.33

To find the number of calculators demanded (Q) when the price per unit is Rs 1650, we can rearrange the equation and solve for Q:

1650 = -10/3Q + 14533.33

-10/3Q = 1650 - 14533.33

-10/3Q = -12883.33

Q = (-12883.33) / (-10/3)

Q = 12883.33 * 3/10

Q ≈ 3865

Therefore, when the price per unit of calculators is Rs 1650, approximately 3865 calculators are demanded.

Now, let's determine the price per unit (p) when 4500 calculators are demanded. We rearrange the equation and solve for p:

4500 = -10/3Q + 14533.33

-10/3Q = 4500 - 14533.33

-10/3Q = -10033.33

Q = (-10033.33) / (-10/3)

Q = 10033.33 * 3/10

Q ≈ 3010

Therefore, when 4500 calculators are demanded, the price per unit should be approximately Rs 3010.

By using the slope-intercept form of a linear equation and the given data points, we can determine the demand equation and solve for various scenarios, including finding quantities demanded at specific prices and determining the appropriate price for a given quantity demanded.

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Answer:

6 inches

Step-by-step explanation:

Volume= Length*Width*Height

720=15*8*H

720=120H

H=6

The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.

The set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.

The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.

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The point-slope form of the equations of the line are listed below:

Case 1: y - 4 = 2 · (x + 2)

Case 2: y - 1 = - 3 · (x - 2)

Case 3: y + 1 = - (x + 4)

Case 4: y + 2 = 5 · (x - 4)

In this problem we must derive the point-slope form of the equation of the line for each of four cases described in statement. This form is introduced below:

y - k = m · (x - h)

Where:

Now we proceed to determine the resulting expression for each case:

Case 1

y - 4 = 2 · (x + 2)

Case 2

y - 1 = - 3 · (x - 2)

Case 3

y + 1 = - (x + 4)

Case 4

y + 2 = 5 · (x - 4)

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The domain of the function graphed in this problem is given as follows:

a) [-3,0].

The values of x from the graph are given as follows:

Hence the domain of the function is given as follows:

[-3, 0].

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Hadey should open the park when the high temperature consistently reaches or exceeds 72°F and close it when it falls below.

To determine the best day to open and close the park each year, Hadey should consider the temperature patterns based on the given information. The temperature in Los Angeles peaked on September 9 at 102°F and reached a low approximately 6 months later, suggesting a periodic pattern.

To find the optimal opening and closing days, Hadey should look for the days when the high temperature is consistently above 72°F. This would ensure a good turnout for the amusement park. He should open the park when the high temperature consistently reaches or exceeds 72°F and close it when the high temperature consistently falls below this threshold. Using the temperature data from the most recent twelve months, Hadey should analyze the high temperature records for each day and identify the earliest day when the high temperature consistently reaches or exceeds 72°F. This would be the opening day of the park. Similarly, he should find the latest day when the high temperature consistently falls below 72°F, which would be the closing day.

It's important to note that Hadey's approach assumes that temperature patterns will remain consistent in the future. However, climate change and other factors can affect temperature variations, so it would be wise to consider long-term climate trends and consult with meteorological experts to ensure the park's success.

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The binary predicate refers to the membership relation denoted by the symbol "€" (read as "belongs to" or "is an element of").

We have,

The binary predicate is a binary relation because it takes two arguments: an element and a set.

The predicate evaluates to true if the element is a member of the set, and false otherwise.

The binary predicate € is used to establish the membership relationship between elements and sets in set theory.

For example, if we have a set A and an element x, we can write "x € A" to indicate that x is an element of A.

The use of a binary predicate in set theory allows for the formulation of statements and properties involving membership.

It enables us to define sets, make assertions about their elements, and perform operations such as union, intersection, and complement.

Thus,

The binary predicate € forms an essential part of the language and logic of set theory.

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Answer:

a) (1, 4)

b) -1, 3

c) 3

Step-by-step explanation:

The turning point is the point when the function changes direction.

The roots are the x-intercepts.

f(0) is the y-intercept.

The expected value (to you) of one raffle ticket is -$2.737.

The expected value (to you) if you purchase 12 raffle tickets is -$32.84.

The expected value (to the PTO) of one raffle ticket is $2.737.

Amount of money raised if 300 tickets are sold is $821.1.

Cost of a ticket = $3

P(winning a ticket) = 1/300

Winning amount = $76

Prize value = 1/300 × $76 = $0.253

Expected value (to you) for 1 ticket = $0.253 + (299/300 × -$3) = -$2.737

Expected value (to you) if you purchase 12 tickets = 12 × -$2.737

                                                                                   = -$32.84

Expected value (to the PTO) of raffle ticket = -$0.253 + (299/300 × $3)

                                                                       = $2.737

If they sell 300 tickets,

Expected value = 300 × $2.737 = $821.1

Amount raised = $821.1

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Step-by-step explanation:

Well, this includes subtraction.

11-1 1/2=11-3/2=22/2-3/2=19/2

So it was 19/2 Inches longer

The " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

The equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.    

" Eight  further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've =  " 3" is the value to which the expression on the left side is equal, so we've 3  Putting it all together the  judgment " Eight  further than the quotient of a number and 7 is equal to 3" can be  restated into the equation ( x/ 7) =  3  

In this equation, x represents the number we're trying to find. To  break for x, we can manipulate the equation using algebraic operations to  insulate x on one side of the equation.  By abating 8 from both sides of the equation, we get ( x/ 7)- 8 =  3- 8  Simplifying, we have  x/ 7 = -5

To  insulate x, we can multiply both sides of the equation by 7  *( x/ 7) = -5 * 7  This gives us  x = -35  thus, the equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

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Considering the given information, we fail to reject the null hypothesis that the proportion of men who own cats is less than or equal to 23% at the 0.10 significance level.

The null and alternative hypotheses are as follows:

H o: p ≤ 0.23 (proportion of men who own cats is less than or equal to 23%)

H a: p > 0.23 (proportion of men who own cats is larger than 23%)

The test is right-tailed because the alternative hypothesis states that the proportion is larger than 23%.

Based on a sample of 40 people, with 15% of them owning cats, we can calculate the p-value.

To find the p-value, we need to use the binomial distribution and calculate the probability of observing a result as extreme or more extreme than the one obtained under the null hypothesis.

Let's calculate the p-value:

p = 0.15 (proportion of men in the sample who own cats)

n = 40 (sample size)

p-value = P(X ≥ 0.15 x 40) = P(X ≥ 6)

Using a binomial calculator or software, we can find that P(X ≥ 6) is approximately 0.162.

Since the p-value (0.162) is greater than the significance level of 0.10, we fail to reject the null hypothesis.

Therefore, based on the given information, we fail to reject the null hypothesis that the proportion of men who own cats is less than or equal to 23% at the 0.10 significance level.

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The empty space is -7.92 cm^3 (rounded to two decimal places).The result is negative, indicating that there is not enough space in the can to fit all the marbles.

To calculate the empty space in the can, we first need to calculate the volume occupied by the marbles and then subtract it from the total volume of the can.

The volume of each marble can be calculated using the formula for the volume of a sphere:

V_marble = (4/3) * π * r^3

where r is the radius of the marble.

Given that the radius of each marble is 1.2 cm, we can calculate the volume of one marble as follows:

V_marble = (4/3) * π * (1.2 cm)^3

≈ 7.238 cm^3 (rounded to three decimal places)

Since there are 5 marbles in the can, the total volume occupied by the marbles is:

V_total_marbles = 5 * V_marble

≈ 5 * 7.238 cm^3

≈ 36.19 cm^3 (rounded to two decimal places)

The volume of the can can be calculated using the formula for the volume of a cylinder:

V_can = π * r^2 * h

where r is the radius of the can and h is the height of the can.

Given that the radius of the can is 1.5 cm and the height of the can is 4 cm, we can calculate the volume of the can as follows:

V_can = π * (1.5 cm)^2 * 4 cm

≈ 28.27 cm^3 (rounded to two decimal places)

To find the empty space in the can, we subtract the volume occupied by the marbles from the total volume of the can:

Empty space = V_can - V_total_marbles

≈ 28.27 cm^3 - 36.19 cm^3

≈ -7.92 cm^3 (rounded to two decimal places)

The result is negative, indicating that there is not enough space in the can to fit all the marbles.

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Answer:

  (b)  $2109.85

Step-by-step explanation:

You want the monthly loan payment on a 15-year loan for a home with a $284,500 purchase price if 20% is put down, and the borrower's credit score is 700.

The table tells you that a 15-year loan for a borrower with a 700 credit score will have a monthly payment of $9.27 per thousand dollars of loan value.

The loan will be for the 80% of the home value that is not already paid by the down payment. In thousands of dollars, that is 284.5 × 0.80.

The monthly payment is the product of the loan value (in thousands) and the payment multiplier:

  $284.5 × 0.80 × 9.27 = $2109.85

The monthly payment is $2109.85.

__

Additional comment

The higher loan cost for a borrower with a low credit score is effectively saying the lender is presuming about 12% of loans to such borrowers will be in default.

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They plan to clean the street for 3 hours.

They plan to clean the park for 3 hours.

The first step is to set up a set of linear equations that describe the information in the question.

3p + 6s = 27 equation 1

6p + 8s = 42 equation 2

Where:

p = number of hours spent cleaning one park

s = number of hours spent cleaning on street

In order to determine the value of s, take the following steps:

Multiply equation 1 by 2

6p + 12s = 54 equation 3

Subtract equation 2 from equation 3

4s = 12

Divide both sides of the equation by 4

s = 12 / 4

s = 3 hours

Substitute for s in equation 1:

3p + 6(3) = 27

3p + 18 = 27

3p = 27 - 18

3p = 9

p = 9/3

p = 3

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Answer:

[tex]\huge\boxed{\sf (4q - 1)\²}[/tex]

Step-by-step explanation:

= 16q² - 8q + 1

We can also write it as:

= (4q)² - 2(4q)(1) + (1)²

a² - 2ab + b² = (a - b)²

So, the above expression becomes:

[tex]\rule[225]{225}{2}[/tex]

In the circle if  ∠BAD is 106 degrees then the measure of arc DE is 74 degrees

In the circle the measure of ∠BAD is 106 degrees

We have to find the measure of the arc DE

∠BAD is equal to ∠CEA because these are vertical angles

106+106=212 degrees

Now let us find the measure of ∠DAE

212 degrees +∠DAE + ∠ABC = 360

212 degrees+∠DAE+∠DAE=360 (∠DAE =∠ABC)

212 degrees+2∠DAE =360

2∠DAE  = 360-212

2∠DAE  = 148

Divide both sides by 2

∠DAE  = 74 degrees

The ∠DAE is equal to measure of arc DE

arc DE = 74 degrees

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Answer:

How to calculate growth rate percentage?

To calculate the percentage growth rate, use the basic growth rate formula:

Subtract the original from the new value and divide the results by the original value. To turn that into a percent increase, multiply the results by 100.

Step-by-step explanation:

Cross multiply to get

8 (x-1) = 2 (x+2)

8x -8 = 2x + 4

6x = 12

x = 2

Based on the paired difference test conducted at a significance level of α = 0.05, there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the two sets of paired data.

In this paired difference experiment, we have the following data: D₁ = 6, D₂ = 10, D₃ = -3, D₄ = 5, D₅ = 7.

Our objective is to determine if there is a significant difference between the two sets of paired data.

To begin the paired difference test, we state the null hypothesis (H₀) and the alternative hypothesis (H₁).

The null hypothesis assumes that the mean difference between the paired data is equal to zero (µd = 0), while the alternative hypothesis suggests that the mean difference is not equal to zero (µd ≠ 0).

Next, we calculate the mean difference (¯d) by summing the differences and dividing by the number of pairs.

In this case, ¯d = (6 + 10 - 3 + 5 + 7) / 5 = 5.

To assess the variability in the data, we calculate the standard deviation of the differences (sᵈ).

This involves computing the sum of squared differences (SSᵈ) by squaring each difference and summing them.

Dividing SSᵈ by the number of pairs minus 1 (n-1), we then take the square root to obtain sᵈ.

With the mean difference (¯d) and standard deviation (sᵈ) calculated, we can determine the test statistic (t) using the formula t = ¯d / (sᵈ / √n), where n is the number of pairs.

Substituting the values, we compute the test statistic.

Next, we identify the degrees of freedom (df) for the test, which is equal to the number of pairs minus 1 (n-1).

Using the significance level α = 0.05, we consult a t-table or use statistical software to find the critical value for the rejection region.

By comparing the absolute value of the test statistic (t) to the critical value, we make a decision to either reject the null hypothesis if t falls within the rejection region or fail to reject the null hypothesis if it does not.

Finally, we state the final conclusion based on our decision.

If we reject the null hypothesis, we conclude that there is a significant difference between the two sets of paired data.

On the other hand, if we fail to reject the null hypothesis, we conclude that there is insufficient evidence to suggest a significant difference.

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The complete question may be like:

A paired difference experiment produced the following results: D₁ = 6, D₂ = 10, D₃ = -3, D₄ = 5, D₅ = 7. Conduct a paired difference test to determine if there is a significant difference between the two sets of paired data. Use a significance level of α = 0.05.

Context: The paired difference experiment involves measuring a variable of interest on two related subjects or under two different conditions. The goal is to determine if there is a significant difference between the two sets of measurements.

The Probability of rolling a number less than 3 on a regular 6-sided die is 1/3 or approximately 0.333.

The probability of rolling a number less than 3 on a regular 6-sided die, we need to determine the number of favorable outcomes and the total number of possible outcomes.

The favorable outcomes are the numbers that meet the condition of being less than 3. In this case, the favorable outcomes are the numbers 1 and 2.

The total number of possible outcomes is the total number of sides on the die, which is 6.

Therefore, the probability of rolling a number less than 3 can be calculated as:

Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)

Probability = 2 / 6

Simplifying the fraction, we have:

Probability = 1 / 3

So, the probability of rolling a number less than 3 on a regular 6-sided die is 1/3 or approximately 0.333.

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The volume of the cylinder with the same radius and double the height is 2πx²h in³.

To find the volume of a cylinder, we use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, we are given a cylinder with a certain radius and height, and we need to find the volume of another cylinder with the same radius but double the height.

Let's assume the radius of the cylinder is x, and the original height is h.

The volume of the original cylinder is V = πx²h.

Now, we need to find the volume of the cylinder with the same radius (x) but double the height (2h).

The volume of this cylinder is V' = πx²(2h) = 2πx²h.

So, the volume of the second cylinder is twice the volume of the first cylinder.

Therefore, the volume of the second cylinder is 2 times the volume of the first cylinder, which can be expressed as 2V = 2πx²h.

Therefore, the volume of the cylinder with the same radius and double the height is 2πx²h in³.

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