You want to place a towel bar that is 24 1⁄4 centimeters long in the center of a door that is 70 1⁄3 centimeters wide. How far should you place the bar from each edge of the door?

The sum of three even consecutive integers if the first integer is y is 3y+6.

What is an expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that the first even integer is y, than the second integer will be 2 more then the first one that is y+2 and the third even integer will be 2 more then the second one that is y+4. Now the sum of all these three integer will be :

sum = first number + second number + third number

       = y + (y+2) + (y+4)

       = 3y + 6

Therefore, the sum of three even consecutive integers if the first integer is y is 3y+6.

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B is the right answer

-2

Answer:   [tex]85.5\ in^2[/tex]

Step-by-step explanation:

Given : A sheet of paper has dimensions of 8.5 in x 11 in.

Then, the area if the sheet of paper will be :_

[tex]\text{Area}=8.5\times11=93.5\text{ in.}^2[/tex]

Also, we cut [tex]2 in^2[/tex] from each corner of the sheet.

Since, there are 4 corner in a sheet , then the combined area we cut will be :-

[tex]4\times2=8\ in.^2[/tex]

Now, the area of the sheet of paper will be  =[tex]93.5\text{ in.}^2-8\text{ in.}^2[/tex]

[tex]=85.5\ in^2[/tex]

Hence, the area of the sheet of paper will be [tex]85.5\ in^2[/tex]

Based on the provided information, statement that is true about angles 1 and 2 is that they are complementary.

complementary angle can be explained as two angles are that has their measures adding to 90 degrees.

We can see that coloured portion is 90°, and  addition of ∠1 and ∠2= 90° since they are on straight line.

Therefore, option C is correct.

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The fraction 2/5 represents 2 of the 5 equal parts into which a whole is divided. This shows how fractions indicate the distribution of a whole into equal parts. Here, 2 slices out of 5 total slices illustrate the concept effectively.

Examples:

Answer:

the answers are

1/3

27

All real numbers

y>0

Step-by-step explanation:

To simplify the function f(x) = 1/3(81)^3x/4, we identify 81 as 3^4 and then apply exponent rules which lead to the simplified form f(x)=3^(3x-1). The base indicates exponential growth, and the exponent determines the growth rate and vertical scaling. Additional analysis would involve graphing to observe its behavior.

To simplify the function f(x)=1/3(81)^3x/4, we must first recognize that 81 is a power of 3, specifically 3^4. Thus, when raised to the 3x/4 power, we multiply these exponents to get 3^(4*3x/4) which simplifies to 3^(3x). Our function now looks like f(x)=(1/3)*3^(3x). By properties of exponents, this can further simplify to f(x)=3^(3x-1).

Key aspects of this function include the base of the exponential (which is 3), indicating that the growth is exponential, and the exponents indicate how quickly this growth occurs. The term '-1' in the exponent shows a vertical scaling factor of 1/3 on the base function 3^x.

To analyze the function in more detail, one could use a graphing calculator or computer software to visualize the growth pattern. However, it should be noted that in this case, a graphing calculator can't solve for x using the zero function as we don't have an equation set to zero.

Answer:

16

Step-by-step explanation:

The number of divisors is the product of the powers of the prime factors after 1 has been added to each. In order for the total number of divisors to be 5, the number must be a prime raised to the 4th power. The only one in the given range is 2^4 = 16.

The divisors of 16 are 1, 2, 4, 8, 16.

_____

The smallest number with 5 prime factors is 2^5 = 32, so we assume you mean "divisors" when you say "factors."

Answer: 50 Km per hour

Step-by-step explanation: divide 300 by 6 and it will give 50 km and per hour means over one so 50 km over 1 which means per hour . The rule for getting the average speed is distance over time so divide 300(distance ) by 5 which is the time . Please brainliest .

Brett will give 9 flowers to each of the 3 people, as calculated by dividing the total number of flowers (27) by the number of people (3).

Brett picked 27 flowers from the garden and he plans to give an equal number of flowers to each of 3 people. To find out how many flowers each person will get, we divide the total number of flowers by the number of people receiving flowers. So, we calculate 27 ÷ 3, which equals 9 flowers per person.

Answer:

64

Step-by-step explanation:

In an exponential distribution scenario like bus waiting times, the formula P(T > t) = e^(-λt) can be used to calculate the probability of waiting more than a certain time. Substituting the given average waiting time in the formula, we get the probability of waiting more than 20 minutes for a bus is approximately 13.5%.

The question describes the waiting time for a bus as being exponentially distributed. In an exponential distribution, the probability that a variable (in this case, time until the next bus arrives) exceeds a certain value is calculated using the formula P(T > t) = e^(-λt) where, λ is the rate parameter - in this case, 1/10 (since the bus arrives every 10 minutes on average).

Thus, if we want to calculate the probability of waiting more than 20 minutes, we simply substitute t = 20 into the formula giving us: P(T > 20) = e^(-1/10 * 20), which simplifies to e^-2.

The number e^-2 is approximately 0.135, so the probability of having to wait more than 20 minutes for the bus is about 13.5%

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the Time required to fill the cranberry juice is 3.8d.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, Jane goes to a juice bar with her friend Neil. She is thinking of ordering her favorite drink, 7/8 orange juice and 1/8 cranberry juice, but the drink is not on the menu, so she decides to order a glass of orange juice and a glass of cranberry juice and do the mixing herself.

Part A:

The initial height of the inlet of the straw from the surface of the cranberry juice is d and the height of the outlet of the siphon from the surface is h. Using Bernoulli's equation, the initial velocity of cranberry juice that flows out of the straw is determined.

for the surface of the upper reservoir:

ν²/2 -gd +Patm/ρ = Constant

The velocity of the surface of the upper reservoir is zero by considering the reservoir would be infinity and then the above equation becomes:

0²/2 -g*0 + Patm/ρ = Constant

Bernoulli's equation for the outlet of the siphon

ν²/2 -g*h +Patm/ρ = Constant

Both these equations are equal as the siphon is a single system, therefore the initial velocity of the outflow is

ν = √(2gh)

Part B:

time = volume/flow rate

Since Volume to be filled:

V = 1/8 * pi * r² * h

V = 6.731* 10⁻⁵ m³

Thus,

Flow rate,

Q = ν*A

Q = √(2gh) * (pi * r² * h)

Q = 1.758 * 10⁻⁵ m³/s

Therefore, the time required to fill the cranberry juice is:

t = V/Q

t = 3.8s

Therefore, the Time required to fill the cranberry juice is 3.8d.

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Complete question:

The greatest number of necklaces that can be made is 4, with each necklace containing 6 jade beads and 6 teak beads. This is determined by finding the GCD of 24 and 30, which is 6.

To determine the greatest number of necklaces the jewelry maker can make with 24 jade beads and 30 teak beads, we need to find the greatest common divisor (GCD) of the two numbers of beads. The GCD of 24 and 30 is 6.

This means the jewelry maker can make necklaces, each containing 6 beads of one type; 24 jade beads can make 4 necklaces, and 30 teak beads can also make 5 necklaces.

However, since each necklace must have the same number of jade and teak beads, the maximum number of necklaces is limited by the jade beads, which can only make 4 necklaces.

Therefore, the greatest number of necklaces that can be made is 4, with each necklace containing 6 jade beads and 6 teak beads.

Final answer:

Fractions 7⁄11, 5⁄2, 9⁄10, and 7⁄15 can be rewritten as division problems by expressing each as the division of the numerator by the denominator.

Explanation:

To rewrite the given fractions as division problems, you simply need to express each fraction as a division of its numerator by its denominator. Here's how the fractions can be rewritten:

7⁄11 can be written as 7 divided by 11.

5⁄2 can be written as 5 divided by 2.

9⁄10 can be written as 9 divided by 10.

7⁄15 can be written as 7 divided by 15.

Each fraction represents a division problem where the numerator is the dividend and the denominator is the divisor.

Final answer:

To prove that a subset b of a well-ordered set a is also well-ordered, we can assume the opposite and show that it leads to a contradiction. If b is not well-ordered, it means that there exists an element in b smaller than all others, but since b is a subset of a this element must also be in a, contradicting the assumption that a is well-ordered. Therefore, b must be well-ordered as well.

Explanation:

To prove that if a is any well-ordered set of real numbers and b is a nonempty subset of a, then b is also well-ordered, we can use the fact that every well-ordered set has the least element. Let's assume that b is not well-ordered and does not have the least element. This means that there exists an element in b that is smaller than all other elements in b. However, since b is a subset of a, this element must also be in a. But this contradicts the assumption that a is well-ordered and has the least element. Therefore, b must be well-ordered as well.

The car used 70 gallons of gas to go 3 miles