Nail Polish. A Specific shade of red nail polish requires 7 parts red to 2 parts yellow. A mixture contains 45 quarts. How many quarts of red? How many quarts of yellow?

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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B is the right answer

-2

To find the number of hamburgers sold on Saturday, we set up a system of equations and solve for the variable x.

To find the number of hamburgers sold, we can set up a system of equations using the given information. Let x represent the number of hamburgers sold. The number of cheeseburgers sold is two times the number of hamburgers sold, so the number of cheeseburgers is 2x. The total number of hamburgers and cheeseburgers sold is 336, so we can write the equation x + 2x = 336. Combining like terms, we have 3x = 336. Dividing both sides by 3, we find x = 112. Therefore, 112 hamburgers were sold on Saturday.

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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

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.

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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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]

Answer:

64

Step-by-step explanation:

Final answer:

The solution to (4x10 to the 3rd power) x (3x10 to the 4th power) is 1.2x10 to the 8th power in scientific notation.

Explanation:

The solution to (4×103) × (3×104) in scientific notation involves multiplying the coefficients (4 and 3) and then adding the exponents of 10 (3 and 4). To multiply the coefficients, you do 4 × 3, which equals 12. To combine the powers of 10, you add the exponents: 103 × 104 becomes 103+4, which is 107. Therefore, the product in scientific notation is 12 × 107. Since scientific notation requires that the coefficient be between 1 and 10, we adjust the coefficient by dividing it by 10 and increasing the exponent by 1, resulting in 1.2 × 108.

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.

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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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 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:

The hourly unit rate of pay for the employee is $5.25.

Option A is the correct answer.

We have,

Let x be the unit rate.

i.e

Hourly rate of pay for the employee.

Then the employee earned a total of:

Total earnings = (hourly rate) x (number of hours worked) + tips

$400 = 28x + $253

Subtracting $253 from both sides, we get:

$147 = 28x

Dividing both sides by 28, we get:

x = $5.25

Therefore,

The hourly unit rate of pay for the employee is $5.25.

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