Which is the best estimate for the length of a piano keyboard?

The length of the sides of a square with a perimeter between 14 and 72 feet inclusive ranges from 3.5 to 18 feet. By dividing the perimeter limits by 4, we find the possible side lengths, leading to the answer: 3.5 ≤ x ≤ 18 (option a)).

The student is asking about the possible lengths of the sides of a square given that the perimeter must be between 14 and 72 feet inclusive. To solve this, we recall that the perimeter (P) of a square with side length (a) is given by P = 4a. Therefore, if P is between 14 and 72 feet, we divide these values by 4 to find the possible values for a.

The lower limit for the side length is 14 ÷ 4 = 3.5 feet, and the upper limit is 72 ÷ 4 = 18 feet. So the possible values for the side length of the square can be represented as 3.5 ≤ x ≤ 18. Hence, the correct answer to the student's question is option a).

This is a clear example of positive reinforcement. Positive reinforcement involves the addition of a positive stimulus that act as a reinforcement to a desired behavior in order to make the behavior more likely happen again in the future. When Jemma praises and hugs his baby, she is using positive reinforcement, so her baby associates the behavior of saying “thank you” with a reward making him more inclined to say thank you again in the future.

We can conclude that Jemma's reinforcement schedule is positive reinforcement.

Final answer:

The volume of the cone with a height of 7.5 inches and a radius of 5.62 inches is calculated using the formula V = (1/3)πr²h and is approximately 589.05 cubic inches.

Explanation:

To find the volume of a cone with a height of 7.5 inches and a radius of 5.62 inches, you use the formula for the volume of a cone, which is V = (1/3)πr²h. Here, r represents the radius and h represents the height of the cone.

First, calculate the area of the base (A) which is π times the radius squared:

A = π × (5.62 in)²

This gives us the area of the base. Then, multiply by the height (7.5 inches) and divide by 3 to find the volume:

V = (1/3) × A × h = (1/3) × π × (5.62 in)² × 7.5 in

Now, plug in the value for π (approximately 3.14159) and calculate:

V ≈ (1/3) × 3.14159 × (5.62²) × 7.5

V ≈ 589.05 cubic inches (rounded to two decimal places).

Therefore, the volume of the cone is approximately 589.05 cubic inches.

Answer:  The required product is [tex]\dfrac{5}{4k^2}.[/tex]

Step-by-step explanation:  We are to calculate the following product:

[tex]P=5\dfrac{k}{6}\times \dfrac{3}{2k^3}.[/tex]

We will be using the following property of exponents:

[tex]\dfrac{a^x}{a^y}=a^{x-y}.[/tex]

We have

[tex]P\\\\\\=5\dfrac{k}{6}\times\dfrac{3}{2k^3}\\\\\\=\dfrac{5}{6}\times\dfrac{3}{2}k^{1-3}\\\\\\=\dfrac{5}{4}k^{-2}=\dfrac{5}{4k^2}.[/tex]

Thus, the required product is [tex]\dfrac{5}{4k^2}.[/tex]

[tex]4\\[/tex] more workers are needed to do this job in 12 hours.

Given,

Three workers can do a job in 28 hours.

Let [tex]x[/tex] no. of worker needed.

workers          3       [tex]x[/tex]

time (hours)   28      12

The fewer workers there are the more the hours that are required,  

and the more workers there are the fewer hours that are required.  

Therefore workers and hours are inversely proportional.

So,  

[tex]3 \times28=x \times12[/tex]

[tex]x=\frac{3 \times28}{12} \\\\x=7[/tex]

So, 7 workers can do that job in 12 hours.

Hence ([tex]7-3=4[/tex]) [tex]4[/tex] more workers needed to do this job in 12 hours.

For more details on Inverse proportion follow the link:

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Final answer:

To complete a job in 12 hours rather than 28, 4 additional workers are needed, considering the work rate is directly proportional to the number of workers.

Explanation:

The question relates to the optimization of workers to complete a job in a certain amount of time, a common problem in work-rate mathematics.

To solve it, we first determine the rate at which three workers complete the job: since they can complete one job in 28 hours, their combined rate is 1 job per 28 hours, or 1/28 job per hour. Now, we need to find out how many workers are required to complete the job in 12 hours. This means we want the workers to work at a rate that completes 1 job in 12 hours, or 1/12 job per hour.

To find the number of workers needed, we set up the proportion: (3 workers)/(1/28 job per hour) = (x workers)/(1/12 job per hour). Solving for x gives us x = (3 workers) × (1/12 job per hour) / (1/28 job per hour), which simplifies to x = 7 workers. Since we already have 3 workers, we need an additional 4 workers to complete the job in 12 hours.

The ratio of the number of children who own a dog to the total number of children in the class is [tex]\frac{ 5 }{ 12}[/tex], after simplifying the fraction [tex]\frac{ 10 }{ 24}[/tex] by dividing both the numerator and denominator by 2.

The question asks to find the ratio of the number of children who own a dog to the total number of children in the class. Ten children own a dog and fourteen do not, making the total number of children in the class twenty-four. To find this ratio, we divide the number of children who own a dog by the total number of children:

Ratio = number of children who own a dog ÷ total number of children in the class

Ratio = [tex]\frac{ 10 }{ (10 + 14)}[/tex]

Ratio = [tex]\frac{ 10 }{ 24}[/tex]

The simplified form of this ratio is found by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

Simplified Ratio = [tex]\frac{ 5 }{ 12}[/tex]

Answer:

y = 9

Step-by-step explanation:

A horizontal line will stay at the same height across the entire domain.  This means that while its x-coordinates change, its y-coordinate does not.  

Since it passes through the point (-5, 9), this means the y-coordinate is 9.  It will be y=9 throughout the entire graph; this means the equation is y=9.

The equation of the horizontal line that passes through the point (−5, 9) is y=9. The correct option is B.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

For a horizontal line, the value of the slope of the line is 0. Therefore, the value of m is 0. Given the point (-5,9) through which the equation passes, therefore, the value of the constant in the equation of the line can be found by substituting values in the equation.

Therefore, the equation can be written as,

y = mx + c

9 = 0(-5) + c

c = 9

Now, substitute the value of slope and constant in the equation of the line.

y = mx + c

y = 0(x)+ 9

y = 9

Hence, the equation of the horizontal line that passes through the point (−5, 9) is y=9.

Learn more about Equation of Line here:

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To find the probability that a person actually has the disease given a positive test result, we can use Bayes' theorem. Given the probabilities of a positive test result given the person has the disease and does not have the disease, as well as the probability of having the disease, we can calculate the conditional probability.

To find the probability that a person actually has the disease given a positive test result, we can use Bayes' theorem. Let's define the events: A = person has the disease, B = person tests positive. We are given that P(B|A) = 0.9 (probability of a positive test given the person has the disease), P(B|A') = 0.06 (probability of a positive test given the person does not have the disease), and P(A) = 0.16 (probability that a person has the disease).

Bayes' theorem states: P(A|B) = (P(B|A) * P(A)) / P(B).

Substituting the given values, we have: P(A|B) = (0.9 * 0.16) / P(B).

We don't have the value of P(B), but we can calculate it as follows: P(B) = (P(B|A) * P(A)) + (P(B|A') * P(A')). Plugging in the values, we have: P(B) = (0.9 * 0.16) + (0.06 * 0.84).

Now we can substitute the value of P(B) into the formula for P(A|B) to calculate the probability.

Therefore, the probability that the person actually has the disease given a positive test result is approximately 0.231.

Answer:

He will bake 300 loaves of bread.

Step-by-step explanation:

Paul bakes loaves of bread and bread rolls in the ratio of 2 : 5

Suppose, the number of loaves of bread he will bake [tex]=x[/tex]

Given that, he bakes 750 bread rolls.

So, according to the given ratio, we will get......

[tex]\frac{loaves\ of\ bread}{bread\ rolls}=\frac{2}{5}\\ \\ \frac{x}{750}=\frac{2}{5}\\ \\ 5x=1500\ [by\ cross\ multiplication]\\ \\ x=\frac{1500}{5}\\ \\ x=300[/tex]

So, he will bake 300 loaves of bread.

Answer:  The correct option is (C) [tex]\dfrac{1}{2}.[/tex]

Step-by-step explanation:  Given that Jane altered by using [tex]\dfrac{3}{4}[/tex] of the amount of butter called for the recipe and she used 6 tablespoons of butter.

We are to find the number of cups of butter that the recipe call for.

Let x represents the total number of teaspoons of butter that the recipe call for.

Then, according to the given information, we have

[tex]\dfrac{3}{4}x=6\\\\\Rightarrow 3x=24\\\\\Rightarrow x=8.[/tex]

So, the total number of tablespoons of butter that the recipe call for is 8.

Now, 16 tablespoons = 1 cup.

Therefore, we get

[tex]8~\textup{tablespoons}=\dfrac{1}{16}\times 8=\dfrac{1}{2}~\textup{cups}.[/tex]

Thus, the recipe call for [tex]\dfrac{1}{2}[/tex] cup of butter.

Option (C) is CORRECT.