Of all rectangles with a perimeter of 21 21​, which one has the maximum​ area? (give the​ dimensions.) let a be the area of the rectangle. what is the objective function in terms of the width of the​ rectangle, w?

Answer:

6.5 km

Step-by-step explanation:

1:50,000

13 cm on a map, multiply both sides by 13 which leaves us with:

13:650,000

However, we need to calculate the distance in kilometers, not centimeters. To do that, we have to divide 650,000 by 100,000 which leaves us with 6.5 km

Final answer:

The roots of the equation 5x³ + 45x² + 70x = 0 are -7 and -2.

Explanation:

This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 5, b = 45, and c = 70. To find the roots of the equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we get:

x = (-45 ± √(45² - 4(5)(70))) / (2(5))

Simplifying further gives us:

x = (-45 ± √(2025 - 1400)) / 10

And finally, calculating the square root and applying the ± gives us the two roots:

x = (-45 ± √625) / 10

x = (-45 ± 25) / 10

which can be further simplified to:

x = -7 or x = -2

The information regarding the sampling shows that the value of cohen's d for this sample is 0.3.

From the information given, the sample of n = 25 individuals is selected from a population with µ = 60 and sigma = 10 and a treatment is administered to the sample. after treatment, and the sample mean is m = 63.

Therefore, the value of cohen's d for this sample will be:

= (M - µ) / 10

= (63 - 60) / 10

= 0.3

In conclusion, the correct option is 0.3.

Learn more about sampling on:

https://brainly.com/question/17831271

Final answer:

Cohen's d for the given sample is 0.3, calculated by subtracting the population mean from the sample mean and dividing by the population standard deviation.

Explanation:

The student's question is regarding the calculation of Cohen's d for a sample after treatment. Cohen's d is a measure of effect size used to indicate the standardized difference between two means. In this case, the following formula can be used: Cohen's d = (M - μ) / σ, where M is the sample mean after treatment, μ is the population mean, and σ is the population standard deviation.

Given that M = 63, μ = 60, and σ = 10, the calculation of Cohen's d is as follows:

Cohen's d = (63 - 60) / 10 = 3 / 10 = 0.3.

Therefore, the value of Cohen's d for this sample is 0.3, which is considered a small effect size according to Cohen's standards.

An open sentence is a mathematical sentence that has an unknown.

The solution set for t is (a) Null set

The equation is given as:

[tex]\mathbf{2t - t = 0}[/tex]

The set is given as:

[tex]\mathbf{\{1,2,3,4\}}[/tex]

First, we solve for t in: [tex]\mathbf{2t - t = 0}[/tex]

[tex]\mathbf{t = 0}[/tex]

The above equation implies that, the value of t is 0

0 is not represented in the given set, [tex]\mathbf{\{1,2,3,4\}}[/tex]

Hence, the solution set for t is (a) Null set

Read more about open sentences at:

https://brainly.com/question/9070320

48.5 out of 50 as a percentage, is 97%.

48.5 out of 50 as a percentage can be calculated by dividing 48.5 by 50 and then multiplying by 100 to get the percentage.

Divide 48.5 by 50: 48.5 / 50 = 0.97

Multiply by 100 to get the percentage: 0.97 * 100 = 97%

Answer:

Fourth-degree trinomial  

Step-by-step explanation:

9x^4 – 3x + 4 is a trinomial expression because it has three parts: 9x^4, –3x and 4, and is a fourth-degree expression because four is the highest exponent applied to the variable x (the other exponents are one and zero).

Apprentice will take [tex]1\frac{1}{2}[/tex] days  to finish the wall.

" Work is defined as when force is applied to move an object in the direction of displacement."

According to the question,

Number of days taken by Vella to build a brick = 4 days

Work done by Vella in 1 day = [tex]\frac{1}{4}[/tex]

Work done  by Vella in 3 days = [tex]\frac{3}{4}[/tex]

Number of days taken by apprentice to build same brick = 6 days

Total days taken by apprentice to complete 3/4 of work =  [tex]\frac{3}{4} of 6[/tex]

                                                     = [tex]\frac{3}{4}[/tex] × 6

                                                     =[tex]\frac{9}{2}[/tex]

                                                     = [tex]4\frac{1}{2}[/tex] days

Number of days apprentice take to finish the wall is = 6 - [tex]4\frac{1}{2}[/tex]

                                                                                       = [tex]1\frac{1}{2}[/tex]

Hence, apprentice will take [tex]1\frac{1}{2}[/tex] days  to finish the wall.

Learn more about work here

https://brainly.com/question/19624236

#SPJ2

Final answer:

Norma can expect the spinner to land on section A 4 times after spinning it 16 times, based on the probability of [tex]\frac{1}{4}[/tex].

Explanation:

The question asks about the expected number of times Norma can anticipate the spinner to land on section A after spinning it 16 times, given that the probability of landing on A is [tex]\frac{1}{4}[/tex]. To find this, we use the concept of expected value, which in this context is the probability of an event happening multiplied by the number of trials. Since the probability of landing on A is [tex]\frac{1}{4}[/tex] and there are 16 spins, the expected number of times landing on A is calculated as [tex]\frac{1}{4}[/tex] multiplied by 16.

Expected number of landings on A = Probability of landing on A × Number of spins = [tex]\frac{1}{4}[/tex] × 16 = 4.

Therefore, Norma can expect the spinner to land on section A four times after spinning it 16 times.

Step 1

Find the slope of the line

Let

[tex]A(0,1)\\B(2,5)[/tex]

the slope is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5-1}{2-0}[/tex]

[tex]m=\frac{4}{2}[/tex]

[tex]m=2[/tex]

Find the equation of the line

we know that

the equation of the line into slope-intercept form is

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

in this problem we have

[tex]m=2[/tex]

[tex]b=1[/tex] ------> the y-intercept is the point A

substitute

[tex]y=2x+1[/tex]

Step 2

Find the equation of the inequality

we know that

the solution is the shaded area above the dotted line

so

above dotted line---------> represent the symbol ([tex]>[/tex])

the inequality is

[tex]y>2x+1[/tex]

therefore

the answer is

[tex]y>2x+1[/tex]

The correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].

Further explanation:

The linear equation of the line is [tex]y=mx+b[/tex] where, [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the [tex]y[/tex]-intercept of the line.

Suppose the line passes through the two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex].

Therefore, the slope of the line can be calculated as follows:

[tex]\boxed{m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]

The symbol [tex]>[/tex] represents the solution set lies above the dotted line and the symbol [tex]<[/tex] represents the solution set below the dotted line.

Given:

The linear inequalities are  given as follows:

[tex]\boxed{\begin{aligned}y&>2x+2\\ y&\geq x+1\\ y&>2x+1\\ y&\geq x+2\end{aligned}}[/tex]

Calculation:

First we will find the equation of the line.

The line cuts the [tex]y[/tex]-axis on the coordinate [tex](0,1)[/tex] as shown in the Figure 1 (attached in the end).

Therefore, the [tex]y[/tex]-intercept is [tex]1[/tex].

Kindly refer the Figure attached to the question.

From the figure 1 (attached in the end) we can see that the line passes through the points [tex](-2,-3)\text{ and }(1,3)[/tex].

The slope of the line can be calculated as follows:

[tex]\begin{aligned}m&=\dfrac{3-(-3)}{1-(-2)}\\&=\dfrac{6}{3}\\&=2\end{aligned}[/tex]    

Therefore, the value of [tex]m[/tex] is [tex]m=2[/tex] and the value of [tex]b[/tex] is [tex]b=1[/tex].

Substitute [tex]2[/tex] for [tex]m[/tex] and [tex]1[/tex] for [tex]b[/tex] in the equation of the line [tex]y=mx+b[/tex].

Second we will find the equation of the inequality.

The shaded region is shown in Figure 1 above the dotted line .  

Therefore, the solution set of the line lie above the dotted line and it will represented by the symbol [tex]>[/tex].

Thus, the inequality [tex]y>2x+1[/tex] satisfies the given graph.

Therefore, the correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].

Learn more:

1. Learn more about the representation of the graph https://brainly.com/question/2491745

2. Learn more about the graph of the quadratic function https://brainly.com/question/2334270

3. Learn more about graphed below of the function  https://brainly.com/question/9590016

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear inequalities

Keywords:  Linear equations, linear inequality, equation, line, slope, intercept, dotted line , coordinate, shaded region, solutions set, graph, curve.

((1+0.1994/12)^12)-1 = 21.87% effective rate

it would advertise the APR because it is lower

Answer:

Step-by-step explanation:

If all were chickens, there would be 26 legs. There are 14 legs more than that. Each pig contributes 2 additional legs, so there must be 14/2 = 7 pigs. The remaining 6 animals are chickens.

___

Check

7×4 + 6×2 = 28 +12 = 40 . . . . total legs

Answer:

easy! 27

Step-by-step explanation:

13- 40 = 27

or 13 + 27 =40

just add up 13 and 27 you'll get 40 in all

edit; btw I'm not the brightest

Answer-

[tex]\boxed{\boxed{QR=12}}[/tex]

Solution-

Triangle Midpoint Theorem-

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

As given in the question,

QV = SV, so V is the mid point of QS,

SU = RU, so R is the mid point of RS.

Hence, UV is the line joining the midpoints of QS and RS.

Applying Triangle Midpoint Theorem,

[tex]\Rightarrow UV=\dfrac{1}{2}QR[/tex]

[tex]\Rightarrow QR=2UV[/tex]

[tex]\Rightarrow QR=2\times 6[/tex]

[tex]\Rightarrow QR=12[/tex]

Therefore, the side length of QR is 12 units.

The value of the derivatives is A'(12) = 24.

We have,

To find the derivative of the area function A(x) with respect to x, we can differentiate the equation for the area of a square:

A(x) = x^2

Using the power rule, we differentiate A(x) with respect to x:

A'(x) = 2x

To find A'(12), we substitute x = 12 into the derivative equation:

A'(12) = 2 * 12 = 24

Therefore,

The value of the derivatives is A'(12) = 24.

Learn more about derivatives here:

https://brainly.com/question/29020856

#SPJ4

Final answer:

To find A'(12), the rate at which the area A(x) changes when the side length x changes, take the derivative of A(x), which is 2x, and evaluate it at x = 12. The derivative of A(x) is 2x, so A'(12) = 2(12) = 24.

Explanation:

To find the rate at which the area A(x) changes with respect to a change in x, we need to take the derivative of A(x) with respect to x. In this case, A(x) represents the area of a square wafer of silicon with a side length x. The derivative with respect to x is A'(x), which represents the rate of change of the area.

We want to find A'(12), which means we want to find the rate of change of the area when the side length is 12 mm. To do this, we need to take the derivative of A(x) and then evaluate it at x = 12.

Since the side length of the wafer is very close to 12 mm, we can assume x = 12.

Let's find the derivative of A(x):

A(x) = x^2

A'(x) = 2x

Now we can evaluate A'(12):

A'(12) = 2(12) = 24

Answer:

Option C is the answer.

Step-by-step explanation:

Option A. [tex]y=\sqrt{x-5}+3[/tex]

For domain of this function

(x - 5) ≥ 0

x ≥ 5

For range of the function

for every value of x ≥ 0

y ≥ 3

Opttion B. [tex]y=\sqrt{x+5}-3[/tex]

For Domain

(x + 5) ≥ 0

x ≥ (-5)

and for every value of x ≥ (-5) range of the function will be

y ≥ (-3)

Option C.

y = -√(x -5) + 3

For domain

x - 5 ≥ 0

x ≥ 5

For range

y ≤ 3

Option D. [tex]y=-\sqrt{x+5}-3[/tex]

For domain (x + 5) ≥ 0

x ≥ -5

For range

y ≤ (-3)

Therefore option C will be the answer.