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What are the solutions to the equation shown?

The rate of change of the area of a square is 12m^2/sec.

What do you mean by rate of change?

The term "rate of change" refers to the rate at which one quantity changes in respect to another. Consequently, if y value is the dependent variable and x value is the independent variable.

Rate of Change is equal to [tex]\frac{Change in y}{Change in x}[/tex].

Change rates may be positive or negative. This reflects a change in the y-value between the two data points, either up or down. Zero rate of change is the state where a quantity does not change over time.

Solution Explained:

Given,

S = 2m and ds/dt = 3m/s

So, we use

Area = s^2

dA/dt = 2s ds/dt

         = 2 X 2 X 3

Therefore, the rate of change of the area is 12m^2/s.

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Answer:

24%

Step-by-step explanation:

Walmart has 152/200 employees, simplify that to a number over 100, you get 76/100. 100-76=24

Answer:

Step-by-step explanation:

152/200 = .76

100-76 = 24

=24%

Therefore, the percentage the amount of workers decrease is by 24%.

Please do tell if this helps!

There were 13 notepads, each of which cost $1.05 when the bookstore reduced the price of various notepads from $2.00 to $1.00.

Given that,

The bookstore reduced the price of various notepads from $2.00 to $1.00 while maintaining the price. The whole lot was sold. The selling of the pads generated a total profit of $29.45.

We have to find what number of notepads were sold and how much did each notepad cost.

We know that,

One approach to solving this issue is to divide $29.45 by each of the values from $1.01 to $1.99. That is the price for each notepad if one of them fits evenly with no leftovers. The number of pads is the quotient (result of division). The number has to be placed evenly because we cannot use half of the pad (leave no remainder).

Although we can check each of them, I realized that $29.45 ends in a 5 and is therefore divisible by 5, so I chose to check 1.05 as a potential price and it entered evenly. 13 is the quotient.

Therefore, There were 13 notepads, each of which cost $1.05 when the bookstore reduced the price of various notepads from $2.00 to $1.00.

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A 90​% confidence interval about μ if the sample​ size, n, is 25 is (111.6, 118.4), a 90​% confidence interval about μ if the sample​ size, n, is 20 is (111.1, 118.9), a 80​% confidence interval about μ if the sample​ size, n, is 25 is (112.4, 117.6) and we need population to be normal. So we can not make intervals.

In the given question,

Sample​ mean, x​, is found to be 115.

Sample standard​ deviation, s, is found to be 10.

(a) We have to construct a 90​% confidence interval about μ if the sample​ size, n, is 25.

We need to build a 90% confidence interval. So p=0.90.

t-score for confidence interval is given by the excel code is

t=1.7109

Using these values, the margin of error is

ME = 1.7109× 10/√25

ME = 3.4

So confidence interval is

CI = (115-3.4, 115+3.4)

CI = (111.6, 118.4)

(b) We have to construct a 90​% confidence interval about μ if the sample​ size, n, is 20.

We need to build a 90% confidence interval. So p=0.90.

t-score for confidence interval is given by the excel code is

t=1.7291

Using these values, the margin of error is

ME = 1.7291× 10/√20

ME = 3.9

So confidence interval is

CI = (115-3.9, 115+3.9)

CI = (111.1, 118.9)

(c) We have to construct a 80​% confidence interval about μ if the sample​ size, n, is 25.

We need to build a 80% confidence interval. So p=0.80.

t-score for confidence interval is given by the excel code is

t=1.3178

Using these values, the margin of error is

ME = 1.3178× 10/√25

ME = 2.6

So confidence interval is

CI = (115-2.6, 115+2.6)

CI = (112.4, 117.6)

​(d) Now we have to check, could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.

To use t-distribution, the population has to be normal.Otherwise we need a sample size of at least 30. Here sample size is less than 30.

So we need population to be normal. So we can not make intervals.

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The right question is:

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 115​, and the sample standard​ deviation, s, is found to be 10.

(a) Construct a 90​% confidence interval about μ if the sample​ size, n, is 25.

​(b) Construct an 90​% confidence interval about μ if the sample​ size, n, is 20.

​(c) Construct an 80​% confidence interval about μ if the sample​ size, n, is 25.

​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.

Answer: 7/12

Step-by-step explanation: First, flip the 4/3 to its reciprocal and change it to multiplication. Then, you can simplify the 9 and 3 to 3 and 1. After that, multiply straight across. Hope this helps! :)

Answer:

1. 7/9 ÷ 4/3 As a fraction) 21/36

2. 7/9 ÷ 4/3=21/36 as a simplified fraction) 7/12

3. 7/9 ÷ 4/3 As a decimal) 0.583

4. 7/9 ÷ 4/3 As a percentage) 58.3%

Let's see how it's done!

7/9 ÷ 4/3:

7/9 ÷ 4/3 (Invert or flip the second fraction and multiply across)

7/9 x 3/4 = 21/36

How to simplify 21/36

21/36 ÷ 3 (Divide the numerator "the top part of the fraction" and the denominator "the bottom part of the fraction" by 3. This will equal 7/12

How to turn 21/36 into a decimal

21 divided by 36 = 0.5833333333333333...

Round to the nearest thousandth: 0.583

How to turn 0.583 into a percent

Move the decimal point 2 places to the left, drop the zero(s)

and add the percent sign! 58.3%

These are all the same answer but in different forms and how to do them!

Hope it helps!

Step-by-step explanation:

so, if I understand correctly :

angle A = 22°

angle B = 53°

angle D = 38°

remember : the sum of all 3 angles in every triangle is always 180°.

so,

180 = 22 + 53 + AEB

angle AEB = 180 - 22 - 53 = 105°

per the attributes of crossing lines the angles between them are the same on both sides of any of the lines (just left-right mirrored).

so, CB and AD are crossing lines, therefore

angle AEB = angle CED = 105°

and then

180 = 105 + 38 + C

angle C = 180 - 105 - 38 = 37°

Answer:

What is the value of √m = ∓ 17

The value of √m = ∓ 17 is undefined.

Answer:

x=2/3

Step-by-step explanation:

3x - 1 = 1

   + 1   + 1

---------------

3x = 2

÷3    ÷3

------------------

x=2/3

-----------------------

using subtraction and division properties of equality, you can simplify the expression to solve it. you can use other properties of equality for different equations as well, but for this one you only need subtraction and division. :)

The period of the solar system's orbit is 2.05 x 108 years.

What is the time period?

A period is a number that in algebraic geometry can be expressed as the integral of an algebraic function over an algebraic domain. Periods form a ring because their sums and products always remain in the same period.

Don Zagier and Maxim Kontsevich presented some theories and gave a survey of the eras. Periods also appear when computing the integrals that result from Feynman diagrams, and extensive work has been done to understand the relationships.

Solution Explained:

Given,

Radius of the solar system, r=25000 light year

Speed v=230 km/s

Calculate time period by

T = 2πr / v

T = 2πr X (25000 X 3 X 10^8 X 365 X 24 X 60 X 6) / (230 X 10^3)

  = 6.46 X 10^15 X (1 year / 365 X 24 X 60 X 60)
  = 2.05 X 10^8 years

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So for the maximum area, the values of the width and length of the  rectangle will  be  2.121.

Since we know that the formula for the area of a rectangle is:

A = XY, where x and y are the width and length

since we are given the are, y=√(9-x²), so

A = √(9-x²)

taking the derivative on both sides and considering it to be zero, we get

A' = (x/√(9-x²)(-2x) + √(9-x²) = 0, after multiplying by √(9-x²)

A' = -x² + 9 -x² = 0

=>-2x² =-9

=>x² = 9/2

=> x = 3/√2

so x=2.121 so the for y = √(9-(2.121)^2) =  √(9-4.498) = 2.121

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A rectangle is bounded by a  semicircle y = radical 9 − x^2 and the x-axis. What length and width should the rectangle be to maximize the area

The domain and range of the function C(t) based on the context of the problem is

The range is calculated from minima and maxima, this will be achieved using derivative

C(t) = -5t² + 10t

C'(t) = 0 = -10t + 10

t = 1

substituting t = 1

C(t) = -5(1)² + 10t = 5

so at point (1, 5) it is either minima or maxima,

The second derivative test will help to confirm if point (1, 5) is minima or maxima

C'(t) = -10t + 10

C''(t) = -10

a negative value means it is a maxima

Hence the highest value of the concentration C(t) is 5 mg/L and this is at t = 1

The concentration cannot be less than zero or negative hence the lowest concentration is 0. and the range is 0 to 5

0 ≤ C ≤ 2

The time cannot be below zero so the lowest time will be zero

The domain is controlled by the input values. considering the least concentration of the drug which will be at C = 0

C(t) = -5t² + 10t

0 = -5t(t - 2)

-5t = 0

t = 0

t - 2 = 0

t = 2

The roots of the quadratic equation gives the domain to be 0 to 2

0 ≤ t ≤ 2

The graph is attached

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Answer:

Step-by-step explanation: find a point and find another point

y=1x+1/2

The inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let's assume that the number would be x

The sum of a number and -4 is at least 8

According to the given question, translate the phrase into an algebraic form :

x - 4 ≥ 8

Add 4 both sides of the above inequality,

x - 4 + 4 ≥ 8 + 4

x ≥ 12

Therefore, the inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

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The expression 0.3d = 0.95 could be used to find the number of dimes he has.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have joe who has dime and nickels in his piggy bank totaling $1.45 the number of nickels. He has is 5 more than twice the number of dimes [d].

We can write the the number of nickels as -

[n] = 2d + 5

0.1d + 0.1(2d + 5) = 1.45

0.1d + 0.2d + 0.5 = 1.45

0.3d = 0.95

Therefore, the expression 0.3d = 0.95 could be used to find the number of dimes he has.

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There are 65, 19-bit sequences of 0s and 1s that start with a 0 and end with a 0 that exist.

Any subsequent 0 in the sequence must come exactly two or three spots down from the previous one.

We begin at point 1 and finish at position 19 in this instance.

That is, we advance along the line a whole of 18 positions.

In order to achieve 18, we must add all series consecutive 2s and 3s.

There are numerous methods for doing this:

Case 1: There is just one possible arrangement for nine 2s.

Case 2: Two 3s with six 2s - thus ⁸C₂ ways = 28 ways

Case 3: Four 3s with three 2s - thus ⁷C₄ ways = 35 ways

Case 4: Six 3s - Only 1 way to arrange.

Thus, the number of arrangements = 1 + 28 + 35 + 1 = 65 .

Therefore ,the total possible number of the sequence that cane be made is 65 .

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the polynomial will be 2x² + 11x+6, with degree less than 3 and be the subspace.

What is vector space?

A collection of vectors collected collectively and multiplied ("scaled") by scalars forms a vector space, also known as a linear space. Real numbers are typically thought of as scalars. Nevertheless, there aren't many instances of scalar multiplication with vector spaces using rational, complex, etc. numbers. Axioms and other preconditions must be met by the vector addition and scalar multiplication techniques. A space made up of vectors is referred to as a vector space when the addition of vectors is governed by the associative and commutative law and when vectors are multiplied by scalars is governed by the associative and distributive process.

W = span (9x-4-2x²,5+x+2x²)

Now, a(9x42x²)+b(5+x+2x²) = 0

⇒(9a+b)x+(2b-2a)x² + (5b-4a) = 0

⇒9a+b= 0; 2b2a = 0; 5b-4a=0

a = b =0

p(x)=(9x-4-2x²) + 2(5+x+2x²) = 9x-4-2x² + 10 + 2x + 4x² = 2x² + 11x+6

Hence the polynomial will be 2x² + 11x+6.

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It will cost his parents $187.5 to invite 15 friends to his party because it cost $12.5 to invite just one.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, may be used to calculate how many kilometers a car would go on one litre of gas if it travels 44 km on two litres of fuel.

Here,

For inviting 20 friends, The cost of party was $250.

So for 1 friend,

=250/20

=$12.5

Now he wish to invite 15 friends,

=12.5*15

=$187.5

The cost of inviting 15 friends to his party will cost $187.5 to his parents as cost of inviting 1 friend was $12.5.

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Answer: y = 1.75x - 1

Step-by-step explanation: The slope of the line is 1.75

The required range of the given function g(x) = -1/2 |x-6| + 1 will be g(x) ≤ 1 or in internal notation form as (-∞, 1]. which is the correct answer would be an option (A).

The function is given in the question below as:

g(x) = -1/2 |x-6| + 1

We have to determine the range of the given function.

As per the given question, we have

⇒ g(x) = -1/2 |x-6| + 1

The range of an absolute function of the form:-

c|ax+b|+k is :f (x) ≤ k

In this case k = 1

⇒ g(x) ≤ 1

[tex]\mathrm{Range\:of\:}-\frac{1}{2}\left|x-6\right|+1:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:1\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:1]\end{bmatrix}[/tex]

Therefore, the required range of the given function will be g(x) ≤ 1 or in internal notation form as (-∞, 1].

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Answer: (3,0)

Hope this helps! :)

Step-by-step explanation: Think of graphing, like regular number lines. The numbers are either positive or negative and depending on the integer you add or subtract, the number on the line will either move left or right.

x= 5 (x on a coordinate plane is left to right)

2 units left

5-2=3

y= -5 (y on a coordinate plane is top to bottom)

5 units up

-5+5=0

(3,0)

Answer:

(3,0)

Step-by-step explanation:

x= 5-2 = 3

y= -5+5 =0

For the factorial study, Dr Rhodes can use the statement  b) effect of variable A depends on variable B

In a factorial study, two intervention comparisons are undertaken side by side. As a result, in addition to behavioral treatment or standard medical care, individuals may be randomly randomized to receive either aspirin or a placebo. In factorial designs, three different sorts of outcomes are pertinent: main effects, interaction effects, and simple effects.

The primary effect is the impact of one independent variable on the dependent variable, averaged over the values of the other independent variable. Dr Rhodes can forecast the relationship between independent variables A and B using the assumption that the effect of variable A depends on variable B.

Complete question

Dr. Rhodes notices an interaction in his factorial study. In describing this, which statement might he use to explain the link between Independent Variable A and Independent Variable B in predicting the dependent variable? TRUE OR FALSE

Variable A cancels out Variable B.

The effect of Variable A depends on Variable B.

The effect of Variable A is confused by Variable B.

Variable A mainly affects Variable B.

The effect of Variable A is mediated by Variable B.

The effect of Variable A depends on Variable B.

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The volume of the cylinder is 10,099.09 inches³.

Here we have to find the volume of the cylinder.

Given data:

Circumference = 46 inches

height(h) = 5 foot = 12 × 5 = 60 inches

Circumference = 2πr

46 = 2 ×π × r

r = 23/π

The formula for the volume of the cylinder = πr²h

Volume = π( 23/π)² 60

               = 529× 60 / π

               = 10,099.09 inches³

Therefore the volume is 10,099.09 inches³.

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The curve with parametric equations x = [tex]e^{- t}[/tex] + t, y = [tex]e^t[/tex] − t, − 2 ≤ t ≤ 2 can be plotted on a graph. The arrow shows the direction where t increases in the interval (-2,2).

The length of a curve of the provided parametric equations is indicated by the arrow pointing in the direction wherein the curve is traced given data.

Think about the equations for the parameterized curve in the x-y plane.

x = x( t )

y = y( t )

where the argument is t. The graph of the curve is created by charting the series of points as the variable t changes (x,y).

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The question is -

Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t increases. x = [tex]e^{- t}[/tex] + t , y = [tex]e^t[/tex] − t , − 2 ≤ t ≤ 2

Answer:

565.9

Step-by-step explanation:

The monthly payment amount a woman has to pay for the car is $462.91.

Here we have to find the monthly payment amount.

The cost of car = $23,800

Down payment = $3,500

Rate(r) = 4.5%

time(t) = 4 years

Periodic interest(i) = 0.045/12

Formula to calculate monthly payment:

A = P i( 1 + i[tex])^{n}[/tex] / ( 1 + i[tex])^{n}[/tex] - 1

Loan amount = 23800 - 3500

                      = $ 20300

A = 20300 ( 0.045 /12 ( 1 + 0.045/12[tex])^{48}[/tex])/ (1 + 0.045/12[tex])^{48}[/tex] - 1

  = 20300× 0.004488 / 0.196814

  = 462.91

Therefore the monthly payment is $462.91.

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Answer:

3

Step-by-step explanation:

75/15=

             __3_________

   15    /   75

          -    75

     ---------------------------------

                   0

Have a great day

From the given information given, the mean and standard deviation of the probability distribution is; Y will be 0.4899 and 0.699 respectively.

How to create the probability distribution?

From the given probability distribution, it should be noted that the probability distribution for y will be:

Y                   0        1.         2

Probability 0.63.   0.25.   0.12

The mean of Y will be:

Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)

Mean = 0 + 0.25 + 0.25

Mean = 0.49

The variance will be 0.4899. Therefore, the standard deviation will be:

standard deviation = ✓0.4899

Standard Deviation = 0.699

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