Use the rules of exponents and your understanding of roots to find the exact value of the following expressions.

Answer:

the minimum sample size required is 139

Step-by-step explanation:

To construct a 95% confidence interval with a maximum error of 0.19 reproductions per hour, we need to use the t-distribution. The t-distribution is used when the population variance is unknown and the sample size is small.

To find the minimum sample size required, we need to use the following formula:

n = (t_(α/2,df) * s / E)^2

where:

n is the minimum sample size

t_(α/2,df) is the critical value of the t-distribution for a confidence level of 95% (α = 0.05) and df is the degrees of freedom

s is the standard deviation of the population

E is the maximum error allowed

We are given that the mean is 12.6 reproductions and the variance is 3.61. The standard deviation is the square root of the variance, so the standard deviation is 1.9.

To find the critical value of the t-distribution, we need to know the degrees of freedom. The degrees of freedom is equal to the sample size minus 1. Since we don't know the sample size yet, we will use a symbol (let's use "df") to represent the degrees of freedom in the formula.

Plugging the values into the formula, we get:

n = (t_(0.025,df) * 1.9 / 0.19)^2

To find the critical value of the t-distribution, we need to use a t-table or a computer program. Looking up the critical value in a t-table or using a computer program, we find that the critical value for a 95% confidence level and df = 9 is 2.262.

Plugging this value into the formula, we get:

n = (2.262 * 1.9 / 0.19)^2

Simplifying the expression, we get:

n = (11.868)^2

n = 138.7

The minimum sample size required is 138.7. Since we can't have a fractional number of samples, we need to round up to the next integer, which is 139.

Therefore, the minimum sample size required is 139.

On factorizing , we get that the   fully factored form of the expression [tex]32a^{3} + 12a^{2}[/tex] can be written as [tex]4a^{2} (8a+3)[/tex] .

The Factorizing is defined as a process of expressing the given number or the  algebraic expression as a product of its factors .

the expression is given as : [tex]32a^{3} + 12a^{2}[/tex] ;

the first term of the expression is ⇒ [tex]32a^{3}[/tex] , it can be expressed as [tex]4\times 8 \times a \times a \times a[/tex] ;

the second term of given expression is ⇒ [tex]12a^{2}[/tex] , it can be expressed as [tex]4\times 3 \times a \times a[/tex] ;

we see that in both terms , the common factor is [tex]4\times a \times a = 4a^{2}[/tex] ;

which means that , it is written as : [tex]4a^{2} (8a+3)[/tex] ;

Therefore , the fully factored form is [tex]4a^{2} (8a+3)[/tex] .

The given question is incomplete , the complete question is

What is fully factored form of the expression [tex]32a^{3} + 12a^{2}[/tex] ?

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Answer:

True.

Step-by-step explanation:

In a reflection, the orientation of a figure changes. This means that the direction of the shape is reversed, as if it were being viewed in a mirror. For example, if a figure is facing to the right, it will appear to be facing to the left after it has been reflected. The shape itself is not altered by the reflection, only its orientation.

The system of linear equations with our defined variables are 2x + 2y = 62 ...eq(i) and x + 4y = 70 ...eq(ii)

A system of linear equations is a collection of two or more linear equations that use the same set of variables. The solution of a system of linear equations is the set of values for the variables that make all of the equations in the system true.

In this problem, let's define our variables as;

The equations can be written as;

2x + 2y = 62 ...eq(i)

x + 4y = 70 ...eq(ii)

Which is synonymous to option D in the question

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Answer:

Step-by-step explanation:

first one

After factoring the value of y^x = 5 or -4.

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators (such as +, -, x, ÷). These expressions can be evaluated to determine their numerical value, but they can also be simplified, factored, and manipulated using the rules of algebra. Examples of algebraic expressions include 2x + 3, x^2 - 4, and (x + y)^2.

Given expression,

y^2x - y^x - 20 = 0

Let y^x = t .

t^2 - t - 20

t^2-5t+4t-20 = 0

t (t-5) + 4 (t-5) = 0

(t-5) (t+4) = 0

so, t-5 = 0

we get , t = -4

and t+4 = 0

so we get , t = 5

Hence, the value of y^x = 5 or -4.

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Answer:

Each DC cost $18.49.

Step-by-step explanation:

[tex](\frac{79.94 - 5.94)}{4}[/tex]  Subtract out the shipping cost of 5.98 from the total cost of $79.94 and divide that amount by 4.  That will get you 18.49 which is the cost of each DVD.

The logarithm rules and the matching equation is as follows

equation                         logarithm rule

[tex]log_{3}(\frac{(x-4)}{(x-1)})[/tex]                      quotient rule

[tex]log_{2}x(x+2})[/tex]                    product rule

[tex]log(x+2)^{3} x^{3}[/tex]                   product rule and power rule

[tex]log_{3}(x-4)-log_{3}(x+4)[/tex]  quotient rule

3 log (x + 2) - 3 log (x)     product rule and power rule

The laws of logarithm are generally rules that describes how problems involving logarithm is being solved

The quotient rule refers to when there is a division, the rul when applied changes division to subtraction.

The power rule takes care if exponents and places the number in the exponents to be just before the log sign

The product rule is used to deal with duplication, it changes multiplication to addition

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The two pair of linear equations are 2x+6y=30 and x+y=7.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Each, x, table cover cost $2 and each, y, center piece cost $6.

Karl spent $30 decorating for the annual holiday party.

So, the equation is 2x+6y=30 --------(I)

Karl bought 7 items total.

Now, x+y=7 --------(II)

From equation (II), x=7-y

Substitute, x=7-y in equation (I), we get

2(7-y)+6y=30

14-2y+6y=30

14+4y=30

4y=16

y=4

Substitute y=4 in equation (II), we get

x=3

Therefore, the two pair of linear equations are 2x+6y=30 and x+y=7.

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2W² + 2W = 264  is the equation that an be used to find the width, W, of the porch. The value w = 11 gives the width of the porch, in feet.

The tools that aid in indicating an object's measurements are length, width, and height. We can calculate the volume of geometric shapes using their length, width, and height.

The length of an object or a figure on a planar surface is its longest measurement. The length of the specified object or figure is indicated.

The width of an object or figure on a planar surface is its smallest dimension. It provides the object or figure's width information.

Height is the measurement of an object's vertical distance from a figure or a planar surface.

Given that a rectangular porch has an area of  264 ft²

L × W = 264 ft²

And

W = L/2 - 1

or

L = 2(W + 1)

Substitute the value of L in area Equation

2(W + 1) × W = 264

2W² + 2W = 264

Putting the equation in quadratic formula we get

x = 11

x = -12

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A convex mirror's generated image is always virtual and situated behind the mirror. The picture is erect and situated at the focal point when the item is far from the mirror.

The radius of curvature is the measurement between the vertex and the center of the curve (represented by R). The sphere from which the mirror was sliced has a radius equal to the radius of curvature. The distance between the vertex of the circle used to create the cylindrical mirror's shape to its center is known as the center of curvature.

In addition, the center of curvature will house the image. The image will be upside-down in this situation. The proportions of the image match those of the object. The image is the same size as the object, actual, and inverted if the object is at the center of the curve. The image is bigger, realer, and inverted if the object lies between the center of curvature and the main focus.

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The value of angle x is 73⁰

You should be aware that a point where two or three straight lines intersect forms an angles.

The parameters that will help us to determine the value of x are

Line B is a straight line. then the sum of angles on a straight line is 180.

⇒110 + b = 180

Making b the subject we have

b = 180 - 110

This means that  b = 70°

Also, a = 52° (Opposite angles)

The sum of all interior angles of a triangle is 180.

This means that a + b + c = 180

substitute for a and b to get c

52 + 70 + c = 180

122 + c = 180

Making c the subject of the relation

c = 180 - 122

⇒c = 58°

On the other hand c + d + e = 180

Substitute for c and d to have 58 + 49 + e = 180

107 + e = 180

Making e the subject of the relation we have

e = 180 - 107

e = 73°

But x = e (opposite angles)

There the value of x is 73⁰

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Answer:

270

Step-by-step explanation:

He read 45 pages an hour.  If we go back to hour 0, we would add 45 pages to 225

Answer:

270 pages

Step-by-step explanation:

In the attachment, we can see that Aiden read 45 pages per hour. Therefore, since he already read for an hour, we need to add 45 to 225

45+225=270

So, Aiden's book has a total of 270 pages.

A senator wants to know what her constituents think of a proposed health bill.  In this scenario, the population would be all of the constituents of the senator.  The sample would be the 222 letters that were received on the subject.

Generally, In statistics, a population is the entire group of individuals or items that you want to study.

A sample is a smaller group of individuals or items that is selected from the population to represent the larger group. The sample is used to make inferences about the population.

For example, let's say you want to study the political opinions of all the registered voters in your city. The population in this case would be all the registered voters in your city.

However, it might not be practical or possible to survey every single registered voter, so you might instead select a sample of registered voters to survey. This sample would be used to make inferences about the political opinions of the larger population of registered voters in your city.

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Integrating this expression, we obtain: −20√4 cosθe−r2 + C, where C is the constant of integration. Therefore, the integral evaluates to this expression.

Using polar coordinates, we have:

20√4 − r cosθ20e−r2 − r sin2θ dr dθ

This simplifies to:

20√4 − r cosθ20e−r2 dr dθ

Now we can integrate:

∫20√4 − r cosθ20e−r2 dr dθ = −20√4 cosθe−r2 + C

Where C is the constant of integration.

This iterated integral can be evaluated by converting to polar coordinates. We first rewrite the integral as: 20√4 − r cosθ20e−r2 dr dθ. Integrating this expression, we obtain: −20√4 cosθe−r2 + C, where C is the constant of integration. Therefore, the integral evaluates to this expression.

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Answer: D

Step-by-step explanation:

The table that shows the correct missing values would be option A = Brain (part) 0.4 1.1 1.6 4

Body (part) 4.4 12.1 17.6 44

Total (whole) 4.8 13.2 19.2 48

Addition is the combination of two or more values which leads to the arrival of a common value.

To calculate for A;

Brain = 0.4

body part = A

Total = 4.8

A = 4.8 -0.4 = 4.4

To calculate for B;

Brain = B

Body part = 12.1

Total = 13.2

B = 13.2 - 12.1 = 1.1

To calculate for C;

Brain = 1.6

Body part = 17.6

Total (C ) = 19.2

To calculate E;

Brain= E

Body= 44

Total = 48

E = 48-44 = 4

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Answer:

12.5

Step-by-step explanation:

The products of two numbers is 6.25 if one of them is 0.5 then find the other Number.​ - 31133581.

0.5 * x = 6.25

x = 6.25 / 0.5

= 12.5

Check the picture below.

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

We use the formula

n= (zc/E)2σ2

Where,

n = sample size

zc = The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

E = margin of error

σ = standard deviation

Substituting the given values,

n= [(1.96*0.95)/1]2*5.72

n= 95.29

Therefore, the minimum sample size n equals 96 (rounded up to the nearest whole number).

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

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Step-by-step explanation:

The account starts at 2000$

2000$×0.06(same as 6%)= 120$

The account gains 120$ yearly

A. After 4yrs that would be 480$ interest

120$×4= 480$

2000$+480$= 2480$ after 4yrs

B. Aftee 16yrs that would be 1920$ interest

120$×16= 1920$

1920$+2000$= 3920$

C. 2500$-2000$= 500$

500$÷120$= 4.16yrs

It will take about 4.2 years for the account to reach 2500$

D. 3000$-2000$= 1000$

1000$÷120$= 8.33yrs

It will take about 8.3yrs for the account to reach 3000$

The polygonal shape of the hexacontakaienneagon has 69 sides.

A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Polygons include shapes like triangles, hexagons, pentagons, and quadrilaterals.

The hexacontakaienneagon shape's number of sides is indicated by the name. For instance, a triangle has three sides, whereas a quadrilateral has four. A two-dimensional closed figure with three or more straight sides is called a polygon. A polygon is any shape with straight edges, such as a triangle or rectangle. Figures with open sides or any curved sides are not considered to be polygons.

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Using the idea of inequality and some simple math calculations, the total number of persons who can visit an amusement park is 4.

Given that a group of friends has a maximum of $160 in this question.

$10.50 is the cost of parking.

The price of each ticket is $32.50.

We must address inequality.

So let's attempt to define inequity.

Inequalities in mathematics describe the connection between two non-equal quantities. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal sign (≠)". However, a number of inequalities are used to compare the numbers and determine whether one is greater than the other.

A relation is called an inequality if two real numbers or algebraic expressions are related by the symbols ">"  "<"  "≥" "≤".

Let's Suppose we have a total of x number of persons.

then the total cost of tickets is 32.5 * x.

cost of parking is $10.50.

So the total cost to visit an amusement park is = 32.5x+ 10.50

Given that the total cost will be no more than $160.

So according to that

32.5x+ 10.50 ≤ 160.

32.5x ≤ 160-10.50

32.5x ≤ 149.5

x ≤ 149.5/32.5

x ≤ 4.6.

The nearest integer will be 4.

So the number of people who can go to an amusement park is 4.

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The group of friends can have no more than 4 people go to the amusement park.

We can use an inequality to determine the number of people who can go to the amusement park. We know that the group has no more than $160 to spend on parking and admission. We also know that parking is $10.50 and tickets cost $32.50 per person, including tax.

The inequality we can use to determine the number of people who can go to the amusement park is: 10.50 + 32.50x ≤ 160

To solve the inequality, we must first subtract 10.50 from both sides of the equation to isolate variable x. This gives us: 32.50x ≤ 149.50

Next, we must divide both sides of the equation by 32.50 to solve for x. This gives us: x ≤ 4.62

Since x is the number of people who can go to the amusement park, we must round down to the nearest whole number. This gives us: x ≤ 4

Therefore, we can conclude that the group of friends can have no more than 4 people go to the amusement park.

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1. The area of the region enclosed by one loop of the curve r = sin(8theta) is 16π.

2. The area of the region enclosed by one loop of the curve r = 7 cos(3theta) is 28π.

The area of a region enclosed by one loop of a curve is calculated by using a method called the “area under the curve”. This method involves integrating the equation of the curve over one full period (or loop) of the curve. For example, in the case of a curve with equation r = sin(8theta), the area of the region enclosed by one loop of the curve is equal to the integral of r = sin(8theta) from 0 to 2π. This integral evaluates to 16π, which is the area of the region enclosed by one loop of the curve. The same method can be applied to a curve with equation r = 7 cos(3theta) to find the area of the region enclosed by one loop of the curve. In this case, the integral of r = 7 cos(3theta) from 0 to 2π evaluates to 28π, which is the area of the region enclosed by one loop of the curve.

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the lot is 90 feet by 110 feet. the fence is to be 6 feet tall. cost for the fence is $3.00 per linear foot, plus $.40 per square foot for labor then the total cost of the fence is 8643 dollar

We have to sum the three distances to get the perimeter.

P= 90 ft + 110 ft+ 6 ft

P = 201 ft

And each foot of material cost $3.00

we get the cost with the distance and de cost of the material:

Cost = 201 ft * 3.00 $ per ft = $603

he needs $603.00 to fence her backyard garden

40 per square labor

then 201*40 = 8040

total = 8040+603= 8643

thus  the total cost of the fence is 8643 dollar

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Answer:

by solution of 4/3 πr^3

volume of sphere= 5.57×10^-3 m^3

hope this would help you!

The total amount that Mikaela spent on the paddleboard is $578.506. which is the correct answer would be option (D)

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that Mikaela purchased a paddleboard originally priced at $899. If all merchandise was on sale for 40% off and the state tax rate is 7.25%.

Here,

Original cost = $899

Discount = 40% = 0.40

State tax rate = 7.25% = 0.0725

Total amount = Original cost × (1 - Discount) × (1 + State tax)

Total amount = 899×(1 - 40%)×(1 + 7.25%)

Total amount = 899×(1 - 0.40)×(1 + 0.0725)

Total amount = 578.506

Thus, the total amount that Mikaela spent on the paddleboard is $578.506

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The total amount that Mikaela spent on the paddleboard is $578.51. The result is obtained by subtracting the discount from the original price and adding the tax.

When we get a discount of a product, the price will get cheaper. The price is subtracted by the discount. When there is a tax, you have to pay for it.

Mikaela purchased a paddleboard with the original price of $899. She got a discount of 40%. The tax rate is 7.25 %. Find the total amount she paid for the paddleboard!

From the information, we get the discount

= 40% × $899

= 0.4 × $899

= $359.6

The tax would be

= 7.25% × $899

= 0.0725 × $899

= $39.11

The total price is

= original price - discount + tax

= $899 - $359.6 + $39.11

= $578.51

Hence, Mikaela spent $578.51 for the paddleboard.

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Answer:

See explanation

Step-by-step explanation:

Every time x increases by 1, y decreases by 3.