Prob-1A random sample of 21 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.12 mm and sample standard deviation is S = 0.14 mm. Construct a 95% two-sided confidence interval for the mean glass thickness.

Answer:

A system of two linear inequalities in two variables is a set of two linear inequalities that involve two variables, such as x and y. A system of two linear equations in two variables is a set of two linear equations that involve two variables, also typically x and y.

There are several key differences between a system of two linear inequalities in two variables and a system of two linear equations in two variables:

Inequalities use symbols such as "less than" or "greater than" to indicate the relationship between the variables, whereas equations use the equal sign (=).

The solution to a system of linear inequalities is a region in the coordinate plane, whereas the solution to a system of linear equations is a single point.

The solution to a system of linear inequalities is found by graphing the inequalities on the coordinate plane and finding the region where they intersect, whereas the solution to a system of linear equations is found by solving the equations for the values of the variables.

The solution to a system of linear inequalities may include an infinite number of points, whereas the solution to a system of linear equations is always a finite number of points.

Overall, the main difference between a system of two linear inequalities in two variables and a system of two linear equations in two variables is the way in which the solutions are represented and found.

Answer: 28 inches

Hope this helps!!! :)

Since the lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey we can use mathematical operations to make different lemonades with the following recipes:

1) To make more lemonade taste the same as the original, we can use the multiplication operation on the above recipe as follows:

Lemons = 10

Cups of water = 4

Tablespoons of honey = 4

2) To make less lemonade taste the same as the original recipe, we can use the division operation as follows:

Lemons = 2.5

Cups of water = 1

Tablespoons of honey = 1

3) To make lemonade that has a stronger lemon taste than the original recipe, we can use the subtraction operation as follows:

Lemons = 4

Cups of water 1

Tablespoons of honey

4) To make lemonade that has a weaker lemon taste than the original recipe, we can use the addition operation as follows:

Lemons = 6

Cups of water 3

Tablespoons of honey = 3

Lemons = 5

Cups of water = 2

Tablespoons of honey = 2

1) Using the multiplication operation to make more lemonade taste the same as the original:

Lemons = 10 (5 x 2)

Cups of water = 4 (2 x 2)

Tablespoons of honey = 4 (2 x 2)

2) Using the division operation to make less lemonade taste the same as the original recipe:

Lemons = 2.5 (5 ÷ 2)

Cups of water = 1 (2 ÷ 2)

Tablespoons of honey = 1 (2 ÷ 2)

3) Using the subtraction operation to make lemonade that has a stronger lemon taste than the original recipe:

Lemons = 4 (5 - 1)

Cups of water 1 (2 - 1)

Tablespoons of honey = 1 (2 - 1)

4) Using the addition operation to make lemonade that has a weaker lemon taste than the original recipe:

Lemons = 6 (5 + 1)

Cups of water 3 (2 + 1)

Tablespoons of honey = 3 (2 + 1)

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The Area of the shaded part is 3.44 cm²

The formula used to find the Area of a circle is given by

Where r is the radius of the circle

The formula used to find the Area of a Square is given by

Here we know

The radius of the circle = 2m

As we know Area of a Circle = 2πr

=> Area of given circle = 2(3.14)2 = 12.56 cm²

Area of circle = 12.56 cm²

As we can see the circle is inscribed in a square

Then the Length of the side square = diameter of the circle

=> Length of side = 2 × Radius of circle = 2 × 2 cm = 4 cm

Length of side = 4 cm

As we know Area of the square = side²

=> Area of given square = 4 × 4 = 16 cm²

Now using the above value we will friend the area of the shaded part

Area of shaded part = Area of the square - Area of the circle

= 16 cm² - 12.56 cm² = 3.44 cm²

Therefore,

The Area of the shaded part is 3.44 cm²

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The graph's representation of the inequality system is

y≤3x-2 and y≥-4x+2. So, option a is correct.

One of the basic ideas of social justice theories is the existence of unequal status, rights, and opportunities. In public conversation, it might be confusing because various people often interpret it differently. There are some frequent variants, though. In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. As an illustration, suppose you wish to get a 250 new bicycle. Different types of inequality are indicated by a variety of notations, including:

A less than sign, such as a, denotes that an is greater than b.

Therefore, The  system of inequalities that is represented by the graph is

y≤3x-2 and y≥-4x+2. So, option a is correct.

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Answer:

Step-by-step explanation:

199/4

The months when the temperature will be 0 °C are May and August.

A trigonometric function is a function that has the trigonometric ratios.

Temperature is the degree of hotness or coldess of a body.

Since the average monthly temperature of a particular city is T(m) = 10cos(πm/6) + 5 where m = number of months of year and January begins at m = 0.

To find the number of months in which the temperature would be 0°C. This means T(m) = 0.

So,  T(m) = 10cos(πm/6) + 5

0 = 10cos(πm/6) + 5

-10cos(πm/6) = 5

cos(πm/6) = 5/10

cos(πm/6) = -0.5

cos⁻¹cos(πm/6) = cos⁻¹(-0.5)

(πm/6) = π - π/6 or (πm/6) = 3π/2 - π/6 (since cos is negative int he second and third quadrant respectively)

πm/6 = 5π/6 or πm/6 = 8π/6

⇒ m = 5π/6 × 6/π or m = 8π/6 × 6/π

⇒ m = 5 or m = 8

Since m = 5 is May and m = 8 is August,

The months when the temperature will be 0 °C are May and August.

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(i) At a total of 100 Songs the Charges for Company A and Company B will be Equal.

(ii) I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

Let, Songs Downloaded be x

Total Charges of Company A = 15 + 0.75*x

Total Charges of Company B = 0.9*x

(i) Total Charges by Company A = Total Charges by Company B

15 + 0.75*x = 0.9*x

15 = 0.15*x

x = 100 songs

(ii) Charges by Company A to Download 150 Songs = 15 + 0.75 * 150

= 15 + 112.5 = $127.5

Charges by Company B to Download 150 Somgs = 0.9 * 150 = $135

I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5

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The total area of the Sea of Japan and the Southern Ocean is 2.1334 × 10⁷ km². The correct option is the first option 2.1334 × 10⁷ km²

From the question, we are to calculate the total area of the sea and ocean

From the given information,

"The area of the Sea of Japan is 1.007 × 106 km²"

and

"The area of the Southern Ocean is 2.0327 × 107 km²"

Thus,

The total area of the sea and ocean = 1.007 × 10⁶ km² + 2.0327 × 10⁷ km²

The total area of the sea and ocean = 0.1007 × 10⁷ km² + 2.0327 × 10⁷ km²

The total area of the sea and ocean = 2.1334 × 10⁷ km²

Hence, the total area is 2.1334 × 10⁷ km²

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Answer:

y = (2 + √2)/4   ;   y = (2 - √2)/4

Step-by-step explanation:

-8y² + 8y - 1 = 0

8y² - 8y + 1 = 0

discriminant = 64 - 4(8) = 64 - 32 = 32 = 2^4 * 2

y = (8 + [tex]\sqrt{2^4 * 2}[/tex])/16

(8 + 2²√2)/16

(8 + 4 √2) / 16

4(2+√2)/16

(2+√2)/4

y = (8 - [tex]\sqrt{2^4 * 2}[/tex])/16

(8 - 4√2) / 16

4(2-√2)/16

(2-√2)/4

The length of the wrench handle 8.4 inches.

What is length?

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.

f = k/l

35 = k/6        

k = 210

f = 210/l

25 =210/l      

l = 8.4 inches

The length "L" (in inches) of a wrench handle has an inverse relationship with the force "F" (in pounds) required to remove a certain bolt. In the case of a handle that is 6 inches long, 35 pounds of power is required. The length of the wrench handle if the bolt needs to be loosened with 25 pounds of force is 8.4 .

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Answer:

Y= -1/9x-9 that's the answer, you're welcome

The equation of line which is perpendicular to the line q is given by

y = ( -1/9 )x - 9

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The point is P ( 9 , -10 )

Let the equation of line q be  y + 7 = 9 ( x + 4 )

Now , on simplifying the equation , we get

y + 7 = 9x + 36

Subtracting 7 on both sides of the equation , we get

y = 9x + 29

Now , the slope of the equation q is m₁ = 9

Now , since the line r is perpendicular to line q

The product of the slope is -1

So , m₁ x m₂ = -1

Substituting the values in the equation , we get

9 x m₂ = -1

Divide by 9 on both sides of the equation , we get

m₂ = -1/9

So , the slope of the line r m₂ = -1/9

The equation of line is given by y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -10 ) = -1/9 ( x - 9 )

On simplifying the equation , we get

y + 10 = -1/9 ( x - 9 )

y + 10 =  ( -1/9 )x + 1

Subtracting 10 on both sides of the equation , we get

y = ( -1/9 )x - 9

Therefore , the value of A is y = ( -1/9 )x - 9

Hence , the equation of line r is y = ( -1/9 )x - 9

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Answer: 246.7

Step-by-step explanation:

The domain of the inverse function is {5,6}. And as a compound inequality the domain is 5<x<6.

A mathematical statement that expresses the inequality between two inequalities combinedly.

from the graph, we have two inequalities, x>5 and x<6

it can be written as 5<x<6

A function that can be obtained by reversing the primary function is termed as inverse of function. it is denoted by f⁻¹.

The graph shown is got from an inverse function whose domain is {5,6} and ranges are {-2, -4}

The graph also refers the inequalities of x>5 And x<6

compound inequalities of domain 5<x<6

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On solving the given equation  y=(x-2)(x-4) the point on the graph are as follows:

(4,0), (2,0), (5,3), (3,-1) &(0,8)

What is a graph?

A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.

It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.

It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.

1)

let   y=0

0=(x-2)(x-4)

i.e. x = 4 and 2

2)

Let x =0

y=(0-2)(0-4)

y=8

3)

Let x = 3

y=(3-2)(3-4)

y=-1

4)

Let x = 5

y=(5-2)(5-4)

y=3

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5.3

80/15=5.3

which means each person completed 5.3 puzzles

Answer:no

Step-by-step explanation:

There is a property with triangles that the sum of two sides of a triangle should always be greater than the 3rd side.

Here if we take the two smaller sides their sum is 7 + 8 = 15 which is equal to the third side.

So it is not possible to construct a triangle with sides 7, 8, and 15 respectively.

The number of sweets left in the box after giving 35% is 325.

There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. The number of sweets left in the box can be calculated as follows:

Therefore, the number of sweet left in the box = 500 - 35% of 500

number of sweet left in the box = 500 - 35 / 100 × 500

number of sweet left in the box = 500 - 17500 / 100

number of sweets left in the box = 500 - 175

= 325

Therefore, the number of sweets left in the box will be 325

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The linear functions in this problem are given as follows:

1. y = 1/3x + 3.

2. y = 2.

3. y = 3x - 1.

4. x = 1.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are given as follows:

For item 1, the points are given as follows:

(-6, 1) and (-3,2).

When x increases by 3, increases by 1, hence the slope is given as follows:

m = 1/3.

Then:

y = 1/3x + b.

When x = -3, y = 2, then the intercept b is calculated as follows:

2 = 1/3(-3) + b

b = 3.

Thus the function is:

y = 1/3x + 3.

Then items 2 and 4 are given as follows:

For item 3, we have an intercept of -1, hence:

y = mx - 1.

When x = 3, y = 8, hence the slope m is calculated as follows:

8 = 3m - 1

3m = 9

m = 3.

Hence the function is:

y = 3x - 1.

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Reciprocal of a = [tex]\frac{1}{a}[/tex]

What is Reciprocal ?

In Mathematics , reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n.

What are real numbers ?

In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions .

According to the given information

a ≠ 0

a is a real number

By the definition of reciprocal

Reciprocal of a will be the inverse of a = [tex]\frac{1}{a}[/tex]

Reciprocal of a = [tex]\frac{1}{a}[/tex]

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The given statement:

"the sum of a number and 10.7 is at most −3.2"

Is equivalent to the following inequality:

x + 10.7 ≤ -3.2

Here we have the following statement:

"the sum of a number and 10.7 is at most −3.2"

So let's define the variable "x" as "the number", we know that the sum between x and 10.7 is at most -3.2, we can say that the sum is equal to or smaller than -3.2

In that case, the symbol we need to use is: ≤

Then the inequality is:

sum ≤ -3.2

x + 10.7 ≤ -3.2

That is the statement written as an inequality.

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Answer:

$0.48/pound

Step-by-step explanation:

$5.76 divided by 12

In the octagon, the measurement of the largest exterior angle is 90°.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words, poly, which means numerous and gon, means sides.

The given exterior angles of the octagon are,

x°, 2x°, 3x°, 4x°, 5x°, 7x°, 8x°, and 10x°.

The sum of the exterior angle of the octagon is 360°.

Implies that,

x + 2x + 3x + 4x + 5x + 7x + 8x + 10x = 360

40x = 360

x = 9

The largest exterior angle = 10 x  = 10 × 9 = 90°.

The required largest exterior angle is 90°.

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Answer:

See below   ( you have it correct !)

Step-by-step explanation:

See image below....sometimes it is easier to see these things if you extend some lines a bit:

Answer:

Before 1913, federal government revenues came mainly from taxes on goods—tariffs on imported products and excise taxes on items like whiskey.

Step-by-step explanation:

What was the tax rate in 1913?

The act levied a tax of one percent on all incomes above the exemption with additional surtax rates imposed for progressively higher incomes. Those surtax rates started at one percent for those making $20,000 or more and topped out at a mere six percent on incomes in excess of $500,000.

[tex]x=-2 \implies y=(1/3)^{-2}=3^{2}=9\\\\x=-1 \implies y=(1/3)^{-1}=3\\\\x=0 \implies y=(1/3)^0=1\\ \\ x=1 \implies y=1/3\\\\x=2 \implies y=(1/3)^2 =1/9[/tex]

Using these points, the correct graph is shown in option C.

She should divide both sides by -5 while multiplying the other side by -5. She also did not replace the > symbol with a symbol.

An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.

From given question :

-5x-3.5>6.5

-5x > 10

X > -50

Since, we have to solve for x

so, we will isolate x on anyone side

step-1:

Add both sides by 3.5

- 5x - 3.5 + 3.5 > 6.5 + 3.5

- 5x > 10

step-2:

Divide both sides by -5

we know that whenever we divide both sides by negative sign , it's inequality gets revered

so, we get

- 5x / -5 < - 50 / -5

we get

x < 10

so,

She should divide both sides by -5 while she multiplied by -5 on other side

and she also did not change the > symbol to a < symbol

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Answer:

B

Step-by-step explanation:

5x + 30 - 18x - 18 = 10

-13x + 12 = 10

Answer:

18.6

Step-by-step explanation: