a sample of size 115 will be drawn from a population with mean 48 and standard deviation 12 . use the ti-83 plus/ti-84 plus calculator. (b) find the 25th percentile of x . round the answer to at least two decimal places. the 25th percentile is

Answer:

4/1 is the answer

Step-by-step explanation:

according to rules 1st divide then multiple

last addition and subtraction

The value of r² + s² is 17.25 if r and s represents the solution of the given quadratic equation 2x² + 9x + 3 = 0.

To find the sum of squares of the solutions of the given quadratic equation, we can use the formula

r² + s² = (r + s)² - 2rs

where r and s are the roots of the quadratic equation.

In this case, we have the equation

2x² + 9x + 3 = 0

We can use the quadratic formula to find the roots:

x = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = 9, and c = 3.

Plugging in these values, we get

x = (-9 ± √(9² - 4(2)(3))) / 4

Simplifying

x = (-9 ± √69) / 4

So the roots are

r = (-9 + √69) / 4

s = (-9 - √69) / 4

To find r² + s², we need to compute (r + s)² - 2rs

(r + s)² - 2rs = ((-9 + √69)/4 + (-9 - √69)/4)² - 2((-9 + √69)/4)((-9 - √69)/4)

Simplifying

= ((-18)/4)² - 2((-9 + √69)/4)((-9 - √69)/4)

= (9/2)² - 2((81 - 69)/16)

= 81/4 - 3/2

= 69/4

= 17.25

Hence, the sum of squares of the solutions of the given quadratic equation 2x² + 9x + 3 = 0 is 17.25.

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Given that diameter of a circle is 7 ft, its area to the nearest tenth is 38.5 square feet.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2 where r is the radius of the circle.

To find the radius, we can divide the diameter by 2: r = d/2 = 7/2 = 3.5 ft

Now we can plug this into the formula for the area:

A = πr^2

A = π(3.5)^2

A ≈ 38.48

Therefore, rounding to the nearest tenth, the area of the circle is approximately 38.5 square feet.

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Answer:

x = -3, y = -0.512

x = -1, y = -3.2

x = 0, y = -8

x = 2, y = -50

Step-by-step explanation:

(x, y) is an element of the set c × d, since x is an element of c and y is an element of d.

Since (x, y) was an arbitrary element in a × b, we can conclude that every element in a × b is also in c × d. Thus, we have shown that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d.

To show that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d, follow these steps:

Step 1: Understand the notation.
a ⊆ c means that every element in set a is also in set c.
b ⊆ d means that every element in set b is also in set d.

Step 2: Consider the Cartesian products.
a × b is the set of all ordered pairs (x, y) where x ∈ a and y ∈ b.
c × d is the set of all ordered pairs (x, y) where x ∈ c and y ∈ d.

Step 3: Show that a × b ⊆ c × d.
To prove this, we need to show that any ordered pair (x, y) in a × b is also in c × d.

Let (x, y) be an arbitrary ordered pair in a × b. This means that x ∈ a and y ∈ b.

Since a ⊆ c, we know that x ∈ c because every element in set a is also in set c.
Similarly, since b ⊆ d, we know that y ∈ d because every element in set b is also in set d.

Now, we have x ∈ c and y ∈ d, so the ordered pair (x, y) belongs to c × d.

Step 4: Conclusion
Since any arbitrary ordered pair (x, y) in a × b also belongs to c × d, we can conclude that a × b ⊆ c × d.

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Answer:

4.4 x 3.9 x 8.7 = 149.292

To find an area multiply all given side lengths and make sure to know what shape you are finding the area too because different shapes have different formula's. Parallelograms such as square rectangle or any parallel pair will be just L x W x H or L x W depends if its 2d or 3d

Answer:

the number that belongs in the green box is 8

In the given options, only option C has the form of a second-degree function, y = x², where a=1, b=0, and c=0.

Therefore, the correct answer is C.

What is the polynomial equation?

A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.

The function y = x² is a second-degree function because it contains a variable, x, raised to the second power.

Option A, y = x, is a first-degree function because it contains a variable, x, raised to the first power.

Option B, y = 3x - 7, is a first-degree function because it contains a variable, x, raised to the first power.

Option D, y = 3, is a constant function because it does not contain any variable raised to any power.

Therefore, the answer is option C, y = x² has the form of a second-degree function.

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The natural breaks, quantile, and equal interval classification schemes are methods used to categorize data for the purpose of creating thematic maps. Each scheme has its own approach and considerations: Natural Breaks, Quantile, Equal Interval.

Natural Breaks (Jenks): This classification scheme aims to identify natural groupings or breakpoints in the data. It seeks to minimize the variance within each group while maximizing the variance between groups. Natural breaks are determined by analyzing the distribution of the data and identifying points where significant gaps or changes occur. This method is useful for data that exhibits distinct clusters or patterns.

Quantile (Equal Count): The quantile classification scheme divides the data into equal-sized classes based on the number of data values. It ensures that an equal number of observations fall into each class. This approach is beneficial when the goal is to have an equal representation of data points in each category. Quantiles are useful for data that is evenly distributed and when maintaining an equal sample size in each class is important.

Equal Interval: In the equal interval classification scheme, the range of the data is divided into equal intervals, and data values are assigned to the corresponding interval. This method is straightforward and creates classes of equal width. It is useful when the range of values is important to represent accurately. However, it may not account for data distribution or variations in density.

In summary, the natural breaks scheme focuses on identifying natural groupings, the quantile scheme ensures an equal representation of data in each class, and the equal interval scheme creates classes of equal width based on the range of values. The choice of classification scheme depends on the nature of the data and the desired representation in the thematic map.

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The smallest representable positive number is 2149, or roughly 1.4*10-45.

Lets take a  32-bit floating point integer (IEEE 754) with the following bits,

0-22 for the mantissa (23 bits), 23-30 for the exponent ( 8 bits), and 31 for the sign (1bit)

The decimal counterpart of this expression would be if we put all zeros in the mantissa and all ones in the exponent.

The way of representing huge numbers in terms of powers is known as an exponent.

Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6.

The exponent is represented by the symbol  ^ . This symbol is known as a carrot . As an illustration, 4 raised to 2 can be expressed as 4^2 .

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Given the diagram shows the shape of a putting green in a miniature golf course.

We will find the area of the putting green by dividing it into 3 sections as shown in the following figure:

Area (1) is the area of a rectangle with dimensions 4.5 and 8 feets

so, the area (1) = 4.5 x 8 = 36 feet²

Area (2) is the area of a square with a side length of 4.5 feet

So, the area (2) = 4.5 x 4.5 = 20.25 feet²

Area (3) is the area of the sector of a circle with a radius = 4.5 feet

The sector represents the quarter of the circle

so, Area (3) =

So, the total area is the sum of the three areas:

Rounding to the nearest square foot

So, the answer will be: Area = 72 feet²

The value of n for the expression nf = 1/2f will be n = 1/2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is nf = 1/2f. The value of n will be calculated as,

n x f = ( 1/2 ) x f

n = ( 1/2 ) x f / f

n = 1/2

The value of n in the expression nf = 1/2f is 1/2.

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The net outward flux across the boundary of the tetrahedron is: 5, using the concept of gradient of function.

The gradient of a function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z).

Given vector field:

F = ( -x, 3y, 2 z )

Δ . F = (i δ/δx + j δ/δy + k δ/δz) (-x, 3y, 2 z )

Δ . F = [δ/δx(-x)] + δ/δy (3y) + δ/δz (2z)]

Δ . F = - 1 + 3 + 2

Δ . F = 4

According to divergence theorem;

Flux =  ∫∫∫ Δ . (F) dv

x+y+z = 1; so, 1st octant

∫₀¹∫₀¹⁻ˣ∫₀¹⁻ˣ⁻y (4) dz dy dx

= 4 ∫₀¹∫₀¹⁻ˣ (1 - x - y) dy dx

= 5

Therefore, we can conclude that the net outward flux across the boundary of the tetrahedron is: 5

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Answer:

coordinates of point g is ( -6, 14)

Step-by-step explanation:

The coordinates of the point which divides the point (x1,y1) and (x2,y2) in m:n ratio is given by (nx1+mx2)/(m+n), (ny1+my2)/(m+n).

___________________________________________

given point

F(-1, -1) to H(-8, 20)

ratio : 5:2

the coordinates of point g is

(2*-1+5*-8)/(5+2), (2*-1+5*20)/(5+2)

=> (-2 -40/7 , -2+100/7)

=> (-42/7, 98/7)

=>( -6, 14)

Thus ,  coordinates of point g is ( -6, 14)

Answer:

6x -2 is the solved answer for the bracketed question.

Step-by-step explanation:

6x- 2 is not = to -6x -2

Answer: x=0

Step-by-step explanation:

if you are sloving fo x

2(3x-1) = -6x-2 cancel equal terms

6x-2=-6x-2 move the variable to the left

6x=-6x  collect like terms

12x=0 divide both sides

x=0

This tells us that c and k must be related such that ck = -0.03.This differential equation tells us that the rate of change of q with time (dq/dt) is equal to a negative constant, -0.03.

This differential equation tells us that the rate of change of q with time (dq/dt) is equal to a negative constant, -0.03. This means that q is decreasing over time. Therefore, c and k must be related such that ck = -0.03, since this constant is the product of c and k. This tells us that c and k must be related, but does not tell us the exact value of either c or k.

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Answer:

12x+5y

Step-by-step explanation:

Combine 3x and 9x to get 12x.

  hope it helped  :)

Answer:

C

Step-by-step explanation:

Answer:

y = 3 + 1/2 * x

Step-by-step explanation:

Answer:

Volume: 16.76 cm^3

Surface area: 40.67 cm^2

Step-by-step explanation:

To find volume, you use the formula V=πr^2*h/3

To find the surface area you use formula A=πr(r+√h^2+r^2)

Answer:

V = 16.76

Surface Area = 40.67

Step-by-step explanation:

V=πr2h

A=πrl+πr2

Answer:

1) Distributive Property of Multiplication (The terms are distributed)

2) Addition property of equality (Adding 14 to both sides)

3) Simplifying (We simplified the expression)

4) Division property of equality (Dividing both sides by 6)

Answer:

\(\boxed{\mathrm{view \: explanation}}\)

Step-by-step explanation:

- 14 + 6m = 10

Distributive Property of Multiplication

2 is distributed to -7 and 3m

- 14 + 14 + 6m = 10 + 14

Addition Property of Equality

Adding 14 to both sides.

6m = 24

Simplifying

Simplifying the equation.

\(\displaystyle \frac{6m}{6} =\frac{24}{6}\)

Division Property of Equality

Dividing both sides by 6.

Answer:

To determine how much Manuela earns for each hour of tutoring based on the given graph, we need to look at the slope of the line. The slope represents the change in earnings for each change in hours.

From the graph, we can see that when Manuela tutors for 2 hours, she earns $20, and when she tutors for 10 hours, she earns $80. So the change in earnings is $80 - $20 = $60.

Similarly, the change in hours is 10 - 2 = 8.

Therefore, the slope of the line (representing Manuela's hourly earnings) is:

slope = change in earnings / change in hours

slope = $60 / 8

slope = $7.50/hour

Therefore, Manuela earns $7.50 for each hour of tutoring.

The limit of sin(2x)/(9x) as x approaches 0 is 0.Therefore lim(x → 0) sin(2x) / (9x) = 0.

To find the limit as x approaches 0 for the function sin(2x)/(9x), we'll use the limit properties and the squeeze theorem.

Step 1: Recognize the limit
The given limit is lim(x → 0) sin(2x) / (9x).

Step 2: Apply the limit properties
According to the limit properties, we can distribute the limit to the numerator and the denominator:
lim(x → 0) sin(2x) / lim(x → 0) (9x).

Step 3: Apply the squeeze theorem
We know that -1 ≤ sin(2x) ≤ 1. Dividing both sides by 9x, we get:
-1/(9x) ≤ sin(2x) / (9x) ≤ 1/(9x).

Now, as x → 0, both -1/(9x) and 1/(9x) approach 0. Therefore, by the squeeze theorem, the limit of sin(2x)/(9x) as x approaches 0 is also 0.

So, lim(x → 0) sin(2x) / (9x) = 0.

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Step-by-step explanation:

Angle of four sides of rhombus is 360

125+p=360

p=360-125

p=235

hope this helps you

have a good day.

Answer:

Nahla can rent the boat for 9 hours.

Step-by-step explanation:

Nahla has $46 and a coupon for $8 off. Which you ADD to the total that she could spend.

46 + 8 = 54

If each hour costs Nahla $6, how many hours can she rent the boat for if she has a total of $54?

54 ÷ 6 = 9

Nahla can rent the boat for 9 hours.

Step 1

Given;

Required; How many ounces of water do 9 bottles hold?

Step 2

To do this we will use the ratio;

Answer;

Answer:

3*x=15

Step-by-step explanation:

i think-

Answer:

m∠6 = 148°

Step-by-step explanation:

From the figure attached,

AB and CD are two parallel line and another transverse line is intersecting these line at two distinct points.

Since, m∠1 = 32°,

∠1 and ∠4 are supplementary angles [Linear pair of angles]

m∠1 + m∠4 = 180°

32° + m∠4 = 180°

m∠4 = 180° - 32°

m∠4 = 148°

Since, ∠4 ≅ ∠6 [Alternate interior angles]

m∠4 = m∠6 = 148°

Therefore, m∠6 = 148°

Answer:

Step-by-step explanation:

see attached