Answer: C
Sn= 7(1-0.7n)
Step-by-step explanation:
The rule that defines S for [tex]a_n = 3(0.7)^n[/tex] is:
[tex]S_n = 7(1 - 0.7^n)[/tex]
The rule of S means that we calculate the rule that defines the sum of n terms of the geometric progression.
Given that:
[tex]a_n = 3(0.7)^n[/tex]
Rewrite as:
[tex]a_n = 3 (0.7)^n \times 1[/tex]
Replace 1 with 0.7/0.7
[tex]a_n = 3 (0.7)^n \times \frac{0.7}{0.7}[/tex]
Rewrite as:
[tex]a_n = 3 *0.7 \times \frac{(0.7)^n}{0.7}[/tex]
Apply law of indices
[tex]a_n = 3 \times 0.7 \times (0.7)^{n-1}[/tex]
[tex]a_n = 2.1 \times (0.7)^{n-1}[/tex]
The n term of a geometric progression is:
[tex]a_n = ar^{n-1}[/tex]
Compare [tex]a_n = ar^{n-1}[/tex] to [tex]a_n = 2.1 \times (0.7)^{n-1}[/tex]
[tex]a = 2.1[/tex] --- the first term
[tex]r = 0.7[/tex]
The sum of n terms of a geometric progression is:
[tex]S_n = \frac{a(1 - r^n)}{1 -r}[/tex]
This gives:
[tex]S_n = \frac{2.1(1 - 0.7^n)}{1 -0.7}[/tex]
[tex]S_n = \frac{2.1(1 - 0.7^n)}{0.3}[/tex]
[tex]S_n = 7(1 - 0.7^n)[/tex]
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Find the area of the segment enclosed by
chord [BC] and the subtended arc with
radius 4 cm and central angle 55⁰.
The area of segment enclosed by chord [BC] is 0.94 [tex]cm^{2}[/tex]
What is an area of Segment?Segment and area of a circle segment:
A segment is essentially the area of a circle between the chord and the arc. A circle is a path that a point equidistant from a single point on the plane can follow; this point is known as the circle's center, and the distance between it and that point is known as the circle's radius. A segment is a section of a circle's interior. A sector is the region that a segment encloses and the angle that a segment occupies. By deducting the triangle formed inside the sector from the sector where the segment is located, one can calculate the area of a circular segment.
Calculation:Given radius and angle subtended by arc on circle is 4 cm and 55° respectively.
So the length of chord [BC] is [tex]\frac{55}{180}[/tex]×π = 3.84 cm.
Required area of segment enclosed = Area of segment subtended by arc [BC] - area of ΔABC
>semi-perimeter of ΔABC is [tex]\frac{(4+4+3.84)}{2} = 5.92[/tex]
>Area of ΔABC is [tex]\sqrt{5.92*(5.92-4)*(5.92-4)*(5.92-3.84)} = 6.74 cm^{2}[/tex]
>Area of segment subtended by arc {BC} = θ/360° × π[tex]r^{2}[/tex]
=[tex]\frac{55}{180}[/tex]×16π
= 7.68[tex]cm^{2}[/tex]
∴The area of segment enclosed by chord [BC] is [tex]7.68-6.74 = 0.94 cm^{2}[/tex]
The area of segment enclosed by chord [BC] is 0.94 [tex]cm^{2}[/tex]
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these are the fees for sending a package by media mail: $\bullet$ $\$2.41$ for the first pound $\bullet$ $\$0.41$ per additional pound for the next six pounds $\bullet$ $\$0.39$ per additional pound after that for example, a two-pound package costs $\$2.82$ to send by media mail. if a package full of books costs $\$7.99$ to send by media mail, how many pounds does the package weigh?
The weight of the package is 15 pound.
What is an linear equation?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.
Given that the fees for sending a package by media mail
For first pound : $2.41
For the next six pounds: $0.41 per pound
For additional pound: $0.39 per pound
The cost of first 7 pounds is = $(2.41 + (0.41 × 6)) =$4.87
$4.87 < $7.99. Thus the weight of the package is more than 7 pounds
Assume that, the weight of the package is (7 + x) pound.
The fee for (7 + x) pounds package is $(4.87 + 0.39x)
According to the question:
4.87 + 0.39x = 7.99
Subtract 4.87 from both sides:
0.39x = 3.12
Divide both sides by 0.39
x = 8
The weight of the package is (8 + 7) = 15 pounds.
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a pole that is 3.2m tall casts a shadow that is 1.48m long. at the same time, a nearby building casts a shadow that is 42.25m long. how tall is the building? round your answer to the nearest meter.
To round to the nearest meter, use the units place and round to the nearest whole number. At the moment, we have a two in place of a one.
Which centimeter is closest?It is two divisions or two tenths of a mile short of the halfway point. Therefore, seven centimeters are the closest centimeters.
To figure out how to round, we look to the right, at the unit in the tens place.
Let x represent the unknown, which is the building's height.
level of post = level of the structure
level of the shadow level of the shadow
3.3 m = x
1.78 m 49. 75 m Find the solution for x: (3.3 m) (49.75 m) = x 1.78 m = x The building is 92 meters high, rounded to the nearest meter.
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4. The temperature is 36 °F. The temperature decreases for 4 hrs. Each hour, the temperature
decreases by 2 °F. Then the temperature rises 10 °F in one hour what is the temperature after 5
hours? (2 points)
a.) 26°F
b.) 38°F
c.) 50°F
d.) 62°F
Show your work:
38 °F is the temperature after 5 hours of time.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the temperature is 36 °F.
The temperature decreases for 4 hrs
Each hour, the temperature decreases by 2 °F.
1 hour= 2 °F.
For 4 hours it will be 4(2)=8 °F.
So the temperature after 4 hours is 36-8=28 °F.
the temperature rises 10 °F in one hour
28 °F+10°F=38 °F
Hence, the temperature after 5 hours is 38 °F.
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Can anyone help me find this answer fast.
Answer:
8cm
Step-by-step explanation:
We can figure out what the side length of this would be by squaring the area.
[tex]\sqrt{64}[/tex] = 8
To check our work, we can multiply the length by the height. (8 and 8)
8 × 8 = 64
Nado's chessboard side length would be 8cm.
What would the ratio be if you partition a line segment at point?
Part A Find the y-intercept and slope of the line.
Answer:
y-intercept = (0,6)
slope = -2
Step-by-step explanation:
⭐What is the slope of a line?
The slope of a line is how steep the line is⭐How can we find the slope of a line?
Use the formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]m = the slope[tex](x_1,y_1)[/tex] is one of the coordinates of the given line[tex](x_2, y_2)[/tex] is another coordinate of the given lineTo find the slope, pick two coordinates you see on the line, substitute them into the slope formula, and solve for the slope!
I am choosing the coordinates (0,6) and (3,0), but you can choose any 2 coordinates that you see on the line.
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{0-6}{3-0}\\m = \frac{-6}{3}\\m = -2[/tex]
∴ The slope of the line is -2.
⭐ What is the y-intercept of a line?
The y-intercept of a line is the point (0,y) at which the line intersects the y-axis⭐How do we find the y-intercept of a line?
Look at the graphFind the corresponding y-coordinate for when x=0When x=0, y=6
∴ The y-intercept of the line is (0,6)
How do you prove a shape is symmetrical?
By drawing a mirror line across the center of a shape and examining if both halves are the same, you may determine whether it is symmetrical.
When anything has two identical parts, it is symmetrical. In other terms, symmetry is the presence of identical pieces facing one another or revolving around an axis.
But what attributes give a shape symmetry? A symmetrical shape has an identical side on the side, also known as symmetry. When mirrored, rotated, or translated, symmetrical shapes retain their original appearance. The four main subcategories of symmetry are translation, rotation, reflection, and glide reflection. However, the primary type of symmetry in mathematics taught in schools is reflectional symmetry, commonly referred to as mirror symmetry or line symmetry.
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Why is f called a linear function?
For a given function f, it is linear if the function has a constant slope and it doesnot contain the power of x greater than 1.
What is a function?An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
What does a linear function represent?A function which is also linear, represents a straight line in the graph. The graphs to the linear functions are straight lines which have constant slope throughout the graph.
A function f is referred to as linear if it meets both of the following criteria:
The slope of the function is constant. This indicates that the slope of the line is constant, independent of the value of x that you enter into the function.
There are no powers of x bigger than 1 in the function. This indicates that there are no terms in the function that have x2, x3, etc.
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Least common multiple of 5y^2-45 and y+3
The common multiple of 5y²- 45 and y + 3 is (y + 3).
What is meant by common multiple?For any two or more expressions, if any one of their factors is common in all of them, then that factor is said to be the common multiple of those expressions.
Calculation:The given expressions are 5y²- 45 and y + 3
On factorizing them, we get
5y²- 45 = 5(y² - 9)
⇒ 5(y² - 3²)
From he binomial formula a² - b² = (a + b)(a - b), we can write
5y²- 45 = 5(y + 3)(y - 3)
Now, the second expression has no further simplification. The expression is itself a factor for it.
So, we can write their factors as
5y²- 45 = 5 × (y + 3) × (y - 3)
y - 3 = 1 × (y - 3)
From this, (y - 3) is the only factor that is a common factor for both the expression.
So, (y - 3) is the common multiple for the given expressions.
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Hi. May i please have help with these problems? Who wrote the book 'Terrible Weather"?" Ag Perez Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke. B. 4 1. 5x - 7 = 4x +3 Y. No Solution X= to N. 10 2. 6 + 2x = 7x - 9 ... X = - 3 1. - 11 3. 8x + 1 = - 8 - x S. -2 X=1 4. -5+ 12x = 18x + 7 P. 3 X=-2 V . -7 5. -4x + 3 = 5x - 13 - x E. 1 6. -10 - 11x + 24 = 3x W. 5 F. - 6 7. 8 + 3x = x + 11 + 2x 0. 3 No sofmar 8. 5 +'17x +9 = 2x + 21x + 14 A. 1 R. 2 9. 6x + 8 - 13x + 10 = 4 - 6x - 11 + 4x W. 8 10. -14 + 5 - X - 3 =x+6+x+3x Y. -13 D. O AYN 9 3 7 1 6 S 8 5 2 10 4 e #20 Solving Equations: Variables on Both Sides and Collecting L
The Answers to the Equation is shown below.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
1. 5x - 7 = 4x +3
5x- 4x = 3 + 7
x= 10
2. 6 + 2x = 7x - 9
7x- 2x = 6+9
5x = 15
x= 3
3. 8x + 1 = - 8 - x
9x = -9
x= -1
4. -5+ 12x = 18x + 7
6x = -12
x= -2.
5. -4x+ 3= 5x- 13 -x
-8x = -16
x= 2
6. -10 - 11x + 24 = 3x
14x = 14
x=1
7. 8 + 3x = x + 11 + 2x
No Solution
8. 5 +17x +9 = 2x + 21x + 14
6x= 0
x=0
9. 6x + 8 - 13x + 10 = 4 - 6x - 11 + 4x
-5x= 25
x= -5
10. -14 + 5 - x - 3 =x+6+3x + x
4x= -14
x= -3.5
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A wood stove burns 24 same sized logs in 5 hours. How many can I burn in 8 hours?
Answer: 38
Step-by-step explanation:
24 divided by 5 = 4.8 per hour
4.8 times 8 = 38.4 or 38 in 8 hours
It can burn 38 in 8 hours
What is slope in graph example?
The level of a line's slope indicates its steepness.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
That is to say,
Determine the coordinates of two locations along the line that one choose.Evaluate the differences in these two positions' y-coordinates (rise).Evaluate the differences in these two locations' x-coordinates (run).In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates.Example -
This line goes through the points (0,0) and (4,4).
Now, slope = (y₂ - y₁) / (x₂ - x₁)
slope = (4 - 0) / (4 - 0)
slope = 4 / 4
slope = 1
So, from the above calculation it is shown that, the slope of the line is 1.
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What are the roots of the quadratic equation √ 2x 2 7x 5 √ 2 0?
x=-5/√2 and x=-√2 are roots of the quadratic equation √2x²+7x+5√2=0
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The given quadratic equation is √2x²+7x+5√2=0
We will factorize the middle term by middle term method
√2x²+2x+5x+5√2=0
√2x(x+√2)+5(x+√2)=0
(√2x+5)(x+√2)=0
√2x+5=0
√2x=-5
Divide both sides by √2
x=-5/√2
and x+√2=0
x=-√2
Hence, x=-5/√2 and x=-√2 are roots of the quadratic equation √2x²+7x+5√2=0
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What is postulate and theorem?
A postulate is an unsupported assertion that is taken to be true. A provable true assertion is referred to as a theorem.
What is meant by postulate ?A claim that is accepted as true without evidence, also referred to as an axiom. For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry. An unsupported assertion is referred to as a postulate. A postulate is also referred to as an axiom. For instance, you would believe Pam if she claimed that all of her siblings are at least five foot one tall if you knew that she is five feet tall and that all of her siblings are taller than her. A postulate is an unsupported assertion that is taken to be true. A provable true assertion is referred to as a theorem.To learn more about postulate refer to:
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Use the order of operations to order the steps to evaluate the expression (60+15)/3-2(4)+2^3
Answer:
25
Step-by-step explanation:
(60+15)/3-2(4)+2^3
75/3 -2 x4 + 2^3
75/3 - 8 +2^3
75/3 - 8 +8
75/3
25
What is HCF and LCM formula?
The HCF and LCM are Highest common factor and Least common multiple respectively
What is HCF and LCM?
The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers
Product of HCF x LCM = product of two numbers
Given data ,
Let the two numbers be A and B
The value of A is A = 160
The value of B = 252
HCF is the product of common prime factors
So , Prime Factorization of 160: 2 x 2 x 2 x 2 x 2 x 5
And , Prime Factorization of 252: 2 x 2 x 3 x 3 x 7
So , HCF = 2 x 2 = 4
Now, finding LCM of 160 and 252
LCM is the product of all factors of both numbers
Prime Factorization of 160: 2 x 2 x 2 x 2 x 2 x 5
Prime Factorization of 252: 2 x 2 x 3 x 3 x 7
LCM= 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7
LCM= 10080
Now , the product of HCF x LCM = product of two numbers
160 x 252 = 40320
4 x 10080 = 40320
Hence , the HCF and LCM are solved
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What is called discontinuity?
A discontinuity in mathematics is when a function is not well defined
How to identify discontinuity?As earlier defined, discontinuity deals with a function that is not well defined.
Different functions have different discontinuity depending on the function
Good examples of discontinuity include
y=1/x this is a discontinuous function.
x=0 is also a discontinuous function as it is not well defined. because there is no value for y
The function TanA is a discontinuous function because it is not well defined.
Other discontinuities include
y=5п/3, 9п/4, 6п8, 4п/3
All these are discontinuous functions
In conclusion, a discontinuity in mathematics is when a function is not well defined
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What to numbers can equal 16?
1, 2, 4, 8, and 16 are the components that make up 16. Similarly, the negative components of 16 are -1, -2, -4, -8, and -16. factors of 16: 1, 2, 4, 8, and 16.
What two numbers make 16?The natural number 16 (or sixteen) comes after the number 15 and before the number 17. Since 42 = 4 4 is a square number, the number 16 is both a composite and a square. It has precisely five correct divisors, making it the lowest number. These are 1, 2, 4, and 8. The numbers 16 and 60 sound remarkably similar in English speech, which might lead to confusion.
There are three factor pairs of 16:
1 × 16 = 16.
2 × 8 = 16.
4 × 4 = 16.
1, 2, 4, 8, and 16 are the 16 factors. Likewise, the unfavorable factors of 16 are -1, -2, -4, -8, and -16. 1, 2, 4, 8, and 16 make up the number 16.
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Estimate the height of the tree 50 years after it was planted. How did you
make your prediction?
Estimate the height of the tree 50 years after it was planted is 15.92 feet
How to Find the height of the tree?DBH (inches) × π = Estimated Age of Tree (years)
Let us Consider inches is X
X *3.14=50
X=50/3.14
X=15.92
sheet of paper :There is no need for math or other instruments!Shadows: Needs a tape measure, a level surface, discernible shadows, and simple mathematics.Pencil: A quick, rough estimate made with a pal and a pencil.The most precise tools are the clinometer or instruments. You can create your own clinometer using common classroom items. If you don't know when a tree was planted, it might be quite difficult to determine its age. However, an approximate estimation method based on the trunk's circumference can be used to determine the age of the tree.The International Society of Arboriculture (ISA) first presented this method, which is based on a straightforward calculation that use the tree's diameter at breast height (DBH), which is the tree's circumference.To learn more about to find height of the tree refer to:
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multiply 17m 25cm by 24
Step-by-step explanation:
To multiply 17m 25cm by 24, you need to first convert the units of measurement to a common unit, such as meters or centimeters.
17m 25cm can be written as 17.25 m, since 1 meter is equal to 100 centimeters. Therefore, to multiply 17.25 m by 24, you can simply perform the calculation as follows:
17.25 m * 24 = 413 m
This means that the result of the multiplication is 413 meters.
Alternatively, you could express the result in centimeters by performing the calculation as follows:
(17 m * 100 cm/m) + (25 cm * 24) = 1700 cm + 600 cm = 2300 cm
This means that the result of the multiplication is 2300 centimeters.
Prove the following statement using the given pieces of information.
Given: Line AB is parellel to Line DC and Line AD is parellel to Line BC.
Prove: Triangle ABC is congrent to Triangle CDA.
Triangle ABC is congruent to Triangle CDA using the SSS rule.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
SSS rule states that,
If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.
To prove:
ΔABC ≅ ΔCDA.
AB = DC ( given)
AD = BC (given)
AC = AC (common to both the triangles)
ΔABC ≅ ΔCDA ( By SSS rule )
Thus,
ΔABC ≅ ΔCDA by SSS rule.
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When can kids sing ABC?
Therefore , the kids can able to sings alphabets ABC by the age of 2 and by age of 4 children frequently know every letter of the alphabet .
What is alphabet?In alphabet, set of graphs, or characters, used to represent the phonemic structure of a language .The characters are often placed in a specific order, or sequence, in most alphabets (e.g., A, B, C, etc.).
Here,
By the age of two, children can sing or say out loud the "ABC" song and begin to recognise some letters.
By the age of three, children may recognise around half of the alphabet's letters and begin to associate letters with their sounds.
(S makes the sound /s/.)
Most kids are familiar with all 26 letters of the alphabet and their order by the time they are four years old.
Therefore , the kids can able to sings alphabets ABC by the age of 2 and by age of 4 children frequently know every letter of the alphabet .
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Children can begin to sing the alphabet by the time they are two years old.
Define the term alphabet.The phonemic structure of a language is represented by an alphabet, which is a system of graphs or symbols. In most alphabets, the characters are frequently arranged in a certain order, or sequence (e.g., A, B, C, etc.).
How many alphabets are there?There are 26 alphabets named from A to Z.
By the time they turn two, kids can sing or say the "ABC" song aloud and start to recognize some letters.
Around half of the alphabet's letters may be recognized by three-year-old, and they are starting to connect letters with sounds.
By the time they are four years old, the majority of children are familiar with all 26 letters of the alphabet and their placement.
As a result, children can begin to sing the alphabet by the time they are two years old, and by the time they are four, many of them are already familiar with all 26 letters.
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Hi! I really need help with this problem
Sandra et the cruie control in her car to 69 mile per hour when he goe on road trip. Which equation can be ued to find how many hour, h, it will take her to drive m mile at her contant peed?
A. B. C. D
Sandra sets the speed to 69 miles per hour. The equation that express how many hours it will take her to drive m miles is: h = m/69.
Speed or velocity 69 miles per hour means: in 1 hour she will travel 69 miles
69 miles need 1 hour
1 miles need 1/69 hours
m miles need m x 1/69 hours.
If h is the amount of time need to take her to drive m miles, then:
h = m x 1/69 = m/69 hours
We can also solve the problem, using formula:
s = vt
Where:
s = distance
v = speed = 69 mph
t = time
In the given problem, the distance is m, hence s = m, and t = h
Hence,
t = s/v
h = m/69
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THIS IS THE QUESTION I NEEED ANWSERED ASAP
For the shaded region given in the diagram the area is obtained as 50.2 cm². The correct option is (A).
What is a circle?A circle is a geometric shape, all of which points are equidistant from a fixed point called as the center.The center of the circle does not lie on it. The angle subtended by the semicircle on its any point is always a right angle.
The diameters of the external and internal circle are 10 cm and 6 cm.
Then, the radius are given as 10/2 = 5 cm and 6/2 = 3 cm
Now, area of the shaded region is given as follows,
Area of external circle - Area of internal circle
= π × 5² - π × 3²
= 16π
= 50.2
Hence, the area of the shaded region is given as 50.2 cm².
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What is the range of f/x )= A x?
On observing the provided question we can say that - the function f(x) = [tex]a^x[/tex] is Domain: (−∞,∞) or all real numbers
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
The answer to the question is that all real numbers or (−∞,∞)
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the dat set for a random sample of 10 baseball players heights compared to their show sizes is summarized in the table. PLEASE!!!!!! HELP!!!!
Answer: a) The equation of the least-squares regression line is y = -1.66x + 78.83. b) Residual = 7.11 inches. c) The residual is the deviation of a data point from the fitted regression line. In this case, the residual is 7.11 inches, indicating that the player who wears a size 9 and is 71 inches tall is taller than what would be expected based on the trend in the data.
Step-by-step explanation:
What is the least square regression and residual?
Least squares regression is a statistical method that is used to find the line of best fit for a set of data points. It involves finding the line that minimizes the sum of the squares of the differences between the actual data points and the predicted values on the line. The residual is the difference between the actual data point and the predicted value on the line.
Part A: The equation for the least-squares regression line can be found by using the following formula: y = bx + a
To find the values for a and b, we need to calculate the following values:
x: the mean of the shoe sizes,
y: the mean of the heights.
S x y: the sum of the products of the differences between the shoe sizes and x and the differences between the heights and y.
S x x: the sum of the squares of the differences between the shoe sizes and x.
X = (7+10+12+8+9.5+10+11.5+12.5+13.5+10) / 10 = 10.5
Y = (64+69+72+67+69+70+75+73+71+68) / 10 = 69.4
To find S x y and S x x, we use:
S x y = ∑(x - x)(y - y)
S x x = ∑(x - x)^2
Inserting the values from the table, we get:
S x y =-47.5
S x x = 28.5
Using values, we can calculate the slope and y-intercept of the least-squares regression line:
b = S x y / S x x = -47.5 / 28.5 = -1.66
a = y - bx = 69.4 - (-1.66)(10.5) = 78.83
So the equation of the least-squares regression line is y = -1.66x + 78.83
Part B: We can use the equation for the least-squares regression line to determine the residual for a player who wears a size 9 and is 71 inches tall. We calculate the player's height using the size 9 into the equation:
y=-1.66x+78.83=63.89 inches.
The residual is then calculated by deducting the expected height from the actual height: 7.11 inches =71- 63.89 inches.
Part C: The residual is the variation between the dependent variable's actual value (height) and its anticipated value according to the least-squares regression line. The athlete in this instance, who wears a size 9 and is 71 inches tall, is taller than what might be anticipated based on the trend in the data, according to the residual of 7.11 inches.
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The equation of the least-squares regression line is y = -1.66x + 78.83. b) Residual = 7.11 inches.
What is the least square regression and residual?
Least squares regression is a statistical method that is used to find the line of best fit for a set of data points. It involves finding the line that minimizes the sum of the squares of the differences between the actual data points and the predicted values on the line. The residual is the difference between the actual data point and the predicted value on the line.
Part A: The equation for the least-squares regression line can be found by using the following formula: y = bx + a
To find the values for a and b, we need to calculate the following values:
x: the mean of the shoe sizes,
y: the mean of the heights.
S x y: the sum of the products of the differences between the shoe sizes and x and the differences between the heights and y.
S x x: the sum of the squares of the differences between the shoe sizes and x.
X = (7+10+12+8+9.5+10+11.5+12.5+13.5+10) / 10 = 10.5
Y = (64+69+72+67+69+70+75+73+71+68) / 10 = 69.4
To find S x y and S x x, we use:
S x y = ∑(x - x)(y - y)
S x x = ∑(x - x)^2
Inserting the values from the table, we get:
S x y =-47.5
S x x = 28.5
Using values, we can calculate the slope and y-intercept of the least-squares regression line:
b = S x y / S x x = -47.5 / 28.5 = -1.66
a = y - bx = 69.4 - (-1.66)(10.5) = 78.83
So the equation of the least-squares regression line is y = -1.66x + 78.83
Part B: We can use the equation for the least-squares regression line to determine the residual for a player who wears a size 9 and is 71 inches tall. We calculate the player's height using the size 9 into the equation:
y=-1.66x+78.83=63.89 inches.
The residual is then calculated by deducting the expected height from the actual height: 7.11 inches =71- 63.89 inches.
Part C: The residual is the variation between the dependent variable's actual value (height) and its anticipated value according to the least-squares regression line. The athlete in this instance, who wears a size 9 and is 71 inches tall, is taller than what might be anticipated based on the trend in the data, according to the residual of 7.11 inches.
c) The residual is the deviation of a data point from the fitted regression line. In this case, the residual is 7.11 inches, indicating that the player who wears a size 9 and is 71 inches tall is taller than what would be expected based on the trend in the data.
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How many terms are there in the expression 2y +10x+ 5 *?
What is the first step in solving a polynomial inequality?
The first step in solving a polynomial inequality is to determine the type of inequality that you are dealing with. There are two types of polynomial inequalities: strict inequalities and non-strict inequalities.
Strict inequalities are inequalities that are either less than or greater than a value, but not equal to it. For example, the inequality x < 4 is a strict inequality because it means that x is strictly less than 4 (i.e., it is less than 4 but not equal to 4).
Non-strict inequalities are inequalities that are either less than or equal to, or greater than or equal to a value. For example, the inequality x <= 4 is a non-strict inequality because it means that x is less than or equal to 4 (i.e., it is either less than 4 or equal to 4).
Once you have determined the type of inequality that you are dealing with, you can proceed to the next step, which is to solve the inequality by isolating the variable and performing the necessary operations to find the solution.
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