Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.
Exponents of polynomials are whole numbers.
Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.
If an operation results in the production of another polynomial, the resulting polynomials will be closed.
The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.
The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.
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What is the smallest positive multiple of $13$ that is greater than $500?$
Answer:
Step-by-step explanation:
The smallest possible multiple of 13 dollars greater than 500 dollars would be 507 which is 13*39 (i assume you mean whole numbers when you say positive numbers, if not the other answer would be 13*38.461)
A group of 36 people from the Nantucket recreation center plans to purchase tickets for a cruise to Permut Bermuda the standard fare for an individual ticket is $1200 the group is informed that because of the size of the group the standard fare will be reduced by 30% with a discount of 30% how much does each member of the Nantucket recreation center have to pay for a cruise ticket show or explain how you got your answer (SOMEONE PLEASE HELP)
The total amount each member of the Nantucket recreation center have to pay after the discount is given by the equation A = $ 840
What is an 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.
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 data ,
Let the total amount for each person after discount be represented as A
Now , the equation will be
The total number of people in the group = 36
The standard fare for each person = $ 1200
So , the total cost of the fare = total number of people x standard fare for each person
Substituting the values in the equation , we get
The total cost of the fare = 1200 x 36
The total cost of the fare = $ 43,200
Now , the discount percentage = 30 %
So , the amount after discount = total cost of the fare - total cost of the fare x discount percentage
Substituting the values in the equation , we get
The amount after discount = 43,200 - ( 30/100 ) x 43,200
The amount after discount = 43200 - 12960
The amount after discount = $ 30,240
Now ,
Total amount for each person after discount A =amount after discount / 36
Total amount for each person after discount A = 30,240 / 36
On simplifying the equation , we get
Total amount for each person after discount A = $ 840
Therefore , the value of A is $ 840
Hence , the amount is $ 840
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At Central Middle School the 108 students who take the AMC 8 meet in theevening to talk about problems and eat an average of two cookies apiece.Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe,1 which makes a pan of 15 cookies, lists this items: 1- cups of flour, 2 eggs, 323 tablespoons butter, cups sugar, and 1 package of chocolate drops. They will 4 make only full recipes, not partial recipes.Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cookies? (Some eggs and some cookies may be left over.)(A) 1(B) 2(C) 5(D) 7 (E) 15
5 half-dozens he should buy to make enough cookies.
What is an average?
Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or a figure that lies halfway between two extremes.
Here, we have
If 108 students eat 2 cookies on average, there will need to be 108× 2 = 216 cookies.
There are 15 cookies per pan, meaning there need to be {216}/{15} = 14.4 pans.
However, since half-recipes are forbidden, we need to round up and make{216}/{15} = 15 pans.
1 pan requires 2 eggs, so 15 pans require 2×15 = 30 eggs.
Since there are 6 eggs in a half dozen,
we need 30/6 = 5 half-dozens of eggs.
Hence, 5 half-dozens he should buy to make enough cookies.
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For what value of k do the pair of linear equations KX − 4y 3 and 6x − 12y 9 have an infinite number of solutions?
The pair of linear equations KX − 4y = 3 and 6x − 12y = 9 have an infinite number of solutions when K = 0.
This can be shown by solving the two equations for K. Solving the first equation for K yields K = (4y/X) + 3. Substituting this into the second equation yields: 0 = (4y/X) + 3 - (12y/6x). Simplifying this yields 0 = (2y/X) - (9/6x). This equation simplifies to 0 = (2y - 9x)/X. Since the denominator of the right side of the equation is not equal to 0, the only way to get 0 = 0 is if the numerator is equal to 0 as well. This happens when 2y - 9x = 0. Since y and x are variables, the only way that this equation can be true for all values of x and y is if the coefficient of both of them is equal to 0. Thus, K = 0 is the only value for which this pair of linear equations has an infinite number of solutions.
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please help me
please help me
pls answer all questions
Spiders are arachnids with eight legs, as do all arachnids. Spiders differ from insects in that they have only six legs.
Do spiders have 6 or 8 legs?Crabs and prawns are also members of the phylum Arthropoda, which includes spiders. Spiders walk on eight legs, but they also have two additional legs that they utilise as hands. The front legs are called pedipalps, or palps for short.
Proteins are secreted by glands on spiders, which aid in the formation of the web. For a number of objectives, including prey capture, prey detection, tunnel lining, egg sacs, and prey wrapping, spiders can create a variety of webs or silks.
Spiders are venomous carnivores who hunt their prey with poison.In Everglades National Park, arachnids such as spiders, scorpions, mites, ticks, whip scorpions, and pseudoscorpions are all common.
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What is the equation of the straight line shown below? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms. Y 14- 13- 12- 11- 10- 9 8- 97654 MNE 7- 6- 5- 4- 3- 2- 1- -10-9-8-7-6-5-4-3-2 0 1 2 3 4 5 6 7 8 9 10 x -1 -2- -3- بنا -4- 56 -5- -6+
Answer:
y = 2x + 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line
m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2
the line crosses the y- axis at (0, 10 ) ⇒ c = 10
y = 2x + 10 ← equation of line
What is the center of a circle (x y) with the equation (x + 3)^2 + (y − 5)^2 = 16
Step-by-step explanation:
the center of the circle is (−3,5) and radius is 16 =
What equation represents this sentence?
5 less than a number is 12.
5=n-12
n-5=12
5-n=12
5=12-n
ill give brainliest its due at 11:59 its 8pm
Answer:
I'm sure its 5=n-12 :))))
If it is 10:00 A.M. Friday in Miami, Florida Eastern time zone (based on 75o W), what is time and day is it in Los Angeles California (120oW), Pacific Time zone
Therefore, the answer to the time dilemma is 7 am on Friday, which is the right choice.
Define time.In mathematics, time is described as a continuously and continuous series of events that take place in chronologically from the past through to the present and into the future. The duration of events, the gaps between them, or even the sequence of occurrences can all be quantified, measured, or compared using time.
Here,
If it is 10 a.m. on Friday in Miami, Florida's Eastern time zone, it is 7 a.m. on Friday in Los Angeles,
California's (120 o W) pacific time region
since Miami, Florida's Eastern time zone is three hours early of Los Angeles.
Thus,
the correct response is 7 am on Friday.
Therefore, the answer to the time dilemma is 7 am on Friday, which is the right choice.
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43 inches tall. Each book 1/2 - inch thick
Answer:
If you're asking how many books there are its 86.
Step-by-step explanation:
If each book is 1/2 thick that means there are 2 books per inch.
Because there are 43 inches you're going to multiply by 2.
43(2)= 86.
Hope that helped, have a good day!
Use Pascal's Triangle to expand (5z + 5x²)³. Express your
answer in simplest form.
The simplest form is 15z+ 15x²
How to simplify the given expression ?In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)n. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.
Because it has so many patterns that can be used to greatly simplify complex calculations, Pascal's triangle is significant.
Given,
(5z+5 x²)3
15z+15x² by simplifying,
3(5z+5 x²)
apply the distributive formula :a (b + c) =ab + ac
3(5z+5 x²) = 5x+3 * 5x²
By simplifying 3 5z+3 , 5x², 15z+15x²
we get
15z+ 15x²
Therefore the simplest form is 15z+ 15x² .
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look at picture please
The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ
What are trigonometric identities?Trigonometric identities are equations which contain the trigonometric ratios.
How to show the equivalent identity of cot²θ + 1?Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.
So, we proceed as follows
Since cot²θ + 1 = 1/tan²θ + 1 (since cot²θ = 1/tan²θ)
Now taking the L.C.M, we have that
1/tan²θ + 1 = (1 + tan²θ)/tan²θ
We know that the trigonometric identity 1 + tan²θ = sec²θ
So, substituting this into the equation, we have that
(1 + tan²θ)/tan²θ = sec²θ/tan²θ
Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that
sec²θ/tan²θ = cot²θsec²θ
So, cot²θ + 1 = cot²θsec²θ
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Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of % in hr
The expression when Buffalo New York had 2ft of snow on the ground before a snowstorm is 2 - 0.25h.
How to illustrate the expression?From the information, Buffalo New York had 2ft of snow and we want to find the. expression based on the information given.
An expression have at least two terms which have to be related by through an operator.
Since Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. The expression will be:
2 - (25% × h)
= 2 - 0.25h
h = number of hours.
The expression is 2 - 0.25h.
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Complete question
Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. Illustrate the expression
- 3 (x + 8) ^ 2 - 3
Answer:
-3x + 549
Step-by-step explanation:
The order of operations is PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction)
So, according to PEMDAS, the first thing that we would do is solve the parenthesis. Since we can't solve the parenthesis because they aren't like terms, we're going to use distributive property to solve it instead.
-3(x+8) = -3(x) + -3(8) = -3x -24
Now we have: -3x - 24 ^ 2 -3
Our next step is to solve the exponent
24 ^ 2 or 24 x 24 = 576
Now we have: -3x - 24 + 576 -3
Our next step would be to add and subtract the like terms
-24 + 576 = 552 and 552 - 3 = 549
Now we have: -3x + 549
This would be the simplest form of the equation because -3x and 549 are not like terms
Write the equation of the given function in vertex- and standard form.
f(x)
-2
2+
N
X
-1
0
1
2
3
4
f(x)
-5
0
3
4
3
0
The standard form of the function is f(x) = -x² +4x, The vertex form isf(x) = -(x-2)² + 4
What is a function?
A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
Given table is
x f(x)
-1 -5
0 0
1 3
2 4
3 3
4 0
Find the difference to find the degree of the given function
f(x) -5 0 3 4 3 0
1st difference 5 3 1 -1 -3
2nd difference -2 -2 -2 -2
The degree of the function is 2.
The general form of a second-degree function is
f(x) = ax²+bx+c
Putting x = 0 and f(0) =0 in f(x) = ax²+bx+c:
f(0) = a×0²+b×0+c
0 = c
Now putting x = 1 and f(1) =3 in f(x) = ax²+bx+c:
f(1) = a×1²+b×1+0 [since c=0]
3 = a + b ....(i)
Now putting x = 2 and f(2) =4 in f(x) = ax²+bx+c:
f(2) = a×2²+b×2+0 [since c=0]
4 = 4a + 2b ....(ii)
Solve equations (i) and (ii) by using the elimination method:
Multiply equation (i) by 2 and subtract it from (ii)
4a + 2b = 4
2a + 2b = 6
(-) (-) (-)
__________
2a = -2
a = -1
Putting a = -1 in equation (i):
-1 + b = 3
b = 3+1
b = 4
The function is f(x) = -x² +4x
Rewrite the given function in vertex form:
f(x) = -(x² - 4x +4-4)
f(x) = -(x-2)² + 4
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Sam recorded the effects of exercise on short-term memory. Which of these is a response variable ?
A. Exercise
B. Neither exercise nor short-term memory
C. Short term memory
D. Both exercise and short-term memory
Short term memory is a response variable as it is dependent. Hence Option C is the answer.
What is response variable?A dependent variable is the response variable. It is reliant on the independent variable, which serves as the explanatory variable.
What is the predicting factor?Explanations for the findings revealed by the response variables are provided by the explanatory or independent variables. Explanatory response is qualitative since it is classified based on a category.
The response variable is what the researcher often measures in research studies. The response variable in the example presented above is short-term memory, which is influenced by exercise.
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The the mesure of……..
The measure of angle B is 82°
What is angle ?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
∠A = 180° - 143°
= 37°
∠A + ∠B + ∠C = 180°
37° + ∠B + 61° = 180
∠B = 180 - 61 - 37
= 82°
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Use pattern blocks to represent each multiplication equation. Use the trapezoid to
represent 1 whole.
a. 3 • 1/3 = 1
b. 3 • 2/3 = 2
when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,
Describe area.The size of a region on a flat or curved surface is expressed mathematically as area. The area of a form is defined as the "space encompassed inside the perimeter or the border." The area of various shapes is calculated using mathematical methods.
given
The trapezoid's surface area is 70 units.
first base is worth 20 units, while second base is worth 10 units.
how long CE
[tex]1/2(b1 + b2)*h is the area of a trapezoid.\\70= 1/2 (20 + 10 )*h\\70 = 1/2(30)*h\\4.6 units of h[/tex]
when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,
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A whale is swimming due north at a speed of 40 kilometers per hour. Just 6 kilometers away,
a whale-watching tour boat is traveling south, directly toward the whale, at a speed of 83
kilometers per hour. How long will it be before they meet?
Answer:
O hrs and 30 minutes is the answer
Step-by-step explanation:
want proof?
Answer:
about 0.04878 hours ≈ 2 minutes 56 seconds
Step-by-step explanation:
You want the time until a whale-watching boat and a whale meet if the boat is traveling south at 83 km/h and the whale is traveling north at 40 km/h when they start 6 km apart.
Closing speedThe speed at which the gap between the boat and the whale is closed is the sum of their respective speeds:
closing speed = 83 km/h + 40 km/h = 123 km/h
TimeThe time it takes to close the 6 km gap is ...
time = distance/speed
time = (6 km)/(123 km/h) ≈ 0.04878 h
Converted to minutes and seconds, that is about ...
0.04878 h ≈ 2 minutes 55.6 seconds
It will be about 2 minutes 56 seconds before the boat and whale meet.
__
Additional comment
NOAA recommends a distance of at least 100 yards be maintained between a boat and a whale. In some areas, the recommended distance is 400 yards when approaching head-on. The recommended boat speed is 15 knots or less, about 28 km/h.
a paint roller has a width of 12 inches and a radius of 3 inches, what is the surface area that can be painted with one complete rotation of the roller
The surface area that can be painted with one complete rotation of the roller is 226.19 inches².
Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.
A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.
SA = 2πrh
where SA = surface area
r = radius of the base = 3 inches
h = height of the cylinder = width = 12 inches
Plug in the values and solve for the surface area.
SA = 2πrh
SA = 2π(3 inches)(12 inches)
SA = 226.19 inches²
Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².
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Please look at image.
Answer:
Step-by-step explanation: its 90
Answer:
y=90°
since,70°+(X+X)+(180°-110°)=180°
or,70°+2X+180°-110°=180°
or,2X-40°=0
or,2X=40°
:.X=20°
Also,
X+y+70°=180°
or,y+90°=180°
:.y=90°
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: Find the pherical coordinate of the point whoe rectangular coordinate are
(-2, 2√3,4)
The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
What is a peripheral coordinate?
A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.
To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:
[tex]r=\sqrt{(x^2 + y^2 + z^2)} = \sqrt{((-2)^2 + (2\sqrt3)^2 + 4^2)} = \sqrt{(4 + 12 + 16)} = \sqrt32 = 4\sqrt2[/tex]
θ = [tex]tan^{-1}(y/x) = tan^{-1}(2\sqrt3/(-2)) = tan^{-1}((-\sqrt3)/1) = -60^o[/tex]
φ = [tex]cos^{-1}(z/r) = cos^{-1}(4/4\sqrt2) = cos^{-1}(1/\sqrt2) = \degree 45 ^o[/tex]
So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
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The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
What is a peripheral coordinate?
A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.
To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:
[tex]r=\sqrt{x^2+y^2+z^2} = \sqrt{(-2)^2+(2\sqrt{3})^2+4^2}=4\sqrt{2}[/tex]
θ = [tex]tan^{-1}(y/x)=tan^{-1}(2\sqrt{3}/(-2))=60^o[/tex]
φ = [tex]cos^{-1}(z/r)=tan^{-1}(4/4\sqrt{4})=45^o[/tex]
So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
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HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
x > 3
Step-by-step explanation:
6x - 2 - 3x + 9 > 16
3x + 7 > 16
3x > 9
x > 3
pls solve me this functions question
On solving the provided question, we can say that - the value of the function is f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]; f(x) = x= it doesn't factor
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
f(x) = [tex](x+3)^2 - 5[/tex]
f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]
f(x) = x= it doesn't factor
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The scale drawing of a building has a height of 10 centimeters. The actual building is 20 feet high. How many centimeters in the scale drawing represent one foot on the actual building?
a. 1/2
b. 30
c. 10
d. 2
Answer: 1/2
Step-by-step explanation:
The question is asking you to find how many centimeters in the scale drawing equal 1 foot on the actual building. The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter, or A.
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ORIGINAL ANSWERS PLEASE
A student's course grade is related to class attendance. The grade can be modeled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. For a student who was in attendance for 75 days and has a grade of 82%, find and interpret the residual.
The residual of the given situation is 0.8
What is residual of a function?The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.
Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,
Finding the actual value,
y = 0.66 × 75 + 33.3
y = 82.8
The predicted value = 82
Residual = actual y value − predicted y value
Therefore,
Residual = 82.8-82 = 0.8
Therefore, y = 0.8
Hence, the residual of the given situation is 0.8
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The top-notch middle school had athletes from all the grades playing on a sports team. 6th grade 7th grade 8th grade basketball 2 4 7 baseball 1 6 5 soccer 7 4 4 football 8 15 10 explain what the ratio 5:73 represents. the ratio 5:73 represents the ratio of 8th grade baseball players to total athletes. the ratio 5:73 represents the ratio of 7th grade football players to total athletes. the ratio 5:73 represents the ratio of total athletes to 7th grade football players. the ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
What is ratio?In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.
Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10
= 73
Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.
There are on one event is where 5 athletes are, that is 8th grade baseball players.
So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
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6 the standard deviation of human body temperatures is equal to 0. 62 F. Identify the null hypothesis and alternative hypothesis in symbolic form
The null hypothesis exists that the standard deviation σ exists equivalent to 0.62. The alternative hypothesis exists that it does not equivalent 0.62.
What are null and alternative hypotheses?Statistical hypothesis testing employs null and alternate hypotheses. While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no association between variables.
A proposed claim or defense in the hypothesis test is referred to as an alternative hypothesis in statistics. In most cases, it supports the research premise and shows that there is a statistical relationship between the variables. It is one of the two statements in statistical hypothesis testing that are mutually exclusive.
H₀: σ = 0.62
H₁: σ ≠ 0.62
The null hypothesis exists that the standard deviation σ exists equivalent to 0.62.
The alternative hypothesis exists that it does not equivalent 0.62.
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How can you tell if a linear system has infinitely many solutions?
A linear system has infinite solutions if it consists of exactly the same equations.
The 3 possible solutions of a linear system are:
- Unique or one solution
- Infinite solutions
- No solution
- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
Example:
3x + 2y = -4 ..... (equation 1)
6x = -4y - 8 ..... (equation 2)
Add 4y to both sides of equation 2:
6x + 4y = -8
Divide both sides by 3:
3x + 2y = -4
Hence, equation 2 is exactly the same as equation 1. If we plot their graphs, they will share the same graph. Any solution of equation 1 is also solution of equation 2. Therefore, this linear system has infinite solutions.
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