When evaluating the likelihood of an outcome, the claim or hypothesis statement is assumed. The required answer is a hypothesis claim or statement.
It is possible to test one's assumptions regarding a population parameter through the statistical analysis known as hypothesis testing. The association between two statistical variables can then be estimated by this hypothesis.
We start by writing the claim mathematically and determining if it is the null or alternative hypothesis. The null hypothesis is the assertion that there is no change or no relationship between the two variables; otherwise, the alternative hypothesis is the assertion that tells that there is a change or relationship.
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What is the measure of n?
28
m
7
n = [?]
Give your answer in simplest form.
The measure of the side length n is equal to 14 for the right triangle.
How to evaluate the length of n in the right triangleConsidering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent m and hypotenuse 28+7= 35;
cosθ = m/35
for the smaller right triangle with adjacent 7 and hypotenuse m
cosθ = 7/m
m/35 = 7/m
m² = 245 {cross multiplication}
m = √245 = 7√5 {take square root of both sides}
(√245)² = 7² + n² {by Pythagoras rule for the smaller right triangle}
245 = 49 + n²
n² = 245 - 49 {collect like terms}
n² = 196
n = √196 {take square root of both sides}
n = 14
Therefore, the measure of the side length n is equal to 14 for the right triangle
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A marble statue of height h1metres is mounted on a pedestal. The angles of elevation of the top and bottom of the statue from a point h2metres above the ground level are αandβrespectively. Show that the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.
So, the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.
To find the height of the pedestal, we can use the concept of angles of elevation. The angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizontal.
From the given information, we know that the angles of elevation of the top and bottom of the statue from a point h2 metres above the ground level are α and β respectively.
We can use the tangent of the angle of elevation to find the height of the object. The tangent of the angle of elevation is equal to the height of the object divided by the distance from the base of the object to the point of observation.
Let's call the height of the pedestal as "h3"
So we can write the following equations:
h1/((h3+h1)-h2)= tan(α)
h1/((h3)-h2)= tan(β)
By solving the above equations we can get the value of h3 which is the height of the pedestal.
((h1−h2)tanβ+h2tanα)/tanα−tanβ
This is the final equation which gives the height of the pedestal.
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what is 15 ones dividend by eight and seven fifty eight thousandths
15 divided by eight and seven fifty eight thousandths will give a quotient of one and seven hundred and three thousandths
What is division operation?One of the four fundamental operations, along with addition, subtraction, and multiplication, is division. A number is split using the straightforward method of division.
The division (/) operator creates the product of its operands, where the dividend is the left operand and the divisor is the right operand.
In the problem written the words the division is done by writing in figure as below
15 ÷ 8.758
Using calculator the quotient is 1.7127 = 1.713 to the nearest thousandth
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Help please
The mathematician Girolamo Cardano is credited with the first use of negative square roots in solving the now-famous problem, "Find two numbers whose sum is 10 and whose product is 40. Show that the complex numbers 5 + iv15 and
5 - i~15 satisfy the conditions of the problem.
View image
Girolamo Cardan or Cardano was an Italian doctor and mathematician who is famed for his work Ars Magna which was the first Latin treatise devoted solely to algebra.
What is Cardano's formula?For which the relation =p/3 holds (such a value of p exists always), the Cardano formula for the roots of (1) has the form: x=3q2+q24+p327+3q2q24+p327.
P and Q are arbitrary complex numbers in the Cardano formula. By substituting y = x + b/3a, the square term is eliminated. Rewrite the aforementioned equation to u3 + v3 + (u+v)(3uv + p) + q = 0 if x = u+v. The equation above is changed to u3 + v3 = -q by setting 3uv + p = 0. We achieve the system in this manner.
With regards to scalability, interoperability, and sustainability issues on cryptocurrency platforms, Cardano is specifically designed to address these. The first issue is the sluggishness of networks and excessive costs brought on by an increase in transaction volume.
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i need help 10 divided by 75.10
quotient.
After divide, the value of quotient is 0.133.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
⇒ 10 divided by 75.10.
Now, We get;
⇒ 10 divided by 75.10
⇒ 10 ÷ 75.10
⇒ 0.133
Thus, The value of quotient after divide = 0.133
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show 2/3 of 4 on the number line.
The position of the value is shown on the number line attached to this answer.
What is a number line?A number line is a ray which extends from -∞ to +∞ as its two extreme ends. Thus all number fall within this range such that all directed numbers can be located on the number line.
A directed number is a any number which has either a positive or negative sign. This implies that the position of all numbers can be shown on the line.
Thus, from the question to show 2/3 of 4 on the number line;
2/3 of 4 = 2/3 x 4
= 8/ 3
= 2 2/3
The position of 2 2/3 is shown on the number line attached to this answer.
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Lian's dog eats
of a bag of dog food each week. Lian currently has of a bag remaining.
How many weeks will it take Lian's dog to finish this remaining food?
weeks
Stuck?
The period that it would take the Dog to finish the remaining food would be a period of 12.5 weeks
How to solve for the period that it would take to finish the foodThe amount that the dog eats weekly is given as 1 / 20 of the food.
The amount that Lian has left in the bag is given as 5 / 8
To get the number of weeks that it would take to finish the food, we would divide 1 / 20 by 5 / 8
1 / 20 ÷ 5 / 8
20 / 1 * 5 / 8
= 100 / 8
= 12.5
Hence it would take 12.5 weeks for the dog to finish the remaining food here.
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'Lian's dog eats 1/20 of a bag of dog food each week. Lian currently has 5/8 of a bag remaining.How many weeks will it take Lian's dog to finish this remaining food?weeksStuck?
Area:
10
Area:
?
Area:
40
Answer: THE CORRECT ANSWER IS 30
Step-by-step explanation:
The compound figure shown is composed of a
semicircle and a rectangle.
Which best represents the area of the composite
figure
A) 88ft2
B) 108 ft2
C) 75 ft2
D) 100ft2
Answer:
A
Step-by-step explanation:
this is a college level question ? oh my ...
to get the total area we need to add the area of the rectangle and the area of the half-circle.
the area of the rectangle is
length × width = 15 × 5 = 75 ft²
the area of the half-circle is
pi×r² / 2
how do we get r (radius) ?
we know, both lengths of the rectangle must be equally long. so, 15 ft.
we see that the remaining length after the half-circle is 9 ft.
so, the diameter of the half-circle is 15 - 9 = 6 ft.
the radius is half the diameter, so r = 6/2 = 3 ft.
the area is therefore
pi×3² / 2 = 9pi /2 = 14.13716694... ft²
in total that makes
75 + 14.13716694... = 89.13716694... ft²
the closest of your answer options is A : 88 ft²
18. Subtract:
8.50
- 4.75
19. Multiply:
X
0.625
5
20. Divide: 0.04)26.4
Answer:
18.
3.25
19.
3.125
20.
-26.36
Step-by-step explanation:
3
Module One - The 2 R's of Infection
Select the one (1) correct answer. Which of these statements is
correct?
There is no need for infection control risk assessments
The infection control risk assessments are not important
There is a need for infection control risk assessment
There is a need for infection control risk assessment is correct statements.
What does risk assessment in infection control accomplish?To evaluate infection hazards and risks and to make sure that they are, if feasible, eliminated, minimised, confined, and managed effectively, an infection control risk assessment must be conducted.Tools called Infection Control Assessment and Response (ICAR) are used to systematically evaluate infection prevention and control (IPC) procedures in healthcare facilities and direct quality-improving initiatives (e.g., by addressing identified gaps).hand cleanliness Personal protective equipment usage (e.g., gloves, masks, eyewear). Coughing manners and respiratory hygiene. Sharps security (engineering and work practise controls).There is a need for infection control risk assessment is correct statements.To learn more about risk assessment refer to:
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For each description below, identify each underlined number as a parameter or statistic. Use appropriate notation to describe each number, e.g., .(a) Nationwide, 84% of people are living in the same house they were living in one year ago. The town council of Pleasant Valley surveys 100 residents and find that 75% of them have not moved in the past year.(b) The mean birthweight of infants in the United States in 2006 was 3.3 kg with a standard deviation of 0.57 kg. An obstetrician determines that among her own patients, the mean birthweight was 3.6 kg.
The mean birthweight of the obstetrician's own patients is higher than the national mean.
In the first description, 84% is a parameter, since it describes the population as a whole. The survey of 100 residents in Pleasant Valley yields a statistic of 75%, since it is a sample of the population.
In the second description, the mean birthweight of infants in the United States in 2006 of 3.3 kg and the standard deviation of 0.57 kg are both parameters. The mean birthweight of the obstetrician's own patients of 3.6 kg is a statistic. To calculate the difference between the two means, we can subtract the two values: 3.6 kg - 3.3 kg = 0.3 kg. This 0.3 kg difference indicates that the mean birthweight of the obstetrician's own patients is higher than the national mean.
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a flat sheet is in the shape of a rectangle with sides of lengths 0.400 m and 0.600 m. the sheet is immersed in a uniform electric field of magnitude that is directed at from the plane of the sheet (fig. e22.2). find the magnitude of the electric flux through the sheet
The magnitude of the electric flux through the sheet will be 6.1 N.m²/C.
What is Electric flux?
The amount of electric lines of force (or electric field lines), which cross a specific area, is referred to as electric flux, a feature of an electric field. According to this theory, electric field lines begin with positive electric charges and end with negative charges.
The following formula can be used to get the electric flux:
∅ = EAcosФ
where,
∅ = Electric flux
E is the Electric field which is 73.9 N/C.
A is Area of the plate which is = (0.4 m)(0.6 m) = 0.24 m²
θ is the angle between normal to the area and electric field lines = 90° - 20° = 70°.
Putting these values in our formula, we get:
∅ = (73.9)(0.24)cos(70°)
∅ = 6.1 N.[tex]m^{2}[/tex]/c.
Therefore the Magnitude of the electric flux through the sheet is 6.1 N.m²/C.
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In a garden,
5
6
6
5
start fraction, 5, divided by, 6, end fraction of the area is filled with native plants. The native plants take up
107
4
m
2
4
107
m
2
start fraction, 107, divided by, 4, end fraction, start text, m, end text, squared. Let
�
gg represent the total area of the garden.
Select
1
11 multiplication and
1
11 division equation to represent the relationship.
Answer:hewwo
Step-by-step explanation:hewwo
Answer: The answer is b and c
Step-by-step explanation:
2. Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00. Carnuba's Car
Rental charges $.15 per mile and has a service of twenty dollars. At how many miles will the
charge for each company be the same?
The charge of each company will be the same at 40 miles.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Let us suppose the miles travelled as x.
Given that:
Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00, this is represented as:
C = 0.10(x) + 40
Carnuba's Car rental charges $.15 per mile and has a service of $20.
D = 0.15(x) + 20
The charge of both the companies would be equal when C = D:
0.10(x) + 40 = 0.15(x) + 20
40 -20 = 0.15x = 0.10x
20 = 0.5x
x = 20/ 0.5
x = 40
Hence, the charge of each company will be the same at 40 miles.
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The table shows the number of smartphones sold at an electronics store each day. A 2-column table with 5 rows. Column 1 is labeled Day with entries Monday, Tuesday, Wednesday, Thursday, Friday. Column 2 is labeled Smartphones sold with entries 8, 13, 12, 10, 15. To the nearest tenth, what is the standard deviation of the data? Use this formula: s = StartRoot StartFraction Sigma-summation (x Subscript I Baseline minus x Overbar) squared Over n minus 1 EndFraction EndRoot 1.5 smartphones 1.9 smartphones 2.1 smartphones 2.7 smartphones
The standard deviation of the data is 2.41 smartphones.
What are the types of representing data?Data refers to the elements that make up persons, things, events, and ideas. It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics. The presentation of data is the name given to such a configuration.
Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.
Given, The number of smartphones sold at an electronic store each day
is represented by the table with two columns and 5 rows.
The mean of the data set is,
= (8 + 13 + 12 + 10 + 15)/5.
= 11.6.
We know the formula for the standard deviation of a data set is,
= [tex]\frac{1}{\sqrt{n}}\sqrt{\sum_{i =1}^{n} (x_i - \overline{x}{}})^2[/tex].
= (1/√5)×√[(-3.6)² + (-1.4)² + (-0.4)² + (-1.6)² +(-3.4)²].
= (1/√5)×[√29.2].
= 2.41.
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Answer:
2.7 Smartphones
Step-by-step explanation: Just did it
a boeing 747 has a wingspan of 195.7 feet and a 6.95 aspect ratio. it cruises at 500 mph at a weight of 550,000 pounds at 35,000 feet (density of 0.000737 slug/ft3). assume that the reynolds number can be approximated using: re
1)Therefore the wing area is determined as 5511 ft2 2) The elliptic chord length is 35.87 f t 3) The Reynolds number for the given elliptical wing is 1.672 X 10^8 4) So, the speed of the plane is 733.33 f t/s.
1) Wing Area
Wing Area determined by using the wingspan and aspect ratio of the Boeing. Where the Aspect ratio of the wing written as,
AR=S^ 2/A
Here s is the wingspan, A is the Wing area and AR is the Aspect ratio.
A=S^ 2/AR=195.7^ 2/6.5=5510.57 FT^ 2
Therefore the wing area is determined as 5511 ft2
2) Average Elliptical chord
Elliptic chord of the Boeing wing determined by the elliptical wing Aspect
ratio,
AR=4xspan/π x chord
chord=4x span/π x AR
chord=4x 195.7/πx6.95=35.87f t
Therefore, the elliptic chord length is determined as35.87 f t
3) Reynolds Number
Reynolds number for the given wing is determined by the average speed and the average chord length
Re=9324xVxc
Here V is the average speed and c is the chord length using the determined values we can find the Reynolds number as,
Re=9324x500x35.87=1.67225x10^ 8
Therefore, the Reynolds number for the given elliptical wing is 1.672 X 10^8
4) Cruise Speed
Where the Speed of the cruise is given as 500 mph to convert the speed mph into the f t/s,
Speed=500x5280/3600=733.33 f t/s
Here 1 mile = 5280 f t and 1 hour = 3600 seconds
So, the speed of the plane is determined in the f t/s as 733.33 f t/s.
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create an equivalent boolean algebra expression for a circuit with 2 inputs a and b, whose output q is true when less than two inputs are true.
An equivalent boolean algebra expression for a circuit with 2 inputs a and b is q = (a XOR b)
One way to represent this circuit using Boolean algebra is to use the logical operators AND, OR, and NOT.
The output of the circuit, q, is true when less than two inputs, a, and b, are true. This can be represented as:
q = (NOT(a) AND NOT(b)) OR (NOT(a) AND b) OR (a AND NOT(b))
This can also be represented using the XOR operator (Exclusive OR) which output is true if one and only one input is true:
q = (a XOR b)
Another equivalent representation can be achieved by using the NOR operator which gives true only when none of the inputs is true:
q = NOT( a NOR b)
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Jupiter has a radius of 44 ,423 miles. As the planet rotates on its axis, a point on its equator travels at 669,883 miles per day.
(a) Find the angular speed of a point on its equator in radians per day.
(b) Find the number of rotations the planet makes per day.
Do not round any intermediate computations, and round your answer to the nearest whole number.
Hey there!
Answers;
(a) 15 radians/day(b) Number of rotations = 2| Explanation |
For part (a):
[tex]v=669,883[/tex] [tex]miles/day[/tex]
[tex]r=44,423[/tex] [tex]miles[/tex]
[tex](a)V=rw[/tex]
[tex]w=\frac{v}{r}[/tex] [tex]=\frac{669883}{44423}[/tex][tex]=15.0796[/tex] [tex]radians/day[/tex]
[tex]15[/tex] [tex]radians/day[/tex]
For part (b):
[tex]Circumference=2\pi r[/tex]
[tex]2*3.14*44423[/tex]
[tex]278976*44[/tex]
Number of rotations = [tex]\frac{669883}{278976*44}[/tex] = [tex]2*40[/tex] ⊥ ≈ [tex]2[/tex]
Hence:
(a) [tex]15[/tex] [tex]radiations/day[/tex]
(b) Number of rotations = [tex]2[/tex]
___________________________________________
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Find the line passing through the point of intersection of the lines xâ3y+1=0,2x+5y=9
and
(i) parallel to yâ2x=0
(ii) perpendicular to 2x+yâ5
the equation of the required line is 3xâ2y+1=3x1â2y1+1.
(i) We are given the parallel line of the given equation, that is yâ2x=0.
So, the equation of the required line will be yâ2x=c, where c is a constant.
Let the point of intersection of the two lines be (x1, y1).
Then, substituting the values of x1 and y1 in the equation yâ2x=c, we get
y1â2x1=c
or, c=y1â2x1
Hence, the equation of the required line is yâ2x=y1â2x1.
(ii) We are given the perpendicular line of the given equation, that is 2x+yâ5=0.
So, the equation of the required line will be 3xâ2y+1=c, where c is a constant.
Let the point of intersection of the two lines be (x1, y1).
Then, substituting the values of x1 and y1 in the equation 3xâ2y+1=c, we get
3x1â2y1+1=c
or, c=3x1â2y1+1
Hence, the equation of the required line is 3xâ2y+1=3x1â2y1+1.
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is 5 a quartly number
Answer:
Step-by-step explanation:
Quarter implies 4. If there were 20 items, and you broke them into quarters, each quarter would have 5 items.
suppose that sum a n and sum b n are series with positive terms. prove that if lim n -> infty a n/b n does not exist, and sum b n diverges, then sum a n also diverges
The comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.
Suppose that [tex]$\sum_{n=1}^{\infty} a_{n}$ and $\sum_{n=1}^{\infty} b_{n}$[/tex] are series with positive terms. We assume that does not exist and that [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex]diverges.
To prove that [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] also diverges, we will use the comparison test. Since [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex] diverges, we can find a number M such that [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges. Since [tex]$\lim_{n\rightarrow \infty} \frac{a_{n}}{b_{n}}$[/tex] does not exist, we can find a number N such that for all [tex]$n \geq N$, $\frac{a_{n}}{b_{n}} > 1$[/tex].
Now, for any [tex]$n \geq \max \{M,N\}$[/tex], we have [tex]$\frac{a_{n}}{b_{n}} > 1$[/tex]. Thus, [tex]$a_{n} > b_{n}$[/tex]. By the comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.If the ratio of two series with positive terms,[tex]$\sum_{n=1}^{\infty}a_n$[/tex] and [tex]$\sum_{n=1}^{\infty}b_n$[/tex], does not converge to a limit as n approaches infinity and [tex]$\sum_{n=1}^{\infty}b_n$[/tex] diverges, then [tex]$\sum_{n=1}^{\infty}a_n$[/tex] must also diverge.
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simplfy : -3 1/2- (-12 1/4)
Answer: 35/4 or 8.75 or 8 3/4
Step-by-step explanation:
First, you start by multiplying the minus sign by the parenthesis.
you multiply a negative sign by a negative sign so it cancels out into a positive one.
Then it will be -3 1/2 + 12 1/4. Change the denominator to do both 4, so we can solve the equation.
-3 2/4 + 12 1/4. That will equal 8 3/4 or 35/4.
The answer is 8 3/4 or 35/4.
Calculate the percent change. Then, describe
the change as an increase or decrease.
20 to 14
The percentage change from 20 to 14 is 30% decrease
How to determine the percentage changeFrom the question, we have the following parameters that can be used in our computation:
20 to 14
The final value (14) is less than the initial value (20)
So, the change is a percentage decrease
The change is then calculated as
Change = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation, so, we have the following representation
Change = (14 - 20)/20 * 100%
Evaluate
Change = -30%
Hence, the percentage decrease is 30%
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Given this equation for converting temperature from Fahrenheit (f) to Celsius (c) is C = [5(f – 32)]/9, what is the Celsius temp when Fahrenheit is 104 degrees?
Answer:
40
Step-by-step explanation:
c= 5*(104-32)/9 =40
The town of Madison has a population of 25{,}00025,00025, comma, 000. The population is increasing by a factor of 1.121.121, point, 12 each year.
Write a function that gives the population P(t)P(t)P, left parenthesis, t, right parenthesis in Madison ttt years from now.
The population after 12 years is 98448 and the formula is[tex]P(t) = 25000(1.121)^{t}[/tex].
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the population of the town is 25000 and increasing at the rate of 1.121.
The expression will be written as:-
[tex]P(t) = 25000(1.121)^{t}[/tex]
[tex]P(12) = 25000(1.121)^{12}[/tex]
P(12) = 98448
Hence, the population after 12 years will be 98448.
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The sum of the measures of angle S and angle T is 120°
*The measure of angle S is (8x + 5).
The measure of angle Tis 35°
What is the value of a ?
A) x=20
B) x=10
C) x=40
D) x=80
The value of x in the angles is 10.
How to find the measure of angles ?The sum of the measures of angle S and angle T is 120 degrees. Therefore, the measure of the angles are as follows:
The measure of angle S is (8x + 5) degreesThe measure of angle T is 35 degreesTherefore, the value of a can be found as follows;
∠S + ∠T = 120
∠S = 8x + 5 degrees
∠T = 35 degrees
Therefore,
8x + 5 + 35 = 120
8x + 40 = 120
8x = 120 - 40
8x = 80
divide both sides by 8
x = 80 / 8
x = 10
Therefore,
x = 10
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which of the following is an integral element that defines sport and therefore distinguishes it from play and dramatic spectacle?
One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.
In sports, there are typically opponents or teams competing against each other to achieve a goal or win a match.
This competitive aspect is not present in play or dramatic spectacles, where the focus is typically on individual or group performance rather than competition against others.
Sports are defined as physical activities that involve a set of rules and are typically competitive in nature. They are typically organized and played by people in order to achieve a goal or win a match. Examples of sports include football, basketball, soccer, tennis, baseball, and golf.
Sports are also a form of recreation, entertainment, and physical activity. They can be played individually or in teams. They help to improve physical fitness, and mental health and also promote teamwork and social interaction.
Therefore, One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.
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State the critical values for a one-sample t test given the following conditions:
1. Two-tailed test, a = .05, n = 12
2. One-tailed test, lower-tail critical, a = .01, df = 15
3. Two-tailed test, a = .01, df = 26
4. One-tailed test, upper-tail critical, a = .05, n = 30
Use the values listed in the table; do not round. Be sure to include the appropriate signs in your answers:
• if positive --> + and the value
. if negative --> - and the value
if both --> +/- and the value
(Privitera, 2019, p. 250, #14)
The critical values for a one-sample t test given the following conditions are +1.796, -1.796 2. -2.60 3. +2.576, -2.576 4. +1.729.
What is value?Value is a term used in many different contexts to refer to the worth or importance of something. It is used to describe the worth of an item or service in terms of its utility, its ability to satisfy a need or desire, or its usefulness in exchange. Value can also refer to the worth of an individual or group in terms of their contribution to society or their inherent worth. Value is subjective and can vary greatly from one person or group to another.
1. +1.796, -1.796
2. -2.60
3. +2.576, -2.576
4. +1.729
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Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.
The congruence theorems used in this problem are given as follows:
9. AAS.
10. SAS.
11. Not similar.
12. SSS.
What are the congruence theorems used?For item 9, the AAS theorem is used, as the two angles, the 72º and the vertical angle, are congruent, along with the another side.
For the item 10, we have that the SAS theorem is used, as we have that the sides between the same angle are proportional.
For item 11, the triangles are not similar, as the side lengths are not proportional.
For item 12, the SSS theorem is used, as the three angles of the similar triangles have the same measure.
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