Its true that the probability of rejecting the null Hypothesis decreases.
What is sample mean?
In mathematics, particularly in statistics, there are various types of means. Each mean summarises a particular set of data, frequently to help determine the overall significance of a particular data set.
The sample mean is a fair estimation of the population mean, according to probability theory. We also observed in our simulations that the means of bigger samples are more likely to be closely grouped around the population mean than the means of smaller samples.
Since, when other things being equal as the sample means get closer to each other.
So, the given statement is true.
Hence, its true that the probability of rejecting the null Hypothesis decreases.
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Solve for x.
Please help
The value of x will be;
⇒ x = 3
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in figure.
Now,
All the sides are given in figure.
By definition of proportionality, we get;
⇒ 3 / (6x - 2 - 10) = (3 + 5) / (6x - 2)
Solve for x as;
⇒ 3 / (6x - 12) = 8 / (6x - 2)
⇒ 3 (6x - 2) = 8 (6x - 12)
⇒ 18x - 6 = 48x - 96
⇒ 96 - 6 = 48x - 18x
⇒ 90 = 30x
⇒ 30x = 90
⇒ x = 90/30
⇒ x = 3
Thus, The value of x will be;
⇒ x = 3
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A local tennis club has an annual tournament to raise money. they allow a total of 128 players to enter. each round eliminates half the players. how many players will be left after 5 rounds?
The total of 4 players left after 5 rounds.
Given information,
Given that a neighborhood tennis club holds a fundraising competition every year. A total of 128 players are permitted to enter. In each round, half the participants are eliminated.
The function will be written as,
[tex]F(x) = 128e^x[/tex]
To know how many players left after 5 rounds,
Round 1 ⇒ 128/2 = 64
Round 2 ⇒ 64/2 = 32
Round 3 ⇒ 32/2 = 16
Round 4 ⇒ 16/2 = 8
Round 5 ⇒ 8/2 = 4
Hence, 4 players will be left after 5 rounds.
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If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively, then the formula for the mean absolute deviation over a range of forecasted values isA) MAD t 1 t 1 B) MAD At C) MAD t 1 At-Ft D) MAD t 1
The correct option is A. The formula for the mean absolute deviation over a range of forecasted values is MAD t 1 t 1.
Forecasting is the method of creating predictions primarily based on past and gift information. Later these can be compared (resolved) against what occurs. for example, a company would possibly estimate their sales in the next yr, then examine it in opposition to the real results. Prediction is similar, but the more preferred time period. Forecasting would possibly confer with particular formal statistical methods using time series, pass-sectional or longitudinal information, or as an alternative to less formal judgmental strategies or the manner of prediction and resolution itself. utilization can range among regions of application:
for example, in hydrology, the phrases "forecast" and "forecasting" are sometimes reserved for estimates of values at sure unique future instances, at the same time as the term "prediction" is used for extra widespread estimates, consisting of the wide variety of times floods will arise over an extended duration.
chance and uncertainty are vital to forecasting and prediction; it's miles generally taken into consideration as an excellent practice to indicate the diploma of uncertainty attached to forecasts. in any case, the information ought to be updated in order for the forecast to be as accurate as possible. In a few instances, the information used to are expecting the variable of the hobby is itself forecast
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Mrs. Stevens bought 5 identical gifts for her children. Each gift was valued at $80. She paid 1/2 of the total cost and financed the remaining balance through her credit union for 18 months at 9 % interest. What was the total amount of money she borrowed?
The total amount of money that she borrowed would be= $227.
What is a credit union?A credit union could be defined as the union that identifies am individual as their members and there offer financial assistance to such an individual.
The number of gifts bought by Mr Steven = 5 identical gifts.
The price for each gift = $80
The total money that Mr Steven spent on gift = 5×80 = $400.
The amount paid was 1/2 of total cost = 1/2×400 = $200
The amount of money she borrowed for her credit union is calculated using simple interest formula;
si = P*T*R/100
si = 200×1.5 × 9/100
si = 2700/100
si = $27
The amount borrowed= 200+27 = $227.
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in a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that group of answer choices the estimated mean of y is 2 when x1 equals zero. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, holding x2 constant. the relationship between x1 and y is significant. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, without regard to x2.
In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that B. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, holding x2 constant
What is a multiple regression?Multiple regression is a statistical technique for examining the relationship between a single dependent variable and a number of independent variables. The goal of multiple regression analysis is to use known independent variables to predict the value of a single dependent variable.
Multiple regression predicts the value of one dependent variable by taking into account the values of the available multiple independent variables. For example, suppose a researcher decides to study the performance of students at a school over time.
In this case, the correct option is B.
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Construct the lowest-degree polynomial given the zeros below. Then, choose the intervals that contain the coefficients of the polynomial in the form x3 + bx? + cr + d. -4 + 4i and 4 I A. b€ (-2.3, 2.2),c € (-3, 10), and d € (-22, -15] B. be[-2.3, 2.2),c € (-14, -6), and d € [11, 19] C. be[-5.4, -1],ce 1-3, 10), and d e [123, 134] D. 6 € (2.1, 5.3],c el-3, 10), and d e f-138, -126] E. None of the above.
Option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].
Here, we are given a polynomial of the form [tex]x^{3}[/tex] + b[tex]x^{2}[/tex] + cx + d
The zeroes of the polynomial are ( -4 + 4i ) and 4
The third root of the cubic equation will be (-4 - 4i) which is the conjugate of (-4 + 4i)
This means that for x = ( -4 + 4i ), ( -4 - 4i ) and 4, the polynomial is equal to 0.
Further, the sum of zeroes of a cubic equation
= -(coefficient of [tex]x^{2}[/tex] )/(coefficient of [tex]x^{3}[/tex])
Thus, -4 + 4i + 4 - 4 - 4i = -b
b = 4
Similarly, the sum of the product of zeroes taken 2 at a time = c
⇒ (-4 + 4i)(-4- 4i) + 4(-4 + 4i) + 4(-4- 4i) = c
c = 16 -16[tex]i^{2}[/tex] - 16 + 16i - 16 - 16i
c = 16 + 16 - 32
c = 0
Further, product of zeroes = -d
-d = (-4 + 4i) (-4- 4i) 4
d = -(16 + 16i - 16i -16[tex]i^{2}[/tex]) 4
d = -(16 + 16)4
d = -128
Thus, we get that option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].
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Which expression is equivalent to log subscript 5 baseline (startfraction x over 4 endfraction) squared? 2 log subscript 5 baseline x + log subscript 5 baseline 4 2 log subscript 5 baseline x + log subscript 5 baseline 16 2 log subscript 5 baseline x + 2 log subscript 5 baseline 4 2 log subscript 5 baseline x + log subscript 5 baseline 4.
The required expression for
[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.
Given,
In the question:
The expression is given as:
Log subscript 5 baseline (startfraction x over 4 endfraction) squared
To find the which expression is equivalent?
Now, According to the question:
The expression is given as:
[tex]log_5(\frac{x}{4} )^2[/tex].
We know that from the properties of logarithm, the following identities
[tex]log m^n = n log m...(1)\\\\log\frac{m}{n} = log m - log n .....(2)[/tex]
Now, [tex]log_5(\frac{x}{4} )^2[/tex] = 2 log [tex]\frac{x}{4}[/tex] (using 1 identity)
Again, Using (2) identity we get,
[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.
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What is the opportunity cost for the congo to produce diamonds? 6 thousand units of corn one-sixth of a thousand units of corn 4 thousand units of corn one-fourth of a thousand units of corn.
The opportunity cost for the Congo to produce additional diamonds is; 4 thousand units of corn.
What is the Opportunity Cost?Opportunity costs are defined as the benefits of an alternative decision when the decision maker is made to reject the alternative.
For example, the opportunity cost of going to college would be the earnings forgone.
The opportunity cost is calculated as the lost benefit when an alternative decision is not followed up.
Fractionally, we can say that the opportunity cost of producing one product A) to another (B) = Units of B/Units of A.
From the attached table, we can deduce the following;
United States opportunity cost to produce diamonds = 60/10 = 6
United States opportunity cost to produce corns = 10/60 = 1/6
Congo's opportunity cost to produce diamonds = 20/5 = 4
Congo's opportunity cost to produce corn = 5/20 = 1/4
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These expressions are equivalent. True or False?
2x−3(x−4) = 5x+12
the answer is -6x and the equation is equivalent
let v be a finite-dimensional vector space. let t : v !v be a linear transformation. if for each eigenvalue of t , the geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.
The geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.
The word "nilpotent" is missing from the title, rather confusing, since being nilpotent is easily seen to be the only possible obstruction against being diagonalisable for a rank 1 operator. After all, by rank-nullity this implies the nullity equals n−1, and this is (by definition) the dimension of the eigenspace for 0. Also Im(T) is always T-stable, so being of dimension 1 its nonzero vectors are eigenvectors, and if this is for a nonzero eigenvalue λ, then the eigenspaces for 0 and for λ are complementary, and so T is diagonalisable.
So the only thing that can go wrong is that the nonzero vectors of Im(T) are eigenvectors for 0, but then clearly T2=0 so T is nilpotent.
It would have been a bit more fun if instead of T not being nilpotent it had been given that T has nonzero trace. Since 0 is a root of the characteristic polynomial χT with multiplicity at least n−1 (which is its geometric multiplicity), the "final" root of χT equals the sum of all its roots, which is the trace of T. This is also the eigenvalue of nonzero vectors in Im(T), and as we have seen it is zero if and only if T is nilpotent if and only if T is not diagonalisable.
Hence the answer is the geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.
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all the real zeros of the given polynomial are integers. find the zeros. (enter your answers as a comma-separated list. enter all answers including repetitions.) p(x)
The zeros of the polynomial P(x) = x³ + 7x² - x - 7 is 1 , - 1 , - 7 .
What is zeros of the polynomial ?In algebraic expressions, exponents may have rational values. A polynomial, on the other hand, is an algebraic assertion with a whole number exponent on any variable. The places where a polynomial turns 0 are referred to as its zeros.
P(x) = x³ + 7x² - x - 7
Now we have to find one zero of given polynomial.
By hit and trial, we get
P(-7) = (-7)³ + 7 (-7)² - (-7) - 7
= 0
Hence we get one zero = -7
So, -7 is the roots of the equation.
Now, by factorisation :
P(x) = x³ + 7x² - x - 7
= x² ( x+7 ) - 1 ( x+3 )
= (x² - 1) ( x+7 )
= ( x-1 )( x+1 )( x+7)
Hence the zeros of the polynomial is 1 , - 1 , - 7.
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THE RIGHT QUESTION ISAll the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x) = x3 + 7x2 − x − 7
A car is moving at a constant speed and travels 48 4/5 miles in 4/5 of an hour. How many miles will this car travel in three hours?
The car travels 183 miles distance in 3 hours.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Distance travelled by car in 4/5 hour = 48⁴/₅ miles or 244/5 miles.
To find distance travelled by car in 3 hours, use ratio property,
4/5 hours = 244/5 miles
⇒1 hour = 61 miles
⇒3 hours = 61×3 = 183 miles
The distance covered by car in 3 hours is 183 miles.
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explanation+answer please
Answer:
-1
Step-by-step explanation:
if the input is 4 you just go through the cycles
4 then subtract 7
4-7
-3
Then divide by 3
-3/3
-1
Hopes this helps please mark brainliest
select the correct answer from each drop-down menu. consider circle c with diameter de. diameter shows a circle centered at c. points d and e lies on the circumference of the circle. point e is labeled (13, 11) and point d is labeled (minus 3, 3). the equation of circle c is ( )2 ( )2
The equation of the circle , with diameter DEis (x - 5)² + (y - 7)² = 80
An equation is an expression that appears as the relationship between two or more variables and numbers. since the standard equation for a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. It is given that the diameter of the circle is at D(-3, 3) and E(13, 11). So the coordinate of the center is:
h = (13 + (-3))/2 = 5
k = (3 + 11)/2 = 7
(h, k) = (5, 7) and the Radius is diameter / 2 = 8√5 ÷ 2 = 4√5.
the equation will be : (x - 5)² + (y - 7)² = (4√5)² => (x - 5)² + (y - 7)² = 80
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Answer:
(x - 5)² + (y - 7)² = 80
Step-by-step explanation:
what is 4 1/3 multplyed by 6?
Answer:
26!
Step-by-step explanation:
let's firstly convert the mixed fraction to improper fraction.
[tex]\stackrel{mixed}{4\frac{1}{3}}\implies \cfrac{4\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{13}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{13}{3}\cdot 6\implies \cfrac{13}{3}\cdot \cfrac{6}{1}\implies \cfrac{13}{1}\cdot \cfrac{6}{3}\implies \cfrac{13}{1}\cdot\cfrac{2}{1}\implies \text{\LARGE 26}[/tex]
The probability of a randomly selected adult having a rare disease for which a diagnostic test has been developed is 0.002. The diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.96 for a person with the disease and 0.01 for a person without the disease. The proportion of adults for which the test would be positive is
The probability of contracting an illness is 0.0475.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is .According to our question-
D: The patient has the illness
ND: the individual without the disease
TD: The results of the test show the patient has the illness.
P(D) will therefore equal 0.001 since only 0.001 of the population is affected by the disease.
P(ND) = 0.991
Because the test successfully identifies a patient with the condition 99% of the time, P(TD/D) = 0.99.
P(TD/ND) = 0.02 because the test indicates that a healthy person contracts the disease 2% of the time.
We are seeking for P(D|TD) and P(ND|TD), respectively.
According to the Bayes formula, 0.00099/0.00099+0.01982 = 0.00099/0.02081 = 0.0475 = (0.99*0.001)/(0.99*0.001)+(0.02*0.991)
And, \s = 1 - \s = 1 - 0.0475 \s = 0.9525
Therefore,
The likelihood of having an illness is 0.0475.
The likelihood of not having any sick people is 0.9525.
Hence, The probability of contracting an illness is 0.0475.
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Which is a way to solve the equation 4x = 128 if you do not know a power of 4 that equals 128?.
When you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is; Find intersections on the graph of y = 4ˣ and y = 128.
Define the term mathematical equation?The explanation of an equation in arithmetic is a mathematics statement that indicates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 is composed of the two equations 3x + 5 and 14, whose are separated by the 'equal' sign.Consider the given equations;
y = 4ˣ and y = 128
Since, the power of 4 equals 128 is unknown.
Thus, draw the graph of equation y = 128. and y = 4ˣ .
Consider the intersected point from the graph.
Thus, when you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is;
Find intersections on the graph of y = 4ˣ and y = 128.
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add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
The correct response is 110.
Consider two numbers that are inside 1000.
324 and 434 are these two numbers.
As a result, for any number abc, the terms a, b, and c each have a place value of 100, 10, and 1.
We will therefore add the corresponding digits and multiply them by their place value when adding the two numbers abc and def.
In order to add 324 and 434, we will
(3+4)×100 + (2+3)×10 + (4+4)×1
The solution is 700+50+8=758.
This is equivalent to (324 + 434 = 758)
Similar steps apply for subtraction; simply choose the larger number and continue the same procedures, changing the + sign in the inner bracket to a -.
(4-3)×100 + (3-2) (3-2)×10 + (4-4)×1
Therefore, the correct response is 110.
This equals (434-324) = 110.
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consider a blackbody of surface area a that cools down with time according to the time-dependent tem- perature function t(t)
The blackbody surface area cools down the area according to time dependent temperature (t)
Radiation that is incident on an object is partially absorbed and partially reflected. At thermodynamic equilibrium, the rate at which an object absorbs radiation is the same as the rate at which it emits it.
Therefore, a good absorber of radiation - any object that absorbs radiation, is also a good emitter. A perfect absorber absorbs all electromagnetic radiation incident on it; such an object is called a blackbody.
The temperature (T) of the object that emits radiation, or the emitter, determines the wavelength at which the radiated energy is at its maximum. For example, the Sun, whose surface temperature is in the range between 5000 K and 6000 K, radiates most strongly in a range of wavelengths about 560 nm in the visible part of the electromagnetic spectrum. The body, when at its normal temperature of about 300 K, radiates most strongly in the infrared part of the spectrum.
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After __ hour, Evelyn and her friends are __ miles from shore
for point (1,4)
After 1 hour, Evelyn and her friends are 4 miles from shore.
for point (3,12)
After 3 hour, Evelyn and her friends are 12 miles from shore.
What is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle ABC?.
2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'
Given,
Triangles ABC and A'B'C' are similar
For ABC;- (x₁, y₁) = (0, 2) and (x₂, y₂) = (2, 2)
For A'B'C' ;- (x₁, y₁) = (-4, -1) and (x₂, y₂) = (1, -1)
We have to find the scale factor of the dilation;
Here,
Find the distance AB and distance A'B' with the formula
Distance, d = [tex]\sqrt{(y_{2} -y_{1})^{2} +(x_{2} -x_{1} )^{2} }[/tex]
Then,
a) Distance of AB
d AB = [tex]\sqrt{(2-2)^{2}+(2-0)^{2} }[/tex]
d AB = [tex]\sqrt{0^{2} +2^{2} }[/tex]
d AB = √4
Distance of AB = 2 units
b) Distance of A'B'
d A'B' = [tex]\sqrt{(-1+1)^{2} +(1+4)^{2} }[/tex]
d A'B' = [tex]\sqrt{0^{2} +5^{2} }[/tex]
d A'B' = √25
Distance of A'B' = 5 units
Now,
Scale factor;
Scale factor = Distance of AB / Distance of A'B'
Scale factor = 5/2
Scale factor = 2.5
Therefore,
2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'
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a deck of cards contains red cards numbered 1,2,3,4, blue cards numbered 1,2,3,4,5,6 and green cards numbered 1,2,3,4,5,6,7,8,9. if a single card is picked at random, what is the probability that the card is blue? give your answer as a fraction.
if a single card is picked and if it is blue card then the probability is 6 / 19 .
What is probability ?Probability means possibility of happening of event, it varies from 0 to 1.
Generally it helps us in determining odds of this situation. Probability expresses that situation.
Probability is defined as the the number of favourable outcomes to the total number of outcomes.
Red Cards = 1, 2, 3, 4
Blue Cards = 1, 2, 3, 4, 5, 6
Green Cards= 1, 2, 3, 4, 5, 6, 7, 8, 9.
Now,
Total number of cards = 19
P ( Blue card ) = [tex]\frac{Number of blue cards}{Total number of cards}[/tex]
= 6 / 19
Hence, if a single card is picked and if it is blue card then the probability is 6 / 19 .
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Alan has a guessing game on his computer.
He estimates that the probability of winning each game is 0.35
Alan decides to play 20 of these games.
How many of these games should he expect to win?
Answer:7
Step-by-step explanation:
100/20 = 5
35/5 = 7
A box holds fewer than 200 apples. either 2, 3, 4, 5, or 6 children could evenly share these apples. how many apples could be in the box?
The number of apples that could be in the box is 180
How to determine the number of apples that could be in the box?From the question, we have the following parameters that can be used in our computation:
Number of apples = Fewer than 200
Children that can share the apples evenly = 2, 3, 4, 5, or 6 children
This means that the number of apples that could be in the box can be a multiple of 2, 3, 4, 5, or 6
Also, the number must be less than 200
The highest number less than 200 that is a multiple of 2, 3, 4, 5, or 6 is 180
Hence, the possible number of apples is 180
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Answer:
Multiples of 60 under 200!
Step-by-step explanation:
your subject-matter expert tells you that her most likely estimate to complete her task is 40 hgours. the task starts on thrusday, january 20, at 8 a.m.
The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.
Given that,
Your subject-matter expert informs you that she believes it will take her 40 hours to finish the work. The project begins on January 20 at 8 a.m. The staff only works throughout the weekdays, eight hours a day.
We have to find when will the assignment be completed.
We know that,
This simple table explains the answer
Thursday, January 20, at 4 p.m. - 8 hours worked
Friday, January 21, at 4 p.m. - 16 hours worked
Monday, January 24, at 4 p.m. - 24 hours worked
Tuesday, January 25, at 4 p.m. - 32 hours worked
Wednesday, January 26, at 4 p.m. - 40 hours worked
Therefore, The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.
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Translate the phrase -19y and 20y is -6 into an algebraic equation.
Answer:
-19y+20y=-6
Step-by-step explanation:
and means plus so its would be -19y+20y
is=equal sign so -19y+20y=-6
Which special segments go through a midpoint?.
Bisectors are the special segments that pass through the mid point of the lines or line segments.
A bisector is the line, line segment or ray that intercepts and/or divided lines or line segments into two equal line segments and thus passes through the midpoint of the given line segment or line segments.
There can be infinite bisector for one particular line or line segment at multiple angles.
The bisector that intercepts and/or cuts a line in half, passes through the midpoint when it is perpendicular (making an angle of 90°) to the line segment is known as the Perpendicular Bisector.
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PLEASE HELP ASAP .................... I will mark brainiest.
Answer:
x>3
Step-by-step explanation:
the answer is x>3 because I took this test in class
Which congruence theorem can be used to prove that the triangles are congruent two sides and non-included right angle?.
According to the Side-Angle-Side Theorem (SAS), two triangles are congruence if their two sides and the angle between them are equal to those of another triangle's two sides and angle.
What in mathematics is a congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Is congruent the same as equal?If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
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in short-track speed skating, the track has straight sections and semicircles 16 m in diameter. assume that a 65 kg skater goes around the turn at a constant 12 m/s .
The horizontal force exerted on the skater 1170 N.
The diameter of the semicircular portion of the track is 16 m.
Therefore its radius is
r = 8 m.
The tangential velocity of the skater is 12 m/s.
Therefore the angular speed is
ω = v/r = (12 m/s)/(8 m) = 1.5 rad/s
The horizontal force on the skater is due to centripetal acceleration of
a = r*ω² = (8 m)*(1.5 rad/s)² = 18 m/s².
The force acting on the 65-kg skater is
F = m*a = (65 kg)*(18 m/s²) = 1170 N
Therefore, the horizontal force exerted on the skater 1170 N. The correct answer is 1170 N.
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