The assumption must be false, which means that either x < 8 or y < 8 must hold true.
What is the Proof by Contradiction?
A proof by contradiction is a method of proof in which we assume the opposite of what we want to prove, and then show that this assumption leads to a contradiction. The contradiction then serves as evidence that the assumption must be false, and therefore the original statement must be true.
In this case, we want to prove that for any positive real numbers x and y, if x · y ≤ 50, then either x < 8 or y < 8.
Suppose for the sake of contradiction that x and y are positive real numbers such that x · y ≤ 50 and x ≥ 8 and y ≥ 8. Then, since x and y are positive, we have x · y = xy ≥ 64, which contradicts the assumption that x · y ≤ 50.
Therefore, we have shown that the assumption that x and y are positive real numbers such that x · y ≤ 50 and x ≥ 8 and y ≥ 8 leads to a contradiction.
Hence, the assumption must be false, which means that either x < 8 or y < 8 must hold true.
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If Sadie spent a total of $2500 this month, how much did she spend on each of the following categories?
Answer: You did not include media attachments, there is not enough information to answer this post.
Step-by-step explanation:
A section of an exam contains six true-false questions, each with two answer choices (listed "T" for true and "F" for false). Assume the outcomes are equally likely.
What is the probability that all six answers are "F"?
What is the probability that at least one answer is "T"?
Answer: a) The probability of answering "F" to a single true-false question is 1/2. Therefore, the probability of answering "F" to all six questions is (1/2)^6 = 1/64.
b) To find the probability that at least one answer is "T", we can use the complement rule and find the probability that all six answers are "F". The complement rule states that the probability of an event happening is equal to 1 minus the probability of it not happening.
So, the probability that at least one answer is "T" is 1 - (1/64) = 63/64.
Step-by-step explanation:
SOLVE THIS AND GET 15 POINTS!!!!!
Explanation:
For any parallelogram, the adjacent angles add to 180.
T+S = 180
(4x+1)+(3x+4) = 180
7x+5 = 180
7x = 180-5
7x = 175
x = 175/7
x = 25
Now we can determine angles T and S.
angle T = 4x+1 = 4*25+1 = 100+1 = 101angle S = 3x+4 = 3*25+4 = 75+4 = 79Notice that they add to 101+79 = 180 to confirm the correct x value, and correct angle measures.
For any parallelogram, the opposite angles are congruent. This allows us to say:
angle T = angle R = 101 degreesangle P = angle S = 79 degreesHELP ASAP WILL GIVE BRAINLIEST
Which of the following tables represents a linear relationship that is also proportional?
X-30 3
y-4-20
X-202
У 0 36
x-303
y-4-3-2
O
x-303
y-202
The table that represents a linear relationship that is also proportional is x-303 and y-202-101-0.
What is values?Values are those principles and beliefs that are important to us and guide our actions, decisions, and behaviors. They are our individual and collective sense of purpose and meaning, and they provide us with a sense of direction and purpose. Values become more important when we are faced with difficult choices or decisions, as it helps us determine what is right and wrong. Values can also be seen as a moral compass, as it helps us determine our actions and behaviors. Values can be influenced by our culture, family, and society, but ultimately, they are our own personal beliefs.
This is an example of a direct proportion, where the ratio of the two values remains the same as they increase or decrease. In this table, the ratio of x to y is 3:2, meaning that for every 3 units of x, there are 2 units of y. This ratio remains the same as the values increase or decrease, so this table represents a linear and proportional relationship.
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name the corresponding parts given ALX≈GIW
Answer:
LX = WI
I = L
A = G
W = X
I = L
LAX = WIG
Erica is making plans to build a fence on her property line. She uses the map shown. Find the m<1
The unknown angle in the hexagon is as follows:
m∠1 = 148 degrees
How to find angles in a polygon?Erica is making plans to build a fence on her property line. Using the map let's find the angle m∠1 as follows:
Therefore, the angle m∠1 is one of the angle in the hexagon.
Therefore, the sum of angles in a hexagon is as follows:
sum of angles in hexagon = 180(n - 2)
where
n = number of sidessum of angles in hexagon = 180(6 - 2)
sum of angles in hexagon = 720 degrees
Therefore,
180 - 45 - 27 = 108 degrees
180 - 108 = 72 degrees
Hence,
m∠1 = 720 - 142 - 148 - 80 - 72 - 130
m∠1 = 148 degrees
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A line passes through the point (8, 9) and has a slope of -3/4 Write an equation in slope-intercept form for this line.
Answer:
y = - [tex]\frac{3}{4}[/tex] x + 15
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 )
here slope m = - [tex]\frac{3}{4}[/tex] , then
y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation
to find c substitute (8, 9 ) into the partial equation
9 = - [tex]\frac{3}{4}[/tex] (8) + c = - 6 + c ( add 6 to both sides )
15 = c
y = - [tex]\frac{3}{4}[/tex] x + 15 ← equation of line
Use this graphic to answer the question. An engineer at an environmentally minded technology company has come up with a process to convert tire waste from the automobile industry into clean energy. Which detail best supports the inference that the auto manufacturing industry supports green solutions? Pyrolysis provides a waste-management solution for tire disposal. Auto manufacturers can profit by selling used tires to pyrolysis plants. Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry. Automobile manufacturers can save raw material costs by using recovered rubber to manufacture new tires.
The detail that best supports the inference that the auto manufacturing industry supports green solutions is -
"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".
What is Pyrolysis?The pyrolysis process is the thermal decomposition of materials at elevated temperatures, often in an inert atmosphere.
Given is that an engineer at an environmentally minded technology company has come up with a process to convert tire waste from the automobile industry into clean energy.
The detail that best supports the inference that the auto manufacturing industry supports green solutions is -
"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".
Therefore, the detail that best supports the inference that the auto manufacturing industry supports green solutions is -
"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".
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Please help meeeeeeeeeee
Answer:
Step-by-step explanation:
USE PYTHAGEROMN THEROME a^2+b^2=c^2
9^2+12^2=a^2
81+144=a^2
255=a^2
15=a
bob and dan are doctors in a medical practice. dan is being sued for malpractice, but it will not affect bob's assets because they formed a(n) partnership.
Since the partnership amount between Bob and Dan is a distinct legal entity, Dan's malpractice claim cannot encumber Bob's assets.
Both Bob and Dan are physicians who work at the same hospital. They established a partnership, which is a distinct legal entity, because they are partners in the company. This indicates that the partnership's assets and liabilities are separate from Bob and Dan's personal assets and liabilities. Therefore, since the action is against the company and not Bob personally, it will not have any effect on Bob's assets if Dan is sued for malpractice. Any obligations resulting from the malpractice lawsuit will be covered by the partnership, and Bob's assets are secure. One of the numerous benefits of creating a partnership is this.
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Given a simplified rate of (1/2), determine the percent change.
Therefore , the solution of the given problem of ratio comes out to be percent change is 50% for the 1/2.
What is ratio?To construct a pair of related variables "a" with "b," whereby "b" may also be bigger than zero, apply the straightforward formula "a / b." Two ratios are combined to form one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. In the group, there are fraction 3/4 girls and 1/4 boys. Parts can be a division between two or more items, a number, or a portion of the volume of a component.
Here,
Given :
Ratio is 1/2
To convert into percentage ,
We multiply it by 100
=> 1/2 * 100
=> 50 %
Thus , percent change is 50%
Therefore , the solution of the given problem of ratio comes out to be percent change is 50% for the 1/2.
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Wellington Elementary School bought a printer one year ago for $3,100. Today, the value of the printer has decreased to $2,170 and is expected to continue decreasing each year.
Write an exponential equation in the form y=a(b)x that can model the value of the printer, y, x years after purchase.
Use whole numbers, decimals, or simplified fractions for the values of a and b
The value of variables are,
⇒ a = 3100
⇒ b = 0.7
What is exponential decay?An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.
The exponential decay function:
Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
Given that;
Wellington Elementary School bought a printer one year ago for $3,100.
And, Today, the value of the printer has decreased to $2,170 and is expected to continue decreasing each year.
Now, An equation in the required exponential form,
A = A₀(1 - r)ˣ
Substituting the values,
A = 3100(1-r)ˣ.
To find the r:
2170 = 3100(1-r)
r = 0.3
So, The equation is,
Aₙ = 3100(1-0.3)ˣ.
y = 3100(0.7)ˣ.
Therefore, The value of variables are,
⇒ a = 3100
⇒ b = 0.7
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What quadrant is the point (2,3) in
Answer:
The point (2, - 3) lies in the third quadrant.
Solution
First quadrant X=positive and Y=positive
Second quadrant X=negative and Y=positive
Third quadrant X=negative and Y=negative
Fourth quadrant X=positive and Y=negative
(2,−3) has X=2, positive and Y=−3, negative
The point lies in the fourth quadrant. Hence, the given statement is False.
a circle has a radius of 13 ft. find the radian measure of the central angle theta that intercepts an arc of length 10 ft. do not round any intermediate computations, and round your answer to the nearest tenth.
The required radian measure of the central angle theta is is 0.872 radians or 0.9 radian.
How to find Central angle?To find the radian measure of the central angle that intercepts an arc of length 10 feet, we can use the formula for the length of an arc:
According to question:Arc Length = Central Angle * Radius
where the central angle is measured in radians.
So, we can write:
10 = Theta * 13
Dividing both sides by 13:
10/13 = Theta
Finally, to convert from degrees to radians,
Radian Measure = (Degree Measure) * (Pi / 180)
So, the radian measure of the central angle is:
Theta = (10/13) * (Pi / 180) = 0.872 radians
Thus, required measurement of angle is 0.872 radians or 0.9 radian.
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Jack Roper is a college student. He pays $17,000 per year in tuition and books, $600 per month in rent, $400 per month for food, and $125 per month for on-campus parking. He gave up a job that pays $45,000 per year to attend college. Given this, the implicit cost of his education equals
The implicit cost of Jack's education is $77,000, which is the amount of foregone income he gave up in order to attend college.
The implicit cost of Jack's education refers to the opportunity cost or the foregone income he gave up in order to attend college. It is a measure of the value of the next best alternative that he had to sacrifice.
First, let's find the total cost of tuition and books. Jack pays $17,000 per year, so the total cost will be 17,000 * 4 = $68,000 over 4 years of college.
Next, let's find the total cost of rent and food. Jack pays $600 per month for rent and $400 per month for food, so the total cost will be 600 + 400 = $1,000 per month. Over 4 years of college, this comes to 1,000 * 12 * 4 = $48,000.
Finally, Jack also pays $125 per month for on-campus parking, so the total cost will be 125 * 12 * 4 = $6,000.
Putting it all together, we can write the equation for the implicit cost of Jack's education as follows:
Implicit Cost = Foregone Income - Total Cost of Tuition, Rent, Food and Parking
Implicit Cost = 45,000 - (68,000 + 48,000 + 6,000)
Implicit Cost = 45,000 - 122,000
Implicit Cost = -77,000
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ANSWER THIS QUESTION ASAP, PLEASEEEEEEE
Write an equation of a line using slope-intercept format goes through the point (4,2) and is parallel to y = 1/2x - 3
Answer: y=1/2x
Step-by-step explanation:
A packing box is 4 ft deep. One side of the box is 1.5 times longer than the other. The volume of the box is 24 ft3 . What are the dimensions of the box?
The dimensions of the packing box are 2 × 3 × 4 feet.
How to calculate the volume of a geometric figure?Based on the information provided, we can reasonably infer and logically deduce that the shape of this packing box is a cuboid.
Mathematically, the volume of a cuboid can be calculated by using this following formula:
Volume = L × W × H
Where:
L represents the length of a cuboid.W represents the width of a cuboid.H represents the height of a cuboid.Substituting the given parameters into the volume of a cuboid formula, we have;
24 = L × (1.5L) × 4
24 = 6L²
L² = 24/6
L = √4
Length, L = 2 feet.
Width, = 1.5L = 1.5(2) = 3 feet.
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The number of days rain per month in London varies depending on the time of year. The data shows the number of wet days per month: 17 13 11 14 13 11 13 12 13 14 16 16(a) For this data, find (i) the median; (ii) the minimum and maximum values. The lower quartile of the data is 12.5 and the upper quartile of the data is 15 (b) Draw a box-and-whisker diagram to represent the data.
As a result, the median is 13. The data has a minimum value of 11 and a maximum value of 17.
What is median?The median is the value in the center of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. For a small data collection, count the number of data points (n) and arrange them in increasing order.
Here,
(a)(i) The median of the data can be found by ordering the data and finding the middle value. In this case, the data has 16 values, so the median is the average of the 8th and 9th values when the data is ordered. The median is therefore 13.
(ii) The minimum value of the data is 11 and the maximum value is 17.
(b) The box-and-whisker diagram is a graphical representation of the distribution of a set of data. It consists of a box, whiskers and dots that show the distribution of the data.
The box represents the interquartile range (IQR), which is the range of the middle 50% of the data. The IQR is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1). In this case, the IQR is 15 - 12.5 = 2.5.
The lower edge of the box is Q1 and the upper edge of the box is Q3. The line inside the box is the median.
Whiskers are drawn to the minimum and maximum values, excluding outliers. Outliers are values that are significantly different from the rest of the data. In this case, there are no outliers.
Dots may be used to represent individual data points.
Here's what the box-and-whisker diagram would look like for this data:
| |
| |
|_13|
12.5 15
The median is therefore 13. The minimum value of the data is 11 and the maximum value is 17.
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Select the correct answer.
Four equivalent forms of a quadratic function are given. Which form displays the zeros of function h?
A. h(x) = -4(x − 2)(x + 2)
B. h(x) = -4(x2 − 4)
C. h(x) = -4x2 + 16
D. h(x) = -2(2x2 − 8)
HELP ASAP QUESTION 2!
Answer:
number 2 or B
Step-by-step explanation:
Please help will give brainliest, math, confused.
Answer:
[tex]\textrm{System A has \boxed{2} real solutions}\\\\\textrm{System B has \boxed{0} real solutions}\\\\\textrm{System C has \boxed{1} real solution}\\[/tex]
Step-by-step explanation:
For a quadratic equation of the form ax² + bx + c = 0
if b² - 4ac > 0 the system will have 2 real roots
if b² -4ac < 0, the system will have 2 imaginary roots(0 real solutions)
if b² -4ac = 0, the system will have exactly one real solution
System A solutions
[tex]x^2 + y^2 = 17\cdots\cdots (1)\\\\y = -\dfrac{1}{2}x\cdots\cdots (2)[/tex]
From equation (2) we get
x = -2y
Substitute this value for x in (1):
(-2y)² + y² = 17
4y² + y² = 17
5y² = 17
y = ±√(17/5)
Both values of y are real, and since x = -2y,x is also real
System B
The equations are:
y = x² - 7x + 10 (1)
y = -6x + 5 (2)
Since left side is y for both:
x² -7x + 10 = -6x + 5
Add 6x to both sides
=> x² -7x + 10 + 6x = -6x + 6x + 5
=> x² -x + 10 = 5
Subtract 5 both sides:
x² - x + 10 - 5 = 0
x² - x + 5 = 0
Comparing to the standard form we get
a = 1, b = -1, c = 5
b²- 4ac = (-1)² - (4 · 1 · 5)
= 1 - 20
= -19
Since b² - 4ac is negative, the system has no real roots
System C
y = -2x² + 9 (1)
8x - y = -17 (2)
In equation(2) isolate y by moving 8x to the right and multiplying by -1
=> -y = -8x - 17
=> y = 8x + 17 (3)
Set right sides of (1) = (3) right side
-2x² + 9 = 8x + 17
Move 8x + 17 to left side
=> -2x² + 9 - (8x + 17) = 0
=> -2x² + 9 - 8x - 17 = 0
=> -2x² - 8x - 8 = 0
we have a = -2, b = -8, c = -8
b² - 4ac = (-8)² - (4)(-2)(-8)
= 64 - (64) = 0
Hence this system has 1 real root
Name a median for ABC.
In the triangle ABC the line segment bisecting AC is the median, i.e. BD.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
The triangle ABC is given.
In Δ ABC, the line segment AC is bisected, so -
AD = CD
The line segment from a vertex to the middle of the other side is what is meant by a median. When the vertex is an angle in an equilateral triangle or the non-congruent angle of an isosceles triangle, it is also an angle bisector.
Since line segment BD bisects AC.
Therefore, the median is BD.
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12/13 x 13/15 x 15/36
Answer:
1/3 or 0.33333
Step-by-step explanation:
To find the product of two fractions, multiply numerators and denominators separately.
You get 2340/7020 which simplifies to 1/3.
Hope that helps.
Answer:
1/3
Step-by-step explanation:
Step 1) 12/13 x 12/15 = 156/195
Step 2) 156/195 x 15/36 = 2340/7020
Step 3) Simplify to get 1/3
At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 30 km/h. How fast is the distance between the ships changing at 4:00 PM?
The distance between the ships is increasing at a rate of approximately 98.82 km/h at 4:00 PM.
How fast is the distance between the ships changing at 4:00 PM?From the question, we have the following parameters that can be used in our computation:
Distance, D = 170 km
Rates = 40 km/h and 30 km/h
Let t be the time elapsed from noon to 4:00 PM
So, we have
t = 4
The distance between the ships to their east-west and north-south distances is represented as
d^2 = (D + rate 1 * t)^2 + (rate 2 * t)^2
So, we have
d^2 = (170 + 40t)^2 + (30t)^2
d^2 = 170^2 + 13600t + 1600t^2 + 900t^2
Differentiate with respect to time (t)
2D d' = 5000t + 13600
So, we have
D d' = 2500t + 6800
Substitute 4 for t
D d' = 16800
So, we have
d' = 16800/D
This gives
d' = 16800/170
d' = 98.82
So the distance between the ships is increasing at a rate of approximately 98.82 km/h at 4:00 PM.
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London borrowed $6,900 from a lender that charged simple interest at a rate of 2.56% for 4 years. What is the amount of interest London paid at the end of the loan?
Answer:
Payment Every Month $151.39
Total of 48 Payments $7,266.66
Total Interest $366.66
Step-by-step explanation:
Hope this helps
Please Choose Brainliest
a. Give an example of a countable collection of disjoint open intervals. !b. Give an example of an uncountable collection of disjoint open intervals, or argue that no such collection exists.!
a. An example of a countable collection of disjoint open intervals is the collection of intervals (0, 1/n), where n is a positive integer. This collection of intervals is countable because it can be put in one-to-one correspondence with the positive integers.
What is the one-to-one correspondence?
In mathematics, a one-to-one correspondence between two sets is a bijective function that maps every element of one set to exactly one element of the other set, and vice versa.
b. An example of an uncountable collection of disjoint open intervals is the collection of intervals (x, x + 1/n), where x is a real number and n is a positive integer. This collection of intervals is uncountable because it can be put in one-to-one correspondence with the real numbers. To see this, note that for any real number x, we can find a positive integer n such that 1/n is smaller than x. Then, the interval (x, x + 1/n) corresponds to x.
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A sample of 12 drivers shows the time that they spent (in minutes) stopped in rush-hour traffic on a specific snowy day last winter. Round your answers to one decimal place.
45 47 46 60 62 61 72 56 59 71 73 59
Find the range, variance, and standard deviation
The range is 28, the variance of the data is 82.75 and the standard deviation is 9.09.
What is measure of dispersion?Data variability is assessed using measures of dispersion. Variance, range, interquartile range, percentiles, and standard deviation are examples of dispersion measurements. Measures of central tendencies, such as mean, mode, and median, are combined with measures of dispersion.
The range is the difference between the largest value and the smallest value. According to the data:
Range = 73 - 45 = 28.
The variance is given as:
V = ∑(x - x')² / n
Where, x is the frequency, x' is the mean and n is the number of elements.
x d = (x - x') d²
45 14.25 203.06
46 13.25 175.56
47 12.25 150.06
56 3.25 1.56
59 0.25 0.065
59 0.25 0.065
60 -1.25 1.56
62 -2.25 5.06
61 -1.75 3.06
72 -12.25 150.06
71 -11.25 126.56
73 -13.25 175.56
∑x = 711 ∑d² = 992.73
x' = 711 / 12 = 59.25
V = ∑d²/ n
V = 992.73 / 12 = 82.75
The standard deviation is given as:
SD = √V = √82.75 = 9.09
Hence, the range is 28, the variance of the data is 82.75 and the standard deviation is 9.09.
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20. in this problem we assume that fish are caught at a constant rate h independent of the size of the fish population. then y satisfies dy dt
the solution of the given derivative will be y = k/2(1±√(1-4h/rk))
What is derivative?
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.
dy/dt = 0
-r/k y²+ry-h=0
y = k/2(1±√(1-4h/rk))
Hence the solution of the given derivative will be y = k/2(1±√(1-4h/rk))
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PLEASE HELP ME!
Anna is considering writing and publishing her own book She estimates her revenue equation as R = 6.56x and her cost equation as C = 10.063 + 1.09x where x is the number of books she sells. Find the minimum number of books she must sell to make a profit
Anna must sell atleast ? books to make a profit.
The minimum number of books she must sell to make a profit is 2.
What is profit?In mathematics, the gain from any business operation is referred to as the profit. Every time a shopkeeper sells a product, his goal is to make a profit by getting something from the customer. Basically, he sells the item for more money than it costs.
Given that Anna estimates her revenue equation as R = 6.56x
And her cost equation as C = 10.063 + 1.09x.
To get profit revenue is greater than cost, i.e.
R>C
6.56x > 10.063 + 1.09x
subtract 1.09x from both sides
6.56x - 1.09x > 10.063
5.47x > 10.063
divide both sides by 5.47
x > 10.063/ 5.47
x > 1.84
So the minimum number of books she must sell to make a profit is 2.
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coach wanted to determine whether the mean sprint speed of his team differed from the national athletics mean speed of 12 seconds. he therefore obtained the speed of members of his team shown below:8,12, 9,7,8,10,9,11,13.5,8.5,10.5,9.5,11.5,12.5,9.5,10.5. write/develop the hypothesis for a two-tailed test and calculate the standard error of the mean for the team .what is your conclusion based on the developed hypothesis in A
It can reject the null hypothesis at a significance level of 0.05 and conclude that the mean sprint speed of the team is significantly different from the national athletics mean speed of 12 seconds.
What is the formula for the standard error of the mean?The formula for the standard error of the mean is:
SE = s / √(n)
where s is the sample standard deviation and n is the sample size.
The null hypothesis for a two-tailed test would be:
H0: The mean sprint speed of the team is equal to 12 seconds.
The alternative hypothesis would be:
Ha: The mean sprint speed of the team is not equal to 12 seconds.
To test this hypothesis, we need to calculate the standard error of the mean for the team.
Using the data provided, we can calculate the sample mean, sample standard deviation, and sample size as follows:
x = (8+12+9+7+8+10+9+11+13.5+8.5+10.5+9.5+11.5+12.5+9.5+10.5) / 16 = 10
s = √(1/(n-1) × ((8-10)² + (12-10)² + ... + (10.5-10)²)) = 1.717
n = 16
Therefore, the standard error of the mean is:
SE = 1.717 / √(16) = 0.429
To test the hypothesis, we can calculate the t-statistic using the formula:
t = (x - μ) / (SE)
where μ is the hypothesized population mean.
Plugging in the values, we get:
t = (10.0625 - 12) / 0.429 = -4.389
Using a t-table with 15 degrees of freedom (n-1), we can find that the probability of obtaining a t-value of -4.389 or more extreme is less than 0.01.
This means that we can reject the null hypothesis at a significance level of 0.05, and conclude that the mean sprint speed of the team is significantly different from the national athletics mean speed of 12 seconds.
Learn more about the standard error here:
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