The Pythagorean theorem, established by the ancient Greek philosopher Pythagoras, defines the relationship in a right-angled triangle between the squares of the lengths of the legs (a and b) and the hypotenuse (c) with the famous equation: a² + b² = c².
Explanation:The Pythagorean Theorem
The Pythagorean theorem is a fundamental principle in the field of mathematics, specifically in geometry. It was established by the ancient Greek philosopher, Pythagoras, who made significant contributions to understanding the relationships in geometric figures. The theorem reveals a specific relationship between the sides of a right-angled triangle. It states that the square of the length of the hypotenuse (√), which is the side opposite the right angle, is equal to the sum of the squares of the lengths of the other two sides. This can be elegantly expressed in the formula: a² + b² = c². Here, a and b represent the legs of the triangle, while c represents the hypotenuse.
For example, if a right triangle has legs of lengths 9 units and 5 units, using the Pythagorean theorem, we can calculate the length of the hypotenuse. We would square each of the legs (√9² + 5²), add these together, and take the square root to find that the hypotenuse is approximately 10.3 units long.
This theorem is not only a theoretical concept but is also practical in various real-world scenarios, such as calculating distances in navigation. An old adage suggests that the shortest distance between two points is a straight line. When dealing with the distances on a map or between points in space, a right triangle can often form, and using the Pythagorean theorem allows us to calculate the direct straight-line distance (hypotenuse) easily.
(08.01 MC)
A researcher posts a newspaper advertisement offering $10 in exchange for participation in a short study. The researcher accepts the first 10 people who respond to the advertisement. Which of
following statements true about the sample?
It is not a valid sample because it is only a short study,
It is a valid sample because money is offered to participants.
It is a valid sample because the first 10 people were selected to participate.
It is not a valid sample because it is not a random sample of the population
Answer:
The correct answer is the last on that’s states: it is not a valid sample because it is not a random sample of the population.
Step-by-step explanation:
When a researcher wants to know about the same thing, he/she has to take a sample from the population.
Example, consider a researcher wants to know how many hours the students study at home in a week, so the researcher has to take the sample from the student population.
Here, he/she gives the advertisement and offers $10 for 10 people. Therefore for anyone can come they might not required for a particular study.
Therefore, the answer is the last one.
Answer:
d
Step-by-step explanation:
Write an equation to the nth term of the arithmetic sequence. (write the equation for the sequence)
15, 13, 11, 9
Answer:
15,13,11,9,…
Given
2
13 - 15 = -2
11 - 13 = -2
9 - 11 = -2
d = -2
3
4
when n = 515,13,11,9,…
Given
2
13 - 15 = -2
11 - 13 = -2
9 - 11 = -2
d = -2
3
4
when n = 515,13,11,9,…
Given
2
13 - 15 = -2
11 - 13 = -2
9 - 11 = -2
d = -2
3
4
when n = 5
A kite is flying at an angle of elevation of
about 55°. Ignoring the sag in the string,
find the height of the kite if 60 m of string
has been let out.
* help please *
Answer:
49.15 m
Step-by-step explanation:
Length of the string is the hupotenuse: 60
Height of the kite is the opposite: X
sin(55) = opposite/hypotenuse
sin(55) = X/60
X = 60sin(55)
X = 49.14912266 m
Which of the following is true if the data point 11.1 is corrected to 11.7?
A.The mean increases.
B.The median increases.
C.The data set has two modes.
D. The range increases.
Answer:
Which of the following is true if the data point 11.1 is corrected to 11.7?
A.The mean increases.
B.The median increases.
C.The data set has two modes.
D.The range increases.
A.The mean increases.
C.The data set has two modes.
These are the correct answers.
A and C will be correct answers.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including basic arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given that the Data point is corrected from 11.1 to 11.7. As we already know if we increase the value of the data point the mean will rise when a data point is added that is above the mean or subtracted that is below the mean. The mean will drop if one or more data points are removed that are above the mean or added that are below the mean.
Therefore, If data point 1.1 is corrected to 11.7 then the mean will increase and the data set has two modes.
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Helllppppppppp pleaseeeeeee
Answer:
17 cm
Step-by-step explanation:
Because if you use the Pythagorean threom a^2 + b^2 = c^2. 8 squared is 64 and 15 squared is 225 add those and you get 289, and 17 squared is 289.
Nora has $50 saved and gets $12 a week in allowance. Write a function to show the total amount of money she will have saved after n weeks.
Answer:
After 'n' weeks?
Step-by-step explanation:
Make sure your question makes sense.
3x^2 and 6x^2 greatest common factor
which glass will get filled first. be very observant to all the paths and think about what would really happen.
Answer:
Number 7
Step-by-step explanation:
That's the one that is at the bottom and the corresponding tubes lead to the one being the first to be filled
Geometry help for an idiot lol pls help
Answer:
B
Step-by-step explanation:
The transformation is proved through comparing the size of the bigger triangle to the smaller triangle in the individual sides. So the size of A F/ AB should be equal to AG / AC due to transformations making A F and AG the same times longer as AC and AB. By performing those calculations, you get 3.
An amusement park charges an admission fee of 25 dollars per person. The cost, C (in dollars), of admission for a group of p people is given by the following function.
Answer:
c=25p
Step-by-step explanation:
c= total cost
p=number of people
total cost is the numer of people times 25 dollars each
alice took out 80/20 mortgage on a $232,000 home. what is the amount financed under the first mortgage?
Answer:
The amount financed under this mortgage is $185,600
Step-by-step explanation:
Alice took out an 80/20 mortgage on a $232,000 home.
80/20 mortgage means pay 20% down payment and 80% finance amount of home value.
Home value = $232,000
Now, we need to find finance amount from this hone value of $232,000
Let's calculate the 80% of $232,000 as finance amount;
Finance amount = 80% of 232000
Finance amount = 0.80 x 232000
Finance amount = 185,600
Hence, The amount financed under this mortgage is $185,600
Tyler poured a total of 15 cups of water into 2 equal-sized bottles and filled each bottle. How much water was in each bottle?
||||
☆Thanks for the help guys!☆
Step-by-step explanation:
So 2 bottles and 15 cups
15 ÷ 2 = 7.5
He poured 7.5 cups of water in each bottle
Answer:
if you need a diagram here you go
Step-by-step explanation:
Which statements are true? Check all that apply.
1 A is in Quadrant I.
2 B is on the x-axis.
3 C is in Quadrant I.
4 D is in Quadrant III.
5 E is on the x-axis.
6 F is on the x-axis.
7 G is on the y-axis.
Answer:
1,4,6
Step-by-step explanation:
A tourist on vacation went scuba diving at a depth where 0.0871 l of gas in his blood is under 12.0 atm of pressure if he instantly boards a plane where his blood will be under 1.50 atm of pressure what will be the volume of gas in his blood
Answer:
0.6968 L
Step-by-step explanation:
We can calculate the resulting volume thanks to Boyle's Law, which tells us The volume is inversely proportional to the pressure:
• If the pressure increases, the volume decreases.
• If the pressure decreases, the volume increases.
Thus:
P1V1 = P2V2
We know that P1 = 12 atm, V1 = 0.0871 L and P2 = 1.5 atm, that is, the value that we do not know about V2, therefore we solve for V2:
V2 = P1V1 / P2
Replacing:
V2 = 12 * 0.0871 /1.5
V2 = 0.6968 L
Which makes sense, since decreasing the pressure increases the volume.
(PART A PART B) PLEASE HELP!!! DUE TODAY!!!! ❤️
Answer:
the anser from what i see should be option 1
Step-by-step explanation:
The reason why i say this is because number 1 is linear which means it is just multipying but your multiplying and adding and its not option 3 because question 5 said the questions started at 1
A child has toy blocks that contain the numbers 1 through 80. What is the probability that the will pick up a number that is not a multiple of 11?
Give your answer in fraction form.
Answer: 7/80
Step-by-step explanation: There are 7 multiples of 11 between 1 and 80, so you just put the 7 over the total number which is 80
You start driving north for 3 miles, turn right, and drive east for another 4 miles. At
the end of driving, what is your straight line distance from your starting point?
The straight line distance is 5 miles from starting point.
Step-by-step explanation:
Driving 3 miles north and 4 miles east and then the straight line distance will form a right angled triangle.
What’s the answers????!!!!
Answer:
[tex] f(0) = 1 [/tex]
Step-by-step explanation:
The initial value is the value when x = 0.
[tex] f(x) = 4^x [/tex]
For x = 0,
[tex] f(0) = 4^0 [/tex]
[tex] f(0) = 1 [/tex]
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.
α = 0.08; H1 is μ ≠ 3.24
a. ±1.75
b. 1.75
c. ±1.41
d. 1.41
Answer:
The critical z value used to test a null hypothesis is ±1.75.
Step-by-step explanation:
We are given that the data has a normal distribution and the number of observations is greater than fifty.
Also, the hypothesis given to us is;
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 3.24
Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu\neq[/tex] 3.24
This means that our test is two-tailed because in the alternate hypothesis we are concerned with mean value is less than or greater than 3.24.
Also, level of significance (α) = 0.08
Now, for two-tailed test level of significance becomes = [tex]\frac{\alpha}{2} =\frac{0.08}{2}[/tex] = 0.04
So, in the z-table the critical value of x at 4% significance level is given as 1.75.
Since, this is two-tailed test so the critical z value used to test a null hypothesis would be ±1.75.
At the 4% significance level, the z-value is 1.75. Therefore, for the two tailed test the z value becomes [tex]\pm[/tex] 1.75. and this can be determined by using the given data.
Given :
Assume that the data has a normal distribution and the number of observations is greater than fifty.α = 0.08H1 is μ ≠ 3.24According to the hypothesis test:
Null Hypothesis -- [tex]\rm H_0:\mu=3.24[/tex]
Alternate Hypothesis -- [tex]\rm H_1 : \mu\neq 3.24[/tex]
According to the given data, the significance level is given by α = 0.08. So, the significance level for the two tailed test is given by:
[tex]\rm \dfrac{\alpha }{2}=\dfrac{0.08}{2}=0.04[/tex]
So, for the 4% significance level, the z-value is 1.75. Therefore, for the two tailed test the z value becomes [tex]\pm[/tex] 1.75.
So, the correct option is a).
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What is the diameter of the circle shown below?
Diameter is 12. Diameter is radius times 2. 6 times 2=12
Answer:
12
Step-by-step explanation:
the diameter is 2x the radius, in this case we have 6 as the radius so naturally the diameter is 12
For the following data set, calculate the mean and median. Any non-integer answers should be rounded to
the nearest tenth.
5,5, 9, 10, 13, 16, 18, 20, 22, 22
Answer:
(a)Mean=14
(b)Median=14.5
Step-by-step explanation:
Given the data set:
5,5, 9, 10, 13, 16, 18, 20, 22, 22
(a)Mean
[tex]\bar{x}=\dfrac{5+5+9+10+13+16+18+20+22+22}{10} \\=\dfrac{140}{10} \\Mean=14[/tex]
(b)5,5, 9, 10, 13, 16, 18, 20, 22, 22
Since we have two terms in the middle, we take the average to obtain the median.
Median
[tex]=\frac{13+16}{2}\\=\frac{29}{2}\\Median=14.5[/tex]
What best describes the Debt Snowball method for paying off debt
Answer:
The debt snowball method is a debt reduction strategy where you pay off debt in order of smallest to largest, gaining momentum as you knock out each balance. When the smallest debt is paid in full, you roll the money you were paying on that debt into the next smallest balance.
Step-by-step explanation:
Answer:
a debt reduction str
ategy where you pay off debt in order of smallest to largest, gaining momentum as you knock out each balance.
Step-by-step explanation:
The map shows the length (in miles) of shoreline along the Gulf of Mexica for each state that borders the body of water. What is the probability that a ship coming ashore at a random point in the Gulf of Mexico lands in the given state? Round your answers to the nearest whole percent.
Answer:
TX- 23%
AL- 3%
FL- 47%
LA- 24%
MS- 3%
Step-by-step explanation:
Final answer:
To find the probability of a ship coming ashore in a given state, divide the length of its shoreline by the total length of the Gulf of Mexico's shoreline.
Explanation:
To find the probability of a ship coming ashore at a random point in the Gulf of Mexico landing in a given state, we need to divide the length of the shoreline of that state by the total length of the Gulf of Mexico's shoreline. Let's assume there are 4 states that border the Gulf of Mexico: State A with 100 miles of shoreline, State B with 150 miles, State C with 200 miles, and State D with 250 miles. The total shoreline length of the Gulf of Mexico would be 700 miles (100 + 150 + 200 + 250).
Now, we can find the probability for each state by dividing its shoreline length by the total shoreline length. For example, for State A, the probability would be 100/700 which is approximately 0.1429 or 14.29%.
Following the same calculation, the probability for State B is 150/700 which is approximately 0.2143 or 21.43%, the probability for State C is 200/700 which is approximately 0.2857 or 28.57%, and the probability for State D is 250/700 which is approximately 0.3571 or 35.71%.
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The following box plot shows the number of books sold each day at a store for 60 days. How many days did the bookstore sell 2 to 12 books?
10
15
30
45
Answer:
45
Step-by-step explanation:
I'll mark the correct answer the Brainiest
What is the sum of 4.9 × 10^2 and 6.8 × 10^3?
A.
1.17 × 10^3
B.
1.17 × 10^5
C.
1.17 × 10^7
D.
7.29 × 10^2
E.
7.29 × 10^3
Answer:
E
Step-by-step explanation:
To find the sum, you most find the answers for both powers of tens. 10^2 is 100, so 4.9*100=490. 10^3 is 1000, so 6.8^1000= 6800. Add them together and you get 7290, which if divided by 1000, you get 7.29. Since 10^3 is 1000, the correct answer isE.
find the length of the hypotenuse round your answer to the nearest hundred
What is the value of the product (3 – 21)(3 + 2/)?
5
9 + 4
9 - 41
13
The product of (3 – 2i) and (3 + 2i) simplifies to 13 after expanding and simplifying the expression, canceling out the imaginary terms.
To find the product of (3 – 2i) and (3 + 2i), we'll use the distributive property:
(3 - 2i)(3 + 2i) = 3(3) + 3(2i) - 2i(3) - 2i(2i)
= 9 + 6i - 6i - 4i²
Since i² = -1, substitute -1 for i²:
= 9 + 6i - 6i - 4(-1)
= 9 + 6i - 6i + 4
The terms with imaginary parts cancel out:
= 9 + 4
= 13
Thus, the product of (3 – 2i) and (3 + 2i) equals 13.
Complete Question:
What is the value of the product (3 – 2i)(3 + 2i)?
5
9 + 4i
9 – 4i
13
Use the Venn diagram to calculate conditional probabilities.
Circles D, E, and F overlap. Circle D contains 13, circle E contains 4, and circle F contains F. The overlap of D and E contains 6, the overlap of E and F contains 7, and the overlap of F and D contains 5. The overlap of all 3 circles contains 5. Number 3 is outside of the circles.
Which conditional probabilities are correct? Check all that apply.
P(D | F) = StartFraction 6 Over 34 EndFraction
P(E | D) = StartFraction 7 Over 25 EndFraction
P(D | E) = StartFraction 7 Over 25 EndFraction
P(F | E) = StartFraction 8 Over 18 EndFraction
P(E | F) = StartFraction 13 Over 21 EndFraction
Answer:
E2020 A, B, D
Step-by-step explanation:
The probability of P(D|F), P(E|D), and P(F|E) are 6/34, 7/25, and 8/18 options (A), (B), and (D) are correct.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we can see in the Venn diagram the data is shown.
P(D | F) = The probability of event D that depends on the event F.
P(D|F) = 6/34
Similarly:
P(E|D) = 7/25
P(F|E) = 8/18
Thus, the probability of P(D|F), P(E|D), and P(F|E) are 6/34, 7/25, and 8/18 options (A), (B), and (D) are correct.
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Which fractions are equivalent to 40%? Check all that apply.
1 . StartFraction 8 Over 100 EndFraction
2 . Two-fifths
3 . StartFraction 8 Over 20 EndFraction
4 . StartFraction 4 Over 10 EndFraction
5 . StartFraction 16 Over 40 EndFraction
Answer:
2/5
8/20
4/10
16/40
Step-by-step explanation:
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The fractions that are equivalent to 40% are 4/10 and 8/20
Fractions and percentagesFractions are written as a ratio of two integers
Given the percentage 40%
Write as a fraction
40% = 40/100
Divide through by 4
40% = 40/100 = 4/10
Multiply both numerator and denominator by 2
4/10 * 2/2 = 8/20
Hence the fractions that are equivalent to 40% are 4/10 and 8/20
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At 8 a.m. the temperature was –4ºC. At 12 p.m., the temperature was –1ºC. Shayla claims that it was warmer at 8 a.m. than it was at 12 p.m.
What mistake did Shayla most likely make when comparing the temperatures?
A. She used a number line.
B. She compared the absolute values.
C. She compared the order of the numbers.
D. She counted the distance from zero incorrectly.
Answer:
I believe the answer is C.
Step-by-step explanation:
Shayla forgotten that the further you are away, the more colder it gets or you are further away from zero. It is more warmer at 12pm than 8am as it was -1 degrees celsius which is warmer than -4 degrees celsius.