find x. provide an explanation
Applying the inscribed angle theorem, the value of x is calculated as: 47 degrees.
How to Apply the Inscribed Angle Theorem?If an inscribed angle intercepts an arc in a circle, according to the inscribed angle theorem, we have:
measure of inscribed angle = 1/2(measure of intercepted arc) or 1/2(measure of central angle)
x is an inscribed angle, while 94 degrees is a central angle. Therefore, we have:
x = 1/2(94)
x = 47 degrees.
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I need some help please
Step-by-step explanation:
'3' is greater than 0 so we use the second portion of f(x)
f(3) = x+1
= 3 + 1 = 4
3 Marcus has 500 g of flour. He uses 200g to bake
bread and 120g to make biscuits.
Work out the percentage of the flour:
A he uses for bread
B he uses for biscuits
C he does not use
Answer:
40% , 24% , 36%
Step-by-step explanation:
first express each as a fraction then multiply the fraction by 100%
A
[tex]\frac{200}{500}[/tex] × 100% = 0.4 × 100% = 40% used for bread
B
[tex]\frac{120}{500}[/tex] × 100% = 0.24 × 100% = 24% used for biscuits
C
percentage not used = 100% - (40 + 24)% = 100% - 64% = 36%
On the way to her babysitting job, Mary rode her bike for the first mile. She stopped at a traffic light and waited a few minutes for the traffic light to turn green. She then walked her bike across the street and up a short steep hill. Finally, she rode the bike at a constant speed for one more mile. If Mary created a graph of her time and distance, which statement describes the part of her graph that would show no change in distance?
Mary used her bike to ride the first mile.
Mary stopped and waited for the traffic light to turn green.
Mary walked her bike across the avenue and up a short hill.
Mary rode her bike at a constant speed for one mile.
The part of the graph that would show no change in distance is when Mary stopped and waited for the traffic light to turn green.
Statement B is correct.
How do we calculate?We know that during this time, Mary did not move forward or cover any distance. Hence, the graph would show a flat line at this point, indicating no change in distance.
Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are.
In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
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UO
Graph each figure and classify it. Then find the area.
6. R(3,-2), S(7, -2), T(8, -6), V(1, -6)
22 unit² is the area of trapezoid .
In arithmetic, what is a polygon?
A polygon is a closed, one-dimensional, flat or planar structure that is circumscribed by straight sides. There are no curves on its sides. Polygonal edges are another name for the sides of a polygon. A polygon's vertices (or corners) are the places where two sides converge.
this is trapezoid .
area of trapezoid = 1/2 * sum of parallel side * height
= 1/2 * (3 + 8 ) * 4
= 22 unit²
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financial planner puts $3,500 into a college savings plan that pays 7.5% simple interest annually. If no additional deposits are made into the savings plan, how much interest is accumulated at the end of 5 years? A. $262.50 |B. $1,312.50* C. $ 2,625.00 D. $4,812.50
Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.
Define about the term simple interest:Simple interest (SI) is calculated as a percentage added to the principle amount deposited or borrowed for a given period of time. SI is typically expressed as years.
As a result, it represents the real expense incurred on the main sum. The accrued interest is not included in this. SI and CI are very dissimilar to one another. CI is the interest rate applied to both the principal amount and the total amount of unpaid interest.Given data:
Principal P = $3,500Simple Interest rate R = 7.5%Time T = 5 yearsSimple interest formula:
SI = PRT / 100
SI = 3500*7.5*5 / 100
SI = 1312.5
Now,
Amount = principal + simple interest
Amount = 3500 + 1312.5
Amount = $4812.50
Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.
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GIVING 50 POINTS, BRAINLYEST, 5 STARS, AND THANKS IF YOU ANSWER CORRECTLY!!!
A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads. (2 points)
Part B: Flip a coin 15 times and record the frequency of each outcome. (4 points)
Part C: Determine the experimental probability of landing on heads. (4 points)
Part D: Compare the theoretical and experimental probabilities. Explain your answer. (2 points)
Answer:
Part A: 1/2 or 0.5
Part B: heads is 8, tails is 7.
Part C: 8/15 or 0.533.
Part D: The theoretical and experimental probabilities are close but not exactly the same. This is because the theoretical probability is based on an ideal situation where the coin is fair, and the outcomes are equally likely. The experimental probability is based on actual data that may vary due to chance or other factors. The more trials we perform, the closer the experimental probability will get to the theoretical probability. It's like when you practice a skill and get better at it over time, but you still make mistakes sometimes.
Step-by-step explanation:
Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. This is because there are two possible outcomes (heads or tails) and only one favorable outcome (heads). This is also the same probability of me winning the lottery, finding a unicorn, or getting a date.
\(∘-∘)/ <-------- single pringle
Part B: I flipped a coin 15 times and got the following results:
H T H H T T H H T H T H T T H
or (in a more orderly fashion)
HHHHHHHH
TTTTTTT
The frequency of heads is 8 and the frequency of tails is 7. This means that I was slightly luckier than average, but not enough to make a difference. Maybe I should have used a different coin, or a different hand, or a different day.
Part C: The experimental probability of landing on heads is the ratio of the frequency of heads to the total number of trials. In this case, it is 8/15 or 0.533. This is slightly higher than the theoretical probability, but still within the margin of error. It's like when you order a pizza and get one extra slice, but it's the one with pineapple.
Part D: The theoretical and experimental probabilities are close but not exactly the same. This is because the theoretical probability is based on an ideal situation where the coin is fair, and the outcomes are equally likely. The experimental probability is based on actual data that may vary due to chance or other factors. The more trials we perform, the closer the experimental probability will get to the theoretical probability. It's like when you practice a skill and get better at it over time, but you still make mistakes sometimes.
✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧
Your friend in college decides to purchase textbooks using his credit card, which has an APR
(Annual Percentage Rate) of 12.5% compounded continuously. He charges $500 for the
textbooks. Without making any payments, after how many years will his credit card balance be
$1360? Round your answer to the nearest year.
The time that it will take for the balance to be of $1360 is given as follows:
8 years.
How to model continuous compounding?The balance of an account after t years, using continuous compounding, is modeled by the equation presented as follows:
A(t) = A(0)e^(kt).
In which:
A(0) is the initial amount.k is the continuous compounding rates.The parameters for this problem are given as follows:
A(t) = 1360, A(0) = 500, k = 0.125.
Hence the time is obtained as follows:
500e^(0.125t) = 1360
e^(0.125t) = 1360/500
0.125t = ln(1360/500)
t = ln(1360/500)/0.125
t = 8 years.
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Find the line parallel to y=5x+3 that includes the point (-1,6)
Write in y-y1=m(x-x1)
Answer:
y=5x-6
Step-by-step explanation:
A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The percentage of people who said they preferred Candidate A was 80%. The margin of error for the survey was 4%. Which of the following is not a reasonable value for the actual percentage of the population that prefers Candidate A? Group of answer choices 75.6% 82.4% 76.4% 83.3%
83.3% is outside the range and therefore not a reasonable value.
How to determine which value is not a reasonable value?
We need to take into account the margin of error in order to determine which value is not a reasonable one for the actual proportion of the population that favors Candidate A. The range within which the actual population value is likely to fall is shown by the margin of error.
We can determine the likely range of the true population value as follows if the sample contained 80% of those who preferred Candidate A and the margin of error was 4%:
The lower bound of the range is 80% - 4% = 76%
The upper bound of the range is 80% + 4% = 84%
Therefore, any value outside of this range is not a reasonable value for the actual percentage of the population that prefers Candidate A.
75.6% is within the range and therefore a reasonable value.
82.4% is within the range and therefore a reasonable value.
76.4% is within the range and therefore a reasonable value.
83.3% is outside the range and therefore not a reasonable value.
So the answer is 83.3%.
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Determina la altura del papalote con respecto al piso considerando los datos presentados.
The length of the string required to fly the kite at a height of 75 meters from the ground is 86.6 meters.
The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is the height of the kite (75 m), and the hypotenuse is the length of the string that we need to find. We can set up an equation using the sine function:
sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = 75/hypotenuse
We can simplify the equation using the value of the sine of 60 degrees, which is √3/2.
√3/2 = 75/hypotenuse
To solve for the length of the string, we can cross-multiply and simplify:
hypotenuse = 75/(√3/2)
hypotenuse = (75*2)/√3
hypotenuse = 150/√3
hypotenuse = (150/√3) * (√3/√3) (to rationalize the denominator)
hypotenuse = (150√3)/3
hypotenuse = 50√3 meters = 86.6 meters.
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Complete Question:
A kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60 ∘ to the horizontal. Find the length of the string, assuming that there is no slack in it. [Take √ 3 =1.732].
Jasmine and her sister are saving to buy MP3 players. Jasmine has $50 and plans to
save $10 per week. Her sister has $80 and plans to save $7 per week. In how many
weeks will Jasmine have more money saved than her sister?
If Jasmine saves $10 per week and her sister saves $7 per week, then Jasmine will have more "money-saved" than her sister in 10 weeks.
Let the number of weeks be denoted by "x",
We know that,
The Jasmine's initial-savings is = $50,
The amount which Jasmine weekly saves is = $10,
Her sister's initial savings is = $80,
The amount which her sister weekly-saves is = $7,
We have to find the value of "x" when Jasmine's savings exceed her sister's savings.
Total saving's of Jasmine after "x" weeks is calculated as,
⇒ Jasmine's total savings = Initial savings + (Weekly savings × Number of weeks),
⇒ $50 + ($10 × x),
Her sister's total savings after "x" weeks can be calculated as:
⇒ Sister's total savings = Initial savings + (Weekly savings × Number of weeks),
⇒ $80 + ($7 × x),
We write the equation to find the value of "x" when Jasmine's total savings exceed her sister's total savings,
⇒ 50 + 10x > 80 + 7x,
⇒ 50 + 10x - 80 > 7x,
⇒ 50 - 80 > 7x - 10x,
⇒ -30 > -3x,
⇒ -30/-3 < x,
⇒ 10 < x,
Therefore, Jasmine will have more money than her sister is after 10 weeks.
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Question 2
Mike deposited $3,000 in the first year of a retirement account, and then increased the deposits by $300 each year. The account earned 8.35%. What was the account value after forty years?
The account value after forty years is approximately $489,074,140.57.
What is formula for the future value of an annuity?To calculate the account value after forty years, we need to use the formula for the future value of an annuity:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods.
In this case, we have:
P = $3,000 in year 1, and then $3,300 in year 2, $3,600 in year 3, and so on
r = 8.35% = 0.0835 (assuming the interest rate is compounded annually)
n = 40 years
To compute the future worth of the annuity, we really want to ascertain the aggregate sum of installments over the 40 years. This should be possible involving the equation for the amount of a number-crunching series:
S = n/2 * [2a + (n-1)d]
where S is the sum, a is the first term, d is the common difference, and n is the number of terms.
In this case, we have:
a = $3,000
d = $300
n = 40
Plugging these values into the formula, we get:
S = 40/2 * [2($3,000) + (40-1)($300)] = $2,340,000
Thus, the aggregate sum of installments more than 40 years is $2,340,000.
We can now enter these figures into the formula for annuity future value:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
[tex]FV = $2,340,000 * [(1 + 0.0835)^{40} - 1] / 0.0835[/tex]
FV = $2,340,000 * 209.251
FV = $489,074,140.57
Consequently, after forty years, the account's value is approximately $489,074,140.57.
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if sally gets scores 73, 85, 93, the 4th score is 20 points less than 5th score which is 2/3 of the average of the first three. what must she score on the 6th and 7th test to average an 85
There is no solution that allows Sally to average an 85 with the given scores.
Let's start by finding the 5th score:
We know that the 4th score is 20 points less than the 5th score, so let's call the 5th score "x". Therefore, the 4th score is "x - 20".
We also know that the 5th score is 2/3 of the average of the first three scores. The average of the first three scores is (73 + 85 + 93)/3 = 83.67. So, (2/3) * 83.67 = 55.78 is the 5th score (rounded to two decimal places).
Therefore, x = 55.78/(2/3) = 83.67 is the 5th score.
Now, let's calculate the total score Sally needs to average an 85:
She already has 73 + 85 + 93 + 83.67 = 334.67 points. To average an 85 over seven tests, she needs a total of 7 * 85 = 595 points.
To find the scores she needs on the 6th and 7th tests, we can subtract the points she already has from the total points she needs:
595 - 334.67 = 260.33
So, Sally needs a total of 260.33 points on the 6th and 7th tests combined.
Let's call the 6th score "y" and the 7th score "z". We can set up an equation to solve for these two scores:
(y + z)/2 = 260.33
Multiplying both sides by 2:
y + z = 520.67
Since Sally needs to average an 85 over seven tests, the sum of all seven scores must be:
7 * 85 = 595
The sum of the first five scores is:
73 + 85 + 93 + 83.67 + 83.67 = 418.34
So, the sum of the last two scores must be:
595 - 418.34 = 176.66
Now we can set up another equation:
y + z = 176.66
We can solve this equation for one of the variables. Let's solve for "y":
y = 176.66 - z
Now we can substitute this into the first equation:
(176.66 - z + z)/2 = 260.33
176.66/2 = 260.33
88.33 = 260.33
This equation does not make sense.
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A recipe calls for 23\frac{2}{3}
3
2
cup of brown sugar. Marilyn is making 5 batches. How many cups of brown sugar should Marilyn use?
Marilyn needs 3 and 1/3 cups of brown sugar to make 5 batches of the recipe.
To find the total amount of brown sugar Marilyn needs, we need to multiply the amount required for one batch by the number of batches.
One batch requires 2/3 cup of brown sugar. To find the amount required for five batches, we can multiply 2/3 by 5.
2/3 * 5 = 10/3
So Marilyn needs 10/3 cups of brown sugar to make 5 batches of the recipe. However, it's usually easier to work with mixed numbers or whole numbers.
To convert the fraction 10/3 to a mixed number, we divide the numerator (10) by the denominator (3) and get a quotient of 3 with a remainder of 1. So:
10/3 = 3 1/3
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PLEASE HELP MY MOMS GONNA KICK MT BUTT AND I JUST DONT GET THIS!!!Add.
(2h + 8) + (9h² + 2h)
Collina’s Italian Café in Houston, Texas, advertises that carryout orders take about 25 minutes (Collina’s website, February 27, 2008). Assume that the time required for a carryout order to be ready for customer pickup has an exponential distribution with a mean of 25 minutes.a. What is the probability than a carryout order will be ready within 20 minutes?b. If a customer arrives 30 minutes after placing an order, what is the probability that the order will not be ready?c. A particular customer lives 15 minutes from Collina’s Italian Café. If the customer places a telephone order at 5:20 P.M., what is the probability that the customer can drive to the café, pick up the order, and return home by 6:00 P.M.?
The probability of a carryout order being ready within 20 minutes is approximately 0.5507
We know that the time required for a carryout order to be ready for customer pickup follows an exponential distribution with a mean of 25 minutes. The probability density function for an exponential distribution is given by
f(x) = λe^(-λx)
where λ is the rate parameter
We can find the rate parameter λ using the mean
mean = 1/λ
λ = 1/mean = 1/25 = 0.04
So the probability of a carryout order being ready within 20 minutes is
P(X ≤ 20) = ∫₀²⁰ λe^(-λx) dx
P(X ≤ 20) = [-e^(-λx)]₀²⁰
P(X ≤ 20) = [-e^(-0.04x)]₀²⁰
P(X ≤ 20) = [-e^(-0.8)] - [-1]
P(X ≤ 20) = 0.5507
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The given question is incomplete, the complete question is:
Collina’s Italian Café in Houston, Texas, advertises that carryout orders take about 25 minutes (Collina’s website, February 27, 2008). Assume that the time required for a carryout order to be ready for customer pickup has an exponential distribution with a mean of 25 minutes. What is the probability than a carryout order will be ready within 20 minutes?
hello! i need help thru out 10-12!!!
what u need to do : decide if each figure is symmetric. then, tell how much lines each figure has
THANKS!!
Please help me this would bring my grade up ALOT!
THANK YOU SO MUCH !!!!!!!!!!!!!!!!!!!!
Answer:
To determine the number of sheets of cardboard in a stack, we need to use the information given in the problem.
We know that each sheet of cardboard is 1 inch thick, and 16 sheets are stacked on top of each other in packages. The height of each stack is 21 inches.
Using the model of a ruler, we can divide the height of the stack (21 inches) by the thickness of each sheet (1 inch) to find the number of sheets in the stack.
21 ÷ 1 = 21
So, there are 21 sheets of cardboard in a stack.
To write an expression that can be used to determine the number of sheets of cardboard in a stack, we can use:
Number of sheets = height of stack ÷ thickness of each sheet
Or, substituting the given values: Number of sheets = 21 ÷ 1 = 21
This expression is simply a representation of the model we used earlier. It shows that we can determine the number of sheets in a stack by dividing the height of the stack by the thickness of each sheet. In this case, the expression yields the same result as the model, which is 21 sheets.
water leaks from a tank at a rate of 2 5t liters/hour, where t is the number of hours after 7 am. how much water is lost between 9 and 11 am?
the total amount of water lost between 9 and 11 am is 5 liters.
To find out how much water is lost between 9 and 11 am, we need to calculate the total amount of water that leaks out during that time period.
First, we need to find the number of hours between 7 am and 9 am, which is 2 hours. Similarly, the number of hours between 7 am and 11 am is 4 hours.
Next, we can use the given rate of water leakage to calculate the amount of water lost during each of these time periods:
Amount of water lost between 7 am and 9 am:
2.5 liters/hour × 2 hours = 5 liters
Amount of water lost between 7 am and 11 am:
2.5 liters/hour × 4 hours = 10 liters
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URGENT! Will give brainliest
The formula =C6*D6 would be found in which cell of this spreadsheet?
A. E6
B. E3
C.D3
D. B6
Answer:A. E6
Step-by-step explanation: Just did it :)
If the dimensions of the following cylinder are tripled, what will be the volume of the new cylinder?
15,260.4 cm 3
61,041.6 cm 3
183,124.8 cm 3
45,781.2 cm 3
Radius 12cm Height 15cm
Answer:
C) 183,124.8 cm^3.Step-by-step explanation:
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
The current volume of the cylinder is:
V = π(12cm)^2(15cm)
V = π(144cm^2)(15cm)
V = 2160π cm^3
If the dimensions of the cylinder are tripled, then the new cylinder will have a radius of 3(12cm) = 36cm and a height of 3(15cm) = 45cm.
The new volume of the cylinder is:
V = π(36cm)^2(45cm)
V = π(1296cm^2)(45cm)
V = 58320π cm^3
Simplifying the expression, we get:
V ≈ 183,124.8 cm^3
Therefore, the volume of the new cylinder, when the dimensions are tripled, is approximately 183,124.8 cm^3.
The answer is C) 183,124.8 cm^3.
Hi,
-The correct answer should be "option 4," 45,781.2 cm ^3.
Let me know if my answer is wrong or not what you were looking for because I would like to help all I can.
If you have any questions let me know and I may be able to help.
I hope that my answer helped you out. :)
Here is the correct figure if anybody needs it. ⇅
a food shop offers 5 different sandwiches and 8 different drink choices. how many choices are possible for a single sandwich and a drink?
Answer:
Step-by-step explanation:
5
Express as a trinomial.
(
2
�
−
3
)
(
3
�
−
4
)
(2x−3)(3x−4)
Answer: 6x^2 - 17x + 12.
Step-by-step explanation:
To multiply these two binomials, we can use the FOIL method, which stands for First, Outer, Inner, Last. This gives us:
(2x - 3)(3x - 4) = (2x)(3x) + (2x)(-4) + (-3)(3x) + (-3)(-4)
Simplifying each term, we get:
(6x^2) + (-8x) + (-9x) + 12
Combining like terms, we can simplify this to:
6x^2 - 17x + 12
Therefore, (2x-3)(3x-4) can be expressed as the trinomial 6x^2 - 17x + 12.
HELP I NEED HELP PLEASE THANKS I HAVE SCHOOL IN 30 MINUTES PLEASE
Answer:
5. 1 line
6. none
7. 2 lines
8. 1 line
9. 1 line
jim tosses a fair coin to decide whether his next vacation will be in hawaii or alaska. if it is a head, jim visits hawaii, or else he decides to visit alaska. if in hawaii, jim surfs during the vacation with a probability of 0.9. if in alaska, jim is going to surf in the ocean with probability 0.1 only. given that we know that jim went on surf- ing during the vacation, what is the conditional probability that his vacation was in alaska?
the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation is 0.1, or 10%.
Let A be the event that Jim's vacation was in Alaska, and let S be the event that Jim went surfing during the vacation. We want to find P(A|S), the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation.
By Bayes' theorem, we have:
P(A|S) = P(S|A) * P(A) / P(S)
We can calculate each term as follows:
P(S|A) = 0.1: the probability that Jim went surfing during the vacation given that he was in Alaska.
P(A) = 0.5: the probability that Jim's vacation was in Alaska, since he tosses a fair coin to decide between Hawaii and Alaska.
P(S) = P(S|A) * P(A) + P(S|H) * P(H) = 0.1 * 0.5 + 0.9 * 0.5 = 0.5: the total probability of Jim going surfing during the vacation, since he either went surfing in Alaska with probability 0.1 or went surfing in Hawaii with probability 0.9.
Therefore, we have:
P(A|S) = P(S|A) * P(A) / P(S) = 0.1 * 0.5 / 0.5 = 0.1
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1870003# gave an answer about Sean and his aquarium in ratios. He had 7 guppies to 12 cichlids which came out to be 7:12 and 4 tetras to 11 catfishes in ratios it is 4:11 and lastly he had a ratio of corydoras catfishes 9 to the total number of fishes is how many ratio to the total number of fish? I had 11:34 is that right?
The simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.
How to find the the ratioTo find the ratio of corydoras catfishes to the total number of fish, we need to add up the number of corydoras catfishes to the total number of fish, and express the ratio as a simplified fraction.
The total number of fish is 7 + 12 + 4 + 11 = 34.
The ratio of corydoras catfishes to the total number of fish is 9:34.
To simplify this ratio, we can divide both sides by the greatest common factor, which is 1 in this case.
So the simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.
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How can 25% of one item be different from 25% of another? Explain
The difference between the two items are depends on sample size, the method of counting, or the criteria for classification can all impact the percentage calculation.
Percentage is a measure of the proportion of one value to another expressed as a fraction of 100. For example, if there are 100 apples, and 25 of them are red, then the percentage of red apples is 25%. Similarly, if there are 200 bananas, and 50 of them are ripe, then the percentage of ripe bananas is also 25%.
However, the context in which these percentages are calculated can be different. For instance, the way in which the 25% of red apples was calculated could be different from how the 25% of ripe bananas was calculated.
To illustrate this, let's consider an example. Suppose there are two cities, A and B, with populations of 10,000 and 5,000, respectively. In city A, 2,500 people have blue eyes, while in city B, 1,250 people have blue eyes. At first glance, it may seem that the percentage of people with blue eyes is the same in both cities, at 25%.
However, if we look closer, we can see that the actual number of people with blue eyes is different between the two cities. City A has twice as many people with blue eyes as city B, even though the percentage is the same.
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2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
a
AC and BD are the diagonals of the MNOP, the diagonals of the rectangle MNOP bisect each other and are congruent.
What is a rectangle and its properties?
A rectangle and a rectangle are quadrilaterals that share the following properties: Opposite sides are equal. Two diagonals are the same length. It has two class 2 reflection symmetries and a rotational symmetry (through 180°). To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following proof:
Proof:
Let MNOP be a rectangle whose diagonal MO and diagonal NP intersect at Q.
First we show that the diagonals bisect each other. Since MNOP is a rectangle, we know that opposite sides are parallel and congruent. Therefore, we can draw segment MP and segment NO which are both parallel and congruent to each other.
Now consider the triangle MON. Since segment MP is parallel to segment NO, we know that angles MNO and MON are alternate interior angles and are congruent. Similarly, the angles NMO and ONM are also congruent. Therefore, triangle MON is an isosceles triangle with legs MO and NO. This means that the height drawn from Q to the side MN (which is the perpendicular bisector of MO and NO) bisects MO and NO. Similarly, the height drawn from Q to the side OP bisects OP. Therefore we have shown that the diagonals of a rectangle bisect each other.
Next, we show that the diagonals are congruent. Since MNOP is a rectangle, we know that opposite sides are parallel and congruent. Therefore, MP is compatible with NO and MO is compatible with NP. Using the fact that the diagonals bisect each other, we can write:
MQ = QO (because the height drawn by Q to the side MN divides MO and NO)
and
NQ = QP (because the height drawn from Q to the side OP divides NP and MO)
Combining these two equations, we get:
MQ + NQ = QO + QP
But we also know that MO is NP-consistent, so we can substitute:
MQ+ NQ = MO + MO
Simplification:
MQ + NQ = 2MO
Therefore, we have shown that the diagonals of a rectangle are congruent. Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent as necessary.
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a company advertises that food preparation time can be significantly reduced with the handy dandy slicer. a sample of 12 individuals prepared the ingredients for a meal with and without the slicer. you are given the preparation times below. preparation times person with slicer without slicer 1 20 22 2 12 18 3 20 18 4 14 22 5 19 19 6 20 21 7 19 18 8 15 12 9 22 18 10 19 25 11 21 26 12 23 20 the null hypothesis should . a. be revised b. not be rejected c. be rejected
For the food preparation time data with or without slicer, the null hypothesis for this sample data should not be rejected. So, option (b) is right answer.
We have a food preparation time data of a company. The time of preparation is significantly reduced with the handy dandy slicer. Sample size, n = 12
We have a table present in above figure which has the preparation times data consists people, with slicer and without slicer. First we calculate difference between with slicer and without slicer data, that d: -2, -6, 2, -8 , 0, -1, 1, 3, 4, -6, -5, 3.
We do all work on the difference, d.
Mean value of difference d, [tex]\bar d = \frac{\sum_{i = 1}^{n} {d_i }}{n}[/tex] = -1.25
Standard deviations, [tex] \sigma = \sqrt{\frac{ \sum {d_i^2 - (\sum d_i)²}}{n - 1}}
[/tex] = 4.115
degree of freedom= 12 - 1 = 11
Let level of significance = 0.05
The null and alternative hypothesis are defined as [tex]H_0 : \mu_d = 0 [/tex]
[tex]H_a: \mu_d < 0[/tex]
Using t-test, [tex]t = \frac{ \bar d} {\frac{ \sigma}{ \sqrt{n}}}[/tex]
[tex]= \frac{ -1.25} {\frac{ 4.115}{ √12}}[/tex]
= - 1.05
Now, using t-distribution table, value of p for t = -1.05 for 11 degree of freedom is -1.796. So, p-value = -1.796 < 0.005, Hence, we should not reject the null hypothesis.
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