The ladder will reach a height of 8 feet, which is greater than 7 feet. So, the ladder will indeed reach 7 feet high, and even higher.
What is Pythagoras theorem?A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
According to question:We can use the Pythagorean theorem to determine if the ladder will reach 7 feet high. Let's let x be the height that the ladder reaches, as shown in the diagram below:
According to the Pythagorean theorem, we have:
[tex]$\begin{align*}x^2 + 6^2 &= 10^2 &= 100 - 36 &= 64 \x &= \sqrt{64} \x &= 8\end{align*}[/tex]
Therefore, the ladder will reach a height of 8 feet, which is greater than 7 feet. So, the ladder will indeed reach 7 feet high, and even higher.
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express in the form n:1
Answer:3/2
Step-by-step explanation:
[tex]\frac{9}{6} = \frac{\frac{9}{3} }{\frac{6}{3} }=\frac{3}{2}[/tex]
The airline industry defines an on-time flight as one that arrives within 15 minutes of its scheduled time. The following table shows the number of on-time and late flights leaving New York and arriving in Miami between November 1 and December 31, 2018, by airlines: Airlines On-Time Late Total United 254 72 326 Delta 292 65 357 American 235 58 683 Total 781 195 a. What is the probability that a randomly selected flight was Delta and was late? b. What is the probability that a randomly selected flight was United or was on-time? c. Given the flight was late, what is the probability that it was from American? d. Given the flight was from Delta, what is the probability that it was late? e. Construct a probability tree for these probabilities.
a) The probability is $\frac{65}{357}$.
b) The probability is $\frac{781}{1000}$.
c) The probability is $\frac{58}{195}$.
d) The probability is $\frac{65}{357}$.
e) We can construct a probability tree for these probabilities. Below is the probability tree:probability tree for airlines. Therefore, the above figure is the probability tree for airlines.
The probability that a randomly selected flight was Delta and was late is $\frac{65}{357}$.Therefore, the probability is $\frac{65}{357}$.
The probability that a randomly selected flight was United or was on-time is $\frac{781}{1000}$.Therefore, the probability is $\frac{781}{1000}$.
Given the flight was late, the probability that it was from American is $\frac{58}{195}$.Therefore, the probability is $\frac{58}{195}$.
Given the flight was from Delta, the probability that it was late is $\frac{65}{357}$.Therefore, the probability is $\frac{65}{357}$.
We can construct a probability tree for these probabilities. Below is the probability tree:probability tree for airlines. Therefore, the above figure is the probability tree for airlines.
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Rohana wants to find the volume of a sphere that has a radius of 10 feet. Which equation chan she use to solve for this value in cubic feet?
The equation change of volume of a sphere Rohana uses to solve for this value in cubic feet is V = (4/3)π(10)³ which gives the value 4,188.79 cubic feet.
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is a constant value approximately equal to 3.14159.
In this problem, the radius of the sphere is given as 10 feet. So, we can substitute this value into the formula to get the volume of the sphere as:
V = (4/3)π(10)³
Simplifying the right side, we get:
V = (4/3) × π × (1000)
V = (4/3) × 3.14159 × 1000
V = 4.18879 × 1000
V = 4,188.79 cubic feet
Therefore, the volume of the sphere with a radius of 10 feet is 4,188.79 cubic feet.
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three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. demetria got a score of 85.1 ; this version has a mean of 61.1 and a standard deviation of 12 . vincent got a score of 299.2 ; this version has a mean of 264 and a standard deviation of 22 . tobias got a score of 7.26 ; this version has a mean of 7.1 and a standard deviation of 0.4 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
The best applicant to fill the only position available based on the test score is Vincent as he scored highest. The method for determining which applicant performed the best on the aptitude test is to use z-scores, which are measurements of how far from the mean a test score falls in standard deviation units.
Since the test is not on the same scale, it is impossible to compare raw test scores. What are Z-scores?A z-score, also known as a standard score, is a score that indicates the number of standard deviations from the mean a raw score is. In other words, a z-score tells you how far from the mean the score is in terms of standard deviations.
In other words, we can use the following formula to calculate the z-score for each person's test result.$$Z = \frac {x - \mu}{\sigma}$$where x is the test score, μ is the test mean, and σ is the standard deviation.The Z-scores for each of the candidates based on their test results are as follows: Demetria:$$Z = \frac {85.1 - 61.1}{12} = 2.00$$,Vincent:$$Z = \frac {299.2 - 264}{22} = 1.6$$,Tobias:$$Z = \frac {7.26 - 7.1}{0.4} = 0.4$$. From the calculations, Vincent has the highest z-score, indicating that he outperformed the other candidates. The candidate with the highest z-score is the best performer, thus Vincent is the best candidate for the job.
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match the equation with its graph
[tex]y=-\frac{2}{3} x+1[/tex]
identify the slope and the y-intercept
( i already did the first part i just need help finding the slope also the y intercept )
Answer:
slope is -2/3, and the y intercept is 1.
Step-by-step explanation:
Using y=Mx+b (slope intercept form), where M=slope, and B = Y intercept , you can find which valurs are which.
he j and k in the jk-ff (and jk-latch) are very much like the s and r in the sr-ff (and sr-latch), respectively. the j acts like the s and the k acts like the r. the only difference for these devices in 3701 is which of the following? group of answer choices j
The only difference for these devices in 3701 is that the jk-FF (or jk-latch) has an additional control input, which is the clock (CK). The CK input is used to enable and disable the device so that the inputs, j and k, do not always affect the output (Q) of the device.
The SR-FF (or SR-latch) has two inputs, S and R, which directly affect the output, Q. When S=1, the output is set to 1, and when R=1, the output is reset to 0.
On the other hand, the jk-FF (or jk-latch) has three inputs, J, K and CK. When CK is 0, the device is disabled and the outputs remain the same. When CK is 1, the J and K inputs can be used to either set (J=1, K=0) or reset (J=0, K=1) the output, Q.
In summary, the j and k in the jk-FF (or jk-latch) are similar to the s and r in the SR-FF (or SR-latch).
So, the only difference is the addition of a clock (CK) input in the jk-FF (or jk-latch). This clock (CK) input enables and disables the device, which allows the inputs, j and k, to affect the output (Q) of the device.
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A coin is flipped and a card is randomly selected from a deck of 52. What is the probability the coin will land on heads and the card will be a club? There are 13 clubs in a deck of cards.
A. 1/8
B. 1/24
C. 4/9
D. 1/2
My answer:
There are 4 cards of number eight in a deck of 52 cards, namely: 8 Spades, 8 Diamond, 8 Clubs, and 8 Hearts. So the probable outcomes are 4 and the total cards are 52. So, x 100 = 1/13. So there is a 1/13 chance for getting an eight, i.e, for every 13 cards, one card will be an eight.
hope it helps :)
also please mark brainliest it means alot
Someone please explain the answer to this problem
Mrs. Williams and her husband went to dinner in NYC last night. The total bill was $265 for the two of them. There was a 7% sales tax added to the bill. They decided to tip the waiter 15% on the bill after tax. How much tip did she leave?
The value of the tip she left is $42.53.
How much tip did she leave?Sales tax is a compulsory amount levied by the government on the sales price of a good or service. Sales price increase the cost of a good or service.
The first step is to determine the total bill after the sales tax has been included.
Total bill after sales tax = (1 + percent sales tax/100) x total bill
(1 + 7/100) x $265
(1 + 0.07) x $265
1.07 x $265
= $283.55
Now, multiply the total bill after sales tax by the percentage value of the tip.
Value of the tip = 15% x $283.55
0.15 x $283.55 = $42.53
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Assessment Practice 18. Data were collected from a random sample of 50 eighth-grade students. It was found that 15 eighth-grade students spent 2 hours each night on homework. If there are 280 eighth graders in the school, how many can you estimate spend 2 hours each night on homework?
We can estimate that 84 eighth graders in the school spend 2 hours each night on homework.We can use the proportion of students in the sample who spend 2 hours each night on homework to estimate the number of students in the school who spend the same amount of time on homework.
We are given that a random sample of 50 eighth-grade students was taken, and 15 of them spent 2 hours each night on homework. Therefore, the proportion of students in the sample who spend 2 hours each night on homework is:
15/50 = 0.3
We can use this proportion to estimate the number of eighth graders in the school who spend 2 hours each night on homework. If we assume that the sample is representative of the larger population, we can multiply the proportion by the total number of eighth graders in the school:
0.3 x 280 = 84
Therefore, we can estimate that 84 eighth graders in the school spend 2 hours each night on homework. It's important to note that this is just an estimate and the actual number may differ due to sampling variability.
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THERMOMETER An outdoor thermometer claims to be accurate within
2 degrees Fahrenheit. One day, the thermometer reads 72°F.
a. Write an absolute value inequality that represents the possible actual
temperature t.
b. What is the range of possible actual temperatures?
Answer:
a. An absolute value inequality that represents the possible actual temperature t is:
|t - 72| < 2
b. To find the range of possible actual temperatures, we can solve the inequality:
|t - 72| < 2
We can split this into two separate inequalities, one for when t is greater than 72 and one for when t is less than 72:
t - 72 < 2 and -(t - 72) < 2
Simplifying these inequalities, we get:
t < 74 and t > 70
Therefore, the range of possible actual temperatures is 70°F < t < 74°F.
Step-by-step explanation:
Consider the equation z^16=(−1−i). Find the value of z which satisfies this equation and which has the second smallest positive argument θ, 0<θ<2π. Express your answer as z=re^iθ where r=______and theta=_________.
Consider the equation z^13=(−1+sqrt3i). Find the value of z which satisfies this equation and which has the second smallest positive argument θ,0<θ<2π. Express your answer as z=re^iθ where r=_________ and theta=__________
I have found the r values of both, I just need help finding theta. Show work so I can practice, please!
After considering and calculating, the modulus of z is r = [tex]2^{1/32}[/tex] and the argument of z is θ = 5π/32.
To solve this equation, we can first express −1−i in polar form as:
−1−i = √2cis(3π/4)
where cis(θ) = cos(θ) + i sin(θ) is the polar form of a complex number.
Now, we can express z in polar form as:
z = r cis(θ)
where r is the modulus of z and θ is its argument. Substituting this into the equation z¹⁶ = √2cis(3π/4), we get:
r¹⁶ cis(16θ) = √2cis(3π/4)
Taking the modulus of both sides, we get:
r¹⁶ = √2
Taking the argument of both sides, we get:
16θ = 3π/4 + 2kπ or 16θ = -3π/4 + 2kπ
where k is an integer. Solving for θ in the range 0 < θ < 2π, we find that the second smallest positive solution is:
θ = (3π/4 + 2π)/16 = 5π/32
Therefore, the value of z is:
z = r cis(θ) = [tex]\sqrt{2}^{1/16}[/tex] cis(5π/32)
We can simplify this as:
z = [tex]2^{1/32}[/tex]cis(5π/32)
So, the modulus of z is:
r = [tex]2^{1/32}[/tex]
And the argument of z is:
θ = 5π/32
Therefore, the answer is:
z = [tex]2^{1/32}[/tex] cis(5π/32)
So, the modulus of z is r = [tex]2^{1/32}[/tex] and the argument of z is θ = 5π/32.
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What is 0.06 written as a percent?
Answer:
6%
Step-by-step explanation:
0.06 is 6% as a decimal
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
the vertex of∠5 is point M
Step-by-step explanation:
Answer: M
Step-by-step explanation: M represents the vertex. Think of the vertex almost like the starting point of an angle.
Brian wants to exchange south African Rand for British pound. If R1 is worth 0. 075199 pound, how many pounds will he get for R2100 if he must pay an agent commission of 1. 5%
After deducting a commission of 1.5%, Brian will receive 155.71 pounds in exchange for R2100.
To find out how many pounds Brian will get, we first need to calculate the amount of commission he will pay. The commission is 1.5% of R2100, which is equal to 0.015 x R2100 = R31.50.
The amount of money he will actually receive in pounds is the remaining R2100 minus the commission, which is R2068.50. To convert this to pounds, we multiply by the exchange rate of R1 = 0.075199 pound:
2068.50 x 0.075199 = 155.706675 pounds
Therefore, Brian will get 155.71 pounds for R2100 after paying the agent commission.
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Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. f(x) = 6x3 + 7x2 + x + 5 The number of variations in sign in f(x) is 3 x. Therefore, the number of positive real zeros of f is either 3 or 0x. The number of variations in sign in f(-x) is 3 . Therefore, the number of negative real zeros of f is either 3 or 0x Need Help? Read It Watch It Talk to a Tutor Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. f(x) = 7x3 - 8x2 - 5x - 4 The number of variations in sign in f(x) is 1 Therefore, the number of positive real zeros of f is 0 The number of variations in sign in f(-x) is 2 . Therefore, the number of negative real zeros of f is either 2 or 0 Need Help? Read It Watch It Talk to a Tutor
The number of negative real zeros of f is either 3 or 0.
Using Descartes's Rule of Signs, the possible numbers of positive and negative zeros of the function f(x) = 6x3 + 7x2 + x + 5 can be determined. The number of variations in sign in f(x) is 3. This means that the number of positive real zeros of f is either 3 or 0. The number of variations in sign in f(-x) is 3. This means that the number of negative real zeros of f is either 3 or 0.
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36 is 15% of what number?
54
240
360
540
Answer:
240
Step-by-step explanation:
15% of 54=8.1
15% of 240=36
15% of 360=54
15% of 540=81
so the answer is 240
36 is 15 percent of 240.
We have,
To find out what number 36 is 15% of, we can set up the equation:
36 = 0.15x
Here, x represents the unknown number we are trying to find.
To solve for x, we divide both sides of the equation by 0.15:
36 / 0.15 = x
Simplifying the right side gives:
240 = x
Therefore,
36 is 15 percent of 240.
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(Please answer quickly!!!)Simplify negative 4 and 1 over 4 minus 6 and 2 over 5.
negative 213 over 20
negative 43 over 20
negative 10 and one third
10 and 13 over 20
Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:
-17/4 * 5/5 = -85/20, 32/5 * 4/4 = 128/20, -85/20 - 128/20 = -213/20
what are fractions?A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers. The depiction of fractions appears easier than when decimal values are used.
A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To simplify:
-4 and 1/4 - 6 and 2/5
For the two mixed integers, we must identify a common denominator. The least frequent multiple of 4 and 5 is 20 since their prime components are 2 and 5. Both mixed numbers can be transformed into improper fractions with a denominator of 20 as follows:
-4 and 1/4 = -17/4
6 and 2/5 = 32/5
Now we can subtract these fractions:
-17/4 - 32/5
We must locate a common denominator in order to subtract fractions. Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:
-17/4 * 5/5 = -85/20
32/5 * 4/4 = 128/20
We can now take the two fractions apart:
-85/20 - 128/20 = -213/20
Therefore, -4 and 1/4 - 6 and 2/5 simplify to -213/20.
So, the answer is negative 213 over 20.
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Evaluate 2^x for (a) x= -2 and (b) x=3. Write your answers in simplest form.
a. The expression is__
when x= -2
b. The expression is__
when x= 3
(a) When [tex]x=-2, 2^x = 2^(-2) = 1/2^2 = 1/4[/tex]. So, the expression 2^x when x=-2 is 1/4.
(b) When [tex]x=3, 2^x = 2^3 = 8[/tex]. So, the expression 2^x when x=3 is 8.
The expression 2^x represents exponential growth, where the base 2 is multiplied by itself x number of times. When x is a negative number, the expression becomes a fraction because we are dividing 1 by the base raised to the absolute value of x. In this case, 2^(-2) is equivalent to 1/2^2, which is equal to 1/4. On the other hand, when x is a positive number, the expression grows exponentially. When x=3, the expression becomes 2^3, which is equal to 2x2x2 = 8.
In summary, the evaluation of 2^x when x is a negative number produces a fraction, whereas when x is a positive number, it produces a positive integer.
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Please help super confused
Answer:
1. 4, 28, 80
2. P(x)=4x
3. P(9.1)=36.4
The perimeter is 36.4 and the side length is 9.1
Step-by-step explanation:
To find perimeter you multiple a squares side length by 4.
Score: 1/6 1/6 answered
Question 1
Given the triangle
H=
* <>
15
/33°
answer to 4 decimal places.
Question Help: Video
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X find the length of side 2 using the Law of Cosines. Round your final
3
27 a
The length of side 2 of the given triangle is 16.22.
What is Law of Cosines?The Law of Cosines is a mathematical formula that is used to calculate the length of sides and angles in a triangle. It is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides
The Law of Cosines helps to solve for the side length in triangles when we are given two sides and the angle between them. In this triangle we are given side 1 (15) and the angle between the two sides (33°). To find side 2, we will use the formula:
c² = a² + b²- 2ab*cosC
Where c is the length of the unknown side, a is the length of the given side, b is the length of the other given side, and C is the angle between the two given sides.
In this case, c is side 2, a is 15, b is unknown, and C is 33°. We will plug in the known values and solve for b:
b² = 15² + c² - 2*15*c*cos(33°)
b² = 225 + c² - 30c*cos(33°)
We can solve this equation for c:
c = (225 + b² - 30b*cos(33°))/2
Now, we can solve for b using the values for c and a given in the problem:
b²= 225 + 27² - 30*27*cos(33°)
b² = 225 + 729 - 690.8
b²= 264.2
b = 16.22
Therefore, the length of side 2 is 16.22.
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Find the volume of a right circular cone that has a height of 3. 5 ft and a base with a diameter of 11. 9 ft. Round your answer to the nearest tenth of a cubic foot
By dividing the diameter by 2, one may get the radius of the cone's base:[tex]r = d/2 = 11.9/2 = 5.95 ft[/tex] The volume of a cone is calculated as follows: V = (1/3)πr^2h Inputting the values provided yields.
[tex]V = (1/3)π(5.95^2)(35) (3.5) V equals 138.2 cubic feet[/tex]. Using tenths of a cubic foot increments, we obtain: V ≈ 138.2 ft^3 Hence, the right circular cone has a volume of around 138.2 cubic feet. some further data on the volume of the cone. The formula: can also be used to express a cone's volume in terms of its height and slant height. V is equal to (1/3)r2h plus (1/3)r2(h2 + r2). where the square root symbol is represented by. Since we already know the height and radius, we can use the Pythagorean theorem to get the slant height.
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Which equation could represent a line that is parallel to y = -2x
+ 4?
a. 1/2+y=1
b.-2x+y=8
c.-2x-y=3
d.-1/2+y=5
The calculated equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.
How to determine the parallel equationThe equation of a line that is parallel to y = -2x + 4 will have the same slope as -2 since parallel lines have the same slope.
Therefore, we need to look for an equation that has a slope of -2.
(a) 1/2x + y = 1 has a slope of -1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
(b) -2x + y = 8 has a slope of 2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
(c) -2x - y = 3 can be rearranged to y = -2x - 3, which has a slope of -2, so it is parallel to y = -2x + 4.
(d) -1/2x + y = 5 has a slope of 1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
Therefore, the equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.
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Which describes a financial product offered by insurance companies that, in
return for an investment, provides fixed payments each month for the
remainder of a person's life?
The financial product described is an annuity.
An annuity is a contract offered by insurance companies, where the buyer makes a lump-sum payment or a series of payments in exchange for regular payments made over time, usually until the end of the buyer's life. An annuity can be either fixed or variable, depending on the type of investment chosen by the buyer.
In a fixed annuity, the payments are predetermined and do not change over time, while in a variable annuity, the payments are based on the performance of the underlying investments. An annuity is often used as a retirement income stream.
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AB=A, B, equals
Round your answer to the nearest hundredth. A right triangle A B C. Angle A C B is a right angle. Angle B A C is forty degrees. Side A C is five. Side A B is unknown
The length of side AB in the right triangle ABC is approximately 3.21 units.
To find the length of side AB in the right triangle ABC, we can use trigonometric ratios.
Given:
Angle BAC = 40 degrees
Side AC = 5 units
Let's use the trigonometric ratio for the sine of angle BAC:
sin(BAC) = opposite/hypotenuse
sin(40°) = AB/AC
Rearranging the equation to solve for AB, we have:
AB = AC * sin(BAC)
Substituting the given values, we get:
AB = 5 * sin(40°)
Using a calculator to evaluate sin(40°), we find:
AB = 5 * 0.6428
≈ 3.21
Therefore, the length of side AB in the right triangle ABC is approximately 3.21 units.
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You are flipping two coins. The probability of flipping two heads is 1/4. What is one way this can be calculated?
A. 1/2 subtracted from 1/2
B. 1/2 multiplied by 1/2
C. 1/2 divided by 1/2
D. 1/2 added to 1/2
Answer:
B. 1/2 multiplied by 1/2
Step-by-step explanation:
To find the probability, you would multiply. If you did not know this, you could solve each answer choice to find which one equals 1/4 since the problem already said the probability of flipping two heads is 1/4.
A. 1/2 - 1/2 = 0
B. 1/2 x 1/2 = 1/4
C. 1/2 / 1/2 = 1
D. 1/2 +1/2 = 1
Pls help me answer this too <3
A race official needs to know how long it takes an average contestant to run an obstacle course. There are a total of 200 contestants. How can he find a reasonable estimate for the amount of time it takes to run the obstacle course?
time any contestant on the course and use that time
time himself on the course and use that time
time 2 contestants and average their times
time 20 contestants and average their times
Time 20 contestants and average their times is the best option to find a reasonable estimate for the amount of time it takes to run the obstacle course. Thus, option D is the correct answer.
A good estimate is an approximation amount of value that is based on analytical reasoning and data available. That estimation must be within a valid margin of error. It is not expected to be accurate, but it is expected to deliver a fair view of the value being estimated.
The official time for 20 contestants is a large sample size which is enough to provide a reasonable estimate of the meantime for all 200 contestants. The actual can average the times for the 20 contestants to calculate the average time for the whole group.
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Solve for vertex algebraically 3x^2+6x+7
if 3 Sin A + 4 cos A= 5 prove that tan A = 3/4
a shopkeeper bought 300 lanterns. he sold 2/3 of them on Saturday and 1/6 of them on Sunday how many lanterns did he have left?
Answer:
150 Lanterns
Step-by-step explanation:
Total lanterns : 300
[tex]\frac{2}{6} * 300 = 100[/tex]
[tex]\frac{1}{6} * 300 = 50[/tex]
so He sold 150 lanterns in total , leaving 300-150 = 150 Lanterns left.