a)Since the height of the basketball is only 6.3 feet when it reaches a height of 17 feet at t = 0.23 seconds, the teenager will not make the basket.
b) To find the height of the teenager, we need more information, such as their arm span or jumping ability.
what is height ?
Height is the measurement of how tall someone or something is, typically referring to the distance from the bottom to the top of an object or person. It can be measured in different units, such as feet, meters, or centimeters
In the given question,
a. To determine if the teenager will make the basket, we need to see if the height of the basketball when it reaches the hoop, which is at a height of 17 feet, is greater than or equal to 17 feet. So, we set h(t) = 17 and solve for t:
-16t² + 20t + 5.5 = 17
-16t² + 20t - 11.5 = 0
Using the quadratic formula, we get:
t = (-20 ± sqrt(20² - 4(-16)(-11.5))) / (2(-16))
t ≈ 1.79 or t ≈ 0.23
Since the basketball will reach a height of 17 feet at two different times, we need to determine the height of the basketball at each of these times and see if it is greater than or equal to 17 feet.
When t = 0.23 seconds:
h(0.23) = -16(0.23)² + 20(0.23) + 5.5 ≈ 6.3 feet
When t = 1.79 seconds:
h(1.79) = -16(1.79)² + 20(1.79) + 5.5 ≈ 17.1 feet
Since the height of the basketball is only 6.3 feet when it reaches a height of 17 feet at t = 0.23 seconds, the teenager will not make the basket.
b. To find the height of the teenager, we need more information, such as their arm span or jumping ability. The function h(t) represents the height of the basketball, not the height of the teenager.
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What steps should be taken to calculate the volume of the right triangular prism? Select three options. A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters. Use the formula A = one-half b h to find the area of the base. Use the formula A = b h to find the area of the base. The area of the base, A, is One-half (7) (8) = 28 meters squared. The area of the base, A, is One-half (8) (14) = 56 meters squared. The volume of the prism, V is (56) (7) = 392 meters cubed.
Answer:
392
Step-by-step explanation:
Volume is the area of the base times the height.
Area of the base:
[tex]\frac{(8x14)}{2}[/tex] = 56
Volume:
area of the base times the height
(56)(7) = 392
Helping in the name of Jesus.
100 points!!!
Express the function graphed on the axes below as a piecewise function.
This means that for x values less than or equal to -2, the function equals -2x - 1. For x values between -2 and 1, the function equals x^2 + 2x - 3. And for x values greater than or equal to 1, the function equals 4.
To express the function graphed on the axes below as a piecewise function, we need to analyze the graph and determine the different intervals where the function behaves differently.
Looking at the graph, we can see that the function is a straight line with a slope of 2 when x is less than or equal to -2. Then, the function changes to a parabola that opens upwards when x is between -2 and 1. Finally, the function becomes a horizontal line when x is greater than 1.
Therefore, the piecewise function that represents this graph is:
f(x) =
-2x - 1, if x ≤ -2
x^2 + 2x - 3, if -2 < x < 1
4, if x ≥ 1
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Mason's mother wants to make 8 curtains that each require 2 1/5 (two, one over five) metres of material in a standard width, but she only has 16 1/4(sixteen, one over four)metres of material. There are to be no seams in her curtains. She asks Mason to buy more material.
a. How much more material must Mason buy?
B. How much material is left over?
The result is negative, meaning there is insufficient material to make the curtains without seams.
EquationsEach curtain requires 2 1/5 meters of material, so for 8 curtains, the total amount of material required is:
8 x 2 1/5 = 17 3/5 meters
However, Mason's mother only has 16 1/4 meters of material, so she needs to buy more material. The amount of additional material needed is the difference between what she has and what she needs:
17 3/5 - 16 1/4 = 1 2/5 meters
Therefore, Mason needs to buy 1 2/5 meters of material.
To determine how much material is left over, we need to subtract the total amount of material needed for the curtains from the amount of material Mason's mother has:
16 1/4 - 17 3/5 = -1 3/20
In this case, Mason's mother would need to either buy more material or adjust the dimensions of the curtains to fit the amount of material she has.
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Can you pls do this i can't do it, it's a little hard and due before 4:00 pm ( Will mark brainliest if 2 answers and 95 pts if you can do it pls and thank you!!)
Answer:
30%
Step-by-step explanation:
(156-120) / 120 × 100％
=36 / 120 × 100％
=30%
Briony needs 8 pieces of curtain material 2 1/4m in length.She has 19 m length of material does she have enough
Yes, Briony has enough material. She needs 18m of material, which is less than the 19m she has.
To find length of material, we need to calculate the length of each
curtain piece using the given length of material.
To convert a mixed number to an improper fraction, multiply the
denominator (the bottom number) by the whole number, and add the
numerator (the top number).
Now, to convert 2 1/4m into an improper fraction, we multiply the
denominator (4) by the whole number (2), then add the numerator (1).
This gives us (2 × 4) + 1 = 9.
Hence, 2 1/4m can be written as 9/4m.
Since Briony needs 8 pieces of curtain material 2 1/4m in length, she will need a total of:
8 × 2 1/4m = 8 × 9/4m = 18 1/4m.
Briony requires 18 1/4m of curtain material. Since she has 19 m length of
material, she has enough to create 8 pieces of curtain material of 2 1/4m
in length.
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In ΔLMN, the measure of ∠N=90°, NM = 9, ML = 41, and LN = 40. What is the value of the cosine of ∠L to the nearest hundredth?
The value of the cosine of ∠L in triangle LMN is approximately 0.98 using Pythagorean Theorem.
To find the cosine of ∠L in triangle LMN, we first need to use the Pythagorean theorem to find the length of side LM, since only have the lengths of NM and LN:
[tex]LM^2 = LN^2 - NM^2\\LM^2 = 40^2 - 9^2\\LM^2 = 1521[/tex]
[tex]LM = \sqrt{1521}[/tex]
LM = 39
Now that we know the length of all three sides of the triangle, we can use the cosine rule to find the cosine of ∠L:
cos(L) = [tex](LM^2 + LN^2 - NM^2)[/tex] / (2 x LM x LN)
cos(L) = [tex](39^2 + 40^2 - 9^2)[/tex] / (2 x 39 x 40)
cos(L) = 0.975
Rounding to nearest hundredth:
cos(L) = 0.98
Therefore, the value of cosine of ∠L in triangle LMN is approximately 0.98.
The ratio of the neighbouring side to the hypotenuse is known as the cosine of an angle in a right triangle. As L is not a straight angle in this situation, its value must be determined using the cosine method. Whether a triangle is a right triangle or not, the cosine rule can be used to relate the lengths of its sides and angles.
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Mrs. Simcox needs to make snickerdoodles for her class for Pi day. She needs 2 ¼ cups flour for each batch of cookies. If she has 9 cups of flour how many complete batches of cookies can she make?
Hellpppp
Mrs. Simcox can make 4 complete batches of snickerdoodles for her class on Pi day, as she has 9 cups of flour and each batch of cookies requires 2 and 1/4 cups of flour.
Mrs. Simcox needs to make snickerdoodles for her class on Pi day and she knows that each batch of cookies requires 2 and 1/4 cups of flour. Therefore, she needs to calculate how many batches of cookies she can make with the 9 cups of flour that she has.
To do this, she divides the total amount of flour she has (9 cups) by the amount of flour required for each batch (2 and 1/4 cups). To simplify this division, she can convert the mixed number (2 and 1/4) to an improper fraction:
2 and 1/4 = (2 x 4 + 1)/4 = 9/4
Therefore, she can rewrite the division as:
9 cups ÷ 9/4 cups per batch
To divide by a fraction, she can multiply by its reciprocal:
9 cups × 4/9 cups per batch = 4 batches
So, Mrs. Simcox can make 4 complete batches of cookies with the 9 cups of flour she has.
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What is the value of p in the equation shown?
p3
= -0.027
The value of p in the equation shown is 0.3
What is equation?
An equatiοn in writing prοving the similarity οf twο phrases. It is made up οf a series οf characters divided intο left and right sectiοns and cοnnected by an equal sign.
Equatiοns are questiοns, and the search fοr methοdical sοlutiοns tο thοse questiοns has fueled the grοwth οf mathematics. Simple algebraic equatiοns with οnly additiοn οr multiplicatiοn tο differential equatiοns, expοnential equatiοns with expοnential fοrmulas, and integral equatiοns are examples οf variοus types οf equatiοns.
The equation that is in the question is given below
p³ = -0.027
or, p=-∛0.027
or, p = -0.3
Hence the value of the p is 0.3
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3dm 5dm 2dm to mm is?
3 dm is equal to 300 mm, 5 dm is equal to 500 mm, and 2 dm is equal to 200 mm.
To convert 3 dm to mm, we multiply by 10 to get 30 cm, and then by another 10 to get 300 mm.
To convert 5 dm to mm, we multiply by 10 to get 50 cm, and then by another 10 to get 500 mm.
To convert 2 dm to mm, we multiply by 10 to get 20 cm, and then by another 10 to get 200 mm.
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Can someone please help me ASAP it’s due today!! I will give brainliest if it’s correct.
Answer:
about 7 days
Step-by-step explanation:
31 · .22
6.82 days
rounded up it would be approximately 7 days
A strawberry patch is 1.7 dam long and 1.4 dam wide. If one person can pick 3 m² of strawberries in an hour, then how many hours will it take for one person to harvest the entire patch?
79 hours will it take for one person to harvest the entire strawberry patch.
What is the conversion of the unit?The same property is expressed using a unit conversion but in a distinct unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other length unit instead of miles.
Finding the strawberry patch's area in square meters and dividing it by the amount that one person can harvest in an hour will give us the total number of hours needed to solve this issue.
The strawberry patch's measurements must first be changed from decameters (dam) to meters.
1 decameter (dam) = 10 meter
Strawberry patch length in meters = 1.7 dam * 10 m/dam = 17 m.
The strawberry patch width in meters = 1.4 dam x 10 m/dam = 14 m.
The strawberry patch's area is therefore:
Area of strawberry patch = length × width = 17 m × 14 m = 238 m²
We must now determine how long it will take one individual to pick 3 m² of strawberries, in hours. We can calculate this by dividing the patch's overall area by the area that a single individual can select in an hour:
[tex]\frac{Area of strawberry patch}{ Area picked per hour }[/tex] = a number of hours needed to harvest the complete patch.
The total harvesting time is [tex]\frac{238 m2 }{3 m2/hour}[/tex] = 79.33 hours nearly equal to 79
Therefore, it would take one person 79 hours to gather the complete strawberry patch.
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y=log(4x-a) for what values of x will the log be positive
The logarithmic function y = log(4x-a) is positive for all values of x which are greater than a/4.
A logarithmic function is what?A function of this type is a logarithmic function. which can be interpreted as "y equals the log, base b, of x" or "y equals the log of x, base b."
Finding the domain of x that makes the argument (4x-a) of the logarithm positive will help us identify the values of x for which the logarithm in the equation y = log(4x-a) is positive.
Remember that a positive number's logarithm is positive and a negative number's logarithm is indeterminate. (in the real number system).
We must therefore identify the x values that meet the inequality:
4x - a > 0
4x > a
x >a/4
After finding x, we obtain:
x > a/4
The equation y = log(4x-a) therefore has the following domain of x for which the logarithm is positive:
In other words, for all values of x larger than a/4, the expression y = log(4x-a) is defined and positive.
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7x-22 is the bottom
3x+10 is the side
wart is a rhombus find WA
x=
WA=
Answer:
x = 8WA = 34Step-by-step explanation:
You want the value of x and the length of side WA in rhombus WART with sides marked 7x-22 and 3x+10.
RhombusThe sides of a rhombus are congruent, so ...
7x -22 = 3x +10
4x = 32 . . . . . . . . add 22-3x
x = 8
3x+10 = 3·8 +10 = 34
The value of x is 8, and side WA is 34 units.
a population of 1200 farm workers, aged 40-55 years, was examined in february 2000. of these workers, 800 were exposed to high levels of pesticide the rest were exposed to low levels of pesticide. at the physical examination, 230 cases of skin cancer were identified, including 185 cases among the high pesticide exposure group. all of the workers who were initially examined and did not have skin cancer were followed by repeat examinations over the next two years. these follow-up exams identified 175 new cases of skin cancer in the total group, including 25 cases among the low-exposure group. what is the incidence of skin cancer over the two years in the high exposure group?
The incidence of skin cancer over the two years in the high exposure group is 24.39%.
To calculate the incidence of skin cancer over the two years in the high exposure group, follow these steps:
1. Determine the number of workers in the high exposure group: 800 workers
2. Subtract the initial skin cancer cases in the high exposure group from the total number of workers in the group to find out the workers without skin cancer:
800 - 185 = 615 workers
3. Calculate the number of new skin cancer cases in the high exposure group by subtracting the new cases in the low-exposure group from the total new cases:
175 - 25 = 150 cases
4. Calculate the incidence rate by dividing the new cases in the high exposure group by the number of workers without skin cancer in the high exposure group:
150 / 615 ≈ 0.2439
5. Multiply the incidence rate by 100 to express it as a percentage:
0.2439 * 100 = 24.39%.
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Can someone please help
The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36 = 0.028
What is probability?The likelihood that a specific occurrence will occur.
The proportion of the total number of possible outcomes to the number of outcomes in an exhaustive set of equally probable outcomes that result in a particular event.
Two six-sided dice are rolled there are 36 possibilities for outcomes which means 6 possibilities for the first dice and 6 for the second dice.
Therefore 36 is the total possibility outcome.
Count the number of outcomes for the one dice show 5 and the second dice show 6.
There is only one possibility two show the (5, 6) from the total s3 outcomes.
so the probability of rolling a 5 and a 6 i = 1/36 or about 0.028.
Therefore, the total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36.
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how long does it take to fly from denver to atlanta on delta airlines? the table below shows 56 observations on flight times (in minutes) for the first week of march 2005.
Based on the given frequency table, it takes between 150 and 160 minutes to fly from Denver to Atlanta on Delta Airlines for 25 out of 56 observations.
The table provides frequency data on flight times (in minutes) for the first week of March 2005 from Denver to Atlanta on Delta Airlines. The frequency table shows that there were 25 flights with a duration between 150 and 160 minutes, which is the most frequent flight duration. The flight times ranged from 140 to 190 minutes.
The frequency data can be used to construct a histogram that displays the distribution of flight times for the Denver to Atlanta route. The histogram can provide further insights into the distribution of flight times, such as whether the distribution is symmetric or skewed, and the location and spread of the data.
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--The complete question is, how long does it take to fly from denver to atlanta on delta airlines? the table below shows 56 observations on flight times (in minutes) for the first week of march 2005.
FROM TO FREQ
140 150 1
150 160 25
160 170 24
170 180 4
180 190 2--
Someone please help me I need help with this homework assignment
Answer:
A
Step-by-step explanation:
A has a positive slope
value for X^2 left for 95% confidence interval when n=15
56% of what number is $21.84?
Percent Proportion-
Percent Equation -
Answer: 39
Step-by-step explanation:
x = (56/100) * y
where x is the amount we're trying to find and y is the total amount.
We're given that 56% of this value is $21.84, so we can substitute these values into the equation:
21.84 = (56/100) * y
To solve for y, we can divide both sides by 56/100:
y = 21.84 / (56/100)
Simplifying this expression, we get:
y = 39
Therefore, the number that represents 56% of this value is $21.84.
Determine the number of 5 MB documents that could fit on a 16 GB flash drive.
Answer:
3200
Step-by-step explanation:
If we know the fact that :
1GB = 1000MB
We can form an equation to show that 16000MB divided by 5MB should give you your answer.
The answer you get is 3200.
This means that you can fit 3200 5 MB files into a 16GB flash drive.
Hoped this helped,
thank you
which inequality represents seven more than a number is no more than 10
Answer: 7>x< 10
Step-by-step explanation:
O is the center of the regular nonagon below. Find its perimeter. Round to the
nearest tenth if necessary.
Thus, the perimeter of the regular nonagon with centre O is found as: 78.57 units.
Explain about the perimeter of regular polygon:A closed, 2D structure with a finite number of line segments is referred to as a polygon. A polygon's number of vertices and its number of line segments are always identical. The perimeter of a closed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides.
P = (Side length) x n
The apothem of each of the 9 isosceles triangles that make up the regular nonagon is 12 cm.
The angle at the circle's centre is 360/9 = 40º.
Hence, the sides of the regular nonagon, if the apothem of a isosceles triangles is 12 cm.
2*12 tan (40/2) = 8.73 cm
Then the perimeter:
P = 9 x 8.73
P = 78.57 units
Thus, the perimeter of the regular nonagon with centre O is found as: 78.57 units.
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The teacher gave a true and false quiz where P(true) = 0.2 for each question. Interpret the likelihood that the first question will be true.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The probability is unlikely.
What is probability ?
A probability is a number that expresses the possibility or liability that a specific event will take place. Chances can be stated as proportions with a range of 0 to 1, or as probabilities with a range of 0 to 100.
Probability is a measure of how likely or likely-possible commodity is to be. For case, there's only one system to admit a head and there are a aggregate of two possible issues, hence the chance of flipping a coin and entering heads is 1 in 2.( a head or tail). P( heads) = 12 is what we write.
The value of the probability and the notation is given as
P(true) = 0.2
As a general rule of probability, we have
Range of probability value = 0 to 1 (inclusive)
Unlikely = less than 0.5
Equally likely and unlikely = 0.5
Likely = greater than 0.5
Using the above as a guide, we have the following:
The value of P(true) = 0.2 is less than 0.5
This that the probability is unlikely.
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I need help please!!
Answer:
8 = 83°
Step-by-step explanation:
4 = 2 (Vertically opp. angles)
2 = 8 (Alternate interior angles)
Therefore 4 = 8
Since 4 = 83°
8 = 83°
Answer:
<8 = 83 degrees
Step-by-step explanation:
<4 and <8 are corresponding angles and corresponding angles are equal if lines are parallel
<4 = 83 so <8 = 83
A=1\3+1\6+1\10+1\15+...+1\45
The value of A is 9/10.
What is binomial?
Binοmial refers tο a type οf prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, where each trial has οnly twο pοssible οutcοmes (success οr failure) and the prοbability οf success is cοnstant acrοss all trials.
The given expressiοn is the sum οf the first several terms οf a harmοnic series. Tο evaluate it, we can use the fοrmula fοr the sum οf the first n terms οf a harmοnic series:
1 + 1/2 + 1/3 + ... + 1/n = ln(n) + γ,
where ln(n) is the natural lοgarithm οf n and γ is the Euler-Mascherοni cοnstant (apprοximately 0.5772).
Using this fοrmula, we can write the expressiοn as:
A = 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/45
= (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... + (1/9 - 1/10)
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10
= 1 - 1/10
= 9/10
Therefore, the value of A is 9/10.
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Complete Question:
Find The value of A
A=1\3+1\6+1\10+1\15+...+1\45
an urn contains 12 balls, five of which are red. the selection of a red ball is desired and is therefore considered to be a success. if a person draws three balls from the urn, what is the probability of three successes?
The probability of selecting three red balls or having three successes when drawing balls from the urn is 0.045, which is equivalent to 4.5%.
The probability of three successes can be calculated using the binomial probability distribution formula. Since there are only two outcomes for each ball drawn (success or failure), and the trials are independent, the binomial distribution applies.
The probability of drawing a red ball on the first attempt is 5/12. Since the ball is not replaced, the probability of drawing a red ball on the second attempt is 4/11. Similarly, the probability of drawing a red ball on the third attempt is 3/10.
To obtain the probability of three successes, we need to multiply these probabilities together:
P(three successes) = (5/12) x (4/11) x (3/10)
P(three successes) = 0.04545 or approximately 0.045
Therefore, the probability of drawing three red balls or three successes from the urn is 0.045 or 4.5%. This means that out of every 100 sets of three balls drawn, we can expect to get three red balls in approximately 4-5 sets.
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Please help me will give brainliest
One real-world situation that could be modeled by the arithmetic sequence f(n) = 100 + 25n, for n ≥ 1, is the cost of a monthly subscription service for an online course.
What is Arithmetic Sequence?An arithmetic sequence is a sequence of numbers where each term is found by adding or subtracting a constant value from the previous term. The constant value is called the common difference and determines the rate at which the sequence increases or decreases.
One real-world situation that could be modeled by the arithmetic sequence f(n) = 100 + 25n, for n ≥ 1, is the cost of a monthly subscription service for an online course.
Assuming that the initial cost of the service is $100 and the subscription fee increases by $25 every month, then the formula
=> f(n) = 100 + 25n
It can be used to calculate the cost of the subscription for any given month n.
For example, the cost of the subscription for the 5th month would be
f(5) = 100 + 25(5) = $225.
Similarly, the cost of the subscription for the 10th month would be
f(10) = 100 + 25(10) = $350.
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discuss how systematic uncertainty can be estimated for a measured value. how is random uncertainty estimated? what is the difference between error and uncertainty?
The deviation of a measurement from the true value, while uncertainty quantifies the reliability of the measurement.
Systematic uncertainty can be estimated for a measured value by identifying and evaluating factors that may cause a consistent deviation in the measurements. These factors may include instrument calibration errors, environmental conditions, or personal bias. To estimate systematic uncertainty, follow these steps:
1. Identify potential sources of systematic error.
2. Quantify the magnitude of each error source.
3. Combine these errors, typically by adding them in quadrature (square root of the sum of squares).
Random uncertainty, on the other hand, arises from unpredictable variations in the measurement process. It can be estimated by performing multiple measurements and analyzing the data. The steps to estimate random uncertainty are:
1. Perform multiple measurements of the same quantity.
2. Calculate the mean (average) of the measurements.
3. Calculate the standard deviation, which represents the spread of the data around the mean.
The difference between error and uncertainty lies in their definitions and how they affect measurements. Error is the difference between the measured value and the true value of a quantity. It can be classified as systematic (consistent and predictable) or random (unpredictable and variable). Uncertainty, however, represents the level of confidence with which the measured value is known, considering the limitations of the measuring process. It is often expressed as a range or interval and encompasses both systematic and random uncertainties. In summary, error is the deviation of a measurement from the true value, while uncertainty quantifies the reliability of the measurement.
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5,30,180 find the 7th term
Answer:
2332805, 30, 180, 1080, 6480, 38880, 233280
The pattern is times 6.
Step-by-step explanation:
You're welcome.
Mr ABA class is making 200 origami cranes for an art project so far they have made 3/4 of the cranes
B. What percent of the cranes have they made?
Step-by-step explanation:
To find the percentage of a fraction you divide the top by the bottom and multiply by 100. So 3/4 = 0.75 then 0.75 x 100 = 75%. Now you need to find 3/4ths or 75 percent of 200. An easy way to do this is find 1/4 of 200. So 200/4 = 50. Now you need 3/4 of 200, not just one fourth so multiply 50 by 3 to get 150. The class has made 150 cranes.