The answer is (d) 100, which is the expected frequency for each group.
How to find the expected frequency?To determine the expected frequency for each group under the assumption of a uniform distribution of opinions, we can use the formula:
Expected frequency = (total sample size) x (proportion of group in population)
The total sample size is 300, and the proportions of Democrats, Republicans, and Independents in the population are not given, so we cannot use those directly. However, if we assume that the population proportions are roughly the same as the sample proportions, we can estimate the expected frequencies as follows:
Expected frequency for Democrats = 300 x (100/300) = 100
Expected frequency for Republicans = 300 x (120/300) = 120
Expected frequency for Independents = 300 x (80/300) = 80
Therefore, the answer is (d) 100, which is the expected frequency for each group if the opinions of the individuals of the three groups are uniformly distributed.
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PLEASE HELP ME IM NOT GOOD AT MATH AND don’t understand!!
The total volume of the cylindrical can is given as follows:
C) 24.54 in³.
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The parameters for this problem are given as follows:
h = 5 in.r = 1.25 in.Hence the volume of the cylinder is obtained as follows:
V = π x 1.25² x 5
V = 24.54 in³.
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Show your work please
Answer:
Perimeter:
[tex]2( \frac{2}{3} + \frac{1}{2} ) = 2( \frac{4}{6} + \frac{3}{6} ) = 2( \frac{7}{6} ) = \frac{7}{3} = 2 \frac{1}{3} [/tex]
The perimeter is 2 1/3 inches.
Area:
[tex] \frac{2}{3} \times \frac{1}{2} = \frac{1}{3} [/tex]
The area is 1/3 of a square inch.
I need help with this. please
The only exponential growth equation is the third one:
y = 2*(4)^x
Which equation will produce a growth?A general exponential equation is:
y = A*(b)^x
if 0 < b < 1, then it is a decay.
if 1 < b, then it is a growth.
So any equation where the base, b, is larger than 1, represents a growth.
Then the correct option is the third one:
y = 2*(4)^x
All the other options are decays.
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a freeway with two northbound lanes is shut down because of an accident. at the time of the accident, the traffic flow rate is 1200 vehicles per hour per lane and the flow remains at this level. the capacity of the freeway is 2200 vehicles per hour per lane when not impacted by an accident. the freeway is shut down completely for 20 minutes after the accident and then one lane is open for 20 minutes and finally both lanes are opened (40 minutes after the accident). what is the average delay per
vehicle?
The average delay per vehicle would be 20 minutes. This is calculated by taking the total time the freeway was shut down (40 minutes) and dividing it by the total number of vehicles that would have been on the freeway during that time (2400 vehicles).
How do I round 9979.03 to the nearest gram?
A factory has 2 x 10^3 workers who make a total of 7 x 10^6 bikes each year. How many bikes does each worker make per year?
Answer:
7,000,000÷2000
= 3,500
Step-by-step explanation:
therefore, each worker makes 3500 bikes per year
Help me please….
it’s due tomorrow!!!
write an expression for the problem and evaluate the expression using the order of operations. bruce charged david and ricky $42 for parts and $12 per hour for labor to repair their motorcycle if he spent 3 hours repairing the bike how much money do david and ricky owe him?
The expression for the problem is:
Total cost = $42 + ($12/hour × 3 hours) × 2 people
How to write the expressionBruce charged David and Ricky a fixed fee of $42 for parts plus an hourly rate of $12 for labor. He spent 3 hours repairing the motorcycle. Since there are two people (David and Ricky), we need to multiply the hourly rate by the number of hours worked (3) and then multiply that by 2. Finally, we add the fixed fee for the parts to get the total cost.
To evaluate the expression using the order of operations, we need to perform the multiplication first and then the addition. So, we have:
Total cost = $42 + ($12/hour × 3 hours) × 2 people
= $42 + ($36) × 2
= $42 + $72
= $114
Therefore, David and Ricky owe Bruce a total of $114 for the motorcycle repair.
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Donna is sharing her snacks with her friends. She went to the store and spent $4 on chips, $2.75 on cookies, $3.37 on fruit snacks, and $11.55 on drinks. How much did she spend in all? How much change did she have left over from $25? Also, she shared ¼ of her bag of chips between her and her 2 friends. How much of the bag did each friend get?
Answer:
3/16
Step-by-step explanation:
hope it help
For each natural number , let ≔ {4, 4 + 1, … ,5}. Find ⋃[infinity] =1 and
⋂[infinity] =1 and prove your answers
The only possible elements that can appear in all the sets are 4 and 5. Since both 4 and 5 appear in each set, they must be in the intersection.
Based on the given set definition, we have:
A₁ = {4, 5}
A₂ = {4, 5, 6}
A₃ = {4, 5, 6, 7}
A₄ = {4, 5, 6, 7, 8}
and so on.
To find the union of all the sets, we need to find all the distinct elements that appear in at least one of the sets. We can do this by listing the elements in each set and removing duplicates:
⋃[infinity] =1 Aᵢ = {4, 5, 6, 7, 8, ...}
We can see that the union includes all the natural numbers greater than or equal to 4. We can prove this by showing that any natural number n greater than or equal to 4 is included in at least one of the sets. Indeed, for any such n, we can choose i = n - 3, which is a natural number since n is at least 4, and then we have n in Aᵢ.
To find the intersection of all the sets, we need to find the elements that appear in all the sets. We can do this by listing the elements in each set and finding the common elements:
⋂[infinity] =1 Aᵢ = {4, 5}
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a prescription for ear drops specifies that the patient put 2 drops in each ear twice a day for 9 days. approx how many millilitres of medication would be needed for this prescription? ( dosage×frequency×day supply )
approximately 3.6 milliliters of medication would be needed for this prescription.
To calculate the total milliliters of medication needed for this prescription, we will use the formula dosage × frequency × day supply.
In this case, the dosage is 2 drops per ear, the frequency is twice a day, and the day supply is 9 days.
First, let's find out how many drops are needed per day:
2 drops/ear × 2 ears = 4 drops
Since the frequency is twice a day, multiply this number by 2:
4 drops × 2 = 8 drops per day
Now, multiply the number of drops per day by the day supply (9 days):
8 drops/day × 9 days = 72 drops
Typically, 1 drop is approximately 0.05 millilitres. To find out how many millilitres of medication are needed, multiply the total number of drops by the volume of one drop:
72 drops × 0.05 mL/drop = 3.6 mL
So, approximately 3.6 millilitres of medication would be needed for this prescription.
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Approximately 1.8 milliliters of medication would be needed for this prescription.
To calculate how many milliliters of medication would be needed for this prescription, we need to use the following formula:
dosage × frequency × day supply.
The dosage is 2 drops, the frequency is twice a day, and the day supply is 9 days.
First, we need to convert drops to milliliters.
One drop is equal to approximately 0.05 milliliters.
2 drops would be equal to 0.1 milliliters.
Next, we can plug in the values into the formula:
[tex]0.1 milliliters/drop \times 2 drops/twice a day \times 9 days = 1.8 milliliters. [/tex]
The patient will be using exactly 2 drops in each ear for each dose, and that there will be no waste or spillage of the medication.
To determine how many milliliters of medicine would be required for this prescription:
dose frequency day supply.
The recommended dosage is 2 drops, twice day, with a 9-day supply.
We must first convert droplets to milliliters.
A drop is around 0.05 milliliters in volume. As a result, 2 drops are equivalent to 0.1 milliliters.
The values may then be entered into the formula as follows:
0.1 milliliters each drop times twice daily for nine days equals 1.8 milliliters.
As a result, this prescription would require about 1.8 milliliters of medicine.
It's crucial to note that this estimate is predicated on the patient applying precisely 2 drops to each ear for each dose.
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rosanne makes 112 liters of strawberry lemonade. she pours 14 of a liter of lemonade into a thermos to take to the park. her brother drinks 25 of the remaining lemonade. how much lemonade does rosanne's brother drink?write your answer as a whole number, fraction, or mixed number. simplify any fractions. liters
If rosanne makes 112 liters of strawberry lemonade, she pours 14 of a liter of lemonade into a thermos to take to the park, rosanne's brother drink 25 liters of lemonade
To solve this problem, we can start by subtracting the 14 liters of lemonade that Rosanne poured into the thermos from the total 112 liters to get the amount of lemonade that remained:
112 - 14 = 98 liters
Next, we need to subtract the amount of lemonade that Rosanne's brother drank, which is 25 liters, from the remaining amount:
98 - 25 = 73 liters
Therefore, Rosanne's brother drank 25 liters of lemonade.
To check our answer, we can add the amount of lemonade in the thermos, the amount that Rosanne's brother drank, and the remaining amount to see if it adds up to the original 112 liters:
14 + 25 + 73 = 112
Since the sum is indeed equal to 112, we can be confident that our answer of 25 liters for the amount of lemonade that Rosanne's brother drank is correct.
In summary, to find the amount of lemonade that Rosanne's brother drank, we subtracted the amount that Rosanne poured into the thermos and the amount that her brother drank from the total amount of lemonade that Rosanne made. The answer is 25 liters.
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Find the surface area of the composite figure. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
· Find the surface area of a cone with a slant height of 8 cm and a radius of 3 cm. SA = B + πrS = (πr2) + πrs = (π(32)) + π(3)(8) = 9π + 24π = 33πcm2 = 103.62cm2. Find the surface area of a rectangular pyramid with a slant height of 10 yards, a base width (b) of 8 yards and a base length (h) of 12 yards.
Find the volume of this object.
Use 3 for T.
Volume of a Cylinder
V= πr²h
12 in
14 in
12 in
V [?]cm
4 in
Enter
3
please help
Answer:
First, we need to convert all the measurements to the same unit. Let's convert everything to inches, since the formula for the volume of a cylinder uses inches:
12 in = 12 in
14 in = 14 in
12 in = 12 in
4 in = 4 in
The object consists of a cylinder with a radius of 4 inches and a height of 12 inches, and a hemisphere with a radius of 4 inches. To find the volume of the object, we need to find the volume of the cylinder and the hemisphere, and then add them together.
Volume of the cylinder:
V_cyl = πr^2h
V_cyl = π(4 in)^2(12 in)
V_cyl = 192π in^3
Volume of the hemisphere:
The volume of a hemisphere is given by:
V_hemi = (2/3)πr^3
Since the radius is 4 inches, we have:
V_hemi = (2/3)π(4 in)^3
V_hemi = (2/3)π(64 in^3)
V_hemi = 128π/3 in^3
Total volume:
V_total = V_cyl + V_hemi
V_total = 192π in^3 + 128π/3 in^3
V_total = (576π + 128π)/3 in^3
V_total = 704π/3 in^3
Now we can substitute the value of π (3) to get the final answer:
V_total = 704π/3 in^3
V_total = 704(3)/3 in^3
V_total = 704 in^3
Therefore, the volume of the object is 704 cubic inches.
1. Write the equation of a circle with a radius of 14 and the center at (-5, 9).
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-5}{h}~~,~~\underset{9}{k})}\qquad \stackrel{radius}{\underset{14}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-5) ~~ )^2 ~~ + ~~ ( ~~ y-9 ~~ )^2~~ = ~~14^2\implies (x+5)^2 + (y-9)^2=196[/tex]
for a normal distribution, a positive value of z indicates that group of answer choices all the observations must have had positive values. the area corresponding to the z is either positive or negative. the sample mean is smaller than the population mean. the sample mean is larger than the population mean.
For a normal distribution ,a positive value of z simply means that the observation or sample mean is above the population mean this implies
none of the options provided is completely accurate.
All the observations must have had positive values,
It is not necessarily true for a positive value of z.
The value of z indicates how many standard deviations away from the mean a particular observation or sample mean is.
A positive value of z simply means that the observation or sample mean is above the population mean.
The area corresponding to the z is either positive or negative,
It is also not accurate.
The area under the normal curve corresponds to probabilities, not positive or negative values.
The area to the right of the mean corresponds to positive z-values, and the area to the left of the mean corresponds to negative z-values.
The sample mean is smaller than the population mean,
It is a possibility when the z-value is negative, indicating that the sample mean is below the population mean.
The sample mean is larger than the population mean,
It is a possibility when the z-value is positive, indicating that the sample mean is above the population mean.
Therefore, the sample mean can be either larger or smaller than the population mean depending on the direction of the z-value.
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help Here is your graph of the points on the previous screen.
Connect the points in order to create polygon `ABCDEF`.
1.2 Enter the length of the segment betwee
The length of the given line AB is 6 units and the polygon ABCDEF has been created.
What is a graph?A graph is a mathematical structure made up of a collection of points called VERTICES and a set of lines connecting some pair of VERTICES that may or may not be empty.
There is a chance that the edges will be directed, or orientated.
If the lines are directed or undirected, respectively, they are referred to as ARCS or EDGES.
Make a sequence of bars on graph paper as an example of a graph.
So, in the given situation the polygon ABCDEF has been created:
(Refer to the graph attached below)
Now, the length of the side AB:
Count the units as follows which comes to 6 units.
Therefore, the length of the given line AB is 6 units and the polygon ABCDEF has been created.
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Correct question:
Help Here is your graph of the points on the previous screen.
Connect the points in order to create polygon `ABCDEF`.
1.2 Enter the length of the segment between A and B.
a frog is placed at the origin on the number line, and moves according to the following rule: in a given move, the frog advances to either the closest point with a greater integer coordinate that is a multiple of $3$, or to the closest point with a greater integer coordinate that is a multiple of $13.$ a move sequence is a sequence of coordinates which correspond to valid moves, beginning with $0,$ and ending with $39.$ for example, $0,\ 3,\ 6,\ 13,\ 15,\ 26,\ 39$ is a move sequence. how many move sequences are possible for the frog?
There are 16 possible move sequences for the frog.
The possible moves that the frog can make.
The frog can move to either the closest point with a greater integer coordinate that is a multiple of 3, or to the closest point with a greater integer coordinate that is a multiple of 13.
Let's consider the first type of move, where the frog moves to the closest point with a greater integer coordinate that is a multiple of 3.
If the frog is at the point [tex]$n$[/tex], then the closest point with a greater integer coordinate that is a multiple of 3 is either [tex]$n+3$ or $n+6$[/tex].
Similarly, if the frog is at the point [tex]$n$[/tex] and wants to move to a multiple of 13, then the closest point with a greater integer coordinate that is a multiple of 13 is either[tex]$n+13$[/tex] or [tex]$n+26$[/tex].
Constructing move sequences.
The sequence starts with 0 and ends with 39.
The frog has two choices for its first move: either move to 3 or move to 13.
Let's assume that the frog moves to 3.
From there, the frog has two choices again:
move to 6 or move to 13. If the frog moves to 6, then it has two choices again: move to 9 or move to 13.
If it moves to 13, then it has two choices: move to 26 or move to 16.
We can continue this process until we reach 39.
We can create a tree diagram to help us keep track of the possible move sequences:
0
|
3 or 13
/ \
6 or 13 13 or 26
/ \ / \
9 13 16 26
/ \ / \ / \ / \
... ... ... ... ... ... ... ...
Each branch represents a different move sequence.
We can see that there are 16 possible move sequences in total.
We can also see that some sequences are longer than others.
The longest sequence has 7 moves, while the shortest sequence has only 2 moves.
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30
The number of tables needed is proportional to the number of
people who are attending a banquet. The table below shows the
relationship.
BANQUET TABLES
D 20
Number of Tables
5
15
25
Number of People Attending
60
180
300
A banquet for 192 people is being held. How many tables are
needed for this banquet?
A 8
B 12
C 16
D 20
[tex]\begin{array}{ccll} tables&persons\\ \cline{1-2} 15 & 180\\ x& 192 \end{array} \implies \cfrac{15}{x}~~=~~\cfrac{180}{192} \implies \cfrac{ 15 }{ x } ~~=~~ \cfrac{ 15 }{ 16 }\implies x=16[/tex]
A person has a bag containing quarters and dimes. There are a total of 52 coins in the bag, and the total value of the coins is $8.35.
There are 23 quarters and 29 dimes in the bag.
How many quarters and dimes are in the bag?Let's denote the number of quarters as "q" and the number of dimes as "d".
We can set up a system of two equations based on the given information:
The total number of coins is 52:
q + d = 52
The total value of the coins is $8.35, where each quarter is worth $0.25 and each dime is worth $0.10:
0.25q + 0.10d = 8.35
To solve this system of equations, we can use substitution, elimination, or any other appropriate method.
Let's use elimination to solve this system of equations.
0.10(q + d) = 0.10(52)
25q + 10d = 835
25q + 10d = 835
0.25q + 0.10d = 8.35 (multiply by 100)
Now, let's multiply both sides of the first equation by 2 and the second equation by 8 to make the coefficients of "q" the same:
50q + 20d = 1670
200q + 80d = 6680
Now, let's subtract the first equation from the second equation to eliminate "q":
200q + 80d - (50q + 20d) = 6680 - 1670
150q + 60d = 5010
Now, let's divide both sides of the resulting equation by 30 to solve for "q":
150q/30 + 60d/30 = 5010/30
5q + 2d = 167
After trying different values, we find that when "q" = 23 and "d" = 29, the equation is satisfied and the condition "q + d = 52" is also satisfied. Therefore, there are 23 quarters and 29 dimes in the bag.
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in order to maintain accuracy, political polling groups must maintain a certain degree of confidence with a small margin of error. fivethirtyeight is a polling company that wishes to survey a population of people, but maintain a margin of error of 0.05 or less with a 99% confidence level. what is the smallest number of consumers they should survey to guarantee this?
A minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.
What is the sample size?Sample size refers to the number of observations or individuals included in a study or experiment. It is the number of subjects or units that are selected from a population to be studied. The sample size is an important consideration in statistical analysis, as it can affect the accuracy and generalizability of the results. A larger sample size generally leads to more precise estimates and stronger statistical power, but it can also be more costly and time-consuming to collect and analyze.
According to the given informationTo calculate the minimum sample size required to maintain a margin of error of 0.05 or less with a 99% confidence level, we can use the formula:
n = (Z² * p * (1-p)) / E²
where n is the sample size, Z is the Z-score for the desired confidence level (2.576 for 99% confidence level), p is the estimated proportion of the population that has a certain characteristic (we can use 0.5 for maximum variability), and E is the margin of error.
Plugging in the values, we get:
n = (2.576² * 0.5 * (1-0.5)) / 0.05²
n = 664.3
Rounding up to the nearest whole number, we get a minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.
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Chester worked for 8hour each day for 5days.He earned P2190.00.How much did he earn per hour?
Answer:
P54.75 per hour.
Step-by-step explanation:
If he earned 2190 pesos on working 8 hours each for 5 days then he earned 54.75
Equation: hours x days / earnings
Therefore, 8 hours x 5 days = 40
2190 / 40 = P54.75 / hour
what is the probability that the larger of two continuous i.i.d. random variable will exceed the population median? stackage
The probability that the greater of the two random variables will surpass the population median is just 0.5 because both events are mutually exclusive.
The i.i.d means two random variable where there is an equal chance that one will be greater then the other.
So, it means there is 50% chances for both of them to be greater then the median.
The probability that the greater of the two random variables will surpass the population median is just 0.5 because both events are mutually exclusive. This conclusion is valid as long as the variable are given to be continuous and i.i.d.
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a monkey types 10 letters on a computer. assume the keyboard contains only letters and that the monkey never repeats letters. what is the probability of seeing the word math in this string of 10 letters?
The probability of seeing the word "math" in a 10-letter string typed by a monkey is 0.0024 (or 0.24%).
To calculate this probability, we first need to determine the total number of possible 10-letter strings that the monkey can type. Since the monkey never repeats letters, the number of possible 10-letter strings is given by the permutation formula:
10P10 = 10!/(10-10)! = 3,628,800
Next, we need to determine the number of 10-letter strings that contain the word "math". We can do this by fixing the position of the "m" and the "a", and then allowing the monkey to freely choose the remaining 6 letters. The number of ways to do this is given by:
8P6 = 8!/(8-6)! = 56
Finally, we divide the number of 10-letter strings containing "math" by the total number of possible 10-letter strings to obtain the probability:
56/3,628,800 = 0.000024 = 0.0024 (or 0.24%)
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a person swims 11 miles downriver in the same time they can swim 7 miles upriver. the speed of the current is 4 miles per hour. find the speed of the person in still water.
The speed of the person in still water is 18 miles per hour
Let's call the speed of the person in still water "x".
When the person swims downriver, they are swimming with the current, so their effective speed is the sum of their swimming speed and the speed of the current, which is "x + 4".
When the person swims upriver, they are swimming against the current, so their effective speed is the difference between their swimming speed and the speed of the current, which is "x - 4".
We know that the person covers 11 miles downriver in the same amount of time it takes them to cover 7 miles upriver. This means that the two distances are equal in terms of time:
[tex]11 / (x + 4) = 7 / (x - 4)[/tex]
To solve for x, we can cross-multiply and simplify:
[tex]11(x - 4) = 7(x + 4)[/tex]
[tex]11x - 44 = 7x + 28[/tex]
[tex]4x = 72[/tex]
[tex]x = 18[/tex]
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three six-sided, fair dice are rolled. what is the probability that none of the outcomes is an even number
the probability that none of the outcomes is an even number is 1/8 or approximately 0.125
The probability of rolling an even number on a fair six-sided die is 3/6 or 1/2, and the probability of rolling an odd number is also 1/2.
To find the probability that none of the outcomes is an even number, we need to calculate the probability of rolling an odd number on all three dice. Since the dice are rolled independently, we can multiply the probabilities together to get the overall probability:
P(rolling odd on one die) = [tex]1/2[/tex]
P(rolling odd on two dice) = [tex](1/2)^2 = 1/4[/tex]
P(rolling odd on three dice) =[tex](1/2)^3 = 1/8[/tex]
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the confidence interval in which you have the most confidence that it captures the population mean must be:
The confidence interval in which you have the most confidence that it captures the population mean is the one with the highest level of confidence.
But keep in mind that this interval will be wider and less precise, so we must balance the level of confidence with the desired precision of your estimate.
The terms confidence interval, population mean, and level of confidence.
A confidence interval is a range of values that is likely to contain the population mean, which is the average value of a certain variable in the entire population.
The level of confidence, expressed as a percentage (e.g., 95%), represents the probability that the confidence interval captures the true population mean.
In general, the confidence interval with the highest level of confidence will give you the most certainty that it captures the population mean.
However, as the level of confidence increases, the width of the confidence interval also increases, making it less precise.
This means that while we have more confidence that the interval contains the population mean, you have less specific information about where the mean lies within that interval.
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2. Allie plans to tile her living room but leave a square area in the upper right-hand corner
for carpet. The squares sides will half the length of the entire area. The entire area has a length
of 18' while the width will be 12'. How big is the tiled area?
The solution is :; 1256.63 tiles would be needed.
We have,
the question is not quite clear but I assume that it is asking how many tiles of length 70cm is required in order to pave the circular area.
Given,
radius(r) = 14m= 1400cm
Area of the circle= πr²= π×1400²
= 6157521.6 cm²
length of square tile(l)= 70cm
area of square= l²= 70×70= 4900cm²
now,
number of tiles required= area of circle ÷ area of tile
= 6157521.6 ÷ 4900
= 1256.63 tiles
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complete question:
A circular room of radius 14 m is to be covered by a square carpet. What will be the maximum area the carpet can cover? If the same area is to be paved with square tiles with a side length of 70 cm, then how many tiles would be needed?
Help with algebra 2 homework
The formula for the volume of an sphere of radius r is given as follows:
V = (2/3)πr³
The radius as a function of the volume is obtained as follows:
r³ = 3V/2π
[tex]r = \sqrt[3]{\frac{3V}{2\pi}}[/tex]
Hence the radius of a sphere of volume 25 in³ is given as follows:
[tex]r = \sqrt[3]{\frac{25}{2\pi}}[/tex]
r = 2.29 in.
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In morning Emily studied 40 minutes for a math exam. Later that evening Emily studied for x more minutes. Write an equation that represents the total number of minutes y emily studied for the math exam
Equation that represents the total number of minutes y Emily studied for the math exam is y = 40 +x.
We can represent the total number of minutes Emily studied for the math exam using the equation,
y = 40 + x
Here, 'y' represents the total number of minutes Emily studied for the math exam, '40' represents the number of minutes she studied in the morning, and 'x' represents the number of minutes she studied later that evening.
By adding the number of minutes studied in the morning to the number of minutes studied later that evening, we can calculate the total number of minutes Emily studied for the math exam.
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