Mathematics High School
Answers
Answer 1
The results related to quadrilaterals, triangles and semicircles are, respectively:
Case 12: A = 467.611 ft²
Case 13: h = 8.7 m
Case 14: b = 27 mm
Case 15: B = 14 ft
Case 16: h = 11.5 in
Case 17: r = 7 km
Case 18: h = 19 ft
Case 19: C = 243.56 USD
How to determine the area of figures
In this problem we find seven area cases related to quadrilaterals and triangles, whose formulae are shown below:
Triangle (Classic formula)
A = 0.5 · b · h
Triangle (Heron's formula)
A = √[s · (s - a) · (s - b) · (s - c)]
s = 0.5 · (a + b + c)
Where:
a, b, c - Side lengthss - Semiperimeter.
Rectangle / Parallelogram
A = b · h
Trapezoid
A = 0.5 · (b + B) · h
Where:
b - BaseB - Alternative base.h - Height
And an area case related to a semicircle:
Semicircle
A = 0.5π · r²
Where r is the radius.
Now we proceed to solve on each case:
Case 12
A = 0.5 · √[(18 ft)² - (8 ft)²] · (8 ft) + √[(18 ft)² - (8 ft)²] · (25 ft)
A = 467.611 ft²
Case 13
h = 211.41 m² / 24.3 m
h = 8.7 m
Case 14
b = 202.5 mm² / [0.5 · (15 mm)]
b = 27 mm
Case 15
193.5 ft² = 0.5 · (29 ft + B) · (9 ft)
29 ft + B = 193.5 ft² / [0.5 · (9 ft)]
B = 14 ft
Case 16
166.75 in² = 0.5 · (21 in + 8 in) · h
h = 166.75 in² / [0.5 · (21 in + 8 in)]
h = 11.5 in
Case 17
76.97 km² = 0.5π · r²
r = 7 km
Case 18
h = 228 ft² / 12 ft
h = 19 ft
And the perimeter is:
p = 2 · (12 ft + 19 ft)
p = 62 ft
Case 19
s = 0.5 · 3 · (15 ft)
s = 22.5 ft
A = √[(22.5 ft) · (22.5 ft - 15 ft)]
A = 12.990 ft²
And the total cost is:
C = (18.75 USD / ft²) · (12.990 ft²)
C = 243.56 USD
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Related Questions
Johnny could wash 120 cars in eight hours at that rate how many cars could johnny wash in 15 hours
Answers
Answer:
225 cars
Step-by-step explanation:
he can wash 120 in 8 hours.
that's 120/8 = 15 cars per hour.
so he can was 15 X 15 = 225 cars
5. a building has 6 homes per floor and 3 floors. on the first floor, there are 4 penguins per home. on the second and third floors, there are 3 penguins per home.
which equation can we use to find, p, the total number of penguins living in the building?
(a) 3.6. (4+3) =p
(b) (4.6) + (3.6) +(3.6) =p
(c) (4.6) + (3.6). 3 =p
Answers
The correct equation to find the total number of penguins living in the building is option (b): (4.6) + (3.6) + (3.6) = p
Let's break down the equation: (4.6) represents the number of penguins per home on the first floor, multiplied by the total number of homes on the first floor (6 homes per floor). (3.6) represents the number of penguins per home on the second floor, multiplied by the total number of homes on the second floor (6 homes per floor).
(3.6) represents the number of penguins per home on the third floor, multiplied by the total number of homes on the third floor (6 homes per floor). By adding these three terms together, we get the total number of penguins, represented by p.
Therefore, option (b) is the correct equation to find the total number of penguins living in the building.
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Ava opened an account first oak with $5000. zoe started an account with $4000 at west united. no additional money was deposited or withdraw from the accounts.
how much more money will be in ava's account than zoe's at the end of three years?
Answers
At the end of three years, Ava's account will have $750 more than Zoe's account.
To calculate the difference in the final amounts, we need to consider the interest earned on the initial deposits over the three-year period. Assuming both accounts earn the same annual interest rate, we can use the formula A = P(1 + r)^n, where A is the final amount, P is the principal (initial deposit), r is the interest rate, and n is the number of years.
For Ava's account, with an initial deposit of $5000, we have A_Ava = 5000(1 + r)^3.
For Zoe's account, with an initial deposit of $4000, we have A_Zoe = 4000(1 + r)^3.
Since no additional money is deposited or withdrawn, the difference in the final amounts will be A_Ava - A_Zoe.
Substituting the values into the equation, we get the difference as $5000(1 + r)^3 - $4000(1 + r)^3.
By simplifying the expression, we find that at the end of three years, Ava's account will have $750 more than Zoe's account.
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A jar contained 18 red marbles, 14 green marbles, and 20 blue marbles. A marble was selected at random, the color was recorded, and the marble was placed back in the jar. The table shows the results after 60 trials.
What was the relative frequency of selecting a blue marble?
Enter your answer rounded to the nearest percent in the box.
Answers
The relative frequency of selecting a blue marble is 33%
A jar contained 18 red marbles, 14 green marbles, and 20 blue marbles.
Let's event A: selecting a blue marble
⇒ n(A) = 20
Here, the number of trials (t) = 60
So, the relative frequency of selecting a blue marble would be,
⇒ f(A) = n(A)/t
⇒ f(A) = 20/60
⇒ f(A) = 1/3
The relative frequency to the nearest percent would be,
⇒ f(A) = (1/3 × 100)%
⇒ f(A) = 33.33%
⇒ f(A) ≈ 33%
Therefore, the relative frequency of selecting a blue marble is 33%
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Complete question:
Twelve synchronized swimmers are forming a circle. the locations of three of those swimmers
Answers
In a circle formed by twelve synchronized swimmers, the locations of three specific swimmers can be described using their positions in relation to the other swimmers.
To describe the locations of three swimmers in a circle formed by twelve synchronized swimmers, we need additional information or specifications about their positions.
In a circle, each swimmer is equidistant from the neighboring swimmers, forming a regular pattern. However, without knowing any specific positions or reference points, it is not possible to pinpoint the exact locations of the three swimmers.
To describe the locations, we can refer to their positions relative to other swimmers, such as "swimmer A is three positions to the left of swimmer B," or "swimmer C is opposite swimmer D." By using such descriptions in relation to other swimmers, we can provide some information about the positions of the three swimmers.
However, without any specific instructions or positions given, it is not possible to provide accurate or definitive information about the locations of the three swimmers within the circle formed by twelve synchronized swimmers.
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Given x = -4, order the following as they would appear on the number line from left to right. X, -x, |3. 5|, -3, |-2. 5|, |5|
Answers
When ordering the given numbers on the number line from left to right, the correct order is:
-4, -(-4) or 4, |3.5| or 3.5, -3, |-2.5| or 2.5, and |5| or 5.
Starting with x = -4, which is already given, we move to -(-4) or 4, which is the positive value of -4. Next, we have |3.5|, which represents the absolute value of 3.5, resulting in 3.5. Moving to -3, we have a negative number. Then, |-2.5| is the absolute value of -2.5, which is 2.5. Finally, |5| is the absolute value of 5, which remains as 5.
Therefore, the numbers on the number line, from left to right, would be -4, 4, 3.5, -3, 2.5, and 5.
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A spinner has three equal sections labeled 1, 2, and 3.
What is the probability of getting two numbers that have a sum of 5 on the spinner?
Ο Α. 2
9
B. 1
3
o
C. 1
6
0 D 4
lo
Answers
The probability of getting two numbers that have a sum of 5 on the spinner is 1/9.
What is the likelihood of obtaining two numbers with a sum of 5 on the spinner?
In probability theory, the probability of an event happening is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, we need to determine the number of favorable outcomes where the sum of two numbers on the spinner is 5. There are two such favorable outcomes: (2, 3) and (3, 2). Since the spinner has three equal sections, the total number of possible outcomes is 3 * 3 = 9.
Therefore, the probability is calculated as 2 favorable outcomes divided by 9 total outcomes, resulting in 2/9 or approximately 0.2222.
Probability theory and calculating probabilities by considering favorable and total outcomes in different scenarios.
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For a sample size of 90 and a sample proportion of 0. 5, what is the standard error of the sampling distribution? Round your answer to three decimal places
Answers
The standard error of the sampling distribution is approximately 0.052 when rounded to three decimal places.
The formula for the standard error of the sampling distribution, denoted as SE, can be calculated using the formula:
SE = √[(p * (1 - p)) / n]
where p is the sample proportion and n is the sample size.
Given:
Sample size (n) = 90
Sample proportion (p) = 0.5
Substituting these values into the formula, we have:
SE = √[(0.5 * (1 - 0.5)) / 90]
= √[(0.25) / 90]
= √0.002777777777777778
≈ 0.052
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For a recent art project, a teacher purchased 94 pieces of red construction paper and 80 What is the exact ratio of red construction paper to blue construction paper?
Answers
In the recent art project, the teacher purchased 94 pieces of red construction paper and 80 pieces of blue construction paper. To determine the exact ratio of red construction paper to blue construction paper, we divide the number of red construction paper pieces by the number of blue construction paper pieces.
The ratio of red construction paper to blue construction paper can be expressed as:94:80
However, we can simplify this ratio by dividing both numbers by their greatest common divisor. In this case, the greatest common divisor of 94 and 80 is 2.
Dividing 94 by 2 gives us 47, and dividing 80 by 2 gives us 40.
Therefore, the exact simplified ratio of red construction paper to blue construction paper is: 47:40
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For an integer n greater than 1, if bn = a, then b is a(n).
of a.
Answers
For an integer n greater than 1, if [tex]b^{n}[/tex] = a, then b is the nth root of a.
How to complete the sentence
In the sentence, we are told about an integer greater than 1. An integer is a whole number that can either be positive or negative or even 0. Now we can assign the number n the integer, 2, and b the number 4
[tex]4^{2} = 16[/tex]
The result a for this expression is 16. This means that the value 4 is the 2nd root of 16. We can express this thus:
[tex]\sqrt[2]{16} = 4[/tex]
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Select an
expression that is
equivalent to 2 4/8
Answers
An expression equivalent to 2 4/8 is 5/2.
What is expression?
Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both.
To simplify the expression 2 4/8, we can convert the mixed number into an improper fraction and then simplify further if needed.
2 4/8 can be rewritten as 2 + 4/8.
First, let's convert the mixed number into an improper fraction:
2 + 4/8 = (2 * 8 + 4)/8 = 16/8 + 4/8 = 20/8
Now, let's simplify the fraction:
20/8 = 10/4 = 5/2
Therefore, an expression equivalent to 2 4/8 is 5/2.
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A teacher has a bag of marbles. there are 10 red, 10 blue, 8 green, 8 purple, and 8 yellow marbles in the bag. as the students enter the classroom, they draw a marble and keep it. if the first student in the room draws a yellow, and the second draws a purple, what is the probability that the third student will draw a red or a blue?
Answers
The Probability that the third student will draw a red or blue marble is 20/44, which simplifies to 5/11 or approximately 0.45.
To find the probability that the third student will draw a red or a blue marble, we need to first calculate the total number of marbles remaining in the bag after the first two students draw theirs.
The first student draws a yellow marble, leaving 9 yellow, 10 red, 10 blue, 8 green, and 8 purple marbles in the bag.
The second student draws a purple marble, leaving 9 yellow, 10 red, 10 blue, 8 green, and 7 purple marbles in the bag.
Therefore, the total number of marbles remaining in the bag is 44.
Of those 44 marbles, there are 10 red and 10 blue marbles, for a total of 20 marbles that the third student could potentially draw.
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What is the volume of 1.35 moles of chlorine gas at rtp?
Answers
According to the question we have the volume of 1.35 moles of chlorine gas at RTP is 31.1 L.
At RTP (room temperature and pressure), the temperature is 25°C (298K) and the pressure is 1 atm. To find the volume of 1.35 moles of chlorine gas at RTP, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
R = 0.08206 L.atm/mol.K
First, we need to convert the temperature from Celsius to Kelvin by adding 273.
T = 298K
Next, we can plug in the values and solve for V.
PV = nRT
V = nRT/P
V = (1.35 mol)(0.08206 L.atm/mol.K)(298K)/(1 atm)
V = 31.1 L
Therefore, the volume of 1.35 moles of chlorine gas at RTP is 31.1 L.
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Your bike was originally purchased for $1,200. it loses about 8% of its original value each year. how many years have passed if the bike is now worth $479.56?
Answers
Answer:
11 years
Step-by-step explanation:
N = A (1 + increase) ^n
Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.
479.56 = 1200(1-0.08)^n
479.56 = 1200 (0.92)^n
0.92^n = (479.56/1200)
takes logs for both sides:
log 0.92^n = log (479.56/1200)
simplify:
n log 0.92 = log (479.56/1200)
n = log (479.56/1200) ÷ log 0.92
= 11.
it will take 11 years for the value to be $479.56
Write two numbers that multiply to the value on top and add to the value on bottom.
30
13
Answers
The two numbers that multiply to 30 and add to 13 are 10 and 3, or 3 and 10.
To find two numbers that multiply to 30 and add to 13, we can use algebraic equations.
Let's assume the two numbers are x and y. According to the given conditions, we have two equations:
Equation 1: x× y = 30
Equation 2: x + y = 13
We can solve this system of equations by substitution or elimination.
Let's solve it using substitution:
From Equation 2, we can express one variable in terms of the other:
x = 13 - y
Substituting this value of x into Equation 1:
(13 - y) × y = 30
Expanding the equation:
13y - y² = 30
Rearranging the equation:
y² - 13y + 30 = 0
Now we can factorize this quadratic equation:
(y - 3)(y - 10) = 0
Setting each factor equal to zero and solving for y:
y - 3 = 0 or y - 10 = 0
Solving these equations:
y = 3 or y = 10
If y = 3, substituting it back into Equation 2:
x + 3 = 13
x = 13 - 3
x = 10
If y = 10, substituting it back into Equation 2:
x + 10 = 13
x = 13 - 10
x = 3
Therefore, the two sets of numbers that satisfy the conditions are:
x = 10, y = 3
x = 3, y = 10
So, the two numbers that multiply to 30 and add to 13 are 10 and 3, or 3 and 10.
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Read this line from fall of the house of usher: in this there was much that reminded me of the specious totality of old wood-work which has rotted for long years in some neglected vault, with no disturbance from the breath of the external air. why does the narrator describe the house in this way? to show that it has a nice design to show that it reminds him of something rotting to show that there are too many people inside to show that the owner had a lot of parties
Answers
The narrator describes the house in this way to convey a sense of decay and deterioration. It is not to show that it has a nice design, remind him of something rotting, indicate the number of people inside, or suggest that the owner had a lot of parties.
The line from "Fall of the House of Usher" describes the house using imagery of old wood-work that has rotted in a neglected vault. This description serves to create a mood of decay and deterioration. The phrase "specious totality of old wood-work" suggests that the once-grand and impressive architecture of the house has fallen into disrepair. By comparing it to something rotting in a neglected vault, the narrator conveys a sense of neglect and isolation. The description emphasizes the dilapidated state of the house, setting the tone for the eerie and decaying atmosphere that permeates the story.
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If an object goes from 60 mph to 30 mph in 5 seconds, what is its acceleration?
Answers
The acceleration of the object can be calculated by determining the change in velocity over the given time interval. In this case, the object decreases its velocity from 60 mph to 30 mph in 5 seconds.
The acceleration can be determined using the formula: acceleration = (final velocity - initial velocity) / time.
Using the given values, we can calculate the acceleration as follows:
Acceleration = (30 mph - 60 mph) / 5 seconds
Acceleration = -30 mph / 5 seconds
Acceleration = -6 mph/s
The negative sign indicates that the object is decelerating or slowing down. The acceleration value of -6 mph/s means that the object's velocity is decreasing by 6 miles per hour every second.
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Line AC is perpendicular to the circle centered at O with radius 1 unit. The length of AC is 1. 5 units. Find the length of segment AB
Answers
The length of segment AB is 1 unit, which is equal to the radius of the circle centered at O.
Since line AC is perpendicular to the circle centered at O, it means that line AC intersects the circle at point A. Given that the length of line AC is 1.5 units, and considering that point A lies on the circle, we can conclude that the distance from point A to the center O is equal to the radius of the circle, which is 1 unit.
Therefore, segment AB represents the distance from the center O to the point of intersection A, which is the radius of the circle. Consequently, the length of segment AB is 1 unit, matching the radius of the circle centered at O.
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2. identify the biased sample.
f. every fifth student is asked for their opinion on school colors.
g. every tenth person at a concert is asked to identify their favorite radio station.
h. every fifth shopper at the mall is asked if they voted.
j. a random sample of people is asked to name their favorite vehicle
Answers
The biased sample is option (h) where every fifth shopper at the mall is asked if they voted.
A biased sample is one that does not accurately represent the entire population due to a systematic bias in the sampling method. In this case, option (h) is biased because it only selects every fifth shopper at the mall and asks if they voted. This method may introduce a bias because it assumes that the opinions of every fifth shopper are representative of the entire population of mall shoppers. However, this may not be the case as there could be certain factors or characteristics that distinguish the fifth shoppers from the rest. To obtain a more representative sample, a random sampling method should be used where each individual has an equal chance of being selected, as in option (j) where a random sample of people is asked to name their favourite vehicle.
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Which of these could be the graph of F(x) = 3 • (0.5)*?
.
A
A. Graph A
B. Graph B
C. Graph C
D. Granh D
B
H
D
Answers
Graph C is the graph of the exponential function [tex]F(x) = 3(0.5)^x[/tex] in this problem.
How to define an exponential function?
An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.
The function for this problem is given as follows:
[tex]F(x) = 3(0.5)^x[/tex]
Hence the parameters are given as follows:
a = 3 -> y-intercept of y = 3.b = 0.5 -> decreasing exponential function.
Hence graph C is the correct graph for this problem.
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Why does christopher collier think new england should be proud of the town hall meeting form of government
Answers
New England should be proud of the town hall meeting form of government because it promotes civic engagement and ensures direct participation in decision-making processes.
What are the reasons behind New England's pride in the town hall meeting form of government?
The town hall meeting form of government is deeply rooted in the history and culture of New England. Christopher Collier, an esteemed historian, believes that this form of government holds significant value and should be a source of pride for the region.
At its core, the town hall meeting allows community members to come together in a direct and democratic setting to discuss and decide on local matters. It fosters civic engagement by providing a platform for individuals to voice their opinions, concerns, and ideas. The participatory nature of these meetings ensures that every citizen has the opportunity to actively contribute to the decision-making process.
Furthermore, the town hall meeting form of government promotes transparency and accountability. By gathering in a public forum, citizens can witness firsthand how decisions are made and hold their elected officials accountable for their actions. This open and inclusive process strengthens the bond between the government and the governed, creating a sense of shared responsibility and trust.
In addition, town hall meetings cultivate a strong sense of community and civic pride. These gatherings provide a space for residents to connect with one another, exchange information, and collaborate on local initiatives. By coming together as a community, New Englanders can collectively address challenges, celebrate achievements, and shape the future of their towns.
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The table represents the number of cheese crackers in the lunchboxes of 9 boys and 9 girls. by looking at the table, does it appear that the degree of variability for the boys' data is greater, less, or the same as the girls' data? compute the interquartile range of each data set. using the interquartile range, compare the degree of variability between the data sets. explain how the comparison supports your first answer.
a) no; boys: iqr: 4.5; girls iqr: 3; the degree of variability for both sets is about the same.
b) no; boys: iqr: 3; girls iqr: 4.5; the degree of variability for both sets is about the same.
c) yes; boys: iqr: 8; girls iqr: 5; the degree of variability is greater for the boys than for the girls.
d) yes; boys: iqr:10; girls iqr:16; the degree of variability for the boys is less than for the boys.
Answers
Hence, the correct option is c) yes; boys: iqr: 8; girls iqr: 5; the degree of variability is greater for the boys than for the girls.
To compute the interquartile range, we need to first find the median of each data set. For the boys' data, the median is 17, and for the girls' data, the median is 15. Then, we find the first and third quartiles by dividing the data set into two halves at the median and finding the median of each half. For the boys' data, the first quartile is 13 and the third quartile is 21, giving an interquartile range of 8. For the girls' data, the first quartile is 12 and the third quartile is 15, giving an interquartile range of 3.
Based on these calculations, we can see that the degree of variability for the boys' data is greater than for the girls' data, as their interquartile range is larger. This supports our initial observation that the boys' data has a greater degree of variability than the girls' data. Answer c) is therefore the correct choice.
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Anna has $30 in her account. she earns $12 per hour at her job. she needs more than $168 to buy a bike. part a create an inequality that represents the number of hours anna needs to work, h, to have enough money to buy a bike.
Answers
The inequality that represents the number of hours anna needs to work, h, to have enough money to buy a bike is 12h > 168
To create an inequality representing the number of hours Anna needs to work, h, to have enough money to buy a bike, we can use the given information.
Let's break down the information provided:
Anna has $30 in her account.
She earns $12 per hour at her job.
She needs more than $168 to buy a bike.
We can create the inequality as follows:
Total earnings > Cost of the bike
Since Anna earns $12 per hour and needs more than $168 to buy a bike, we can multiply her hourly earnings by the number of hours she needs to work to have enough money:
12h > 168
This inequality states that the total earnings, which is 12 times the number of hours Anna needs to work (h), must be greater than $168.
Therefore, the inequality representing the number of hours Anna needs to work, h, to have enough money to buy a bike is:
12h > 168
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A random sample of 10 subjects have weights with a standard deviation of 8. 9105 kg. What is the variance of their weights? Be sure to include the appropriate units with the result
Answers
The variance measures the spread or dispersion of the weights in the random sample. To calculate the variance, we square the standard deviation. Given that the standard deviation is 8.9105 kg, we square this value to obtain the variance.
The variance of the weights for the random sample of 10 subjects is approximately 79.36 kg^2, rounded to two decimal places. This means that, on average, the weights in the sample deviate from the mean weight by approximately 79.36 kg^2.
It's important to note that the variance is expressed in square units, representing the squared units of the original data (weights). It quantifies the variability or spread of the weights within the sample, providing insight into the dispersion of the data points.
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2 which survey question could have been asked to produce this data display? how many bags of dog food do you buy each month? how many times do you feed your dog each day? how much does your bag of dog food weigh? how much does your dog weigh?
Answers
The survey question that could have been asked to produce this data display is "How many bags of dog food do you buy each month?"
The data display provided suggests that the information being analyzed relates to the frequency of dog food purchases. The question "How many bags of dog food do you buy each month?" would directly elicit the specific data required to create such a display. By asking dog owners about the number of bags they purchase monthly, the survey collects quantitative data that can be organized and displayed graphically or numerically. This information can be used to identify patterns, trends, or variations in dog food consumption, providing insights for retailers, manufacturers, and pet owners. It allows for comparisons between different demographic groups or regions and can help inform marketing strategies or product development related to dog food. Overall, this survey question provides a clear and focused inquiry into the purchasing habits of dog owners, generating data that can be visually represented and analyzed for various purposes.
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The canopy of a parachute is a semicircle with a radius of 13 feet. A company that is making parachutes for a Fourth of July celebration wants each parachute to be made from equal parts of red, white, and blue fabric. Approximately how much fabric of each color will be needed to make a single parachute canopy? 88. 5 ft 88. 5 ft² 265. 5 ft 265. 5 ft².
Answers
A single parachute canopy will require roughly 88.48 [tex]ft^2[/tex] of each colour (red, white, and blue).
Approximately how much fabric of each color will be needed to make a single parachute canopy?
The canopy of the parachute is a semicircle with a radius of 13 feet. The area of a semicircle is given by the formula:
[tex]A = (\pi * r^2) / 2[/tex]
where A represents the area and r represents the radius.
Calculate the area of the semicircle canopy:
[tex]A = (\pi * 13^2) / 2 = (\pi * 169) / 2 = 265.45 ft^2[/tex] (rounded to two decimal places).
Since the company wants each parachute to be made from equal parts of red, white, and blue fabric, divide the total area by 3 to determine the amount of fabric needed for each color.Calculate the amount of fabric needed for each color:
[tex]265.45 ft^2 / 3 = 88.48 ft^2[/tex] (rounded to two decimal places).
Therefore, approximately 88.48 ft² of each color (red, white, and blue) will be needed to make a single parachute canopy.
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What four specific ideas does lincoln ask his listeners to commit
themselves to at the end of this speech?
Answers
The reference to "Lincoln" in this context is most likely about Abraham Lincoln's famous speech, the Gettysburg Address. In the Gettysburg Address, Lincoln asks his listeners to commit themselves to four specific ideas at the end of the speech. The ideas are as follows:
1. "That from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion." Lincoln urges the listeners to honor and remember the sacrifice of those who died in the Civil War and to be even more dedicated to the cause for which they fought.
2. "That we here highly resolve that these dead shall not have died in vain." Lincoln emphasizes the importance of ensuring that the deaths of those who fought in the war were not in vain. He encourages the listeners to work towards preserving the principles and ideals for which they fought.
3. "That this nation, under God, shall have a new birth of freedom." Lincoln expresses his hope for a renewed sense of freedom and unity in the nation, emphasizing that the war and its aftermath should lead to a stronger and more inclusive nation.
4. "And that government of the people, by the people, for the people, shall not perish from the earth." Lincoln underscores the importance of a democratic government that is founded on the principles of the people, by the people, and for the people. He asserts that such a government should endure and continue to exist.
These four ideas encapsulate the core messages and calls to action in Lincoln's Gettysburg Address.
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What does outer space lack that allows spaceships to fly?
force
friction
gravity
inertia
Answers
Outer space lacks friction, which allows spaceships to fly.
Friction is a force that opposes motion between two surfaces in contact, and in the vacuum of space, there is no air or other matter to create friction. This absence of friction allows spaceships to move freely without the need to overcome the resistance that friction would normally provide. However, it is important to note that spaceships still experience other forces, such as gravity and inertia, which need to be considered and accounted for in space exploration and spacecraft navigation.
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Jake is moving homes, and lifts a box straight up to put it on the moving truck. if he uses 1,074 w to lift the box 1.7 m, and it takes him 6.04 s to put it on the truck, calculate the mass of the box.
Answers
To find the mass of the box, we need to use the formula:
Work = force x distance
Power = work / time
We know the power used by Jake is 1,074 W and the distance he lifted the box is 1.7 m. Therefore, the work done by Jake is:
Work = power x time
Work = 1,074 W x 6.04 s
Work = 6,494.96 J
Next, we need to find the force used by Jake to lift the box. We can do this by rearranging the first formula:
Force = work / distance
Force = 6,494.96 J / 1.7 m
Force = 3,823.50 N
Finally, we can find the mass of the box by using the formula:
Force = mass x gravity
where gravity is approximately 9.81 m/s².
Mass of the box = Force / gravity
Mass of the box = 3,823.50 N / 9.81 m/s²
Mass of the box = 389.52 kg
Therefore, the mass of the box that Jake lifted is approximately 389.52 kg.
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Describe how the student's hand motion could be changed to make a wave with a greater frequency.
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To make a wave with a greater frequency, the student's hand motion would need to become faster. The frequency of a wave is determined by the number of waves that pass a given point in a unit of time.
So, by increasing the speed of the hand motion, the waves created would pass the same point more frequently, resulting in a higher frequency. Alternatively, the amplitude (height) of the waves could be decreased, as the frequency of a wave is inversely proportional to its wavelength (the distance between two consecutive peaks or troughs of a wave). By reducing the wavelength through decreasing the amplitude, the frequency would increase.
To make a wave with a greater frequency, the student's hand motion should be changed as follows:
1. Increase the speed of hand motion: Move the hand back and forth more quickly. This will create more waves in the same amount of time, resulting in a higher frequency.
2. Decrease the wavelength: By moving the hand in smaller, more rapid motions, the distance between each wave crest will decrease, leading to an increase in frequency.
By making these changes to the hand motion, the student will create a wave with a greater frequency.
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