Answers
The finished table contains the following amount of cans per day:
- 4 1 - 5 2/5- 6 1 ¹/₂- 7 1 ³/₄- 8 2- 9 2¹/₄- 10 2¹/₂- 11 2³/₄- 12 3- 13 3¹/₈- 14 3³/₁₀- 15 3³/₄How to determine fractions?To find out how many cans of food per day to give a cat, divide the cat's weight by 4. If the weight is not a multiple of 4, the result will be a fraction, which represents a fraction of a can of food.
A 5-pound cat needs 5/4 or 1.25 cans of food per day. Simplify this fraction to 1 ¹/₄ or 1.25.
Others include:
6/4 = 1.5
7/4 = 1.75
8/4 = 2
9/4 = 2.25
10/4 = 2.5
11/4 = 2.75
12/4 = 3
13/4 = 3.25
14/4 = 3.5
15/4 = 3.75
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Related Questions
Use the following for #5-6 A middle school science teacher wants to conduct some experiments. There are 15 students in the class. The teacher selects the students randomly to work together in groups of five. 5) In how many ways can the teacher combine five of the students for the first group if the order is not important? 6) After the first group of five is selected, in how many ways can the teacher combine five of the remaining students if the order is not important?
Answers
Answer:
5) 3003 ways;6) 252 ways.---------------------------------
5) Use the combination formula:
C(n, r) = n! / (r!(n-r)!)In this case, n = 15 (total students) and r = 5 (students in a group).
Substitute and calculate:
C(15, 5) = 15! / (5!(15-5)!) C(15, 5) = 15! / (5!10!) C(15, 5) = 3003The teacher can combine the students in 3003 ways for the first group.
6) After the first group of five is selected, there are 10 students remaining.
Again use the combination formula, with n = 10 and r = 5:
C(10, 5) = 10! / (5!(10-5)!) C(10, 5) = 10! / (5!5!) C(10, 5) = 252The teacher can combine the remaining students in 252 ways for the second group.
Which of the following tables represent a proportional relationship?
verbal:
a. y/x= 40/1 76/2 112/3 148/4
b. y/x= 48/2 96/3 144/4 192/5
c. y/x= 18/1 54/3 90/5 126/7
d. 24/1 21/2 18/3 15/4
picture:
Answers
a. y/x = 40/1, 76/2, 112/3, 148/4 does not represent a proportional relationship. . y/x = 48/2, 96/3, 144/4, 192/5 does not represent a proportional relationship. c. y/x = 18/1, 54/3, 90/5, 126/7 represents a proportional relationship.
How to determine a proportional relationshipA proportional relationship means that the ratio of y to x is constant throughout the table. Let's check each table:
a. y/x = 40/1, 76/2, 112/3, 148/4
If we simplify the fractions, we get y/x = 40, 38, 37.33, 37. This is not a constant ratio, so this table does not represent a proportional relationship.
b. y/x = 48/2, 96/3, 144/4, 192/5
If we simplify the fractions, we get y/x = 24, 32, 36, 38.4. This is not a constant ratio, so this table does not represent a proportional relationship.
c. y/x = 18/1, 54/3, 90/5, 126/7
If we simplify the fractions, we get y/x = 18, 18, 18, 18. This is a constant ratio, so this table represents a proportional relationship.
d. y/x = 24/1, 21/2, 18/3, 15/4
If we simplify the fractions, we get y/x = 24, 10.5, 6, 3.75. This is not a constant ratio, so this table does not represent a proportional relationship.
Therefore, the table that represents a proportional relationship is c. y/x = 18/1, 54/3, 90/5, 126/7.
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ASAP THX!!! ANSWER GETS BRAINLIEST
Rachel went to the grocery store and spent $68. She now has only $23 to get gasoline with before she returns home. How much money did Rachel have before she went grocery shopping? Create an equation to represent the situation. Make sure to identify and label your variable. Solve for the variable and describe your answer. Show your work and prove your solution to be correct
Answers
The solution is correct, as both sides of the equation are equal.
To find out how much money Rachel had before she went grocery shopping, we can create an equation using a variable.
Let x represent the amount of money Rachel had before grocery shopping.
The equation for the situation would be: x - $68 = $23
Now, let's solve for x:
Step 1: Add $68 to both sides of the equation:
x = $23 + $68
Step 2: Calculate the sum:
x = $91
So, Rachel had $91 before she went grocery shopping.
To prove the solution is correct, we can plug the value of x back into the equation:
$91 - $68 = $23
$23 = $23
Hence, both are equal.
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3
type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
the measurement of an angle is 40°, and the length of a line segment is 8 centimeters.
the number of unique rhombuses that can be constructed using this information is _____
please hurry
Answers
The number of unique rhombuses that can be constructed using this information is three.
How many unique rhombuses can be constructed using a 40° angle and an 8 cm line segment?When given a 40° angle and an 8 cm line segment, we can construct three distinct rhombuses. A rhombus is a quadrilateral with all sides of equal length, and opposite angles are congruent.
In this scenario, the given 40° angle determines the orientation of the rhombus, while the 8 cm line segment determines its side length. By connecting the endpoints of the line segment with congruent opposite angles, we can create three different rhombuses.
Each rhombus formed will possess an angle measure of 40° and a side length of 8 cm. However, these rhombuses will vary in terms of their overall shape and orientation. Each one represents a unique configuration that satisfies the given angle and side length criteria.
Therefore, the correct answer is that three distinct rhombuses can be constructed using the given information.
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Work out the size of an exterior angle of a regular hexagon
Answers
The size of an exterior angle of a regular hexagon is 60 degrees.
Working out the size of an exterior angleIn a regular hexagon, all the interior angles are equal and are given by the formula:
Interior angle = (n-2) x 180 / n
where n is the number of sides of the polygon.
For a hexagon, n = 6, so the interior angle is:
Interior angle = (6-2) x 180 / 6 = 120 degrees
An exterior angle is the supplement of an interior angle, which means it is the angle that when added to the interior angle, will equal 180 degrees.
So, exterior angle = 180 - interior angle = 180 - 120 = 60 degrees.
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Two different box-filling machines are used to fill cerealboxes on the assembly line. The critical measurement influenced bythese machines is the weight of the product in the machines. Engineers are quite certain that the variance of the weight ofproduct is σ^2=1 ounce. Experiments are conducted using bothmachines with sample sizes of 36 each. The sample averages formachine A and B are xA=4. 5 ounces and xB =4. 7 ounces. Engineers seemed surprisedthat the two sample averages for the filling machines were sodifferent.
a. Use the central limit theorem to determine
P(XB- XA >= 0. 2)
under the condition that μA=μB
b. Do the aforementioned experiments seem to, in any way,strongly support a conjecture that the two population means for thetwo machines are different?
Answers
a. By central limit theorem, P(XB- XA >= 0. 2) is approximately 0.0228 under the condition that μA=μB.
b. Yes, we can conclude that the observed difference in sample means does provide evidence that the two population means for the two machines are different.
a. Using the central limit theorem, we know that the sampling distribution of the difference in means (XB - XA) is approximately normal with mean (μB - μA) and standard deviation (σ/√n), where σ is the population standard deviation (σ=1 ounce) and n is the sample size (n=36 for both machines).
So, P(XB - XA >= 0.2) can be calculated by standardizing the difference in means:
Z = (XB - XA - (μB - μA)) / (σ/√n)
Z = (4.7 - 4.5 - 0) / (1/√36)
Z = 2
Looking up the probability of Z being greater than or equal to 2 in a standard normal distribution table, we find P(Z >= 2) = 0.0228.
Therefore, P(XB - XA >= 0.2) is approximately 0.0228 under the condition that μA=μB.
b. The difference in sample means (XB - XA = 0.2) is relatively small compared to the population standard deviation (σ=1 ounce). However, the calculated probability in part a (0.0228) suggests that the observed difference in sample means is statistically significant at a significance level of 0.05 (since P(XB - XA >= 0.2) < 0.05).
Therefore, we can conclude that the observed difference in sample means does provide evidence that the two population means for the two machines are different. However, further testing or analysis may be necessary to confirm this conclusion.
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A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 0.5 s and t=1.4 s? Use Galileo's formula u(t) = -32t ft/s.
Answer = _______
Answers
The distance is negative because it's a fall, so the cat falls 27.36 ft between t = 0.5 s and t = 1.4 s.
To find the distance the cat falls between t = 0.5 s and t = 1.4 s, we need to use the formula for velocity and distance.
we first need to find the position at each of these times using the given formula u(t) = -32t ft/s.
The formula for distance fallen is:
distance(t) = initial position + initial velocity × t + (1/2) × acceleration × t²
Since the cat falls with zero initial velocity and starts from the tree, we can simplify the formula:
distance(t) = (1/2) × acceleration × t²
First, let's find the velocity of the cat at t = 0.5 s and t = 1.4 s using Galileo's formula:
u(0.5) = -32(0.5) = -16 ft/s
and, u(1.4) = -32(1.4) = -44.8 ft/s
Now, we can use the formula for distance:
distance = (velocity at t = 0.5 s + velocity at t = 1.4 s) / 2 x (t = 1.4 s - t = 0.5 s)
⇒ distance = (-16 ft/s + (-44.8 ft/s)) / 2 x (1.4 s - 0.5 s)
⇒ distance = (-60.8 ft/s) / 2 x (0.9 s)
⇒ distance = -27.36 ft/s x s
Therefore, the cat falls 27.36 feet between t = 0.5 s and t = 1.4 s.
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true or false
Solids can be "unfolded" to form different net arrangements.
Answers
Solids can be "unfolded" to form different net arrangements is a true statement.
What is the unfolding?A net refers to a flat, two-dimensional shape that can be transformed or manipulated to form a three-dimensional object. A solid has the potential to create a variety of nets through various unfolding methods.
The term "net" for a solid refers to a flat shape that can be folded to form the solid object. it is possible to manipulate a three-dimensional object in various manners in order to produce distinct two-dimensional patterns. One can create various nets by cutting different edges of a cube and arranging the resultant faces.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answers
Answer:
The three equivalent equations are x+1=4, -5+x=-2, and 2+x=5. The x equals 3.
Step-by-step explanation:
A cylinder has a base area of 64π m2. Its height is equal to twice the radius. Identify the volume of the cylinder to the nearest tenth
Answers
The volume of the cylinder is approximately 1024π cubic meters.
We are given the base area of the cylinder as 64π square meters, which means that the radius of the cylinder is 8 meters (since the area of a circle is given by πr^2). We are also given that the height of the cylinder is twice the radius, which means that the height is 16 meters.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Substituting the given values, we get V = π(8^2)(16) = 1024π cubic meters. Therefore, the volume of the cylinder is approximately 1024π cubic meters.
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Answer:
[tex]3217.0 m ^{3}[/tex]
Step-by-step explanation:
2. A social media company claims that over 1 million people log onto their app daily. To test this claim, you record the number of people who log onto the app for 65 days. The mean number of people to log in and use the social media app was discovered to be 998,946 users a day, with a standard deviation of 23,876. 23. Test the hypothesis using a 1% level of significance.
Answers
The hypothesis test suggests that there is not enough evidence to reject the claim made by the social media company that over 1 million people log onto their app daily, as the t-value (-1.732) is less than the critical value (-2.429).
Null hypothesis, The true mean number of people who log onto the app daily is equal to or less than 1 million.
Alternative hypothesis, The true mean number of people who log onto the app daily is greater than 1 million.
Level of significance = 1%
We can use a one-sample t-test to test the hypothesis.
t = (X - μ) / (s / √n)
where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Substituting the values, we get
t = (998,946 - 1,000,000) / (23,876 / √65)
t = -1.732
Using a t-distribution table with 64 degrees of freedom and a one-tailed test at a 1% level of significance, the critical value is 2.429.
Since the calculated t-value (-1.732) is less than the critical value (-2.429), we fail to reject the null hypothesis. There is not enough evidence to support the claim that more than 1 million people log onto the app daily.
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The cost to produce x cases of Thingamabobs is given by the function C = 50x + 1000 where Cis in hundreds of dollars. If production is growing at a rate of 20 cases per day when the production level is x= 50 cases, find the rate at which the cost of production is changing.
Answers
The rate at which the cost of production is changing is 1000 hundred dollars per day or $100,000 per day.
To find the rate at which the cost of production is changing, we'll use the given cost function C = 50x + 1000, and the information that production is growing at a rate of 20 cases per day when x = 50 cases.
First, differentiate the cost function with respect to x to get the rate of change of the cost with respect to the number of cases produced (dC/dx):
dC/dx = 50
The derivative, 50, tells us that the cost increases by 50 hundred dollars for each additional case produced.
Now, we're given that dx/dt = 20 cases per day when x = 50 cases. To find dC/dt, the rate at which the cost of production is changing, multiply the rate of change of the cost with respect to the number of cases (dC/dx) by the rate of change of the number of cases with respect to time (dx/dt):
[tex]dC/dt = (dC/dx) × (dx/dt) = 50 × 20[/tex]
dC/dt = 1000
So, the rate at which the cost of production is changing is 1000 hundred dollars per day or $100,000 per day.
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Need help on unit 2 review
Answers
a^2+b^2=c^2
12 is the hypotenuse because it is opposite the right angle.
10^2+b^2=144
100+b^2=144
b^2=44
b=sqrt44
Use linear approximation to approximate √125.04 as follows Let f(x) = ³√ x, and find the linearization of f(x) at x = 125 in the form y = mx+ b Note: The values of m and bare rational numbers which can be computed by hand. You need to enter expressions which give m and b exactly You should not have a decimal point in the answers to either of these parts m= b = Using these values, find the approximation Also, for this part you should be entering a rational number, not a decimal approximation ²√ 125.04≈
Answers
To approximate √125.04 using linear approximation, first find the linearization of f(x) = ³√x at x = 125. Then use the point-slope form of the equation to find the equation of the tangent line and plug in x = 125.04 to get the approximation.
To approximate √125.04 using linear approximation and the function f(x) = ³√x, first find the linearization of f(x) at x = 125 in the form y = mx + b. Calculate f(125) and f'(x).Calculate f'(125): Use the point-slope form of the equation
1: Calculate f(125) and f'(x).
f(125) = ³√125 = 5
f'(x) = (1/3)x^(-2/3)
2: Calculate f'(125).
f'(125) = (1/3)(125)^(-2/3) = 1/15
3: Use the point-slope form of the equation y - y1 = m(x - x1) to find the equation of the tangent line.
y - 5 = (1/15)(x - 125)
4: Rearrange to find y in terms of x.
y = (1/15)(x - 125) + 5
5: Determine the values of m and b.
m = 1/15
b = (1/15)(-125) + 5
6: Plug in x = 125.04 to approximate √125.04.
²√125.04 ≈ (1/15)(125.04 - 125) + 5
The linearization of f(x) at x = 125 is y = (1/15)x + b, with m = 1/15 and b = (1/15)(-125) + 5. Using these values, the approximation of √125.04 is (1/15)(125.04 - 125) + 5.
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Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)
Answers
The area of the triangle is 6 square units.
How to solveOnce you have the points they make a 3-4-5 triangle.
The two legs are 3 and 4, so the hypotenuse has to be 5.
Or you could use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5
then find area
A=1/2bh
1/2(3*4)
6
Thus, the area of the triangle is 6 square units.
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Use this data set, which shows how many miles Tisha ran each week for 10 weeks
4,9,8,6,14,8,16,12
Find the statistical measures that you need tomake a box plot of Tisha's running distances.
(what’s a statistical measure)
Answers
Statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.
A statistical measure is a numerical value that provides information about a specific aspect of a dataset's distribution, such as its central tendency, spread, or variability. Box plots require several statistical measures to be constructed, including:
Minimum: The smallest value in the dataset. In this case, the minimum value is 4.
Maximum: The largest value in the dataset. In this case, the maximum value is 16.
Median: The middle value of the dataset when it is arranged in numerical order. In this case, the median is the average of the two middle values, which are 8 and 9. The median is therefore (8 + 9) / 2 = 8.5.
First Quartile (Q1): The value below which 25% of the data falls. In this case, the first quartile is the median of the first half of the data, which is 6.
Third Quartile (Q3): The value below which 75% of the data falls. In this case, the third quartile is the median of the second half of the data, which is 14.
With these statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.
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8-73.
For each diagram below, write and solve an equation for x
Answers
Answer:
a.x=100 equation: 540=(125·2)+90+(2x)
b. x=3 equation: 6x+18=2x+30
Step-by-step explanation:
a. We know that the interior angles of a pentagon have to equal 540 degrees.
So:
540=125+125+90 (hence the square) + x + x
simplify:
540=340+2x
simplify:
200=2x
x=100
b. Using the alternate exterior angles theorem we can say:
6x+18=2x+30
simplify:
4x+18=30
4x=12
x=3
An athletic Beld is a 50 yd-by-100 yd rectangle, with a semicircle at each of the short sides. Arunning track 10 yd wide surrounds the field. If the track is divided into eight lanes of equal width, with lane 1 being the inner-most and lane 8 being the outer-most lane, what is the distance around the along the inside edge of each lane?
Answers
The distance along the inside edge of each lane is 170 yards, 180 yards, 190 yards, 200 yards, 210 yards, 220 yards, 230 yards, and 240 yards.
Length of the Beld = 100 yd
Width of the Beld = 50 yd
The radius of the lane = 50/2 = 25 yards
To calculate the length of the overall length of the lane including semicircles is:
100 yards + 2 × 25 yards = 150 yards
The length of the innermost lane is:
150 yards + 2 × 10 yards = 170 yards
To calculate the length of the other lanes is:
170 yards + 10 yards = 180 yards
The length of lane 3 is:
180 yards + 10 yards = 190 yards
The distance between the two lanes is 10 yards. Then the remaining lengths of the lanes will be 200 yards, 210 yards, 220 yards, 230 yards, and 240 yards
Therefore, we can conclude that the distance between the two lanes along the inside edge of each lane is 10 yards.
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Set up the partial fraction decomposition for a given function. Do not evaluate the coefficients. f(x) = 16x3 + 12x2 + 10x + 2 / (x4 – 4x2)(x2 + x + 1)2(x2 – 3x + 2)(x4 + 3x2 + 2)
Answers
We can decompose the given rational function as follows:
f(x) = (16x^3 + 12x^2 + 10x + 2) / [(x^4 – 4x^2)(x^2 + x + 1)^2(x^2 – 3x + 2)(x^4 + 3x^2 + 2)]
To find the partial fraction decomposition, we first factor the denominator completely:
x^4 – 4x^2 = x^2(x^2 – 4) = x^2(x – 2)(x + 2)
x^2 + x + 1 = (x + 1/2)^2 + 3/4
x^2 – 3x + 2 = (x – 1)(x – 2)
x^4 + 3x^2 + 2 = (x^2 + 1)(x^2 + 2)
Substituting these factorizations into the denominator, we get:
f(x) = (16x^3 + 12x^2 + 10x + 2) / [x^2(x – 2)(x + 2)(x + 1/2)^2(3/4)^2(x – 1)(x – 2)(x^2 + 1)(x^2 + 2)]
We can now write the partial fraction decomposition as:
f(x) = A/x + Bx + C/(x – 2) + D/(x + 2) + E/(x + 1/2) + F/(x + 1/2)^2 + G/(x – 1) + H/(x^2 + 1) + I/(x^2 + 2)
where A, B, C, D, E, F, G, H, and I are constants to be determined.
Note that the term E/(x + 1/2) has a repeated linear factor (x + 1/2)^2, so we need to include a second term F/(x + 1/2)^2 in the decomposition.
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H 고 Assignment Law of Cosli Progress saved Submit and End Assignment Law of Cosines 5 points possible 0/5 answered 6 VO : Question 1 > 1 pt 1 Details A pilot flies in a straight path for 1 hour 45 minutes. She then makes a course correction, heading 35 degrees to the right of her original course, and flies 2 hours 15 minutes in the new direction. If she maintains a constant speed of 235 mi/h, how far is she from her starting position? Give your answer to the nearest mile. She is miles from her starting position
Answers
Round the answer to the nearest mile: She is 398 miles from her starting position.
To solve this problem, we'll use the Law of Cosines.
Here are the steps to find the distance from the starting position:
1. Convert the given time to hours: 1 hour 45 minutes = 1.75 hours 2 hours 15 minutes = 2.25 hours
2. Calculate the distance traveled in each direction:
Distance1 = Speed × Time1 = 235 mi/h × 1.75 h = 411.25 miles
Distance2 = Speed × Time2 = 235 mi/h × 2.25 h = 528.75 miles
3. Use the Law of Cosines to find the distance between the starting position and her final position:
Distance = √(Distance1² + Distance2² - 2 × Distance1 × Distance2 × cos(35°))
4. Plug in the values and solve for the distance:
Distance = √(411.25² + 528.75² - 2 × 411.25 × 528.75 × cos(35°))
Distance ≈ 397.69 miles
5. Round the answer to the nearest mile: She is 398 miles from her starting position.
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The foutain in the of a park is circular with a diameter of 16 feet. There is a walk way that is 3 feet wide that goes around the fountain what is the approximate are of the walkway?
Answers
The approximate area of the walkway is 179 square feet.
To find the area of the walkway, we need to subtract the area of the inner circle (fountain) from the area of the outer circle (walkway + fountain).
The radius of the fountain is half the diameter, which is 16/2 = 8 feet.
The radius of the outer circle is the radius of the fountain + the width of the walkway, which is 8 + 3 = 11 feet.
The area of a circle is πr², where π (pi) is approximately 3.14.
So, the area of the fountain is:
π(8)² ≈ 201 square feet
And the area of the walkway plus fountain is:
π(11)² ≈ 380 square feet
To find the area of just the walkway, we subtract the area of the fountain from the area of the walkway plus fountain:
380 - 201 ≈ 179 square feet
So, the approximate area of the walkway is 179 square feet.
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Differentiate between absolute and relative measure of dispersion
Answers
Absolute measures of dispersion give the actual spread or variability in the original units of measurement, while relative measures of dispersion express the dispersion relative to the mean or some other characteristic of the data.
Measures of dispersion are used to describe the spread or variability of a set of data. There are two common types of measures of dispersion: absolute measures and relative measures.
Absolute measures of dispersion, such as the range, interquartile range (IQR), and standard deviation, give an actual value or measurement of the spread in the original units of measurement.
For example, the range is simply the difference between the maximum and minimum values in a data set, while the standard deviation is a measure of how far each value is from the mean.
Relative measures of dispersion, such as the coefficient of variation (CV), express the dispersion relative to the mean or some other characteristic of the data. These measures are useful when comparing the variability of different sets of data that have different units of measurement or different means
For example, the CV is the ratio of the standard deviation to the mean, expressed as a percentage, and it can be used to compare the variability of different data sets that have different means.
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The volume of a box in the shape of a
rectangular prism can be represented by
the polynomial 8x² + 44x + 48, where x is
a measure in centimeters. Which of these
measures might represent the dimensions
of the box?
Answers
The possible dimensions of the rectangular prism are (2x + 3) cm, (x + 4) cm, and 4 cm, or (2x + 3) cm, 4 cm, and (x + 4) cm, where x is a measure in centimeters.
The polynomial 8x² + 44x + 48 represents the volume of a rectangular prism in cubic centimeters, where x is a measure in centimeters.
To find the possible dimensions of the box, we need to factor the polynomial into three factors that represent the length, width, and height of the rectangular prism.
First, we can factor out the greatest common factor of the polynomial, which is 4:
8x² + 44x + 48 = 4(2x² + 11x + 12)
Next, we can factor the quadratic expression inside the parentheses:
2x² + 11x + 12 = (2x + 3)(x + 4)
Therefore, the polynomial can be factored as:
8x² + 44x + 48 = 4(2x + 3)(x + 4)
This means that the dimensions of the rectangular prism could be (2x + 3), (x + 4), and 4, where x is a measure in centimeters. Alternatively, the dimensions could be (2x + 3), 4, and (x + 4).
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4. Let A be a 3 x 4 matrix and B be a 4 x 5 matrix such that ABx = 0 for all x € R5. a. Show that R(B) C N(A) and deduce that rank(B) < null(A) b. Use the Rank-Nullity theorem to prove that rank(A) + rank(B) < 4.
Answers
a. To show that R(B) is a subset of N(A), let y be any vector in R(B):
This means that there exists a vector x in R4 such that Bx = y.
Now, since ABx = 0 for all x in R5, we can write:
A(Bx) = 0
But we know that Bx = y, so we have:
Ay = 0
This shows that y is in N(A), and therefore R(B) is a subset of N(A).
To deduce that rank(B) is less than null(A), recall that by the Rank-Nullity theorem, we have:
rank(B) + null(B) = dim(R5) = 5
rank(A) + null(A) = dim(R4) = 4
Since R(B) is a subset of N(A), we have null(A) >= rank(B).
Therefore, using the above equations, we get:
rank(B) + null(A) <= null(B) + null(A) = 5
which implies:
rank(B) <= 5 - null(A) = 5 - (4 - rank(A)) = 1 + rank(A)
This shows that rank(B) is less than or equal to 1 plus the rank of A.
Since the rank of A can be at most 3 (since A is a 3 x 4 matrix),
we conclude that:
rank(B) < null(A)
b. To use the Rank-Nullity theorem to prove that rank(A) + rank(B) < 4
We simply add the equations:
rank(A) + null(A) = 4
rank(B) + null(B) = 5
to get:
rank(A) + rank(B) + null(A) + null(B) = 9
But since R(B) is a subset of N(A), we know that null(A) >= rank(B), and therefore:
rank(A) + rank(B) + 2null(A) <= 9
Using the first equation above, we can write null(A) = 4 - rank(A), so we get:
rank(A) + rank(B) + 2(4 - rank(A)) <= 9
which simplifies to:
rank(A) + rank(B) <= 1
Since rank(A) is at most 3,
we conclude that:
rank(A) + rank(B) < 4
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Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Answers
The dot plot that most accurately displays Miss Little's class data is illustrated below.
To create a dot plot, we first need to determine the range of the data, which is the difference between the highest and lowest values. In this case, the range is from 8 to 16. We then draw a number line that spans the range, and mark each data point along the line with a dot.
Let's take a look at the first data set: 13, 14, 9, 12, 16, 11, and 10. The range is from 9 to 16, so we draw a number line from 9 to 16. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 13, one dot above 14, two dots above 9, one dot above 12, one dot above 16, one dot above 11, and one dot above 10.
We repeat this process for the second data set: 9, 8, 10, 10, 11, 15, and 10. The range is from 8 to 15, so we draw a number line from 8 to 15. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 9, one dot above 8, three dots above 10, one dot above 11, one dot above 15, and zero dots above 14.
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Complete Question:
Miss. Little wants to know how many pairs of shoes each of her students owns. She decides to ask each of her students to write the number of pairs of shoes that he or she owns. This data is displayed in the provided chart. Plot the dot plot that most accurately displays Miss Little's class data.
13 14 9 12 16 11 10
9 8 10 10 11 15 10
My office is 10 ft by 12 ft. I want to buy border for the top of my wall. I have a 3ft door on a 10 ft wall and a 3 ft window directly across from it. How much wallpaper border should I buy?
a. 24
b. 44
c. 38
Answers
You should buy 38 feet of wallpaper that cover the border for the top of the wall using the perimeter of the room. Thus, option C is correct.
Length of office = 10 feets
width of office = 12 feets
Door length = 3 feet
Wall length = 10 feet
Window length = 3 feet
To estimate the length of the wallpaper border needed, we need to calculate the perimeter of the room that needs the bordering of wallpaper. It is given that only the top of the roof needs bordering.
We need to add the lengths of all 4 sides of the walls and subtract the lengths of the door and window.
Mathematically,
The perimeter of the room =(sum of the length of sides of the room) - (length of the window) - (length of the door)
Perimeter of room = (10 + 12 + 10 + 12) - 3 - 3
Perimeter of room = 38 ft
Therefore, we can conclude that we need to buy 38 feet of the wallpaper border.
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Niamh was driving back home following a business trip.
She looked at her Sat Nav at 17:30
Time: 17:30
Distance: 143 miles
Niamh arrived home at 19:42
Work out the average speed of the car, in mph, from 17:30 to 19:42
You need to show all your working
:)
Answers
Answer:
65 mph
Step-by-step explanation:
To calculate the average speed of Niamh's car, we need to use the formula:
Average speed = Total distance ÷ Total time
First, we need to calculate the total time elapsed from 17:30 to 19:42:
Total time = 19:42 - 17:30 = 2 hours and 12 minutes
To convert the minutes to decimal form, we divide by 60:
2 hours and 12 minutes = 2 + (12 ÷ 60) = 2.2 hours
Now we can calculate the average speed:
Average speed = Total distance ÷ Total time
Average speed = 143 miles ÷ 2.2 hours
Average speed = 65 mph
Therefore, the average speed of Niamh's car from 17:30 to 19:42 was 65 mph.
A fisherman kept records of the weight in pounds of the fish caught on the fishing trip 10, 9, 2, 12, 10, 12, 8, 14, 11, 3, 6, 9, 7, 15. What does the shape of the distribution in the histogram tell you about the situation
Answers
The shape of the distribution in the histogram can tell us about the distribution of weights of fish caught by the fisherman.
Looking at the given data set, we can see that the weights of the fish caught vary from as low as 2 pounds to as high as 15 pounds. The histogram of this data set can help us to fantasize the distribution of these weights. Grounded on the shape of the histogram, we can see that the distribution is kindly slanted to the right, with a long tail extending towards the advanced end of the weights.
This suggests that there were further fish caught that counted lower than the mean weight of the catch, with smaller fish caught that counted further than the mean weight. also, the presence of a many outliers( similar as the fish that counted 15 pounds) suggests that there may have been some larger or unusual fish caught on the trip.
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Question 3
3.1 simplify the following ratios:
3.1.1 500g : 3 kg
3.1.2 12cm : 1m
Answers
The simplified ratios are: 1:6 & 3:25
To simplify the first ratio, we need to convert the units so they are the same. We can either convert 500g to kilograms or 3kg to grams. Let's convert 3kg to grams since it will be easier to compare with 500g.
3 kg = 3000g
Now the ratio becomes:
500g : 3000g
We can simplify this ratio by dividing both sides by 500:
500g/500 = 1 and 3000g/500 = 6
So the simplified ratio is:
1 : 6
For the second ratio, we need to convert either 12cm to meters or 1m to centimeters. Let's convert 1m to centimeters since it will be easier to compare with 12cm.
1m = 100cm
Now the ratio becomes:
12cm : 100cm
We can simplify this ratio by dividing both sides by 4:
12cm/4 = 3 and 100cm/4 = 25
So the simplified ratio is:
3 : 25
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This question: 1 pt
15 of 30
identify the type 1 error. the epa claims that fluoride in children's drinking water should be at a mean level of less than 1. 2 ppm, or parts per million, to reduce the number of dental cavities.
Answers
The type 1 error in this scenario would be rejecting the null hypothesis that the mean level of fluoride in children's drinking water is less than 1.2 ppm, when in reality it is true.
The EPA claims that fluoride in children's drinking water should have a mean level of less than 1.2 ppm to reduce the number of dental cavities. A type 1 error occurs when we reject the null hypothesis when it is actually true. In this case, the null hypothesis (H0) would be that the mean fluoride level is less than or equal to 1.2 ppm, and the alternative hypothesis (H1) would be that the mean fluoride level is greater than 1.2 ppm.
A type 1 error would occur if we incorrectly conclude that the mean fluoride level is greater than 1.2 ppm when, in reality, it is less than or equal to 1.2 ppm. This could lead to unnecessary actions being taken to reduce fluoride levels when they are already at an acceptable level.
In other words, falsely concluding that the mean level of fluoride in the water is above 1.2 ppm and therefore causing harm to the children's dental health by not reducing the number of dental cavities.
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