The students do not spend nmore time reading in April than in July
How to solve for the evidenceFind the mean
5 + 2+ 7+23+3+6+3+1+10 / 10
= 64 / 10
= 6.4
standard deviation = √368.4 / 9 = 6.398
test statistic = 6.4 / 6.398/√10
= 3.1633
degree of freedom= 10 - 1
= 9
p v alue = 0.005745
This shows that the students do not spend nmore time reading in April than in July
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Find the value of x in the following equation
3.6(2x+5)=7.2x+18
Maxine graphs the function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8). Ricardo graphs p(x) = (x+3)² +4
Maxine thinks that both functions have the same axis of symmetry equation. Do you agree or disagree?
Therefore, both functions have the same axis of symmetry equation, which is x = -3.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are one of the central objects of study in mathematics and have many applications in various fields such as physics, economics, engineering, and computer science. A function is typically represented using a mathematical expression or equation, and it can be analyzed and manipulated using a variety of mathematical techniques.
Here,
Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.
For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.
For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.
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jackie converted the fallowing decimals to fractions.
explain plisssss
Answer:
Step-by-step explanation:
To convert a fraction to a decimal, you divide the numerator by the denominator. The line in the middle of a fraction is essentially a large division sign.
Let's check Jackie's work
1/200 = 0.005
3/10 = 0.3
7/8 = 0.875
4/5 = 0.8
Jackie listed 7/8 as 0.625, which is incorrect. 7/8 is 0.875
So, 0.625 is your answer.
John and Mary are young professionals who both have good jobs with
possibilities for advancement. They are trying to decide whether to rent or to buy
their housing. They are relocating to a large urban area with the availability of
public transportation. They have a dog that needs to be exercised. They need a
home office because they will be working from home part of the time.
List AT LEAST three reasons John and Mary should buy AND AT LEAST three
reasons John and Mary should rent.
Some reasons why John and Mary should buy a house could be investment, control and stability. The reasons why they should rent could be flexibility, maintenance costs and lower upfront.
What would be the best decision for them?When considering whether to rent or buy a home, there are many factors to take into account, including financial considerations, lifestyle preferences, and personal circumstances.
Therefore, the decision to rent or buy a home is a complex one that involves many factors. By carefully considering these factors and weighing the pros and cons of each option, John and Mary can make an informed decision that is best for their needs and goals.
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Find the closing cost, to the nearest cent: house value of $89,548, two points, attorney's fees $324, title fees $105.
a 4,439. 92
b 2,219. 96
c 2,114. 96
d 1324. 48
If the house value of $89,548 and two points, attorney's fees $324, title fees $105, then closing cost is option (b) $2,219.96
Closing costs are fees associated with the purchase or refinance of a property that are paid at the closing of the transaction.
To calculate the closing cost, we need to add up all the fees associated with the purchase of the house.
First, we need to calculate the cost of the points. Two points on a house value of $89,548 would be
2 x $89,548 x 0.01 = $1,790.96
Next, we need to add the attorney's fees and title fees
$1,790.96 + $324 + $105 = $2,219.96
Therefore, the correct option is (b) $2,219.96
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3. In raising a 7000 N motorcycle with a pulley system, the workers note that for every 3 m of rope pulled down- ward, the piano rises 0. 3 m. Show that 700 N is required to lift the motorcycle
If workers note that for every "3 m" of rope pulled down-ward, the piano rises 0.3 m, then we have shown that 700 N is required force to lift the motorcycle.
The term "Mechanical advantage" (MA) is defined as ratio of "output-force" to "input-force" in a machine.
In this case, the output force is the weight of the motorcycle (7000 N) and the input force is the force applied to pull the rope downward.
We use the formula for mechanical advantage in a pulley system, which is given by:
⇒ MA = (distance moved by the effort) / (distance moved by the load),
In this case, the distance moved by the effort is 3 m, and
The distance moved by the load is 0.3 m,
Substituting the values,
We get,
⇒ MA = 3/0.3,
⇒ MA = 10,
So, mechanical advantage of "pulley-system" is 10.
Now, we use mechanical advantage to calculate the required force to lift the motorcycle.
Since mechanical advantage is defined as the ratio of output force to input force, we can rearrange the formula as:
⇒ Input force = (Output force)/(Mechanical advantage),
Substituting values for "output-force" as 7000 N and "mechanical-advantage" as 10,
We get,
⇒ Input force = 7000/10,
⇒ 700 N,
Therefore, the required force to lift motorcycle is 700 N.
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at ignus school there are 425 students. of these students 351 study mathematics, 71 study latin, and 203 study chemistry. there are 199 students who study more than one of these subjects, and 8 students who do not study any of these subjects. find the number of students who study all three of these subjects.
Answer: 9 study all three subjects
Step-by-step explanation:
0.4 centimeters converted into millimeters
Answer: 4 milimeters
Step-by-step explanation:
1 centimeters = 10 millimeters
0.4 centimeters= 4 miliimeters
Discuss the similarities and the differences between the Empirical Rule and Chebychev's Theorem What is a similarity between the Empirical Rule and Chebychev's Theorem? 0 A. O B. ° C. Both apply only to symmetric and bell-shaped distributions. Both do not require the data to have a sample standard deviation. Both calculate the variance and standard deviation of a sample. D. Both estimate proportions of the data contained within k standard deviations of the mean What is a difference between the Empirical Rule and Chebychev's Theorem? A. The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions O B. Chebychev's Theorem estimates proportions of data contained within infinite standard deviations and the Empirical Rule has a limit of 5 standard deviations ° C. The Empirical Rule assumes a small data set (less than 50 values) where Chebychev's Theorem has no limit on data size. O D. Chebychev's Theorem applies only to distributions which are approximately symmetric or bell-shaped and the Empirical Theorem has no restrictions
A. The correct option for similarity is option D - Both estimate proportions of the data contained within k standard deviations of the mean.
Both the Empirical Rule and Chebyshev's Theorem are used to estimate the proportion of data contained within a certain number of standard deviations from the mean.
Therefore, option 'D' is the correct answer: Both estimate proportions of the data contained within k standard deviations of the mean.
B. The correct option for difference is option A - The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.
The Empirical Rule assumes that the distribution is approximately symmetric and bell-shaped, while Chebyshev's Theorem makes no assumptions about the shape of the distribution.
Another difference is that the Empirical Rule is only applicable for normal distributions, while Chebyshev's Theorem can be applied to any distribution.
Therefore, option 'A' is the correct answer: The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.
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Between which two integers does 7/3 lie Answer A 4 and 5 Answer B 1 and 2 Answer C 2 and 3 Answer D 3 and 4
We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,
To determine between which two integers 7/3 lies, we can use division and rounding.
Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:
7/3 = 2 + 1/3
Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.
This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.
Answer C, 2 and 3, is the correct answer.
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In circle C, FG and FE are tangent segments, m
Choose the two answers that represent the angle measures of the central and circumscribed angles.
The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
What is angle?Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.
The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.
In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
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Evaluate: a = 3, b = 6, c = 4 a •b + c
Answer:
Step-by-step explanation:(3)(6)+(4) = 18+4= 22
An engineer has a 50:1 scale drawing of a bridge. The dimensions of the scaled bridge deck are 24 inches by four and one fifth inches. What is the area of the actual bridge deck in square feet?
120 square feet
875 square feet
1,750 square feet
3,500 square feet
Thus, the area of the actual bridge deck is found as 1750 square feet.
Explain about the scale factor:A scale factor refers to the amount by which an object is multiplied to produce a second object of different size but with the same appearance. Just a larger or smaller version of the original is created, not an exact copy.
Given dimension-
Length l = 24 inches
width w = 4 1/5 = 21/5 inches
Convert inches to feet:
1 foot = 12 inches.
Scaled length = 24 inches ÷ 12 inches/foot = 2 feet
Scaled width =21/5 inches ÷ 12 inches/foot = 21 / 5*12 = 0.35 feet
Now, scale factor = 50.: 1
Actual length = Scaled length × Scale factor
Actual length = 2 feet × 50 = 100 feet
Actual width = Scaled width × Scale factor
Actual width = 0.35 feet × 50 = 17.5 feet
Area of actual bridge deck:
Area = Actual length × Actual width
Area = 100 feet × 17.5 feet
Area = 1750 square feet
Thus, the area of the actual bridge deck is found as 1750 square feet.
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Completely factor x^4 - 81
Answer: (x + 3) (x - 3) (x^2 + 9) (x^2 - 9)
Step-by-step explanation: We can use the difference of squares formula to factor x^4 - 81 as (x^2 + 9)(x^2 - 9).
Then, we can use the difference of squares formula again to factor x^2 - 9 as (x + 3)(x - 3).
Therefore, the complete factorization of x^4 - 81 is (x + 3)(x - 3)(x^2 + 9)(x^2 - 9).
a pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. this plan randomly selects and tests 27 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. what is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 11% rate of defects?
The probability of accepting the whole shipment is 0.384, or about 38.4%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
This is a binomial probability problem, where the probability of a defect (or non-conformance) is p=0.11 and the sample size is n=27. We want to find the probability of having at most one defect in a sample of 27 tablets.
Let X be the number of defects in the sample. Then X follows a binomial distribution with parameters n=27 and p=0.11. We want to find P(X ≤ 1), which is the probability of having 0 or 1 defects in the sample.
Using the binomial distribution formula, we have:
P(X ≤ 1) = P(X = 0) + P(X = 1)
= (27 choose 0) * [tex](0.11)^{0}[/tex] * [tex](0.89)^{27}[/tex] + (27 choose 1) * [tex](0.11)^{1}[/tex] * [tex](0.89)^{26}[/tex]
= (1) * (1) * [tex](0.89)^{27}[/tex] + (27) * (0.11) * [tex](0.89)^{26}[/tex]
= 0.384
Therefore, the probability of accepting the whole shipment is 0.384, or about 38.4%.
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highway accidents: dui the u.s. department of transportation, national highway traffic safety administration, reported that 77% of all fatally injured automobile drivers were intoxicated. a random sample of 27 records of automobile driver fatalities in kit carson county, colorado, showed that section 8.3 testing a proportion p 479 15 involved an intoxicated driver. do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in kit carson county? use a 5 0.01.
The highway accident evidence to reject the null hypothesis that the population proportion is equal to 77%.
No, these data do not indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County.
The sample proportion of 15 out of 27 is 56.25%, which is not significantly different from the population proportion of 77%.
The p value for this test is 0.788, which is greater than the alpha level of 0.01.
The p value of this test indicates that the sample proportion of 15 out of 27 (56.25%) is not significantly different from the population proportion of 77%.
This means that there is not enough evidence to reject the null hypothesis that the population proportion is equal to 77%.
The p value of 0.788 is greater than the alpha level of 0.01, meaning that the results of this test are not statistically significant enough to support the alternative hypothesis that the population proportion is less than 77%.
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Find the length of the rectangular prism.
The length of the rectangular prism given the volume, width and height is 19 yd.
What is the length of the rectangular prism?Volume of a rectangular prism = length × width × height
Volume of the prism = 2,280 yd³
Width of the prism = 20 yd
Height of the prism = 6 yd
Length of the prism = x
So,
Volume of a rectangular prism = length × width × height
2,280 = x × 20 × 6
2,280 = 120x
divide both sides by 120
x = 2,280 / 120
x = 19 yd
Therefore, the length is 19 yd
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Please help me with this homework
Answer:
14
Step-by-step explanation:
c = 2[tex]\pi r[/tex]
c = 2[tex]\pi[/tex]7
x = 14[tex]\pi[/tex]
Helping in the name of Jesus.
State the most specific name for each figure
PLS HELP
1.) parallelogram
2.) trapezoid
3.) kite
4.) parallelogram
What are the qualities of a parallelogram?The parallelogram is a type of quadrilateral that has the following unique properties such as:
The opposite sides are parallel and equal.The opposite angles are equal.The consecutive or adjacent angles are supplementary.If any one of the angles is a right angle, then all the other angles will be at right angle.The two diagonals bisect each other.The kite is also a type of quadrilateral that has two pairs of adjacent equal sides with a pair of opposite angles that are equal.
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Solve the triangle
A
B
C
(h² − h) + (5h + 6)-(3h² +4h - 9)
Answer in expanded form
The expanded form of the given expression (h² − h) + (5h + 6)-(3h² +4h - 9) is -2h² + 15.
What is the expanded form of the given expression?Given the expression in the question;
(h² − h) + (5h + 6) - (3h² + 4h - 9)
Expanding an algebraic expression means to remove any parentheses and simplify the expression as much as possible.
In the given expression, we have three sets of parentheses:
(h² − h)
(5h + 6)
(3h² +4h - 9)
To expand the expression, we will remove the parentheses and simplify the resulting terms.
(h² − h) becomes h² - h
(5h + 6) remains the same
(3h² +4h - 9) becomes 3h² + 4h - 9
Putting all the terms together, we get:
h² - h + 5h + 6 - (3h² + 4h - 9)
Now, we will distribute the negative sign to all the terms inside the parentheses:
h² - h + 5h + 6 - 3h² - 4h + 9
Simplifying further by combining like terms, we get:
h² - 3h² - h + 5h - 4h + 6 + 9
-2h² + 15
Therefore, the expanded form is -2h² + 15.
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I WILL GIVE BRAINLIEST TO THE BEST/CORRECT ANSWER
Point U is located at (5,2) on the coordinate plane. Point U is reflected over the y-axis to create point U'. Point U' is the reflected over the x-axis to create point U". What ordered pair describes the location of U"?
Answer:
(-5,-4)
Step-by-step explanation:
i think this is correct because i tried to solve in paper.
Please help ASAP!
A clinical trial is performed to test a new drug designed to lower blood sodium levels. One hundred fifty participants are randomly assigned to take the new drug, and 150 participants are randomly assigned to take a placebo. After 6 months of treatment, blood sodium levels are measured and compared to the starting levels. For those who took the new drug, the blood sodium levels had a mean reduction of 27 points with a standard deviation of 5.2, while for those who took the placebo, the blood sodium levels showed a mean reduction of 22 points with a standard deviation of 3.9. Assuming the standard deviations are true for the entire population, calculate 90% confidence intervals and evaluate whether there is evidence the new drug is working.
A: The interval for the new drug is from 26.168 to 27.832 points. The interval for the placebo is from 21.376 to 22.624 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is working.
B: The interval for the new drug is from 26.302 to 27.698 points. The interval for the placebo is from 21.476 to 22.524 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is not working.
C: The interval for the new drug is from 26.302 to 27.698 points. The interval for the placebo is from 21.476 to 22.524 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is working.
D: The interval for the new drug is from 26.168 to 27.832 points. The interval for the placebo is from 21.376 to 22.624 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is not working.
The answer to the question is C
How many 6-digit numbers can be found using the digits from 1 to 6 if the number is less than 400000 and the even digits occupy the even places in descending order, answer should be 4
Answer
Step-by-step explanation:
Answer
Answer step-by-step explanation
What is the first step to solve this equation? (4)/(x)+(1)/(2)=(5)/(x) The first step in solving the equation is to multiply both sides by
The first step in solving the equation is to multiply both sides by the least common multiple (LCM) of the denominators.
To solve the equation (4)/(x) + (1)/(2) = (5)/(x):
Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 2x.
Multiply the left side of the equation by 2/2 to get:
(8)/(2x) + (1)/(2) = (5)/(x)
Combine the two fractions on the left side of the equation:
(8+1)/(2x) = (9)/(2x)
Set the left side of the equation equal to the right side:
(9)/(2x) = (5)/(x)
Cross-multiply:
9x = 10x
Simplify:
x = 0
Therefore, the solution to the equation is x = 0.
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you want to display data on average number of points scored by the top 5 uci basketball players in the history of uci. which type of graph would be best?
A The histogram is the best graph showing the average scores of 5 UCI volleyball teams in UCI history. Because it allows us to divide the data into as many or as few groups as we want and clarify the comparison between them.
We would like to view the average points data of the top 5 UCI basketball players in UCI history. There are two types of charts used to present data. The first is a histogram and the second is a scatterplot. We have to decide which picture is the best. Now, as we know, scatter charts are used to plot observations based on points to show the relationship between two data sets. A histogram is a type of bar chart in which all values are divided. Divides the range of results in the data into classes or groups. It can help identify outliers or gaps in the data. After discussing the features of the two graphs, shows the average score of 5 UCI basketball players in UCI history, the histogram is the best choice here because it allows us to divide and share the difference between clearly.
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complete question:
The above figure complete the question..
you want to display data on average number of points scored by the top 5 uci basketball players in the history of uci. which type of graph would be best?
The area of a semicircle is 1. 2717 square meters. What is the semicircles diameter
The diameter of the semicircle for the given area of the semicircle 1. 2717 square meters is equal to 1.8 meters.
Area of a semicircle = 1. 2717 square meters
The area of a semicircle is given by the formula,
A = πr^2 / 2
where A is the area
And r is the radius of the semicircle.
Rearrange the formula to solve for r,
r = √(2A/π)
Substituting the given value of A = 1.2717 square meters into this formula, we get,
⇒ r = √(2 × 1.2717 / π)
⇒ r = 0.9 meters
Since the diameter of a semicircle is twice the radius,
The diameter of this semicircle is equal to,
d = 2r
= 2 × 0.9
= 1.8 meters
Therefore, the diameter of the semicircle is equal to 1.8meters.
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Calculate the area of each of the polygons with the following dimensions.
1. Triangles
B = 4in, H = 5in
B = 6ft, H= 10ft
B = 12m, H = 15m
Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?
2. Parallelogram (H = height) and (B = base)
H = 9in, B = 6in
H = 5 ft, B = 2ft
H = 7yds, B = 3yds
Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?
Hint: Use the formula. Substitute the given values and then solve as an equation.
3. Rectangle (L = length) and (w = width)
rect. DKIF with L = 8 ft and w = 6 ft
rect. AOPU with L = 13 ft and w = 5 ft
Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.
4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)
rhombus with d1 = 12 yds and d2 = 12 yds
rhombus with d1 = 10 ft and d2 = 25 ft
rhombus with d1 = 16 in and d2 = 22 in
Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?
5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)
b1 = 6 ft, b2 = 7 ft, H = 10 ft
b1 = 5 yds, b2 = 8 yds, H = 4 yds
c. b1 = 9 in, b2 = 11 in, H = 13 in
d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?
The total area of two triangle tablecloths for one table = 8ft²,
height = 6mm,
The total area of the den = 430ft²,
height of the rhombus = 12ft,
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Triangles:
a) Area of triangle = 1/2 * base * height = 1/2 * 4in * 5in = 10in²
b) Area of triangle = 1/2 * base * height = 1/2 * 6ft * 10ft = 30ft²
c) Area of triangle = 1/2 * base * height = 1/2 * 12m * 15m = 90m²
Total area of two triangle tablecloths for one table = 2 * 1/2 * 2ft * 4ft = 8ft²
Parallelogram:
a) Area of parallelogram = base * height = 6in * 9in = 54in²
b) Area of parallelogram = base * height = 2ft * 5ft = 10ft²
c) Area of parallelogram = base * height = 3yds * 7yds = 21yds²
height = Area/base = 78mm²/13mm = 6mm
Rectangle:
a) Area of rectangle = length * width = 8ft * 6ft = 48ft²
b) Area of rectangle = length * width = 13ft * 5ft = 65ft²
Total area of the den = (2 * 9ft * 15ft) + (2 * 8ft * 10ft) = 270ft²+ 160ft² = 430ft². Charles has enough paint because one gallon of paint will cover 440 square feet of wall space.
Rhombus:
a) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 12yds * 12yds = 72yds²
b) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 10ft * 25ft = 125ft²
c) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 16in * 22in = 176in²
height of the rhombus = 2(area/diagonal1) = 2(72ft²/12ft) = 12ft
Trapezoid:
a) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (6ft + 7ft) * 10ft = 65ft²
b) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (5yds + 8yds) * 4yds = 26yds²
c) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (9in + 11in) * 13in = 130.5in²
d) Height of trapezoid = 2(area/(base1 + base2)) = 2(32km²/16km) = 4km
Hence, the total area of two triangle tablecloths for one table = 8ft²,
height = 6mm,
The total area of the den = 430ft²,
height of the rhombus = 12ft,
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To help determine what types of clubs to offer at harding middle school the principal surveyed fifty 8th grades. Does the sampl fairly represent the population ? explain
To determine if the sample fairly represents the population, we need to consider whether the sample is representative and whether there is any bias present in the sampling process.
If the principal surveyed fifty 8th graders in a way that ensures that each 8th grader in the population has an equal chance of being selected, then the sample can be considered representative. This means that the sample accurately reflects the characteristics of the population, and any conclusions drawn from the sample can be applied to the population.
However, if the sampling process was biased in some way, the sample may not be representative of the population. For example, if the principal only surveyed 8th graders in one class or in one particular group, the sample may not be representative of the entire 8th-grade population at Harding Middle School. In this case, any conclusions drawn from the sample may not accurately reflect the entire population.
Therefore, the key factor in determining whether the sample fairly represents the population is the sampling method used. If the sampling method is random and unbiased, then the sample can be considered representative of the population.
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A rectangular pen is to be constructed with three equal sections. One side of the pen will be enclosed with the side of the barn. All other sides need to be fenced. If the total amount of fencing available is 510 feet, calculate the dimensions of each rectangular pen that would maximize the fenced area. State the maximum area as well. Show all work.
Answer:
Let x be width and y = length of barn wall y + 2x =20Area = xy= x(20 - 2x)=20x -2x^2dA/dx = 20 - 4xmax at dA/dx =0 so 20 - 4x = 0x=5 y=10 max area is 50 sq ft