The cost of wax to cover the floor is $1569.75.
How to find the cost that will cover the floor?The area of the floor is calculated and multiplied by the unit cost ($1.38) to get the total cost
The floor is segmented and the area is calculated and added together
1. Area of rectangle joining the right triangle = 15 * (30 - 20) = 150 square feet
2. Area of right triangle = 1/2 * 15 * (35 - 10) = 187.5 square feet
3. Area of the large rectangle = 40 * 20 = 800 square feet
total area = 800 + 187.5 + 150 = 1137.5
cost of wax to cover the floor = total area * unit cost
cost of wax to cover the floor = 1137.5 * 1.38 = $1569.75
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Complete Question
A maintenance worker needs to wax a restaurant floor shaped like the image shown. A six-sided figure. There is a horizontal base of 35 feet then another horizontal base below it of 20 feet. The longest side is to the right and is 40 feet. The top is 30 feet. There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet. If the wax cost $1.38 a square foot, how much will the wax cost to cover the floor?
$1,224.75
$1,569.75
$2,104.50
$2,449.50
Solve for x. Round to the nearest hundredth.
17
18°
х X
what trigonometric function would you use to find x?
O Cosine
Sine
Tangent
O Secant
O Cosecant
Answer:
5
Step-by-step explanation:
like i dont know probably 5 its kinda weird. it definitely has to be 5
f(1)= -34
f(n)=f(n−1) - 3
Find an explicit formula for f(n).
Answer:
f(n) = -34 -3(n - 1)
Step-by-step explanation:
The explicit formula for f(n) is given below:
Given that
f(1)= -34
f(n)=f(n−1) - 3
Based on the above information
f(n) = a1 +d(n -1)
a1 = -34
d = -3
So
f(n) = -34 -3(n - 1)
This above represent an explicit formula
Kaylee has $0.90 worth of nickels and dimes. She has a total of 14 nickels and dimes altogether. By following the steps below, determine the number of nickels, x,x, and the number of dimes, y,y, that Kaylee has. You need 3 different solutions.
Answer:
kaylee has 4 dimes and 10 nickles.
Mutiply 4 by ten that equals 40 then multiply 10 by 5 and get 50
2. in second soution
Nickels are worth 0.05 and dimes are worth 0.10 so if nickes + dimes = 10 and 0.05 *nickles 0.10*dimes = $0.90, then there are 2 nickels and 8 dimes.
Step-by-step explanation:
On Thursday the basketball coach ordered 12 pizzas for 36 players who came in for practice. How many pizzas does the coach need to order if 12 players turned up for practice the next day
Answer:16
Step-by-step explanation:Next day there will be (36+12) or 48 players.
For 36 players 12 pizzas are needed
For 1 player 12/36 pizzas are needed
For 48 players 12/36*48 or 16 pizzas are needed
The number of pizzas that 12 players will need is 4 based on the given ratio.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
The ratio of pizza to players = 36/12
With the same ratio,
The number of pizzas required for x number of 12 players,
12/x = 36/12
x = 144/36 = 4
Hence "Based on the above ratio, 12 players will require 4 pizzas.".
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Which expression is equivalent to 83 ⋅ 8−7? (1 point)
a
fraction: 1 over 8 to the power 10
b
1 over 8 to the power 4
c
810
d
84
\(8^{3} \cdot 8^{-7} =8^{-4}=\boxed{\frac{1}{8^4}}\)
You were given a Starbucks gift card for your birthday. One day, you used the gift card to order 3 drinks that cost $5.20 each. When you looked at your receipt, you noticed that there was a remaining balance of $26.00 on the gift card.
Write an equation in point-slope form that represents the total balance left on the gift card, y, in terms of the number of drinks ordered, x.
Answer:
The card had 41.60 originally
Step-by-step explanation:
3 x 5.20 = 15.60
15.60 + 26.00 = 41.60
unless there is tax
uppose that a certain data set contains the variable HEIGHT (giving a person's height) and the variable GENDER (coded O=female, 1=male). Then the y-intercept of the regression equation predicting HEIGHT from GENDER is given by: Select one: a. how much shorter females are than males, on average. b. how much taller males are than females, on average. c. the average height of females in the data set. d. the average height of males in the data set. e. the proportion of females in the data set. f. the proportion of males in the data set. g. it is not appropriate to interpret the y-intercept in this case.
The data set contains the variable height (giving a person's height) and the variable gender (coded O=female, 1=male). Then the y-intercept of the regression equation predicting height from gender is given by: option c) the average height of females in the data set.
The y- intercept of a direct retrogression relationship represents the value of one variable when the value of the other is zero. Non-linear retrogression models also live, but are far more complex. Retrogression analysis is a important tool for uncovering the associations between variables observed in data, but can not fluently indicate occasion. The data set contains the variable height (giving a person's height) and the variable gender (enciphered O = womanish, 1 = manly). also the y- intercept of the retrogression equation prognosticating height from gender is given by option c) the average height of ladies in the data set.
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Using the basic form of Euclid’s algorithm, compute the
greatest common divisor of:
Use only the Euclidean algorithm (table form) and a
calculator.
7579 and 3724
3769 and 5001
1) The GCD of 7579 and 3724 is: 1.
2) The GCD of 3769 and 5001 is 7.
How to use Euclidean Algorithm?The Euclidean Algorithm for finding GCD(A,B) is as follows:
If A = 0 then GCD(A,B)=B, since the GCD(0,B)=B, and we can stop. If B = 0 then GCD(A,B)=A, since the GCD(A,0)=A, and we can stop. Write A in quotient remainder form (A = B⋅Q + R)
1) Computing the greatest common divisor of 7579 and 3724 using the Euclidean algorithm gives:
7579 = 2 * 3724 + 1301
3724 = 2 * 1301 + 222
1301 = 5 * 222 + 191
222 = 1 * 191 + 31
191 = 6 * 31 + 5
31 = 6 * 5 + 1
5 = 5 * 1 + 0
The remainder becomes 0, and the last divisor is 1
2) 5001 = 1 * 3769 + 1232
3769 = 3 * 1232 + 273
1232 = 4 * 273 + 140
273 = 1 * 140 + 133
140 = 1 * 133 + 7
133 = 19 * 7 + 0
The remainder becomes 0, and the last divisor is 7.
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The length of a rectangle is 7 inches longer than it is wide. If the perimeter is 34 inches, what are the dimensions of the rectangle
the expected number of heads in 90 tosses of an unbiased coin is:
The expected number of heads in 90 tosses of an unbiased coin is 45.
The probability of obtaining a head is 0.5, and the probability of obtaining a tail is 0.5. Since there are only two possible outcomes, heads and tails, a coin is classified as a binomial distribution.
Binomial distribution can be used to calculate the expected number of heads in 90 tosses of an unbiased coin. The expected value of a binomial distribution is μ = np. where n is the number of trials, and p is the probability of success.In the given case, n = 90, and p = 0.5.
Thus, the expected value of the number of heads would be:
μ = npμ = 90 x 0.5
μ = 45.
The expected number of heads in 90 tosses of an unbiased coin is 45. The expected value can be used to predict the outcomes of a large number of tosses.
However, it cannot predict the exact outcome of any single toss since the result of each toss is a random variable that is independent of the previous tosses.
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What is (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001) in standard form?
The standard form of the given numbers is 207360 × 10¹⁷.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Given the numbers is (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001)
Now standard form means we need to write the exponents form.
So,
5 x 6 x 4 x 8 x 3 x 2 x 4 x 9 = 207360
And
1,000,000 x 100000 x 10000 x 1000 x 100 x 10 x 0.1 x 0.001 = 10¹⁷
So, combine 207360 x 10¹⁷
Hence "The standard form of the given numbers is 207360 × 10¹⁷".
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A line passes through the point (-7,3) an has a slope of -3. Write an equation in slope intercept form
Answer:
-3x + 5
Step-by-step explanation:
y = mx + bm = -3y = -3x + bFind b from the given point.-7 = -3(4) + bb = 5y = -3x + 5
4x+9/y+11=0 and 6/y -3x=8
9514 1404 393
Answer:
(x, y) = (-2 12/17, -51)
Step-by-step explanation:
Here is the answer to ...
\(4x+\dfrac{9}{y}+11=0\\\\\dfrac{6}{y}-3x=8\)
If you mean something else, then parentheses are needed.
__
Let z = 1/y. Then the equations in general form are ...
\(4x+9z+11=0\\3x-6z+8=0\)
The solution (cross multiplication method) is ...
x = (9·8 -(-6)·11)/(4(-6)-3·9) = 138/-51 = -2 12/17
z = (11·3 -8·4)/-51 = -1/51
y = 1/z = -51
The solution is (x, y) = (-2 12/17, -51).
What sentence represents the number of test questions in the problem
below?
A test is worth 50 points. Multiple-choice questions are worth point, and
short-answer questions are worth 3 points. If the test has 20 questions, how
many multiple-choice questions are there?
A. The number of multiple-choice questions plus the number of
short-answer questions is 50.
B. The number of multiple-choice questions minus the number of
short-answer questions is 50.
• C. The number of multiple-choice questions times the number of
short-answer questions iS 20.
D.
The number of multiple-choice questions plus the number of
short-answer questions is 20.
Answer:
D
Step-by-step explanation:
The number of questions is 20; it's the total points that are worth 50 and the question is asking for number of questions
A grain silo has a cylindrical shape. Its radius is 9.5ft, and its height is 39ft. Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact volume of the silo. Write your answer in termis of π
.
Exact volume: (b) Using the ALEKS calculator, approximate the volume of the silo, To do the approximation, use your answer to part (a) and the π button on the calculator. Round your answer to the nearest hundredth.
a. The exact volume of the silo is 3515.975π cubic feet.
b. The approximate volume of the silo is 10578.50 cubic feet.
(a) The exact volume of a cylinder can be calculated using the formula:
Volume = π * radius^2 * height
Given that the radius is 9.5 ft and the height is 39 ft, we can substitute these values into the formula:
Volume = π * (9.5 ft)^2 * 39 ft
= π * 90.25 ft^2 * 39 ft
= 90.25π * 39 ft^3
= 3515.975π ft^3
Therefore, the exact volume of the silo is 3515.975π cubic feet.
(b) To approximate the volume of the silo using the ALEKS calculator, we can use the value of π provided by the calculator and round the answer to the nearest hundredth.
Approximate volume = π * (radius)^2 * height
≈ 3.14 * (9.5 ft)^2 * 39 ft
≈ 3.14 * 90.25 ft^2 * 39 ft
≈ 10578.495 ft^3
Rounded to the nearest hundredth, the approximate volume of the silo is 10578.50 cubic feet.
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Priscilla decides to order a delivery from the local sandwich shop. Her order comes to $12.74 and there is a $2.30 delivery charge. When the food is delivered, Priscilla adds on to her receipt a charge of 15% of her total, not including the delivery charge, as a tip for the driver. When Priscilla goes to check her debits on her online bank statement, what amount should she expect as her total debit?
a.
$14.65
b.
$15.04
c.
$16.95
d.
$17.30
Including the cost of the order, the delivery charge, and the tip, the total cost will be $17.30
How to get the total cost?We know that the cost of the order is $12.74, there is a $2.30 delivery charge, and there is a tip of 15% of her total.
Then for the order and the delivery charge we have:
C = $12.74 + $2.30 = $15.04
If we now add a 15% of that amount for the tip, we will get:
$15.04 + (15%/100%)*$15.04 = $17.30
So the correct option is d.
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g) (12d + 3) +-14d what's the answer
Answer: -2d+3
Step-by-step explanation:
For every additional hour, on average, the number of miles goes up by thousand. For every additional thousand miles, on average, the time goes up by hours.
The given information describes a linear relationship between miles and time, with a rate of change of 1000 miles per hour and 1 hour per 1000 miles.
the rate of change between the number of miles and time is as follows: for every additional hour, the number of miles increases by a thousand, and for every additional thousand miles, the time increases by an hour.
This indicates a linear relationship between miles and time, with a constant rate of change. For every additional hour, the number of miles traveled increases by a thousand, implying a slope of 1000/1 in the miles-time graph. Similarly, for every additional thousand miles, the time taken increases by an hour, resulting in a slope of 1/1000 in the time-miles graph.
The given information allows us to determine the rates of change or slopes in both directions, indicating a linear relationship between miles and time. However, without specific values or equations, we cannot calculate the exact measure of angle y or provide further analysis.
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The Transportation Security Administration (TSA) is responsible for airport security. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such flight has 76 passengers (12 in first class and 64 in coach). TSA officers selected an SRS of 10 passengers for screening. Let p-hat be the proportion of first class passengers in this sample. So, assuming that you are checking for the probability of choosing a first class passenger out of all passengers on the flight. Is the 10% condition met in this case? Justify your answer. (POS 447#31)
- Yes, 10 passengers out of 76 is less than 10% of the population of the flight.
- yes, 10 passengers out of all passengers on all flights is less than 10% of the population
- No, 10 passengers is the population being studied and is not less than 10% of the 10 total
- No, 10 passengers out of 76 is more than 10% of the population of the flight.
Use a parameterization to find the flux doubleintegral_S F middot n do of F = 5xy i - 2z k outward (normal away from the z-axis) through the cone z = 6 squareroot x^2 +y^2 0 lessthanorequalto z lessthanorequalto 6. The flux is (Type an exact answer, using pi as needed.)
The flux of the vector field F through the cone is zero.
To find the flux of the vector field F = 5xy i - 2z k outward through the cone z = 6 square root x^2 +y^2 with 0 ≤ z ≤ 6, we need to first parameterize the cone. Let x = r cos θ and y = r sin θ, where r ≥ 0 and 0 ≤ θ ≤ 2π, then we have z = 6r for the cone.
Now we can compute the unit normal vector n as n = (zr/6) cos θ i + (zr/6) sin θ j + (z/6) k, and then calculate the dot product F · n as F · n = 5xy (zr/6) - 2z (z/6) = (5/6)zr^2 cos θ sin θ - z^2/3.
The double integral of F · n over the cone is then given by:
doubleintegral_S F · n dS = doubleintegral_R (5/6)zr^2 cos θ sin θ - z^2/3 r dr dθ
where R is the region in the xy-plane that corresponds to the base of the cone.
Integrating with respect to r first, from 0 to 6, we get:
doubleintegral_S F · n dS = integral_0^(2π) integral_0^6 (5/18)z^3 cos θ sin θ - (1/9)z^3 r dr dθ
Evaluating the integral with respect to r and then θ, we obtain:
doubleintegral_S F · n dS = 0
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The length of a book marker is (x + 1) cm as shown in diagram 2. If the width is 5 cm less than its length and the area of the book marker is 24 cm², calculate the perimeter of the book marker.
The perimeter of the book marker is 22cm
What is perimeter of a shape?Perimeter is the outside boundary of a shape.
Analysis:
Length = x + 1
Width = x+1 - 5= x - 4
Area = 24 square centimeters = length x width
(x-4)(x+1) = 24
x2 -3x -4 = 24
x2 -3x -28 = 0
x2 -7x + 4x - 28 = 0
x(x-7) + 4(x - 7) = 0
(x+4)(x-7) = 0
since dimension cannot be negative x = 7
Length = 7 + 1 = 8 cm
Width = 7 - 4 = 3cm
Perimeter = 2(8 + 3 ) = 2 x 1 1 = 22cm
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Write a rule for the nth term of the arithmetic sequence. Then graph the first six terms of the sequence.
a14=42,d=3
The arithmetic sequence with a first term of 14, a common difference of 3, and the 14th term being 42 can be described by the formula: aₙ = 14 + (n - 1) * 3.
In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. The general formula for the nth term of an arithmetic sequence is given as aₙ = a₁ + (n - 1) * d, where aₙ represents the nth term, a₁ is the first term, n is the position of the term in the sequence, and d is the common difference.
Given that a₁₄ = 42 and d = 3, we can substitute these values into the formula to find the nth term. Plugging in the values, we have a₁₄ = 14 + (14 - 1) * 3, which simplifies to 14 + 13 * 3, resulting in a₁₄ = 14 + 39 = 53. Therefore, the 14th term of the arithmetic sequence is 42.
To graph the first six terms of the sequence, we can substitute n = 1, 2, 3, 4, 5, and 6 into the formula. The corresponding terms are as follows:
a₁ = 14 + (1 - 1) * 3 = 14
a₂ = 14 + (2 - 1) * 3 = 17
a₃ = 14 + (3 - 1) * 3 = 20
a₄ = 14 + (4 - 1) * 3 = 23
a₅ = 14 + (5 - 1) * 3 = 26
a₆ = 14 + (6 - 1) * 3 = 29
Plotting these values on a graph, we would have the following points: (1, 14), (2, 17), (3, 20), (4, 23), (5, 26), and (6, 29). Connecting these points would result in a straight line with a positive slope, representing the arithmetic sequence.
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helpppppppppppppppppp
Answer:
Step-by-step explanation:
a. Expand the area of the graph that has some small deviations from an otherwise coherent line. By magnifying those particular points, a sense of greater error is portrayed.
b. Shrink the axes so that data are moved closer together.
PLEASE HELP!!
Find the equation of the line that is perpendicular to the line
6x – 4y = 3 and passes through the point (6,-1).
(a) Find the slope of the given line 6x – 4y = 3.
(b) What is the slope of a line that is perpendicular to the above line?
(c) Now, find the equation of the perpendicular line that passes through (6,-1).
Answer:
a). y = 3/2x - 3/4 b).-2/3 c).y = -2/3x + 3
Step-by-step explanation:
a). 6x – 4y = 3
-4y = -6x + 3
y = 3/2x - 3/4
- The slope is 3/2.
b). The slope of a perpendicular line would be the opposite: -2/3
c). y = -2/3x + b
-1 = -2/3(6) + b
-1 = -4 + b
3 = b
y = -2/3x + 3
4.43 overweight baggage. suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. most airlines charge a fee for baggage that weigh in excess of 50 pounds. determine what percent of airline passengers incur this fee.
The percentage of airline passengers covered by this fee is 85.99%.
If the distribution is normal, use the Z-score formula. For a set of means and standard deviations, the measure's z-score X is given by z-score measures how many standard deviations a measure is from its mean. After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is
less than X, the percentile of X Subtracting 1 from the p-value gives the probability that the value of the measure is greater from X means 46 pounds with a standard deviation of 3.7 pounds.
This is the p-value of Z for X = 50 minus 1 as a
ratio. So the p-value of is 0.8599or 0.8599× 100 = 85.99%
So, 85.99% of the airline passengers pay this fee.
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Create and solve the EQUATION. 4. The sum of seven times a number and 16 is 163.
An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.
The solution is 21.
How to determine the two unknown numbers?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:
Let the variable n represent the unknown number.
Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;
7n + 16 = 163
7n = 163 - 16
7n = 147
n = 147/7
n = 21.
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Are teacher evaluations independent of grades? Halfway through the term, 3 random sample of 284 students were asked to evaluate teacher performance. The students also were asked to supply their midterm grade in the course being evaluated. In this study, only students with a passing grade ( A,B, or C) were included in the summary table. Use a S\% level of significance to test the claim that teacher evaluations are independent of students midterm grades. To test the hypothesis, which of the following is the alternative hypotheres? Find the expected value for the category: Grade C and Negative Teacher Evaluation. Round to the nearest whole number. Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 30 b 38 c 23 d. 35
The claim that teacher evaluations are independent of students' midterm grades is that there is a relationship or dependence between the two variables. The provided answer choices (30, 38, 23, and 35) are not sufficient to determine the expected value accurately.
The specific alternative hypothesis can be stated as follows: The teacher evaluations are not independent of students' midterm grades.
To determine the expected value for the category "Grade C and Negative Teacher Evaluation," we need to calculate the expected frequency for this category. The expected frequency is calculated based on the assumption of independence between the variables.
1. Set up the null and alternative hypotheses:
Null hypothesis (H0): Teacher evaluations are independent of students' midterm grades.
Alternative hypothesis (Ha): Teacher evaluations are not independent of students' midterm grades.
2. Conduct a chi-square test of independence using the observed frequencies from the sample data.
3. Calculate the expected frequencies for each category in the contingency table under the assumption of independence. To calculate the expected frequency for a particular category, use the formula:
Expected frequency = (row total * column total) / sample size
4. Determine the degrees of freedom (df) for the chi-square test. The degrees of freedom can be calculated using the formula:
df = (number of rows - 1) * (number of columns - 1)
5. Calculate the chi-square test statistic by comparing the observed and expected frequencies for each category in the contingency table.
6. Determine the critical value for the specified significance level (S%) and the calculated degrees of freedom. Compare the chi-square test statistic to the critical value to make a decision about rejecting or failing to reject the null hypothesis.
7. Finally, interpret the results. If the p-value associated with the chi-square test statistic is less than the specified significance level, reject the null hypothesis and conclude that there is evidence of a relationship between teacher evaluations and students' midterm grades.
Regarding the expected value for the category "Grade C and Negative Teacher Evaluation," we would need the observed frequencies and the specific contingency table to calculate it. The provided answer choices (30, 38, 23, and 35) are not sufficient to determine the expected value accurately.
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A water supply system is to be installed at a distance of 54 meters using 6 meters long PVC pipe with a diameter of 100mm. determine the number of length of PVC pipe to be used? a. 7 b. 8 c. 9 d. 10
To determine the number of lengths of PVC pipe to be used, we need to divide the total distance to be covered (54 meters) by the length of each PVC pipe (6 meters) and round up to the nearest whole number.
Number of lengths of PVC pipe = Total distance / Length of each PVC pipe
Number of lengths of PVC pipe = 54 meters / 6 meters
Number of lengths of PVC pipe = 9
Therefore, the number of lengths of PVC pipe to be used is 9.
So, the answer is option c. 9.
The moment of inertia depends on the distribution of masses relative to the axis of rotation. It is a measure of an object's resistance to rotational motion. The formula for the moment of inertia varies depending on the specific shape and distribution of masses.
If you can provide more details about the arrangement of masses and the axis of rotation, I can help you derive the expression for the moment of inertia in terms of m and l.
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FencingYou purchase a 50-meter roll of fencing, at a cost of $14.95 per meter, in order to build a dog run that is 340 cm wide and 1380 cm long. After you cut the four pieces of fencing from the roll, how much of the fencing is left on the roll
After cutting the four pieces of fencing for the dog run, there will be approximately 33.5 meters of fencing left on the roll.
The amount of fencing left on the roll, we need to determine the total length of the four pieces cut from the roll and subtract it from the initial length of the roll (50 meters).
The perimeter of the dog run can be calculated by summing the lengths of all four sides. For a rectangle with width 340 cm and length 1380 cm, the perimeter is given by 2 * (width + length), which equals 2 * (340 cm + 1380 cm) = 2 * 1720 cm = 3440 cm.
To convert the perimeter from centimeters to meters, we divide by 100: 3440 cm / 100 = 34.4 meters.
Therefore, the total length of the four pieces cut from the roll is approximately 34.4 meters. Subtracting this from the initial length of 50 meters gives us the remaining fencing on the roll: 50 meters - 34.4 meters = approximately 15.6 meters. Hence, approximately 33.5 meters of fencing will be left on the roll after cutting the four pieces.
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The sum of 2 consecutive numbers is 69. What are the numbers?
Answer:
34, 35Step-by-step explanation:
z - some integer
then the consecutive integer would be:
z+1, (or z-1)
the sum is 69 so:
z + z+1 = 96
2z = 68
z = 34
z+1 = 34 + 1 = 35
(or:
z + z-1 = 69
2z = 70
z = 35
z-1 = 35 - 1 = 34)