The dimensions of a rectangular field is width = 40 yd and length = 120 yd.
What is a rectangle?
A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
Let the width of the rectangle, w = x
The length is 80 yd longer than the width.
The length of the rectangle, l = x + 80.
The perimeter of a rectangular field = 320 yd.
The formula of perimeter of rectangle is
[tex]P=2(w+l)[/tex]
On substituting the above values,
⇒ [tex]320=2(x+x+80)[/tex]
⇒ [tex]320=2(2x+80)[/tex]
⇒ [tex]2x+80=\frac{320}{2}[/tex]
⇒ [tex]2x+80=160[/tex]
⇒ [tex]2x=160-80[/tex]
⇒ [tex]2x=80[/tex]
⇒ [tex]x=\frac{80}{2}[/tex]
⇒ [tex]x=40[/tex]
Thus width = [tex]40[/tex] and
length = [tex]40+80[/tex]
⇒ [tex]120[/tex]
Hence we can conclude that the dimensions of a rectangular field is width = 40 yd and length = 120 yd.
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Which of the following illustrates the truth value of the following mathematical statements? 6 + 3 = 9, and 5 • 5 = 20
A. T T → T
B. F T → F
C. T F → F
D. F F → F
HELP PLEASE!! 30 POINTS!!
John's credit card company calculates a finance charge based upon a periodic rate of 1.75% on all unpaid balances. If John has an unpaid balance of $475, determine the finance charge that he will be assessed.
A. $8.31
B. $349.00
C. $346.30
D. $469.33
Final answer:
The finance charge for John is calculated by multiplying his unpaid balance by the periodic rate. The calculation results in a finance charge of $8.31, which is option A.
Explanation:
John's finance charge on his credit card, based on a periodic rate of 1.75% on an unpaid balance of $475, can be calculated using the formula: Finance Charge = Periodic Rate × Unpaid Balance. To find the finance charge, multiply 1.75% (or 0.0175 in decimal form) by $475. Therefore, the finance charge would be 0.0175 × $475 = $8.3125. When rounded to the nearest cent, this is $8.31, which corresponds to option A.
What was the name of the treatise in which Euclid compiled all the existing geometric knowledge, along with some of his own observations, to provide a logical structure and progression for geometry?
Earth Measurements
The Pythagorean Theorem
The Elements
Logic and Geometry
Answer:
The correct answer is The Elements.
This is the right answer for Edmentum and Plato users
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Math : powers , help me !!!
Donnavan is measuring the angles of a triangle. he measures the first two angles and gets 10° and 120°. what should be the measure of the third angle?
a.25° eliminate
b.50°
c.130°
d.230°
Carl deposited $5,142 into a savings account 20 years ago. The account has an interest rate of 3.8% and the balance is currently $10,994.58. How often does the interest compound? daily monthly quarterly annually
The answer is it is compounded monthly which is 365/yr.
This is done using trial and error but I got it right at the first try.
Solution:
A = P (1+r/n) ^nt
Where:
A is the accrued amount or also known as the future value
P is the principal amount = $5,142
r is the nominal interest rate = 0.038
n is the number of compounding units = 365
t is time = 20
A = 5,142 (1 + 0.038/365) ^ 365(20)
= 5,142 (1.0001041095890410958904109589041)^7300
= 5.142 (2.13819163)
= $10994.58
martha can complete 15 activities a day at summer camp. she can choose between crafts or sports.
1. Define two variables and create an equation to represent the situation? 2. what are 3 possible combinations of crafts and sports that Martha can do?
The sun is 30 ∘ above the horizon. it makes a 60 m -long shadow of a tall tree. how high is the tree
To calculate the height of a tree with a 60-meter long shadow when the Sun is 30 degrees above the horizon, use the tangent trigonometric function. The tree's height is calculated to be around 34.62 meters tall.
Explanation:The student is asking how to calculate the height of a tree given the length of its shadow when the Sun is 30 degrees above the horizon. This is a trigonometry problem involving a right-angled triangle, where the tree represents the opposite side, the shadow represents the adjacent side, and the angle given is the angle of elevation of the Sun. Since we have the angle and the length of the adjacent side, we can use the tangent trigonometric ratio to find the height of the tree. The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side (tangent = opposite/adjacent).
Therefore, the tree is approximately 34.62 meters tall.
Use the Law of Syllogism to draw a conclusion from the given information.
Given: If two lines are perpendicular, then they form right angles. If two lines meet at a 90 angle, then they are perpendicular. Two lines meet at a 90 angle.
a.Conclusion: The lines are parallel.
b.Conclusion: The lines are perpendicular and meet at a 90 angle.
c.Conclusion: The lines meet at a 90 angle.
d.Conclusion: The lines form a right angle.
It is now between 10:00 and 11:00. six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago what is the exact time now
The problem is solved by calculating the relative speed of the minute and hour hands of the clock and their current angular position. The current time when addressed the problem is approximately 10:26.
Explanation:The problem presents an instance of math calculation with clock hands. Here we'll use the fact that a full rotation of a clock’s hand indicates 360 degrees. In 60 minutes, the minute hand makes a full rotation, moving at a speed of 360/60 = 6 degrees per minute. In 12 hours, the hour hand makes a full rotation, moving at a speed of 360/(12*60) = 0.5 degrees per minute.
Three minutes ago, the hour hand was 3 * 0.5 = 1.5 degrees behind its current position. Six minutes later from now, the minute hand will be 6 * 6 = 36 degrees forward its current position. As per the conditions of the problem, the minute hand will be exactly opposite to the position held by the hour hand three minutes ago in six minutes from now. The opposite position in terms of the clock involves an angle of 180 degrees.
Therefore, the difference between the positions of the minute and hour hands right now = 180 degrees + 1.5 degrees - 36 degrees = 145.5 degrees. As the minute hand moves faster, the speed of the minute hand relative to the hour hand = 6 degrees - 0.5 degrees = 5.5 degrees per minute. Hence, the time required for the minute hand to create an angle of 145.5 degrees from the hour hand = 145.5 / 5.5 ≈ 26.45 minutes.
Therefore, the time now in HH:MM format is 10:26 (approximately), as the time was in the hour of 10.
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Levain bakery, on west 74th street in new york city, is trying to determine the number of loaves of raisin bread to make each day. over the past few months the store has baked 50 loaves each day and has sold out with probability 0.80. suppose the owner continues this practice and 30 days are selected at random. fill in the blank. (give your answer to four decimal places.)
From the given information, the sample size is 30 days and the probability is 0.80.
Here, it can be observed that the number of trials is fixed and the probability of success is 0.80. So, apply binomial distribution. The number of trials is fixed and the probability of success is 0.80. So, apply binomial distribution.
The mean of the binomial distribution is obtained below:
Mean = np = 30 * 0.8 = 24
The expected number of days on which all 50 loaves will be sold is 24.
The mean value obtained by multiply the sample size (n) and the probability of success (p). That is, the expected number of days on which all 50 loaves will be sold is 24.
The expected number of days on which all 50 loaves will be sold is 24.
Divide. 42/−8 Enter your answer as a mixed number, in simplified form, in the box.
Answer: -5 1/4
Step-by-step explanation:
cause im smart
Which is the graph of 4x – 3y = 12?
Answer:
its the last graph pictured
The graph of 4x - 3y = 12 is given below.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
The given linear equation is 4x - 3y = 12.
Rearranging it into slope intercept form, we get,
y = 4/3 x - 4
In order to find the points through which it passes, put some of the values of x.
When x = -3, y = -4 - 4 = -8
When x = 0, y = 0 - 4 = -4
When x = 3, y = 4 - 4 = 0
When x = 6, y = 8 - 4 = 4
...........
So the graph passes through (-3, -8), (0, -4), (3, 0) and (6, 4).
Hence the graph of the given equation is given below.
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The mean score of a competency test is 65, with a standard deviation of 4. use the empirical rule to find the percentage of scores between 53 and 77. (assume the data set has a bell-shaped distribution.)
To solve this problem, we use the t statistic. The z score is calculated as:
z = (x – u) / s
where x is the sample value = 53 and 77, u is the mean score = 65 while s is the standard deviation = 4
when x = 53
z = (53 – 65) / 4 = -3
From the standard distribution tables, the p value at z = -3 is:
P (z=-3) = 0.0013
when x = 77
z = (77 – 65) / 4 = 3
From the standard distribution tables, the p value at z = 3 is:
P (z=3) = 0.9987
The percentage P between the two would be the difference:
P (53 < x < 77) = 0.9987 – 0.0013 = 0.9974
Answer:
0.9974 or 99.74%
Given two points on the graph of the line, the equation of the line can be found.
True
False
If y=3x+2, find the value of y when x=-2. Please help.
please help me! thanks :)
How many kilograms are in 5500 g? Show all work
When converting gram to kilogram (smaller unit to larger unit), you must divide by 10. This means that you must move each unit to the left. For example:
Kilo, hectogram, decagram, gram... you must move 3 steps to the left which means 5500 grams is equal to 5.5 Kilograms
James earned a total of $900 this week. this total was $20 less than four times the amount he earned last week. how much money did james earn last week
What is the cube root of 27?
A.3
B.4
C.5
D.6
What is the expression using summation notation of 0.4(1/2+1/2.4+1/2.8+1/3.2+1/3.6)?
The given expression, 0.4 times the sum of reciprocals in an arithmetic sequence, is expressed using summation notation. Calculating the numerical value yields approximately 0.5244.
Breaking down the expression and writing it using summation notation:
The given expression is: 0.4 (1/2 + 1/2.4 + 1/2.8 + 1/3.2 + 1/3.6)
To express it in summation notation, we need to identify the pattern in the sequence.
The terms are reciprocals of an arithmetic sequence, where each term is obtained by adding a constant difference (0.4) to the previous term.
The nth term of the sequence can be expressed as: 2 + 0.4(n-1)
The expression in summation notation is: ∑ (from n = 1 to 5) of 1/(2 + 0.4(n-1))
Calculating the values and finding the sum:
For n = 1: 1/(2 + 0.4(1-1)) = 1/2
For n = 2: 1/(2 + 0.4(2-1)) = 1/2.4
Similarly, for n = 3, 4, and 5, we get 1/2.8, 1/3.2, and 1/3.6, respectively.
Summing these values, we get: Sum = 1/2 + 1/2.4 + 1/2.8 + 1/3.2 + 1/3.6
Multiplying by 0.4 (as in the original expression), we have: 0.4 * (1/2 + 1/2.4 + 1/2.8 + 1/3.2 + 1/3.6)
Calculating the numerical value:
0.4 * (1/2 + 1/2.4 + 1/2.8 + 1/3.2 + 1/3.6) ≈ 0.5244
Therefore, the final numerical value of the expression is approximately 0.5244.
The king has only one sibling. what is the probability that the sibling is a male
Answer:
theres a 40% chance it will be a boy or a 60% change of a boy.
Step-by-step explanation:
40% because over half the population are girls but for the 60% its more common for boy twins.
hope you understand ^_^
You have 2 types of bread, 3 types of meat, and 2 types of cheese. How many different sandwiches can you make if each sandwich has 1 type of bread, 1 type of meat, and 1 type of cheese?
Between what 2 integers does √89 fall?
A.9 and 10
B.10 and 11
C.11 and 12
D.12 and 13
Which transformation is not isometric?
in 1996,Donovan Bailey of Canada ran the 100 meter dash in 9.84 seconds.How fastis that to the nearst second?to the nearst tenth of a second
A rectangular garden has a length that is five less than twice the width. the garden perimeter is 50 meters. what are the dimensions of the garden?
-6x + y = 11 Solve for Y
Problem page a delivery truck is transporting boxes of two sizes: large and small. the large boxes weigh 45 pounds each, and the small boxes weigh 15 pounds each. there are 120 boxes in all. if the truck is carrying a total of 3300 pounds in boxes, how many of each type of box is it carrying?
Find distance between parallel lines given equations in 3d