The correct answer is option D. 1/35. To count the number of rectangles that can be formed, we need to consider the two cases where the diagonals of the rectangle are parallel to the sides of the octagon, and where the diagonals are perpendicular to the sides of the octagon.
In the first case, there are four choices for which side the diagonals are parallel to, and once that side is chosen, there are two choices for which pair of vertices lie on that side. Therefore, there are $4 \cdot 2 = 8$ rectangles of this type.
In the second case, there are four choices for which vertex the diagonals intersect, and once that vertex is chosen, there are two choices for which pair of vertices lie on the same side of the intersection point as the chosen vertex. Therefore, there are $4 \cdot 2 = 8$ rectangles of this type.
Altogether, there are $8 + 8 = 16$ rectangles. Therefore, the probability that the quadrilateral formed by the four vertices is a rectangle is
$\frac{16}{70} = \frac{16}{{8 \choose 4}}= \frac{1}{{8 \choose 4}/16}
= \frac{1}{{8 \choose 4}/2^4}
= \frac{1}{{8 \choose 4}/2^4}
= \boxed{\text{(D) } 1/35}$.
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Given that △DEF is a right triangle and that ∠E=90° with sides DE¯¯¯¯¯=3, DF¯¯¯¯¯=5, and FE¯¯¯¯¯=4, which ratio would be equal to sin(D)?
9514 1404 393
Answer:
sin(D) = 4/5
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation ...
Sin = Opposite/Hypotenuse
sin(D) = FE/DF
sin(D) = 4/5
mhairi invest 1000 for 5 years at 4% compound interest p.a calculate how much interest she has gained over the 5 years
Answer:
Step-by-step explanation:
$1000×1.04⁵ ≅ $1216.65
interest ≅ $216.65
You have one type of nut that sells for $4.50/lb and another type of nut that sells for $8.00/lb. You would like to have 28 lbs of a nut mixture that sells for $7.80/lb. How much of each nut will you need to obtain the desired mixture?
You will need
lbs of the cheaper nut
and
lbs of the expensive nut.
Answer:
I will need 26.4 pounds of the expensive nuts and 1.6 pounds of the cheap nuts.
Step-by-step explanation:
Since I have one type of nut that sells for $ 4.50 / lb and another type of nut that sells for $ 8.00 / lb, and I would like to have 28 lbs of a nut mixture that sells for $ 7.80 / lb, to determine how much of each nut will I need to obtain the desired mixture, the following calculation must be performed:
8 x 0.95 + 4.5 x 0.05 = 7.825
8 x 0.94 + 4.5 x 0.06 = 7.79
0.94 x 28 = 26.32
26.4 x 8 + 1.6 x 4.5 = 218.4
218.4 / 28 = 7.8
Thus, I will need 26.4 pounds of the expensive nuts and 1.6 pounds of the cheap nuts.
wyoming electric coop owns a steam-turbine power-generating plant. because wyoming is rich in coal deposits, the plant generates its steam from coal. this, however, may result in emission that does not meet the environmental protection agency (epa) standards. epa regulations limit sulfur dioxide discharge to 2000 parts per million per ton of cual burned and smoke discharge from the plant stacks to 20 ib per hour. the coop receives two grades of pulverized coal, c1 and c2, for use in the steam plant. the two grades are usually mixed together before burning. for simplicity, it can be assumed that the amount of sulfur pollutant discharged (in parts per million) is a weighted average of the proportion of each grade used in the mixture. the following data is based on the consumption of 1 ton per hr of each of the two coal grades. sulfur discharge smoke discharge steam generated coal grade in parts per million in ih per hour in ib per hour cl 1800 2.1 12,000 c2 2100 3 9,000 (a) determine the optimal ratio for mixing the two coal grades. (b) determine the effect of relaxing the smoke discharge limit by 1 ib on the amount of generated steam ner hour.
The reverse of adding 6 is:
A. dividing by 6
B. adding 1/6
C. subtracting 6
D. adding 6
E. multiplying by 6
F. subtracting 1/6
Answer:
C. subtracting 6
Step-by-step explanation:
If you add 6 to a number then subtract t you get the same number because they are inverse operations
Hope I helped! (p.s. maybe brainliest answer)
PLEASE HELP ACED + +++++++++
What is 4 1/7 in simplest form ??
Answer:28
Step-by-step explanation:
Answer:
29/7 or in decimal form: 4.1428...
please help and show work
la masa de un camión de 45000000
Explicación:
conversión de 45.000.000 gr a kg
45.000.000 gr ( 1 kg / 1000 gr) = 45.000 kg
conversión de 45.000 kg a toneladas
45.000 kg ( 1 ton / 1000 kg) = 45 ton
Respuesta: Espero te sirva...
Which list shows the numbers NOT in order from least to greatest?
4.036 < 4.08 < 42<4.201
3.09 < 3.1 < 3.507 < 3.9
6.4 < 6.51 < 6.387 < 6.995
7.315 < 7.38 < 7.406 < 7.5
You have $400,000.00 saved in a retirement account paying 4% interest compounded monthly and are ready to start your retirement. You have to figure out how much money you can safely take out of your account every month because you don't want to run out of money before you die.
How much money can you take out each month if you expect to live another 25 years?
9514 1404 393
Answer:
$2,104.33 at the beginning of the month, or
$2,111.35 at the end of the month
Step-by-step explanation:
The amount you can withdraw at the end of the month is given by the annuity formula ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where principal P is earning annual rate r for t years
A = $400,000(0.04/12)/(1 -(1 +0.04/12)^(-12·25)) ≈ $2,111.35
If the withdrawal is at the beginning of the month, then the amount is less by a factor of (1+0.04/12) ≈ 1.003333. It will be $2,104.33.
what is 381.7 rounded to the nearest tenth?
A merchant sells goods which cost $240 for $299. What percentage is his profit of the cost price?
Answer:
24.58%
Step-by-step explanation:
Given that,
Initial cost = $240
Final cost = $299
We need to find the percentage in his profit of the cost price.
Profit = Final cost - Initial cost
= $299 - $240
= $59
Percentage,
[tex]\%=\dfrac{59}{240}\times100\\\\=24.58\%[/tex]
So, the required percentage is equal to 24.58%.
What is the y value in the system of equations shown below?
y = 5 - 1/2x
3x - 2y = 6
If 55% of a number is 209 and 35% of the same number is 133, find 90% of that number.
Answer:
205 is 55% of 372 and is 335 90% of 372
Step-by-step explanation:
When the length of each edge of a cube is increased by 1 cm, the volume is increased by 37 cm3.
What is the length (in centimeters) of each edge of the original cube?
original length =3cm
Answer:
solution given;
let length be x
its
volume be x ³
we have when length is increased by 1cm volume increased by 37cm³ so
(x+1)³=x³+37cm³
x³+1³+3x²+3x=x³+37
3x²+3x-36=0
3(x²+x-12)=0
x²+4x-3x-12=0
x(x+4)-3(x+4)=0
(x+4)(x-3)=0
either
x=-4 rejected
or
x=3cm
The length (in centimeters) of each edge of the original cube will be 3.
How do you calculate the volume of a cube?Assume the side length of the cube under consideration is L units. The volume of the cube is then equal to L³ cubic units.
We have when length is increased by 1 cm volume increased by 37 cm³, so from the given condition the equation formed as;
(L+1)³=L³+37 cm³
Open the bracket and apply the necessary identities;
L³+1³+3L²+3L=L³+37
3L²+3L-36=0
3(x²+x-12)=0
Applying the factorization method;
L²+4L-3L-12=0
L(L+4)-3(L+4)=0
(L+4)(L-3)=0
L=-4 cm (Negative length is not possible.)
L=3cm
Hence,the length (in centimeters) of each edge of the original cube will be 3.
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Plz help I am very confused on this
Answer:
(-4, 0)
Step-by-step explanation:
(-4, 0)
what is is distance between (0,2) and (5,2)
You randomly select one card from a 52-card deck. Find the probability of selecting a two or a five.
Answer:
2/13
Step-by-step explanation:
there are 4 5s and 4 2s so
8/52
simplified is 2/13
5. A bag contains 21 red marbles and 29 blue marbles. A marble is picked at
random from the bag. What is the probability of picking a red marble?
Answer:
i dont know
Step-by-step explanation:
uhhh
Answer:
42% chance
Step-by-step explanation:
Since there are 21 red marbles and 29 blues ones, the total amount of marbles is 50. There are only 21 red marbles out of 50 marbles so there is a 21/50 chance that you will pick a red marble.
Joel went to the market to buy a juicy watermelon and found the volume was 523.6 mm. what is the radius of the watermelon? round to the nearest whole number.
Answer:
The radius of the watermelon was 5 milimeters.
Step-by-step explanation:
Since Joel went to the market to buy a juicy watermelon and found the volume was 523.6 square mm., To determine what is the radius of the watermelon, the following calculation must be performed, knowing that the volume of a sphere is equal to four thirds multiplied by pi, multiplied by the radius cubed:
4/3 x 3.14 x X^3 = 523.6
4.186 x X^3 = 523.6
X^3 = 523.6 / 4.186
X = 3√ 125.06
X = 5
Therefore, the radius of the watermelon was 5 milimeters.
-7.66666, \sqrt(50,) -(157)/(20), -7.64 list these from least to greatest.
Answer:
From least to greatest, the correct order is: [tex]-\frac{157}{20}[/tex]; -7.666....; -7.64; and [tex]\sqrt{50}[/tex].
Step-by-step explanation:
Since [tex]\sqrt{50}[/tex] is the only positive number, that means that it will be the greatest number on the list. [tex]-\frac{157}{20}[/tex] is equivalent to -7.85, which makes it the smallest number. So you can conclude that the correct order is [tex]-\frac{157}{20}[/tex]; -7.666...; -7.64; and [tex]\sqrt{50}[/tex].
A cylinder has a volume of 8792 cubic units. If the height is 7 cubic u it’s which of the following is the radius
Answer:
20 units
Step-by-step explanation:
Volume of a cylinder = πr²h
V = πr²h
height, h = 7
V = π * r² * 7
V = 8792
8792 = 21.991148 * r²
r² = 8792 / 21.991148
r² = 399.79722
r = √399.79722
r = 19.99unit
r = 20 units
Any help would be appreciated
Please help thank you
Answer:
x = 140
Step-by-step explanation:
Using the exterior angle rule ( an exterior angle of a triangle is equal to the opposite interior angles of a triangle )
x is the interior angle and the given angles ( 50 and 90 ) are the opposite interior angles
So
x = 50 + 90
50 + 90 = 140
x = 140
Note: there is a right angle ( indicated by the little square. A right angle has a measure of 90 degrees so that's where the 90 came from)
Please answer quickly! Will mark brainliest
Answer: C) 1/a^12•b^8
Step-by-step explanation:
B= R/E - T, solve for E
Please give me the correct answer
Answer:
-63
Step-by-step explanation:
5×9 = 45
45/-5 = -9
-9×7 = -63
How do u go pro at skateboarding? Also why is my baseball cup so uncomfortable?
Answer:
You can probably go pro at skating by just practicing a ton and learning new skills and tricks that separates you from other skaters. Its not very hard to be a "pro", its hard to make money off of skating because of the lack of audience it has. Also, I assume your baseball cap is uncomfortable because of the material or your hair.
Hope that helps
PLEASE HELP!!! I GIVE 15 POINTS!
Flaws in a carpet tend to occur randomly and independently at a rate of one every 260 square feet. What is the probability that a carpet that is 7 feet by 14 feet contains no flaws?
Probability =
Enter your answer in terms of e.
Answer:
The probability that a carpet that is 7 feet by 14 feet contains no flaws is 99.996%.
Step-by-step explanation:
Given that flaws in a carpet tend to occur randomly and independently at a rate of one every 260 square feet, to determine what is the probability that a carpet that is 7 feet by 14 feet contains no flaws, the following calculation must be performed:
7 x 14 = 98
1/260 = 0.003
98 = 100
0.003 = X
0.003 x 100/98 = X
0.0039 = X
100 - 0.0039 = 99.996
Thus, the probability that a carpet that is 7 feet by 14 feet contains no flaws is 99.996%.