Answer:
17
Step-by-step explanation:
Rachael has 20 thin rods whose lengths, in centimetres, are 1, 2, 3, ... 20. Any two rods can be connected at their ends. Rachael selects three rods to make a triangle, then three other rods to make a second triangle, and so on. a Only one of Rachael's rods cannot be the side of a triangle. Determine which one. b Rachael uses six of her rods that are no more than 7 cm to make two triangles. In how many ways can she do this? c Show how Rachael could use 15 of her rods to make five triangles, each with an even perimeter. d Rachael wants to use 18 rods to form a set of six triangles with equal perimeters. Either find such a set or explain why no such set exists.
9514 1404 393
Answer:
a) 1
b) 3
c) {{3, 6, 7}, {8, 12, 14}, {9, 10, 17}, {11, 13, 16}, {15, 18, 19}
d) cannot do. The numbers cannot add up.
Step-by-step explanation:
a) The minimum difference between rod lengths is 1. A unit-length rod cannot be used, because the sum of that and another length cannot exceed a third length. 1 + 2 = 3; is not greater than 3.
__
b) The 3 possible pairs of triangles are
{2, 3, 4}, {5, 6, 7}
{2, 4, 5}, {3, 6, 7}
{2, 6, 7}, {3, 4, 5}
__
c) There are numerous ways to make 5 triangles having an even perimeter. One is shown above. Several more are ...
{5, 12, 15}, {7, 17, 18}, {8, 10, 16}, {9, 13, 20}, {11, 14, 19}
{5, 15, 16}, {6, 9, 13}, {7, 14, 19}, {8, 11, 17}, {10, 12, 18}
{3, 9, 10}, {5, 15, 16}, {7, 13, 18}, {8, 11, 17}, {12, 14, 20}
{4, 9, 11}, {5, 12, 13}, {7, 18, 19}, {8, 15, 17}, {10, 16, 20}
{5, 12, 13}, {7, 18, 19}, {8, 11, 15}, {9, 17, 20}, {10, 14, 16}
__
d) No such set exists.
The sum of the 19 rod lengths is 209. Even if we throw out the rod of length 20 (to make a set of 18 rods), the perimeter must be at least 2(19)+1 = 39. Six triangles with that perimeter would require a total rod length of 6(3) = 234. The total length of rods is insufficient to make the required triangles.
A square originally starts with an area of 64 cm. If each side of the square is increased by 2 cm, what is the area of the new square? A. 68 cm2 B. 72 cm2 C. 81 cm? D. 100 cm2
Answer:
D
Step-by-step explanation:
pls answer fast will give branliest
if u send links will report so mf fast
Answer:
m∠1= 17°
m∠2=73°
m∠3=90°
m∠4=51°
m∠5=17°
m∠6=129°
Step-by-step explanation:
Hope it helps...
Have a great day!!
Suppose a caravan (5 cars) travels 100 km, beginning in front of one tollbooth, passing through a second tollbooth, and nishing just after a third tollbooth. The distance between two tollbooths is 50 km. Each car takes 12 sec to serve. The tollbooth starts to serve the caravan when the entire caravan is lined up. The caravan can only dispatch a tollbooth after all cars in the caravan are served. What is the end-to-end delay (from when the caravan is lined up before 1st tollbooth till the caravan is served by the 3rd tollbooth)
Answer:
1 hr 2 min 30 secs
Step-by-step explanation:
Assume Propagation speed = 100 km/hr
number of cars = 5
distance between booths = 50 km
Total distance = 100 km
take taken to serve each car = 12 secs
Determine the end to end delay
first calculate the propagation delay = Total distance / propagation speed
= 100 / 100 = 1 hr
next calculate : Time taken to serve 5 cars in each Tollbooth
= 5 * 12 secs = 60 secs
Next calculate : transmission delay ( time taken by three tollbooth to reach 5 cars )
= 60 secs * 3 = 180 secs = 2 min 30 secs
therefore end-end delay
= propagation delay + transmission delay
= 1 hr 2 min 30 secs
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x^2-8x-3
Answer:
x = 1 and vertex = (1, - 7 )
Step-by-step explanation:
Given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 )
The the equation of the axis of symmetry which is also the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 4x² - 8x - 3 ← is in standard form
with a = 4, b = - 8 , then
x = - [tex]\frac{-8}{8}[/tex] = 1
That is equation of axis of symmetry is x = 1
Substitute x = 1 into the function for y- coordinate of vertex
y = 4(1)² - 8(1) - 3 = 4 - 8 - 3 = - 7
vertex = (1, - 7 )
Harper can do 5 math problems in 1 2/3 minutes.How many problems can she complete in 1 minute?.
Answer:
bjrkhfjehrukfe
Step-by-step explanation:
rnfewklnfeklr
Answer:
Step-by-step explanatioN
30
What is an example of a quadrilateral?
solve 3 - x/2 ≥ 15.
A. x ≤ - 24
B. x ≥ - 6
C. x ≥ - 24
D. x ≤ 6
Answer:
A
Step-by-step explanation:
subract the three on both sides to get 12. then multiple by -2. when multiplying or dividing by negatives you want to flip the sign
Answer:
A. X ≤ -24
Step-by-step explanation:
(3 - X/2 ≥ 15)2
6 - X ≥ 30
-X ≥ 30-6
-X ≥ 24
-X/-1 ≤ 24/-1
X ≤ -24
PLEASE HELP REALLY URGENT
Step-by-step explanation:
[tex]2 + \sqrt{2} [/tex]
Hi im sorry to ask for help but im really stressed about this IN OWN WORDS PLEASE. and sorry to add more but please no scam<3
Answer:
1008
Step-by-step explanation:
volume formula: l×w×h
18×8×7=1008
Answer:
Volume = 1008 ft.
Step-by-step explanation:
The process to solving volume is L x W x H (length times width times hight). 18 ft. x 8 ft. x 7 ft. = 1008 ft. total.
hi could anyone please help me with this
A Ferris wheel has a radius
of 72 feet. What is the
distance a passenger will
travel one time around the
Ferris wheel?
Answer:
144
Step-by-step explanation:
radius is half of a diameter so that means you need to multiply 72 times 2
MAFS.912. G-GMD. 1.3
A regular pyramid has a square base. The perimeter of the base is 36
inches and the height of the pyramid is 15 inches. What is the volume of
the pyramid in cubic inches?
A. 180
B. 405
C. 540
D. 1215
Answer:
b
Step-by-step explanation:
The volume of the square pyramid is 405 cubic inches.
The correct answer is option (B).
What is the volume of the square pyramid?V = 1/3 × base area × h,
where h is the height of the pyramid.
What is the perimeter of square?P = 4 × a
where, 'a' represents the side of the square
For given example,
Let 'a' be the side length of the square base.
We have been given the perimeter of the square base is 36.
⇒ P = 36
⇒ 4 × a = 36
⇒ a = 9
So, the length of the side of the square base is 9 in.
Using the formula of the volume of the pyramid,
⇒ V = (1/3) × base area × h
⇒ V = (1/3) × a² × h
⇒ V = (1/3) × (9)² × 15
⇒ V = 27 × 15
⇒ V = 405 cubic inches
Therefore, the volume of the square pyramid is 405 cubic inches.
The correct answer is option (B).
Learn more about the volume of the square pyramid here:
https://brainly.com/question/23323560
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5. Select all of the ordered pairs that are a solution of y= 8x-1*
Please do asap
I need point really sorry :/ksjsjs
- cx9gwtu5rd
What is 2×2×2×5÷5÷100×100-100+1000
Answer:
908
Step-by-step explanation:
Answer:
908
Step-by-step explanation:
simplify the variable expression: g-16/4
Answer:
im not sure if this is what ur looking for but id k hopefully yes
Step-by-step explanation:
-16/4=-4
g-4
The solution after simplifying the variable expression by evaluating its numerical part is (g - 4).
Given that,
The expression is,
[tex]g - \dfrac{16}{4}[/tex]
Used the concept of expression by combining the like terms.
Now, simplify each term as,
[tex]g - \dfrac{16}{4}[/tex]
Here, [tex]\dfrac{16}{4} = 4[/tex]
So, we get;
[tex]= g - 4[/tex]
Therefore, the solution is (g - 4).
To learn more about the equation visit:
brainly.com/question/28871326
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Find the domain of the following function: f(t) = √(t + 9)(t - 5)
Please help ASAP!! Thank you!!
Answer:
{ t | t ≥ − 9 }
Step-by-step explanation:
You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53. 2 3 5 5 7 8 8 9 9 10 11 11 12 12 12 12 13 13 13 14 15 15 15 16 16 17 17 18 18 19 At the 5% level of significance, the conclusion of the test is that the
Answer:
At 5% level of significance the conclusion of the test is that the number of intervals used to test the hypothesis is : 5
Step-by-step explanation:
At 5% level of significance the conclusion of the test is that the number of intervals used to test the hypothesis is : 5
since each interval contains equal number of values lets divide the data into 6 groups i.e. frequency in the third group = 30 /6 = 5
hence we can say that the number of intervals used to test the hypothesis is 5
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator
0.30 cm to 0.42 cm
Answer:
[tex]\dfrac{5}{7}[/tex]
Step-by-step explanation:
Given numbers are :
0.30 cm and 0.42 cm
We need to find the ratio of the above whole numbers.
Taking 0.3 cm on the numerator and 0.42 cm on the denominator. So,
[tex]\dfrac{0.3}{0.42}=\dfrac{\dfrac{3}{10}}{\dfrac{42}{100}}\\\\=\dfrac{3}{10}\times \dfrac{100}{42}\\\\=\dfrac{10\times 3}{42}\\\\=\dfrac{10}{14}\\\\=\dfrac{5}{7}[/tex]
So, the required fraction is equal to [tex]\dfrac{5}{7}[/tex].
One hundred tomato plants were randomly selected from a large garden, and a 90% confidence interval was computed to determine the true proportion of plants that produce useable tomatoes. The interval is 0.86 to 0.92. What would happen to the width of the confidence interval if the sample size was quadrupled
Answer:
D. the interval would be half the original width.
Step-by-step explanation:
Sandra has a bag of marbles, in the bag she has 7 yellow, 6 blue, and 3 red marbles.
1. Find the sample space of all the possible outcomes if she were to pick two marbles from the bag without replacement.
Answer:
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How are you today? Have you had anything to eat? What's ur fav color? I'm just here to talk. I hope everyone has been staying safe!
Answer:
How are you today?
im good
Have you had anything to eat?
hot pocket
What's ur fav color?
Blue and Black
I'm just here to talk. I hope everyone has been staying safe!
Step-by-step explanation:
Complete the point-slope equation of the line through (-9,6) and (−7,−8)
y−6=
Answer:
its 9 :)
Step-by-step explanation:
hkjgh
A grocery store bought milk for $2.60 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 15 half gallons. If the remaining milk is sold for $4.08 per half gallon, how many half gallons did the store buy if they made a profit of $69.04?
Answer:
88 half gallons
Step-by-step explanation:
We can solve this problem by creating an equation. First we will need a variable. Since we are trying to find how many half gallons the store bought, that will be what our variable represents.
Let g = the number of half gallons
Since the store bought milk for $2.60 per half gallon, the amount of money they spent will be 2.6g.
The remaining milk is sold for $4.08 per half gallon. Remember, the store lost 15 half gallons so the number of gallons is currently g-15. This means that to find the amount of profit they made, we use 4.08(g-15).
We already know that the profit is $69.04, so we can make this into an equation.
This profit is the amount of money made minus the cost.
4.08(g-15) - 2.6g = 69.04
We can begin to solve this by simplifying the left side.
4.08(g-15) - 2.6g
4.08g - 61.2 - 2.6g
1.48g - 61.2
This makes our new equation:
1.48g - 61.2 = 69.04
We can begin to isolate our variable, g, by adding 61.2 to both sides.
1.48g = 130.24
Then we divide both sides by 1.48.
g = 88
Pls help me and explain!!
Answer:
22.919 or 23 degrees
Step-by-step explanation:
Use the theta or x in place of the usual angle. the lengths are adjacent and hypotenuse (a/h) so you use cosine. cos(x)=35/38 or cos(θ)=35/38
A square flag includes three colors: yellow, black, and green. The colors of the flag appear in the proportion 3:2:1, with yellow accounting for the greatest area and green accounting for the least. If a total of 48 square inches of the flag is black, what are the dimensions of the flag?
Answer:
423
Step-by-step explanation:
2313
Can somebody please help? It would be very appreciated. C:
Answer:
31/100
Step-by-step explanation:
Answer:
5/58 = 0.0862...
So, multiply that by 100.
8.62%.
There were 16 skittles in a bag there were 3 yellow, 4 red, 2 purple, 6 orange, and 1 green. What is the probability of pulling a red skittle (simplify your answer). The probability of a red is /
Answer:
1 out of 8, or 12.5 percent.
Step-by-step explanation:
There were 2 red skittles out of 16 total skittles, and then we divide the numbers by 2, then we get 1 out of 8. Converting it into a percentage, there is a 12.5% chance of pulling out a red skittle.
Wells Fargo has realized that they lose home mortgage business to other banks that can process the loan applications with less variability in the time it takes to process each application. The bank recently studied this problem, and found that the processing time T is normally distributed with a mean of 13 days. They didnt measure the standard deviation, but they know that 50% of all applications were processed in between 10.5 and 15.5 days. After learning all this, they then fired half of their mortgage loan officers and replaced them with new recruits. They then sampled 25 applications, and found a sample mean of 13 days (same as the old) and a sample standard deviation of 2.5 days.
(a) Test whether their actions have significantly changed their processing time T.
(b) Based on the sample of 25 applications, give a 90% confidence interval for the parameter that
has changed.
Answer: B
Step-by-step explanation:
I don’t know it help me pls
Answer:
its the yellow one hope this helps
Step-by-step explanation:
i did the math and checked !!!