Answer:
6
Step-by-step explanation:
use mathematical induction to prove the statement is true for all positive integers n. 6 + 12 + 18 + ... + 6n = 3n(n + 1)
Answer:
Step-by-step explanation:
6+12+18+....6n=3n(n+1)
Proof by induction
True for n = 1
6 = 3(1)(1+1)
Assume true for n = k
6+12+18+....6k=3k(k+1)
Then show that
6+12+18+....6(k+1)= 3(k+1)(k+1+1)
We add 6(k+1) to both sides of
6+12+18+....6k=3k(k+1)
6+12+18+....6k +6(k+1) =3k(k+1) + 6(k+1)
= 3(k+1)(k + 2)
= 3(k+1)(k+1+1)
So true for n = k+1
Since true for n=1 it is true for n=2,3,...
Thus true for all natural numbers n by mathematical induction
At 100°F, a certain Insect chirps at a rate of 97 times per minute, and at 102°F, they chirp 111 times per minute. Write an equation in slope-intercept form that represents the situation.
Answer:
y = 7x - 603
Step-by-step explanation:
We start by determining the slope:
m = y2 - y1/x2 - x1 = 111 - 97/102 - 100 = 14/2 = 7,
Now we substitute the slope into the slope-intercept equation y = mx + b, solving for the y-intercept [b]:
111 = 7(102) + b,
b = -603
Equation: y = 7x - 603
A kite is flying 76 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 589. Find the length of the string. Round your answer to the
nearest tenth
Answer:
Answer: The length of string from kite to the ground is 111.5 feetStep-by-step explanation:Given ... of the ground, and its string is pulled tout. The angle of elevation of the kite is 43. Find the length of the string. Round your answer to the ... The height from the ground at which kite is flying = BC = h = 76 feet.
Step-by-step explanation:
Two number cubes are rolled.
What is the probability that the first lands on an odd number and the second lands on an even number?
Enter you answer, as a fraction in simplified form, in the box
Answer:
1/4
Step-by-step explanation:
Assuming the number cube is a six-faced die, you have
1 2 3 4 5 6
three odd numbers, and three even numbers. Therefore, the chance of it landing on an odd number or even number is 3/6, which equals 1/2. That means you have a 50% chance to get an odd number, or an even number.
So, you have two die. Both have a 50/50 chance of getting an even or odd number. So what's the chance of one landing on an odd number, and the other landing on an even number?
You would have a 25% chance for an even and then an even numberYou would have a 25% chance for an odd and then an odd numberYou would have a 25% chance for an even and then an odd numberYou would have a 25% chance for an odd and then an even number.25% as a simplified fraction is 1/4. Therefore, 1/4 is your answer.
Answer:
1/4
Step-by-step explanation:
help please I gotta get my grade up!
First step: you got to add y to both sides in the math problem Ex: 15x - y + y < 12 + y
Second step: simplify 15x < 12 + y
Third Step: This you got to divide both sides by 15 like this: 15x/15 < 12/15 + y/15
Last and Fourth step: Simplify and thats your answer x < 12 + y/15
Can someone help me with this. Will Mark brainliest.
Answer: ur answer would be (1,5)
Step-by-step explanation:
Hope this helps! Have a good day! :)
Find the exact value of each variable.
x=
y=
z=
Step-by-step explanation:
hope it helps
have a great day!!
Timberly spent 3 4/5 hours in Misty spent 2 1/10 hours at gymnastics practice over the weekend. How many more hours did Timberly spend than Misty at the gymnastics practice?
Answer:
Step-by-step explanation:
The common denominator of these 2 fractions is 10.
Turn the mixed number 3 4/5 into an improper fraction which would be
19/5.
Then multiply the numerator and denominator with 2 to get the denominator to be 10.
19/5 x 2 = 38/10
Now turn 2 1/10 into an improper fraction= 21/10
Now subtract...
38/10 - 21/10 = 17/10
So Timberly spent 17/10 or 1 7/10 more hours then Misty at the gymnastics practice
please help i’ll give brainliest if you help thanks
Answer:
84
Step-by-step explanation:
What I did was simple. I just plugged it into my calculator and let it get to work. If you don't have a calculator, use your phone or computer. There should be calculators on both of these.
Please let me know if you need any more help. Hope this helps!
A 25 foot ladder and a 10 foot ladder are leaning against a building at the same angle,
and the base of the 25 foot ladder is 7.5 feet from the building. How far is the base of
the 10 foot ladder from the building?
Answer:
33.33 feet
Step-by-step explanation:
First you want to divide 25 to 7.5 so that you can find out how far the ladder is if it was a foot-long your answer should be 3.33. Then you want to multiply the 3.33 to 10 and the answer would be 33.33
Match the word to its description.
The most frequent value = mode
The middle value = median
The average = mean
The difference between the lowest and highest value = range
Answer:
Mode is the most frequent value
Mean is the average
Median Is the middle value
Range is the difference between etc...
The afternoon crew at Yummy Yummy Subbys can make a submarine sandwich once every 45 seconds. The evening crew can only make a submarine sandwich once every 50 seconds. If both crews work together, how many seconds will it take them to make 38 submarine sandwiches?
Answer: 900
Step-by-step explanation:
The number of seconds it will take both the crew together to make 38 sandwiches is 900.
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
The time taken by the afternoon crew to make a sandwich is 45 seconds. The time taken by the evening crew to make a sandwich is 50 seconds. Taking the LCM of the timing of the two crew, to know at what time they both will finish making a sandwich together.
LCM of 45 and 50 is 450.
Therefore, the number of sandwiches made by the afternoon crew in 450 seconds is 10, while the number of sandwiches that will be made by the evening crew is 9. Thus, in a time period of 450 seconds, both crews together will make 19 sandwiches.
Now, since it takes 450 seconds to make 19 sandwiches the time it will take to make double the number of sandwiches therefore, 38 sandwiches will also be double.
Hence, the number of seconds it will take both the crew together to make 38 sandwiches is 900.
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please help, i will give 20 points
4. Overall, there are 45 students.
13 students achieved a mark over 65
[tex]\frac{13}{45} *100[/tex] = 29%
Therefore the answer is b. 29%
5. b is incorrect.
This is because retrievers account for 10% of the dogs, not 15%.
100%-(35% + 45% + 10%) = 10%
What is 1% of 4,935 ?
O A. 0.04935
O B. 0.4935
O C. 4.935
D. 49.35
E. 493.5
Answer:
D. 49.35
Step-by-step explanation:
[tex]\frac{4935}{100 X 100}[/tex] X 100 = 49.35
math (not too hard answer asap) :)
Answer:
A and CStep-by-step explanation:
A. 134 is the mode, correct, repeated 5 timesB. 111 is appears 3 times, incorrect , this number is not part of data setC. There are more data values between 130 and 139, correct, there are 8 of themD. There are 20 data values, incorrect , there are 23I'm very confused on what the answer to this one is
Answer:
(-3,1.5) (0,3) (3'3)
Step-by-step explanation:
multiply all the coordinates by 1/2
please please please helpppp
Each side of a square piece of plastic is 2 centimeters long. What is the piece of plastic's area?
Answer:
4cm because area is length times width
Step-by-step explanation:
Answer:
4 cm2
Step-by-step explanation:
[tex]area = side {}^{2} = (2cm) {}^{2} = 4cm {}^{2} [/tex]
Kala deposits $7000 into an account that pays simple Interest at a rate of 4% per year How much interest will she be paid in the first 4 years?
Please help me! I’m giving brainliest to whoever is right first
Answer:
y = 10
x = 17
Step-by-step explanation:
4y - 3 = 37
4y = 37 + 3
4y = 40
y = 40 / 4
y = 10
3x - 9 = 42
3x = 42 + 9
3x = 51
x = 51 / 3
x = 17
Hope that helps!
Answer:
x = 17
y = 10
Step-by-step explanation:
Parallel sides are equal in length, so set them equal to each other.
3x - 9 = 42 --> Add 9 to both sides.
3x = 51 --> Divide both sides by 3.
x = 17
4y - 3 = 37 --> Add 3 to both sides.
4y = 40 --> Divide both sides by 4.
y = 10
Use the table. What inference can you make by comparing the measures of variability? Use the drop-down menus to explain your answer.
Finish Times of 30 Runners
in the 100-meter Dash
Mean MAD
Last Year 16.2s 1.2
This Year 14.7s 1.9
The is greater for this year’s 100-meter dash, which suggests that all 30 students equally.
Answer:
The first one is mean absolute deviation and the second one is did not improve
Step-by-step explanation:
I took the test
The MAD is greater for this year’s 100-meter dash, which suggests that all 30 students did not improve equally.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
The given table is:
Mean MAD
Last Year 16.2 s 1.2
This Year 14.7 s 1.9
Looking at this table we can see that this year, the meantime is smaller than the one from last year, so the runners are faster on average.
The mean absolute deviation is bigger, but the change in the mean is bigger.
difference of the mean 16.2 - 14.7 = 1.5
difference of the MAD 1.9 - 1.2 = 0.7
This means that the average speed of the runners increased since last year,
and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike as last year.
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PLEASE HELP ME :)))Micheal is making scale drawings of rectangular rooms using a scale of 1in to 1 1/2 feet
Answer:
a) 256 ft^2 No
b) 150 ft^2 Yes
c) 300 ft^2 NO
d) 192 ft^2 Yes
w=8.5 in
l=11 in
A=w•l
A=8.5•11=93.5 in^2
Scale:
1in:1.5 ft
1in^2:2.25 ft^2
1in ^2. 2.25ft^2
93.5 in^2. Xft^2
X=2.25•93.5
X=210.375
Step-by-step explanation:
The required answers are below the scale drawings for each of these rooms:
a. 16 feet by 16 feet: No
b. 10 feet by 15 feet: es
c. 15 feet by 20 feet: NO
d. 12 feet by 16 feet: Yes
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.
a. 16 feet by 16 feet:
The width of the room on the scale drawing will be 16/1.5 = 10.67 inches, and the length will also be 10.67 inches. Since both dimensions are greater than the width and length of the paper, the scale drawing will not fit on one piece of paper.
Answer: No.
b. 10 feet by 15 feet:
The width of the room on the scale drawing will be 10/1.5 = 6.67 inches, and the length will be 15/1.5 = 10 inches. The length dimension of the scale drawing fits on the paper, Therefore, the scale drawing will fit on one piece of paper.
Answer: Yes.
c. 15 feet by 20 feet:
The width of the room on the scale drawing will be 15/1.5 = 10 inches, and the length will be 20/1.5 = 13.33 inches. Both dimensions are greater than the width and length of the paper, so the scale drawing will not fit on one piece of paper.
Answer: Not.
d. 12 feet by 16 feet:
The width of the room on the scale drawing will be 12/1.5 = 8 inches, and the length will be 16/1.5 = 10.67 inches. Both dimensions are less than the width and length of the paper, so the scale drawing will fit on one piece of paper.
Answer: Yes.
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Two different functions are shown below.
1st function:
2nd function: y=3x
Which of the following statements is true?
Both functions have a positive slope
Both functions have a negative slope
Both Functions Are Proportional
Answer:
I think it's C if not D, but more likely C. Hope this helps, sorry if it doesn't.
Step-by-step explanation:
please tell me what this answer is
Simplify
-3(y+4)+4y
Please ANSWER FAST!!!!!
Answer: y-12
Step-by-step explanation:
-3(y+4)+4y
first distribute teh -3 to the y and the 4, so you get -3y and -12. Then combine like terms. -3y-12+4y, add the -3y and 4y, you get y. So the answer is y-12.
Answer:
y = 12
Step-by-step explanation:
here's your solution
=> -3(y + 4) + 4y = 0
=> -3y -12 +4y = 0
=> y -12 = 0
=> y = 12
hope it helps
At a school, there are 526 students and 263 are girls. About how likely is it that a randomly chosen student will be a boy?
◯ unlikely
◯ somewhat likely
◯ very likely
◯ equally as likely as unlikely
ABC is dilated by a scale factor of 1/2 to produce A’B’C’. What is A’B, the length AB after the dilation? What is the measure of
...It's A on Ap3x......
I NEED HELP!!! ASAP!
The image of point (2,1) under a rotation -540 degrees about the origin is:
a. (-1,2)
b. (-2,-1)
c. (1,2)
d. (2,1)
e. none of the above
You go to dinner with your family. The bill before tax is $60.00. How much is your bill when 7.25% tax added on?
If you can answer BOTH CORRECTLY you'll get brainliest
Answer:
Sorry the pictures re not clear. Could u zoom in? :)