Answer:
252
Step-by-step explanation:
One way we could think about this problem is by grouping the numbers together into pairs: -103+104 would be a pair, -105+106 would be a pair and et cetera up to the pair -199+200.
As you can see, each of these pairs add to 1 (-103+104=1, -199+200=1 etc.), so to solve this problem we can simply find how many of these pairs there are and multiply the number by 1 since each pair will total to 1.
To find how many pairs there are we need to find the number of numbers between 103 and 200 (incl.) and divide it by 2.
200-103= 97 numbers, adding 1 to count the one we started with gives us 98 numbers between 103 and 200 (incl.).
98/2 = 49 pairs of numbers. Since each pair totals 1, 1x49 is the total sum of all these pairs of numbers.
Now we need to address the other two numbers. The sequence started with 101+102 before we looked at the remaining pairs, so to find the sum, we just need to add together 101+102+49.
101+102+49 = 252
Hope this helped!
1
Select the correct answer.
Consider the formula for the average vělocity, v, of a moving particle. In the formula, d, and de represent the distance traveled by the particle at
times t, and to respectively.
V=
t₂-t₁
Which of the following equations is equivalent to the formula for velocity?
Equatio 15: Mastery Test
OA. d₂= v(t₂-t₁) + di
v (d₂d₁) + ti.
OB. t₂ =
OC. t₁:
OD. d₁=
=
v (d₂d₁) - t₂
v (t₂-t₁) - d₂
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help me pease this is confussing will give brainlidt
[tex]\stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} \\\\\\ 6\cdot 2\frac{3}{4}\implies \cfrac{6}{1}\cdot \cfrac{11}{4}\implies \cfrac{66}{4}\implies \cfrac{33}{2}\implies {\LARGE \begin{array}{llll} 16\frac{1}{2} \end{array}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{mixed}{3\frac{1}{3}}\implies \cfrac{3\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{10}{3}} ~\hfill \stackrel{mixed}{3\frac{2}{5}}\implies \cfrac{3\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{17}{5}} \\\\\\ -3\frac{1}{3}\cdot -3\frac{2}{5}\implies -\cfrac{10}{3}\cdot -\cfrac{17}{5}\implies +\cfrac{170}{15}\implies \cfrac{34}{3}\implies {\LARGE \begin{array}{llll} 11\frac{1}{3} \end{array}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} ~\hfill \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}} \\\\\\ -4\frac{1}{2}\cdot 8\frac{2}{3}\implies -\cfrac{9}{2}\cdot \cfrac{26}{3}\implies -\cfrac{234}{6}\implies \cfrac{-39}{1}\implies \text{\LARGE -39} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{mixed}{1\frac{5}{6}}\implies \cfrac{1\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{11}{6}} \\\\\\ 1\frac{5}{6}\cdot (-9)\implies \cfrac{11}{6}\cdot \cfrac{(-9)}{1}\implies -\cfrac{99}{6}\implies -\cfrac{33}{2}\implies \LARGE \begin{array}{llll} -16\frac{1}{2} \end{array}[/tex]
A zumba instructor charges according to the number of participants. If there art 15 participants or below, the instructor charges 500.00 for each participant per month. If the number of participants is between 15 and 30 , he charge 400.00 for each paetricipants pe month . If there are 30 partricipantsor more . he charge 350.00 for each partricipas per month
The piecewise function that describes what the instructor charges is; f(x) = 500x , 0 < x ≤ 10
400x , 10 < x < 25
350x , x ≥ 25
How to create piecewise functions?
Let x represent the number of participants and let y represent the charge per participant.
Now, y depends on x, and as such we can say that;
f(x) = y
For, 0 < x ≤ 10, the total charges is 500x,
f(x) = 500x , 0 < x ≤ 10
For 10 < x < 25, total charge is 400x,
f(x) = 400x , 10 < x < 25
For x ≥ 25, the total charge is 350
f(x) = 350x x ≥ 25
Therefore, we can say that;
f(x) = 500x , 0 < x ≤ 10
400x , 10 < x < 25
350x , x ≥ 25
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Write the piecewise function that describes what the instructor charges.
what is 2 -x/15=-3 pls give in step by step explatorn or do work in paper
Answer:
2 + -x/15 = -3 the answer is x = 75Step-by-step explanation:
2+-x15 = -3
15.2 2 /15 -x =3
30 -x /15 = -3 x= 75
how many seconds are in 10 1/2 minutes
Answer:
630 seconds
Step-by-step explanation:
1 minute = 60 seconds
Number of minutes × Number of seconds per minute = Number of seconds in total
60 × 10 ½ = 630 seconds
Hope this helped! ^^
Find the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 15-inch long picture frame.
Answer:
The length is 5.
Step-by-step explanation:
Since the proportions are the same, 3 is 3 times less than 9. The same applies to 15, which 3 times less would be 5. It has a ratio of 3:5.
Compare the functions shown below: f(x) = (x + 3)2 − 2 g(x) linear graph with y intercept of negative 3 over 2 and x intercept of 3 h(x) x y −3 2 −2 7 −1 14 0 23 1 34 2 47 3 62 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3?
Answer:
For f (x):
f (x) = (x + 3) ^ 2 - 2
For x = -1
f (-1) = (-1 + 3) ^ 2 - 2
f (-1) = (2) ^ 2 - 2
f (-1) = 4 - 2
f (-1) = 2
For x = 3
f (3) = (3 + 3) ^ 2 - 2
f (3) = (6) ^ 2 - 2
f (3) = 36 - 2
f (3) = 34
AVR = ((34) - (2)) / ((3) - (- 1))
AVR = 8
For g (x):
linear graph with and intercept of negative 3 over 2 and x intercept of 3
y = mx + b
b = -3/2
For me we have:
0 = m (3) - 3/2
3m = 3/2
m = 1/2
The function g (x) is:
g (x) = (1/2) x - 3/2
For x = -1
g (-1) = (1/2) (- 1) - 3/2
g (-1) = -1/2 - 3/2
g (-1) = -4/2
g (-1) = -2
For x = 3
g (3) = (1/2) (3) - 3/2
g (3) = 3/2 - 3/2
g (3) = 0
AVR = ((0) - (- 2)) / ((3) - (- 1))
AVR = 1/2
For h (x):
Using the table we have:
AVR = ((62) - (14)) / ((3) - (- 1))
AVR = 12
Step-by-step explanation:
Answer:
from least to greatest:
1) g (x)
2) f (x)
3) h (x)
Step-by-step explanation:
Number 33, Im not sure how to start so if anyone could write the steps down in order or explain it, I would be so happy.
Answer:
A = 26 B = 82
Step-by-step explanation:
The angle A = 180 - ∅
So A is:
180 - (4x+10)
180 - 4x - 10
170 - 4x
The total angle of a triangle is 180, so A + B + C = 180
(170 - 4x) + (2x + 10) + 72 = 180
170 - 4x + 2x + 10 + 72 = 180
170 - 2x +82 = 180
252 - 2x = 180
252 - 180 = 2x
72 = 2x
72/2 = x
36 = x
A = (170 - 4x) = (170 - 4(36)) = 26
B = (2x + 10) = (2(36) + 10) = 82
C = 72
Snorkel's age 15 years ago was 22. How old is Snorkel today?
A hiker first hiked down into a canyon 1,345 feet below sea level. She then hiked 950 feet up the side of a mountain. What was the final altitude of the hiker? Please explain
The final altitude of the hiker 395 feet.
How to compute the value?From the information, the hiker first hiked down into a canyon 1,345 feet below sea level and she then hiked 950 feet up the side of a mountain.
This will be:
= -1345 + 950
= 395
Therefore, the final altitude of the hiker 395 feet.
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M
80.7°
Solve x
29°
N
Answer:
So what's M and N?
Step-by-step explanation:
What is the difference between the value of the 4 in 25.48 and 12.64
The difference between the values of 4 is 0.36.
We need to understand the place value and face value of a digit in a number.
Place value of digit is decided by putting the number of zeroes equal to the number of digits after that digit.
And the face value of a number is the number itself.
Here the two numbers given is 25.48 and 12.64. And we have to find the difference in place value of 4 in the given number.
The value of 4 in 25.48 is 0.40.
The value of 4 in 12.64 is 0.04.
Required difference = 0.40-0.04
= 0.36
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Help me with 15 and 17. I need this done today
Answer:
15. x = 4
17. AB = 9
Step-by-step explanation:
15.
Since B is in the middle of AC, AB + BC = AC
So,
x + 5 + 2x - 4 = 13
3x + 1 = 13
3x = 12
x = 4
17.
Since B is in the middle of AC, AB + BC = AC
So,
x + 16 + x + 17 = 19
2x + 33 = 19
2x = -14
x = -7
Going back to the question, it says to find the length of AB.
AB = x + 16 = -7 + 16 = 9
90 = 10(x + 7) solve for x
show steps & describe the number of solutions
Answer:
x = 2
Step-by-step explanation:
Simplifying
90 = 10(x + 7)
Reorder the terms:
90 = 10(7 + x)
90 = (7 * 10 + x * 10)
90 = (70 + 10x)
Solving
90 = 70 + 10x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-10x' to each side of the equation.
90 + -10x = 70 + 10x + -10x
Combine like terms: 10x + -10x = 0
90 + -10x = 70 + 0
90 + -10x = 70
Add '-90' to each side of the equation.
90 + -90 + -10x = 70 + -90
Combine like terms: 90 + -90 = 0
0 + -10x = 70 + -90
-10x = 70 + -90
Combine like terms: 70 + -90 = -20
-10x = -20
Divide each side by '-10'.
x = 2
Simplifying
x = 2
A group of friends wants to go to the amusement park. they have $154.25 to spend on parking and admission. parking is $11.25, and tickets cost $35.75 per person, including tax. how many people can go to the amusement park?
4 people can go to the amusement park.
Let the number of people that can go to amusement park be x.
The parking fee will be paid once only, while cost of ticket will be multiplied based on the number of people.
Forming equation as per the given information in question -
11.25 + 35.75 × x = 154.25
Solving the equation as per the operators -
Shifting 11.25 to Right Hand Side of the equation
35.75x = 154.25 - 11.25
Performing subtraction on Right Hand Side of the equation
35.75x = 143
Shifting 35.75 to Right Hand Side of the equation
x = 143 ÷ 35.75
Performing division on Right Hand Side of the equation
x = 4
Therefore, 4 people can go to the amusement park.
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Lisa works a weekend job for some extra money during school. She works Friday for 5 hours, Saturday for 8 hours and Sunday for 3 hours.
On Friday she makes $55.
On Saturday she makes $88.
On Sunday she makes $33.
How much money does Lisa make per hour at her job?
HOW TO DO???
- First you have to find how much money does she get per hour on each day
- Then add the amounts together
SLOVE
Lisa get: 55 : 5= 11$ per hour on Friday
Lisa get: 88 : 8= 11$ per hour on Saturday
Lisa get: 33 : 3= 11$ per hour on Sunday
At the end Lisa get: 11$ x 3= 33$ per hour at her job
{ I think my English isn't very good either because I'm just intermediate so I hope you understand it.}
3z^2 -4z+10 3z 2 −4z+10
Answer:
106z2−8z+10Step-by-step explanation:
3z2 − 4z + 103z2 −4z + 10
3z2 + − 4z+ 103z2 +− 4z + 10
Combine Like Terms:3z2 +− 4z+ 103z2 + − 4z + 10
( 3z2 + 103z2 ) + ( −4z+−4z ) + ( 10 )
106z2 + − 8z + 10
5 less than 2/3 of a number is 19. Find the number
Answer:
the anser in 60
Step-by-step explanation:
Let the original number be x.
According to the question we can write as (2/3)x+20x
On rearranging x−(2/3)x=20
Now taking the L.C.M od 1 and 3 is 3
(3x−2x)/3=20
x/3=20
Again by transposing x=60
So the original number is 60
Evaluate Piecewise Functions, please help asap! Thank you!
Answer:
4, -1, 5, -2
Step-by-step explanation:
Segments AD and BC intersect at point O.
Prove that AC = BD,
m∠ABC=m∠BAD.
Since both triangles are congruent, then we can conclude that AC = BD by Angle - Side - Angle congruence theorem.
How to prove Congruent Angles?
In ΔOAC and ΔODB, we have the following observations
CO = DO because it is shown that they are congruent
∠AOC = ∠BOD because vertical angles are congruent
∠ACO = ∠BDO because we are given that they are congruent
Now, the congruency theorem that we can use here is ASA which means Angle - Side - Angle. This implies that 2 corresponding angles and the included side are congruent.
If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by Angle - Side - Angle congruence theorem.
Since both triangles are congruent, then we can conclude that AC = BD by Angle - Side - Angle congruence theorem.
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y varies directly as the square root of x, and y = 12, when x = 49. Find the value of y when x = 225.
Answer:
180/7
Step-by-step explanation:
Direct variation:
y varies directly as k
y = kx
y varies directly as √x
y = k√x
We need to find k. We use the given data to find k.
y = 12 when x = 49
12 = k√49
12 = 7k
k = 12/7
The equation of direct variation is
y = (12/7)√x
x = 225
y = (12/7)√225
y = (12/7)(15)
y = 180/7
Unit 2 Logic and Proof Homework 1 Inductive reasoning
Answer:
The answers for this question is given below in the explanation section, kindly refer.
Step-by-step explanation:
Find the next 5 terms:
1) 28 < 33, 38, 43, 48, 53 => In every next term 5 is added.
2) 64 < 32, 16, 8, 4, 2 => In every next step the term is divided by 2.
3) 64 < 125, 216, 343, 512, 729 => In every next step it is a cube of next number.
4) 13 < 17, 19, 23, 29, 31 => In every next term it is the next prime number.
5) V < VI, VII, VIII, IX, X => In every next term it is the next roman numeral.
6) 8 < 13, 21, 34, 56, 90 => In every next term it is the sum of previous two terms.
7) => In every next term the arrows rotate clockwise in direction.
T/F:
8) False => 17+19 = 36, which is not a prime number.
9) True
10) True
11) True
12) True
13) True
14) False => ostrich, penguin, etc.
15) True
16) False => (a + b)² = a² + b² + 2ab
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Identify the transformation that maps the figure onto itself. A Reflect across the line x = 3 Reflect across the line x = 3, B Rotate 180° about the point (3, -3)Rotate 180° about the point (3, -3) C Rotate 180° about the point (5, -5)Rotate 180° about the point (5, -5) D Reflect across the line y = -3
Answer:
D Reflect across the line y = -3
Step-by-step explanation:
The only way you can divide the trapezoid so that there are two congruent parts is when you draw a line on y=-3.
Help I don’t know how to do this
Answer:
∠1 is 101 ∠4 is 79 and ∠2 is 79
Step-by-step explanation:
This is because ∠1 is a vertical angle of ∠3 so they have the same angle
For ∠4 and ∠2 you would do 101-180 because they are supplementary do they add up to 180
Evaluate the expression [8(2)-4^2]+7(4)
The value of expression using PEMDAS rule is 28 .
Given : expression [ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )
To find : value of expression
Calculation : Using V-BODMAS
[ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )
= [ ( 8 * 2 ) - ( 4 * 4 ) ] + ( 7 * 4 )
= [ 16 - ( 4 * 4 ) ] + ( 7 * 4 )
= [ 16 - 16 ] + ( 28 )
= [ 0 ] + ( 28 )
= 28
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Given that 12q x + 16p + 10p = 192x + 312. Find the values of p and q
Answer:
p = 12, q = 16,
Step-by-step explanation:
The following values represent the amount of money (in dollars) 10 people have in their wallets: 10, 12, 19, 5, 6, 8, 1, 13, 4, 7 what is the median?
The median of all these numbers in dollars is 7.5.
How to obtain median when no. of given data are odd ?When the no. of given data are odd we arrange those nos. in an order increasing or decreasing order and the middle no. is the median of the given odd numbers.
According to the given question the following values represent the amount of money (in dollars) 10 people have in their wallets: 10, 12, 19, 5, 6, 8, 1, 13, 4, 7 and we have to find the median.
First we observe that no. of people is even so there will be two middle nos.
Now lets arrange these nos. in an order from least to greatest which is
1, 4, 5, 6, 7, 8, 10, 12, 13, 19 in this 7 and 8 are middle numbers.
So, to find the median of all these nos. we will divide these two middle nos. by 2.
∴ ( 7 + 8 )/2
= 15/2
= 7.5.
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Solve the equation v² = 36. What’s the value of v?
Answer:
6
Step-by-step explanation:
6 x 6 = 36
Will mark brainliest! HELP MEEE!!
Answer:
He needs to get 100% on his next test
Explanation:
(59 + 80 + 65 + 96 + 100) / 5
After san jose, ca banned plastic bags, in 2012, bag litter choking the city's storm drains dropped by
62% down to 80 bags per site tested. what was the number of bags per site tested before 2012 based
on this study?
Number of bags per site tested before 2012 based on study it dropped by 62% down to 80 bags per site in 2012 is 129 (approximately).
As given,
In 2012, bag per site tested dropped by 62%
Let n be the number of bags per site before 2012
As per condition,
62% of n = 80
⇒(62/100) × n = 80
⇒ n = (80 × 100)/62
= 129.03
≈ 129
Therefore, number of bags per site tested before 2012 based on study it dropped by 62% down to 80 bags per site in 2012 is 129 (approximately).
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