2AI + 3H₂SO4
To show that the reaction conserves matter, how many hydrogen (H) atoms
will the right side of the equation need to have?
A. 6
B. 3
C. 2
OD. 5
Answer:
A. 6
Step-by-step explanation:
You have 3 molecules of H2SO4, each molecule has two atoms of H and you have 3 molecules, so 3*2=6 atoms of H
Suitable average for averaging the shoe sizes of children is
Select one:
a. Mean
b. Harmonic Mean
c. Geometric Mean
d. Percentile
e. Mode
PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS )
Find the measure of arc GW.
Answer:c
Step-by-step explanation:
faste او انوار کو کسی Q2. 3 balls are drawns from the box containing six white balls five red balls and four blue balls find the probabi- lity. that they are draw from the other blue red and white if each ball is (i) Replaced (ii) Not replace.
The probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.
To calculate the probability of drawing three balls from a box containing six white balls, five red balls, and four blue balls, we need to consider two scenarios: with replacement and without replacement.
(i) With replacement:
When each ball is replaced after it is drawn, the total number of balls remains the same for each draw. Therefore, the probability of drawing a specific color on each draw remains constant.
The probability of drawing a blue ball on each draw is 4/15, the probability of drawing a red ball is 5/15, and the probability of drawing a white ball is 6/15 (assuming all colors are equally likely to be drawn).
To find the probability of drawing a blue, red, and white ball consecutively, we multiply the probabilities together since the events are independent:
P(Blue, Red, White) = (4/15) * (5/15) * (6/15) = 120/3375
(ii) Without replacement:
When the balls are not replaced after being drawn, the total number of balls decreases for each subsequent draw. This affects the probability of each color being drawn on subsequent draws.
For the first draw, the probability of drawing a blue ball is 4/15, a red ball is 5/15, and a white ball is 6/15.
For the second draw, the probability of drawing a blue ball is 3/14, a red ball is 5/14 (as one blue ball is already drawn), and a white ball is 6/14.
For the third draw, the probability of drawing a blue ball is 2/13, a red ball is 4/13 (as two blue balls and one red ball are already drawn), and a white ball is 6/13.
To find the probability of drawing a blue, red, and white ball consecutively without replacement, we multiply the probabilities together:
P(Blue, Red, White) = (4/15) * (5/14) * (6/13) = 120/2730
Therefore, the probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.
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1. Find (f + g)(1), when f(x) = x + 6 and g(x) = x - 3.
Answer:
(f + g)(1) = 5
Step-by-step explanation:
(f + g) means we are going to add f(x) and g(x). But also, the (1) part means we are going to let x be equal to 1. We're going to fill in 1 in place of x. You can do this in either order.
Generally speaking its "easier" to fill in the 1 for x first and then do the adding part.
f(x) = x + 6
f(1) = 1 + 6 = 7
and,
g(x) = x - 3
g(1) = 1 - 3 = -2
add the 7 and -2 together:
7 + - 2
= 5
It works out the same if you add first:
f(x) + g(x)
= x + 6 + x - 3
= 2x + 3
then put the 1 in:
= 2×1 + 3
= 2 + 3
= 5
Hope this helps!
You just inherited a sum of money from a distant uncle. The only stipulation is that you need to save it for 10 years and then you can do whatever you want with it. The amount of the inheritance is $25,000.
Option one: You can put it into a saving account that earns 6% compounded quarterly.
Option two: You can put it into a checking account that earns 4% compounded monthly.
Option three: You can place it into a money market account that earns 3% compounded daily.
Which option is best for you? Why?
Submit a report detailing the reasons you have for the decision you make.
This flexibility of a money market account makes it an ideal option for people who need to save money without risking their inheritance.
After inheriting $25,000 from a distant uncle, you would like to save it for ten years before doing anything with it. Since you want to save the money, there are several options for keeping it safe and earning interest, including a savings account, a certificate of deposit (CD), and a money market account.
Money market accounts, in my opinion, would be the best place to keep the inheritance. The money market account is a low-risk account with high-interest rates, making it an attractive option for someone who wants to save their money. As a result, it would be reasonable to place the inheritance into a money market account that pays a daily compounded rate of 3%.There are several reasons for choosing this option.
Firstly, the daily compounded interest will generate a higher return over the ten-year period than the simple interest or monthly compounded interest offered by other accounts. Second, the account is FDIC-insured, which means that the account holder is guaranteed to receive their money in the event of a bank failure.
Furthermore, the money market account provides easy access to the account holder's money while still earning interest. Most money market accounts have a limit on the number of withdrawals a person can make per month. Still, the account holder can easily transfer funds into a checking account or withdraw money from an ATM if needed.
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Hannah and Becky are learning to type on a computer keyboard. Hannah's
typing speed is represented by the equation y = 11x where y is the number of
words she types and x is the number of minutes. Becky's typing speed is
given by the graph.
Number of words
60
48
36
24
12
2
3
Time (minutes)
Choose the statement that correctly compares their unit rates.
Adr
A. Hannah's unit rate is 2 more words per minute than Becky's unit
rate.
B. Hannah's unit rate is 1 more word per minute than Becky's unit
rate.
C. Hannah's unit rate is equal to Becky's unit rate.
D. Hannah's unit rate is 1 fewer word per minute than Becky's unit
rate
The correct statement is D. Hannah's unit rate is 1 fewer word per minute than Becky's unit rate.
To compare the unit rates, we need to determine the rate at which each person types words per minute.
For Hannah, the equation y = 11x represents her typing speed, where y is the number of words and x is the number of minutes. This means that Hannah types 11 words per minute (11 words/minute).
Looking at Becky's graph, we can determine her unit rate by calculating the change in the number of words divided by the change in time.
The change in words is 48 - 2 = 46, and the change in time is 3 - 2 = 1. So, Becky's unit rate is 46 words per minute (46 words/minute).
Comparing the unit rates:
Hannah's unit rate: 11 words/minute
Becky's unit rate: 46 words/minute
Therefore, Hannah's unit rate is 35 words per minute less than Becky's unit rate.
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5h-6-8+7h what’s the answer ?
Question #2
Solve for x
2
O Saved 1
4
3
Q
69x + 2
R
70°
Can some please help me I don’t understand this?
Please due tmr morning thanks!
The numbers to complete the pythagorean triple in the equation (n² - 1)² + k² = (n² + 1)² are B. 35 and 37
What is the pythagorean triple?A pythagorean triple is a set of 3 numbers that obey the pythagorean theorem.
Given the equation
(n² - 1)² + k² = (n² + 1)², we need to find the remaining numbers generated by the equation when k = 12. So, we proceed as follows/
Since we have the equation
(n² - 1)² + k² = (n² + 1)²
Subtracting (n² + 1)², from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = (n² + 1)² - (n² + 1)²
(n² - 1)² - (n² + 1)² + k² = 0
Now, subtracting k from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = 0
(n² - 1)² - (n² + 1)² + k² - k² = 0 - k²
(n² - 1)² - (n² + 1)² + 0 = - k²
(n² - 1)² - (n² + 1)² = - k²
Using the difference of two squares a² - b² = (a + b)(a - b)
(n² - 1)² - (n² + 1)² = - k²
(n² - 1 + n² + 1)[n² - 1 - (n² + 1)] = - k²
(n² + n² - 1 + 1)[n² - n² - 1 - 1)] = - k²
(2n² + 0)[0 - 2)] = - k²
(2n²)(- 2) = - k²
-4n² = - k²
4n² = k²
n² = k²/4
Taking square root of both sides, we have that
n = √(k²/4)
n = k/2
Since k = 12, we have that
n = 12/2
n = 6
So, the first number is (n² - 1) = (6² - 1)
= 36 - 1
= 35
The second number is (n² + 1) = (6² + 1)
= 36 + 1
= 37
So, the numbers are B. 35 and 37
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Solve it for me please
1a.) The amount that the eldest son received would be =GHç 1,360
b .) The amount received by the daughter would be =G Hç 2176
c.) The difference between the amount the two sons received would be =GHç1,904
How to calculate the amount received by the eldest son?For 1a.)
The amount that the land is worth= $8,600
The amount received for various purposes= $1,800
The remaining amount shared to the sons= 8,600-1800= $6,800
The percentage amount received by the eldest son= 20% of 6800
That is;
= 20/100×6800/1
= 136000/100
= $1,360
The remaining amount= 6800-1360= $5,440
For 1b.)
The ratio that the remaining amount was shared between the other son and the daughter = 3 : 2 respectively.
The total ratio= 3+2=5
For daughter= 2/5× 5440
= 10880/5 = 2176
The other son= 5440-2176 = 3264
For 1c.)
The difference between the amount the two sons received would be =3264-1,360 = GHç1,904.
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In order to compute a sample mean by hand, first the data values must be added up. Then the sum is divided by the
sample size.
x = xx
Given the data set below, compute the summation, identify the sample size, and calculate the sample mean.
19
10
15
17
16
a.) Ex =
b.) n =
c.) x =
a) The summation (Ex) of the given data set, we add up all the values
Ex = 77
b) n = 5
c) x = 15.4
a) To compute the summation (Ex) of the given data set, we add up all the values:
19 + 10 + 15 + 17 + 16 = 77
b) The sample size (n) is the total number of data points in the set. In this case, there are 5 data points, so:
n = 5
c) To calculate the sample mean (x), we divide the summation (Ex) by the sample size (n):
x = Ex / n
x = 77 / 5
x = 15.4
Therefore, the answers are:
a) Ex = 77
b) n = 5
c) x = 15.4
The summation is 77, the sample size is 5, and the sample mean is 15.4.
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In an election 177 votes are cast. How many votes are needed
The number of votes needed in an election can vary depending on various factors such as the type of election, voting rules, and specific requirements.
Without additional context or information about the specific election, it is challenging to provide an exact number of votes needed.The number of votes needed in an election is typically determined by factors such as the majority threshold, minimum vote requirement, or any specific criteria outlined in the election rules.
For example, in some elections, a candidate may need a simple majority (more than half) of the votes cast to win, while in others, a candidate may need a specific number or percentage of votes to secure victory.To determine the number of votes needed, it is essential to refer to the specific guidelines or rules established for that particular election.
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PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS)
Identify the arc length of MA◠ in terms of a and rounded to the nearest hundredth.
The length of the arc in terms of π and the actual length is as follows;
8.17π m²
25.68 m²
How to find arc length?Let's find the length of the arc of the circle as follows:
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleHence,
∅ = 180 - 88 = 92 degrees
r = 16 m
length of an arc MA = 92 / 360 × 2 × π × 16
length of an arc MA = 2944π / 360
length of an arc MA = 8.17π
Therefore,
length of an arc MA = 25.68 m²
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1. Brandon went to a Formula One car race and used his stopwatch to time how fast his favorite driver, Fernando Alonso, went around the 4.7-kilometer track. Brandon started the timer at the beginning of the second lap, when the cars were already going fast. When he stopped the timer at the beginning of the third lap, one minute and three seconds had passed.
b. If you graphed the distance Fernando had traveled at the beginning of the lap and at the end of the lap, what would the coordinates of these points be? What would the
- and
-axes on this graph represent?
c. Find the equation of the line between these two points. What does this line represent?
d. If Fernando continues to average this speed, about how long do you think it would take him to finish the entire race? The race is 500 km.
Step-by-step explanation:
b. To determine the coordinates of the points on the graph, we need to consider the information given.
At the beginning of the second lap, one minute and three seconds had passed. Since each lap is 4.7 kilometers long, we can calculate the distance traveled at the beginning of the lap using the formula:
Distance = (Number of laps - 1) × Length of each lap
For the beginning of the second lap:
Distance = (2 - 1) × 4.7 km = 4.7 km
At the beginning of the third lap, one minute and three seconds had passed. Therefore, the distance traveled at the beginning of the third lap is:
Distance = (3 - 1) × 4.7 km = 9.4 km
The coordinates of the points on the graph would be:
Point A: (4.7 km, 4.7 km)
Point B: (9.4 km, 9.4 km)
On the graph, the x-axis would represent the distance traveled at the beginning of the lap, and the y-axis would represent the distance traveled at the end of the lap.
c. To find the equation of the line between the two points, we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept.
Using the coordinates of the two points (4.7 km, 4.7 km) and (9.4 km, 9.4 km), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
= (9.4 km - 4.7 km) / (9.4 km - 4.7 km)
= 4.7 km / 4.7 km
= 1
The slope of the line is 1.
Since the line passes through the origin (0, 0), the y-intercept (b) is 0.
Therefore, the equation of the line is:
y = 1x + 0
y = x
This line represents a one-to-one relationship between the distance traveled at the beginning of the lap and the distance traveled at the end of the lap.
d. To estimate how long it would take Fernando to finish the entire race if he continues to average the same speed, we need to find the time it takes for one lap.
In the given scenario, Brandon timed Fernando's lap for one minute and three seconds. Since there are 3 laps in total, we can divide the total time by the number of laps to find the average time per lap:
Average time per lap = Total time / Number of laps
= 1 minute and 3 seconds / 3
= 21 seconds
Since each lap is 4.7 kilometers long, we can calculate the speed:
Speed = Distance / Time
= 4.7 km / (1 minute + 21 seconds)
To estimate the time it would take Fernando to finish the entire race, we divide the total race distance by the speed:
Total race time = Total race distance / Speed
= 500 km / (4.7 km / (1 minute + 21 seconds))
To calculate the time, we need to convert 1 minute and 21 seconds to a decimal form:
1 minute + 21 seconds = 1 minute + (21 seconds / 60 seconds)
= 1 minute + 0.35 minutes
= 1.35 minutes
Substituting the values:
Total race time = 500 km / (4.7 km / 1.35 minutes)
= 500 km × (
1.35 minutes / 4.7 km)
= 500 km × 0.28723...
≈ 143.615 minutes
Therefore, it would take approximately 143.615 minutes for Fernando to finish the entire race if he continues to average the same speed.
Will give brainlieest. 50 points. (8x + 2x³ - 4x²) - (4 + x³ + 6x)
Answer:
[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2x - 4
Step-by-step explanation:
(8x + 2[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex]) - (4 + [tex]x^{3}[/tex] + 6x)
= 8x + 2[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] - 4 - [tex]x^{3}[/tex] - 6x
= 2x + [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] - 4
= [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2x - 4
Choose an amount between $60.00 and $70.00 to represent the cost of a grocery bill for a family. Be sure to include dollars and cents.
Part A: If the family has a 25% off coupon, calculate the new price of the bill. Show all work or explain your steps. (6 points)
Part B: Calculate a 7% tax using the new price. What is the final cost of the bill? Show all work or explain your steps. (6 points)
Answer:
A: $51.00
B: $54.57
Step-by-step explanation:
Let amount = $68.00
Part A:
Since the coupon is for 25%, the family pays 75% of $68.00
75% of $68.00 = 0.75 × $68.00 = $51.00
The new price is $51.00
Part B:
The tax is 7% of $51.00
7% of $51.00 = $3.57
The total price is the sum of $51.00 and the amount of tax, $3.57
Total price = $51.00 + $3.57 = $54.57
given the line y= -6x +5 what is the line nslope and the y - intercept
According to slope intersept form : y = mx+b
m is slope and b is y intersept
so y = -6x+5
slope(m) = -6
y intersept = 5
HOPE IT HELPS
PLEASE GIVE BRAINLIEST
You are working on your second project as an equity research intern at a bulge investment bank. Your focus is in retail space, especially in the health and fitness sector. Currently, you are gathering information on a fast-growing chain fitness company called LuluYoga. You are interested in calculating the free cash flow of the firm.
LuluYoga offers yoga classes in several major cities in the United States. Two major revenue resources are selling workout gear and membership passes for class access.
Assume at the beginning of year 2016, LuluYoga has zero inventory.
In year 2016, LuluYoga purchased 10,000 yoga mats at a price of $10 each. The company sells 6,000 mats at a price of $15 in year 2016 and sells the remaining at a price of $20 in year 2017.
In year 2016, LuluYoga sells 1,000 membership passes for $2,000 each. 80% of the classes purchased were used in 2016 and the rest are used in 2017.The yoga master’s compensation to teach classes are $300K in year 2016 and $200K in year 2017.
LuluYoga pays corporate tax of 35%
What is the deferred revenue in 2016?
The number of membership passes that will contribute to deferred revenue in 2016 is: 1,000 (total passes sold) x 20% (passes utilized in 2017) = 200 passes.
To calculate the deferred revenue in 2016 for LuluYoga, we need to consider the membership passes that were sold but not yet utilized.
In 2016, LuluYoga sold 1,000 membership passes for $2,000 each. We know that 80% of the classes purchased were used in 2016, which means 20% of the classes will be utilized in 2017.
Therefore, the number of membership passes that will contribute to deferred revenue in 2016 is:
1,000 (total passes sold) x 20% (passes utilized in 2017) = 200 passes
The revenue generated from these 200 passes will be realized in 2017 when the classes are utilized. Therefore, the revenue from these passes should be deferred to the following year.
To calculate the deferred revenue, we need to multiply the number of passes by the price per pass:
200 (passes) x $2,000 (price per pass) = $400,000
Hence, the deferred revenue in 2016 for LuluYoga is $400,000.
Deferred revenue represents the amount of revenue that has been received but has not yet been earned. In this case, LuluYoga has received payment for the membership passes, but the revenue associated with the unused classes will be recognized in the subsequent year when the classes are actually utilized.
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A charged particle produces an electric field with a magnitude of 2.0 N/C at a point that is 50 cm away from the particle. a) Without finding the charge of the particle, determine the electric field produced by this charge at a point 25 cm away from it. b) What will happen to the Electric field at the distance 50 cm, if you double the charge? c) What is the magnitude of the particle’s charge?
To solve these problems, we can use Coulomb's Law, which states that the magnitude of the electric field produced by a charged particle is directly proportional to the charge and inversely proportional to the square of the distance from the particle.
a) Without finding the charge of the particle, we can use the inverse square relationship. If the electric field magnitude is 2.0 N/C at a distance of 50 cm, then at half the distance (25 cm), the electric field would be four times stronger. Therefore, the electric field at 25 cm would be 4 * 2.0 N/C = 8.0 N/C.
b) Doubling the charge would result in doubling the electric field magnitude. So, if the electric field at a distance of 50 cm was initially 2.0 N/C, it would become 4.0 N/C after doubling the charge.
c) To determine the magnitude of the particle's charge, we need to use the equation for the electric field:
E = k * (|q| / r^2)
where E is the electric field magnitude, k is the electrostatic constant, |q| is the magnitude of the charge, and r is the distance from the particle.
Using the known values of E = 2.0 N/C and r = 50 cm (or 0.5 m), we can rearrange the equation to solve for |q|:
|q| = E * r^2 / k
Substituting the values and the known value of k, we can calculate the magnitude of the charge.
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Suppose the bear population in the Allegheny National Forest have weights that produce a normal density curve as shown.
74——————-200————————-326
From the graph shown, use the 69-95-99.7% (empirical) rule to estimate the standard deviation of the bear weights.
The estimated standard deviation of the bear weights, based on the given graph and using the 69-95-99.7% rule, is approximately 63.
The 69-95-99.7% (empirical) rule, also known as the 3-sigma rule, is a rule of thumb that applies to data that follows a normal distribution. According to this rule:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In the given graph, if we assume the bear weights follow a normal distribution, we can estimate the standard deviation using the 69-95-99.7% rule.
Based on the graph, we know that the midpoint of the distribution (mean) is 200. Assuming the graph is symmetric, we can estimate one standard deviation as half the distance between the mean (200) and either end (74 or 326).
To calculate this, we subtract the mean from one of the endpoints and divide by 2:
Standard Deviation ≈ (326 - 200) / 2 ≈ 126 / 2 ≈ 63
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Consider this equation
1/x-1 = | x-2 |
Using three iterations of successive approximation, what is the approximate solution to the equation? Use the graph as a starting point.
A. x ≈ 43/16
B. x ≈ 21/8
C. x ≈ 41/16
D. x ≈ 19/8
The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.
To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.
Given that the equation involves absolute value, we will consider two cases:
Case 1: x - 2 ≥ 0
In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.
Case 2: x - 2 < 0
In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).
Now, let's perform the successive approximation:
Iteration 1:
Let's start with an initial guess, x = 2.
Case 1: When x - 2 ≥ 0,
1/(2-1) = 2-2,
1/1 = 0,
which is not true.
Case 2: When x - 2 < 0,
1/(2-1) = -(2-2),
1/1 = 0,
which is not true.
Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.
Iteration 2:
Let's try x = 3.
Case 1: When x - 2 ≥ 0,
1/(3-1) = 3-2,
1/2 = 1,
which is not true.
Case 2: When x - 2 < 0,
1/(3-1) = -(3-2),
1/2 = -1,
which is not true.
Again, our guess did not satisfy the equation in either case.
Iteration 3:
Let's try x = 2.5.
Case 1: When x - 2 ≥ 0,
1/(2.5-1) = 2.5-2,
1/1.5 = 0.5,
which is true.
Case 2: When x - 2 < 0,
1/(2.5-1) = -(2.5-2),
1/1.5 = -0.5,
which is not true.
Our guess of x = 2.5 satisfies the equation in Case 1.
Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.
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The cost to buy p pounds of potatoes at $0.32 per pound and n
pounds of onions at $0.48 per pound can be determined by using
the expression 0.32p + 0.48n. How much will it cost to buy 4.5
pounds of potatoes and 2.5 pounds of onions?
lion plays trumpet for a minmium of 45 mins on the days that he practices. if x is the number of days that lionel practices and y is the total number of hours he spends practicing, which inequality represents this situation
The inequality representing the situation is "y ≥ 0.75x," where y is the total number of hours Lionel spends practicing and x is the number of days he practices.
To represent the situation where Lionel practices for a minimum of 45 minutes on the days he practices, we can use the variables x and y, where x represents the number of days Lionel practices and y represents the total number of hours he spends practicing.
We know that Lionel practices for a minimum of 45 minutes on each day. Since there are 60 minutes in an hour, this is equivalent to 0.75 hours. Therefore, for each day Lionel practices, he spends at least 0.75 hours.
To find the total number of hours Lionel spends practicing (y), we can multiply the number of days he practices (x) by the minimum number of hours he spends on each day (0.75). This gives us the equation:
y ≥ 0.75x
This inequality states that the total number of hours Lionel spends practicing (y) must be greater than or equal to 0.75 times the number of days he practices (x). It ensures that Lionel practices for a minimum of 45 minutes (0.75 hours) on each day he practices.
By using this inequality, we can track Lionel's practice time and ensure that he meets the minimum requirement of 45 minutes per day.
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Please answer ASAP I will brainlist
Answer:
A) The y-intercept(s) is/are 2
Step-by-step explanation:
Y-intercepts are where the graph of a function cross over the y-axis. In this case, the line passes through y=2, which is the y-intercept.
Which inequality is equivalent to the given inequality? -4(x + 7) < 3(x - 2)
Answer:
Step-by-step explanation:
We must simplify and rearrange the variables to divide x in order to determine the comparable inequality to the supplied inequality, -4(x + 7) 3(x - 2).
Below are the steps to solve the problem:
-4(x + 7) < 3(x - 2)
Expanding the equation:
-4x-28<3x-6
Gather the variable term on one side and constants on the other:
Adding -4x and 28 on both sides:
-4x + 4x - 28 + 28 < 3x + 4x - 6 + 28
=>0 < 7x + 22
To make the coefficient of x positive, we divide the entire inequality by 7:
0/7 < (7x + 22)/7
=> 0 < x + 22/7
Consider the following pair of points.
(8,−8)
and (−5,−1)
Step 2 of 2 : Determine the midpoint of the line segment joining the pair of points.
The midpoint of the line segment joining the pair of points (8, -8) and (-5, -1) is (1.5, -4.5).
To find the midpoint, we need to take the average of the x-coordinates and the average of the y-coordinates of the two given points.
For the x-coordinate: (8 + (-5))/2 = 3/2 = 1.5
For the y-coordinate: (-8 + (-1))/2 = -9/2 = -4.5
Thus, the midpoint of the line segment is (1.5, -4.5).
In more detail, the midpoint formula is derived by averaging the x-coordinates and y-coordinates separately. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint (xm, ym) is given by:
xm = (x1 + x2)/2
ym = (y1 + y2)/2
In this case, the x-coordinates are 8 and -5, and their average is (8 + (-5))/2 = 1.5. The y-coordinates are -8 and -1, and their average is (-8 + (-1))/2 = -9/2 = -4.5.
Therefore, the midpoint of the line segment joining the two given points is (1.5, -4.5).
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87,959 to the nearest hundred
two points A and B, due to two spheres X and Y 4.0m apart, that are carrying charges of 72mC and -72mC respectively. Assume constant of proportionality as 9×10^9Nm²/C². Find the electric field strength at points A and B due to each spheres presence
Point B: Electric field strength due to sphere X = 2073.6 NC⁻¹ and Electric field strength due to sphere Y = -2073.6 NC⁻¹.
data: Spheres X and Y are 4.0 m apart. The charge on sphere
X = + 72 mC = 72 × 10⁻³ C.
The charge on sphere
Y = -72 mC = -72 × 10⁻³ C.
The constant of proportionality = 9 × 10⁹ Nm²/C².
The formula to calculate the electric field strength due to a point charge is
E = k q / r²
where E is the electric field strength, k is the Coulomb's constant (= 9 × 10⁹ Nm²/C²), q is the magnitude of the charge, and r is the distance from the charge.The electric field due to sphere X at point A is
EaX = [tex]k q / r²where r = 4.0 m, q = + 72 × 10⁻³ CSo, EaX = 9 × 10⁹ × 72 × 10⁻³ / (4.0)²EaX = 9 × 9 × 2 × 2 × 2 × 2 / 10[/tex]EaX = 2592 / 10EaX = 259.2
NC⁻¹The electric field due to sphere Y at point A is
[tex]EaY = k q / r²where r = 4.0 m, q = -72 × 10⁻³ CSo, EaY = 9 × 10⁹ × 72 × 10⁻³ / (4.0)²EaY = -9 × 9 × 2 × 2 × 2 × 2 / 10EaY = -2592 / 10EaY = -259.2[/tex]
NC⁻¹The electric field due to sphere X at point B is
[tex]EbX = k q / r²where r = 4.0 m, q = + 72 × 10⁻³ C + 72 × 10⁻³ C = 144 × 10⁻³ C.So, EbX = 9 × 10⁹ × 144 × 10⁻³ / (4.0)²EbX = 9 × 9 × 4 × 4 × 4 × 4 / 10EbX = 20736 / 10EbX = 2073.6[/tex]
NC⁻¹The electric field due to sphere Y at point B is
[tex]EbY = k q / r²where r = 4.0 m, q = -72 × 10⁻³ C - 72 × 10⁻³ C = -144 × 10⁻³ C. So, EbY = 9 × 10⁹ × -144 × 10⁻³ / (4.0)²EbY = -9 × 9 × 4 × 4 × 4 × 4 / 10EbY = -20736 / 10EbY = -2073.6 NC⁻¹[/tex]
Therefore, the electric field strength at points A and B due to each sphere's presence are: Point A: Electric field strength due to sphere X = 259.2 NC⁻¹ and Electric field strength due to sphere Y = -259.2 NC⁻¹.
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3,20,110 _1715 This is an mathematics question
The pattern between the numbers 3, 20, 110, and 1715 can be found using a mathematical method. In order to get the following number from each, there is a sequence that must be applied.Let's take a look at the sequence that was used to generate these numbers:
The first number is multiplied by 2 and then increased by 14 to get the second number. For example:
3 x 2 + 14 = 20
Then, the second number is multiplied by 3 and 20, and 110 is added.
20 x 3 + 110 = 170
The third number is multiplied by 4 and then increased by 110.
110 x 4 + 110 = 550
Finally, the fourth number is multiplied by 5 and then increased by 110.
550 x 5 + 110 = 2825
Therefore, using the above formula, the next number in the sequence can be calculated:
1715 x 6 + 110 = 10400
As a result, the sequence of numbers 3, 20, 110, 1715, 10400 can be calculated using the mathematical formula stated above.
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