what is the sum of the infinite geometric series? –288 –216 –144 –72
The sum of the infinite geometric series –288 –216 –144 –72 is -1152.
The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.
Given series, -288, -216, -144, -72, ...
The sum of the infinite geometric series can be calculated as:
Sum = [tex]\dfrac{a}{1 -r}[/tex]
Here, 'a' is the first term of the series and 'r' is the common ratio.
a = -288
The common difference can be calculated as:
r = [tex]\dfrac{(-216)}{(-288)}[/tex]
= [tex]\dfrac{3}{4}[/tex]
Substitute the values in the sum formula:
Sum = [tex]\dfrac{-288}{1 - \dfrac{3}{4}}[/tex]
It can be simplified as:
Sum = -288 [tex]\times[/tex] 4
= -1152
So, the sum of the infinite geometric series is -1152.
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vlad the impaler promotes many of his soldiers into generals (don't ask what happened to the past generals). vlad was told by his informers that the proportion is about 62%, but wants to estimate the proportion better by sampling soldiers until her margin of error for a 97% confidence interval is less than 0.007. how many soldiers should haley sample?
Vlad should sample 1733 soldiers to estimate the proportion with a margin of error of less than 0.007 and a 97% confidence level.
We can use the formula for the margin of error of a proportion:
ME = zsqrt(p(1-p)/n)
where ME is the margin of error, z is the critical value for a 97% confidence interval (which can be found using a table or calculator and is approximately 2.17), p is the estimated proportion (0.62), and n is the sample size.
We want to find n, so we can rearrange the formula and solve for n:
n = (z^2 * p * (1-p)) / ME^2
Substituting the values given, we get:
n = (2.17^2 * 0.62 * 0.38) / 0.007^2
n ≈ 1732.92
Since we need a whole number of soldiers, we round up to n = 1733.
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what punishment should be given to students
In school suspension
given COS x = 0.8, whas sine X? enter answer as decimal
Answer:
±0.6
Step-by-step explanation:
Pythagorean identity:
sin² x + cos² x = 1
sin² x + (0.8)² = 1
sin² x + 0.64 = 1
sin² x = 0.36
sin x = ±0.6
Find each set if R is the universal set.
{x∈R:[tex]x^2\geq 0[/tex]}^c
The set {x∈R:[tex]x^2\geq 0[/tex]}^c is the empty set, as there are no real numbers that are not included in the set of all real numbers.
To find the set {x∈R:[tex]x^2\geq 0[/tex]}^c, we first need to understand what the statement [tex]x^2\geq 0[/tex] means. This inequality simply states that any real number squared is always non-negative. Therefore, the set {x∈R:[tex]x^2\geq 0[/tex]} is equivalent to the set of all real numbers.
Now, to find the complement of this set, we need to look for all the elements that are not in the set of all real numbers. Since the universal set is R, which is the set of all real numbers, the complement of {x∈R:[tex]x^2\geq 0[/tex]} will be the empty set, since there are no real numbers that are not included in the set of all real numbers.
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Trig I’m so lost I tried and i just can’t get it
The value of the missing sides are;
1. 12. 9
2. 2. 0
3. 4. 6
4. 5. 3 degrees
How to determine the valueWe have that their are six trigonometric identities. These identities are;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Using sine identity
sin 57 = 10.8/x
cross multiply the values
x = 12. 9
2. Using cosine identity
cos 47 = x/3
cross multiply
x = 2. 0
3. Using the tangent identity;
tan 41 = 4/x
cross multiply
x = 4. 6
4. The angle of depression is ;
sin X = 27.6/300
sin X = 0. 092
X = 5. 3 degrees
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A shipping plane is flying from New York to Berlin, Germany. The total distance of the flight is 3960 miles. The flight is scheduled to reach Berlin in 7 hours. The airplane has traveled 2100 miles in the first 5 hours
The airplane traveling from New York to Berlin, Germany, has covered 2100 miles in the first 5 hours of its 7-hour journey, leaving a remaining distance of 1860 miles to cover to reach its destination.
To determine the remaining distance that the airplane needs to cover to reach Berlin, we can subtract the distance already traveled from the total distance of the flight. In this case, the airplane has covered 2100 miles in the first 5 hours of its 7-hour journey. Therefore, the remaining distance can be calculated as:
Total distance - Distance covered = 3960 - 2100 = 1860 miles
This means that the airplane still needs to cover a distance of 1860 miles to reach Berlin. We can use this information to estimate the speed at which the airplane needs to travel for the remaining two hours to reach its destination on time. To do this, we can divide the remaining distance by the remaining time:
Speed = Distance / Time = 1860 / 2 = 930 miles per hour
Therefore, the airplane needs to maintain a speed of 930 miles per hour to reach Berlin on time. It's important to note that weather conditions, air traffic, and other factors can affect the actual speed of the airplane during the remaining two hours of the flight, which should be taken into account by the pilot and the flight crew to ensure a safe and timely arrival at the destination.
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Solve the Application. In one week, Keith earns $896 in regular pay and $672 in overtime pay. A total of $275 is deducted from his paycheck for taxes. What is his take-home pay?
To calculate Keith's take-home pay, we need to subtract the taxes deducted from his total earnings.
Regular pay: $896
Overtime pay: $672
Total earnings: $896 + $672 = $1568
Taxes deducted: $275
Take-home pay: Total earnings - Taxes deducted
Take-home pay: $1568 - $275 = $1293
Therefore, Keith's take-home pay is $1293.
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please help plsssssss
1. 2x = 14 --> divide both sides by 2 --> x = 14/2 --> x = 7
2. x + 4 = 3 --> subtract 4 from both sides --> x = 3-4 --> x = -1
3. 3x + 6 = 12 --> subtract 6 from both sides --> 3x = 12-6 --> 3x = 6
4. 2x + 8 = 14 --> factor 2 out on the left side --> 2(x+4) = 14 --> divide both sides by 2 --> x + 4 = 14/2 --> x + 4 = 7
5. x + 5 = 4 --> factor -1 out on the left side --> -(-x-5) = 4 --> divide both sides by -1 --> -x-5 = 4/-1 --> -x-5 = -4
6. 2x + 4 = 3x - 5 --> subtract 2x from both sides --> 4 = 3x - 5 - 2x --> add 5 on both sides --> 4 + 5 = 3x - 2x --> 3x - 2x = 9
7. x - 8 = 24 --> add 8 on both sides --> x = 24 + 8 --> x = 32
8. 21 - 5x = 2 --> subtract 21 from both sides --> -5x = 2 - 21 --> -5x = -19 --> divide both sides by -1 --> 5x = -19/-1 --> 5x = 19
9. 4x + 2 = 8 --> add 2 on both sides --> 4x + 2 + 2 = 8 + 2 --> 4x + 4 = 10 --> factor 4 out on the left side --> 4(x+1) = 10 --> divide both sides by 4 --> x + 1 = 10 / 4 --> x + 1 = 2.5
10. (x-5) / 7 = 10 --> multiply both sides by 7 --> x-5 = 10 * 7 --> x-5 = 70
Solve the application.
A mason's assistant's rate of pay is $0.75 per cubic foot of earth moved. He moves 220 cubic feet of earth to dig a trench. What is his pay for this job?
$_________
The mason's assistant's pay for the job is $165.
To find the mason's assistant's pay for the job, we need to multiply the rate of pay per cubic foot by the number of cubic feet moved.
Rate of pay per cubic foot = $0.75
Number of cubic feet moved = 220
Pay for the job = $0.75 x 220 = $165
Therefore, the mason's assistant's pay for the job is $165.
The mason's assistant will earn $165 for this job.
To calculate the pay for the mason's assistant, follow these steps:
1. Determine the rate of pay per cubic foot: $0.75
2. Determine the total amount of cubic feet moved: 220 cubic feet
3. Multiply the rate of pay by the total cubic feet moved: $0.75 x 220
By multiplying the rate of pay ($0.75) by the total cubic feet moved (220), you get the total pay for the job:
$0.75 x 220 = $165
The mason's assistant will be paid $165 for moving 220 cubic feet of earth to dig the trench.
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meeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
See attached. ∠A is a right angle, ∠B and ∠D are acute, ∠C is obtuse.
Step-by-step explanation:
A right angle is defined as an angle equal to 90 degrees.
An acute angle is defined as an angle less than 90 degrees.
An obtuse angle is defined as an angle greater than 90 degrees.
Using this information we will classify all of the four given angles.
∠A is a right angle, 90 = 90
∠B is acute angle, 60 < 90
∠C is obtuse angle, 160 > 90
∠D is acute angle, 70 < 90
What is the remainder after dividing 2x^3 + 5x^2 – 3x + 1 by (x + 4)?
The remainder after dividing 2x³ + 5x² - 3x + 1 by x+4 is 9x+1
We have to find the remainder when we divide 2x³ + 5x² - 3x + 1 by x+4
Dividend is the number which is getting divided by some other number
2x² - 3x + 15 is the dividend
Divisor is the number which divides a number
x+4 is the divisor
In the given division the
2x² - 3x + 15
------------------
x + 4|2x³ + 5x² - 3x + 1
- (2x³ + 8x²)
--------------
-3x²- 3x
+(-3x² - 12x)
--------------
9x + 1
Hence, the remainder is 9x+1 when we divide 2x³ + 5x² - 3x + 1 by x+4
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What is 637000 in scientific notation
Answer:
6.37 x 10^5
This is it
an electric water heater consumes 5 kw for 2 hours per day. what is the cost of running it for one month (30 days) if electricity costs 12 cents/kw.h?
The cost of running the electric water heater for one month (30 days) would be $36, assuming the electricity costs 12 cents per kilowatt-hour.
To calculate the cost of running the electric water heater for one month, we need to determine the total energy consumption and multiply it by the cost per kilowatt-hour.
The water heater consumes 5 kW for 2 hours per day, so the daily energy consumption can be calculated as follows:
Daily energy consumption = Power (kW) × Time (hours) = 5 kW × 2 hours = 10 kWh
Next, we calculate the total energy consumption for one month (30 days):
Total energy consumption = Daily energy consumption × Number of days = 10 kWh/day × 30 days = 300 kWh
Finally, we multiply the total energy consumption by the cost per kilowatt-hour (12 cents/kWh) to find the cost of running the water heater for one month:
Cost = Total energy consumption × Cost per kilowatt-hour = 300 kWh × $0.12/kWh = $36
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when solving linear trig equations in terms of only sine or cosine, how do we know whether there will be solutions?
For linear trigonometric equations involving only sine or cosine, there will be solutions if the constant term on the other side of the equation falls within the range of -1 to 1.
When solving linear trigonometric equations in terms of only sine or cosine, we can determine whether there will be solutions by considering the range of values that sine and cosine can take.
For sine (sin) and cosine (cos), their values range from -1 to 1. If the equation involves only sine or cosine and is linear, it means the variable is not squared or involved in any higher powers. In such cases, the equation will have solutions if the constant term on the other side of the equation is within the range of -1 to 1.
For example, if we have the equation sin(x) = 0.5, it will have solutions because 0.5 is within the range of -1 to 1. However, if we have the equation sin(x) = 2, it will not have any solutions because 2 is outside the range of -1 to 1.
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3.2.2 Determine how many boxes of tiles Tshego will need if an extra 10% of the number of tiles must be added for cutting and breakages. (9)
The number of required tiles including the breakage and cut-offs are 37.
Firstly we will calculate the number of required tiles based on below mentioned formula-
Number of tiles required to cover the floor = Area covered by one tile × Total area to be tiled
Number of required tiles = 33.984
Rounding off the number
Number of required tiles = 34
Number of extra tiles required for breakage and cut-offs = 34 + 10% × 34
Number of extra tiles = 34 + 10/100×34
Performing multiplication, division, addition along with cancelling common zeroes of the number
Number of extra tiles = 34 + 3.4
Adding the values
Number of extra tiles = 37.4
Again rounding off the number
Number of extra tiles = 37
Hence, the total required number of tiles are 37 according to stated percentage of waste.
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Is -0.614035088 a rational number?
Yes, -0.614035088 is a rational number.
We know, A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers.
We have the number -0.614035088.
In this case, -0.614035088 can be expressed as the fraction -1227/1999, where both the numerator and denominator are integers.
Thus, Yes, -0.614035088 is a rational number.
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DUE TOMORROW!!
Whoever answers this first will get a prize
The prize is:
you get these girls messages that are saying your AMAZING!!
dentify whether this angle is acute, obtuse, right, or straight. (1 point)
angle that measures one hundred eighty degrees
a
Acute
b
Obtuse
c
Right
d
Straight
In conclusion, the correct answer is d) Straight.
The correct answer is d) Straight.
In geometry, an angle is formed by two rays that have a common endpoint. Angles can be classified based on the measure of their degree. A straight angle measures 180 degrees, which is the same as a straight line. It is formed by two opposite rays that point in opposite directions, and they create a straight line.
Therefore, an angle that measures 180 degrees is called a straight angle. In a straight angle, the two rays point in opposite directions and form a straight line. This angle is not acute, obtuse, or right because it doesn't form a triangle, and the degree measure is not less than 90 degrees or greater than 90 degrees.
In conclusion, the correct answer is d) Straight.
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If all questions answered and are correct I will give brainlessly
Answer:
13) 225
14) 289
15) 64
16) 8
Find F, Write your answer as an integer or as a decimal rounded to the nearest tenth.
The value of the length f is 6. 7
How to determine the valueTo determine the value, we have to know the different trigonometric identities.
These trigonometric identities are enumerated as;
sinecosinetangentcotangentsecantcosecantTo determine the length of f
Let us use the tangent identity, we have that;
tan θ = opposite/adjacent
substitute the values, we have;
tan 24 = f/15
Multiply the values, we get;
f = 0. 4452(15)
multiply the values
f = 6. 7
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y = 6x + 8
y =14× + 4
pretty please and PLEASE step by step.
methods either substitution, elimination, or equal values
Answer:
Step-by-step explanation:
1. Put the equations in order:
-14x+y=4(1)
-6x+y=8(2)
2. Eliminate a variable.
In this case, we want to eliminate y, so subtract the second equation from the first
(1)-(2) -8x=-4
x=-4/8
x=1/2
3. Now that we have one variable, we can use it to solve for y:
6(1/2) + 8=y
3+8=y
y=11
(1/2,11) is the answer.
Another way to do this is to set the first equation equal to the second equation:
6x+8=14x+4
8x=4
x=1/2
y=11
(1/2,11) is the answer!
We used elimination and equal values!
Please help!! I need it!! Will give brainliest!!!
find the length of the curve r(t) = sqrt(2)ti
To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.
First, we need to find r'(t):
r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i
The magnitude of r'(t) is ||r'(t)|| = sqrt(2).
So, the length of the curve is:
L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)
Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).
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Which statement about the graphs of these two functions is true?
I need help‼️‼️‼️‼️
Answer: #4- both graphs intersect the x-axis to the right of 0
Step-by-step explanation: put them in a graphing calculator or work it out by first solving for x then imputing that answer into the equation
Names of TV shows taped in New York are an example of which type of data? Answer a. Qualitative b. Statistic c. Quantitative d. Parameter
Option (A) Names of TV shows taped in New York are an example of qualitative data. Qualitative data is descriptive in nature and does not involve numerical values or measurements.
It deals with qualities or attributes that cannot be expressed numerically. In this case, the names of TV shows are characteristics that describe the nature of the data. Quantitative data, on the other hand, is numerical data that can be measured and expressed in numbers. A parameter is a measurable factor or variable that can be used to define a system, while statistics is a branch of mathematics that deals with data collection, analysis, and interpretation. In conclusion, since the names of TV shows are descriptive in nature and do not involve numerical values, they are an example of qualitative data.
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pls help asap i really need to get my homework done
Based on the information, we can infer that the area of the prism is: 981.3m²
How to calculate the area of the prism?To calculate the area of the prism we must calculate the area of each of the faces and then add them as shown below:
15m * 13m = 195 m²13m * 9m / 2 = 58.5m²15m * 15.81m = 237.15m²Now we must multiply each value by 2 because we have two faces of each in the prism. Additionally, we must add the results to obtain the total area:
195m² * 2 = 390m²58.5m² * 2 = 117m²237.15m² * 2 = 474.3m²390m² + 117m² + 474.3m² = 981.3m²Learn more about surface area in: https://brainly.com/question/29298005
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Please help me thanks. everything i need help with is due this week.
Answer: 80
Step-by-step explanation:
10x5=50 10x2=20 2x5=10
What is the difference in the intensity between a a 3.2 and a 6.5 earthquake. how is earthquake intensity a logarithmic equation
A 4.2 earthquake's energy release is 10 times more than a 3.2 earthquake's energy release despite the 3.2 earthquake's amplitude being 10 times smaller.
Now, A 3.2- to 6.5-magnitude earthquake has a substantial difference in intensity.
In actuality, a 6.5 earthquake has a magnitude almost 1000 times greater than a 3.2 earthquake.
The Richter scale, which uses a logarithmic scale to assess earthquake intensity, is the reason behind this.
Since, the Richter scale uses a seismograph to estimate the amplitude of earthquake waves, it is a logarithmic equation.
Each unit increase on the Richter scale causes an exponential increase in the energy released by the earthquake, which is proportional to the amplitude of the earthquake waves.
For instance, a 4.2 earthquake's energy release is 10 times more than a 3.2 earthquake's energy release despite the 3.2 earthquake's amplitude being 10 times smaller.
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F(x)=(x-5)^2-20 for all real numbers x what the range of f
The range of the function f include the following: [-20, ∞].
What is a range?In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:
Range = [-20, ∞] or -20 ≤ y ≤ ∞.
Domain = [-∞, ∞] or -1 < x < ∞.
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PLEASE HELP< DONT UNDERSTAND!!!!!!
The corresponding IQ score for a z-score of 1.86 is 127.9.
Option A.
What is the corresponding IQ?If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Given a z-score of 1.86, the corresponding IQ score is calculated as follows;
The formula for IQ score is given as;
IQ = (z-score x standard deviation) + mean
Substituting the given values, the value of IQ score is calculated as;
IQ = (1.86 x 15) + 100
IQ = 27.9 + 100
IQ = 127.9
Therefore, the corresponding IQ score for a z-score of 1.86 is 127.9. The answer is A.
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