The required simplified value of the given expression [tex]\dfrac{2^{3x+1}-2^{3x}}{4*2^{3x - 1}}[/tex] is 1/2.
What is a rational expression?A rational expression is a mathematical expression that is the ratio of two polynomial expressions. That is, a rational expression is formed by dividing one polynomial expression by another polynomial expression.
Here,
Given expression,
[tex]=\dfrac{2^{3x+1}-2^{3x}}{4*2^{3x - 1}}[/tex]
Rewriting the equation by splitting the terms in numerator and denominator in order to take common terms out and make the expression more simple.
We can write [tex]2^{3x+1} = 2^{3x} * 2[/tex] and [tex]2^{3x-1} = 2^{3x} /2[/tex] so,
Given expression becomes, hence cancel the common terms.
[tex]=\dfrac{2^{3x}*2-2^{3x}}{4*2^{3x}/2}\\=1/2[/tex]
Thus, the required simplified value of the given expression [tex]\dfrac{2^{3x+1}-2^{3x}}{4*2^{3x - 1}}[/tex] is 1/2.
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please help me asap i will give brainliest
Answer:
x = 5.88
Step-by-step explanation:
by simplifying both sides of the equation, then isolating the variable.
A cylinder is sliced parallel to its base. The area of the cross section is 36π in2 . What is the radius of the cylinder?
If a cylinder is sliced parallel to its base. The area of the cross section is 36π inch square, then the radius of the cylinder is 6 inches
If we slice a cylinder parallel to its base, we get a circle with the same radius as the cylinder.
We are given that the area of the cross section is 36π in square units. Since the cross section is a circle, we can use the formula for the area of a circle to find the radius.
The formula for the area of a circle is:
A = πr^2
where A is the area of the circle and r is the radius of the circle.
We are given that the area of the cross section is 36π. So, we can set A = 36π and solve for r:
36π = πr^2
Dividing both sides by π:
36 = r^2
Taking the square root of both sides:
r = ±6 inches
Since radius cannot be negative, the radius of the cylinder is 6 inches
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Rosetta drives 85 kilometres in 1 hour 15 minutes. Work out her average speed in kilometres per hour.
Answer:
68 kilometers per hour
Step-by-step explanation:
Rosetta's average speed is 85 kilometers per hour. This can be determined by dividing the total distance traveled (85 kilometers) by the total time taken (1 hour and 15 minutes, or 1.25 hours). Therefore, 85 kilometers divided by 1.25 hours is equal to 68 kilometers per hour.
Answer: 68 kilometers per hour (look at the image for the explanation)
Step-by-step explanation:
Alex and his father took a taxi cab that charges $2.60 per mile plus $3.00 for the two passengers, and they paid a total of $18.60. Alex wrote the equation 18.60=2.60b+3.00 for this situation and found b=6, where b represents the number of miles the taxi traveled. How could Alex correctly solve this problem without using the equation?
Answer:
Answer is explained Below
Step-by-step explanation:
He could subtract 3 from both sides of the equation first. Then he could divide both sides to get D alone. When you do the D=
Estadio Azteca, a stadium in Mexico City, has a capacity of 1. 04 X 10% people. One day,
spectators filled Estadio Azteca in 25 minutes. What was the average number of people
who entered the stadium per minute? Express your answer in scientific notation.
1. What division expression represents the average number of people
per minute?
2. How would you express the divisor in scientific notation?
3. Rewrite your division expression from Exercise 1 with the divisor
expressed in scientific notation.
4. Use the Associative Property to regroup. Then simplify.
5. In scientific notation, what was the average number of people who
entered Estadio Azteca per minute?
1. The division expression represents the average number of people per minute is (1.04 x 10⁶) / 25
2. The divisor in scientific notation is (2.5 x 10¹)
3. The rewritten expression is (1.04 x 10⁶) / (2.5 x 10¹)
4. The simplified expression is (1.04 x 10⁶) / (2.5 x 10¹)
5. The average number of people who entered Estadio Azteca per minute is 4.16 x 10⁴.
1. The division expression that represents the average number of people per minute is the total number of spectators who filled Estadio Azteca (1.04 x 10⁶) divided by the amount of time it took them to enter (25 minutes). This expression can be written as
=> (1.04 x 10⁶) / 25
2. To express the divisor (25) in scientific notation, we would need to move the decimal point three places to the left, giving us
=> (2.5 x 10¹)
3. Rewriting the division expression from Exercise 1 with the divisor expressed in scientific notation, we get
=> (1.04 x 10⁶) / (2.5 x 10¹)
4. We can use the Associative Property to regroup the expression as
=> (1.04 x 10⁶) / (2.5 x 10¹)
=> 4.16 x 10⁴.
5. In scientific notation, the average number of people who entered Estadio Azteca per minute was 4.16 x 10⁴.
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If 3 pizzas cost $26.97, one pizza is $ ____
What is the binomial probability formula used for?
The binomial probability formula is used to calculate the probability of a specific number of successes in a fixed number of independent trials, where each trial can only result in success or failure. It is used to model situations where there are only two possible outcomes for each trial, and where the trials are independent and identically distributed.
The formula for binomial probability is:
[tex]P(x) = (n choose x) * p^x * (1 - p)^{n-x}\\[/tex]
where P(x) is the probability of x successes in n trials, p is the probability of success on each trial, (n choose x) is the binomial coefficient which gives the number of ways to choose x successes from n trials, and (1 - p) is the probability of failure on each trial.
The binomial probability formula can be used in a variety of applications, such as:
Predicting the probability of a certain number of defective products in a production runEstimating the likelihood of a certain number of people out of a sample having a particular characteristicAnalyzing the probability of winning a certain number of games in a sports seasonFor more questions on Binomial Probability
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Please help
The step function g(x) is defined as shown
For given Step function also known as piecewise function, The range of g(x) is {-3,2,5} i.e. C.
What exactly is a piecewise function?
A piecewise function has several definitions in various x intervals. The graph of a piecewise function is split into sections that correspond to each of its definitions. The absolute value function is an outstanding example of a piecewise function. Let us look at why it was given that name. We know that an absolute value function is defined as f(x) = |x|.
f(x)=(x if x x≥0)
-x if x<0)
This piecewise function should be interpreted as
When x is higher than or equal to 0, f(x) equals x.
When x is less than zero, f(x) equals -x.
Now,
As range of a given function is given by its y values, here it will be given by values of g(x) and as we can see from question for values of x, g(x) is always equal to -3,2,5.
Hence,
The range of g(x) is {-3,2,5}.
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How many pounds is 5 kg in pounds?
5 kilograms (kg) is equivalent to 11.02 pounds (lbs). To convert kilograms to pounds, you need to use the conversion factor of 2.20462 pounds per kilogram.
This means that you can multiply the number of kilograms by this conversion factor to get the equivalent weight in pounds. The conversion from kilograms to pounds is commonly used in daily life, especially for weighing objects such as produce, parcels, and personal belongings.
Understanding how to convert between different units of weight is also important for international travel and trade, where different countries may use different units of measurement.
It's important to note that while kilograms and pounds are both units of weight, they are not interchangeable with other units of measurement such as volume or length. Additionally, some countries use different units of weight such as grams or ounces, so it's important to pay attention to the units used in a given context.
In summary, 5 kilograms is equal to 11.02 pounds, and understanding how to convert between different units of weight is important in daily life, international trade, and other applications that involve measuring weight.
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Which theorem or postulate proves that △ABC and △DEF are similar?
Select from the drop-down menu to correctly complete the statement.
The two triangles are similar by the ________.
A. AA Similarity Postulate
B. SSS Similarity Theorem
C. SAS Similarity Theorem
Option A. AA Similarity Postulate. The AA Similarity Postulate is a geometric principle that states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
This means that their corresponding sides are in proportion, and the triangles have the same shape, but not necessarily the same size. This postulate is one of the ways to prove the similarity of two triangles. In the case of the given question, if we know that two angles of one triangle are congruent to the two angles of another triangle, then we can use the AA Similarity Postulate to prove that the triangles are similar. This principle is widely used in geometry and helps to establish relationships between different shapes and figures.
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Thuli invests R5000 for 3 years at 8% p.a simple interest.What is the total value of Thuli's investment after 3 years?Calculate the answer.
The total value of Thuli's investment after 3 years is R6200
What is the total value of Thuli's investment after 3 years?From the question, we have the following parameters that can be used in our computation:
principal, P = 5000
Rate = 8%
Time = 3 years
Using the above as a guide, we have the following:
Amount = P * (1 + RT)
Substitute the known values in the above equation, so, we have the following representation
Amount = 5000 * (1 + 8% * 3)
Evaluate
Amount = 6200
Hence, the amount is R6200
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What size is 65 inch in CM?
The value of length of 65-inch after converting in decimals is 165.1 centimeters.
The conversion is important because some countries, such as those in Europe and Asia, use the metric system, which is based on centimeters, while others, such as the United States, use the imperial system, which is based on inches.
Knowing the conversion rate between these two systems can be useful in many situations, especially when it comes to purchasing electronics or other goods that are measured in different units of measurement.
Here, to convert inches to centimeters the formula used is:
1inch is equal to 2.54 cm.
In this case, 65 x 2.54 equals 165.1 centimeters.
The length of 65-inch is equal to approximately 165.1 centimeters.
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A football club increases the number of seats in its stadium to 66,000 The manager of the club states they can now seat exactly 45% more people than previously. Explain why the manager cannot be correct
The manager's claim that the new stadium can seat exactly 45% more people than previously is not correct. Instead, the new stadium can accommodate 145% of the previous number of seats, which is an increase of 45% over the original capacity
If a football club increases the number of seats in its stadium by 45%, it means that the new stadium can accommodate 145% of the previous number of seats.
Suppose the previous capacity of the stadium was x seats. Then, the new capacity of the stadium can be calculated by multiplying the previous capacity by 1.45 (which represents the 45% increase in capacity):
New capacity = x × 1.45 = 1.45x
However, the manager of the club claims that the new capacity of the stadium is exactly 45% more than the previous capacity, which means that the new capacity should be:
New capacity = x + (0.45x) = 1.45x
This equation suggests that the increase in capacity is not 45%, but rather an increase of the original capacity by 45%. This is not the same as the increase of 45% over the original capacity.
Therefore, the manager's claim that the new stadium can seat exactly 45% more people than previously is not correct. Instead, the new stadium can accommodate 145% of the previous number of seats, which is an increase of 45% over the original capacity.
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special right triangles calculator
Online calculators can solve for sides, angles, area, and perimeter of special right triangles, such as 45-45-90 and 30-60-90.
There are numerous web-based number crunchers that can assist you with addressing exceptional right triangles, like the 45-45-90 and 30-60-90 triangles. A few instances of extraordinary right triangle mini-computers are:
Calculator.net: This site has a unique right triangle number cruncher that can settle for the sides, points, and area of 45-45-90 and 30-60-90 triangles.
Omni Number cruncher: This site has a unique right triangle mini-computer that can settle for the sides, points, region, and border of 45-45-90 and 30-60-90 triangles.
Mathsisfun.com: This site has an intelligent apparatus that can help you comprehend and address exceptional right triangles, including 45-45-90 and 30-60-90 triangles.
These adding machines can save you time and assist you with rapidly tackling extraordinary right triangles, particularly assuming that you are chipping away at calculation issues or developments.
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The complete question is:
Explain about special right triangles calculator.
What is r?
150°
115⁰
130⁰
O
110°
105°
r
Answer:
r = 110
Step-by-step explanation:
We can see that we have a polygon that has 6 sides. So we can use the formula [tex]S = (n-2) * 180[/tex] to get the answer to create our algebraic equation, n being the number of sides of the polygon.
[tex]S=(6-2) * 180[/tex]
Solve
[tex]4*180[/tex]
[tex]s=720[/tex]
Now that we have our number, we just have to create an algebraic equation to solve for r
[tex]r+110+150+115+130+105=720[/tex]
Add like terms
[tex]r+610=720[/tex]
Subtract 610 on both sides
[tex]r=110[/tex]
To check our work, we can add all of our angle measurements together.
[tex]110+110+150+115+130+105=720[/tex]
Because this equals 720, we know for sure r = 110.
Instructions & Problem in picture
The temperature (in degrees Celsius of)Delhi during a particular Fortnight in the month of June is given below 38,40,42,43,45,39,40,37,38,41,44,44,40,42,40 rearrange the data in descending order and find the range
Answer:
Arranging the temperature data in descending order, we get:
45, 44, 44, 43, 42, 42, 41, 40, 40, 40, 39, 38, 38, 37, 36
The range of a set of data is the difference between the highest and lowest values.
Here, the highest temperature is 45°C and the lowest temperature is 36°C. Therefore, the range is:
Range = highest value - lowest value = 45°C - 36°C = 9°C
So the range of the temperature data is 9°C.
What is the conversion of 45 c to fahrenheit ?
The converted value of Celsius to Fahrenheit represented as 45 Celsius equals to 113 Fahrenheit.
Temperature is measured by the standard units which is defined as Celsius and Fahrenheit .
Formula which defines the relation of Celsius and Fahrenheit is equal to
(°C × 9/5) + 32 =°F
Now Substitute the given value 45 degree Celsius and convert into Fahrenheit we have,
(45°Celsius × 9/5) + 32
= ( 405 / 5 ) + 32
= ( 81 ) + 32
= 113°Fahrenheit
Therefore, the converted value from Celsius to Fahrenheit for the given temperature 45 Celsius is given by 113 Fahrenheit.
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what is the roman numeral l?
The Roman numeral number I means the number "1".
In roman numerals, the counting is represented by using the basic English alphabets in the Upper Case.
The roman numeral I means the number "1". For representing 10 we use "X".
When we have to write 1, 2, 3 we use I, II, III respectively and when we use want to show 5 we use "V" in roman numerals. More English letters like L, C etc. are also used to depicts certain other big numbers in the roman numbers. It is to be noted that one alphabet cannot be used more than three times in an number.
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how many minutes are in 24 hrs
Answer:
There are 1440 minutes in 24 hours.
Step-by-step explanation:
24 x 60 = 1440
Hope this helped. Have a good day!
What is the Z Score for a 99 confidence interval?
The Z score for a 99% confidence interval is approximately 2.576.
A confidence interval is a range of values that, with a given degree of certainty, is likely to contain the real value of a population parameter.
For example, a 99% confidence interval means that if we were to take repeated samples of the same size from the same population
To figure the interval estimate for each sample,
Approximately 99% of these intervals would contain the true population parameter.
To find the Z score for a 99% confidence interval,
We can make use of a calculator or a conventional normal distribution table.
The Z score for a 99% confidence interval corresponds to the point on the standard normal distribution
Where the area to the right of the Z score is 0.01
(As the confidence interval is split evenly into two tails, each with a probability of 0.005).
Utilizing a standard normal distribution table or calculator,
We find that the Z score for a 99% confidence interval is approximately 2.576.
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What is a value of inches to the nearest hundredth? 1/22
Answer:
Step-by-step explanation:
0.14285714285714286
How to convert 1.77 meters to feet?
After converting 1.77 meters to feet its value is equal to 5.8071 feet ( approximately ) .
Conversion of meters to feet we get,
Meter and feet both are the units used to measure length.1 meter is equal to 3.28084 feet
Substitute the value given meters to convert into feet.
Now convert 1.77 meters to feet
⇒ 1.77 meters = ( 1.77 ) × ( 3.28084 ) feet
⇒ 1.77 meters = 5.8070868 feet
⇒ 1.77 meters = 5.8071 feet ( approximately )
Therefore, the conversion unit of 1.77 meters to feet is given by 5.8071 feet ( approximately ) .
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On a scale drawing of a basketball court, 1 inch equals 8 feet. What is the actual area, in square feet, of the basketball court if the scale drawing is 11.75 inches by 6.25 inches
Therefore , the solution of the given problem of area comes out to be
the actual area of the basketball court is 4,700 square feet.
What is a Surface Area ?Its surface area is a reliable indicator of its overall size. When figuring out the right triangle's squared, the environment is taken into account. The surface area of everything determines its overall size. The total of the volumes from each of the twelve vertical sides makes up the water volume inside a cuboid. Utilize the following formula to get the box's dimensions: The region is represented by 2lh, 2lw, & 2hW. (SA). The area is represented by the flexible shape's entire surface area.
Here,
First, let's find the length and width of the basketball court in feet using the scale:
Length = 1 inch on the drawing represents 8 feet in reality
Length of the drawing = 11.75 inches
Actual length = 8 feet/inch × 11.75 inches = 94 feet
Width = 1 inch on the drawing represents 8 feet in reality
Width of the drawing = 6.25 inches
Actual width = 8 feet/inch × 6.25 inches = 50 feet
Now, we can find the actual area of the basketball court:
Actual area = Actual length × Actual width
Actual area = 94 feet × 50 feet
Actual area = 4,700 square feet
Therefore, the actual area of the basketball court is 4,700 square feet.
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what is 5pm military time
5:00 pm in military time is 1700 hours. Military time, also known as the 24-hour clock, is a system of timekeeping used by the military, emergency services, and other organizations around the world.
In this system, the day is divided into 24 hours, starting at midnight (0000 hours) and ending at midnight the following day (2400 hours).
To convert from standard time (AM/PM) to military time, you can simply add 12 hours to any time after 12:00 pm. For example, to convert 5:00 pm to military time, you would add 12 hours to 5:00 pm, which gives you 17:00 or 1700 hours.
Military time is commonly used in situations where time needs to be communicated clearly and without confusion, such as in aviation, transportation, and healthcare. It can also be useful in everyday life to avoid confusion and ensure accurate scheduling.
In summary, 5:00 pm in military time is equivalent to 1700 hours, and understanding how to convert between military time and standard time can be useful in a variety of contexts where clear and accurate timekeeping is important.
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f(x)=x^2+7
find x if f(x) = 24
Write in ascending order
x= _______ and ______
Answer:
[tex]\huge\boxed{\sf x = \pm \sqrt{17} }[/tex]
Step-by-step explanation:
Given function:f(x) = x² + 7
Given that, f(x) = 24
24 = x² + 7
Subtract 7 from both sides24 - 7 = x²
17 = x²
Take square root on both sides x = ±√17So,
x = √17 or x = -√17
[tex]\rule[225]{225}{2}[/tex]
what is 10000m to miles?
To convert meter into miles we simply have to divide meter by 1609.34 so we have 1000 m as 6.21 miles.
Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.
The SI base unit of length is the metre (or metre; US spelling), which is denoted by the letter m.
first described in 1793 as a ten millionth of the distance between the equator and the North Pole, but was later redefined in 1799 to refer to a prototype metre bar (this bar was changed again in 1889).
The imperial unit system uses the symbol mi to designate the mile as a unit of length.
Although it was initially an English unit, it was adopted by numerous nations, each of which had a somewhat different definition. However, the English mile is 63,360 inches, 5280 feet, or 1760 yards.
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HELP ASAP
The table shows input and output values of a function given a rule. Which function
represents the rule?
Input: x, a number; Output: y, 3 less than 2 times x
Input, x: -2 -1 0 1 2
Output, y: -7 -5 -3 -1 1
y=2x+3
y=2x-3
y=-3x+2
y=2x
Answer:I think its A.
Step-by-step explanation:
I'm too lazy too explain you got your answer please be happy
Measurement math word problems. 25 pts, show working out!
Answer:
bumps down
Step-by-step explanation:
65+82+14+0=161/4=40.25
40.25/65=0.619 this is lowest, so highest accurate
40.25/82=.490
40.25/14=2.875
subtract
6 1/2 - 3 9/11
Answer: 2 15/22
Step-by-step explanation: To solve this, let's first turn the mixed numbers into improper fractions. When we do so, we get 13/2 and 42/11. Now, we make a common denominator. We can turn both denominators into 22. When we do so, we get 143/22 and 84/22. Now, we subtract. When we subtract the two fractions, we get 2 15/22.