We can use the trigonometric identities to find the exact values of the expressions.
First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:
cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25
cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)
Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):
sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425
cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85
Finally, we can use the quotient identity for tangent to find tan(alpha + beta):
tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85
Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.
A baseball team has the starting and relief pitchers shown in the table. The manager selects a pitcher at random. Find the probability that the pitcher is left-handed.
Pitchers on Baseball Team (Table)
Pitchers Number
Left-handed starters 1
Right-handed starters 4
Left-handed relievers 2
Right-handed relievers 1
Okay, here are the steps to find the probability the randomly selected pitcher is left-handed:
1) There are 1 left-handed starter, 4 right-handed starters, 2 left-handed relievers and 1 right-handed reliever.
2) In total, there are 1 + 4 + 2 + 1 = 8 pitchers.
3) Of the 8 pitchers, 1 + 2 = 3 are left-handed.
4) So the probability the randomly selected pitcher is left-handed = (3/8) = 3/8 = 0.375
Therefore, the probability that the randomly selected pitcher from the team is left-handed is 0.375.
Let me know if you have any other questions!
A hamster runs at a speed of 16 centimeters per second in a wheel of radius 15 centimeters.
a) What is the angular velocity of the wheel? (in radians/sec)
b) How fast will the wheel spin in revolutions per minute?
a) The angular velocity of the wheel is approximately 1.0667 radians per second. b) The wheel will spin at approximately 10.16 revolutions per minute.
What is angular velocity?Angular velocity is a measure of how quickly an object rotates or revolves around a fixed point, such as an axis or a center of rotation. It is a vector quantity that describes the rate of change of an object's angular position with respect to time, and is usually expressed in units of radians per second (rad/s) or degrees per second (deg/s).
According to given information:a) To find the angular velocity of the wheel, we can use the formula:
angular velocity = linear velocity / radius
In this case, the linear velocity of the hamster is 16 centimeters per second, and the radius of the wheel is 15 centimeters. So, we have:
angular velocity = 16 / 15
angular velocity = 1.0667 radians per second
Therefore, the angular velocity of the wheel is approximately 1.0667 radians per second.
b) To find the speed of the wheel in revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute. There are 2π radians in one revolution, and 60 seconds in one minute. So, we can use the following formula:
angular velocity (in revolutions per minute) = angular velocity (in radians per second) * 60 / 2π
Plugging in the angular velocity we found in part (a), we get:
angular velocity (in revolutions per minute) = 1.0667 * 60 / 2π
angular velocity (in revolutions per minute) ≈ 10.16 revolutions per minute
Therefore, the wheel will spin at approximately 10.16 revolutions per minute.
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Given cos A = 3/10 and tan A < 0 , find sin A .
Answer: Since we know that cos A = 3/10, we can use the Pythagorean identity to find sin A:
sin^2 A + cos^2 A = 1
sin^2 A = 1 - cos^2 A
sin A = sqrt(1 - cos^2 A)
Substituting cos A = 3/10, we get:
sin A = sqrt(1 - (3/10)^2)
sin A = sqrt(1 - 9/100)
sin A = sqrt(91)/10
Since we also know that tan A < 0, we know that the sine and tangent of A have opposite signs, and therefore sin A is negative.
Therefore:
sin A = -sqrt(91)/10
Step-by-step explanation:
A chef makes batches of dumpling wrappers for shrimp dumplings. She uses 2 cups of flour
for each batch and a total of an additional cup of flour to keep the dough from sticking.
She uses 21 cups of flour to make n batches of dumpling wrappers. How many batches of
dumpling wrappers does the chef make?
Answer:
7 batches
hope this helps
Step-by-step explanation:
1 n (batches of dumpling wrappers) = 3 cups flour
n = 21 / 3
n = 7
The chef can make 7 batches of dumpling wrappers :D.
A bakery owner wants to keep his bakery open a few more hours every evening. He wants to
conduct a survey to determine whether extending the bakery's hours would be what customers
want. Which survey method would likely produce the most representative sample?
A. Ask 20 of the bakery's employees as they arrive for work.
B. Ask the first 20 customers who enter the bakery tomorrow.
C. Ask 20 of the bakery's regular suppliers as they make deliveries.
D. Ask 20 customers as they visit the bakery over the course of a day.
"Ask 20 customers as they visit the bakery over the course of a day." would likely produce the most representative sample.
What is sample?In statistics, a sample refers to a group of individuals or objects that are selected from a larger population and used to represent that population for the purpose of statistical analysis and inference. A sample is often used because it is impractical or impossible to examine every member of the population, so a smaller group is chosen that is expected to be representative of the larger population. The goal of sampling is to obtain accurate and reliable information about the population by studying the characteristics of the sample.
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Consider the statement “If you are under age 17, then you cannot attend this movie.”
a. Write the converse.
b. Write the inverse.
c. Write the contrapositive.
a. The converse, inverse and contrapositive are "If you cannot attend this movie, then you are under age 17.", "If you are over age 16, then you can attend this movie." and "If you can attend this movie, then you are not under age 17."
Writing the other versions of the statementThe original statement is an example of a conditional statement, which is a statement of the form "if A, then B." The part that comes after "if" is called the hypothesis, and the part that comes after "then" is called the conclusion.
To find the converse of the statement, we switch the hypothesis and conclusion. The converse of a conditional statement may or may not be true. In this case, the converse is not true.
To find the inverse of the statement, we negate both the hypothesis and conclusion. The inverse of a conditional statement may or may not be true. In this case, the inverse is not true.
To find the contrapositive of the statement, we switch and negate both the hypothesis and conclusion. The contrapositive of a conditional statement is always true if the original statement is true. In this case, the contrapositive is true.
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ANSWER Quick Due in 5 minutes!!!!!!
The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 18, with an IQR of 16 Bus 47, with an IQR of 24 Bus 18, with a range of 16 Bus 47, with a range of 24
IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers.
Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.
WHAT IS IQR?An indicator of statistical dispersion used to describe the variability of a dataset is the interquartile range (IQR). It is derived by subtracting a dataset's 75th percentile (Q3) from its 25th percentile (Q1). When compared to other measures of variability like range, the IQR represents the middle 50% of the data and is less susceptible to outliers.
We must contrast the measurements of variability for the two buses in order to determine which one is more reliable. We can utilize range and interquartile range as measurements of variability. (IQR).
The range of a dataset is the difference between its maximum and minimum values.
The range for Bus 18 is 16 (22 - 6), whereas the range for Bus 47 is 24. (28 - 4).
As a result, Bus 47's range is greater than Bus 18's.A measure of variability that is less impacted by outliers than the range is the interquartile range (IQR). It is determined as the difference between a dataset's third and first quartiles (Q3 and Q1, respectively).
The IQR is 16 for Bus 18 (Q3 - Q1 = 22 - 6)
The IQR for Bus 47 is 24 (Q3 - Q1 = 28 - 4"). Bus 18 therefore has a lower IQR than Bus 47.IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers. Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.
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in the number below, how many times greater is the number represented by the digit in the thousands place than the number represented by the digit in the hundreds place?
57,762
Answer:
Ten times greater
Step-by-step explanation:
700 x 10 = 7000
Answer:
it will be ten times greater
Step-by-step explanation:
What is the least whole number that rounds to 570 when rounded to the nearest ten?
What is the greatest whole number that rounds to 570 when rounded to the nearest ten?
Use the number pad to enter your answers in the boxes.
Least number:
Greatest number:
Answer:
Least: 565
Greatest: 574
Step-by-step explanation:
564 would round down to 560 and 575 would round to 580
Helping in the name of Jeus.
The least whole number that rounds to 570 when rounded to the nearest ten is 570. The greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
Explanation:To find the least whole number that rounds to 570 when rounded to the nearest ten, we need to look at the digit in the tens place. In this case, the tens digit is 7. Since the number can only round up or down, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 570 than to 580, we can round down to 570. Therefore, the least whole number that rounds to 570 when rounded to the nearest ten is 570 itself.
On the other hand, to find the greatest whole number that rounds to 570 when rounded to the nearest ten, we again need to look at the digit in the tens place. Since the tens digit is 7, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 580 than to 570, we can round up to 580. Therefore, the greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
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Does standard deviation means independent events
Standard deviation does not mean independent events.
Does standard deviation means independent events?No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.
Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.
Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.
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What’s the length of side AB?
tan = 1/√3= perpendicular/ base
1/√3 = AB / AC
AB / 6 = 1/√3
AB = 6/√3
4. Assuming that the rectangles have whole number side lengths, why is it possible to draw two different rectangles that have an area of 30 square inches but not possible to draw two rectangles with an area of 7 square inches?
Answer:
hm
Step-by-step explanation:
The reason why it is possible to draw two different rectangles that have an area of 30 square inches is that there are multiple pairs of whole numbers that multiply to 30. For example, a rectangle with dimensions 5 inches by 6 inches has an area of 30 square inches, and so does a rectangle with dimensions 2 inches by 15 inches.
However, the number 7 is a prime number, which means it can only be divided evenly by 1 and itself. Therefore, the only way to get an area of 7 square inches for a rectangle is by multiplying 1 and 7, which means the dimensions of the rectangle would be 1 inch by 7 inches. Since there are no other pairs of whole numbers that multiply to 7, it is not possible to draw two different rectangles with an area of 7 square inches.
I need help with this please
Answer:
Step-by-step explanation:
just add the two numbers up 576x1 1/2= 864
Hurry please combine Leon’s results and Celia’s results to find the experimental probability of spinning a 4
The experimental probability of spinning a 4 will equals to 0.3.
How to find the experimental probability of spinning a 4?Outcome Tally Frequency
1 IIII 4
2 III 3
3 IIIIIIII 7
4 IIIIII 6
Total 20
The probability of spinning a 4:
= 6/20
= 3/10
= 0.3
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Which missing x-value would make the table a function?
we can replace the second occurrence of x = -2 with x = 1:
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
For the table to be a function, each x-value must correspond to a unique y-value. To determine the missing x-value, we need to find if there are any repeated x-values with different y-values.
The x-value 3 is paired with y-values -3 and -1, which means that the table is not a function. Therefore, we need to replace one of the x-values that appears twice with a different value.
Since x = 0 is already paired with y = 5, we cannot use 0 as the replacement. The only other x-value that appears more than once is x = -2. Therefore, we can replace one of the occurrences of x = -2 with a different value.
For example, we can replace the second occurrence of x = -2 with x = 1:
x y
3 -3
1 4
-2 -1
-2 -2
0 5
Now each x-value corresponds to a unique y-value, so the table represents a function.
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You own 23 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
The probability that the CDs are in alphabetical order is
The probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.
What is combination?
In mathematics, a combination is a way of selecting objects from a larger group of objects, where the order of selection is not important. A combination is a subset of objects that are chosen from a larger set without regard to the order in which they are selected.
The formula is given by:
C(n, r) = [tex]\frac{n!}{r!* (n - r)!}[/tex]
The total number of ways to choose 5 CDs from a collection of 23 CDs is given by the combination formula:
C(23, 5) = [tex]\frac{23!}{5!* (23 - 5)!}[/tex]
= 33649
This means there are 33649 different ways to arrange 5 CDs out of the 23 CDs.
Out of these 33649 ways, only one arrangement is alphabetical. For this to happen, the first CD chosen must be the first one alphabetically, the second CD chosen must be the second one alphabetically, and so on.
The first CD can be any of the 23 CDs. However, once the first CD is chosen, there is only one CD that can be the second one alphabetically, two CDs that can be the third one alphabetically, and so on. Therefore, the probability of choosing 5 CDs in alphabetical order is:
P = 1 / C(23, 5)
P = 1 / 33649
P ≈ 0.00003
So the probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.
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A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.6 in. The slant height of the pyramid is 88.9 in. What is the height of the pyramid?
NEED AN ANSWER ASAP! IT'S DUE TOMORROW
find the smallest number that is a multiple off all 2,3,4,5,6,8 and 9
PLSSS HELP ME ITS DUE TOMORROW!!!!!
What is the height, h, of the rectangular prism shown below?
Round your answer to the nearest tenth.
h
The height is
4
√34
units.
3
The height is 3 units.
We have,
l = 4 and b= 3
Using Pythagoras theorem
d² = l² + b²
d² = 4² + 3²
d² = 16 + 9
d² = 25
d= 5 unit
let h be the height.
Again, using Pythagoras theorem
34 = 25 + h²
h² = 9
h= 3 unit
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Find the area of the figure. Round to the nearest hundredth when necessary.
6in
14in
26in
15in
The answer is 1,764 in^2
which of the following describes the graph
Therefore, the graph of the given set is: closed circles on 1 and 4 with a line segment between.
How should an equation be set up to determine the value of x?A common form for an algebraic expression is one of the following: addition, subtraction, multiplication, or division. Simplify the values to determine the result.
The expression (x I x ≤ 1) U (x I x ≥ 24) represents the set of all values of x that are less than or equal to 1 or greater than or equal to 24.
the graph of this set will have a closed circle at x=1 and a closed circle at x=24
The arrows pointing outward indicate that the set continues indefinitely in both directions.
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what is the ratio between yellow to red?
6 yellow = 5 green
4 green = 3 purple
5 purple = 2 red
A.3 to 1
B.4 to 1
C.5 to 1
D.6 to 1
The ratio between yellow to red is 1 to 2 or 1:2. Answer: not listed.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
First, we can use the given information to find the ratio between green and yellow:
6 yellow = 5 green
=> green/yellow = 6/5
Next, we can use the given information to find the ratio between purple and green:
4 green = 3 purple
=> purple/green = 4/3
Finally, we can use the given information to find the ratio between red and purple:
5 purple = 2 red
=> red/purple = 5/2
To find the ratio between yellow and red, we can combine these ratios and simplify:
green/yellow = 6/5
=> yellow/green = 5/6
purple/green = 4/3
=> green/purple = 3/4
red/purple = 5/2
=> purple/red = 2/5
yellow/green * green/purple * purple/red = yellow/red
(5/6) * (3/4) * (2/5) = 1/2
Therefore, the ratio between yellow to red is 1 to 2 or 1:2. Answer: not listed.
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Nate is renting a compact car for 8 days and wants to buy the additional insurance. Using the information below, what is the total cost of the car rental if Nate fills the gas tank before he returns the car? Vehicle Type Daily Rental Rate Compact $56 Luxury Sedan $75 SUV $98 Minivan $90 Optional insurance cost is $10 per day. Gasoline charge of $3.50 per gallon if car returned not full.
the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $[tex]570.[/tex]
What is the total cost?To calculate the total cost of the car rental, we need to first determine the rental rate for a compact car for 8 days, including the optional insurance.
The daily rental rate for a compact car is $ [tex]56,[/tex] and the optional insurance costs $10 per day. Therefore, the total daily cost of renting a compact car with insurance is:
[tex]56 + 10 = 66[/tex]
To determine the total cost of renting the compact car for 8 days, we simply multiply the daily cost by the number of days:
[tex]66 \times 8 = $528[/tex]
Next, we need to determine the cost of gasoline if Nate returns the car without a full tank. The gasoline charge is $ [tex]3.50[/tex] per gallon, but we don't know how many gallons Nate will need to fill up the tank.
If we assume that a compact car has a gas tank capacity of around 12 gallons, and that Nate will need to refill the tank to its full capacity, then the gasoline charge would be:
$[tex]3.50 \times 12 = $42[/tex]
Finally, we can calculate the total cost of the rental, including the optional insurance and the gasoline charge if Nate returns the car without a full tank:
$[tex]528 + $42 = $570[/tex]
Therefore, the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $[tex]570[/tex].
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Circle B is shown, with GHJK inscribed in the circle. The mGHJ = (3x+50)°, and mzHJK = (4x)° and mLGK] = (4x-10)°.
Find HGK and JHG
The value of
m∠GHJ = (3(20°)+50)° = 110°.
m∠GkJ = (4(20°)-10)° = 70°
m∠HJK = (4(20°))° = 80°
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
Given: Circle B is shown, with GHJK inscribed in the circle. The m∠GHJ = (3x+50)°, and m∠HJK = (4x)° and mLGK] = (4x-10)°.
we have to find the value of HJK and JHG.
We know that
m∠GHJ + m∠GkJ = 180°
(3x+50)° + (4x-10)° = 180°
7x + 40 = 180°
7x = 140°
x = 20°
Hence, the value of
m∠GHJ = (3(20°)+50)° = 110°.
m∠GkJ = (4(20°)-10)° = 70°
m∠HJK = (4(20°))° = 80°
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A random sale of 40 flower shop customers was surveyed to find customers' favorite flowers. The table shows the results. The shop expects to sell 50 bunches of flowers on Sunday. How many bunches of each flower should the shop order?
Answer:
below
Step-by-step explanation:
To find out how many bunches of each flower the shop should order, we need to calculate the percentage of customers who preferred each flower, and then use that percentage to estimate the number of bunches needed for each flower.
First, we need to calculate the total number of customers who were surveyed:
Total customers surveyed = 8 + 4 + 8 + 20 = 40
Next, we can calculate the percentage of customers who preferred each flower:
Percentage of customers who preferred daisy = (8/40) x 100% = 20%
Percentage of customers who preferred gardenia = (4/40) x 100% = 10%
Percentage of customers who preferred mum = (8/40) x 100% = 20%
Percentage of customers who preferred rose = (20/40) x 100% = 50%
Now, we can use these percentages to estimate how many bunches of each flower to order.
Let's assume that each bunch contains 10 flowers (this is just an example, the actual number may vary):
Number of bunches of daisy to order = 20% of 50 bunches = 10 bunches
Number of bunches of gardenia to order = 10% of 50 bunches = 5 bunches
Number of bunches of mum to order = 20% of 50 bunches = 10 bunches
Number of bunches of rose to order = 50% of 50 bunches = 25 bunches
So, the shop should order 10 bunches of daisy, 5 bunches of gardenia, 10 bunches of mum, and 25 bunches of rose to meet the expected demand on Sunday.
Find the value of x. Write your answer in simplest form.
Answer:
C
Step-by-step explanation:
using the sine ratio and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 5[tex]\sqrt{2}[/tex]
At a local play, student tickets cost $6 each and adult tickets cost $11 each. If ticket sales were $3,000 for 400 tickets, how many students attended the play?
120
180
220
280
Answer:
If ticket sales were $3,000 for 400 tickets then 280 students attended the play.
Step-by-step explanation:
Write an Algebraic Equation for each problem (include a let statement) and use it to solve the world problem
On number is eight less than five times another. If the the sum of the two numbers is 28, find the two numbers.
The smaller number is __.
The larger number is __.
The smaller number is 6 .
The larger number is 22
To solve this problem
Let's let x be the smaller number and y be the larger number.
From the problem, we know that one number is eight less than five times the other, so we can write:
y = 5x - 8
We also know that the sum of the two numbers is 28, so we can write:
x + y = 28
Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.
Let's solve the first equation for x
x = (y + 8)/5
Now we can substitute this expression for x into the second equation:
(y + 8)/5 + y = 28
Multiplying both sides by 5 to eliminate the fraction, we get:
y + 8 + 5y = 140
Combining like terms, we get:
6y + 8 = 140
Subtracting 8 from both sides, we get:
6y = 132
Dividing both sides by 6, we get:
y = 22
Now we can use the equation y = 5x - 8 to solve for x:
22 = 5x - 8
Adding 8 to both sides, we get:
30 = 5x
Dividing both sides by 5, we get:
x = 6
Therefore, the smaller number is 6 and the larger number is 22.
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Class: Algebra 2
I need help with these Natural Logarithms problems!!!!!
I will give lots of points!!!!
The solutions are: x = ln(2) for 2eˣ = 4, x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.
Solving equations using natural logarithmTo solve these equations using natural logarithm, we can use the following rules:
If a = eᵇ, then b = ln(a).If ln(aᵇ) = b ln(a).Using these rules, we can solve the given equations as follows:
2eˣ = 4
Divide both sides by 2 to get
eˣ = 2.
Take the natural logarithm of both sides to get
ln(eˣ) = ln(2).
Using rule 1 above, we can simplify ln(eˣ) to x, and we get
x = ln(2).
e⁴ˣ = 25
4x = ln(25).
Divide both sides by 4 to get
x = ln(25)/4.
eˣ = 72
Take the natural logarithm of both sides to get
x = ln(72).
e³ˣ = 124
Take the natural logarithm of both sides to get
3x = ln(124).
Divide both sides by 3 to get
x = ln(124)/3.
For the second set of equations, we use the same rule as above
So, we have
ln(x - 3) = 2
x - 3 = e²
x = e² + 3.
x ≈ 10.389.
Therefore, the solution is x ≈ 10.389.
ln(2t) = 4
2t = e⁴
t = 0.5 * e⁴
t ≈ 27.299.
Therefore, the solution is t ≈ 27.299.
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