Answer:
The arithmetic mean of two numbers is found by adding them together and dividing the sum by 2.
So, the arithmetic mean of 4 and 18 is:
(4 + 18) / 2 = 22 / 2 = 11
Therefore, the arithmetic mean of 4 and 18 is 11.
Step-by-step explanation:
Answer:
STEP 1:let the arithmetic mean be p, q, r hence 4,p, q, r, 18
STEP 2:U5=18=a+4d
a+4d=18
we're a=4 therefore
4+4d=18
STEP 3:4d/4=(18-4)÷4=14/4
d=14/4=3.5
p=U2=a+d=4+3.5=7.5
q=U3=a+2d=4+(2×7.5)
=
$4,500 is invested at 10% annual interest, which is compounded continuously, what is the account balance after 3 years
The account balance after 3 years of continuous compounding at 10% annual interest is $6,074.32.
To solve this problem, we can use the formula for continuous compounding, which is:
[tex]A = Pe^{(rt)[/tex]
where A is the account balance after t years, P is the principal amount invested, r is the annual interest rate expressed as a decimal, and e is the mathematical constant approximately equal to 2.71828.
In this problem, P = $4,500, r = 0.10, and t = 3. Substituting these values into the formula, we get:
[tex]A = 4500 * e^{(0.10 * 3)[/tex]
[tex]A = 4500 * e^{(0.30)[/tex]
A = 4500 * 1.34986
A = $6,074.32 (rounded to the nearest cent)
Therefore, the account balance after 3 years of continuous compounding at 10% annual interest is $6,074.32.
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The complete question is :
If $4500 is invested at 10% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?
Why am I not getting correct anwsers on my geometry questions
Maybe you're bad at math.
But I don't think that's true.
Try reading the questions more carefully and properly reading/understanding the material.
If you have any future questions, please ask me! I would be glad to help with your geometry work.
pls pls help pls pls
The length of Jennifer's garden is 25 feet.
What is rectangle?A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length. It is a type of quadrilateral, a polygon with four sides. The length of the sides that are parallel to each other is called the base, and the length of the sides that are perpendicular to the base is called the height.
Let's suppose that the length of the garden is x feet.
We know that the width of the garden is 5 feet, so the total length of the edging required for the two widths is 2 x 5 = 10 feet.
The remaining edging is used for the two lengths of the garden, so we can write an equation based on the total length of the edging:
2(5 + x) = 60
Simplifying this equation, we get:
10 + 2x = 60
2x = 50
x = 25
Therefore, the length of Jennifer's garden is 25 feet.
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PLEASE ANSWER ASAP I NEED IT.
Answer:
[tex]\huge\boxed{\sf 18^{-3}}[/tex]
Step-by-step explanation:
Given expression:[tex]\displaystyle \frac{18^4}{18^7}[/tex]
According to exponent rule:[tex]\displaystyle \frac{a^m}{a^n} = a^{m-n}[/tex]So, the expression becomes:
= [tex]18 ^{4-7}[/tex]
= [tex]18^{-3}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Mr. Apo Man borrowed K 2 000 from a bank to finance an extension to his home. He agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. a) What is the amount of each yearly payment? (2 marks)
If he agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. The amount of each yearly payment is K 368.51.
How to find the yearly payment?To calculate the amount of each yearly payment, we can use the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^-n) / r]
where:
PV = present value of the loan
A = annual payment
r = interest rate per year
n = number of years of the annuity
In this case, Mr. Apo Man borrowed K 2 000 from the bank at an interest rate of 14% p.a. compound interest, and agreed to pay back the loan in 8 yearly payments.
So, we have:
r = 14% = 0.14
n = 8
PV = K 2 000
We can solve for A by rearranging the formula:
A = PV * r / [(1 - (1 + r)^-n)]
Substituting the values, we get:
A = K 2 000 * 0.14 / [(1 - (1 + 0.14)^-8)]
A = K 2 000 * 0.14 / 0.7598
A = K 368.51
Therefore, the amount of each yearly payment that Mr. Apo Man needs to make to repay the loan in 8 years at 14% p.a. compound interest is K 368.51.
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Pls help There is a 20% chance that a customer walking into a store will make a purchase. A computer was used to generate 5 sets of random numbers from 0 to 9, where the numbers 0 and 1 represent a customer who walks in and makes a purchase.
A two column table with title Customer Purchases is shown. The first column is labeled Trial and the second column is labeled Numbers Generated.
What is the experimental probability that at least one of the first three customers that walks into the store will make a purchase?
A) 60%
B) 13%
C) 40%
D) 22%
Answer:
it's D
Step-by-step explanation:
hope this helps lol.....
X^2(4x-3)(5x-1)=0 solve for x
Answer:
x = 0, 3/4, 1/5
Step-by-step explanation:
This equation is already factored into 3 terms.
For this expression to equal 0, any of the terms must be equal to 0. Set each factor equal to 0 and solve for x.
x^2 = 0
x = 0
4x - 3 = 0
4x = 3
x = 3/4
5x - 1 = 0
5x = 1
x = 1/5
The solutions are x = 0, 3/4, 1/5
How much interest would you pay if you borrowed $4700 for 4 years at 8% simple yearly
interest. Use the formula. Make sure to label each variable. must show your work.
After answering the presented question, we can conclude that Therefore, the interest paid would be $1504.
what is interest ?In mathematics, interest is the amount of money earned or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest every year for three years, for a total of $15.
To calculate the amount of interest paid on a simple interest loan, we use the following formula:
Interest = Principal x Rate x Time
where:
Principal is the amount borrowed
Rate is the annual interest rate as a decimal
Time is the length of the loan in years
In this case, we have:
Principal = $4700
Rate = 0.08 (8% expressed as a decimal)
Time = 4 years
So, the interest paid on this loan would be:
Interest = $4700 x 0.08 x 4
Interest = $1504
Therefore, the amount of interest paid would be $1504.
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A water station table at a marathon starts with 200 plastic cups on it. Every minute, 15 cups are taken from the table. How many minutes could have passed if there are fewer than 65 cups on the table?
[tex]15x < 65[/tex]
Solve for x to get
[tex]x < 4.33[/tex].
So 4.33 minutes could have passed if there are fewer than 90 cups on the table.
Answer:
x=10
Step-by-step explanation:
work out the value of (√7^)^2
Answer:
Step-by-step explanation:
Puedo ayudarte con tu cálculo. (√7) 2 es lo mismo que √(7^2), que es igual a 7. Por lo tanto, el valor de (√7) 2 es 7.
rovide an appropriate response.
Determine the number of classes in the frequency table below.
tableau3 ( (Class Frequency)(23-24 7)(25-26 2)(27-28 6)(29-30 4)(31-32 1) )
2
5
6
20
There are 5 classes in the frequency table.
What is frequency table?The frequency of each data point or interval in a dataset is displayed in a frequency table. It is a technique for arranging data such that patterns and connections within the data may be examined. Two columns are normally present in the table: one for the intervals or data points (referred to as classes) and the other for the frequency of recurrence for each class. The classes may be intervals of equal size or they may be determined by the data's relevant categories or values.
From the given table we have:
Class 1: 23-24 (frequency of 7)
Class 2: 25-26 (frequency of 2)
Class 3: 27-28 (frequency of 6)
Class 4: 29-30 (frequency of 4)
Class 5: 31-32 (frequency of 1)
There are 5 classes in the frequency table.
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How to write this standard form? 2y=3x+5
The standard form of the equation is as follows:
3x -2y + 5 = 0
Define equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is known as an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
In the question,
The given equation is: 2y = 3x + 5
Standard form: ax + by + c = 0
Now,
2y = 3x + 5
Subtracting 2y from both the sides:
0 = 3x + 5 - 2y
Rearranging the equation we get,
3x -2y + 5 = 0
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A and B started a business investing Rs. 90,000 and Rs 20,000
espectively. In what ratio the profit earned after 2 years be divided
between A and B respectively?
Dividing the profit ratio after two years into equal portions for A and B is 9:2.
Explain about the ratio of the number?Ratios frequently appear in daily life and, by putting numbers into perspective, help to systematize many of our interactions. By making quantities easier to comprehend, ratios enable us to measure as well as express quantities.
One of the most typical ways to write a ratio with a colon as a the whole comparison, like in the example above with the children and adults. Ratios can also be expressed as a fraction because they are straightforward division problems.
Given data:
Investments by A = 90,000
Investments by B = 20,000
ratio of profit after 2 years:
profit of A / profit of B = Investments by A / Investments by B
profit of A / profit of B = 90,000 / 20,000
profit of A / profit of B = 9/2
Thus, dividing the profit after two years into equal portions for A and B is 9:2.
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Complete question:
A and B started a business investing Rs. 90,000 and Rs 20,000
respectively. In what ratio the profit earned after 2 years be divided
between A and B respectively?
Area between curves questions
Answer:
16.739
Step-by-step explanation:
2 Al gives food pellets to the animals on the farm.
• Rabbits: 0.3 kilogram
• Chickens: 1,300 grams
• Ducks: 0.7 kilogram
How many more grams of pellets does Al give
the chickens than he gives the rabbits and
ducks combined?
A 1,000 g
B 2,300 g
C 3,000 g
D 300 g
By answering the presented question, we may conclude that As a result, inequality the correct answer is D) 300 g.
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions and shows the relationship between them, usually using the symbols > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).
For example, "3 > 2" is an inequality that states that 3 is greater than 2. Similarly, "x ≤ 5" is an inequality that states that the value of x is less than or equal to 5.
Inequalities are used to represent ranges of possible values and are commonly used in algebra, calculus, and other branches of mathematics. They are often used to describe constraints in optimization problems, such as finding the maximum or minimum of a function subject to certain conditions.
To begin, we must convert the weights to the same units. We can convert rabbit weight to grammes as follows:
300 grammes = 0.3 kilos
We can also convert duck weight to grammes:
700 grammes = 0.7 kilos
We can now multiply the weights of rabbits and ducks:
300 grammes plus 700 grammes equals 1000 grammes
300 grammes plus 1300 grammes plus 700 grammes equals 2300 grammes.
To calculate how many more grammes of pellets Al feeds the chickens than the rabbits and ducks combined, subtract the total weight of pellets fed to the rabbits and ducks from the weight of pellets fed to the chickens:
1300 grammes minus 1000 grammes equals 300 grammes
As a result, the correct answer is D) 300 g.
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1. How many ways are there to get from the point (-3,2) to (-1,-1) if you only step down and to the right
2. How many ways are there to get from the point (-1,-2) to (4,0) if you only step up and to the right
calculated using the binomial coefficient:
6 choose 3 = 6! / (3! * (6-3)!) = 20 ways
The binomial coefficient can be used to compute the following:
7 select 2 is equal to 7 / (2! * (7-2)!) = 21 ways.
1. We simply need to take three steps down and three steps to the right in order to move from (-3,2) to (-1,-1) by doing so. It doesn't matter in whatever sequence we do these stages.
As a result, the number of ways to select 3 steps out of a total of 6 steps is the number of ways to travel from (-3,2) to (-1,-1). The binomial coefficient can be used to compute the following:
6 select 3 is equal to 6!/(3!*(6-3)!) = 20 ways.
2. We need to take 5 steps to the right and 2 steps up in order to move from (-1,-2) to (4,0) by simply moving up and to the right. It doesn't matter in whatever sequence we do these stages.
Hence, the variety of routes to and from The range of options for selecting 2 stages out of a total of 7 steps is from (-1,-2) to (4,0). The binomial coefficient can be used to compute the following:
7 select 2 is equal to 7 / (2! * (7-2)!) = 21 ways.
Describe the binomial coefficient?The number of possibilities to choose k things randomly from a set of n items is represented mathematically by the binomial coefficient. The formula: It is represented by the symbol "n pick k" or "C(n,k)" and can be calculated.
C(n,k) = n!/(k!*(n-k))!
where the factorial function is shown by "!" A non-negative integer's factorial is the sum of all positive integers that are less than or equal to that number. 5!, for instance, equals 5 x 4 x 3 x 2 x 1 = 120.
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How much will I have by the end of the year if I clean the yards of roughly 6 houses for 25$ every month?
If you clean the yards of 6 houses for $25 every month, you will earn $1,800.
$25/month * 6 houses = $150/month . If you continue earning $150 every month for a year (12 months), then your total earnings for the year will be: $150/month * 12 months = $1,800
Therefore, you will have approximately $1,800 by the end of the year if you clean the yards of roughly 6 houses for $25 every month. However, please note that this assumes that you will be able to consistently clean the yards of all 6 houses every month for the entire year.
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Rita has coins worth $3.00. If the coins are all dimes, how many dimes does she have?
Answer:
300 dimes I believe because 3.00 is 100 dimes?
Step-by-step explanation:
Multiply and simplify the following complex numbers: ( − 4 + 4 � ) ⋅ ( 3 + 2 � ) (−4+4i)⋅(3+2i)
Answer:
Step-by-step explanation:(−4+4i)⋅(3+2i);
= -4(3+2i)+4i(3+2i);
=-12-8i+12i-8;
= -20+4i
Where v
is the final velocity (in m/s), u
is the initial velocity (in m/s), a
is the acceleration (in m/s²) and s
is the distance (in meters).
Find v
when u
is 6 m/s, a
is 3 m/s², and s
is 29 meters.
the final velocity is approximately 14.5 meters per second.
Define accelerationThe rate at which an object's velocity alters over time is known as acceleration. It is a vector quantity, which means it has both magnitude (a numerical value) and direction.
Using the formula: v² = u2 + 2as
We can plug in the values given:
u = 6 m/s (initial velocity)
a = 3 m/s² (acceleration)
s = 29 m (distance)
v² = (6 m/s)² + 2(3 m/s²)(29 m)
v² = 36 m²/s² + 174 m²/s²
v²= 210 m²/s²
To solve for v, we need to take the square root of both sides of the equation:
v = √(210 m²/s²)
v ≈ 14.5 m/s (rounded to one decimal place)
Therefore, the final velocity is approximately 14.5 m/s.
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The complete question is:
v²=u²+2as
Where v
is the final velocity (in m/s), u
is the initial velocity (in m/s), a
is the acceleration (in m/s²) and s
is the distance (in meters).
Find v
when u
is 6 m/s, a
is 3 m/s², and s
is 29 meters.
The table shows the numbers of feet and the equivalent numbers of inches. Lionel painted a wall that is 12 feet long. How many inches long is the wall that Lionel painted?
A. 144
B. 122
C. 156
D. 132
The wall is 144 inches long that Lionel painted
What are unit cοnversiοns?Unit cοnversiοn is the prοcess οf cοnverting οne unit οf measurement tο anοther unit οf measurement that is equivalent tο the οriginal unit.
Given table:
Number οf feet's Number οs inches
3 36
5 60
8 96
10 120
Tο cοnvert feet tο inches, we need tο multiply the number οf feet by 12 since there are 12 inches in οne fοοt.
Fοr 12 feet, we have:
12 feet = 12 x 12 inches = 144 inches
Hence, the answer is A. 144.
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The image of the point (8,1) under a translation is (9,2). Find the coordinates of
the image of the point (5,5) under the same translation.
Answer:
Since the translation has shifted the point (8,1) to (9,2), we can determine the displacement vector between these two points as:
(9,2) - (8,1) = (1,1)
This vector represents the amount and direction of the translation. To find the image of the point (5,5) under the same translation, we need to add this vector to the coordinates of the point:
(5,5) + (1,1) = (6,6)
Therefore, the image of the point (5,5) under the same translation is (6,6).
Simplify the following
8⁶÷8
Answer: 8^5
Step-by-step explanation:
To simplify this expression, we can use the rules of exponents which state that when we divide two exponential terms with the same base, we can subtract their exponents. So we have:
8⁶ ÷ 8 = 8^(6-1) = 8^5
Therefore, the simplified expression is 8^5.
Length of rectangle is 2 more than its Width and the perimeter is 48 cm sqaure find length width and area of the rectangle
Answer:
the width of the rectangle is 11 cm, the length is 13 cm, and the area is 143 cm^2.
Step-by-step explanation:
Let's assume that the width of the rectangle is "x" cm.
According to the problem, the length of the rectangle is 2 more than its width, which means:
Length = x + 2
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Substituting the given values, we get:
48 = 2(x + 2 + x)
48 = 2(2x + 2)
48 = 4x + 4
44 = 4x
x = 11
So, the width of the rectangle is 11 cm and the length is:
Length = 11 + 2 = 13 cm
The formula for the area of a rectangle is:
Area = length x width
Substituting the given values, we get:
Area = 11 x 13 = 143 cm^2
Therefore, the width of the rectangle is 11 cm, the length is 13 cm, and the area is 143 cm^2.
Answer:
Length = 13 cm Breadth = 11 cm Area of rectangle = 143 cm²Step-by-step explanation:
Length of rectangle is 2 more than its Width.
Let width be x and length be x +2.
If Perimeter is 48 cm .
Perimeter of rectangle = 2(l +b)=> 48 = 2(x + 2 + x)
=> 48 = 2(2x +2)
=> 48 = 4x + 4
=> 48 - 4 = 4x
=> 44 = 4x
=> x = 44/4
=> x = 11 cm
Hence,
Length of rectangle = x +2 = 13 cm
Breadth of rectangle = 11 cm
Now,
Area of rectangle = l × b=> 11 × 13
=> 143 cm²
A sample of maximum pressure from 12 trials with a stamping machine yielded a mean of 7.2 thousand psi and a standard deviation of 1.2 thousand psi. The histogram of the sample data is approximately normal. Calculate a 90% confidence interval.
The 90% confidence interval for the mean pressure is calculated equivalent to (6.39, 7.99).
What is t-distribution table?A t-distribution table is a statistical table that lists critical values of the t-distribution for various levels of significance and degrees of freedom. The t-distribution is a probability distribution that is used when the sample size is small or when the population standard deviation is unknown.
The table is organized by degrees of freedom (df), which is calculated as n-1, where n is the sample size. It also lists different levels of significance, usually ranging from 0.01 to 0.5 or more. The critical values are listed in the table corresponding to the degrees of freedom and the significance level. To use a t-distribution table, you need to know the degrees of freedom and the level of significance.
To calculate the 90% confidence interval for the mean pressure, we can use the formula:
CI = X' ± Z*(σ/√n)
Where X' is the sample mean, σ is the sample standard deviation, n is the sample size, and Z is the critical value for a 90% confidence interval.
Since the sample size is 12, we need to use a t-distribution with 11 degrees of freedom to find the critical value, because we are estimating the population standard deviation from the sample. Using a t-distribution table or calculator, we can find that the critical value for a 90% confidence interval with 11 degrees of freedom is approximately 1.796.
Substituting the values into the formula, we get:
CI = 7.2 ± 1.796*(1.2/√12)
= 7.2 ± 0.81
Therefore, the 90% confidence interval for the mean pressure is:
(7.2 - 0.81, 7.2 + 0.81) or (6.39, 7.99)
So, we can say with 90% confidence that the true mean pressure of the machine lies between 6.39 thousand psi and 7.99 thousand psi.
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Question
Jim's music store bought a guitar at the wholesale price of $1,200. Jim marked up the price 50%. Find the list price.
Answer: $1,800
Step-by-step explanation:
What is the bagel’s circumference, in inches?
The circumference of the bagel is 4.71 inches
How to determine the bagel’s circumference?
The circumference is the distance around the edge of a circle. It is the length of the boundary that encloses the circle.
The bagel’s circumference can be calculated using the formula:
C = 2πr
where r is the radius of the bagel.
Substituting r = 0.75 inches in the formula, we have:
C = 2 * 22/7 * 0.75
C = 4.71 inches
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Complete Question
If the radius of the bagel's hole is 0.75 inches, what is the hole's circumference, in inches?
Six friends were discussing the amount of time per week they spend on social media, including online videos and music. The list below has the names and the sex for the 6 friends.
Andre, male
Bella, female
Carlos, male
Desirae, female
Edgar, male
Frances, female
Which of the following graphs is the sampling distribution of the sample proportion of males for all samples of size n = 3 for these six friends?
The correct answer is the bar graph with bars centered on the values 0.00, 0.33, 0.67, and 1.00, which corresponds to option (d).
To find the sampling distribution of the sample proportion of males for all samples of size n = 3, we need to consider all possible samples of size 3 that can be taken from the population of 6 friends. There are a total of 20 such samples, which are:
Andre, Bella, Carlos
Andre, Bella, Desirae
Andre, Bella, Edgar
Andre, Bella, Frances
Andre, Carlos, Desirae
Andre, Carlos, Edgar
Andre, Carlos, Frances
Andre, Desirae, Edgar
Andre, Desirae, Frances
Andre, Edgar, Frances
Bella, Carlos, Desirae
Bella, Carlos, Edgar
Bella, Carlos, Frances
Bella, Desirae, Edgar
Bella, Desirae, Frances
Bella, Edgar, Frances
Carlos, Desirae, Edgar
Carlos, Desirae, Frances
Carlos, Edgar, Frances
Desirae, Edgar, Frances
For each sample, we can compute the sample proportion of males by counting the number of males in the sample and dividing by 3. We can then list all the sample proportions of males and count how many times each value appears. The resulting distribution is the sampling distribution of the sample proportion of males.
To make it easier to visualize the distribution, we can create a frequency table and a bar graph. The frequency table lists all the distinct values of the sample proportion of males and their frequencies, while the bar graph shows the frequencies as bars of different heights.
The sample proportion of males' Frequency
0.00 - 1
0.33 - 8
0.67 - 8
1.00 - 3
Frequency
0 1 8 8 3
0.00 0.33 0.67 1.00
The sample proportion of males
The x-axis represents the possible values of the sample proportion of males, and the y-axis represents the frequency of each value. The bars are centered on the values 0.00, 0.33, 0.67, and 1.00, and their heights correspond to the frequencies of these values in the sampling distribution.
Therefore, the correct answer is the bar graph with bars centered on the values 0.00, 0.33, 0.67, and 1.00, which corresponds to option (d).
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Amy is making salt dough for an art project. Her recipe calls for cup of salt
for each batch of salt dough she makes. She has 3 cups of salt. How
many batches of salt dough can Amy make?
If Amy has 3 cups of salt and each batch of salt dough requires 1 cup of salt, then she can make:
3 batches = 3 cups of salt / 1 cup of salt per batch
So, Amy can make 3 batches of salt dough with the amount of salt she has.
Answer:
3 batches of salt dough
Step-by-step explanation:
What is the measure of angle P?
Enter your answer as a decimal in the box.
Round only your final answer to the nearest hundredth.
P = ___
Therefore, the measure of angle P is approximately 22.62 degrees (rounded to the nearest hundredth).
So, the final answer is P ≈ 22.62.
What is triangle?A triangle is a closed geometric shape that has three sides, three angles, and three vertices (or corners). It is one of the most basic and important shapes in geometry. The sum of the angles in a triangle is always 180 degrees, and the length of each side can be calculated using the Pythagorean theorem or other geometric formulas. Triangles can be classified into different types based on the length of their sides and the size of their angles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are used extensively in mathematics, science, engineering, and many other fields.
To find the measure of angle P, we can use the Pythagorean theorem and trigonometric functions. Here's the step-by-step solution:
From the given information, we know that one angle of the triangle is 90 degrees, and the lengths of the adjacent sides are 5 and 13.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 5^2 + 13^2
c^2 = 194
c = sqrt(194)
c ≈ 13.93
So the length of the hypotenuse is approximately 13.93 units.
Now, we can use the trigonometric function sine to find the measure of angle P:
[tex]sin(P) = opposite / hypotenuse[/tex]
[tex]sin(P) = 5 / 13.93[/tex]
[tex]P = sin^{-1(5/13.93)}[/tex]
P ≈ 22.62 degrees
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