Answer:
its a
Step-by-step explanation:
8 divided by 1.6 is 5 , have a good day <3
If the hypotenuse of a 30°-60°-90° triangle is 8 cm, what is the measure of the longer leg of the triangle?
The measure of the longer leg of the triangle is given as follows:
6.93 cm.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The longer leg is opposite to the angle of 60º, hence the sine relation is used to find the length, as follows:
sin(60º) = x/8
x = 8 x sine of 60 degrees
x = 6.93 cm.
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You own a life insurance company called PeaceOfMind. PeaceOfMind offers only one type of insurance policy that works in the following way. Each policyholder pays PeaceOfMind a fixed "premium" of GHSX per year, starting (for the sake of simplicity) from birth until death. In turn, PeaceOfMind pays each policyholder’s family a "pay-out" of GHS1 million upon the policyholder’s death. The database shows that 60% of PeaceOfMind’s policyholders are male, and 40% are female. Actuarial studies have shown that in this country a man’s life expectancy (also called lifespan) obeys a Normal distribution with mean 75 years and standard deviation 8 years, a women’s life expectancy obeys a Normal distribution with mean 78 and standard deviation 6 years, and all individuals’ life expectancies are independent of one another. Suppose that PeaceOfMind’s policyholders have the same life expectancy distributions as the population of the entire country. PeaceOfMind is not allowed to charge different premiums to men and women because doing so would violate anti-discrimination laws.
c What is the probability that a randomly selected policyholder (who could be either male or female) lives for more than 80 years?
d) A MALE policyholder just turned 80 years old today. Given this fact, what is the probability that he will live for at least three more years?
(a) The probability that a randomly selected policyholder lives more than 80 years is approximately 0.3106. (b) Given that a male policyholder just turned 80, the probability that he will live for at least three more years is approximately 0.6166.
(a) To find the probability that a randomly selected policyholder lives more than 80 years, we need to calculate the cumulative probability of survival beyond 80 for both males and females separately, and then weigh them based on the gender distribution.
For males: Using the normal distribution with mean 75 and standard deviation 8, we find the probability of survival beyond 80 is approximately 0.3446.
For females: Using the normal distribution with mean 78 and standard deviation 6, we find the probability of survival beyond 80 is approximately 0.2847.
The weighted probability for a randomly selected policyholder is (0.60 * 0.3446) + (0.40 * 0.2847) = 0.3106.
(b) Given that a male policyholder just turned 80 years old today, we can use conditional probability to calculate the likelihood of him living for at least three more years.
Using the normal distribution with mean 75 and standard deviation 8, the probability of survival beyond 83 (80 + 3) is approximately 0.8621.
Therefore, the probability that a male policyholder, who just turned 80, will live for at least three more years is 0.8621.
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Suppose that there is a 30% chance Clyde is injured and earns $50,000, and a 70% chance he is healthy and will earn $500,000. Suppose further that his utility function is the following (utility = square root of income) U= Income Clyde's utility if he earns $50,000 is and his utility if he earns $500,000 is 50,000;500,000 223.6;707.1100;264.58707.1;223.6 264.58;100
The Clyde's expected utility is approximately 562.05.
To determine Clyde's expected utility, we need to calculate the expected value of his utility for each possible outcome.
Let's start by calculating the expected utility if Clyde is injured and earns $50,000. According to the given utility function, his utility in this case is √50,000, which is approximately 223.6. Next, let's calculate the expected utility if Clyde is healthy and earns $500,000. Again, using the utility function, his utility in this case is √500,000, which is approximately 707.1.
Now, we can calculate the expected utility by multiplying the probability of each outcome by its corresponding utility, and then summing them up.
The probability of Clyde being injured is 30%, so the expected utility in this case is 0.3 * 223.6 = 67.08.
The probability of Clyde being healthy is 70%, so the expected utility in this case is 0.7 * 707.1 = 494.97.
Adding these expected utilities together, we get a total expected utility of approximately 562.05.
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3 + 2x = y Given x = 4 y =
Answer:
\(y = 9\)
Step-by-step explanation:
\(3 + 2x = y\)
\(y = 3 + 6\)
\(y = 9\)
Hope it is helpful...Ellie is renting a paddle boat. The boat rents for a 5 plus 3.50 per hour. She wants to spend under $30 altogether Write an inequality to determine how long she can rent the paddle boat
What is K(4-17) in math
Answer: -13K.
Step-by-step explanation:
To simplify the expression "K(4-17)" in math, we can start by evaluating the parentheses:
4 - 17 = -13
Now, the expression becomes "K(-13)".
x^2+3x=40 (complete the square!)
Hello there. To solve this quadratic equation using the method of completing squares, we need to remember some properties on binomial expansions.
First, remember that (a + b)² = a² + 2ab + b².
With this in mind, we want to find a value b that we can sum into x² + 3x and reach something like the expression in the line above.
So, we divide the second term coefficient by two
3/2
Now, square this term
9/4
Sum this term on both sides of the equation
x² + 3x + 9/4 = 40 + 9/4
Sum the fractions on the right hand side
x² + 3x + 9/4 = 169/4
Now, we can make the LHS return to its power form:
(x + 3/2)² =
Help Asap!
Determine the period of each function.(show step by steps on problem 1 and 2)
1. The period of the function is π
2. The period of the function is 6
How to determine the period of the functionFrom the question, we have the following parameters that can be used in our computation:
The graphs
By definition, the period of the function is calculated as
Period = Difference between cycles or the length of one complete cycle
Graph 1
Using the above as a guide, we have the following:
Period = 2π - π
Evaluate
Period = π
Graph 2
Using the above as a guide, we have the following:
Period = 9 - 3
Evaluate
Period = 6
Hence, the period of the functions are π and 6
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Pls urgent help needed Bcz exam tmrw
The simplification of the expression 4a + 3b - a + 3b + 6 is 3(a + 2b + 2)
The expression im terms of x for the perimeter of the triangle is 31 = (3x - 5) + (2x - 1) + (x + 1)The value of x is 6How to find the perimeter of a triangle?Simplify 4a + 3b - a + 3b + 6
collect like terms
= 4a - a + 3b + 3b + 6
= 3a + 6b + 6
factorize
= 3(a + 2b + 2)
side a = 3x - 5
side b = 2x - 1
side c = x + 1
Perimeter = 31 cm
The perimeter of a triangle = side a + side b + side c
31 = (3x - 5) + (2x - 1) + (x + 1)
31 = 3x - 5 + 2x - 1 + x + 1
31 = 6x - 5
Add 5 to both sides
31 + 5 = 6x
36 = 6x
divide both sides by 6
x = 36/6
x = 6
Therefore, the value of x from the perimeter of the triangle is 6
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PLSSS HELP!! Select the number that would make this statement true: 628 ÷ ________ = 0.628
10 to the power of 1
10 to the power of 2
10 to the power of 3
10 to the power of 4
Answer:
10 to the power of 3
Step-by-step explanation:
i used a calculator (´-﹏-`;) - Hope this helps
Find the height a 17-foot ladder can reach on the side of a building when it
hits the ground at a 65° angle.
A. 7.2 ft
B. 15.4 ft
C. 36.5 ft
D. 48 ft
E 224 ft
SHOW EXPLANATION
Answer:
B. 15.4 ft
Step-by-step explanation:
this answer, without any formulas used, can be answered correctly and logically.
answer c, d and e are eliminated as the opposite side cant be greater than the hypotenuse.
now we have to find which is correct between a and b
the answer will be 'B' as the value of sine of an angle keeps increasing as the angle itself increases. thus, giving a bigger value of the opposite side (required height). as 15.4 ft.
mathematically,
sin65° = x/17
17 × sin65° = x
where x is height of the side of the building.
helpppp please !!!!
Answer:
To add integers having the same sign, keep the same sign and add the absolute value of each number. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite.
help me please. Very much appreciated
Answer:
73 m^2
Step-by-step explanation:
Well divide this into 3 shapes
The 3 dimensions will be
3X9
7X4
2X9
You;d gets 73
Answer:
This is your answer. If I'm right so,
Please mark me as brainliest. thanks!!!
Help plzdlkkdkkdkdnnzkzkzkskskeme
Answer:
ofc 8 there are 8 post card ♦️
Answer:
222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222
Step-by-step explanation:
22222222222222222222222222222222222222
Place the following numbers in order from largest to smallest.
Answer:
D
Step-by-step explanation:
pi = 3.14 --> round pi to 3 --> pi/2 = 1.5 --> pi^2 = 9
6 > sqrt(28) > 5
4> \sqrt[3]{28\\} > 3
Thus D
if it take a person 3 hours to do something and another person 6 hours to do the same thing how much time will it take to do that thing if they work together
It will take them 2 hours to do the whole task if they work together.
If one person can do a task in 3 hours and another person can do the same task in 6 hours, then we can calculate their individual rates of work as follows:
The first person can do 1/3 of the task per hour (since it takes them 3 hours to do the whole task).
The second person can do 1/6 of the task per hour (since it takes them 6 hours to do the whole task).
When they work together, their rates of work will add up, so their combined rate of work is:
1/3 + 1/6 = 1/2
This means that working together, they can do 1/2 of the task per hour. To find out how long it will take them to do the whole task, we can use the formula:
time = work ÷ rate of work
Since the whole task is 1 unit of work, and their combined rate of work is 1/2 units per hour, we can plug in these values to get:
time = 1 ÷ (1/2) = 2 hours
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SOLVE PLS! WILL GIVE BRAINLIST
-2x-9y=-25
-4x-9y=-23
What is the solution? and show all steps
Answer:
x = -1 and y = 3
Step-by-step explanation:
Let's solve your system by elimination.
−2x−9y=−25;−4x−9y=−23
Multiply the second equation by -1, then add the equations together.
(−2x−9y=−25)
−1(−4x−9y=−23)
Becomes:
−2x−9y=−25
4x+9y=23
Add these equations to eliminate y:
2x=−2
x = -1
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
−2x−9y=−25
Substitute−1forxin−2x−9y=−25:
(−2)(−1)−9y=−25
−9y+2=−25(Simplify both sides of the equation)
−9y+2+−2=−25+−2(Add -2 to both sides)
−9y=−27
y = 3
Find the value of y for which the value of 8y+3 is 7 more than the value of 6y
How do you write 143% as a decimal
Answer:
1.43
Step-by-step explanation:
1.43 or 1 43/100 turned into a percent is 143%
Answer:
1.43 because 1 = 100 percent and the 43 is your 43 remaining
From the age of a person if two fifth of his age is subtracted, the result becomes 24 years. Find the age of the person .
Answer:
40 years old.
Step-by-step explanation:
\(x - \frac{2}{5} x = 24 \\ \frac{3}{5} x = 24 \\ x = 24 \div \frac{3}{5} = 40\)
What is the prime factorization of 45. Using exponents when appropriate and order the factors from least to greatest
Answer:
3to the power of 2 times 5
Step-by-step explanation:
yeah thats all hehe
An advertising company is purchasing a new industrial-sized color printer. The company has been approved for a $75,000 loan at two different
banks. The terms of each loan are:
Offer 1: 4.99% annual simple interest, with a total account balance of $91,529.38 after a 53-month term
Offer 2: 3.5% annual interest compounded monthly for a 62-month term
Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest
penny.
O $1,624.49
$1,686.87
$1,894.02
O $2,207.67
The difference in the account balances at the end of the loan terms is given as follows:
$1,686.87.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for the offer 2 are given as follows:
P = 75000, r = 0.035, n = 12, t = 62/12.
Hence the balance of the offer 2 is given as follows:
B = 75000 x (1 + 0.035/12)^(12 x 62/12)
B = $89,842.51.
The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:
91529.38 - 89842.51 = $1,686.87.
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Mikes plumbing charges 68 for coming to your house and 17 per hour for labor if I paid him 357, how many hours, h, was mike at my house ? Write and solve an equation that is represented in this scenario.
Answer:
b. \( 68 + 17h = 357 \)
f. 17 hours
Step-by-step explanation:
Charges for coming to my house = $68 (this will be the constant of the equation)
Amount charged per hour labor = $17
hours = h
Total amount paid to Mike = 357
The equation that represents this situation can be expressed as:
\( 68 + 17h = 357 \)
Solve for h
\( 68 + 17h - 68 = 357 - 68 \) (subtraction property of equality)
\( 17h = 289 \)
\( \frac{17h}{17} = \frac{289}{17} \) (division property of equality)
\( h = 17 \)
Mike was in my house for 17 hours.
Can someone please help me ASAP?? It’s due tomorrow!! I will give brainliest If It’s correct.
Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:
A. Perpendicular to the base: Rectangle
B. Parallel to the base: Triangle with dimensions equal to the base
C. Diagonal from vertex to vertex: Triangle with unknown dimensions
which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?8, 10, 149, 12, 1510, 14, 1712, 15, 19
The correct option is option( A).
Using the property of Obtuse Triangle, the triangle with sides { 8, 10, 14 } is an Obtuse Triangle.
Obtuse Triangle:
An obtuse triangle is a triangle with one interior angle greater than 90 degrees. In geometry, a triangle is represented as a closed 2D figure with three sides of equal or unequal length and three angles of equal or unequal measurements.
Obtuse triangle property:
The longest side of the triangle is opposite the obtuse angle.A triangle can have only one obtuse angle.The sum of the other two angles of an obtuse triangle is always less than 90°.In an obtuse triangle, the sum of the squared lengths of the two short sides is less than the squared length of the longest side.we have given the sides of triangle so, we use the fourth property for check the triangle formed by given sides are obtuse triangle or not .
8² + 10² = 164; 14² = 196 -> obtuse
9² + 12² = 225; 15² = 225 -> not obtuse
10² + 14²= 296 ; 17²= 289 --> not obtuse
12² + 15² = 369; 19²= 361 --> not obtuse
Hence, the required triangle is triangle with sides 8, 10, 14.
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Complete Question:
which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle
A. 8, 10, 14
B. 9, 12, 15
C. 10, 14, 17
D. 12, 15, 19
Answer: the answer is A 8, 10, 14.
Step-by-step explanation: it show below.
what is the constant term for -2a3b2+5ab5+7b4+8
Hey there!
Constant terms are the terms where no variables are there (only the constant, i.e, the number). So, here the term 8 is the constant term because it doesn't have any variables.
Hope it helps ya!
Hello there! :)
The constant is 8.
Keep in mind that constant terms have no variables next to them. In other words, a constant is just a number.
Hope this helps!
~Just a felicitous girlie
#CarryOnLearning
\(SilentNature :)\)
according to government data, 51% of employed women have never been married. rounding to 4 decimal places, if 15 employed women are randomly selected: a. what is the probability that exactly 2 of them have never been married? b. that at most 2 of them have never been married? c. that at least 13 of them have been married?
a) The probability that exactly 2 of them have never been married is\(0.0026 \text{ or }2.6*10^{-3}\)
b) The probability that at most 2 of them have never been married is\(0.0029\text{ or }2.9*10^{-3}\)
c) The probability that at least 13 of them have been married is \(0.0046 \text{ or } 4.6*10^{-3}\)
a) What is the probability that exactly 2 of them have never been married?
By applying binomial probability distribution method,
\(P(x)=^{n}C_{x}p^{x}q^{n-x}\)
Substitute,
P(x) =Binomial probability = 51% = 0.51
x = No. of times of an outcome = 2
n = No. of trials = 15
q = Probability of failure = 49% = 0.49
\(^{n}C_{x}\) = No. of combinations
\(P(2)=^{15}C_{2}*(0.51)^{2}*(0.49)^{15-2}\\\\P(2)=\frac{15!}{13!2!} *(0.51)^{2}*(0.49)^{13}\\\\P(2)=0.0026 \text{ or }2.6*10^{-3}\)
b) What is the probability that at most 2 of them have never been married?
By applying binomial probability distribution method,
\(P(x)=^{n}C_{x}p^{x}q^{n-x}\)
Substitute,
P(x) =Binomial probability = 51% = 0.51
x = No. of times of an outcome = 0,1,2
n = No. of trials = 15
q = Probability of failure = 49% = 0.49
\(^{n}C_{x}\) = No. of combinations
\(P(0-2)=^{15}C_{0}*(0.51)^{0}*(0.49)^{15-0}+^{15}C_{1}*(0.51)^{1}*(0.49)^{15-1}+^{15}C_{2}*(0.51)^{2}*(0.49)^{15-2}\\\\P(0-2) = 2.253*10^{-5}+15*0.51*4.59987*10^{-5}+2.563*10^{-3}\\\\P(0-2)=0.0029 \text{ or }2.9*10^{-3}\)
c)What is the probability that at least 13 of them have been married?
By applying binomial probability distribution method,
\(P(x)=^{n}C_{x}p^{x}q^{n-x}\)
Substitute,
P(x) =Binomial probability = 51% = 0.51
x = No. of times of an outcome = 13,14,15
n = No. of trials = 15
q = Probability of failure = 49% = 0.49
\(^{n}C_{x}\) = No. of combinations
\(P(13-15)=^{15}C_{13}*(0.51)^{13}*(0.49)^{15-13}+^{15}C_{14}*(0.51)^{14}*(0.49)^{15-14}+^{15}C_{15}*(0.51)^{15}*(0.49)^{15-15}\\\\P(13-15)= 105*(0.51)^{13}*(0.49)^{2}+15* (0.51)^{14}*(0.49)+(0.51)^{15}\\\\P(13-15)= 0.0046 \text{ or } 4.6*10^{-3}\)
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A tortoise starts running a length of 400 m. After one day, the tortoise found it has only come 4/5 of the total journey. What is the distance the tortoise has still to cover?
plz explain it..
Answer:
The distance that the tortoise has still to cover is equal to 80 meters.
Step-by-step explanation:
When it says that she has only come 4/5 of the total journey that means that if we were to divide the journey into 5 parts of the same length, the turtle would already be done with 4 parts and has only 1 more part to do before finishing the journey.
Since all the parts are of the same length then the distance of that one part that she still has to cover is equal to...
400 / 5 = 80 m
Therefore the distance that the tortoise has still to cover is equal to 80 meters
Step-by-step explanation:
Given,
A tortoise starts running a length of 400 m.
after one day , the tortise found it has come only 4/5 tortise.
so, the total distance is : 4/5 of 400 m.
then it will come :320m.
Ans: 320m.
Given that f(x) = (2x+1)/ (1-x)
(a) Find domain and range of f(x)
(b) Sketch the graphs of f(x), f^-1(x) on the same axes.
(c) Solve the equation f^-1(x) = f(x)
Thank You
The domain and the range of f(x) are x ≠ 0 and y < -2 or y > -2
The solution to the equation f^-1(x) = f(x) is x = -0.5
The domain and the range of f(x)From the question, we have the following parameters that can be used in our computation:
f(x) = (2x + 1)/(1 - x)
Set the denominator to 0, to determine the domain
So, we have
1 - x = 0
Evaluate the like terms
x = 1
This means that the domain is all set of values except 0
i.e. x ≠ 0
For the range, the function does not have values at y = -2
This means that the range is
y < -2 or y > -2
The graph of the functionsSee attachment for the graphs of f(x), f^-1(x) on the same axes.
The solution of the equationStart by calculating the inverse of f(x)
So, we have
y = (2x + 1)/(1 - x)
Swap x and y
x = (2y + 1)/(1 - y)
When we solve the equation for y, we have
y = (x - 1)/(2 + x)
Substitute y = (x - 1)/(2 + x) in y = (2x + 1)/(1 - x)
(x - 1)/(2 + x) = (2x + 1)/(1 - x)
Cross multiply
So, we have
(x - 1)(1 - x) = (2x + 1)(2 + x)
x - x² + 1 + x = 4x + 2x² + 2 + x
Evaluate
3x + 3x² + 1 = 0
Using a graphing calculator, we have
x = -0.5
Hence, the solution is x = -0.5
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the table layout and relationship structure of a relational database is called its:
The table layout and relationship structure of a relational database is called its schema.
A schema in a relational database refers to the overall structure and organization of tables, their attributes (columns), and the relationships between them. It defines the blueprint for how the data is organized and stored in the database.
The schema includes information such as the table names, column names, data types, constraints, and the relationships established through keys (such as primary keys and foreign keys). It provides a logical representation of the database structure and helps ensure data integrity and consistency.
The schema serves as a guide for creating, modifying, and querying the database tables. It defines the structure that enforces rules and relationships between tables, facilitating data manipulation and retrieval.
By designing a well-defined schema, database administrators and developers can establish the foundation for efficient data storage, retrieval, and management within a relational database system.
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