Step-by-step explanation:
The prime factor of the 144 is 24 x 32. The exponents in the prime factorisation are 4 and 2. Add the number 1 with the exponents and multiply it. (4+1)(2+1) = 5 x 3 = 15.
A term life insurance policy will pay a beneficiary a certain sum of money upon the death of the policyholder. These policies have premiums that must be paid annually. Suppose a life insurance company sells a $250,000 one-year term life insurance policy to a 49-year-old female for $780. The probability the female will survive the year is 0.997. (a) Compute the expected profit of this policy to the insurance company. (b) Interpret the value of expected profit in (a) in the context of the problem.
(a) The expected profit of this policy to the insurance company is $520.10.
(b) The interpretation value of expected profit in (a) in the context of the problem is small probability of the policyholder's death.
(a) The expected profit to the insurance company can be calculated as follows:
Expected Profit = (Probability of Survival * Premium) - (Probability of Death * Death Benefit)
Probability of Survival = 0.997
Probability of Death = 1 - Probability of Survival = 1 - 0.997 = 0.003
Premium = $780
Death Benefit = $250,000
Expected Profit = (0.997 * $780) - (0.003 * $250,000) = $520.10
Therefore, the expected profit to the insurance company from selling this policy is $520.10.
(b) The expected profit of $520.10 represents the average profit that the insurance company can expect to earn from selling this type of policy to similar customers over time.
In the context of this problem, it means that if the insurance company sells many policies like this one, they can expect to make a profit of about $520.10 per policy, on average, after accounting for the small probability of the policyholder's death.
To know more about insurance policy here.
https://brainly.com/question/17479291
#SPJ4
5. A population of bumble bees starts at 20 bees in the spring. Every week, the
population of bumble bees triples. Write the geometric sequence formula and
find the number of bees after 32 weeks. Show all of your work.
After 32 weeks, the population of bumble bees will be 6.77315 x 10¹⁴ bees.
Solving for the population of bumble bees after 32 weeks:The population of bumble bees triples every week, so the common ratio is 3. The starting population is 20 bees.
The formula for a geometric sequence is:
a_n = a_1 * rⁿ⁻¹
where,
a_n = the nth term in the sequence
a_1 = the first term
r = the common ratio
n = the number of terms.
Using this formula, we can find the number of bees after 32 weeks:
a_32 = 20 * 3³²⁻¹
a_32 = 20 * 3³¹
a_32 = 6.773150 × 10¹⁴
Therefore, after 32 weeks, the population of bumble bees will be approximately 6.77315 x 10¹⁴ bees.
Learn more about geometric sequence on
https://brainly.com/question/13008517
#SPJ1
The second angle of the triangle is 25 degrees larger than the first, while the third angle of the triangle is 3 times the second. How big is the first angle? Remember, the sum of the angles in any triangle is 180 degrees.
Answer: look at the image for the answer and the explanation
Step-by-step explanation:
Answer: 16 degrees
Step-by-step explanation:
how to determine the sum of all the factors of 100
Answer:
5, 10 20, etc.
Step-by-step explanation:
You can skip count like you do in multiplying.
what is the quotient of 25 divide by 25,704 use long division
The quotient of 25 divided by 25,704 is approximately 0.00097 (rounded to five decimal places).
How would one describe long division?When splitting huge numbers, the task is divided into several sequential steps using the long division approach. The dividend is divided by the divisor, just like in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.
The long division for 25 divided by 25,704 is shown below:
code :
0.00097
-------
25704 | 25.00000
0
--
250
257
---
-7
As a result, the result of 25 divided by 25,704 is almost 0.00097. (rounded to five decimal places).
To know more Long Division visit:
https://brainly.com/question/28824872
#SPJ1
calculate 10% of 360km
Answer:36
Step-by-step explanation:360 * 0.1 = 36 or 360/10 = 36
HELP PLEASEEE
Write en equation of a Line that goes through (1, 2) slope = 7. Put in point slope
The height h of the triangle is 8cm greater than its corresponding base. HELP PLSSS
The area of the triangle is 120 square centimeters.
A = 120 cm².
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
The area of the triangle = 1/2 x base x height.
Given:
The height h of the triangle is 8cm greater than its corresponding base.
That means
the height = 20 + 8 = 20 cm.
The area of the triangle,
= 1/2 x base x height
= 1/2 x 12 x 20
= 120 square centimeters.
Therefore, the area is 120 square centimeters.
To learn more about the area;
https://brainly.com/question/27683633
#SPJ1
Cody is selling scarves at a craft fair. Cody uses the
expression np - (m + 10) to calculate profit, where n is
equal to the number items sold, p is the price per item, m is
the amount Cody spent on materials, and the 10 represents
the fee to sell at the fair.
If Cody sold 9 scarves at $25 each and spent $34 on
materials, what was his profit, in dollars?
Cody's profit from selling 9 scarves at $25 each, after spending $34 on materials and paying a $10 fee to sell at the craft fair, was $181.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
To calculate Cody's profit using the expression np - (m + 10), we need to substitute the given values:
n = 9 (number of scarves sold)
p = $25 (price per scarf)
m = $34 (amount spent on materials)
Using these values, we can calculate Cody's profit as:
= np - (m + 10)
= (9 * 25) - (34 + 10)
= 225 - 44
= $181
Therefore, Cody's profit from selling 9 scarves at $25 each and spending $34 on materials is $181.
Learn more about Mathematical operations here:
https://brainly.com/question/20628271
#SPJ9
The population of a country is growing by 1. 5% per year. A census taken in 1999 showed a population of 9,800,000. Assume the country's population growth remains constant. What will the population be in 2009?
Population growth is usually an exponential equation. By forming and solving an exponential equation the population in 2009 will be 11,373,300.08
The exponential equation for population growth is,
P = P₀ ( 1+r)ⁿ
P₀ is the initial population, r is the rate and n is the time.
Here r = 1.5% = 1.5/100 = 0.015
n is 10 years and P₀ is 9800000
Substituting the values in equation,
P = 9800000 ( 1+0.015)¹⁰
= 9800000 × 1.160 = 11,373,300.08
So with the growth rate of 1.5% over 10 years, the population will grow and reach 11,373,300.08.
For more information regarding exponential growth, kindly refer
https://brainly.com/question/14355665
#SPJ4
what is linear interpolation formula
The formula of linear interpolation(y) = [tex]y_{1} +\frac{(x - x_{1}) (y_{2} -y_{1}) }{x_{2} -x_{1} }[/tex]
The formula to calculate linear interpolation is:
Linear Interpolation(y) = [tex]y_{1} +\frac{(x - x_{1}) (y_{2} -y_{1}) }{x_{2} -x_{1} }[/tex]
where,
[tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the first coordinates[tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the second coordinatesx is the point to perform the interpolationy is the interpolated value.It allows users to interpolate (interpolation is a mathematical technique for estimating any value between two known points) data points between the sets(two sets) of points or coordinates.
Take the two known points and calculate the value of the point that lies between them. This has been used in as many engineering applications as estimating the value of a point on a graph or table. This calculator helps in estimating the value of a point that lies between two known points on a line.
To know more about Linear Interpolation:
brainly.com/question/23984064
#SPJ4
15. Prove inductively and deductively that the sum of six consecutive numbers is divisible by 3. (4
marks)
Deductive Reasoning
The required proof is inductively and deductively that the sum of six consecutive numbers is divisible by 3 in the solution part.
What is deductive reasoning?Deductive reasoning is a method of reasoning in which conclusions are drawn based on premises that are known or assumed to be true.
Let's assume that the six consecutive numbers are n, n+1, n+2, n+3, n+4, and n+5.
We have to show that the sum of these numbers is divisible by 3.
First, we can express the sum of the six numbers as follows:
n + (n+1) + (n+2) + (n+3) + (n+4) + (n+5)
Simplify the expression by combining like terms:
6n + 15
Next, factor out 3 from the expression:
6n + 15 = 3(2n + 5)
Since 2n + 5 is an integer, we can see that 3(2n + 5) is divisible by 3. Therefore, the sum of six consecutive numbers is divisible by 3.
This is an example of deductive reasoning because we started with a premise (the assumption that the six consecutive numbers are n, n+1, n+2, n+3, n+4, and n+5) and used logical steps to arrive at a conclusion (that the sum of the six numbers is divisible by 3).
Learn more about deductive reasoning here:
https://brainly.com/question/971917
#SPJ9
how to calculate inverse tangent?
The Inverse tangent is defined as the mathematical function that returns the angle whose tangent is a given number and the step to calculate the inverse tangent has been explained
Inverse tangent (also known as arctangent) is a mathematical function that returns the angle whose tangent is a given number. The inverse tangent function is denoted by "tan^-1" or "arctan".
To calculate the inverse tangent of a number, you can follow these steps:
Determine the input value (the number whose inverse tangent you want to find).
Use the inverse tangent function on your calculator.
The output of the inverse tangent function will be in radians. If you want the result in degrees, you can convert it using the formula: degrees = radians * (180/π), where π (pi) is approximately 3.14159
Learn more about inverse tangent here
brainly.com/question/14998181
#SPJ4
Write each phrase as an algebraic expression.
14. n divided by 8.
15. p multiplied by 4
16. b plus 14.
17. 90 times x,
18. a take away 16.
19. k less than 24
20. 3 groups of w
21. the sum of 1 and q
22. the quotient of 13 and z.
23. cadded to 45
Each phrase can be epressed as an algebraic expression as:
n/8
4p,
b+14
90x
-16
24-k
3(w)
1+q
13/z
45+c
w-8
What is algebraic expression?An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). A good example of an algebraic expression is 3x2 2xy + c.
A variable expression can be described using its terms and operations on the terms as an algebraic expression. For instance, "3 more than x" can be used to describe x + 3.
Learn more about algebraic expression at:
https://brainly.com/question/4344214
#SPJ1
two vectors are linearly dependent if and only if they are collinear.
true
false
If the sun is 59 degrees above the horizon, find the length of the shadow cast by a building 52 feet tall, round your answer to the nearest tenth
Answer:44.5
Step-by-step explanation:
To solve this problem, we can use the tangent function, which relates the angle of elevation to the length of the opposite side (the shadow) and the adjacent side (the height of the building).Let x be the length of the shadow.
Then, we have:tan(59°) = 52/xTo solve for x, we can cross-multiply and simplify:x = 52 / tan(59°)
x ≈ 44.5 feet (rounded to the nearest tenth)Therefore, the length of the shadow cast by the building is approximately 44.5 feet.
Find the missing length. The triangles in each pair are similar.
Answer: 56
Step-by-step explanation: Since we know both triangles are similar, we want to first find the scale factor between the two triangles, knowing side UP and side PQ are corresponding we can find that 84/60 or in simplified terms, 7/5 is the scale factor. Now we know that side VP and side PR are corresponding so 40 x 7/5 gives us 56 which is side PR. Hope this helped! :)
Find the value of each markup or discount. 1. original $10.00 percent of markup: 20%
The value of the markup is $12
How to determine the value of the markupFrom the question, we have the following parameters that can be used in our computation:
Original $10.00 percent of markup: 20%
The markup price is calculated as
Markup Price = Original; * (1 + Markup)
Substitute the known values in the above equation, so, we have the following representation
Markup Price = 10 * (1 + 20%)
Evaluate
Markup Price = 12
Hence, the price is $12
Read more about markup at
https://brainly.com/question/19104371
#SPJ1
solve for y and state how many solutions there will be. y+2=2x
This is a linear equation with a slope of 2 and a y-intercept of -2. There is exactly one solution for y for every value of x.
Describe Equation?In mathematics, an equation is a statement that two expressions are equal. It usually contains one or more variables, which are unknown quantities that can take on different values. Equations are used to represent relationships between quantities, and they can be used to solve problems by finding the values of the variables that make the equation true.
An equation typically consists of two sides, separated by an equal sign. Each side can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. For example, the equation:
2x + 3 = 7
contains the variable x, as well as constants 2, 3, and 7, and mathematical operations of addition and multiplication.
Equations can be solved by applying algebraic techniques to isolate the variable on one side of the equation. For example, to solve the above equation for x, we can first subtract 3 from both sides to get:
2x = 4
Then, we can divide both sides by 2 to get:
x = 2
This is the solution to the equation, which means that x must be equal to 2 in order to make the equation true.
Equations are used in many areas of mathematics, including algebra, calculus, geometry, and trigonometry. They are also used in physics, engineering, and other sciences to model physical phenomena and solve problems related to them.
To solve for y, we need to isolate y on one side of the equation.
y + 2 = 2x
Subtract 2 from both sides:
y + 2 - 2 = 2x - 2
Simplify:
y = 2x - 2
Therefore, the solution for y is y = 2x - 2.
This is a linear equation with a slope of 2 and a y-intercept of -2. There is exactly one solution for y for every value of x.
To know more about intercept visit:
https://brainly.com/question/14180189
#SPJ1
what is 56 as a decimal?
Answer: 56 as a decimal is 0.56
Step-by-step explanation: Just simply add a decimal point in front of 56, and you’ll get 0.56
56 = 0.56
Hope this helps!
- Critique Reasoning Amanda calculated 34÷8= 3 R10. Is Amanda's answer correct? If not, what is the correct answer? Explain.
Amanda's answer correct is not correct. The correct answer is 4 R2, because she might have incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead
Amanda's answer, 3 R10, is not correct.
When we divide 34 by 8, we want to know how many times 8 goes into 34, and what is left over. We start by dividing 8 into the first digit of 34, which is 3. 8 cannot go into 3, so we move on to the next digit, which is 34.
We can see that 8 goes into 34 four times, because 8 x 4 = 32. This means that the whole number part of the answer is 4.
But there is still a remainder left over. To find the remainder, we subtract 32 from 34, which gives us 2.
Therefore, the correct answer is 4 R2.
Amanda's mistake may have been to incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead.
Learn more about division here
brainly.com/question/2339009
#SPJ4
Helpppp math asappp 25 points
Answer:
2*4*3
Step-by-step explanation:
The number of blocks is the same as the volume. So start with the formula for the volume of a rectangular prism, that being length*width*height. Then use the picture to count out that the length is 4 blocks, width is 2 blocks and height is 3 blocks. Then we can plug these values into our equation and get the answer: 2*4*3
what is mm to meters?
The method to convert milimeter to meters will be through multiplication of [tex] {10}^{-3} [/tex] with the quantity in milimeter.
The abbreviation mm is representative of milimeters. Now, we know that milimeters is 1/1000 meters and hence is smaller unit in comparison to meters.
Based on the above mentioned fact, we can multiply the same number (smaller unit) with negative exponent. It will be carried out like this -
Quantity in meters = quantity in milimeter ×
[tex] {10}^{-3} [/tex], where [tex] {10}^{-3} [/tex] has negative exponent. Let us say we have 10⁹ milimeters and need to convert in into meters.
So, quantity in meter = 10⁹ × [tex] {10}^{-3} [/tex],
Performing multiplication which will be done through subtraction of powers
Quantity in meters = 10⁶ meters
Hence, mm to meters will be multiplication with [tex] {10}^{-3} [/tex].
Learn more about unit conversion -
https://brainly.com/question/13016491
#SPJ4
for a period of time, an island's population grows exponentially. If the population doubles every 34 years and the current population is 1233, what will the population be 6 years from now?
As a result, the island's population will be about 1397.33 persons in 6 years.
What is exponent?An exponent, also called a power or index, is a mathematical operation that indicates the number of times a base number is multiplied by itself. Exponents are written as a superscript number to the right of the base number. Exponents can be positive or negative, and they can be whole numbers or fractions. A positive exponent tells us to multiply the base number by itself, while a negative exponent tells us to divide the base number into 1. Exponents can be used to simplify and solve many mathematical problems, and they are an important part of many areas of mathematics, including algebra, calculus, and geometry.
Here,
If the population of the island doubles every 34 years, we can use the exponential growth formula to determine the population after a certain period of time:
P = P0 * 2ⁿ÷³⁴
where P is the population after time t, P0 is the initial population, and t is the time elapsed in years.
We know that the current population is 1233, so P0 = 1233. We want to find the population 6 years from now, so t = 6. Plugging these values into the formula, we get:
P = 1233 * 2⁶÷³⁴
P ≈ 1397.33
Therefore, the population of the island will be approximately 1397.33 people 6 years from now.
To know more about exponent,
https://brainly.com/question/11709654
#SPJ1
Find the length of X
Answer:
Below
Step-by-step explanation:
21 is to 27 as x-3 is to x-1
21/27 = x-3/x-1 cross multipliy , solve for x = 10
Answer:
x = 10Step-by-step explanation:
x-3/21 = x-1/27
27(x-3) = 21(x-1)
27x-81 = 21x-21
27x-21x = -21+8
6x = 60
x = 60/6
x = 10
_____________________
Hope this helps! :)
2/3(3-6x)=-3(8x-4).
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Solve for x
[tex]\frac{2}3}(3-6x)=-3(8x-4)[/tex]
Distribute [tex]\frac{2}{3}[/tex] and -3.
[tex]2-4x=-24x+12[/tex]
Simplify
[tex]-4x+2=-24x+12[/tex]
Subtract 2 on both sides
[tex]-4x=-24x+10[/tex]
Subtract -24x on both sides
[tex]20x=10[/tex]
Divide by 20
[tex]x=\frac{1}{2}[/tex] or 0.5
List the prime numbers between 20 and 30
25 and 29
23 and 29
21 and 23
23 and 27
The numbers between 20 and 30 are: 21,22,23,24,25,26,27,28,29 Even numbers, other than 2 are not prime because by definition of being even they are divisible by 2.
What are prime numbers?
Prime numbers are numbers that can only be divisible by themselves or 1. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. In this tutorial, you will learn how to check if a number is a prime number. We will discuss how to write a prime number program in python – this program prints numbers that are prime numbers within a given range.
There is just one perfect number between 20 and 30. The number 28 is a perfect number. Its factors are 1, 2, 4. 7, 14, and 28. Why is 2 the only prime number? Two is a prime because it is divisible by only two and one. All the other even numbers are not prime because they are all divisible by two. That leaves only the odd numbers.
Hence, The numbers between 20 and 30 are: 21,22,23,24,25,26,27,28,29 Even numbers, other than 2 are not prime because by definition of being even they are divisible by 2.
Learn more about prime numbers here: https://brainly.com/question/23039018
#SPJ3
How is Z 1.96 at 95 confidence?
The value of the average normal distribution with a 95% degree of confidence is Z 1.96 as 95% of the area under the standard normal distribution curve should fall between -Z and Z, hence Z should be selected to reflect this.
In statistics, the standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. The region beneath the curve between any two values represents the chance of seeing a value inside a given range.
At a 95% confidence level, the value of Z should be chosen so that 95% of the area under the standard normal distribution curve is between -Z and Z. Using a calculator or a generic table of the normal distribution, we may determine Z = 1.96 with a 95% confidence interval. In 95% of the situations, the values of the classic normal distribution lie between +/- 1.96 standard deviations from the mean.
For more such questions on confidence
https://brainly.com/question/15712887
#SPJ4
The area of the rectangle is 34.56cm squared. The diamtetr is 2.75cm. WHAT is the surface area.
The total surface area is 46.43 square centimeter.
What is surface area?The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.
Given that, the area of the rectangle is 34.56 cm².
Here, the diameter is 2.75 cm, so radius =2.75/2=1.375 cm
Cylinder is made up of 1 rectangle and 2 circles.
Now, area of 2 circles =2πr²
= 2×3.14×1.375²
= 11.87 cm²
So, total surface area = 34.56+11.87
= 46.43 cm²
Therefore, the total surface area is 46.43 square centimeter.
Learn more about the total surface area here:
https://brainly.com/question/8419462.
#SPJ1
what is steps per mile?
Steps per mile is a measure of how many steps a person takes to walk one mile, Which is 2000 steps.
It takes over 2,000 steps to walk one mile and 10,000 steps would be almost 5 miles, as the average person has a stride length of approximately 2.1 to 2.5 feet.
The number of steps required to walk a mile can vary from person to person depending on their height, weight and stride length. And Generally, taller people with longer strides take fewer steps per mile, while shorter people with shorter strides take more steps per mile.
To know more about Steps per mile:
brainly.com/question/30403088
#SPJ4
