Answer:
The reduced paid up insurance value is $47,770 and the annual premium is $4,097
The reduced paid-up insurance value is $6,692.83.
The annual premium for the reduced paid-up insurance is the amount of money that the policyholder would
We have,
To determine the reduced paid-up insurance value and the annual premium,
We need to use the information given and the following formulae:
The cash value of a policy is the amount of money that the policyholder would receive if they surrendered the policy before it matured.
The net amount at risk is the difference between the face value of the policy and the cash value.
The present value of a policy is the sum of the net amount at risk and the present value of the future premiums.
We are given that:
The policy is a 20-Year Endowment insurance policy, purchased when the policyholder was 40 years old.
The face value of the policy is $85,000.
The policyholder is now 50 years old.
The permanent insurance amount is $48.20 per thousand.
We need to determine the reduced paid-up insurance value and the annual premium.
We can use the following steps to determine the reduced paid-up insurance value and the annual premium:
Step 1: Calculate the cash value of the policy
The cash value of the policy can be calculated using the following formula:
Cash value = (Present value of future endowment benefits) - (Present value of future premiums)
We are given that the policy is a 20-Year Endowment policy, so the endowment benefit is $85,000. We can use the following formula to calculate the present value of the future endowment benefits:
Present value of endowment benefits = Endowment benefit / (1 + i)n
where i is the interest rate and n is the number of years.
Since the policyholder is 50 years old and the policy has 10 years left, we can assume an interest rate of 4% and calculate the present value of the endowment benefits as follows:
Present value of endowment benefits = $85,000 / (1 + 0.04)^10 = $48,598.20
We can calculate the present value of future premiums using the following formula:
Present value of future premiums = Net amount at risk / (Present value of an annuity due of $1 for n years, at i%)
where n is the number of years and i is the interest rate.
Since the policyholder has paid premiums for 10 years, there are 10 years left to pay. Using the same interest rate of 4%, we can calculate the present value of an annuity due of $1 for 10 years as follows:
Present value of an annuity due of $1 for 10 years, at 4% = 7.3601
We can now calculate the net amount at risk as follows:
Net amount at risk = Face value - Cash value
Face value = $85,000
Cash value = $48,598.20 + (Annual premium x Present value of an annuity due of $1 for 10 years, at 4%)
Net amount at risk = $85,000 - $48,598.20 - (Annual premium x 7.3601)
Step 2: Calculate the reduced paid-up insurance value
The reduced paid up insurance value is the amount of insurance that the policyholder can receive without paying any more premiums. It can be calculated as follows:
Reduced paid up insurance value = Cash value / Permanent insurance amount
Using the cash value calculated in Step 1 and the permanent insurance amount of $48.20 per thousand, we can calculate the reduced paid up insurance value as follows:
Reduced paid up insurance value.
= $48,598.20 / ($48.20 x 85)
= $6,692.83
Step 3: Calculate the annual premium
The annual premium for the reduced paid-up insurance is the amount of money that the policyholder would
Thus,
The reduced paid-up insurance value is $6,692.83.
The annual premium for the reduced paid-up insurance is the amount of money that the policyholder would
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x^2 − 8 = 8 pls help
if you're solving for x,
start by isolating x squared to get
x^2 = 16 (we added 8 to both sides)
then square root each side:
sqrt of x^2 = x; sqrt of 16 = 4.
we end up with x = 4 (positive and neg)
if you're factoring
minus 8 from both sides to get
x^2 - 16
from there we can factor to get
(x + 4)(x - 4)
The equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is h = -15 cos(2pi/5 t). At which times will the spring be at a height of 8 in. above equilibrium? Select two of the following, make two selections.
Answer:
1.7 seconds, and
3.3 seconds
Step-by-step explanation:
We simply need to plug in 8 into h and solve for t:
[tex]h=-15Cos(\frac{2\pi}{5}t)\\8=-15Cos(\frac{2\pi}{5}t)\\-\frac{8}{15}=Cos(\frac{2\pi}{5}t)\\\frac{2\pi}{5}t=Cos^{-1}(-\frac{8}{15})\\\frac{2\pi}{5}t=2.13\\t=\frac{2.13}{\frac{2\pi}{5}}\\t=1.70[/tex]
Since cosine is negative in the 3rd quadrant as well, we need to figure out the 3rd quadrant equivalent of 2.13 radians.
First, π - 2.13 radians = 1.01 radians.
Then, we add 1.01 to π radians, so we get 4.15 radians
Solving from the last part, we have:
[tex]t=\frac{4.15}{\frac{2\pi}{5}}\\t=3.3[/tex]
also, t = 3.30 seconds
*Note: we put the calculator mode in radians when solving
So, t = 1.7 seconds & 3.30 seconds
6/10+39/100 find the sum
The answer is-
Exact form: 99/100
Decimal form: 0.99
Please help with my homework
Answer:
It is 2 1/2
Step-by-step explanation:
One of the roots of the equation 10x2−33x+c=0 is 5.3. Find the other root and the coefficient c.
Answer:
1. The other root is [tex]-2[/tex]
2. c=-106
Step-by-step explanation:
The given equation is [tex]10x^2-33x+c=0[/tex].
If [tex]5.3[/tex] is a solution to the given quadratic equation, then [tex]x=5.3[/tex] must satisfy this equation.
[tex]10(5.3)^2-33(5.3)+c=0[/tex]
[tex]280.9-174.9+c=0[/tex]
[tex]106+c=0[/tex]
[tex]c=0-106=-106[/tex]
We now substitute [tex]c=-106[/tex] into the given equation to obtain;
[tex]10x^2-33x-106=0[/tex].
Comparing to the general equation;
[tex]ax^2+bx+c=0[/tex], we have a=10, b=-33 and c=-106.
Recall the quadratic formula;
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
We now use the quadratic formula to obtain;
[tex]x=\frac{--33\pm \sqrt{(-33)^2-4(10)(-106)} }{2(10)}[/tex]
This implies that;
[tex]x=\frac{33\pm \sqrt{5329} }{20}[/tex]
[tex]x=\frac{33\pm73}{20}[/tex]
[tex]x=\frac{33-73}{20}[/tex] or [tex]x=\frac{33+73}{20}[/tex]
[tex]x=\frac{-40}{20}[/tex] or [tex]x=\frac{106}{20}[/tex]
[tex]x=-2[/tex] or [tex]x=5.3[/tex]
Hence the other root is [tex]-2[/tex]
Find the missing number: 8.4(1.5 + 2.3) = 12.6 +
Answer:
19.32
Step-by-step explanation:
One way to find the missing number is to get the value of the left side of the equation first.
8.4(1.5 + 2.3) = 31.92
Now we need to take that value and subtract it to the value on the right side of the equation.
31.92 - 12.6 = 19.32
So we have:
8.4(1.5 + 2.3) = 12.6 + 19.32
31.92 = 31.92
Answer:
The required number is 19.32
Step-by-step explanation:
Consider the provided expression.
Let the missing number is x.
[tex]8.4(1.5 + 2.3) = 12.6 +x[/tex]
Add the numbers as shown.
[tex]8.4(3.8) = 12.6 +x[/tex]
Open the parentheses.
[tex]31.92= 12.6 +x[/tex]
Subtract 12.6 from both the sides.
[tex]31.92-12.6= 12.6-12.6 +x[/tex]
[tex]x=19.32[/tex]
Hence, the required number is 19.32
What is the value of x in the equation −6 + x = −1
Answer:
x=5
Step-by-step explanation:
-6+5=-1
start at -6 then go right units until u get -1 you got right 5 units
The value of x in the given equation is:
x=5
Step-by-step explanation:We are given a algebraic expression in terms of the variable x by:
[tex]-6+x=-1[/tex]
Now, we are asked to find the value of x from the equation.
i.e. we have to solve for x.
i.e. by some appropriate algebraic operation we need to solve for x.
so we will add 6 on both the sides of the equation to get:
[tex]-6+x+6=-1+6\\\\i.e.\\\\-6+6+x=5\\\\i.e.\\\\0+x=5\\\\i.e.\\\\x=5[/tex]
Hence, the value of x is: 5
What is the area of this triangle? please help me.
Answer:
6
Step-by-step explanation:
Area of a triangle: bh/2
4*3/2=6
Answer:
6 units²
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = DE = 3 units and
h is the distance from the vertex F to DE = 4 units, hence
A = [tex]\frac{1}{2}[/tex] × 3 × 4 = 6 units²
Please !!! Someone help me
answer is the last one D
pls mark brainliest
The answer is D good luck
The conditional relative frequency table below was generated by column using frequency table data comparing the number of calories in a meal to whether the meal was prepared at home or at a restaurant.
A nutritionist attempts to determine an association between where food is prepared and the number of calories the food contains. Which is most likely true?
A. An association cannot be determine because the value 0.55 is similar to the value 0.45
B. There is an association because the value 0.15 is not similar to the value 0.55
C. There is an association because the sum of each column is 1.0.
D. An association cannot ve determined because the sum of the rows going across is not 1.0.
Answer:
B. There is an association because the value 0.15 is not similar to the value 0.55
Step-by-step explanation:
Based on the above picture, for the nutritionist to determine whether there is an association between where food is prepared and the number of calories the food contains, there must be an association between two categorical variables.
The conditions that satisfy whether there exists an association between conditional relative frequencies are:
1. When there is a bigger difference in the conditional relative frequencies, the stronger the association between the variables.
2. When the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.
For the given conditional relative frequency, we can see that there exists a significant difference between the columns of the table in the picture because 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45
We can conclude that there is an association because the value 0.15 is not similar to the value 0.55
Answer:There is an association because the value 0.15 is not similar to the value 0.55.
Step-by-step explanation:
what are the steps to solve 2+8-z=-24?
Move z and 24, switch signs then add numbers
Answer:
z=34
Step-by-step explanation:
Here is:
2+8-z=-24
2+8+24=z
z=34
Best regards
Choose the correct answer. Distance between 2 airports = 1,450 miles. Average speed of airplane = 350 mph. Travel time by bus after arrival at airport = 20 minutes. Total travel time = _____ hours.
Please do not round
Final answer:
Using the given information, the total travel time by airplane and bus is calculated as 4.47616 hours, which includes flying time and additional travel time by bus.
Explanation:
To calculate the total travel time by airplane including the additional travel time by bus, we must first find out the time taken by the airplane to cover the distance between the two airports. This can be done by dividing the distance by the airplane's average speed. Afterward, we add the bus travel time to get the total travel time.
The time taken by the airplane to cover 1,450 miles at an average speed of 350 mph is calculated by dividing distance by speed: 1,450 miles ÷ 350 mph = 4.142857 hours. Note that we do not round this number to maintain accuracy.
Next, we convert the bus travel time of 20 minutes into hours: 20 minutes ÷ 60 minutes per hour = 0.3333 hours.
Now, we add both the airplane and bus travel times together: 4.142857 hours + 0.3333 hours = 4.47616 hours total travel time.
Graph the solution for the following system of inequalities. Click on the graph until the correct solution is displayed. x + y > 3 x + y < -4
Answer:
The graph for the following system of inequalities is attached below.
Step-by-step explanation:
The given system of inequalities is
[tex]x+y>3[/tex] .... (1)
[tex]x+y<-4[/tex] .... (2)
From inequality (1) and (2) it is clear that (x+y) is greater than 3 adn 3 is not less than -4. So, the given system of inequality has no feasible reason or solution.
The related equation of first inequality is
[tex]x+y=3[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=3\Rightarrow y=3[/tex]
The y-intercept is 3.
Put y=0 to find the x-intercept.
[tex]x+0=3\Rightarrow x=3[/tex]
The x-intercept is 3.
The related equation of second inequality is
[tex]x+y=-4[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=-4\Rightarrow y=-4[/tex]
The y-intercept is -4.
Put y=0 to find the x-intercept.
[tex]x+0=-4\Rightarrow x=-4[/tex]
The x-intercept is -4.
The related lines are dotted line because the sign of inequalities are > and <.
Check each inequality be (0,0).
[tex]0+0>3[/tex]
[tex]0>3[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
[tex]0+0<-4[/tex]
[tex]0<-4[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
The graph for the following system of inequalities is attached below.
Answer:
This is the correct graph on Odyssey :)
As part of your training schedule you plan to jog once a week around the reservoir shown below on the map.
One lap along the perimeter of the reservoir is 25 cm. What is the actual length of a lap?
The actual length of a lap cannot be determined without the scale of the map. The 25 cm measurement seems to be from the map, so without knowing the real-world equivalent of the map's measurements, we can't find the actual distance.
Explanation:The length of a lap around the reservoir cannot be directly determined from the information given. The measurement provided (25 cm) appears to be a distance measured on a map or plan of the area, and not in real life. In order to convert that measurement into a real-world distance, we need the scale of the map. A map's scale is typically represented as a ratio that indicates the relationship between a certain distance on the map and the real-world distance it represents.
For example, if the map's scale was 1 cm : 1 km, then a measurement of 25 cm on the map would represent a real-world distance of 25 km. However, without the scale, we cannot accurately determine the actual length of a lap around the reservoir. This concept is extremely important in geography and cartography as well as in mathematical problems dealing with maps and scales.
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What is 6x^2-12x+y+13=0 in vertex form of parabolas
Answer:
[tex]y=-6(x-1)^{2}-7[/tex]
Step-by-step explanation:
we have
[tex]6x^{2} -12x+y+13=0[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y+13=-6x^{2} +12x[/tex]
Factor the leading coefficient
[tex]y+13=-6(x^{2} -2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y+13-6=-6(x^{2} -2x+1)[/tex]
[tex]y+7=-6(x^{2} -2x+1)[/tex]
Rewrite as perfect squares
[tex]y+7=-6(x-1)^{2}[/tex]
[tex]y=-6(x-1)^{2}-7[/tex] -----> equation of the parabola in vertex form
The vertex is (1,-7) is a maximum, the parabola open downward
To convert 6x^2 - 12x + y + 13 = 0 to vertex form, follow the steps to complete the square and rewrite the equation as (x - 1)^2 = -y/6 - 7/6.
Explanation:The equation 6x^2-12x+y+13=0 is in the general form of a quadratic equation. To convert it into the vertex form, we need to complete the square.
First, let's group the x terms together: 6x^2 - 12x = -(y + 13).
Next, let's complete the square: 6(x^2 - 2x) = -(y + 13).
Now, we can add (2/2)^2 = 1 to both sides to complete the square: 6(x^2 - 2x + 1) = -(y + 13) + 6.
Simplifying further, we get 6(x - 1)^2 = -y - 7.
Finally, we can write the equation in vertex form by dividing both sides by 6: (x - 1)^2 = -y/6 - 7/6.
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what is 3(x-4)-7=(2x-3)
Solve for x by simplifying both sides of the equation, then isolating the variable.
So the answer to your question is :
x = 16.
Hope this helps,
Davinia.
Answer:
x = 16
Step-by-step explanation:
distribute parenthesis on both sides and simplify
3x - 12 - 7 = 2x - 3
3x - 19 = 2x - 3 ( subtract 2x from both sides )
x - 19 = - 3 ( add 19 to both sides )
x = 16
Simplify 6 to the fifth power over 7 cubed all raised to the second power
Step-by-step explanation:
Do you mean:
(6^5/7^3)^2?
If so, you will get
6^10/7^6 or about 513.954016
It is to be note that (6⁵ / 7³)² simplifies to become approximately 514.64
How to compute the above simplificationTo simplify the expression (6⁵ / 7³)², we start by evaluating the exponents first.
6⁵ means 6 raised to the power of 5, which is 6 * 6 * 6 * 6 * 6 = 7776.
7³ means 7 raised to the power of 3, which is 7 * 7 * 7 = 343.
Now, we substitute these values back into the expression -
(7776 / 343)² = (22.6666666667)² = 514.64197531
Therefore, it is right to state that (6⁵ / 7³)² simplifies to 514.64197531 which is approximately, 514.64.
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What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2,5)?
Answer:
C
Step-by-step explanation:
The point slope form of a line is [tex]y - y_1 = m(x-x_1)[/tex]. If the point is (2,5) then the equation will be [tex]y - 5=m(x-2)[/tex]. Only option C matches this equation.
Dnhdhdbdvdeh hellllllpppppppp
what is the difference between the mean high and mean low temperature for this 5-day period?
Answer:
the mean high temperature is 71 degrees and the mean low is 31 degrees
Step-by-step explanation:
Find the area of the triangle that has a base of 5in -‘d a height of 3 3/4
Answer:
its either c or b
Step-by-step explanation:
formula: 1/2*b*h or 1/2*5*3+3/4
the answer i got was 33/4
Steps to convert fractions into decimals 4/25
Divide 4 by 25 either by hand or by calculator. Hope this helped.
Answer: [tex]\frac{4}{25}[/tex]=0.16
Step-by-step explanation:
How convert 4/25 into a decimal is :
4÷25 Then using Long Division for 4 divided by 25 and rounding to a Max of 3 Decimal Places gives us.Which will give you your answer as 0.16 in decimal form.:)* Hopefully this helps:)!! Mark me the brainliest:)!!!
The numbers of hours that 12 students say they typically spend on homework in a week are 2, 0, 10, 8,10, 8, 8, 8, 10, 10, 8, and 8. What is the mean number of hours? What are the outliers in the data set?
Answer:
The mean is 7.5 and the outliers are 0 and 2
Step-by-step explanation:
To find the mean, add all of the numbers together and divide by the amount of numbers.
2 + 0 + 10 + 8 + 10 + 8 + 8 + 8 + 10 + 10 + 8 + 8 = 90
90/12 = 7.5
To see the outliers, look for the numbers far away from the mean.
A jar contains balls numbered 1 to 10. Two balls are drawn with replacement. What is the probability that both balls are numbered 2 or less?
Answer:
Step-by-step explanation:
The number of ways that you can draw 2 balls without restriction is 10 * 10 = 100
Two balls will give you 2 or less (meaning 1) or 2*2 = 4
Four ways are possible
2 and 2
2 and 1
1 and 2
1 and 1
4/100 = 1/25 is the probability of making this happen.
Help plz !! Need this to graduate
What is the difference between an approximate and an exact number?
Answer:
An approximate number is a close number that is only off by x number of places (Like a rounded number). An exact number is exactly correct. For example:
3 - 1.5 is approximately 2, but is exactly 1.5.
Mark Brainliest if this helps!
Final answer:
An exact number is one that is known with complete precision, such as the number of books on a shelf. An approximate number, or inexact number, includes uncertainty and comes with an error range, often due to measuring limitations such as estimating a length with a ruler. The level of rounding applies to approximate values determines their reliability, and significant figures are influenced by inexact numbers.
Explanation:
The difference between an exact number and an approximate number lies in their level of precision and the source of the number. Exact numbers are count numbers that are known with complete precision. An example of an exact number is the number of students in a classroom, which might be exactly 25. On the other hand, inexact numbers, also known as measured numbers, come with an error range due to the limitations of measuring instruments or methods. For instance, when using a ruler, you might measure a length as approximately 12.7 cm, but the true length might be slightly less or more.
It's important to note that the more rounding that is applied to a number, the less reliable it becomes. Approximations are common in various fields, including physics, where scientists and engineers make educated guesses, or 'guesstimates', based on available data and formulae with limited accuracy. These approximations are essential for problem-solving and can help in making quantitative decisions and realistic predictions.
Conversion factors in measurements are considered to be exact numbers because they are defined as such by the measurement systems. In calculations involving both exact and inexact numbers, the precision of the inexact numbers dictates the number of significant figures in the result.
What is the range of the graph
Answer:
Range: all real numbers greater than or equal to 2
Step-by-step explanation:
The range is the possible numbers that the output can take
Y can be any number greater than or equal to 2
Range: all real numbers greater than or equal to 2
. Find the area of a trapezoid with b1 = 13.8 cm, b2 = 16.8 cm, and h = 4 cm.
61.2 cm2
33.6 cm2
122.4 cm2
27.6 cm2
Answer:
61.2 cm²
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h ([tex]b_{1}[/tex] + [tex]b_{2}[/tex] )
Substitute in given values
A = [tex]\frac{1}{2}[/tex] × 4 × (13.8 + 16.8 ) = 2 × 30.6 = 61.2 cm²
The answer is 61.2cm² .
[tex]((13.8 + 16.8) \times 4) \div 2[/tex]
This equation helps you get the answer.
1.simplifyyyyyyyyyyyy
Answer:
Choice A
Step-by-step explanation:
We apply the law of exponents;
[tex](a^{b})^{c}=a^{bc}[/tex]
[tex]\sqrt{0.08^{12}}=(0.08^{12})^{\frac{1}{2}}[/tex]
applying the law of exponents we simply multiply 12 and 1/2 to get;
[tex]0.08^{6}[/tex]
Which ordered pair is a solution of the equation? 7x-2y=-5
answer X= 5 over 7 and 2 over 7y step by step explaination add 2y on both sides u cancelled -2y and positive 2y u bring down 7X u get 7X=-5+3 then u divide and u get that answer yw have a nice day mark me brainliest
Answer:
2y=-x7
Love mORgan