The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011 $5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020)..
Answers
The given data plot will look thus:
a) Building a model using just the 1999 and 2019 years:
[tex]\begin{gathered} 1999\rightarrow0\rightarrow2196 \\ 2019\rightarrow20\rightarrow7186 \\ \text{Havng} \\ x_1=0,y_1=2196 \\ x_2=20,y_2=7186 \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}_{} \\ \text{The model will be:} \\ P_t=249.5t+2196 \end{gathered}[/tex]b) The cost of insurance in 2030
[tex]\begin{gathered} P_t=249.5t+2196 \\ t=2030-1999=31 \\ \text{The cost of insurance in 2030 therefore will be:} \\ =249.5(31)+2196 \\ =7734.5+2196 \\ =\text{ \$9930.5} \end{gathered}[/tex]c) When do we expect the cost to reach $12,000
[tex]\begin{gathered} P_t=249.5t+2196 \\ 12,000=249.5t+2196 \\ 12000-2196=249.5t \\ 9804=249.5t \\ \frac{9804}{249.5}=\frac{249.5t}{249.5} \\ 39.2946=t \\ Since\text{ t = year -1999} \\ 39.2946+1999=\text{year} \\ 2038.2946=\text{year} \\ Since\text{ we are to give our answer as an exact year} \\ \text{The year will be }2039. \end{gathered}[/tex]
Related Questions
A bank features a savings account that has an annual percentage rate of 4.8 % with interest compounded monthly. Umbrosia deposits $6,500 into the account.
How much money will Umbrosia have in the account in 1 year?
What is the annual percentage yield (APY) for the savings account?
Answers
S(8)=3500(1+(.047/4))^32
S(8)=$5086.40 in the account after 8 years.
a)The relative growth rate is .25, or 25%
b)at t=0, the population is 955e^.25(0)=955
c)at t=5; the population is 955*e^.25(5)=955*3.49=3333.28 bacterium.
Do the following lengths form an acute, right, or obtuse triangle? 99 90 39 O Acute, 7921 < 7921 Right, 7921 = 7921 Obtuse, 7921 > 7921
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As we can see the interior angles of this triangle are less than 90° , therefore this triangle is an ACUTE TRIANGLE
How do I find the gif and distributive property
Answers
By using the GCF and distributive property, the sum of 15+27 = 42
The expression is
15 + 27
GCF is the greatest common factor, the greatest common factor is the highest number that divides exactly into two or more numbers.
The distributive property states that multiplying the sum of two or more variables by a number will produce the same result as multiplying each variables individually by the number and then adding the products together.
The expression is
= 15 + 27
= 3(5 + 9)
= 3 × 14
= 42
Hence, by using the GCF and distributive property, the sum of 15 + 27 = 42
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NEED TO FINISH BEFORE 9!!! PLEASE HELP!!!
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A rational value that is less than zero is -√4.
An irrational value greater than five is 5 1/9.
A rational value between 10 and 20 is √225.
What are rational numbers and irrational numbers?A rational number is a number that can be expressed as a fraction of two integers. A rational number can either be a positive number, negative number, whole number, decimal or fraction. Examples of rational numbers are 100, -0.5.
A irrational number is a number that cannot be expressed as a fraction of two integers. An irrational number can either be a positive number, negative number, whole number, decimal or fraction. Examples of irrational numbers are 22/7, 1-/9.
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HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
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By the midpoint formula, the real number - 5 / 12 is between the rational numbers - 1 / 3 and - 1 / 2.
How to find a rational number between two rational numbers
Rational numbers are real numbers of the form m / n, where m and n are integers and n is non-zero. There are more than one choice between the rational numbers - 1 / 3 and - 1 / 2, one option can be found by obtaining the midpoint between the two numbers:
x = (1 / 2) · (- 1 / 3) + (1 / 2) · (- 1 / 2) Given
x = - 1 / 6 - 1 / 4 Multiplication of rational numbers
x = - 4 / 24 - 6 / 24 Modulative, commutative and associative properties / Existence of multiplicative inverse
x = - 10 / 24 Addition of fraction with same denominator
x = - 5 / 12 Simplification / Result
The real number - 5 / 12 is between the rational numbers - 1 / 3 and - 1 / 2.
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Find the equation of the line, in slope-intercept form, that passes through the points (-2, -4) and (2,8).A) y = 1/3x + 22/3B) y = 3x + 14C) y = 3x + 2 D) y = - 3x + 14
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
x1 and y1 are the x and y coordinates of the initial point
x2 and y2 are the x and y coordinates of the final point
From the information given, the initial point is (- 2, - 4) and final point is (2, 8)
Thus,
x1 = - 2, y1 = - 4
x2 = 2, y2 = 8
By substituting these values into the slope formula,
m = (8 - - 4)/(2 - - 2) = (8 + 4)/(2 + 2) = 12/4 = 3
We would find the y intercept, c by substituting m = 3, x = - 2 and y = - 4 into the slope intercept equation. We have
- 4 = 3 * - 2 + c
- 4 = - 6 + c
Adding 6 to both sides of the equation,
- 4 + 6 = - 6 + 6 + c
c = 2
By substituting m = 3 and c = 2 into the slope intercept equation, the equation of the line is
C) y = 3x + 2
WW Solve the system by substitution. -10x + 4y = -18 and x= y Submit Answer
Answers
Substitute second expression (x=y) in the first expression.
[tex]\begin{gathered} -10x+4y=-18 \\ -10\times y+4y=-18 \\ -6y=-18 \\ y=\frac{-18}{-6} \\ y=3 \end{gathered}[/tex]Substitute the above value of y in the expression number 2.
[tex]\begin{gathered} x=y \\ x=3 \end{gathered}[/tex]Thus, the value of x=3 and the value of y=3.
Factor the common factor1) -36m + 16
Answers
Given:
-36m + 16
To factor out the common factor, let's find the Greatest Common Factor (GCF) of both values.
GCF of -36 and 16 = -4
Factor out -4 out of -36 and 16:
[tex]-4(9m)-4(-4)[/tex]Factor out -4 out of [-4(9m) - 4(-4)] :
[tex]-4(9m\text{ - 4)}[/tex]ANSWER:
[tex]-4(9m-4)[/tex]Match the following reasons to the statements given.Given:ABEF isEBDCProve:ACDF is
Answers
Solution
For this case we can do the following:
2. Part of lines FE and AB
4. Transitive
1. Given
5. Definition of parallelogram
3. Opposite sides of a parallelogram are II
In a garden, there are 10 rows and 12 columns of mango trees. The distance between two trees is 2 meters and a distance of one meter is left from all sides of the boundary of the garden. What is the length of the garden?
Answers
Answer:
20m
Step-by-step explanation:
(10-1)x2+1x2=20m
x – a is the factor of a polynomial P(x) if P(a) is equal to
Answers
we know that
If (x-a) is a factor of P(x)
then
For x=a
the value of P(a)=0
therefore
the answer is option D9=3(x+2) simplified
Answers
x=1
Explanation
Step 1
[tex]9=3(x+2)[/tex]apply distributive property
[tex]\begin{gathered} 9=3(x+2) \\ 9=3x+6 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} 9=3x+6 \\ \text{subtract 6 in both sides} \\ 9-6=3x+6-6 \\ 3=3x \end{gathered}[/tex]Step 3
finally, divide both sides by 3
[tex]\begin{gathered} 3=3x \\ \frac{3}{3}=\frac{3x}{3} \\ 1=x \end{gathered}[/tex]so, the answer is x=1
I hope this helps you
Find the time. Round to the nearest day given the following:Principal: $74,000Rate: 9.5%Interest: $2343.33
Answers
Explanation
Simple Interest is calculated using the following formula:
[tex]I=\text{PRT}[/tex]where P is the principal ( initial amount)
R is the rate ( in decimal)
T is the time ( in years)
so
Step 1
Let
[tex]\begin{gathered} P=74000 \\ \text{rate}=\text{ 9.5\% =9.5/100= 0.095} \\ T=t\text{ ( unknown)} \\ \text{Interest}=\text{ 2343.33} \end{gathered}[/tex]now, replace
[tex]\begin{gathered} I=\text{PRT} \\ 2343.33=74000\cdot0.095\cdot t \\ 2343.33=7030t \\ \text{divide both sides by 7030} \\ \frac{2343.33}{7030}=\frac{7030t}{7030} \\ 0.3333=t\text{ } \end{gathered}[/tex]so, the time is 0.333 years
Step 2
convert 0.333 years into days
[tex]1\text{ year }\Rightarrow365\text{ days}[/tex]so
[tex]\begin{gathered} 0.333years(\frac{365}{1\text{ year}})=121.66 \\ \text{rounded} \\ 122\text{ days} \end{gathered}[/tex]therefore, the answer is
122 days
Calculate the average rate of change for the function f(x) = 3x4 − 2x3 − 5x2 + x + 5, from x = −1 to x = 1.
a
−5
b
−1
c
1
d
5
Answers
Average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from
x =-1 to x=1 is equal to -1.
As given in the question,
Given function :
f(x) = 3x⁴ -2x³ -5x² +x +5
Formula for average rate of change for (a, f(a)) and (b, f(b))
[f(b) -f(a)] / (b-a)
Substitute the value of a=-1 and b=1
f(-1)=3(-1)⁴ -2(-1)³-5(-1)² +(-1) +5
= 3+2-5-1+5
=4
f(1)=3(1)⁴ -2(1)³-5(1)² +(1) +5
= 3-2-5+1+5
= 2
Average rate of change = (2-4)/(1-(-1))
= -2/2
=-1
Therefore, average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from x =-1 to x=1 is equal to -1.
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A building is 5 feet tall. the base of the ladder is 8 feet from the building. how tall must a ladder be to reach the top of the building? explain your reasoning.show your work. round to the nearest tenth if necessary.
Answers
The ladder must be 9.4 ft to reach the top of the building
Here, we want to get the length of the ladder that will reach the top of the building
Firstly, we need a diagrammatic representation
We have this as;
As we can see, we have a right triangle with the hypotenuse being the length of the ladder
We simply will make use of Pythagoras' theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides
Thus, we have;
[tex]\begin{gathered} x^2=5^2+8^2 \\ x^2=\text{ 25 + 64} \\ x^2\text{ = 89} \\ x=\text{ }\sqrt[]{89} \\ x\text{ = 9.4 ft} \end{gathered}[/tex]Which of the following points is in the solution set of y < x2 - 2x - 8? O 1-2. -1) O 10.-2) 0 (4.0)
Answers
Given the functon
[tex]yExplanation
To find the points that lie in the solution set we will lot the graph of the function and indicate the ordered pirs.
From the above, we can see that the right option is
Answer: Option 1
1.23 × 10 to the 5th power
=
Answers
Answer:
1.23 x 10 to the 5th power is 123,000.
Step-by-step explanation:
math.
I am having so much trouble with my assignment. can you please help me with number 8 and 10.
Answers
We have to solve this system of equations by substitution.
8) First, we find the value of one of the variables in function of the other using one of the 2 equations (first equation, in this case). Then, we use the other equation and replace the variable we just cleared (x, int his case) and solve for the other variable (y).
Then, after calcualting y, we can use the first equation to calculate x.
[tex]\begin{gathered} x+4y=0 \\ x=-4y \end{gathered}[/tex][tex]\begin{gathered} 3x+2y=20 \\ 3(-4y)+2y=20 \\ -12y+2y=20 \\ -10y=20 \\ y=\frac{20}{-10} \\ y=-2 \end{gathered}[/tex][tex]\begin{gathered} x=-4y=-4(-2) \\ x=8 \end{gathered}[/tex]Answer: x=8, y=-2.
10)
[tex]\begin{gathered} x-3y=-2 \\ x=3y-2 \end{gathered}[/tex][tex]\begin{gathered} 10x+8y=-20 \\ 10(3y-2)+8y=-20 \\ 30y-20+8y=-20 \\ 38y=-20+20 \\ 38y=0 \\ y=0 \end{gathered}[/tex][tex]x=3y-2=3\cdot0-2=0-2=-2[/tex]Answer: x=-2, y=0
A random sample of 41 people is taken. What is the probability that the main IQ score of people in the sample is less than 99? Round your answer to four decimal places if necessary(See picture )
Answers
Solution:
Given:
[tex]\begin{gathered} \mu=100 \\ \sigma=15 \\ n=41 \\ x=99 \end{gathered}[/tex]From the Z-scores formula;
[tex]\begin{gathered} Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}} \\ Z=\frac{99-100}{\frac{15}{\sqrt{41}}} \\ Z=-0.42687494916 \\ Z\approx-0.4269 \end{gathered}[/tex]From Z-scores table, the probability that the mean IQ score of people in the sample is less than 99 is;
[tex]\begin{gathered} P(xTherefore, to 4 decimal places, the probability that the mean IQ score of people in the sample is less than 99 is 0.3347
26.219 Miles in 128 minutes. what is speed in km per minute?
Answers
26.219 Miles in 128 minutes.
First we have to convert miles to km:
Since 1 mile = 1,609 km
26.219 x 1,609 = 42,041.561 km
Then divide the distance by the time:
42,041.561/ 128 = 192.85 km per minute
Not everyone pays the same price for the same model of a car that the figure is the streets a normal distribution for the price paid for the particular model of a new car the meanest $24,000 and a standard deviation is $1000 user 68–95-99.7 Raw to find a percentage of buyers who paid more than $27,000
Answers
The Solution:
The correct answer is 0.15%
Given the data in the given question,
We are required to find the percentage of buyers who paid more than $27,000.
The percentage of the total buyers is 100%
The percentage of buyers that paid between $21,000 and $27,000 is given to be 99.7%
This means that the total percentage of buyers who paid less than $21,000 and the buyers who paid more than $27,000 is
[tex]100-99.7=0.3\text{ \%}[/tex]Since the distribution is a normal distribution, it follows that half of 0.3% is the percentage of buyers who paid more than $27,000.
[tex]\frac{0.3}{2}=0.15\text{ \%}[/tex]Thus, the percentage of buyers who paid more than $27,000 is 0.15%
what is the factored form of his expression ? 2x^3+5x^2+6x+15
Answers
The given expression is:
[tex]2x^3+5x^2+6x+15[/tex]It is required to write the expression in factored form.
[tex]\begin{gathered} \text{ Factor out }x^2\text{ in the first two terms of the expression:} \\ x^2(2x+5)+6x+15 \end{gathered}[/tex]
Next, factor out 3 in the last two terms of the expression:
[tex]x^2(2x+5)+3(2x+5)[/tex]Factor out the binomial 2x+5 in the expression:
[tex](2x+5)(x^2+3)[/tex]The expression in factored form is (2x+5)(x²+3).Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
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The derivative of the function y = -1/x-2 is 1/(x-2)².
Given, the function is y = -1/x-2
Differentiate the function with respect to x.
dy/dx = d/dx (-1/x-2)
the function is in the form of :
d/dx [f(x)g(x)] = f(x)d/dx((x)) + g(x)d/dx(f(x))
here d/dx [f(x)g(x)] = d/dx [(-1)(1/x-2)]
therefore, d/dx [(-1)(1/x-2)] = (-1)d/dx(1/x-2) +(1/x-2)d/dx(-1)
⇒ d/dx [(-1)(1/x-2)] = (-1)(-1)(x-2)⁻¹⁻¹ + (1/x-2)d/dx(0)
⇒ d/dx [(-1)(1/x-2)] = 1(x-2)⁻² + 0
⇒ d/dx [(-1)(1/x-2)] = 1/(x-2)²
Hence the derivative of the function is 1/(x-2)²
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it takes a rat 65 seconds to run from its food source to its home. If the rat has to run 28 meters which is going faster: the rat, or a child on a bike moving at 2 m/s?
Answers
Given data:
The given distance covered by rat is d= 28 m.
The given time is t= 65 seconds.
The speed of the child is s'=2 m/s.
The expression for the speed is,
[tex]\begin{gathered} s=\frac{28}{65}\text{ m/s} \\ =0.43\text{ m/s} \end{gathered}[/tex]As the speed of the child is greater than speed of the rat, so child is going faste.
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Show instructionsQuestion 1 (1 point)Does the point (0,5) satisfy the equation y = x + 5?TrueFalse
Answers
The equation is
[tex]y=x+5[/tex]The point given is:
[tex](x,y)=(0,5)[/tex]The x coordinate given is 0 and the y coordinate given is 5.
We put the respective point and see if the equation holds true or not.
Thus,
[tex]undefined[/tex]State the domain and range for each graph and then tell if the graph is a function(write yes or no)
Answers
For the point 1)
- The domain will be: (note that this is not an interval, it is a set of two points)
[tex]\mleft\lbrace-3,2\mright\rbrace[/tex]-The range is the set R of all real numbers (since the line extends to infinite)
-The first graph is NOT a function
For the point 2)
-The domain will be the interval
[tex](-5,5\rbrack[/tex]-The range is the interval:
[tex]\lbrack-2,2\rbrack[/tex]-The second graph is a function.
The Adventure Club has scheduled a trip to hike a nearby mountain. Since the group started hiking, they gained 456 feet in altitude from their start position. The current altitude is 437 feet, but there is no record of their starting altitude.write a equation to represent this situation Explain what your variable representssolve your equation please someone help me ill give you a star anything please ♡
Answers
Let h be the altitude of the starting position.
Since the group has gained 456 feet from the start position, then the current altitude is:
7n + 2 - 7n How can I simplify the expression by combining like terms
Answers
In order to simplify this expression, we can combine the terms with the variable n, like this:
[tex]\begin{gathered} 7n+2-7n \\ =(7n-7n)+2 \end{gathered}[/tex]Since the terms with the variable n have opposite coefficients (+7 and -7), the sum will be equal to zero:
[tex]\begin{gathered} (7n-7n)+2 \\ =(0)+2 \\ =2 \end{gathered}[/tex]Therefore the simplified result is 2.
the endpoints of line segment DEF are D(1,4) and and F(16,14). Determine and state the coordinates of E, if DE:EF = 2:3.
Answers
The coordinates can be obtained using section formula
[tex]\begin{gathered} \text{Let the coordinates of D be (x}_{1_,}y_1)andFbe(x_2,y_2) \\ \text{The point E divides the line in m:n ratio.} \\ U\sin g\text{ section formula, coordinates of E is} \\ \frac{mx_2+nx_1}{m+n},\text{ }\frac{my_2+ny_1}{m+n} \\ \end{gathered}[/tex][tex]\begin{gathered} (x_1,y_1)=(1,4),(x_2,y_2)=(16,14),\text{ m:n=2:3} \\ \text{Substitute the values in section formula} \\ \frac{2\ast16+3\ast1}{2+3},\text{ }\frac{2\ast14+3\ast4}{2+3} \\ \frac{32+3}{5},\text{ }\frac{28+12}{5} \\ \frac{35}{5},\text{ }\frac{40}{5} \\ 7,\text{ 8} \end{gathered}[/tex]The x coordinate of E is 7 and y coordinate is 8.
Find a unit vector u in the direction of v. Verify that ||0|| = 1.v = (4, -3)U =
Answers
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
