using calculations show that the height of the barrel of oil is 96.82cm
The use of calculations to show that the height of the barrel of oil is 96.82cm is given below:
The volume is given as V = 42 gal
The radius is given as r = 18/2 = 9 in
The height is given as h= 96.83 cm
How to solveUsing the formula:
V = πr²h
h = V/(πr²)
The volume is given as V = 42 gal
42 gal x 3.7854 l/gal = 158.987 l
158.987 l = 158,987 ml = 158,987 cm³
The radius is given as r = 18/2 = 9 in
9 in x 2.54 cm/in = 22.86 cm
The height is given as h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm
depending on how you round, the more precise answer is 96.8285 ≈ 96.83 cm
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Brent starts with 16 identical white socks in his sock drawer. Imagine he receives 2 identical black socks as a gift and mixes them in with his 16 white socks. If he draws one sock without looking to put on his left foot, then draws a second sock without looking to put on his right foot, what is the probability that he draws mismatched socks?
The probability that Brent draws mismatched socks is approximately 31/153.
After adding 2 identical black socks, Brent has a total of 18 socks in his drawer. The probability of drawing a white sock on the first draw is 16/18 (since there are 16 white socks out of 18 total socks).
After drawing a white sock on the first draw, there are 15 white socks and 2 black socks left in the drawer. The probability of drawing a black sock on the second draw is 2/17 (since there are 2 black socks out of 17 total socks left). So the probability of drawing a white sock followed by a black sock is;
(16/18) × (2/17) = 32/306
Similarly, the probability of drawing a black sock followed by a white sock is;
(2/18) × (15/17) = 30/306
However, the probability of drawing mismatched socks is;
32/306 + 30/306 = 62/306
= 31/153
Therefore, the probability will be 31/153.
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PLEASE HELP ME WITH THE WHOLE PROBLEM PLEASEEEE
The probability of getting blue or green is 1/3, the probability of getting blue is 3/4 and there are 8 blue marbles.
What is the probability in each case?a) If the probability of getting a yellow marble is 2/3, then the probability of getting a blue or green marble is:
P(blue or green) = 1 - P(yellow) = 1 - 2/3 = 1/3
b) If the probability of getting a green marble is 1/4, then the probability of getting a blue marble is:
P(blue) = 1 - P(green) = 1 - 1/4 = 3/4
c) The total number of marbles in the bag is 24. Let x be the number of blue marbles. Then the number of yellow marbles is 2x, and the number of green marbles is 24 - x - 2x = 24 - 3x. We know that:
2x/24 = 2/3 (probability of getting a yellow marble is 2/3)
=> x = 8
Therefore, there are 8 blue marbles in the bag.
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) In the figure below, two secants are drawn to a circle from exterior point U.
Suppose that UW=40, UY=64, and UX= 8. Find UZ.
U
Applying the Intersecting Secants and Tangents Theorem, the measures are: CD = 19.5 units; UZ = 12.8 units
How to Apply the Intersecting Secants and Tangents Theorem?a. Apply the intersecting secant-tangent theorem to create the equation below:
EG² = EC * ED
Plug in the values:
13² = 6.5 * (6.5 + CD)
169 = 42.25 + 6.5CD
169 - 42.25 = 6.5CD
126.75/6.5 = CD
CD = 19.5 units
b. Apply the intersecting secants theorem to create the equation below:
UX * UY = UZ * UW
Plug in the values:
8 * 64 = UZ * 40
512/40 = UZ
UZ = 12.8
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Given the circle below with secants
�
�
�
‾
KLM
and
�
�
�
‾
ONM
. If
�
�
=
13
,
�
�
=
12
LM=13,NM=12 and
�
�
KL is
3
3 less than
�
�
ON, find the length of
�
�
‾
ON
. Round to the nearest tenth if necessary.
The length of ON for the intersecting secants is derived to be equal to 14
What is the intersecting secant theoremThe intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
MK × KL = MO × MN
note that KL = (ON - 3) so;
[13 + (ON - 3)] × 13 = (12 + ON) × 12
13(10 + ON) = 144 + 12ON
130 + 13ON = 144 + 12ON
13ON - 12ON = 144 - 130 {collect like terms}
ON = 14
Therefore, the length of ON for the intersecting secants is derived to be equal to 14
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College Level Trigonometry Question Any Help will do
The expression of angle in radian is -0.071.
What is the measure of angles in radian?Angles can be measured in two units: degrees and radians.
Radian is a unit of measurement for angles, and it is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
To be more precise, an angle of one radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
The expression of angle in radian is calculated as follows;
θ = tan⁻¹ (-0.071)
θ = -0.071
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2. Ricky wants to make rice cream. Of 1 kilogram of rice, milk2/5 is rice and 1/6 is sugar. Find the quantity of rice and sugar needed for 1 kg of rice milk.
The quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.
To solve the above problem, we can use the following equation:
Rice + Milk + Sugar = 1 kg
Rice = 2/5 (1 kg) = 0.4 kg
Milk = 2/5 (1 kg) = 0.4 kg
Sugar = 1/6 (1 kg) = 0.167 kg
Therefore, the quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.
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In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company, and a measure of flexibility was recorded for each. The data are as follows:
Company A: 9.3; 8.8; 6.8; 8.7; 8.5; 6.7; 8.0; 6.5; 9.2; 7.0
Company B: 11.0; 9.8; 9.9; 10.2; 10.1; 9.7; 11.0; 11.1; 10.2; 9.6
i. Calculate the sample mean and median for the data for the two companies.
ii. Plot the data for the two companies on the same line/chart and give your impression regarding any apparent differences between the two.
iii. Is there any relation between the two companies? Compare using the 90% confidence interval of the mean.
iv. Which company you will recommend
i. The sample mean and median for the data for the two companies are 8.1 and 8.25 respectively.
ii. The line graph of the data is illustrated below.
iii. Yes, The steel rods supplied by Company B may be more flexible than those supplied by Company A.
iv. If you are looking for steel rods with higher flexibility, I would recommend Company B based on the higher median, the apparent differences in the box and whisker plot, and the confidence interval indicating a higher mean flexibility for their rods.
For Company A, the sample mean can be calculated by adding all the values and dividing by the number of values:
Mean of Company A = (9.3 + 8.8 + 6.8 + 8.7 + 8.5 + 6.7 + 8.0 + 6.5 + 9.2 + 7.0) / 10 = 8.1
To find the median, we first need to arrange the data in ascending order:
6.5, 6.7, 6.8, 7.0, 8.0, 8.5, 8.7, 8.8, 9.2, 9.3
Since there are an even number of values, the median is the average of the two middle values:
Median of Company A = (8.0 + 8.5) / 2 = 8.25
For Company B, the sample mean can be calculated similarly:
Mean of Company B = (11.0 + 9.8 + 9.9 + 10.2 + 10.1 + 9.7 + 11.0 + 11.1 + 10.2 + 9.6) / 10 = 10.2
Arranging the data in ascending order, we get:
9.6, 9.7, 9.8, 9.9, 10.1, 10.2, 10.2, 10.2, 11.0, 11.1
Since there are an odd number of values, the median is the middle value:
Median of Company B = 10.2
Next, let's plot the data for both companies on the same chart and observe any apparent differences. We can use a box and whisker plot to do this.
Looking at the box and whisker plot, we can see that the median of Company B (represented by the line in the middle of the box) is higher than the median of Company A. Additionally, the box for Company B is taller than the box for Company A, indicating that the range of values for Company B is greater than that of Company A. These observations suggest that the steel rods supplied by Company B may be more flexible than those supplied by Company A.
To determine if there is a significant difference between the means of the two companies, we can use a 90% confidence interval of the mean. This interval gives us a range within which we can be 90% confident that the true population mean lies.
Using a t-distribution with 18 degrees of freedom (10 + 10 - 2), we can find the 90% confidence interval for the difference between the means of the two companies. The formula for the confidence interval is:
Difference in means ± (t-value x standard error of difference in means)
The t-value for a 90% confidence interval with 18 degrees of freedom is approximately 1.734.
Now, we can calculate the margin of error by multiplying the t-value (1.734) by the standard error:
Margin of Error = 1.734 * 0.393 ≈ 0.682
Finally, we can construct the 90% confidence interval for the difference in means as:
Difference in means ± Margin of Error
Calculating the difference in means (mean of Company B - mean of Company A), we have:
Difference in means = 10.2 - 8.1 = 2.1
Therefore, the 90% confidence interval is:
2.1 ± 0.682
This means that we can be 90% confident that the true population mean difference between the two companies' steel rods lies between 1.418 and 2.782.
Based on this analysis, we can conclude that Company B tends to supply steel rods that are more flexible compared to Company A. However, it's important to note that this study was conducted on a small sample size, so further investigation with larger sample sizes would be beneficial to confirm the findings.
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Sonji went to a sandwich shop for lunch with 8 of her friends. Part of the group ordered only a sandwich for $5, and the
rest of the group ordered à combo for $8. The bill for all 9 people totaled $66.00. Which system of equations represents
the number of meals of each type that Sonji and her friends purchased?
Answer:
x+y=9
5x+8y=66
Step-by-step explanation:
Find the exact value of each of the following:
a)4sin(π/6)+tan(π/4)
b)cos(4π/3) tan(330°)-sin(3π/4)
The exact values for both equations are as follows:
a) 3
b) -√3/2 - √2/2
How to solvea) In order to ascertain the precise value of 4sin(π/6) + tan(π/4), we must first evaluate the trigonometric functions involved: sin(π/6) = 1/2 and tan(π/4) = 1.
Now, by substituting these values in the equation, we get
4(1/2) + 1 = 2 + 1 = 3.
b) To calculate cos(4π/3) tan(330°) - sin(3π/4), it is necessary to convert 330° into radians: (330 * π) / 180 = 11π/6.
After setting this conversion, evaluate the trigonometric functions present: cos(4π/3) = -1/2, tan(11π/6) = √3, and sin(3π/4) = √2/2.
When these values are used within the equation, the result is (-1/2)(√3) - (√2/2) which equals -√3/2 - √2/2.
Ergo, the exact values for both equations are as follows:
a) 3
b) -√3/2 - √2/2
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If cosθ=-1/3 and θ is in quadrant III, find the exact values of sinθ,tanθ,secθ,cscθ,and cotθ. You can use the identities or x, y, r.
The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
Given: cosθ = -1/3 and θ is in quadrant III.
This means that sinθ = ± √(1 - (cosθ)2).
We know that cosθ is negative, so sinθ will be negative.
Therefore, sinθ = -√(1 - (-1/3)2 )
sinθ = - √(1 - 1/9)
sinθ = -√8/9
tanθ = sinθ/cosθ
tanθ = (-√8/9)/-1/3
tanθ = √8/3
secθ = 1/cosθ
secθ = 1/-1/3
secθ = -3
cscθ = 1/sinθ
cscθ = 1/-√8/9
cscθ = -√9/8
cotθ = cosθ/sinθ
cotθ = -1/3/-√8/9
cotθ = √9/8
Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
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The formula v= √√2gh gives the velocity v, in feet per second, of an object after it falls h feet accelerated by gravity g, in feet
per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 96 feet
per second.
We can rearrange the formula to solve for h:
v = √√2gh
Squaring both sides: v^2 = 2gh
Dividing both sides by 2g: h = v^2 / 2g
Substituting v = 96 ft/s and g = 32 ft/s^2, we get:
h = (96 ft/s)^2 / (2 × 32 ft/s^2)
h = 288 ft
Therefore, the object has fallen 288 feet.
Function g is a transformation of f(x) = 2x. Compare the graphs of the functions. Select all that apply.
g(x)
(Table)
0 1 2 3 4
1/2 1 2 4 8
A.They have the same y-intercept.
B.They have the same asymptote.
c. They have the same range.
D.They have the same domain.
The functions have the following characteristics:
A. They have the same y-intercept.
D. They have the same domain.
How to compare the graphs of the functionsWhen a function f(x) is transformed by multiplying its input by a constant "a", it results in a new function g(x) = f(ax). In this case, f(x) = 2x, so when we multiply x by a constant "a", we get g(x) = f(ax) = 2ax.
Therefore, the functions f(x) = 2x and g(x) = 2ax have the same y-intercept (0,0) and the same domain (-∞, +∞).
The range of g(x) is determined by the value of "a", which is different from the range of f(x), so option C is not correct. Asymptotes are not relevant for linear functions, so option B is not correct.
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Step 1: Understand the Problem
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 190 miles per week to commute to work. With gas prices currently at $
2.9 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 18 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $
770 per year (as long as nothing serious goes wrong).
The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $
6,500 over a three-year loan process. This car gets 32 miles per gallon and would only require an average of $
10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
Step 3: Apply Quantitative Tools
Use computational and algebraic tools to quantify the total costs (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Scenario
Total Cost for Three Years
Keep the old car
$
Number
Buy the fuel-efficient used car
$
Number
I Need help with this question
Answer:
The answer is A.
Step-by-step explanation:
For this graph, you are using the linear equation formula: y = mx + b
m is the slope (rise/run)b is the y-intercept (where the line crosses zero at the y-intercept)Find the slope of the line represented
by the data below.
x 2 4 6 8
-3 39
3
9 15
y|-3
Simplify completely.
Slope = [?
Hint: The slope of a line is the
Change in y
Change in x
What integer is closest to the radius of a circle with a circumference of 50.27?
The integer which is closest to the radius of a circle with a circumference of 50.27 as required is; Choice A; 8.
Which answer choice is closest to the radius of the circle?It follows from the task content that the integer which is closest to the radius of the circle whose circumference is; 50.27 is to be determined.
Recall; Circumference, C = 2πr
r = C / 2π
r = 50.27 / 2π
r = 8.000718989
Ultimately, the integer which is closest to the radius is; Choice A; 8.
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A company sells cereal in two different-sized boxes. The smaller box has the dimensions shown below. The height of the smaller box is 80% of the height of the larger box, while the other two dimensions are the same for both boxes. What is the volume of the two boxes?
Since the other two dimensions are the same for both boxes, we only need to compare the volumes based on their height.
Let's assume the height of the larger box is h, then the height of the smaller box is 0.8h.
The volume of the larger box is:
V1 = lwh = (8)(11)(h) = 88h
The volume of the smaller box is:
V2 = lwh = (8)(11)(0.8h) = 70.4h
Therefore, the volume of the larger box is 88h and the volume of the smaller box is 70.4h.
What is 124.8 as a fraction? Please help
Find the value of 11 3/8 -7/8
The value of 11 3/8 -7/8 is 10 1/2
What is subtraction?Subtraction is the operation or process of finding the difference between two numbers or quantities . For examples, if out 100 students In a school , 40 are boys , the number of girls in the school is calculated by subtracting the number of boys from the total number of students.i.e 100 - 40 = 60
Solving 11 3/8 -7/8
= 91/8 - 7/8
= (91-7)/8
= 84/8
= 21/2
= 10 1/2
Therefore the value of 11 3/8 -7/8 is 10 1/2
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MN=3X+2 AND NP=X+4 WHAT IS THE VALUE OF X
Answer:
N = M + 10/3P
Step-by-step explanation:
A tunnel is shaped in the form of a semi-ellipse. The width of the tunnel is 20 feet and the height of the tunnel is 12 feet. A train is 10 feet wide and centered in the tunnel. Determine whether a 10-foot high train would have clearance to pass through. If so, by how much? If not, by how much? (Nearest inch.)
what is equilivent to 28/2
Answer:
14
Step-by-step explanation:
28/2 is equivalent to 14. This is because when you divide a number by 2, you are essentially cutting it in half. So, 28/2 is the same as cutting 28 into two equal parts, which is 14.
Answer:
28
2
looks like a fraction but it is actually the whole number 14.
There is an infinity number of equivalent fractions to 28
2
.
To find an equivalent fraction to 28
2
, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By dividing the original fraction by 2, we get:
28 ÷ 2
2 ÷ 2
= 14
1
By multiplying the original fraction by 2, we get:
28 × 2
2 × 2
= 56
4
Here is the full list of equivalent fractions to 28
2
.
14
1
, 28
2
, 42
3
, 56
4
, 70
5
, 84
6
, 98
7
, 112
8
, 126
9
, 140
10
, 154
11
, 168
12
, 182
13
, 196
14
, 210
15
, 224
16
, 238
17
, 252
18
, 266
19
, 280
20
...
HOW TO SOLVE LINEAR REGRESSIONS
Alexander deposits $3,200 into a savings account that has a simple interest rate of 1%. If interest is calculated quarterly, which statement is true?
Select one:
a.
He will earn $8 in interest each quarter, totaling $32 in interest for the year
b.
He will earn $32 in interest at the end of one year
c.
He will earn $0.80 in interest each quarter, totaling $3.20 in interest for the year
d.
He will earn $3.20 in interest at the end of one year
The TRUE statement about Alexander's deposit of $3,200 into a savings account that has a simple interest rate of 1% calculated quarterly is a. He will earn $8 in interest each quarter, totaling $32 in interest for the year.
What is the simple interest?Simple interest describes an interest system that does not compound the interest.
Compounding involves charging interest on both interest and principal.
For the simple interest system, the interest amount is computed only on the principal, using the following SI formula.
Principal deposit, P = $3,200
Interest rate, R = 1%
Interest period, P = 1 year
Interest system = Simple interest quarterly
Simple interest (SI) formula = P x R x T
Simple interest for each quarter = $8 ($3,200 x 0.01 x 1/4)
Simple interest for the year = $32 ($3,200 x 0.01)
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PLEASE HELP!!!
The surface area of a triangular pyramid is 400 square meters. The surface area of a similar triangular pyramid is 25 square meters.
What is the ratio of corresponding dimensions of the smaller pyramid to the larger pyramid?
Enter your answer by filling in the boxes.
Answer:
can i get a picture\
Step-by-step explanation:
thanks
Answer:
Step-by-step explanation:
1:4
Select the correct location on the table.
Darian knows the area of a ring-shaped figure, and wants to determine the radius of the outer circle. His teacher tells him the following formula for finding the area of a ring based on the radius of the smaller circle, r, and the radius of the outer ring, R.
An illustration of two concentric circles. The radius of the inner circle is lower case r and the radius of the outer circle is upper case R.
Darian decides to rewrite the equation to solve for the radius of the outer ring. His work is shown below. Determine if Darian made a mistake when rewriting the equation, and if so, select the step where Darian made his first error.
There was no error in the procedure as we can see below.
What is the change of subject in a formula?In algebra, a formula expresses a relationship between two or more variables. Changing the subject of a formula means isolating a specific variable on one side of the equation. This is done by applying inverse operations in a specific order to eliminate all other variables and isolate the desired one.
We have the formula as;
[tex]A = \pi R^2 - \pi r^2\\A = \pi(R^2 - r^2)\\A/ \pi = R^2 - r^2\\R^2 = A/ \pi + r^2\\R = \sqrt{} A/ \pi + √r^2\\R = \sqrt{} A/ \pi + r[/tex]
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The vertices of AABC are A (-3, -6), B (-3,5), and C (5,5).
What is the area of AABC?
Answer:
44 units²-----------------------------
AB is vertical with same x-coordinates, and BC is horizontal with same y-coordinates.
Hence this is a right triangle.
Its area is:
A = 1/2 × AB × BCA = 1/2(5 - (-6))(5 - (-3)) = 1/2(11)(8) = 44 units²Consider the graph of the function f(x)=(1/4)^x
Which statements describe key features of function f?
The horizontal asymptotes of the function is y = 0 and the y-intercepts is (0, 1).
What is graph of exponential functionAn exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.
In this problem, the graph of the function f(x) = (1/4)ˣ is attached below the question and the characteristics of the graph are;
1. The domain of the function is {x|x ∈ R}
2. The range of the function is {y|y > 0}
3. The horizontal asymptotes is y = 0
4. The x-intercepts does not exists
5. The y-intercepts are (0, 1)
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An employee started a new job and must enroll in a new family health insurance plan. One of the options involves prescription drug coverage. The employee estimates that the entire family will fill 6 prescriptions per month, totaling $850. The monthly premium for the plan is $34, with 90% coverage for the first $500 in prescription costs, then 80% coverage for all prescription costs over $500. What is the total out-of-pocket expense for one month?
$120
$154
$696
$764
the deductible, and the coinsurance. Here are the steps to calculate the total out-of-pocket expense: the total out-of-pocket expense for one month is $ [tex]154[/tex] .
What is the total out-of-pocket expense?To calculate the out-of-pocket expense for one month, we need to take into account the monthly premium.
Step 1: Calculate the deductible
The deductible is the amount that the insured person needs to pay before the insurance starts covering the costs.
In this case, the deductible is $500 because that's the threshold for the 90% coverage. Since the family will fill 6 prescriptions per month, we need to calculate the average cost per prescription:
Average cost per prescription = Total prescription costs / Number of prescriptions
Average cost per prescription = $ [tex]850 / 6 = $141.67[/tex]
Since the deductible is $500, the insurance will cover 90% of the first $500, which is $450. The remaining $50 will be paid by the insured person. Therefore, the deductible is $ [tex]500 - $450 = $50.[/tex]
Step 2: Calculate the coinsurance
After the deductible is met, the insurance will cover 80% of the remaining prescription costs, and the insured person will be responsible for the remaining [tex]20[/tex] %.
To calculate the coinsurance, we need to subtract the deductible from the total prescription costs and multiply the result by 0.2:
Coinsurance = (Total prescription costs - Deductible) x 0.2
Coinsurance = [tex]($850 - $500) \times 0.2[/tex]
Coinsurance = $ [tex]70[/tex]
Step 3:
Calculate the total out-of-pocket expense
The total out-of-pocket expense is the sum of the monthly premium, the deductible, and the coinsurance:
Total out-of-pocket expense = Monthly premium + Deductible + Coinsurance
Total out-of-pocket expense = $ [tex]34 + $50 + $70[/tex]
Total out-of-pocket expense = $154
Therefore, the total out-of-pocket expense for one month is $ [tex]154[/tex] .
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