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
Answers
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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Related Questions
Write an equation in standard form
Answers
The equation of the quadratic with a directrix of x = 2 and vertex of (0 , 0) is: y² = -8x
The equation of the quadratic with a directrix of y = 4 and vertex of (1, 3) is: (x - 1)² = -4 (y - 3)
How to write the equation of parabola with directrix of x = 2 and vertex of (0, 0)Quadratic equation when the directrix is at x direction is of the form:
(y - k)² = 4P (x - h)
OR
standard vertex form, x = a(y - k)² + h where a = 1/4p
The vertex
v (h, k) = (0, 0)
P in this problem, is the distance between the vertex and the directrix
P = 0 - 2 = -2
substitution of the values into the equation gives
(y - k)² = 4P (x - h)
(y - 0)² = 4 x -2 (x - 0)
y² = -8x
Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (1, 3)
P in this problem, is the distance between the vertex and the directrix
P = 3 - 4 = -1
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - 1)² = 4 * -1 (y - 3)
(x - 1)² = -4 (y - 3)
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What the correct answer??
Answers
The angle of the turn at Deer Trail is of 105 degrees.
What is the angle of the turn?Notice that both of the lines that go up to the left are parallel, thus, the angles formed betwen the intersections are all equal (for the respective lines).
Now, also know that two adjacent angles in an intersection should add up to 180°.
We can see that the angle to the right of deer trail has a measure of 75°, then the angle to the left (which is adjacent) must have a measure M such that:
M + 75° = 180°
M = 180° - 75°
M = 105°
That is the angle of the turn.
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Find the areas of the trapezoids.
Answers
The areas of the trapezoids is,
A = 48 sq units.
Since, The formula to find the area of a trapezoid of a trapezoid is,
⇒ A = 1/2(b₁ + b₂ )h.
Hence, it is stated that the height of each unit is 2.
Now let's substitute the variables in the formula with the actual bases and heights as;
A = 1/2(8 + 4)8,
A = 6 × 8,
A = 48 sq units.
Thus, the areas of the trapezoids is,
A = 48 sq units.
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Select all the polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base?
Answers
The polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base include :
B. SquareC. RectangleE. CircleHow to find the polygons ?If a plane intersects three distinct vertices of the cube while bypassing any other vertices, a triangle is produced. To visualize this, suppose a corner of the cube were removed with a knife; picture that cut surface as a triangle.
On the other hand, if a plane coincides with four points on the cube and outlines a square shape, it creates what's called a "square cross-section." This transpires when said plane parallels one side of the cube while intersecting only the midpoints of its opposite face's edges.
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Full question is:
Select all the polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base
A triangle
B square
C. rectangle
D pentagon
E circle
8. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. (i) What is the car's angular speed in radians per hour? (ii) What is the car’s linear speed in miles per hour?
Answers
Answer:
the car's angular speed is 72,000π radians per hour.
the car's linear speed is approximately 100.53 miles per hour.
Step-by-step explanation:
To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.
The formula for angular speed is:
ω = 2πf
where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.
In this case, the wheel is spinning at a rate of 10 revolutions per second, so:
ω = 2π(10) = 20π radians per second
To convert this to radians per hour, we can multiply by the number of seconds per hour:
20π radians per second × 3600 seconds per hour = 72,000π radians per hour
To find the car's linear speed in miles per hour, we can use the formula:
v = rω
where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.
The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:
9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles
Now we can substitute the values we have found:
v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)
v ≈ 100.53 miles per hour
Answer:
(i) 10 revolutions = 10(2π) = 20π radians
10 revolutions/sec =
(20π radians/sec)(3,600 sec/hr) =
72,000π radians/hr
(ii) C = 18π inches
10 revolutions × 18π inches =
180π inches
(180π in./sec)(3,600 sec/hr) =
(648,000π in./hr)(1 mi./63,360 in.)
= 225π/22 miles/hour
= about 32.13 miles/hour
pls help very much appreciate it
Answers
Gruden Company produces golf discs which it normally sells to retailers for $7 each. The cost of manufacturing 20,000 golf discs is:
Answers
Answer:
$140,000
Step-by-step explanation:
7*20,000 = 140,000
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 66 m wide.
Find the area of the training field. Use the value 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
0
$6 m
808
m
X
m²
5
m²
Answers
The area of the training field that has the shape of a rectangle and two semicircle would be = 9,755.46m²
How to calculate the area of the training field?To calculate the area of the training field, the area of the rectangle and the two semicircles should be determined and added together.
The area of rectangle = length×width
where:
length = 96m
width = 66m
area of rectangle = 66×96 = 6,336m²
Area of the two semicircle = Area of a circle = πr²
radius = diameter/2 = 66/2 = 33m
area of a circle= 3.14×33×33 = 3419.46m²
Therefore the area of the training field = 6,336m²+3419.46m² = 9,755.46m²
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Can someone give me the answer to the following 4 trig questions using sum and difference formulas
Answers
1. Therefore, the exact value of cos(105°) is (√2 - √6)/4.
2. Therefore, the exact value of sin(75°) is (√6 + √2)/4.
3. Therefore, the exact value of tan(105°) is (√3 + 1)/(3 - √3).
4. Therefore, the exact value of cos(105°)cos(15°) is (2 + 2√3)/8.
What is trigonometry?A branch of mathematics known as trigonometry is concerned with the study of triangles and the correlations between their sides and angles.
It entails computing different triangle measurements and attributes using trigonometric functions including sine, cosine, and tangent.
Trigonometry is an essential component of calculus and other advanced mathematical studies, and it has applications in many disciplines including engineering, physics, navigation, astronomy, and architecture.
1. We can use the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with A = 60° and B = 45°. Then:
cos(105°) = cos(60° + 45°)
= cos(60°)cos(45°) - sin(60°)sin(45°)
= (1/2)(√2/2) - (√3/2)(√2/2)
= (√2 - √6)/4
Therefore, the exact value of cos(105°) is (√2 - √6)/4.
2. We can use the formula sin(A + B) = sin(A)cos(B) + cos(A)sin(B) with A = 45° and B = 30°. Then:
sin(75°) = sin(45° + 30°)
= sin(45°)cos(30°) + cos(45°)sin(30°)
= (√2/2)(√3/2) + (√2/2)(1/2)
= (√6 + √2)/4
Therefore, the exact value of sin(75°) is (√6 + √2)/4.
3. We can use the formula tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B)) with A = 60° and B = 45°. Then:
tan(105°) = tan(60° + 45°)
= (tan(60°) + tan(45°))/(1 - tan(60°)tan(45°))
= (√3 + 1)/(3 - √3)
Therefore, the exact value of tan(105°) is (√3 + 1)/(3 - √3).
4. We can use the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with A = 60° and B = -45°. Then:
cos(105°)cos(15°) = cos(60° - 45°)cos(15°)
= [cos(60°)cos(-45°) - sin(60°)sin(-45°)]cos(15°)
= [(1/2)(√2/2) - (√3/2)(-√2/2)]cos(15°)
= (√2 + √6)/4 * cos(15°)
= (√2 + √6)/4 * (√6 + √2)/4
= (2 + 2√3)/8
Therefore, the exact value of cos(105°)cos(15°) is (2 + 2√3)/8.
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26) What is the area of Rectangle A?
is 1 unit square.
Rectangle A
Answers
The required area of the rectangle is 8 sq. units
What is rectangle?Any mathematical statement with numbers, variables, and an arithmetic operation between them is an expression or algebraic expression. For instance, the expression 4m + 5 is one in which the terms 4m and 5 and the variable m are separated by the arithmetic sign +.
According to question:From the diagram
Length = 4 units, width = 2 units
Area of rectangle = length×width
Area of rectangle = 4×2
Area of rectangle = 8 sq. units
Thus, required area of the rectangle is 8 sq. units
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help me please Which statement could be made based on the diagram below?
A) m∠3 + m∠6 = 90
B) ∠3 = ∠6
C) ∠3 = ∠5
D) m∠4 + m∠5 = 180
Answers
Answer:
A) m∠3 + m∠6 = 90
Step-by-step explanation:
Angles 3 and 6 are complementary angles. This means they add up to 90 degrees. Since you know the angle that is a right angle due to the box, you know these angles add up to 90 degrees
Round-off 108.76 to the nearest tens.
Answers
Answer:
108
You rounded to the nearest tens place.
The 0 in the tens place rounds up to 1
Step-by-step explanation: because the digit to the right in the ones place is 8.
110
When the digit to the right is 5 or greater we round away from 0.
108 was rounded up and away from zero to 110
There are 200 end-of-the-year school dance tickets available. Students who have perfect attendance are able to purchase them in advance. If 18 tickets were purchased in advance, what percent of the tickets were purchased in advance?
Answers
Thus, 9 percent of the total dance tickets available is found to be purchased in advance.
Explain about the percentage:Although the usage of percent and percentage differs slightly, they both signify the same thing. It is customary to use percent or the symbol (%) along with a numerical value. One tenth of something is one percent.
Hence, it can be expressed as a fraction as well as a decimal. In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. The Latin word "per centum," which meaning "per 100," is where the word "percent" comes from. % is the symbol used to represent percentages.Given data:
Total dance tickets = 200
Advanced purchased tickets = 18
Let x be the percentage of advance booked tickets.
Then,
x% of 200 = 18
x*200 / 100 = 18
2x = 18
x = 18/2
x = 9%
Thus, 9 percent of the total dance tickets available is found to be purchased in advance.
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I need the best answer to this question complete sentences (I will give 20 points for the full question answered how it says to do it.)
Answers
The three types of rock are igneous, sedimentary, and metamorphic.
What are the three types of rock?There are three types of rocks as explained below.
Igneous rocks are formed from the cooling and solidification of molten rock, either on the Earth's surface (extrusive) or beneath the surface (intrusive). Examples of igneous rocks include basalt, granite, and pumice.
Sedimentary rocks are formed from the accumulation and cementation of sediment particles (such as sand, silt, and clay) or the precipitation of minerals from a solution. Examples of sedimentary rocks include sandstone, limestone, and shale.
Metamorphic rocks are formed from the alteration of pre-existing rocks by heat, pressure, and chemical reactions. Examples of metamorphic rocks include marble, slate, and gneiss.
The rock cycle is the process by which one type of rock can be changed into another type of rock.
The rock cycle involves three main processes:
Weathering and erosionDeposition and lithificationMelting and solidificationTherefore, one type of rock can be changed into another type of rock through the rock cycle by undergoing weathering, erosion, deposition, lithification, metamorphism, melting, and solidification, depending on the specific conditions and processes involved.
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If the profit function for a product is
P(x) = 2800x + 85x^2 − x^3 − 109,000
dollars, selling how many items, x, will produce a maximum profit?
Find the maximum profit.
Answers
The maximum profit that for the equation p(x) = 2800x - 85x² - x³ - 109000 is $672500
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Given the profit function:
p(x) = 2800x - 85x² - x³ - 109000
The profit is maximum at:
p'(x) = 0
p(x) = 2800 + 170x - 3x²
2800 + 170x - 3x² = 0
x = 70
p(70) = 2800(70) - 85(70)² - (70)³ - 109000 = 672500
The maximum profit is $672500
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Suppose that you are taking a course where the total class grade is the weighted average of your homework, worksheets, quizzes and tests.
The homework is worth 15% of the course grade, worksheets are worth 20% of the course grade, the quizzes are worth 25% of the course grade, and tests are worth 40% of the course grade. To get a B in the course, you must have an overall average of at least 80%.
Your current grades in each category are:
Homework =
73
%, Worksheets =
79
%, and Quizzes =
84
%.
What is the minimum test average you need to get a B in the course?.
Your answer is:
% (Round to at least 1 decimal place)
Answers
The minimum grade you need to get a B in the course is given as follows:
x = 80.625.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The grades and their percentages are given as follows:
73 worth 15%.79 worth 20%.84 worth 25%.x worth 40%.You want a grade of 80, hence the minimum test average is obtained as follows:
0.15 x 73 + 0.2 x 79 + 0.25 x 84 + 0.4x = 80
47.75 + 0.4x = 80
x = (80 - 47.75)/0.4
x = 80.625.
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to manufacturing floor
T
30 in.
72 in.
to loading dock
D
48 in.
36 in.
g) What is the longest rod that can be carried to the loading dock? Round to
the nearest tenth of an inch.
Answers
Answer:
To determine the longest rod that can be carried to the loading dock, we want to find the shortest distance from point T to line segment CD. We can use the Pythagorean theorem for this.
First, we need to find the equation of the line containing segment CD. We can find the slope of the line CD as:
m = (y2 - y1) / (x2 - x1) = (36 - 48) / (48 - 0) = -12/48 = -1/4
where (x1, y1) = (0, 48) and (x2, y2) = (48, 36).
Using point-slope form, we get the equation of the line CD as:
y - 48 = (-1/4)(x - 0)
y = (-1/4)x + 48
Now, we can find the perpendicular distance from point T to the line CD as follows:
d = |(-1/4)(30) + 72 - 48| / sqrt((-1/4)^2 + 1)
d = 42 / sqrt(17) ≈ 10.21
Therefore, the longest rod that can be carried to the loading dock is approximately 10.2 inches long (rounded to the nearest tenth of an inch).
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects.
Before treatment, 23 subjects had a mean wake time of 105.0 min. After treatment, the 23 subjects had a mean wake
time of 82.1 min and a standard deviation of 23.3 min. Assume that the 23 sample values appear to be from a
normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a
population with drug treatments. What does the result suggest about the mean wake time of 105.0 min before
the treatment? Does the drug appear to be effective?
Answers
The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.
what is mean ?In statistics, mean is a measure of central tendency that represents the average value of a set of data. It is commonly referred to as the "arithmetic mean" or simply the "average." To calculate the mean, you add up all the values in the data set and divide the total by the number of values. For example, if you have the following data set: 2, 5, 8, 9, 12, the mean would be calculated as follows:(2 + 5 + 8 + 9 + 12) ÷ 5 = 7.2 . So the mean of this data set is 7.2. The mean is a useful measure of central tendency because it takes into account all the values in the data set and provides a single representative value that can be used to describe the overall characteristics of the data.
given
For a population receiving pharmacological treatments, the mean wake time was estimated with a 95% confidence interval.
where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.
When we enter the provided values, we obtain:
s = 23.3
n = 23
t0.025,22 = 2.074
The mean wake time estimate with a 95% confidence interval for a population receiving medication is thus:
82.1 ± 2.074 * (23.3/√23)
which is equivalent to:
(71.4, 92.8)
The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.
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use synthetic division
PLEASE HELP 30 PTS
Answers
Answer:
The quotient is
[tex]8 {x}^{2} + 15x - \frac{1}{8} [/tex]
and the remainder is
[tex] \frac{63}{64} [/tex]
Find the volume of the composite solid. Round your answer to the nearest hundredth.
Answers
Therefore, the volume of the composite solid is approximately 1357.28 cubic feet, rounded to the nearest hundredth.
What is volume?Volume is a measure of the amount of space occupied by an object or a substance. In other words, it is the three-dimensional space that an object or substance occupies. The SI unit for volume is cubic meters (m³), although other units such as cubic centimeters (cm³) and liters (L) are also commonly used.
Here,
The composite solid is made up of a hemisphere and a cone with the same base radius and height. The volume of the hemisphere is given by (2/3)πr³, and the volume of the cone is given by (1/3)πr²h, where r is the radius and h is the height. Given that the radius is 6 feet and the height is 12 feet, we can find the volumes of the hemisphere and the cone as follows:
Volume of hemisphere = (2/3)π(6³)
= 288π cubic feet
Volume of cone = (1/3)π(6²)(12)
= 144π cubic feet
The total volume of the composite solid is the sum of the volumes of the hemisphere and the cone, which is:
Total volume = Volume of hemisphere + Volume of cone
= 288π + 144π
= 432π
To find the numerical value of this volume, we can use the approximation π ≈ 3.14 and round the result to the nearest hundredth:
Total volume ≈ 432(3.14)
= 1357.28 cubic feet
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What is the solution set for −4x−38<2
Answers
The solution set for the inequality is x < -10
What are inequalities?The different signs for representing inequalities are;
< represents the sign for less than> represents the sign for greater than≥ represents greater than or equal to≤ represents less than or equal toFrom the information given, we have that;
−4x−38<2
To solve for the value of x, take the steps;
collect the like terms
-4x> 2 + 38
Add the values
-4x> 40
Divide both sides by the coefficient of x, we have;
x > -10
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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
Answers
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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please help! it is matrices, so it should be rlly easy.
Answers
B is a 2 by 2 matrix, and the determinant of B written as |B| is equal to -1.
How to find the determinant of the matrix BWe can find |B|, the determinant of the matrix B by subtracting the multiple of row column and row 2 column 1 from the multiple of row column 1 and row 2 column 2 as follows:
|B| = (-2 × -2) - (1 × 5)
|B| = 4 - 5
|B| = -1.
Therefore, the determinant of the 2 by 2 matrix B written as |B| is equal to -1.
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Kara wants to paint the four outside walls of her dogs house. She will not paint the roof or the door on the front of the house. What is the area of surface that Kara needs to paint?
Answers
Total area to paint: (15 + 10) - 1.5 = 23.5 sq ft
How to solveCalculate the area of each wall, subtract the door area, and sum the areas.
Front and back walls: (3 * 2.5) * 2 = 15 sq ft
Next, we calculate the area of the side walls:
Side walls: (2 * 2.5) * 2 = 10 sq ft
Door area: 1.5 * 1 = 1.5 sq ft
Total area to paint: (15 + 10) - 1.5 = 23.5 sq ft
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The Complete Question
Kara wants to paint the four outside walls of her dog's house, excluding the roof and door. The dog house measures 3 feet in length, 2 feet in width, and 2.5 feet in height. The door is 1.5 feet tall and 1 foot wide. What is the area of the surface she needs to paint?
A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 28.4 units of niacin and 37,335 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.11 unit of niacin and 190 units of retinol per gram. Food B contains 0.35 unit of niacin and 95 units of retinol per gram. How many grams of each food does she feed this group of rats each day?
Answers
The grams of each food she feeds this group of rats each day is 80 grams of food A and 100 grams of food B each day.
Let us consider that the researcher feeds x grams of food A and y grams of food B each day. Then we can restructure the two equations on the basis of the amount of niacin and retinol present in the food
0.11x + 0.35y = 28.4 (equation 1)
190x + 95y = 37,335 (equation 2)
We can evaluate this system of equations applying the substitution or elimination method.
Let us apply substitution method:
In case of equation 1, we can evaluate concerning x:
x = (28.4 - 0.35y) / 0.11
Staging this value for x in equation 2
190[(28.4 - 0.35y) / 0.11] + 95y
= 37,335
Applying simplification and evaluating for y
y = 100
Staging this value for y in equation 1 to evaluate x
x = 80
Then, the researcher feeds 80 grams of food A and 100 grams of food B each day.
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Please help me this is so hard. Please if you help i give you 60 points. This is really hard for me and i dont get this.
Answers
Answer:
The discriminant is:
(-3)^2 - 4(1)(18) = 9 - 72 = -63
Since this discriminant is negative, f(x) does not have any real number solutions.
George went to the store to buy notebooks.
- He had $36 to spend.
- He purchased 4 notebooks.
- After buying the notebooks, George had less than $12 left.
-What is the solution set for x, the cost of each notebook?
Answers
Thus, the solution set for the cost of each notebook that can be bought by George is: (0 ≤ x ≤ 6).
Explain about the one variable linear equation:A linear equation is a one-variable equation of the a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.
Given that:
Total amount George has = $36.Number of books = 4Left amount = $12Let the cost of each notebook 'x'.So, the linear equation follows
Amount for 4 notebooks + Left amount = total amount
4*x + 12 ≤ 36
4x ≤ 36 - 12
4x ≤ 24
x ≤ 24/4
x ≤ 6
So, (0 ≤ x ≤ 6)
Thus, the solution set for the cost of each notebook that can be bought by George is: (0 ≤ x ≤ 6).
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solve the following system of equations algebraically for all values of x and y
Answers
The values of x, y, and z based on the system of equations will be (-2,4,7).
How to solve the equationx + 3y + 5z = 45
6x - 3y + 2z = - 10
------------------------add
7x + 7z = 35
6x - 3y + 2z = -10
-2x + 3y + 8z = 72
----------------------add
4x + 10z = 62
7x + 7z = 35....multiply by 4
4x + 10z = 62...multiply by -7
---------------------
28x + 28z = 140 (result of multiplying by 4)
-28x - 70z = - 434 (result of multiplying by -7)
--------------------add
- 42z = - 294
z = -294/-42
z = 7
4x + 10z = 62
4x + 10(7) = 62
4x + 70 = 62
4x = 62 - 70
4x = - 8
x = -8/4
x = -2
x + 3y + 5z = 45
-2 + 3y + 5(7) = 45
-2 + 3y + 35 = 45
3y + 33 = 45
3y = 45 - 33
3y = 12
y = 12/3
y = 4
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Solve the following system of equations algebraically for all values of x,y and z
x+3y+5z=45
6x-3y+2z=-10
-2x+3y+8z=72
Brynen is driving to a new job five days this week. He drives 27 miles each way. His car gets 35 miles per gallon of gas. How many gallons of gas will he use driving to and from work this week? Round to the nearest tenth.
Answers
The number of gallons of gas Brynen will use in driving to and from work, during the week, obtained using arithmetic operations is 7 5/7 gallons
What are arithmetic operations?Arithmetic operations are operations involving addition, subtraction, multiplication, and division.
The distance Brynen travels each way to his new job = 27 miles
The distance his car gets per gallon of gas = 35 miles
The number of gallons he will use in a week (five days of driving in the week), can therefore, be found by arithmetic operations follows;
The distance Brynen travels = 27 × 2 × 5 = 270 miles
The number of gallons = 270 miles/(35 miles/gallon) = 270/35 = 7 25/35
7 25/35 = 7 5/7
The volume of gas he will use to and from work this week is; 7 5/7 gallons
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Santiago is going to see a movie and is taking his 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $4.50 each. How much total money would Santiago have to pay for his family if he were to buy 6 snacks for everybody to share? How much would Santiago have to pay if he bought x snacks for everybody to share?
Answers
Answer:
25$ if the tickets were involved it would be 70$
Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.
Explanation:The topic of this question is
Mathematics
, specifically about using multiplication and addition in problem-solving.
Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.
Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.
Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.
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