So the handwriting is a bit messy.
A dosage requires a patient to receive 58.3 mg of medicine for every 9 kg of body weight for every 4 hours. How many grams of medication does a patient, who weights 63 kg, need in 12 hours?
Based on proportional multiplication, the quantity of medication in grams that the patient, who weighs 63 kg needs in 12 hours is 1,224.3 mg.
What is proportional multiplication?Proportional multiplication involves the cross-multiplication of two fractional ratios, which are equated to each other.
Proportions involve the equation of two ratios.
The dosage required by a patient in 4 hours with a weight of 9 kg = 58.3 mg
Proportionately, the dosage required by a patient in 12 hours with a weight of 63 kg = 1,224.3 mg (58.3 x 63/9 x 12/4).
Thus, if a patient weighing 9 kg receives 58.3 mg of medicine in 4 hours, proportionately, in 12 hours, a patient weighing 63 kg will receive 1,224.3 mg.
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Janet hikes a trail at a local forest each day. The trail is 23.6 miles long, and she has hiked 5 days in the past week. How many miles has Janet hiked in the past week?
Answer:18
Step-by-step explanation:
x -3,0,5
y- 5,2,-3
Draw the straight line y=2-x
The graph of straight line y = 2 - x with the given points are shown in graph.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The equation of straight line is,
⇒ y = 2 - x
Now, We have to given that;
Points on the graph are,
x = -3, 0, 5
y = 5, 2, -3
Hence, We can plot the points and join all the points.
We get;
The graph of straight line with the given points as shown in figure.
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What is the area of this figure?
___ units 2
Answer:
Step-by-step explanation:
7 + 28 + 7 = 42 units^2 see image below
pa8 11.project Daffynition Decoder
Daffynition Decoder is a fun and challenging word puzzle that requires both creativity and logical thinking to solve. It is often found in puzzle books, newspapers, and online puzzle websites.
What is Daffynition Decoder?Daffynition Decoder is a word puzzle game that involves decoding phrases or sentences by using a letter-substitution method. The game provides a list of numbered words, where each word is a cryptic definition of a common word or phrase. The solver's goal is to figure out what each word represents and then use the letters from those words to decode a secret message. The game is typically played by filling in a chart or grid, where each row corresponds to a numbered word in the list, and each column represents a letter in the decoded message. The solver uses the numbered words to fill in the corresponding letters in the grid, eventually revealing the hidden message.
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Complete question:
What is project Daffynition Decoder?
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 84
months, with a variance of 100
.
If he is correct, what is the probability that the mean of a sample of 99
computers would differ from the population mean by less than 2.5
months? Round your answer to four decimal places.
SEE ATTACHED SOLUTION
A rectangular sheet of metal 360mm by 240mm has four equal squares cut out the corners. The sides are then turned up to form a rectangular box. Find the length of the sides of the squares cut out so that the volume of the box may be as great as possible, and find this maximum volume.
Answer: Let x be the side length of each square cut out from the corners.
After cutting out the squares, the dimensions of the resulting rectangle will be:
length = 360 - 2x
width = 240 - 2x
The height of the box will be equal to the side length of the squares cut out, which is x.
The volume of the box is given by the formula:
V = length × width × height
Substituting the expressions for length, width, and height, we get:
V = (360 - 2x)(240 - 2x)x
Expanding this expression, we get:
V = x(86400 - 120x + 4x^2)
To find the maximum volume, we need to find the value of x that maximizes the expression for V.
We can do this by finding the critical points of the function V(x) and then determining whether these points correspond to a maximum or a minimum.
Taking the derivative of V(x) with respect to x, we get:
V'(x) = 86400 - 240x + 8x^2
Setting V'(x) = 0 to find the critical points, we get:
8x^2 - 240x + 86400 = 0
Dividing both sides by 8, we get:
x^2 - 30x + 10800 = 0
Using the quadratic formula to solve for x, we get:
x = (30 ± √(30^2 - 4(1)(10800))) / 2
x = (30 ± 210) / 2
We can discard the negative solution, since x represents a length and therefore must be positive. Thus, we get:
x = (30 + 210) / 2
x = 120
Therefore, the side length of the squares cut out from the corners should be 120 mm in order to maximize the volume of the box.
To find the maximum volume, we can substitute x = 120 into the expression for V:
V = x(86400 - 120x + 4x^2)
V = 120(86400 - 120(120) + 4(120)^2)
V ≈ 27648000 mm^3
Therefore, the maximum volume of the box is approximately 27,648,000 mm^3, and this maximum is achieved when the side length of each square cut out from the corners is 120 mm.
Step-by-step explanation:
Need help with this equation please
Answer:
-1/5(x-6)^2+3
Step-by-step explanation:
+3 makes the graph go up by 3
-6 makes the graph go right 6
we put a negative outside of (x-6) since this goes down and is a -x^2 parabola
no clue about 1/5 just kept putting numbers outside of (x-6) to eventually get the width.
does anyone know the answer??? plsss i need the answer ASAP
Step-by-step explanation:
closest to all points on the graph
Exponential Functions Problems
Please help me, thank you!
The graph of both the exponential functions y = 3(11)ˣ and y = (1/12)ˣ can be plotted by assuming some arbitrary values of 'x' that correspond to
different values of 'y'.
What are exponential functions?A function is said to be n exponential function when the independent variable is the exponent.
For example -: aˣ.
The two exponential functions can be graphed by assuming some arbitrary values of 'x'.
In y = 3(11)ˣ.
At x = 1, y = 33.
At x = - 1, y = 3/11.
At x = 2, y = 363.
So, The points are (1, 33), (- 1, 3/11) and (2, 363).
Now we can plot these points and join them by free hand.
Similarly, y = (1/12)ˣ can also be graphed in a similar manner.
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Solve for the variable. I NEED HELP PLS:) THIS HW IS DUE IN A HOUR
The solution to the variable x is 60/7
How to determine the solution to the variableFrom the question, we have the following parameters that can be used in our computation:
The similar polygons
The scale factor from the big to the small polygon is represented as
Scale factor = 5/7
Using the above as a guide, we have the following:
x = 12 * 5/7
Evaluate
x = 60/7
Hence, the solution is 60/7
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4) A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in
11 hours? What is the rate of speed of the jet?
The rate of speed of the jet is given by S = 98 miles per hour
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the rate of speed of the jet be represented as S
Now , the value of S is
The distance traveled by the jet D = 490 miles
The time taken by the jet to travel 490 miles T = 5 hours
So , the speed of the jet is given by
Speed = Distance / Time
On simplifying , we get
The speed of the jet S = 490 / 5
The speed of the jet S = 98 miles per hour
Now , the distance traveled by the jet in 11 hours be D₁
The time taken to travel D₁ distance is 11 hours
where D₁ = Speed x Time
On simplifying , we get
D₁ = 98 x 11
D₁ = 1,078 miles
Hence , the distance traveled at a speed of 98 mph for 11 hours is 1,078 miles
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Need help fast response
The value of (p o g)(-1) is -2 and the value of (q o p)(-1) is 15 which represents the composite of the function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function p and q:
p(x) = 2x - 2
q(x) = x² - 1
= (p o q)(-1)
Find the value of q(-1):
q(-1) = 0
Plug the above value in the function p(x):
(p o q)(-1) = p(q(-1)) = -2
= (q o p)(-1)
Find the value of p(-1):
p(-1) = -4
(q o p)(-1) = q(p(-1)) = 15
Thus, the value of (p o g)(-1) is -2 and the value of (q o p)(-1) is 15 which represents the composite of the function.
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If $10,000 is invested at 6% annual interest compounded annually, how long would it take for the account balance to reach $20,000? Round your answer to the nearest tenth
It would take approximately 11.6 years for the account balance to reach $20,000 if compounded annually.
What is the difference between compound interest and simple interest?The costs a borrower pays a lender for a loan are known as interest. For instance, banks charge interest on the loans that consumers take out.
Simple interest is the term used to describe interest that is based on the principle amount that a person borrows or invests. Contrarily, compound interest is computed on the principle borrowed or invested by the individual as well as the accrued interest from the prior period.
The formula for compound interest is:
A = P(1 + r/n)ⁿˣ
where, A is the amount
P is the principal amount = $10,000
r is the rate = 6% = 0.06
x is time.
n = 1
Substituting the values,
$20,000 = $10,000(1 + 0.06/1)¹ˣ
2 = (1.06)ˣ
Taking the natural logarithm of both sides:
ln(2) = t * ln(1.06)
t = ln(2) / ln(1.06) ≈ 11.6
Therefore, it would take approximately 11.6 years for the account balance to reach $20,000.
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32% of 120 is 38.4. pls help
Answer:
Step-by-step explanation:
pls finish question first
A tunnel connecting two portions of a space station has a circular cross-section of radius 15 feet. Two walkway decks are constructed in the tunnel. Deck A
is… A tunnel connecting two portions of a space station has a circular cross-section of radius 15 feet. Two walkway decks are constructed in the tunnel. Deck A is along a horizontal diameter and another parallel Deck B is 2 feet below Deck A. Because the space station is in a weightless environment, you can walk vertically upright along Deck A, or vertically upside down along Deck B. You have been assigned to paint "safety stripes" on each deck level, so that a 6 foot person can safely walk upright along either deck. Determine the width of the "safe walk zone" on each deck
Deck A the safe walk zone must be painted at the points 13.74 units left and right of the edge of the circle, whereas for Deck B it must be painted at 12.68 units.
What is maximum height?Maximum Height refers to the vertical distance between the Reference Level and the highest point of a building's roof surface, including parapet walls, mechanical equipment installed on the roof, authorised Signage, and other permissible projections of any type.
The equation of the given circular space station is:
[tex]x^2 + y^2 = 15^2\\\\x^2 + y^2 = 225[/tex]
Given that, a 6-foot person can walk through the circular station.
Substitute the value of y = 6.
[tex]x^2 + 6^2 = 225\\\\x^2 = 225 - 36\\\\x = \sqrt{189}\\ \\x = \pm 13.74[/tex]
Also, Deck B is 2 feet below deck A thus,
[tex]x^2 + 8^2 = 225\\\\x^2 = 225 - 64\\\\x = \sqrt{161}\\ \\x = \pm 12.68[/tex]
Hence, for Deck A the safe walk zone must be painted at the points 13.74 units left and right of the edge of the circle, whereas for Deck B it must be painted at 12.68 units.
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Find the total year costs for 5
years, 10
years, and 15
years for purchasing and renting a house. Then compare your answers to those in the following table.
Length of Time Purchase Home Rent Home
5
years $78,559.20
$54,900.00
10
years $127,118.40
$115,200.00
15
years $175,677.60
$180,900.00
Purchase Home
Total 5-
year cost: $30,000.00+5×12×$809.32=$78,559.20
Total 10-
year cost: $30,000.00+10×12×$809.32=$127,118.40
Total 15-
year cost: $30,000.00+15×12×$809.32=$175,677.60
Rent Home
Total 5-
year cost: (4×12×$900)+(1×12×$975)=$54,900
Total 10-
year cost: (4×12×$900)+(4×12×$975)+(2×12×$1050)=$115,200
Total 15-
year cost: (4×12×$900)+(4×12×$975)+(4×12×$1050)+(3×12×$1125)=$180,1900
Recall the pros and cons of buying a house and which conditions make it better to to purchase a home. Also, think about the pros and cons of renting a house and which conditions make it better to rent. Use this information along with the total costs you found to answer the following prompts. Make sure to write your answer in complete sentences.
Does renting or purchasing makes the most sense for the Bainters if they live in the house 1
year? 5
years? 10
years? 15
years?
For each interval, explain why you think the Bainters should rent or purchase a home. Use mathematical evidence to support your conclusions.
The table makes it abundantly evident that buying costs less than renting does. Buying a house is therefore better over the course of 15 years. By buying a home instead of renting one, you can save $5,222.4.
How are lengths determined?Every object's length can be determined using measuring tools like a ruler, measuring tape, etc. For example, a ruler may be utilized to measure the length in inches of a pencil. A foot scale can be used in a classroom to gauge the heights of the students.
Step 1
Buying a home is more advantageous if someone is looking for somewhere to live for an extended period of time. Second, if a person buys the home, it can be sold at a higher price in the future since rental prices after a specified term and after a few years, say 10 or 15, cumulative rental charges become greater than the initial purchase price.
However, according to the above table, renting a property is preferable if the need for the home is for a shorter duration, like fewer then 5 or 10 years, in order to save money.
Step 2
1 year
The cost for Purchasing a house = 30,000 + 1 × 12 × 809.32 = $39,711.84
The cost of renting a house = 1 × 12× 900 = $10,800
So, it is evident that there's a difference between buying and renting a home of $28,911.84. So, renting a home is preferable.
Step 3
5 year
The cost of purchasing the home for five years is listed as $78559.20, whereas the cost of renting the home for five years was $54,900.
Again, renting is more affordable than buying. By renting a home, one could save $23,659.2 (78559.20-54900).
10 years
The cost of purchasing the home over 10 years is shown as $127,118.40, while the cost of renting the home for 10 years was $115,200.
Renting is less expensive than buying. Yet, buying a house is advantageous if it can be bought or rented out; otherwise, leasing one is advantageous.
Step 4
15 years
The table clearly shows that purchasing is less expensive than renting. Over the period of fifteen years, purchasing a home is therefore preferable. You can save $5,222.4 by buying a house instead of renting one.
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1. A hot piece of meat is removed from an oven and its surface temperature
is given by the formula S(t) = 72 +238•0.97^t, in degrees Fahrenheit, at time t
minutes after it was removed.
(a) What was the initial surface temperature of the meat?
I am not understanding how to do this at all could someone please help me & show the work for it??
Answer:
[tex]310 ^\circ F[/tex]
Step-by-step explanation:
The formula relating surface temperature in °F and time in t minutes after removal from the oven is given as
[tex]S(t)= 72 + 238 (0.97^t)\\\\\text{The initial temperature is when t = 0}\\\\\text{At t = 0}\\\\S(0) = 72 + 238(0.97^0)\\\\0,97^0 = 1 \text{ since any number raised to 0 = 1}\\\\\text{Therefore}\\S(0) = 72 + 238 \cdot 1\\= 72 + 238\\\\= 310 ^\circ F[/tex]
write another ratio that is equivalent to the ratio 4:6
Answer:
2:3 , 8:12
Step-by-step explanation:
Equivalent ratio means, multiply/divide the numerator and the denominator of the fraction with the same number. So, we need to multiply the numerator and the denominator with the same number. Hence, another ratio that is equivalent to 4 : 6 is 8 : 12
Hope this helped :D
The scale of the model is 1 inch = 9 feet. The fountain at the center of the city is 18 1/2 feet wide. How wide is the fountain in the model
Therefore , the solution of the given problem of unitary method comes out to be fountain's diameter in the model is roughly 2.0556 inches.
What is an unitary method?The measurements taken from this nanosecond variable section must be multiplied by two in order to complete the task using the unitary technique. In essence, the characterised by a group and the colour sections are both removed from the unit expression method when a desired object is present. For example, 40 pens with a variable price would pay Inr ($1.01).
Here,
We can use proportionality to determine the breadth of the fountain in the model if the scale is 1 inch = 9 feet. The following percentage can be configured:
Model fountain width divided by one inch equals actual fountain width multiplied by nine feet.
The diameter of the fountain is stated to be 18 1/2 feet in real life, which is the same as 18.5 feet. Adding this number to the proportion results in:
1 inch of the model fountain's diameter divided by 18.5 feet by 9 feet
If we simplify, we get:
diameter of the model's fountain / 1 = 2.0556
By dividing the two edges by one inch, we obtain:
Modeled fountain width is 2.0556 inches.
As a result, the fountain's diameter in the model is roughly 2.0556 inches.
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Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
5(x2 + 4x + 4) = –7 + 20
x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot
5(x2 + 4x) = 7
5(x2 + 4x + 4) = 7 + 20
5(x2 + 4x) = –7
Steps he could use to solve the quadratic equation by completing the square is 5(x² + 4x) = –7
What are quadratic equations?A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants. It typically has two solutions, which can be found using the quadratic formula or factoring the equation.
Solution:
The three steps that Sergey could use to solve the quadratic equation by completing the square are:
1.Write the equation in the form ax² + bx + c = 0
2.Add and subtract (b/2)² to complete the square, resulting in an expression of the form a(x + p)^2 + q = 0
3.Solve for x by isolating (x + p)² and taking the square root, resulting in x = (-b ± sqrt(b² - 4ac)) / 2a
Therefore, the three options that correspond to these steps are:
5(x² + 4x + 4) = –7 + 20
x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot
5(x² + 4x) = –7
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Amir got $100 for his birthday. He wants to buy a pitching machine that costs $44 and as many baseballs as he can with the money. The baseballs cost $1.25 each. Amir found a coupon for 20% off the baseballs at the sporting goods store but he isn't sure if the coupon is expired. Determine the number of baseballs he can buy if he can use the coupon, and how many he can buy if he can't use the coupon.
Answer:
Without coupon: 44 baseballs
With coupon: 56 baseballs
Step-by-step explanation:
Amount that Amir got as a birthday present = $100Cost of pitching machine = $44Amount left over for buying baseballs = 100 - 44 = $56Cost of each baseball without coupon = $1.25Number of baseballs that Amir can buy at $1.25 per baseballIf the coupon works, the cost per baseball is reduced by 20%20% = 20/100 = 0.2 in decimalDiscount in $ at 20% discount = 1.25 x 0.2 = $0.25Cost after discount = $1.25 - $0.25 = $1Therefore number of baseballs that can be bought with coupon
You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 14 by 24 ft brick patio installed.
Therefore, we can estimate that having a 14 ft by 24 ft brick patio installed would cost around $3,033.33.
What does "cost concept" mean?Cost is a key concept in economics. The price that was paid in return for any products or services is referred to. Cost is a monetary evaluation of the materials, labour, risks, expenses, and time required to purchase goods and services.
We can use proportions to estimate the cost of having a 14 ft by 24 ft brick patio installed based on the given information.
Let's use x to represent the estimated cost of having a 14 ft by 24 ft brick patio installed.
We can set up a proportion:
15/20 = 2275/x
To solve for x, we can cross-multiply and simplify:
15x = 20 x 2275
15x = 45500
x = 3033.33
So the estimated cost of having a 14 ft by 24 ft brick patio installed is approximately $3,033.33.
Therefore, we can estimate that having a 14 ft by 24 ft brick patio installed would cost around $3,033.33.
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what is the mean absolute deviation of 42, 45, 47, 50, 53, 56, 58, 65
The mean absolute variation for the group of integers 42, 45, 47, 50, 53, 56, 58, and 65 is therefore roughly 6.5.
How does one standard deviation mean?What one standard deviation (SD) means. on a normal or bell-shaped distribution of the data. The region of a bell curve starting at position 13 on the y axis is approximately filled by 1 SD = one standard deviation = 68% of a ratings or data values.
Here's how to find the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65:
Find the mean:
mean = (42 + 45 + 47 + 50 + 53 + 56 + 58 + 65) / 8
mean = 50.375
Find the absolute difference between each number and the mean:
|42 - 50.375| = 8.375
|45 - 50.375| = 5.375
|47 - 50.375| = 3.375
|50 - 50.375| = 0.375
|53 - 50.375| = 2.625
|56 - 50.375| = 5.625
|58 - 50.375| = 7.625
|65 - 50.375| = 14.625
Find the average of these absolute differences:
mean absolute deviation = (8.375 + 5.375 + 3.375 + 0.375 + 2.625 + 5.625 + 7.625 + 14.625) / 8
mean absolute deviation ≈ 6.5
Therefore, the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65 is approximately 6.5.
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step by step answer. differentiate/simplify
The derivative of given ƒ(x) is:
[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]
What is differentiation ?Differentiation is a mathematical process used to find the rate at which a function changes with respect to one of its variables. It is the process of finding the derivative of a function, which is a measure of how much the function changes as its input changes. The derivative is used to analyze the behavior of functions, find maximum and minimum values, and solve optimization problems. It is an important concept in calculus and is used in many areas of mathematics, science, and engineering.
According to given information :We can use the quotient rule to differentiate ƒ(x):
[tex]f(x) &= \frac{2+3\log(x)}{x^2+5} \ \\ \\ \\f'(x) &= \frac{(x^2+5)\frac{d}{dx}(2+3\log(x)) - (2+3\log(x))\frac{d}{dx}(x^2+5)}{(x^2+5)^2} \\ \\\ &\\= \frac{(x^2+5)\left(0+\frac{3}{x}\right) - (2+3\log(x))(2x)}{(x^2+5)^2} \\\ \\ \\ &= \frac{3x^2-6-6\log(x)}{x(x^2+5)^2}[/tex]
Therefore, the derivative of given ƒ(x) is:
[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]
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Solve for y. Explain all steps.
y/3 - 8 = -15
Answer:
y = -21
Step-by-step explanation:
Hope this helps! :))
An experiment published in The American Biology Teacher studied the efficacy of using 95% ethanol and 20% bleach as disinfectants for removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue cultured. Five cuttings per plant were placed on a petri dish, disinfected using each agent, and stored at 25 Celsius for 4 weeks. The observations reported were the number of uncontaminated eggplant cuttings after the 4 weeks of storage. Relevant data is given in the following table. Are you willing to assume that the underlying population variances are equal?
Disinfectant Sample mean Sample variance Sample size
95% Ethanol 3.73 2.78095 15
20% Bleach 4.80 0.17143 15
Since t = -2.41 < -2.145, reject [tex]H_o[/tex] and conclude Ha, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.
How to solve(a) Are you willing to assume that the underlying variances are equal?
Absolutely not! The variances can NOT be assumed equal.
H_o: sigma1^2 = sigma2^2
H_a: sigma1^2 =/ sigma2^2
F = s1^2 / s2^2 = 2.78095 / 0.17143 = 16.222
alpha = .05, dfnum = 15-1 = 14 and dfdenom = 15-1 = 14
F-critical values
= .33573 = F.INV(.025,14,14) using Excel
= 2.978588 = F.INV(.025,14,14) using Excel
Since F = 16.222 > 2.978588, reject H_o and conclude H_a, i.e. that the population variances significantly differ.
Or, using the p-value from the TI-84... p-value = 5.59E-6 = .00000559 < alpha = .05, so we can reject H_o and conclude H_a, i.e. that the population variances significantly differ.
(b) Using the information from part a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested ?
Note: Since the population variances ARE significantly different, we can NOT use the pooled t-test as rapunzel shows.
H_o: mu1 = mu2
H_a: mu1 =/ mu2
t = (xbar1-xbar2) / sqrt(s1^2/n1 + s2^2/n2)
t = (3.73 - 4.80) / sqrt(2.78095/15 + .17143/15)
Note: We do NOT square the variances. They are already squared.
t = -2.41
t-critcal values
df = smaller of n1-1 and n2-1, i.e. the smaller of 15-1 = 14 and 15-1 = 14
--> df = 14
left tail critical value = -2.145 <-- alpha/2 = .025, df = 14
right tail critical value = +2.145 <-- alpha/2 = .025, df = 14
Since t = -2.41 < -2.145, reject H_o and conclude H_a, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.
Or, using the p-value from the TI-84... p-value = .028486... < alpha = .05, so we can reject H_o and conclude H_a, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.
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An experiment published in The American Biology Teacher studied the efficacy of using 95% ethanol and 20% bleach as a disinfectant in removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue being cultured. Five cuttings per plant were placed on a petri dish for each disinfectant and stored at 25 centigrades for 4 weeks. The observation reported was the number of uncontaminated eggplant cuttings after the 4-week storage.
Disinfectant 95% Ethanols 20% Bleach
Mean 3.73 4.80
Variance 2.78095 0.17143
Pooled variance: 1.47619
Are you willing to assume that the underlying variances are equal?
Using the information from part a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested ?
Denniel chooses to never do homework. If he gets a 70 as his final grade for the class, and he knows that he did equally well on classwork and exams, what was his classwork average?
Grading System:
Tests: 40% of the grade
Classwork: 40% of the grade
Homework: 20% of the grade
Answer:
Step-by-step explanation:
Let's start by finding out what Denniel's weighted average grade is, given the grading system:
Tests: 40% of 70 = 0.4 x 70 = 28
Classwork: ? (we don't know this yet)
Homework: 0 (since he never does homework)
Weighted average grade: 0.4 x 28 + 0.4 x ? + 0.2 x 0 = 0.4 x ?
We know that his overall weighted average grade is 70, so we can set up an equation to solve for his classwork average:
0.4 x ? = 70 - 0.4 x 28 - 0.2 x 0
0.4 x ? = 42
? = 42 / 0.4
? = 105
So Denniel's classwork average is 105.
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The value of sin (x/2) is -√(26/27).
The value of cos (x/2) is -√(2/27)
The value of tan (x/2) is 1/12.
What is the value of sine, cosine and tan functions?
We know that sin(x) = -2/27 in Quadrant 3, which means that x lies between 180 degrees and 270 degrees.
a. To find sin(x/2), we can use the half-angle formula:
sin(x/2) = ±√[(1-cos(x))/2]
Since x lies in Quadrant 3, we know that cos(x) is negative. To find cos(x), we can use the Pythagorean identity:
sin²(x) + cos²(x) = 1
(-2/27)² + cos²(x) = 1
cos²(x) = 1 - (-2/27)²
cos(x) = -√(1 - (-2/27)²)
cos(x) = -25/27
Now we can substitute cos(x) into the half-angle formula:
sin(x/2) = ±√[(1-(-25/27))/2]
sin(x/2) = ±√[(27/27 + 25/27)/2]
sin(x/2) = ±√[52/54]
sin(x/2) = ±√(26/27)
Since x is in Quadrant 3, sin(x/2) is negative.
Therefore;
sin(x/2) = -√(26/27)
b. To find cos(x/2), we can use the half-angle formula:
cos(x/2) = ±√[(1+cos(x))/2]
Again, we know that cos(x) is negative, so we can use the value we found earlier:
cos(x/2) = ±√[(1-25/27)/2]
cos(x/2) = ±√[2/27]
Since x is in Quadrant 3, cos(x/2) is also negative.
Therefore;
cos(x/2) = -√(2/27)
c. Finally, to find tan(x/2), we can use the identity:
tan(x/2) = sin(x)/(1+cos(x))
We already know sin(x) and cos(x), so we can substitute them in:
tan(x/2) = (-2/27)/(1-25/27)
tan(x/2) = (-2/27)/(-24/27)
tan(x/2) = 1/12
Therefore,
tan(x/2) = 1/12
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Describe the conditions that would create an ambiguous case with two possible solutions.
In order to resolve the ambiguity and find the correct solution, we need to use additional information such as the Law of Sines or the Law of Cosines.
what is a Triangle ?
Triangle can be defined in which it consists three sides, three angles and sum of three angles is always 180 degrees.
An ambiguous case in geometry refers to a situation where, given certain information about a triangle, there are two possible solutions for one of the unknown angles or sides. This situation arises in trigonometry when we have to solve a triangle using the Law of Sines or the Law of Cosines.
The conditions that create an ambiguous case with two possible solutions are as follows:
Given two sides and an angle opposite one of the sides:
If we are given two sides and an angle opposite one of the sides, there can be two possible solutions for the triangle. For example, if we are given side lengths of 4 and 5, and an angle of 40 degrees opposite the side of length 4, there are two possible triangles that can be formed.
Given two angles and a side opposite one of the angles:
If we are given two angles and a side opposite one of the angles, there can be two possible solutions for the triangle. For example, if we are given angles of 30 degrees and 60 degrees, and a side length of 4 opposite the 30-degree angle, there are two possible triangles that can be formed.
In both of these cases, the ambiguous case arises when the given information is not sufficient to uniquely determine the triangle.
Therefore, In order to resolve the ambiguity and find the correct solution, we need to use additional information such as the Law of Sines or the Law of Cosines.
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