Therefore, the linearization predicts that f(2.9, 4.1) is approximately 4.142.
To find the linearization of the function f(x, y) = √x^2 + y^2 at the point (3, 4), we need to find the partial derivatives of f with respect to x and y, evaluate them at (3, 4), and use them to write the equation of the tangent plane to the surface at that point.
First, we have:
∂f/∂x = x/√(x^2 + y^2)
∂f/∂y = y/√(x^2 + y^2)
Evaluating these at (3, 4), we get:
∂f/∂x(3, 4) = 3/5
∂f/∂y(3, 4) = 4/5
So the equation of the tangent plane to the surface at (3, 4) is:
z - f(3, 4) = (∂f/∂x(3, 4))(x - 3) + (∂f/∂y(3, 4))(y - 4)
Plugging in f(3, 4) = 5 and the partial derivatives, we get:
z - 5 = (3/5)(x - 3) + (4/5)(y - 4)
Simplifying, we get:
z = (3/5)x + (4/5)y - 1
This is the linearization of f(x, y) = √x^2 + y^2 at the point (3, 4).
To approximate f(2.9, 4.1), we plug in x = 2.9 and y = 4.1 into the linearization:
z = (3/5)(2.9) + (4/5)(4.1) - 1
z ≈ 4.142
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The value of an investment at simple interest is given by the formula
a
=
p
+
p
r
t
.
a is the final value after t years at the interest rate r (as a decimal) if the initial amount p is invested.
solve for t and solve for how long $200 must be invested at 8% interest to reach a value of $248?
It would take 15 years of investing $200 at 8% interest to reach a value of $248.
To solve for t, we can rearrange the formula:
a = p + prt
a - p = prt
t = (a - p) / (pr)
To solve for how long $200 must be invested at 8% interest to reach a value of $248, we can plug in the given values into the formula and solve for t:
a = 248
p = 200
r = 0.08
t = (a - p) / (pr)
t = (248 - 200) / (200 * 0.08)
t = 15
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A tile maker makes triangular tiles for a mosaic. Two triangular tiles form a square. what is the area of one of the triangular tiles
Answer: [tex]\frac{x^2}{2}[/tex]
Step-by-step explanation:
If two of the tiles form a square together, then one of them must be half of a square. this means that the square is split diagonally.
If you've ever done trigonometry, you'll know this is a 45-45-90 special right triangle. The side lengths are in the ratio of x, x, and xsqrt(2).
so we know the area of one of these tiles will be [tex]\frac{x^2}{2}[/tex], where x is the side length of the square formed.
let EF be a diameter of circle O. if D and G are opposite side of EF and DG and EF intersect at H and m(<EOG)=82,m(<DOE)=76then find others
In triangle EOD, angle EOD = 14 degrees, angle DOE = 76 degrees, and angle DEO = 90 degrees. In triangle GOD, angle GOD = 98 degrees, angle DOG = 90 degrees, and angle GDO = 76 degrees.
Since EF is a diameter of circle O, we know that angle EOG is a right angle, because it is an inscribed angle that intercepts the diameter EF. Therefore, angle EOG = 90 degrees.
We also know that angle DOE = 76 degrees, so angle GOH (which is opposite angle DOE) must be 180 - 76 = 104 degrees.
Similarly, angle EOG = 82 degrees, so angle GOD (which is opposite angle EOG) must be 180 - 82 = 98 degrees.
Now, we can use the fact that angles in a triangle add up to 180 degrees to find angle DOG:
angle DOG = 180 - angle GOD - angle GOH
= 180 - 98 - 104
= -22
This result doesn't make sense, because angles can't be negative. However, we made a mistake when calculating angle GOH earlier. Since D and G are opposite sides of EF, they must be collinear.
Therefore, H must be at the point where EF intersects DG, and angle GOH must be a straight angle (180 degrees), not 104 degrees.
With this correction, we have:
angle GOH = 180 degrees
angle GOD = 98 degrees
angle DOG = 180 - angle GOD - angle GOH
= 180 - 98 - 180
= -98
Again, this result doesn't make sense because angles can't be negative. We made another mistake when calculating angle DOG.
Since EF is a diameter of circle O, angles DOG and DEG must be right angles. Therefore, we have:
angle DOG = 90 degrees
angle DEG = 90 degrees
Finally, we can use the fact that angles on a straight line add up to 180 degrees to find angle EOD:
angle EOD = 180 - angle DOG - angle DOE
= 180 - 90 - 76
= 14
Therefore, the angles in triangle EOD are:
angle EOD = 14 degrees
angle DOE = 76 degrees
angle DEO = 90 degrees
And the angles in triangle GOD are:
angle GOD = 98 degrees
angle DOG = 90 degrees
angle GDO = 180 - angle GOD - angle DOG
= 180 - 98 - 90
= -8
Once again, we have a negative angle, which doesn't make sense.
However, we can correct this by recognizing that angles DOG and EOD are adjacent angles that add up to 90 degrees. Therefore, we have:
angle GDO = 90 degrees - angle EOD
= 90 - 14
= 76 degrees
Therefore, the angles in triangle GOD are:
angle GOD = 98 degrees
angle DOG = 90 degrees
angle GDO = 76 degrees
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 Part C
The rectangular sides of the treasure box will be cut from wooden planks
5
9 feet long and foot wide. How many planks will Mr. Penny need so
9
16
that his 18 students can each construct one treasure box?
Mr. Penny will require a total of 20 square feet of wooden planks for all 18 students to construct their treasure boxes.
To determine the number of planks required, we need to calculate the total amount of wood needed for all 18 students' treasure boxes.
Each treasure box has two identical rectangular sides.
Each side is cut from a wooden plank that is 5/9 feet long and 1 foot wide.
Therefore, the area of each side is [tex](5/9) \times 1 = 5/9[/tex] square feet.
Since there are two identical sides for each treasure box, the total area of wood needed for one treasure box is [tex](5/9) \times 2 = 10/9[/tex] square feet.
To find the total wood needed for 18 students' treasure boxes, we multiply the area per treasure box by the number of treasure boxes:
Total wood needed [tex]= (10/9) \times 18 = 20[/tex] square feet.
So, Mr. Penny will require a total of 20 square feet of wooden planks for all 18 students to construct their treasure boxes.
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Question: What is the number of planks required for Mr. Penny's 18 students to each construct one treasure box if the rectangular sides of the treasure box will be cut from wooden planks that are 5/9 feet long and 1 foot wide?
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 32 randomly selected people who train in groups, and finds that they run a mean of 49. 0 miles per week. Assume that the population standard deviation from group runners is known to be 4. 2 miles per week
Our calculated t-value (-2.54) is beyond this critical value, we can reject the null hypothesis and conclude that there is a significant difference between the mean number of miles run per week by group runners and individual runners.
To test if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons, we can use a two-sample t-test.
Let's assume that the population standard deviation for the individual runners is also 4.2 miles per week.
We can set up the hypotheses as follows:
Null hypothesis: The mean number of miles run per week by group runners and individual runners is the same.
Alternative hypothesis: The mean number of miles run per week by group runners and individual runners is different.
Mathematically, we can write:
H0: μ1 = μ2
Ha: μ1 ≠ μ2
where μ1 is the population mean for group runners and μ2 is the population mean for individual runners.
We are given the sample mean for the group runners, which is 49.0 miles per week. We do not know the sample mean for the individual runners. Let's assume that we collect a random sample of 32 individual runners and find that their sample mean is 52.0 miles per week.
We can calculate the test statistic as follows:
t = (X1 - X2) / sqrt((s1^2/n1) + (s2^2/n2))
where X1 and X2 are the sample means for group runners and individual runners, s1 and s2 are the population standard deviations for group runners and individual runners, and n1 and n2 are the sample sizes for group runners and individual runners.
Plugging in the values, we get:
t = (49.0 - 52.0) / sqrt((4.2^2/32) + (4.2^2/32))
t = -3.0 / 1.182
t = -2.54
Using a t-distribution table with 62 degrees of freedom (32 + 32 - 2), we can find that the critical value for a two-tailed test with a significance level of 0.05 is approximately ±2.0. Since our calculated t-value (-2.54) is beyond this critical value, we can reject the null hypothesis and conclude that there is a significant difference between the mean number of miles run per week by group runners and individual runners.
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Tim wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3 4 m by 3 1 2 m. Find the area the grass seed needs to cover. Solve on paper. Then check your work on Zearn
The area of the grass seed needs to cover is 38.625 m².
What is the area of the rectangle?
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
Here, we have
Given: Tim wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3/4 m by 3 1/2 m.
We have to find the area the grass seed needs to cover.
Let the area of the grass seed needs to cover be A
Now , the area of the lawn L = ( 11 3/4 ) x 5 m²
The area of the lawn L = 58.75 m²
where the length of the pool l= ( 5 3/4 ) m = 5.75 m
The width of the pool is w = ( 3 1/2 ) m = 3.5 m
Now, Area of Rectangle = Length x Width
On simplifying, we get
Area of the pool P = 5.75 x 3.5 = 20.125m²
Now, the area of the grass seed needs to cover A = L - P
The area of the grass seed needs to cover A = 58.75 m² - 20.125 m²
The area of the grass seed needs to cover A = 38.625 m²
Hence, the area of the grass seed needs to cover is 38.625 m².
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MAGIC SHOW A magician currently sells tickets to his shows for $15 and averages 180 spectators per show. He estimates that he can sell 10 more tickets for each $0.75 decrease in price. a. Let x represent the number of $0.75 price decreases. Write a function P(x) to represent the price of a ticket and a function T(x) to represent the number of tickets sold. b. Write a function R(x) that can be used to find the revenue from ticket sales. c. If the magician decides to sell the tickets for $12, find his revenue. m
On the basis of given data & Using combining-functions, We can say that
a).The function P(x) which represents the price of a ticket can we given by where x represents the number of 0.75 price decreases= ($15 - 0.75x)
b). the function T(x) which represents number of tickets sold on a day
=(180 + 10x)
c). the revenue would be if the magician decides to sell the tickets for
$12 = $ 2640
What are combining-functions?The process of composition, in which the result of one function becomes the input of another, allows us to create complex functions from basic ones. A complicated function may occasionally need to be broken down into two or more simpler ones, using the opposite method.
Given that:
Current price of ticket = $15
Average tickets sold per day = 180
Price decrease each time = $0.75
Number of price decreases = x
Total Price decrease = 0.75x
Increase in number of tickets with price decrease each time = 10
Total increase in number of tickets with x times price decrease = 10x
a). Function to represent total price of tickets
P(x) = current price - total price decrease
= ($15 - 0.75x)
Function to represent number of tickets T(x)
= average number of tickets+ total increase in tickets
= (180 + 10x)
b)Function to represent total revenue R(x) = total tickets x total price
= T(x) . P(x)
= (180 + 10x) ($15 - 0.75x)
c)Given that total price of tickets=$12
P(x)=$12
($15 - 0.75x) = $12
- 0.75x = $12 - $15
- 0.75x = - $3
x = 3 ÷ 0.75
x = 4 times
The number of times price decreased=4
Total tickets sold T(x) =(180 + 10x)
=(180 + 10(4))
=180+40
=220 tickets
Total revenue= T(x) . P(x)
= 220 x 12
=$2640
Total revenue earned on 220 tickets at $12 is $ 2640
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Hi can someone please help me with this
Answer:
Since Q is a center of gravity, we can apply these formulas
Polynomial in standard form (6d+6) (2d-2)
Answer:
I think the answer is 8d + 4.
Step-by-step explanation:
Combine the like terms, 6d + 2d = 8d. 6 - 2 = 4.
In which quadrant does 0 lie if the following statements are true: cos 0 > and sin> 0
The angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.
Based on the given information that cos(θ) > 0 and sin(θ) > 0, we can determine the quadrant in which the angle θ lies.
Recall that there are four quadrants in a Cartesian coordinate system: Quadrant I (both x and y are positive), Quadrant II (x is negative, y is positive), Quadrant III (both x and y are negative), and Quadrant IV (x is positive, y is negative). The cosine function, cos(θ), represents the x-coordinate of a point on the unit circle, while the sine function, sin(θ), represents the y-coordinate.
Since cos(θ) > 0, the angle θ must be in a quadrant where the x-coordinate is positive. This means that θ can lie in either Quadrant I or Quadrant IV. Next, since sin(θ) > 0, the angle θ must be in a quadrant where the y-coordinate is positive. This narrows down the possibilities to only Quadrant I, where both x and y coordinates are positive.
Therefore, the angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.
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A container ship left port last week carrying some goods that weighed a total of 60,010 tons. Today, it stopped in another port to unload. The weight of the goods on the ship is now 30,005 tons. By what percent has the weight of the goods on the ship decreased?
The weight of the goods on the ship decreased by 50 percent.
To find the percentage decrease in the weight of goods on the ship, we need to calculate the difference between the initial weight and the final weight, divide it by the initial weight, and then multiply by 100 to get the percentage decrease.
The initial weight of the goods on the ship was 60,010 tons and the final weight after unloading was 30,005 tons.
The difference between the initial weight and the final weight is 60,010 - 30,005 = 30,005 tons.
To find the percentage decrease, we divide the difference by the initial weight:
30,005 / 60,010 = 0.5
Multiplying by 100 gives us the percentage:
0.5 x 100 = 50%
Therefore, the weight of goods on the ship has decreased by 50 percent.
In conclusion, the percentage decrease in the weight of goods on the ship is 50 percent. This means that the ship has unloaded half of its initial weight and now carries only half of the weight it carried when it left the port last week. This calculation can be helpful for the shipping company to determine the efficiency of their transportation and to plan for future shipments.
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Write the equation below in standard and factored form y= -(x-1)^2+25
Sam lives 8 miles from work and Mike lives 30 miles from work. How much farther is Mike's trip to work than Sam's?
Find The Area Of This Shape.
The expression for the area of the triangle is given as follows:
A = 6x² - 7x - 3.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The dimensions for this problem are given as follows:
Base of b = 4x - 6.Height of h = 3x + 1.Hence the expression for the area of the triangle is given as follows:
A = 0.5(4x - 6)(3x + 1)
A = 0.5(12x² - 14x - 6)
A = 6x² - 7x - 3.
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Find a quadratic function that models the
number of cases of flu each year, where y is years since 2012. What is the coefficient of x? Round your answer to the nearest hundredth
The quadratic function that models the number of cases of flu each year, where y is years since 2012 is y = -0.02x^2 + 0.5x + 10. The coefficient of x is 0.5.
Suppose the number of cases of flu each year initially increases rapidly, but then starts to level off and eventually decline. We can model this behavior with a quadratic function of the form:
y = ax^2 + bx + c
where y is the number of cases of flu, and x is the number of years since 2012. Estimate the coefficients a, b, and c.
Assume the number of cases of flu was initially very low in 2012, so the y-intercept c is small value, say 10.
Next, assume that the number of cases of flu initially increased rapidly, but then started to level off around 2018.
y = ax^2 + bx + 10
where a is negative and b is positive.
Suppose the coefficient of the linear term is small, since we expect the trend to level off rather than continue to increase at a constant rate.
So, a possible quadratic function that models the number of cases of flu each year is:
y = -0.02x^2 + 0.5x + 10
The coefficient of x in this function is 0.5, which represents the rate of change of the number of cases of flu each year after 2012.
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How do I fill this chart with the information given?
Fill the two-way frequency table as shown in the image attached.
How to fill the chart with the information given?A two-way frequency table is a way of displaying frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
For the frequency table:
Total = 82
Apple
Total = 24
Students = 22
Teachers = 24 - 22 = 2
Grape
Total = 82 - 25 -24 = 33
Students = 33 - 4 = 29
Orange
Teachers = 25 - 24 = 1
Students
Total = 22 + 29 + 24 = 75
Teachers
Total = 2 + 4 + 1 = 7
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Christie builds a model airplane that has a wingspan of 11. 8 inches. The model airplane has a scale of 1 inch to 2. 5 feet. What is the wingspan, in feet, of actual airplane?
A. 4. 72
B. 9. 30
C. 14. 30
D. 29. 50
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!
The correct answer is D. 29.50.
To find the wingspan of the actual airplane, we will use the given scale factor and the wingspan of the model airplane.
Given information:
Model airplane wingspan = 11.8 inches
Scale factor = 1 inch to 2.5 feet
Step 1: Convert the model wingspan to feet using the scale factor.
1 inch on the model represents 2.5 feet on the actual airplane. To convert 11.8 inches to feet, multiply by the scale factor.
Step 2: Calculate the actual wingspan.
Actual wingspan = Model wingspan * Scale factor
Actual wingspan = 11.8 inches * 2.5 feet/inch
Step 3: Perform the multiplication.
Actual wingspan = 29.5 feet
So, the wingspan of the actual airplane is 29.5 feet.
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Help on problem 2 and 3!
(I already did 1. Stepby step please ASAP!)
The missing angles ;
22.6°
53.1°
28.1°
Right triangleA right triangle is a type of triangle that has one of its angles measuring 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs or catheti.
We have that;
[tex]Sin \alpha = 5/13\\ \alpha = Sin-1(5/13)\\ \alpha = 22.6[/tex]
[tex]Tan \alpha = 16/12\\\alpha = Tan-1 (16/12)\\= 53.1[/tex]
[tex]Sin \alpha = 8/17\\\alpha = Sin-1(8/17)\\\alpha = 28.1[/tex]
Right triangles have many practical applications, such as in trigonometry, engineering, and architecture.
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Subtract.3 1/3−5enter your answer as a simplified mixed number by filling in the boxes.
The result of subtracting 5 from 3 1/3 is -2 2/3.
To subtract 5 from 3 1/3, we need to first convert the mixed number to an improper fraction. This can be done by multiplying the whole number (3) by the denominator of the fraction (3), and adding the numerator (1) to get 10/3. Therefore, 3 1/3 is equivalent to 10/3.
Next, we can subtract 5 from 10/3 by finding a common denominator of 3, which gives 15/3 - 10/3 = 5/3. This is the result in improper fraction form.
To convert back to a mixed number, we can divide the numerator (5) by the denominator (3), which gives a quotient of 1 and a remainder of 2. Therefore, the answer is -2 2/3.
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A scale drawing of a rectangular park had a scale of 1 cm = 90 m.
What is the actual area of the park in meters squared?
The calculated value of the actual area of the park in meters squared is 8100x
What is the actual area of the park in meters squared?From the question, we have the following parameters that can be used in our computation:
A scale drawing of a rectangular park had a scale of 1 cm = 90 m.
This means that
Scale factor = 90/1
Evaluate
Scale factor = 90
The actual area of the park in meters squared is calculated as
Area = Area of scale * Scale factor^2
Substitute the known values in the above equation, so, we have the following representation
Area = Area of scale * 90^2
Evaluate
Area = Area of scale * 8100
Let Area of scale = x
So, we have
Area = 8100x
Hence, the actual area of the park in meters squared is 8100x
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Write an expression for the sequence of operations described below.
Three increased by the sum of five and six
Type x if you want to use a multiplication sign. Type / if you want to use a division sign. Do not simplify any part of the expression.
The sequence U is defined by: Un +2 = 2 * Un+1+1* Un for n > 2 with given up and u uo 3 U = 1 List the first four terms uo, 21, U2, U3. Enter your answer as: value of uo, value of u1, value of uz, value of uz Enter answer here
The given values for uo and u3 are uo = 1 and u3 = 21. We can use the recurrence relation Un+2 = 2 * Un+1+1* Un to find the remaining terms:
U1 = U3 - 2U2 - 1*U0
U1 = 21 - 2U2 - 1*1
U1 = 20 - 2U2
U2 = U1 - 2U0 + 1*U0
U2 = 20 - 2U0 + 1*1
U2 = 19 - 2U0
Therefore, the first four terms are: 1, 19, -17, -53
So, the answer is: 1, 19, -17, -53.
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solve for x when x^2 = 0,0025
Each theme park charges an entrance fee plus an additional fee per ride. Write a function for each park. (3 points)
a) write a function rule for Big Wave Waterpark
b) write a function rule for Coaster City
c) write a function rule for Virtual Reality Lan
(a) The function rule for Big Wave Waterpark, f(x) = 2.5x + 5. where f(x) is total cost and x is number of slides ridden.
b) The function rule for Coaster City is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden and f(x) is total cost.
c) The function rule for Virtual Reality Lan is, f(x) = 3x + 10, where f(x) is total cost and x is the number reality rides ridden.
(a) Let f(x) = ax +b be the function which represents the total cost of Big Wave Park where x represents the number of taken ride.
We can see that f(2) = 10; f(4) = 15 and f(6) = 20.
Therefore, 2a + b = 10 and 4a + b = 15
So, 2(2a + b) - (4a + b) = 2*10 - 15
4a + 2b - 4a - b = 20 - 15
b = 5
Now, f(6) = 20
6a + b = 20
6a + 5 = 20 [putting the value of 'b']
6a = 20 - 5 = 15
a = 15/6 = 5/2 = 2.5
Hence, the function rule for Big Wave Waterpark is, f(x) = 2.5x + 5.
(b) The function rule for Coaster city is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden.
(c) Let the total cost for Virtual Reality Lan is, f(x) = cx + d, where x is the number reality rides ridden.
From the given graph we can see that, f(10) = 40; f(20) = 70; f(30) = 100.
So, 10c + d= 40 ........... (i)
20c + d = 70 ............... (ii)
Solving (i) and (ii) we get,
2(10c + d) - (20c + d) = 2*40 - 70
20c + 2d - 20c - d = 80 - 70
d = 10
So putting the value d = 10 in f(30) = 100 we get,
30c + 10 = 100
30c = 100 - 10 = 90
c = 90/30 = 3
So the function rule is, f(x) = 3x + 10.
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Fruit fly thorax lengths fruit flies are used frequently in genetic research because of their quick reproductive cycle. the length of the thorax (in millimeters) was measured for each fly in a random sample of 49 male fruit flies. the mean length was a=0.8004 mm, with a standard deviation of 8 = 0.0782 mm. a. construct and interpret a 90% confidence interval for the true mean thorax length of a male fruit fly.
The confidence level for length of the thorax of 49 fruit fly males is (0.7820 mm, 0.8188 mm).
Here the sample size (n=49), the sample mean (a=0.8004 mm), and the sample standard deviation (s=0.0782 mm), we can calculate the confidence interval as follows:
1. Determine the critical value (z-score) for a 90% confidence level. You can use a z-table or calculator to find the z-score, which is approximately 1.645.
2. Calculate the margin of error using the z-score, sample standard deviation, and sample size:
Margin of Error = z-score * (s / √n)
Margin of Error = 1.645 * (0.0782 / √49)
Margin of Error ≈ 0.0184 mm
3. Add and subtract the margin of error from the sample mean to obtain the confidence interval:
Lower Limit = a - Margin of Error = 0.8004 - 0.0184 ≈ 0.7820 mm
Upper Limit = a + Margin of Error = 0.8004 + 0.0184 ≈ 0.8188 mm
So, the 90% confidence interval for the true mean thorax length of a male fruit fly is approximately (0.7820 mm, 0.8188 mm). This means that we are 90% confident that the true mean thorax length of a male fruit fly falls within this range.
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Sausage is 1/2 inch thick roll is 6 inches long how many pieces can be cut
If you cut a 6-inch long sausage roll that is 1/2 inch thick, you can make 12 pieces.
How many pieces can a 6-inch sausage roll with 1/2 inch thickness be cut into?To understand how to arrive at this answer, we need to use some basic math.
First, we need to determine the volume of the sausage roll. We can do this by multiplying the length, width, and height of the roll. In this case, the length is 6 inches, the width is 1/2 inch, and the height is also 1/2 inch. So:
Volume = Length x Width x Height
Volume = 6 x 1/2 x 1/2
Volume = 1.5 cubic inches
Next, we need to determine the volume of each individual piece. To do this, we divide the total volume of the sausage roll by the number of pieces we want to make. In this case, we want to make two equal pieces, so we divide the total volume by 2:
Volume per piece = Total volume / Number of pieces
Volume per piece = 1.5 / 2
Volume per piece = 0.75 cubic inches
Finally, we can determine the dimensions of each individual piece by using the volume per piece and the thickness of the sausage roll. We can calculate the length of each piece by dividing the volume per piece by the thickness:
Length per piece = Volume per piece / Thickness
Length per piece = 0.75 / 0.5
Length per piece = 1.5 inches
So each piece will be 1.5 inches long. To determine how many pieces we can make, we divide the total length of the sausage roll by the length of each piece:
Number of pieces = Total length / Length per piece
Number of pieces = 6 / 1.5
Number of pieces = 4
However, since we are cutting the sausage roll in half, we can make 2 sets of 4 pieces, for a total of 8 pieces.
Alternatively, if we want to make only one cut, we can make two 3-inch long pieces from each half, for a total of 12 pieces.
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Connie’s team won 12 out of 16 games this season what percentage of game did her team lose
Connie's team lost 4 out of 16 games this season. To calculate the percentage of games lost, we can divide the number of games lost by the total number of games and then multiply by 100.
In this case, 4 divided by 16 is equal to 0.25, or 25% as a percentage. Therefore, Connie's team lost 25% of their games this season.
We first note that the total number of games played is 16. Connie's team won 12 of these games, so the number of games they lost is 16 - 12 = 4. To calculate the percentage of games lost, we divide the number of games lost by the total number of games and then multiply by 100. This gives:
(4 / 16) * 100 = 25%
Therefore, Connie's team lost 25% of their games this season.
It is important to understand how to calculate percentages in order to solve problems like this. In this case, we used the formula:
percentage = (part / whole) * 100
where the "part" is the number of games lost and the "whole" is the total number of games played. By substituting the appropriate values into this formula, we were able to calculate the percentage of games lost by Connie's team.
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in a survey of some people, it was found that the ratio of the people who liked pop songs and rap songs is 7:9. out of which, 60 people liked both songs, 30 liked rap songs only and 40 liked none of the songs. find the number of people who did not like pop songs.
Solve with steps.
The number of people who did not like pop songs is 175.
Given data :
In a survey, the ratio of people who liked pop songs and rap songs is 7: 9.
The number of people who liked both songs = 60.
The number of people who liked only rap songs = 30.
The number of people who liked none of the songs = 40
First of all, we will find the number of people who only like pop songs. We are given a ratio of 7:9 for the people who liked pop songs and rap songs. Let us assume that the number of people who liked pop songs is x and those who liked rap songs is y. According to the ratio given,
[tex]\frac{x}{y} = \frac{7}{9}[/tex] .....(1)
As we know the number of people who only liked rap songs are 30. Therefore, y - x = 30
x = y - 30
We will substitute the value of x in equation 1.
[tex]\frac{y - 30}{y} = \frac{7}{9}[/tex]
9y - 270 = 7y
2y = 270
y = 135
Now, x = 135 -30
x = 105
Total number of people in survey = x + y + 40
105 + 135 + 40 = 280
Out of 280, the number of people who liked pop songs is 105. So, the number of those who did not like pop songs is ( 280 - 105) = 175.
Therefore, the number of people who did not like pop songs are 175.
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Solve this system and identify the solution.
Select one:
a.
(5,-2)
b.
infinite solutions
c.
no solutions
d.
(2,-5)
The correct statement regarding the solution to the system of equations is given as follows:
b. Infinite solutions.
How to solve the system of equations?The system of equations in the context of this problem is defined as follows:
3y - 6x = 24.8 + 2x = y.Replacing the second equation into the first, the value of x is obtained as follows:
3(8 + 2x) - 6x = 24
24 + 6x - 6x = 24
24 = 24.
24 = 24 is a statement that is always true, hence the system has an infinite number of solutions, and thus option B is the correct option for this problem.
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[tex]\sqrt[4]{81} -8(\sqrt[3]{216} )+15(\sqrt[5]{32} )+\sqrt{225}[/tex]
[tex]\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}[/tex] when simplified gives 0
What are Indices?Indices are small number that tells us how many times a term has been multiplied by itself. Indices are also the power or exponent which is raised to a number or a variable.
How to determine this
[tex]\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}[/tex]
When all of then are perfect square
[tex]\sqrt[4]{81}[/tex]= 3 * 3 *3 *3
[tex]\sqrt[3]{216}[/tex] = 6 * 6 * 6
[tex]\sqrt[2]{32}[/tex] = 2 * 2 * 2 * 2 * 2
[tex]\sqrt{225}[/tex] = 15 * 15
Therefore,
3 - 8(6) + 15(2) + 15
3 - 48 + 30 + 15
By collecting like terms
3 + 30 + 15 - 48
48 - 48
= 0
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