The mean amount of D-glucose in cockroach hindguts is 44.24 micrograms, with a standard deviation of 26.16 micrograms. The 96% confidence interval for the mean is (20.19, 68.29) micrograms.
We will first calculate the mean, standard deviation, and then the 96% confidence interval for the given data on D-glucose amounts in cockroach hindguts.
Data: 55.95, 68.24, 52.73, 21.5, 23.78
1. The mean is calculated as follows.
Mean = (55.95 + 68.24 + 52.73 + 21.5 + 23.78) / 5 = 221.2 / 5 = 44.24
The mean amount of D-glucose in cockroach hindguts is approximately 44.24 micrograms.
2. To find the standard deviation, we calculate the variance first:
Variance = [(55.95 - 44.24)^2 + (68.24 - 44.24)^2 + (52.73 - 44.24)^2 + (21.5 - 44.24)^2 + (23.78 - 44.24)^2] / (5 - 1) = 2739.736 / 4 = 684.934
Standard Deviation = √684.934 = 26.16 (rounded to two decimal places)
The standard deviation of D-glucose in cockroach hindguts is approximately 26.16 micrograms.
3. To calculate the 96% confidence interval, we need to find the margin of error:
Margin of Error = (Critical value * Standard Deviation) / √sample size
For a 96% confidence interval, the critical value (z-score) is approximately 2.05.
Margin of Error = (2.05 * 26.16) / √5 ≈ 24.05
Now, we can find the confidence interval:
Lower limit: Mean - Margin of Error = 44.24 - 24.05 = 20.19
Upper limit: Mean + Margin of Error = 44.24 + 24.05 = 68.29
The 96% confidence interval for the mean amount of D-glucose in cockroach hindguts approximately is (20.19, 68.29) micrograms.
Note: The question is incomplete. The complete question probably is: To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts: Amounts of D-glucose 55. 95, 68. 24, 52. 73, 21. 5, 23. 78. The researchers gave a 96% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions. The insects are a random sample from a uniform population grown in the laboratory. We therefore expect responses to be Normal. What is the mean, standard deviation, and confidence interval?
Learn more about Confidence interval:
https://brainly.com/question/20309162
#SPJ11
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.
You can read more about scale factor at https://brainly.com/question/25722260
#SPJ11
A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likel voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0. 014, 0. 064). What was the difference (pre- debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
The difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.
The range of the 95% confidence interval for the actual difference between the proportions of probable voters who would support this candidate before and after the debate was (-0.014, 0.064). To find the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate, we need to find the midpoint of the confidence interval, which is the point estimate of the true difference.
In the given question, the interval is (-0.014, 0.064), then the expression for the likely difference is
(0.064 + (-0.014))/2 = 0.050/2
= 0.025
Hence, the difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.
Learn more about confidence intervals here
brainly.com/question/25890103
#SPJ4
If my refrigerator uses 300 watts when the motor is running, and the motor runs for 30 minutes of every hour, then how much energy does it use per day? How many BTU of energy would that be equal to?
The amount of energy the refrigerator uses per day is 3.6 kilowatt-hour (kWh)
The refrigerator energy usage per day in BTU is 12283.704 BTU
What is the BTU?The BTU is an acronym for the British Thermal Unit, which is a measure of heat, which is specified in energy units.
The duration the refrigerator fan runs per hour = 30 minutes
The amount of energy the refrigerator uses every hour = 300 watts × 0.5 hour/hour = 150 watts
The amount of energy the refrigerator uses per hour = 150 watt-hour
The amount of energy the refrigerator uses per day = 24 × 150 watt-hour = 3600 watt-hour = 3.6 kilowatt-hour (kWh)1 kWh = 3412.14 BTU
Therefore;
3.6 kWh = 3.6 × 3412.14 BTU = 12283.704 BTUThe amount of energy in BTU the refrigerator uses per day = 12283.704 BTU
Learn more on the BTU here: https://brainly.com/question/14252954
#SPJ1
help pls. my mom is mad bc i don’t have this done.
_______________________________
A = L × B = 7.3cm × 9cm= 65.7cm= 65.7cm × 90m= 5,913m²_______________________________
Which statement is true about the relationship between the diameter and circumference of a circle?
A. The diameter and circumference of a circle have a proportional relationship.
B. The diameter is a product of the circumference and pi.
C. The constant of proportionality between the diameter and circumference of a circle is a rational number.
D. The circumference of a circle is the quotient of the diameter and pi.
Option A The diameter and circumference of a circle have a proportional relationship is True .
What is diameter and circumference?Diameter
The diameter is the length acrοss the circle at its widest pοint, measured frοm center tο center . The radius, a related measurement, is a line that extends frοm the circle's centre tο its edge. The diameter is equivalent tο twice the radius. (A chοrd is a line that crοsses the circle but is nοt at the widest pοint.)
Circumference
The circle's perimeter, οr the distance arοund it, is knοwn as its circumference. Imagine encircling a circle with a string. Imagine taking the string οut and extending it in a straight line. This string's length, if measured, wοuld represent yοur circle's circumference.
Learn more about Diameter
https://brainly.com/question/5501950
#SPJ!
Find the cosine of K.
24
Save answer
26
blo
J
10
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
cos (K) =
K
Skip to
Step-by-step explanation:
remember the original trigonometric triangle inside the norm circle (radius = 1).
sine is the up/down distance from the triangle baseline or corresponding circle diameter.
cosine is the left/right distance from the center of the circle (and the point of the angle).
for larger triangles and circles all these function results need to be multiplied by the actual radius (which we skipped for the norm circle, as a multiplication by 1 is not changing anything).
when you look at the triangle with K representing the angle, we have 10 a the cosine value, 24 as the sine value and 26 as the radius.
so,
10 = cos(K) × 26
cos(K) = 10/26 = 5/13
On the curve y = x3, point p has the coordinates (2, 8). what is the slope of the curve at point p?
The slope of the curve y = x^3 at point P(2, 8) is 12.
To find the slope of the curve y = x^3 at point P with coordinates (2, 8), we need to determine the derivative of the function and then evaluate it at x = 2.
Step 1: Find the derivative of the function y = x^3.
The derivative, dy/dx, represents the slope of the curve. To find the derivative of y = x^3, apply the power rule: d(x^n)/dx = n * x^(n-1).
So, dy/dx = 3 * x^(3-1) = 3x^2.
Step 2: Evaluate the derivative at the given point P (2, 8).
To find the slope at point P, substitute the x-coordinate (2) into the derivative: 3 * (2)^2 = 3 * 4 = 12.
Thus, the slope of the curve y = x^3 at point P(2, 8) is 12.
To learn more about derivative
https://brainly.com/question/30466081
#SPJ11
PLEASE SHOW ALL YOUR WORK AS NEATLY AS POSSIBLE: 1) Given f(x) = 3sqrt(x + 2)^2 a) Find the derivative, f'(x). b) Solve f'(x) = 0
The only critical point of f(x) is x = -2.
a) To find the derivative of f(x), we can use the chain rule and the power rule of differentiation.
f(x) = 3sqrt(x + 2)^2
f'(x) = 3 * 2 * sqrt(x + 2) * (x + 2)^1/2-1 * (1)
Applying the power rule, we simplify the expression as:
f'(x) = 6(x + 2)^1/2
Therefore, the derivative of f(x) is f'(x) = 6(x + 2)^1/2.
b) To solve f'(x) = 0, we set f'(x) equal to zero and solve for x:
f'(x) = 6(x + 2)^1/2 = 0
Dividing both sides by 6, we get:
(x + 2)^1/2 = 0
Squaring both sides, we get:
x + 2 = 0
Subtracting 2 from both sides, we get:
x = -2
Therefore, the only critical point of f(x) is x = -2.
To learn more about critical point visit: https://brainly.com/question/31017064
#SPJ11
Express this number in scientific notation.
9 ten thousandths
Answer: 9 x 10^4
Step-by-step explanation:
9 ten thousands in standard form is written like this: 90,000
To convert this into scientific notation, we simply count how many spaces we want to move the decimal point.
So far, our number looks like this with a decimal point: 90000.0
To make this number equal to 9, we have to move the decimal point 4 spaces to the left.
The 4 then becomes our exponent.
So now we have 9 by itself, and all we do is multiply it by 10 with an exponent of 4, to show you are multiplying 10 four times.
Therefore, 9 ten thousands written in scientific notation is 9 x 10^4
I need help ASAP PLEASE! Z-score question
The weights of logs in a wood pile are normally distributed with a mean of 17 pounds and a standard deviation of 3. 4 pounds
The majority of logs in the pile will have a weight close to the mean of 17 pounds, with a smaller number of logs having a weight that is farther away from the mean.
In statistics, the normal distribution is a commonly used continuous probability distribution.
It is also referred to as a Gaussian distribution, and it has a bell-shaped curve that is symmetrical around the mean.
The mean is the center of the distribution, and the standard deviation describes how spread out the data is around the mean.
In this case, the weights of logs in a wood pile are normally distributed with a mean of 17 pounds and a standard deviation of 3.4 pounds.
This means that the majority of logs in the pile will have a weight close to the mean of 17 pounds, with a smaller number of logs having a weight that is farther away from the mean.
To know more about Gaussian distribution, refer here:
https://brainly.com/question/13390425#
#SPJ11
Frank cuts a piece of cork to make trivet that has the shape and dimensions as shown.Find The Area Of The Trivet.Round Your Answer to the nearest tenth if needed
Answer:
52.5
Step-by-step explanation:
First, we can see that the base is 14m. The top is 7m, and the height is 5m. Since the formula for a trapezoid is
top + base / 2 ∙ h,
we plug in our numbers to get
7 + 14 / 2 ∙ 5.
We can solve to get
21 / 2 ∙ 5
10.5 ∙ 5
52.5
Construct a square, and a regular Pentagon with equal side equal to 0. 5 inch.
To construct a square and a regular pentagon with equal side lengths of 0.5 inch, we need to use basic geometric constructions.
How can I create a square and a regular pentagon with equal side lengths of 0.5 inch?To construct a square and a regular pentagon with equal side length of 0.5 inch, follow these steps:
(a) Construct a Square:
Draw a horizontal line segment of length 0.5 inch.From the endpoints of the line segment, draw two perpendicular lines of length 0.5 inch each, meeting at the endpoints of the original line segment.From the endpoints of these new line segments, draw two more perpendicular lines of length 0.5 inch each, meeting at the endpoints of the second line segment.Connect the endpoints of the four line segments to form a square.
(b) Construct a Regular Pentagon:
Draw a circle with a radius of 0.5 inch. This will be the circumcircle of the pentagon.Draw a horizontal line through the center of the circle.Mark the points where the line intersects the circle. These will be the vertices of the pentagon.Draw a line segment connecting two adjacent vertices of the circle.Using a compass, copy the length of this line segment to the next vertex, and connect the two vertices to form a line segment of the pentagon.Repeat this process for all five vertices of the circle to form the regular pentagon.
A geometric construction is a method of drawing a figure using only a straightedge (an unmarked ruler) and a compass.
For the square, we start by drawing a horizontal line segment of length 0.5 inch. We then draw two perpendicular lines of length 0.5 inch each, meeting at the endpoints of the original line segment.
These two new line segments represent the adjacent sides of the square. We then repeat this process to create the remaining two sides of the square, and connect all four endpoints to form the complete square.
For the regular pentagon, we need to construct a circle with a radius of 0.5 inch. This will be the circumcircle of the pentagon, meaning that all five vertices of the pentagon will lie on the circle.
We draw a horizontal line through the center of the circle, and mark the points where the line intersects the circle. These five points will be the vertices of the pentagon.
We then draw line segments connecting adjacent vertices, using a compass to copy the length of each line segment from the previous one.
This process will create all five sides of the pentagon, and the figure will be a regular pentagon with equal side lengths of 0.5 inch.
Learn more about regular Pentagon
brainly.com/question/929013
#SPJ11
007 10.0 points An advertisement is run to stimulate the sale of cars. After t days, 1 st = 54, the number of cars sold is given by N(t) = 8000 + 36t2 – On what day does the maximum rate of growth of sales occur? 1. on day 12 2. on day 11 3. on day 14 4. on day 10 5. on day 13
The advertisement generates the maximum rate of growth of car sales on the first day.
How to find the day of maximum growth rate?The rate of growth of sales is given by the derivative of N(t) with respect to time t:
dN/dt = 72t
To find the day when the maximum rate of growth of sales occurs, we need to find the value of t that maximizes this expression.
Setting dN/dt = 0, we get:
72t = 0
t = 0
However, since we are interested in finding the day when the maximum rate of growth of sales occurs, we need to consider the second derivative of N(t):
d2N/dt2 = 72
Since this is a positive constant, it tells us that N(t) is a convex function and has a minimum value at t = 0. Therefore, the maximum rate of growth of sales occurs on the day when t = 0, which corresponds to the first day of the advertisement.
Answer: 1. on day 12
Learn more about maximum growth rate.
brainly.com/question/29217326
#SPJ11
Drag each number to the correct location. classify each number according to its value. 4. 2 × 10-6 2. 1 × 10-3 3. 1 × 10-2 3. 2 × 10-5 3. 5 × 10-4 5. 8 × 10-3 5. 2 × 10-4.
Each number is classified according to its value in the given image.
We are given some numbers and we have to drag each number to the correct location according to its value. The numbers given are 4.2×[tex]10^{-6}[/tex], 2.1×[tex]10^{-3}[/tex], 3.1×[tex]10^{-2}[/tex], 3.2×[tex]10^{-5}[/tex], 3.5×[tex]10^{-4}[/tex], 5.8×[tex]10^{-3}[/tex], 5.2×[tex]10^{-4}[/tex].
We will classify these numbers in the categories given in the table.
(a) Now the numbers which are greater than 3.1×[tex]10^{-3}[/tex] are:
3.1×[tex]10^{-2}[/tex] and 5.8×[tex]10^{-3}[/tex].
(b) Numbers falling between 3.1 × [tex]10^{-3}[/tex] and 4.3 × [tex]10^{-5}[/tex] are:
2.1×[tex]10^{-3}[/tex], 3.5×[tex]10^{-4}[/tex], and 5.2×[tex]10^{-4}[/tex]
(c) Numbers that are less than 4.3 × [tex]10^{-5}[/tex] are:
4.2×[tex]10^{-6}[/tex]and 3.2×[tex]10^{-5}[/tex]
So, the numbers are classified according to their values in the table given in the image.
To learn more about classifying numbers;
https://brainly.com/question/13029444
#SPJ4
PLS HELP ASAP 50 POINTS AND BRAINLEIST!!!
Explain how the arc BX, central angle BCX, and inscribed BNX are connected. what are the relationships between them?
Answer:
see explanation
Step-by-step explanation:
the arc BX is equal to the measure of the central angle BCX
the measure of the inscribed angle BNX is half the measure of its intercepted arc BX
TASK CARD 1
-2x³
a) Write the polynomial in standard form
b) Determine the degree
c) Determine the lead coefficient
Answer: The given polynomial is -2x³.
a) To write the polynomial in standard form, we arrange the terms in descending order of degrees:
-2x³
b) The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the degree of the polynomial is 3.
c) The lead coefficient is the coefficient of the term with the highest degree. In this case, the lead coefficient is -2.
Step-by-step explanation:
find scale factor of the dilation
Answer:
Step-by-step explanation:
The original image is the the black one. The dilated image is blue. It got bigger. So it is an enlargment.
Each side got bigger by times 2
So the dilation is 2
The figure below has a net for a right rectangular prism. 15cm 11cm 11cm 11cm 11cm 14cm What is the surface area of the right rectangular prism, in square centimeters
The surface area of the right rectangular prism is 880 cm².
Given Top and bottom measurements of the rectangular prism = 15 cm and 11 cm
The front and back measurements of the rectangular prism = 11cm and 11cm
The two sides measurements of the rectangular prism = 11 cm and 14 cm
To find the surface area of the rectangular prism, we have to substitute the above values in the below equation,
Surface area = (top*bottom) + (front*back) + (sides)
Surface area = (15 cm * 11 cm) + (11 cm * 11 cm) + (11 cm * 14 cm)
Surface area = 330 cm² + 242 cm² + 308 cm²
Surface area = 880cm²
To know more about rectangular prism,
https://brainly.com/question/30337697
#SPJ1
I. Suppose you a business owner and sell clothing. The following represents the number of items sold and the cost for each item: Use matrix operations to determine the total revenue over the two days:
Monday: 3 T-shirts at GH¢10 each, 4 hats at GH¢15 each, and 1 pair of shorts at GH¢20.
Tuesday: 4 T-shirts at GH¢10 each, 2 hats at GH¢15 each, and 3 pairs of shorts at GH¢20.
The total revenue over the two days is GH¢305.
We can represent the number of items sold and the cost for each item in matrices as follows:
[tex]\begin{equation}A = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix}\end{equation}[/tex]
Here, matrix A represents the number of items sold on each day, and matrix B represents the cost per item. To find the total revenue, we need to multiply the two matrices and then take the sum of all the elements in the resulting matrix:
[tex]\begin{equation}A \cdot B = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix} = \begin{bmatrix} 95 \ 140 \end{bmatrix}\end{equation}[/tex]
Therefore, the total revenue over the two days is GH¢(95 + 140) = GH¢305.
For more questions like Matrix click the link below:
https://brainly.com/question/28180105
#SPJ11
A box of tissues is shaped like a rectangular prism and has a volume of 288 cubic inches.
We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.
How to find the volume?To find the dimensions of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:
V = l x w x h
where V is the volume, l is the length, w is the width, and h is the height.
We know that the volume of the box of tissues is 288 cubic inches. We want to find the length, width, and height.
We can start by listing all the factors of 288:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
We can see that some of these factors are repeated, so we can pair them up to find the dimensions of the rectangular prism.
For example, we can pair 2 and 144, since 2 x 144 = 288. This means that the length of the rectangular prism could be 144 inches and the width could be 2 inches.
We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.
We can continue pairing the factors until we find all the possible combinations. Once we have all the possible combinations, we can choose the one that makes the most sense based on the context of the problem (in this case, the dimensions of a box of tissues).
Learn more about volume
brainly.com/question/29868754
#SPJ11
Solve this quick please thank you.
Answer:
[tex]y=-\dfrac{8}{x}[/tex]
Step-by-step explanation:
Inverse proportions can be represented by an equation in the form:
[tex]\boxed{y=\dfrac{k}{x}}[/tex]
where:
y and x are the two quantities in the proportion.k is the constant of proportionality.To write an expression for the graphed function, first input the given point (-2, 4) into the inverse proportion equation and solve for k:
[tex]\implies y=\dfrac{k}{x}[/tex]
[tex]\implies 4=\dfrac{k}{-2}[/tex]
[tex]\implies 4 \cdot (-2)=\dfrac{k}{-2}\cdot (-2)[/tex]
[tex]\implies -8=k[/tex]
[tex]\implies k=-8[/tex]
Therefore, the expression for the graphed function is:
[tex]\boxed{y=-\dfrac{8}{x}}[/tex]
what percentage is equivalent to 96/160
Answer:
60%
Step-by-step explanation:
Take 96 and divide it by 160.
(easier if done on a calculator.)
For example: Find A/B as a percentage: take "A" and divide it by "B"
On the average the time spent by college students every week on computer gaming is 15 hours with a standard deviation 3. a random sample of 350 students were taken. find the best point estimated of the population mean and 95% confidence interval for the population mean
The best point estimate is 15 hours. The 95% confidence interval for the population mean is (14.71, 15.29).
The best point estimate of the population mean is the sample mean, which is 15 hours since it was stated in the problem that the average time spent by college students on computer gaming is 15 hours.
To calculate the 95% confidence interval for the population mean, we use the formula:
CI = [tex]\bar{X}[/tex] ± z*(σ/√n)
where [tex]\bar{X}[/tex] is the sample mean, z is the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96), σ is the population standard deviation (given as 3), and n is the sample size (given as 350).
Plugging in the values, we get:
CI = 15 ± 1.96*(3/√350)
Simplifying, we get:
CI = 15 ± 0.29
To know more about confidence interval, refer here:
https://brainly.com/question/17212516#
#SPJ11
Each deck of cards in a a box has a weight of 3.4 oz.the box contains 64 decks of cards.what is the total weight of the cards inside the box?teh oz are rounded to the nearest oz
The total weight of the cards inside the box is approximately 217.6 oz.
Each deck of cards weighs 3.4 oz, and there are 64 decks of cards in the box. Therefore, the total weight of the cards inside the box is 3.4 oz/deck x 64 decks = 217.6 oz. As the answer needs to be rounded to the nearest ounce, we round 217.6 to the nearest ounce, which gives us 218 oz.
However, the question asks for the weight of the cards, which is only accurate to one decimal place. Therefore, we round 217.6 to one decimal place, which gives us 217.6 oz. Hence, the total weight of the cards inside the box is approximately 217.6 oz.
For more questions like Cards click the link below:
https://brainly.com/question/31598744
#SPJ11
HELP PLS!! I AM LACKING BRAIN CELLS RN!! :(
Answer:
17.5 feet
Step-by-step explanation:
The picnic are shortest side is 5 units long on the scale drawing
Since each unit on the scale drawing is 1 inch, the shortest side length on the drawing is 5 inches
Each inch on the drawing corresponds to an actual size of 3.5 feet
Therefore 5 inches corresponds to 5 x 3.5ft = 17.5 feet
Therefore the actual length of the shortest side of the picnic area is 17.5 feet
Pleasee help
f(x) = 3x² - 7x + 4
f(2)= [?]
Answer:
f(2) = 2
Step-by-step explanation:
We are given
f(x) = x² - 7x + 4
To find f(2), just plug in 2 wherever you see an x and simplify
f(2) = 3 · 2² - 7 · 2 + 4
= 3 · 4 - 7 · 2 + 4
= 12 - 14 + 4
= 2
Assuming that the daily wages for
workers in a particular industry
averages Birr 11. 90 per day and the
standard deviation is Birr 0. 40. If the
wages are assumed to be normally
distributed, determine what percentage
of workers receive wages
A. Between Birr 10. 90 and Birr 11. 90
B. Between Birr 10. 80 and Birr 12. 40
C. Between Birr 12. 20 and Birr 13. 10
D. Less than Birr 11. 00
E. More than Birr 12. 95
Using statistics, we can calculate the following percentages:
A. The percentage of workers who receive wages between Birr 10.90 and Birr 11.90 is approximately 49.38%.
B. The percentage of workers who receive wages between Birr 10.80 and Birr 12.40 is approximately 89.15%.
C. The percentage of workers who receive wages between Birr 12.20 and Birr 13.10 is approximately 22.53%.
D. The percentage of workers who receive wages less than Birr 11.00 is approximately 1.22%.
E. The percentage of workers who receive wages more than Birr 12.95 is approximately 0.47%.
These percentages are obtained by calculating the areas under the normal distribution curve using z-scores and the standard normal distribution table.
We are given that the daily wages in a particular industry are normally distributed with a mean of Birr 11.90 and a standard deviation of Birr 0.40.
A. To find the percentage of workers who receive wages between Birr 10.90 and Birr 11.90, we need to calculate the z-scores for both values and use the standard normal distribution table.
z1 = (10.90 - 11.90) / 0.40 = -2.50
z2 = (11.90 - 11.90) / 0.40 = 0
From the standard normal distribution table, the area to the left of z = -2.50 is 0.0062, and the area to the left of z = 0 is 0.5000. Therefore, the percentage of workers who receive wages between Birr 10.90 and Birr 11.90 is:
0.5000 - 0.0062 = 0.4938, or approximately 49.38%.
B. To find the percentage of workers who receive wages between Birr 10.80 and Birr 12.40, we need to calculate the z-scores for both values.
z1 = (10.80 - 11.90) / 0.40 = -2.75
z2 = (12.40 - 11.90) / 0.40 = 1.25
From the standard normal distribution table, the area to the left of z = -2.75 is 0.0029, and the area to the left of z = 1.25 is 0.8944.
Therefore, the percentage of workers who receive wages between Birr 10.80 and Birr 12.40 is:
0.8944 - 0.0029 = 0.8915, or approximately 89.15%.
C. To find the percentage of workers who receive wages between Birr 12.20 and Birr 13.10, we need to calculate the z-scores for both values.
z1 = (12.20 - 11.90) / 0.40 = 0.75
z2 = (13.10 - 11.90) / 0.40 = 3.00
From the standard normal distribution table, the area to the left of z = 0.75 is 0.7734, and the area to the left of z = 3.00 is 0.9987. Therefore, the percentage of workers who receive wages between Birr 12.20 and Birr 13.10 is:
0.9987 - 0.7734 = 0.2253, or approximately 22.53%.
D. To find the percentage of workers who receive wages less than Birr 11.00, we need to calculate the z-score for this value.
z = (11.00 - 11.90) / 0.40 = -2.25
From the standard normal distribution table, the area to the left of z = -2.25 is 0.0122. Therefore, the percentage of workers who receive wages less than Birr 11.00 is approximately:
0.0122, or approximately 1.22%.
E. To find the percentage of workers who receive wages more than Birr 12.95, we need to calculate the z-score for this value.
z = (12.95 - 11.90) / 0.40 = 2.63
From the standard normal distribution table, the area to the left of z = 2.
To know more about statistics refer here:
https://brainly.com/question/29821285?#
SPJ11
what is 2X (2² + sin 3) = ?
2X (2² + sin 3) can be simplified as 8X + 2X sin 3
How to simplify the functionTo solve the expression, we will first have to compute the values inside the parentheses and then apply the given operations. so we Calculate the values inside the parentheses by multiplying across the bracket:
2² is equal to 4, and sin 3 is a trigonometric function that returns the sine of the angle 3
Therefore, the expression 2X (2² + sin 3) simplifies to:
2X (4 + sin 3)
or
8X + 2X sin 3
where X is an unknown variable and sin 3 is a trigonometric function
Read more on trigonometric function here:https://brainly.com/question/25618616
#SPJ1
Answer:
Solution
verified
Verified by Toppr
I=∫e
2x
sin3xdx
I=sin3x∫e
2x
dx−∫(
dx
d
sin3x∫e
2x
dx)dx
I=sin3x
2
e
2x
−∫
2
3
cos3xe
2x
dx
I=sin3x
2
e
2x
−
2
3
∫cos3x∫e
2x
dx−∫(
dx
d
cos3x∫e
2x
dx)dx
I=sin3x
2
e
2x
−
2
3
[
2
cos3xe
2x
−∫(−sin3x
2
e
2x
)dx]
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
−
4
3
∫sin3xe
2x
dx
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
−
4
3
I
I+
4
3
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
4
7I
=
4
2e
2x
sin3x−3cos3xe
2x
I=
7
e
2x
(2sin3x−3cos3x)
∴∫e
2x
sin3dx=
7
e
2x
(2sin3x−3cos3x)
Solve any question of Integrals with:-
Patterns of problems
Patterns of problems
>
Solve :∫e xe e xe e e x
dx
Medium
View solution>Solve:-∫ a 2b 2(a 2 −b 2) 2
Step-by-step explanation:
pls brain
A trip to white mountains of new hampshire from boston will take you 2 3/4 hours. assume you have traveled 1/11 of the way. how much longer will the trip take?
The trip will take another 1 hour to complete.
If a trip from Boston to the White Mountains of New Hampshire takes 2 3/4 hours, and you have already traveled 1/11 of the way, then the remaining distance is:
1 - 1/11 = 10/11 of the total distance.
To find how much longer the trip will take, we can use the proportion:
time taken for 10/11 of the trip = x (time taken for the whole trip)
distance traveled for 10/11 of the trip = 1 - 1/11 = 10/11 of the total distance
Since the time taken is proportional to the distance traveled, we can set up the following equation:
2 3/4 hours / (1 - 1/11) = x
where x is the time it will take for the whole trip.
Simplifying the left side of the equation, we get:
2 3/4 hours / (10/11) = x
Multiplying both sides by (11/10), we get:
x = (2 3/4 hours) × (11/10) = 3 1/4 hours
Therefore, the remaining time to complete the trip is:
3 1/4 hours - 2 3/4 hours = 1 hour
So the trip will take another 1 hour to complete.
To learn more about hour, click here:
https://brainly.com/question/3164396
#SPJ11
What is the quotient of 223 + 3x2 + 5x – 4 divided by 22 +2+1?
Pls I need help
The quotient is -58x2 + 131x - 234 with a remainder of -5898.To solve this problem, we need to use long division. The dividend is 223 + 3x2 + 5x - 4 and the divisor is 22 + 2 + 1, which simplifies to 25.
We start by dividing 2 into 22, which gives us 11. We then write 11 above the 2 and multiply it by 25, which gives us 275. We subtract 275 from 223, which gives us -52. We bring down the 3, which gives us -523. We then repeat the process by dividing 2 into 52, which gives us 26. We write 26 above the 5 and multiply it by 25, which gives us 650. We subtract 650 from -523, which gives us -1173. We bring down the 1, which gives us -11731. We divide 2 into 117, which gives us 58.
We write 58 above the x and multiply it by 25, which gives us 1450. We subtract 1450 from -1173, which gives us -2623. We bring down the -4, which gives us -26234. We divide 2 into 262, which gives us 131. We write 131 above the 5 and multiply it by 25, which gives us 3275. We subtract 3275 from -2623, which gives us -5898. Therefore, the quotient is -58x2 + 131x - 234 with a remainder of -5898.
To know more about quotient click here
brainly.com/question/24367754
#SPJ11
