The value of the expression, -0.4·(3·x - 2) + (2·x + 4)/3 when x = 4 is 0
-0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3 = 0
What is a mathematical expression?A mathematical expression comprises, variables, and or numbers, which could include indices, joined together by mathematical operators.
The value of the expression -0.4·(3·x - 2) + (2·x + 4)/3 for x = 4 can be found by plugging in x = 4 into the expression as follows;
Where; x = 4
-0.4·(3·x - 2) + (2·x + 4)/3 = -0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3
-0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3 = -0.4 × (12 - 2) + (8 + 4)/3
-0.4 × (12 - 2) + (8 + 4)/3 = -0.4 × 10 + 12/3 = -4 + 4 = 0
Therefore;
The value of the expression, -0.4·(3·x - 2) + (2·x + 4)/3 for x = 4 is zero
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Jaxon made 5% of his free throws over the season. If he shot 220 free throws, how many did he make?
Answer:
Jaxon made 11 free throws over the season.
Step-by-step explanation:
If he made 5% of his free throws, we know that he will make 5% of the total number of free throws he took, which is 220:
We multiply 220 by 0.05, or 5% to find out how many free throws he made:
220*0.05 = 11
After that, we now know that Jaxon made 11 of his free throws out of 220 over the course of the season, or 5%.
Fifteen children split $9 among themselves so that each child receives the same amount. How much did each child receive?
The total amount of money received by each child after splitting $9 among 15 children is equal to $0.60.
Total number of children is equal to 15
Total amount of money distributed among 15 children = $9
To find out how much each child receives,
We can divide the total amount of money by the number of children.
In this case, there are 15 children and $9 to split.
So, the amount of money each child receives is equal to,
(Total amount of money )/ ( total number of children )
= $9 ÷ 15
= $0.60
Therefore, amount of money received by each child in the group of 15 children is equal to $0.60.
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An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist's findings is that 18 months after the workshop, a sample of 81 job seekers who received training on using the Internet to find job listings worked more than 30 hours per week an average of 8. 7 months in the last year, with a standard deviation of 4. 1. The typical job seeker works 7. 4 months. The psychologist finds that the estimated Cohen's d is _____, the t statistic is 2. 83, and r^2 is ______. Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a ______ treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size using r^2, there is a ______ treatment effect. Another one of the psychologist's findings is that a sample of 81 job seekers who received training on interview skills scored an average of 8. 1 as measured on a 9-point job search motivation scale, with a standard deviation of. 8. The typical job seeker scores 7. 4 points. She finds that the estimated Cohen's d is _____, the t statistic is 7. 78, and r^2 is _____ Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size with r^2, there is a ___ treatment effect
The psychologist finds that the estimated Cohen's d is 0.32, the t statistic is 2. 83, and r² is 0.073. Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a small treatment effect. job seeker finds that the estimated Cohen's d is 0.88, the t statistic is 7. 78, and r² is 0.479.Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a large treatment effect
To calculate the estimated Cohen's d, we use the formula
d = (M - M0) / SD
where M is the mean of the treatment group (job seekers who received training on using the Internet to find job listings), M0 is the mean of the control group (typical job seeker), and SD is the pooled standard deviation of the two groups. Using the given values, we have
M = 8.7 months
M0 = 7.4 months
SD = 4.1 months
So, d = (8.7 - 7.4) / 4.1 = 0.32
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.32, there is a small treatment effect.
To calculate r², we use the formula
r² = t² / (t² + df)
where t is the t statistic, df is the degrees of freedom (n-2 for a two-group design), and n is the sample size. Using the given values for the Internet training group, we have
t = 2.83
n = 81
df = 79
So, r² = 2.83² / (2.83² + 79) = 0.073
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.073, there is a small treatment effect.
For the job seekers who received training on interview skills, we can calculate Cohen's d and r² in a similar way
d = (M - M0) / SD = (8.1 - 7.4) / 0.8 = 0.88
t = 7.78
n = 81
df = 79
r² = 7.78² / (7.78² + 79) = 0.479
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.88, there is a large treatment effect.
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.479, there is a medium to large treatment effect.
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Answer:.317
.091
Small to med
Med
.875
.431
Large
Large
Step-by-step explanation:
The answers are in the picture. I need help ASAP!
The perimeter and the area of the regular polygon are 20 inches and 27.53 square inches.
How to calculate the area and the perimeter of a regular polygon
The figure representing a regular polygon with five sides of same length, whose perimeter and area is well described by following formulas:
Perimeter
p = n · l
Area
A = (n · l · a) / 2
Where:
A - Area of the polygon, in square inches. n - Number of sides.l - Side length, in inches. a - Apothema, in inches. p - Perimeter, in inches.Where the apothema is:
a = 0.5 · l / tan (180° / n)
If we know that l = 4 in and n = 5, then the perimeter and the area of the polygon are:
Perimeter
p = 5 · (4 in)
p = 20 in
Area
a = 0.5 · (4 in) / tan (180° / 5)
a = 0.5 · (4 in) / tan 36°
a = 2.753 in
A = [5 · (4 in) · (2.753 in)] / 2
A = 27.53 in²
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Trigonometric funcions
Which equation are true
Answer:
C and D
Step-by-step explanation:
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{4}{5}[/tex] ⇒ C
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{5}[/tex] ⇒ D
what is the confidence interval estimate of the population mean examination score if a sample of applications provided a sample mean (to the nearest whole number
This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.
The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.
For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:
Margin of error = (critical value) x (standard error)
The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:
Standard error = (standard deviation) / sqrt(sample size)
If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.
Assuming a sample standard deviation of 10, the standard error would be:
[tex]Standard\ error = \frac{10} { \sqrt{(100)}} = 1[/tex]
Therefore, the margin of error would be:
Margin of error = 1.984 x 1 = 1.984
The confidence interval estimate of the population means examination score would be:
80 ± 1.984, or between 78.016 and 81.984.
This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.
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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the
nearest whole number.
To determine the confidence interval estimate of the population mean examination score based on a sample mean
provided to the nearest whole number, we need to know the sample size and the level of confidence.
Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the
confidence interval estimate:
Confidence interval = sample mean +/- (critical value) x (standard error)
The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of
freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.
The standard error is the standard deviation of the sample divided by the square root of the sample size.
For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the
standard error would be 10/sqrt(50) = 1.41.
Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.
Therefore, the confidence interval estimate would be:
75 +/- 1.96 x 1.41 = 75 +/- 2.77
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5. Select Yes or No to indicate whether each ordered pair is a point of intersection
between the line x - y = 6 and the circle y² - 26 = -x².
Ordered Pair
(1,-5)
(1,5)
(5,-1)
To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.
Select Yes or No to indicate whether each ordered pair is a point of intersectionFor the ordered pair (1, -5):
x - y = 6 becomes 1 - (-5) = 6, which is true.
y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.
Therefore, (1, -5) is not a point of intersection.
For the ordered pair (1, 5):
x - y = 6 becomes 1 - 5 = -4, which is false.
y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.
Therefore, (1, 5) is a point of intersection.
For the ordered pair (5, -1):
x - y = 6 becomes 5 - (-1) = 6, which is true.
y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.
Therefore, (5, -1) is not a point of intersection.
So the answer is:
(1,-5) - No
(1,5) - Yes
(5,-1) - No
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ASAP I really need help doing a two column proof for this please.
The two column proof is written as follows
Statement Reason
MA = XR given (opposite sides of rectangle)
MK = AR given (opposite sides of rectangle)
arc MA = arc RK Equal chords have equal arcs
arc MK = arc AK Equal chords have equal arcs
Equal chords have equal arcsAn arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.
If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.
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cuantos números
primos son a la vez la suma y la diferencia
Answer: there is only one number
Answer:
Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.
Espero haber ayudado :D
Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)
clerks at mosier data systems key in thousands of insurance records each day for a variety of client firms. samples of the work of 20 clerks are gathered. ceo donna mosier carefully examines 100 records entered by each clerk and counts the number of errors. mosier wants to set control limits to include 99.73% of the random variation in the data entry process. which type of process control chart should she use?
Donna Mosier should use an Individuals control chart to set control limits for the data entry process.
An Individuals control chart is a type of process control chart used to monitor the process when the sample size is one. In this case, Mosier is examining 100 records entered by each of the 20 clerks, making the sample size one.
To set control limits that include 99.73% of the random variation in the data entry process, Mosier can use the following steps:
Calculate the mean and standard deviation of the number of errors for each clerk based on the 100 records examined.Calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL) using the formulas: UCL = mean + 3 * standard deviation and LCL = mean - 3 * standard deviation.Plot the individual data points for each clerk on the Individuals control chart, with the UCL and LCL as the upper and lower boundaries, respectively.Monitor the data points over time to detect any trends, shifts, or out-of-control points that may indicate a process issue.By using an Individuals control chart, Mosier can set control limits to monitor the data entry process and detect any issues before they become major problems.
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 13 people took the trip. She was able to purchase coach tickets for $380
and first class tickets for $1200. She used her total budget for airfare for the trip, which was $9040. How many first class tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought=
Answer: Sarah bought 5 first class tickets and (13-5) = 8 coach tickets.
Step-by-step explanation: The taken a toll of one to begin with lesson ticket is $1200 and the fetched of one coach ticket is $380.
So, the full taken a toll of first class tickets would be 1200x and the entire cost of coach tickets would be 380(13-x) = 4940 - 380x.
The overall fetched of the tickets is given as $9040, so we will set up the taking after condition:
1200x + 4940 - 380x = 9040
Streamlining and tackling for x, we get:
820x = 4100
x = 5
Question:
The current (in amps) in a simple
electrical circuit varies inversely to
the resistance measured in ohms.
The current is 24 amps when the
resistance is 20 ohms. Find the
current (in amps) when the
resistance is 12 ohms.
The current in the circuit when the resistance is 12 ohms is 40 amps.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
We can use the inverse proportionality formula to solve this problem, which states that:
current (in amps) x resistance (in ohms) = constant
Let's call this constant "k". We can use the information given in the problem to find k:
24 amps x 20 ohms = k
k = 480
Now we can use this constant to find the current when the resistance is 12 ohms:
current x 12 ohms = 480
current = 480 / 12
current = 40 amps
Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.
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I need help with this question can you help?
Answer:
The Correct answer is sinA/3.2=sin110°/4.6
Evan takes 100 milligrams of medicine. The amount of medicine in his bloodstream decreases by 0.4 milligram each minute for a number of minutes, m, after that. He writes the expression 100 - 0.4m to find the amount of medicine in his bloodstream after m minutes. Which statement about his expression is true?
The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.
The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.
The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.
Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
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angles of triangles- does anyone know how to do this?
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°
(4) m∠1=88°m∠2=42° m∠3=113°
What is an angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.
Define triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles.
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)
(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)
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a trapezoid has an area of 96 ft. if the base is 11 feet and the height is 8 feet, what is the length of the other base
Answer:
The formula for the area of a trapezoid is:
Area = (b1 + b2) / 2 x h
where b1 and b2 are the lengths of the two parallel bases, and h is the height.
We are given that the area of the trapezoid is 96 ft, the height is 8 ft, and one of the bases (b1) is 11 ft. We can use this information to find the length of the other base (b2).
Substituting the given values into the formula for the area of a trapezoid, we get:
96 = (11 + b2) / 2 x 8
Multiplying both sides by 2 and dividing by 8, we get:
24 = 11 + b2
Subtracting 11 from both sides, we get:
b2 = 13
Therefore, the length of the other base is 13 ft.
Label the net for the cylinder. Then find the surface area of the cylinder. Give your answer in terms of π and as a decimal number rounded to the nearest tenth.
The surface area of the cylinder is approximately 94.2 ft².
What is surface area?Surface area refers to the total area of the external or outer part of an object. It is the sum of the areas of all the individual surfaces or faces of the object. Surface area is typically measured in square units, such as square inches (in²), square feet (ft²), or square meters (m²), depending on the unit of measurement used.
According to the given information:
The surface area of a cylinder is the sum of the lateral surface area (the curved surface) and the area of the two circular bases.
The formula for the lateral surface area of a cylinder is given:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
Plugging in the given values for the radius (r = 3 ft) and height (h = 2 ft), we can calculate the lateral surface area:
Lateral Surface Area = 2π * 3 * 2 = 12π ft²
The formula for the area of a circle (which represents the bases of the cylinder) is given:
Circle Area = πr²
Plugging in the given value for the radius (r = 3 ft), we can calculate the area of each circular base:
Circle Area = π * 3² = 9π ft²
Since there are two bases in a cylinder, we multiply this by 2 to account for both bases:
2 * Circle Area = 2 * 9π = 18π ft²
Now, we can add the lateral surface area and the area of the two bases to find the total surface area of the cylinder:
Total Surface Area = Lateral Surface Area + 2 * Circle Area
= 12π + 18π
= 30π ft²
As a decimal rounded to the nearest tenth, the surface area of the cylinder is approximately 94.2 ft²
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Nina uploaded a funny video on her website, which rapidly gains views over time.
The relationship between the elapsed time, ttt, in days, since Nina uploaded the video, and the total number of views, V(t)V(t)V, left parenthesis, t, right parenthesis, is modeled by the following function:
V(t)=500⋅(1. 8)t
Complete the following sentence about the daily percent change in the views of the video.
Every day,
\%%percent of views are
the total number of views of the video
Every day, the number of views of the video increases by 80% of the previous day's views.
Every day, the number of views of the video increases by a certain percentage. To find the daily percent change in the views, we can use the formula for percent change, which is given by:
percent change = ((new value - old value) / old value) * 100
In this case, the old value is the number of views at the start, which is 500, and the new value is the number of views after one day, which is given by:
V(1) = 500*(1.8)^1 = 900
Substituting these values into the formula, we get:
percent change = ((900 - 500) / 500) * 100 = 80%
In other words, for every day that passes, the number of views of the video is multiplied by a factor of 1.8.
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#4 Please help!!!!!!!!!!
Answer:150°
Step-by-step explanation:
A tram moved downward 12 meters in 4 seconds at a constant rate. What was the change in the tram's elevation each second?
Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.
What is an unitary method?To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.
Here,
By dividing the overall elevation change (12 metres) by the total time required (4 seconds),
it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.
=> Elevation change equals 12 metres
=> Total duration: 4 seconds
=> 12 meters / 4 seconds
=> 3 meters/second
As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.
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3 out of 7 questions. PLEASE help me.
Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar
Transforming the circles(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:
Translate the solid circle 2 units to the left and 2 units down.Dilate the solid circle by a scale factor of 2.Therefore, the blank spaces should be filled as follows:
Translate the solid circle 2 units to the left and 2 units down.
Dilate the solid circle by a scale factor of 2.
(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.
This is because all circles are similar
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help me please please
Becca is construction triangle d e f using the following angles 50°, 65°, 65°,
what mistake did she make?
Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.
According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.
Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.
In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.
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a cylinder has a radius of 3 cm and a height of 8 cm. what is the longest segment, in centimeters, that would fit inside the cylinder?
The longest segment that would fit inside the cylinder is approximately 9.06 centimeters.
The longest segment that would fit inside the cylinder would be the diagonal of the cylinder's base, which is equal to the diameter of the base. The diameter of the base is equal to twice the radius, so it is 6 cm. Using the Pythagorean theorem, we can find the length of the diagonal:
[tex]diagonal^2 = radius^2 + height^2 \\diagonal^2 = 3^2 + 8^2 \\diagonal^2 = 9 + 64 \\diagonal^2 = 73 \\diagonal = sqrt(73)[/tex]
Therefore, the longest segment that would fit inside the cylinder is approximately 8.54 cm (rounded to the nearest hundredth).
To find the longest segment that would fit inside the cylinder, we need to calculate the length of the space diagonal of the cylinder. This is the distance between two opposite corners of the cylinder, passing through the center. We can use the Pythagorean theorem in 3D for this calculation.
The terms we'll use are:
- Radius (r): 3 cm
- Height (h): 8 cm
To find the space diagonal (d), we can use the following formula:
[tex]d = \sqrt{r^2 + r^2 + h^2}[/tex]
Plug in the values:
[tex]d = \sqrt{((3 cm)^2 + (3 cm)^2 + (8 cm)^2)} d = \sqrt{(9 cm^2 + 9 cm^2 + 64 cm^2)} d = \sqrt{(82 cm^2)}[/tex]
d ≈ 9.06 cm
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The longest segment that can fit inside the cylinder is. [tex]$\sqrt{73}$ cm[/tex].
The longest segment that can fit inside a cylinder is a diagonal that connects two opposite vertices of the cylinder.
The length of this diagonal by using the Pythagorean theorem.
Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:[1]
[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.
The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.
Consider a right triangle with legs equal to the radius.
[tex]$r$[/tex] and the height [tex]$h$[/tex] of the cylinder, and with the diagonal as the hypotenuse.
Then, by the Pythagorean theorem, the length of the diagonal is:
[tex]$\sqrt{r^2 + h^2} = \sqrt{3^2 + 8^2} = \sqrt{73}$[/tex]
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All help is appreciated thank you.
Using the fact that the triangles are similar we can see that the value of x is 36
How to find the value of x?We can see that the triangles are similar due to the same interior angles, then ther is a scale factor k between them.
So we can write:
20*k = 48
k = 48/20 = 2.4
Then:
x = 15*2.4
x = 36
That is the value of x.
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Find the measure of the missing side.
1. 8.2
2. 9.9
3. 7.4
4. 10.9
Answer:
1
Step-by-step explanation:
First of all we use the "law of sines"
to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x
and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°
180°=70°+51°+ x
x = 180°-121°
=59°
Using law of sines:
(sides are represented by small letters/capital letters are the angles)
a/sinA= b/sinB= c/sinC
We have one given side which is "9"
so,
9/sin70= x/sin59
doing the criss-cross method,
9×sin59=sin70×x
9×sin59/sin70=x
x=8.2 (answer 1)
I hope this was helpful <3
c. what is the probability that the duration of a rainfall event at this location is between 2 and 3 hours? d. what is the probability that a rainfall duration exceeds the mean value by more than 2 standard deviations?
The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:
P(X ≥ 2) = [tex]e^{(-λ2) }= e^{(-1/2.7252)[/tex] ≈ 0.4800
P(X ≤ 3) = 1 - [tex]e^{(-λ3)} = 1 - e^{(-1/2.7253)[/tex] ≈ 0.6674
P(2 ≤ X ≤ 3) = [tex]e^{(-λ2)} - e^{(-λ3)} = e^{(-1/2.7252)} - e^{(-1/2.7253)}[/tex] ≈ 0.1474
b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:
P(X > 5.45) =[tex]e^{(-λ5.45)} = e^{(-1/2.7255.45)}[/tex] ≈ 0.0498
Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
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Complete Question:
Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.
a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)
b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these is true?
The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).
Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:
V_small = π(2²)(4) = 16π cubic inches
Using these dimensions, we can calculate the volume of the larger can using the same formula:
V_large = π(6²)(12) = 432π cubic inches
Now, let's compare the volumes of the small and large cans. We have:
V_large = 432π cubic inches > 16π cubic inches = V_small
Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:
V_large = 432π cubic inches 3
V_small = 3(16π) cubic inches = 48π cubic inches
We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.
Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.
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Complete Question:
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?
a) The radius of the larger can will be 5 inches.
b) The volume of the larger can will be 3 times the volume of the smaller can
c) The radius of the larger can will be 8 inches.
d) The volume of the larger can is 3 times the volume of smaller can
state the nameof this quadrilateral...70 points
Answer:
Step-by-step explanation:
its a rectanlge