Mobile ladder stands with a top step over 10 feet high and 20 inches or more in depth must be equipped with a safety cage or body belt and lanyard to provide protection against a fall.
The cage should be at least 30 inches tall and should be fully enclosed on all four sides. Additionally, the top step should be enclosed and provided with a grab bar. The ladder must be securely supported and stabilized. Non-skid materials should be applied to the steps and platform. Finally, the ladder must meet safety requirements outlined in the Occupational Safety and Health Administration's (OSHA) regulations.
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A Venn Diagram comparing swimmers and weightlifters is shown below:
An image of a Venn diagram is shown labeled swimmers and weightlifters. The label in the swimmer's portion is B. The label in the intersection of the two circles is A. The label in the weightlifter's portion is C. The label outside the circles is D.
Which area represents elements contained in open parentheses swimmers intersection weightlifters close parentheses complement?
A
D
B, C, D
A, B, C
Answer:
The area that represents elements contained in the complement of the intersection of swimmers and weightlifters is the region outside the circles labeled as D. Therefore, the answer is D.
Step-by-step explanation:
chatgpt
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the number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.5 . what is the probability of observing exactly 4 errors in the carpet? round your answer to four decimal places.
The probability of observing exactly 4 errors in the carpet is 0.0165 or 1.65%.
The number of weaving errors in a twenty-foot by ten-foot roll of carpet follows a Poisson distribution with a mean of 0.5. We can use the Poisson probability distribution formula to find the probability of observing exactly 4 errors in the carpet:
[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4![/tex]
where X is the random variable representing the number of weaving errors. Plugging in the values, we get:
[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4! = 0.0165[/tex] (rounded to four decimal places)
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calculate the probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460. (use salt. round your answer to four decimal places.)
The probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460 is very low, almost zero.
To calculate the probability of obtaining a sample result of a mean of $470 or more, we need to use the sampling distribution of the mean.
Assuming that the sample size is large enough and that the sample means are normally distributed, we can use the central limit theorem to approximate the sampling distribution of the mean to a normal distribution. We can standardize the sample mean using the formula
z = (x - μ) / σ,
where x is the sample mean, μ is the population mean, and σ is the standard error of the mean.
In our case, we want to find the probability of obtaining a sample mean of $470 or more. We can convert this to a z-score by standardizing it using the formula
z = (470 - 460) / (σ / √n),
where n is the sample size.
If the sample size is 100 and the population standard deviation is 10, then the standard error of the mean is 1. We can then calculate the z-score as
=> z = (470 - 460) / (1 / √100) = 10.
We can look up the probability of obtaining a z-score of 10 or greater in a standard normal distribution table, which is almost zero.
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The Computer has labeled the lines you graphed a and b. What are the equations of the lines? Enter them into the table below
The equation of the line is 9x+8y + 19 = 0 and 5x - 4y+ 19 = 0 According to the given graphs, these are the equations of the graph.
Consider two points on the blue line.
The points are (5, -8) and ( -3,1 ).
Equation of the blue line is:
y - 1 = [tex]\frac{-8-1}{5+3} (x+3)[/tex]
8 (y - 1) = -9 ( x + 3)
8y - 8 = -9x -27
9x + 8y + 19 = 0
Therefore, the Equation of the blue line is 9x + 8y + 19 = 0.
Consider two points on the red line.
The points are (-3, 1) and ( 1,6 ).
Equation of the red line is:
y - 1 = [tex]\frac{6-1}{1+3} (x+3)[/tex]
4 (y - 1) = 5 (x + 3)
4y - 4 = 5x + 15
5x - 4y+ 19 = 0
Therefore, the Equation of the red line is 5x - 4y+ 19 = 0.
Hence, the equations for the given blue and red lines are completed.
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On pose, pour tout n E N, Un = Un - 5.
(a) Montrer que (Un) est une suite géométrique; préciser sa raison et son premier terme.
(b) Donner l'expression de Un en fonction de n: en déduire l'expression de un en fonction de n.
(c) En déduire la valeur de U12
Answer:
(a) Pour montrer que la suite (Un) est géométrique, il suffit de vérifier que le quotient de deux termes consécutifs est constant. Soit n un entier naturel non nul. Alors :
Un+1 / Un = (Un-4) / (Un) = 1 - 5/Un
Donc, pour tout n E N*, on a :
Un+1 / Un = 1 - 5/Un = (Un / Un) - (5/Un) = (Un - 5) / Un
On a bien trouvé une raison q = -5/1, et un premier terme U1 = U1 - 5.
(b) La raison de la suite (Un) est q = -5/1. En utilisant la formule générale de la suite géométrique, on obtient :
Un = U1 * q^(n-1) = (U1 - 5) * (-5)^(n-1)
En particulier, on a :
U_n = U_1 * q^{n-1} = (U_1 - 5) * (-5)^{n-1} = U_12 = (U_1 - 5) * (-5)^{12-1}
(c) On n'a pas suffisamment d'informations pour déterminer la valeur de U1, donc on ne peut pas calculer directement la valeur de U12.
The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 3 comma negative 2, a point at negative 5 comma 2, and a point at negative 1 comma 2.
What is the equation of g(x) in vertex form?
g(x) = (x − 3)2 − 2
g(x) = (x − 3)2 + 2
g(x) = (x + 3)2 − 2
g(x) = (x + 3)2 + 2
Answer:
g(x) = (x + 3)2 - 2
Step-by-step explanation:
I think that's the one I just did this class so
A video goes viral on social media, the number of views per day can be modeled with the equation y = -0.75x² +9.75x where is the number of days after the video is posted and y is the number of views per day in thousands. According to the model, after how many days do people stop watching the video?
Answer:
Step-by-step explanation:
To find when people stop watching the video, we need to find the maximum point of the quadratic function y = -0.75x² + 9.75x.
The x-coordinate of the maximum point of a quadratic function can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic function.
Using the formula with a = -0.75 and b = 9.75, we get:
x = -9.75 / 2(-0.75)
x = -9.75 / -1.5
x = 6.5
Therefore, the maximum number of views per day will occur on the 6.5th day after the video was posted.
To determine when people stop watching the video, we need to check the values of y after this point.
When x > 6.5, the quadratic function becomes negative, which means that the number of views per day will start to decrease. Therefore, people stop watching the video after 6.5 days (or sometime around the 7th day).
Select the correct answer.
A graph with a y-axis and an x-axis in positive and negative planes. Two lines L I and I J are formed by connecting points (Negative 4,3), (5,3), and (5, Negative 3).
I(5, 3), J(5, -3), and L(-4, 3) are three vertices of rectangle IJKL. What are the coordinates of the fourth vertex, K, of rectangle IJKL?
A.
(-4, -3)
B.
(5, 3)
C.
(5, -3)
D.
(-4, 3)
The cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).
Thus, οptiοn D is cοrrect.
What is the cοοrdinate geοmetry?Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetry using the principles οf algebra.
The rectangle IJKL is fοrmed by cοnnecting the pοints I, J, K, and L in a clοckwise οr cοunterclοckwise manner. Since I and J have the same x-cοοrdinate and are οn οppοsite sides οf the x-axis, and L and K have the same y-cοοrdinate and are οn οppοsite sides οf the y-axis, it fοllοws that the diagοnals οf the rectangle IJKL intersect at the οrigin (0,0).
Therefοre, the cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).
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Describe a series of transformations that moves the blue figure to the red figure. If there is a : Translation - show number and direction Reflection - give axis of reflection
Rotation - give direction (clockwise or counterclockwise) and degree amount
Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.
Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.
Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.
This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.
To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.
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a town doubles its size every 38 years. if the population is currently 6,790, what will the population be in 76 years?
Population will be 43,160 in 76 years if a town doubles its size every 38 years if the current population is 6,790.
Since the town doubles in size every 38 years, we can use the formula:
P = P0 * 2^(t/T)
where P0 is the initial population, P is the population after time t, and T is the doubling time (38 years in this case).
We know that the current population is P0 = 6,790, and we want to find the population in 76 years, which is t = 76. Plugging these values into the formula, we get:
P = 6,790 * 2^(76/38)
P = 6,790 * 2^2
P = 6,790 * 4
P = 27,160
Therefore, the population of the town will be 27,160 in 76 years.
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The 15 Chihuahua puppies ate 63 cups of food last week. If each puppy ate the same amount of food, how many cups of puppy food did each puppy eat?
15 StartLongDivisionSymbol 63.0 EndLongDivisionSymbol minus 60 = a remainder of 30 and a quotient of 4.blank.
How many cups of food did each puppy eat?
4 cups
4.1 cups
4.2 cups
4.ModifyingAbove 2 with bar cups
Answer:c 4.2 cups
Step-by-step explanation:
just do 63 divided 15
Do anybody know this?
The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)
What are the coordinates of the division of the line segment?The formula for the division of line segments in the ratio m:n is
P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}
We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)
Thus, if the ratio is 2:5, we have:
U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}
U(x, y) = (84/7), (42/7)
U(x, y) = (12, 6)
Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.
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It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box, which holds 15 cups of sugar. Double the dimensions of the box. Hint: given k, areas are scaled by ____ and volumes are scaled by ____ Approximately how much paint would the new box need? How much sugar would it hold?
The new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.
To find out how much paint the new box would need and how much sugar it would hold, follow these steps:
1. The original box holds 15 cups of sugar, and it takes 2 ounces of paint to cover it completely. When you double the dimensions of the box, areas are scaled by [tex]k^2[/tex] (k is the scale factor), and volumes are scaled by[tex]k^3.[/tex]
2. Since you double the dimensions, the scale factor k is 2.
3. The surface area of the box will be scaled by [tex]k^2, which is 2^2 = 4.[/tex]So, the new box will need 4 times the amount of paint that the original box needed. Since the original box needed 2 ounces of paint, the new box will need 2 × 4 = 8 ounces of paint.
4. The volume of the box will be scaled by [tex]k^3, which is 2^3 = 8[/tex]. So, the new box will hold 8 times the amount of sugar that the original box held. Since the original box held 15 cups of sugar, the new box will hold 15 × 8 = 120 cups of sugar.
In conclusion, the new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.
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A rectangle has an area of 717. 8m2. One of the sides is 7. 4m in length. Work out the perimeter of the rectangle
The perimeter of the rectangle is approximately 208.9 meters.
To find the perimeter of the rectangle, we need to know the length of the other side.
Let's use the formula for the area of a rectangle:
area = length x width
We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:
length = area / width
length = 717.8 / 7.4
length ≈ 97.05 m
Now we have both the length and width of the rectangle, so we can find the perimeter:
perimeter = 2 x (length + width)
perimeter = 2 x (97.05 + 7.4)
perimeter = 2 x 104.45
perimeter = 208.9 m
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A student was asked to factor
During bracket off, when 6x⁴ * 6x⁴= 36x⁸ instead of 36x¹⁶ using Perfect square method.
When 4y² * 4y² = 16y^4 instead of 25y⁴⁴ gotten in the question. To correct the error, using the perfect square method, it can be corrected.
The answer will be (6x⁸ - 5y²)(6x⁸ + 5y²)The last error found is sign rule-4y^2 x -4y^2 = +16y⁴ instead of -4y² * +4y² = -16y⁴
What is a Perfect Square?Perfect square is is a number that is generated by multiplying two equal integers by each other.
Given 36x¹⁶ - 25y⁴
The rule = A difference of two perfect squares, A² - B²² can be factored into (A+B) x (A-B)36x¹⁶ is a perfect square = 6₂ * x⁸2)= (6x⁸)^225y⁴ is also a perfect square= 5² * x²(2)= (5x²)²
Using the rule for Perfect square,
When A² - B² = (A + B) x (A - B)
So,(6x⁸)₂ - (5x²)²
=(6x⁸ + 5x²) * (6x⁸ - 5x²)
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GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Answer:
x > 3
Step-by-step explanation:
This is an open circle, meaning there will be no equal sign.
The line is going to the right of 3, meaning x > 3
So, our inequality is x > 3
does the confidence interval suggest that the difference, if any, observed in this sample will also generalize to the larger population?
In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.
What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.
A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.
A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.
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Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real objects.
Using the scale factor of 4:1, the side lengths of the real objects are:
B. Side a is 5 inches long and side b is 4.5 inches long.
What is a Scale Factor?A scale factor is a number that represents the ratio of the size or dimensions of an object in relation to another object. It is a proportional relationship between two similar objects, where the scale factor is the ratio of any corresponding lengths or dimensions.
Thus, given that the scale factor is 4:1, it means 4 inches of the scale drawing represents 1 inch of the real object.
Therefore, the sides would be:
Side a = 20/4 = 5 in.
Side b = 18/4 = 4.5 in
The answer is B.
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suppose the amount of time (in minutes) per day that you spend watching netflix is in the 90th percentile of all account users. which interpretation(s) of this quantity are correct? select all that apply.
The correct interpretations of the given quantity are C and E.
C. Your daily viewing time is greater than 90% of all Netflix users.
E. 90% of all Netflix users viewing times per day are less than your daily viewing time.
To understand the correct interpretation, we need to first understand what the 90th percentile means. It refers to the value below which 90% of the data falls.
If your daily viewing time is in the 90th percentile of all Netflix users, it means that your viewing time is greater than 90% of all users. In other words, only 10% of users watch more Netflix than you, and your viewing time is greater than the viewing time of 90% of users.
Therefore, options C and E are the correct interpretations.
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Complete Question:
Suppose the amount of time (in minutes) per day that you spend watching Netflix is in the 90th percentile of all account users. Which interpretation(s) of this quantity are correct? Select ALL that apply.
A. You spend approximately 90 minutes per day watching Netflix.
B. 90% of all viewers spend more time on Netflix per day than you.
C. Your daily viewing time is greater than 90% of all Netflix users.
D. There is a 90% probability that a randomly selected viewer spends less time than you watching Netflix per day.
E. 90% of all Netflix user viewing times per day are less than your daily viewing time.
F. 90% of all Netflix user viewing times per day are less than or equal to your daily viewing time.
the smith family has $4$ cats and $3$ dogs. in how many ways can these $7$ pets be placed in a row of $7$ chairs such that at least $2$ cats are next to each other?
There are 4896 ways of arranging 7 pets in a row of 7 chairs such that at least 2 cats are next to each other.
Arrangement of entities can be done using permutation and combination in mathematics.
Consider the distributions where 2 cats are not next to each other as
C D C D C D C.
There are 4! ways to seat the cats, and 3! ways to seat the dogs that gets us N=4! 3! = 144
There are a total of 7!=5040 possible ways to seat both cats and dogs.
At least 2 cats seat together= All possible arrangements- None of the cat seat together.
Thus the number of seatings where at least 2 cats are adjacent is
5040-144 = 4896
So, there are 4896 arrangements can be made so that at least 2 of the cats seat together.
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Can anybodyhelp me with these please? I need help please!
1: The measure of arc JML is: arc JML = 176°
3: m∠WXY = 59°
5: The measure of the arc is: arc FE = 54°
7: The measure of the angles are: m∠A = 79° and m∠B = 112°
9: The value of x is: x = 9
How to find the angle or arc measure in a circle?
No. 1
The measure of inscribed angle is half the measure of its intercepted arc. That is:
∠ JKL = 1/2 * arc JML
88 = 1/2 * arc JML
arc JML = 2 * 88
arc JML = 176°
No. 3
arc WY = 360 - 86 - 156 = 118° (sum of angles in a circle)
m∠WXY = 1/2 * arc WY
m∠WXY = 1/2 * 118
m∠WXY = 59°
No. 5
An angle inscribed in a semicircle is a right angle. Thus, m∠DFE = 90°
m∠EDF = 180 - 90 - 63 = 27° (sum of angles in a triangle)
m∠EDF = 1/2 * arc FE
27° = 1/2 * arc FE
arc FE = 2 * 27
arc FE = 54°
No. 7
The opposite angle in a cyclic quadrilateral add up to 180°. That is:
m∠A + m∠C = 180°
m∠A + 101 = 180
m∠A = 180 - 101
m∠A = 79°
m∠B + m∠D = 180°
m∠B + 68 = 180
m∠B = 180 - 68
m∠B = 112°
No. 9
67 = 1/2 * (16x - 10)
67 * 2 = (16x - 10)
16x - 10 = 134
16x = 134 + 10
16x = 144
x = 144/16
x = 9
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please answer!! A rectangle is 1/3 yards long and 2/3 yards wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form by filling in the boxes
Answer:
2/9yd²
Step-by-step explanation:
We know that area is calculated by length × width, so we will do the same here. To get the area, we must multiply 1/3 by 2/3.
1/3 × 2/3 is 2/9. So, the area of the rectangle is 2/9yd². :D
Describe how it is possible to calculate the enthalpy of formation for a compound that cannot be synthesized directly from the constituent elements.
The enthalpy change of each step in the cycle must be added together to obtain the enthalpy of formation of the desired compound.
The enthalpy of formation of a compound that cannot be synthesized directly from the constituent elements can be calculated using the Hess's Law. Hess's Law states that the enthalpy change of a reaction is independent of the route taken from reactants to products. This law allows for the enthalpy of formation of a compound to be determined by summing the enthalpy changes of a series of known reactions, referred to as a ‘thermochemical cycle’, which lead to the compound of interest. To use this law, the enthalpy of formation of the intermediate species formed during the reaction must be known.
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all the edges of a cube are expanding at a rate of 4 4 in. per second. how fast is the volume changing when each edge is 10in. 10 in. long?
Answer:
Step-by-step explanation:
every second we are increasing the sides by 4.4 in all 3 dimensions. This must mean that we need to do 4.4x4.4x4.4 to get
85.184in^3 per second
Find and explain the error in the student’s work below.
Solve 2x² - 5x -12 = 0 using the Quadratic Formula.
The error made by the student is in simplifying the expression inside the square root.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The student made an error in simplifying the expression inside the square root.
The expression should be simplified as follows:
25 + 4(2)(-12) = 25 - 96 = -71
So the correct expression inside the square root is -71, not 121.
Therefore, the correct solution using the Quadratic Formula is:
x = (-(-5) ± √((-5)² - 4(2)(-12)))/(2(2))
x = (5 ± √(25 + 96))/4
x = (5 ± √121)/4
x = (5 ± 11)/4
Hence, the solutions are x = -3 and x = 4/2, which simplifies to x = 2.
Therefore, the error made by the student is in simplifying the expression inside the square root.
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show that 2 2/3/6=4/9
2 and 2/3 divided by 6 equals 4/9.
So, 2 and 2/3 divided by 6,
we can simplify it step by step as follows:
First, we need to convert the mixed numbers 2 and 2/3 to an improper fraction:
2 and 2/3 = (2 × 3 + 2) / 3 = 8/3
Therefore, the expression becomes:
8/3 ÷ 6
To divide fractions, we need to invert the second fraction and multiply:
8/3 ÷ 6 = 8/3 × 1/6
Simplifying the multiplication of fractions:
8/3 × 1/6 = (8 × 1) / (3 × 6) = 8/18
Now, we can simplify the fraction 8/18 by dividing both the numerator and denominator by their greatest common factor, which is 2:
8/18 = (8 ÷ 2) / (18 ÷ 2) = 4/9
Therefore, 2 and 2/3 divided by 6 equals 4/9.
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What is the volume of the composite figures?
Total volume of the composite figure using volume of cuboid formula is = 120ft³.
Define volume?A cuboid's volume is a measurement of how much room it occupies. A three-dimensional shape with dimensions of length, breadth, and height is the cuboid. We can keep stacking them, starting with a rectangular sheet, until we achieve a shape with a particular length, breadth, and height.
The shape of this stack of sheets is a cuboid, which has 6 faces, 12 edges, and 8 vertices. The (unit)³ is used to represent a cuboid's volume.
In the given figure,
Length of cuboid = 6ft.
Breadth of cuboid = 3ft.
Height of cuboid = 5ft.
Length of second cuboid = 4ft.
Height of second cuboid = 5ft.
Breadth of second cuboid = 3ft.
Volume of first cuboid = length × breadth × height.
= 6 × 3 × 5
= 90ft³
Volume of second cuboid = 4 × 3 × 5
= 60ft³
Now the second cuboid is half.
So, volume becomes = 60/2
= 30ft³.
So, total volume of the figure = 90 + 30 = 120ft³.
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Down below are the coordinates after dilation but it says its wrong
Answer:
For the original triangle:
A is at (-3, 6), B is at (1, 2), C is at (-5, 1).
For the new triangle:
A' will be at (-3 - 3, -(6 + 2)) = (-6, -8)
B' will be at (1 - 3, -(2 + 2)) = (-2, -4)
C' will be at (-5 - 3, -(1 + 2)) = (-8, -3)
a die is continuously rolled 104 104 times. what is the probability that the total sum of all rolls does not exceed 375 375 ?
The probability that the total sum of all rolls does not exceed 375 is approximately 0.7165
Assuming the die is a fair six-sided die, the possible outcomes for each roll are numbers 1 through 6, each with a probability of 1/6.
Let X be the total sum of all rolls. Then X follows a discrete uniform distribution with parameters n = 104 (number of rolls) and a = 1 (minimum value of each roll). The expected value of X is:
E(X) = n × (a + b) / 2 = 104 × (1 + 6) / 2 = 365
The variance of X is
Var(X) = n × (b - a + 1)^2 / 12 = 104 × 6^2 / 12 = 312
The standard deviation of X is
SD(X) = sqrt(Var(X)) = sqrt(312) = 17.67
To calculate the probability that the total sum of all rolls does not exceed 375, we need to calculate the cumulative distribution function (CDF) of X and evaluate it at 375
P(X <= 375) = F(375)
where F(x) = P(X <= x) is the CDF of X.
Using the normal approximation to the binomial distribution, we can approximate X as a normal distribution with mean E(X) = 365 and standard deviation SD(X) = 17.67
Z = (X - E(X)) / SD(X)
Z follows a standard normal distribution with mean 0 and standard deviation 1.
P(X <= 375) = P(Z <= (375 - E(X)) / SD(X))
= P(Z <= (375 - 365) / 17.67)
= P(Z <= 0.566)
Using a standard normal distribution table or a calculator, we can find that P(Z <= 0.566) is approximately 0.7165.
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The given question is incomplete, the complete question is :
A die is continuously rolled 104 times. what is the probability that the total sum of all rolls does not exceed 375 ?
A trazpodizi has an aera of 35 mm2 what is the height
The height of the trapezium is 5mm, given that the two parallel sides have lengths of 6mm and 8mm, and the area of the trapezium is 35mm².
To find the height of a trapezium given its area and the lengths of its parallel sides, we use the formula:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides, h is the height, and Area is the area of the trapezium.
In this case, we are given that the area of the trapezium is 35mm², and we know that the two parallel sides have lengths 6mm and 8mm. So, we can substitute these values into the formula and solve for h:
35 = (6+8) x h/2
Simplifying the right-hand side of the equation, we can combine the two lengths of the parallel sides and multiply by h, and then divide by 2 to get:
35 = 14h / 2
Multiplying both sides by 2, we get:
70 = 14h
Dividing both sides by 14, we get:
h = 5
Therefore, the height of the trapezium is 5mm.
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