To find the projection of b onto the subspace W spanned by vi and v2, we need to first find the orthogonal projection of b onto W.
We can use the formula for orthogonal projection:
projW b = ((b ⋅ vi)/(vi ⋅ vi))vi + ((b ⋅ v2)/(v2 ⋅ v2))v2
where ⋅ denotes the dot product.
Plugging in the given values:
projW b = ((1*3 + 2*1 - 1*0 - 5*(-1))/(3*3 + 1*1 + 0*0 + (-1)*(-1)))vi + ((1*0 + 2*1 - 1*3 - 5*1)/(0*0 + 1*1 + 3*3 + 1*1))v2
Simplifying:
projW b = (22/11)vi + (-6/11)v2
Therefore, the projection of b onto the subspace W is given by (22/11, -6/11, 0, 0).
To find the projection of vector b onto the subspace W spanned by vectors v1 and v2, we will use the following formula:
proj_W(b) = (b · v1 / v1 · v1) * v1 + (b · v2 / v2 · v2) * v2
First, calculate the dot products:
b · v1 = (1 * 3) + (2 * 1) + (-1 * 0) + (-5 * -1) = 3 + 2 + 0 + 5 = 10
b · v2 = (1 * 0) + (2 * 1) + (-1 * 3) + (-5 * 1) = 0 + 2 - 3 - 5 = -6
v1 · v1 = (3 * 3) + (1 * 1) + (0 * 0) + (-1 * -1) = 9 + 1 + 0 + 1 = 11
v2 · v2 = (0 * 0) + (1 * 1) + (3 * 3) + (1 * 1) = 0 + 1 + 9 + 1 = 11
Now plug the dot products into the formula:
proj_W(b) = (10 / 11) * v1 + (-6 / 11) * v2
proj_W(b) = (10/11) * (3, 1, 0, -1) + (-6/11) * (0, 1, 3, 1)
Perform scalar multiplication:
proj_W(b) = (30/11, 10/11, 0, -10/11) + (0, -6/11, -18/11, -6/11)
Finally, add the two vectors:
proj_W(b) = (30/11, 4/11, -18/11, -16/11)
So the projection of b onto subspace W is:
proj_W(b) = (30/11, 4/11, -18/11, -16/11)
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1ST ONE TO ANSWER MY QUESTION WILL BE MARKED BRAINLIESTT! ANSWER 1 QUESTION!
2x²t + 7xy
Step-by-step explanation:To simplify, we will combine like terms.
Given:
5xy - x²t + 2xy + 3x²t
Reorder like terms:
5xy + 2xy + 3x²t - x²t
Combine like terms:
➜ 5 + 2 = 7
➜ 3 - 1 = 2
7xy + 2x²t
Reorder by degree:
2x²t + 7xy
18. Mr. Kamau wishes to buy some items for his son and daughter. The son's item costs sh. 324 while
the daughter item costs sh. 220 each. Mr. Kamau would like to give each of them equal amount of
money.
a) How many items will each person buys.
Answer:
if Mr. Kamau wants to give each of his children an equal amount of money, he can either:
Buy 1 item for his son (costing sh. 324) and 0 items for his daughter, giving each child sh. 162.
Buy 1 item for his son (costing sh. 324) and 1 item for his daughter (costing sh. 220), giving each child sh. 272.
Step-by-step explanation:
Let x be the number of daughter items that Mr. Kamau will buy for his daughter. Since the son's item costs sh. 324, we know that each child should receive sh. (324 + 220x)/2.
We want to find how many items each child will buy, so we need to solve for x in the equation:
(324 + 220x)/2 = 220
Multiplying both sides by 2, we get:
324 + 220x = 440
Subtracting 324 from both sides, we get:
220x = 116
Dividing both sides by 220, we get:
x = 0.527
Since we can't buy a fraction of an item, Mr. Kamau should buy either 0 or 1 daughter item for his daughter. If he buys 0 daughter items, he can give his son sh. (324 + 2200)/2 = sh. 162. If he buys 1 daughter item, he can give each child sh. (324 + 2201)/2 = sh. 272. Therefore, the possible scenarios are:
Mr. Kamau buys 0 daughter items. His son buys 1 item and his daughter buys 0 items.
Mr. Kamau buys 1 daughter item. His son buys 1 item and his daughter buys 1 item.
A ship sailed from Port X to Port Y. It traveled 20 kilometers due north and then 25 kilometers due west. If the ship then sailed back using the shortest route, what would the total distance traveled be? Round to the nearest kilometer.
The total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.
What is Kilometer ?
Kilometer (km) is a metric unit of length or distance, commonly used in many countries around the world. It is equal to 1000 meters, or approximately 0.62 miles.
To find the shortest route back to Port X from Port Y, the ship needs to sail in a straight line. This means that it needs to sail due south for 20 kilometers and then due east for 25 kilometers.
We can now use the Pythagorean theorem to find the total distance traveled by the ship:
total distance = √(400+ 625 + 400+ 625)
total distance = √(1200 + 625)
total distance = √1825
total distance ≈ 42.73 kilometers (rounded to the nearest kilometer)
Therefore, the total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.
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Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)
The area of the triangle is 6 square units.
How to solveOnce you have the points they make a 3-4-5 triangle.
The two legs are 3 and 4, so the hypotenuse has to be 5.
Or you could use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5
then find area
A=1/2bh
1/2(3*4)
6
Thus, the area of the triangle is 6 square units.
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The ratio of English books to Math books is 5:9.If there 28 more Math books than English books. How many Math and English books are there?
Answer: 35 English Books and 63 Maths Books
Step-by-step explanation:
5:9
x:(x+28)
Cross multiplication...
9x=5x+140
9x-5x=140
4x=140
14/4 = 35 = x
English Books = x= 35
Maths Books = x+28 = 63
All of these rectangles have an area of 12 square inches. Each square represents 1 square inch. Which rectangles do not have a perimeter of 14 inches?
The rectangles with dimensions 1 x 12 and 2 x 6 do not have a perimeter of 14 inches. These rectangles have perimeters of 26 inches and 16 inches, respectively.
To determine which rectangles with an area of 12 square inches do not have a perimeter of 14 inches, we will first find the possible dimensions of the rectangles and then calculate their perimeters.
1. Since the area of a rectangle is given by length x width, let's find the factors of 12:
- 1 x 12
- 2 x 6
- 3 x 4
2. Now, let's calculate the perimeters for each of these rectangles using the formula 2(length + width):
- For the 1 x 12 rectangle, the perimeter is 2(1+12) = 2(13) = 26 inches
- For the 2 x 6 rectangle, the perimeter is 2(2+6) = 2(8) = 16 inches
- For the 3 x 4 rectangle, the perimeter is 2(3+4) = 2(7) = 14 inches
The rectangles with dimensions 1 x 12 and 2 x 6 do not have a perimeter of 14 inches. These rectangles have perimeters of 26 inches and 16 inches, respectively.
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Find parametric equations for a line in the direction of the vector 57 - 7 and through the point
(0, 0, - 3).
Write the equations so that one term is just the parameter - t.
х (t) = y(t) =
z(t) =
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
To find the parametric equations for a line in the direction of the vector 57 - 7 and through the point (0, 0, - 3), we can use the vector form of the equation of a line:
r = r0 + tv
where r is a point on the line, r0 is the given point (0, 0, -3), t is a parameter, and v is the direction vector (57, -7, 0).
Substituting the given values, we have:
r = (0, 0, -3) + t(57, -7, 0)
Expanding, we get:
x(t) = 0 + 57t
y(t) = 0 - 7t
z(t) = -3 + 0t
Simplifying, we have:
x(t) = 57t
y(t) = -7t
z(t) = -3
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
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A manufacturer measures the number of cell phones sold using the binomial 0. 015c+2. 81. She also measures the wholesale price on these phones using a binomial 0. 011c+3. 52. Calculate her revenue if she sells 100,000 cell phones. Revenue = (numberofcellphones)(wholesaleprice) = (0. 015c+2. 81)(0. 011c+3. 52)
When the manufacturer sells 100,000 cell phones, her revenue will be approximately $1,657,993.39.
To find the revenue for selling 100,000 cell phones, we will first evaluate both binomials for the given number of cell phones (c = 100,000) and then multiply them together.
Step 1: Evaluate the first binomial (number of cell phones sold) for c = 100,000:
0.015c + 2.81 = 0.015(100,000) + 2.81 = 1,500 + 2.81 = 1,502.81
Step 2: Evaluate the second binomial (wholesale price) for c = 100,000:
0.011c + 3.52 = 0.011(100,000) + 3.52 = 1,100 + 3.52 = 1,103.52
Step 3: Calculate the revenue by multiplying the results of the two binomials:
Revenue = (1,502.81)(1,103.52) = 1,657,993.3912
So, when the manufacturer sells 100,000 cell phones, her revenue will be approximately $1,657,993.39. This calculation is based on the binomial expressions provided for the number of cell phones sold (0.015c+2.81) and the wholesale price (0.011c+3.52).
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1. A triangle, △DEF, is given. Describe the construction of a circle with center C circumscribed about the triangle. (3-5 sentences)
2. ⊙O and ⊙P are given with centers (−2, 7) and (12, −1) and radii of lengths 5 and 12, respectively. Using similarity transformations on ⊙O, prove that ⊙O and ⊙P are similar
Answer: Finally, translate the circles back to their original positions. This will not change their similarity. Therefore, ⊙O and ⊙P are similar.
Step-by-step explanation:
To construct a circle circumscribed about triangle △DEF, follow these steps:
Draw the perpendicular bisectors of the sides of the triangle. Each bisector should intersect the opposite side of the triangle at a point.
Find the point of intersection of any two perpendicular bisectors. This point is the center of the circle.
Measure the distance from the center to any of the vertices of the triangle. This distance is the radius of the circle.
Draw the circle with the center and radius found in the previous steps. The circle should pass through all three vertices of the triangle.
To prove that ⊙O and ⊙P are similar using similarity transformations, follow these steps:
Translate both circles so that their centers coincide with the origin. This will not change their relative positions.
Scale one of the circles by a factor equal to the ratio of the radii of the two circles. This will make the two circles have the same size.
Since both circles are centered at the origin and have the same size, they must be similar. This is because any two circles with the same size are either congruent or similar.
Finally, translate the circles back to their original positions. This will not change their similarity. Therefore, ⊙O and ⊙P are similar.
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How can you use your knowledge of evaluating expressions involving square roots to
identify and correct an error in calculating the period of a pendulum?
the period of a pendulum is the time in seconds) it takes the pendulum to swing back
and forth. the period t is represented by t = 1.1vi, where l is the length of the
pendulum (in feet).
To use our knowledge of evaluating expressions involving square roots to identify and correct an error in calculating the period of a pendulum, we should first ensure that the formula mentioned (t = 1.1vi) is accurate.
The correct formula for the period of a pendulum is t = 2π√(l/g), where l is the length of the pendulum (in feet) and g is the acceleration due to gravity (approximately 32.2 ft/s²).
When evaluating the period t, make sure to use the correct formula and follow these steps:
1. Substitute the given length of the pendulum (l) into the formula.
2. Divide the length by the acceleration due to gravity (g).
3. Calculate the square root of the result.
4. Multiply the square root by 2π.
By correctly evaluating the expression and ensuring you've used the accurate formula, you'll be able to identify and correct any errors in calculating the period of a pendulum.
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QUESTION IN PHOTO I MARK BRAINLIEST
The value of x in the given circle is 13.9.
Given that a circle D, having an inscribed angle ∠CFE = 57° and the arc opposite it arc CE = 10x-25, we need to find the measure of x,
Using the inscribed angle theorem,
It states that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circumference of the circle.
So,
m ∠CFE = arc CE / 2
57 = 10x-25 / 2
10x-25 = 114
10x = 139
x = 13.9
Hence the value of x in the given circle is 13.9.
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A building is 210 m tall. A scale model is built using a scale factor of 0. 5.
a) Determine the height of the model to the nearest centimeter, if necessary.
b) What are the actual dimensions of the bed, couch, and desk?
a) The height of the scale model is 105 m. b) The actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
a) To determine the height of the scale model, we multiply the height of the actual building by the scale factor of 0.5:
Height of scale model = 0.5 x 210 m = 105 m.
b) Since the scale factor is 0.5, the actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
For example, if the length of the couch in the scale model is 10 cm, then the actual length of the couch is 2 x 10 cm = 20 cm. Similarly, if the width of the desk in the scale model is 8 cm, then the actual width of the desk is 2 x 8 cm = 16 cm.
Therefore, to find the actual dimensions of the bed, couch, and desk, we simply multiply the corresponding dimensions in the scale model by 2.
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400 people attended a concert 10% of the people came from Scotland 25% of the people came form Wales How many more pepole came from Wales than Scotland
If 400 people attended a concert 10 percent of the people came from Scotland 25 percent of the people came form Wales, there were 60 more people from Wales than from Scotland.
To find out how many more people came from Wales than Scotland at a concert with 400 attendees, we'll first calculate the number of people from each region.
1. Determine the number of people from Scotland:
Since 10% of the people came from Scotland, we'll multiply the total attendees (400) by 10% (0.10).
400 * 0.10 = 40 people from Scotland.
2. Determine the number of people from Wales:
Since 25% of the people came from Wales, we'll multiply the total attendees (400) by 25% (0.25).
400 * 0.25 = 100 people from Wales.
3. Calculate the difference between the number of attendees from Wales and Scotland:
Subtract the number of people from Scotland (40) from the number of people from Wales (100).
100 - 40 = 60 more people from Wales than Scotland.
In conclusion, at the concert with 400 attendees, there were 60 more people from Wales than from Scotland.
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Team A purchases 3 soccer balls and 7 basketballs for a total cost of $1240. Team B purchases 5 soccer balls and 10 basketballs for a cost of $1900. If team C purchases 4 soccer balls and 6 basketballs, how much would they expect to pay?
The total cost for team C would be $760 + $600 = $1360.
How to calculate how much would they expect to payWe can start by setting up a system of equations based on the given information. Let x be the cost of one soccer ball and y be the cost of one basketball. Then we have:
3x + 7y = 1240 (equation 1)
5x + 10y = 1900 (equation 2)
We can solve this system of equations by using either substitution or elimination method. Let's use elimination method here:
Multiplying equation 1 by 2 and subtracting it from equation 2, we get:
5x + 10y - (6x + 14y) = 1900 - 2(1240)
-x - 4y = 420
Now we can use either equation 1 or equation 2 to solve for x or y. Let's use equation 1:
3x + 7y = 1240
3x + 3y = 840 (multiplying both sides by -1 and adding to the previous equation)
4y = 400
y = 100
So one basketball costs $100. Now we can substitute this value back into either equation 1 or equation 2 to solve for x. Let's use equation 1:
3x + 7y = 1240
3x + 7(100) = 1240
3x = 570
x = 190
So one soccer ball costs $190.
Now we can use these values to find the cost for team C:
4 soccer balls cost 4 x $190 = $760
6 basketballs cost 6 x $100 = $600
So the total cost for team C would be $760 + $600 = $1360.
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A triangle has side lengths of (7m – 2) centimeters, (9m - 5) centimeters, and
(6n – 1) centimeters. which expression represents the perimeter, in centimeters, of
the triangle?
The expression that represents the perimeter, in centimeters, of the triangle is (7m - 2) + (9m - 5) + (6n - 1).
How to find the perimeter of a triangle?The perimeter of a triangle is the sum of the lengths of its sides. Therefore, to find the perimeter of the triangle with side lengths (7m - 2) cm, (9m - 5) cm, and (6n - 1) cm, we need to add these lengths together.
Thus, the expression that represents the perimeter of the triangle is (7m - 2) cm + (9m - 5) cm + (6n - 1) cm.
Simplifying this expression, we get 16m + 6n - 8 cm, which is the final answer. Therefore, the perimeter of the triangle is 16m + 6n - 8 cm.
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An angle measure 94 less than the measure of its supplementary angle. What is the measure of each angle?
The angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.
What is the supplementary angle?In geometry, the supplementary angle of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. In other words, two angles are supplementary if their sum is 180 degrees.
For example, if an angle measures 60 degrees, its supplementary angle would measure 120 degrees, since 60 degrees + 120 degrees = 180 degrees.
According to the given informationLet x be the measure of the angle in degrees.
By definition, the supplementary angle of x measures 180 - x degrees.
We are given that the angle measures 94 degrees less than its supplementary angle, so we can write:
x = (180 - x) - 94
Simplifying and solving for x, we get:
2x = 180 - 94
2x = 86
x = 43
Therefore, the angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.
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a manufacturing machine has a 80% defect rate. if 109 items are chosen at random, answer the following. a) which is the correct wording for the random variable? select an answer b) pick the correct symbol: ?
The correct words are number of defective items from the sample of 109 items chosen at random and correct symbol is X ~ B(109, 0.8).
Percent of defective rate in manufacturing machine = 80%
Random number of items chosen = 109
The correct wording for the random variable in this situation is,
The number of defective items in a sample of 109 items chosen at random from the manufacturing machine.
Number of defective items is successes.
A common symbol for the number of successes in a binomial distribution is X.
Use X to represent the random variable in this situation.
The notation for the binomial distribution is usually written as,
X ~ B(n, p)
where X is the random variable,
n is the sample size,
and p is the probability of success on each trial.
X ~ B(109, 0.8).
Therefore, the correcting wording is number of defective items in a sample of 109 items chosen at random and the correct symbol is equal to X ~ B(109, 0.8).
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In right triangle RST, ST = 5, RT = 12, and RS = 13. Find tan (s)
In right triangle RST, the value of tan (s) is 12/5.
To find tan(s), we first need to determine which side is opposite angle S and which side is adjacent to angle S.
In this case, RT is the side opposite angle S, and ST is the side adjacent to angle S. Since tangent (x) or tan(x) is defined as the ratio of the length of the opposite side to the length of the adjacent side, we can write the formula for tan(s) as follows:
tan(s) = (opposite side) / (adjacent side)
Now we can plug in the given side lengths to calculate the value of tan(s):
tan(s) = RT / ST
tan(s) = 12 / 5
Thus, tan(s) = 12 / 5.
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The volume of this prism is 2990cm3. the area of the cross-section is 65cm2. work out x
After considering the given values provided in the question the value of x is 46cm, under the condition that the volume of this prism is 2990cm³. the area of the cross-section is 65cm².
The evaluated volume of a prism refers to the area of the cross-section multiplied by its length. Then, considering the volume of this prism is 2990cm³ and the area of the cross-section is 65cm², we can finally formulate a formula to evaluate the length of the prism by dividing the volume by the area of the cross-section.
So,
Length = Volume / Area of cross-section
= 2990 / 65
= 46
Then the value of x = 46cm.
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The complete question is
The volume of this prism is 2990cm³. The area of the cross-section is 65cm². Work out x
Diagram is not drawn to scale
If a triangle given by the matrix [235-102] is dialed by a scale factor of 2, what will will happened to the side lengths and angle measure of triangle?
If the triangle given by the matrix [235-102] is scaled by a factor of 2, the side lengths of the triangle will be doubled. The angle measures of the triangle will remain the same since scaling does not affect the angles.
When a triangle is scaled by a factor of 2, the side lengths will be doubled, but the angle measures will remain the same. Here's a step-by-step explanation:
1. The original matrix is [2 3 5; -1 0 2].
2. Apply the scale factor of 2 to each of the side lengths by multiplying the matrix by 2: [4 6 10; -2 0 4].
3. The side lengths of the triangle have been doubled, but the angle measures remain the same.
So, after scaling the triangle by a factor of 2, the side lengths will be doubled while the angle measures will stay the same.
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Choose the system for the graph.
The system of equations which represents the given graph is:
(C) y ≥ 2/5x + 1 and y ≤ 7/3x + 3
What are systems of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
A group of equations comprising one or more variables is known as a system of equations.
The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
So, the lines have slopes of 7/3 and 2/5, based on the solutions. (We could verify this by close examination of the graph.)
The shade is above (greater than) the line with a slope value of 2/5, and below (less than) the line with a slope value of 7/3.
So, using the symbols, we need to find two inequalities:
y ≥ 2/5x ...
y ≤ 7/3x ...
Choice C contains this combo.
Therefore, the system of equations which represents the given graph is:
(C) y ≥ 2/5x + 1 and y ≤ 7/3x + 3
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To solve 6÷1/4, james thinks about how the distance from his home to the store is 1/4 mile and he wonders how many times he would have to walk that distance to walk 6 miles. what is the quotient of 6 and 1/4? enter your answer in the box.
The quotient of 6 and 1/4 is 24.
We have applied division operation to this question. Firstly, we will understand the meaning of a proper fraction. A fraction in which the numerator is less than the denominator is called a proper fraction. This means that the denominators will always be bigger than the numerators for appropriate fractions.
We can represent this condition in either of the two ways.
Denominator < Numerator
(Or)
Numerator > Denominator
We are given a numerical expression which is 6÷ 1/4 and we have to solve this.
To convert this division sign into a multiplication sign, we will take the reciprocal of 1/4.
The reciprocal of 1/4 is 4.
Therefore,
6÷ 1/4
= 6 × 4
= 24
Therefore, the quotient of 6 and 1/4 is 24.
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Gebhardt Electronics produces a wide variety of transformers that it sells directly to manufacturers of electronics equipment. For one component used in several models of its transformers, Gebhardt uses a 3-foot length of. 20 mm diameter solid wire made of pure Oxygen-Free Electronic (OFE) copper. A flaw in the wire reduces its conductivity and increases the likelihood it will break, and this critical component is difficult to reach and repair after a transformer has been constructed. Therefore, Gebhardt wants to use primarily flawless lengths of wire in making this component. The company is willing to accept n more than a l in 20 chance that a 3-foot length taken from a spool will be flawless. Gebhardt also occasionally uses smaller pieces of the same wire in the manufacture of other compo- nents, so the 3-foot segments to be used for this component are essentially taken randomly from a long spool of. 20 mm diameter solid OFE copper wire Gebhardt is now considering a new supplier for copper wire. This supplier claims that its spools of. 20 mm diameter solid OFE copper wire average 50 inches between flaws. Gebhardt now must determine whether the new supply will be satisfactory if the supplier's claim is valid. Managerial Report In making this assessment for Gebhardt Electronics, consider the following three questions:
1. If the new supplier does provide spools of. 20 mm solid OFE copper wire that aver age 50 inches between flaws, how is the length of wire between two consecutive flaws distributed?
2. Using the probability distribution you identified in (I), what is the probability that Gebhardt's criteria will be met (i. E. , a l in 20 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless)
3. In inches, what is the minimum mean length between consecutive flaws that would result in satisfaction of Gebhardt's criteria
4. In inches, what is the minimum mean length between consecutive flaws that would result in a l in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless?
we need to determine the minimum mean length between consecutive flaws that would result in a 1 in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless.
First, we need to convert the length of the wire provided by the new supplier (50 inches) into feet, which is 4.17 feet (50 inches divided by 12).
Next, we can use the Poisson distribution formula to calculate the probability of getting at least one flaw in a 3-foot segment of wire:
P(X >= 1) = 1 - e^(-λ)
Where X is the number of flaws in a 3-foot segment, and λ is the mean number of flaws per 3-foot segment.
Since the supplier claims that the average length between flaws is 4.17 feet, we can calculate λ as:
λ = 1/4.17 = 0.239
Now, we can plug in the values and solve for the probability:
P(X >= 1) = 1 - e^(-0.239) = 0.208
This means that there is a 20.8% chance of getting at least one flaw in a 3-foot segment of wire provided by the new supplier.
To find the minimum mean length between consecutive flaws that would result in a 1 in 100 (or 0.01) chance of getting a flawless 3-foot segment, we can rearrange the Poisson formula:
P(X = 0) = e^(-λ)
0.01 = e^(-λ)
ln(0.01) = -λ
λ = 4.605
This means that the mean length between consecutive flaws would need to be at least 4.605 feet (55.26 inches) in order to have a 1 in 100 chance of getting a flawless 3-foot segment from the new supplier.
In conclusion, if the new supplier's claim is valid and the mean length between consecutive flaws is at least 55.26 inches, then Gebhardt Electronics can expect to get a flawless 3-foot segment of wire with a 1 in 100 probability.
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Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.
Sample Standard Deviation
red box 3.868
blue box 2.933
Then complete each statement.
The sample size of the session regarding the number of people would purchase the red box,
, is
.
The sample size of the session regarding the number of people would purchase the blue box ,
, is
.
The standard deviation of the sample mean differences is approximately
.
The standard deviation of the sample mean differences is; 0.6898
How to find the standard deviation of the mean differences?From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45
From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60
Formula for standard deviation of the sample mean differences is;
σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]
Thus;
σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]
σm₁ - σm₂ = 0.6898
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A hotel offers two activity packages. One costs $192 and includes 3h of horseback riding and 2h of parasailing. The second costs $213 and includes 2h of horseback riding and 3h of parasailing. What is the cost for 1h of each activity?
Answer:
Step-by-step explanation:
Step-by-step explanation:
let's assumed that
x = 1h of horseback
y = 1h of parasailing
3h of horseback = 3x
2h of parasailing = 2y
and
2h of horseback = 2x
3h of parasailing = 3y
if
3x + 2y = 192
2x + 3y = 213
to find y we have to remove the x
(3x + 2y = 192) × 2
(2x + 3y = 213) × 3
6x + 4y = 384
6x + 9y = 639
___________ -
-5y = -255
y = 51
substitute y to any equation to find x
3x + 2y = 192
3x + 2(51) = 192
3x + 102 = 192
3x = 192 - 102
3x = 90
x = 30
so the answers are 1h of horseback = $30 and 1h of parasailing = $51
#CMIIWTaylor is making a large banner that
measures 6 yards in length. He split the
banner into 18 sections for him and
some of his friends to work on. How
many inches long is each section?
Answer:
12 is the answer
Step-by-step explanation:
6 y = 6 × 36 in. ( y = yards, in = inches )
do the math:
6(36) ÷ 18 = 12 ( for 18 sections of course )
12 × 18 = 6 × 36
becuase;
12 × 18 = 216 \
——- They are the same
6 × 36 = 216 /
= 216
Divide
216 ÷ 18 = 12
12 being the answer
Answer:
12 inches long
Step-by-step explanation:
One yard is equal to 36 inches, so 6 yards is equal to:
[tex]\sf:\implies 6 \times 36 = 216\: inches[/tex]
To find the length of each section, we need to divide the total length of the banner (216 inches) by the number of sections (18):
[tex]\sf:\implies 216 \div 18 = \boxed{\bold{\:\:12\:\:}}\:\:\:\green{\checkmark} [/tex]
Therefore, each section is 12 inches long.
Question 1(Multiple Choice Worth 2 points)
(Circle Graphs MC)
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 3(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Question 5(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Answer:
Step-by-step explanation:
Car are the preferred transportation for 168 residents.Together, Walk and Streetcar are the preferred transportation for 55 residents.Bus is the preferred transportation for 45 residents.Bicycle is the preferred transportation for 50 residents.Question 2(Multiple Choice Worth 2 points)(Appropriate Measures MC)The box plot represents the number of tickets sold for a school dance.A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the numb
What is the surface area of the square pyramid?
Answer:
3456 [tex]m^{2}[/tex]
Hope this helps!
Step-by-step explanation:
A square pyramid is comprised of a square and four triangles.
The square has an area of 1296 m ( 36m × 36m ) ( length × width ).
A triangle has an area of 540 m ( [tex]\frac{1}{2}[/tex] × 36m × 30m ) ( [tex]\frac{1}{2}[/tex] × width × ( slant ) height ).
The total surface area would be 1296 m + 4 × ( 540 m ) : ( Multiply 4 because there are 4 triangles ).
The total surface area is 3456 [tex]m^{2}[/tex].
Answer: 3,456 m^2
Step-by-step explanation:
The formula is SA = 2bs + b^2.
SA = 2 (36) (30) + 36^2
= 72 (30) + 1,296
= 2,160 + 1,296
= 3,456 m^2
the battery life of the iphone has an approximately normal distribution with a mean of 10 hours and a standard deviation of 2 hours. if you randomly select an iphone, what is the probability that the battery will last more than 10 hours?
If you randomly select an iphone, The probability that the battery will last more than 10 hours is 0.5000.
Population mean, µ = 10
Population standard deviation, σ = 2
The likelihood that the battery will survive more than 10 hours is equal to
[tex]= P( X > 10)\\= P( (X-\mu)/\sigma > (10 - 10)/2)\\= P( z > 0)\\= 1- P( z < 0)\\[/tex]
Using excel function:
= 1- NORM.S.DIST(0, TRUE)
= 0.5000
The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that describes a large class of phenomena observed in nature, social sciences, and engineering. It is often called the bell curve because of its characteristic shape, which is symmetric and bell-shaped.
The mean and the standard deviation are the two factors that define the normal distribution. The mean is the center of the distribution, and the standard deviation measures how much the data varies from the mean. The normal distribution has several important properties, including that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
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f (x) = ¹4 - 6. Find the inverse of f(x) and its domain.
O A. f¹(x) =
6 + 4, where x #-6
O B. f¹(x) =
6 +4, where x #4
O c. f¹(x) =
¹6-4, where x 4
OD. f¹(x) = 2¹6-4, where x#-6
The correct option is the first one, and the domain is the set of real numbers except for x = -6.
How to find the inverse?The inverse will be a function such that when we take the composition we get the identity, then we can write:
[tex]f(g(x)) = \frac{1}{g(x) - 4} - 6 = x[/tex]
We need to solve that for g(x), we will get:
[tex]\frac{1}{g(x) - 4} - 6 = x\\\\\frac{1}{g(x) - 4} = x +6\\\\g(x) - 4 = \frac{1}{x + 6} \\g(x) = \frac{1}{x + 6} + 4[/tex]
That is the inverse function, and notice that if x = -6 the denominator becomes zero, so that value is not in the domain.
Then the correct option is the first one.
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