The trigonometric ratios of sine, cosine, and tangent can be used to find the lengths of the sides of the triangle.
How do you solve the right triangles?A right triangle has one angle that measures exactly 90 degrees. Identify this angle in the triangle.
Label the sides of the triangle as the hypotenuse, adjacent, and opposite sides, relative to one of the non-right angles. The hypotenuse is always the side opposite the right angle.
We know that;
Tan 45 = 5.9/w
w = 5.9/Tan45
w = 5.9
Then;
Tan 35 = 5.9/w + x
0.7 = 5.9/5.9 + x
0.7(5.9 + x) = 5.9
4.13 + 0.7x = 5.9
x = 2.5
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one of the most notable intellectual achievements of the maya was their use of what mathematical concept? multiplication the zero decimal system a calendar
One of the most notable intellectual achievements of the Maya civilization was their use of the mathematical concept known as the zero decimal system.
The Maya developed a sophisticated numerical system that allowed them to perform complex calculations, which was essential for their advancements in various fields such as astronomy, agriculture, and architecture.
The zero decimal system used by the Maya was a base-20 (vigesimal) system that incorporated the concept of zero as a placeholder. This was a significant breakthrough in mathematics, as it enabled the Maya to perform complex calculations and record large numbers more efficiently.
Here's a step-by-step explanation of how the Maya zero decimal system worked:
1. The Maya used a combination of dots and bars to represent numbers. A dot represented the number 1, and a bar represented the number 5.
2. Numbers from 1 to 19 were written using a combination of dots and bars. For example, the number 7 would be represented as one bar (5) and two dots (1 + 1).
3. To represent the number zero, the Maya used a unique symbol called a shell glyph.
4. The Maya zero decimal system was positional, meaning that the value of a digit depended on its position within a number. For example, in the number 24, the digit 2 is in the 20s position, and the digit 4 is in the ones position.
5. To write numbers larger than 19, the Maya used a vertical arrangement of glyphs, with the ones at the bottom, the 20s above them, the 400s above that, and so on.
The use of the zero decimal system allowed the Maya to excel in various fields, such as creating an accurate calendar system, predicting celestial events, and planning agricultural activities. This mathematical achievement is a testament to the advanced intellectual capabilities of the Maya civilization.
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Katie is a surveyor for an engineering firm. Her firm was hired to determine the slope of the lot before construction of a new building could begin.
What is the slope of the lot?
Round to the nearest hundredth.
The calculated slope of the lot is 25/cos(angle)
from the question, we have the following parameters that can be used in our computation:
The figure
The slope of the lot is the length of the hypotenuse
So, we have
cos(angle) = 25/slope
This gives
slope = 25/cos(angle)
Hence, the slope is 25/cos(angle)
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A circular spinner from a board game is divided into 8 equal sections. What is the measure of the inner angle (with the vertex at the spinner) of one of the sections?
Answer: Three of eight sectors do not move the token; this area is 35.9 in2.
To find the radius of the spinner: A = pi · r2
35.9 = (3/8) · pi · r2
35.9 = 1.1781 · r2
30.73 = r2
r = 5.5 in
Step-by-step explanation:
if zeros are reciprocal of each other then find k. (1-3k)x2 +4x-5
Answer: Let's assume that the zeros of the given quadratic equation are a and 1/a, since they are reciprocals of each other. By the sum-product relationships for zeros of a quadratic equation, we have:
a + 1/a = -b/a1 = -4/(1-3k) (where b = 4 and a1 = 1-3k)
Multiplying both sides by a1, we get:
a1(a + 1/a) = -4
Expanding the left-hand side, we get:
a1a + a1/a = -4
Multiplying both sides by a, we get:
a1a² + a1 = -4a
Substituting a1 = 1-3k, we get:
(1-3k)a² + (1-3k) = -4a
Rearranging, we get:
(1-3k)a² + 4a + (3k-1) = 0
Since a is one of the zeros of the quadratic, we know that the quadratic can be factored as:
(1-3k)(a - r)(a - s) = 0
where r and s are the other two roots of the quadratic. By expanding the left-hand side, we get:
(1-3k)(a² - (r+s)a + rs) = 0
Comparing with the expanded form of the quadratic, we see that:
r + s = -4/(1-3k)
rs = (3k-1)/(1-3k)
By Vieta's formulas, we know that rs = c/a1, where c is the constant term of the quadratic. Substituting c = -5 and a1 = 1-3k, we get:
rs = -5/(1-3k)
Equating this with the expression we obtained earlier for rs, we get:
-5/(1-3k) = (3k-1)/(1-3k)
Multiplying both sides by 1-3k and simplifying, we get:
-5 = (3k-1)(3k-2)
Expanding the right-hand side, we get:
-5 = 9k² - 15k + 2
Simplifying, we get:
9k² - 15k - 7 = 0
Using the quadratic formula, we get:
k = (15 ± sqrt(15² + 497))/18
k = (15 ± sqrt(429))/18
Therefore, the two possible values of k are:
k = (15 + sqrt(429))/18 ≈ 1.57
k = (15 - sqrt(429))/18 ≈ -0.24
Note that both of these values of k satisfy the condition that the zeros of the quadratic are reciprocals of each other.
Step-by-step explanation:
a researcher conducting a qualitative study knows that saturation of information has occurred when group of answer choices data collected confirms theoretical models additional sampling reveals redundant information subjects participating are representative of the general population the desired sample size has been reached flag question: question 44
The most relevant answer to this question is researcher conducting a qualitative study knows that saturation of information has occurred when data collected confirms theoretical models.
In qualitative research, data saturation refers to when the collection of new data no longer leads to additional ideas or themes.
In other words, saturation occurs when data has been thoroughly explored and little or no new information or new patterns emerge.
so, the researcher can be sure that he or she has collected enough data to answer the research question, and collecting more data is unlikely for new insights.
Therefore, Using the data provided, we can calculate:
x = (38.1 + 38.4 + 38.3 + 38.2 + 38.2 + 37.9 + 38.7 + 38.6 + 38.0 + 38.2) / 10 = 38.25
In a t distribution table or calculator, find the t value with 9 (n-1) degrees of freedom and 95% confidence intervals. This is approximately 2.262.
Substituting these values into the formula gives:
therefore, the most relevant answer to this is data collected confirms theoretical models.
This means that the researcher has collected enough data to confirm or disprove their original theoretical models, and collecting more data is unlikely to change those models.
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Please help with this ASAP
Answer:
The second one is correct
Step-by-step explanation:
1. Replace x in the equation with the given x (from the table):
y = 2x - 3
x = -1, y = 2 × (-1) - 3 = -2 - 3 = -5
x = 0, y = 2 × 0 - 3 = 0 - 3 = -3
x = 1, y = 2 × 1 - 3 = 2 - 3 = -1
x = 2, y = 2 × 2 - 3 = 4 - 3 = 1
x = 3, y = 2 × 3 - 3 = 6 - 3 = 3
.
2. y = -x + 6
x = -1, y = -(-1) + 6 = 1 + 6 = 7
x = 0, y = -0 + 6 = 6
x = 1, y = -1 + 6 = 5
x = 2, y = -2 + 6 = 4
x = 3, y = -3 + 6 = 3
) What is the area of this figure?
7 yd
4 yd
5 yd
6 yd
8 yd
2 yd
2 yd
6 yd
According to the information, the area of the irregular octagon is approximately 111.8 square yards.
How to calculate the area of the figure?To find the area of a figure with 8 sides and given side lengths, we need to first determine what type of figure it is. Based on the side lengths provided, it is not immediately clear what type of figure it is. However, we can calculate the perimeter of the figure to gain some insights.
Perimeter = sum of all the side lengthsPerimeter = 7 yd + 4 yd + 5 yd + 6 yd + 8 yd + 2 yd + 2 yd + 6 ydPerimeter = 40 ydThe perimeter of the figure is 40 yards, which suggests that it might be an octagon (a polygon with 8 sides). To confirm this, we can check if the side lengths satisfy the necessary condition for an octagon, which is that all 8 sides have to be equal or else they should be grouped in pairs of equal lengths. From the given side lengths, we can see that there are no pairs of equal lengths, so it is an irregular octagon.
To find the area of the irregular octagon, we can divide it into smaller shapes such as triangles and rectangles. One way to do this is to draw lines from one vertex to all the other vertices, dividing the octagon into 6 triangles and 2 rectangles. Then we can calculate the area of each individual shape and add them up to get the total area of the octagon.
This process can be tedious and time-consuming, so we can also use a formula to calculate the area of the irregular octagon. One common formula is the Brahmagupta's formula, which states that the area of an irregular quadrilateral (such as an octagon) can be calculated as:
Area = sqrt((s-a)(s-b)(s-c)(s-d) - abcd*cos^2((B+D)/2))where a, b, c, and d are the lengths of the sides, B and D are the opposite angles, and s is the semiperimeter (half the perimeter):
s = (a + b + c + d)/2Using the given side lengths and the formula above, we can calculate the area of the irregular octagon. The calculations can be a bit involved, but using a calculator or spreadsheet can help make it easier.
After plugging in the side lengths and evaluating the formula, we get:
Area ≈ 111.8 square yardsTherefore, the area of the irregular octagon is approximately 111.8 square yards.
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When Zak first planted his flower garden, there were only 5 weeds. Every week, the number of weeds doubles. Assuming he never removes the weeds, when will there first
be 3000 weeds in his garden? (Round your answer to the nearest week)
There will be 3,000 weeds in Zak's garden after
***
A weeks.
which of the fallowing represents a constant from the explosion given ?
The constant in the given expression is
C. 9
What is a constant in a mathematical expression?In a mathematical expression, a constant is a value that does not change and remains the same throughout the expression or equation.
It is a fixed numerical value, coefficient, or term that is independent of the variable(s) in the expression.
For example, in the expression 15x^2 + 2x + 9, the constant is 9, as it remains the same regardless of the value of x.
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What would be the probability Carlos draws a blue marble, does not replace it, and then draws
another blue marble?
7/105
6/225
1/35
2/90
The probability of Carlos drawing a blue marble, not replacing it, and then drawing another blue marble is E. 2/15.
How to calculate the probabilityThe probability of drawing a blue marble on the first draw is 4/10 (since there are 4 blue marbles out of a total of 10 marbles in the bag).
If Carlos does not replace the first blue marble, then there will be 9 marbles left in the bag, of which 3 will be blue. So the probability of drawing another blue marble on the second draw is 3/9.
To find the probability of both events occurring, we multiply the probabilities together:
Probability of drawing a blue marble on the first draw: 4/10
Probability of drawing a blue marble on the second draw, given that the first draw was blue: 3/9
Probability of drawing two blue marbles in a row: (4/10) * (3/9) = 2/15, or approximately 0.133.
Therefore, the probability of Carlos drawing a blue marble, not replacing it, and then drawing another blue marble is approximately 0.133.
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A bag has 6 red and 4 blue marbles. What is the probability Carlos draws a blue marble, does not replace it, and then draws another blue marble?
7/105
6/225
1/35
2/90
2/15
I need to show my work please help me
The value of angle RTS is determined as 75⁰.
What is the value of angle RTS?The value of angle RTS depends on the value of the arc angle SR.
The value of arc angle SR is calculated by finding the value of x, and we will have the following equation.
38x - 2 + 18x - 2 + 34x + 4 = 360 (sum of angles in a circle)
90x = 360
x = 360/90
x = 4
The value of arc angle SR = 38x - 2
= 38(4) - 2
= 150⁰
The value of angle RTS is equal to half of arc angle SR (based on intersecting chord theorem)
∠RTS = ¹/₂ x 150⁰
∠RTS = 75⁰
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(01.08 mc) when a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic pressure, s(t), can be measured by the following piecewise defined function: where t is the time, in hours, since taking the medication. based on the graph of the piecewise function, if the patient takes the blood pressure medication at 8 a.m., in which interval will their systolic pressure be lowest?
The patient's systolic pressure will be the lowest during the time interval 5 < t < 8, when they take the medication at 9 a.m.
The given piecewise function for systolic pressure S(t) has two segments, one for the time interval 5 < t < 8 and another for 8 ≤ t ≤ 12.
For 5 < t < 8, the systolic pressure is a constant value of 115. Therefore, the systolic pressure remains the same during this time interval, and it will not be the lowest.
For 8 ≤ t ≤ 12, the systolic pressure increases linearly with time, starting from 140 and increasing by 9 units every hour. Therefore, the systolic pressure at the beginning of this interval is 140, and it increases until it reaches the maximum value of 211 at t=12.
Since the systolic pressure is highest at the end of the second interval, the lowest value of the systolic pressure must occur in the first interval, which is 5 < t < 8. Therefore, the patient's systolic pressure will be lowest during this time interval, and it will be a constant value of 115.
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The given question is incomplete, the complete question is:
When a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic pressure, S(t), can be (140-5tif Osts 5 measured by the following piecewise defined function: S(t) = 115 if 5<t<8 - where t is the time, in hours, since 43 +9t if 8sts 12 taking the medication. Based on the graph of the piecewise function, if the patient takes the blood pressure medication at 9 a.m., in which interval will their systolic pressure be lowest?
what is the perimeter of the garden?
D) 20 ft.
If the area of a square garden is 25 square feet, it means that the length of each side of the square is the square root of 25, which is 5 feet.
To find the perimeter of the square garden, we need to add up the lengths of all four sides. Since all sides of a square are equal, we can simply multiply the length of one side by 4 to get the perimeter.
Perimeter = 4 x length of one side
Perimeter = 4 x 5 ft
Perimeter = 20 ft
Therefore, the perimeter of the square garden is 20 feet.
Can a non-complex equation have 2 horizontal asymptotes? Excluding piecewise equations, o course. Also, what about 2 vertical asymptotes? And using a complex number as x could an equation pass the vertical asymptote? What about the horizontal one?
The answer of the given question is , part 1 - No, a non-complex equation cannot have two horizontal asymptotes , part 2- a non-complex equation cannot have two vertical asymptotes , part 3- vertical behavior does not apply to complex numbers.
What is Horizontal asymptotes?A horizontal asymptote is horizontal line that function approaches as x goes to positive or negative infinity. In other words, it describes the long-term behavior of the function as x gets very large or very small.
For a function f(x), if the values of f(x) get closer and closer to a specific number L as x approaches infinity or negative infinity, then the line y = L is a horizontal asymptote of the function.
No, a non-complex equation cannot have two horizontal asymptotes. A horizontal asymptote represents the behavior of a function as x approaches positive or negative infinity, and it is determined by the highest power of x in the denominator and numerator of the function. A non-complex equation can only have one horizontal asymptote, which can be a horizontal line or a slant asymptote.
Similarly, a non-complex equation cannot have two vertical asymptotes. A vertical asymptote occurs when the denominator of a function approaches zero and the numerator does not. A non-complex equation can have multiple vertical asymptotes, but they must be distinct values of x.
If a complex number is used as x, an equation could pass through a vertical asymptote because the notion of vertical behavior does not apply to complex numbers. However, the concept of horizontal asymptotes still applies to complex numbers, and an equation cannot have two horizontal asymptotes in the complex plane.
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Twelve squares are placed in a row forming the grid below. Each square is to be filled with an integer. After the third square, each integer in a square is the sum of the previous three integers. If we know the third integer is 6, the sixth integer is 11, and the eleventh integer is 14, determine all of the integers in the grid.
The integers in the grid are 1, 2, 6, 45, 53, 11, 109, 169, 322, 600, 14, and 1042.
We can start by filling in the third, sixth, and eleventh squares with the given values:
_ _ 6 _ _ 11 _ _ _ _ 14 _
Now we can use the rule that each integer is the sum of the previous three integers to fill in the rest of the grid. We can work from left to right, filling in one square at a time.
For the fourth square, we know that it must be the sum of the first three squares, which are currently unknown. However, we know that the product of the three unknown integers is 84, so we can use this information to find the possible combinations of integers:
1 × 2 × 42
1 × 3 × 28
1 × 4 × 21
1 × 6 × 14
2 × 3 × 14
2 × 4 × 7
3 × 4 × 7
Since the digits are increasing from left to right, the only possible combination is 1, 2, 42. Therefore, the fourth square is 45.
Continuing in this way, we can fill in the rest of the squares:
1 2 6 45 53 11 109 169 322 600 14 1042
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Circle P is shown. What is the area of the sector QPR?
As a result, the sector QPR's area is roughly 60.3 m².
How is area of a sector determined?We must apply the following algorithm to determine the sector QPR's area:
Sector QPR area = θ/360°(r²)
where r is the circle's radius, is a constant equal to roughly 3.14, and is the sector's angle in degrees.
We can substitute these numbers into the calculation and simplify it because the angle in this example is provided as 80 degrees and the radius r as 8 meters:
QPR sector area = (108/360)(8)²
QPR sector area = (0.3)(64)
QPR sector area = 19.2
QPR sector area = 19.2
QPR sector area = 60.318°
As a result, the sector QPR's area is roughly 60.3 m².
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A computer can perform 4.66 x 10^8 instructions per second. How many instructions is that
per hour? Use scientific notation to express this.
Answer asap and show work pls
Thank you
There are 60 seconds in a minute and 60 minutes in an hour. To find the total number of instructions the computer can perform in an hour, we need to multiply the number of instructions per second by the number of seconds in an hour.
Number of seconds in an hour = 60 seconds/minute × 60 minutes/hour = 3600 seconds/hour
Total number of instructions per hour = instructions per second × seconds per hour
= 4.66 × 10^8 instructions/second × 3600 seconds/hour
= 1.6776 × 10^12 instructions/hour
Therefore, the computer can perform 1.6776 x 10^12 instructions per hour.
two cities have the same longitude. the latitude of city a is 6 degrees north and the latitude of city b is 38 degrees north. assume the radius of the earth is 3960 miles. find the distance between the two cities round to the nearest hundredth of a mile
The distance between City A and City B is approximately 2300.55 miles, rounded to the nearest hundredth of a mile.
How we find the distance between City A and City B?Let's assume that City A is at latitude 6 degrees north and City B is at latitude 38 degrees north. Since they have the same longitude, we can assume a longitude of 0 degrees for both cities. We also have the radius of the Earth, which is 3960 miles.
Using the Haversine formula, the distance (d) between the two cities can be calculated as:
d = 2r * arcsin( sqrt( sin²((latB - latA)/2) + cos(latA) * cos(latB) * sin²((lonB - lonA)/2)) )
where r is the radius of the Earth, latA and latB are the latitudes of City A and City B in radians, and lonA and lonB are the longitudes of City A and City B in radians.
Converting the latitudes and longitudes to radians, we get:
latA = 6° * pi / 180 = 0.10472 radians
latB = 38° * pi / 180 = 0.66323 radians
lonA = 0° * pi / 180 = 0 radians
lonB = 0° * pi / 180 = 0 radians
Substituting the values in the formula, we get:
d = 2 * 3960 * arcsin( sqrt( sin²((0.66323 - 0.10472)/2) + cos(0.10472) * cos(0.66323) * sin²((0 - 0)/2)) )
Simplifying the expression, we get:
d ≈ 2300.55 miles
Therefore, the distance between City A and City B is approximately 2300.55 miles, rounded to the nearest hundredth of a mile.
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What is the slope of the line?
100 points!!!
A movie theater charges for a ticket based on the age of the moviegoer. For individuals under the age of 12, the price is $5. For those who are 12 or older, but younger than 55, tickets are $9. A special rate for those 55 and over is available for the scenario.
Write a piecewise function to represent the scenario.
f(x) =
How much would it cost a 16 year-old to see the movie?
How much would it cost at 12 year old to see the movie?
For moviegoers who are younger than 12 years old, the ticket price is a fixed amount of $5. This is represented by the first rule of the piecewise function
f(x) = $5 if x < 12For moviegoers who are 12 years old or older, but younger than 55, the ticket price is also a fixed amount, but this time it is $9. This is represented by the second rule of the piecewise function
$9 if 12 <= x < 55For moviegoers who are 55 years old or older, a special rate is available, and the ticket price is $7. This is represented by the third rule of the piecewise function
$7 if x >= 55So, for a 16 year-old, the ticket price would be $9.
For a 12 year-old, the ticket price would also be $5.
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a cylindrical tank with radius 3 m is being filled with water at a rate of 4 m 3 /min . how fast is the height of the water increasing?
Thus, the height of the water in the tank is increasing at a rate of approximately 4 / (9π) meters per minute
To solve this problem, we need to find the rate at which the height of the water is increasing. Let's call the height of the water in the tank h(t), and the rate at which it is increasing dh/dt. We know that the volume of a cylinder is given by the formula[tex] V = πr^2h[/tex], where V is the volume, r is the radius, and h is the height.
Given information:
- The radius of the cylindrical tank, r, is 3 m.
- The volume of water, V, is being filled at a rate of 4 m^3/min.
We want to find dh/dt. First, we need to find the expression for the volume of the water in the tank with respect to time, V(t):
V(t) = π(3)^2*h(t)
V(t) = 9π*h(t)
Now, we can find the derivative of V(t) with respect to time:
dV/dt = 9π*dh/dt
We know that dV/dt = 4 m^3/min. Therefore:
4 = 9π*dh/dt
Now, we can solve for dh/dt:
dh/dt = 4 / (9π)
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find these degrees
m
m
Answer:
x = 14
Step-by-step explanation:
m∠B and m∠D are congruent angles, which means they are equal in measurement.
We can write the following equation to find the value of x:
5x - 7 = 3x + 21
Transfer like terms to the same side of the equation5x - 3x = 21 + 7
Add/subtract like terms2x = 28
Divide both sides by 2x = 14
To find the measure of m∠B, replace x with 14:
5 × 14 - 7 = 63°
m∠B and m∠C are supplementary angles, so we can find the measure of m∠C using this information:63 + m∠C = 180
Subtract 63 from both sidesm∠C = 117°
A side of the triangle below has been extended to form an exterior of 65. Find the value of x.
Check the picture below.
Enlarge the picture below by a scale factor of 3. What are
the new length and width of this picture?
Use multiplication to enlarge this picture.
7ft
5ft
Therefore , the solution of the given problem of area comes out to be the picture's revised dimensions are 21 feet long and 15 feet wide.
What is scale factor?
A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.
What exactly does an area mean?
Its total size can be determined by figuring out how much area would be required to completely enclose its exterior. When choosing a comparable product for the rectangular design, the surrounding area is taken into account. The total measurements of something are determined by its surface area. The volume of water a cuboid can contain depends on the number in sides between its four trapezoidal shapes.
Here,
The initial image's length and width must be multiplied by 3 in order to enlarge it by a scale factor of 3.
=> 7 feet in length at first.
=> 5 foot original diameter
=> New length = 7ft x 3 = 21ft
=> New width = 5ft x 3 = 15ft
As a result, the picture's revised dimensions are 21 feet long and 15 feet wide.
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Tucker has 122.00 in one,five,ten dollar bills if he has 15 bills in all how many of each bills does he have?
Answer:
Tucker has 2 one-dollar bills, 1 five-dollar bill, and 12 ten-dollar bills.
Step-by-step explanation:
a company has a customer retention rate of 70% per year. it is testing a new customer experience plan. what is the minimum number of customers that need to be included in the test to determine if the new plan has more than a 6 percentage point effect on customer retention, with 90% confidence? use the normal approximation
The minimum number of customers that need to be included in the test is 1492 members to determine if the new plan has more than a 6% point effect on customer retention, with 90% confidence.
The z-score corresponding to the desired confidence level of 90% = 1.645
The retention rate under the old plan = 1-p = = 0.7
The margin of error = E = 6 percentage points = 0.06
To calculate the minimum number of customers needed for the test, we can use the following formula:
[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]
[tex]n = (1.645^2 * p * (1-p)) / 0.06^2[/tex]
assuming that p = 0.5
n = (1.645^2 * 0.5 * (1-0.5)) / 0.06^2
n = 1492
Therefore we can conclude that the minimum number of customers that need to be included in the test is 1492 members.
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suppose set a contains 57 elements and the total number elements in either set a or set b is 136. if the sets a and b have 6 elements in common, how many elements are contained in set b?
The number of the elements which are present in the set B is given by the term 85.
The symbol "" can be used to represent the intersection of sets. According to the definition given above, the intersection of two sets A and B is the collection of all the items that are shared by both sets. The intersection of A and B can be conceptualised as A B.
The largest set containing all the items shared by X and Y is the intersection of two given sets, let's say X and Y. The intersection of two sets can be an empty set, meaning that there are no elements in the intersection set, or it can be a set containing at least one member. If A and B are two sets with the relationship A B =, then A and B are referred to be disjoint sets. Hence, there are no elements at the point where A and B meet.
The set A contains 57 elements so,
n(A) = 57
total number elements in either set A or set B is 136.
n(A ∪ B) = 136
if the sets A and B have 6 elements in common,
n(A ∩ B) = 6
By using the formula for Union and Intersection of Sets,
n (A ∪ B) = n (A) + n (B) – n (A ∩ B)
136 = 57 + n(B) - 6
136 = 51 + n(B)
n(B) = 85.
Therefore, the number of element in B is 85.
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a pearson's correlation of -.65 was found between number of minutes studying for a test and test performance in a sample of 300 students. which of the following conclusions can be drawn from this finding? group of answer choices there was a weak negative relationship between the time spent studying and test performance spending more time studying causes students to perform more poorly. study time accounted for 65% of the variance in test performance on average, students who spent more time studying performed worse on the test
Based on this finding, the following conclusion can be drawn:
On average, students who spent more time studying performed worse on the test.
The correlation coefficient only accounts for the relationship between the two variables and not the variance,
so we cannot say that study time accounted for 65% of the variance in test performance.
From the student question, a Pearson's correlation of -0.65 was found between the number of minutes studying for a test and test performance in a sample of 300 students.
Based on this finding, the following conclusion can be drawn:
On average, students who spent more time studying performed worse on the test.
This is because the Pearson's correlation of -0.65 indicates a moderate negative relationship between study time and test performance.
However, it's important to note that correlation does not imply causation, so we cannot conclude that spending more time studying causes students to perform more poorly.
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Two sides of a triangle are 6 and 18. What is the range of possible third sides?
Answer:24
Step-by-step explanation:
below is some output from the regression on the furniture factory data. what does the r-square value tell us?
The R-square value represents the correct output for the regression models by 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift
The R-square value in regression analysis tells us the proportion of the variability in the response variable.
That can be explained by the regression model.
In this case, the output states that the R-square value is 0.7059.
This means that 70.59% of the variability in the number of chairs produced.
This can be explained by the independent variables in the model which is whether the shift is in the morning or evening and whether it is a weekday or weekend shift.
Therefore, the correct option for the regression model is 'That 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift.'
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The above question is incomplete, the complete question is:
Below is some output from the regression on the furniture factory data. What does the R-square value tell us?
That we cannot reject the null hypothesis
That there is multicollinearity between the independent variables
That on average, 0.7059 more chairs are produced during weekday shifts than during weekend shifts.
That 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift.