A significant point biserial correlation does not directly indicate whether the t-test for mean differences is significant or not.
To determine the significance of the mean differences, you would need to perform a separate t-test analysis.
Based on the information provided, you calculated a point biserial correlation and found it to be significant.
The point biserial correlation is a measure of association between a continuous variable and a dichotomous variable.
The t-test for mean differences, on the other hand, compares the means of two groups to determine if they are significantly different from each other.
Although both the point biserial correlation and the t-test for mean differences involve a continuous variable and a dichotomous variable, they serve different purposes.
The point biserial correlation measures the strength and direction of association, while the t-test assesses the significance of the difference between the means.
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Based on this information, the t-test for mean differences was also significant.
Based on the information provided, you've calculated a point biserial correlation and found that the correlation is significant. To determine if the t-test for mean differences was significant, follow these steps:
1. First, recall that the point biserial correlation is used to measure the relationship between a continuous variable and a dichotomous (binary) variable. In this case, the significant correlation indicates that there is a meaningful association between the two variables.
2. Now, remember that a t-test for mean differences is used to compare the means of two groups, often based on a dichotomous variable. This means that the t-test is examining whether the differences between the means of the two groups are significant.
3. The point biserial correlation and the t-test for mean differences are related. Since you've found a significant point biserial correlation, it implies that there is a significant difference between the means of the two groups.
4. Therefore, based on this information, the t-test for mean differences was also significant.
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Lauren gets a 12% commission for every piece of jewelry she sells. How much will she earn if she sells a $3,200 bracelet?
Answer:
$384
Step-by-step explanation:
$3,200 x 0.12 = $384
Help with algebra 2 homework
The formula for the volume of an sphere of radius r is given as follows:
V = (2/3)πr³
The radius as a function of the volume is obtained as follows:
r³ = 3V/2π
[tex]r = \sqrt[3]{\frac{3V}{2\pi}}[/tex]
Hence the radius of a sphere of volume 25 in³ is given as follows:
[tex]r = \sqrt[3]{\frac{25}{2\pi}}[/tex]
r = 2.29 in.
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Find the area of the parallelogram 13cm 13cm 16cm
angle opposite 16 = [tex]sin-1(\sqrt(1 - cos2(angle opposite 16))[/tex] angle opposite 16 = [tex]sin-1(\sqrt(1 - (-0.442)2)[/tex]angle opposite 16 = 118.7 degrees
What is parallelograms?In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of parallel sides. A parallelogram is a kind of quadrilateral in which both sets of opposite sides are parallel and equal. Parallelograms are classified into four types, three of which are unique. The four distinct shapes are parallelograms, squares, rectangles, and rhombuses. A quadrilateral is a parallelogram when it has two sets of parallel sides. The opposing sides and angles of a parallelogram are both the same length. The internal angles on the same side of the horizontal line are also angles. The total number of internal angles is 360.
To calculate the area of a parallelogram, multiply the base by the height. Nevertheless, the height is not mentioned in this situation. Alternatively, we may use the following formula to calculate the area of a parallelogram:
The area is defined as follows: base x height x sin (angle between base and height)
[tex]16^2 = 13^2 + 13^2 - 2(13)(13) (13)[/tex]
cos(opposite angle 16) 256 = 338 − 338
cos(opposite angle 16) cos(opposite angle 16) = -0.442
We know the angle is between 90 and 180 degrees since the cosine is negative. To get the angle in that range, we may use the inverse sine function:
angle opposite 16 = [tex]sin-1(\sqrt(1 - cos2(angle opposite 16))[/tex] angle opposite 16 = [tex]sin-1(\sqrt(1 - (-0.442)2)[/tex]angle opposite 16 = 118.7 degrees
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Find the volume of this object.
Use 3 for T.
Volume of a Cylinder
V= πr²h
12 in
14 in
12 in
V [?]cm
4 in
Enter
3
please help
Answer:
First, we need to convert all the measurements to the same unit. Let's convert everything to inches, since the formula for the volume of a cylinder uses inches:
12 in = 12 in
14 in = 14 in
12 in = 12 in
4 in = 4 in
The object consists of a cylinder with a radius of 4 inches and a height of 12 inches, and a hemisphere with a radius of 4 inches. To find the volume of the object, we need to find the volume of the cylinder and the hemisphere, and then add them together.
Volume of the cylinder:
V_cyl = πr^2h
V_cyl = π(4 in)^2(12 in)
V_cyl = 192π in^3
Volume of the hemisphere:
The volume of a hemisphere is given by:
V_hemi = (2/3)πr^3
Since the radius is 4 inches, we have:
V_hemi = (2/3)π(4 in)^3
V_hemi = (2/3)π(64 in^3)
V_hemi = 128π/3 in^3
Total volume:
V_total = V_cyl + V_hemi
V_total = 192π in^3 + 128π/3 in^3
V_total = (576π + 128π)/3 in^3
V_total = 704π/3 in^3
Now we can substitute the value of π (3) to get the final answer:
V_total = 704π/3 in^3
V_total = 704(3)/3 in^3
V_total = 704 in^3
Therefore, the volume of the object is 704 cubic inches.
When Ranim started karate, her highest kick went
11
0
∘
110
∘
110, degrees from the ground. Her instructor asked her to practice until her highest kick goes
15
5
∘
155
∘
155, degrees from the ground. Which equation will tell us the measure of the additional angle,
a
aa, that Ranim's kick needs to go to reach
15
5
∘
155
∘
155, degrees from the ground?
Choose 1 answer:
The equation that will tell us measure of additional angle, a, that Ranim's kick needs to go to reach 155 degrees from the ground is given option 155 - 110 = a.
Highest kick went when Ranim started karate from the ground is
= 110 degrees
Highest kick limit given by instructor from the ground = 155 degrees
This equation represents the difference between the final desired angle of 155 degrees and the initial angle of 110 degrees.
Which Ranim's kick went when she started karate.
The result of this subtraction will give us the measure of the additional angle, a.
That Ranim needs to add to her kick to reach the new desired angle.
Therefore, equation representing the measure of the additional angle a, of Ranim karate kick is equal to 155 - 110 = a.
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The above question is incomplete, the complete question is:
When Ranim started karate, her highest kick went 110 degrees from the ground. Her instructor asked her to practice until her highest kick goes 155 degrees from the ground. Which equation will tell us the measure of the additional angle, a, that Ranim's kick needs to go to reach 155 degrees from the ground?
155−110=a
155+110=a
180−110=a
155+90=a
How many times do the graphs of the equations y = 2x + 4 and y = −x + 4 intersect?
Answer: They both intersect once.
Step-by-step explanation: Solving for x, we get:
3x = 0
x = 0
Now we can substitute x = 0 into either equation to find the y-coordinate:
y = 2(0) + 4 = 4
So the two lines intersect at the point (0,4).
Therefore, the graphs of the equations y = 2x + 4 and y = −x + 4 intersect once.
Answer:
It intersects once.
Step-by-step explanation:
To plot y = 2x + 4, you start at the y-intercept which is 4. Then you go up 2 times, and to the right once.
To plot y = -x + 4, you start at the y-intercept which is also at 4. Then you go down once and to the right one time.
The graph will intersect at (0, 4).
I NEED HELP ON THIS ASAP! I JUST NEED HELP WITH THE QUESTION BELOW THE TABLE
All of these ratios are equal to b, and we have shown that there is a constant ratio between consecutive output values.
What is ratio between consecutive output?The common ratio is the ratio that remains constant between successive function output values. The behaviour of a geometric sequence, which is a series of numbers where each term is produced by multiplying the one before it by a set number (the common ratio), depends on the common ratio. The sequence is rising exponentially if the common ratio is bigger than 1. The sequence decreases exponentially if the common ratio is between 0 and 1.
To show that the function form shows a constant ratio we take:
[tex](x+1) / f(x) = (ab^{(x+1)}) / (ab^x) = b[/tex]
Similarly, we have:
[tex]f(x+2) / f(x+1) = (ab^{(x+2)}) / (ab^{(x+1)}) = b[/tex]
Hence, all of these ratios are equal to b, and we have shown that there is a constant ratio between consecutive output values.
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Chester worked for 8hour each day for 5days.He earned P2190.00.How much did he earn per hour?
Answer:
P54.75 per hour.
Step-by-step explanation:
If he earned 2190 pesos on working 8 hours each for 5 days then he earned 54.75
Equation: hours x days / earnings
Therefore, 8 hours x 5 days = 40
2190 / 40 = P54.75 / hour
The points (2, −4) and (2, 7) are on a
coordinate plane. What is the distance
between the points?
The distance between the points (2, -4) and (2, 7) is 11 units.
What is distance?
In mathematics, the distance between two points is a numerical value that represents the amount of space between them. The distance between two points is calculated using the Pythagorean theorem, which applies to any two points in a two-dimensional or three-dimensional space.
The two points have the same x-coordinate of 2, so they lie on a vertical line. To find the distance between them, we need to find the difference between their y-coordinates.
The y-coordinate of the first point is -4 and the y-coordinate of the second point is 7. Therefore, the difference between the y-coordinates is:
7 - (-4) = 7 + 4 = 11
So the distance between the two points is 11 units.
Therefore, the distance between the points (2, -4) and (2, 7) is 11 units.
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explain how to do this, please!
The solution to the system of inequalities is given by the image presented at the end of the answer.
One point on the solution set is given as follows:
(-9,3).
What is a system of inequalities?A system of inequalities is a set of two or more inequalities involving one or more variables. In a system of inequalities, the solution is a set of values for the variables that satisfy all of the given inequalities simultaneously.
The solution is the shaded region on the graph given by the image presented at the end of the answer.
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what is the probability that the larger of two continuous i.i.d. random variable will exceed the population median? stackage
The probability that the greater of the two random variables will surpass the population median is just 0.5 because both events are mutually exclusive.
The i.i.d means two random variable where there is an equal chance that one will be greater then the other.
So, it means there is 50% chances for both of them to be greater then the median.
The probability that the greater of the two random variables will surpass the population median is just 0.5 because both events are mutually exclusive. This conclusion is valid as long as the variable are given to be continuous and i.i.d.
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PLEASE HELP ME IM NOT GOOD AT MATH AND don’t understand!!
The total volume of the cylindrical can is given as follows:
C) 24.54 in³.
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The parameters for this problem are given as follows:
h = 5 in.r = 1.25 in.Hence the volume of the cylinder is obtained as follows:
V = π x 1.25² x 5
V = 24.54 in³.
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If the sum of zeroes of polynomial px^2 + 5x + 8p is equal to the product of zeroes , find the value of p
The value of p would be could be approximately -0.391 or 0.321.
Let's start by using the quadratic formula to find the roots of the polynomial [tex]px^2 + 5x + 8p[/tex]
[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]
Plugging in the coefficients, we get:
[tex]x = (-5 ± √(5^2 - 4p(8p))) / 2p[/tex]
Simplifying, we get:
[tex]x = (-5 ± √(25 - 32p^2)) / 2p[/tex]
Now, we know that the sum of the roots is equal to -b/a, and the product of the roots is equal to c/a. So:
Sum of roots = [tex](-5 + √(25 - 32p^2)) / 2p + (-5 - √(25 - 32p^2)) / 2p = -5/p[/tex]
Product of roots = [tex][(-5 + √(25 - 32p^2)) / 2p] * [(-5 - √(25 - 32p^2)) / 2p] = (25 - 32p^2) / 4p^2[/tex]
Since we're given that the sum of the roots is equal to the product of the roots, we can set these expressions equal to each other and solve for p:
[tex]-5/p = (25 - 32p^2) / 4p^2[/tex]
Multiplying both sides by 4p^2 gives:
[tex]-20p = 25 - 32p^2[/tex]
Adding [tex]32p^2[/tex] to both sides and rearranging, we get:
[tex]32p^2 + 20p - 25 = 0[/tex]
Now we can use the quadratic formula again to solve for p:
[tex]p = (-b ± √(b^2 - 4ac)) / 2a[/tex]
Plugging in the coefficients, we get:
[tex]p = (-20 ± √(20^2 - 4(32)(-25))) / 2(32)[/tex]
Simplifying, we get:
[tex]p = (-20 ± √1560) / 64[/tex]
p ≈ -0.391 or p ≈ 0.321
Therefore, the value of p could be approximately -0.391 or approximately 0.321.
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Jose is wrapping a stack of 100 coins in a paper holder. Each coin is 18
inch thick and has a diameter of
1 inch. How many square inches of paper will Jose need to cover the stack of coins?
Jose needs 61.23 square inches of paper to cover the stack of coins.
How many square inches of paper will Jose need to cover the stack of coins?The total thickness of the stack of 100 coins is 100 x 0.18 = 18 inches. The diameter of each coin is 1 inch, so the radius of each coin is 0.5 inches.
To find the amount of paper needed to cover the stack of coins, we need to calculate the total surface area of the stack.
The area of each circle is given by:
πr^2 where r is the radius of the coin.
The area of the top and bottom circles is:
2 x π x (0.5)^2 = 0.5π
The circumference of the circle is given by:
2πr
So, the circumference of each coin is:
2π(0.5) = π
The height of the stack is 18 inches, so the area of the curved surface is:
π x 18 = 18π
Therefore, the total surface area of the stack is:
1.5π + 18π = 19.5π
To cover the stack of coins with paper, Jose will need 19.5π square inches of paper.
19.5π ≈ 19.5 x 3.14 ≈ 61.23 square inches.
Therefore, Jose will need approximately 61.23 square inches of paper to cover the stack of coins.
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A factory has 2 x 10^3 workers who make a total of 7 x 10^6 bikes each year. How many bikes does each worker make per year?
Answer:
7,000,000÷2000
= 3,500
Step-by-step explanation:
therefore, each worker makes 3500 bikes per year
Habib drew a new diagram that has an area of [tex]6+4s^2[/tex].
What is the area of Habib's diagram when [tex]s=1/2[/tex]?
The area of Habib's diagram when s = 1/2 is 7.
What is circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.
To find the area of Habib's diagram when s = 1/2, we just need to substitute s = 1/2 into the expression for the area:
Area = 6 + 4s²
Area = 6 + 4(1/2)²
Area = 6 + 4(1/4)
Area = 6 + 1
Area = 7
Therefore, the area of Habib's diagram when s = 1/2 is 7.
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Solve for s.
q+1+s=P
Answer:
s = p - q - 1
Step-by-step explanation:
q + 1 + s = p Subtract q and 1 from both sides
q -q +1 - 1 + s = p - q -1
s = p - q - 1
Helping in the name of Jesus.
Using Trig to find a side.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 9.0
Step-by-step explanation:
sin E = CD/EC = CD/x
<=> sin 50 = 6.9/x <=> x = 6.9/sin 50 ≅ 9.0
What is the measure of angle A in this triangle?
Answer:
The Answer is 40°
Step-by-step explanation:
Base angles of an isosceles triangle are equal
x+30=70
x=70-30
x=40°
so,
<C=70°
<A+<B+<C=180°
let <A be X
X+70+70=180°
X+140=180°
X=180-140
X=40°
X=2x-10
40°=2x-10
2x=40+10
2x=50°
divide both sides by 2
x=25°
do less republicans (group a) than democrats (group b) favor the government investing billions of dollars to improve the country's train system? one thousand republicans and one thousand democrats were asked if they favored spending billions to improve the country's train system. how would we write the alternative hypothesis?
The alternative hypothesis can be written as H₁: pA < pB.
The alternative hypothesis would be that there is a difference in the proportion of Republicans (Group A) and Democrats (Group B) who favor the government investing billions of dollars to improve the country's train system. Expressly, it would state that the proportion of Republicans who favor this investment is less than the proportion of Democrats who favor it:
H₁: pA < pB
where pA denotes the proportion of Republicans who favor the investment and pB denotes the proportion of Democrats who favor the investment.
In the alternative hypothesis, we actually create the relationship between the variables which are being tested in that situation. According to these, we come across the comparison among the variables and how much they differ from each other. The alternative hypothesis is the statement the researcher tries to prove by conducting a statistical analysis.
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The value of a new 2022 Jeep Wrangler Rubicon was $67,035 when it went on the market. The value of the car depreciates at a rate of 9.7% per year. Which function models the car's value, V, t years since 2022?
If the value of the 2022 Jeep Wrangler Rubicon depreciates at a rate of 9.7% per year, then its value after t years can be modeled by:
V(t) = 67,035(1 - 0.097)^t
Simplifying the right side:
V(t) = 67,035(0.903)^t
Therefore, the function that models the car's value, V, t years since 2022 is V(t) = 67,035(0.903)^t.
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
· Find the surface area of a cone with a slant height of 8 cm and a radius of 3 cm. SA = B + πrS = (πr2) + πrs = (π(32)) + π(3)(8) = 9π + 24π = 33πcm2 = 103.62cm2. Find the surface area of a rectangular pyramid with a slant height of 10 yards, a base width (b) of 8 yards and a base length (h) of 12 yards.
ASAP please someone help me do a two column proof. I don’t get it
It should be noted that to prove that arc AB is equal to arc CD, we can use the fact that vertical angles are equal. Specifically, the angles formed by radii OA and OB are vertical angles with angles formed by radii OC and OD.
How to explain the proofingLet's call the angle formed by radii OA and OB angle x, and the angle formed by radii OC and OD angle y. Since ZAOB is a central angle of circle O, we know that arc AB is equal to twice angle x. Similarly, since COD is a central angle of circle O, we know that arc CD is equal to twice angle y.
Now, since angles x and y are vertical angles, they are equal. Therefore, arc AB is equal to twice angle x, which is equal to twice angle y, which in turn is equal to arc CD.
Therefore, we have proven that arc AB is equal to arc CD.
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Assuming line ABCD is a diameter. The proof is not valid in general for any chord.
What is circle theorem?To prove AB = CD, we show triangles ABO and DCO are congruent.
1. OB=OC radius of inner circle
2. OA=OD radius of outer circle
3. angle ABO = angle DCO
4. SSA = SSA indicates congruent triangles
Therefore AB = CD
Angles ABC and DCB are straight angles.
Angles OBC and OCB are congruent triangle OBC is isosceles with OB=OC
Therefore angle ABO = ABC - OBC = DCB - OCB = DCO
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Write the point-slope form of the equation of the horizontal line that passes through the point (2, 1). Include your work in your final answer. Type your answer in the box provided to submit your solution.
Therefore , the solution of the given problem of equation comes out to be y = 1 is the equation for the horizontal line.
What is quadratic equation?For one-variable problems, regression modelling employs the polynomial solution answers x = ax2 + b + c=0. There is only room for one solution, according to the Fundamental Principle of Algebra, because it has an additional order. Both straightforward and intricate solutions are accessible. A "non-linear algorithm" has four variables, as the name implies. This suggests that there might be a single squared word.
Here,
=> y = k, where k is the y-coordinate of any point on the horizontal line, is the equation of a horizontal line in the point-slope form.
The y-coordinate of the given point (2, 1) will be the same as the y-coordinate of any other point on the line because
the given line is horizontal and passes through that location.
Therefore, the equation of the horizontal line going through the point (2, 1) has the following point-slope form:
=> y - 1 = 0
or merely:
=> y = 1
Consequently, y = 1 is the equation for the horizontal line.
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Callie owns a business and wants to know if the majority of her customers are satisfied. She surveys a random sample of 25 customers, and 17 customers report being satisfied. In a second random sample of 25 customers, 12 customers report being satisfied. The results of the third and fourth surveys of random samples of 25 customers finds 14 and 9 satisfied customers, respectively. Which statement BEST describes the sample mean absolute deviation for this data set?
Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.
To calculate the mean absolute deviation (MAD), we first need to find the mean of each sample.
Sample 1:[tex]17/25 = 0.68[/tex]
Sample 2: [tex]12/25 = 0.48[/tex]
Sample 3: [tex]14/25 = 0.56[/tex]
Sample 4: [tex]9/25 = 0.36[/tex]
Next, we calculate the deviation of each observation from its respective sample mean:
Sample 1: |0.68 - x1|, |0.68 - x2|, ..., |0.68 - x25|
Sample 2: |0.48 - x1|, |0.48 - x2|, ..., |0.48 - x25|
Sample 3: |0.56 - x1|, |0.56 - x2|, ..., |0.56 - x25|
Sample 4: |0.36 - x1|, |0.36 - x2|, ..., |0.36 - x25|
where xi is the satisfaction rating (0 or 1) of the Ith customer in the sample.
The MAD is the average of these deviations:
MAD = (|0.68 - x1| + |0.68 - x2| + ... + |0.36 - x25|)/100
Since we don't know the actual ratings of the customers, we cannot calculate the MAD exactly. However, we can say that the MAD is likely to be higher for samples 2 and 4, which have lower satisfaction rates, compared to samples 1 and 3, which have higher satisfaction rates. Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.
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suppose coach bennet selects one senior and one junior as the first two players. the coach then randomly selects the third player from either group. taylor and jamie are both juniors on the team. if taylor is selected as one of the first two players, what is the probability that jamie will be selected as the third player? type in the correct answer in the box. use numerals instead of words. if necessary, round your answer to the nearest tenth.
If Taylor is selected as one of the first two players out of ten players on the team, the probability of Jamie being selected as the third player is 4/9.
Using the multiplication rule of probability, the overall probability of both events happening is 8.9%
How to find the probability of Jamie being selected?Assuming that there are only seniors and juniors on the team, the probability of Taylor being selected as one of the first two players is 2/10, since there are two juniors out of ten total players.
If Taylor is selected as one of the first two players, then there are nine players left, of which four are juniors, including Jamie.
Therefore, the probability of Jamie being selected as the third player, given that Taylor is already selected, is 4/9.
Using the multiplication rule of probability, the overall probability of both events happening is:
P(Taylor and Jamie) = P(Taylor) x P (Jamie | Taylor)
P(Taylor and Jamie) = 2/10 x 4/9
P(Taylor and Jamie) = 8/90
P(Taylor and Jamie) = 0.089 or 8.9% (rounded to the nearest tenth)
Therefore, the probability of Jamie being selected as the third player, given that Taylor is already selected as one of the first two players, is 8.9%.
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suppose the customers arrive at a starbucks shop at an average rate of 1/min. use a poisson process to model the arrival of customers. what is the probability that at least one customer arrives at the shop during a one-minute interval? 0.736 0.368 0.632 0.264
The probability that at least one customer arrives at the shop during a one-minute interval is 0.632.
Since the arrival of customers at a Starbucks shop can be modeled as a Poisson process with an average rate of 1/min, the probability of exactly k customers arriving in a one-minute interval is given by the Poisson probability mass function:
P(k arrivals) = (λ^k * e^(-λ)) / k!
where λ is the average rate of arrivals (in this case, 1/min), e is the mathematical constant e, and k! is the factorial of k.
To find the probability that at least one customer arrives during a one-minute interval, we can use the complement of the probability that zero customers arrive (i.e., the probability of at least one arrival is 1 minus the probability of zero arrivals).
Thus, the probability of at least one customer arriving during a one-minute interval is:
P(at least one arrival) = 1 - P(0 arrivals)
P(at least one arrival) = 1 - [([tex]1^{0}[/tex] * [tex]e^{-1}[/tex]) / 0!] = 1 - [tex]e^{-1}[/tex] = 0.632
Therefore, the probability that at least one customer arrives at the shop during a one-minute interval is 0.632.
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please help me…i’ll give brainliest
The cone have measures for the base, lateral, and surface areas as 77.6 mm², 330 mm², and 408.6 mm² respectively.
How to evaluate for the areas of the coneThe formula for the surface area of a cone is:
A = πr² + πrs
Where: A = surface area r = radius of the base s = slant height of the cone
Base area = 22/7 × 5 mm × 5 mm
Base area = 78.6 mm²
Lateral area = 22/7 × 5 mm × 21 mm
Lateral area = 330 mm³
Surface area = 78.6 mm + 339 mm²
Surface area = 408.6 mm²
Therefore, the cone have measures for the base, lateral, and surface areas as 77.6 mm², 330 mm², and 408.6 mm² respectively.
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If x - 2 is a factor polynomial f(x), which of the following statements does NOT have to be true?
Answer:
b)
Step-by-step explanation:
If x - 2 is a factor polynomial f(x), then the polynomial can be expressed as f(x) = (x - 2) g(x), where g(x) is another polynomial.
Using this information, we can check each statement to see which one does NOT have to be true:
A) f(2) = 0:
If x - 2 is a factor of f(x), then plugging in x = 2 gives f(2) = (2 - 2) g(2) = 0. This statement has to be true.
B) f(-2) = 0:
If x - 2 is a factor of f(x), then plugging in x = -2 gives f(-2) = (-2 - 2) g(-2) = -4 g(-2). This statement does NOT have to be true. For example, if g(-2) = 1/(-4), then f(-2) would not equal 0.
C) 2 is a root of f(x):
If x - 2 is a factor of f(x), then 2 is a root of f(x), meaning f(2) = 0. This statement has to be true.
D) 2 is a zero of f(x):
The term "zero" can be interpreted in different ways, but if it means the same as a root or a solution, then this statement is the same as statement C and has to be true.
Therefore, the statement that does NOT have to be true is B) f(-2) = 0.
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used. 6 one sixth 3 one third
The scale factor used for the dilation of the triangle ABC to A'B'C' is 3.
To find the scale factor, we can compare the corresponding side lengths of the two triangles. Let's start by finding the length of side AB in both triangles.
Length of AB in the original triangle ABC:
AB = √[(3-(-3))² + (3-(-3))²]
= √[6² + 6²]
= 6√(2)
Length of A'B' in the dilated triangle A'B'C':
A'B' = √[(9-(-9))²+(9-(-9))²]
= √[18² + 18²]
= 18√(2)
Now we can find the scale factor by dividing the length of A'B' by the length of AB:
scale factor = A'B'/AB
= (18√(2))/(6√(2))
= 3
Therefore, the scale factor used is 3. The dilation has enlarged the triangle by a factor of 3.
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