Answer: The amount of planes of symmetry a right pyramid with an isosceles triangle base has four.
Hope this helps!
3-10 A gable roof with a slope of 9 inches per foot has a rake slope of 1.25. If the run is 10 feet and the eaves length is 30 feet. What is the roof area in square foot?A. 300.B. 450.C. 700.D. 800.
The roof area is 468.75 square feet.
To find the roof area, we need to follow these steps:
Determine the rise (vertical distance) using the slope of 9 inches per foot:
Since the run is 10 feet, the rise is 9 inches/foot × 10 feet = 90 inches.
Convert the rise to feet: 90 inches ÷ 12 inches/foot = 7.5 feet.
Calculate the length of the rafter using the Pythagorean theorem:
Rafter length = √(run² + rise²) = √(10² + 7.5²) = √(100 + 56.25) = √156.25 = 12.5 feet.
Determine the total length of the gable roof:
Since the rake slope is 1.25, we have Total length = Rafter length × Rake slope = 12.5 feet × 1.25 = 15.625 feet.
Calculate the roof area:
Roof area = Eaves length × Total length = 30 feet × 15.625 feet = 468.75 square feet.
None of the given options matches the calculated roof area.
It is possible there is a mistake in the question or the provided options.
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given the following situation, determine if the data is rank data. a publix manager wants to measure the difference in the total value sales on a saturday vs. a monday. he randomly selects sales data from 20 saturdays and 20 mondays from the previous year and he analyzes his data. is this rank data? group of answer choices not rank data rank data
2.) Let's consider a Stackelberg version of monopolistic competition. Suppose market demand is given by P = 30 – Q and there are ""n"" firms in the market with the first firm denoted as the leader
The specific numerical solution will depend on the number of firms in the market and their behavior.
In a Stackelberg version of monopolistic competition, there is a leader firm that sets its output first, and all the other firms in the market act as followers and choose their outputs simultaneously.
Suppose there are "n" firms in the market, with the first firm denoted as the leader. Let's assume that each firm has a constant marginal cost of $10 per unit. Then, the leader firm's profit-maximizing output level can be found by solving the following problem:
max (30-Q1-Q2-...-Qn)Q1 - 10Q1
subject to Q1 >= 0
where Q1 is the output level of the leader firm, and Q2, Q3, ..., Qn are the output levels of the follower firms.
Taking the first-order condition by differentiating with respect to Q1 and setting it equal to zero, we get:
d/dQ1 [(30-Q1-Q2-...-Qn)Q1 - 10Q1] = 0
Simplifying this expression, we get:
30 - Q1 - Q2 - ... - Qn - 2Q1 = 0
Solving for Q1, we get:
Q1 = (30 - Q2 - ... - Qn)/3
This equation gives us the leader firm's profit-maximizing output level as a function of the follower firms' output levels.
Now, let's consider the follower firms' profit-maximizing output levels. Since each follower firm is a price-taker, its profit-maximizing output level can be found by equating marginal cost to market price, which is equal to the market demand curve divided by the total quantity produced by all firms in the market. Therefore, the profit-maximizing output level of the jth follower firm can be expressed as:
Qj* = (1/n) * (30 - Q1 - Q2 - ... - Qj-1 - Qj+1 - ... - Qn - 10)
where Qj* is the follower firm's profit-maximizing output level, and j = 2, 3, ..., n.
Using these expressions for the leader and follower firms' profit-maximizing output levels, we can solve for the equilibrium outputs and profits in the Stackelberg version of monopolistic competition. However, the specific numerical solution will depend on the number of firms in the market and their behavior.
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Dean loves rocks. Altogether, they have 6 66 pieces of granite, 3 33 pieces of marble, and 14 1414 pieces of sandstone.
What is the ratio of pieces of sandstone to total pieces of rock in Dean's collection?
(Choice A)
9
:
14
9:149, colon, 14
A
9
:
14
9:149, colon, 14
(Choice B)
14
:
9
14:914, colon, 9
B
14
:
9
14:914, colon, 9
(Choice C)
14
:
23
14:2314, colon, 23
C
14
:
23
14:2314, colon, 23
(Choice D)
23
:
14
23:1423, colon, 14
D
23
:
14
23:14
Answer:
a maybe
Step-by-step explanation:
Find the volume of a cylinder with a diameter of 28 meters and a height of 7 and one half meters. Approximate using pi equals 22 over 7.
210 cubic meters
1,575 cubic meters
4,620 cubic meters
The formula for the volume (V) of a cylinder is given by:
V = πr^2h
where r is the radius of the cylinder and h is its height.
We are given the diameter of the cylinder as 28 meters, so the radius (r) is half of that, or 14 meters.
Using the given height of 7 and one half meters, we can now calculate the volume of the cylinder as follows:
V = πr^2h = (22/7) * (14)^2 * (7.5) = 4,620 cubic meters (rounded to the nearest whole number)
Therefore, the approximate volume of the cylinder is 4,620 cubic meters.
25% off original price! The original price of a trampoline is $68. What is the sale price?
Answer: To find the sale price of the trampoline, you have to subtract 25% or a quarter of the original price ($68) from the original price ($68)
Step-by-step explanation:
To find a quarter of 68, you can simply divide this by 4 and now you have a quarter of the original price, $68. 68/4 = 17
Then you subtract a quarter of the original price from the original price.
68-17= sales price
68-17= 51
Sales Price = $51
Hope this helps :D
In a social group, 62 members enjoy dancing and 28 members enjoy hiking. If each of the 75 members in the group enjoys dancing or hiking, how many members enjoy both dancing and hiking?
Answer: 162
Step-by-step explanation:
so you will have to do 62+28+75=162
15 member enjoy both dancing and hiking.
What is Conditional Probability?The likelihood of the preceding event is multiplied by the probability of the subsequent, or conditional, occurrence to determine the conditional probability. Conditional probability examines the likelihood that one event will occur given the likelihood that a related event will occur beforehand.
We have,
Member enjoy dancing, n(D) = 62
Member enjoy hiking, n(H) = 28
Member enjoy dancing or hiking, n(D ∪ H) = 62
Using Conditional probability
n (D ∪ H) = n(D) + n(H) - n (D ∩ H)
75 = 62 + 28 - n (D ∩ H)
75 - 90 = - n (D ∩ H)
n (D ∩ H) = 15
Thus, 15 member enjoy both dancing and hiking.
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Quiz Active
Does anyone know the answer
Answer:c the third one
Step-by-step explanation: because i did it!
Visual work of 44. 4 divided by 100 with decimal moves
By division rule of fraction, dividing 44.4 by 100 results to 0.444, that is shifts three decimal places (to right).
We can divide 44.4 by 100 using simple rule of division.
Rewriting 44.4 in fractional form we get,
44.4 = 444/10
Dividing 444/10 by 100 we can write it in fractional form as 444/10*100.
Therefore, 44.4 divided by 100 in fractional form can be written as 444/1000.
Applying division rule of fractions,
Dividend is 444 and divisor is 1000.
Since the denominator of the fraction has three zeros (in divisor 1000) by properties of fraction the decimal place of the numerator shifts three places to its right.
Also something divided by one is the same value as its initial value.
Thus as 444 shifts to three decimal places (on its right) it becomes 0.444 as the denominator is 1*1000.
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Complete the table.
f(u) = u² + 2u + 3 f(u) U
-20 -10 0 10
Explain.
Answer: see below
Step-by-step explanation:
To complete the table, we need to evaluate the function f(u) = u² + 2u + 3 for the given values of u.
f(u) U
-20 (-20)² + 2(-20) + 3 = 403
-10 (-10)² + 2(-10) + 3 = 117
0 0² + 2(0) + 3 = 3
10 10² + 2(10) + 3 = 123
The table can be filled as follows:
f(u) U
403 -20
117 -10
3 0
123 10
The function f(u) = u² + 2u + 3 is a quadratic function, which has a parabolic shape. The coefficient of u² is positive, which means the parabola opens upward. The vertex of the parabola is at the point (-1, 2), which is the minimum point of the function.
As u increases or decreases from 0, the function increases. This is reflected in the table, where we see that the values of f(u) increase as u moves away from 0.
The table gives us a set of ordered pairs that represent the function f(u) for the given values of u. These ordered pairs can be plotted on a coordinate plane to draw the graph of the function.
When the explanatory variable is categorical and the response variable is quantitative, what type of plot would be appropriate?
When the explanatory variable is categorical and the response variable is quantitative, a box plot or a bar plot would be appropriate to display the relationship between the two variables.
When the explanatory variable is categorical and the response variable is quantitative, a box plot or a bar plot would be appropriate.
A box plot (also known as a box-and-whisker plot) displays the distribution of the response variable within each category of the explanatory variable. It shows the median, quartiles, and outliers of the data, making it useful for visualizing differences in central tendency and spread between categories.
A bar plot (also known as a bar chart) displays the mean, median, or sum of the response variable for each category of the explanatory variable. It is useful for comparing the values of the response variable between categories.
Both box plots and bar plots are effective in displaying the relationship between a categorical variable and a quantitative variable. The choice between the two would depend on the specific research question, the nature of the data, and the intended audience.
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These plots help visualize the distribution of the quantitative response variable across different categories in the explanatory variable.
When the explanatory variable is categorical and the response variable is quantitative, a bar chart or a box plot would be appropriate. A bar chart displays the mean or median of each category, while a box plot displays the distribution of each category including the median, quartiles, and outliers. These plots help to visualize the relationship between the categorical and quantitative variables and identify any patterns or differences between categories.
When the explanatory variable is categorical and the response variable is quantitative, an appropriate type of plot to use would be a box plot or a violin plot. These plots help visualize the distribution of the quantitative response variable across different categories in the explanatory variable.
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the angle from a lookout at the top of a lighthouse (a) boat located at point c is 30 angle the boat travels towards the lighthouse and after 1 minute has travelled a distance of 50 meter and is now located at point b. the angle of elevation from the boat at b up to the lighthouse lookout is 60 angle. find the height of the lighthouse and find the speed of the boat in meters per second from c to b
We can use the fact that angle ACB is 30° to find v. We can use the tangent function:DB = CD - 50
DB = 2950 / v
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
To solve this problem, we will use trigonometry and geometry.
First, let's draw a diagram to better understand the situation:
/|
/ |
/ | h
b / |
----
d
a c
|\ |
| \ |
H | \ h' |
| \ |
| \ |
| \ |
| \ |
| \ |
| \|
------------
D
In this diagram, we have the lighthouse at point A with height H, the boat at point C, and after traveling for 1 minute at a constant speed, it reaches point B. We are given that angle ACB is 30°, angle AHB is 90°, and angle ABH is 60°.
We need to find the height of the lighthouse and the speed of the boat from C to B.Let's start by finding the height of the lighthouse. We can use the tangent function:
tan(ABH) = H / d
tan(60) = H / d
sqrt(3) = H / d
H = sqrt(3) * d
Now, let's find the distance d. We can use the law of cosines:scss
d² = h² + (AB)² - 2 * h * AB * cos(ABH)
We know that AB = 50 meters, ABH = 60°, and h = CD - h', where CD is the distance the boat traveled from C to D and h' is the height of the boat at point D. We can also use the tangent function to find h':
tan(ACH) = h' / CD
tan(30) = h' / (CD + DB)
1/sqrt(3) = h' / (CD + 50)
h' = (CD + 50) / sqrt(3)
Substituting h' in the previous equation:
d² = (CD - (CD + 50) / sqrt(3))² + 50² - 2 * (CD - (CD + 50) / sqrt(3)) * 50 * cos(60)
d² = (CD² + 2 * CD * 50 / sqrt(3) + 2500 / 3) + 2500 - (CD² - CD * 50 / sqrt(3) + 2500 / 3)
d² = 10000 / 3 + CD * 100 / sqrt(3)
Finally, we can use the fact that angle ACB is 30° to find v. We can use the tangent function:
tan(ACB) = h' / (CD + DB)
tan(30) = (CD + 50) / sqrt(3) / (CD + DB)
1 / sqrt(3) = (CD + 50) / sqrt(3) / (CD + DB)
DB = CD - 50
DB = 2950 / v
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Find the value of sin Q rounded to the nearest hundredth, if necessary.
√95
P
7
To find sin(Q), we first calculated the length of the hypotenuse using the Pythagorean theorem. Then we used the sine function to find sin(Q) which is approximately 0.78 rounded to the nearest hundredth.
We can use the Pythagorean theorem to find the length of the third side, which is the hypotenuse
h = √(P² + Q²)
h = √(7² + √95²)
h = √(49 + 95)
h = √144
h = 12
Now, we can use the sine function to find sin(Q)
sin(Q) = opposite/hypotenuse = √95/12
Using a calculator, we get
sin(Q) ≈ 0.78
Rounding to the nearest hundredth, we get
sin(Q) ≈ 0.78
Therefore, the value of sin(Q) rounded to the nearest hundredth is 0.78.
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--The given question is incomplete, the complete question is given
" Find the value of sin Q rounded to the nearest hundredth, if necessary.
Q= √95
P= 7 "--
Use the net as an aid to compute the surface area (rounded to the nearest integer) of the triangular pyramid with an equilateral triangle base.
The surface area of the triangular pyramid in the image given is calculated as: C. 323 square inches.
How to Find the Surface Area of a Triangular Pyramid Using its Net?To find the surface area of the triangular pyramid, find the area of each face and the base as shown in the net given and add all together.
Area of the three triangular faces = 3(1/2 * base * height)
= 3(1/2 * 15 * 10)
= 3(75)
= 225 square inches
Area of the triangular base = 1/2 * base * height
= 1/2 * 15 * 13
= 97.5 square inches
The surface area = 225 + 97.5 = 322.5
≈ 323 square inches.
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Samuel is folding his laundry. The table shows the proportional relationship between the number of shirts he folds and the time, in minutes, it takes him to fold them.
Number of Shirts 2 4 ?
Time (minutes) 0.4 0.8 3
How many shirts can Samuel fold in 3 minutes?
21 shirts
15 shirts
8 shirts
6 shirts
I’d say 30 shirts.
Step-by-step explanation:
30 seconds = 3 shirts 1 minute 30 seconds = 9 shirts 30 seconds per each 3 shirts.
shirts: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30minutes: .5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5
Answer:
15 (B).
Step-by-step explanation:
I took the test.
A teacher purchased a fish tank for her classroom. The dimensions of the tank are 34 inches by 58 inches by 42 inches. What is the maximum amount of water that the tank can hold? a. 82,824 in3 c. 41,412 in3 c. 2,436 in3 d. 1,972 in3
The maximum amount of water that the tank can hold is 82,824 cubic inches, which corresponds to option (a) in the given answer choices.
To find the maximum amount of water that the tank can hold, we need to find the volume of the tank. The volume of a rectangular prism (which is what a fish tank is) can be found by multiplying the length, width, and height of the prism.
Volume = length x width x height
Plugging in the given dimensions of the fish tank, we get:
Volume = 34 in x 58 in x 42 in
Volume = 82,824 in^3
Therefore, Correct option is A.
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a cylinder has a height of 13 inches and a radius of 7 inches l. What is its volume? use 3.14 amd round you answer to the nearest hundredth
The formula for the volume of a cylinder is:
V = πr^2h
where r is the radius and h is the height of the cylinder.
Substituting the given values, we get:
V = π(7^2)(13)
= 1274π
≈ 3993.87 cubic inches (rounded to the nearest hundredth)
Therefore, the volume of the cylinder is approximately 3993.87 cubic inches.
The manager of a local nursery wants to know which types of plants his customers buy most often. What is the population from which the manager should choose a sample to answer her question?
A. The first 25 adults who come into the nursery during one business day.
B. The list of customers who purchased plants from the nursery.
C. Every adult who enters the nursery during one business day.
D. Subscribers to a gardening magazine.
The population from which the manager should choose a sample to answer her question is: B. The list of customers who purchased plants from the nursery.
How to distinguish between population and sample?A population is a term that goes by the definition of it being the entire group that we specifically intend to get conclusions about. Meanwhile, we ca sample is defined as the specific group that you will collect data from. The size of the given sample is normally always less than that of the total size of the given population. In research, it is noticed that a population doesn't always mean we are referring to people.
Now, we are told that the manager wants to know which types of plants his customers buy most often.
Looking at the options, the most appropriate population from which a sample could be gotten from is the list of customers who purchased plants from the nursery.
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low securitymedium securitymaximum securitytotalatlanta7016070300los angeles100150150400detroit155100245500total3254104651,200what is the appropriate degrees of freedom for this test?
Using the given data, we have r = 4 and c = 3. Therefore, the degrees of freedom would be (4-1)(3-1) = 6.
Explanation
The given data is in the form of a table, which represents the number of facilities in different locations with varying levels of security. To determine the appropriate degrees of freedom for this test, we need to know the type of statistical analysis that is being performed.
Since the question does not provide any context or information about the statistical analysis, we cannot determine the appropriate degrees of freedom. It is possible that the degrees of freedom may not even be relevant to the analysis being performed.
However, if we assume that a chi-square test is being conducted to determine whether there is a significant association between the location and the security level of facilities, then the appropriate degrees of freedom would be (r-1)(c-1), where r is the number of rows and c is the number of columns in the table.
In summary, the appropriate degrees of freedom for this test would be 6 if a chi-square test is being conducted to determine the association between the location and the security level of facilities.
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At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer chili on a hot dog?
5,070
3,380
2,986
2,084
Answer:3,380
Step-by-step explanation:
we need to apply cross-multiplication to the ratio of chili preferences in the sample (60) against the total attendance (8450). This gives us:
(60/150) = (x/8450)
where x is the number of people in attendance who would prefer chili on a hot dog.
Simplifying this equation, we get:
x = (60/150) * 8450x = 3,380
helpp will give brainlest ASAPPPPPP
Answer:
1) She needs (35 × 2) + 8 = 78 inches
please please please please please please please please please please help me out
You would want to find the slope of the line (for this, look at the coordinate pairs and the y intercept). The slope equation is y2-y1/x2-x1. Once you find this out, rewrite in y = mx + b
Plug in 6 for x, then solve for y.
83x37 pls show me a picture of how to do this it’s my homework
Right answer gets brainliest and 25 points‼️‼️‼️‼️
Answer: d
Step-by-step explanation:
Answer:
B: Range of round 1 were higher than the range of Round-2.
Step-by-step explanation:
Please give me Brainliest.
which graph shows the solution to the system of linear equations?
y = 1/3x
x + 3y = 6
Answer:
The top right graph shows the solution to this system of linear equations.
bruce has a pet worm that fell into a well. the well is 26 feet deep. each day, the worm climbs up 8 feet, but each night, it slides back down 2 feet. how many days will it take for bruce’s worm to get to the top of the well
To obtain certification for a certain occupation, candidates take a proficiency exam. The exam consists of two sections, and neither section should be more difficult than the other. To investigate whether one section of the exam was more difficult than the other, a random sample of 50 candidates was selected. The candidates took the exam and their scores on each section were recorded. The table shows the summary statistics
The test statistic for the appropriate test to determine if there is a significant mean difference between the percent correct on the two sections for all candidates similar to the one in the investigation is given by t = 75 - 65 / [8 / √(50)], option (A) is correct.
The appropriate test to determine if there is a significant mean difference between the percent correct on the two sections is a two-sample t-test assuming equal variances.
The test statistic for this hypothesis test can be calculated using the formula:
t = x' / ([tex]s{p}[/tex] × √n')
where x' is the sample means for the first and second sections, respectively, [tex]s{p}[/tex] is the pooled standard deviation, and n' is the sample sizes for the first and second sections.
Using the information given in the question, we can calculate the values needed for the test statistic:
x₁ = 75, x₂ = 65, s₁ = 10, s₂ = 5, n' = 50
x’ = x₁ - x₂ = 75 - 65 = 10
The pooled standard deviation is given by [tex]s_{p}[/tex] = 8
We can calculate the test statistic:
t = (x') / [[tex]s_{p}[/tex] / √(n)]
t = 75 - 65 / [8 / √(50)]
Further simplifying:
t = 10 / [8 / √(50)]
t = 8.8356
Hence, option (A) is correct.
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– The question is incomplete, The complete question is:
To obtain certification for a certain occupation, candidates take a proficiency exam. The exam consists of two sections, and neither section should be more difficult than the other. To investigate whether one section of the exam was more difficult than the other, a random sample of 50 candidates was selected. The candidates took the exam and their scores on each section were recorded.
The summary of the statistics are as follows:
-For the first section, Mean Percent Correct is 75 and Standard Deviation Percent Correct is 10
-For the second section, Mean Percent Correct is 65 and Standard Deviation Percent Correct is 5
-The difference is, Mean Percent Correct is 10, and the pooled Standard Deviation Percent Correct is 8
Which of the following is the test statistic for the appropriate test to determine if there is a significant mean difference between the percent correct on the two sections (first minus second) for all candidates similar to the one in the investigation?
A) t = 75 - 65 / (8 / √(50))
B) t = 75 - 65 / [√(10² / 50 + 5² / 50)]
C) x² =(75 - 70)² / 70 + (65-70)² / 70
D) x² = (75-70)² / 65 + (65-70)² / 65
please i need your help for today please i would really appreciate it
Answer:80
Step-by-step explanation:
Is ΔABC ~ ΔDEF? Explain.
Answer:
ΔABC and ΔDEF are similar by (AA).
option (2)
Step-by-step explanation:
Here to test if the two triangles are similar based on the information given I will attempt to see if they are similar using
Angle-Angle (AA) Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Δ = 180°
therefore using the givens:
m∠CAB = 18°
m∠ABC = 110°
m∠ACB = 180°-110°-18° = 52°
now for ΔDEF
because we know corresponding parts of similar triangles are proportional
∠DEF ≅ ∠CAB
and because m∠ACB = 52° and m∠FDE = 52°
∠FDE ≅ ∠ACB
Therefore by AA, we have proven that these two triangles ΔABC and ΔDEF are similar.
so option (2)
if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used? assume confidence.
The recommended sample size for estimating the population mean time for previews at movie theaters with a margin of error of one minute and a confidence level of 95% would be n = 1.
To determine the sample size needed to estimate the population mean time for previews at movie theaters with a margin of error of one minute, we would need to know the confidence level desired. The confidence level is the level of certainty we want to have in our estimate.
Let's assume a confidence level of 95%, which is commonly used in many statistical analyses. This corresponds to a Z-score of 1.96, which is the critical value for a 95% confidence level in a standard normal distribution.
The formula for calculating the sample size needed for estimating a population mean with a given margin of error and confidence level is:
n = ( [tex]Z^2[/tex] * [tex]σ^2[/tex] ) / [tex]E^2[/tex]
where:
n = sample size
Z = Z-score for the appropriate level of confidence
σ = standard deviation of the population (if known)
E = margin of error
Since the population standard deviation (σ) is not given, we will assume it is unknown and use a conservative estimate of 0.5 as a typical standard deviation for movie theater preview times.
Plugging in the values into the formula:
n = ( [tex]1.96^2[/tex] * [tex]0.5^2[/tex] ) / [tex]1^2[/tex]
n = (3.8416 * 0.25) / 1
n = 0.9604 / 1
n ≈ 0.9604
As sample sizes must be whole numbers, we round up to the nearest whole number to ensure we have enough sample size to meet the desired margin of error and confidence level.
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To estimate the population mean time for previews at movie theaters with a margin of error of one minute and a certain confidence level, we need to use the formula for sample size calculation.
To estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, you'll need to calculate the sample size. Assuming you want a certain confidence level, you'll use the following formula:
n = (Z^2 * σ^2) / E^2
Where:
- n is the sample size
- Z is the Z-score, which depends on the desired confidence level (e.g., 1.96 for 95% confidence)
- σ is the population standard deviation (you'll need to have an estimate of this value)
- E is the margin of error (1 minute in this case)
Once you have the estimated standard deviation, you can plug the values into the formula and calculate the sample size required to achieve the desired margin of error and confidence level.
Since we do not know the standard deviation of the population, we can use a conservative estimate of 5 minutes as the standard deviation. For a 95% confidence level, the z-score is 1.96. Substituting these values into the formula, we get:
n = (1.96^2 * 5^2) / (1^2) = 96.04
Rounding up, we can say that a sample size of at least 97 previews would be needed to estimate the population mean time for previews at movie theaters with a margin of error of one minute and a 95% confidence level.
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