Answer:
All of them
Step-by-step explanation:
Answer:
A,B,C,D,E,F
Step-by-step explanation:
to sum it up all of them !
Find the perimeter of a triangle with these vertices (5,1),(-2,1),(-2,-4)
Answer:
12+√74 ≈ 20.60
Step-by-step explanation:
The side lengths of this right triangle are 5 and 7 units, so the length of the hypotenuse is ...
b² = a² +c² = 5² +7² = 74
b = √74
The perimeter is ...
P = a + b + c = 5 + √74 + 7
P = 12+√74 ≈ 20.60
On a coordinate plane, an absolute value graph has a vertex at (1, negative 2.5). The graph shows the function f(x) = |x – h| + k. What is the value of k? k = –2.5 k = –1 k = 1 k = 2.5
9514 1404 393
Answer:
(a) k = –2.5
Step-by-step explanation:
When the function f(x) is transformed to f(x -h) +k, the graph is translated h units right and k units up.
If the absolute value function has its original vertex of (0, 0) moved to (1, -2.5), then (h, k) = (1, -2.5).
The value of k is -2.5.
_____
Additional comment
The above answer applies to the given problem statement. The question asked in the comment has a vertex of (0, 2.5), so (h, k) = (0, 2.5) for that question.
If you're going to copy the answer, make sure it is the answer to the question you're looking at.
In an absolute value function expressed as f(x) = |x – h| + k, the value of k corresponds to the y-coordinate of the function's vertex. In this case, as the vertex is at the point (1, -2.5), the value of k is -2.5.
The student's question relates to the concepts of Two-Dimensional (x-y). Graphing and the graphing of the absolute value function. It is vital to remember that the vertex of an absolute value graph in the form f(x) = |x – h| + k corresponds to the point (h, k) on the Cartesian coordinate plane. The student states that the vertex is at the point (1, -2.5), so based on our function analysis, the value of k, which represents the y-coordinate of the vertex, is -2.5. Therefore, the correct answer is k = -2.5.
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In a random sample of 41 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 51 months, with a standard deviation of 11 months. Construct and interpret a 95% confidence interval for the mean length of sentencing for this crime.
Answer:
95% confidence interval for the mean length of sentencing for this crime is [47.53 months , 54.47 months].
Step-by-step explanation:
We are given that in a random sample of 41 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 51 months, with a standard deviation of 11 months.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean length of sentencing = 51 months
[tex]s[/tex] = sample standard deviation = 11 months
n = sample of criminals = 41
[tex]\mu[/tex] = population mean length of sentencing
Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.021 < [tex]t_4_0[/tex] < 2.021) = 0.95 {As the critical value of t at 40 degree of
freedom are -2.021 & 2.021 with P = 2.5%}
P(-2.021 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.021) = 0.95
P( [tex]-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]51-2.021 \times {\frac{11}{\sqrt{41} } }[/tex] , [tex]51+2.021 \times {\frac{11}{\sqrt{41} } }[/tex] ]
= [47.53 , 54.47]
Therefore, 95% confidence interval for the mean length of sentencing for this crime is [47.53 months , 54.47 months].
The Bureau of the Census reports the average commuting time for citizens of both Baltimore, Maryland, and Miami, Florida. To see if their commuting times appear to be any different in the winter, random samples of 40 drivers were surveyed in each city and the average commuting time for the month of January was calculated for both cities. The results are provided below. Miami (X1) Baltimore (X2) Sample size 40 40 Sample mean 28.5 min 35.2 min Population standard deviation 7.2 min 9.1 min At the 0.05 level of significance, can it be concluded that the commuting times are different in the winter? What is the test statistic? Round to 3 decimal places.
Answer:
[tex]z=\frac{28.5-35.2}{\sqrt{\frac{7.2^2}{40}+\frac{9.1^2}{40}}}}=-3.652[/tex]
Now we can calculate the p value since we are conducting a bilateral test the p value would be:
[tex]p_v =2*P(z<-3.652)=0.00026[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis that the true means are equal at 5% of significance.
Step-by-step explanation:
Information provided
[tex]\bar X_{1}=28.5[/tex] represent the mean for Miami
[tex]\bar X_{2}=35.2[/tex] represent the mean for Baltimore
[tex]\sigma_{1}=7.2[/tex] represent the population standard deviation for Miami
[tex]\sigma_{2}=9.1[/tex] represent the population standard deviation for Baltimore
[tex]n_{1}=40[/tex] sample size selected for Miami
[tex]n_{2}=10[/tex] sample size selected for Baltimore
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test
Hypothesis to analyze
We want to check if the commiting times are different in the winter for the two cities, so then the system of hypothesis are:
Null hypothesis:[tex]\mu_{1} = \mu_{2}[/tex]
Alternative hypothesis:[tex]\mu_{1} \neq \mu_{2}[/tex]
Since we know the population deviations the statistic for this case is given by:
[tex]z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
Replacing the info provided we got:
[tex]z=\frac{28.5-35.2}{\sqrt{\frac{7.2^2}{40}+\frac{9.1^2}{40}}}}=-3.652[/tex]
Now we can calculate the p value since we are conducting a bilateral test the p value would be:
[tex]p_v =2*P(z<-3.652)=0.00026[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis that the true means are equal at 5% of significance.
An oblique prism has a base area of 3x2 square units. An oblique prism has a base area of 3 x squared square units. The base of the prism is a quadrilateral. The distance from the top quadrilateral to the bottom quadrilateral is 13. A right triangle is drawn outside of the prism and has the side with length 13 as its hypotenuse. The base length of the triangle is 5. What expression represents the volume of the prism, in cubic units? 15x2 24x2 36x2 39x2
Answer: 36x^2
Step-by-step explanation:
just took eg quiz
The expression represents the volume of the prism, in cubic units is
39x². (Option D) This is because the formula for the volume of a prism is: V = Bh
What is a prism?Any 3-dimensional shape with two identical shapes facing each other is called a Prism.
Recall that the oblique prism is described as having a base area of 3x², If the height is 13 (that is the distance between the top of the quadrilateral and the bottom) hence,
V = 3x² * 13
→ V = 39x², therefore, Option D is the correct answer.
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When measuring miles using a telescope, surveyors made an error of 6.5 feet per mile. If the total error was 55.25 feet, how
many miles were measured?
A 8.5
B
48.75
C
61.75
D
359.125
A. 8.5.
55.25 feet / 6.5 feet = 8.5 miles.
what is a telescope?A telescope is an optical tool using lenses, curved mirrors, or a combination of both to look at distant objects, or various devices used to look at distant objects by means of their emission, absorption, or reflection of electromagnetic radiation.
There are three main types of telescope. These are
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Miranda says that the triangle below represents the cross section of the rectangular pyramid shown.What mistake might miranda have made
Answer:
Miranda may have made the mistake of mismatching
Step-by-step explanation:
See attached a rough sketch of Cross sections of rectangular and triangular pyramids
Miranda made the mistake of not properly identifying the cross section of a rectangular pyramid which has a cross section of a rectangle.
A triangular pyramid has a triangular cross section
4. Determine which of the following relations on the given sets are reflexive, symmetric, antisymmetric and/or transitive: a) ℛ = {(1,5), (5,1), (1,1), (2,2), (3,3)(4,4)} oooo ???????? = {1,2,3,4,5} Write the matrix representation of this relation. b) ???????? = {(1,4), (1,2), (2,3), (3,4), (5,2), (4,2), 1,3)} oooo ???????? = {1,2,3,4,5} Write the matrix representation of this relation.
Answer:
(a)
Reflexivity
Is not reflexive
Symmetry
Is symmetric
Anti-Symmetry
is not antisymmetric.
Transitivity
It is transitive
[tex]R = \begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 & 0 \\0 & 0& 1 & 0 & 0 \\0 & 0& 0 & 1 & 0 \\0 & 0& 0& 0 & 1 \end{pmatrix}[/tex]
(b)
Reflexivity
Is not reflexive
Symmetry
Is not symmetric
Anti-Symmetry
It is antisymmetric
Transitivity
So is NOT transitive.
[tex]R = \begin{pmatrix} 0 & 1 & 1 & 1 & 1 \\0 & 0 & 1 & 0 & 0 \\0 & 0& 0 & 1 & 0 \\0 & 1& 0 & 0& 0 \\0 & 1& 0& 0 & 0 \end{pmatrix}[/tex]
Step-by-step explanation:
(a)
Reflexivity
Is not reflexive because 5 is not related to 5.
Symmetry
Is symmetric because 1R5 .and 5R1
Anti-Symmetry
If it is symmetric then it is not antisymmetric.
Transitivity
It is transitive because 1R5 5R1 and 1R1.
[tex]R = \begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 & 0 \\0 & 0& 1 & 0 & 0 \\0 & 0& 0 & 1 & 0 \\0 & 0& 0& 0 & 1 \end{pmatrix}[/tex]
(b)
Reflexivity
Is not reflexive no element of the set is related to itself.
Symmetry
Is not symmetric because (1,4) belongs to the relation but (4,1) does not belong to the relation . And similarly you can do the same with all pairs and none of them will satisfy the condition.
Anti-Symmetry
It is symmetric because for every element if aRb then "b" is NOT related to "a"
Transitivity
A relation can't be antisymmetric and transitive. So is NOT transitive.
[tex]R = \begin{pmatrix} 0 & 1 & 1 & 1 & 1 \\0 & 0 & 1 & 0 & 0 \\0 & 0& 0 & 1 & 0 \\0 & 1& 0 & 0& 0 \\0 & 1& 0& 0 & 0 \end{pmatrix}[/tex]
Please help me with the math question
Answer:
neither even nor odddegree 5LC negativeroots {-6, -4, 0, 2, 3}Step-by-step explanation:
The function's graph is not symmetrical about the origin, so it is not an odd function. It is not symmetrical about the y-axis, so is not an even function.
The function is neither even nor odd.
There are 5 zero-crossings and no places where y=0 and the graph does not cross. This means the function is of degree 5, at least.
The general shape of the function is down and to the right, so the sign of the function for large values of x is opposite the sign of x. The leading coefficient must be negative.
As we noted, there are 5 zero-crossings. These are the real roots. They are found at x-values in the set {-6, -4, 0, 2, 3}.
x=23y+4 solve for x and graph
Answer:
X=4
for the graph, the point would be (4,0)
solve for
3x + 12= -12
Answer:
x = -8
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 12 from both sides:
3x + 12 (-12) = -12 (-12)
3x = -12 - 12
3x = -24
Next, divide 3 from both sides:
(3x)/3 = (-24)/3
x = -24/3
x = -8
x = -8 is your answer.
~
Answer:
x = -8
Step-by-step explanation:
3x + 12= -12
3x = -24
x = -24/3
x = -8
A right rectangular prism with square bases has a height of 20cm and a volume of 800 cubic centimeters. Which statements describe the prism?
Answer:
The area of the rectangular prism is 40cm²
Step-by-step explanation:
To calculate the volume of a rectangular prism we have to use the following formula:
a = area
v = volume = 800 cm³
h = height = 20 cm
v = a * h
we replace the values that we know
800cm³ = a * 20cm
800cm³ / 20cm = a
40cm² = a
v = 70ft³
The area of the rectangular prism is 40cm²
1 point) The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 65 with a standard deviation of 5.3. Assume that the distribution is approximately normal. (a) What is the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg
Answer:
The probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg is 0.9970.
Step-by-step explanation:
The random variable X can be defined as the amount of oxygen an athlete takes in.
The mean maximum oxygen uptake for elite athletes is, μ = 65 ml/kg.
The standard deviation is, σ = 5.3 ml/kg.
The random variable X is approximately normally distributed.
Now to compute probabilities of a normally distributed random variable, we first need to convert the value of X to a z-score.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The distribution of these z-scores is known as a Standard normal distribution, i.e. [tex]Z\sim N(0, 1)[/tex].
A normal distribution is a continuous distribution. So, the probability at a point on a normal curve is 0. To compute the exact probabilities we need to apply continuity correction.
Compute the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg as follows:
P (X ≥ 50) = P (X > 50 + 0.50)
= P (X > 50.50)
[tex]=P(\frac{x-\mu}{\sigma}>\frac{50.50-65}{5.3})[/tex]
[tex]=P(Z>-2.74)\\=P(Z<2.74)\\=0.99693\\\approx 0.9970[/tex]
Thus, the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg is 0.9970.
10. The scores on the verbal section of the Graduate Records Examination (GRE)
are approximately normally distributed with a mean of 150 and a standard
deviation of 8.5. What is the probability that a randomly selected score on the
verbal section is higher than 1657
Answer:
The probability that a randomly selected score on the verbal section is higher than 165 is 0.0392
Step-by-step explanation:
We are given that The scores on the verbal section of the Graduate Records Examination (GRE) are approximately normally distributed with a mean of 150 and a standard deviation of 8.5.
Mean = [tex]\mu = 150[/tex]
Standard deviation =[tex]\sigma = 8.5[/tex]
We are supposed to find the probability that a randomly selected score on the verbal section is higher than 165 i.e.P(x>165)
Formula :[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{165-150}{8.5}[/tex]
Z=1.76
Refer the z table for p value
P(x<165)=0.9608
P(x>165)=1-P(x<165)=1-0.9608=0.0392
Hence the probability that a randomly selected score on the verbal section is higher than 165 is 0.0392
a classmate says the first step to solve the equation 12(3g-9)=99 is to add to both sides do you agree
Answer:
NoStep-by-step explanation:
[tex]12(3g - 9) = 99 \\ 36g - 108 = 99 \\ 36g = 99 + 108 \\ 36g = 207 \\ \frac{36g}{36} = \frac{207}{36} \\ g = 5.75[/tex]
The Central Company manufactures a certain specialty item once a month in a batch production run. The number of items produced in each run varies from month to month as demand fluctuates. The company is interested in the relationship between the size of the production run (x) and the number of hours of labor (y) required for the run. The company has collected the following data for the ten most recent runs. Number of items: 40 30 70 90 50 60 70 40 80 70 Labor (hours): 81 60 137 180 99 117 140 74 159 143 (a) Find a point estimate for the number of hours of labor required, on average, when 60 units are produced. (Round your ans
Answer:
p value = 0.0000 < 0.05
We reject H0
Hence the claim is significant
Step-by-step explanation:
See attached image
The file CEOSAL2.RAW contains data on 177 chief executive officers and can be used to examine the effects of firm performance on CEO salary. (i) Estimate a model relating annual salary to firm sales and market value. Make the model of the constant elasticity variety for both independent variables. Write the results out in equation form. (ii) Add profits to the model from part (i). Why can this variable not be included in logarithmic form
Find the given attachment for the solution
A model relating a CEO's annual salary to firm's sales, market value, and profits is proposed. The equation takes a logarithmic form of sales and market value for the elasticity. Profits cannot take a logarithmic form due to the possibility of negative values.
Explanation:The objective of this question is to build a model relating CEO's annual salary to firm sales, market value, and profits, using the data from CEOSAL2.RAW. The model would be a constant elasticity variety for the sales and market variables. The standard form of a constant elasticity model is ln(Y) = a + b1*ln(X1) + b2*ln(X2) + u, where Y represents the dependent variable (CEO's annual salary), X1 and X2 represent independent variables (firm sales and market value).
Now adding profits to the model, your equation would be: ln(Y) = a + b1*ln(X1) + b2*ln(X2) + b3*X3 + u, where X3 denotes the firm's profits. It is not in logarithmic form because profits can be negative, and the natural log of a negative number is undefined in real numbers.
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Use the triangle shown to find the ratios.
cos(A) =
tan(C) =
Triangle A B C is shown. Angle A B C is a right angle. The length of A B is 10 feet, the length of C B is 24 feet, and the length of hypotenuse A C is 26 feet.
Answer:
cos (A) =5/13
tan (C) =5/12
Step-by-step explanation:
The triangle for the problem is produced and attached.
cos (A)=Adjacent/Hypotenuse
cos (A) = 10/26 =5/13
Similarly,
tan (C)=Opposite/Adjacent
tan (C)=10/24 =5/12
Answer:
Cos(A) = 5/13 or 10/26
Tan(C) = 5/12 or 10/24
Step-by-step explanation:
I did it on edge :)
What is the area of the rectangle, in square centimeters? A rectangle with length 12 centimeters and width 5 centimeters. 17 34 30 60
En un mapa, 1 cm medido en el papel representa a 100 km
a. que distancia en la realidad habrá entre dos puntos que en el papel distan 3,3 cm?
b. que distancia en el papel habrá si en la realidad hay 1 800 km
porfa respondan
I want to know if mammals usually have more teeth than reptiles
Answer: yes reptiles have no teeth at all while mammals have two sets of teeth
Step-by-step explanation:
Answer:
dot plot
Step-by-step explanation:
gay gay
If a basketball player makes 2 baskets for every 5 shots and he keeps getting baskets at the same rate, how many baskets will he get if he takes 100 shots?
Answer:
i thinl it would be 200 or 1000
A manufacturer of cream filled donuts wants to make sure that it's automatic filling process is on target. Based On sample of 25 donuts the mean weight of cream filling is estimated to be 15 grams with a standard deviation of 1.5 grams. however, the quality control inspectors wish to estimate the mean wright of cream filling mor accurately so that they can be 99% confident that it is within 0.25 grams of the true mean. How many donuts should they sample?
To estimate the true mean weight of the cream filling within 0.25 grams with 99% confidence, the quality control inspectors should sample approximately 384 donuts. This is calculated using statistical techniques for sample size determination.
Explanation:In order to find out how many donuts the quality control inspectors should sample, we need to utilize the formula for sample size in statistics, which is n = (Z^2 * σ^2 * N) / E^2 . In this case, 'Z' is the Z-score which corresponds to the desired confidence level, σ is the standard deviation of the sample data, E is the desired margin of error, and N is the population size.
For a 99% confidence level, the Z-score is 2.58. Given the standard deviation(σ) is 1.5 grams, and the desired margin of error(E) is 0.25 grams, we can substitute these values into the equation to calculate the sample size(n).
Substituting these values: n = (2.58^2 * 1.5^2) / 0.25^2. n becomes approximately 384.
Therefore, the quality control inspectors should sample approximately 384 donuts to be 99% confident that their estimate of the true mean weight of cream filling is within 0.25 grams of the true mean.
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Consider the system of equations.
y = -x + 3
y=-x-3
The graph of the first equation is shown by the orange
line.
ty
What is the slope of the orange line?
If the second equation was drawn on the same graph,
what would be its slope?
If the lines of both equations were shown on the same
graph, they would
The system of equations has
Answer:
slope of orange Line = -1
slope of other line = -1 (also)
would be parallel
no solution
Step-by-step explanation:
how do i know. I did the assignment. Can i get brainlyest. I need it please.
This question is based on system of linear equation. thus, there is no solution of equations.
Given:
y = - x + 3 ...(1)
y = -x - 3 ...(2)
We know that ,
Equation of line is y = mx+c ...(3)
Now, calculate the slope of equation (1) is m= -1 (by comparing equation (1) and (3).
Now, calculate the slope of equation (2) is m= -1 (by comparing equation (2) and (3).
Therefore, both lines are parallel to each other.Thus, never meet ech other so, the equation has no solution.
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Best gets Brainliest! Please help im desperate
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms:
2 – 11 x 2 – 8 x + 6 x 2
Giving brainliest for CORRECT awnser.
Answer:
12
Step-by-step explanation:
x^2 -bx +36
A perfect square trinomial is of the form
a^2 -2abx +b^2
x^2 -bx +6^2
a =1 and b = 6
2ab = 2*1*6 = 12
Pls help me I reallyyyyy don't understand
Answer:
9
Step-by-step explanation:
range is the range from the lowest # through the biggest # in other words subtract the smaller number from the bigger number
write the equation of the circle graphed below
Answer:
The equation of the circle is
(x + 2)² + (y + 2)² = 9
Centered at (-2, -2), with radius of 3 units.
Step-by-step explanation:
The general equation of a circle is given as
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.
Looking at the graph, the center is the red dot. It corresponds to -2 on the y-axis, and -2 on the x-axis. So, the center (h, k) is (-2, -2).
The radius is the distance from the center of the circle to the edge of the circle. The red dot is the edge of the circle, there are 3 lines that represent 3 units, so we have a radius of 3 units.
Using these in the general equation, we have
[x - (-2)]² + [y - (-2)]² = 3²
(x + 2)² + (y + 2)² = 9
And this is the equation.
Answer:
(x+2)^2 + (y+2)^2= 0.5625
Step-by-step explanation:
In which quadrant does the point (5, -13) lie?
A.
Quadrant IV
b. Quadrant !
c. Quadrant III
D.
Quadrant II
Answer:
IV
Step-by-step explanation:
Since x is positive, the two possible quadrants are I and IV.
Since y is negative, the two possible quadrants are III and IV.
The point lies in quadrant IV.
Enzo is studying the black bear population at a large national park. He finds that the relationship between the elapsed time (t), in years, since the beginning of the study, and the black bear population B(t) in the park is modeled by the following function:
B(t) = 2,500×2^0.01t
According to the model, what will the black bear population be at that national park in 25 years?
according to the model, the black bear population at the national park after 25 years will be approximately 2,973.
To find the black bear population at the national park after 25 years using the given function [tex]\( B(t) = 2,500 \times 2^{0.01t} \)[/tex], we substitute [tex]\( t = 25 \)[/tex] into the function:
[tex]\[ B(25) = 2,500 \times 2^{0.01 \times 25} \][/tex]
[tex]\[ B(25) = 2,500 \times 2^{0.25} \][/tex]
[tex]\[ B(25) = 2,500 \times 2^{1/4} \][/tex]
[tex]\[ B(25) = 2,500 \times \sqrt[4]{2} \][/tex]
Now, let's compute the value:
[tex]\[ B(25) = 2,500 \times 1.1892 \][/tex]
[tex]\[ B(25) \approx 2,973 \][/tex]
Therefore, according to the model, the black bear population at the national park after 25 years will be approximately 2,973.