Answer:
∠BIJ ≅ ∠CGJ and ∠BJI ≅ ∠CJG
Step-by-step explanation:
To prove similarity, you must show two corresponding angles are congruent. Thus, you can ignore any answer choices involving congruence of segments. The angles in the 2nd answer choice are not corresponding, so that, too, can be eliminated.
The appropriate choice is the last one:
∠BIJ ≅ ∠CGJ and ∠BJI ≅ ∠CJG
Please PLease PLEASE HELP ME!!!!!!!!!!!!!! Consider what would happen if you were to slice a face at a vertex (cut a corner) of a particular polyhedron. You would see a new polygonal face where the old vertex used to be. What type of polygon would a slice of a hexahedron at a vertex create? Explain how you know. What type of polygon would a slice of an icosahedron at a vertex create? Explain how you know.
Answer:
A triangle
Step-by-step explanation:
The plane which cuts a corner intersects the polyhedron in n faces that depend on the specific polyhedron as seen in the attachment
And here's a cube, and three faces intersect. Because the intersection of two planes is a line, and that there are three planes with which to intersect, the polygon has three sides.
Therefore in the given situation, the polygon is a triangle
I NEED HELP PLEASE THANKS!
Jenny is sitting on a sled on the side of a hill inclined at 15°. What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds? (Show work)
Answer:
23.29 lbs
Step-by-step explanation:
The force on Jenny due to gravity can be resolved into components perpendicular to the hillside and down the slope. The down-slope force is ...
(90 lbs)sin(15°) ≈ 23.29 lbs
In order to keep Jenny in position, that force must be balanced by an up-slope force of the same magnitude.
There is a set of 100 obserations with a mean of 46 and a standard deviation of 0. What is the value of smallest obserstion in a set?
Answer:
Solution = 46
Step-by-step explanation:
I believe you meant standard deviation. Standard deviation is defined as the variation of the data set, or the differences between the values in this set. In order for the standard deviation to be 0, all values should be the same.
Now if the mean is 46, the smallest possible number of each value in the data set should be 46 as well. This is considering the mean is the average of the values, and hence any number of values in the data set being 46 will always have a mean of 46. Let me give you a demonstration -
[tex]Ex. [ 46, 46, 46 ], and, [46, 46, 46, 46, 46]\\Average = 46 + 46 + 46 / 3 = 46,\\Average = 46 + 46 + 46 + 46 + 46 / 5 = 46[/tex]
As you can see, the average is 46 in each case. This proves that a data set consisting of n number of values in it, each value being 46, or any constant value for that matter, always has a mean similar to the value inside the set, in this case 46. And, that the value of the smallest standard deviation is 46.
pls help help me pls
Answer:
b
Step-by-step explanation:15 x 5 = 75 and 20 x 4 = 80 making 155 and 15 x 3 = 45 and 20 x 2 = 40 making 85
Four different digits from 1 to 9 are required to open a safe.
1. The sum of the digits is 20.
2. The first digit is greater than the third.
3. The second and fourth digits differ by at least 5.
4. Exactly two digits are squares.
5. The first and fourth digits add up to a prime number.
6. The fourth digit is the lowest.
Can you find the four-digit combination?
Answer: 5942
Step-by-step explanation:
Clue 4 states exactly two of the digits = 1, 4, or 9
Clue 1 leaves us with the following combinations:
1, 9, 2, 8
1, 9, 3, 7 eliminate by clue 5
4, 9, 2, 5
1, 4, 7, 8
Clue 5 directs us to the following order for 1,9,2,8
2 __ __ 1 --> 2981 or 2891 eliminate by clue 2
9 __ __ 8 --> 9128 or 9218 eliminate by clue 6
9 __ __ 2 --> 9182 or 9812 eliminate by clue 6
Clue 5 directs us to the following order for 4,9,2,5
5 __ __ 2 --> 5492 or 5942 eliminate 5492 by clue 2
9 __ __ 2 --> 9452 or 9542 eliminate by clue 3
Clue 5 directs us to the following order for 1,4,7,8
4 __ __ 1 --> 4781 or 4871 eliminate by clue 2
The only combination not eliminated is 5-9-4-2, which satisfies all six clues.
1) 5 + 9 + 4 + 2 = 20
2) 5 > 4
3) 9 - 2 > 5
4) 4 & 9 but not 1 are included
5) 5 + 2 = 7, which is a prime number
6) 2 < 5, 9, 4
The school band is going to a competition. Five members play the flute. There are three times as many members who play the trumpet. There are eight fewer trombone players than trumpeters, and eleven more drummers than trombone players. There are twice as many members that play the clarinet as members that play the flute. There are four fewer tuba players than there are trombone player, but three more members play the French horn than play the trombone. The band director, his assistant and six parent volunteers are also going. How many seats are needed on the bus?
Answer:
76
Step-by-step explanation:
Flute players- 5
Trumpet player- 3 times flute players -15
Trombone players- 8 fewer than trumpet-7
Drummers- 11 more than trombone-18
Clarinet- 2 times flute- 10
Tuba-4 fewer than trombone-3
French horn- 3 more than trombone- 10
Band director- 1
Assistant-1
Volunteers- 6
5+15+7+18+10+3+10+1+1+6=76
Sequence of numbers 1.5,2.25,3.0,3.75 in a recursive formula?
Answer:
f(n + 1) = f(n) + 0.75
Step-by-step explanation:
Plz I need help with this question
Answer:
adjacentobtuseStep-by-step explanation:
The angles marked 1 and 2 share the vertical line as a common side, so they are "adjacent" angles. Each is the sum of an acute angle and a right angle, so is "obtuse."
None of the other descriptors apply.
Complete a frequency distribution for the following data that represents the recent sales prices (in $1,000s) of homes in Midwestern County. As this is quantitative data, calculate five classes, report the cumulative frequency, relative frequency, and cumulative relative frequency.
Sales price:
115 290 271 267 290
271 242 223 221 269
245 336 236 265 270
249 216 335 237 295
Frequency Cumulative Frequency Relative Frequency Cumulative Relative Frequency
100 upto 150
Answer:
Given the quantitative data, the five classes would be:
Number of data given, n = 20
________________________
100 to 150:
Frequency = 1
Cumulative frequency = 1
Relative frequency [tex] = \frac{1}{20} = 0.05 [/tex]
Cumulative relative frequency [tex] = \frac{1}{20} = 0.05 [/tex]
__________________________
150 to 200:
Frequency = 0
Cumulative frequency = 0 + previous cumulative frequency = 0 + 1 = 1
Relative frequency = 0
Cumulative relative frequency [tex] = \frac{1}{20} = 0.05 [/tex]
__________________________
200 to 250:
Frequency = 8
Cumulative frequency = 9 + previous cumulative frequency = 8 + 1 = 9
Relative frequency [tex] = \frac{8}{20} = 0.4 [/tex]
Cumulative relative frequency [tex] = \frac{9}{20} = 0.45 [/tex]
__________________________
250 to 300:
Frequency = 9
Cumulative frequency = 9 + previous cumulative frequency = 9 + 9 = 18
Relative frequency [tex] = \frac{9}{20} = 0.45 [/tex]
Cumulative relative frequency [tex] = \frac{18}{20} = 0.9 [/tex]
__________________________
300 to 350:
Frequency = 2
Cumulative frequency = 2 + previous Cumulative frequency = 2 + 18 = 20
Relative frequency [tex] = \frac{2}{20} = 0.1 [/tex]
Cumulative relative frequency [tex] = \frac{20}{20} = 1 [/tex]
__________________________
Members of the school committee for a large city claim that the population mean class size of a middle school class within the district is exactly 20 students. Karla, the superintendent of schools for the city, thinks the population mean is less. She selects a random sample of 35 middle school classes across the city. The sample mean is 18.5 students with a sample standard deviation of 3.7 students. The test statistic t for a hypothesis test of H0:μ=20 versus Ha:μ<20 is t≈−2.40. If 0.01
Answer:
At a level of dignificance of 0.01, there is not enough evidence to support the claim that the population mean class size of a middle school class within the district is less than 20.
P-value = 0.011
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean class size of a middle school class within the district is less than 20.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=20\\\\H_a:\mu< 20[/tex]
The significance level is 0.01.
The sample has a size n=35.
The sample mean is M=18.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.7.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.7}{\sqrt{35}}=0.625[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{18.5-20}{0.625}=\dfrac{-1.5}{0.625}=-2.398[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=35-1=34[/tex]
This test is a left-tailed test, with 34 degrees of freedom and t=-2.398, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-2.398)=0.011[/tex]
As the P-value (0.011) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population mean class size of a middle school class within the district is less than 20.
Newton's second law says force (f) is equal to mass (m) times acceration (a). A scientist wants to calculate the force of an object where the acceleration of gravity (g) is 9.8 m/s2. Use the function to calculate the force for an object with a mass (m) of 0.29 kilograms. 9.51 Newtons 2.8 Newtons 34 Newtons 0.029 Newtons
Answer:
Force = mass×acceleration
F=ma
m=0.29kg
a=9.8m/s²
F=0.29kg×9.8m/s²
F= 2.84N=2.8N
Answer:Answer:
Force = mass×acceleration
F=ma
m=0.29kg
a=9.8m/s²
F=0.29kg×9.8m/s²
F= 2.84N=2.8N
Step-by-step explanation:
A homeowner puts a passcode-enabled lock on her front door. To choose a passcode, she must choose a number, a letter from a list of 5 letters, and then another number.
Number Letter Number
0 A 0
1 E 1
2 I 2
3 O 3
4 U 4
5 5
6 6
7 7
8 8
9 9
How many possible passcodes can she make?
Answer:
500
Step-by-step explanation:
I assume each number is from 0 to 9. Also there are 5 letters.
10 * 5 * 10 = 500
You want to study how the number of popped kernels in a microwave popcorn bag is affected by brand, microwave power, and time in microwave. You manipulate three different factors: brand, power, and time. There are three brands, two power settings, and three different microwave times. a. How many unique treatment combinations are there
Answer:
Number of unique treatment combinations = 8
Step-by-step explanation:
Given:
Number of brands = 3
Number of power settings = 2
Number of microwave times = 3
Find:
Number of unique treatment combinations.
Computation:
Number of unique treatment combinations = Number of brands + Number of power settings + Number of microwave times
Number of unique treatment combinations = 3 + 2 + 3
Number of unique treatment combinations = 8
Solve each equation (images provided).
Answer:
+-2
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
When you solve the equation you should get two parallel lines with x-intercepts at (-2,0) & (2,0)
Dylan wants to determine a 90 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. How large of a sample must he have to get a margin of error less than 0.03
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]
And rounded up we have that n=748
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
The best estimatr for the proportionis 0.5 since we don't have any other info provided. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]
And rounded up we have that n=748
pls help me hepl me
Answer:
b at most 199
Step-by-step explanation:so the total was 121 and there is a flat fee of 21.50 so you subtract that out and gat 99.5 since its .5 per mile its going to be divided giving 199 and that is the most she could have driven.
how do i round 17.875 to the nearest tenth
Answer:
17.9
Step-by-step explanation:
The tenth place is the digit 8. After the tenth place is 7, which is higher or equal to 5. Therefore, we must add +1 to the tenth place followed by zeros.
Not sure how I would solve this
Answer:
7/6
Step-by-step explanation:
m = (y2-y1)/(x2-x1)
Using the given points
m = (-2 - -9)/(2 -8)
= (-2+9) / (-6)
= 7/6
Describe how you can determine the quadrant in which the terminal side or angle a lies if sin a =-1/4
Step-by-step explanation:
Well it's easy, you can write sin a=y/r
in which y is the y coordinate and r the hipotenuse.
so if sin a is negative that must mean that "a" is where y is negative and that happens in the third and fourth quadrant
Choose the equation of the horizontal line that passes through the point (−5, 9). y = −5 y = 9 x = −5 x = 9
Answer:
y = 9
Step-by-step explanation:
Since we are trying to find a horizontal line, our line would have to be y = [a number]. That takes our x = -5 and x = 9 out as answer choices. We are left with y = -5 and y = 9. y = 9 is correct because the horizontal line is the y-values, and since in (-5, 9), our y-value is 9, our line is y = 9.
Gelb Company currently manufactures 54,000 units per year of a key component for its manufacturing process. Variable costs are $5.15 per unit, fixed costs related to making this component are $73,000 per year, and allocated fixed costs are $80,500 per year. The allocated fixed costs are unavoidable whether the company makes or buys this component. The company is considering buying this component from a supplier for $3.90 per unit.
Calculate the total incremental cost of making 54,000 units.
Answer:
$351,100
Step-by-step explanation:
The total incremental cost of making 54,000 units = Variable Cost Per Unit (54,000 unit) + Fixed Manufacturing Costs
Fixed Manufacturing Costs = $73,000
Variable costs are $5.15 per unit
Variable Cost Per Unit = $5.15 * 54,000 unit = $278,100
Hence, the total incremental cost of making 54,000 units = $278,100 + $73,000 = $351,100
When 21 volts are applied the arlent is a amperes. What is the current when 47 volts are applied round to decimal
Answer:
Since it is directly related, then the current is one third of the voltage.
57 / 3 = 19 amperes
Step-by-step explanation:
Thomas and Randy had some blue and yellow handkerchiefs. 1/4 of Thomas' handkerchief and 3/7 of Randy's handkerchiefs are blue. Thomas and Randy have the same amount of yellow handkerchiefs. If the difference between the number of handkerchiefs they have is 10, how many handkerchiefs do they have in total?
Answer:
74 handkerchief
Step-by-step explanation:
Let the number of Thomas' and Randy's handkerchief be T and R respectively.
Thomas
blue ----- ¼T
yellow ----- 1T -¼T= ¾T
Randy
blue ----- [tex] \frac{3}{7} [/tex]R
yellow ----- [tex] \frac{4}{7} [/tex]R
Since they have the same number of yellow handkerchiefs,
¾T= 4/7 R
Multiply by 28 on both sides,
(since 28 is the lowest common multiple of 4 and 7)
21T= 16R -----(1)
From this we can see that R is greater than T.
Hence, given that the difference between R and T is 10,
R= T +10 -----(2)
Subst. (2) into (1):
21T= 16 (T +10)
21T= 16T +160 (expand)
21T -16T= 160
5T= 160 (simplify)
T= 160 ÷5 (÷5 on both sides)
T= 32
Subst. into (2):
R= 32 +10
R= 42
Thus, total number of handkerchief
= 32 +42
= 74
Can anyone explain how you got the answer please.
Answer:
Option A
Step-by-step explanation:
The first thing we want to do here is identify whether or not the diagonals are perpendicular, which helps much to know to prove what angle AOB.
_____
Let us say that this is a rhombus. That would make the diagonals perpendicular, and hence ∠AOB should be 90 degrees, but let's not jump to conclusions. We need to calculate the length of BO. By Pythagorean Theorem it should be the following length -
[tex]( BC )^2 = ( BO )^2 + ( OC )^2,\\( 10 )^2 = ( BO )^2 + ( 7.8 )^2,\\100 = BO^2 + 60.84,\\BO^2 = 39.16,\\\\BO = ( About ) 6.26\\[/tex]
_____
Knowing BO, to prove that this is a rhombus we can find the length of BO another way, and match it to the length 6.26 -
Δ ABD = Equilateral,
BD = 10 cm,
" Coincidence Theorem " - BO = 5 = OD.
Here BO = 5. 5 is close to 6.26 but not exactly, so the measure of angle AOB is not 90, but better yet 80.
A=2 b=2 c=1 Find the value of 2abcosC
Answer:
[tex]2abCosC = 1[/tex]
Step-by-step explanation:
The cosine rule is
=> [tex]a^2= b^2+c^2-2abCosC[/tex]
For 2abCosC, it becomes
=> [tex]2abCosC = b^2+c^2-a^2[/tex]
=> [tex]2abCosC = (2)^2+(1)^2-(2)^2[/tex]
=> [tex]2abCosC = 1[/tex]
Find the value of x to the nearest tenth
Answer:
X = 5.3Step-by-step explanation:
To do: Find the value of X
Concept : Angle bisector formula
Now,
[tex] \frac{a}{b} = \frac{c}{d} [/tex]
[tex] \frac{6}{9} = \frac{x}{8} [/tex]
[tex]x \times 9 = 6 \times 8[/tex]
( cross multiplication)
[tex]9x = 48[/tex]
Divide both sides by 9
[tex] \frac{9x}{9} = \frac{48}{9} [/tex]
Calculate
[tex]x = 5.3[/tex]
Hope this helps..
Good luck on your assignment...
The left and right page numbers of an open book are two consecutive integers whose sum is 389. Find these page numbers
Step-by-step explanation:
Maybe the page numbers can be 143 and 246
143 + 246 = 389
Answer:
194 and 195
Step-by-step explanation:
x = 1st page
x + 1 = 2nd page
x + x + 1 = 389
2x + 1 = 389
2x = 388
x = 194
x + 1 = 195
if p(A)=0.30,p(B)=0.40and p(AB) =0.20,then p(A/B) is
Answer:
p(A|B) = 2/3Step-by-step explanation:
Given p(A)=0.30,p(B)=0.40and p(A∩B) =0.20,then p(A/B) is expressed as shown:
p(A|B) = p(A∩B)/p(A)
p(A|B) means B is independent and A depends on B.
In your problem P(A)=0.65, P(A∩B) =0.1
Substituting the given values,
p(A|B) = 0.2/0.30
p(A|B) = 2/10 * 10/3
p(A|B) = 2/3
onsider the equation below. (If an answer does not exist, enter DNE.) f(x) = 8 cos2(x) − 16 sin(x), 0 ≤ x ≤ 2π (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) (No Response) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (No Response) (b) Find the local minimum and maximum values of f. local minimum value (No Response) local maximum value (No Response) (c) Find the inflection points. (x, y) = (No Response) (smaller x-value) (x, y) = (No Response) (larger x-value)
Answer:
(a) Increasing:[tex]\frac{\pi}{2}< x< \frac{3\pi}{2}[/tex] and Decreasing:[tex]0< x< \frac{\pi}{2}\ \text{or}\ \frac{3\pi}{2}< x< 2\pi[/tex]
(b) The local minimum and maximum values are -16 and 16 respectively.
(c) The inflection points are [tex](\frac{\pi}{6},\ -2)\ \text{and}\ (\frac{5\pi}{6},\ -2)[/tex]
Step-by-step explanation:
The function provided is:
[tex]f(x)=8cos^{2}(x)-16sin( x);\ 0\leq x\leq 2\pi[/tex]
(a)
[tex]f(x)=8cos^{2}(x)-16sin( x);\ 0\leq x\leq 2\pi[/tex]
Then, [tex]f'(x)=-16cos(x)sin(x)-16cos(x)=-16cos(x)[1+sin(x)][/tex]
Note, [tex]1+sin(x)\geq 0\ \text{and }\ sin(x)\geq 1\\[/tex]
Then, [tex]sin(x)=-1\Rightarrow x=\frac{3\pi}{2}[/tex] for [tex]0\leq x\leq 2\pi[/tex].
Also [tex]cos(x)=0[/tex].
Thus, f (x) is increasing for,
[tex]f'(x)>0\\\Rightarrow cos(x)<0\\\Rightarrow \frac{\pi}{2}< x< \frac{3\pi}{2}[/tex]
And f (x) is decreasing for,
[tex]f'(x)<0\\\Rightarrow cos(x)>0\\\Rightarrow 0< x< \frac{\pi}{2}\ \text{or}\ \frac{3\pi}{2}< x< 2\pi[/tex]
(b)
From part (a) f (x) changes from decreasing to increasing at [tex]x=\frac{\pi}{2}[/tex] and from increasing to decreasing at [tex]x=\frac{3\pi}{2}[/tex].
The local minimum value is:
[tex]f(\frac{\pi}{2})=8cos^{2}(\frac{\pi}{2})-16sin(\frac{\pi}{2})=-16[/tex]
The local maximum value is:
[tex]f(\frac{3\pi}{2})=8cos^{2}(\frac{3\pi}{2})-16sin(\frac{3\pi}{2})=16[/tex]
(c)
Compute the value of f'' (x) as follows:
[tex]f''(x)=16sin(x)[1+sin(x)]-16cos^{2}(x)\\\\=16sin(x)+16sin^{2}(x)-16[1-sin^{2}(x)]\\\\=32sin^{2}(x)+16sin(x)-16\\\\=16[2sin(x)-1][sin (x)+1][/tex]
So,
[tex]f''(x)>0\\\Rightarrow sin(x)>\frac{1}{2}\\\Rightarrow \frac{\pi}{6}<x<\frac{5\pi}{6}[/tex]
And,
[tex]f''(x)<0\\\\\Rightarrow sin(x)<\frac{1}{2}\ \text{and}\ sin (x)\neq -1\\\\\Rightarrow 0<x<\frac{\pi}{6}\ \text{or} \frac{5\pi}{6}<x<\frac{3\pi}{2}\ \text{or}\ \frac{3\pi}{2}<x<2\pi[/tex]
Thus, f (x) is concave upward on [tex](\frac{\pi}{6},\ \frac{5\pi}{6})[/tex] and concave downward on [tex](0,\ \frac{\pi}{6}), (\frac{5\pi}{6},\ \frac{3\pi}{2})\ \text{and}\ (\frac{3\pi}{2},\ 2\pi)[/tex].
If [tex]x=\frac{\pi}{6}[/tex], then f (x) will be:
[tex]f(\frac{\pi}{6})=8cos^{2}(\frac{\pi}{6})-16sin(\frac{\pi}{6})=-2[/tex]
If [tex]x=\frac{5\pi}{6}[/tex], then f (x) will be:
[tex]f(\frac{5\pi}{6})=8cos^{2}(\frac{5\pi}{6})-16sin(\frac{5\pi}{6})=-2[/tex]
The inflection points are [tex](\frac{\pi}{6},\ -2)\ \text{and}\ (\frac{5\pi}{6},\ -2)[/tex].
11. What are the vertices of the ellipse whose equation is (x2)/9 + (y2)/4 = 1? please show the work
Answer: I think that this is the answer
standard form of equation for ellipse with vertical major axis (a^2 under y^2):
(x-h)^2/b^2+(y-k)^2/a^2=1,a>b, (h,k) being the (x,y) coordinates of the center.
For given equation: x^2/9+y^2/36=1
center: (0,0)
a^2=36
a=√36=6
length of vertical major axis=2a=12
Vertices are end points of major axis=(0,0�a)=(0,0�6)=(0,-6) and (0,6)
Vertices are at (0,-6) and (0,6)
Step-by-step explanation:
Answer:
Explanation: General formula for vertical ellipse Given: x24+y29=1 ... Use the equation provided above, and "plug it" in.