Answer:
2.83
Step-by-step explanation:
For a normally distributed data :
Mean = 3.1 inches
Standard deviation = 0.4 inches
Find the value of the quartile Q1:
The quartile Q1 represents the first quartile which is the Lower 25% of the distribution
25% = 0.25
Using the z-table :
0.25 = - 0.68
The z- score formula
Z-score = ( x - mean / standard deviation)
-0.68 = ((x - 3.1) / 0.4)
x - 3.1 = (-0.68 * 0.4)
x - 3.1 = - 0.272
x = - 0.272 + 3.1
x = 2.828
x = 2.83
3/4 + 20 (2/5 x 4/7)
Answer:
i believe the answer is 5.3
PLEASE HELP
If a = -1, b = 2.5, and c = 3, then evaluate a+2[c^(2)-(b+c)].
Answer:
6
Step-by-step explanation:
Let a = -1, b = 2.5, and c = 3.
-1 + 2(3² - (2.5 + 3))
-1 + 2(9 - 5.5)
-1 + 2(3.5)
-1 + 7
6
A box contains12 balls in which 4 are white,3 blue and 5 are red.3 balls are drawn at random from the box.Find the chance that all three balls are of sifferent color.(answer in three decimal places)
[tex]|\Omega|=_{12}C_3=\dfrac{12!}{3!9!}=\dfrac{10\cdot11\cdot12}{2\cdot3}=220\\|A|=4\cdot3\cdot5=60\\\\P(A)=\dfrac{60}{220}=\dfrac{3}{11}\approx0,273[/tex]
Answer:
0.273
Step-by-step explanation:
Total number of balls is 4+3+5 = 12
There are 6 ways to draw 3 different colors (WBR, WRB, BWR, BRW, RWB, RBW) each with a chance of 4/12 · 3/11 · 5/10 = 1/22
So the total chance is 6 · 1/22 = 6/22 = 3/11 ≈ 0.273
Stuck on this problem
9514 1404 393
Answer:
-8,257,536·u^5·v^10
Step-by-step explanation:
The expansion of (a +b)^n is ...
(c0)a^nb^0 +(c1)a^(n-1)b^1 +(c2)a^(n-2)b^2 +... +(ck)a^(n-k)b^k +... +(cn)a^0b^n
Then the k-th term is (ck)a^(n-k)b^k, where k is counted from 0 to n.
The value of ck can be found using Pascal's triangle, or by the formula ...
ck = n!/(k!(n-k)!) . . . . where x! is the factorial of x, the product of all positive integers less than or equal to x.
This expansion has 11 terms, so the middle one is the one for k=5. That term will be ...
5th term = (10!/(5!(10-5)!)(2u)^(10-5)(-4v^2)^5
= (252)(32u^5)(-1024v^10) = -8,257,536·u^5·v^10
I need help please help me!
Answer:
36ft³
Step-by-step explanation:
Bottom rectangular prism: 2x2x6=24
Top rectangular prism: 2x2x3=12
24+12=36ft³
Answer:
[tex]\boxed{36ft^3}[/tex]
Step-by-step explanation:
Hey there!
Well to solve for V we need to find the volume of the 2 rectangular prism's given.
Rec#1: 2•3•2 = 12
Rec#2: 6•2•2 = 24
Rec#1 + Rec#2 = V
12 + 24 = 36ft³
Hope this helps :)
A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 7 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to discard a given lot on the basis of the number of defective chips in a simple random sample. They decide they can afford to test 100 chips from each lot. You are hired as their statistician.
There is a tradeoff between the cost of eroneously discarding a good lot, and the cost of warranty claims if a bad lot is sold. The next few problems refer to this scenario.
Problem 8. (Continues previous problem.) A type I error occurs if (Q12)
Problem 9. (Continues previous problem.) A type II error occurs if (Q13)
Problem 10. (Continues previous problem.) Under the null hypothesis, the number of defective chips in a simple random sample of size 100 has a (Q14) distribution, with parameters (Q15)
Problem 11. (Continues previous problem.) To have a chance of at most 2% of discarding a lot given that the lot is good, the test should reject if the number of defectives in the sample of size 100 is greater than or equal to (Q16)
Problem 12. (Continues previous problem.) In that case, the chance of rejecting the lot if it really has 50 defective chips is (Q17)
Problem 13. (Continues previous problem.) In the long run, the fraction of lots with 7 defectives that will get discarded erroneously by this test is (Q18)
Problem 14. (Continues previous problem.) The smallest number of defectives in the lot for which this test has at least a 98% chance of correctly detecting that the lot was bad is (Q19)
(Continues previous problem.) Suppose that whether or not a lot is good is random, that the long-run fraction of lots that are good is 95%, and that whether each lot is good is independent of whether any other lot or lots are good. Assume that the sample drawn from a lot is independent of whether the lot is good or bad. To simplify the problem even more, assume that good lots contain exactly 7 defective chips, and that bad lots contain exactly 50 defective chips.
Problem 15. (Continues previous problem.) The number of lots the manufacturer has to produce to get one good lot that is not rejected by the test has a (Q20) distribution, with parameters (Q21)
Problem 16. (Continues previous problem.) The expected number of lots the manufacturer must make to get one good lot that is not rejected by the test is (Q22)
Problem 17. (Continues previous problem.) With this test and this mix of good and bad lots, among the lots that pass the test, the long-run fraction of lots that are actually bad is (Q23)
Step-by-step explanation:
A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 7 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to discard a given lot on the basis of the number of defective chips in a simple random sample. They decide they can afford to test 100 chips from each lot. You are hired as their statistician.
There is a tradeoff between the cost of eroneously discarding a good lot, and the cost of warranty claims if a bad lot is sold. The next few problems refer to this scenario.
Problem 8. (Continues previous problem.) A type I error occurs if (Q12)
Problem 9. (Continues previous problem.) A type II error occurs if (Q13)
Problem 10. (Continues previous problem.) Under the null hypothesis, the number of defective chips in a simple random sample of size 100 has a (Q14) distribution, with parameters (Q15)
Problem 11. (Continues previous problem.) To have a chance of at most 2% of discarding a lot given that the lot is good, the test should reject if the number of defectives in the sample of size 100 is greater than or equal to (Q16)
Problem 12. (Continues previous problem.) In that case, the chance of rejecting the lot if it really has 50 defective chips is (Q17)
Problem 13. (Continues previous problem.) In the long run, the fraction of lots with 7 defectives that will get discarded erroneously by this test is (Q18)
Problem 14. (Continues previous problem.) The smallest number of defectives in the lot for which this test has at least a 98% chance of correctly detecting that the lot was bad is (Q19)
(Continues previous problem.) Suppose that whether or not a lot is good is random, that the long-run fraction of lots that are good is 95%, and that whether each lot is good is independent of whether any other lot or lots are good. Assume that the sample drawn from a lot is independent of whether the lot is good or bad. To simplify the problem even more, assume that good lots contain exactly 7 defective chips, and that bad lots contain exactly 50 defective chips.
Problem 15. (Continues previous problem.) The number of lots the manufacturer has to produce to get one good lot that is not rejected by the test has a (Q20) distribution, with parameters (Q21)
Problem 16. (Continues previous problem.) The expected number of lots the manufacturer must make to get one good lot that is not rejected by the test is (Q22)
Problem 17. (Continues previous problem.) With this test and this mix of good and bad lots, among the lots that pass the test, the long-run fraction of lots that are actually bad is (Q23)
6x - 10 = 4(x + 3) x = ? x = 9 x = 10 x = 11 x = 12
Answer:
x=11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
6x - 10 = 4(x+3)
6x - 10 = 4*x + 4*3
6x - 10 = 4x + 12
6x - 4x = 12 + 10
2x = 22
x = 22/2
x = 11
check:
6*11 - 10 = 4(11+3)
66 - 10 = 4*14 = 56
Suppose that X; Y have constant joint density on the triangle with corners at (4; 0), (0; 4), and the origin. a) Find P(X < 3; Y < 3). b) Are X and Y independent
The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]
where T is the set
[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]
(a) I've attached an image of the integration region.
[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]
(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.
Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:
[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]
[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]
Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.
1. Find the length of the side indicated.
6
9.1
?
Answer:
10.9
Step-by-step explanation:
[tex]a^2+b^2=c^2[/tex]
[tex]9.1^2+6^2=c^2[/tex]
[tex]82.81+36=c^2[/tex]
[tex]c^2=118.81[/tex]
[tex]c=\sqrt{118.81} =10.9[/tex]
which rate can you set 7 miles over 1 hour equal to in order to find the distance traveled in 49 hours at 7 miles per hour
Answer:
Step-by-step explanation:
time = 49 hours
speed = 7 miles/hour
speed = distance / time
∴ distance = speed × time
= 7 × 49
= 343 miles
Nathan saves 5 1/4% of his weekly salary. Naban earns $380.00 per week. How much
does he save per week?
.
A.$19.95
B.$20.52
C.$21.95
D.$25.20
Answer:
19.95
Step-by-step explanation:
Take the amount of his salary and multiply by 5 1/4 %
380 * .0525
19.95
10 - 2x, when x = 3
Answer:
4
Step-by-step explanation:
Plug in 3 as x in the expression:
10 - 2x
10 - 2(3)
10 - 6
= 4
Answer:
4
Step-by-step explanation:
10 - 2x
Let x =3
10 -2(3)
10 -6
4
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
In 8 cups it is possible to measure the 2kg or 2000 grams but in three weighs it is not possible to measure the 2kg or 2000 grams.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
You have 9kg of oats and cup scales that gears of 50g and 200g.
Total oats need to measure = 9kg
As we know in 1 kg there are 1000 grams.
1 kg = 1000 grams
9kg = 9000 grams
2kg = 2000 grams
Cup scales that gears: 50g and 200g
The number of cups if consider one cup is of 250 grams( = 200 + 50)
Number of cups = 2000/250
Number of cups = 8
In three weighs it is not possible to measure the 2kg or 2000 grams.
Thus, in 8 cups it is possible to measure the 2kg or 2000 grams but in three weighs it is not possible to measure the 2kg or 2000 grams.
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Help with question b please
9514 1404 393
Answer:
(a) 5.82 cm (correctly shown)
(b) 10.53 cm
Step-by-step explanation:
a) The length BC can be found from the law of sines:
BD/sin(C) = BC/sin(D)
BC = BC·sin(C)/sin(D) = (6 cm)sin(48°)/sin(50°) ≈ 5.82 cm
__
b) The angle ABD is the sum of the angles shown:
angle ABD = 50° +48° = 98°
We know the lengths BA and BD and the included angle ABD, so we can use the law of cosines to find AD.
AD² = BA² +BD² -2·BA·BD·cos(98°)
AD² ≈ 8² +5.82² -2(8)(5.82)(-0.139173) ≈ 110.8411
AD ≈ √110.8411 ≈ 10.53 . . . . cm
Circle O has a circumference of approximately 28.3 cm. Circle O with radius r is shown. What is the approximate length of the radius, r? 4.5 cm 9.0 cm 14.2 cm 28.3 cm
Answer:
4.5cm
Step-by-step explanation:
Circumference = 2[tex]\pi[/tex]r
28.3=2[tex]\pi[/tex]r
28.3/2[tex]\pi[/tex]=r
4.456
The radius of the circle O is 4.5 cm.
What is radius?A radius is a measure of distance from the center of any circular object to its outermost edge or boundary.
Given that, a circle having a circumference of approximately 28.3 cm, we need to find its radius,
So, Circumference = 2 π × radius
2 π × radius = 28.3
Radius = 28.3 / 2π
Radius = 28.3 / 6.28
Radius = 4.5
Hence, the radius of the circle O is 4.5 cm.
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Is this a function help
Write a few sentences to describe the picture below. Can you use the words “slide”, “flip”or “turn”in your description?
Answer:
Turn
Step-by-step explanation:
you could say that, "No matter which way you turn the image, it stays the same".
hope this helps :D
Can some help with the answer please it’s very much needed and apprIeciated
Answer:
A
Step-by-step explanation:
The degree of the Polynomial is 3
You can often use geometric figures to model objects in the real world. You can transfer your knowledge of the properties of these figures to better understand and describe the objects that they represent. For each shape the table, list three examples of real-world objects that could be modeled by the shape. Use your experiences, the Internet, newspapers, magazines, or other resources to uncover examples.
Geometric figures are basically figures that have a boundary. The geometric figures and their real life examples are:
Rectangular prism: Building block, Gift box, CabinetTriangular prism: Tomblerone, Triangular roofs, Camping tentsCylinder: Pencil holders, Toilet paper rolls, Drink cansCone: Funnel, Party hat, Traffic conePyramid: Pyramids of Egypt, Pyramid roof, Pyramid tentsSphere: Soccer ball, Golf ball, PlanetsTo determine the real life object of each geometric figure, we simply identify objects that have similar features as the geometric figure.
For instance, a rectangular prism has 6 rectangular faces; building blocks, some gift box and cabinets also have 6 rectangular faces.
So, these three real life objects can be used as examples of a rectangular prism.
When the above explanation is applied to the other geometric figures, we come up with the following list:
Triangular prism: Tomblerone, Triangular roofs, Camping tentsCylinder: Pencil holders, Toilet paper rolls, Drink cansCone: Funnel, Party hat, Traffic conePyramid: Pyramids of Egypt, Pyramid roof, Pyramid tentsSphere: Soccer ball, Golf ball, PlanetsRead more about geometric figures at:
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In the photo are a couple possible answers you could use.
In the diagram below, ΔABC ≅ ΔDEF. Complete the statement AB¯¯¯¯¯¯¯¯≅ __
A. BC
B. DF
C. FE
D. DE
Answer:
The answer would be D. DE
Step-by-step explanation:
same prob
Congruent triangles are exact same triangles, but they might be placed at different positions. The correct option is D.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes the length of line segment AB, and so on for others).
Given that ΔABC ≅ ΔDEF. Therefore, the given sentence can be completed as AB ≅ ΔDE.
Hence, the side AB ≅ ΔDE
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The parallelogram to be a square,x=?
Answer:
7°
Step-by-step explanation:
for this paralellogram to be a square, the sides should be perpendicular.
Woch means that 4x+17° = 45°
● 4x +17° = 45°
Substract 17 from both sides.
● 4x +17°-17° = 45°-17°
● 4x = 28°
Divide both sides by 4
● 4x/4 = 28°/ 4
● x = 7°
Help please, I’m confused about this question.
Answer:
The order, least to greatest, is:
Lemon, Cherry, Grape.
Step-by-step explanation:
Adding all these values up, we get to 1. This means that the smallest values will be the least likely and the highest values will be the most likely.
With the numbers 0.2, 0.16, and 0.64, we can sort these by value.
0.16 is the smallest.
0.2 is the next biggest
and 0.64 is the largest number.
So, the order is Lemon, Cherry, Grape.
Hope this helped!
Solve the equation for y. Identify the slope and y- intercept. Then graph the equation. 2y-3x=10
Answer:
y=3/2x+5
The slope is 3/2 and the y-intercept is 5
Step-by-step explanation:
Solving for y will give us the slope and y-intercept
Isolate y
2y/2=10+3x/2
y=5+3/2x
The slope is 3/2 and the y-intercept is 5
Graph it by graphing (0,5) and using the slope (up 3 over 2) to put other points
Which of the following theorems verifies that AABC - ASTU?
A. AA
B. HL
C. HA
D. LL
Answer:
AA
Step-by-step explanation:
See In Triangle ABC and Triangle STU
[tex]\because\begin{cases}\sf \angle A=\angle S=90° \\ \sf \angle B=\angle T=31°\end{cases}[/tex]
Hence
[tex]\sf \Delta ABC~\Delta STU(Angle-Angle)[/tex]
By AA similarity triangle ABC is similar to triangle SUT. Therefore, option A is the correct answer.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
In the given triangle ABC, ∠C=180°-90°-31°
∠C=59°
In the given triangle SUT, ∠U=180°-90°-31°
∠U=59°
Here, ∠B=∠T (Given)
∠C=∠U (Obtained using angle sum property of a triangle)
So, by AA similarity ΔABC is similar to ΔSUT.
Therefore, option A is the correct answer.
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One car travels 390 miles in the same amount of time it takes a second car traveling 3 miles per hour slower than
the first to go 372 miles. What are the speeds of the cars?
The speed of the cars are
miles per hour.
The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time hr and y = RBOT time min for 12 oil specimens.TOST 4200 3575 3750 3700 4050 2770 4870 4500 3450 2675 3750 3300RBOT 370 340 375 310 350 200 400 380 285 220 345 280Required:Calculate the value of the sample correlation coefficient. Round your answer to four decimal places. r = _____
Answer:
0.9259
Step-by-step explanation:
Given the following data :
TOST(x) :4200 3575 3750 3700 4050 2770 4870 4500 3450 2675 3750 3300
RBOT(y) : 370 340 375 310 350 200 400 380 285 220 345 280
The correlation Coefficient tells about the strength of the statistical relationship which exists between two variables. The value of correlation Coefficient ranges from - 1 to +1.
The closer the value of correlation Coefficient is to ±1 , the stronger the correlation Coefficient with a negative and positive values signifying a negative and positive relationship respectively. Value of 1 depicts a perfect correlation while 0 means no relationship exists between them. Values close to zero denotes weak relationship.
Using the online Coefficient of correlation calculator ;
The r value of the data above is 0.9259 which signifies a very strong positive relationship between the variables.
In this exercise we have to calculate the value of the coefficient which can be descriptive statistics as:
0.9259
Given the following data :
[tex]TOST(x) :\\4200\\ 3575\\ 3750 \\3700\\ 4050\\ 2770\\ 4870\\ 4500\\ 3450\\ 2675\\ 3750\\ 3300[/tex][tex]RBOT(y) : \\370 \\340 \\375\\ 310\\ 350\\ 200\\ 400\\ 380\\ 285\\ 220\\ 345\\ 280[/tex]
The correlation Coefficient tells about the strength of the statistical relationship which exists between two variables. The value of correlation Coefficient ranges from - 1 to +1.
The closer the value of correlation Coefficient is to ±1 , the stronger the correlation Coefficient with a negative and positive values signifying a negative and positive relationship respectively. Value of 1 depicts a perfect correlation while 0 means no relationship exists between them. Values close to zero denotes weak relationship.
Using the online Coefficient of correlation calculator, the r value of the data above is 0.9259 which signifies a very strong positive relationship between the variables.
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1
1 point
mZABD = 79
D
C
V
(5x + 4)
(8x - 3)
В B.
A
x= type your answer...
2
1 point
Answer:
x = 6
Step-by-step explanation:
∠ DBC + ∠ ABC = ∠ ABD , substitute values
5x - 4 + 8x - 3 = 79
13x + 1 = 79 ( subtract 1 from both sides )
13x = 78 ( divide both sides by 13 )
x = 6
Jamie kept track of the total hours and minutes she worked this week at the local health food store.
Monday - 3 hours
Thursday - 5 hours 30 minutes
Saturday - 3 hours 30 minutes
Sunday - 6 hours 45 minutes
How many decimal hours did Jamie work this week? (2 points)
17.11
18.05
18.75
Answer:
18.05
Step-by-step explanation:
A 7ft board is to be cut into three pieces, two equal length ones and the third 6 inches shorter than each of the other two. If the cutting does not result in any length being lost, how long are the pieces?
Answer:
The two boards of equal length are 30 inches long, and the third board is 24 inches long
Step-by-step explanation:
First, convert the length of the board to inches. There are 12 inches in a foot, so multiply 7 by 12:
7(12)
= 84
Let x represent the length of the two boards of equal length. The length of the third board can be represented by x - 6, since it is 6 inches shorter than the other two.
Create an equation to represent this and solve for x:
(x) + (x) + (x - 6) = 84
3x - 6 = 84
3x = 90
x = 30
So, the two boards of equal length are 30 inches long.
Subtract 6 from this to find the length of the third board:
30 - 6
= 24
The two boards of equal length are 30 inches long, and the third board is 24 inches long.
Given the exponential function f(x) = 16(0.75)", classify the function as exponential growth or decay and determine the percent rate of growth or decay.
Exponential growth, 75% increase
O Exponential decay, 75% decrease
O Exponential growth, 25% increase
Exponential decay, 25% decrease
Answer:
D
Step-by-step explanation:
To determine if a function is exponential decay or growth, simply look at the rate. If the rate is less than one, it is decay. It it's greater than one, it's growth.
The rate in the given function is 0.75 or 75%. 0.75 is less than one so it's exponential decay.
To determine the percent decrease, simply subtract the rate into 1 or 100%. Thus:
[tex]1-0.75=0.25[/tex]
Therefore, it is a 0.25 or 25% decrease.
The answer is D.
Answer: D
Step-by-step explanation:
1-0.75=0.25
Therefore, it decreases Exponential decay,25 percent decrease