According to the given information value of X =16.06
What is the volume of right cone?The volume of a cone defines the space or the capacity of the cone. A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex. A cone is formed by a set of line segments, half-lines or lines connecting a common point, the apex, to all the points on a base that is in a plane that does not contain the apex.
A cone can be seen as a set of non-congruent circular disks that are stacked on one another such that the ratio of the radius of adjacent disks remains constant.
According to the given information:Cone volume formula
A cone is a solid that has a circular base and a single vertex. To calculate its volume, you need to multiply the base area (area of a circle: π × r²) by height and by 1/3:
volume = (1/3) × π × r² × h
5677 = (1/3) x 22/7 x r² x 21
x = 16.06
Therefore, according to the given information value of X =16.06
To know more about click:
brainly.com/question/10625069
#SPJ1
What is the y-intercept of the line with the equation y = 4 x + 2?
a. -2
b. 4
c. 2
d. -1/2
Answer:
C. 2-----------------------------------
The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.
To find the y-intercept, substitute 0 for x in the equation y = 4x + 2:
y = 4*0 + 2 y = 2The y-intercept is 2 and matching choice is C.
Answer:
2
Step-by-step explanation:
We need to find out the y intercept of the given equation which is y = 4x + 2 .
y intercept is a point where the graph of the equation cuts the y axis. So at y intercept x coordinate will be 0 , so plug in x = 0 , in the given equation as ;
y = 4x + 2
y = 4(0) + 2
y = 0 + 2
y = 2
Therefore the y intercept of the line is 2 . ( option C )
find bases for the null spaces of the matrices given in exercises 9 and 10. refer to the remarks that follow example 3 in section 4.2.
In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.
The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.
The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.
for such more questions on Gauss-Jordan elimination
https://brainly.com/question/20536857
#SPJ11
a tank is being filled with water at the rate of 2 3 450t gallons per hour with t > 0 measured in hours. if the tank is originally empty, how many gallons of water are in the tank after 5 hours?
The rate of filling water in the tank is 23450t gallons per hour.
Let's assume that the time taken to fill the tank is t hours.
The volume of water filled into the tank at time t is given by the expression V(t) = 23450t.
The tank is originally empty, which means its volume = 0 gallons.
After 5 hours,
t= 5 hours
The volume of water filled in is given by [tex]V(5) = 23450 * 5= 1,17,250[/tex] gallons of water.
Therefore, 1,17,250 gallons of water are filled in the tank after 5 hours.
For more information on the rate of change, refer to:
brainly.com/question/29012717
#SPJ11
0 | 40
1 | 40.75
3 | 42.5
5 | 44
7 | 45.25
Use the line segment that connects ______ and _______ to estimate the vine length after 4 days.
After 4 days, the vine length is about ______.
The top is a chart Please help me!!!
Use the line segment that connects (3, 42.5) and (5, 44) to estimate the vine length after 4 days.
How to determine the lengths after 4 daysGiven the table of values
To do this, we make use of linear interpolation
Such that the points closest to day 4 are (3, 42.5) and (5, 44)
The slope of the line passing through the two points can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (3, 42.5) and (x2, y2) = (5, 44).
Thus, we have:
m = (44 - 42.5) / (5 - 3) = 0.75
So, we have
y = 0.75x + b
Using the point (3, 42.5), we get:
42.5 = 0.75(3) + b
Solving for b, we get:
b = 42.5 - 0.75(3)
b = 40.25
So, the equation is
y = 0.75x + 40.25
To estimate the vine length after 4 days, we substitute x = 4 into the equation and solve for y:
y = 0.75 * 4 + 40.25
y = 43.25
Therefore, the vine length after 4 days is estimated to be about 43.25 units.
Read more about linear regression at
https://brainly.com/question/10209928
#SPJ1
find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. calculatot
Therefore, the volume of the solid obtained by rotating the region bounded by the curves y = x^2, y = 0, x = 0, and x = 1 about the line x = 2 is (5/6)π cubic units.
To find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line, we use the method of cylindrical shells. The formula for the volume of a cylindrical shell is given as,
Volume = 2πrh * Δx
Where, r is the distance of the shell from the axis of rotation, h is the height of the shell, and Δx is the thickness of the shell. The factor 2π accounts for the entire circumference of the shell.
Example problem: Find the volume of the solid generated by rotating the region bounded by the curves y = x^2, y = 0, x = 0, and x = 1 about the line x = 2.
Solution:
Step 1: Draw the graph of the region to be rotated
Step 2: Identify the shell radius and height
For a shell at position x, the radius is given by r = 2 - x (the distance of the line x = 2 from the axis of rotation)
The height of the shell is given by h = x^2 (the difference between the top and bottom curves)
Step 3: Write the volume formula
Volume = 2πrh * Δx
Step 4: Integrate to find the total volume
The limits of integration are from 0 to 1 since the curves intersect at (0,0) and (1,1).
[tex]∫ 2π(2 - x)(x^2) dx from 0 to 1[/tex]
= [tex]2π [∫ 2x^2 - x^3 dx from 0 to 1][/tex]
= [tex]2π [(2/3) - (1/4)][/tex]
= 2π [5/12][tex]2π [5/12][/tex]
= (5/6)π cubic units
for such more questions on integration
https://brainly.com/question/22008756
#SPJ11
Can someone please help me with this?
The measure of the side MR is given as 20
How to solve for the side MRWe have to first find the value of the angle
∠TQR = 180 - (35 + 25)
= 180 - 60
= 120 degrees
180 - 120 = 60 degrees
angle TPR = 90 degrees
next we have to find ∠PTQ
= 180 - (90 + 60)
= 180 - 150
= 30 degrees
given that TMN = TQR
TNP = PTQ
So if TMN = 35 degrees since TQR = 35 degrees
PTQ = 30, so TNP = 30 degrees
The measure of QR = 4 since MN = 4
NP = pq
np = 6
Hence the measure of MR
= 4 + 6 + 6 + 4
= 20
Read more on angles here:https://brainly.com/question/25770607
#SPJ1
Simplify n+1 combination 3 - n+1 combination 3
The simplified form of the combination is (3n² - 5n + 3)/3
Now let's return to the problem at hand. We have the expression ⁿ⁺¹C₃ − ⁿ⁻¹C₃, which involves two combinations with slightly different values of n. To simplify this expression, we need to first expand each combination using the formula we just discussed.
Starting with ⁿ⁺¹C₃, we have:
ⁿ⁺¹C₃ = (n + 1)!/(3!(n - (3 + 1))!)
We can simplify this further by noting that (n - 4)! is the same as (n - 3 - 1)! and pulling out the common factors:
(n + 1)!/(3!(n - 4)!) = (n + 1)(n)(n - 1)/(3 x 2 x 1)
Next, let's expand ⁿ⁻¹C₃:
ⁿ⁻¹C₃ = (n - 1)!/(3!(n - (3 - 1))!)
Again, we can simplify by noting that (n - 2)! is the same as (n - 1 - 1)!:
(n - 1)!/(3!(n - 2)!) = (n - 1)(n - 2)(n - 3)/(3 x 2 x 1)
Now we can substitute these expressions back into the original equation:
ⁿ⁺¹C₃ − ⁿ⁻¹C₃ = (n + 1)(n)(n - 1)/(3 x 2 x 1) - (n - 1)(n - 2)(n - 3)/(3 x 2 x 1)
We can simplify this by finding a common denominator and combining like terms:
[(n + 1)(n)(n - 1) - (n - 1)(n - 2)(n - 3)]/(3 x 2 x 1)
Simplifying further, we can expand the terms:
[(n³ - n) - (n³ - 7n² + 11n - 6)]/(6)
Which gives us:
(6n² - 10n + 6)/6
We can simplify this by factoring out a 2 from each term in the numerator and denominator:
2(3n² - 5n + 3)/2(3)
And finally, we can cancel out the 2s to get:
(3n² - 5n + 3)/3
To know more about combination here
https://brainly.com/question/28998705
#SPJ4
Complete Question:
Simplify:
ⁿ⁺¹C₃ − ⁿ⁻¹C₃
Question 1 0.5 pts A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept focused on the man. Place the steps below in the correct order that they should be performed in order to the determine the rate at which the searchlight is rotating when the man is 15 ft from the point on the path closest to the searchlight. 1. Step 1 Draw a picture 2. Step 2 Write down the numerical info 3. Step 3 Determine what you are asket 4. Step 4 Write an equation relating the 5. Step 5 Plug in your known informatic 6. Step 6 Differentiate both sides of the h at a speed of 4 ft/s. A searchlight is located on the ground 20 ft d on th [Choose ] ey the de Differentiate both sides of the equation with respect to t on the 1 Determine what you are asked to find Write down the numerical information that you know Write an equation relating the variables Draw a picture Plug in your known information to solve the problem Write down the numerical info v V Determine what you are asker
In order to determine the rate at which the searchlight is rotating when the man is 15 ft from the point on the path closest to the searchlight, the following steps should be performed in this order
Learn more about Equation
brainly.com/question/24169758
#SPJ11
a family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. each member of the family averages 8 minutes in the shower per day. in a 30-day period, how many fewer gallons of water will the family use with the new showerheads? responses 60 60 800 800 2,400 2,400 3,600 3,600 7,200
The family will use 3,600 fewer gallons of water with the new showerheads in a 30-day period.
A family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. Each member of the family averages 8 minutes in the shower per day. In a 30-day period, the family will use 3,600 fewer gallons of water with the new showerheads. How many fewer gallons of water will the family use with the new showerheads?
Calculate the number of gallons used per person per shower before:
5 gal/min x 8 min = 40 gallons per person per shower.
The number of gallons used per person per shower after:
2 gal/min x 8 min = 16 gallons per person per shower.
The number of gallons used per person per day before:
40 gallons x 1 shower = 40 gallons per person per day.
The number of gallons used per person per day after:
16 gallons x 1 shower = 16 gallons per person per day
The number of gallons used per family per day before:
40 gallons x 5 people = 200 gallons per day
The number of gallons used per family per day after:
16 gallons x 5 people = 80 gallons per day
The number of gallons used per month before:
40 gallons x 5 people x 30 days = 6,000 gallons per month
The number of gallons used per month after:
16 gallons x 5 people x 30 days = 2,400 gallons per month
The family will use 6,000 - 2,400 = 3,600 fewer gallons of water with the new showerheads in a 30-day period. Therefore, the answer is 3,600.
To learn more about water gallon problems refer :
https://brainly.com/question/14700882
#SPJ11
An experiment was conducted to test the effect of a new cholesterol medicine. Fifteen people were treated with medicine X and 15 with medicine y for a month; then the subjects' cholesterol level was measured. A
significance test was conducted at the 0. 01 level for the mean difference in cholesterol levels between medicine X and medicine Y. The test resulted in t - 2. 73 and p = 0. 3. If the alternative hypothesis in
question was Mo: px - WY* 0, where wx equals the mean cholesterol level for subjects taking medicine X and by equals the mean cholesterol level for subjects taking medicine Y, what conclusion can be drawn? (2
points)
There is sufficient evidence that there is a difference in mean cholesterol level when using medicine X and medicine Y.
There is not a significant difference in mean cholesterol level when using medicine X and medicine Y.
There is sufficient evidence that medicine X towers cholesterol levels more than medicine Y.
The proportion of subjects who lowered their cholesterol level with medicine X is greater than the proportion of subjects who lowered their cholesterol level with medicine Y.
There is insufficient evidence that the proportion of people who lowered cholesterol level on medicine X and Y is different.
The right answer is provided by: Taking into account the hypothesis tested and the p-value of the test.
There is enough proof to conclude that using drugs X and Y results in different mean cholesterol levels.
What theories are being tested?
If there is no difference in the cholesterol levels, then the null hypothesis is tested, which is:
H₀:Hₓ-H
It is determined whether there is a difference at the alternative hypothesis, so:
H₀:Hₓ-H≠0
The p-value of 0.003 0.01 leads us to reject the null hypothesis and determine that there was a difference, hence the following is the right response:
There is enough proof to conclude that using drugs X and Y results in different mean cholesterol levels.
To know more about hypothesis tests, click the below link
brainly.com/question/26454209
#SPJ4
just need help with part (b) please
In response to the stated question, we may state that As a result, the formula for the sequence's nth term is: [tex]a_n = a _1 * r^{(n-1) (n-1)}[/tex]
What is Sequences?In mathematics, a sequence is an ordered list of items. Elements can be numbers, functions, or other mathematical objects. A series is commonly expressed by putting the phrases in parentheses and separating them with commas. A natural number series, for example, can be denoted as: (1, 2, 3, 4, 5, ...) Similarly, the even number series is labelled as follows: (2, 4, 6, 8, 10, ...) A series can be finite or infinite depending on whether it has a finite or infinite number of words.
a. Since the difference between subsequent terms is constant, the series 5, 7, 8,... is an arithmetic sequence. The usual difference is 2, specifically. As a result, the formula for the sequence's nth term is:
[tex]a_n = a_1 + (n-1)d[/tex]
where a 1 represents the first term, d represents the common difference, and n represents the term number. Using the provided values, we get:
[tex]a_n = 5 + (n-1)2\\a_n = 2n + 3[/tex]
b. Since the ratio between subsequent terms is constant, the series 6, 30, 150,... is a geometric sequence. The common ratio is 5, specifically. As a result, the formula for the sequence's nth term is:
[tex]a_n = a _1 * r^{(n-1) (n-1)}[/tex]
where a 1 denotes the first term, r the common ratio, and n the term number
[tex]a_n = 6 * 5^{(n-1) (n-1)}[/tex]
To know more about Sequences visit:
https://brainly.com/question/21961097
#SPJ1
PLEASE HELP!!! WILL MARK BRANLIEST!!!
Answer:
The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.
Step-by-step explanation:
qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]
where r = |z| = magnitude of z and theta = arg(z) = argument of z.
Calculate the magnitude of z:
|r| = sqrt((3)^2 + (4)^2) = 5
And the argument of z:
theta = arctan(4/3) = 0.93 radians
Now, find the two square roots of z:
sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]
= +/- 1.58 * [cos(0.47) + i sin(0.47)]
= +/- 1.58 * [0.89 + i*0.46]
Using a calculator, simplify this expression to:
sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8
A triangle has a side that is 5 inches long that is adjacent to an angle of 61. In addition, the side oppositethe 61 angle is 4,8 inches long. There are two triangles with these measurements. For each one,determine the other two angles of the triangle and the length of the third side..acute:(a) The triangle in which the angle opposite the 5-inch side-The angle between the two given sides measuresnearest tenth of a degree.)The third angle measuresThe remaining side is approximatelyan inch.)(b) The triangle in which the angle opposite the 5-inch side is obtuse:The angle between the two given sides measuresnearest tenth of andegree.)WThe third angle measuresThe remaining side is approximatelyan inch.)degrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)Ainches long. (Round to the nearest tenth ofdegrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)inches long. (Round to the nearest tenth of an inch
The two remaining angles are 58°, and the length of the third side of the triangle is 6.5 inch.
In order to determine the other two angles of each triangle as well as the length of the third side, we need to use the Cosine Rule. According to the Cosine Rule, for any triangle with sides of length a, b, and c, and angles of A, B, and C, the following equation holds:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
For the first triangle, we are given that the side of length 5 is adjacent to an angle of 61°. Therefore, a = 5, C = 61°. Using the information provided, we can also determine that b = 4.8. Substituting these values into the Cosine Rule equation, we get:
[tex]c^2 = (5)^2 + (4.8)^2 - 2(5)(4.8) cos(61°)[/tex]
We can solve this equation to get c = 6.5. Therefore, the length of the third side in the first triangle is 6.5. Additionally, we can use the Triangle Angle Sum theorem to determine the other two angles. According to this theorem, the sum of the three angles of a triangle is 180°. Therefore, for the first triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.
For the second triangle, we use the same process, but with the given side lengths reversed. That is, we set a = 4.8, b = 5, and C = 61°. Again, substituting these values into the Cosine Rule equation, we get:
[tex]c^2 = (4.8)^2 + (5)^2 - 2(4.8)(5) cos(61°)[/tex]
We can solve this equation to get c = 6.5. Therefore, the length of the third side in the second triangle is also 6.5. We can use the Triangle Angle Sum theorem again to determine the other two angles. Again, for the second triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.
In conclusion, for each triangle, the two remaining angles are 58°, and the length of the third side is 6.5 inch.
Learn more about cosine rule: https://brainly.com/question/21568111
#SPJ11
24 354÷5 (use long division)
Please help me guys i need this right now
Answer:
487
or
4870
Step-by-step explanation:
(I might not have done it right)
is it 24,354 / 5 or 2,435 / 5?
Because I got 487
But to check an answer you must multiply
When I multiplied 5 x 487 the answer is 2,435
But 5 x 4870 is 24,350
It has to be one of these
a) What is the mean proportional between 3 and 12?
b) What is the geometric mean of 3 and 12?
Answer:
a. 6
b. 6
Step-by-step explanation:
A. mean proportion
3:x::x:12
product of mean = product of extreme
3 x 12 = x^2
x^2= 36
now take square root on both sides
x = 6
as sqaure root will cancel the square on x and square root of 36 is 6.
B. the geometric mean is the product of all
the numbers in a set, with the root of how many numbers there are. here, there are two numbers, so a square root is used. the value of the geometric mean of 3 and 12 is 6.
Hope's it helps...
Find the distance between A and B.
A. 4 (square root of 7) units
B. 11 units
C. (Square root of 14) units
D. (Square root of 130) units
Answer:
I think it's answer is no.B
PLEASE HELP a) Calculate the scale factor from shape A to shape B.
b) Find the value of t.
Give each answer as an integer or as a fraction (preferable) in its simplest form.
Question attached, Thank you!
Answer:
see explanation
Step-by-step explanation:
(a)
the scale factor is the ratio of corresponding sides, shape B to shape A
scale factor = [tex]\frac{12}{15}[/tex] = [tex]\frac{4}{5}[/tex]
(b)
t is then [tex]\frac{4}{5}[/tex] of 7 = [tex]\frac{4}{5}[/tex] × 7 = [tex]\frac{28}{5}[/tex]
what is the surface area
Answer: 24
Step-by-step explanation:
Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units.
= 2[(2*2)+(2*2)+(2*2)]
= 2[4+4+4]
=2[12]
24
ax+by=ac
make 'a' as the subject
The required equation in terms of 'a' is: a = (ac - by)/x.
What is Subject in equation?The number being calculated is the formula's subject. On one side of the equals symbol, it is identifiable as the letter on its own.
According to question:To make 'a' the subject of the equation:
Ax + by = ac
we can start by isolating 'a' on one side of the equation.
Ax = ac - by
Then, we can divide both sides by 'x':
a = (ac - by)/x
Therefore, the equation in terms of 'a' is:
a = (ac - by)/x
To know more about equation visit:
brainly.com/question/28243079
#SPJ1
Complete questiion:
Find the subject of the equation ax+by=ac.
Find the value of x.
Answer:
x=1.9
Step-by-step explanation:
[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]
[tex]11x=21.16[/tex]
[tex]X=1.9[/tex]
the amount of bacteria present in a medium after t hours is given by a (t )equals 16 e to the power of 0.32 t end exponent. at what rate is the amount of bacteria changing after 12 hours?
The rate at which the amount of bacteria is changing after 12 hours is 21.698 units/hour.
What is the rate at which the amount of bacteria changing after 12 hours?The given formula for the amount of bacteria present in a medium after t hours is:
[tex]a(t) = 16e^ (0.32t)[/tex]
Now, we need to find out at what rate the amount of bacteria is changing after 12 hours.
This means we need to find out the derivative of a(t) with respect to t and then substitute t = 12 in the derivative formula to get the rate of change of bacteria after 12 hours.
Differentiating the given formula for a(t) with respect to t, we get:
a'(t) = [tex]16(0.32)e^(0.32t)[/tex]
On substituting, t = 12, we get
a'(12) = [tex]16(0.32)e^ (0.32X12)[/tex]
On solving this, we get a'(12) = 21.698.
Therefore, the rate at which the amount of bacteria is changing after 12 hours is 21.698 units/hour.
Learn more about Bacteria here:
https://brainly.com/question/14067407
#SPJ11
The cost price of a book is Rs 20 . It is sold at 10% profit. Find its sale price
Answer:
Cost price (CP) = Rs20
% Profit = 10%
Selling price (SP) = y
By formula:
% Profit = (Profit/CP) x 100%
But Profit= SP - CP
Therefore;
% Profit = [(SP-CP)/C.P)] x 100%
Substituting, we have:
10% = [(y-20)/20] x 100%
10/100 = (y-20)/20
1/10 = (y-20)/20
1 = (y-20)/2
Cross multiply
y - 20 = 2
y = 2 + 20
y = 22
Therefore, the Sale price is Rs 22
Consider the following exponential probability density function. f(x) = 1/3 4 e^-x/3 for x > 0 a. Write the formula for P(x < x_0). b. Find P(x < 2). c. Find P(x > 3). d. Find P(x < 5). e. Find P(2 <.x <5).
The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.
The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:
F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx
a. Write the formula for P(x < x_0):
Using integration, we can solve this formula as follows:
F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]
= [-4e^(-x_0/3) + 4]/3
b. Find P(x < 2):
To find P(x < 2), we simply substitute x_0 = 2 in the above formula:
F(2) = [-4e^(-2/3) + 4]/3
≈ 0.4866
Therefore, the probability that x is less than 2 is approximately 0.4866.
c. Find P(x > 3):
To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:
P(x > 3) = 1 - P(x < 3) = 1 - F(3)
= 1 - [-4e^(-1) + 4]/3
≈ 0.3528
Therefore, the probability that x is greater than 3 is approximately 0.3528.
d. Find P(x < 5):
To find P(x < 5), we simply substitute x_0 = 5 in the above formula:
F(5) = [-4e^(-5/3) + 4]/3
≈ 0.6321
Therefore, the probability that x is less than 5 is approximately 0.6321.
e. Find P(2 < x < 5):
To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:
P(2 < x < 5) = P(x < 5) - P(x < 2)
= F(5) - F(2)
= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3
≈ 0.1455
Therefore, the probability that x is between 2 and 5 is approximately 0.1455.
To learn more about probability
https://brainly.com/question/30034780
#SPJ4
Y=5x+17 Y=-2x+4 solve with substitution
Answer:
x = -13/7, y = 54/7
Step-by-step explanation:
- Set equations equal to each other
[tex]5x + 17 = -2x +4[/tex]
Add 2x to both sides
[tex]7x +17 = 4[/tex]
Subtract 17 from both sides
[tex]7x = -13[/tex]
divide both sides by 7
[tex]x = -13/7[/tex]
Then substitute x into one of the equations. I picked the first one.
[tex]y = 5 (-13/7) + 17[/tex]
I multiplied 5 by -13 to get -65/7. Then I turned 17 into sevenths: 17 x 7 = 119, so that's 119/7. 119 + -65 = 54, so 54/7 for y.
Let me know if this helped by hitting thanks or brainliest. If not, please comment and I'll get back to you ASAP!
Which of the following algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order? A Heap Sort B Quick Sort Merge Sort (D Radix Sort
B) Quick Sort is algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order
What is Merge Sort Algorithm?Merge Sort is an effective algorithm for sorting the data items of a list or an array. This algorithm's fundamental idea is to break the unsorted list into many sub-lists until every sub-list contains only one item.
The merging procedure then recombines all of the sublists, resulting in a sorted list. Divide-and-conquer is the name given to this merging process. Merge Sort divides the original list into N sublists, each of which contains one element.
The Merge Sort algorithm is faster than other sorting algorithms when it comes to time complexity. The time complexity of Merge Sort is O (n log n), which is better than Bubble Sort and Insertion Sort.
It is a more efficient sorting algorithm than other algorithms, such as bubble sort, which has a higher time complexity of O (n²).
Therefore, we can say that Merge Sort is the most efficient algorithm to sort an array in ascending or descending order.
Learn more about Merge Sort Algorithm at
https://brainly.com/question/13152286
#SPJ11
what is the variance inflation factor measuring? (select all that apply) group of answer choices the variance of the error term how much the explanatory variables are associated with one another the variance of the coefficient estimates the collinearity of the explanatory variable
The Variance Inflation Factor (VIF) measures the degree of correlation or the collinearity of the explanatory variables.
VIF quantifies how much each explanatory variable is correlated with a linear combination of the other variables in a multiple regression model. This can help identify variables that are redundant, irrelevant, or harmful to the model's accuracy. The VIF is calculated for each explanatory variable by dividing the variance of the regression coefficient estimates by the variance of the regression coefficient estimates when that variable is excluded from the model.
If the VIF is greater than 1, it indicates that the variance of the regression coefficient estimate for that variable is inflated by the presence of the other variables, which reduces the model's accuracy. Therefore, a VIF greater than 1 is considered to be an indication of collinearity or multicollinearity in the explanatory variables. The VIF measures the degree of correlation or the collinearity of the explanatory variables, and it can identify variables that are redundant, irrelevant, or harmful to the model's accuracy.
Learn more about Variance Inflation Factor (VIF) here: https://brainly.com/question/28941844
#SPJ11
what is the value of y in the solution to the system of equations below.
y=-x+6
2x-y=-9
Answer:
I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.
for the first equation y=-x+6, y intercept is (0,6)
for equation two 2x-y=-9, y intercept is (0,9)
In both of the equations the x value is 1.
Solving for y without graphing. Y=9+2x
and x=-1
Step-by-step explanation:substitute i
HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5
It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.
Lightbulbs act as resistors. Janine is building a circuit that contains two lightbulbs in parallel. One of the lightbulbs has a resistance of 120 ohms, but the resistance of the second lightbulb is unknown. She models the total resistance in the circuit, t, with this equation, in which r represents the resistance of the second lightbulb. T = 120 r r + 120 Find the inverse of Janine’s equation. Big fraction Parentheses Vertical bars Square root Root Superscript (Ctrl+Up) Subscript (Ctrl+Down) Plus sign Minus sign Middle dot Multiplication sign Equals sign Less-than sign Greater-than sign Less-than or equal to Greater-than or equal to Pi Alpha Beta Epsilon Theta Lambda Mu Rho Phi Sine Cosine Tangent Arcsine Arccosine Arctangent Cosecant Secant Cotangent Logarithm Logarithm to base n Natural logarithm Bar accent Right left arrow with under script Right arrow with under script Angle Triangle Parallel to Perpendicular Approximately equal to Tilde operator Degree sign Intersection Union Summation with under and over scripts Matrix with square brackets
Lightbulbs act as resistors. Janine is building a circuit that contains two lightbulbs in parallel. One of the lightbulbs has a resistance of 120 ohms, but the resistance of the second lightbulb is unknown. Therefore, The inverse of Janine's equation is r = -120/(t - 120).
Equation:
An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign. An equation is a formula that expresses that two expressions are equal by joining them with the equal sign =.The word comparison and its cognates in other languages may have subtly different meanings; for example, in French, an equation is defined to contain one or more variables, and in English any well-formed formula composed of two expressions linked by equal signs is an equation.
According to the Question:
In algebra, an equation is a mathematical statement that determines whether two mathematical expressions are equal.
The type of comparison is identity or conditional comparison.
For each potential value, the variable provides an identifier. Only certain combinations of variable values allow conditional comparisons to be true.
In order to find the inverse of Janine's equation, we will to solve for r in terms of t.
First, we can rearrange the equation to get
⇒ t - 120 = 1/r.
divide both sides of the equation by 1/r to get
⇒ t/r - 120/r = 1.
divide both sides of the equation by -120/r to get
⇒ r = -120/(t - 120).
Therefore, the inverse of Janine's equation is r = -120/(t - 120).
Learn more about Equation:
https://brainly.com/question/29538993
#SPJ4
Simplify the expression 3(x+2)+5x and find the value of x=2
Answer:
12.
Step-by-step explanation:
Given: 3(x + 2) + 5x
Put in x:
3(2 + 2) + (5 x 2)
(3 x 4) + 10
12 + 10
= 12.
Proving Triangle Similarity
The proof is completed using two column proof as follows
Statement Reason
QT ⊥ PT Given
∠ QRP ≅ ∠ SRT = 90 definition of perpendicularity
∠ QPR ≅ ∠ STR Given
Δ PQR is similar to Δ TSR AA similarity theorem
What is AA similarity theorem?The AA similarity theorem, also known as the Angle-Angle Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.
In the given triangle, the two angles given to be equal are
∠ QRP ≅ ∠ SRT = 90 and ∠ QPR ≅ ∠ STRHence the triangles are similar
Learn more about AA similarity theorem at:
https://brainly.com/question/26462153
#SPJ1
Answer:
:)
Hopefully this helps you guys :)
good luck :D