Yes, if there are more concordant pairs in the rank order, it makes sense that the Kendall correlation will be positive, as it suggests a tendency for the two variables to move in the same direction more often.
In Kendall correlation,
Rank values of each observation for the two variables are compared to determine the level of agreement or disagreement between them.
A concordant pair is when the rank order of the two variables is the same both increase or decrease together.
A discordant pair is when the rank order is different one variable increases while the other decreases.
If there are more concordant pairs, it means that the two variables tend to move in the same direction more often.
Which suggests a positive correlation relationship between them.
Conversely, if there are more discordant pairs, it means that the two variables tend to move in opposite directions more often.
Which suggests a negative relationship between them.
Example ,
two variables, X and Y, that are positively correlated.
If we plot the observations of X and Y on a scatter plot.
Expect to see a pattern where as the values of X increase, the values of Y also tend to increase.
Learn more about correlation here
brainly.com/question/19263847
#SPJ4
Help with problem in photo
The measures of the arc angle AP is 63° using the Angles of Intersecting Chords Theorem
What is the Angles of Intersecting Chords Theorem
The Angles of Intersecting Chords Theorem states that the angle formed by the intersection of the chords is equal to half the sum of the intercepted arcs, and conversely, that the measure of an intercepted arc is half the sum of the two angles that intercept it.
109° = (AP + RQ)/2
109 = (AP + 155)/2
AP + 155 = 2 × 109 {cross multiplication}
AP + 155 = 218
AP = 218 - 155 {collect like terms}
AP = 63°
Therefore, the measures of the arc angle AP is 63° using the Angles of Intersecting Chords Theorem
Read more about chords here:https://brainly.com/question/13950364
#SPJ1
A student drilled a hole into a six-sided die and filled it with a lead weight, then proceeded to roll the die 200 times here are the observed frequencies 27 31 42 40 28 and 32 use a 0. 05 significance level to test the claim that the outcomes are not equally likely find the test statistic x^2 and critical value for the goodness-of-fit needed to test the claim
To test the claim that the outcomes of rolling the modified die are not equally likely, we can use a chi-square goodness-of-fit test. We will use a significance level of 0.05.
The null hypothesis is that the outcomes are equally likely. The alternative hypothesis is that the outcomes are not equally likely.
First, we need to calculate the expected frequencies assuming that the outcomes are equally likely.
Since the die has six sides, each outcome has a probability of 1/6. Therefore, the expected frequency for each outcome is 200/6 = 33.33.
To calculate the test statistic [tex]x^2[/tex], we can use the formula:
[tex]x^2 = Σ (observed frequency - expected frequency)^2 / expected frequency[/tex]
where Σ is the sum over all outcomes.
Using the observed and expected frequencies given in the problem, we get:
[tex]x^2 = (27 - 33.33)^2 / 33.33 + (31 - 33.33)^2 / 33.33 + (42 - 33.33)^2 / 33.33 + (40 - 33.33)^2 / 33.33 + (28 - 33.33)^2 / 33.33 + (32 - 33.33)^2 / 33.33[/tex]
[tex]x^2 = 3.02[/tex]
The degrees of freedom for this test is 6 - 1 = 5 (since there are 6 sides on the die).
Using a chi-square distribution table (or calculator), we can find the critical value for a significance level of 0.05 and 5 degrees of freedom to be 11.070.
Since the test statistic x^2 = 3.02 is less than the critical value of 11.070, we fail to reject the null hypothesis.
Therefore, we do not have enough evidence to conclude that the outcomes of rolling the modified die are not equally likely.
To know more about significance level refer here
https://brainly.com/question/13947717#
#SPJ11
The box plot displays the number of push-ups completed by 9 students in a PE class.
A box plot uses a number line from 12 to 58 with tick marks every 2 units. The box extends from 27.5 to 42.5 on the number line. A line in the box is at 37. The lines outside the box end at 15 and 55. The graph is titled Push-Ups In PE and the line is labeled Number of Push-Ups.
Which of the following represents the value of the lower quartile of the data?
27.5
37
42.5
55
the answer is Q1 = 27.5
009 10.0 points Let f be a function defined on (-1, 1] such that f(-1) = f(1) = . Consider the following properties that f might have: A. f(1) = 2; x | | B. f continuous on (-1, 1]; C. Which properties ensure that there exists cin (-1, 1) at which f'(c) = 0? - f(x) = 22/3 = x2 1. B and C only 2. none of them 3. all of them 4. B only 5. C only 6. A and C only 7. A only 8. A and B only
Properties B and C together ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0.
Your answer: 1. B and C only
Which properties ensure that there exists ?
a 'c' in (-1, 1) at which f'(c) = 0, given f(-1) = f(1) = and the properties A, B, and C.
First, let's define the properties:
f(1) = 2
f is continuous on (-1, 1]
f(x) = (22/3) - x^2
To ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0, we will use the Mean Value Theorem (MVT). MVT states that if a function is continuous on a closed interval and differentiable on an open interval, then there exists at least one 'c' in the interval where the derivative is 0.
Looking at property B, it states that f is continuous on (-1, 1], which satisfies the first condition of the MVT. Property C provides a specific function for f(x), which is differentiable on (-1, 1) since it is a polynomial function. Therefore, properties B and C together ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0.
Your answer: 1. B and C only
Learn more about Mean Value Theorem.
brainly.com/question/30403137
#SPJ11
Draw a triangle with side lengths that are 3 inches, 5 inches, and 6 inches long. Is this the only triangle that you can draw using these side lengths? Explain
The combination of these side lengths uniquely determines the shape of the triangle.
Hi! To draw a triangle with side lengths 3 inches, 5 inches, and 6 inches, make sure that the sum of any two sides is greater than the third side. In this case, 3 + 5 > 6, 3 + 6 > 5, and 5 + 6 > 3, so a triangle can be formed.
Yes, this is the only triangle you can draw using these side lengths.
The reason is that the side lengths are fixed, and according to the triangle inequality theorem, the combination of these side lengths uniquely determines the shape of the triangle.
The combination of these side lengths uniquely determines the shape of the triangle.
To know more about triangle refer here
https://brainly.com/question/2773823#
#SPJ11
A velociraptor runs 5m [e] , 10 m [w], 3m [s], & 2m [w] in 10 seconds. calculate speed & velocity.
The velociraptor's speed is 2 m/s, and its velocity is -0.3 m/s [w].
What is the total distance covered?
To calculate the speed and velocity of the velociraptor, we need to first find the total distance it covered and the displacement.
Total distance = 5m + 10m + 3m + 2m = 20m
Displacement = Final position - Initial position
Displacement = (2m [w]) - (5m [e])
Displacement = -3m [w]
Velocity is defined as displacement per unit time, while speed is defined as distance per unit time.
Velocity = Displacement / Time
Velocity = -3m [w] / 10s
Velocity = -0.3 m/s [w]
Speed = Total distance / Time
Speed = 20m / 10s
Speed = 2 m/s
Therefore, the velociraptor's speed is 2 m/s, and its velocity is -0.3 m/s [w].
Learn more about velociraptors
brainly.com/question/15557097
#SPJ11
Ann lives on the shoreline of a large lake. A market is located 20 km south and 21 km west of her home on the other side of the lake. If she takes a boat across the lake directly
toward the market, how far is her home from the market in km?
If Ann takes a boat then the distance between Ann's home and the market across the lake is approximately 29 km.
To find the distance from Ann's home to the market, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, Ann's home, the market, and the point where she crosses the lake form a right triangle, with the distance she travels across the lake being the hypotenuse.
To calculate the distance, we can use the following formula:
c^2=a^2+b^2
where c is the distance from Ann's home to the market, a is the distance from her home to the point where she crosses the lake, and b is the distance from the market to the point where she crosses the lake.
We know that a = 20 km and b = 21 km, so we can plug these values into the equation:
c^2=20^2+21^2
c^2=400+441
c^2=841
To solve for c, we take the square root of both sides of the equation:
c=sqrt(841)
c=29
Therefore, the distance from Ann's home to the market is approximately 29 km, when she takes the shortest path across the lake directly toward the market.
To know more about distance refer here:
https://brainly.com/question/28768362#
#SPJ11
What are the coordinates of the vertices of d(3, a)(△abc) for a(0, 4), b(−2, 5), and
c(3, 7)? does the perimeter increase or decrease?
The coordinates of the triangle after the dilation are given as follows:
a(0, 12), b(-6, 15) and c(9, 21).
The perimeter of the triangle increases, as the side lengths are multiplied by 3, hence the perimeter is also multiplied by 3.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The scale factor for this problem is given as follows:
k = 3.
The scale factor is greater than 1, meaning that the figure is an enlargement, and thus the perimeter increases.
The original vertices of the triangle are given as follows:
a(0, 4), b(−2, 5), and c(3, 7)
Hence the vertices of the dilated triangle are given as follows:
a(0, 12), b(-6, 15) and c(9, 21).
(each coordinate of each vertex is multiplied by the scale factor of 3).
More can be learned about dilation at brainly.com/question/3457976
#SPJ1
3 cm
H
8 cm
12 cm
What is the volume of the table tent?
The volume of the table tent 3 cmH8 cm12 cm is 288 cubic cm.
How to determine the volume of the table tentThe volume of the table tent can be found by multiplying the length, width, and height of the tent.
Volume = length x width x height
In this case, the length is 12 cm, the width is 8 cm, and the height is 3 cm.
Volume = 12 cm x 8 cm x 3 cm
Volume = 288 cubic cm
Therefore, the volume of the table tent is 288 cubic cm.
Learn more about volume at https://brainly.com/question/463363
#SPJ1
WILL MARK BRAINLIEST QUESTION IS IN THE PHOTO
The value of measure of RU is,
⇒ 149°
We have to given that;
In circle,
m RS = 88 degree
m ST = 35 degree
Hence, We can formulate;
The value of measure of RU is,
⇒ 360° - ( 88° + 35° + 88°)
⇒ 360° - 211°
⇒ 149°
Thus, The value of measure of RU is,
⇒ 149°
Learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ1
Suppose M and C each represent the position number of a letter in the alphabet, but M represents the letters in the original message and C represents the letters in a secret code. The equation c=m+2 is used to encode a message.
The equation that can be used to decode the secret code is m = c - 2
How so you find the equation to decode the secret code?For you to decode the secret message, you need to turn the the encoding process around. Find the inverse.
Since the encoding process uses the equation c = m + 2, to decode the message, all that need to be found is the value of m. This can be done by rearranging the encoding equation to solve for m
move 2 to c side. it becomes m = c-2
The above answer is in response to the full question below;
Suppose M and C each represent the position number of a letter in the alphabet, but M represents the letters in the original message and C represents the letters in a secret code. The equation c=m+2 is used to encode a message.
Write an equation that can be used to decode the secret code into the original message.
Find more exercises on decoding;
https://brainly.com/question/29976739
#SPJ1
Mary creates a stack of 10 of piece am and a stack of 8 of piece N. Both stacks have equal volumes. Create an equation relating h and k
Let's assume that the pieces am and N have heights of h_am and h_N respectively, and let k be the number of times the height of piece N fits into the height of piece am (i.e., k is the ratio of the height of piece am to the height of piece N).
We know that the volume of each stack is equal. Let's use the following variables:
- h for the height of each piece of A
- k for the height of each piece of N
- 10 for the number of pieces in stack A
- 8 for the number of pieces in stack N
The equation for the volume of each stack is:
Volume of stack A = h x 10
Volume of stack N = k x 8
Since we know the volumes are equal, we can set the two equations equal to each other:
h x 10 = k x 8
To create an equation relating h and k, we can solve for one variable in terms of the other:
h = (8/10)k
or
k = (10/8)h
Either equation shows how h and k are related to each other. For example, if we know the value of h, we can use the first equation to find k.
Learn more about equation at https://brainly.com/question/26170143
#SPJ11
Solve the following system of equations using Gauss-Jordan elimination method. (Hint: your given Ax=b, you should solve for the inverse of A and obtain x= A A. 4x1 + 3x2 + x3 = 2
B. x1 + x2 + x3 = 3 C. 2x1 + 5x2 + 2x3 = 1
The Gauss-Jordan elimination method is used to obtain the inverse of a matrix and solve a system of equations. The solution for the given system is x1 = 2/3, x2 = 5/3, x3 = 2/3.
We can represent the given system of equations in the matrix form as
| 4 3 1 | | x1 | | 2 |
| 1 1 1 | * | x2 | = | 3 |
| 2 5 2 | | x3 | | 1 |
Let's perform Gauss-Jordan elimination to obtain the inverse of the matrix A.
Augment the matrix with an identity matrix of the same order:
| 4 3 1 | | 1 0 0 | | ? ? ? |
| 1 1 1 | * | 0 1 0 | = | ? ? ? |
| 2 5 2 | | 0 0 1 | | ? ? ? |
Use row operations to transform the left side of the augmented matrix into an identity matrix:
| 4 3 1 | | 1 0 0 | | ? ? ? | | 1 0 0 |
| 1 1 1 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 2 5 2 | | 0 0 1 | | ? ? ? | | 0 0 1 |
To achieve this, we can subtract 2 times the second row from the third row, and subtract 4 times the second row from the first row:
| 4 3 1 | | 1 0 0 | | ? ? ? | | 1 0 0 |
| 1 1 1 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 0 3 0 | | 0 -2 1 | | ? ? ? | | 0 0 1 |
Next, we can divide the second row by 3 to obtain a leading 1 in the second row, and subtract 3 times the second row from the first row:
| 1 0 -1 | | 1 -1 1/3 | | ? ? ? | | 1 0 0 |
| 0 1 0 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 0 0 1 | | 0 -2 1 | | ? ? ? | | 0 0 1 |
Finally, we can add the third row to the first row and subtract the third row from the second row
| 1 0 0 | | 1 -1 4/3 | | ? ? ? | | 1 0 0 |
| 0 1 0 | * | 0 1 2 | = | ? ? ? | =>| 0 1 0 |
| 0 0 1 | | 0 -2 1 | | ? ? ? | =>| 0 0 1 |
Hence, we have obtained the inverse of the matrix A as
| 1 -1 4/3 |
| 0 1 2 |
| 0 -2 1 |
We can now find the solution vector x by multiplying the inverse of A with the vector b
| x1 | | 1 -1 4/3 | | 2 |
| x2 | = | 0 1 2 | * | 3 |
| x3 | | 0 -2 1 | | 1 |
Performing the matrix multiplication, we get
| x1 | | 2/3 |
| x2 | = | 5/3 |
| x3 | | 2/3 |
Therefore, the solution of the given system of equations is
x1 = 2/3
x2 = 5/3
x3 = 2/3
To know more about Gauss-Jordan elimination method:
https://brainly.com/question/12090959
#SPJ4
Debnil has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3 to 1. How many tablespoons of salt does Debnil have?
Answer: Debnil has 2 Tablespoons of salt.
Step-by-step explanation:
3/1 is the ratio for teaspoons to tablespoons.
Substitute the 1 with the 6. What is six divided by three? 2.
In survey 55%of those surveyed said that they get news from local television station,three-fifths said that they get the news from daily news paper and 0. 4 said they get they get their news form the internet. Which new source has the most users
The daily newspaper has the most users among those surveyed.
To determine which news source has the most users, we need to compare the percentages of those who use each source.
According to the survey:
55% get news from local television station
60% get news from daily newspaper
40% get news from the internet
To compare these percentages, we can either convert them to fractions or decimals. Let's convert them to decimals:
55% = 0.55
60% = 0.60
40% = 0.40
Now we can compare them directly. We see that the source with the highest percentage is the daily newspaper, with 60% of those surveyed saying they get news from it. Therefore, the daily newspaper has the most users among the surveyed population.
Learn more about survey at https://brainly.com/question/14563335
#SPJ11
PLEASE HELP THIS A FRESHMEN QUESTION
Answer:
The total area of the "t" figure is 20 square units.
The figure is made up of a triangle, a square, and a rectangle.
The area of the triangle is (1/2)(base)(height) = (1/2)(4)(3) = 6 square units.
The area of the square is 4^2 = 16 square units.
The area of the rectangle is 2(4)(3) = 24 square units.
The total area of the figure is 6 + 16 + 24 = 46 square units.
However, the question asks for the area of the composite region, which is the shaded region in the figure. The shaded region is a triangle with base 4 units and height 3 units. The area of this triangle is (1/2)(base)(height) = (1/2)(4)(3) = 6 square units.
Therefore, the area of the composite region is 6 square units.
Here is a diagram of the figure with the areas of each shape labeled:
[Image of the "t" figure with the areas of each shape labeled]
Answer:
Step-by-step explanation:
I don't have enough information to answer this.
Order from least to greatest
30.
4,0.91,8
50
Answer:
0.91
30.4
850
Step-by-step explanation:
Emma is sick a lot and as a result has to go to the doctor regularly. Each time she goes there is a $20 copay that she uses her FSA to pay for. Last month she went to the doctor 9 times. She earns $20 an hour at her job. How many hours (round up) would she have to work to pay these bills without an FSA/HSA? (She pays 17 percent in taxes. )
She would have to work for 11 hours to pay these bills without her FSA/HSA.
Emma went to the doctor 9 times last month, which means she had to pay a total of 9 x $20 = $180 in copays.
Without her FSA/HSA, she would have to work to earn $180 after taxes. Since she pays 17 percent in taxes, the amount she would have to earn before taxes is $180 / (1 - 0.17) = $216.87.
To earn $216.87, she would have to work for $216.87 / $20 per hour = 10.84 hours.
Rounding up, she would have to work for 11 hours to pay these bills without her FSA/HSA.
To know more about hours refer here
https://brainly.com/question/13533620#
#SPJ11
can someone help me please
Answer:
3. 254.34 mm^2
4. 615.44 cm^2
5. 314 in^2
6. 7.065 in^2
7. 3.14 cm^2
8. 1.76625 ft^2
Step-by-step explanation:
AREA FORMULA: π * r^2
This question is asking to use 3.14 or 22/7 for x.
The following steps will use 3.14.
3. r = 9 mm (r^2 = 81 mm)
A = 81 * 3.14 = 254.34 mm^2
4. r = 14 cm (r^2 = 196 cm)
A = 196 * 3.14 = 615.44 cm^2
5. r = 10 in (r^2 = 100 in)
A = 100 * 3.14 = 314 in^2
Questions 6-8 show the diameter of the circle.
Divide by 2 to find the radius, then plug that into the area formula
6. r = 1.5 in (r^2 = 2.25 in)
A = 2.25 * 3.14 = 7.065 in^2
7. r = 1 cm (r^2 = 1 cm)
A = 1 * 3.14 = 3.14 cm^2
8. r = 0.75 ft (r^2 = 0.5625 ft)
A = 0.5625 * 3.14 = 1.76625 ft^2
Maria records random speeds from three different Internet providers in the table. ProviderDownload Speed (megabits per second)CityNet3. 6, 3. 7, 3. 7, 3. 6, 3. 9Able Cable3. 9, 3. 9, 4. 1, 4. 0, 4. 1Tel-N-Net3. 9, 3. 7, 4. 0, 3. 6, 3. 8 Which company offers the fastest mean downloading speed?  00:00 CityNet  00:00 Able Cable  00:00 Tel-N-Net  00:00 Impossible to determine from the information given
Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.
How to determine the fastest internet provider?We can calculate the mean (average) download speed for each provider and compare them to determine which company offers the fastest mean downloading speed.
Based on the given data, the mean download speed for each provider is:
City Net: (3.6 + 3.7 + 3.7 + 3.6 + 3.9) / 5 = 3.7 megabits per second (Mbps)
Able Cable: (3.9 + 3.9 + 4.1 + 4.0 + 4.1) / 5 = 4.0 Mbps
Tel-N-Net: (3.9 + 3.7 + 4.0 + 3.6 + 3.8) / 5 = 3.8 Mbps
Therefore, Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.
Learn more about speed
brainly.com/question/28224010
#SPJ11
In the diagram below, congruent figures 1, 2 and 3 are drawn.
Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3
A sequence of transformations that maps figure 1 onto figure 2 and then figure 2 onto figure 3 include the following: D. a translation followed by a rotation.
What is a translation?In Mathematics and Geometry, a translation can be defined as a type of rigid transformation which moves every point of the object in the same direction, as well as for the same distance.
This ultimately implies that, a translation is a type of rigid transformation that does not change the orientation of the original geometric figure (pre-image).
What is a rotation?In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Read more on transformation here: https://brainly.com/question/15832612
#SPJ1
Complete Question:
Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?
a reflection followed by a translation
a rotation followed by a translation
a translation followed by a reflection
a translation followed by a rotation
Find the value of X of the circle
The circle's x value will continue to be the same as the arc ST. So, x has a value of 40 degrees.
What is circle?A circle's centre is the point from which all of the distances to the other points on the circle are equal. The radius of the circle is the measurement at issue.
Every point on a circle is a geometric shape that is equally separated from the centre.
The location of any point that is evenly separated from the fixed point known as the circle's centre can also be characterised as it.
The distance from any point on a circle to the centre is known as the radius of the circle.
To know more about arc visit:
brainly.com/question/30688993
#SPJ1
£1800 is put into an account. It gathers simple interest at a rate of 3%
per year.
to task
a) How much money is added to the account each year?
b) How much money will be in the account after two years?
Give your answers in pounds (£).
Answer:
a) £54
b) £1908
Step-by-step explanation:
a) use £1800 × 3% = £54
b) use £1800 + ( 54 × 2) = £1908
To the nearest hundredth, what is the value of x?
Use a trigonometric ratio to compute a distance
Therefore, the value of x to the nearest hundredth is approximately 72.73 units.
What is triangle?A triangle is a geometrical shape that consists of three straight sides and three angles. It is a polygon with three vertices, and the sum of its interior angles always adds up to 180 degrees. Triangles are classified based on the length of their sides and the measure of their angles. The most common types of triangles are equilateral, isosceles, and scalene, based on the length of their sides, and acute, right, and obtuse, based on the measure of their angles. Triangles have a wide range of applications in mathematics, physics, engineering, and other fields.
Here,
Therefore, in this triangle, sin(67°) = 67/x, where x is the length of the hypotenuse.
We can rearrange this equation to solve for x:
x = 67 / sin(67°)
Using a calculator, we find that sin(67°) is approximately 0.921, so:
x = 67 / 0.921
x ≈ 72.73
To know more about triangle,
https://brainly.com/question/28600396
#SPJ1
Sand falls from an overhead bin and accumulates in a conical pile with a radius that is alwavs two times its heiaht. Suppose the height of the pile increases at a rate of 2 cm/s when the pile is 11 cm high. At what rate is the sand leaving the bin at that instant?
To solve this problem, we need to use related rates. Let's start by drawing a diagram:
```
/\
/ \
/ \
/ \
/ \
/__________\
```
We know that the radius of the conical pile is always two times its height, so we can label the diagram as follows:
```
/\
/ \
/ \
/ \
/ \
/__________\
/| r=2h \
/ |___________\
```
Now we need to find an equation that relates the height of the pile to its radius. We can use the formula for the volume of a cone:
```
V = (1/3)πr^2h
```
We want to solve for h in terms of r:
```
V = (1/3)πr^2h
3V/πr^2 = h
```
Now we can differentiate both sides of this equation with respect to time:
```
d/dt (3V/πr^2) = d/dt h
0 = (3/πr^2) dV/dt - (2/πr^3) dr/dt
```
We're given that the height is increasing at a rate of 2 cm/s when the pile is 11 cm high, so we know that:
```
dh/dt = 2 cm/s
h = 11 cm
```
We want to find the rate at which sand is leaving the bin, which is given by `dV/dt`. We can solve for this using the equation we derived:
```
0 = (3/πr^2) dV/dt - (2/πr^3) dr/dt
dV/dt = (2/3)πr^2 (dh/dt) / r
```
Now we just need to plug in the values we know:
```
dh/dt = 2 cm/s
h = 11 cm
r = 2h = 22 cm
dV/dt = (2/3)π(22)^2 (2) / 22
dV/dt = 264π/3
```
So the rate at which sand is leaving the bin when the pile is 11 cm high is `264π/3 cm^3/s`.
To solve this problem, we can use the relationship between the radius and height of the conical pile, as well as the given rate of height increase.
Since the radius (r) is always two times the height (h), we have r = 2h. The volume (V) of a cone is given by the formula V = (1/3)πr^2h. We can substitute r with 2h, so V = (1/3)π(2h)^2h.
Now, let's differentiate both sides with respect to time (t):
dV/dt = (1/3)π(8h^2)dh/dt
When the height is 11 cm, the rate of height increase (dh/dt) is 2 cm/s. We can substitute these values into the equation:
dV/dt = (1/3)π(8(11)^2)(2)
Solving for dV/dt:
dV/dt ≈ 2046.92 cm³/s
At that instant, the sand is leaving the bin at a rate of approximately 2046.92 cm³/s.
Learn more about radius here: brainly.com/question/30106091
#SPJ11
In triangle abc, point d is on side ac, ab=bd=dc=12 inches, and measurement of angle bdc= 2 times the measurement of angle abd. find ac
The length of AC in triangle ABC is 24 inches.
In triangle ABC, let point D be on side AC such that AB = BD = DC = 12 inches. We are given that the measure of angle BDC is twice the measure of angle ABD.
To find the length of AC, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we can apply the Law of Cosines to triangle ABD to find the length of AD:
AD^2 = AB^2 + BD^2 - 2 * AB * BD * cos(ABD)
Since AB = BD = 12 inches, we have:
AD^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(ABD)
AD^2 = 288 - 288 * cos(ABD)
Now, let's consider triangle BDC. We are given that the measure of angle BDC is twice the measure of angle ABD. Let's denote the measure of angle ABD as x. Therefore, the measure of angle BDC is 2x.
Since the sum of angles in a triangle is 180 degrees, we can write:
x + 2x + angle BCD = 180
3x + angle BCD = 180
angle BCD = 180 - 3x
Now, let's apply the Law of Cosines to triangle BDC to find the length of BC:
BC^2 = BD^2 + CD^2 - 2 * BD * CD * cos(BDC)
BC^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(2x)
BC^2 = 288 - 288 * cos(2x)
Since AD = DC, we have AD = 12 inches. Now we can write the equation for the total length AC:
AC = AD + DC
AC = 12 + 12
AC = 24 inches
Therefore, the length of AC in triangle ABC is 24 inches.
Learn more about triangle,
https://brainly.com/question/28470545
#SPJ11
A radioactive isotope is decaying at a rate of 18% every hour. Currently there
are 120 grams of the substance.
Write an equation that will represent the number of grams, y, present after
hours.
=
Can you tell me the answer please
The decay of the radioactive substance can be modeled by the exponential decay function:
y = a(1 - r)^t
where:
- y is the amount of substance present after t hours
- a is the initial amount of substance (in grams), which is 120 grams in this case
- r is the decay rate per hour, which is 18% or 0.18 in decimal form
- t is the time elapsed in hours
Plugging in the values we get:
y = 120(1 - 0.18)^t
Simplifying:
y = 120(0.82)^t
So this is the equation that represents the number of grams, y, present after t hours, given the initial amount of 120 grams and a decay rate of 18% per hour.
#SPJ11
Need help please show work
Answer:
Add the lengths:
5x - 16 + 2x - 4 = 7x - 20
Can someone give me an explanation for how to factor this:
x4 − 2x^3 − 16x^2 + 2x + 15
The factored form of the polynomial x⁴ - 2x³- 16x² + 2x + 15 is [x³(x - 2) - (4x + 3)(4x - 5)].
Factoring the polynomial?
x⁴- 2x³ - 16x² + 2x + 15.
First, look for any common factors among the terms. In this case, there are none.
Next, try factoring by grouping. To do this, group the first two terms and the last three terms: (x⁴ - 2x³) - (16x² - 2x - 15).
Factor out the greatest common factor from each group: x³(x - 2) - 1(16x² - 2x - 15).
Now, we have a difference of two expressions, but there isn't a common factor to factor further. Therefore, we must use other methods to factor the quadratic expression 16x²- 2x - 15.
Factor the quadratic expression using the "ac method." Multiply the leading coefficient (16) by the constant term (-15) to get -240. Find two numbers that multiply to -240 and add up to the linear coefficient (-2). These numbers are 12 and -20.
Rewrite the middle term using the two numbers found: 16x² + 12x - 20x - 15.
Group the terms in pairs: (16x² + 12x) + (-20x - 15).
Factor out the greatest common factor from each group: 4x(4x + 3) - 5(4x + 3).
Factor out the common binomial factor: (4x + 3)(4x - 5).
Now, put everything together: x³(x - 2) - (4x + 3)(4x - 5).
So, the factored form of the polynomial x⁴ - 2x³- 16x² + 2x + 15 is [x³(x - 2) - (4x + 3)(4x - 5)].
Learn more about binomial factor.
brainly.com/question/30142650
#SPJ11
Yvette cuts a hole from a rectangular panel to make a window. She wants to determine how
much of the panel is left after she cuts the hole. She writes:
(fraction left)
(area of panel) - (area of hole)
(area of panel)
If the panel is 3 feet by 2 feet, and the hole is 1 foot by foot, what is the fraction left?
The area of the panel left after she cuts the hole is 5.215 ft²
Given that a circular hole of 1 foot by foot has been cut out of a rectangular panel of 3 feet by 2 feet,
We need to find the area of the remaining part after the cutting of the hole,
So, we will find the same by subtracting the area of the hole from the area of the panel.
So, area of the hole = π×radius² = 3.14×0.5² = 0.785 ft²
Area of the panel = length × width = 3 × 2 = 6 ft²
Area remaining part = 6-0.785 = 5.215 ft²
Hence the area of the panel left after she cuts the hole is 5.215 ft²
Learn more about area click;
https://brainly.com/question/27683633
#SPJ1