Step-by-step explanation:
Volume is = 4ft × 4ft × 8ft
= 128 cubic feet
Find the distance from the point (9, –2) to the line y = 3∕2x + 4. Choices are in the attachment...
===================================================
Work Shown:
y = (3/2)x + 4
2y = 3x + 8 .... multiply both sides by 2
0 = 3x + 8 - 2y
3x-2y+8 = 0
The original equation transforms to 3x-2y+8 = 0. It is in the form Ax+By+C = 0. We see that A = 3, B = -2, C = 8. This form is very useful to help find the distance from a point to this line.
The formula we will use is
[tex]d = \frac{|A*p+B*q+C|}{\sqrt{A^2+B^2}}\\\\[/tex]
where A,B,C were the values mentioned earlier. The p,q are the x and y coordinates of the point given. So p = 9 and q = -2
Plugging all that in gives...
[tex]d = \frac{|A*p+B*q+C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|3*9+(-2)*(-2)+8|}{\sqrt{3^2+(-2)^2}}\\\\d = \frac{|27+4+8|}{\sqrt{9+4}}\\\\d = \frac{|39|}{\sqrt{13}}\\\\d = \frac{39}{\sqrt{13}}\\\\d = \frac{39\sqrt{13}}{\sqrt{13}\sqrt{13}} \ \text{ rationalizing denominator}\\\\d = \frac{39\sqrt{13}}{13}\\\\d = 3\sqrt{13}\\\\d = \sqrt{9}*\sqrt{13}\\\\d = \sqrt{9*13}\\\\d = \sqrt{117}\\\\[/tex]
Name the major arc and find its measure.
Answer:
ADB = Major Arc
arc measure = 310
Step-by-step explanation:
major arc measure = 360 - 50 = 310
please help fast ! Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the fractions with equivalent percentages.
Answer:
13/20<--->65%
21/25<--->84%
3/4<--->75%
2/5<--->40%
3/5<--->60%
To find the matching pairs, divide the fraction and move the decimal point to your answer 2 places to the right to then get a percentage.
Ex: 1/2= .50->5.0->50.->50%
The image did not show the rest of the answers, but I worked with what information I received from the current image, producing 5 sets of answers. If there are more than 5 sets, please send a second image with your question so we can help you with the rest.
Hence the correct match of fractions to their equivalent percentages are;
13/20 = 65%
21/25 = 84%
3/4 = 75%
2/5 = 40%
3/5 = 60%
Percentages and fractionsFractions are written as a ratio of two integers. In order to convert fractions to percentage, we will simply multiply the fraction given by 100.
For the fraction 13/20
13/20 * 100 = 13 * 5
13/20 = 65%
For the fraction 21/25
21/25 * 100 = 21 * 4
21/25 = 84%
For the fraction 3/4
3/4 * 100 = 3 * 25
3/4 = 75%
For the fraction 2/5
2/5 * 100 = 2 * 20
2/5 = 40%
For the fraction 3/5
3/5 * 100 = 3* 20
3/5 = 60%
Hence the correct match of fractions to their equivalent percentages are;
13/20 = 65%
21/25 = 84%
3/4 = 75%
2/5 = 40%
3/5 = 60%
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Suppose that P(A) = 1/3, P(B) = 1/3, and P(A ∩ Bc ) = 2/9. Are A and B independent? Why or why not?
A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.
Given that are two events P(A) = 1/3, P(B) = 1/3, and P(A ∩ B) = 2/9.
We need to determine if the events are independent or not.
The chance of occurrences A and B intersecting (P(A B)) must be compared to the sum of both events' individual probabilities (P(A) × P(B)) in order to assess if events A and B are independent.
Two events A and B are independent if and only if:
P(A ∩ B) = P(A) × P(B)
Let's check if this condition holds for the given probabilities:
P(A) = 1/3
P(B) = 1/3
P(A ∩ B) = 2/9
Next, add up the odds of each separately:
P(A) × P(B) = (1/3) × (1/3) = 1/9
We can infer that A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.
In other words, the likelihood that one event (A) occurs influences the likelihood that another event (B) occurs, and vice versa.
The probability of both events happening at once (P(A B)) would be equal to the product of their individual probabilities (P(A) × P(B)) if A and B were independent, but this is not the case in this situation.
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Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 15 ft high
Answer:
The height increase by
20/49π when pile is 14ft high
Step by step Explanation
Given:
rate of 20 ft3/min
To asolve this quest we will be using the volume of a cone then find the partial derivative
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
I need help pls pls pls
Answer: D
Step-by-step explanation:
Domain is to x as range is to y. Thus, according to the graph, when y is 11.4, x is 3.6. The only choice that contains 3.6 is D.
Edit: Just got Ace on this question :))
Answer: D
Step-by-step explanation:
Find the first four iterates of the function f(z)=z^2-2-2i with an initial value of z0=2+i
Obtain the next iterate by plugging the previous iterate into the function.
First iterate:
[tex]z_0=2+i\implies z_1=f(z_0)=(2+i)^2-2-2i=1+2i[/tex]
Second iterate:
[tex]z_2=f(z_1)=(1+2i)^2-2-2i=-5+2i[/tex]
Third iterate:
[tex]z_3=f(z_2)=(-5+2i)^2-2-2i=19-22i[/tex]
Fourth iterate:
[tex]z_4=f(z_3)=(19-22i)^2-2-2i=-125-838i[/tex]
Use an iterated integral to find the area of the region bounded by the graphs of the equations.
y = 16 − x2 y = x + 4
Answer:
use photomath and it will solve ur problem
In how many ways can the letters in the world ballon be arranged?
Answer:
900
Step-by-step explanation:
=IF(5 > = 2 * 4,11,IF(25/2 > 5 * 3,15, a friend tells you that they always call people they would like to date. identify the converse error 74))
Answer:
4+10-284-4819+2948929
For what values of k does the function y = cos(kt) satisfy the differential equation 81y'' = -100y? k = (smaller value) k = (larger value)
Answer:
k = -10/9 and k = 10/9
Step-by-step explanation:
given y = cos(kt) and the differential equation 81y'' = -100y
y' = -ksin(kt)
y'' = -k²cos(kt)
Substituting the value of y and y'' in the differential equation we have;
81 (-k²cos(kt))= -100 (cos(kt))
-81k²cos(kt)) = -100cos(kt))
-81k² = -100
k² = 100/81
k = ±[tex]\sqrt{\frac{100}{81} }[/tex]
k = ±10/9
k = -10/9 and k = 10/9
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90% confidence interval for the mean score, muμ, of all students taking the test?
Answer:
29.5+/-1.11
= ( 28.39, 30.61)
Therefore, the 90% confidence interval (a,b) =( 28.39, 30.61)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 29.5
Standard deviation r = 5.2
Number of samples n = 59
Confidence interval = 90%
z-value (at 90% confidence) = 1.645
Substituting the values we have;
29.5+/-1.645(5.2/√59)
29.5+/-1.645(0.676982337100)
29.5+/-1.113635944529
29.5+/-1.11
= ( 28.39, 30.61)
Therefore, the 90% confidence interval (a,b) =( 28.39, 30.61)
Does anyone mind explaining? I have been stuck on this for a while.
The base of the pyramid is a regular hexagon. Find the volume of the pyramid. Round your answer to the nearest tenth.
Answer:
vol = 62 in³
Step-by-step explanation:
First determine r (see attached image) by using pythagorean theorem.
a² = b² + c²
a = 3 in
b = 3/2 = 1.5 in
c = r
3² = 1.5² + r²
r = [tex]\sqrt{3^{2}-1.5^{2} }[/tex]
r = 2.598 in
Get the area = n/2 * a * r
n = number of sides = 6
r = 2.598 in
Area = 6/2 * 3 * 2.598
Area = 23.38 in²
get the volume = 1/3 * Area * h
Area = 23.38 in²
h = 8 in (as given)
vol = 1/3 * 23.38 * 8
vol = 62 in³
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y = x ; about x = 3
Answer:
Volume = π [ 2/3 - 12/2].
Step-by-step explanation:
So, in this question we are asked to find or Calculate for or determine the value of volume v of the solid obtained by rotating the region bonded by the given curves about the specified lines = ? (Unknown). In addition, we are given that y = x, y = x , so, about x = 3.
Volume = π ∫ [ (3 - y)^2 - (3 - y)^2 ] dy.
(Taking 0 and 1 as the lower and upper limit).
Volume = π ∫ 9 - 6y + y^2 - 9 - 6y + y^2 dy.
(Taking 0 and 1 as the lower and upper limit).
Volume = π ∫ 2y^2 - 12y dy.
(Taking 0 and 1 as the lower and upper limit).
(Solving the quadratic equation above, we have; Roots: -6, 0
Root Pair: -3 ± 3
Factored: f(x) = 2(x + 6)x)
Also,
Volume = π [ 2y^3 / 3 - 12y2/2]
Volume = π [ 2/3 - 12/2] cubic units.
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 39 in. by 21 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume.
Answer:
Length=29.8 inches
Width=11.8 inches
Height=4.6 inches
Volume=1,617.54 cubic inches
Step-by-step explanation:
Let the side of congruent square cut =x inches
So the length of the rectangular box=(39-2x)
width = (21-2x)
height = x
The volume V=Length*Width*Height
= (39-2x)*(21-2x)*x
dV/dx= (39-2x)(21-4x)-2x(17-2x)=0
Simplify the equation above
819-156x-42x+8x^2-34x+4x^2=0
We have,
12x^2 -232 +819=0
Solve the quadratic equation using formula
a=12
b= -232
c=819
x= -b +or- √b^2-4ac/2a
= -(-232) +- √(-232)^2 - (4)(12)(819) / (2)(12)
= 232 +or- √53824 - 39312 / 24
= 232 +or- √14512 / 24
= 232 +or- 4√907 / 24
x= 232 / 24 + 4√907 / 24
=14.6861
Or
x=232 / 24 - 4√907 / 24
=4.64726
x=4.6 inches
Length=(39-2x)
={39-2(4.6)}
= 29.8 inches
Width=(21-2x)
={21-2(4.6)}
= 11.8 inches
Height=x= 4.6 inches
Volume=(39-2x)*(21-2x)*x
={39-2(4.6)}*{21-2(4.6)*4.6
=(39-9.2)*(21-9.2)*4.6
=29.8*11.8*4.6
=1,617.544
Approximately 1,617.54
Volume=1,617.54 cubic inches
Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c. sin(B) = sin(A) sin(B) = cos(90 – B) cos(B) = sin(180 – B) cos(B) = cos(A)
Answer:
sin(B) = cos(90 – B)
Step-by-step explanation:
Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.
sin(B) = sin(A)
sin(B) = cos(90 – B)
cos(B) = sin(180 – B)
cos(B) = cos(A)
Assuming the angles are in degrees, the second relation is always true.
By definition of sine,
sin(B) = AC/AB
cos(90-B) = cos (A) = AC/AB
therefore the second relation is true, for arbitrary values of B.
Answer:
sin(B) = cos(90 – B)
Step-by-step explanation:
Which relationship in the triangle must be true?
Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.
here are approximately 400 million trees currently growing in the Amazon Rainforest, which covers approximately 5.5 million square kilometers. The rainforest is being cleared at a rate of 20,000 square kilometers per year to make way for new farmland and to harvest wood for building supplies. Before this year, 250,000 square kilometers had already been cleared. A preservation consortium is trying to mitigate the loss of rainforest by planting new trees. They have already planted 3,000 square kilometers of trees and plan to plant 100 square kilometers of trees each year. What are the y-intercepts for each function? What do these y-intercepts represent?
Answer: y-intercepts: 250,000 & 3,000
Step-by-step explanation:
The first equation represents the trees cleared. The starting/original amount cleared was 250,000.
The second equation represents the trees planted. The starting/original amount planted was 3,000.
The slope of a line is 1, and the y-intercept is -1. What is the equation of the line written in slope-intercept form? y = 1 - x y = -x - 1 y = x - 1
all my points!!!!!!!!!!!!!! Brainleist will be given
Answer:
18-22 = 1
23-27 = 3
28-32 = 3
33-37 = 3
Answer:
18-22 = 1
23-27 = 3
28-32 = 3
33-37 = 3
In a circle, diameter AB¯¯¯¯¯¯¯¯ is perpendicular to chord CD¯¯¯¯¯¯¯¯ at point L. Which statement will always be true about this circle?
Answer:
CL = LD
Step-by-step explanation:
In a circle, diameter AB is perpendicular to chord CD at point L. Which statement will always be true about this circle?
1) (CL)(LD)=AB
2) AL > LB
3) CL = LD
4) BL > AB
Answer: The chord is CD and the diameter AD of the circle are perpendicular to each other at point L. According to the perpendicular bisector theorem, if the diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arc. This means that chord CD is bisected by the diameter of the circle at point L.
Since CD is bisected at point L, CL = LD
Also CD = 2CL = 2LD
A quadrilateral has three angles that measure 80°, 110°, and 75°. Which is the measure of the fourth angle? A. 50° B. 90° C. 95° D. 125°
Answer: 95 degrees.
Step-by-step explanation:
A quadrilateral has a total combined angle measure of 360 degrees. If you do 360-(80+110+75) it would equal 95.
Answer:
95°Option C is the correct option
Solution,
The sum of the angles in the quadrilateral is 360°
Let the forth angle be X
X + 80° + 110° + 75° = 360°
Calculate the sum:
X + 265° = 360°
Subtract 265° on both sides
X + 265° - 265° = 360° - 265°
Calculate the difference
X = 95°
Hope this helps...
Good luck on your assignment...
If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?
Answer:
The range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).
Step-by-step explanation:
The complete question is:
The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?
Solution:
As the sample size is large, i.e. n = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.
So,[tex]\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})[/tex]
The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.
The critical value of z for 98% confidence level is,
z = 2.33
Compute the 98% confidence interval as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)[/tex]
Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).
What is the y-intercept of the line described by the equation below?
y = 7x+ 4
A. (0,4)
B. (0,-4)
C. (0,7)
D. (0, -7)
Answer:
A. (0, 4)
Step-by-step explanation:
y=mx+b
y=7x+4
7x<-- mx
4<-- b
b=y intercept
The value of the y-intercept of the line described by the equation is,
⇒ (0, 4)
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The equation of line is,
y = 7x + 4
Now, We know that;
The equation of line is,
y = mx + c
Where, c is y - intercept.
Hence, We get;
The value of the y-intercept of the line described by the equation is,
⇒ y = 4
⇒ (0, 4)
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Two fair dies are rolled. What is the conditional probability thatat least one lands on 6 given that the dies land on different numbers?
Answer:
33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
All outcoms of the dices:
Format(Dice A, Dice B)
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
36 in all
Total outcomes:
In this question, we want all with no repetition.
There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.
Desired outcomes:
One landing on six:
(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).
10 desired outcomes.
Probability:
10/30 = 0.3333
33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers
What is 3x squared times x squared?
Answer:
9x^4
Step-by-step explanation:
(3x)^2 * x^2
9x^2 * x^2
Add the exponents
9x^(2+2)
9x^4
differentiate 1_x² over 1+x²
Answer:
Dy/Dx=-4x/(1+x²)²
Step-by-step explanation:
The differential of 1_x² over 1+x²
First of all
1_x² over 1+x² = (1_x²) / (1+x²)
Let (1_x²) = u
Let (1+x²) = v
Differential = Dy/Dx
Dy/Dx of (1_x²) / (1+x²)
= (VDu/Dx -UDv/Dx)V²
u = (1-x²)
Du/Dx = -2x
(VDu/Dx) =(1+x²)(-2x)
V = 1+x²
Dv/Dx = 2x
UDv/Dx= (1-x²)(2x)
v² = (1+x²)²
Dy/Dx = ((1+x²)(-2x) - (1-x²)(2x))/(1+x²)²
Dy/Dx= ((-2x -2x³)-(2x-2x³))/(1+x²)²
Dy/Dx=( -2x -2x - 2x³ +2x³)/(1+x²)²
Dy/Dx=-4x/(1+x²)²
X+X-X=15. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
You want to remove the opposites which will leave you with x = 15
Hope this helped! :)
Hey there!
ORIGINAL PROBLEM/EQUATION:
x + x - x = 15
CONVERSION/NEW EQUATION:
1x + 1x - 1x = 15
COMBINE the LIKE TERMS:
2x - 1x = 15
1x = 15
DIVIDE 1 to BOTH SIDES
1x/1 = 15/1
SIMPLIFY AFTER CANCELING OUT 1/1 BECAUSE IT GAVE YOU 1 & KEEPING 15/1 BECAUSE IT HELP/GIVE YOU THE x-value
NEW EQUATION: x = 15
Therefore, your answer is: x = 15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.)
Answer:
(0, 16]
Step-by-step explanation:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)
According to the ratio test, if we define L such that:
L = lim(n→∞) |aₙ₊₁ / aₙ|
then the series will converge if L < 1.
aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)
aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)
Plugging into the ratio test:
L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |
L = lim(n→∞) | -n (x−8) / (8 (n+1)) |
L = (|x−8| / 8) lim(n→∞) | n / (n+1) |
L = |x−8| / 8
For the series to converge:
L < 1
|x−8| / 8 < 1
|x−8| < 8
-8 < x−8 < 8
0 < x < 16
Now we check the endpoints. If x = 0:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -1 / n
This is a harmonic series, and diverges.
If x = 16:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° (-1)ⁿ⁺¹ / n
This is an alternating series, and converges.
Therefore, the interval of convergence is:
0 < x ≤ 16
Or, in interval notation, (0, 16].
Pls help see (pic posted)
Answer:
AB=8.4 inchesAC=13.05 inchesSolution,
[tex] \frac{ab}{bc} = tan \: 40 \\ ab = bc \times tan \: 40 \\ ab = 10 \times 0.84 \\ ab = 8.4 \: inches \: [/tex]
[tex] \frac{bc}{ac} = cos \: 40 \\ \frac{bc}{cos \: 40} = ac \\ ac = \frac{10}{cos \: 40} \\ ac = 13.05 \: inches[/tex]
Hope this helps...
Good luck on your assignment..
Find the value of the variable.
6 x (10+ 6) = 8 x (8 +x)
Simplify:
96 = 64 + 8x
Subtract 64 from both sides:
32 = 8x
Divide both sides by 8
X = 4