Step-by-step explanation:
For a geometric sequence,
[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}[/tex]
1. The sequence is :
3, 13, 23, 33,...
[tex]\dfrac{13}{3}\ne \dfrac{23}{13}[/tex]
It is not geometric. It is false
2. The sequence is :
5, -25, 125, -625
[tex]\dfrac{-25}{5}=\dfrac{125}{-25}\\\\-5=-5[/tex]
So, the sequence is geometric as the common ratio is same. It is true.
work out the area of this shape
Answer:
75.5
Step-by-step explanation:
First, the picture is not to scale.
The Area of the bottom (2) rectangle is 33
base x height = A
11 x 3 = 33 (where did I get 3? Total height of shape is 8. Trapezoid is 5)
(8-5 = 3)
Area of the trapezoid:
A = [tex]\frac{h (B_{1} + B_{2}) }{2}[/tex]
= [tex]\frac{(5)(6 + 11)}{2}[/tex]
= [tex]\frac{5(17)}{2}[/tex]
= [tex]\frac{85}{2}[/tex]
= 42.5
42.5 + 33 = 75.5
A bus started from Kathmandu and reached khanikhola,26km far from Kathmandu, in one hour. if the bus had uniform acceleration, calculate the final velocity of the bus and acceleration.
Answer:
a = 0.0040 m/s², v = 14.4 m/s.
Step-by-step explanation:
Given that,
The distance between Kathmandu and Khanikhola, d = 26 km = 26000 m
Time, t = 1 hour = 3600 seconds
Let a is the acceleration of the bus. Using second equation of motion,
[tex]d=ut+\dfrac{1}{2}at^2[/tex]
Where
u is the initial speed of the bus, u = 0
So,
[tex]d=\dfrac{1}{2}at^2\\\\a=\dfrac{2d}{t^2}\\\\a=\dfrac{2\times 26000}{(3600)^2}\\\\a=0.0040\ m/s^2[/tex]
Now using first equation of motion.
Final velocity, v = u +at
So,
v = 0+0.0040(3600)
v = 14.4 m/s
Hence, this is the required solution.
Find the missing number?
Answer:
65 solve theprob
Step-by-step explanation:
sinolove ko po yan paki brainly
Question 1a) Suppose you sample 100 times at random with replacement from a population in which 26% of the individuals are successes. Write a Python expression that evaluates to the chance that the sample has 20 successes.
Answer:
from math import comb
n = 100
x = 20
p = 0.26
q = 0.76
print(comb(n, x)*(p**x)*(q**(n-x)))
Step-by-step explanation:
Given that :
Number of trials, n = 100
P(success), p = 26% = 0.26
P(success)' = 1 - p = 1 - 0.26 = 0.74
Chance that sample has 20 successes = x
This problem meets the condition for a binomial probability distribution :
p(x = 20)
Recall :
P(x = x) = nCx * p^x * q^(n-x)
Using python :
comb is an built in function which calculate the combination of two arguments it takes ; and returns the combination value.
** mean raised to the power and
* is used for multiplication
The Python code as per the given question is provided below.
Program explanation:
The number of trials,
100Probability of success,
20% or 0.26Size of array generated,
2000The output that shows chances of 20 success,
SProgram code:
import numpy as np
S=sum(np.random.binomial(100,0.26,2000)==20)/2000
S
Learn more about Python expression here:
https://brainly.com/question/21645017
A machine has two components both of which have a lifespan, in months, that is exponentially distributed with mean 8. The lifespan of the two components are independent. Find the probability both components are functioning in 12 months.
Answer:
0.0498
Step-by-step explanation:
In this question,
x~exponential
we have
mean = 1/λ = 8
from here we cross multiply, when we do
such that
λ = 1/8
probability of x functioning in 8 months
= e^-λx
= e^-1/8x12
= e^-1.5
= 0.2231
i got this value through the use of a scientific calculator
then the probability that these two are greater than 12
= 0.2231²
= 0.04977
= approximately 0.0498
therefore the probability that both components are functioning in 12 months is 0.0498
13, 5, 4, 9, 7, 14, 4 The deviations are _____.
A. "5, -3, -4, 0, 1, 6, 4"
B."5, -3, -4, 1, -1, 6, -4"
C."6, -3, -4, 1, 2, 6, -4"
D."-5, 3, 4, -1, 1, 6, 4 "
Answer:
B."5, -3, -4, 1, -1, 6, -4"
Step-by-step explanation:
We are given that
13,5,4,9,7,14,4
We have to find the deviation.
Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]
Using the formula
[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]
[tex]Mean,\mu=\frac{56}{7}=8[/tex]
Deviation=[tex]x_i-\mu[/tex]
[tex]x_i-\mu[/tex]
13 5
5 -3
4 - 4
9 1
7 -1
14 6
4 - 4
Hence, option B is correct.
The circumference of a circle is 14 inches. Find the circle's radius and diameter.
Please help :)
what number must you add to complete the square x^2+12x=40
Step-by-step explanation:
x²+12x=40
(x+6)²-6²-40=0
(x+6)²-76 = 0
Express each ratio as a fraction in its lowest terms.
18 hours to 2 days
Answer:
3/8.
Step-by-step explanation:
First convert days to hours:
2 days = 2 * 24 = 48 hours.
The greatest common factor of 18 and 48 = 6 so the required fraction is
18/48
= (18/6) / (48/6)
= 3/8.
Write the quadratic equation in standard form:
3x2 – 3x = 11
Answer:
[tex]3x^{2} -3x-11 = 0[/tex]
Step-by-step explanation:
Dada la función f(x)=1+6Sen(2x+π/3) . Halle: Período, amplitud y desfase (1.5 puntos) Dominio y rango de la función (1.5 puntos) Grafique la función trigonométrica (2 puntos)
Dada una ecuación de la forma
y = A sin(B(x + C)) + DTenemos que:
la amplitud es Ael periodo es 2π/Bel desfase es C (a la izquierda es positivo)el desplazamiento vertical es DSabemos que:
f(x)=1+6Sen(2x+π/3)
Y podemos reescribirla como:
f(x)=6Sen(2(x+π/6))+1
Siendo:
A = 6 → AmplitudT = 2π/B = 2π/2 = π → PeríodoC = π/6 → DesfaseEl dominio de un a función trigonométrica es todo el conjunto de los números reales (x ∈ R ).La imagen de una función trigonométrica de esta forma es:
y ∈ [-A+D,A+D]
y ∈ [-6+1, 6+1]
y ∈ [-5,7]
La gráfica se adjunta.
The sum of two numbers is 125. Their difference is 47. The two numbers are:
a)39 and 86.
b)40 and 85.
c)47 and 78.
d)None of these choices are correct.
Answer:
let x represent the bigger number
x+x-47=125
2x-47=125
2x=125+47
2x=172
2x/2=172/2
x=86
the smaller number=x-47
86-47
39
therefore the answer is a) 39 and 86
Answer:
A
Step-by-step explanation:
To find the sum of 125, you have to add the numbers.
39+86 = 125
To find the difference of 47, you have to subtract the numbers.
86-39 = 47
How is the graph of
y=-3(5)*-
- 3 translated from the graph of y=
=30594?
A. reflected across the y-axis and 3 units down
B. reflected across the x-axis and 3 units down
C. reflected across the x-axis and 3 units left
D. reflected across the y-axis and 3 units right
Answer:
Purplemath
Introduces reflections in the x- and y-axes. ... To see how this works, take a look at the graph of h(x) = x2 + 2x – 3. ... The previous reflection was a reflection in the x-axis. ... f (x – b) shifts the function b units to the right.
integrate G(x,y,z)=yz over the surface of x+y+z=1 in the first octant.
Parameterize the surface (I'll call it S) by
r(u, v) = (1 - u) (1 - v) i + u (1 - v) j + v k
with 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1.
Take the normal vector to this surface to be
n = ∂r/∂u × ∂r/∂v = ((v - 1) i + (1 - v) j) × ((u - 1) i - u j + k) = (1 - v) (i + j + k)
with magnitude
||n|| = √3 (1 - v)
Then in the integral, we have
[tex]\displaystyle\iint_SG(x,y,z)\,\mathrm ds = \int_0^1\int_0^1 G((1-u)(1-v),u(1-v),v) \|\mathbf n\| \,\mathrm du\,\mathrm dv \\\\= \sqrt3 \int_0^1\int_0^1uv(1-v)^2\,\mathrm du\,\mathrm dv \\\\= \boxed{\frac1{8\sqrt3}}[/tex]
Alternatively, if you're not familiar with parameterizing surfaces, you can use the "projection" formula:
[tex]\displaystyle\iint_S G(x,y,z)\,\mathrm ds = \int_{S_{xy}}G(x,y,z)\sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2}\,\mathrm dx\,\mathrm dy[/tex]
where I write [tex]S_{xy}[/tex] to mean the projection of the surface onto the (x, y)-plane, and z = f(x, y). We would then use
x + y + z = 1 ==> z = f(x, y) = 1 - x - y
and [tex]S_{xy}[/tex] is the triangle,
{(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}
Then the integral becomes
[tex]\displaystyle\int_0^1\int_0^{1-x}y(1-x-y)\sqrt{1+(-1)^2+(-1)^2}\,\mathrm dy\,\mathrm dx \\\\= \sqrt3\int_0^1\int_0^{1-x} y(1-x-y)\,\mathrm dy\,\mathrm dx \\\\= \frac{\sqrt3}{24} \\\\= \boxed{\frac1{8\sqrt3}}[/tex]
A, B and C are collinear points. B is between A and C. AB=3x+4 BC=4x-1 AC=8x-9 Find AC
Answer:
[tex]AC = 87[/tex]
Step-by-step explanation:
Given
[tex]AB = 3x + 4[/tex]
[tex]BC = 4x -1[/tex]
[tex]AC = 8x - 9[/tex]
Required
The value x
Since A, B and C are collinear, then;
[tex]AC = AB + BC[/tex]
This gives:
[tex]8x - 9 =3x+4+4x-1[/tex]
Collect like terms
[tex]8x - 3x - 4x = 9 + 4-1[/tex]
[tex]x = 12[/tex]
We have:
[tex]AC = 8x - 9[/tex]
[tex]AC = 8*12 - 9[/tex]
[tex]AC = 87[/tex]
Can someone help asap?
Answers:
sin = -5/13tan = 5/12csc = -13/5sec = -13/12cot = 12/5=============================================
Explanation:
The angle theta is between pi and 3pi/2, excluding both endpoints.
This places theta in the third quadrant (Q3) between 180 degrees and 270 degrees. The third quadrant is in the southwest.
Plot point A at the origin. 12 units to the left of this point, will be point B. So B is at (-12,0). Then five units lower is point C at (-12,-5). Refer to the diagram below. Notice how triangle ABC is a right triangle.
The angle theta will be the angle BAC, or simply angle A.
Since cos(theta) = -12/13, this indicates that
AB = -12 = adjacent
AC = 13 = hypotenuse
Technically, AB is should be positive, but I'm making it negative so that we can then say
cos(angle) = adjacent/hypotenuse
cos(theta) = AB/AC
cos(theta) = -12/13
------------------
If you apply the pythagorean theorem, you should find that BC = 5, which I'll make negative since we're below the x axis. Then we can say
sin(theta) = opposite/hypotenuse
sin(theta) = BC/AC
sin(theta) = -5/13
------------------
If you divide sine over cosine, then you'll get 5/12. The 13's cancel out. This is the value of tangent.
Or you could say
tan(theta) = opposite/adjacent
tan(theta) = BC/AB
tan(theta) = (-5)/(-12)
tan(theta) = 5/12
------------------
To find csc, aka cosecant, you apply the reciprocal to sine
sin = -5/13 which means csc = -13/5
sec, or secant, is the reciprocal of cosine
cos = -12/13 leads to sec = -13/12
and finally cotangent (cot) is the reciprocal of tangent
tan = 5/12 leads to cot = 12/5
------------------
Note: everything but tan and cot is negative in Q3.
Round 948070 to the nearest hundred? Hurry please
Answer:
9.48
Step-by-step explanation:
The following measurements (in picocuries per liter) were recorded by a set of argon gas detectors installed in a research facility:
381.3,394.8,396.1,380
Using these measurements, construct a 95% confidence interval for the mean level of argon gas present in the facility. Assume the population is approximately normal.
Answer:
The 95% confidence interval for the mean level of argon gas present in the facility is (374.4, 401.7).
Step-by-step explanation:
Before building the confidence interval, we have to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{381.3+394.8+396.1+380}{4} = 388.05[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(381.3-388.05)^2+(394.8-388.05)^2+(396.1-388.05)^2+(380-388.05)^2}{3}} = 8.58[/tex]
Confidence interval:
We have the standard deviation for the sample, so the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 4 - 1 = 3
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{8.58}{\sqrt{4}} = 13.65[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 388.05 - 13.65 = 374.4
The upper end of the interval is the sample mean added to M. So it is 388.05 + 13.65 = 401.7
The 95% confidence interval for the mean level of argon gas present in the facility is (374.4, 401.7).
Please help NO LINKS
[tex]\bar{x} = 0[/tex]
[tex]\bar{y} =\dfrac{136}{125}[/tex]
Step-by-step explanation:
Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:
[tex]f(x) = x^2 + 1[/tex]
[tex]g(x) = 6x^2[/tex]
The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:
[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]
The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by
[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= 0[/tex]
The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by
[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]
[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]
XYZ has side lengths that measure 20 centimeters each. Which of the
following best describes this type of triangle?
A. Obtuse triangle
B. Right triangle
C. Scalene triangle
D. Equilateral triangle
Answer:
it's and equilateral triangle because
all sides are equal
Answer:
equilateral triangle i have a math proffesor helping me
Step-by-step explanation:
I have a math proffesor helping me
Rearrange 2x = y/w to make w the subject
What is the area of area of 7 meters, 15 meters and 9 meters?
Answer:
10
Step-by-step explanation:
10-7 do it yourself and don't vheat
The graph shows a line of best fit for data collected on the average temperature, in degrees Fahrenheit, during a month and the
number of inches of rainfall during that month.
у
90
801
70
Average Temp
20
10
Inches of Rain
The equation for the line of best fit is y=-3.32x +97.05.
Based on the line of best fit, what would be the prediction for the average temperature during a month with 13.25 inches of rainfall?
Answer:
53.06°F
Step-by-step explanation:
Given the equation of best fit :
y=-3.32x +97.05.
The average temperature for a month with 13.25 inches of Rainfall
Amount of Rainfall = x
Average temperature = y
To make our prediction ; put x = 13.25 in the equation and solve for y ;
y = -3.32x +97.05
Put x = 13.25
y = -3.32(13.25) +97.05
y = - 43.99 + 97.05
y = 53.06°F
remove bracket and simplify 6x-(3x+2)
Answer: 3x - 2
Step-by-step explanation:
First to solve this, we need to know some basic information such as:
1. (-) × (-) = +
2. (+) × (-) = -
3. (+) × (+) = +
Therefore, 6x-(3x+2)
= 6x - 3x - 2
= 3x - 2
The answer to the question after removing the bracket will be 3x - 2.
HW HELP PLZZZZ ASAPPPP
Answer:
[tex]\frac{3v}{a^{2}} = h[/tex]
Step-by-step explanation:
[tex]v = \frac{1}{3} a^{2} h[/tex]
[tex]3v = a^{2} h[/tex]
[tex]\frac{3v}{a^{2}} = h[/tex]
A paper weight is made in the shape of a triangular pyramid.The dimensions of the paper weight are shown The formula for the volume of a triangular pyramid is V = 1/3 Bh .Which expression can be usef to find the value of B the area of the base of the pyramid
Answer:
[tex]B = \frac{3V}{h}[/tex]
Step-by-step explanation:
Given
[tex]V = \frac{1}{3}Bh[/tex]
Required
Solve for B
We have;
[tex]V = \frac{1}{3}Bh[/tex]
Multiply by 3
[tex]3V = Bh[/tex]
Make B the subject
[tex]B = \frac{3V}{h}[/tex]
Which of the following is the solution set of -2|x| < -8 {x | -4 > x > 4} {x | x < -4 or x > 4} {x | -4 < x < 4}
Answer:
the second one
Step-by-step explanation:
For the function, tell whether the graph opens up or opens down, identify the vertex, and tell whether the graph is wider, narrower, or the same width as the graph of y = |x|.
y = 2|x – 1| - 3
opens up, (1, 3), wider
opens up, (1, 3), narrower
opens up, (-1, -3), wider
opens up, (1, -3), narrower
Answer:
The answer is D, the last one.
9514 1404 393
Answer:
(d) opens up, (1, -3), narrower
Step-by-step explanation:
The factor of +2 multiplying the function tells you the graph is expanded vertically by a factor of 2. The parent function opens upward, and the positive sign on this expansion factor does not change that. The expansion means that y-values will be farther from the vertex for the same x-value distance from the vertex. This give the appearance of a narrower graph.
As always, the transformation ...
f(x -h) +k
moves the vertex from (0, 0) to (h, k). Here, you have (h, k) = (1, -3), so that is the location of the vertex of the transformed function.
PLEASE ANSWER QUICKLY Find the distance between points (4, 2) and (7, 2) on the coordinate
plane.
Answer:
3 units
Step-by-step explanation:
(4,2) (7,2)
Subtract 4 from 7 = 3
Subtract 2 from 2 = 0
This means that (7,2) is 3 units up from (4,2).
:) ur welcome
Answer:
Step-by-step explanation:
D=√(x2-x1)²+(y2-y1)²
D=√(7-4)²+(2-2)²
D=√(3)²+0
D=3²*½
D=3
Julie and Mona know that that Earth’s average distance from the Sun is approximately 93 million miles and it takes 1 year to complete an orbit of the Sun. A new asteroid has been discovered orbiting the Sun at an average distance of 1,488 million miles. How long will it take for the asteroid, in Earth years, to complete one orbit of the Sun.
Answer:
16 years
Step-by-step explanation:
Given that :
Earth's distance from sun = 93 million miles
Number of years to complete an orbit = 1 year
Average orbiting distance of new asteroid = 1488 million miles
Number of years to complete an orbit = x
93,000,000 Miles = 1
1488000000 miles = x
Cross multiply :
93000000x = 1488000000
x = 1488000000 / 93000000
x = 16 years
Period taken to orbit the sun = 16 years
Answer: 64 Earth years...
