Answer:
1/6
Step-by-step explanation:
We need to find the common ratio for the given Geometric Series . We know that ,
Geometric Series:- When a common number is multiplied to each term to obtain the next term of the Series is called Geometric Series .
Common Ratio :- The number which is multiplied to obtain the next term of the series .
Here the given series is ,
[tex]\rm\implies Series = 72 , 12 , 2 , \dfrac{1}{3},\dfrac{1}{18} [/tex]
We can find the common ratio by dividing the consecutive terms , As ,
[tex]\rm\implies Common \ Ratio (r) = \dfrac{ n \ th \ term }{ ( n - 1)th \ term } [/tex]
Substitute the respective values ,
[tex]\rm\implies Common \ Ratio (r) = \dfrac{ 12 }{ 72 } [/tex]
Simplify by dividing the term in RHS ,
[tex]\rm\implies \boxed{\blue{\rm Common \ Ratio (r) = \dfrac{ 1 }{ 6 } }}[/tex]
Hence the common ratio is 1/6 .
I can't figure this out, please help
1. A rectangle is formed by the intersection of the lines x = −1, y = −1, x = 5
and y = 3. What is the perimeter and area of the rectangle
Step-by-step explanation:
The length along the x-axis is 5 - (-1) = 6. The length along the y-axis is 3 - (-1) = 4. The perimeter of this rectangle can be calculated as
[tex]P = 2x + 2y = 2(6) + 2(4) = 20\:\text{units}[/tex]
The area of the rectangle can be calculated as
[tex]A = xy = (6)(4) = 24\:\text{units}^2[/tex]
Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give two exams, one to a class of size 25 and the other to a class of size 64.
Required:
a. Approximate the probability that the average test score in the class of size 25 exceeds 80.
b. Repeat part (a) for the class of size 64.
c. Approximate the probability that the average test score in the larger class exceeds that of the other class by over 2.2 points.
Answer:
a) Hence the probability that the average test score in the class of size 25 exceeds 80.
P ( X > 74) = 0.9838
P ( Z > 2.14) = 0.0162
b) Hence the probability that the average test score for the class of size 64
P ( X > 74) = 0.9838
P ( Z > 2.14) = 0.0003
c) Probability of the difference exceeding 2.2 = 0.9936
P (Z < 2.49) = 0.0064
Step-by-step explanation:
Let's assume a normal distribution.
Now,
a) For a class of 25
[tex]P ( X > 74) = P (Z > 80 - 74/ 14\sqrt(25) )\\\\= P (Z < 6 / 2.8)\\\\= P ( Z < 2.14)\\= 0.9838\\[/tex]
[tex]P ( Z > 2.14) = 1- 0.9838\\= 0.0162[/tex]
b)
Similarly:
For the class of 64
[tex]P ( X > 74) = P (Z > 80 - 74/ 14\sqrt(64) )\\\\= P (Z < 6 / 1.75)= P ( Z < 3.428)\\= 0.9838\\[/tex]
[tex]P ( Z > 2.14) = 1- 0.9997\\= 0.0003[/tex]
c) Probability of the difference exceeding 2.2
[tex]= P (Z > 2.2/\sqrt{14 * {(1/25) + (1/64}\\[/tex]
[tex]= P (Z > 2.49)\\= 0.9936[/tex]
P (Z < 2.49)
= 1 - 0.9936
= 0.0064
the line that passes through the point (-4, 2) and has a
What is the equation of
slope of
2?
Answer:
y = 2x + 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2 , then
y = 2x + c ← is the partial equation
To find c substitute (- 4, 2 ) into the partial equation
2 = - 8 + c ⇒ c = 2 + 8 = 10
y = 2x + 10 ← equation of line
The winter group provides tax advice
what? ;-;.............
What is the measurement of N?
Answer:
the measurement of N is D, 81.
Step-by-step explanation:
The angle measurement of a Right Angled Triangle is 90 degrees. And based off the angle dimension given in the image above ( 9 degrees ), you need to subtract 90 ( the angle dimension of the triangle) with the angle dimension given (9 degrees) which gets you to an answer of 81 degrees.
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker with explaination simple method for class 5
Answer:
$150
Step-by-step explanation:
So, 60 dollars is 40% of the original price. So 30 dollars is 20% of the original price, and 150 dollars is 100% of the original price. So, the original value of the rice cooker is 150 dollars.
Answer:
The price of the Rice Cooker was 150$.
Step-by-step explanation:
So if you buy an item at $150 with 60% discounts, you will pay $60 and get 90 cashback rewards ... interest per annum, dollars, pounds, coupons,60% off, 60% of price or something, we ... For example 5% of 20, which is the same thing as fraction x/100 * 20=5%. ... Formula and equation for % of something or whole numbers.
write the numeral of twelve Arab sixty core
Answer:
12600000000
Step-by-step explanation:
write the numeral of twelve Arab sixty core
The numeral of twelve Arab sixty core is
=> 12600000000
hope it is helpful to you
Step-by-step explanation:
the numeral from is 12600000000
A professor, transferred from Toronto to New York, needs to sell his house in Toronto quickly. Someone has offered to buy his house for $220,000, but the offer expires at the end of the week. The professor does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with his realtor, the professor believes the price he will get by leaving the house on the market for another month is uniformly distributed between $210,000 and $235,000. If he leaves the house on the market for another month, what is the probability that he will get at least $225,000 for the house
How does the rate of change of f(x)=3x+5 compare to the rate of change of g(x)=2x+5 ?
HELP I NEED ANSWERS
Answer:
The rate of change of f(x) is faster than the rate of change of g(x).
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
*Note:
Rate of Change is determined by slope.
Step 1: Define
f(x) = 3x + 5
↓ Compare to y = mx + b
Slope m = 3
g(x) = 2x + 5
↓ Compare to y = mx + b
Slope m = 2
Step 2: Answer
We can see that the slope of f(x) is greater than g(x).
∴ the rate of change of f(x) would be greater than g(x).
In a normally distributed data set with a mean of 19 and a standard deviation of 2.6, what percentage of the data would be between 13.8 and 24.2?a) 95% based on the Empirical Ruleb) 68% based on the histogramc) 68% based on the Empirical Ruled) 95% based on the histogram
Step-by-step explanation:
check the attachment above.
The length of rectangular garden is 8 feet longer than the width. If the area of the garden is 20 square feet, find the length and width of the garden.
The length is ____________ ft
The width is _____________ ft
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Answer:
length: 10 ftwidth: 2 ftStep-by-step explanation:
Two integer factors of 20 that differ by 8 are 2 and 10.
The garden is 10 feet long and 2 feet wide.
What is the area of the figure
Answer:
72 in. sq.
Step-by-step explanation:
6 x 6 = 36
6 x 6 = 36 / 2 = 18
6 x 6 = 36 / 2 = 18
18 + 18 + 36 = 72.
Hope this helps!
If there is something wrong just let me know.
Solve 5 to x-4 power =7
Answer:The value of x is 4.
Step-by-step explanation:
Given : Expression .
To find : Solve for x ?
Solution :
Applying exponential property,
Comparing the base,
Step-by-step explanation:
Directions: Use the figure to write the symbol for each.
1. I ray
2. a plane
А
3. 3 points
4. 2 lines
5. 3 angles
6. 3 line segments
D
Geometry
156
Total Math Grade 6
I need help ASAP please due tomorrow 6th grade geometry
The work done by a machine in 2 minutes is 480J. Calculate the power of the machine
Answer:
I think the power is 4
Step-by-step explanation:
480J / 120 = 4
Put 2 mins into seconds which is 120 seconds
Sorry if it is wrong :)
Answer:
[tex]4\text{ watts}[/tex]
Step-by-step explanation:
In physics, the power of a machine is given by [tex]P=\frac{W}{\Delta t}[/tex], where [tex]W[/tex] is work in Joules and [tex]\Delta t[/tex] is time in seconds.
Convert 2 minutes into seconds:
2 minutes = 120 seconds.
Substitute [tex]W=480[/tex] and [tex]\Delta t=120[/tex] to solve for [tex]P[/tex]:
[tex]P=\frac{480}{120}=\boxed{4\text{ watts}}[/tex]
whats 2 plus 2
*just trying to help someone get points* :)
Answer:4 ma boi
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
because I am god at meth and very smart
5 = –6x2 + 24x
5 = –6(x2 – 4x)
inside the parentheses and
.
–19 = –6(x – 2)2
StartFraction 19 Over 6 EndFraction = (x – 2)2
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot = x – 2
The two solutions are
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot.
Answer:
x = 2 - sqrt(19/6)
x = 2 + sqrt(19/6)
Step-by-step explanation:
Answer:
add 4
subtract 24 from 5
2
Step-by-step explanation:
Regarding the violation of multicollinearity, which of the following description is wrong?
Complete question is;
Regarding the violation of multicollinearity, which of the following description is wrong?
a. It changes the intercept of the regression line.
b. It changes the sign of the slope.
c. It changes the slope of the regression line.
d. It changes the value of F-tests.
e. It changes the value of T-tests
Answer:
a. It changes the intercept of the regression line
Step-by-step explanation:
Multicollinearity is a term used in multiple regression analysis to show a high correlation between independent variables of a study.
Since it deals with independent variables correlation, it means it must be found before getting the regression equation.
Now, looking at the options, the one that doesn't relate with multicollinearity is option A because the intercept of the regression line is the value of y that is predicted when x is 0. Meanwhile, multicollinearity from definition above does in no way change the intercept of the regression line because it doesn't predict the y-value when x is zero.
If h(x) = −3x − 10, find h(−3). (1 point)
Answer:
h(- 3) = - 1
Step-by-step explanation:
Substitute x = - 3 into h(x) , that is
h(- 3) = - 3(- 3) - 10 = 9 - 10 = - 1
Please helpppppp me!!!!!!!!
Answer:
A --> y=cot(x)
Step-by-step explanation:
if you graph tan(x), it has a period of just PI, because tan(x) is just sin(x)/cos(), and cot(x) is the same because it is just sec(x)/csc(x).
trigonometry Ration
Lesson Goals
Understand
relationships.
Define a function in
Identify the domain
Determine whether or
terms of its
and
of
not a
and output.
a relation.
is a function.
W
2K
Words to know
स्ज्द्ज्ज्ग्जेज्दिविफ्ज्र्ज्स्ज्स्ज्ग्झ्क्व्जेफिक
A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance σ2 = 42.3. In a different section of Chaco Canyon, a random sample of 28 transects gave a sample variance s2 = 48.3 for the number of sites per transect.
Required:
Use a 5% level of significance to test the claim that the variance in the new section is greater than 42.3.
Answer:
There is significant evidence to conclude that carina e in New section is greater than 42.3
Step-by-step explanation:
Given :
Sample variance, s² = 48.3
Population variance, σ² = 42.3
Sample size, n = 28
α = 0.05
The hypothesis :
H0 : σ² = 42.3
H0 : σ² > 42.3
The test statistic, χ² : (n-1)*s²/σ²
χ² = [(28 - 1) * 48.3] / 42.3
χ² = (27 * 48.3) / 42.3
χ² = 1304.1 / 42.3
χ² = 30.829787
χ² = 30.830
The Critical value at α = 0.05 ; df = (28-1) = 27
Critical value(0.05, 27) = 27.587
Reject H0 if χ² statistic > Critical value
Since, 30.830 > 27.587 ; Reject H0 ; and conclude that variance in the new section is greater than 42.3
ASAP PLSSS!!!!!!!!!!1!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: i think its the last one bc if you multiply 9 and 3 in its gets you 18
Step-by-step explanation:
Answer:
V=(1/3)πr²h
v=
[tex] \frac{1}{3} \times {3}^{2} \times 9 \times \pi \\ = 27\pi[/tex]
27pi in³
27pi in³First option
Brainliest please~
Find the x and y intercepts and graph 2x − y = −8
Answer:
-2
Step-by-step explanation:
2x-y=-8-1equation
2x=-8+y
x=-8+y -2equation
2
then, taking 1st equation;
2x-y=-8
2(-8+y/2)-y=-8
-16+2y-y=-8
4
-16+2y-4y=-8
4
-16-2y=-8*4
-2y=-32+16
y=-16/-2
y=4
for x
x=-8+y
2
x=-8+4
2
x=-4
2
x=-2
Find the values of c such that the area of the region bounded by the parabolas y = 4x2 − c2 and y = c2 − 4x2 is 32/3. (Enter your answers as a comma-separated list.)
Answer:
-2,2
Step-by-step explanation:
Let
[tex]y_1=4x^2-c^2[/tex]
[tex]y_2=c^2-4x^2[/tex]
We have to find the value of c such that the are of the region bounded by the parabolas =32/3
[tex]y_1=y_2[/tex]
[tex]4x^2-c^2=c^2-4x^2[/tex]
[tex]4x^2+4x^2=c^2+c^2[/tex]
[tex]8x^2=2c^2[/tex]
[tex]x^2=c^2/4[/tex]
[tex]x=\pm \frac{c}{2}[/tex]
Now, the area bounded by two curves
[tex]A=\int_{a}^{b}(y_2-y_1)dx[/tex]
[tex]A=\int_{-c/2}^{c/2}(c^2-4x^2-4x^2+c^2)dx[/tex]
[tex]\frac{32}{3}=\int_{-c/2}^{c/2}(2c^2-8x^2)dx[/tex]
[tex]\frac{32}{3}=2\int_{-c/2}^{c/2}(c^2-4x^2)dx[/tex]
[tex]\frac{32}{3}=2[c^2x-\frac{4}{3}x^3]^{c/2}_{-c/2}[/tex]
[tex]\frac{32}{3}=2(c^2(c/2+c/2)-4/3(c^3/8+c^3/28))[/tex]
[tex]\frac{32}{3}=2(c^3-\frac{4}{3}(\frac{c^3}{4}))[/tex]
[tex]\frac{32}{3}=2(c^3-\frac{c^3}{3})[/tex]
[tex]\frac{32}{3}=2(\frac{2}{3}c^3)[/tex]
[tex]c^3=\frac{32\times 3}{4\times 3}[/tex]
[tex]c^3=8[/tex]
[tex]c=\sqrt[3]{8}=2[/tex]
When c=2 and when c=-2 then the given parabolas gives the same answer.
Therefore, value of c=-2, 2
A humanities professor assigns letter grades on a test according to the following scheme.
A: Top 8% of scores
B: Scores below the top 8% and above the bottom 62%
C: Scores below the top 38% and above the bottom 18%
D: Scores below the top 82% and above the bottom 9%
E: Bottom 9% of scores Scores on the test are normally distributed with a mean of 67 and a standard deviation of 7.3.
Find the numerical limits for a C grade.
Answer:
The numerical limits for a C grade are 60.6 and 69.1.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 67 and a standard deviation of 7.3.
This means that [tex]\mu = 67, \sigma = 7.3[/tex]
Find the numerical limits for a C grade.
Below the 100 - 38 = 62th percentile and above the 18th percentile.
18th percentile:
X when Z has a p-value of 0.18, so X when Z = -0.915.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.915 = \frac{X - 67}{7.3}[/tex]
[tex]X - 67 = -0.915*7[/tex]
[tex]X = 60.6[/tex]
62th percentile:
X when Z has a p-value of 0.62, so X when Z = 0.305.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.305 = \frac{X - 67}{7.3}[/tex]
[tex]X - 67 = 0.305*7[/tex]
[tex]X = 69.1[/tex]
The numerical limits for a C grade are 60.6 and 69.1.
what is the area of this whole shape
Answer:
104 m²
Step-by-step explanation:
Area of the whole shape = area of the triangle + area of the rectangle
= ½*b*h + L*W
Where,
b = 8 m
h = 6 m
L = 10 m
W = 8 m
Plug in the values into the equation
Area of the whole shape = ½*8*6 + 10*8
= 24 + 80
= 104 m²
.
you invested $
7000
7000
between two accounts payin
6
%
6
%
and
8
%
8
%
annual interet, respectively. if the total interest earned for the year was $
480
,
480
,
how much was invested at each rate
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Answer:
$3000 at 8%$4000 at 6%Step-by-step explanation:
Let x represent the amount invested at 8%. Then the total interest earned is ...
0.06(7000 -x) +0.08x = 480
420 +0.02x = 480 . . . . . . . . . eliminate parentheses
0.02x = 60 . . . . . . . . . . subtract 420
x = 60/0.02 = 3000 . . . . . divide by the coefficient of x
$3000 was invested at 8%; $4000 was invested at 6%.
Use the procedures developed to find the general solution of the differential equation. (Let x be the independent variable.)
2y''' + 15y'' + 24y' + 11y= 0
Solution :
Given :
2y''' + 15y'' + 24y' + 11y= 0
Let x = independent variable
[tex](a_0D^n + a_1D^{n-1}+a_2D^{n-2} + ....+ a_n) y) = Q(x)[/tex] is a differential equation.
If [tex]Q(x) \neq 0[/tex]
It is non homogeneous then,
The general solution = complementary solution + particular integral
If Q(x) = 0
It is called the homogeneous then the general solution = complementary solution.
2y''' + 15y'' + 24y' + 11y= 0
[tex]$(2D^3+15D^2+24D+11)y=0$[/tex]
Auxiliary equation,
[tex]$2m^3+15m^2+24m +11 = 0$[/tex]
-1 | 2 15 24 11
| 0 -2 - 13 -11
2 13 11 0
∴ [tex]2m^2+13m+11=0[/tex]
The roots are
[tex]$=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]
[tex]$=\frac{-13\pm \sqrt{13^2-4(11)(2)}}{2(2)}$[/tex]
[tex]$=\frac{-13\pm9}{4}$[/tex]
[tex]$=-5.5, -1$[/tex]
So, [tex]m_1, m_2, m_3 = -1, -1, -5.5[/tex]
Then the general solution is :
[tex]$= (c_1+c_2 x)e^{-x} + c_3 \ e^{-5.5x}$[/tex]
