Answer:
Step-by-step explanation:
Given that:
A set of numbers is transformed by taking the log base 10 of each number. The mean of the transformed data is 1.65. What is the geometric mean of the untransformed data.
To obtain the geometric mean of the untransformed data,
X = set of numbers
N = number of observations
Arithmetic mean if transformed data = 1.65
Log(Xi).... = transformed data
Arithmetic mean = transformed data/ N
Log(Xi) / N = 1.65
(Πx)^(1/N), we obtain the antilog of the aritmétic mean simply by raising 10 to the power of the Arithmetic mean of the transformed data.
10^1.65 = 44.668359
please help me with this question.
Answer:
[tex] \purple{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]
Step-by-step explanation:
[tex]y = \frac{1}{ {x}^{11} } \\ y = {x}^{ - 11} \\ \frac{dy}{dx} = \frac{d}{dx} {x}^{ - 11} \\ \frac{dy}{dx} = - 11{x}^{ - 11 - 1} \\ \frac{dy}{dx} = - 11{x}^{ - 12} \\ \\ \frac{d}{dx} \bigg(\frac{dy}{dx} \bigg) = \frac{d}{dx} ( - 11 {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11\frac{d}{dx} ( {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11( - 12{x}^{ - 13} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = 132{x}^{ - 13} \\ \\ \huge \red{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]
The first term of a G.p are as follows: m, m^2+4, 16m find the 5th term
Answer:
512
Step-by-step explanation:
In a geometric sequence, the ratio between the second term and the first term is equal to the ratio between the third term and the second term.
(m² + 4) / m = 16m / (m² + 4)
Solve:
(m² + 4)² = 16m²
m² + 4 = 4m
m² − 4m + 4 = 0
(m − 2)² = 0
m = 2
The first three terms of the geometric sequence are therefore 2, 8, 32.
The common ratio is 4, and the first term is 2. So the 5th term is:
a = 2 (4)⁵⁻¹
a = 512
i need help on this question: Expand the expression 8( 7 + t) this is algabra.
Answer:
[tex]\huge \boxed{8t + 56}[/tex]
Step-by-step explanation:
[tex]8(7 + t)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]8(7) + 8(t)[/tex]
[tex]56 + 8t[/tex]
If the sin 30° is 1 over 2, then the cos ____° = _____.
Answer:
Below.
Step-by-step explanation:
(sine) [tex]sin=30=1/2[/tex]
[tex]=cos [90-30][/tex]
Which means cos=60
Same as:
(cosine) [tex]cos=60=1/2[/tex] or [tex]Sin30=Cos 60=1/2[/tex]
Hence, the answer is...
cos 60° = ½....
By:✨ RobloxYt ✨
The value of the trigonometric ratio cos60 is 1 / 2.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the value of sin 30° is 1 over 2. The value of cos(90-30) will be calculated as:-
sin(30) = cos(90-30) = cos60
sin(30) = cos(90-30) = 1 / 2
Hence, the value of the cos60 is 1 / 2.
To know more about Trigonometry follow
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Jackie ordered a set of wood and metal clothes pins. Of the 276 pins, 172 were wood. What percentage of the clothes pins were wood? Round to the nearest hundredth.
Answer:
62.32%
Step-by-step explanation:
172/276 * 100%
= 62.32%
Explain how do you do it If you put only the answer i will report you
Answer:
[tex] d = \sqrt{113} = 10.63014 [/tex]
Step-by-step explanation:
Distance between the endpoints of the graph, (-3, 3) and (5, -4), can be calculated using distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex].
Where,
[tex] (-3, 3) = (x_1, y_1) [/tex]
[tex] (5, -4) = (x_2, y_2) [/tex]
Thus,
[tex] d = \sqrt{(5 - (-3))^2 + (-4 - 3)^2} [/tex]
[tex] d = \sqrt{(8)^2 + (-7)^2} [/tex]
[tex] d = \sqrt{64 + 49} = \sqrt{113} [/tex]
[tex] d = \sqrt{113} = 10.63014 [/tex]
What is 0=3x^2-16x +15 solved for x? there should be two numbers
Answer: x = ⅓ or 5
Step-by-step explanation:
From the quadratic equation, we are asked to find the root of the equation. Therefore, we may use any of the methods.
Here I am using grouping method.
3x² - 16x + 15 = 0
3x² - 15x -x + 15 = 0, we now factorize
3x( x - 5 ) - ( x - 5 ) = 0, we now collect like terms.
( 3x - 1 )( x - 5 ) = 0
Now to find x, we equate each in brackets to zero and then solve.
3x - 1 = 0
x = ⅓ , and if
x - 5 = 0
x = 5, .
Now , the solution of the equation will be
x = ⅓ or 5
using addition formula solve tan 15
Answer:
2 - [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the addition formula for tangent
tan(A - B) = [tex]\frac{tanA-tanB}{1+tanAtanB}[/tex] and the exact values
tan45° = 1 , tan60° = [tex]\sqrt{3}[/tex] , then
tan15° = tan(60 - 45)°
tan(60 - 45)°
= [tex]\frac{tan60-tan45}{1+tan60tan45}[/tex]
= [tex]\frac{\sqrt{3}-1 }{1+\sqrt{3} }[/tex]
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
The conjugate of 1 + [tex]\sqrt{3}[/tex] is 1 - [tex]\sqrt{3}[/tex]
= [tex]\frac{(\sqrt{3}-1)(1-\sqrt{3}) }{(1+\sqrt{3})(1-\sqrt{3}) }[/tex] ← expand numerator/denominator using FOIL
= [tex]\frac{\sqrt{3}-3-1+\sqrt{3} }{1-3}[/tex]
= [tex]\frac{-4+2\sqrt{3} }{-2}[/tex]
= [tex]\frac{-4}{-2}[/tex] + [tex]\frac{2\sqrt{3} }{-2}[/tex]
= 2 - [tex]\sqrt{3}[/tex]
PLEASE HELP! A) 9 B) 8.6 C) 26.3 D) 5.7
Answer:
x = 9.0
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos 39 = 7/x
x cos 39 = 7
x = 7/cos 39
x =9.007316961
x = 9.0
Can the sine rule relationship in trigonometry be used with non right angled triangle?
Answer:
Yes
Step-by-step explanation:
The sine rule works on all triangles (not just right-angled triangles) where a side and it's opposit angles are known.
Given A = {a, b, c, d} and B = {1, 2, 3, 4} , sets A and B can be defined as?
Answer:
Answer: {4,5}. 13) ∪ . Put the sets together in one large set. {1,2,3,5} ... {2,3,1,5}. There are no duplicates to remove, but I can write this in a nicer order.
Step-by-step explanation:
Given f(x) = -2x^2 + 4, determine the slope of the secant line over the interval [-1, 2].
Answer: -2
Step-by-step explanation:
We know that the slope of a secant line over a interval [a,b] is given by :-
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
Given f(x) =[tex]-2x^2 + 4[/tex]
Then, the slope of the secant line over the interval [-1, 2] is given by :-
[tex]m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1[/tex]
Hence, the slope of the secant line over the interval [-1, 2] is -2.
solve for q
-9 = q - 4.8
q = ?
(Thank you :3)
Answer:
[tex]-4.2=q[/tex]
Step-by-step explanation:
To do this you would just add 4.8 to both sides to get rid of the -4.8 so then the equation would look like [tex]-4.2=q[/tex] and that would be our answer.
Answer:
q=-4.2
Step-by-step explanation:
-9 = q - 4.8
Add 4.8 to each side
-9+4.8 = q - 4.8+4.8
-4.2 = q
q=-4.2
Suppose x and y are related by the given equation and use implicit differentiation to determine dydx.x7y+y7x=7.
Looks like the equation is
[tex]x^7y+y^7x=7[/tex]
Differentiate both sides with respect to [tex]x[/tex], taking [tex]y[/tex] to be a function of [tex]x[/tex].
[tex]\dfrac{\mathrm d[x^7y+y^7x]}{\mathrm dx}=\dfrac{\mathrm d[7]}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm d[x^7]}{\mathrm dx}y+x^7\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\mathrm d[y^7]}{\mathrm dx}x+y^7\dfrac{\mathrm dx}{\mathrm dx}=0[/tex]
[tex]7x^6y+x^7\dfrac{\mathrm dy}{\mathrm dx}+7y^6x\dfrac{\mathrm dy}{\mathrm dx}+y^7=0[/tex]
Solve for [tex]\frac{\mathrm dy}{\mathrm dx}[/tex]:
[tex](x^7+7y^6)\dfrac{\mathrm dy}{\mathrm dx}=-(7x^6y+y^7)[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{7x^6y+y^7}{x^7+7y^6}[/tex]
The heights of North American women are nor-mally distributed with a mean of 64 inches and a standard deviation of 2 inches. a. b. c. What is the probability that a randomly selected woman is taller than 66 inches? A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches? What is the probability that the mean height of a random sample of 100 women is greater than
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]P(X > 66) = P(Z> 1 ) = 0.15866[/tex]
b
[tex]P(\= X > 66) = P(Z> 2 ) = 0.02275[/tex]
c
[tex]P(\= X > 66) = P(Z> 10 ) = 0[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 64 \ inches[/tex]
The standard deviation is [tex]\sigma = 2 \ inches[/tex]
The probability that a randomly selected woman is taller than 66 inches is mathematically represented as
[tex]P(X > 66) = P(\frac{X - \mu }{\sigma } > \frac{ 66 - \mu }{\sigma} )[/tex]
Generally [tex]\frac{ X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X > 66) = P(Z> \frac{ 66 - 64 }{ 2} )[/tex]
[tex]P(X > 66) = P(Z> 1 )[/tex]
From the z-table the value of [tex]P(Z > 1 ) = 0.15866[/tex]
So
[tex]P(X > 66) = P(Z> 1 ) = 0.15866[/tex]
Considering b
sample mean is n = 4
Generally the standard error of mean is mathematically represented as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{4} }[/tex]
=> [tex]\sigma _{\= x} = \frac{2 }{\sqrt{4} }[/tex]
=> [tex]\sigma _{\= x} = 1[/tex]
The probability that the sample mean height is greater than 66 inches
[tex]P(\= X > 66) = P(\frac{X - \mu }{\sigma_{\= x } } > \frac{ 66 - \mu }{\sigma_{\= x }} )[/tex]
=> [tex]P(\= X > 66) = P(Z > \frac{ 66 - 64 }{1} )[/tex]
=> [tex]P(\= X > 66) = P(Z> 2 )[/tex]
From the z-table the value of [tex]P(Z > 2 ) = 0.02275[/tex]
=> [tex]P(\= X > 66) = P(Z> 2 ) = 0.02275[/tex]
Considering b
sample mean is n = 100
Generally the standard error of mean is mathematically represented as
[tex]\sigma _{\= x} = \frac{2 }{\sqrt{100} }[/tex]
=> [tex]\sigma _{\= x} = 0.2[/tex]
The probability that the sample mean height is greater than 66 inches
[tex]P(\= X > 66) = P(Z > \frac{ 66 - 64 }{0.2} )[/tex]
=> [tex]P(\= X > 66) = P(Z> 10 )[/tex]
From the z-table the value of [tex]P(Z > 10 ) = 0[/tex]
[tex]P(\= X > 66) = P(Z> 10 ) = 0[/tex]
-2/3(6/5x-7/10)17/20
Piecewise Function - The domain is split
Answer:
The piecewise function would be as follows :
[tex]\mathrm{C(g) = \left \{ {{25\:if\: 0 < g < 2} \atop {10g\:if\:g>2}} \right. }[/tex]
Step-by-step explanation:
This piecewise function is composed of one segment, and a ray. Let's start by identifying the properties of this segment.
Segment : As you can see the segment extends from 0 to 2 on the x - axis. This is at y = 25. Therefore our first expression would be 'C(g) = 25 at {0 < g < 2}.'
Ray : As this is ray, we have C(g) = 10g, as the slope is apparently 10. As you can see the rise is 10, over a run of 1, given the points (2, 25) and (3, 35) lie on the plane. The ray starts at the coordinate (2, 25), leaving us with the inequality g > 2.
So now that we have the expressions 'C(g) = 25 at {0 < g < 2}' and 'C(g) = 10g at {g > 2}' we can combine them to create the following piecewise function,
[tex]\mathrm{C(g) = \left \{ {{25\:if\: 0 < g < 2} \atop {10g\:if\:g>2}} \right. }[/tex]
Solve for x x - 8.9 = 7.18 x =
Answer:
x = 16.08
Step-by-step explanation:
x - 8.9 = 7.18
Add 8.9 to each side
x - 8.9+8.9 = 7.18+8.9
x = 16.08
What is an example of polynomials that are in standard form?
Answer:
standard form means that the terms are ordered from biggest exponent to
lowest exponent. The leading coefficient is the coefficient of the first term in a
polynomial in standard form . For example, 3x^4 + x^3 - 2x^2 + 7x.
Suppose a bag of marbles has 4 green, 2 red, 5 yellow, 1 brown, and 7 blue marbles. What is the probability of picking a green marble, replacing it, and then picking a brown marble? The probability of a student having a skateboard is 0.49 and the probability of having rollerblades is .57. What is the probability that a student has both a skateboard and roller blades? If 50% of your friends like coffee and 70% like hot cocoa, what is the probability that one of your friends likes both coffee and hot cocoa?
Answer:
1. There are a total of 19 marbles in the bag. The probability of picking a green marble out of them is 4/19 since there are only 4 green ones. The probability of picking a brown marble after replacing what has been initially picked is 1/19. The final probability is the product of the two probabilities and that is 4/361.
2. ?
3. 60%
Step-by-step explanation:
write -0.1... as a fraction
Answer:
THE ANSWER IS :
-(1/10)
Kim is watching a satellite launch from an observation spot 6 miles away. Find the angle of elevation from Kim to the satellite, which is at a height of 0.7 miles.
Answer:
Angle of elevation from Kim to the satellite launch = 6.654°
Step-by-step explanation:
The distance from Kim to the satellite launch
= 6 miles
Height of the satellite launch
= 0.7 miles
Angle of elevation from Kim to the satellite launch = b
Tan b = height of satellite/distance from Kim
Tan b= 0.7/6
Tan b= 0.1166667
b = tan^-1 (0.1166667)
b= 6.654°
Angle of elevation from Kim to the satellite launch = 6.654°
In the given diagram if AB || CD, ∠ABO = 118° , ∠BOD = 152° , then find the value of ∠ODC.
please help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
90°
Step-by-step explanation:
Through point O draw a ray on left side of O which is || to AB & CD and take any point P on it.
Therefore,
∠ABO + ∠BOP = 180° (by interior angle Postulate)
118° + ∠BOP = 180°
∠BOP = 180° - 118°
∠BOP = 62°.... (1)
Since, ∠BOP + ∠POD = ∠BOD
Therefore, 62° + ∠POD = 152°
∠POD = 152° - 62°
∠POD = 90°.....(2)
∠POD + ∠ODC = 180° (by interior angle Postulate)
90° + ∠ODC = 180°
∠ODC = 180° - 90°
[tex] \huge\red {\boxed {m\angle ODC = 90°}} [/tex]
A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3. Using the .05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis
Answer:
We conclude that the population mean is greater than 10.
Step-by-step explanation:
The complete question is: A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3. Using the 0.05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis [tex]H_0= \mu \leq 10[/tex] and [tex]H_A=\mu >10[/tex].
We are given that a random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3.
Let [tex]\mu[/tex] = population mean
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq 10[/tex] {means that the population mean is less than or equal to 10}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 10 {means that the population mean is greater than 10}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 12
s = sample standard deviation = 3
n = sample of observations = 10
So, the test statistics = [tex]\frac{12-10}{\frac{3}{\sqrt{10} } }[/tex] ~ [tex]t_9[/tex]
= 2.108
The value of t-test statistics is 2.108.
Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the population mean is greater than 10.
The growth of a city is described by the population functionwhereis the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at
Complete question:
The growth of a city is described by the population function p(t) = P0e^kt where P0 is the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at
Answer:
27,800
Step-by-step explanation:
We need to obtain the initial population(P0) and constant value (k)
Population function : p(t) = P0e^kt
At t = 0, population = 19,000
19,000 = P0e^(k*0)
19,000 = P0 * e^0
19000 = P0 * 1
19000 = P0
Hence, initial population = 19,000
At t = 3; population = 23,000
23,000 = 19000e^(k*3)
23000 = 19000 * e^3k
e^3k = 23000/ 19000
e^3k = 1.2105263
Take the ln
3k = ln(1.2105263)
k = 0.1910552 / 3
k = 0.0636850
At t = 6
p(t) = P0e^kt
p(6) = 19000 * e^(0.0636850 * 6)
P(6) = 19000 * e^0.3821104
P(6) = 19000 * 1.4653739
P(6) = 27842.104
27,800 ( nearest whole number)
what value should go in the red box
Answer: y = 4
Step-by-step explanation: If y = x + 2, then the value of y will correspond
to the values that are located in the x-column.
In other words, for the first column, we know that 2 = x.
So if y = x + 2, then y = 2 + 2 or y = 4.
To the nearest meter, how many meters are in 160 inches?
Answer:
4
Step-by-step explanation:
When you convert 160 inches to meters you get 4 meters
Answer:
4.064 Meters
Step-by-step explanation:
The length of a rectangle is 5 mm less than 4 times the width. If the perimeter is 75 mm, what is the length of the rectangle?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{29 \: mm}}}}}[/tex]
Step-by-step explanation:
Let the width of a rectangle be 'w'
Length of a rectangle be 4w - 5
Perimeter of a rectangle = 75 mm
First, finding the width of the rectangle ( w )
[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(length + width)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 2(4w - 5 + w)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 2(5w - 5)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 10w - 10}}[/tex]
[tex] \dashrightarrow{ \sf{10w - 10 = 75}}[/tex]
[tex] \dashrightarrow{ \sf{10w = 75 + 10}}[/tex]
[tex] \dashrightarrow{ \sf{10w = 85}}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{10w}{10} = \frac{85}{10} }}[/tex]
[tex] \dashrightarrow{ \sf{w = 8 .5 \: mm}}[/tex]
Replacing / substituting the value of width of a rectangle in order to find the length of a rectangle
[tex] \sf{length \: of \: a \: rectangle = 4w - 5}[/tex]
[tex] \dashrightarrow{ \sf{4 \times 8.5 - 5}}[/tex]
[tex] \dashrightarrow{ \sf{34 - 5}}[/tex]
[tex] \dashrightarrow{ \sf{29 \: mm}}[/tex]
Length of a rectangle = 29 mm
Hope I helped!
Best regards! :D
Solve this equation: Y/9 + 5 = 0.
Answer:
y = -45
Step-by-step explanation:
Y/9 + 5 = 0
y/9 = -5
y = -45
Write this in a Algebraic expression. (Use x as your variable) The sum of x squared and y
Answer:
x^2+y
Step-by-step explanation:
simply because you have x squared and a variable y that needs to be added.