Answer:
The 99% confidence interval is [tex]97.94 < \mu < 98.26[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 110
The sample mean is [tex]\= x = 98.1 \ F[/tex]
The standard deviation is [tex]\sigma = 0.64 \ F[/tex]
Given that the confidence level is 99% the level of significance i mathematically evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution, the values is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]
[tex]E = 0.1574[/tex]
Generally the 99% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]
[tex]97.94 < \mu < 98.26[/tex]
Answer:
Step-by-step explanation:
g If A and B are disjoint events, with P( A) = 0.20 and P( B) = 0.30. Then P( A and B) is: a. .00 b. .10 c. .50 d. 0.06
Answer: A) 0
P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.
We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.
A ladder 10 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 6 ft/sec, how fast is the height of the top changing (this will be a negative rate) when the lower end is 6 feet from the wall?
Answer:
-4.5ft per sec
Step-by-step explanation:
Assume that vertical wall has a distance of y and the horizontal floor is x (6 ft).
This forms a triangle with the ladder as the hypothenus of length 10ft
We have dy/dt = 6ft per sec
According to Pythagoras law the relationship between x and y is
(x^2) + (y^2) = (hypothenus ^2) = 10^2
When we differentiate both sides of the equation
2x(dx/dt) + 2y(dy/dt) = 0
dy/dt = (x/y) * (dx/dt)
y= √(10^2) - (6^2) = 8ft
So dy/dt = (6/8)* (6/1)= -4.5 ft per sec
It is a negative rate
Which of the following statements is TRUE about the stepwise selection procedure?
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
B. Backward stepwise procedure and forward stepwise procedure would end up with the same "best" model.
C. The "best" model determined by the stepwise selection method is the same model as what would be selected by complete search but stepwise method is usually faster.
D. Different choices of alpha limits for variable selection may end up with different final models.
Answer:
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
Step-by-step explanation:
Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.
A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and the string vibrates forming 8 loops. When the stone is immersed in water 10 loops are formed. The specific gravity of the stone is close to
A) 1.8
B) 4.2
C) 2.8
D) 3.2
Answer:
correct option is C) 2.8
Step-by-step explanation:
given data
string vibrates form = 8 loops
in water loop formed = 10 loops
solution
we consider mass of stone = m
string length = l
frequency of tuning = f
volume = v
density of stone = [tex]\rho[/tex]
case (1)
when 8 loop form with 2 adjacent node is [tex]\frac{\lambda }{2}[/tex]
so here
[tex]l = \frac{8 \lambda _1}{2}[/tex] ..............1
[tex]l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}[/tex]
and we know velocity is express as
velocity = frequency × wavelength .....................2
[tex]\sqrt{\frac{Tension}{mass\ per\ unit \length }}[/tex] = f × [tex]\lambda_1[/tex]
here tension = mg
so
[tex]\sqrt{\frac{mg}{\mu}}[/tex] = f × [tex]\lambda_1[/tex] ..........................3
and
case (2)
when 8 loop form with 2 adjacent node is [tex]\frac{\lambda }{2}[/tex]
[tex]l = \frac{10 \lambda _1}{2}[/tex] ..............4
[tex]l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}[/tex]
when block is immersed
equilibrium eq will be
Tenion + force of buoyancy = mg
T + v × [tex]\rho[/tex] × g = mg
and
T = v × [tex]\rho[/tex] - v × [tex]\rho[/tex] × g
from equation 2
f × [tex]\lambda_2[/tex] = f × [tex]\frac{1}{5}[/tex]
[tex]\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}[/tex] .......................5
now we divide eq 5 by the eq 3
[tex]\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}[/tex]
solve irt we get
[tex]1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}[/tex]
so
relative density [tex]\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}[/tex]
relative density = 2.78 ≈ 2.8
so correct option is C) 2.8
A plane is flying at the height of 5000 meter above the sea level. at a particular point, it is excatly above a submarine floating 1200 meter below the sea level. what is the vertical distance between them ?
Answer:
3800 meters
Step-by-step explanation:
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 72 58 62 38 44 66 42 49 76 52 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
72 58 62 38 44 66 42 49 76 52 ( arrange it!)
38 42 44 49 52 58 62 66 72 76 (done!)
Median: Find the number in the middle after we arranged, so the answer is (52+58)/2= 110/2 = 55
Mode : None (there is no number appear more than other number)
Mean = (38+42+44+49+52+58+62+66+72+76)/10
=559/100
=5,5
Hope it helps ^°^
Find the distance between (8,4) and (8,8).
Answer:
From the given points above, the distance between them is 4 units.
Step-by-step explanation:
In order to find the distance between the two points, we must know the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now, we plug in our numbers from the coordinate points that we are given to their respectful places.
[tex]d=\sqrt{(8-8)^2+(8-4)^2}[/tex]
Now, we solve. First, simplify the terms in parentheses. So, subtract 8 from 8 and subtract 4 from 8.
[tex]d=\sqrt{(0)^2+(4)^2}[/tex]
Next, solve for the exponents.
[tex]d=\sqrt{0+16}[/tex]
Add the numbers in the radical.
[tex]d=\sqrt{16}[/tex]
Solve the radical.
[tex]d=4[/tex]
So, the distance between the two given points is 4 units.
please help me guys please find the value of 3x°
Answer:
finding the value of x first
2x + 3x + 10 = 180 (linear pair)
5x = 180 - 10
x = 170 / 5
x = 34
3x = 102
An animal population is increasing at a rate of 13 51t13 51t per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years.
Answer:
ΔP = 567
Step-by-step explanation:
The increasing rate of the population is 13,51*t.
That rate by definition is:
dP/dt where P is the population therefore
dP/dt = 13,51*t
dt = 13,51*t*dt
Integrating on both sides of the equation we get:
∫dp = ∫ 13,51*t*dt
P = 13,51*t²/2 + K ( K is population for t = 0 )
Now the population in 10 years P(₁₀)
P(₁₀) = 13,51* (10)² /2 + K
P(₁₀) = 675,5 + K (1)
And P(₄) is
P(₄) = 13,51*(4)²/2 * K
P(₄) = 108,08 + K (2)
Then substracting
P(₁₀) - P(₄) = ( 675,5 + K ) - ( 108,08 + K )
ΔP = 567,42
But we don´t have fraction of animal, then
ΔP = 567
Which is one of the transformations applied to the graph of f(x) = X^2 to change it into the graph of g(x) = -x^2 +16x - 44
Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
Step-by-step explanation:
Let's construct g(x) in baby steps.
Ok, we start with f(x) = x^2
The first thing we have is a horizontal translation of A units (where A is not known)
A vertical translation of N units to the right, is written as:
g(x) = f(x - N)
Then we have:
g(x) = (x - A)^2 = x^2 - 2*A*x + A^2
Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.
Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)
Then if we apply also a reflection over the x-axis, we have:
g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44
Then:
2*A = 16
A*A = 44.
The first equation says that A = 16/2 = 8
But 8^2 is not equal to 44.
Then we need another constant coefficient, which is related to a vertical translation.
If we have a relation y = f(x), a vertical translation of N units up, will be
y = f(x) + N.
Then:
g(x) = -f(x - A) + B
-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44
Now we have:
2*A = 16
-A^2 + B = - 44
From the first equation we have A = 8, now we replace it in the second equation and get:
-8^2 + B = -44
B = -44 + 64 = 20
Then we have:
The transformation is:
First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
Find the function h(x) = f(x) - g(x) if f(x) = 3^x and g(x) = 3^2x - 3^x. A.h( x) = 0 B.h( x)=-3^2x C.h( x) = 3^x (2 - 3^x) D.h( x) = 2(3^2x)
Answer:
3^x( 2-3^x)
Step-by-step explanation:
f(x) = 3^x and g(x) = 3^2x - 3^x
h(x) = f(x) - g(x)
3^x - ( 3^2x - 3^x)
Distribute the minus sign
3^x - 3^2x + 3^x
2 * 3^x - 3 ^ 2x
Rewriting
We know that 3^2x = 3^x * 3^x
2 * 3^x - 3^x* 3^x
Factoring out 3^x
3^x( 2-3^x)
Reduce 18/24 to its lowest terms
Answer:
3/4
Step-by-step explanation:
find a common number that 18 and 24 are both divisible by. I chose 6. So when i divide 6 by 18, I got 3. Which I put on my numerator, when I divided 24 by 6 I got 4 which I put on my denominator. My end result was 3/4
Answer:
3/4
Step-by-step explanation:
18/24
=2*9=18
=2*12=24
=9/12
=3/4
illustrate the distributive property to solve 144/8
Answer:
8 (19) or 8 (18 +1)
Step-by-step explanation:
Distributive property means to distribute.
HCF of 144 and 8.
=> 8 is the HCF of 144 and 8
8 (18 + 1)
=> 8 (19)
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 80 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 20°. How far away from the building is the sculpture? Round your answer to the nearest hundredth.
Answer:
219.80 feet
Step-by-step explanation:
Tan 20= 80/b
Tan 20= 0.363970234266
(0.363970234266)b=80
b= 219.80 feet
The distance between the sculpture and the bottom of the building is required.
The distance between the building and sculpture is 219.80 feet.
Trigonometry[tex]\theta[/tex] = Angle of depression = Angle of elevation = [tex]20^{\circ}[/tex]
p = Height of building = 80 feet
b = Required length
From the trigonometric ratios we have
[tex]\tan\theta=\dfrac{p}{b}\\\Rightarrow b=\dfrac{p}{\tan\theta}\\\Rightarrow b=\dfrac{80}{\tan 20}\\\Rightarrow b=219.80\ \text{feet}[/tex]
Learn more about trigonometry:
https://brainly.com/question/23899312
From her purchased bags, Rory counted 110 red candies out of 550 total candies. Using a 90% confidence interval for the population proportion, what are the lower and upper limit of the interval? Answer choices are rounded to the thousandths place.
Answer:
The Confidence Interval = (0.172, 0.228)
Where:
The lower limit = 0.172
The upper limit = 0.228
Step-by-step explanation:
The formula to be applied or used to solve this question is :
Confidence Interval formula for proportion.
The formula is given as :
p ± z × √[p(1 - p)/n]
n = Total number of red candies = 550 red candles
p = proportion = Number of red candies counted/ Total number of red candies
= 110/550 = 1/5 = 0.2
z = z score for the given confidence interval.
We are given a confidence interval of 90%. Therefore, the z score = 1.6449
Confidence Interval = p ± z × √[p(1 - p)/n]
Confidence Interval = 0.2 ± 1.6449 × √[0.2(1 - 0.2)/550]
= 0.2 ± 1.6449 √0.2 × 0.8/550
= 0.2 ± 1.6449 × 0.0170560573
= 0.2 ± 0.0280555087
Hence, the Confidence Interval = 0.2 ± 0.0280555087
0.2 - 0.0280555087 = 0.1719444913
Approximately = 0.172
0.2 + 0.0280555087 = 0.2280555087
Approximately = 0.228
Therefore, the Confidence Interval = (0.172, 0.228)
Where:
The lower limit = 0.172
The upper limit = 0.228
Answer:
Lower Limit: 0.172
Upper Limit: 0.228
Step-by-step explanation:
A leaf blower was marked up 100% from an original cost of $152. If Eva bought the leaf blower and paid 7% sales tax, how much in total did she pay?
Answer:
$325.28
Step-by-step explanation:
152+152=304
304x1.07=325.28
Answer:
325.28
Step-by-step explanation:
increase the price by 100 %
152* 100%
152
Add this to the original price
152+152 = 304
Now find the sales tax
304 * 7%
304 * .07
21.28
Add this to the amount of the purchase price
304+21.28
325.28
Johnny and a robot standing 5 melo (units of length) apart (in a flat area) on the
planet Rote. They spot a flying object hovering in the sky at the same time. If the
angle of elevation from Johnny to the flying object is 29°, and the angle of elevation
from the robot to the flying object is 42°, find the distance from the flying object to
the ground. For this problem, assume that the heights of Johnny and the robot are
neligible. [8 marks]
Answer:
distance from the flying object to
the ground
= 7.2 melo(unit of measurement)
Step-by-step explanation:
The distance between the robot and Jo is 5 melo( unit Of measurement)
Let the distance between the flying object and the ground= y
Let's the remaining length of the closest between robot and Jonny and the ground be x.
Y/(x+5)= tan 29.... equation 1
Y/x= tan 42.... equation 2
Equating the value of y
Tan 29(x+5) = tan42(x)
Tan29/tan 42 = x/(x+5)
0.61562(x+5)= x
3.0781= x- 0.61562x
3.0781= 0.38438x
3.0781/0.38438= x
8.008= x
8= x
Y/x= tan 42
Y/8= 0.9004
Y= 7.203
Y= 7.2 melo (unit of measurement )
_______% of 44 = 22
Answer:
50%
Step-by-step explanation:
22 is half of 44.
So, this means 50% of 44 is 22.
What is 28% of 58?
Hhhhhhh
Answer:
16.24
Step-by-step explanation:
of means multiply
28% * 58
Change to decimal form
.28 * 58
16.24
Answer:
[tex]\Large \boxed{\mathrm{16.24}}[/tex]
Step-by-step explanation:
[tex]28\% \times 58[/tex]
[tex]\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}[/tex]
[tex]\displaystyle \frac{28}{100} \times 58[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{1624}{100} =16.24[/tex]
A European study of thousands of men found that the PSA screening for prostate cancer reduced the risk of a man’s dying from prostate cancer from 3.0 percent to 2.4 percent. "But it’s already a small risk. I don’t think a difference of less than 1 percent would be of practical importance," said Ed. Do you agree with Ed’s conclusion?
Answer:
Following are the answer to this question:
Step-by-step explanation:
In the given statement, we don't agree with Ed’s conclusion, because it is not relevant simply since it is not statistically significant. The reduction of prostate cancer is the death risk, which is highly significant even if it decreases significantly. It can also be something statistically important without becoming important.
Vhat is the volume of the right rectangular prism?
Will mark brainliest
Answer:
432 mm³
Step-by-step explanation:
Volume of a Rectangular Prism: V = lwh
Step 1: Define variables
l = 8
w = 6
h = 9
Step 2: Plug into formula
V = 8(6)(9)
Step 3: Evaluate
V = 48(9)
V = 432
And we have our answer!
Of 900 people surveyed, 480 were male and 410 had cell phones. Of those with cell phones, 290 were female. What is the probability that a person surveyed was either male or had a cell phone? A. 600/900 = 0.6667 B. 770/900 = 0.8556 C. 360/900 = 0.40 D. 820/900 = 0.9111
Answer:
C. 360/900 = 0.40
Step-by-step explanation:
The number of the males that are using cellphone and the females who are using cell phones are in total 410. The total people surveyed are 900 people. There are total 480 males and rest 420 are females. Among the 420 females there are 290 females who use cellphones. The probability for males can be given by 360/900.
(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) (a) σ = 18, n = 9 (b) σ = 18, n = 36 (c) σ = 18, n = 144
Answer:
a) 6.00
b) 3.00
c) 1.50
Step-by-step explanation:
Sample error of the mean is expressed mathematically using the formula;
SE = σ /√n where;
σ is the standard deviation and n is the sample size.
a) Given σ = 18, n = 9
Standard error of the mean = σ /√n
Standard error of the mean = 18/√9
Standard error of the mean = 18/3
Standard error of the mean = 6.00
b) Given σ = 18, n = 36
Standard error of the mean = σ /√n
Standard error of the mean = 18/√36
Standard error of the mean = 18/6
Standard error of the mean = 3.00
c) Given σ = 18, n = 144
Standard error of the mean = σ /√n
Standard error of the mean = 18/√144
Standard error of the mean = 18/12
Standard error of the mean = 3/2
Standard error of the mean = 1.50
A movie theater is having a special. If a group of four pays $7.25 each for tickets, each person can get popcorn and a drink for $5.75. Use the expression 4(5.75 + 7.25) to find the total cost for 4 friends.
Answer:
The price for 4 people is 52 dollars.
4 × (5.75 + 7.25) = 52
The total cost including drink and popcorn is $52 according to a given condition.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Cost of movie ticket = $7.25/person
Cost of popcorn and drink = $5.75/person
Total cost per person = 5.75 + 7.25 = $13
Now,
Number of people = 4
So,
4(5.75 + 7.25) = 4(13) = $52
Hence "The total cost including drink and popcorn is $52 according to a given condition".
For more about the equation,
https://brainly.com/question/10413253
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what is the value of x?
Answer:
[tex]\boxed{\sf x = 80}[/tex]
Step-by-step explanation:
A quadrilateral inscribed in a circle has opposite sides equal to 180.
So,
x + x + 20 = 180
2x + 20 = 180
Subtracting 20 from both sides
2x = 180 - 20
2x = 160
Dividing both sides by 2
x = 80
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 80
▹ Step-by-Step Explanation
x + x + 20 = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 80
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
If 2 x 2 + 13 x − 7 = 0 , then x could equal which of the following?
Hi there! :)
Answer:
x = 1/2 or -7.
Step-by-step explanation:
(I'm assuming the expression is 2x² + 13x - 7 = 0)
Factor the equation to solve for the possible values of "x":
2x² + 13x - 7 = 0
When factored, we get:
(2x - 1) ( x + 7) = 0
Use the Zero-Product property to solve for the roots:
2x - 1 = 0
2x = 1
x = 1/2.
-----------
x + 7 = 0
x = -7.
Therefore, possible values of x are x = -1/2, 7.
Answer:
x = 1/2 x=-7
Step-by-step explanation:
2 x^2 + 13 x − 7 = 0
Factor
(2x-1)(x+7)=0
Using the zero product property
2x-1 =0 x+7=0
2x=1 x =-7
x = 1/2 x=-7
find the value of X from the given picture
Answer:
x = 108
Step-by-step explanation:
The sum of a circle is 360
90 + x/2 + x+x = 360
Combine like terms
90 + 2x+x/2 = 360
90 + 5/2 x = 360
Subtract 90 from each side
5/2x = 270
Multiply each side by 2/5
5/2x * 2/5 = 270*2/5
x =108
What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level
Answer:
their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster
∠ACB is a circumscribed angle. Solve for x. 1) 46 2) 42 3) 48 4) 44
Answer:
[tex]\Huge \boxed{x=44}[/tex]
Step-by-step explanation:
The circumscribed angle and the central angle are supplementary.
∠ACB and ∠AOB add up to 180 degrees.
Create an equation to solve for x.
[tex]3x+10+38=180[/tex]
Add the numbers on the left side of the equation.
[tex]3x+48=180[/tex]
Subtract 48 from both sides of the equation.
[tex]3x=132[/tex]
Divide both sides of the equation by 3.
[tex]x=44[/tex]
Answer:
4)44
Step-by-step explanation:
Please help!! find the value of the expression
Answer:
7
Step-by-step explanation:
First plug in the variable amounts so the expression now looks like this:
(3 × 4 - 12) + 1/2(4 × 6 - 10)
Now, start by solving the multiplication parts first, so it now looks like this:
(12 - 12) + 1/2(24 - 10)
Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)
Next, solve the multiplication part, so it now looks like this: 0 + 7
Solve that and the answer is 7.
