Answer:
When the sample size is [tex]n_1 = 5[/tex] ,
[tex]P( X < 11) = 0.9875[/tex]
When the sample size is [tex]n_2 = 6[/tex] ,
[tex]P( X < 11) = 0.993[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 9 \ min[/tex]
The standard deviation is [tex]\sigma = 2 \ min[/tex]
The first sample size is [tex]n_1 = 5[/tex]
The second sample size is [tex]n_2 = 6[/tex]
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{x} = \frac{\sigma}{ \sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{2}{ \sqrt{5} }[/tex]
When the sample size is [tex]n_1 = 5[/tex] ,
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{x} = \frac{\sigma}{ \sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{2}{ \sqrt{5} }[/tex]
=> [tex]\sigma_{x} = 0.894[/tex]
Generally the probability that the sample average amount of time taken on each day is at most 11 min is mathematically represented as
[tex]P( X < 11) = P( \frac{X - \mu }{\sigma } < \frac{11 - 9 }{0.8944 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P( X < 11) = P( Z < 2.24 )[/tex]
From the z table the area under the normal curve to the left corresponding to 2.24 is
[tex]P( Z < 2.24 ) = 0.9875[/tex]
=> [tex]P( X < 11) = 0.9875[/tex]
When the sample size is [tex]n_2 = 6[/tex] ,
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{x} = \frac{\sigma}{ \sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{2}{ \sqrt{6} }[/tex]
=> [tex]\sigma_{x} = 0.816[/tex]
Generally the probability that the sample average amount of time taken on each day is at most 11 min is mathematically represented as
[tex]P( X < 11) = P( \frac{X - \mu }{\sigma } < \frac{11 - 9 }{0.816 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P( X < 11) = P( Z < 2.45 )[/tex]
From the z table the area under the normal curve to the left corresponding to 2.24 is
[tex]P( Z < 2.45 ) = 0.993[/tex]
=> [tex]P( X < 11) = 0.993[/tex]
Question in the picture
I will find x, so 4x-4=180, so 4x=184, so x=46
Sorry if i answered wrong I don't understand what it is asking for.
-46 − 8x > 22.
A. x -8.5 D. x > 8.5
Answer:
x < -8.5
Step-by-step explanation:
-46 - 8x > 22
-8x > 68 -- when you divide by a negative number in an inequality, you flip the inequality sign
Therefore, x < -8.5
7=6-4, +4r
Please help
Answer:
R=5/4
Or
R=1.25
Step-by-step explanation:
Water runs into a conical tank at the rate of [tex]9ft^{3}/min.[/tex] The tank stands point down and has a height of 10 ft and a base of 5 ft. How fast is the water level rising when the water is 6 ft deep?
Answer:
[tex]\frac{1}{\pi} \frac{\text{ft}}{\text{min}}[/tex] is the rate at which the water is rising when the water is 6 ft deep.
Step-by-step explanation:
See the attached diagram that I drew to represent this problem.
To solve related rates problems, let's use the recommended steps:
Draw a diagram.Label all quantities and their rates of change.Relate all quantities in the same equation.Differentiate (implicitly) with respect to time.Use the resulting equation to answer the question in context.Step 1:I already drew the diagram; see attached image.
Step 2:I labeled the quantities we are given in the problem. h = 10 ft, and r = 5 ft. We are also told that the change in volume is 9 ft³/min; dV/dt = 9 ft³/min.
We want to find dh/dt when h = 6.
[tex]\frac{dh}{dt}\ \vert \ _h_=_6 =\ ?[/tex] Step 3:We know that we are dealing with a cone in this problem, and we are given the volume of the cone. Therefore, we can use the formula for the volume of a cone in order to relate all of the quantities in the same equation.
[tex]V=\frac{1}{3} \pi r^2 h[/tex]Since we only want the two variables, V and h, we can solve for r in terms of h and substitute this value for r in the formula.
This is because when we perform implicit differentiation, we do not have the change in r (dr/dt) but we do have dh/dt, which is what we are trying to solve for.
We know that r = 5 ft, and h = 10 ft. Therefore, we can say that [tex]\frac{r}{h}=\frac{5}{10} \rightarrow \frac{r}{h} = \frac{1}{2}[/tex]. Multiply h to both sides to solve for the variable r: [tex]r=\frac{h}{2}[/tex].
Substitute this into the volume of a cone equation:
[tex]V=\frac{1}{3} \pi(\frac{h}{2})^2 h[/tex]Simplify this equation.
[tex]V=\frac{\pi}{3}\cdot \frac{h^2}{4} \cdot h[/tex] [tex]V=\frac{\pi}{12}h^3[/tex] Step 4:Perform implicit differentiation on the volume equation.
[tex]\frac{dV}{dt} =\frac{\pi}{12}3h^2 \cdot \frac{dh}{dt}[/tex] Step 5:Substitute known values and solve for dh/dt to find the change in height, or the rise in water level, when the water is 6 ft deep (h = 6).
We know that:
[tex]\frac{dV}{dt} =9[/tex] [tex]h=6[/tex]Plug these values into the implicitly differentiated volume equation.
[tex]9=\frac{\pi}{12}3(6)^2\cdot \frac{dh}{dt}[/tex] [tex]9=\frac{3\pi}{12}\cdot 36 \cdot \frac{dh}{dt}[/tex] [tex]9=9\pi\frac{dh}{dt}[/tex] [tex]\frac{dh}{dt} =\frac{9}{9\pi}= \frac{1}{\pi}[/tex]Answering the question in context:
Since dh/dt = 1/π when h = 6 ft, we can say that the water is rising at a rate of [tex]\frac{1}{\pi} \frac{\text{ft}}{\text{min}}[/tex] when the water is 6 ft high.
Hey there!
We can create some variables to denote some of the things we are working with.
v = volume
h = height
r = radius
We know that [ dv/dt = (π/3)r²h ]. We also know that [ r/h = 5/10 = 1/2 ] which resembles the parts of a triangle.
Solution:
v = π/3*h/2²
h = πh³/(4)(3)
~Differentiate both sides
dv/dt = (3πh³/4*3)(dh/dt)
~Simplify
dh/dt = (4dv/dt)/πh²
~Use chain rule
(4)(9)/π6²
1/π
Thus, the speed of the water level rising is [ 1/π ft/min ] when the water is 6ft deep.
Best of Luck!
Vector Calculus
A particle of mass m move along the path σ(t)={t^2,sin t, cos t} Calculate the force acting on the particle t=0.
It seems like σ(t) is the positive function of the particle. Compute its acceleration by differentiating this function twice.
σ(t) = {t ², sin(t ), cos(t )}
σ'(t) = {2t, cos(t ), -sin(t )}
σ''(t) = {2, -sin(t ), -cos(t )}
When t = 0, the acceleration on the particle is
σ'' (0) = {2, -sin(0), -cos(0)} = {2, 0, -1}
Then the force acting on the particle at time t = 0 is
F = {2m, 0, -m}
by Newton's second law.
which of the following would be neither perpendicular nor parallel to the following equation. y=3x-7. equations: y=-1/3x-7, y=-1/3x+5, y=1/3x+6, y=3x+1
Answer:
y=1/3x+6
Step-by-step explanation:
Equations parallel to each other have the same slope so that rules out the fourth answer. Perpendicular equations have opposite and reciprocal slopes, which in this case would be [tex]\frac{-1}{3}[/tex], which rules out all of the others except for the third option.
An apartment of the same square footage today is $716 unfurnished making a cost of living increase of 44.69%. If Della and Jim's apartment was $32 per month with furnishings included and they signed a lease for 13 months, what is the total weekly cost in 1905?
An apartment of the same square footage today is $716 unfurnished making a cost of living increase of 44.69%. If Della and Jim's apartment was $32 per month with furnishings included and they signed a lease for 13 months, what is the total weekly cost in 1905? Answer: $1340.80
Find the 11th term of the geometric sequence 7,35, 175, ...
Answer:
68,359,375. Using a calculator, you can multiply each new number by 5.
11th term of the given geometric sequence is [tex]a_{n}= 7(5^{n-1})[/tex]
What is Geometric sequence?In a Geometric Sequence each term is found by multiplying the previous term by a constant.
Given geometric sequence = 7,35,175,..
Nth term of the geometric sequence [tex]a_{n}=a_{1}.r^{n-1}[/tex]
[tex]a_{1}=7[/tex]
[tex]r=\frac{35}{7}=5[/tex]
Nth term of the geometric sequence
[tex]a_{n}= 7(5^{n-1})[/tex]
Hence, the Nth term of the given geometric sequence is [tex]a_{n}= 7(5^{n-1})[/tex]
Learn more about Geometric sequence here
https://brainly.com/question/13008517
#SPJ2
How do I get numbers 1-20 with only using four 2's
Answer: 1-20 can be made with four 2's when you use a power on the 2's like this 2 to the power of 4 + (2 to the power of 2+2 to the power of 2)= 20
Step-by-step explanation:
A selective university advertises that 96% of its bachelor’s degree graduates have, on graduation day, a professional job offer or acceptance in a graduate degree program in their major area of study. In a sample of 227 recent graduates this was true of 209 of them. The probability of obtaining a sample proportion as low as or lower than this, if the university’s claim is true, is about:________
a. 0.015
b. 0.001
c. 0.131
d, 0.084
Answer:
The probability is [tex]P( p < 0.9207) = 0.0012556[/tex]
Step-by-step explanation:
From the question we are told
The population proportion is [tex]p = 0.96[/tex]
The sample size is [tex]n = 227[/tex]
The number of graduate who had job is k = 209
Generally given that the sample size is large enough (i.e n > 30) then the mean of this sampling distribution is
[tex]\mu_x = p = 0.96[/tex]
Generally the standard deviation of this sampling distribution is
[tex]\sigma = \sqrt{\frac{p (1 - p )}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{0.96 (1 - 0.96 )}{227} }[/tex]
=> [tex]\sigma = 0.0130[/tex]
Generally the sample proportion is mathematically represented as
[tex]\^ p = \frac{k}{n}[/tex]
=> [tex]\^ p = \frac{209}{227}[/tex]
=> [tex]\^ p = 0.9207[/tex]
Generally probability of obtaining a sample proportion as low as or lower than this, if the university’s claim is true, is mathematically represented as
[tex]P( p < 0.9207) = P( \frac{\^ p - p }{\sigma } < \frac{0.9207 - 0.96}{0.0130 } )[/tex]
[tex]\frac{\^ p - p}{\sigma } = Z (The \ standardized \ value\ of \ \^ p )[/tex]
[tex]P( p < 0.9207) = P(Z< -3.022 )[/tex]
From the z table the area under the normal curve to the left corresponding to -3.022 is
[tex]P(Z< -3.022 ) = 0.0012556[/tex]
=> [tex]P( p < 0.9207) = 0.0012556[/tex]
which strategy demonstrates the correct use of properties of operations to evaluate 5×( -7÷ 1/8)
the answer to the equation is -280
√50, √8, whats the area of the triangle no picture
Answer:
Area = 10
Step-by-step explanation:
([tex]\sqrt{50}[/tex]×[tex]\sqrt{8}[/tex]) ÷ 2 = 10
which polynomial function has a leading coefficient of 1, roots -2 and 7 with miltiplicity
1, and root 5 with multiplicity 2?
Answer:
f(x)=(x+2)(x-7)(x-5)(x-5)
Step-by-step explanation:
With the use of the roots and leading coefficient, you can easily write out the polynomial as I have above.
Answer:
f(x)= (x-7)(x-5)(x-5)((x+2)
Step-by-step explanation:
Edge answer D
katie is planting a garden for her science fair project. she needs 2/3 of a cup of soil to go in 8 different pots.how many cups of total does she need in total
Answer:
5 and 1/3 cups of soil
Step-by-step explanation:
Hello there, in this problem we can solve for the amount of soil that Katie will need by multiplying the factor for one of them by the number of pots we have, 8. We get 16/3 cups of soil, or 5 and 1/3 cups of soil.
Hope this helps!
-HM
Answer:
Katie need 5.6 cups of soil.
Step-by-step explanation:
To solve this equation, we just need to multiply 8 by 2/3. Though to make this equation easier, I will turn 2/3 into a decimal by dividing the numerator (2) by the denominator (3.)
2 ÷ 3 = 0.7 when rounded to the nearest tenth.
Now, let's multiply 0.7 by 8.
8 x 0.8 = 5.6
Therefore, Katie need 5.6 cups of soil.
Hope this helps! :)
does kageyama get an award? for like best setter?
Answer:
of course.
he's the king of the court
Answer:
He's a great setter but he never gets an award like Oikawa does...
Step-by-step explanation:
*spoiler*
-
-
-
-
buuut he does get accepted to the Japan Youth Training camp where only elites go (Ushijima when there) ;)
Find the value of X.
Answer:
x = 9
Step-By-Step Explanation:
1. 3x + 5 + 6x + 4 = 90
2. 9x + 9 = 90
3. 9 + -9
4. 90 + -9
5. 9x = 81
6. x= 9 Substituting X:
3 X 9 + 5 = 27 + 5 = 32
6 X 9 + 4 = 54 + 4 = 58 58 + 32 = 90, so X = 9
Answer:
Step-by-step explanation:
The reason I say the answer above is wrong is because their answer equals up to a angle of 100 degrees however your angle is equaling up to 90 degrees. First off we know this angle is going to be 90 degrees right so we put it into the eqution:
=90
but we don't know what x is in order to solve the degrees that add up to 90, so since these equations add up to 90 we put them into the equation:
(3x + 5)+ (6x + 4) = 90
we then add all the numbers that have the same variables or are simply numbers in the equation
3x + 6x and 5 + 4 to get 9x + 9 = 90
we then subtract 9 from both sides (because what you do to one side you do to the other) to get 81
the equation now looks like this: 9x = 81 so now we divide 9 from both sides to get x = 9
Now how do we know if x is really 9 well we plug it into the equations (3x + 5) and (6x + 4) making them look like this (3(9) + 5) and (6(9) + 4)
and you get (3(9) + 5)= 32
(6(9) + 4)= 58
and when you add them together you get 90
32 + 58 = 90
Sorry it took so long to answer back. I hope this helps you
Let's say you are in the market to buy a car that will cost you $20,000. Shopping around for financing, you manage to get $20,000 loan at 4% interest for 60 months. Which of the following will be the closest final cost of your car including the interest/finance charges?
Answer:
oof
Step-by-step explanation:
A customer/member owes $11.02 and pays $100.00 in cash. Change due is $88.98.
Answer:
Correct
Step-by-step explanation:
Use the distributive property to rewrite the expression: 1.5(2x-20) WILL MAKE BRAINLISTT
Answer:
-60...make me brainlistt
Step-by-step explanation:
Is it a nonliner or a linear function
Answer:
linear, it can be solved for y
Answer:
A. Linear
Step-by-step explanation:
It's a straight line when you graph it etc. etc.
Larry fills his bathtub at a constant rate. The amount of water in his tub is proportional to the amount of time he spends filling it. This relationship is described in the following graph:
Answer:
7 but im not sure
Step-by-step explanation:
Answer:
its A and B
Step-by-step explanation:
Do NOT hit none of the above, that's wrong
Find the value of x and y.
Answer:
Triangle= 180 degrees
180 degrees-20 degrees=140
140/2=70
Step-by-step explanation:
Hope this helps! Consider Brainiest!
solve for h: -2/3h-4=4/3
Isolate the variable by dividing each side by factors that don't contain the variable.
h = −8
The sides of the square shown below have a length of
2v3
. What would be the length of a diagonal across the square?
Answer:2[tex]\sqrt{6}[/tex]because it is a 45 45 90
Step-by-step explanation:
Type your number answer in decimal form. Do not round.
3,000 millimeters = meters.
Answer: 3.0 meters
Step-by-step explanation:
3000 millimetres is the same as 3 meters.
3 as a decimal is the same as 3.0
What is the DOMAIN of this graph? Need help!!
I'm using system of equations and I have to use either substitution or elimination. My two equations are
2x - 6y = 13
8x - 24y = 8
A real estate sales agent receives a salary of $250 per week plus a commission of 2% of sales.
a. Identify the Slope m _________
b. Identify the initial value b ________________
c. Write an equation that gives the weekly income y in terms of sales x ______________.
d. What is his weekly income if the sales were $600.00?
Answer:
a. The slope m is 0.02
b. The initial value b is 250
c. y = 0.02x + 250
d. His weekly income is $262 if the sales were $600.00
Step-by-step explanation:
the form of the linear equation is y = m x + b, where
m is the slope (rate of change)b is the y-intercept (constant amount)∵ A real estate sales agent receives a salary of $250 per week
→ This is a fixed amount every week
∴ b = 250
∵ They give a commission of 2% of sales
→ This value depends on the sales (rate of change)
∵ 2% = 2 ÷ 100 = 0.02
∴ m = 0.02
a. The slope m is 0.02
b. The initial value b is 250
∵ y represents the weekly income
∵ x represents the sales
∵ m = 0.02 and b = 250
∴ The equation is y = 0.02x + 250
c. y = 0.02x + 250
∵ The sales were $600.00
∴ x = 600
→ Substitute it in the equation to find y
∵ y = 0.02(600) + 250
∴ y = 12 + 250
∴ y = 262
d. His weekly income is $262 if the sales were $600.00
You paint of a wall in hour. At that rate, how long will it take you to paint one wall? pls help now
Answer:
3/4 hour
Step-by-step explanation:
What is an equivalent to -16m^2n-(-25m^2n)+(-7m^2n)
Answer:
The equivalent expression is:
[tex]-16m^2n-\left(-25m^2n\right)+\left(-7m^2n\right)=2m^2n[/tex]
Step-by-step explanation:
Given the expression
[tex]-16m^2n-\left(-25m^2n\right)+\left(-7m^2n\right)[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a,\:-\left(-a\right)=a[/tex]
[tex]=-16m^2n+25m^2n-7m^2n[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:-16m^2n+25m^2n-7m^2n=2m^2n[/tex]
[tex]=2m^2n[/tex]
Therefore, the equivalent expression is:
[tex]-16m^2n-\left(-25m^2n\right)+\left(-7m^2n\right)=2m^2n[/tex]