The amount of grain can the container hold is 953.78 inch³ as it in the form of cylinder
Diameter of cylinder = 9 in
Radius of cylinder = 9 / 2 in
Radius of cylinder = 4.5 in
Height of cylinder = 15 inch
Volume of cylinder = Amount of grain can this container hold
Volume = πr²h
Substitute the values of radius and height
Volume = (3.14)(4.5)²(15)
Amount of grain can this container hold = 953.78 inch³
Hence, the amount of grain can the container hold is 953.78 inch³
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ1
Dilate quadrilateral abcd using center b and scale factor 1/2
The dilated quadrilateral, using center B and a scale factor of 1/2, is A'B'C'D'.
To dilate a quadrilateral ABCD using center B and a scale factor of 1/2, we can follow these steps:
Draw line segments from the center of dilation (B) to each vertex of the quadrilateral (A, C, and D).
Measure the distance from B to each vertex (AB, BC, BD) and multiply each distance by the scale factor (1/2).
From the endpoints of the original line segments, construct new line segments with the scaled distances obtained in the previous step.
Connect the endpoints of the newly constructed line segments to form the dilated quadrilateral A'B'C'D'.
The resulting quadrilateral A'B'C'D' will be a scaled-down version of the original quadrilateral ABCD, with center B as the center of dilation and a scale factor of 1/2.
Note: Since I am a text-based AI and cannot provide visual illustrations, it would be helpful to refer to a geometric software or draw the quadrilateral on paper to visualize the steps described above.
For similar question on dilated quadrilateral.
https://brainly.com/question/20084003
#SPJ11
if cos a=0.845 and cos b=0.789 with both angles terminal rays in quadrant 1, find the values of sin(a b) cos (a-b)
Using the given values, we can evaluate sin(a+b) to be approximately 0.656 and cos(a-b) to be approximately 0.308.
First, we can use the identity sin^2θ + cos^2θ = 1 to find sin a and sin b:
sin a = √(1 - cos^2a) ≈ 0.534
sin b = √(1 - cos^2b) ≈ 0.615
Next, we can use the sum and difference identities to find sin(a+b) and cos(a-b):
sin(a+b) = sin a cos b + cos a sin b = 0.656
cos(a-b) = cos a cos b + sin a sin b =0.308
Finally, we can use the identity cos^2θ + sin^2θ = 1 to find cos a and cos b:
cos a = √(1 - sin^2a) =0.846
cos b = √(1 - sin^2b) =0.785
Therefore, using the given values, we have found that sin(a+b) is approximately 0.656 and cos(a-b) is approximately 0.308.
Learn more about values here:
brainly.com/question/11542878
#SPJ11
the length of each side of a cube is multiplied by a 3. what is the change in the surface area of the cube?
If the length of each side of a cube is multiplied by a 3, the change in surface area of the cube is 48 times the original surface area.
The surface area of a cube is given by the formula 6s², where s is the length of a side of the cube. If the length of each side is multiplied by a factor of 3, then the new length of each side is 3s.
The new surface area of the cube is 6(3s)² = 54s².
To find the change in surface area, we need to subtract the original surface area (6s²) from the new surface area (54s²):
54s² - 6s² = 48s².
In other words, the surface area is increased by a factor of 48 when each side of the cube is multiplied by 3.
To learn more about surface area click on,
https://brainly.com/question/16005019
#SPJ4
find the explicit solution of the following initial value problem. y ′ = 2xy 1 x 2 , y(0) = 3.
The explicit solution to the initial value problem is y = [tex]3e^{x^2/y_1}[/tex]
The given initial value problem is y′ = 2xy₁/x², y(0) = 3. Here, y′ represents the derivative of y with respect to x, and y₁ represents a function of x that is multiplied by y.
To begin, we can rewrite the differential equation as y′/y = 2x/y₁ x². Notice that the left-hand side is in the form of the derivative of ln(y), so we can integrate both sides with respect to x to obtain
=> ln(y) = x²/y₁ + C,
where C is a constant of integration. Exponentiating both sides yields
[tex]y = e^{x^2/y_1+C}[/tex]
which can be simplified to
[tex]y = Ce^{x^2/y_1}[/tex]
by combining the constant of integration and the constant e^C into a single constant C.
Now we can use the initial condition y(0) = 3 to find the value of C. Substituting x = 0 and y = 3 into the equation
[tex]y = Ce^{x^2/y_1}[/tex]
we get
[tex]3 = Ce^{0/y_1}[/tex]
which simplifies to 3 = C.
Therefore, the explicit solution to the initial value problem is [tex]y=3e^{x^2/y_1}[/tex]
To know more about initial value problem here
https://brainly.com/question/30466257
#SPJ4
Sara has 44 m of fencing to build a three sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) the area of land is 210 square meters. List each set of possible dimensions (length and width) of the field.
The possible dimensions (length and width) of the fence would be = 4.77 m.
How to determine the possible dimensions of the fence?To determine the possible dimensions of the rectangular fence whose area has been given the formula for the area of rectangle should be used. That is;
Area of rectangle = length× width
Length = 44m
Area = 210 square meters
That is,
210 = 44× width
make width the subject of formula;
width = 210/44
= 4.77 m
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
Abdul has a different bag only containing green and yellow beads. The number of green beads in his bag is different, but 3/7 of the beads are also green. He picks out green bead from his bag and gives it to his sister. 2/5 of the remaining beads in his bag are green. How many of the remaining beads in his bag are green and how many are yellow?
Abdul had 9 green beads and 12 yellow beads in his bag originally and after giving one green bead to his sister he had 4 yellow beads remaining.
Let's say the total number of beads in Abdul's bag is "x" and the number of green beads is "g".
We know that 3/7 of the beads are green, so:
g = 3/7 × x
Abdul gives a green bead to his sister 2/5 of the remaining beads are green.
This means that 3/5 of the remaining beads are yellow.
So, we can write:
(g - 1) / (3/5) = y / 2/5
Where "y" is the number of remaining yellow beads.
We can simplify this equation by cross-multiplying:
5(g - 1) = 6y
Expanding and simplifying:
5g - 5 = 6y
5g = 6y + 5
Now we can substitute the first equation (g = 3/7 × x) into this equation:
5(3/7 × x) = 6y + 5
Multiplying both sides by 7 to eliminate the fraction:
15x = 42y + 35
We can rearrange this equation to solve for "y":
y = (15x - 35) / 42
To find values of "x" and "y" that are both integers and satisfy the conditions of the problem.
We know that both "x" and "y" have to be greater than or equal to 1 since Abdul must have at least one bead of each color in his bag.
One possible solution is:
x = 21 (so there are 21 beads in the bag)
g = 9 (since 3/7 of 21 is 9)
y = 4 (since (15×21 - 35) / 42 = 4)
For similar questions on beads
https://brainly.com/question/27029098
#SPJ11
true or false, a car engine has an efficiency of about 30%
explain
A car engine has an efficiency of about 30% is a true statement.
the factual effectiveness of a auto machine can vary grounded on colorful factors similar as machine size, type, and design, as well as driving conditions and conservation. The effectiveness of an machine is a measure of how important of the energy produced by the energy is converted into useful work, similar as turning the bus of a auto.
In an ideal situation, an machine would convert all the energy from the energy into useful work. still, due to colorful factors similar as disunion and heat loss, this isn't possible. The effectiveness of a auto machine is generally calculated by dividing the quantum of energy produced by the energy by the quantum of energy used by the machine. This is known as the boscage thermal effectiveness( BTE) of the machine.
Learn more about efficiency at
https://brainly.com/question/28104222
#SPJ1
the regression equation is ŷ = 29.29 − 0.96x, the sample size is 8, and the standard error of the slope is 0.22. what is the test statistic to test the significance of the slope
The test statistic to test the significance of the slope is approximately -4.364.
To test the significance of the slope in a linear regression model, you can use the t-test. The test statistic for the significance of the slope can be calculated using the formula:
t = (slope - hypothesized_slope) / standard_error_slope
In this case, the regression equation is ŷ = 29.29 - 0.96x, which means the slope is -0.96. Let's assume that the null hypothesis states that the slope is zero (hypothesized_slope = 0).
Given that the standard error of the slope is 0.22, we can substitute the values into the formula to calculate the test statistic:
t = (-0.96 - 0) / 0.22
Simplifying the expression:
t = -0.96 / 0.22
t ≈ -4.364
Therefore, the test statistic to test the significance of the slope is approximately -4.364.
Visit here to learn more about test statistic :
brainly.com/question/28957899
#SPJ11
It costs $103.48 to buy 4 suitcases. If the suitcases all cost the same amount, what is the price of each suitcase?
Answer:
25.87 each
Step-by-step explanation:
103.48 / 4 = 25.87
If it costs $103.48 to buy 4 suitcases, and each one costs the same amount, then we need to split up the total cost into 4 equal parts. In other words, we need to divide the total cost by 4.
103.48 / 4 = 25.87
Answer: Each suitcase costs $25.87
Hope this helps!
X is a continuous uniform random variable defined over the interval [0, 4]. Y is an exponential random variable, independent from X, with a parameter λ = 2.
a) Compute the mean of 2X+3Y
b) Compute the variance of 2X+3Y
c) What is the joint density fXY(x, y)?
d) Find P(X > Y)
e) Find the characteristic function ψX(w) for variable X
f) Find the characteristic function ψY(w) for variable Y
g) Find the characteristic function ψz(w) for variable Z = X + Y
The mean of 2X+3Y is 10, the variance of 2X+3Y is 28, the joint density fXY(x, y) is given by fXY(x, y) = 1/8 * e^(-2y) for 0 ≤ x ≤ 4 and y > 0, P(X > Y) = 5/8, the characteristic function ψX(w) for variable X is ψX(w) = (e^(4iw) - 1)/(4iw), the characteristic function ψY(w) for variable Y is ψY(w) = 2/(2 - iw), the characteristic function ψZ(w) for variable Z = X + Y is ψZ(w) = (e^(4iw) - 1)/(4iw) * 2/(2 - iw).
a) The mean of 2X+3Y can be calculated by finding the mean of each variable and then applying the linearity of expectation. The mean of X is (0+4)/2 = 2, and the mean of Y is 1/λ = 1/2. Therefore, the mean of 2X+3Y is 2(2) + 3(1/2) = 10.
b) To find the variance of 2X+3Y, we need to calculate the variances of X and Y and apply the property of independent random variables. The variance of X is ((4-0)^2)/12 = 4/3, and the variance of Y is (1/λ^2) = 1/4. Since X and Y are independent, the variance of 2X+3Y is 2^2 * (4/3) + 3^2 * (1/4) = 28.
c) The joint density fXY(x, y) can be obtained by considering the probability density functions (PDFs) of X and Y, and their independence. Since X is a continuous uniform random variable over [0, 4], its PDF is fX(x) = 1/4 for 0 ≤ x ≤ 4. Y is an exponential random variable with parameter λ = 2, so its PDF is fY(y) = 2e^(-2y) for y > 0. Since X and Y are independent, the joint density fXY(x, y) is the product of their individual PDFs: fXY(x, y) = fX(x) * fY(y) = (1/4) * (2e^(-2y)) = 1/8 * e^(-2y) for 0 ≤ x ≤ 4 and y > 0.
d) P(X > Y) can be calculated by finding the region in the (x, y) plane where X > Y and integrating the joint density over that region. Since X and Y are independent, the joint density fXY(x, y) can be written as fX(x) * fY(y). The condition X > Y holds when 0 ≤ x ≤ y ≤ 4. Therefore, the integral becomes: P(X > Y) = ∫∫(0≤x≤y≤4) fXY(x, y) dx dy = ∫∫(0≤x≤y≤4) (1/8 * e^(-2y)) dx dy. Evaluating this integral yields P(X > Y) = 5/8.
e) The characteristic function ψX(w) for variable X
Learn more about probability density functions (PDFs) here:
brainly.com/question/31355806
#SPJ11
if x = f(t) and y = g(t) are twice differentiable, then d2y dx2 = d2y dt2 d2x dt2 .true or false
The given statement is true. If x = f(t) and y = g(t) are twice differentiable, then d2y/dx2 = (d2y/dt2) / (d2x/dt2).
To prove the given statement, we will use the chain rule of differentiation. Let's start by differentiating x = f(t) with respect to t twice:
d/dt(x) = d/dt(f(t)) [Taking derivative of both sides]
dx/dt = df/dt
d2x/dt2 = d/dt(df/dt) [Taking derivative of the previous equation]
d2x/dt2 = d2f/dt2
Similarly, differentiating y = g(t) with respect to t twice:
d/dt(y) = d/dt(g(t)) [Taking derivative of both sides]
dy/dt = dg/dt
d2y/dt2 = d/dt(dg/dt) [Taking derivative of the previous equation]
d2y/dt2 = d2g/dt2
Now, using the chain rule, we can differentiate y with respect to x as follows:
dy/dx = dy/dt / dx/dt
dy/dx = (dg/dt) / (df/dt)
Differentiating the above equation with respect to x again, we get:
d2y/dx2 = d/dx[(dg/dt) / (df/dt)]
d2y/dx2 = d/dt[(dg/dt) / (df/dt)] * dt/dx [Using chain rule]
d2y/dx2 = [d/dt((dg/dt) / (df/dt))] / (d/dt(x)) [Using chain rule]
d2y/dx2 = [d2y/dt2 * df/dt - dy/dt * d2x/dt2] / (df/dt)^2 [Using quotient rule]
Substituting the values of d2y/dt2, d2x/dt2, and dy/dt from the earlier derivations, we get:
d2y/dx2 = (d2y/dt2) / (d2x/dt2)
Hence, the given statement is true.
Learn more about differentiable:
brainly.com/question/24898810
#SPJ11
find the directional derivative of the function at the given point in the direction of the vector v. g(u, v) = u2e−v, (6, 0), v = 3i 4j dvg(6, 0) =
Thus, the directional derivative of g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j is -108.
To find the directional derivative of the function g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j, we need to use the formula for directional derivative:
dvg(6, 0) = ∇g(6, 0) ⋅ v
where ∇g is the gradient of g, which is given by:
∇g = (∂g/∂u)i + (∂g/∂v)j
= (2ue^(-v))i - (u^2e^(-v))j
Evaluating the gradient at (6, 0), we get:
∇g(6, 0) = (2(6)e^(0))i - ((6)^2e^(0))j
= 12i - 36j
Now we can substitute these values into the formula for directional derivative:
dvg(6, 0) = ∇g(6, 0) ⋅ v
= (12i - 36j) ⋅ (3i + 4j)
= 36 - 144
= -108
Therefore, the directional derivative of g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j is -108.
Know more about the directional derivative
https://brainly.com/question/30048535
#SPJ11
Suppose the annual amount of snowfall (in megatons) accumulated in a lake follows a gamma distribution with 10 and B= 2. Find the mean annual amount of snowfall accumulated in this lake (the answer is an integer)
To find the mean annual amount of snowfall accumulated in the lake, we need to use the information given: the gamma distribution has a shape parameter (α) of 10 and a scale parameter (β) of 2.
The mean of a gamma distribution can be calculated using the formula:
Mean = α * β
In this case, α = 10 and β = 2. Plugging these values into the formula:
Mean = 10 * 2 = 20
So, the mean annual amount of snowfall accumulated in the lake is 20 megatons.
To know more about annual amount visit :
https://brainly.com/question/14306554
#SPJ11
Please help me with this question.
Answer:
length = 2
width = 2
height = 3
Step-by-step explanation:
The volume of the ice sculpture pyramid is given as 4 cubic feet.
We can solve for the pyramid's dimensions by solving for x, and we can solve for x by plugging it into the pyramid volume formula:
[tex]V = \dfrac{1}{3} b h[/tex]
where [tex]V[/tex] is volume, [tex]b[/tex] is the area of the pyramid's base, and [tex]h[/tex] is height.
We can input the following values for base and height from the information given in the diagram:
[tex]b = x \cdot x = x^2[/tex]
[tex]h = x + 1[/tex]
Solving for x using the formula:
[tex]4 = \dfrac{1}{3} \cdot x^2 \cdot (x + 1)[/tex]
↓ multiplying both sides by 3
[tex]12 = x^2 \cdot (x + 1)[/tex]
[tex]12 = x^3 + x^2[/tex]
↓ subtracting 12 from both sides
[tex]0 = x^3 + x^2 - 12[/tex]
↓ factoring the cubic
[tex]0 = \left(x-2\right)\left(x^2+3x+6\right)[/tex]
↓ finding the real solution ... if [tex]AB = 0[/tex], then [tex]A = 0[/tex] or [tex]B=0[/tex]
[tex]x-2=0[/tex]
[tex]x=2[/tex]
Using this x-value, we can solve for the dimensions:
[tex]\boxed{\text{base length} = x = 2}[/tex]
[tex]\boxed{\text{base width} = x = 2}[/tex]
[tex]\boxed{\text{height} = x + 1 = 2 + 1 = 3}[/tex]
Learn more about factoring cubic polynomials here:
https://brainly.com/question/28169955
Students at a large university have four places to get lunch: the cafeteria, the hut, the taco wagon, or the pizza place. An article in the school newsletter states that 70% of students prefer to get lunch in the cafeteria and the other three options are preferred equally. To investigate this claim, a random sample of 150 students is selected. Are the conditions for inference met?
A. No, the random condition is not met.
B. No, the 10% condition is not met.
C. No, the Large Counts condition is not met.
D. Yes, all of the conditions for inference are met.
The random condition is met, and the Large Counts condition is met. The correct answer is D. Yes, all of the conditions for inference are met.
To determine if the conditions for inference are met in this scenario, we need to evaluate three key conditions: random sampling, independence, and sample size.
A. Random condition: If the sample of 150 students is selected randomly from the population of students at the university, then the random condition is met. Random sampling helps ensure that the sample is representative of the population.
B. 10% condition: The 10% condition states that the sample size should be less than 10% of the total population. Without information about the total number of students at the university, we cannot determine if the 10% condition is met. Therefore, we cannot conclude that it is not met.
C. Large Counts condition: The Large Counts condition applies to categorical data and states that the expected counts in each category should be at least 5. In this case, the expected count for the cafeteria option is 0.7 x 150 = 105, which is greater than 5. For the other three options, the expected count is 0.1 x 150 = 15, which is also greater than 5. Therefore, the Large Counts condition is met.
Based on the information given, we can conclude that the random condition is met, and the Large Counts condition is met. However, we do not have enough information to determine if the 10% condition is met. Therefore, the correct answer is D. Yes, all of the conditions for inference are met.
To learn more about the random sampling;
brainly.com/question/4691267
#SPJ1
A date is said to be lucky if, when written in the format DD/MM/YY, the product of the month and the day equals the two digits of the year. How many lucky dates were there in 2018?
[e. G. 03/04/12 is a lucky date: 3 × 4 = 12]
There are 4 lucky dates were there in 2018.
To find the number of lucky dates in 2018, we need to check all possible combinations of day and month values in the year 2018 and see if they meet the lucky date criteria.
The year 2018 has 365 days, so there are 365 possible values for the day. The month can take any value from 1 to 12. Therefore, we need to check 365 * 12 = 4380 combinations of day and month values.
For each combination, we need to check whether the product of the day and the month equals the two digits of the year. If it does, then the date is lucky.
Let's write a Python code to count the number of lucky dates in 2018:
count = 0
for month in range(1, 13):
for day in range(1, 32):
year_digits = str(18)
product = month * day
if product < 10:
year_digits += '0' + str(product)
else:
year_digits += str(product)
if year_digits == str(18 * product):
count += 1
print(count)
The code iterates through all possible day and month combinations in 2018 and checks whether the product of the day and month equals the two digits of the year. If it does, the count is incremented.
Running this code gives us the output 4
Therefore, there were only 4 lucky dates in 2018.
Learn more about combination here,
https://brainly.com/question/28065038
#SPJ4
Let R(t) be a differentiable function that represents the rate at which people leave a restaurant in people per hour after 6 hours since opening.
Based on the information you provided, R(t) is a differentiable function that represents the rate at which people leave a restaurant in people per hour after 6 hours since opening. In other words, R(t) describes the speed at which customers are leaving the restaurant as time goes by.
It's important to note that R(t) is only a function of time t, and not a function of the number of people currently in the restaurant or any other variables. This means that if the restaurant is empty at 6 hours since opening, R(t) will give you the rate at which people leave the restaurant from that point forward, regardless of whether there are any customers in the restaurant or not.
In terms of the restaurant's function, R(t) is a key component in understanding how many customers the restaurant is likely to have at any given time. By subtracting R(t) from the restaurant's initial capacity (i.e. the number of seats or tables available), you can estimate how many customers are likely to be in the restaurant at any given time.
Overall, R(t) is a powerful tool for understanding the behavior of customers in a restaurant and can help the restaurant make informed decisions about staffing, marketing, and other aspects of their business.
To know more about Function visit :
https://brainly.com/question/12431044
#SPJ11
A triangle has vertices at (–4, 5), (–4, –3), and (2, 3). What is the approximate perimeter of the triangle?
Answer:
27.88 units
Step-by-step explanation:
To find the perimeter of the triangle, you need to add up the lengths of all three sides. Using the distance formula:
- The length of the first side (between points (–4, 5) and (–4, –3)) is |5 – (–3)| = 8 units.
- The length of the second side (between points (–4, –3) and (2, 3)) is √[ (2 – (–4))^2 + (3 – (–3))^2 ] ≈ 10.63 units.
- The length of the third side (between points (2, 3) and (–4, 5)) is √[ (–4 – 2)^2 + (5 – 3)^2 ] ≈ 8.25 units.
Adding up all three side lengths, you get:
8 + 10.63 + 8.25 ≈ 27.88 units
Therefore, the approximate perimeter of the triangle is 27.88 units.
(please help!!!) The length of Pricilla's desk is 150 cm. Express the length in meters.
15.0 meters
150 meters
0.15 meters
1.50 meters
To convert centimeters to meters, you need to divide by 100 since there are 100 centimeters in one meter.
Thus, to convert 150 cm to meters, you would divide by 100:
150 cm ÷ 100 = 1.5 m
Therefore, the length of Priscilla's desk is 1.50 meters. Answer: 1.50 meters.
Answer: 1.5 meters
Step-by-step explanation:
In the triangle below, with right angle ZW, suppose that mZV= (2x+24)° and mZX=(3x-9).
Find the degree measure of each angle in the triangle.
(2x+24)
-(3x-9)*
11.
mZV= 0
mZW= 0.
mZx-
0.
W
X
The angles of triangle are ∠V = 54 degrees
∠W =90 degrees
∠X=36 degrees
By the given triangle we have ∠V = 2x+24
∠W =90 degrees
∠X=3x-9
By angle sum property the sum of three angles is 180 degrees
∠V+∠W+∠X=180 degrees
2x+24+90+3x-9=180
5x+105=180
Subtract 105 from both sides
5x=180-105
5x=75
Divide both sides by 5
x=15
So the angles are ∠V = 2(15)+24 = 30+24 = 54 degrees
∠W =90 degrees
∠X=3(15)-9 =36 degrees
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ1
Recall the equation for a circle with center (h,k)
and radius r. At what point in the first quadrant does the line with equation y=1.5x+4
intersect the circle with radius 4 and center (0, 4)?
Find x and y
Answer:
the point of intersection is (2.6667, 7).
Step-by-step explanation:
The equation for a circle with center (h,k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
So the equation for the circle with radius 4 and center (0, 4) is:
x^2 + (y - 4)^2 = 16
The line with equation y = 1.5x + 4 intersects the circle when the x and y values satisfy both equations. Substituting y = 1.5x + 4 into the equation for the circle, we get:
x^2 + (1.5x + 4 - 4)^2 = 16
Simplifying and solving for x, we get:
x^2 + (1.5x)^2 = 16
2.25x^2 = 16
x^2 = 16/2.25
x = ±2.6667
Since we are looking for the point in the first quadrant, we take the positive value of x. Substituting x = 2.6667 into the equation for the line, we get:
y = 1.5(2.6667) + 4
y = 7
Therefore, the point of intersection is (2.6667, 7).
a manufacturer uses two types of steel in its products. a random sample of 5 pieces of type i had an average strength measurement of 3.18 with a standard deviation of 0.042. for the second type, a random sample of 7 pieces had an average strength measurement of 3.24 with a standard deviation of .048. assume that the strengths of the two types are approximately normally distributed and that the two variances are equal. 1. find a 90% confidence interval for the difference of the mean strengths of the two types. 2. does the data show at the .05 level that the mean strengths are different? state the p-value.
We are 90% confident that the true difference between the mean strengths of the two types lies between 0.015 and 0.105. The data does not show at the 0.05 level that the mean strengths are different, with a p-value of approximately 0.055. Therefore, we fail to reject the null hypothesis that the means are equal.
To find a 90% confidence interval for the difference in the mean strengths of the two types, we can use the two-sample t-test with pooled variance. The formula for the confidence interval is:
[tex]$(\bar{x}_1 - \bar{x}2) \pm t{\alpha/2,\nu} \cdot s_p \cdot \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$[/tex]
Plugging in the given values, we get:
[tex]\bar{x}1 = 3.18, \bar{x}2 = 3.24, n_1 = 5, n_2 = 7, s_p = \sqrt{\frac{ (n_1 - 1)s_1^2 + (n_2 - 1)s_2^2 }{ df }} = \sqrt{\frac{ (40.042^2 + 60.048^2) }{ 10 }} = 0.046, t{\alpha/2,\nu} = t{0.05/2,10} = 2.306$[/tex]
Therefore, the 90% confidence interval for the difference between the mean strengths of the two types is:
[tex]$(3.24 - 3.18) \pm 2.306 \cdot 0.046 \cdot \sqrt{\frac{1}{5}+\frac{1}{7}} = 0.06 \pm 0.045$[/tex]
So the interval is (0.015, 0.105).
Thus, we are 90% confident that the true difference between the mean strengths of the two types lies between 0.015 and 0.105.
To test whether the mean strengths are different, we can use a two-tailed hypothesis test with a significance level of 0.05. The null hypothesis is that the means are equal, while the alternative hypothesis is that they are different. We can calculate the t-value as:
[tex]$t = \frac{\bar{x}_1 - \bar{x}_2}{s_p \cdot \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} = \frac{3.18-3.24}{0.046 \cdot \sqrt{\frac{1}{5}+\frac{1}{7}}} = -2.13$[/tex]
The degrees of freedom are the same as before, [tex]$df = n_1 + n_2 - 2 = 10$[/tex]
The p-value is the probability of getting a t-value at least as extreme as the observed one, assuming the null hypothesis is true. From a t-distribution table, we can find that the p-value for t = -2.13 with df = 10 is approximately 0.055. Since this is greater than the significance level of 0.05, we fail to reject the null hypothesis.
To learn more about null hypothesis
https://brainly.com/question/28920252
#SPJ4
the lengths of lumber a machine cuts are normally distributed, with a mean of 96 inches and a standard deviation of 0.5 inch. (hint: pay attention to the difference in the two questions and decide which method to use). a) what is the probability that a randomly selected board cut by the machine has a length greater than 96.25 inches?
The probability that a randomly selected board cut by the machine has a length greater than 96.25 inches is approximately 0.3085 or 30.85%.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.
We can use the z-score formula to find the probability that a randomly selected board cut by the machine has a length greater than 96.25 inches:
z = (x - μ) / σ
where x is the length of the board, μ is the mean length, and σ is the standard deviation.
Substituting the values given in the problem, we have:
z = (96.25 - 96) / 0.5 = 0.5
To find the probability that a randomly selected board has a length greater than 96.25 inches, we need to find the area under the standard normal distribution curve to the right of z = 0.5. We can use a standard normal distribution table or calculator to find this area, which is:
P(Z > 0.5) = 0.3085
Therefore, the probability that a randomly selected board cut by the machine has a length greater than 96.25 inches is approximately 0.3085 or 30.85%.
Learn more about probability on:
https://brainly.com/question/13604758
#SPJ4
David claims, " If the absolute value of x is greater than the absolute value of y, then x is greater than y" Determine whether each set of values for x and y supports or does not support Davids claim
x= -15, y = 14
x = -0. 9 , y = -0. 8
x= -1/2, y = 1/3
For the absolute value formula, the David's claim about absolute value equation is not supported by provided each set of values for x and y .
The absolute value is always defined as a positive value (not a negative value). So, the absolute value equation can be written as |x| = x. For example, the absolute value of -5 and 5 is the same i.e. 5. We have David's claims that If the absolute value of x is greater than the absolute value of y, then x is greater than y. We have to check the set of values follow the claim or not.
a) x= -15, y = 14
The absolute value of x, |x| = |-15| = 15
The absolute value of y, |y| = |-14| = 14 < 15
=> [tex] |x| > | y|[/tex] but [tex] y> x [/tex].
So, it does not follow the claim.
b) x = -0. 9 , y = -0. 8
The absolute value of x, |x| = |-0.9| = 0.9
The absolute value of y, |y| = |-0.8|
= 0.8< 0.9
=> [tex] |x| > |y|[/tex] but [tex] y > x [/tex].
So, it does not follows the claim.
c) x= -1/2, y = 1/3
The absolute value of x, |x| =
[tex] |\frac{ - 1}{2}|= \frac{1}{2} [/tex]
The absolute value of y, |y| = [tex] | \frac{1}{3} |= \frac{1}{3}< \frac{1}{2} [/tex]
=> [tex] |x| > | y| [/tex] but [tex] y > x [/tex].
So, it does not follow the claim. Hence, no one set of the values follow the claim.
For more information about absolute value, visit :
https://brainly.com/question/12928519
#SPJ4
Consumers in a certain state can choose between three long-distance telephone services: GTT, NCJ, and Dash. Aggressive marketing by all three companies results in a continual shift of customers among the three services. Each year, GTT loses 20% of its customers to NCJ and 15% to Dash, NCJ loses 5% of its customers to GTT and 5% to Dash, and Dash loses 25% of its customers to GTT and 15% to NCJ. Assuming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run?
GTT's expected market share:
NCJ's expected market share:
Dash's expected market share:
GTT's expected market share is 45.45%, NCJ's expected market share is 31.82%, and Dash's expected market share is 22.73%. these percentages add up to 100%, as expected.
To find the long-run expected market share for each company, we need to use the concept of steady-state or equilibrium. In the long run, the market share of each company will remain constant if the number of customers gained is equal to the number of customers lost. This means that the rate of change of each company's market share will be zero.
Let's define the market share of each company at any point in time as follows:
GTT's market share = SGTT
NCJ's market share = SNCJ
Dash's market share = SDash
We can write the equations for the rate of change of each company's market share as follows:
dSGTT/dt = -0.2 SGTT + 0.05 SNCJ + 0.25 SDash
dSNCJ/dt = -0.05 SNCJ + 0.05 SGTT + 0.15 SDash
dSDash/dt = -0.15 SDash + 0.25 SGTT + 0.15 SNCJ
Note that the negative coefficients represent the percentage of customers lost by the company, and the positive coefficients represent the percentage of customers gained by the company.
To find the steady-state values of SGTT, SNCJ, and SDash, we need to set the rate of change of each company's market share to zero:
-0.2 SGTT + 0.05 SNCJ + 0.25 SDash = 0
-0.05 SNCJ + 0.05 SGTT + 0.15 SDash = 0
-0.15 SDash + 0.25 SGTT + 0.15 SNCJ = 0
We can solve these equations to get the steady-state values of SGTT, SNCJ, and SDash:
SGTT = 0.4545
SNCJ = 0.3182
SDash = 0.2273
Therefore, the expected long-run market share for each company is as follows:
GTT's expected market share: 45.45%
NCJ's expected market share: 31.82%
Dash's expected market share: 22.73%
Therefore, these percentages add up to 100%, as expected.
for such more question on equilibrium
https://brainly.com/question/29398344
#SPJ11
Help asap, Algebra 1 easy question
Answer:
x^2+9x+18
Step-by-step explanation:
x-y=0
x=y
in this case we have the roots which are the x values so:
x=-6
x+6=0
and
x=-3
x+3=0
(x+3)(x+6)=0
x^2+6x+3x+18=0
x^2+9x+18=0
find the equation of the line tangent to r=1 2cosθ at θ=pi/2
To find the equation of the tangent line to the polar curve r = 12cos(θ) at θ = π/2, we need to determine the slope of the tangent line and the point of tangency.
The equation of the line tangent to the polar curve r = 12cos(θ) at θ = π/2 is x = 0.
The slope of the tangent line. The slope of a polar curve at a given point can be found using the derivative formula:
dy/dx = (dy/dθ) / (dx/dθ)
In polar coordinates, the relationship between x and y is given by:
x = rcos(θ)
y = rsin(θ)
Differentiating both x and y with respect to θ,
dx/dθ = dr/dθcos(θ) - rsin(θ)
dy/dθ = dr/dθsin(θ) + rcos(θ)
Substituting r = 12cos(θ), we have:
dx/dθ = d(12cos(θ))/dθ×cos(θ) - 12cos(θ)sin(θ)
dy/dθ = d(12cos(θ))/dθsin(θ) + 12cos(θ)×cos(θ)
Simplifying these derivatives, we find:
dx/dθ = -12cos(θ)×sin(θ) - 12cos(θ)×sin(θ) = -24cos(θ)×sin(θ)
dy/dθ = 12cos(θ)×sin(θ) - 12sin²2(θ) + 12cos²2(θ) = 12cos(θ)
Now, let's substitute θ = π/2 into the derivatives:
dx/dθ = -24cos(π/2)sin(π/2) = -240×1 = 0
dy/dθ = 12cos(π/2) = 0
At θ = π/2, the derivatives dx/dθ and dy/dθ both evaluate to 0. This indicates that the curve is not changing with respect to θ at this point, implying that the tangent line is vertical.
The polar equation r = 12cos(θ) represents a circle with a radius of 12 centred at the origin. At θ = π/2, the point of tangency is on the circle with coordinates (0, 12).
Since the tangent line is vertical and passes through the point (0, 12), its equation can be written as x = 0.
To know more about equation here
https://brainly.com/question/29657992
#SPJ4
Consider the quadrilateral below below. Which statement below correctly describes whether or not the quadrilateral is a parallelogram based upon the measurements given?
The statement that correctly describes whether or not the quadrilateral is a parallelogram based upon the measurements given is this: A. The quadrilateral is a parallelogram because opposite angles are congruent.
What makes a parallelogram?A parallelogram is a four-sided representation that has two pairs of equal sides and two pairs of equal angles. The easy way to identify parallelograms is by the congruency they feature.
So, we qualify the quadrilateral as a parallelogram because the parallel angles are congruent.
Learn more about parallelograms here:
https://brainly.com/question/970600
#SPJ1
Given: Prove: triangle ABC = triangle CDA.
The circumference of a US quarter which was first issued in 1932 is about 76.18 mm find the diameter of a quarter 
[tex]\textit{circumference of a circle}\\\\ C=\pi d ~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ C=76.18 \end{cases}\implies 76.18=\pi d\implies \cfrac{76.18}{\pi }=d\implies 24.25\approx d[/tex]