a. Salt flows into tank A at a rate of
(y(t)/500 lb/gal) * (50 gal/min) = y(t)/10 lb/gal
and out at a rate of
(x(t)/500 lb/gal) * (50 gal/min) = x(t)/10 lb/gal
so the net rate of change of the amount of salt in tank A is
[tex]x'(t)=\dfrac{y(t)}{10}-\dfrac{x(t)}{10}[/tex]
Similarly, you would find
[tex]y'(t)=\dfrac{x(t)}{10}-\dfrac{y(t)}{10}[/tex]
b. We have
[tex]x'=-\dfrac x{10}+\dfrac y{10}\implies x''=-\dfrac{x'}{10}+\dfrac{y'}{10}[/tex]
Notice that x' = -y', so
[tex]x''=-{2x'}{10}\implies 5x''+x'=0[/tex]
Solve for x: the characteristic equation
[tex]5r^2+r=r(5r+1)=0[/tex]
has roots [tex]r=0[/tex] and [tex]r=-\frac15[/tex], so
[tex]x(t)=C_1+C_2e^{-t/5}[/tex]
Again using the fact that y' = -x', we then find
[tex]x'(t)=-\dfrac{C_2}5e^{-t/5}\implies y'(t)=\dfrac{C_2}5e^{-t/5}\implies y(t)=C_1-C_2e^{-t/5}[/tex]
Given that x(0) = 0 and y(0) = 10, we find
[tex]\begin{cases}0=C_1+C_2\\10=C_1-C_2\end{cases}\implies C_1=5,C_2=-5[/tex]
(5) In the center of the monument are two concentric circles of igneous rock pillars, called bluestones. The construction of these circles was never completed. These circles are known as the Bluestone Circle and the Bluestone Horseshoe. The stones in these two formations were transported to the site from the Prescelly Mountains in Pembrokeshire, southwest Wales. Excavation at the center of the monument revealed an antler, an antler tine, and an animal bone. Each artifact was submitted for dating. It was determined that this sample of three artifacts had a mean age of 2193.3 BCE, with a standard deviation of 104.1 years. Assume that the ages are normally distributed with no obvious outliers. Use an α = 0.05 significance level to test the claim that the population mean age of the Bluestone formations is different from Corbin's declared mean age of the ditch, that is, 2950 BCE.
Answer:
There is enough evidence, at a significance level of 0.05, that the population mean age of the Bluestone formations is different from 2950 BCE.
Step-by-step explanation:
We have a sample and we want to perform a hypothesis test on the mean.
The null hypothesis is the Corbin's declared age (2950 BCE). The alternative hypothesis states that the age differ from that value.
They can be expressed as:
[tex]\H_0:\mu=2950\\\\H_a:\mu\neq2950[/tex]
The significance level is 0.05.
The sample has a size of n=3, a mean of 2193.3 BCE and a standard deviation of 104.1 years.
As the standard deviation is estimated from the sample, we have to calculate the t-statistic.
[tex]t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{2193.3-2950}{104.1/\sqrt{3}}=\dfrac{-756.7}{60.1}=-12.59[/tex]
The degrees of freedom for this test are:
[tex]df=n-1=3-1=2[/tex]
The critical value for a two side test with level of significance α=0.05 and 2 degrees of freedom is t=±4.271.
As the statistic t=-12.59 lies outside of the acceptance region, the null hypothesis is rejected.
There is enough evidence, at a significance level of 0.05, that the population mean age of the Bluestone formations is different from 2950 BCE.
(4x^2-10x+6) divide (4x+2)
Answer:
x = 1 or x = 3/2
Step-by-step explanation:
Solve for x:
(4 x^2 - 10 x + 6)/(4 x + 2) = 0
Multiply both sides by 4 x + 2:
4 x^2 - 10 x + 6 = 0
The left hand side factors into a product with three terms:
2 (x - 1) (2 x - 3) = 0
Divide both sides by 2:
(x - 1) (2 x - 3) = 0
Split into two equations:
x - 1 = 0 or 2 x - 3 = 0
Add 1 to both sides:
x = 1 or 2 x - 3 = 0
Add 3 to both sides:
x = 1 or 2 x = 3
Divide both sides by 2:
Answer: x = 1 or x = 3/2
An architect is making a model of a proposed office building with the dimensions shown. To fit on a display, the longest side of the architect's
model must be 30 inches long. To make the model geometrically similar to the proposed building, what should the width and the height of the
model be?
A. Width = 20 inches, height = 8 inches
B. Width = 20 inches, height = 12 inches
C. Width = 25 inches, height = 16 inches
D. Width = 25 inches, height = 20 inches
E. Width = 20 inches, height = 25 inches
Answer:
25 20
Step-by-step explanation:
D. Width = 25 inches, height = 20 inches
Mandy wants to buy a variety of beverages for her birthday party. She wants to make sure she has enough to drink for all her friends, so she decides to buy 10 liters of beverages. If she buys at least one container of each beverage, what combination of beverages can she buy to equal exactly 10 liters? Beverages at the store:
2,000 millilitres of soda, 2.5 liters of apple juice, 1,500 millilitres of fruit punch, 2 liters of lemonade
Answer:
Soda x 2
Apple Juice x 1
Fruit Punch x 1
Lemonade x 1
and
Soda x 1
Apple Juice x 1
Fruit Punch x 1
Lemonade x 2
Step-by-step explanation:
Amounts:
Soda 2L
Apple Juice 2.5L
Fruit Punch 1.5L
Lemonade 2L
S + A + FP + L = 8L
So we need 2 L more. The only way of doing this is by either having 2 lots of soda or 2 lots of lemonade.
The combination of beverages she can purchased;
Soda = 2 container
Apple juice = 1 container
Fruit punch= 1 container
Lemonade = 1 container
Logical reasoning:The quantity of Beverages present at the store ;
Soda = 2000ml = 2L
Apple Juice = 2.5L
Fruit Punch = 1.5L
Lemonade = 2L
We have to buy exactly 10 liters but it should be at least one container of each beverage.
Soda + Apple juice + Fruit Punch + Lemonade = 8L
So we need 2 L more.
The only way of doing this is by either having 2 container of soda or 2 container of lemonade.
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What type of symmetry can the graph of a quadratic function have?
A. Symmetry about the x-axis
B. Symmetry about the y-axis
C. Symmetry about the line y=x
D. No symmetry
Answer:
B
Step-by-step explanation:
Option B is correct. A quadratic function can have symmetry about the y-axis.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
A quadratic function can have symmetry about the axis of symmetry, which is a vertical line that passes through the vertex of the parabola. The axis of symmetry is given by the equation x = -b/(2a)
where a and b are the coefficients of the quadratic function ax² + bx + c.
If a quadratic function has symmetry about the x-axis, then its equation is of the form y = ax² + c, where a and c are constants.
If it has symmetry about the y-axis, then its equation is of the form y = ax², where a is a constant.
Therefore, Option B is correct. A quadratic function can have symmetry about the y-axis.
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Can somone help me with 1,2,3 ????
Answer:
This is a weird assignment
Step-by-step explanation:
1) 7.5 minute per mile
10 convert hours to min (900 min) and then simply the unit of 6771 miles by 900 min. The objective is to know how far you travel in one minute.
3) Chose any country in South America:
Brazil, Argentina, Peru, Columbia, Venezuela, Bolivia, etc.
A certain front-loading washing machine has a drum of diameter 23.3 inches. A small tennis ball placed inside spins in a vertical circle pressed against the inner wall of the drum. How quickly would the drum have to spin (in radians per second) in order to ensure that the tennis ball remained pinned against the wall for the entire cycle without falling off?
Answer:
33.12 rad/s
Step-by-step explanation:
We are given that
Diameter=d=23.3 in
Radius,=[tex]r=\frac{d}{2}=\frac{23.3}{2}=11.65 in=11.65\times 0.0254= 0.29591 m[/tex]
1 in=0.0254 m
We have to find the angular speed of drum would have to spin.
Force=[tex]mg[/tex]
Centripetal force=[tex]m\omega^2 r[/tex]
[tex]mg=m\omega^2 r[/tex]
[tex]\omega^2=\frac{g}{r}[/tex]
[tex]\omega=\sqrt{\frac{g}{r}}[/tex]
Where [tex]g=9.8m/s^2[/tex]
[tex]\omega=\sqrt{\frac{9.8}{0.29591}[/tex]
[tex]\omega=33.12 rad/s[/tex]
Factor the expression completely 8x^2-18 Please help
Answer:
2 (2x - 3) x (2x + 3)
What is the range of the data below?
—
—
50
60
70
80
90
100
оооо
Answer:
50 all you have to do is subtract the least and the biggest number
Step-by-step explanation:
please answer all of them there are 3 pages cuz i couldnt fit them all only 10 questions tho please answer it like this
1:
2:
3:
4:
Answer:
1:C
2:B
3:A
4:B
5:D
6:D
7:A
8:C
9:C
10:B
Step-by-step explanation:
consider circle O, in which arc XY measures 16 pie cm. The length of a radius of the circle is 32 cm. What is the circumference of the circle?
Answer:64 pi units
What is the ratio of the arc length to the circumference?Answer: 1/4
What is the measure of central angle XOY?Answer: 90 degrees
Answer:
1. 64 pi units
2. 1/4
3. 90°
Step-by-step explanation: edge
Follow the steps to finish solving the equation –3x + 18 = 7x.
1. Add 3x to both sides to isolate the variable term.
2. Divide both sides by 10.
18/10
Step-by-step explanation:
Answer:
18/10
Step-by-step explanation:
Just did the question
An experiment was performed to compare the wear of two different laminated materials. Twelve pieces of material 1 were tested by exposing each piece to a machine measuring wear. Ten pieces of material 2 were similarly tested. In each case, the depth of wear was observed. The samples of material 1 gave an average (coded) wear of 85 units with a sample standard deviation of 4, while the samples of material 2 gave an average of 81 with a sample standard deviation of 5. Can we conclude at the 0.05 level of significance that the abrasive wear of material 1 exceeds that of material 2 by more than two units? Assume the populations to be approximately normal with equal variances pdf
Answer:
At 0.05 level of significance, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units
Step-by-step explanation:
We hypothesize that mean difference between abrasive wear of material 1 and material 2 is greater than 2.
So we write the null hypothesis [tex]H_0 : \mu_1 - \mu_2 >2[/tex],
and the alternative hypothesis [tex]H_1: \mu_1 - \mu_2 \leq 2[/tex].
We will find the T-score as well as the p-value. If the p-value is less than the level of significance, we will reject the null hypothesis, i.e. we will conclude that the abrasive wear of material 1 is less than that of material 2. Otherwise, we will accept the null hypothesis.
Since the variance is unknown and assumed to be equal, we will use the pooled variance
[tex]s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} = 20.05[/tex],
where [tex]n_1 = 12, n_2 =10, s_1 =4, s_2 = 5[/tex].
The mean of material 1 and material 2 are [tex]\mu_1 =85, \mu_2=81[/tex] respectively and mean difference [tex]d[/tex] is equal to 4. The hypothesize difference [tex]d_0[/tex] is equal to 2.
To find the T-score, we use the following formula
[tex]T = \frac{d - d_0}{\sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2} }}[/tex]
Substituting all the values into the T-score formula gives us [tex]T = 1.04[/tex], and the respective p-value is equal to 0.31. This means we have enough statistical evidence not to reject the null hypothesis, and at 5% significance level, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units.
What is the measure of angle DEG on circle O? Please help! Picture included!
I don't know how to do that. Only one angle is given and no relationships between the triangles or any lines are given.
Answer:
The answer is 50.
Step-by-step explanation:
A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 279 vinyl gloves, 60% leaked viruses. Among 279 latex gloves, 14% leaked viruses. See the accompanying display of the technology results. Using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. Identify: null, alternative hypothesis, test statistic, and P-value.
The P-value is (1) the significance level ?, so (2) the null hypothesis. There is (3) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
1) greater than / less than 2) reject / fail to reject 3) sufficient / insufficient
(Table at bottom of question)
Technology results:
Pooled proportion: 0.37
Test statistic, z: 11.3049
Critical z: 1.2816
P-value: 0.0000
80% Confidence interval: 0.4163430 < p1 ? p2 < 0.5083882
Answer:
a) H0: Null Hypothesis: P1 = P2
HA: Alternative Hypothesis:P1> P2
The P-value is less than the significance level.
Therefore, Reject the null hypothesis
In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
Step-by-step explanation:
(a) From the information given, we can identify the null hypothesis and alternative hypothesis.
H0: Null Hypothesis: P1 = P2
HA: Alternative Hypothesis:P1> P2
(b) n1 which is size of sample 1 = 279
p1 which is proportion of sample 1= 0.60
n2 which is size ofsample 2 = 279
p2 which is proportion of sample 2 = 0.14
P=n1p1+n2p2 / n1+n2
=279 × 0.60+279 × 0.14/279+279
=0.37
Q = 1- P = 0.63
SE= √PQ(1/n1+1/n2)
= √ 0.37 × 0.63(1/279+1/279)=0.0409
So,
Test statistic is:
Z = (p1 - p2) /SE
= (0.60 - 0.14)/0.0409
= 11.3049
(c) The able of Area Under Standard Normal Curve gives the following area =
0.5 approximately.
So,
P-value = 0.5 - 0.5 nearly =0 nearly
(d)From the information derived, the P-value is less than the significance level.
Therefore, Reject the null hypothesis
In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
To every linear transformation T from ℝ2 to ℝ2, there is an associated 2×2 matrix. Match the following linear transformations with their associated matrix. B 1. The projection onto the x-axis given by T(x,y)=(x,0) A 2. Counter-clockwise rotation by π/2 radians C 3. Clockwise rotation by π/2 radians A 4. Reflection about the y-axis B 5. Reflection about the x-axis F 6. Reflection about the line y=x A. (−1001) B. (1000) C. (100−1) D. (0−110) E. (01−10) F. (0110) G. None of the above
Answer:
1. B
2. D
3. E
4. A
5. C
6. F
Step-by-step explanation:
1. The projection onto the x-axis is given by T(x, y) = (x, o) =(1 0 0 0) B
2. Counter-clockwise rotation by π/2 radians C
= (0 - 1 1 0) D
3. Clockwise rotation by π/2 radians
= (0 1 - 1 0) E
4. Reflection about the y-axis
= (-1 0 0 1) A
5. Reflection about the x-axis = (1 0 0 - 1) C
6. Reflection about the line y=x
(0 1 1 0) F
For every line in a plane, there is a linear transformation that reflects the vector about that line. The easiest way to answer a question like this is to figure out where the standard basic vector is, e1 and e2. Write the answers at the column of the matrix. Letting As be the matrix corresponding to the linear transformation s. It is easier to see that e1 gets carried to e2 and e2 gets carried to - e1
As= (0 - 1 1 0)
The answer identifies and correlates different types of linear transformations in ℝ2 to ℝ2 space with their corresponding 2×2 matrices, considering operations such as projection onto axis, clockwise and counter-clockwise rotations, and reflections about axes or a line.
Explanation:The question is about matching linear transformations with their associated 2×2 matrices.
The projection onto the x-axis given by T(x,y)=(x,0) would be represented by a matrix that eliminates the y-component, so its matrix is (1000). Counter-clockwise rotation by π/2 radians corresponds to the matrix (01−10), as it reverses the entries and changes the sign of the y-component. Clockwise rotation by π/2 radians corresponds to the matrix (0−110), as it also switches the entries, but with a positive sign for the y-component. Reflection about the y-axis inverts the sign of the x-component, corresponding to the matrix (−1001). Reflection about the x-axis influences the sign of the y-component, thus corresponding to the matrix (010-1). Lastly, reflection about the line y=x equates to exchange the roles of x and y and hence represented by the matrix (0110).
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A food safety inspector is called upon to investigate a restaurant with a few customer reports of poor sanitation practices. The food safety inspector uses a hypothesis testing framework to evaluate whether regulations are not being met. If he decides the restaurant is in gross violation, its license to serve food will be revoked.
What is a Type 1 Error in this context?
Answer:
P (Type I Error) = P (Revokes the license | Restaurant is not in gross violation)
Step-by-step explanation:
A type I error occurs when we reject a true null hypothesis (H₀). It is the probability of rejecting the null hypothesis when the null hypothesis is true.
The type I error is also known as the level of significance. It is denoted by α .
P (Type I Error) = P (Rejecting H₀ | H₀ is true) = α.
In this case, the food inspector uses a hypothesis testing framework to evaluate whether regulations are not being met.
He decides the the restaurant's license to serve food will be revoked if the restaurant is in gross violation.
So the hypothesis is defined as:
H₀: The restaurant is not in gross violation.
Hₐ: The restaurant is in gross violation.
The type I error will be committed by the food inspector if he concludes that the the restaurant is in gross violation and revokes their license, when in fact the restaurant is not in gross violation.
α = P (Revokes the license | Restaurant is not in gross violation)
A Type 1 Error in this context would be when the food safety inspector incorrectly identifies the restaurant as violating sanitation regulations when in reality, it was following all necessary practices. It’s the wrongful rejection of the null hypothesis.
Explanation:In statistical hypothesis testing, a Type 1 Error occurs when a true null hypothesis is rejected. In the context of the food safety inspector's investigation, the null hypothesis would likely be that the restaurant is abiding by all required sanitation practices. Therefore, a Type 1 Error would be if the food safety inspector concludes that the restaurant is in serious violation of sanitation regulations and revokes its license, but in actuality, the restaurant was not violating any regulations, i.e., the inspector incorrectly identified the restaurant as unclean and unhealthy.
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206, 254, 240, 203, 191, 208, 218, 235, 242, 237, 213, 222, 228, 201, 225, 186 whats the 25th percentile
Answer:
Q1 or the 25th percentile is 204.5
Step-by-step explanation:
Combine all data values in TI-84, excel, or other software and make a box and whisker plot. The Q1 is the first vertical line on the plot
Evaluate and simplify the expression when x=1 and y=2. 3(×+2y)-2x+10=?
Answer:
Step-by-step explanation:
Just for some extra closure lol the answer is indeed 23. :)
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 411 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 406 grams with a variance of 225. Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
0.0445937
Step-by-step explanation:
-Given that the sample statistic has a mean of 406 grams, standard deviation of sq root(225) and the null statistic is 411 grams.
-Assuming normal distribution, the test statistic is calculated as:
[tex]z=\frac{Sample \ statistic-Null \ statistic}{\sigma/\sqrt{n}}\\\\=\frac{406-411}{\sqrt{225/26}}\\\\=-1.6997[/tex]
-we then find the p-value of the test statistic from the z-tables:
P-value=0.0445937
Suppose that two balanced dice, a red die, and a green die, are rolled. Let Y denote the value of G - R where G represents the number on the green die and R represents the number on the red die. What are the possible values of the random variable Y?
Answer:
-5,-4,-3,-2,-1,0,1,2,3,4,5
Step-by-step explanation:
The sample space for the two balanced dice, a red die, and a green die is given below in the pair (G,R)
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
For each pair, Y=G-R is presented below:
0 -1 -2 -3 -4 -5
1 (2,2) (2,3) (2,4) (2,5) (2,6)
2 (3,2) (3,3) (3,4) (3,5) (3,6)
3 (4,2) (4,3) (4,4) (4,5) (4,6)
4 (5,2) (5,3) (5,4) (5,5) (5,6)
5 (6,2) (6,3) (6,4) (6,5) (6,6)
The first column and row is representative of the values which will be obtained throughout the table.
Therefore, the possible values of the random variable Y are:
-5,-4,-3,-2,-1,0,1,2,3,4,5
The possible values of Y are its sample space, and the values are 0, -1, -2, -3, -4, -5, 5, 4, 3, 2 and 1
The sample space of the green die is:
[tex]G= \{1,2,3,4,5,6\}[/tex]
The sample space of the red die is:
[tex]R= \{1,2,3,4,5,6\}[/tex]
When the numbers on both dice are combined, we have the following possible outcomes
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) , (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) , (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) , (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) , (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) , (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Subtract the second outcomes from the first, to get Y
(0) (-1) (-2) (-3) (-4) (-5) , (-1) (0) (-1) (-2) (-3) (-4) , (2) (1) (0) (-1) (-2) (-3) , (3) (2) (1) (0) (-1) (-2) , (4) (3) (2) (1) (0) (-1) , (5) (4) (3) (2) (1) (0)
List out the unique numbers:
(0) (-1) (-2) (-3) (-4) (-5) (5) (4) (3) (2) (1)
Hence, the possible values of Y are 0, -1, -2, -3, -4, -5, 5, 4, 3, 2 and 1
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An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. If the volume V of the box is a function of the length x of the side of the square cut from each corner, for what value of x is V the largest
The value of x that maximizes the volume V is x = 2 inches.
This means that by cutting 2-inch squares from each corner of the 24-inch square cardboard, you'll create an open box with the largest possible volume.
We have,
To solve this problem, we need to express the volume of the open box in terms of the length x of the side of the square cut from each corner, and then find the value of x that maximizes this volume.
Let's denote:
Side length of the original square cardboard = 24 inches
Side length of the cut square from each corner = x inches
The dimensions of the resulting box would be:
Length = (24 - 2x) inches (since we're removing x from both sides)
Width = (24 - 2x) inches (same as length)
Height = x inches
The volume V of the box can be calculated by multiplying these dimensions:
V = Length * Width * Height
V = (24 - 2x) * (24 - 2x) * x
Now, we'll simplify this expression for V:
V = x * (24 - 2x)²
To find the value of x that maximizes V, we need to find the critical points of the function and then analyze the behaviour around those points.
Take the derivative of V with respect to x:
dV/dx = 24x - 12x²
Set the derivative equal to zero and solve for x to find the critical points:
24x - 12x² = 0
12x(2 - x) = 0
This gives us two critical points: x = 0 and x = 2.
Now we need to determine which critical point corresponds to a maximum value of V.
To do this, we can analyze the second derivative of V with respect to x:
d²V/dx² = 24 - 24x
Evaluate the second derivative at each critical point:
For x = 0: d²V/dx² = 24 (positive value)
For x = 2: d²V/dx² = 24 - 24(2) = -24 (negative value)
Since the second derivative is negative at x = 2, it indicates that this critical point corresponds to a maximum.
Therefore,
The value of x that maximizes the volume V is x = 2 inches.
This means that by cutting 2-inch squares from each corner of the 24-inch square cardboard, you'll create an open box with the largest possible volume.
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To find the value of x that maximizes the volume of the box, we need to express the volume as a function of x. Then, we can take the derivative of the volume function with respect to x, set it equal to zero, and solve for x. Finally, we substitute the value of x back into the volume function to find the maximum volume.
Explanation:To find the value of x that maximizes the volume of the box, we need to express the volume as a function of x. Let's start by finding the dimensions of the box after cutting out the squares from each corner. Since the original square has sides of 24 inches, each side of the base of the box will be 24 - 2x inches. The height of the box will be x inches.
The volume of a box is given by the formula V = length x width x height. In this case, the length and width of the base of the box are the same, so we can simplify the formula to V = (24 - 2x)^2 * x.
To find the value of x that maximizes the volume, we can take the derivative of the volume function with respect to x, set it equal to zero, and solve for x. Once we find the value of x, we can substitute it back into the volume function to find the maximum volume.
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5 inches +?inches = 1 foot?
Answer:
7 inches hope this helps
Step-by-step explanation:
Answer:
7 inches
Step-by-step explanation:
12 inches is a foot
the second and third terms in the following fibonacci sequence are X and Y. write down algebraic expressions for the first, fourth and fifth terms
Answer:
(Y-X), X, Y, (X+Y), (X+Y)+Y, ...
Step-by-step explanation:
FIBONACHI SEQUENCE IS A SPECIAL MATHEMATICAL SEQUENCE IN W/C YOU HAVE TO ADD THE LAST AND THE NEXT TERM TO GET THE FOLLOWING TERM, IF SO.. TO GET THE LAST TERM, JUST REDUCE THE 3RD TERM TO YOUR 2ND TERM
TO GET THE 4RTH AMD 5TH TERM, JUST ADD THE FLLOWING CONSECITIVE TERM AS SHOWN IN THE ANSWER
A test of [tex]H_{0}[/tex]: μ = 20 versus [tex]H_{1}[/tex]: μ > 20 is performed using a significance level of ∝ = 0.05. The value of the test statistic is z = 1.47.
If the true value of μ is 25, does the test conclusion result in a Type I error, a Type II error, or a Correct decision?
Answer:
Type II error
Step-by-step explanation:
Type 1 error occurs when:
We reject a True Null Hypothesis
Type 2 error occurs when:
We fail to reject a wrong Null Hypothesis.
The given hypothesis are:
[tex]H_{o}: \mu=20\\\\ H_{a}:\mu>20[/tex]
Level of significance = α = 0.05
The calculated z test statistic = z = 1.47
In order to make a decision we first need to convert z = 1.47 to its equivalent p-value. From the z-table the p value for z score being greater than 1.47 comes out to be:
p-value = 0.0708
Since, p-value is greater than the level of significance, we fail to reject the Null Hypothesis.
It is given that the true value of μ is 25. If the true value of μ is 25, then the Null hypothesis was false. But from the test we performed, we failed to reject the Null Hypothesis.
Since, we failed to reject a False Null Hypothesis, the conclusion resulted in a Type II error.
What is the equation of the line that has a slope of -3 and goes through the point (3,-1)
Answer:
y = -3x+8
Step-by-step explanation:
We can use the slope intercept form of an equation
y = mx+b where m is the slope and b is the y intercept
y = -3x+b
Substitute the point into the equation
-1 = -3(3)+b
-1 = -9+b
Add 9 to each side
-1+9 = -9+9+b
8 =b
y = -3x+8
What is the arc measure of the minor arc BC in degrees?
285
(20y - 11)
(4y+6)
(7y - 7)
Answer:
Step-by-step explanation:
131
The radius of a cylinder is 3 cm and the height is 6 cm.
Find the Surface Area. (hint: Use the answer from the previous question.)
Answer
Step-by-step explanation:
A=2πrh+2πr2=2·π·3·6+2·π·32≈169.646
A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with millimeters. A random sample of 15 rings has a mean diameter of . Construct a 99% two-sided confidence interval on the true mean piston diameter and a 95% lower confidence bound on the true mean piston diameter. Round your answers to 3 decimal places. (a) Calculate the 99% two-sided confidence interval on the true mean piston diameter.
Complete Question:
A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with ? = 0.001 millimeters. A random sample of 15 rings has a mean diameter of \bar{X}= 74.106. Construct a 99% two-sided confidence interval on the true mean piston diameter and a 95% lower confidence bound on the true mean piston diameter.
(Round your answers to 3 decimal places.)
(Calculate the 99% two-sided confidence interval on the true mean piston diameter.
Answer:
99% true sided confidence Interval on the true mean Piston diameter = (74.105, 74.107)
Step-by-step explanation:
Check the attached file for the complete solution
Write an expression that gives the requested sum.
The sum of the first 20 terms of the geometric sequence with first term 6 and common ratio 3
s20 =
Step-by-step explanation:
To find the sum of first 20 terms,
a = 6, r = 3
By formula, [tex]S_{n} = \frac{a(r^{n}-1) }{r-1}[/tex]
substitute the values in the above formula, the equation becomes,
[tex]S_{20} = \frac{6(3^{20}-1) }{3-1}[/tex]
[tex]S_{20} = \frac{6(3^{20}-1) }{2}[/tex]
[tex]S_{20}[/tex] = [tex]{3(3^{20}-1) }[/tex]