Among all rectangles that have a perimeter of 188, find the dimensions of the one whose area is largest.

The diameters of bearings used in an aircraft landing gear assembly have a standard deviation of ???? = 0.0020 cm. A random samp

vovikov84 [41]

Answer:

(a) We conclude after testing that mean diameter is 8.2500 cm.

(b) P-value of test = 2 x 0.0005% = 1 x $10^{-5}$ .

(c) 95% confidence interval on the mean diameter = [8.2525 , 8.2545]

Step-by-step explanation:

We are given with the population standard deviation, $\sigma$ = 0.0020 cm

Sample Mean, Xbar = 8.2535 cm and Sample size, n = 15

(a) Let Null Hypothesis, $H_0$ : Mean Diameter, $\mu$ = 8.2500 cm

Alternate Hypothesis, $H_1$ : Mean Diameter, $\mu$ $\neq$ 8.2500 cm{Given two sided}

So, Test Statistics for testing this hypothesis is given by;

$\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ follows Standard Normal distribution

After putting each value, Test Statistics = $\frac{8.2535-8.2500}{\frac{0.0020}{\sqrt{15} } }$ = 6.778

Now we are given with the level of significance of 5% and at this level of significance our z score has a value of 1.96 as it is two sided alternative.

Since our test statistics does not lie in the rejection region{value smaller than 1.96} as 6.778>1.96 so we have sufficient evidence to accept null hypothesis and conclude that the mean diameter is 8.2500 cm.

(b) P-value is the exact % where test statistics lie.

For calculating P-value , our test statistics has a value of 6.778

So, P(Z > 6.778) = Since in the Z table the highest value for test statistics is given as 4.4172 and our test statistics has value higher than this so we conclude that P - value is smaller than 2 x 0.0005% { Here 2 is multiplied with the % value of 4.4172 because of two sided alternative hypothesis}

Hence P-value of test = 2 x 0.0005% = 1 x $10^{-5}$ .

(c) For constructing Two-sided confidence interval we know that:

Probability(-1.96 < N(0,1) < 1.96) = 0.95 { This indicates that at 5% level of significance our Z score will lie between area of -1.96 to 1.96.

P(-1.96 < $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96\frac{\sigma}{\sqrt{n} }$ < $Xbar - \mu$ < $1.96\frac{\sigma}{\sqrt{n} }$ ) = 0.95

P( $-Xbar-1.96\frac{\sigma}{\sqrt{n} }$ < $-\mu$ < $1.96\frac{\sigma}{\sqrt{n} }-Xbar$ ) = 0.95

P( $Xbar-1.96\frac{\sigma}{\sqrt{n} }$ < $\mu$ < $Xbar+1.96\frac{\sigma}{\sqrt{n} }$ ) = 0.95

So, 95% confidence interval for $\mu$ = [ $Xbar-1.96\frac{\sigma}{\sqrt{n} }$ , $Xbar+1.96\frac{\sigma}{\sqrt{n} }$ ]

= [ $8.2535-1.96\frac{0.0020}{\sqrt{15} }$ , $8.2535+1.96\frac{0.0020}{\sqrt{15} }$ ]

= [8.2525 , 8.2545]

Here $\mu$ = mean diameter.

Therefore, 95% two-sided confidence interval on the mean diameter

= [8.2525 , 8.2545] .

6 0

2 years ago

Read 2 more answers

A photographer offers a photo shoot for a $85 flat fee. Customers may purchase prints for $5 per sheet. How many sheets can a cu

professor190 [17]

To find the answer you must first make the equation which is

(5x)+85=150

subtract 85 from 150

(5x)=65

now divide 65 by 5

resulting in the answer

X=13

To check this

(5 x 13)+85=160

(5x)+85≤150

4 0

3 years ago

How do I write an equation with 5he restrictions x does not equal 14, x does not equal 2 and x does not equal 0???

Oxana [17]

Diffusion- The process by which molecules spread themselves out evenly in a given area. This happens by natural molecular movement.How do particles move across membranes?- by osmosis, active transport, simple diffusion and facilitated diffusionSimple/Passive Diffusion- No energy
- Happens across cell membrane
- From high to low concentration ("down the concentration gradient")Controlled/Facilitated Diffusion- diffusion across a membrane through specific protein channels in the membrane, with no energy costOsmosis- Simple diffusion of waterActive Transport- Requires energy
- Happens only at specific channels
- From low to high concentration ("against the concentration gradient")Concentration Gradient- difference in concentration of a substance between one area and anotherGradient- Different or unevenSemi-Permeability- a type of biological membrane that will allow certain molecules or ions to pass through it by diffusion
(- maintain a balance of water in the cell
- ability to differentiate materials that are needed and those that are not needed in the cell, keeping the cell healthy
- ability to control the amount and kind of substances through the cell membranes )What must we understand? (homeostasis- cells)- Cells constantly change concentrations to their benefit and to maintain stable internal conditions.Endocytosis- the movement of bulk liquids or solids into a cell, by the indentation of the plasma membrane to form vesicles containing the substance; active process requiring ATPEndo--means 'inside'Exocytosis- the movement of bulk liquids or solids out of a cell by fusion of vesicles containing the substance with the plasma membrane; active process requiring ATPExo--means 'outside'How many types of Endocytosis are there?- 3 types of endocytosis-- phagocytosis, pinocytosis and receptor mediated endocytosisPhagocytosis- In endocytosis, if the substances being taken in are particles, such as bacteria, then process is called phagocytosisPinocytosis- In endocytosis, if the substances are in solution, such as the end products of digestion, then the process is called pinocytosisReceptor-Mediated Endocytosis- is an endocytotic mechanism in which specific molecules are ingested into the cell.Water Potential- the tendency of water molecules to move from an area of higher concentration to an area of lower concentrationPlasmolysis- Shrinkage of protoplasm away from the cell wall of a plant or bacterium due to water loss from osmosis, therefore resulting in gaps between the cell wall and cell membrane.Protoplasm- the fluid living content of the cell-- composed mainly of nucleic acids, proteins, lipids, carbohydratesTypes of Solutions- hypotonic
- isotonic
- hypertonicHypotonic- concentration of dissolved substances is greater INSIDE the cell
- through osmosis, H2O diffuses INTO the cell
- hippos get fat, so will the cell
[a less concentrated solution (one with a more negative water potential) than the cell solution]Isotonic- concentration of dissolved substances is EQUAL INSIDE and OUTSIDE the cell
- H2O diffuses INTO the cell and OUT of the cell at the same rateHypertonic- concentration of dissolved substances is greater OUTSIDE the cell
- through osmosis, H2O diffuses OUT of the cell
- this cell will shrink
[a more concentrated solution (one with a less negative water potential) than the cell solution]Gene- a length of DNA at a specific location on a chromosome that controls a specific heritable characterisicStandard Deviation (SD)- measures the spread of the data in a set by describing how far the numbers are from the mean
(- a valuable method of analysis
- it takes into account all values & it's not affected by extreme values
- gives you a hint on how accurate the data is- if the method is good- if you can draw a valid conclusion)Equation for Standard Deviationn= # of data pointsHow do you find the mean?- in a data set, add all the values together then divide by the total number of values in the setHigh SD- the data is widely spread (less reliable)Low SD- the data is clustered closely around the mean (more reliable)Cell Membrane- controls what comes in and out of the cellCell Wall- composed of cellulose and other carbohydrates, giving plant cells further support and a more rigid structure than animal cellsNucleus- the brain and control center of the cell:
contains DNA
controls all cellular functions in the cellNucleolus- small body found in the nucleus of eukaryotic cells where ribosomal RNA is synthesisedCytoskeleton- in the structural support;

3 0

2 years ago

Evaluate the function for the given value: f(x)=2x (to the power of 2) -5x-17, find f(-3)

lions [1.4K]

Answer:

f(-3) = 16

Step-by-step explanation:

You substitute -3 to x.

f(-3) = 2(-3)² - 5(-3) - 17

f(-3) = 16.

As for the coordinates, the coordinates plotted in the graph above are (1,-1) and (2,-2).

7 0

2 years ago

Read 2 more answers

Please help if possible :)

n200080 [17]

9514 1404 393

Answer:

(a) no

(b) no

Step-by-step explanation:

The two questions are asking essentially the same thing. There is nothing that indicates DC ≅ DB or that AC ≅ AB. One (both) of these conditions is (are) required for ΔBAC to be isosceles, so that AD is both a perpendicular bisector of BC and a bisector of angle BAC.

There is not enough information to answer either question affirmatively.

8 0

2 years ago