Answer:
all real numbers expect 1.
Step-by-step explanation: This is a rational function. when we usually the find the domain of a rational function we would look at the bottom because you don't want the denomonatior to be zero because dividing by zero in math makes the range undefined. so we use the equation and set it up to zero to find the domain. 1-x=0 -x=-1, divide by -1 and we get 1. So x can be any numbers expect 1. Interval notation: (-∞,1)∪(1,+∞)
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<span>- No energy
- Happens across cell membrane
- From high to low concentration ("down the concentration gradient")</span>Controlled/Facilitated Diffusion- diffusion across a membrane through specific protein channels in the membrane, with no energy costOsmosis- Simple diffusion of waterActive Transport<span>- Requires energy
- Happens only at specific channels
- From low to high concentration ("against the concentration gradient")</span>Concentration Gradient- difference in concentration of a substance between one area and anotherGradient- Different or unevenSemi-Permeability<span>- 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 )</span>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<span>- hypotonic
- isotonic
- hypertonic</span>Hypotonic<span>- 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]</span>Isotonic<span>- concentration of dissolved substances is EQUAL INSIDE and OUTSIDE the cell
- H2O diffuses INTO the cell and OUT of the cell at the same rate</span>Hypertonic<span>- 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]</span>Gene- a length of DNA at a specific location on a chromosome that controls a specific heritable characterisicStandard Deviation (SD)<span>- 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)</span>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<span>- the brain and control center of the cell:
contains DNA
controls all cellular functions in the cell</span>Nucleolus- small body found in the nucleus of eukaryotic cells where ribosomal RNA is synthesisedCytoskeleton<span>- in the structural support; </span>
Answer:
When we have a rational function like:
The domain will be the set of all real numbers, such that the denominator is different than zero.
So the first step is to find the values of x such that the denominator (x^2 + 3) is equal to zero.
Then we need to solve:
x^2 + 3 = 0
x^2 = -3
x = √(-3)
This is the square root of a negative number, then this is a complex number.
This means that there is no real number such that x^2 + 3 is equal to zero, then if x can only be a real number, we will never have the denominator equal to zero, so the domain will be the set of all real numbers.
D: x ∈ R.
b) we want to find two different numbers x such that:
r(x) = 1/4
Then we need to solve:
We can multiply both sides by (x^2 + 3)
Now we can multiply both sides by 4:
Now we only need to solve the quadratic equation:
x^2 + 3 - 4*x - 4 = 0
x^2 - 4*x - 1 = 0
We can use the Bhaskara's formula to solve this, remember that for an equation like:
a*x^2 + b*x + c = 0
the solutions are:
here we have:
a = 1
b = -4
c = -1
Then in this case the solutions are:
x = (4 + 4.47)/2 = 4.235
x = (4 - 4.47)/2 = -0.235
Answer:
The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).
Step-by-step explanation:
The formula for estimating the population proportion by a confidence interval is given by:
Where:
is the sample's proportion of success, which in this case is the people that regularly lie during surveys,
is the critical value needed to find the tails of distribution related to the confidence level,
is the sample's size.
<u>First</u> we compute the value:
<u>Next</u> we find the z-score at any z-distribution table or app (in this case i've used StatKey):
Now we can replace in the formula with the obtained values to compute the confidence interval:
