The logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x is-
[tex]g(x)[/tex] = ㏑[tex](x) / 0.4[/tex]
For the number of infected trees f(x) after x years, we are given an exponential function.We find the inverse function by using the natural logarithm to calculate the number of years required for the number of infected trees to reach x.The equation can be written as-
[tex]y = f(x) = e x^{0.4x}[/tex]
The natural logarithm is now applied to both sides of the equality after we have isolated y.
[tex]0.4y = ln x[/tex][tex]y = ln x / 0.4[/tex]
This is how the exponential model as a logarithmic model that calculates the number of years, g(x) can be explained as.
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true or false: if and are mutually exclusive and exhaustive with and , and is an event in , then
If A1 and A2, are mutually exclusive and exhaustive with P(A1)>0 and P(A2) >0, and B is an event in S. then P(B) = P(A1 ∩B) + P(A2∩ B). [TRUE]
IntersectionThe sets A and B are the sets of all objects that are members of set A and members of set B. In written notation form:
A ∩ B = {x | x ∈ A and x ∈ B}
Here's how to determine the separation of two sets:
One set which is another subset if A ⊆ B then A ∩ B = A and vice versa.
The sets are equal if A = B, then A ∩ B = (A = B).
Sets are mutually exclusive if A // B, then A ∩ B = … and vice versa.
The sets are not mutually exclusive.
UnionThe union of sets A and B is the set of all objects that are members of set A or members of set B. In written notation form:
A ∪ B = {x | x ∈ A or x ∈ B}
Here's how to determine the union of two sets:
A set that is a set in other parts if A ⊆ B, then A ∪ B = B and vice versa.
The set is equal if A = B then A ∪ B = (A = B).
Sets are mutually exclusive if A // B, then A ∪ B = {x | x ∈ A or x ∈ B} and vice versa.
The sets are not mutually exclusive if A ⊃⊂ B, then A ∪ B = {x | x ∈ A, x ∈ B or x ∈ (A ∩ B)}.
Your question is incomplete but most probably your full question was:
If A, and A, are mutually exclusive and exhaustive with P(A)>and P(A2) >0, and B is an event in s. then P(B) = P(ALB) + P(ANB). True False
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please fill in the "if ___" part!
The expression can be simplified as follows:
2(x - y)/[y(x + y)]
The condition for the expression is given as follows:
x ≠ y, y ≠ 0.
How to simplify the expression?The expression for this problem is defined as follows:
[(x - y)²]/(2xy + 6y) x (4x + 12)/(x² - y²)
The factors of the expression can be simplified as follows:
2xy + 6y = 2y(x + 3).4x + 12 = 4(x + 3).x² - y² = (x + y)(x - y).The terms that can be simplified are given as follows:
4(x + 3)/2y(x + 3) = 2/y.(x - y)²/[(x + y)(x - y)] = (x - y)/(x + y).Hence the product is given as follows:
(x - y)/(x + y) x 2/y
2(x - y)/[y(x + y)]
As the expression is a fraction, the denominator cannot be zero, hence the conditions are given as follows:
x ≠ y, y ≠ 0.
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janet gross salary is 24000 per month her tax free allowances are shown in the table below national insurance 2 1\2 ,personal allowances is 20000 what is her total tax allowances for the year
Janet's total tax allowances for the year are $27,200.
How are the tax allowances determined?The first step is to convert the monthly gross salary to the annual gross salary by multiplying it by 12.
The insurance allowance is computed by applying the rate to the annual gross salary.
The personal and insurance allowances are added to determine the total tax allowances.
Generally, tax allowances reduce the taxpayer's taxable income.
Gross salary per month = $24,000
Annual gross salary = $288,000 ($24,000 x 12)
Personal allowances per year = $20,000
National insurance = 2¹/₂%
= $7,200 ($288,000 x 2¹/₂%)
Total allowances for the year = $27,200 ($20,000 + $7,200)
Thus, Janet is entitled to a total tax allowance of $27,200 for the year.
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On parallelogram PQRS, P is located at (-1, 6) and S is located at (-7,-3). What is the
slope of segment QR?
P Р
R
rimblr an impronar fraction
How do I solve this?
According to the parallelogram, the slope of the segment QR is 3/2
In math the term called parallelogram is a closed quadrilateral with parallel and congruent opposite sides is referred to as a parallelogram and the opposite pairs of sides have the same slope and the sum of two adjacent angles is 180 degrees.
Here we have know that values of P is located at (-1, 6) and S is located at (-7,-3). Then the slope of QR is calculated by using the the slope formula for a line segment passing through two points,
It can be calculated as,
=> m = (-3 - 6) / (-7 - (-1)
When we simplify this one then we get,
=> m = -9/-6
=> m = 3/2
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if PQ+PR=72 cm, then what is the value of sinR? (look at the file)
The exact value of the sine of angle R is equal to 1 / 2.
How to determine the exact value of a trigonometric function
In this problem we find the representation of a right triangle, where two side lengths are known and the exact value of a trigonometric function must be found. First, determine the length of side PR:
PR = 72 cm - PQ
PR = 72 cm - 24 cm
PR = 48 cm
Second, determine the length of side PQ by Pythagorean theorem:
RQ = √[PR² - PQ²]
RQ = √[(48 cm)² - (24 cm)²]
RQ = 24√3 cm
Third, determine the exact value of a trigonometric function of angle R by definition of sine:
sin R = PQ / PR
sin R = (24 cm) / (48 cm)
sin R = 1 / 2
Fourth, determine the exact value of a trigonometric function of angle R by definition of cosine:
cos R = RQ / PR
cos R = (24√3 cm) / (48 cm)
cos R = √3 / 2
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PLEASE HELP!!!!!!! PHOTO BELOW
State the equation of the graphed function.
The equation of the graphed function for this problem is given as follows:
y = x³ - 6x² - 7x - 6.
How to obtain the function?The function for this problem is obtained using the Factor Theorem, as a product of the linear factors of the function.
The zeros of the function are given as follows:
x = 1.x = 2.x = 3.Hence the linear factors are given as follows:
(x - 1).(x - 2).(x - 3).Then the function is given as follows:
y = a(x - 1)(x - 2)(x - 3).
In which a is the leading coefficient.
The y-intercept is at y = -6, hence the leading coefficient is given as follows:
-6a = -6
a = 1.
Hence the function is:
y = (x² - 3x + 2)(x - 3)
y = x³ - 6x² - 7x - 6.
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Six friends are going to run a relay race that is 3.12 miles long. Each friend will run an equal distance. How many miles will each friend run? (I WILL GIVE BRAINLIEST!!)
In a relay race each friend run a distance of 0.52 miles.
How to find distance?The distance of the race divided by the runners' times will give you their average velocities.
We are given that
Total distance covered in a race = 3.12 miles
Total number of persons = 6
Each person runs equal parts of the race.
We have to find the miles run by each person.
To find the distance covered by each person we will divide the total distance by total number of persons who took part in a race.
Each person runs = Total distance/ Total number of persons
Each person runs= 3.12 / 6 miles
Each person runs = 0.52 miles
Hence, each person runs 0.52 miles.
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Find the quotient of 6y^4+10y^3-8y^2divided by 2y.
The quotient of 6y^4 + 10y³ - 8y² by 2y is given as follows:
6y³ + 10y² - 4y.
How to obtain the quotient?The dividend is given as follows:
6y^4 + 10y³ - 8y²
The common factors are given as follows:
Constants 6, 10 and -8: 2, which is the greatest common factor of the three numbers.Exponents 2, 3 and 4: 2, which is the lowest exponent.Hence the dividend can be simplified as follows:
2y²(6y² + 10y - 4).
Simplifying by 2y, the result of the quotient is given as follows:
y(6y² + 10y - 4) = 6y³ + 10y² - 4y.
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A girl of height 0.9 m is walking away from the base of a lamp-post and covered 4.8 m. If the lamp is 3.6 m above the ground, find the length of her shadow.
If the lamp is 3.6 m above the ground, the length of her shadow is 1.2 m.
What is proportionality?In algebra proportionality is equality between two ratios. In the mathematical expression a/b = c/d, a and b are in the same proportion as c and d.
Height of the girl = 0.9 m.
Height of the lamp = 3.6 m.
Distance between the lamp and the girl = 4.8 m.
Let the length of her shadow = x m.
From proportionality relation:
3.6 : 4.8 = 0.9 : x
3.6/4.8 = 0.9/x
3.6x = 4.8 × 0.9
x = (4.8 × 0.9) ÷ 3.6
x = 1.2
Hence, the length of her shadow is 1.2 m.
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A company manufactures and sells shirts the daily profit. The company makes depends on how many shirts they sell the profit in dollars when the company sells X shirts can be found using the function F (X)equals 6X -90 find the interpret the given function values and determine inappropriate domain for the function f(-9)
profit of
of the problem.
=
f(27)
profit of
of the problem.
=
f(17.5) =
profit of
of the problem.
meaning if the company sells |
dollars. This interpretation
meaning if the company sells
dollars. This interpretation
, meaning if the company sells
dollars. This interpretation
shirts, they would make a
in the context
shirts, they would make a
in the context
shirts, they would make a
in the context
The increase in earnings brought on by producing one extra unit is known as the marginal profit. The proper domain for functions is the integers (0, 1, 2, ...).
Explain about the Marginal profit?By dividing marginal revenue by marginal cost, one can compute marginal profit. Because it can help determine whether to raise or lower the level of output, marginal profit analysis is useful.
Any quantity of output below the one at which marginal profit equals zero has a positive marginal profit, meaning that profit can be increased by producing more of that quantity. Conversely, any quantity of output above the one at which marginal profit equals zero has a negative marginal profit, meaning that profit can be increased by producing less of that quantity.
A company that manufactures and sells shirts. Daily profit of...
A company that manufactures and sells shirts. The daily profit the company makes depends on the number of shirts sold. The profit in dollars if a company sells x shirts can be found using the function f(x)=7x-40. Locates and interprets given function values to determine the appropriate domain for the function.
f(-10) = -110, which means that if the company sells -10 shirts, it will make a profit of -$110. This interpretation makes no sense in the context of the problem.
f(10) = 26.5, so if the company sells 9.5 of his shirts, he makes a profit of $26.5. This interpretation makes no sense in the context of the problem
f(9.5) = 26.5, so if the company sells 9.5 shirts, it makes a profit of $26.5. This interpretation makes no sense in the context of the problem.
Therefore, based on the above observations, it is clear that the proper domain for functions is the integers (0, 1, 2, ...).
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Square root of 50 in simplist radical form
Answer:
The square root of 50 can be simplified to the radical form of 5*sqrt(2)
Step-by-step explanation:
To simplify the square root of 50, we factor the number 50, which is 50 = 510 = 552. The square root of any number that is a perfect square, such as 55, is equal to the number inside the square root, which is 5 in this case. The square root of any number that is not a perfect square, such as 2, remains under the radical sign.
Therefore, the simplified radical form of the square root of 50 is √50 = 5√2.
The square root of 50 in simplest radical form is 5√2.
To find the square root of 50 in simplest radical form, we need to determine if there are any perfect square factors in 50 that can be taken outside the square root symbol.
The prime factorization of 50 is 2 × 5².
We can see that 5² is a perfect square factor of 50.
Therefore, we can rewrite the square root of 50 as the square root of (2 × 5²).
Using the property of square roots, we can split the square root of a product into the product of the square roots of each factor:
√(2 × 5²) = √2 × √(5²)
The square root of 5² simplifies to 5, so we have:
√(2 × 5²) = √2 × 5
Therefore, the square root of 50 in simplest radical form is 5√2.
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the half-life of radon (rn-222) is 3.82 days. how much (what fraction) of a sample remains after 11.46 days?
Radon-222 was initially present in a sample of 3.82 mg. Only 0.375 mg of the radon-222 in the sample were still present after 11.46 days, after which three half-lives had gone.
As per the data given in the above question are as bellow,
A material has a half-life when it takes a particular length of time for half of it to disappear or change.
11.46 days have 3 half lives because 11.46 x 3.82 Equals 3.
We thus split the 3 mg sample in half three times.
3 ÷ 2 = 1.5
1.5 ÷ 2 = 0.75
0.75 ÷ 2 = 0.375
After 11.46 days, there will only be 0.375mg of radon-222 left.
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Which is a correct solution for the following system of Inequalities
Answer:
I think the answer is C
-3,-2
Find the solution to the system of equations.
Answer: (-5, -2)
Step-by-step explanation:
We will substitute the first equation into the second and then solve for x. Then we will substitute x into the equation and solve for y.
Given:
5x + 3y = -31
Substitue:
5x + 3(x + 3) = -31
Distribute:
5x + 3x + 9 = -31
Combine like terms:
8x + 9 = -31
Subtract 9 from both sides of the equation:
8x = -40
Divide both sides by 8:
x = -5
Given:
y = x + 3
Substitute x into the equation and solve for y.
y = (-5) + 3
Combine like terms:
y = -2
We can also graph it. The point of intersection is the solution, see below.
Karis ran 3 and 2/3rds miles on Monday. Benita ran 1/2 of the distance that Karis ran. How far did Benita run?
The required distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.
This problem is related to the chapter fractions. The relation between the distances travelled by both the people is given, so that we can calculate the actual distance travelled by the second person.
Karis ran 3 2/3 miles on Monday.
It is said that Benita ran half of the distance ran by Karis.
So, the distance ran by Benita would be,
⇒ 3 2/3 × 1/2
⇒ 11/3 × 1/2
⇒ 11/6 miles
Thus, the distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.
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joan earns 8% commission on her sales this month Joan had $6000 in sales what was her commission
The amount of commission that Joan earns this month on sales will be $480.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Joan earns an 8% commission on her sales this month Joan had $6000 in sales.
Let 'x' be the commission. Then the equation is given as,
x / $6,000 = 0.08
x = 0.08 · $6,000
x = $480
The amount of commission that Joan earns this month on sales will be $480.
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Please help just number 10 and 11 thank you.
Answer: 10. 3
Step-by-step explanation: 4x3=12, ad 3x3 is 9 so all the sides of the triangle are multiplied by 3
find the soulotion to this in eqaulity a
> –3
A graph of the solution to this inequality a > -3 is shown on the number line attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).In this exercise, we would use an online graphing calculator to plot the given inequality a > -3 as shown on the number line (graph) attached below.
In conclusion, the circle on the number line (graph) is open because of the greater than (>) symbol and it increases to the right of the number line.
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Complete Question:
Find the solution to this inequality a > –3.
There are 25 pieces of candy in a bowl, and 15 of them are chocolate. What percentage of pieces of candy in the bowl are chocolate?
60% of the pieces of candy in the bowl are chocolate.
(15/25)*100 = 60%
A town has a population of 20000 and grows at 5% every year. To the nearest tenth of a year, how long will it be until the population will reach 41600?
If the town has a population of 20000 and grows at 5% every year , then the time required for the population to reach 41600 is 15 years .
To find out how long it will take for the town's population to reach 41600, we can use the formula :
⇒ A = P(1 + r)ⁿ
Where:
A = final population of town , P = initial population o town
r = percent increase (as a decimal)
let n = number of years for population to reach 41600 .
We know the final population is 41600, the initial population is 20000, the percent increase is 5% = 0.05 and we have to solve for n.
Substituting the values ,
we get ;
⇒ 41600 = 20000(1 + 0.05)ⁿ ;
⇒ 41600 = 20000(1.05)ⁿ ;
⇒ 41600/20000 = (1.05)ⁿ ;
taking "log" on both sides ,
we get ;
⇒ log(41600/20000) = n × log(1.05) ;
⇒ n = log(41600/20000)/log(1.05) ;
⇒ n = 15.0105 ≈ 15
Therefore , it will take approximately 15 years for the town's population to reach 41600, to the nearest tenth of a year.
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Evaluate the following: −3 − (−8)
Answer: The answer is 5
Step-by-step explanation:
-3-(-8)
-3+8
5
Answer: 5
Step-by-step explanation:
First the negative 3 adds to 8. Because if you see “- -“ it will be +. So we just have -3 + 8 = 5
Calculator
During a construction project, heavy rain filled construction cones with water. The diameter of a cone is 12 in. and the height
What is the volume of the water that filled one cone?
nter your answer as a decimal in the box. Use 3.14 for pi.
in³
1 2
3
A
4
5
6
7 8 9
10
The volume of One cone held 1.1017.36 inches3 of water when it was full.
A method for determining a cone's volume?A cone's volume is determined using the following formula:
V = 1/3πr²h
R is the radius, and H is the height.
the aforementioned conditions
A cone's volume is determined using the following ,
V = 1/3πr²h
R is the radius, and H is the height.
the aforementioned conditions
r = 12/2 = 6in
h =27in
Discover the volume V = 1/3(3.14)(6)2*27
V = 1.1017.36
In light of this, one cone held 1.1017.36 inches of water.
One cone held 1.1017.36 inches of water.
The complete question is,
Construction cones were soaked with water while a project was underway due to a strong downpour. A cone has a 12 inch diameter and a 27 inch height.
How much water was used to fill each cone?
Put a decimal in the box for your response. Pi is equal to 3.14; in3
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12. Estimate the average rate of change of p between peak, p(8), and closing, p(14). What is
the meaning of the rate of change in the context of this problem? Show all work.
The meaning of the rate of change in the context of this problem is 4/7.
What is the change's speed?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one thing by the equal amount of change in another.The term "rate of change" (ROC) describes the rate at which something changes over time. Thus, it is not the amount of individual changes themselves but rather the acceleration or slowdown of changes (i.e., the pace). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.The formula R = D/T may often be used to tackle rate-of-change problems.P-8 / p(14)
8p / p(14) =4/7
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Find x please help asap
Answer:
68888jours 9999999888
Ashley invested $59,000 in an account paying an interest rate of 3 (1/8)% compounded
daily. Fwam invested $59,000 in an account paying an interest rate of 2 (3/4)%
compounded annually. After 15 years, how much more money would Ashley have in
her account than Fwam, to the nearest dollar?
Answer:
5650
Step-by-step explanation:
3 (1/8)% =3.125% but compound daily = 3.125% /365 = 0.00856%
so everyday the money grows at 1.00856%, so compound 365 times, it'll become 1.00856%^365 =3.1742% annually equivalent.
so now you can compare the 2 - apples to apples.
so 3.1742%^15years * 59000 = $94,279.80
2.75%^15years * 59000 = $ $88,629.74
diff is 5650$
Kate is firing off her homemade rockets for a project in physics class. The
maximum height of any of her rockets can be represented by the equation
h-701-162, where h is the height (in feet) of the rocket after t seconds.
The domain and range for the function for the maximum height of the rockets Kate fires is; h = 70·t - 16·t² are;
Domain; 0 ≤ t ≤ 4.375
Range; 0 ≤ h ≤ 39.06
What is a mathematical function?A function is a rule that defines the relationship between input variables and output variables, such that the each value from the set of input variables are assigned to exactly on variable from the set of output variables.
The possible specified function in the question is; h = 70·t - 16·t², and the possible required details is the domain and range that best represent the situation.
The domain of the above function is the set of possible input (t) values, which is found by the time it takes the rocket to land after flight as follows;
At ground level, h = 0, therefore;
h = 70·t - 16·t² = 0
(70 - 16·t)·t = 0
A possible solution is therefore, t = 0
The other solution is found as follows;
(70 - 16·t) = 0
70 = 16·t
16·t = 70
t = 70/16 = 4.375
The other solution or time at which the rocket is at ground level is t = 4.375
The domain is therefore; 0 ≤ t ≤ 4.375The range is the set of possible h values, which is obtained as follows;
The maximum point of the quadratic function, f(x) = a·x² + b·x + c, is the point, x = -b/2·a. Therefore, comparison between the function, f(x) = a·x² + b·x + c, and h = 70·t - 16·t², we get;
a = -16
b = 70
c = 0
The maximum height reached, therefore is obtained at the point, at which; t = -70/(2 × (-16)) = 2.1875
The maximum height, [tex]h_{max}[/tex], is therefore;
[tex]h_{max}[/tex] = 70 × 2.1875 - 16 × 2.1875² = 76.5625
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19. In the energy category, Khalil scored low on the intuitive function. Since Khalil has low intuition, he must have
scored high on the function, which involves looking for the facts, focusing on specifics, taking realistic
approaches to problem-solving, planning for the immediate, and embracing practical solutions.
A. observant
B. turbulent
C. judging
D. prospecting
If in the energy category, Khalil scored low on the intuitive function in which he must he have scored high on the function, which involves looking for the facts, focusing on specifics, taking realistic. This is an example of : A. observant
What is Observant?To be observant can be defined as the way in which a person tend to watch others or when a person observe the event happening around him/her .
This scenario is an example of observant based on the fact that this person watch the event happening in Khalil life and this was done by carefully observing Khali and things that happen around Khali.
Therefore the correct option is A.
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What number line models the expression 1/8-(-3/4)
A number line that models the expression 1/8 - (-3/4) is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Next, we would evaluate and add the given numbers together as follows:
Number = 1/8 - (-3/4)
Number = 1/8 + 3/4
Number = 7/8
In conclusion, you would start at 1/8 on the number line and move 3/4 places to the right.
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A measure computed from the entire population is called
a. a statistic.
b. a qualitative value.
c. a mean.
d. a parameter.
A measure computed from the entire population is called a parameter. Option D is the correct answer.
A parameter is a numerical characteristic of the population, and it is usually estimated from a sample of the population. Parameters are usually unknown and are estimated using a variety of mathematical methods.
Examples of parameters include the population means, median, and standard deviation. Parameters can also be used to describe the characteristics of a population, such as the percentage of people who are a certain color, race, or gender.
Parameters are usually reported in summary form, such as the mean or median of a population. In contrast, a statistic is a measure computed from a sample and is not representative of the entire population. Statistics are used to make estimates and predictions about a population and are usually reported in the form of a confidence interval.
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in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, mark has scored 90, 86, and 85 on the first three. what range of scores on the fourth test will give mark a c for the semester (an average between 70 and 79, inclusive)? assume that all test scores have a non-negative value.
Answer:
b/w 19 & 55
Step-by-step explanation:
average of four equally weighted 100-point tests,
mark has scored 90, 86, and 85 on the first three.
C average = 70 and 79
90+86+85+x = 4*70 = 280, so x=19
90+86+85+x = 4*79 = 316, so x=55