Answer: For all three functions, the direction of fastest increase at the point (1, 1, 1) is the direction of the gradient vector of the function at that point.
For function (a), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[2/x³, 2y, 22] = [2, 2, 22].
The direction of this gradient vector is given by the direction in which each of its components is increasing the most rapidly. In this case, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
For function (b), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[4y + 4z, 4x + 4z, 4x + 4y] = [4, 4, 4].
Again, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
For function (c), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[2x, 2y, 2z] = [2, 2, 2].
As before, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
Therefore, for all three functions, the direction of fastest increase at (1, 1, 1) is the direction of the positive x, y, and z axes.
Step-by-step explanation:
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Four hemispheres are present in the shaded area. One large hemisphere and three smaller hemispheres each have a radius of 18 cm.
What is the perimeter of the hemisphere's formula?Consequently, the hemisphere's total surface area is 3(pi)R2. A semicircle has a curved line and a straight line that are both equal to the circle's diameter. The curving line is 2R in length while the straight line is (pi)R in length. So, 2R + (pi)R is the semicircle's total perimeter.
The shaded regions' area is calculated as follows:
initially, area of a hemisphere = 2r2 square units
the area of three small hemispheres
(2*3.14*6 r).3 = 226.08 cm2
Area of the larger hemisphere
2*3.14*18^2 = 2034.72cm^2
Total area of the shaded regions = 226.08 + 2034.72 = 2260.8cm^2
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Find the value of x that makes the equation true 7x=70
x=10
x=9
x=0
x=11
Answer: x = 10
Step-by-step explanation:
1. To find x, you need x to be by itself and the only way for it be like that in this situation is by dividing both sides by 7.
2. 7 divided by 7 cancels out and 70 divided by 7 = 10. This means x = 10.
Answer:
10
Step-by-step explanation:
since we have 7x=70
the multiply goes and becomes divide we get 70/7
and by dividing it we get the ans 10
Which of the following can you determine, when you use deduction and start
from a given set of rules and conditions?
A. What may be true
B. What must be true
C. None of these
D. What may be false
k
The correct option is B.Because when i use deduction and start from a given set of rules and condition is what must be true.If you analyze it to be true then it must be definitely true.
What is deduction in math?Deduction is a conclusion from something known or assumed. This is the type of reasoning we use in almost every step in a mathematical argument. For example to solve 2x = 6 for x we divide both sides by 2 to get 2x/2 = 6/2 or x = 3.
What is deduction rule in logic?In mathematical logic a deduction theorem is that justifies doing conditional proofs—to prove an implication A → B, assume A as an hypothesis and then proceed to derive B—in systems that do not have an explicit inference rule for this.
Now we able to know
Deduction is a term used to known as validated principle.This is when you analyze points through logic from a given set of rules and condition.
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In in1965 the population of country A wa 2,714,000. In 2015 the population wa 3,663,900. Determine the percentage increae in the population from 1965 to 2015
The percentage increase in the population from 1965 to 2015 is 35 %.
To calculate the population growth rate (PG), take the difference (subtraction) between the original population and the population at time point 1, divide by the original population, and multiply by 100. The population growth rate (PGR) for that period (10 years) was 12%.
Given:
In the year 1965, the population of country A was 2714000.
In the year 2015, the population of country A was 3663900.
Percentage increase in population 50 years
= [tex]\frac{(3663900-2714000)}{2714000}[/tex] × 100
= 35 %
Thus, the percentage increase in the population from 1965 to 2015 , i.e, 50 years is 35%.
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How to find the side of a triangle given two angles and one side?
If you know two angles and one side of a triangle, you can use the Law of Cosines to find the length of the other two sides.
The Law of Cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite to those sides, the following formula holds:
c² = a² + b² - 2ab cos(C)
Where C is the angle opposite to side c.
So, if you know the measures of two angles (A and B) and the length of one side (c), you can use the Law of Cosines to find the lengths of the other two sides (a and b) by using the following formulas:
a = √(c² + b² - 2bc cos(A))
b = √(c² + a² - 2ac cos(B))
You can use the above equations to find the sides of the triangle, if you have the measures of two angles and one side.
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Pls answer asap I’m literally stumped it’s not that hard tho
Answer:
[tex]d=11.3125[/tex]
Step-by-step explanation:
Given
[tex]\frac{-4(-8.625+2d)}{-8} +3=10[/tex]
Lets solve for [tex]d.[/tex]
Start on the left side with the fraction.
Factor -4 out of -8.
[tex]\frac{-4(-8.625+2d)}{-4(2)} +3=10[/tex]
Cancel the common factor of -4.
[tex]\frac{-8.625+2d}{2} +3=10[/tex]
Subtract 3 from both sides.
[tex]\frac{-8.625+2d}{2} =7[/tex]
Multiply both sides by 2.
[tex]\frac{-8.625+2d}{2} *2=14[/tex]
Cancel the common factor of 2.
[tex]-8.625+2d=14[/tex]
[tex]2d-8.625=14[/tex]
Add 8.625 to both sides.
[tex]2d=22.625[/tex]
Divide both sides by 2.
[tex]d=11.3125[/tex]
8
In the expression (3) (0.2)³(0.8)5, which value
represents the number of successes?
0.8
C. 0.8 D. (0.8)5
A. 8/3 B. 0.2 C.
Answer: In the expression (3)(0.2)³(0.8)5, the value that represents the number of successes is 0.8.
This value is associated with the probability of success in the given expression, usually represented as "p" in a binomial distribution.
0.8 is probability of success
(0.8)5 represents number of successes.
It is important to note that 0.8 is a probability of success which means the probability of getting a success outcome in a single trial, and (0.8)5 is the probability of getting five successful outcomes in five trials.
Step-by-step explanation:
just need help with #7. A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
Surface Area : Volume = 6 : s
What is cube ?A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
Surface Area of a Cube = 6a² in a square units
Volume of cube = a³ cubic units
where a is the side length of the cube.
Given length of the cube = s
Surface Area of cube A = 6s²
Volume of cube V = s³
Ratio between Surface Area and volume:
Surface Area / Volume = 6s² / s³
Surface Area / Volume = 6 / s
Surface Area : Volume = 6 : s
Hence the ratio between Surface area and volume of cube is 6 : s.
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Can you guys answer the top question thanks?
The required solution are as follows,
(A) Kyra's equation of line, passes through 15 pts.
(B) Liam's equation of line, passes through 20 pts.
(C) the equation of line passes through 30 pts is y = 4/3x + 5.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
here,
Drawing the graph on the graph and evaluating which line pass through which points,
(A)
Kyra's equation of a line is y = 1/2 x
And from the graph, it is seen that the line passes through 15pts
Similarly,
(B) passes through 20 pts
(C)
from the graph, it is seen that equation y = 4/3x + 5 passes through 30 points.
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Triangle abc is to triangle efg because a vertical translation of units and a horizontal translation of units maps triangle abc onto triangle efg
Triangle ABC is translated to triangle EFG because a vertical translation of 10 units and a horizontal translation of 5 units maps triangle ABC onto triangle EFG.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
Triangle ABC.
A = (-9, -2)
B = (-9, -7)
C = (-7, -7)
Triangle EFG.
E = (-4, 8)
F = (-4, 3)
G = (-2, 3)
Now,
With a vertical translation of 10 units up on triangle ABC and 5 units right of the horizontal translation will give us triangle EFG.
i.e,
(-9, -2) = (-9 + 5, - 2 + 10) = (-4, 8)
(-9, -7) = (-9 + 5, -7 + 10) = (-4, 3)
(-7, -7) = (-7 + 5, -7 + 10) = (-2, 3)
Thus,
Vertical translation of 10 units up and horizontal translation of 5 units right.
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Answer:
1: Congruent
2: 10
3: 5
Step-by-step explanation:
4. Automotive Trades At the beginning of the day on Monday, the parts
department has on hand 520 spark plugs. Mechanics in the service depart-
ment estimate they will need about 48 plugs per day. A new shipment of
300 will arrive on Thursday. Write out a mathematical statement that gives
the number of spark plugs on hand at the end of the day on Friday. Calcu-
late this total.
StS estimate
Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.
Describe the equation.Using the equals symbol (=), a mathematical equation appears to be a formula that connects two statements and denotes equality. A scientific assertion that supports the equality of two mathematical abstraction is known as an equation in algebra. For instance, the equal sign is present between the variables ptdc + 6 and 12 in the output obd + 6 = 12. The link between the syllable on either side of either a letter is described by a mathematical formula. In many cases, the logo and the say — are identical.
Here,
Given: A new supply of 300 spark plugs will come on Thursday,
and 520 spark plugs require 48 plugs per day.
To determine an equation to determine however many plugs will just be left at the end of Friday:
So,
where n is the no of days
=> 520 - 48*n + 300
=> 520 - 48*5 + 300
=> 520 - 240 + 300
=> 520 + 60
=> 580
Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.
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What is 5c−3d−12c+d−6 written in simplest form?
To simplify the expression 5c−3d−12c+d−6, we can combine like terms:
5c − 12c + d − d − 6 = (-12c + d) + (-6)
Therefore, the expression 5c−3d−12c+d−6 can be simplified to -12c + d - 6.
What is a 2 step equation that equals to 14
Answer:
2x + 1 = 29
Step-by-step explanation:
There are a lot of answers.
2x + 1 = 29
2x + 1 = 29 Subtract 1 from both sides
2x = 28 Divide both sides by s
x = 14
Start off knowing that x will be 14, then multiply 14 by some number and then add or subtract some number from that and put that on the other side of the equal sign.
x = 14
14 x 2 = 28 and then add 1 to that to get 29
2x + 1 = 29
Answer: Do you want x=14 or for it to equal 14, because I have it both ways. For x=14, an acceptable two step equation would be 2x-5=23. If you want it to equal 14, then you can write 5x-1=14
Step-by-step explanation:
For x=14:
2x-5=23
Add 5 on both sides
2x=28
x=14
For the equation to equal 14:
5x-1=14
Add one on both sides
5x=15
x=3
A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have
With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.
How to interpret a standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.
We have given,
Mean weight of Eskimo dogs is μ = 30 pound
Standard deviation of Eskimo dogs is σ = 2 pound
The range of weights would 99.7% of the dogs have,
R = μ ± 3σ
R = 30 ± 3*2
R = 30 ± 6
R = (30 - 6) , (30 + 6 )
R = 24, 36
With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.
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Which expression is the factored form of X^3 2x^2 5x 6?
The factors of the given equation x³ - 2x² - 5x + 6 is (x - 1)(x + 2)(x - 3) with the help of synthetic division.
Let f(x) = x³ - 2x² - 5x + 6
Substitute x = 1
f(1) = (1)³ - 2(1)² - 5(1) + 6
⇒ f(1) = 1 - 2 - 5 + 6
⇒ f(1) = -1 + 1
⇒ f(1) = 0
As x = 1 is the root of the given equation therefore one of the factor of the given equation is (x-1)
Now use long division method, we get (x² - x - 6) as another factor.
⇒ f(x) = (x - 1)(x² - x - 6)
⇒ f(x) = (x - 1)(x² - 3x + 2x - 6)
⇒ f(x) = (x - 1)(x(x-3) + 2(x-3))
⇒ f(x) = (x - 1)(x - 3)(x + 2)
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How do you know if a graph is logarithmic or exponential?
exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph and if the log term involved in the given function then it is a logarithmic
How do you identify an exponential function from a graph?
Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph
and if the log term involved in the given function then it is a logarithmic
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The question is in the picture I would appreciate if you could explain how to get the answer thank you.
(0.818 , 1.546) is the point that is part of solution.
point (0,2) and (2,0) are not the part of solutions.
3y - 2x ≤ 3
y + 3x ≤ 4
these are the system of inequalities.
What are Inequalities?
Inequality is a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Given in this question,
There are two lines L1 and L2.
From the graph we can find the two points that lies on the line L1 be
(0,1) and (3,3).
similarly From the graph we can find the two points that lies on the line L2 be
(0,4) and (2,-2).
From the two points (x1 , y1) and (x2,y2) we can write the equation of the Line from the following formula :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]. This is the equation of line for given two points.
Equation of line L1 :
[tex]y-1=\frac{3-1}{3-0} (x-0)[/tex]
3y - 3 = 2x ----------(ii)
Equation of line L1 : 3y - 2x = 3.
Equation of line L2 :
[tex]y-4=\frac{-2-4}{2-0} (x-0)[/tex]
y = -3x + 4 ----------(ii)
Equation of line L2 : y + 3x = 4.
The point that is the part of the solution :
putting the value of y from equation (ii) in equation (i).
3(-3x+4) -3 = 2x
-9x-2x = -12+3
-11x = -9
x = 0.818
y = -3(0.818) +4 = +1.546
so Point of intersection is (0.818 , 1.546)
This is the point that is part of solution.
The point that is not below both the lines are not part of solution.
the point that are not part of solution are:
3y - 2x ≥ 3 -> (0,2)
y + 3x ≥ 4 -> (2,0)
point (0,2) and (2,0) are not the part of solutions.
Inequalities are for shaded portion :
3y - 2x ≤ 3
y + 3x ≤ 4
these are the system of inequalities.
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if g varies inversely as the square root of h, and g = 9 when h = 121, find g when h = 81.
If g varies inversely as the square root of h, this means that the product of g and the square root of h is constant. We can represent this relationship using the equation g*sqrt(h) = k, where k is the constant value.
We are given that g = 9 when h = 121, so we can substitute these values into the equation to find the constant:
9sqrt(121) = k
Simplifying this expression gives us:
k = 911 = 99
Now that we know the value of the constant, we can use the equation to find g when h = 81:
g*sqrt(81) = 99
Solving for g gives us:
g = 99/sqrt(81) = 99/9 = 11
Therefore, when h = 81, g = 11.
What is −30y − 15 if y is 7?
Answer:
-225
Step-by-step explanation:
-30*7=-210
-210-15=-225
please give brainliest
What are the domain and range of the logarithmic function?
The domain and range of the logarithmic function is given by:
Domain= [ 0 , ∞ ) and Range = { y ∈ R }.
As given in the question,
Let y = logₐ x be the given logarithmic function.
Logarithmic function is defined for all the positive values.
Domain of the logarithmic function is given by x∈ R , x > 0.
Range of the logarithmic function is inverse of the domain of the exponential function.
x = e^y
Here y is set of all the real numbers.
Range of logarithmic function is set of all the real numbers.
Therefore, domain of the logarithmic function is set of all real number greater than zero and range of the logarithmic function is the set of all the real numbers.
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A recipe for tropical punch calls for 222 liters of pineapple juice and 333 liters of orange juice. Jo creates a drink by mixing 333 liters of pineapple juice with 444 liters of orange juice. How does Jo's drink compare to the tropical punch recipe
Amount of pineapple juice is more in Jo's drink and amount of Orange juice is less in Jo's drink as compare than the tropical punch recipe because these are not in that ratio as in the tropical punch recipe.
What is the ratio?Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.
The Number of cups of pineapple juice = 222 liters
The Number of cups of orange juice = 333 liters
Thus ,
Total number of cub of juice = 222+333
= 555 cups
In Jo's drink
The Number of cups of pineapple juice = 333 liters
The Number of cups of orange juice = 444 liters
Thus Total number of cub of juice = 333+444
= 777 cups.
The ratio of amount of pineapple juice and amount of Orange juice is 2:3 in the tropical punch recipe
Whereas the ratio of amount of pineapple juice and amount of Orange juice is 3:4 in Jo's drink
Thus we can see that Amount of pineapple juice is more in Jo's drink And Amount of Orange juice is less in Jo's drink.
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Consider the division of 8y2 - 12y + 4 by 4y.
What are the values of a and b?
=a+b++
O a = 2y and b = 3
O a= { and b = -3y
O a= 2y and b = -3
O a = ? and b = 3y
Mark this and return
Save and Exit
Next
Sub
By solving the given Algebraic expression, the correct answer is Option (C) ,a = 2y and b = –.
What is an Algebraic Expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are different components of an algebraic expression. Let us have a look at the image given below in order to understand the concept of Variables, Constants, Terms, and Coefficients of any algebraic expression.
Assume that 8y2 - 12y + 4 has terms with a=8y² , b=-12y, c=4
Now, to divide 8y2 - 12y + 4 by the monomial (single term) 4y,
The easy way is divide each term of the dividend by the monomial:
8y2 - 12y + 4 /4y
=(8y²-12y+4)/4y
=(8y²/4y)-(12y/4y)+(4/4y)
=2y-3+1/y
After performing the division we get that now a = 2y and b = –3
We can conclude that the correct answer is a = 2y and b = –3
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What is the coefficient form of X³ 2 *?
Let x= the co-efficient of x^2. So the co-efficient of given function is x=1.
Define co-efficient.
The term "coefficient" refers to a number or symbol that multiplies another number or symbol (used as a mathematical variable).
Write an example of co-efficient.
An amount multiplied by a variable is known as a coefficient. As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.
Let x= the co-efficient of x^2 So the co-efficient of given function is x=1.
The term multiplied with x^3 is the co-efficient of this expression. As there is not term with x^2 so it is 1.
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Alaska is the biggest state in the United States of America. Write the given definition as a biconditional. A. A state is Alaska if and only if it is the smallest state in the United States of America. B. A state is the biggest state in the United States of America if and only if it is not Alaska. C. If a state is Alaska, then it is the biggest state in the United States of America. D. A state is Alaska if and only if it is the biggest state in the United States of America
D. A state is Alaska if and only if it is the biggest state in the United States of America is the correct biconditional statement.
Give reason for your answer.This is the correct biconditional statement because it accurately reflects the information given. The statement states that a state is Alaska if and only if it is the biggest state in the United States of America. This is true, as the given information states that Alaska is the biggest state in the United States of America.
Option A is incorrect because it says that a state is Alaska if and only if it is the smallest state in the United States of America which contradicts the given information.Option B is incorrect because it says that a state is the biggest state in the United States of America if and only if it is not Alaska, and that is not true. Alaska is the biggest state in the United States of America and it contradicts the given information.Option C is correct, but it is not a biconditional statement, it is a conditional statement, it states that if a state is Alaska, then it is the biggest state in the United States of America, but it doesn't have the "if and only if" part.Therefore, statement D is the correct biconditional statement that reflects the given information that Alaska is the biggest state in the United States of America.
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ALGEBRA 2 - Exponential and Logarithmic Functions
Simone’s parents invested $1,500 in an account such that the value of the investment doubles every seven years. The value of the investment, V, is determined by the equation V= p · t^r/7, where p represents the amount invested and t represents the number of years since the money was deposited. How many years, to the nearest tenth of a year, will it take the value of the investment to reach $1,000,000?
It will take approximately 4687.9 years for an investment principal of $1500 to reach $1000000 at an interest rate of 14.2% per year
What is Simple InterestSimple interest is a type of interest calculated only on the principal amount of a loan or deposit, without taking into account the compound interest earned on that principal. It is calculated by multiplying the principal amount, the interest rate and the time period.
The formula of simple interest is given as;
A = P(1 + rt)
where;
A = Simple InterestP = principalr = ratet = time period.In this problem, we have to find the rate first.
The investment doubles after 7 years.
A = p(1 + rt)
2 = 1(1 + r * 7)
2 = (1 + 7r)
2 = 1 + 7r
7r = 2 - 1
7r = 1
r = 1 / 7
r = 0.142
r = 14.2%
The rate is 14.2 %
Now, we can proceed to determine how many years it will take to reach a value of 1000000
Using simple interest formula again;
A = P(1 + rt)
100000 = 1500(1 + 0.142 * t)
1000000 = 1500(1 + 0.142t)
t = 4687.8 years
It will take approximately 4687.8 years
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What type of data collection might be best to study how voters might decide an upcoming ballot issue
Observational data collection might be best to study how voters might decide an upcoming ballot issue.
What kinds of information is observed?The majority of big data is observational data, such as bank transaction records, user viewing patterns on video streaming services, or social media posts. Observational data, however, can also be sparse data (based on just a few people).
The observational study method is what?In observational research, participants and phenomena are observed in their most natural environments. Instead of using structured environments like research labs or focus groups, this allows researchers to observe how their subjects make decisions and respond to situations in their everyday lives.
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1.) what is the length of the apothem in this regular pentagon?
2.) What is the area of the regular pentagon?
3.)What is the length of the apothem in this regular pentagon ?
On solving the provided question, we can say that - the each angle of pentagon is x = 108
what is a pentagon?A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.
since all sum of pentagon is 540
so, 5x = 540
x = 108
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i have help with this q
The slope of the graph is equivalent to 6 units.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the graph showing the amount of water in the tank after the several minutes of it being turned off.
We can write the slope of the graph as -
m = (16 - 10)/(2 - 1)
m = 6
Therefore, the slope of the graph is equivalent to 6 units.
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he distribution of the diameters of a particular variety of apples is approximately normal with a standard deviation of 0.2 inches. How does the diameter of an apple at the 34th percentile compare with the mean diameter
Using the normal distribution, we have that diameters at the 0.34th percentile are 0.2 standard deviations, that is, 0.127 inches above the mean.
Which of the following can be true about an event's probability?Probability is the likelihood that a particular experiment result will appear a certain number of times. It cannot be less than zero or greater than one. A 100% chance of an outcome occurring exists if the outcome is 1, for example. If the result is greater than 1, there is a greater chance that it will occur.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
It measures how many standard deviations the measure X is from the mean.
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
34th percentile is X when Z has a p-value of 0.34, so X when Z = 0.6331.
It means that the diameter is 0.44 standard deviations = 0.6331x0.2 = 0.127 inches above the mean.
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If a student scored 75 points on a test where the mean score was 83. 5 and the standard deviation was 6. 1. The student's z score is ________. Round to 2 decimal places
The z score of the student is -1.39. The value z score is rounded to 2 decimal places.
What is mean?
The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.
The formula for the z-score is
z = (x - μ)/σ
x = standard value
μ = mean
σ = standard deviation
Given that the scored 75 points. The mean score of the student was 83.5 and the standard deviation was 6. 1.
Putting x = 75, μ = 83.5 and σ = 6.1
z = (75 - 83.5)/6.1
z = -1.3934
z ≈ -1.39
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