The probabilities are P(X = 2) = 0.14 and P(X ≥ 2) = 0.30
The mean and the standard deviation are 0.96 and 0.90
How to determine the probabilitiesP(x = 2)
From the question, we have the following parameters that can be used in our computation:
X 0 1 2 3
P(X) 0.12 0.20 0.14 0.16
From the above table, we have
P(X = 2) = 0.14
P(x ≥ 2)
From the question, we have the following parameters that can be used in our computation:
X 0 1 2 3
P(X) 0.12 0.20 0.14 0.16
From the above table, we have
P(X ≥ 2) = P(2) + P(3)
Substitute the known values in the above equation, so, we have the following representation
P(X ≥ 2) = 0.14 + 0.16
Evaluate the sum
P(X ≥ 2) = 0.30
The mean and the standard deviationThe mean is calculated as
μx = sum of the products of x and P(x)
So, we have
μx = 0 * 0.12 + 1 *0.20 + 2 * 0.14 + 3 * 0.16
Evaluate
μx = 0.96
The standard deviation is calculated as
ox = the square root of sum of the products of x and P(x) * (1 - P(x)
So, we have
ox = √[(0 * 0.12 * 0.88) + (1 * 0.20 * 0.80) + (2 * 0.14 * 0.86) + (3 * 0.16 * 0.84)]
Evaluate
ox = 0.90
Hence, the standard deviation is 0.90
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answer please have no idea how to start or do it just please show the workings aswell.
The evaluation of P10–Focus 1 indicates that we get by using the equation for the volume of a cuboid and by calculus;
(a) [tex]L = 4\times x + 4\times 2\cdot x + 4\times \frac{81}{2\cdot x} =12\cdot x + \frac{162}{x^2}[/tex]
(b) [tex]L_{min}[/tex] = 54 cm
(c) L'' at x = 3, (where [tex]L_{min}[/tex] = 54 cm) is positive, therefore, x = 3 is a minimum point
P10-Focus2
The area = [tex]2\times x \times y+\frac{\pi\cdot x^2}{4} =4[/tex], therefore, [tex]y = \frac{16- \pi \cdot x^2}{8 \cdot x}[/tex]
The minimum point, which is an extremum point is a point where the derivative of the function is 0.
(a) The length of the cuboid = 2·x
The width of the cuboid = x
The volume of the cuboid = 81 cubic centimeters
The thickness of the cuboid is therefore;
Thickness = 81/(2·x × x) = 81/(2·x²)
The sum of the length of the twelve edges, L, is therefore;
[tex]L=x + x + x + x + x + 2\cdot x + 2 \cdot x + 2 \cdot x + 2\cdot x + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2}[/tex]
Therefore;
[tex]L=4\times x + 4\times 2\cdot x + 4\times \frac{81}{2 \cdot x^2} =12\cdot x + \frac{162}{x^2}[/tex]
The sum of the lengths of the twelve edges, L, is [tex]L = 12\cdot x + \frac{162}{x^2}[/tex]
(b) The minimum value of L can be found using calculus by finding the point at which dL/dx = 0 as follows;
[tex]\frac{dL}{dx} = 12 - \frac{324}{x^3} =0[/tex]
Therefore;
[tex]12-\frac{324}{x^3}=0[/tex]
[tex]12 = \frac{324}{x^3}[/tex]
x³ = 324 ÷ 12 = 27
x = ∛(27) = 3
x = 3
The minimum value of L can be obtained when x = 3 as follows;
[tex]L = 12\cdot x + \frac{162}{x^2}[/tex]
[tex]L_{min} = 12\times 3 + \frac{162}{3^2} = 54[/tex]
The [tex]L_{min}[/tex] = 54
The minimum value of L is 54 centimeters
(c) The value of the minimum value of L can be confirmed by further differentiation using the second derivative, L'' as follows;
At the x-value of a minimum point of a function, the value of the further derivative is larger than zero
The further derivative of the specified function is found as follows;
[tex]L'' = \frac{dL'}{dx} =\frac{972}{x^4}[/tex]
At the critical number, x = 3, from the first derivative, we get;
[tex]L'' = \frac{972}{3^4} = 12 > 0[/tex]
The value of the further derivative of the function at the point x = 3, is L'' = 12 > 0, therefore the point x = 3 is a relative minimum.
(b) The radius of the quarter circle = x
The area of the figure = 4 m²
The sum of the area of the composite figures are;
[tex]A = 2 \times x \times y + \frac{\pi \cdot x^2}{4} = 4[/tex]
Therefore;
[tex]y =\frac{\left(4 - \pi \cdot \frac{x^2}{4}\right)}{2\cdot x} = 16 - \frac{\pi \cdot x^2}{8\cdot x}[/tex]
Rearranging the right hand side expression as a fraction, we get;
[tex]y = \frac{16-\pi \cdot x^2}{8\cdot x}[/tex]
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Graph y=1/2x=+1
Use the table or identify m and b if it helps you graph.
Answer: 1/3
Step-by-step explanation:
50 POINTS IF ANSWERED PLSS!!!!!
Mr. Hansen has three sticks that measure 5 inches, 10 inches, and 17 inches. If he connects the sticks ends, will the three sticks form a triangle?
Answer:
This would not form a triangle
Step-by-step explanation:
due to the triangle inequality theorem, in order to find out if three numbers can form a triangle, you have to have each pair of numbers add up to more than the remaining number. The first combination added is 5+10 which is 15, and that is not greater than 17, so the answer is no, this is not a triangle.
hope this helps! :3
Assuming they are charging simple interest annually and the interest rate was 21.24%, what steps would I need to do in order to solve this problem??
50000x6000000000000 what is it?
Answer: 300000000000000000
Step-by-step explanation:
50000x6000000000000 can be written as 3 times 10^17
So the answer is 300000000000000000
Walmart has cashews that sell for $2 a pound and peanuts that sell for $1.50 a pound. Meijer sells cashews for
$2.50 a pound and peanuts for $1 a pound. Mike paid $26 at Walmart and Jim paid $29 at Meijer for the same
amount of nuts. How many pounds of cashews and peanuts did they buy?
Let "c" represent the amount of cashews they each bought.
Let "p" represent the amount of peanuts they each bought.
Mike: 2c + 1.5p = 26
Jim: 2.5c + 1 p = 29
That's the system you need to solve. We can do this with substitution.
Start with Jim:
2.5c + p = 29
p = 29 - 2.5c
Substitute that into Mike and solve for c:
2c + 1.5p = 26
2c + 1.5(29 - 2.5c) = 26
2c + 43.5 - 3.75c = 26
-1.75c + 43.5 = 26
-1.75c = - 17.5
c = 10
Now substitute that back into Jim's last equation:
p = 29 - 2.5c
p = 29 - 2.5(10)
p = 29 - 25
p = 4
So they each bought 10 pounds of cashews and 4 pounds of peanuts.
If co(x)= 2/3 and x i in quadrant I, then find exact value for (without olving for x) in(2x)
If cos x= 2/3 and x is in quadrant I, then the exact value of sin(2x) is (4/3)sin x.
What is trigonometry?A branch of mathematics called trigonometry examines the connections between triangles' angles and sides. It is predicated on the idea of right triangles, where one angle is 90 degrees and two sides are perpendicular to one another. The six fundamental functions of trigonometry—sine, cosine, tangent, cotangent, secant, cosecant. These values of functions can be used to address real-world angle and length issues, such as determining the height of a structure or the distance between two locations. Calculus, geometry, and other areas of mathematics are all strongly connected to trigonometry.Modeling actual phenomena like item motion, wave behaviour, and light dispersion is possible with these functions. Physics, engineering, and astronomy are just a few of the disciplines that use trigonometry extensively.
How to solve?
In quadrant I, cos x = 2/3 and sin x > 0.
sin(2x) = 2sin x cos x
sin(2x) = 2 * 2/3 * (sin x)
sin(2x) = (4/3)sin x
If sin x > 0, then sin(2x) = (4/3)sin x > 0.
The exact value of sin(2x) is (4/3)sin x
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The population of a heard of buffalo after t
years is represented by the function
() = 2186(0.954)^t
What does the value 0.954 represent in this
situation?
a. The initial population of the town is 0.954
b. The population of the town increases by 0.954
each year.
c. The population of the town decreases by 0.954
each year.
d. The population of the town is 0.976 times the
population of the town in the previous year.
0.954 represents population of the town increases by 0.954 each year.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The population of a heard of buffalo after t
years is represented by the function
[tex]f(x)=2186(0.954)^{t}[/tex]
We need to find the what does the value 0.954 represent in this
situation.
In the given function 2186 represent the initial population.
t represents the time in years
and 0.954 represents population of the town increases by 0.954 each year.
Hence, 0.954 represents population of the town increases by 0.954 each year.
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Choose the correct name for the set of numbers.
{-₁ √11, 21.6555..., 16,
The correct name for the set of numbers {-1, √11, 21.6555..., 16} include the following;
A. Real numbers
B. Integers
C. Irrational numbers
E. rational numbers
What are the types of numbers?In Mathematics, there are six (6) common types of numbers and these include the following:
Irrational numbersReal numbersRational numbersIntegersNatural (counting) numbersWhole numbersWhat is an irrational number?In Mathematics, an irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11 or √11.
In conclusion, when the square root of 11 or √11 is taken, the output is neither a terminating decimal nor a repeating decimal. Therefore, it would be classified as an irrational number.
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Complete Question:
Choose the correct name for the set of numbers. {-√11, 21.6555..., √16, 1/9}.
real numbers
integers
irrational numbers
natural numbers
rational numbers
whole numbers
16. Translate the phrase "Two-tenths of a number" into an algebraic expression. Let x represent the real number.
The algebraic expression of the phrase Two-tenths of a number is 2x/10. The simplest form of the expression is x/5.
What is a phrase?
A mathematical expression is an expression that contains numbers, variables, and/or operations on those numbers and variables. A mathematical phrase is a verbal phrase that contains words and/or figures that can be turned into a mathematical expression.
Given phrase is Two-tenths of a number.
The value of two tenths is 2/10.
Assume that x be the number.
Two-tenths of x is 2/10 × x = 2x/10
Divide the denominator and numerator by 2:
= x/5
The expression is x/5.
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How does a number change in total when it is decreased by 60% and increased by 80%? PLEASE HELP ASAP!
The number will be decreased by a percentage of 32%.
How does the number change?
If a number N is increased by a percentage X, then the new value is:
N' = N*(1 + X/100%)
If instead the number is decreased, then the new value is:
N' = N*(1 - X/100%)
So if we apply a decrease by 60% followed by an increase of 80%, we will have:
N' = N*(1 - 60%/100%)*(1 + 80%/100%)
N' = N*(1 - 0.6)*(1 + 0.8)
N' = N*(0.4)*(1.8)
N' = N*0.72
We can rewrite that as:
N' = N*(1 - 0.32)
0.32 = 32%/100%
So that is equivalent to a decrease by 32%
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a cup of coffee starts at temperaryre 180 in a room where the surroundings temperature is 80. after 10 minutes, the coffee has cooled to 130. find an equation for the temperature t of the coffee as a function of time. simplify your answer as much as you can and make sure there are no unknown constants
The final equation for the temperature of the coffee as a function of time is [tex]T = 80 + 100*e^{(-4t)[/tex]. There are no unknown constants in this equation.
The temperature of a substance will naturally cool down over time due to heat transfer to the surrounding environment. The rate at which the substance cools down is described by Newton's law of cooling, which states that the rate of change of the temperature of a substance is proportional to the difference in temperature between the substance and the surroundings. Mathematically, this can be expressed as:
dT/dt = k(T - Ts)
Where T is the temperature of the substance, Ts is the temperature of the surroundings, t is time, and k is the cooling coefficient, which is a constant that depends on the properties of the substance and the surroundings.
Since we know that the initial temperature of the coffee is 180 and the temperature of the surroundings is 80, and the temperature of the coffee after 10 minutes is 130, we can write the following equation:
(180 - 130)/10 = k(180 - 80)
Solving for k, we get:
k = -4
Substituting this value back into the equation for the rate of change of temperature, we get:
dT/dt = -4(T - 80)
This is the equation for the temperature of the coffee as a function of time. To find the temperature of the coffee at any time t, we can integrate this equation with respect to time. The resulting equation will be:
[tex]T = 80 + C*e^{(-4t)[/tex]
Where C is an unknown constant of integration. Since we are given that the initial temperature of the coffee is 180, we can solve for C by substituting t = 0 and T = 180 into the equation:
[tex]180 = 80 + C*e^0[/tex]
Solving for C, we get:
C = 100
Substituting this value back into the equation for T, we get the final equation for the temperature of the coffee as a function of time:
[tex]T = 80 + 100*e^{(-4t)[/tex]
This is the final, simplified equation for the temperature of the coffee as a function of time. There are no unknown constants in this equation.
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Josue has $0.33 worth of pennies and nickels. He has a total of 13 pennies and nickels altogether. Write a system of equations that could be used to determine the number of pennies and the number of nickels that Josue has. Define the variables that you use to write the system.
Josue has 8 pennies and 5 Nickels and N+P=13 and 0.01P + 0.05N ≥ 0.33 are system of equations that could be used to determine the number of pennies and the number of nickels that Josue has
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Josue has $0.33 worth of pennies and nickels.
total of 13 pennies and nickels altogether.
Let N be number of Nickels and P be number of Pennies
P + N =13..(1)
Therefore
0.01P + 0.05N ≥ 0.33..(2)
From 1,
P=13-N
0.01(13-N)+0.05N ≥ 0.33
0.13-0.01N+0.05N ≥ 0.33
0.13+0.04N ≥ 0.33
0.04N≥ 0.33-0.13
0.04N≥ 0.33-0.13
0.04N≥ 0.2
Divide both sides by 0.04
N=5
From 1, N+P=13
5+P=13
Subtract 5 from both sides
P=13-5
P=8
Hence, Josue has 8 pennies and 5 Nickels and N+P=13 and 0.01P + 0.05N ≥ 0.33 are system of equations that could be used to determine the number of pennies and the number of nickels that Josue has
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The function g(x) = f(x – 7) + 3. Which of the following is true about the graph of g(x)
the graph of g(x) is shifted 7 units to the right and 3 units below the graph of f(x).
The graph of g(x) is shifted 7 units to the left and 3 units below the graph of f(x).
The graph of g(x) is shifted 7 units to the right and 3 units above the graph of f(x).
The graph of g(x) is shifted 7 units to the left and 3 units above the graph of f(x).
Answer:
Step-by-step explanation:
the graph of g(x) is shifted 7 units to the right and 3 units below the graph of f(x).
The graph of g(x) is shifted 7 units to the left and 3 units below the graph of f(x).
The graph of g(x) is shifted
7 units to the right and 3 units above the graph of f(x).
The graph of g(x) is shifted 7 units to the left and 3 units above the graph of f(x)
A sign made of aluminum is in the shape of a pyramid. The base is a triangle with a base of 3 feet and a height of 5 feet. The height of the sign is 6 feet. The aluminum costs $8 per cubic foot. What is the cost of the sign?
A) $722
B) $240
C) $120
D) $168
The cost of the pyramid shape sign is $240.
What is a pyramid?A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.
We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.
∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,
= (1/3)×6×3×5 cubic feet.
= 30 cubic feet.
Given, The aluminum costs $8 per cubic foot.
∴ The total cost of the pyramid is = (30×8) = $240.
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Please help!!! And show your work or not I don’t care I need the answers
Answer:
Step-by-step explanation:
1. Lin, Tyler, and Jada's information is missing.
2. 9 1/8 = 73/8
1 2/8 = 10/8
73/8 - 10/8 = 63/8.
His shoe length was 63/8 inches.
solve each of these equations.
Answer:
a.) x=6 b.) y=-7 c.) a=0.25
Step-by-step explanation:
a.) 2(3x+2)=2x+28
6x+4=2x+28
subtract 4 on both sides
6x=2x+24
subtract 2x on both sides
4x=24
divide both sides by 4
x=6
b.) 5y+13=-43-3y
add 43 on both sides
5y+56=3y
subtract 5y on both sides
56=-8y
divide both sides by 8
-7=y or y=-7
c.) 4(2a+2)=8(2-3a)
8a+8=16-24a
add 24a on both sides
32a+8=16
subtract 8 on both sides
32a=8
divide both sides by 32
a=0.25
(hope you understood how I solved for each equation..)
A recently televised broadcast of a popular television show had a 15 share, meaning that among 5000 monitored households with TV sets in use, 15% of them were tuned to the show. A 0.01 significance level is used to test an advertiser’s claim that among the households with TV sets in use, less than 20% were tuned in to the show. Find the P-value.
1.9998
0.9999
0.0001
0.0002
The p-value of the given hypothesis is; 0.9999
How to find the p-value of the statistics?The formula for the z-score of proportions is;
z = (p^ - p)/√(p(1 - p)/n)
where;
p^ is sample proportion
p is population proportion
n is sample size
We are given;
p^ = 15% = 0.15
p = 20% = 0.2
n = 5000
Thus;
z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)
z = -8.8388
From p-value from z-score calculator, we have;
P(Z < -8.8388) = 1 - 0.0001 = 0.9999
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please help it about calculus
The question is based on the calculus and the derivative for given equation [tex]t^{4} - 24t^{2} \\ \\[/tex] is t = 0.
What is calculus?Calculus is a discipline of mathematics that focuses on rates of change, to put it simply. For instance, you could wish to determine how quickly an automobile will slow down when it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!
Calculus is a tool used by engineers to calculate things like rates of change and areas; in fact, calculus is the mathematical "backbone" for dealing with problems where variables change with time or some other reference variable. Calculus is concerned with two basic operations: differentiation and integration.
We are given
x(t) = [tex]t^{4} - 24t^{2} \\ \\[/tex]
we need to find its derivative only then we can comment on its increasing decreasing nature
x'(t) = [tex]4t^3 -48t\\\\[/tex]
we will check where derivative is zero
[tex]4t^3 - 48t = 0\\\\4t^2(t-4) = 0\\\\\\t = 0 \\\\t = 4\\[/tex]
hence increasing for all x E R except interval (0,4)
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A block of ice contains 40 three-ounce portions of shaved ice. A food truck owner wants to use the block of ice to make as many spheres of ice as possible, each weighing 18 lb. How many spheres can she make?
The maximum number of spheres that can be made through ice will be 135.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
As per the given,
Number of ice portions = 40
Weight of one ice portion = 3 ounce
Since, 1 lb = 16 ounce
3 ounce = 3/16 lb
Weight of 40 portion = 120/16 lb
The weight of one sphere of ice = 18 lb
Number of possible spheres = (120/16)/18
⇒ 120/16 x 18
⇒ 135 sphere
Hence "135 spheres are the most that can be produced by ice".
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a researcher obtains a negative value for the chi square test. what can you conclude because the value is negative?
A researcher obtains a negative value for the chi square test.1 is the value is negative .
What is chi-square value?
The difference between the frequencies of results of a collection of events or variables that were observed and those that were expected is measured by the chi-square (2) statistic.
Such variations in categorical variables can be examined using chi-square, particularly when they are nominal in nature.
We know that the chi-square is the sum of square of difference between observed and expected frequencies divided by the expected frequency. So, it is clear that the chi-square value can never be negative because sum of squares is always positive.
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what is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the
$150 is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer.
What is RAM?RAM is a type of volatile memory, which means that data is only stored there while the chip is powered and is completely erased when the computer is turned off. In gigabytes, RAM memory is measured (GB).
Random access memory is referred to as RAM. Because the data may be swiftly read and updated in any sequence, it is termed random access. Compared to previous storage devices like CD-RWs, which access data in a slower, predetermined order, this is faster.
There are much more methods through which we can improve computer performance but by spending the least amount of money we can do it by upgrading your RAM. We can upgrade the RAM of the system to 8 GB and 16 GB. If we want to upgrade the RAM to 8 GB then it can be done for around $75 and If we want to upgrade the RAM to 16 GB then it can be done for around $150.
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The complete question is as follows:
What is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer?
A shop increased the price of a shirt by 10% , then decided to decrease the price of the shirt by 10%. What was the percent change in price of the shirt. Explain your answer using words
Answer:
Step-by-step explanation:
1. Increase of 10% in price of shirt.
2. Decrease of 10% in price of shirt.
Hence- both amounts cancel out, therefore there is 0% change in price of shirt as both percentages cancelled out, or we can say nullified each other. Because they added the same amount to the item and then subtracted the same percent leading to no change.
Use the reciprocal property to solve for a 36/15 8/a
Applying reciprocal property the equation 36 / 5 = 8 / a is solved to find the value of a as 10/9
What is reciprocal property?The definition of reciprocal in mathematics is the inverse of a value or a number.
If n is a real number, then 1/n will be n's reciprocal.
Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9.
The result of multiplying a number by its reciprocal now equals one. multiplicative Inverse is another name for it.
Similarly, 36 / 5 = 8 / a
the reciprocal is 5 / 36 = a / 8
cross multiplying
5 * 8 = 36 * a
36a = 40
a = 40 / 36
a = 10/9
The value of a is 10/9
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a tennis player makes a successful first serve 70% of the time- what is the probability she makes at least 65
The probability she makes at least 65 is 0.0139.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
[tex]\begin{aligned}P(x \geq 65) & =1-P(x < 65) \\& =1-P\left(\frac{x-\mu}{n} < \frac{65-56}{4.0988}\right) \\& =1-P(z < 2.1958) \\& =1-0.9861 \\& =0.0139\end{aligned}[/tex]
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Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
2y + 5x = 13
2y-3x = 5
Answer:
Step-by-step explanation:
To solve the system of equations 2y + 5x = 13 and 2y-3x = 5 using the substitution method, you can follow these steps:
Begin by solving one of the equations for one of the variables. For example, you could solve the first equation for y:
2y + 5x = 13
2y = 13 - 5x
y = (13 - 5x) / 2
Substitute the expression for y into the second equation and solve for x:
2((13 - 5x) / 2) - 3x = 5
13 - 5x - 3x = 5
-8x = -8
x = 1
Substitute the value of x into the expression for y to find the value of y:
y = (13 - 5(1)) / 2
y = (13 - 5) / 2
y = 8 / 2
y = 4
The solution to the system of equations is (1,4).
Therefore, the correct ordered pair is (1,4).
Find the slope of the line that passes through (1, 1) and (7, 8).
Answer:
[tex] slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
[tex] slope=\frac{8-1}{7-1} [/tex]
[tex] slope=\frac{7}{6} [/tex]
slope = 7/6
6/22, 3:45 PM
Kris said, "The Rawlings Rockets basketball team does not have any really tall players." These are the players'
heights in inches:
70, 77, 75, 68, 88, 70, and 72.
a. Which number does not seem to fit this set of data? 1
b. Do you agree or disagree with Kris?
2
Answer:
a. 88
b. I disagree with Kris
Step-by-step explanation:
88 is by far the biggest outlier here being 11 numbers away from the second highest being 77. This means there is one kid that is much higher than the rest of the group.
Triangle ABC is a right triangle, with right angle B. Side AC has a length of 10. Side CB has a length of 6. Find the length of side AB.
The length of side AB is 8 units. Option B is the correct option.
What is right angle triangle?
A triangle is a area that bounded by three sides. The length of the sides may not be equal. A right triangle is a triangle with 90 degree angle. The rest two angles are acute angle.
Given that △ABC is a right triangle with right angle at B.
The length of side AC is 10 units. The length of side CB is 6 units.
Pythagoras theorem: The square of hypotenuse is equal to the sum of square of legs.
The legs of △ABC is AB and BC. The hypotenuse of triangle ABC is AC.
Therefore,
AB² + BC² = AC²
AB² + 6² = 10²
AB² + 36 = 100
Subtract 36 from both sides:
AB² = 100 - 36
AB² = 64
Take square root on both sides:
AB = √64
AB = 8
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........ i need help past due
Part a: y = -6x + 5 is : Not proportional.
Part b: y = 7/8x proportional: proportionality constant = 7/8.
Explain the term proportional relation?Relationships among two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.For the stated question;
Part a: y = -6x + 5
To check the proportional relation, put value of 'x' and find the corresponding value of 'y'.
The ratio = y/x must be same.
For x = 1, y = -1
y/x = -1
And, for x = 2, y = 7
y/x = 7/2
Thus, ratio is not equal, Not proportional.
Part b: y = 7/8x
For x = 1, y = 7/8
y/x = 7/8
Now, For x = 2, y = 14/8
y/x = 7/8, both ratios are equal.
Thus, y = 7/8x proportional: proportionality constant = 7/8.
To know more about the proportional relation, here
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