The inverse cosine function to find the measures of the = arccos(-sqrt)
What is measure of angles?
Angle measure can be defined as the measure of the angle formed by the two rays or arms at a common vertex.
To find the measures of the angles of a triangle, you can use the Law of Cosines, which states that the square of the length of a side of a triangle is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of the other two sides and the cosine of the angle opposite the side in question.
In this case, we are given the coordinates of the vertices of the triangle and we want to find the measures of the angles. To do this, we can use the distance formula to find the lengths of the sides of the triangle and then use the Law of Cosines to find the cosines of the angles.
The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
where d is the distance between the two points with coordinates (x1, y1, z1) and (x2, y2, z2).
Using this formula, we can find the lengths of the sides of the triangle as follows:
PR = sqrt((4 - 1)^2 + (0 - 2)^2 + (2 - 3)^2) = sqrt(9 + 4 + 1) = sqrt(14)
PQ = sqrt((3 - 1)^2 + (4 - 2)^2 + (2 - 3)^2) = sqrt(4 + 4 + 1) = sqrt(9)
QR = sqrt((4 - 3)^2 + (0 - 4)^2 + (2 - 2)^2) = sqrt(1 + 16 + 0) = sqrt(17)
Now we can use the Law of Cosines to find the cosines of the angles:
cos A = (PR^2 + PQ^2 - QR^2) / (2 * PR * PQ)
= (14 + 9 - 17) / (2 * sqrt(14) * sqrt(9))
= (-4) / (2 * sqrt(14) * sqrt(9))
= -2 / (sqrt(14) * sqrt(9))
cos B = (QR^2 + PQ^2 - PR^2) / (2 * QR * PQ)
= (17 + 9 - 14) / (2 * sqrt(17) * sqrt(9))
= (2) / (2 * sqrt(17) * sqrt(9))
= 1 / (sqrt(17) * sqrt(9))
cos C = (QR^2 + PR^2 - PQ^2) / (2 * QR * PR)
= (17 + 14 - 9) / (2 * sqrt(17) * sqrt(14))
= (12) / (2 * sqrt(17) * sqrt(14))
= 6 / (sqrt(17) * sqrt(14))
Finally, we can use the inverse cosine function to find the measures of the angles:
A = arccos(-2 / (sqrt(14) * sqrt(9)))
= arccos(-2 / (2 * sqrt(7) * sqrt(3)))
= arccos(-1 / sqrt(7) * sqrt(3))
= arccos(-sqrt)
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please help me!!! this is due tomorrow
Answer:
Below
Step-by-step explanation:
Multiply L number and Bottom number ...then add the R number to get the top number
? = 100 - (3*24) = 28
△JKL∼△STU Which statements are true? more than one are right? ∠K≅∠T
JK≅ST
KL/TU=JK/ST
JL=SU
m∠J=m∠S
∠K≅∠T , KL/TU=JK/ST and m∠J=m∠S are true .
Given: △JKL∼△STU
When two triangles are similar , then their corresponding sides are proportional and Corresponding angles of one triangle is equal to corresponding angles of another Triangle.
The two Triangles can be similar by following Similarity axiom
1. AA
2. S A S
3. S S S
The Options are
→∠K≅∠T( True) Corresponding angles are equal.
→JK≅ST (False)
→KL/TU=JK/ST (True) Because sides are proportional.
→JL=SU (False)
→m∠J=m∠S (True) Corresponding angles are equal.
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Find the probability that when a couple has six children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
The probability of having a boy when a couple has six children is 63 / 64.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.
Given:
A couple has six children, n = 6
The wanted event, p = 1 / 2
Calculate the probability of having a boy given by the following formula,
[tex]P(X) = nC_x px (1-p)n-x[/tex]
Here, [tex]X[/tex] = number of boys,
So,
P(X >= x) = 1 - P(X = 0)
P (X) = 1 - 6C₀ × (1 / 2) 0 × (1/2) 6
P (X) = 63 / 64
Therefore, the probability of having a boy when a couple has six children is 63 / 64.
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Tommy made s sandwiches for them to eat when they get hungry. Tommy put 3 slices of turkey and 3 slices of ham on each sandwich.
Pick all the expressions that represent how many slices of meat Tommy used on the sandwiches.
Answer:
Step-by-step explanation:het
Here is a picture of the Mostar Bridge in Bosnia.The diagram shows one side of the bridge find the area of the bridge (yellow part). show your work.
The area of the bridge(yellow part) is 297.9 m².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
From the given diagram the area of the bridge is the total area of the larger rectangle - the area of a semicircle - the area of the smaller rectangle.
We know the area of a rectangle is (length×width) and the area of a semicircle is (1/2)πr².
∴ The area of the bridge is = {(34×20) - (24×6.5) - (1/2)π(12)²} m².
= {680 - 156 - 226.1} m².
= 297.9 m².
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solve the following expression
(12 × 4²) + 9/3²
Answer: 193
Step-by-step explanation:
(12 x 16) + 9/9 = 192 + 1 = 193
Assuming second term is 9/(3²)?
In 2010, the U.S. Congress passed the Tax Relief, Unemployment Insurance Reauthorization, and Job Creation Act of 2010. The act reduced the self-employment tax rate from 15.3% to 13.3%. Estimate the reduction in self-employment tax for an individual whose taxable earnings totaled $50,319.
Answer:A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
A conical-shaped reservoir has a depth of 20 feet and a radius of 10 feet. Water is leaking out so that the surface is falling at the rate of 1/2ft/hr. Find the rate, in cubic feet per hour at which water is draining when the water is 8 feet deep. V=1/3πr2h
The rate at which water is draining when the water is 8 feet deep is calculated to be 2.54 ft³/ h
The vertex angle of the conical-shaped reservoir can be given as follows;
tan θ = R/H
Here R represents the radius and H illustrates the depth
so here we can say that the vertex angle will remain constant; therefore;
r/y = R/H
r/8 = 10/20
r = (10/20) × 8
r = 4
now for the volume, we can say;
V=1/3πr^2h
also, we can say;
r = y/2
Therefore here we will have;
V = 1/3π(y/2)^2y = 1/12 πy³
now for volume flow rate, we can determine as follows;
Q = dV/dt = 3/12πy²(dy/dt)
Q = 1/4 πy²v
Substituting the values as follows;
Q = 1/4 π(8)²(1/2)ft³/h
Q = 2.54 ft³/ h
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Which equation is represented by the graph below?
Answer:
(4,2) may be the answer
I guess!!
what is 6845.86 rounded to the nearest cent?
Answer: 6,845.9, or to whole number 6,846
Step-by-step explanation:
Find the length of side AC in the right triangle ABC with sides AC = 13 cm, BC = 5 cm and
The length of AB is equal to 12cm
How to find the length of a triangle?
If leg an is the missing side, change the equation such that an is on one side and compute the square root of that number: a = √(c² - b²)
Leg b = √(c² - a²) if leg b is unknown.
The equation is c = √(a² + b²) for the hypotenuse c that is absent.
What is the side length of a triangle?According to the law of the sides of a triangle, the lengths of any two of the triangle's sides added together are always more than the length of the third side. The triangle inequality theorem is another name for this condition. This indicates that a triangle with the dimensions 3, 4, and 9 is impossible because 3 + 4 =7 < 9.
a = √(c² - b²)
a=?,b=5,c=13
a=√169-25
a=12cm
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Usain Bolt masses 94 kg and runs at 10 m/s. How much kinetic energy does he have?
Usain’s brother, Insane Bolt, runs twice as fast and has the same mass. How much kinetic energy does he have?
If you double the mass of an object, how does this affect its kinetic energy?
You serve a volleyball with a mass of 2.1 kg. The ball leaves your hand with a speed of 30 m/s.
A car is traveling with a velocity of 40 m/s and has a mass of 1120 kg.
Determine the kinetic energy of a 1000-kg roller coaster car that is moving with a speed of 20.0 m/s.
Usain bolt with a mass of 94 kg and speed 10m/s has kinetic energy 4700j
What is kinetic energy and what is its formula?
The energy that an object has as a result of motion is known as kinetic energy. It is described as the amount of effort required to move a mass-determined body from rest to the indicated velocity. The formula of kinetic energy is [tex]\frac{1}{2}mv^2[/tex]
We are given that the mass of usain bolt is 94 kg and that he runs at a speed of 10m/s
That means the value of m and v are 94 kg and 10 m/s respectively
Substituting the values in the formula we get
Kinetic energy = [tex]\frac{1}{2}94*10^2[/tex]
Kinetic energy = [tex]47*100\\[/tex]
Kinetic energy = [tex]4700 j[/tex]
Hence the kinetic energy of Usain bolt is 4700 j
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Suppose that the scatterplot of log x and log y shows a strong positive correlation close to 1. Which of the following is true?
a. The variables x and y also have a correlation close to 1 b. A scatterplot of the variables log x andy shows a strong nonlinear pattern c. The residual plot of the variables and y shows a random pattern d. A scatterplot of the variables x andy shows a strong nonlinear pattern e. A residual plot of the variables log x and log y shows a nonrandom pattern
The correct options are;
a. The variables x and y also have a correlation close to 1 .
b. A scatterplot of the variables log x and y shows a strong nonlinear pattern .
The correlation is a measurement of a dependence between 2 variables. If the logarithm of the correlation function shows a linear tendency, it because the correlation between x and y shows a exponential tendency.
This mean that x and y are non linear correlated, but them are correlated.
For this type of data is used a non linear correlation technique know it as logarithm correlation.
Option c is incorrect because random patterns have a correlation value close to 0, which is not the case.
So ,
The correct options are;
a. The variables x and y also have a correlation close to 1
b. A scatterplot of the variables log x andy shows a strong nonlinear pattern
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4. Are these two functions inverses of each other?
g(x)=1/4 x
f(x)= 4x
Answer:
Yes
Step-by-step explanation:
g(x) = 1/4 x
g(x) = x/4
f(x) = 4x
If you plugin f(x) in g(x) and g(x) into f(x), you should get x:
f(g(x))=
4(g(x)= => plugin g(x) for x in f(x)
4(x/4)=
4*x/4=x √
g(f(x))=
f(x)/4= ==> plugin f(x) for x in g(x)
4x/4 = x√
Hence, f(x) and g(x) are inverse of each other.
what is the result of adding the system of equations 2x y 43x y 6x 10x y 25x 10
Therefore the result of adding the system of equations 2x + y = 4 ,
6=3x-y is 5x =10
Describe equation:Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS is used. You can solve equations to find the value of an unknown variable that stands in for an unknown quantity. If a sentence lacks a "equal to" sign, it is not considered an equation. It will be considered to be a phrase.
Here,
Given:
we have to solve the system of equations given. .Each equation is added together to remove the variable Y.
2x + y = 4
+
3x - y = 6
________
=> 5x =10
Therefore the result of adding the system of equations 2x + y = 4 ,
6=3x-y is 5x =10
The value of x :
x =10 / 5 = 2
⇒ x=2
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The vertex form of the quadratic function f(x) = -6x² - 60x - 151 is
f(x)= a(x - h)² + k.
What is the value of a?
What is the value of h?
What is the value of k?
This is one way of writing a quadratic function:
[tex]f(x)= a(x-h)^2+k[/tex]
(h,k) = vertexa = vertical stretchSolving the QuestionWe're given:
[tex]f(x) = -6x^2 - 60x - 151[/tex]
To write a quadratic function in vertex form, we must complete the square.
⇒ Put parentheses around the first two terms containing x and x²:
[tex]f(x) = (-6x^2 - 60x) - 151[/tex]
⇒ Factor out -6 (keeping the x's in the parentheses):
[tex]f(x) = -6(x^2+10x) - 151[/tex]
⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.
⇒ In this case, the coefficient of x is 10.⇒ Half of this value is 5.⇒ The square of 5 is 25.⇒ Add this inside the parentheses:[tex]f(x) = -6(x^2+10x+25) - 151[/tex]
⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:
[tex]f(x) = -6(x^2+10x+25) - 151-(-6*25)\\f(x) = -6(x^2+10x+25) - 151-(-150)\\f(x) = -6(x^2+10x+25) - 151+150\\f(x) = -6(x^2+10x+25) - 1[/tex]
⇒ Finally, complete the square.
Remember: [tex](a+b)^2=a^2+2ab+b^2[/tex]In this case, a is x, and b is 5:[tex]f(x) = -6(x+5)^2 - 1[/tex]
Answer[tex]f(x) = -6(x+5)^2 - 1[/tex]
a = -6h = -5h = -1A prestigious university wants to estimate the average starting salary of its graduates. The alumni outreach department sends an email to the most recent address they have on file for every graduate. The email asks the graduates to participate in a survey about their employment history and starting salary.
What are some possible concerns?
Some graduates won't check their emails and therefore won't respond (non-response bias)
Graduates might claim they make more $ than they actually do (response bias)
The correct option is option C i.e., current students are not included in the sample for the survey.
Current students are not required to participate in this survey because its main objective is to learn about respondents' career histories and starting salaries .
Survey could mean:
Research into humans and statistics.
A statistical survey is a technique for gathering numerical data on constituents of a population.
Type of survey
Spatial measurement : measuring places and distances on Earth using the technique and science of surveyingPhotogrammetry, a method of collecting information using aerial photographs and satellite imageryCadastral surveyors provide paperwork, diagrams, plats, and maps to prove who owns the land.
Most of Western Canada is divided into one-square-mile pieces using the Dominion Land Survey technique for agricultural and other uses. Identifying and surveying land parcels in the United States using the Public Land Survey System.
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FILL IN THE BLANK. before employing inferential statistics, alberto selects the probability level required for statistical significance. this level is referred to as the___\of the test.
Alberto chooses the probability threshold needed for statistical significance and then use inferential statistics. This level layer is described known as the test's significance level.
The significance level refers to the threshold at which one may agree that an event was statistically significant.
To evaluate statistical significance, researchers utilize a measurement called the p-value: whereas if the p-value was lower than the significance level, the result is considered statistically significant. The implies as well as standard deviations of both the data samples determine the p-value.
The confidence level would be the inverse of the significance level and is computed as 1 minus the significance level.
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Find the angle θ , in radians, in the given right triangle. The length of the side adjacent to θ is 16 and the length of the side opposite θ is 10. A right triangle with height 10 opposite from angle theta and base 16 adjacent to angle theta. 10 16 Round your answer to the nearest hundredth
Angle θ is equal to 0.56 radian.
What do you mean by inverse trignometry?
Inverse trigonometric functions are just the sine, cosine, tangent, cotangent, secant, and cosecant functions of the fundamental trigonometric functions. The terms arcus functions, antitrigonometric functions, and cyclometric functions are also used to describe them. To find the angle for any trigonometric ratio, apply these inverse trigonometric functions.
It is given that in right angle triangle, base of the triangle is 16 and height of the triangle is 10.
Now to find θ, from the given right angled triangle. Using the formula for tanθ
tanθ = P/B = 10/16 = 5/8
θ = [tex]tan^{-1}(5/8) = tan^{-1}(0.625) = 0.56[/tex] radian.
Therefore, angle θ is equal to 0.56 radian.
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A person is riding a Ferris wheel has a radius of 50ft. find the linear speed of the person in feet per minute if the Ferris wheel revolves twice per minute.
The linear speed of a person on this Ferris wheel is about 628.2 ft/min.
What is Linear Speed ?As a body travels a circular path, it has both a linear speed and an angular speed. The rate it travels on that path is the linear speed, and the rate it turns around the center of that path is the angular speed. The linear speed (v) and angular speed (ω) are related by the radius (r) or v = rω .
Given that ;
Radius = r = 50 ft
Frequency = f = 2 rev/min
The angular speed is the product of the angular displacement for one complete turn, namely 2π radians per revolution, and the frequency (f). That is, the angular speed is equal to ω = 2πf. Substituting this into the formula for linear speed (v), we get:
v = r (2πf)
= (50 ft) ( 2π / rev) ( 2 rev/min)
= 200π ft/min
≈ 628.2 ft/min
The linear speed of a person on this Ferris wheel is about 628.2 ft/min.
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.
What is the slope indicated in the table below
Answer:
y=5x
Step-by-step explanation:
On January 1, a nasty species of algae is mistakenly introduced into Lake Skinner. It grows in such a way that it doubles every day. If it continues to grow like this, the lake will be totally covered and the fish in the lake will suffocate. At the rate it is growing, this will happen on January 30.
1). When will Lake Skinner be covered halfway?
2). On January 26, you convince your friend that the lake will be completely covered soon. Your friend laughs. Why is your friend skeptical?
3). One January 29 a cleanup crew arrives and is able to remove most of the algae. When they are done on February 1, only 1 % of the surface is covered. How well does this solve the problem in Lake Skinner?
Answer: If the algae in Lake Skinner doubles every day, then on the 15th day (halfway between the 1st and 30th) the lake will be covered halfway.
If the algae doubles every day, then on January 26 it would have only doubled six times, meaning it would only cover 1/64 of the lake's surface. This is why your friend may be skeptical that the lake will be completely covered soon.
The cleanup crew's efforts on January 29 were able to remove most of the algae, but by February 1 only 1% of the lake's surface was still covered. This means that while the problem has been greatly reduced, it is not completely solved and there may still be some risks to the fish in the lake. Continued monitoring and efforts to prevent future algae blooms may be necessary to fully protect Lake Skinner.
Step-by-step explanation:
17. You probably know the Fibonacci numbers 1,1,2,3,5,8,⋯ , where f n+2 =f n+1 +f n and we number as f 1 =1,f 2 =1 . Try applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers? As a function or formula of n , how long does it take?
Applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers is GCD of that numbers .
Given :
You probably know the Fibonacci numbers 1 , 1 , 2 , 3 , 5 , 8 , ⋯ , where f n+2 = f n+1 + f n and we number as f 1 = 1,f 2 = 1 . Try applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers .
Euclidean algorithm :
The Euclidean Algorithm is a technique for quickly finding the GCD of two integers .
GCD ( 1 , 2 )
2 = 1 * 2 + 0
GCD ( 1 , 0 )
hence GCD ( 1 , 2 ) is 1 .
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Y-9=-4/3x+5 slope intercept form
Answer:
y=-4/3x+13
Step-by-step explanation:
formula:y=mx+b
you need to add 9 on both sides of the equation
so it's look like this:y-9=-4/3x+5
+9 +9
so combine the like terms
y=-4/3x+13
Please help :(
Solve each equation for I. Show all steps.
A) 50=10log base10 I
B) 60=10log base10 I
The solution of the logarithm equation are as follows:
a. l = 100000
b. l = 1000000
How to solve logarithm equation?Any equation in the variable x that contains a logarithm is called a logarithmic equation.
Let's solve the logarithm equation as follows:
a.
50 = 10 log₁₀ l
Using logarithm law,
50 = 10 log₁₀ l
50 = log₁₀ l¹⁰
10⁵⁰ = l¹⁰
multiply both sides of the exponents by 1 / 10
Hence,
l = 10⁵
Hence, the value of l = 100000
b.
60 = 10 log₁₀ I
Using logarithm rule,
60 = 10 log₁₀ I
60 = log₁₀ l¹⁰
10⁶⁰ = l¹⁰
multiply both sides of the exponents by 1 / 10
l = 10⁶
Hence, the value of l = 1000000
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If the translation T maps point A(-3,1) onto point A'(5,5), what is he translation T?
Answer: Translation T = (x + 8, y + 4)
Step-by-step explanation:
The x coordinate moved to the right by 8 and the y coordinate moved up by 4.
Franklin rolls a pair of six-sided fair dice with sides numbered 1 through 6.
The probability that the sum of the numbers rolled is either even or a multiple of 5 is
. The probability that the sum of the numbers rolled is either a multiple of 3 or 4 is
.
The probability that the sum of the numbers rolled is either even or a multiple of 5 is 61.11%.
What is Probability?Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,
Probability = Number of outcomes / Total number of outcomes
The total number of outcomes = 36
The number of outcomes whose sum is either even or a multiple of 5 = 22
The number of outcomes whose sum is either a multiple of 3 or 4 = 20
Now, the probability that the sum of the numbers rolled is either even or a multiple of 5 is,
Probability
= number of outcomes whose sum is either even or a multiple of 5 / total number of outcomes
= 22 / 36
= 11 / 18
= 0.61111
= 61.11%
Further, the probability that the sum of the numbers rolled is either a multiple of 3 or 4 is,
Probability
= number of outcomes whose sum of the numbers rolled is either a multiple of 3 or 4 / total number of outcomes
= 20 / 36
= 5/9
= 0.5555
= 55.55%
Hence, The probability that the sum of the numbers rolled is either a multiple of 3 or 4 is 55.55%.
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Here are the first four terms of a sequence. -1 4 9 14 Write an expression for the n th term of this sequence.
Answer:
The nth term is aₙ = 5n - 6-------------------------------------
Given sequence:
-1, 4, 9, 14, ...We observe that it has a linear increase and common difference of terms is 5:
4 - (-1) = 9 - 4 = 14 - 9 = 5So d = 5, a₁ = - 1, find the nth term:
aₙ = a₁ + (n - 1)daₙ = - 1 + (n - 1)*5 = - 1 + 5n - 5 = 5n - 6Scores on an IQ test are normally distributed. A sample of 18 IQ scores had standard deviation s=8.
(a) Construct a confidence interval for the population standard deviation . Round the answers to at least two decimal places.
(b) The developer of the test claims that the population standard deviation is 3. Does this confidence interval contradict this claim? Explain.
a) The 95% confidence interval for the population standard deviation is given as follows: (5.25, 10.49).
b) Since the interval does not contain 3, yes, it contradicts the claim of the developer.
What is the confidence interval for the standard deviation?The bounds of the confidence interval for the variance are given as follows:
[tex]\frac{(n - 1)s^2}{\chi^{2}_{\frac{\alpha}{2}}} \leq \sigma \leq \frac{(n - 1)s^2}{\chi^{2}_{1 - \frac{\alpha}{2}}}[/tex]
The parameters are given as follows:
n is the sample size.s is the sample standard deviation.[tex]\chi^2[/tex] represents the critical values.The critical values of the chi-square distribution with a confidence level of 95% and 18 - 1 = 17 df are given as follows:
7.5641 and 30.191.
Hence the lower bound of the interval for the variance is given as follows:
17 x 7²/30.191 = 27.59.
The upper bound of the interval is of:
17 x 7²/7.5641 = 110.13.
The standard deviation is the square root of the variance, hence the bounds are given as follows:
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The change in temperature after y minutes for a chemical in a lab can be represented by the expression −4(y − 3). Which other expression can be used to represent the change?
Other expression can be used to represent the change in temperature after y minutes is -4y + 12.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
The distributive property is a( b + c) = ab + ac.
Given expression that represents the change in temperature after y minutes for a chemical in a lab can be represented by the expression −4(y − 3).
Given expression is
-4(y - 3)
Applying distributive property:
= -4 × y - (-4)×3
= -4y + 12
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