It's important to evaluate the fit of the equation to the data before making any predictions or decisions based on it.
To determine the linear equation that best represents the trend line for a given scatter plot, we need to find the line of best fit. The line of best fit is a straight line that represents the general trend of the data and can be used to make predictions or estimates based on the data.
One way to find the line of best fit is by using the method of least squares. This involves finding the line that minimizes the sum of the squared differences between each data point and the line itself.
Once we have the line of best fit, we can express it as a linear equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To determine the linear equation that best represents the trend line for a given scatter plot, we would need to perform the following steps:
Plot the scatter plot of the given data points.
Visually inspect the scatter plot to see if there appears to be a linear relationship between the variables.
Calculate the line of best fit using the method of least squares.
Express the line of best fit as a linear equation of the form y = mx + b.
Use the equation to make predictions or estimates based on the data.
It's important to note that the linear equation that best represents the trend line for a scatter plot may not always be a good predictor of the data, especially if the data is not linear or if there are outliers present.
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In the figure, each small cube has edges that are 1/3 yd long. Which expression can you use to find the volume of the rectangular prism is cubic yards?
The expressiοn (B) 2 × 4 × 5 × 1/3 × 1/3 × 1/3 can be used tο find the vοlume οf the rectangular prism is cubic yards.
What is equatiοn?A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.
Vοlume is calculated using the fοrmula LWH
Here each cube has side 1/3 yd
Sο vοlume = (2 × 1/3) × (4 × 1/3) × (5 × 1/3)
It can be written as 2 × 4 × 5 × 1/3 × 1/3 × 1/3
Thus, οptiοn B is cοrrect.
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Complete question:
Audrey’s university English teacher Mr. Dalton has told her she will have 28 assignments this semester. Audrey has discovered that she needs to spend 2.5 hours on each assignment.
How many hours will Audrey spend on her English assignments?
AND
How many days will it take Audrey to complete her assignments?
Answer:
70 and 2.91 days
hope this helped
Hellllllllllllllllp meeeeeeeeeeeee
Answer: Option B is the correct answer
Step-by-step explanation:
Area of lateral surface = 3 x Area of rectangle
The rectangle is of 5 inches wide and 14 inches long.
Area of rectangle = 5 x 14 = 70 square inches
Area of lateral surface = 3 x Area of rectangle
Area of lateral surface = 3 x 70 = 210 square inches
Option B is the correct answer.
Keith who runs a daycare center bought 14 gallons of paint to do up the classroom how many classrooms can he get painted in all if each room requires 7/4 gallons of paint
Answer:
Keith bought 14 gallons of paint, and each classroom requires 7/4 gallons of paint.
To find how many classrooms can be painted, we can divide the total amount of paint by the amount of paint needed per classroom:
14 ÷ (7/4) = 8
Therefore, Keith can paint 8 classrooms in total.
What is 23.5% of 855? Give your answer to three decimal places
Find the relative maxima and minima, if any, of the function or
DNE. f(x) = x + 9/x + 5
The relative maxima.
To find the relative maxima and minima of the function f(x) = x + 9/x + 5, we need to first find the derivative of the function.
The derivative of f(x) is f'(x) = 1 - 9/x^2.
Next, we need to set the derivative equal to zero and solve for x to find the critical points.
1 - 9/x^2 = 0
9/x^2 = 1
x^2 = 9
x = ±3
So, the critical points are x = 3 and x = -3.
To determine if these are relative maxima or minima, we need to use the second derivative test.
The second derivative of f(x) is f''(x) = 18/x^3.
Plugging in x = 3, we get f''(3) = 18/27 = 2/3, which is positive. This means that x = 3 is a relative minima.
Plugging in x = -3, we get f''(-3) = 18/-27 = -2/3, which is negative. This means that x = -3 is a relative maxima.
Therefore, the relative maxima is at x = -3 and the relative minima is at x = 3.
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Find the length of the missing side.
Answer:
8
Step-by-step explanation:
Let's call the unknown side [tex]c[/tex].
The Pythagorean Theorem states that in any right triangle, [tex]a^{2} + b^2 = c^2[/tex]
Now plug in the known values.
[tex]6^2 + (2\sqrt 7)^2 = c^2\\36 + 4(7) = c^2\\36 + 28 = c^2\\64 = c^2\\c = \sqrt{64} = 8[/tex]
Which value shows the point on the number line?
The value shown on the number line is 3 8/10
How to determine the value shown on the number lineThe number line represents the given parameter
On the number line, we have the point located between 3 and 4
Such that the point is at 0.8 between 3 and 4
When the above expression is represented as a number, we have
Number = 3 + 0.8
Express the decimal as a fraction
So, we have
Number = 3 + 8/10
Evaluate
Number = 3 8/10
Hence, the solution is 3 8/10
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Mr. Ling is adding a pond in the shape of a semicircle in his backyard. What is the area of the pond? Use 3.14 for n. Round to the nearest
hundredth if necessary.
Next Question
ft²
Check Answer
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The area of the pond after rounding to the nearest hundredth is 39 feet²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
To find the area of a semicircle, we need to first find the radius of the pond.
Let's assume the diameter of the pond is 10 feet.
Since a semicircle is half of a circle, the radius of the pond is half the diameter, which is 5 feet.
Now we can use the formula for the area of a semicircle, which is:
A = (1/2)πr²
where A is the area and r is the radius.
Plugging in the values, we get:
A = (1/2) × 3.14 × 5²
A = 39.25
Rounding to the nearest whole number, the area of the pond is approximately 39 square feet.
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2. Kim, Doug, and Conner all run on the cross country team. In the last race Doug finished first, Kim finished 3 minutes after Doug, and Conner finished with a time that was twice Doug’s time.
a. What is the sum of their times?
b. What property or properties did you use?
c. Evaluate the expression if Doug ran the race in 27 minutes.
a) The sum of their times is of 4x + 3.
b) The property used is the combination of like terms, which we use to add the terms with the variable x.
c) If Doug ran the race in 27 minutes, the total time for the team is of 111 minutes.
How to obtain the expression?Doug finished first, and the times of the other two athletes are as function of Doug, hence the variable x represents the time needed for Doug to finish the race, that is:
D = x.
Kim finished 3 minutes after Doug, hence:
K = D + 3
K = x + 3.
Conner finished with a time that was twice Doug’s time, hence:
C = 2x.
Then the total time is given as follows:
T = D + K + C
T = x + x + 3 + 2x
T = 4x + 3.
If Doug ran the race in 27 minutes, the total time for the team is obtained as follows:
T = 4 x 27 + 3
T = 111 minutes.
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7. Use a half-angle identity to find each exact value. a. sin 195 b. cos 165
8. Find the following: a. cos θ/2 given sin θ = - 4/5 with 180º < θ < 270º. b. cot θ/2, given tan θ = - √5 / 2 with 90° < θ < 180°.
The exact values are sin 195 = 0.9763, cos 165 = 0.6088, cos θ/2 = 0.8944, and cot θ/2 = -0.2764.
To find the exact value of sin 195 and cos 165 using a half-angle identity, we need to use the following formulas:
sin(x/2) = √[(1-cosx)/2] and cos(x/2) = √[(1+cosx)/2]
For sin 195, we can use the half-angle identity for sine:
sin(195/2) = sin(97.5) = √[(1-cos195)/2] = √[(1+0.9063)/2] = √(0.9532) = 0.9763
For cos 165, we can use the half-angle identity for cosine:
cos(165/2) = cos(82.5) = √[(1+cos165)/2] = √[(1-0.2588)/2] = √(0.3706) = 0.6088
For question 8, we can use the given values and the half-angle identities to find the exact values of cos θ/2 and cot θ/2.
For cos θ/2 given sin θ = -4/5 with 180º < θ < 270º, we can use the half-angle identity for cosine:
cos(θ/2) = √[(1+cosθ)/2] = √[(1+√(1-sin^2θ))/2] = √[(1+√(1-(-4/5)^2))/2] = √[(1+√(1-(16/25)))/2] = √[(1+√(9/25))/2] = √[(1+(3/5))/2] = √(0.8) = 0.8944
For cot θ/2 given tan θ = -√5/2 with 90° < θ < 180°, we can use the half-angle identity for cotangent:
cot(θ/2) = (1+cosθ)/sinθ = (1+√(1-sin^2θ))/sinθ = (1+√(1-(1/tan^2θ)))/(1/tanθ) = (1+√(1-(1/(-√5/2)^2)))/(-√5/2) = (1+√(1-(4/5)))/(-√5/2) = (1+√(1/5))/(-√5/2) = (1+(1/√5))/(-√5/2) = (1-(1/√5))/(-√5/2) = -0.2764
Therefore, the exact values are sin 195 = 0.9763, cos 165 = 0.6088, cos θ/2 = 0.8944, and cot θ/2 = -0.2764.
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please someone complete this ive never struggled so bad
Answer:
Step-by-step explanation:
Im not really sure what the heck you doing because im only in 8th grade but right now im in central and i'm kind of good at math but i'll try. Lets see........ I think they would all just be $11.50, but like i said im only in 8th grade and not that good at this kind of math so before you answer it please check with someone else to see if i got it right for you, cause i don't want to give you the wrong answer and you fail it.
LetP(x)=10x5−35x4+22x3+13x2+4x+4. (a) Use the Rational Roots Theorem to find all possible rational roots ofP(x). LetP(x)=10x5−35x4+22x3+13x2+4x+4. (b) Find all roots ofP(x)
The Rational Roots Theorem states that the possible rational roots of a polynomial equation are the factors of the constant term divided by the factors of the leading coefficient. Therefore, the possible rational roots of P(x) are ±1, ±2, ±4, and ±4.
To find the exact roots of P(x), we can use synthetic division. Synthetic division is an efficient way of dividing a polynomial by a number. Using this method, we can determine that there are three roots for P(x): 1, -2, and -3. To verify this, we can evaluate P(x) for each of the three roots and confirm that the result is zero.
We can also use the quadratic formula to find the remaining two roots. Since P(x) is a 5th degree polynomial, the two remaining roots are complex and can be found using the quadratic formula. The complex roots of P(x) are -0.5 ± 0.5i.
In conclusion, the roots of P(x) are 1, -2, -3, -0.5 ± 0.5i. All of these results can be verified by evaluating P(x) and confirming that the result is zero.
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What is the intersection of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14-37
The intersection set, A∩ B, of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14 } is equals to the { 6, 14}.
For any two sets A and B, the intersection, A∩ B (read as A intersection B) lists all the elements that are present in both sets, and are the common elements of A and B. The intersection of sets is denoted by the symbol '∩'. It is subset of both of sets, A and B. For example, if Set A = {1,2,3,4,5} and Set B
= {3,4,6,8}, A ∩ B = {3,4}.
Here, we have two sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14 }
The common elements in sets A and B
= { 6,14 }
Therefore, the intersection of A and B,
A ∩ B = { 6, 14}.
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Complete question:
What is the intersection of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14}?
I REALLY NEED HELP ON THESE QUESTIONS!
The surface areas of these cylinders are 75.39 cm, 835.76 cm, 1324.11 cm, and 3543.71 cm.
How to calculate the surface area of a cylinder?The surface area of a cylinder can be calculated by using the formula 2π r h + 2π r², which means we need the radius and the height to calculate the area. Let's now use this formula to know the area of each cylinder:
Cylinder 1:
2π 2 4+ 2π 2² = 75.39 cm
Cylinder 2:
2π 7 12+ 2π 7² = 835.76 cm
Cylinder 3:
2π 8.2 17.5+ 2π 8.2² = 1324.11 cm
Cylinder 4:
2π 12 35 + 2π 12r² = 3543.71 cm
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Find x to the nearest degree
The nearest value of x is 56°. We solve this question using Pythagoras theorem for that we also find one of its side which is not given.
What is Pythagoras theorem?The square on the hypotenuse of a right-angled triangle has the same area as the sum of the squares on the other two sides, according to a Pythagorean theorem.
Given AB = 5 and AC = 9
By Using Pythagoras theorem,
AB² + BC² = AC²
5² + BC² = 9²
BC² = 9² - 5²
BC² = 81 - 25
BC = 7.48 (Approx.)
Now, we will find the value of x°
[tex]So, tan\ x^{\circ} = \frac{BC}{AB}[/tex]
[tex]tan \ x^{\circ} = \frac{7.48}{5}[/tex]
[tex]tan\ x^{\circ} = 1.496[/tex]
[tex]x^{\circ} =tan^{-1} 1.496[/tex]
[tex]x^{\circ} = 56.24^{\circ}[/tex] , which is close to 56°
So the nearest value of x is 56°.
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Solving Trigonometric Functions 6. a. Solve the following equations using algebra. You must show your algebra steps for full marks. You may use desmos to verify, but the marks will be allocated to the process not just the solution.
i. 2 sin^2 θ = 1, 0 < θ < 2π
ii. sin 1/2 θ = 1, - π < θ < 2π
iii. 4 cos(θ-45º) + 7 = 10, 0 < θ < 360 º
The solutions to the given trigonometric equations are:
i. θ = π/4, 3π/4, 5π/4, 7π/4
ii. θ = π/2, 3π/2
iii. θ ≈ 76.96º, 13.04º
To solve the given trigonometric equations using algebra, we need to rearrange the equations and use trigonometric identities to find the values of θ that satisfy the equations.
i. 2 sin^2 θ = 1, 0 < θ < 2π
First, we rearrange the equation to isolate sin^2 θ:
sin^2 θ = 1/2
Next, we take the square root of both sides:
sin θ = ±√(1/2)
Using the identity sin θ = cos (π/2 - θ), we can find the values of θ that satisfy the equation:
θ = π/4, 3π/4, 5π/4, 7π/4
ii. sin 1/2 θ = 1, - π < θ < 2π
First, we rearrange the equation to isolate θ:
sin θ = 2
Next, we use the identity sin θ = 1/csc θ to find the values of θ that satisfy the equation:
θ = π/2, 3π/2
iii. 4 cos(θ-45º) + 7 = 10, 0 < θ < 360 º
First, we rearrange the equation to isolate cos(θ-45º):
4 cos(θ-45º) = 3
cos(θ-45º) = 3/4
Next, we use the identity cos θ = sin (π/2 - θ) to find the values of θ that satisfy the equation:
θ = 45º + cos^-1(3/4), 45º - cos^-1(3/4)
Using desmos, we can verify our solutions and find the approximate values of θ:
θ ≈ 76.96º, 13.04º
Therefore, the solutions to the given trigonometric equations are:
i. θ = π/4, 3π/4, 5π/4, 7π/4
ii. θ = π/2, 3π/2
iii. θ ≈ 76.96º, 13.04º
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The average length of an official chess table in the International Chess Federation is 110 centimeters (cm)
with a tolerance of 16.5 cm. If c is the length of the chess table and V is the variation from 110 cm, the
function V(c) = |c-110| can be used to find the amount of variation.
Complete the statements by typing decimal values in the blank spaces.
Answer:
1. What is the maximum length of a chess table that is still within the tolerance limit?
To find the maximum length of a chess table that is still within the tolerance limit, we add the tolerance to the average length:
110 cm + 16.5 cm = 126.5 cm
Therefore, the maximum length of a chess table that is still within the tolerance limit is 126.5 cm.
2. What is the minimum length of a chess table that is still within the tolerance limit?
To find the minimum length of a chess table that is still within the tolerance limit, we subtract the tolerance from the average length:
110 cm - 16.5 cm = 93.5 cm
Therefore, the minimum length of a chess table that is still within the tolerance limit is 93.5 cm.
Step-by-step explanation:
Use simple interest to find the ending balance.
$36,000 at 6.3% for 4 years
Answer:
$45072
Step-by-step explanation:
I = Prt
I = 36000(6.3/100)(4)
I = 9072
ending balance = 36000 + 9072
= 45072
60 students went on a school trip to the zoo. 32 of the students bought a packed lunch
From the given information provided, the number of students who brought a packed lunch and did not visit the gift shop is 32.
The number of students who brought a packed lunch and did not visit the gift shop can be calculated by subtracting the number of students who visited the gift shop from the number of students who bought a packed lunch:
32 - 0 = 32
A frequency tree is a visual representation of data that shows how the total number of individuals or items is distributed among different categories or groups. It is commonly used in statistics and probability to organize and analyze data in a hierarchical structure.
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using a table of values what is an approximate solution to the equation f(x)=g(x) to the nearest quarter of a unit
The desired solution is to the nearest quarter of a unit, the approximate solution is x=2.25.
What is a quarter?A quarter is a fraction that represents one-fourth of a whole number or quantity. It can be written as a ratio, a decimal, or a percentage. A quarter is one of the simplest fractions, and it can be used to divide an object or number into four equal parts. It is also used to calculate percentages and proportions.
A table of values is a great way to approximate a solution to an equation. To approximate a solution to the equation f(x)=g(x) to the nearest quarter of a unit, the table of values must contain the x-values and the corresponding f(x) and g(x) values.
For example, if the equation was f(x)=2x+3 and g(x)=x+2, the table of values would look like this:
x f(x) g(x)
0 3 2
1 5 3
2 7 4
3 9 5
4 11 6
To find the approximate solution to f(x)=g(x), the table must be examined for the first x-value where the f(x) and g(x) values are equal. In this case, the x-value is 2 and the corresponding f(x) and g(x) values are both 7. Since the desired solution is to the nearest quarter of a unit, the approximate solution is x=2.25.
This method of using a table of values to approximate a solution to an equation is very simple and quick. It is a great way to get a rough answer to an equation without having to solve it. It is also a useful tool for double-checking the exact solution to an equation.
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If k is a real number, then the vectors(1,k),(k,3k+18)are linearly independent precisely whenk=a,b, wherea=,b=, anda
The vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.
If k is a real number, then the vectors (1,k), (k,3k+18) are linearly independent precisely when k≠a,b, where a=-18 and b=1/3. This is because for the vectors to be linearly independent, the equation c1(1,k) + c2(k,3k+18) = (0,0) should only have the trivial solution of c1 = c2 = 0. If k = a or k = b, then there will be nontrivial solutions for c1 and c2, making the vectors linearly dependent.
To find the values of a and b, we can set the equations for the x and y components equal to 0 and solve for k:
c1 + c2k = 0
c1k + c2(3k+18) = 0
From the first equation, we can solve for c1 in terms of c2 and k:
c1 = -c2k
Substituting this into the second equation:
-c2k^2 + c2(3k+18) = 0
c2(-k^2 + 3k + 18) = 0
Since c2 cannot be 0, we can divide both sides by c2 and solve the quadratic equation for k:
-k^2 + 3k + 18 = 0
(k-1/3)(k+18) = 0
So k = 1/3 or k = -18. Therefore, the vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.
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A parallelogram has an area of
102 1/2
square inches , with a height of 10 inches. How many inches long is the base of the parallelogram?
The length of the base of the parallelogram is 10.25 inches.
given that,
the area of parallelogram=102 1/2 square inches
height=10 inches
The following formula determines the area of a parallelogram:
Base + height = area.
The parallelogram's area and height are provided. By entering these values in the above formula we obtain:
102 1/2 = base × 10
We can divide both sides by 10 to find the base:
102 1/2 ÷ 10 = base
By dividing 1 by 2, we may convert the mixed number 1/2 to a decimal:
102 1/2 ÷ 10 = 102.5 ÷ 10 = 10.25
therefore, the length of the base of the parallelogram is 10.25 inches long.
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Wse the Law of Cosines to determine the indicated angle e0. (Assume \( a=69.01, b=39.28 \), and \( c=42.65 \), Round your answer to two decimal places.) \[ d= \] Neod Help?
The final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.
To determine the indicated angle, we can use the Law of Cosines, which states that: \[ c^2 = a^2 + b^2 - 2ab\cos(C) \]We can rearrange this equation to solve for the cosine of the indicated angle: \[ \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \]Plugging in the given values for a, b, and c, we get: \[ \cos(C) = \frac{69.01^2 + 39.28^2 - 42.65^2}{2(69.01)(39.28)} \]Simplifying the expression, we get: \[ \cos(C) = 0.7664 \]Now, we can use the inverse cosine function to find the indicated angle: \[ C = \cos^{-1}(0.7664) \]This gives us an angle of 40.32 degrees. However, the question asks us to round our answer to two decimal places, so the final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.
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Nathan's orchestra has 18 string
musicians, 9 percussion musicians,
15 brass musicians, and 12 woodwind
musicians. Six of the musicians cannot
play in the next performance. If the
remaining musicians plan to sit in rows
of 6 chairs, how many rows of chairs
are needed?
Rows of chairs that are needed to make 48 musicians sit is 8 rows.
What is division?The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.
Given,
Number of musicians in orchestra
18 string musicians, 9 percussion musicians,
15 brass musicians, and 12 woodwind musicians
Total number of musicians
= 18 + 9 + 15 + 12
= 54
Six of the musicians cannot play in the next performance
Number of musicians playing in next performance
= 54 - 6
= 48
48 musicians will sit on 48 chairs
Number of chairs in one row = 6
Number of rows for 48 chairs = 48/6 = 8
Hence, 8 rows of chairs are needed to make 48 musicians sit.
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i need help with finding the domain and range for this will give brainliest
For the given function we have:
domain [0, 76,867] and range [$0, $12,375,587]
How to find the domain and range?We know that x represents the number of people in atendance, then:
R(x) = 161*x
Represents the revenue.
The domain is the set of possible inputs, and it will go between 0 and 76,867 (total number of seats).
The range will go between:
R(0) = 161*0 = 0
R(76,867) = 76,867*161 = 12,375,587
Then the domain is all the integers in [0, 76,867] and the range is [$0, $12,375,587]
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f(x)=x^4−19x^3+135x^2+2 - Fias the toe crical nambers a,b of f′ (that is. the values at which f′′′ is zero or undetined) and lat thoir euact values in the fiet colume of the tibie below (n ancendeng order, a
Local Minima is 5 and 80
The critical numbers, a and b, of f'(x)=x^4−19x^3+135x^2+2 can be found by setting the derivative f'(x) = 0 and solving for x.
The derivative is: f'(x) = 4x^3 − 57x^2 + 270x
By setting the derivative equal to 0, we get:
4x^3 − 57x^2 + 270x = 0
Solving for x, we get:
x = 0, x = 5, x = 9
The critical numbers of f'(x) are 0, 5 and 9. The second derivative f''(x) is undefined at x = 0, so this is a local maximum point, while x = 5 and 9 are local minimum points.
Table:
Critical number | Second derivative (f''(x)) | Value
0 | Undefined | Local Maximum
5 | -80 | Local Minimum
9 | 80 | Local Minimum
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A blue print of a house has a scale of 1. 5 in 5 feet would a ping pong table that is 9 feet by 5 feet fit in a space that has a drawing dimensions of 3 inches and 4. 8 inches if so how much space in feet square will remain after the table is put in the room
There will be about 111.25 square feet of space remaining in the room after the ping pong table is put in.
First, we need to convert the scale of the blueprint to a real-world scale. Since the scale is 1.5 in 5 feet, we can write this as:
1.5 inches : 5 feet
To convert this to a ratio that we can use, we can divide both sides by 1.5 inches:
1 inch : 3.33 feet
Now we can use this ratio to convert the dimensions of the room from the blueprint to real-world dimensions:
3 inches x 3.33 feet/inch = 9.99 feet
4.8 inches x 3.33 feet/inch = 15.96 feet
So the room is approximately 10 feet by 16 feet.
Next, we need to see if the ping pong table will fit in the room. The table is 9 feet by 5 feet, which means it needs at least a space of 9 feet x 5 feet = 45 square feet. To convert this to the scale of the blueprint, we can use the inverse of the ratio we calculated earlier:
1 foot : 1/3.33 inches
So the table needs at least a space of 9 feet x (1/3.33 inches/foot) = 27 inches by 5 feet x (1/3.33 inches/foot) = 15 inches on the blueprint.
The space in the room is 3 inches x 4.8 inches on the blueprint, which is equivalent to 3 inches x (1/1.5 inches/foot) = 2 feet and 4.8 inches x (1/1.5 inches/foot) = 1 foot 7.8 inches in real-world dimensions.
Since the table will fit on the blueprint, we can now calculate the remaining space in the room. The total area of the room is approximately 10 feet x 16 feet = 160 square feet.
The area taken up by the ping pong table is approximately 9 feet x 5 feet = 45 square feet, or 27 inches x 15 inches on the blueprint. To convert this to square feet, we can use the ratio we calculated earlier:
27 inches x (1/12 feet/inch) x 15 inches x (1/12 feet/inch) = 3.75 square feet
So the remaining space in the room is approximately 160 square feet - 45 square feet = 115 square feet - 3.75 square feet
= 111.25 square feet.
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I don’t understand how to solve this when one number is missing! Pls help
Given:
5yd
To find:
The area of the hexagon
Solution:
[tex]area \: of \: hexagon = 6s[/tex]let the area of hexagon here be x. [tex] = 5 \times 6 \\ = 30yd[/tex]Learn more about area and perimeter:https://brainly.ph/question/14127685Help anything is useful!!
The value of x in the triangle based on Pythagoras Theorem will be 13
What is Pythagoras theorem?Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a²+b²=c². However, it can also be written in the form of c²=a²+b²
This will be:
x² = 12² + 5²
x² = 144 + 25
x² = 169
x = ✓169
x = 13
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