Answer:
Probability of the sticks weight being 2.44 oz or greater is 0.01017 .
Step-by-step explanation:
We are given that the manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz.
Also, it is given that the weight of the drumsticks is normally distributed.
Let X = weight of the drumsticks, so X ~ N([tex]\mu = 2,\sigma^{2} = 0.19^{2}[/tex])
The standard normal z distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
Now, probability of the sticks weight being 2.44 oz or greater = P(X >= 2.44)
P(X >= 2.44) = P( [tex]\frac{X-\mu}{\sigma}[/tex] >= [tex]\frac{2.44-2}{0.19}[/tex] ) = P(Z >= 2.32) = 1 - P(Z < 2.32)
= 1 - 0.98983 = 0.01017
Therefore, the probability of the sticks weight being 2.44 oz or greater is 0.01017 .
Final answer:
The probability of the sticks weighing 2.44 oz or more is approximately 0.01017.
Explanation:
Given that the manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz, we know the weight of the drumsticks is normally distributed.
Let X represent the weight of the drumsticks, with X being normally distributed with a mean (μ) of 2 and a variance [tex](\sigma^2) \ of \ 0.19^2[/tex]
To find the probability of the sticks weighing 2.44 oz or more, we need to calculate P(X ≥ 2.44).
We can standardize X using the formula Z = (X - μ) / σ, which results in a standard normal distribution with mean 0 and standard deviation 1.
So, to find P(X ≥ 2.44), we compute P((X - μ) / σ ≥ (2.44 - 2) / 0.19), which simplifies to P(Z ≥ 2.32).
From the standard normal distribution table or a calculator, we find that P(Z < 2.32) is approximately 0.98983.
Therefore, P(Z ≥ 2.32) = 1 - P(Z < 2.32) = 1 - 0.98983 = 0.01017.
Hence, the probability of the sticks weighing 2.44 oz or more is approximately 0.01017.
What is Fermat’s Last Theorem?
Answer:
That is a VERY famous math problem first published in 1637 by Pierre Fermat. He said that in an equation of the type
x^n + y^n = z^n
you will ONLY find solutions when "n" is no greater than 2. He said he had a proof but the margin in his note book was too small to fit it in.
(It is now believed he never had any such proof.)
Anyway, we can find an infinite number of solutions when n = 2
3^2 + 4^2 = 5^5
5^5 + 12^2 = 13^2
but you cannot find any solutions when n = 3 or higher.
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem
Finally in 1995, (358 YEARS after Fermat first published this theorem), the British mathematician Andrew Wiles published his own proof of this theorem.
https://en.wikipedia.org/wiki/Andrew_Wiles
Step-by-step explanation:
Final answer:
Fermat's Last Theorem is a famous mathematical conjecture proposed by Pierre de Fermat in the 17th century, stating that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. The theorem remained unproven for over 350 years until Andrew Wiles presented a proof in 1994.
Explanation:
Fermat's Last Theorem is a famous mathematical conjecture proposed by Pierre de Fermat in the 17th century. The theorem states that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. In other words, there are no whole number solutions to this equation when n is greater than 2.
This conjecture remained unproven for over 350 years and became one of the most elusive problems in mathematics. However, in 1994, the British mathematician Andrew Wiles presented a proof of Fermat's Last Theorem, which is considered one of the most significant achievements in the history of mathematics.
twin bothers, collin and cameron get jobs immediately after graduating from college at the age of 22. collin opts for the higher starting salary, $55,000 and stays with the same company until he retires at age 65. his salary doubles every 15 years. cameron opts for the lower starting salary, $35,000 but moves to a new job every few years so that he doubles his salary every 10 years until he retires at age 65. what is the annual salary of each brother upon retirement?
Collin
22 years = 55,000 USD
+15 years
37 years = 2 x 55,000 = 110,000 USD
+15 years
52 years = 2 x 110,000 = 220,000 USD
Cameron
22 years = 35,000 USD
+10 years
32 years = 2 x 35,000 = 70,000 USD
+10 years
42 years = 2 x 70,000 = 140,000 USD
+10 years
52 years = 2 x 140,000 = 280,000 USD
+10 years
62 years = 2 x 280,000 = 560,000 USD
Retirement Salaries
Collin = 220,000 USD
Cameron = 560,000 USD
consider the diagram below. which of the following statements are correct? select all that apply
Answer:
• ΔCFB ~ ΔEDB by the AA similarity
• mCE = 46°
Step-by-step explanation:
No lengths are marked equal on the diagram, so we cannot assume any of the chords is the same length as any other. Then there is no evidence that the conditions for SAS congruence are met for the given triangles. Likewise, there is no evidence that arcs DE and CF are the same length, which they would have to be to have measure 108°.
The angles with vertices C and E subtend the same arc, so have equal measures. Likewise for the angles with vertices D and F. The angles CBF and EBD are vertical angles, so also congruent. Hence the two triangles are AA similar.
The angle labeled 72° is half the sum of the measures of arcs CE and DF, so we have ...
(CE + 98°)/2 = 72°
CE = 144° -98° = 46° . . . . . multiply by 2 and subtract 98°
Answer:
Answer:
• ΔCFB ~ ΔEDB by the AA similarity
• mCE = 46°
Step-by-step explanation:
Rectangle moat has vertices m(1,2), p(1,3), a(3,3) and t(3,2). Rectangle moat was translated 1 unit right and 2 units up to produce rectangle m’p’a’t’. Which coordinates describes the vertices of the image?
Answer:
M'(2,4), P'(2,5), A'(4,5), T'(4,4)
Step-by-step explanation:
The translation 1 unit to the right and 2 units up has the rule
(x,y)→(x+1,y+2)
Rectangle MPAT has vertices at points M(1,2), P(1,3), A(3,3) and T(3,2). The image rectangle is rectangle M'P'A'T'. According to translation rule:
M(1,2)→M'(2,4);P(1,3)→P'(2,5);A(3,3)→A'(4,5);T(3,2)→T'(4,4).Solve the problem of exponential growth. In 1985 an antique automobile club had 23,000 members. Since then its membership has grown at an average rate of 5% per year. Assuming this trend continues, how many members will there be in 2020? Round to the nearest thousand.
Answer:
[tex]127,000\ members[/tex]
Step-by-step explanation:
In this problem we have an exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
The base is equal to
b=1+r
r is the average rate
In this problem we have
a=23,000 members
r=5%=5/100=0.05
b=1+0.05=1.05
substitute
[tex]f(x)=23,000(1.05)^{x}[/tex]
x ----> is the number of years since 1985
How many members will there be in 2020?
x=2020-1985=35 years
substitute in the function
[tex]f(x)=23,000(1.05)^{35}=126,868\ members[/tex]
Round to the nearest thousand
[tex]126,868=127,000\ members[/tex]
Please help ASAP on #4,6 please I'll give you brainliest
Answer: 4) 0.8/(1/6)=4.8 miles per hour
6) 100%-16%=84%
500*0.84=420 mL
Step-by-step explanation:
4) rate=miles/hour
(pre-calc) WILL GIVE BRAINLIEST Find the direction angle of vector v to the nearest thenth of a degree
Please show work!
[tex]v[/tex] starts at the point (-5, 0) and ends at the point (7, 2). It points in the same direction as the vector [tex]w[/tex] where
[tex]w=(7,2)-(-5,0)=(12,2)[/tex]
which starts at the origin and ends at (12, 2). Its direction [tex]\theta[/tex] is such that
[tex]\tan\theta=\dfrac2{12}=\dfrac16[/tex]
[tex]w[/tex] terminates in the first quadrant, so both [tex]w[/tex] and [tex]v[/tex] have direction
[tex]\theta=\tan^{-1}\dfrac16\approx9.5^\circ[/tex]
Solve. x 5 + 3 = 2
a) -5
b) 25
c) 5
d) - 1/5
The answer is D. Have a nice day.
Your answer should be d!
Salska and colleagues (2008) studied height preferences among dating partners. In their first study, they reviewed Yahoo personals for heterosexual individuals living within 250 miles of Los Angeles, California, and recorded the acceptable range of heights for their dating partners. The following table lists some of the results. Overall, did men or women show greater variability in their responses? Explain.Women MenPreferences M SD M SDShortestacceptableheight, inches 68.9 2.6 60.6 3.7Tallestacceptableheight, inches 75.3 2.2 69.8 2.7a) Women showed greater variability overall because the standard deviations for women were smaller than for men. b) Women showed greater variability overall because the means for women were larger than for men. c) Men showed greater variability overall because the means for men were smaller than for women.d) Men showed greater variability overall because the standard deviations for men were larger than for women
Answer:
D
Step-by-step explanation:
The larger standard deviation, the greater the variability. So even before looking at the data, we can eliminate a) and c).
The standard deviations of men's preference of shortest and tallest acceptable height (3.7 and 2.7, respectively) were more than the standard deviations of women's preference of shortest and tallest acceptable height (2.6 and 2.2, respectively).
So men showed greater variability overall because the standard deviations for men were larger than for women. Answer D.
Final answer:
Men showed greater variability in their height preferences for dating partners than women, as indicated by the larger standard deviations in men's responses.
Explanation:
The question asks whether men or women showed greater variability in their height preferences among dating partners based on a study by Salska and colleagues (2008). In the given study, variability is indicated by the standard deviation (SD) values. A larger standard deviation signifies greater variability in the responses. For the shortest acceptable height, men had an SD of 3.7 inches, while women had an SD of 2.6 inches. Likewise, for the tallest acceptable height, men had an SD of 2.7 inches versus women's 2.2 inches. These SD values clearly show that men displayed greater variability in their height preferences compared to women.
A kite has a height of 36 inches and a width of 30 inches. Explain how to use the area formula for a triangle to find the area of the kite. 34
Answer:
You can view a kite as 4 triangles
Step-by-step explanation:
A geometric kite can easily be viewed as 4 triangles. The formula to calculate the area of a kite (width x height)/2 is very similar to the one of a triangle (base x height)/2.
According to the formula to calculate the area of a kite, we would get:
(36 x 30)/2 = 540.
If we take the approach of using 4 triangles, we could imagine a shape formed by 4 triangles measuring 18 inches wide with a height of 15.
The area of each triangle would then be: (18 x 15)/2 = 135
If we multiply this 135 by 4... we get 540.
Answer:
Draw a vertical line to break the kite into two equal triangles with a base of 36 and a height of 15. Use the formula A = 1/2bh to find the area of each. The sum of the areas is the area of the kite.
Step-by-step explanation:
Factor the expression. 6x^2 + 31x + 28
A.) (x + 4)(6x + 7)
B.) (x + 2)(6x + 14)
C.) (3x + 7)(3x + 4)
D.) (x + 14)(6x + 2)
Answer:
(6 x + 7) (x + 4) thus A:
Step-by-step explanation:
Factor the following:
6 x^2 + 31 x + 28
Factor the quadratic 6 x^2 + 31 x + 28. The coefficient of x^2 is 6 and the constant term is 28. The product of 6 and 28 is 168. The factors of 168 which sum to 31 are 7 and 24. So 6 x^2 + 31 x + 28 = 6 x^2 + 24 x + 7 x + 28 = 4 (6 x + 7) + x (6 x + 7):
4 (6 x + 7) + x (6 x + 7)
Factor 6 x + 7 from 4 (6 x + 7) + x (6 x + 7):
Answer: (6 x + 7) (x + 4)
The factored form of the expression '6x^2 + 31x + 28' is '(x + 4) (6x + 7)', which corresponds to option A.
Explanation:In factoring the expression '6x^2 + 31x + 28', we need to find two numbers whose product equals '6x2 * 28' (the product of the first and the last term), and sum equals '31x' (the middle term). The numbers that fit these conditions are '4' and '7'.
So, this means you can factor out 'x' from the terms '6x^2' and '31x' to get '6x*(x + 4)'. Then, you will be left with '+ 28'. The number '7' fits perfectly here, because '4 * 7 = 28'. Hence, the factored form of the expression is '(x + 4) (6x + 7)'.
This corresponds to the answer choice A.) (x + 4) (6x + 7).
Learn more about Factoring expressions here:https://brainly.com/question/34538246
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Tickets to see a movie is $16 for an adult and $10 for students. If they sold 400 tickets, which totaled $4,600, how many of each type did they sell?
Answer:
300 student tickets100 adult ticketsStep-by-step explanation:
Let "a" represent the number of adult (highest price) tickets sold. Then 400-a is the number of student tickets, and the revenue is ...
16a +10(400 -a) = 4600
6a = 600 . . . . . . . . . . . . . . . simplify, subtract 4000
a = 100 . . . . . . . . . . . . . . . . . divide by the coefficient of a
100 adult and 300 student tickets were sold.
_____
Note that the above can be described by the verbal reasoning: If all the tickets sold were the (lower price) student tickets, revenue would be $4000. It was actually $600 more than that. Each adult ticket sells for $6 more than a student ticket, so there must have been $600/$6 = 100 adult tickets sold.
_____
Another way to work this problem is as a "mixture" problem. The average selling price per ticket is $4600/400 = $11.50. The differences between this price and the adult and student ticket prices are 4.50 and 1.50, so the ratio of student tickets to adult tickets is 4.50:1.50 = 3:1. That is, there were 300 student tickets sold and 100 adult tickets sold.
Find the volume of a rectangular solid with a width 16 mm, length 22 mm and height 21 mm.
Check the picture below.
Find the volume of the square pyramid shown. Round to the nearest whole number. The diagrams are not drawn to scale.
Base: 12 cm
Height: 11 cm
NEED HELP ASAP!!!!!!!!!!!!!!
Answer:
528 cm^3
Step-by-step explanation:
The volume of a pyramid is given by the formula ...
V = 1/3·Bh
where B is the area of the base and h is the height.
The area of a square of side length s is given by ...
A = s^2
Then the area of the base of the pyramid is ...
A = (12 cm)^2 = 144 cm^2
So, the volume of the pyramid is ...
V = 1/3·(144 cm^2)(11 cm) = 528 cm^3
The function f(x) = x2 - 6x + 9 is shifted 5 units to the left to create g(x). What is
g(x)?
ANSWER
[tex]g(x) = {x}^{2} + 4x + 4[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} - 6x + 9[/tex]
This can be rewritten as:
[tex]f(x) = {(x - 3)}^{2} [/tex]
If this function is shifted 5 units to the left to create g(x), the
[tex]g(x) = f(x + 5)[/tex]
We substitute x+5 into f(x) to get:
[tex]g(x) = {(x + 5 - 3)}^{2} [/tex]
[tex]g(x) = {(x + 2)}^{2} [/tex]
We expand to get:
[tex]g(x) = {x}^{2} + 4x + 4[/tex]
Answer:
g(x) = x^2 + 4x + 4
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 6x + 9
a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;
g(x) = f(x+5)
g(x) = (x+5)^2 - 6(x+5) + 9
g(x) = x^2 + 10x + 25 - 6x -30 + 9
g(x) = x^2 + 4x + 4
Find the surface area of the tool box. Round your answer to the nearest tenth and explain your answer. Pls I NEED THE ANSWER NOW ASAP!!!
Answer:
807.8 in^2
Step-by-step explanation:
The total area of the box is the sum of the areas of all faces of the box. The top, bottom, front, and back faces are rectangles 18 in long. The end faces each consist of a rectangle and a triangle. We can compute the sum of these like this:
The areas of top, bottom, front, and back add up to be 18 inches wide by the length that is the perimeter of the end: 2·5in +2·8 in + 9.6 in = 35.8 in. That lateral area is ...
(18 in)(35.6 in) = 640.8 in^2
The area of the triangle on each end is equivalent to the area of a rectangle half as high, so we can compute the area of each end as ...
(9.6 in)(8.7 in) = 83.52 in^2
Then the total area is the lateral area plus the area of the two ends:
640.8 in^2 + 2·83.52 in^2 = 807.84 in^2 ≈ 807.8 in^2
Cole walked 2 1/2 kilometers on Monday. Isabella walked twice as many kilometers as coke. How many meters did cole and Isabella walk alotogether?
Answer:
7500 meters
Step-by-step explanation:
Isabella walked 2 × 2.5 km = 5 km. Together, they walked ...
2.5 km + 5 km = 7.5 km = 7.5×1000 m = 7500 m
Cole and Isabella walked 7500 meters altogether.
_____
"kilo-" is a prefix meaning "one thousand". So one kilometer is 1000 meters. Then 7.5 kilometers is 7.5 times 1000 meters, or 7500 meters.
Graph the functions on the same coordinate plane.
f(x) = x^2 - 4x + 3
g(x) = -x^2 + 3
What are the solutions to the equation where f(x) = g(x)?
Question options:
−1
0
1
2
3
Answer:
x=0, x=2
Step-by-step explanation:
Here is the graph: desmos.com/calculator/thpubranfo
As we can see, the two functions have two points of intersection. (0, 3) and (2, -1).
If the value of the functions is the same. Then the value of x will be 0 and 2.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
Graph the functions on the same coordinate plane.
f(x) = x² - 4x + 3
g(x) = -x² + 3
If the value of the functions is the same. Then the value of x will be
f(x) = g(x)
x² - 4x + 3 = -x² + 3
x² - 4x + 3 + x² - 3 = 0
2x² - 4x = 0
x (x - 2) = 0
x = 0, 2
The graphs are given below.
Then the correct options are B and D.
More about the function link is given below.
https://brainly.com/question/5245372
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x-12/x-8 rational expression
It is a rational expression.
A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on top, where the radius of the hemisphere is to be the same length as the radius of the base of the cylinder. The farmer would like the height of the silo’s cylinder portion to be 3 times the diameter of the base of the cylinder. What should the radius of the silo be if the silo is to hold 22,500 cubic feet of grain?
Answer:
about 10.24 ft
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . where h is the height and r is the radius
The formula for the volume of a sphere is ...
V = (4/3)πr³ = πr²·(4/3r) . . . . equivalent to a cylinder of height 4/3r
__
We have a cylinder of height 3d = 3(2r) = 6r. It has half a sphere on top, so the equivalent height of that is (1/2)·(4/3r) = 2/3r.
Then our total volume is equivalent to a cylinder with radius r and height (6 2/3)r = (20/3)r. That is, ...
22,500 ft³ = πr²·(20/3)r = (20π/3)r³
Multiplying by the inverse of the coefficient of r³, then taking the cube root, we have ...
r = ∛(22,500·3/(20π)) ft ≈ 10.24 ft
The radius of the silo should be about 10.24 feet.
Answer:
10.24 ft
Step-by-step explanation:
745 mmHg into psi
727 mmHg into kPa
55.5kPa into atm
Answer:
14.4059 psi96.9254 kPa0.5181347 atmStep-by-step explanation:
Google is your friend for such conversions. It will generally give answers correct to 6 significant figures.
___
Normal atmospheric pressure is defined as 1 atmosphere.
1 atm = 101,325 Pa = 760 torr (mmHg) ≈ 14.695 948 775 514 2 psi
To convert 745 mmHg into psi, divide the value by 51.71. 745 mmHg is approximately equal to 14.41 psi. To convert 727 mmHg into kPa, divide the value by 7.5. 727 mmHg is approximately equal to 96.93 kPa. To convert 55.5 kPa into atm, divide the value by 101.325. 55.5 kPa is approximately equal to 0.55 atm.
Explanation:To convert 745 mmHg into psi, divide the value by 51.71. Therefore, 745 mmHg is approximately equal to 14.41 psi.
To convert 727 mmHg into kPa, divide the value by 7.5. Therefore, 727 mmHg is approximately equal to 96.93 kPa.
To convert 55.5 kPa into atm, divide the value by 101.325. Therefore, 55.5 kPa is approximately equal to 0.55 atm.
Last question please help me I’m lost
30.8% ≅ 31%. The probability in percent that a given graduate student is on financial aid is 31%.
The key to solve this problem is using the conditional probablity equation P(A|B) = P(A∩B)/P(B). Conditional probability is the probability of one event occurring with some relationship to one or more other events.
From the table we can see P(A∩B) which is the intersections of event A and event B, in this case the intersection is the amount of graduates students receiving financial aid 1879. Then P(A∩B) = 1879/10730.
From the table we can see P(B) which is the probability of the total of students undergraduate and graduate and the total of the students of the university data. Then P(B) = 6101/10730
P(A|B) = (1879/10730)/(6101/10730) = 0.307982
Round to nearest thousandth 0.308
Multiplying by 100%, we obtain 30.8% or ≅ 31%
NEED HELP ASAP!
Find the area of the shaded region. All angles are right angles.
Answer:
166 m^2
Step-by-step explanation:
The enclosing rectangle is 9m by 29m, so is 261 m^2. From that, the white space of 5m by 19m = 95 m^2 must be subtracted. The result is that the shaded area is ...
261 m^2 -95 m^2 = 166 m^2
3) Solve each equation using the quadratic formula. Show
a. x2 – 3x – 10 = 0
Answer:
x = -2 or x = 5Step-by-step explanation:
The quadratic formula of a quadratic equation
[tex]ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{If}\ b^2-4ac=0\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}[/tex]
[tex]\text{If}\ b^2-4ac<0\ \text{then the equation has no solution}[/tex]
We have:
[tex]x^2-3x-10=0\to a=1,\ b=-3,\ c=-10\\\\b^2-4ac=(-3)^2-4(1)(-10)=9+40=49>0\\\\x=\dfrac{-(-3)\pm\sqrt{49}}{2(1)}=\dfrac{3\pm7}{2}\\\\x=\dfrac{3-7}{2}=\dfrac{-4}{2}=-2\\or\\x=\dfrac{3+7}{2}=\dfrac{10}{2}=5[/tex]
Help with IXL please
Answer:
$77.18
Step-by-step explanation:
Fill in your equation like this:
[tex]B=70(1+.05)^2[/tex] and
[tex]B=70(1.05)^2[/tex] and
[tex]B=70(1.1025)[/tex] so
B = $77.18
PLEASE HELP MATH CIRCLES
Answer:
The measure of DE is 12
Step-by-step explanation:
* Lets study the figure to solve the problem
- There are two intersected circles B and C
- BA is a radius of circle B and CE is a radius of circle C
- AD is a tangent to the two circles touch circle B in A and touch
circle C in E
- The line center BC intersects the tangent AD at D
- There are two triangles in the figure Δ BAD and Δ CED
* Now lets solve the problem
∵ AD is a tangent to circles B and C
∵ BA and CE are radii
∴ BA ⊥ AD at A
∴ CE ⊥ AD at E
- Two lines perpendicular to the same line, then the two lines are
parallel to each other
∴ BA // CE
- From the parallelism
∴ m∠ABD = m∠ECD ⇒ corresponding angles
∴ m∠BAD = m∠CED ⇒ corresponding angles
- In any two triangles if their angles are equal then the two triangles
are similar
- In the two triangles BAD and CED
∴ m∠ABD = m∠ECD ⇒ proved
∴ m∠BAD = m∠CED ⇒ proved
∵ ∠D is a common angle of the two triangle
∴ The two triangle are similar
- There are equal ratios between their sides
∴ BA/CE =AD/ED = BD/CD
∵ BD = 50 , AD = 40 , CD = 15
∴ 40/ED = 50/15 ⇒ using cross multiplication
∴ ED(50) = 15(40)
∴ 50 ED = 600 ⇒ divide both sides by 50
∴ ED = 12
Let f(x)=x^2−9 and g(x)=x^2−7x+12 . What is (f/g)(x) ?
The answer is:
[tex]\frac{f(x)}{g(x)}=\frac{x+3}{x+4}[/tex]
Why?To solve the problem, we need to factorize the quadratic functions in order to be able to simplify the expression.
We can factorize quadratic functions in the following way:
[tex]a^{2}-b^{2} =(a-b)(a+b)[/tex]
Also, we can factorize/simplify quadratic expressions in the following way, if we have the following quadratic expression:
[tex]ax^{2}+bx+c[/tex]
We can factorize it by finding two numbers which its products give as result "c" (j) and its algebraic sum gives as result "b" (k), and then, rewrite the expression in the following way:
[tex](x+j)(x+k)[/tex]
Where,
x, is the variable.
j, is the first obtained value.
k, is the second obtained value.
We are given the functions:
[tex]f(x)=x^{2} -9\\g(x)=x^{2} -7x+12[/tex]
Then, factoring we have:
First expression,
[tex]f(x)=x^{2} -9=(x+3)(x-3)[/tex]
Second expression,
[tex]\g(x)=x^{2} -7x+12[/tex]
We need to find two number which product gives as result 12 and their algebraic sum gives as result -7. Those numbers are -4 and -3.
[tex]-4*-3=12\\-4-3=-7[/tex]
Now, rewriting the expression we have:
[tex]\g(x)=x^{2} -7x+12=(x-4)(x-3)[/tex]
So, solving we have:
[tex](f/g)(x)=\frac{f(x)}{g(x)}=\frac{(x+3)(x-3)}{(x+4)(x-3)}=\frac{x+3}{x+4}[/tex]
Have a nice day!
find the width of the rectangular prism if the volume is 165,000 the length is 100 mm and the height is 55
Answer:
30 mm
Step-by-step explanation:
The volume of a rectangular prism is the product of its three dimensions. To find the missing dimension, divide the volume by the product of the two that are given:
(165000 mm^3)/((100 mm)(55 mm)) = 165000/5500 mm^3/mm^2 = 30 mm
Answer:
30mm
Step-by-step explanation:
30mm
please respond asap!!!
ANSWER
[tex]9(\pi - \frac{ \sqrt{3} }{2} )[/tex]
Approximately, A=20
EXPLANATION
The circle has radius r=3 units.
The height of the triangle is ,
[tex]h = 6 \cos(60 \degree) = 3[/tex]
The base of the triangle is
[tex]b = 6 \sin(60 \degree) = 3 \sqrt{3} [/tex]
The area of the triangle is
[tex] \frac{1}{2} bh[/tex]
[tex] = \frac{1}{2} \times 3 \sqrt{3} \times 3[/tex]
[tex] = \frac{9}{2} \sqrt{3} [/tex]
The area of the circle is
[tex]\pi {r}^{2} [/tex]
[tex] = {3}^{2} \pi[/tex]
[tex] = 9\pi[/tex]
The difference between the area of the circle and the triangle is
[tex]9\pi - \frac{9}{2} \sqrt{3} = 9(\pi - \frac{ \sqrt{3} }{2} )[/tex]
Answer:
Difference = 20.47 square units
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where r - Radius of circle
Area of triangle = bh/2
Where b - Base and h- Height
It is given a circle with radius 3 units
And a right angled triangle with angles 30, 60 and 90 and hypotenuse = 6 units
To find the area of circle
Here r = 3 units
Area = πr²
= 3.14 * 3 * 3
= 28.26 square units
To find the area of triangle
Here sides are in the ratio Base : Height : hypotenuse = 1 : √3 : 2
= Base : Height : 6
= 3 : 3√3 : 6
Base b = 3 and height h = 3√3
Area = bh/2
= (3 * 3√3)/2
= 7.79 square units
To find the difference
Difference = 28.26 - 7.79
= 20.47 square units
find the area of a regular hexagon inscribed in a circle of radius 6 cm
Answer:
C
Step-by-step explanation:
If the hexagon is regular, that means that all of its sides are the same length, all of its interior angles are equal, as are the central angles formed by the triangles within in it. It is one of these triangles that we are concerned about.
If the regular hexagon is inscribed in a circle with a radius of 6, that means that the radius of the hexagon is also 6. The radii of the regular hexagon start at its center and go to each one of the 6 pointy ends (vertices). There are 6 sides so that means that there are 6 radii. That also means that each pair of radii create a triangle. There are 6 triangles inside this hexagon, and all of them are congruent. Because there are 6 central angles and because the degree measure around the outside of a circle is 360 degrees, we can find the vertex angle of each one of these 6 triangles by dividing 360 by 6 to get 60 degrees. The Isosceles Triangle Theorem tells us that if two sides of a triangle are congruent, then the angles opposite those congruent sides are also congruent. So 180 - 60 (the vertex angle) = 120, and 120 divided in half is 60. So this is an equilateral/equiangular triangle. Since all the angles measure 60, that means that all the sides measure the same, as well. So they all measure 6 cm. That gives us that one side of the hexagon measures 6 cm and we will need that for the formula for the area of said hexagon. The altitude of one of those equilateral triangles serves as the apothem that we also need for the area of the hexagon. If we split one of those triangles in half at the altitude, the base will measure 3 and the vertex angle will measure 30 degrees. In the Pythagorean triple for a 30-60-90, the side across from the 30 angle measures x, the side across from the 60 angle measure x times the square root of 3, and the hypotenuse measure 2x. That means that the apothem (which is the altitude of this triangle) is the length across from the 60 angle. So if x measures 3, then the side across from the 60 measures [tex]3\sqrt{3}[/tex]
The formula for the area of a regular polygon is
[tex]A=\frac{1}{2}ap[/tex]
where a is the apothem and p is the perimeter around the hexagon. We found one side to be 6 cm, so 6 times the 6 sides of the hexagon is 36 cm. The apothem is [tex]3\sqrt{3}[/tex]
so putting it all together in our formula looks like this:
[tex]A=\frac{1}{2}(3\sqrt{3})(36)[/tex]
Do the math on that and you will get
[tex]A=54\sqrt{3} cm^2[/tex]
93.53 cm².
The area of a regular hexagon inscribed in a circle of radius 6 cm can be calculated using the formula for the area of a regular hexagon.
Calculate the area of one of the equilateral triangles formed by the hexagon inscribed in the circle.
Multiply the area of one triangle by 6 to find the total area of the regular hexagon.
In this case, the area of the regular hexagon is approximately 93.53 cm².