The area of the original fountain was 16π square yards at the Palace of Versailles due to the radius of the fountain on a scale of 1 : 4.
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
A = πr²
where 'r' is the radius of the circle
The radius of the fountain using a scale of 1 : 4 in New York
The area of the fountain in New York is 1,600π square yards.
To determine the area of the original fountain at the Palace of Versailles
We can write this as a ratio as
A₁ : A₂ = πr² : π(4r)²
A₁ : 1,600π = πr² : π(4r)²
A₁ / 1,600π = πr² / π(4r)²
A₁ = (πr²/ π 16r²)(1,600π )
A₁ = 1,600π/16
A₁ = 16π square yards
Therefore, the area of the original fountain was 16π square yards at the Palace of Versailles.
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John works at the mall 20 hours a week and makes $8.50 an hour. He is saving for a car and needs a down payment of $500.
The will have to work for 3 weeks in order to save money for down payment of car.
What is the unitary method?Unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given in the question is a story of john works at the mall, 20 hours a week and makes $8.50 an hour. He is saving for a car and needs a down payment of $500.
Assume that he has to work 'x' number of weeks for down payment.
For 1 hour, John earns → $8.50
Number of hours he work in the mall per week → 20 hours
Amount of money collected in one week → $8.50 x 20 = $170
Money needed for down payment → $500
In 1 week, John earns → $170
So, he earns $1 in → 1 / 170 weeks
Therefore, he will earn $500 in →
(1 / 170) x 500 = 2.94 = 3 weeks (approx.)
Therefore, he will have to work for 3 weeks in order to save money for down payment of car.
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How can the discriminant be used to determine the number of solutions for a trinomial
in standard form?
See below for the explanation on how discriminant be used to determine the number of solutions
How can the discriminant be used to determine the number of solutions?Let a trinomial in standard form be represented as
y = ax^2 + bx + c
The discriminant (d) is calculated as
d = b^2 - 4ac
The solutions are dependent on the following conditions
If d = 0, the trinomial has 1 real solutionIf d < 0, the trinomial has imaginary solutionsIf d > 0, the trinomial has 2 different real solutionsRead more about discriminant at
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Hector is picking out some movies to rent, and he is primarily interested in documentaries and foreign films. He has narrowed down his selections to 11 documentaries and 15 foreign films.
Step 1 of 2 : How many different combinations of 4 movies can he rent?
Hector can have a total of 14950 number of combinations of 4 movies, from his shortlist of 11 documentaries and 15 foreign films, that he can rent.
As per the question statement, Hector has shortlisted 11 documentaries and 15 foreign films, from which he wants to rent any 4 movies.
We are required to calculate the total of number of combinations of 4 movies from his above mentioned shortlist.
Total number of movies Hector has shortlisted = (11 + 15) = 26.
That is, we will have to calculate the total of number of combinations of 4 movies, Hector can rent from a lot of 26 movies.
Now, we need to know the formula of combination which goes as [tex][nCr=\frac{n!}{r!(n-r)!} ][/tex],
When "r" objects are to be selected from a set of "n" objects, such that order of selection does not matter.
Here, (n = 26) and (r = 4), and using these values in the above mentioned equation of nCr, we get
[tex]26C4=\frac{26!}{4!(26-4)!} =\frac{26!}{4!*22!}=\frac{22!*23*24*25*26}{24*22!}=(23*25*26)=14950[/tex]
That is, Hector can have a total of 14950 number of combinations of 4 movies, from his shortlist of 11 documentaries and 15 foreign films, that he can rent.
Combination: In mathematics, combination is a method of selecting items from a set, where the order of selection does not matter.To learn more about Combinations, click on the link below.
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Multiply 39.341 × 0.72 =
what is the answer to 114 to 118 in my 7th-grade math?
Answer:
what do you mean like answer to what
Answer:
there's literally no way to answer that
How to solve that question?
Answer:
(i) (x√x)/3 -(√x)/2
(ii) f(x) = x³/27 +3x -5
Step-by-step explanation:
You want the value of the integral in each case. One integral is indefinite, the other has conditions specified.
In each case, the power rule applies:
[tex]\displaystyle \int{x^n}\,dx=\dfrac{x^{n+1}}{n+1}[/tex]
(i) indefinite integralThe integral can be rewritten as the sum of two integrals involving half powers.
[tex]\displaystyle \int{\dfrac{2x-1}{4\sqrt{x}}}\,dx=\dfrac{1}{2}\int{x^{\frac{1}{2}}}\,dx-\dfrac{1}{4}\int{x^{-\frac{1}{2}}}\,dx=\dfrac{x^{\frac{3}{2}}}{2\left(\dfrac{3}{2}\right)}-\dfrac{x^{\frac{1}{2}}}{4\left(\dfrac{1}{2}\right)}\\\\=\boxed{\dfrac{1}{3}x\sqrt{x}-\dfrac{1}{2}\sqrt{x}}[/tex]
(ii) f'(x)=ax²+bYou are given the derivative and three conditions:
f'(x) = ax² +bf'(3) = 4f(3) = 5f(0) = -5Together with the integral, the conditions give rise to three equations in the three unknown coefficients.
[tex]\displaystyle f(x) = \int{ax^2+b}\,dx=\dfrac{a}{3}x^3+bx+c[/tex]
Then the equations we can write for a, b, c are ...
f'(3) = 4 ⇒ a(3²) +b = 4
f(3) = 5 ⇒ (a/3)(3³) +b(3) +c = 5
f(0) = -5 ⇒ a(0³) +b(0) +c = -5
The last equation gives the value of c = -5, so the remaining equations become ...
9a +b = 4
9a +3b = 10
Subtracting the first from the second, we have ...
(9a +3b) -(9a +b) = (10) -(4)
2b = 6
b = 3
Using this in the first equation, we find 'a' to be ...
9a +3 = 4
a = 1/9
Then f(x) is ...
[tex]\boxed{f(x)=\dfrac{1}{27}x^3+3x-5}[/tex]
Find the circumference of this circle
using 3 for TT.
C≈ [?]
7
C = 27Tr
Enter
The circumference of the circle with radius 7 and value of pie 3, using the formula C= 2pie r is 42 unit.
Circumference of this circle using 3 for TT and 7 as radius.
The circumference of a circle is the distance around the outside of the circle. It is like the perimeter of other shapes like squares. You can think of it as the line that defines the shape. For shapes made of straight edges this line is called the perimeter but for circles this defining line is called the circumference. There are two other important distances on a circle, the radius (r) and the diameter (d). The radius, the diameter, and the circumference are the three defining aspects of every circle. Given the radius or diameter and pi you can calculate the circumference.
Circumference of circle = π x Diameter of circle.
You can also work out the circumference of a circle if you know its radius. Remember that the diameter is double the length of the radius. We already know that C = πd. If r is the radius of the circle, then d = 2r. So, C = 2πr.
Here, π = 3, r = 7,
So C = 2*7*3 = 42 units.
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how to translate by the rule (x,y)->(x +6,y -3) then reflect image over the y axis
Transformation of Reflect image over the y axis for this equation (x ,y)->(x +6,y -3) is (3, -1)
Reflecting point (-6,1) on y = x
gives (1, -6)
Translating, (1, -6) by 2,5 is
(1 + 2, - 6 + 5) = (3, - 1)
Therefore, reflect image over the y axis translate by rule (x ,y)->(x +6,y -3) is (3, - 1)
transformation :A function, f, itself is called the transformation, i.e., f: X → X. After the transformation the pre-image X becomes the image X. This transformation can be any part or the mixture of operations such as translation, reflection, rotation and dilation. The translation is working a function in a particular direction, rotation is rotate the function to a point, reflection is the mirror image of the function, and dilation is the ascend of a function.
Translation, rotation, reflection, and dilation are the four most prevalent types of transformations. From the transformation, we have a rotation about any point, reflection over any line, and translation along any angle. The picture is congruent to its pre-image in these stiff transformations.. They are also called as isometric transformations. Dilation is performed at about any point of angle and it is non-isometric.
Rules for Transformations
Consider a function f(x). On a coordinate grid, we use the x-axis and y-axis to check the movement. Here are the rules for transformations of function that could be applied to the all graphs of functions. Transformations can be shown algebraically and graphically. Transformations are commonly found in algebraic functions. We can use the formula of transformations in graphical functions to obtain the graph just by transforming the fundamental or the parent function, and thereby move the graph around, rather than tabulating the coordinate values. We can visualize and learn algebraic equations with the aid of transformations.
Formula of Transformations
Let us consider the graph f(x) = [tex]x^{2}[/tex]
Suppose we have need to graph f(x) = [tex]x^{2}[/tex] -3, we shift the vertex 3 units down.
Suppose we have need to graph f(x) = 3 [tex]x^{2}[/tex]+ 2, we shift the vertex two units above and extend vertically by 3 factor
Suppose we have need to graph f(x) = 2(x-1)^2, we shift the vertex one unit to the right and extend vertically by 2 factor
Thus, we know the formula of transformations as
f(x) =a(bx-h) n + k
where k is the vertical shift,
h is the horizontal shift,
a is the vertical stretch and
b is the horizontal stretch
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The common ratio of a sequence is 1/2. Two terms in the sequence are a5=1 and a8=1/8
what is the recursive formula?
Answer:
Since r = 1/2, and the fifth term = 1
1 = A×[(1/2)^(5-1)]
1 = A×[(1/2)^4]
1 = A× (1/16)
Step-by-step explanation:
please help! i don’t get axioms and my teacher is unavailable for questions right now
Answer:
2nd option ==> closure rule
Step-by-step explanation:
Four students plan to rent a minivan for the weekend and equally share the rental cost. By adding one more people, they can each save $6. How much is the total rent of the car?
The amount of the total rent is 120 dollars.
How to find the total rent using average?Four students plan to rent a minivan for the weekend and equally share the rental cost.
By adding one more people, they can each save $6.
Therefore, the 4 students equally share the rent.
Hence,
average for 4 student = total amount shared / number of student
average for 4 student = x / 4
When you add one more person,
average for 5 student = x / 5
Therefore, the difference, will give you the total amount of the rent.
x / 4 - x / 5 = 6
5x - 4x/ 20 = 6
x / 20 = 6
cross multiply
x = 20 × 6
x = 120
Therefore, the amount of the total rent is 120 dollars.
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I need help please. I think its C but i want to be sure!
Is this relation a function? Justify your answer.
A. No, because two points with the same x-value have different y-values.
B. Yes, because every x- and y-value is positive.
C. Yes, because the number of x-values is the same as the number of y-values.
D. No, because two points with the same y-value have different x-values.
Answer:
A. No, because two points with the same x-value have different y-values.
Step-by-step explanation:
You want to know if the graph represents a function.
FunctionA function is a relation that maps any input value to exactly one output value. On a graph, any vertical line will intercept a function graph in exactly one place.
ApplicationOn the given graph, the vertical line x=10 intersects the graph in two places (y=6 and y=9, different y-values). The graphed relation is not a function.
Lisa wants to buy some new shirts are her favorite store. Each shirt costs $15 and she wants to buy a pair of shoes that are $35. Lisa only has $137 to spend.
Let S represent the number of shirts that Lisa buys.
Which inequality describes this scenario?
137 > 15s + 35
137 ≥ 15s + 35
137 < 15s + 35
137 ≤ 15s + 35
In some racing events, downhill skiers receive the average of their times for three trials. Would you prefer the average time to be the mean or the median if you had… one very good time and two average times?
Answer:
Median
Step-by-step explanation:
i think median would be better than mean. This is because with mean, your adding it together then dividing it(by 3 in this case), making the end number higher. tou dont want a higher number in this case.
ex: your numbers are 50, 55,and 90
median = 55 (as it's the middle number)
mean = 65 ( 90+ 55+ 50 / 3)
so median is the lower number, meaning it would be better in this** case.
Six workers can build a house in 30 days. Assuming that all of the workers work at the same rate, how many workers would it take to build a house in 10 days?
Solve the inequality for x.
Show work
Answer:
x > 1
Step-by-step explanation:
to make everything under the same denominator
multiply everything by 2
7x + 1 > 8
now subtract 1 to both sides
7x > 7
divide everything by 7
x > 1
that is your asnwer
Select the correct answer.
68600
A) 6.86 × 104
C) 0.686 × 10²
B) 0.686 × 10¹
D) 6.86 x 10²
Answer:
A) 6.86×10⁴
Step-by-step explanation:
You want to write 68600 in scientific notation.
Expanded formThe number 68600 can be written in expanded form with exponents as ...
68600 = 6×10⁴ +8×10³ +6×10² +0×10¹ +0×10⁰
The left-most term of this sum tells you the exponent in scientific notation:
68600 = 6.86×10⁴
Solve the system of equations.
2x-5y-2z= -2
6x-15y-6z=20
2x-2y-5z = 4
Answer:
No solution
Step-by-step explanation:
2x-5y-2z= -2
6x-15y-6z=20
2x-2y-5z = 4
3rd eq - 1st eq
3y - 3z = 6
2nd eq - 3 × 1st eq
0 = 26
This is a false statement. Therefore, there is no solution.
Answer: No solution
What’s the answer
|z/4+5|=-7
Answer:
No solutions
Step-by-step explanation:
To solve systems of inequations with absolute values you need to isolate the items inside of the absolute value brackets then solve for x.
[tex]|\frac{x}{4}+5|=-7\\\frac{x}{4}+5=-7\\\frac{x}{4}=-12 \\x=-48[/tex]
Therefore our answers would be -48 and 48, however there are no answers to this solution as if you try either it does not equal -7. Furthermore graphing both sides of the equations shows there is no intersection.
Evaluate 3√-512.
A. Write your answer as an integer.
B. Explain how you can check that your result is correct.
:) Please help
The value of number 3[tex]\sqrt{-512}[/tex] as complex number is equal to 67.88i.
Given that the number is 3[tex]\sqrt{-512}[/tex].
We are required to find the value of the given number.
We have to first find out the square root of 512. Since we cannot find the square root of a negative number so we have to assume it as complex number and we will multiply the resultant number with i.
A complex number is basically an element of a number system that extends the real numbers with a specific element denoted i called the imaginary unit and satisfying the equation i² = −1 every complex number can be expressed in the form a + bi where a and b are real numbers.
3[tex]\sqrt{-512}[/tex] =3*22.627
=67.88i
It is not an integer and we cannot solve it further.
Hence the value of 3[tex]\sqrt{-512}[/tex] as an complex number is equal to 67.88i.
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There is something wrong in the statement of the question because the solution of 3[tex]\sqrt{-512}[/tex] will not be an integer.
what's that symbol mean?
Answer:
Every element in B is in B.
Step-by-step explanation:
The students in Mrs. Mangione's class attempt to guess the number of marbles in a jar to earn 2 extra credit points on their next exam. Suppose there are 1206 marbles in a jar and a student makes a guess of m marbles. Which expression represents the difference between the student's guess and the actual number of marbles.
The expression which reflects the difference between the student's guess and the actual number of marbles is m-1206.
Given that there are 1206 marbles in the jar and student makes a guess of m marbles.
We are required to find the expression that represents the difference between the student's guess and the actual number of marbles.
Expression is the combination of numbers, symbols, fraction, coefficients and are found to be without the equal to sign.
Total number of marbles in the jar=1206
Number of marbles that student guesses=m
The expression that shows the difference between the student's guess and the actual number of marbles is m-1206.
Hence the expression which reflects the difference between the student's guess and the actual number of marbles is m-1206.
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Larissa is picking out some movies to rent, and she is primarily interested in horror films and foreign films. She has narrowed down her selections to 19 horror films and 18 foreign films. Step 1 of 2 : How many different combinations of 3 movies can she rent?
Based on the number of horror films and the number of foreign films, the number of different combinations of 3 movies that Larissa is able to rent are
How many combinations can be rented?The total number of movies that Larissa has narrowed down are:
= 19 + 18
= 37 movies
The number of combinations of 3 movies that Larissa can select are:
= Total number of movies! / ( ( Total number of movies - Number of combinations)! x Number of combinations!)
= 37! / ( (37 - 3)! - 3!)
= 46,620 combinations
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40 oz= ___pounds
••••••••••••••••••••••••
Answer:
[tex]2.5[/tex] pounds,
OR
[tex]2 \frac{1}{2} [/tex] pounds
Therefore, option C is the answer
Answer:
Option C is the correct answer.
In Question 1-2, determine the type of reasoning for each statement, (GEOMETRY)
1. IN ORDER TO PARTICIPATE IN SCHOOL SPORTS, STUDENTS MUST HAVE A MINIMUM GPA OF 2.0, JIM HAS A GPA OF 2.75 THEREFORE HE CAN PARTICIPATE IN SCHOOL SPORTS.
2. EVERY TUESDAY THAT YOLANDA FAMILY HAS VISITED A SPECIFIC LOCAL RESTAURANT , THE KIDS MEAL HAVE BEEN FREE. WHEN YOLANDA FAMMILY VISITS THAT RESTAURANT NEXT TUESDAY, the kids meal will bee free.
Answer:
uyrddfhjjki
Step-by-step explanation:
A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 14 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 19 minutes.
The distance, D, is 5,760,000 divided by 2,160, which is 2666.67 (approx)
What exactly does "time function" mean?The TIME function is included as part of Excel's Date and Time features. With the assistance of TIME, we are able to create a time by employing various components for the hours, minutes, and seconds.
While conducting financial analysis, it's possible that we'll need to date a report. Under these conditions, the TIME function may be used to convert a text string into a format that presents the time as a decimal representation of the seconds, minutes, and hours.
Additionally, the function's capabilities include the ability to merge several values into a single time value.
formula= TIME (hour, minute, second)
distance = rate X time
D = RT
T = D/R
720 feet in a minute is equal to 12 feet per second.
480 feet per minute is equal to 8 feet per second.
The number of minutes to go to the flowerbed plus 14 minutes plus the number of minutes to get back to the hive equals 19 minutes.
(D/R) + 14 + (D/R) = 19
(D/R) + 14 + (D/R) = 19
In conclusion, The calculation that we may use to get the distance from the flowerbed to the hive is (D/720 ) plus 14 plus (D/480), which is 19.
(D/720 ) + (D/480) = 5
(D(1200)(480))/1200 + (D(720 )(480))/960 = 5(1200)960
480D + 1200D = 5(720 )480
1200D= 1728000
D=1440
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Answer Questions.
Round off decimals
1) 0.67 (1 decimal place)
2) 9.699 (2 decimal place)
Answer:
1. 0.7
2. 9.7
Step-by-step explanation:
1. 0.67->0.7
2. 9.699->9.7
solve by inverse matrix method 2x-y=1, 3y-x-z=8, y-2z=5
please help me my exam is tomorrow
Best's Computers claims that of its 4280 items in inventory, 3636 items are IBM PC, while the rest are Apple. What percent of total
inventory is Apple? Round to the nearest tenth of a percent.
select one :
A. 6.6%
B. 15.0%
C. 85.0%
D. 0.8%
The percent of total inventory is Apple, rounded to the nearest tenth of a percent is 15.0%
How do we determine the percentage of claims in Apple?
Out of the total claims of 4,280 items in inventory, the number of claims in Apple is determined as the total claims minus the number of claims attributable to IBM, such that the percentage of total inventory in Apple is computed as the number Apple's claims divided by total claims
number of claims in Apple=total claims-number of claims in IBM
total claims=4,280
number of claims in IBM=3636
number of claims in Apple=4280-3636
number of claims in Apple=644
% of claims in Apple=number of claims in Apple/total claims
% of claims in Apple=644/4280
% of claims in Apple=15.0%(rounded to 1 decimal place as shown in the options provided)
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Need help with math problem
