Answers
Answer: 5*sqrt(2pi)/pi
-----------------------
Work Shown:
r = sqrt(A/pi)
r = sqrt(50/pi)
r = sqrt(50)/sqrt(pi)
r = (sqrt(50)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(50pi)/pi
r = sqrt(25*2pi)/pi
r = sqrt(25)*sqrt(2pi)/pi
r = 5*sqrt(2pi)/pi
Note: the denominator is technically not able to be rationalized because of the pi there. There is no value we can multiply pi by so that we end up with a rational value. We could try 1/pi, but that will eventually lead back to having pi in the denominator. I think your teacher may have made a typo when s/he wrote "rationalize all denominators"
============================================================
Part b)
Answer: 3*sqrt(3pi)/pi
-----------------------
Work Shown:
r = sqrt(A/pi)
r = sqrt(27/pi)
r = sqrt(27)/sqrt(pi)
r = (sqrt(27)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(27pi)/pi
r = sqrt(9*3pi)/pi
r = sqrt(9)*sqrt(3pi)/pi
r = 3*sqrt(3pi)/pi
Note: the same issue comes up as before in part a)
============================================================
Part c)
Answer: sqrt(19pi)/pi
-----------------------
Work Shown:
r = sqrt(A/pi)
r = sqrt(19/pi)
r = sqrt(19)/sqrt(pi)
r = (sqrt(19)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(19pi)/pi
The radius can be found by taking the square root of A divided by pi under the root sign.
Formula
r = sqrt(A / pi)
r = sqrt(A * pi/( pi * p)i)
the root of pi^2 is pi
r = sqrt(A * pi)/pi
Problem A
r = √(50 * π) / π <<<< answer
Comment
For each problem, all you need do is put in the given areas in A B C. I don't know what your input will do with the square root sign; you can write sqrt(50 * pi) / pi
B
r = √(27*π) / π
C
r = √(19* π) / π
Related Questions
Which of the following holds about 800 milliliters o f water?
Answers
Mr zucco baked a total of 270 cupcakes and muffins. After ue sold 1/3 of the cupcakes and baked 18 more miffins, he had twice as many cupcakes as muffins. How many cupcakes and muffins did mr. Zucco bake to begin with?
Answers
c + m = 270
After 1/3 of cupcakes are sold (leaving 2c/3) and 18 more muffins are baked (m + 18), there are twice as many cupcakes as muffins:
2c/3 = 2(m + 18)
2c/3 = 2m + 36
c = 3m + 54
Substituting into the original equation:
3m + 54 + m = 270
4m = 216
m = 54 muffins
c = 3(54) + 54 = 216 cupcakes
After the hairdresser Jenny had 27 centimeters cut off her hair how many decimeters of hair did jenny have cut off
Answers
Answer:
2.7 dm
Step-by-step explanation:
You want to know the number of decimeters in 27 centimeters.
SI PrefixesThe SI prefix "deci-" means 1/10.
The SI prefix "centi-" means 1/100.
This tells you that 10 cm = 1 dm.
27 cm = (27 cm) × (1 dm)/(10 cm) = 2.7 dm
Jenny had 2.7 dm of hair cut off.
Question 11 please solve
Answers
We can conclude that you will need 6 segments to connect each point to every other point.
4+2= 8
the answer is 8 4 plus 2 equals 8 even if the circle has four dots you draw four more which equals 8 either one
Miss Nelson Has a rectangular flower box that is 5 ft long 2 ft tall she wants the width of the box to be no more than 5 ft if the width is a whole number what are the possible volumes for the flower box
Answers
17.5% as a fraction in simplest form?
Answers
A restaurant uses 290 pounds of onions every 2 and a half weeks. If they continue to use onions at the same rate, how many pounds of onions will they use in 6 weeks?
Answers
116 * 6 = 696 pounds
290/2.5 = 116
Now that we have a single rate, we find the amount for 6 weeks:
116*6 = 696
696 pounds are used in 6 weeks
Find the length of AB , given that DB is a median of the triangle and AC = 24.
Answers
Answer:
AB = 12 units
Step-by-step explanation:
We are given the following information in the question:
DB is the median of the triangle.
AC = 24 units
Property of median of a triangle:
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.Thus, a median divides the side of triangle in two equal parts.Thus, DB divides AC in two equal parts.
Thus, we could say:
AB = BC
We have to find the length of AB.
[tex]\text{AB} = \displaystyle\frac{AC}{2} = \frac{24}{2} = 12\text{ units}[/tex]
Thus, AB is 12 units.
hello can you please help me posted picture of question
Answers
If Disc > 0, the function has two distinct roots
If Disc = 0, the function has repeated roots
If Disc < 0, the function has complex roots
The turning away of the function indicates a repeated root at that point.
Thus, the given quadratic equation has a repeated root at x = 2. So the discriminant of the function is zero.
Therefore, the correct answer is option B
Hey can you please help me posted picture of question
Answers
In given case, Karen has to find the probability of a number greater than 4 which can appear when a die is rolled. The possible outcomes in this case are 2 i.e. 5 and 6
Since, the number of possible outcomes is more than 1, the event is a compound event.
So answer is true
5.
Find the present value of the annuity.
Amount Per Payment: $6,225
Payment at End of Each: Quarter
Number of Years: 6
Interest Rate: 8%
Compounded: Quarterly
Answers
where
[tex]PV[/tex] is the present value
[tex]P[/tex] is the periodic payment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]k[/tex] is the number of payments per year
[tex]t[/tex] is the number of years
We know for our problem that [tex]P=6225[/tex] and [tex]t=6[/tex]. To convert the interest rate to decimal form, we are going to divide it by 100%:
[tex]r= \frac{8}{100} [/tex]
[tex]r=0.08[/tex]
Since the interest is compounded quarterly, it is compounded 4 times per year, so [tex]n=4[/tex]. Similarly, since the payment is made at the end of each quarter, it is made 4 times per year; therefore, [tex]k=4[/tex].
Lets replace the values in our formula:
[tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{(-kt)} }{ \frac{r}{n} }] [/tex]
[tex]PV=6225[ \frac{1-(1+ \frac{0.08}{4})^{(-(4)(6)} }{ \frac{0.08}{4} }] [/tex]
[tex]PV=117739.19[/tex]
We can conclude that the present value of the annuity is $117,739.19
11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball?
Answers
[tex] |\Omega|=25\cdot24=600\\
|A|=11\cdot14+14\cdot13=154+182=336\\\\
P(A)=\dfrac{336}{600}=\dfrac{14}{25}=56\% [/tex]
A bakery has total receipts for the month of $24,150 including sales taxes. if the sales tax rate is 5%, what are the bakery's sales for the month?
a.$24,000
b.$23,000
c.$23,100
d.$22,943
Answers
Option B= $23000 is the answer.
Explanation:
Let the bakery's sales for the month be represented by = x
As given, the bakery has total receipts for the month = $24150
Rate of sales tax = 5%
This implies that total monthly sales(x) + sales tax on 'x' = 24150
[tex]x+\frac{5x}{100}=24150[/tex]
[tex]x+0.05x=24150[/tex]
[tex]1.05x=24150[/tex]
x=23000
Hence, the bakery's sale for the month is $23,000
The problem is in the picture
Answers
Answer:
∠1 and ∠2,
∠3 and ∠4,
∠5 and ∠6
Explanation:
Supplementary angles are angles opposite each other that share the same line that is being dissected by a perpendicular line. The sum of their angles will always equal 180 degrees.
Angles 1 and 2 are an example of such supplementary angles. They share the horizontal line but are being dissected by descending line which creates their angles.
Angles 3 and 4 are more of the same. They share the somewhat-vertical line and are dissected by a different descending line that created them.
Lastly, Angles 5 and 6 are also supplementary angles. They share the somewhat-vertical line and are dissected by the horizontal line, resulting in their angles.
Angles 7 and 8 are not supplementary angles. Rather, they are vertically-opposite angles, or vertical angle pairs, two angles lying opposite each other existing at the point where two lines intersect. These angles have the same exact measurement and their sum will never equal 180 degrees.
Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?
Number on cube:1,2,3,4,5,6
Number of times event occurs:3,6,1,5,3,2
A.0.2
B.0.3
C.0.6
D.0.83
Answers
[tex] \frac{4}{20} = 0.2[/tex]
The answer is A.
solve the system of equations 5x-2y=88 3x+4y=58 show all work
Answers
5x - 2y = 88
3x + 4y = 58
Multiplying the 1st equation by 2, we get the new set of equations as:
10x - 4y = 176
3x + 4y = 58
Adding the two equations, we get:
10x - 4y + 3x + 4y = 176 + 58
13x =234
x = 18
Using the value of x in 1st equation, we get:
5(18) - 2y = 88
- 2y = 88 -5(18)
-2y = -2
y = 1
So, the solution of the equation is (18, 1)
[tex]3x+4\cdot(2.5x-44)=58\\3x+10x-176=58\\13x-176=58\ \ \ |\text{add 176 to both sides}\\13x=234\ \ \ \ |\text{divide both sides by 13}\\x=18\\\\\text{substitute value of x to the equation}\ 1^o\\\\y=2.5\cdot18-44=45-44=1\\\\Answer:\ \boxed{\left\{\begin{array}{ccc}x=18\\y=1\end{array}\right}[/tex]
Lucia is not yet 80 years old. each of her sons has as many sons as brothers. the combined number of lucias sons and grandsons equals her age, and her oldest grandson is 29. how old is lucia? place your numerical answer in the corresponding answer blank.
Answers
You randomly select one card from a 52-card deck. find the probability of selecting a black seven or a red three.
Answers
Number of back sevens = 2
Number of red three = 2
P(Black seven or red three) 4/52 = 1/13
Answer: 1/13
The probability of selecting a black seven or a red three will be 1/13.
What is Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
You randomly select one card from a 52-card deck.
Now,
Number of black sevens = 2
Number of red three = 2
So, The probability of selecting a black seven or a red three is;
= (2 + 2) / 52
= 4 / 52
= 1 / 13
Thus, The probability of selecting a black seven or a red three will be 1/13.
Learn more about the probability visit:
https://brainly.com/question/24756209
#SPJ2
A homeowner plants two flowerbeds around his garage. What is the total area he will have planted. Round to nearest tenth.
Answers
What is the vertex of the quadratic y=-2x^2-4x-5
Answers
We will need to complete square to write the equation in the vertex form.
y=-2(x²+2x)-5
y=-2(x²+2x+1)-5+2
y=-2(x+1)² - 3
Vertex (-1,-3)
Answer:
(-1,-3)
Step-by-step explanation:
I just took the test, and I got 100%!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 108x + 6, [−3, 4]
Answers
The absolute minimum on the interval is -237 at x=3.
The absolute maximum on the interval is 138 at x=-2.
Answer:
The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.
Step-by-step explanation:
To find the absolute extrema values of [tex]f(x) = 6x^3 - 9x^2 - 108x + 6[/tex] on the closed interval [−3, 4] you must:
1. Locate all critical values. We need to find the derivative of the function and set it equal to zero.
[tex]\frac{d}{dx}f(x)= \frac{d}{dx}\left(6x^3-9x^2-108x+6\right)=\\\\f'(x)=\frac{d}{dx}\left(6x^3\right)-\frac{d}{dx}\left(9x^2\right)-\frac{d}{dx}\left(108x\right)+\frac{d}{dx}\left(6\right)\\\\f'(x)=18x^2-18x-108[/tex]
[tex]18x^2-18x-108=0\\18\left(x^2-x-6\right)=0\\18\left(x+2\right)\left(x-3\right)=0\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=-2,\:x=3[/tex]
2. Evaluate f(x) at all the critical values and also at the two values -3 and 4
[tex]\left\begin{array}{cc}x&f(x)\\-3&87\\-2&138\\3&-237\\4&-186\end{array}\right[/tex]
3. The absolute maximum of f(x) on [-3, 4] will be the largest number found in Step 2, while the absolute minimum of f(x) on [-3, 4] will be the smallest number found in Step 2.
Therefore,
The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.
The hyperbola (x-5)^2/7 - (y+3)^2/9 = 1 is shifted to the right by 4 units and upward by 3 units. the new center of the hyperbola is
Answers
(5, -3) +(4, 3) = (9, 0)
Answer:
( 9 ,0)
Step-by-step explanation:
Given : [tex]\frac{(x -5)^{2}}{7} - \frac{(y+3)^{2}}{9} = 1.[/tex] is shifted to the right by 4 units and upward by 3 units
To find : New center of the hyperbola .
Solution : We have given
[tex]\frac{(x -5)^{2}}{7} - \frac{(y+3)^{2}}{9} = 1.[/tex]
Center of hyperbola is ( 5 , -3)
By the transformation rule f(x) →→ f(x -h) + k it mean f(x) is shifted to right by h unit and k unit up.
Then Center of hyperbola is shifted to the right by 4 units and upward by 3 units.
( 5 , -3) →→ (5 + 4 , -3 + 3
( 5 , -3) →→ ( 9 ,0)
Therefore, new center is ( 9 ,0).
The soup can is 6 cm tall and has a radius of 3.5cm. If you were to pull the label off the can in one complete piece,what would the area of the label be ? Use 22/7 for p.
Please help !!!
A)22 sq.cm
B)42 sq.cm
C)132 sq.cm
D)152 sq.cm
Answers
3,14*7=21.98
21.98*6=131,88≈132
The soup can is 6 cm tall and has a radius of 3.5cm. If you were to pull the label off the can in one complete piece,what would the area of the label be ? Use 22/7 for p.
Please help !!!
A)22 sq.cm
B)42 sq.cm
C)132 sq.cm
D)152 sq.cm
Solution:
Radius of cylindrical soup can= 3.5 cm
Height of cylindrical soup can= 6 cm
Area of cylinder =2πrh
So, Area of label of cylindrical soup can=2πrh
Plugging in the value of r and h in the formula
Area of label=2*π*3.5*6
Multiplying the constants, we get
Area=2*π*21
Area=42π
Plugging in the value of π
Area=42*[tex]\frac{22}{7}[/tex]
Multiplying the numerators
Area=[tex]\frac{924}{7}[/tex]
Area=132 sq.cm
Answer: Option (C)
Area of label= 132 sq. cm
Heong cut a slice of birthday cake. The slice formed the angle shown. What is the measure of the angle shown?
Answers
What is the surface area of a rectangular prism that has a length of 9 feet, a width of 5 feet, and a height of 7.5 feet?
Answers
A = 2(LW +H*(L +W))
Filling in the given information, we have
A = 2((9 ft)*(5 ft) +(7.5 ft)*(9 ft +5 ft))
A = 2(45 ft² +(7.5 ft)*(14 ft)) = 2(150 ft²)
The surface area of the rectangular prism is 300 ft².
Answer: 300 ft²
Step-by-step explanation:
Linda needs 20 gallons of juice that has 75%fruit juice. she has a mixture that has 80% fruit juice and another mixtures that has 60% fruit juice. how much of each mixture should she use to get what she need?
Answers
15 gallons of 80% juice
5 gallons of 60% juice
_____
Let g represent the number of gallons of 80% juice needed. Then (20-g) is the number of gallons of 60% juice Linda will use. The amount of juice in the mixture can be written as
0.80g +0.60(20 -g) = 0.75×20
0.20g = 20(0.75 -0.60) = 20×0.15
g = 20×0.15/0.20 = 15
The amount of 80% juice needed is 15 gallons, so 5 gallons of 60% juice are needed.
hello can you please help me posted picture of question
Answers
[tex] \frac{25-y^2}{16} + \frac{y^2}{9} = 1[/tex]
Explanation:
For the first given equation, we will need to isolate the x². This can be done as follows:
x² + y² = 25
x² + y² - y² = 25 - y²
x² = 25 - y² ..................> I
For the second given equation:
We will remove every x² and substitute with its equivalence from I as follows:
[tex] \frac{x^2}{16} + \frac{y^2}{9} = 1[/tex]
[tex] \frac{25-y^2}{16} + \frac{y^2}{9} = 1[/tex]
Hope this helps :)
It is the c)25-y^2-y^2 by 16-9 = 1
What is the perimeter of the rectangle? Write your answer in scientific notation. The area is 2.76 x 10 pw12
the width is 4.6 x 10 pw5
pw is the power
Answers
To calculate the perimeter of a rectangle given the area and the width, divide the area by the width to find the length, then use the formula Perimeter = 2(Length + Width), adjusting for scientific notation as necessary. This will provide the perimeter in scientific notation.
Explanation:To find the perimeter of the rectangle when we have the area and the width, we need to first calculate the length of the rectangle using the formula Area = Length × Width. The width is given as 4.6 x 105 and the area is 2.76 x 1012. To find the length, we divide the area by the width:
Length = Area ÷ Width = (2.76 x 1012) ÷ (4.6 x 105)
After performing the division, we obtain the length in scientific notation. The next step is to use the formula Perimeter = 2(Length + Width). After calculating the sum of the length and width, we multiply by 2 to obtain the perimeter of the rectangle in scientific notation.
Let's assume after performing the calculation that the length is found to be L x 10n where L and n are specific numbers. The perimeter now would be calculated as:
Perimeter = 2((L x 10n) + (4.6 x 105))
Be sure to adjust the exponents so they match before adding the length and width together. This might involve converting one or the other so that you can add them directly. Once that is done, you can multiply by 2 to find the total perimeter of the rectangle and express it in scientific notation.
(-8,7),(-9,-5) write in Ax+By=C
Answers
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. find the probability that the number drawn is a multiple of 77 or a multiple of 4.
Answers
Multiples of 77: 1, 7, 11
Multiples of 4: 1, 2, 4
Therefore, multiples of 77 or 4 are: 1, 2, 4, 7, 11 = 5 numbers
P (multiples of 7 or 4) = 5/25 = 1/5 = 0.2