The area of a circle is 64 pi ft squared. What is the circumference, in feet? Express your answer in terms of pi
Answers
r
is given by
2
π
r
and area is
π
r
2
.
As
2
π
r
=
64
π
i.e.
r
=
64
π
2
π
=
64
2
=
32
,
Hence, area is
π
(
32
)
2
=
1024
π
Related Questions
If a book costs N10,000, at what price will the book be sold to make a profit of 15%?
Answers
We have,
Cost price of a book (CP) = N10,000
Profit percent (p%)= 15%
Now,
Using profit percent formula we get,
P% = (Sp-Cp)/ Cp*100
15 = (Sp-10,000)/10,000*100.
15*10000=100Sp-1000000
150000+1000000=100Sp
1150000/100=Sp
Sp=11500
Hence,
A book should be sold at 11500
Answer:
11,500
Step-by-step explanation:
cost price of a book (CP) = 10000
profit percent = 15%
selling price of a book (SP) = ?
SP = CP + profit% of CP
=10000 + 15 / 100 * 10000
=1000000 + 150000/100
=1150000/100
=11500
Therefore, the book will cost 11,500
Question 35 of 49
Which description best describes parallel lines?
A. Lines that are not in the same plane and will never intersect
O B. Lines that intersect at a right angle
O C. Lines that intersect
D. Lines that lie in the same plane but will never intersect
SUBM
Answers
Answer:
D.lines that lie in the same plane but will never intersect
Step-by-step explanation:
parallel lie in the same plane but never meet
Given that 9x – 6y= 19
Find y when x=-6
Give your answer as an improper fraction in its simplest form.
Answers
[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} [/tex]
Given that 9x – 6y= 19
Find y when x=-6
[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]
[tex] \red{Equation - > } \\ \blue{9x – 6y= 19} \\ \purple{x = - 6 \: \: (given)}[/tex]
[tex] \tiny\pink{SO \: PUTTING \: VALUE} \: \orange{OF \: x \: FOR \: \: VALUE \: OF \: y}[/tex]
[tex] \red{Equation - > } \\ \blue{9x – 6y= 19} \\ {9( - 6) – 6y= 19} \\ - 54 - 6y = 19 \\ 6y = - 54 - 19 \\ - 73 = 6y \\ \green{ \frac{ - 73}{6} = y}[/tex]
[tex] \red{VARIFICATION - > }[/tex]
PUTTING VALUES IN EQUATION TO VARIFY THE ANSWER:-
[tex] \pink{Equation - > } \\ \blue{9x – 6y= 19} \\ \purple{x = - 6 \: \: (given)} \\ \green{y = \frac{ - 73}{6}} [/tex]
PUTTING VALUE
[tex] \pink{Equation - > } \\ \blue{9x – 6y= 19} \\ 9( - 6) - 6( \frac{ - 73}{6} ) = 19 \\ - 54 \cancel{-}^{ \tiny{+} } \cancel{6} \frac{ \cancel{- }73}{ \cancel{6}} = 19 \\ - 54 + 73 = 19 \\ 19 = 19 \\ \orange{L.H.S} \purple{=} \green{ R.H.S}[/tex]
Answer:
y = 73 / -6
Step-by-step explanation:
Given ;
9x - 6y = 19
Where, x = - 6
Solve for y
9x - 6y = 19
plug the value of x
9 ( -6 ) - 6y = 19
- 54 - 6y = 19
Add 54 to both sides
- 54 + 54 - 6y = 19 + 54
-6y = 73
divide both side by -6
-6y / -6 = 73 / -6
y = 73 / -6
Doris has a fish pond 15 by 18 ft. She wants to put grass in a strip of uniform with around the pond. She has enough grass seed for 234 ft squared. How wide will the strip be? Round your answer to the nearest tenth, when appropriate
Answers
Check the picture below.
so if we simply subtract the strip area with the pond and the area of the pond only, what's leftover is the area of the strip alone, so
[tex]\stackrel{\textit{area of the grass \underline{with} pond}}{(15+2x)(18+2x)}-\stackrel{\textit{area of the pond}}{(15)(18)}=\stackrel{\textit{their difference}}{232} \\\\\\ 270+30x+16x+4x^2-270=232\implies 46x+4x^2=232 \\\\\\ 23x+2x^2=116\implies 2x^2+23x-116=0[/tex]
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+23}x\stackrel{\stackrel{c}{\downarrow }}{-116}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-23\pm \sqrt{23^2-4(2)(-116)}}{2(2)}\implies x = \cfrac{-23\pm \sqrt{1457}}{4}[/tex]
now, the negative root will simply yield a negative value, which is not applicable here, so we'll only use the positive root, since it's the only feasible one for the phenomena
[tex]x = \cfrac{-23+ \sqrt{1457}}{4}\implies x \approx 3.792667341996157\implies \stackrel{\textit{rounded up}}{x = 3.8}[/tex]
Answer:
3 feet
Step-by-step explanation:
Let x be the width of the grass strip.
So the length of the grass strip=18+2x
Area of the grass strip =2(18+2x)(x)+2(15)(x)=2(18x+2x^2)+2(15x)=(36x+4x^2)+30x=4x^2+66x^2
But the available grass seed is enough for 234 ft squared
4x^2+66x=234
4x^2+66x-234=0
x={-66+-[(66)^2–4(4)(-234)]^1/2}/2(4)
x={-66+-[4356+3744]^1/2}/8={-66+-[8100]^1/2}/8
x={-66+-(90)}/8
Two values of x: x=(-66+90)/8=24/8=3 and the other value of x=(-66–90)/8=-19.5. Adopt the positive value of x=3 feet (answer)
So the width of the strip is 3 feet.
Check for the area of grass strip around the fish pond : Area=2(18+6)(3)+2(15)(3)=2(24)(3)+90=144+90=234 square feet
Other area check =4x^2+66x=4(3)^2+66(3)=36+198=234 square feet
Therefore the strip is 3 feet wide
Select all the numbers that are rational.
Answers
Answer:
-14/2 , 1/3 and 0.325 are the rational numbers
what is the sum of the rational expressions x-4/2x+3x/2x-1
Answers
Answer:
May the ans will help you.
Consider rolling two fair dice and observing the number of spots on the resulting upward face of each one. Letting A be the event that at least one of the dice results in 6 spots on its upward face, and E be the event that exactly one of the dice results in 6 spots on its upward face, give the value of P(E|A). (Note: This value can be easily obtained by looking at p. 2.3 of the class notes and using a reduced sample space. In fact, such an approach makes the solution so trivial, that for this problem, you don’t have to give any justification for your answer.)
Answers
Answer:
[tex]P(E|A)= \frac{10}{11}[/tex]
Step-by-step explanation:
Given
Two rolls of die
[tex]E \to[/tex] one of the outcomes is 6
[tex]A \to[/tex] atleast one is 6
Required
P(E|A)
First, list out the outcome of each
[tex]E = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]
[tex]A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]
So:
[tex]P(E|A)= \frac{n(E\ n\ A)}{n(A)}[/tex]
Where:
[tex]E\ n\ A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]
[tex]n(E\ n\ A) = 10[/tex]
[tex]n(A) = 11[/tex]
So:
[tex]P(E|A)= \frac{10}{11}[/tex]
Oakton Manufacturing makes two types of rocking chairs specifically designed for men and women known as the His and Hers models. Each chair requires four legs and two rockers but differing numbers of wooden dowels. Each His chair requires four short dowels and eight long dowels while each Hers chair requires eight short dowels and four long dowels. Each His chair contributes $10 in profit while each Hers chair contributes $12. The company has 900 legs, 400 rockers, 1200 short dowels, and 1056 long dowels available. The company wants to maximize its profit while also ensuring that it makes at least half as many His chairs as Hers chairs.
Required:
a. Formulate an LP model for this problem.
b. Sketch the feasible region for this problem.
c. Find the optimal solution.
Answers
Answer:
x = 76 y = 112 z (max) = 2104 $
Step-by-step explanation:
legs rockers short dowels long dowels Profit $
Model His (x) 4 2 4 8 10
Model Her (y) 4 2 8 4 12
Availability 900 400 1200 1056
From the table above we find z
Objective Function z :
z = 10*x + 12*y to maximize
Subject to
Constraint 1 quantity of legs available: 900
4*x +4*y ≤ 900
Constraint 2 quantity of rockers available: 400
2*x + 2*y ≤ 400
Constraint 3 quantity of short dowels available: 1200
4*x 8*y ≤ 1200
Constraint 4 quantity of long dowels available: 1056
8*x + 4*y ≤ 1056
Constraint 5 condition between x and y
x ≥ 0.5*y
The model:
z = 10*x + 12*y to maximize
Subject to:
4*x +4*y ≤ 900
2*x + 2*y ≤ 400
4*x 8*y ≤ 1200
8*x + 4*y ≤ 1056
x ≥ 0.5*y or x - 0.5*y ≥ 0
General constraints:
x ≥ 0 y ≥ 0 both integers
After 6 iterations with AtomZmath on-line solver optimal solution is:
x = 76 y = 112 z (max) = 2104 $
Seven times a number decreased by three-fourths of the same number is 25. What is the number?
Answers
Answer:
103/28
Step-by-step explanation:
Let the number be 'x'
Equation:-
7x - 3/4 = 25
7x = 25 + 3/4
7x = 100/4 + 3/4
7x = 103/4
x = 103/(4 x 7)
x = 103/28
Answer:
if we make this a algebraic equation it will look like this
7x-3/4x=25
6.25x=25
25 divided by 6.25=4
x=4
to check
28-3=25
Hope This Helps!!!
Use the table to approximate AB in the triangle below.
Answers
Answer:
Answer is 6.1 units
Step-by-step explanation:
The measure of length of AB in the triangle ABC is 6.1 units.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given triangle ABC, BC=5 and ∠A=55°.
We know that, sinθ= Opposite leg length/Hypotenuse length
Here, sinA=BC/AB
sin55°=5/AB
0.82=5/AB
AB=5/0.82
AB=6.1 units
Therefore, the measure of length of AB in the triangle ABC is 6.1 units.
Learn more about the trigonometric ratios here:
brainly.com/question/25122825.
#SPJ2
100 Brainly points!! Need help ASAP :)
In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B’. What is the scale factor of dilation?
A. 1
B. 2
C. 0.5
D. -0.5
Answers
Answer:
B
Step-by-step explanation:
I'm not really shure tho
Answer:
D. -0.5
Step-by-step explanation:
AB dilated by scale factor -0.5 to produce AB'.
the length of AB = 4 units and the length of AB' = 2 units, the direction is backward, so the scale factor is - 2/4 = -0.5
A city is designing a new trail system that will be
6 1/6 miles long. They plan on placing 49 mileage signs to show the distance. How far apart will each sign be?
Answers
Step-by-step explanation:
the answer is 6.125 and its will be divided by 125
You roll a die with the sample space s=1,2,3,4,5,6. you define A as (1,2,4) B as (2,3,4,5,6) C as (3,4) and D as (2,4,5). Determine which of the following events are exhaustive and/or mutually exhaustive.
Exhaustive Mutually exclusive
A and B
A and C
A and D
Band C
Answers
Answer:
A and B are exhaustive.
Step-by-step explanation:
Given
[tex]A = \{1,2,4\}[/tex]
[tex]B = \{2,3,4,5,6\}[/tex]
[tex]C =\{3,4\}[/tex]
[tex]D = \{2,4,5\}[/tex]
Solving (a): The mutually exclusive events
These are events that have no common or mutual elements
Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.
Solving (b): Exhaustive events.
Two events X and Y are said to be exhaustive if:
[tex]S = P(X\ n\ Y)[/tex]
i.e. if the sample space equals the intersection of X and Y
For events A to D, we have:
[tex]A\ n\ B = \{1,2,3,4,5,6\}[/tex]
and the sample space is:
[tex]S = \{1,2,3,4,5,6\}[/tex]
By comparison;
[tex]A\ n\ B = S[/tex]
Hence, A and B are exhaustive.
Data with 950 observations are drawn from a bell-shaped distribution with a mean of 78 and a standard deviation of 19. Approximately how many observations are more than 116
Answers
Answer: there are 22 observations that are more than 116.
Step-by-step explanation:
Let x be the random variable.
Given: Sample size = 950
Mean = 78
Standard deviation = 19
The probability that the observations are more than 116 is given by :-
[tex]P(X>116)=P(\dfrac{X-mean}{standard \ deviation}>\dfrac{116-78}{19})\\\\=P(Z>2)\\\\=1-P(Z<2)\\\\=1-0.9772\ \ \ [\text{Using p-value calculator}]\\\\=0.0228[/tex]
Number of observations are more than 116 = [tex]0.0228\times950[/tex]
[tex]=21.66\approx22[/tex]
Hence, there are 22 observations that are more than 116.
Choose each of the following that ARE a function
Answers
Given the line segment AB=36 cm and a point C on directed line segment AB that partitions AB into the ratio 1 to 2, find the lengths of the line segments AC and CB
Answers
Explanation: so we know that the ratio is 2:1, which can be expressed as 2x and x.
we know that 2x+x must equal 36, so we can set up the equation 2x+x=36
we then add 2x to x to make 3x=36, divide both sides by 3, and get x=12.
now that we know what x equals, 2(12) is 24 and (12) is 12 :)
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
Answers
Given:
In the given circle, the measure of major arc TV is 220 degrees.
To find:
The measure of angle TUV.
Solution:
In a circle, the measure central angle of arc is equal to its corresponding arc measure and according to central angle theorem, the measure of subtended angle on an arc is half of the measure of central angle of that arc.
So, the measure of subtended angle is half of the measure of its corresponding arc.
[tex]m\angle TUV=\dfrac{1}{2}\times \text{Measure of major arc TV}[/tex]
[tex]m\angle TUV=\dfrac{1}{2}\times 220^\circ[/tex]
[tex]m\angle TUV=110^\circ[/tex]
Therefore, the measure of angle TUV is 110 degrees.
Find the measure of WX and show work
Answers
Ans : the measure of WX = 8
Find the angle measurements of the intersections for the two equations f(x) = 4x - 5 and g(x) = 2x^2 - 5.
Multiple answers
63
7 (This is one of the answers already)
20
76
90
Answers
Answer:
76° is the other one
Step-by-step explanation:
nope, no precise calculation here. the option are thankfully enough apart that solving it graphically is just fine. look at the screenshot. the upper intersection is the one with the 7° angle
the lower one is somewhat less than 90° :P
Answer:
76 is the other
Step-by-step explanation:
What would be the amount of his last monthly bill in order. The bill amount to be 110 for all 12 months
Answers
1199/11 = 109
B. 109 answer
I got 7 to go :( help plz
Answers
Answer:
I think the second one is the answer ; 2√b
How should I tell my crush I like her? She's my friend and I asked her if she liked me yesterday and she said no but I think she was lying because she typed and then stoped typing and said no
Answers
Answer:
U just have to make her feel comfortable to trust u that she can tell u that she actually likes u....dont push anything just make her feel appreciated ok?
Step-by-step explanation:
that's all
please help me please
Answers
Answer:
30,000
Step-by-step explanation:
can someone pls help me quickkk
Answers
Answer:
(-4) ^6
Step-by-step explanation:
(-4)*(-4)*(-4)*(-4)*(-4)*(-4)
There are six (-4)'s multiplied together
(-4) is the base and 6 is the exponent
(-4) ^6
Answer:
A.(-4)^6
Step-by-step explanation:
-4 is being multiplied by itself 6 times
So you would get rid of all but one negative for and add ^-6
Nadia has $1.35 in nickels. How many nickels
does she have?
Answers
Answer:
27 Nickels
Step-by-step explanation:
Divide 1.35 by 0.05
= 27
2)
110°
18x + 2
A) 8
C) 6
B) 12
D) -10
Answers
Answer:
C) 6
Step-by-step explanation:
Alternate interior angles are congruent meaning that they are equal to each other sp 18x+2=110 is simplified to 18x=108. Then divide by 18 to get x equal to 6. Hope this helped and post more :)
Find the equation (in terms of x ) of the line through the points (-2,5) and (3,4)
y=
Answers
Answer:
y = (-1/5)x + 23/5
Step-by-step explanation:
Given:
Two points;
(-2,5) and (3,4)
Find:
Equation of slope
Computation:
y = mx + b
5 = m(-2) + b
5 = -2m + b .......... Eq1
4 = m(3) + b
4 = 3m + b .......... Eq2
Eq2 - Eq1
-1 = 5m
m = -1/5
5 = -2m + b
5 = -2(-1/5) + b
5 = 2/5 + b
b = 23/5
y = mx + b
y = (-1/5)x + 23/5
There are red, blue, and white buttons in a box. The ratio of the
number of red buttons to the number of white buttons is 4:7.
The ratio of the number of blue buttons to the number of red buttons
is 3:2. There are 280 white buttons.
How many buttons are there altogether?
Please help i’m very confused
Answers
Answer:
680
Step-by-step explanation:
Ratio of red to white 4 : 7
Number of white = 280
White + red buttons = x
7x / 11 = 280
7x = 280 * 11
7x = 3080
x = 3080 / 7
x = 440
Number of red buttons 440 - 280 = 160
Number of red bottons ;
Blue + red buttons = x
3 : 2 ; blue : red
3 + 2 = 5 ;
2x / 5 = 160
2x = 160 * 5
2x = 800
x = 800 / 2
x = 400
Number of Blue buttons :
400 - 160 = 240
Total :
White + red + blue
280 + 160 + 240 = 680 buttons
A health clinic dietician is planning a meal consisting of three foods whose ingredients are summarized as follows: One Unit ofFood I Food II Food IIIUnits of Protein 10 15 20Units of Carbohydrates 1 2 1Units of Iron 4 8 11Calories 80 120 100The dietician wishes to determine the number of units of each food to use to create a balanced meal containing at least 40 units of protein, 6 units of carbohydrates, and 12 units of iron, and with as few calories as possible. Use solver to find how many units of each food should be used in order to minimize calories.
Answers
Answer:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
Step-by-step explanation:
Protein Carbohydrates Iron calories
Food 1 (x₁) 10 1 4 80
Food 2 (x₂) 15 2 8 120
Food 3 (x₃) 20 1 11 100
Requirements 40 6 12
From the table we get
Objective Function z :
z = 80*x₁ + 120*x₂ + 100*x₃ to minimize
Subjet to:
Constraint 1. at least 40 U of protein
10*x₁ + 15*x₂ + 20*x₃ ≥ 40
Constraint 2. at least 6 U of carbohydrates
1*x₁ + 2*x₂ + 1*x₃ ≥ 6
Constraint 3. at least 12 U of Iron
4*x₁ + 8*x₂ + 11*x₃ ≥ 12
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
With the help of an on-line solver after 6 iterations the optimal solution is:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
Simplify: (5x + 3) – (3x – 2)
Answers
Answer: 2x+5
Step-by-step explanation:
(5x + 3) – (3x – 2)
5x+3-3x+2
2x+5
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
╭⋟───────────────
[tex](5x+ 3) - (3x - 2) \\ = 5x + 3 - 3x + 2 \\ = 5x - 3x + 3 + 2 \\ = 2x + 5[/tex]
───────────────⋞╯
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