The expression is equal to 3sqrt(517)/5
A motion sensor has a range of 65 meters as shown. The ultrasonic waves sweeping out from the sensor span an angle of 135°.
A figure shows the appendix cone has a range of 65 meters in which waves with an angle of 135 degrees.
What is the approximate area that is within range of the motion sensor? Use the value = 3.14.
The approximate area that is within range of the motion sensor is 4975 square meters
How to determine the area of the range?The figure is not given, however the area of the range can be calculated without the figure.
The given parameters are:
Angle, ⊕ = 135°
Radius, r = 65 meters
The area of the range is calculated using the following sector area
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
This gives
[tex]A = \frac{135}{360} * 3.14 * 65^2[/tex]
Evaluate
A = 4974.9375
Approximate
A = 4975
Hence, the approximate area that is within range of the motion sensor is 4975 square meters
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Evaluate the expression below when x = 6 and y = 2. 6x2y3
Answer:
I think that the answer is 432.
Step-by-step explanation:
6x2y3.We have x as 6 and y as 2.So we replace them with their numbers.
We'll have 6*6*2*2*3 which will give us 432. I HOPE THIS HELPS.
calculate time if distance is 53km and speed is 60km/hour?
Suppose that 50% of all babies born in a particular hospital are boys. If 6 babies born in the hospital are randomly selected, what is the probability that fewer than 3 of them are boys?
Using the binomial distribution, it is found that there is a 0.3438 = 34.38% probability that fewer than 3 of them are boys.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, the values of the parameters are given as follows:
n = 6, p = 0.5.
The probability that fewer than 3 of them are boys is given by:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.5)^{0}.(0.5)^{6} = 0.0156[/tex]
[tex]P(X = 1) = C_{6,1}.(0.5)^{1}.(0.5)^{5} = 0.0938[/tex]
[tex]P(X = 2) = C_{6,2}.(0.5)^{2}.(0.5)^{4} = 0.2344[/tex]
Then:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0156 + 0.0938 + 0.2344 = 0.3438[/tex]
0.3438 = 34.38% probability that fewer than 3 of them are boys.
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Need your help now please; the assignment is due tonight and this is the last problem I am having trouble with. The red box is the value I keep getting wrong
The region R is bounded by the x-axis, the straight line in the graph and the vertical line x=2.
The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
What is the volume of the solid (R) on the X-axis?If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
From the given graph:
The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:
[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]
here:
(x₁, y₁) and (x₂, y₂) are two points on the straight lineSuppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:
[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]
y = 4x
Now, our region bounded by the three lines are:
y = 0 x = 2y = 4xSimilarly, the change in polar coordinates is:
x = rcosθ, y = rsinθwhere;
x² + y² = r² and dA = rdrdθTherefore;
rsinθ = 0 i.e. r = 0 or θ = 0rcosθ = 2 i.e. r = 2/cosθrsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)⇒ r = 0 to r = 2/cosθ θ = 0 to θ = tan⁻¹ (4)Then:
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
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In the given triangles, PR ≅ AC and ∠P ≅ ∠A.
Which additional fact is needed in order to use the ASA criterion to prove that the two triangles are congruent?
Answer:
option c and d are correct
Step-by-step explanation:
if there is only one choosing option you can choose option c
A bottle of coke cost 3/4 as much as a $5 milkshake. How much would 3 bottles of coke and 2 milkshakes cost?
Answer:
Total, 2 milkshakes, and 3 cokes would cost $12.50
Step-by-step explanation:
The cokes cost $11.50 and the milkshakes $10.00
Cynthia beach wants to buy a rug for a room that is 22 ft wide and 31 ft long.she wants to leave a uniform strip of floor around the rug.she can afford to buy 580 square feet of carpeting.what dimensions should the rug have?
The dimensions the rug should have is 20 by 29
How to determine the dimension?The dimension of the rug is given as:
22 ft by 31 ft
The area of the carpet is given as:
Area = 580
Represent the length of the empty space with x.
So, the dimension of the carpet is:
22 - 2x by 31 - 2x
The area is calculated as:
Area = (22 - 2x) * (31 - 2x)
Expand
Area = 682 - 62x - 44x + 4x^2
Evaluate the difference
Area = 682 -106x + 4x^2
Substitute Area = 580
682 -106x + 4x^2 = 580
Subtract 580 from both sides
102 -106x + 4x^2 = 0
Rewrite as:
4x^2 - 106x +102 = 0
Using a graphing calculator, we have:
x = 1 and x = 22.5
Substitute these values in 22 - 2x by 31 - 2x
So, we have:
Length = 22 - 2(1) = 20 or Length = 22 - 2(22.5) = -23
Width = 31 - 2(1) = 29 or Length = 31 - 2(22.5) = -14
The dimensions cannot be negative.
So, we have:
Length = 20 and Width = 29
Hence, the dimensions the rug should have is 20 by 29
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Which is equivalent to 64 1/4
Answer:
4*64=256
256+1=256
there fore 64 1/4 is equivalent to 257/4
Write a doubles fact that can help you find the
sum. Write the sum.
3+4
Step-by-step explanation:
4 + 4 = 8 is one of the two closest double to 3 + 4
W.K.T(we know that )..
4 is 1 more than 3 this means ;
4 + 4 will be 1 more than 3 + 4
4 + 4 = 8 ,so finding 1 Less ;
3 + 4 = 7
here is the answer hope It helped U
please mark as BRAINLIEST
I really had some trouble with this problem:( & I need some help
can someone help me on part B please? I've done the answer to the rest please thanks!
Answer:
84 circular tiles are needed to make pattern number 20
4(20+1)
Step-by-step explanation:The number of circular tiles is 1 more than the pattern number on each side of the square.
circular tiles = 4(n +1)
factoring / gcf ??? (in picture)
got really sick and missed a bunch of school, would really appreciate the help !
Step-by-step explanation:
hope this will help you....
Suppose there is a simple index of three stocks, stock ABC, stock XYZ, and stock QRS. Stock ABC opens on day 1 with 8000 shares at $4.25 per share. Stock XYZ opens on day 1 with 5000 shares at $2.90 per share. Stock QRS opens on day 1 with 2000 shares at $6.40 per share. The price of stock ABC on day 8 begins at $3.90. The price of stock XYZ on day 8 begins at $2.50. Stock QRS opens on day 8 with a price of $6.10 per share. Assume that each stock has the same number of shares that it opened with on day 1. What is the rate of change of this simple index over 1 week?
The rate of change of this simple index over 1 week is - 8.81%
What is the rate of change ?The rate of change is the ratio of the difference in the value of the simple index to the original value of simple index.
Total value of the simple index at day 1 = (8000 x $4.25) + (5000 x $2.90) + (2000 x $6.40) = $61,300
Total value of the simple index at day 8 = (8000 x $3.90) + (5000 x $2.50)+(2000*6.10) = 55900
the rate of change of this simple index over 1 week
= (55900-61300)/ 61300 * 100 %
= -8.81 %
the rate of change of this simple index over 1 week is - 8.81%
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y-intercept: 4
-: x-intercepts: -2, 5, 7
-: Relative maximum at (0,4)
-: Relative maximum at (6, -3)
-: As → −∞, → −∞
-: As → ∞, →
The attached figure represents the sketch of the graph
The missing part of the questionThe complete question requires that we sketch the graph that follows the given parameters
How to sketch the graph?The given parameters are:
y-intercept: 4x-intercepts: -2, 5, 7Relative maximum at (0,4)Relative maximum at (6, -3)As x → −∞, y → −∞As x → ∞, y → ∞To start with, we plot the points on an empty coordinate plane.
Next, we connect the points using a rough curve
Lastly, the points are labelled
See attachment for the sketch of the graph
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Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
The equation that can be used to represent the situation is y = 5.5 + x
How to write and solve equation?Whole wheat flour = 5.5 cupsWhite flour = x cupsTotal flour = yThe equation:
Total flour = Whole wheat flour + White flour
y = 5.5 + x
Therefore, the equation that can be used to represent the situation is y = 5.5 + x
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Answer:
C
Step-by-step explanation:
using the figure below identify 1 pair of the following angle relationships
Answer:
\begin{gathered}\\1) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\end{gathered}
1)
Alternateinteriorangles:
\begin{gathered} \sf \implies \: 2\: \: and \: \: 7\\\end{gathered}
⟹2and7
\begin{gathered} \sf \implies \: 6\: \: and \: \: 3\\\\\end{gathered}
⟹6and3
\begin{gathered}\\2) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\\\end{gathered}
2)
Alternateinteriorangles:
\begin{gathered} \sf \implies \: 1\: \: and \: \: 8\\\end{gathered}
⟹1and8
\begin{gathered} \sf \implies \: 5\: \: and \: \: 4\\\\\end{gathered}
⟹5and4
\begin{gathered}\\3) \: \: \underline{ \sf{ Corresponding \: angles \: \: : }}\\\end{gathered}
3)
Correspondingangles:
\begin{gathered} \sf \implies \: 3\: \: and \: \: 1\\\end{gathered}
⟹3and1
\begin{gathered} \sf \implies \: 5\: \: and \: \: 7\\\end{gathered}
⟹5and7
\begin{gathered} \sf \implies \: 4\: \: and \: \: 2\\\end{gathered}
⟹4and2
\begin{gathered} \sf \implies \: 6\: \: and \: \: 8\\\\\end{gathered}
⟹6and8
\begin{gathered}\\4) \: \: \underline{ \sf{ Consecutive\: Interior \: angles \: \: : }}\\\end{gathered}
4)
ConsecutiveInteriorangles:
\begin{gathered} \sf \implies \: 2\: \: and \: \: 3\\\end{gathered}
⟹2and3
\begin{gathered} \sf \implies \: 6\: \: and \: \: 7\\\\\end{gathered}
⟹6and7
\begin{gathered}\\5) \: \: \underline{ \sf{ Consecutive\: Exterior \: angles \: \: : }}\\\end{gathered}
5)
ConsecutiveExteriorangles:
\begin{gathered} \sf \implies \: 1\: \: and \: \: 4\\\end{gathered}
⟹1and4
\begin{gathered} \sf \implies \: 5\: \: and \: \: 8\\\\\end{gathered}
⟹5and8
what are the missing values
Answer:
The answer is on the image, which is color coordinated with the how i got it
5. Solve for x.
21
4
Answer: 10
Step-by-step explanation:
By the geometric mean theorem, if we let the length of the altitude to the hypotenuse be [tex]y[/tex], this means that [tex]y^{2}=84 \longrightarrow y=\sqrt{84}[/tex].
So, by the Pythagorean theorem, [tex]x=\sqrt{(\sqrt{84})^{2}+4^{2}}=\boxed{10}[/tex]
what is the area of the figure?
Answer:
area = 62ft
Step-by-step explanation
so you section the polygon into a big rectangle and 2 small rectangles
the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft
the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft
now add the areas you got, 50+12 which is 62ft
hope this helps:)
Which graph represents the function f(x) = |x + 3|?
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
Answer:
Graph of Modulus
The graph of a modulus or absolute value function is in a form of a 'V' shape whose vertex depends upon the coordinates. The equation for the graph is given as,
where,
(a, b) are the coordinates of the vertex of 'v' in the form of (x, y),
And h shows how wider or lean will be the function, for h=0, it is a straight line, while for a negative value the graph will face downwards and opposite for a positive value.
Given to us
y = |x-3|
On the coordinate plane
The graph will be in the shape of a 'V' whose vertex will lay at the coordinates (3, 0). As the value of a is 1 the graph will face upwards. As shown below on the graph.
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Step-by-step explanation:
Answer:
C
Step-by-step explanation:
edge 23
Which graph shows the solution to the following system of inequalities x+y>4
The solution to this system of inequalities x + y>4 , x + y <3 is Option A
The complete question is
Which graph shows the solution to this system of inequalities? x + y>4 x + y <3
The image are attached with the answer.
What are Inequality ?When an expression is equated with another expression by an Inequality operator (< , > < etc) then the mathematical statement formed is called Inequality.
The inequalities are
x+y>4
x + y <3
After plotting both the inequalities in the graph the following graph that is attached with the answer is obtained.
Therefore the correct answer is Option A
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I need some help please
Answer:
HexagonHeptagonStep-by-step explanation:
The first shape has 6 sides. Hence, it is called a hexagon.
The second shape has 7 sides. Hence, it is called a heptagon.
The mathematical name for the given 2 polygons.
Solution:The first polygon has 6 sides with an angle sum of 720°, which means the mathematical name given for this polygon is,
[tex]\large\boxed {Hexagon}[/tex]
The second polygon has 7 sides with an angle sum of 900°, which means the mathematical name given for this polygon is,
[tex]\large\boxed {Heptagon}[/tex]
Hence, the first polygon is a hexagon and the second polygon is a heptagon.
heIp??
everyone??
Brainliest = Good Answer/Solution
To Find = Diameter, Area
Solution :
Diameter = 2 × Radius
Diameter = 2 × 6cm
Diameter = 12 cm
Area = 2πr
[tex]area \: = 2 \times \frac{22}{7} \times 6cm[/tex]
[tex]area \: = \frac{264}{7} [/tex]
[tex]area \: = 37.7 \: cm[/tex]
____________________________________2. Given : Diameter = 8 DM
( 1dm = 10 cm
8dm = 8 × 10 = 80cm )
To find : Radius , area
Solution :
[tex]raduis \: = \frac{1}{2} \times diameter[/tex]
[tex]radius \: = \frac{1}{2} \times 80cm[/tex]
[tex]radius \: = 40 \: cm \: or \: 4dm[/tex]
Area = 2πr
[tex]area \: = 2 \times \frac{22}{7} \times 40[/tex]
[tex]area \: = \frac{1760}{7} [/tex]
[tex]area \: = 251.4cm \: \: \: or \: 25.14dm[/tex]
____________________________________3. Given : Radius = 2.5m
To find : Diameter , Area
Solution :
Diameter = 2 × radius
Diameter = 2 × 2.5m
Diameter = 5m
Area = 2πr
Area = 2 × 22/7 × 5m
Area = 220/7
Area = 31.4m
Determine whether the relation represents a function. State the domain and range of the relation.
{(-2,-9).(-4,-4). (1,5), (5, -7)}
Answer:
It is a functionDomain: {-4, -2, 1, 5}Range: {-9, -7, -4, 5}Step-by-step explanation:
A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).
Express 5 1/2 and 2 1/2 as a ratio of whole numbers
Answer:
your answers are 5.5 and 2.5 as they both have a half extra
The graph of the absolute value parent function, f(x) = |x, is stretched
orizontally by a factor of 3 to create the graph of g(x). What function is g(X)
Answer:
g(x) = 1/3 • |x|
Step-by-step explanation:
To stretch a parent function, you multiply by whatever you want to stretch it with. If you multiplied by 3, it would be a vertical stretch... if you multiplied by 1/3, it makes it horizontal.
Hope this helps!
Given f(x) = x² + 4x - 3, find f(-3)
O -3
O -6
O 0
O 18
Answer:
f(-3) = -6
Step-by-step explanation:
f(x) = x^2 + 4x - 3
f(-3) means to put -3 in place of x and then do the calculation.
f(-3)
= (-3)^2 + 4(-3) - 3
= 9 - 12 - 3
= -3 - 3
= -6
First square -3, its 9. Then multiply -3 and 4, that's -12. Then add everything.
f(-3) = -6
The graph of y= (x + 2)(x-2)(x + 1) is shown.
4
3
2-
D
-6-5-4-3-2-1₁
23 456x
D
76
B
C
Which point is a relative minimum?
OA
OD
Answer:
Point C
Step-by-step explanation:
At point C, the graph is changing from decreasing to increasing.
Joe went shopping and purchased a pair of pants for $56 and a pair of shoes for $45. The tax in Joe's city is 4%. How much will Joe pay when he checks out ?
Answer:
$105.04
Step-by-step explanation:
First add $56 plus 45$ and you will get $101, then times $101 and 1.04 together.
Your answer should be $105.04.