The estimated perimeter of an ellipse if the major axis has a length of 15 ft and the minor axis has a length of 7.5 ft id found to be 37.3 feet .
Perimeter is calculated as
= 2*pi*r*r
= 2 *3.14 * sqrt (15/2² +7.5/2²)/2
= 6.28 x sqrt (56.25+14.0625/2 6.28) *sqrt (35.15625) 6.28 * 5.929270613
= 37.235 feat
An ellipse is the locus of all the points on a plane whose distances from two fixed points in the plane are always same. The fixed points, which are encompassed by the curve, are known as foci , singular of focus.
The constant ratio is the eccentricity of the ellipse and the fixed line is directrix. Eccentricity is an element of ellipse which denotes elongation and is symbolized by the letter 'e'.
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A cone with a height of 15 yards has a volume of 475.17 yd^3 find the diameter of the cone
Answer: h = 15 yards
Volume = 475.17 cubic yards
Diameter = 5.5*2 = 11.0 = 11 yards
HOPE THIS HELPS
What role does place value have in finding 10% and 1% of a number? Write at least two complete sentences.
The fractions of the numbers are found as follows:
10% of a number is found moving the decimal digit one unit right.1% of a number is found moving the decimal digit two units right.How to divide a number by powers of 10?To divide a number by the nth power of 10, the decimal digit in the number is moved n units to the right.
The fraction that represents 10% of a number is given as follows:
10/100 = 1/10.
Meaning that the number is divided by 10, which is the first power of 10, and thus the decimal digit is moved one unit right in the number.
The fraction that represents 1% of a number is given as follows:
1/100.
Meaning that the number is divided by 100, which is the second power of 10, and thus the decimal digit is moved two units right in the number.
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There are 120 five-digit numbers that can be made from the digits 1, 2, 3, 4, 5 if each digit is used once in the number. That smallest is 12,345 and the largest is 54,321. If these 120 numbers are listed in order from smallest to largest, what is the 73rd number in the list?
Answer:
41235
Step-by-step explanation:
There are 120 five-digit numbers that can be made from the digits 1, 2, 3, 4, 5 if each digit is used once in the number,
The total number of times where each number will occur or be at first place is calculated as:
4! = 4 × 3 × 2 × 1
= 24
Hence,
24th number = The last number where 1 is at first place
We can write this out as:
12345
12354
12435
12453
12534
12543
13245
13254
13425
13452
13524
13542 e.t.c.
48th number = The last number where 2 is at first place
72nd place = The last number where 3 is at first place.
This means, the 73rd number is the first number where 4 is at first place.
Therefore, the 73rd number based on pattern is 41235
Use ruler and compasses to draw a triangle ABC with:
AB of length 3 cm, AC of length 4.5 cm and BC of length 2 cm.
According to the information we can infer that the triangle and its internal angles are: 76.7°, 125.2°, and 21.9°.
How to draw the triangle with the given measurements?To draw the triangle with the given measures we must take into account the internal angles so that the triangle is correct. Additionally we must take into account that it is a scalene triangle.
In this case, the internal angles are the most important part because it gives the shape of the triangle. These angles are:
76.7°125.2°21.9°So, according to the above, this triangles is scalene and its sides are:
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Write an equivalent expression (2x+3y)+(4x+y)
Answer:
[tex]2 \times + 3y[/tex]
Edition:
(2x + 3y) + (4x + y) =
6x + 4y
Sorry, I did the wrong method, I used FOIL instead of combining like terms in order to write an equivalent expression.
The correct answer is 6x + 4y.
How many ways are there to arrange $6$ beads of distinct colors in a $2 \times 3$ grid if reflections and rotations are considered the same
There are 90 ways to arrange 6 beads of distinct colors in a 2*3 grid if reflections and rotations are considered the same.
In order to reach this result, we may use Burnside's Lemma, which states that the average number of arrangements of a symmetric object's symmetric parts, is taken throughout the set of all possible symmetry operations of the object.
You may fix one element and position the rest around it because of the rotation. You now have a total of 90 configurations available.
Thus, If reflections and rotations are treated equally, there are 90 ways to arrange 6 beads of different colors on a 2*3 grid.
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Beatrice has a rectangular swimming pool in her backyard. The dimensions are 16 feet by 8 feet. She decides to build a deck of uniform
width around the pool. Together the pool and the deck will have an area of 384 square feet.
a) write the expression to represent the length and the width of the swimming pool with the deck around it
b) find x, the width of the deck
Use the illustration below to determine which statements are true. Select the two statements that are true statement 1: Points A, E, and C are collinear. statement 2: Lines I and m intersect at point D. statement 3: AE and DC are line segments on line I. statement 4: EA and EC are rays on the line m.
The required true statements for the given lines are 1 and 4.
What is line segments?An element or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
According to question:Statement A: E and C are co-linear.
It is true, E and C are lie in same line
statement 2: Lines I and m intersect at point D.
It is false, I and m intersect at point E.
statement 3: AE and DC are line segments on line I
It is false,because AE and DC are line segments placed in different line.
statement 4: EA and EC are rays on the line m.
It is true, as EA and EC are in same line m.
Thus, required true statements are 1 and 4.
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Answer:
1 and 4
Step-by-step explanation:
What is the circumference of a circle with sector area 9π and arc measure 90 degrees?
By using the area of circle formula, the solution of the given problem of circle comes out to be 6 + π cm
Describe the circle.Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.
Here,
A 9 Pi square centimeter circle's sector has a 60 degree center angle. The sector's exterior border is
Circle area is equal to. πR² = 9π
Circumference =2πR
=> 2π*3 = 6π cm
Arc length equals (60/360)*6 to cm
Arc's perimeter is calculated as follows: Radius + Length of Arc + Radius = π +3 + 3 = 6 + π cm
Therefore , the solution of the given problem of circle comes out to be
6 + π cm.
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By using the area of circle formula and circumference of a circle formula, the solution of the given problem of circle comes out to be 12π cm
Describe the circle.Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.
Here,
sector area of circle = 9π
arc measure = 90°
Area of sector = (arc/360°)*πr²
⇒ 9π = (90°/360°)πr²
⇒ 9π = (1/4)πr²
⇒ 4*9π = πr²
⇒ 36 = r²
⇒ 6² = r²
r = 6
and Circumference of circle = 2πr
=> 2π*6 = 12π cm
Therefore , the solution of the given problem of circle comes out to be
12π cm.
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.
If sin (A + B) = 1 and tan (A - B) = 1/v3, find the value of:
i) tan A+ tan B
ii) sec A- cosec B
If sin (A + B) = 1
and tan (A - B) = 1/√3
To Find :-value of:
i) tan A+ tan Bii) sec A- cosec BSolution :-We know that,
sin 90 = 1tan 30 = 1/√3So,
sin(A + B) = sin90(A+B)=90tan(A - B) =tan 30(A-B)=30A + B + A - B = 90 + 30
(A + A) + (B - B) = 120
2A = 120
A = 120/2
A = 60By putting value of A in 2
A - B = 30
60 - B = 30
-B = 30 - 60
-B = -30
B = 30Finding valuestan 60 + tan 30
We know that
tan 60 = √3tan 30 = 1/√3√3 + 1/√3
√3 × √3 + 1/√3
3 + 1/√3
[tex]4/√3[/tex]
sec A- cosec B
sec 60 - cosec 30
We know that
sec 60 = 2cosec 30 = 22 - 2 = [tex]0[/tex]
Hence,tan A+ tan B=4/√3
sec A- cosec B=0
The null and alternative hypotheses divide all possibilities in to:
a. two sets that may or may not overlap .
b. as many sets as necessary to cover all possibilities c. two non-overlapping sets d. two sets that overlap reset selection
Answer:
Step-by-step explanation:
b
3. A prism has a right triangular base with legs of 2 and 6 inches, meaning the legs are the base and height of the triangle. The height of the prism is 4 inches. What is the volume of the
prism?
12 inches
24 inches
32 inches
48 inches
4. You are choosing between two different cheese wedges at the grocery store. Assume both wedges are triangular prisms with bases that are isosceles triangles. The first wedge has a base that is 2.5 in. wide and a height of 4.5 in., with the entire wedge being 3 inthick. The second wedge has a base that is 3 in. wide and a height of 4 in., with the entire wedge being 3.5 in. thick. Which wedge has a greater volume of cheese, and by how much?
A. The first wedge by 6.375 cubic inches
B. The first wedge by 12.75 cubic inches
C. The second wedge by 8.25 cubic inches
D. The second wedge by 4.125 cubic inches
5. A triangular prism has a base area of 43 square meters and a volume of 645 cubic meters. What is the height of the prism?
A. 12 m
B. 15 m
C. 25 m
D. 32 m
Answer:
c
b
Step-by-step explanation:
The figure below to the left is a graph of f(x), and below to the right is g(x).
The figure below to the left is a graph of f(x), a
(a) What is the average value of f(x) on 0≤x≤2? avg value = __________
(b) What is the average value of g(x) on 0≤x≤2? avg value = __________
(c) What is the average value of f(x)?g(x) on 0≤x≤2? avg value = _________
(d) Is the following statement true?
Average(f)?Average(g)=Average(f?g)
A. Yes
B. No
The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.
avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.
a)
Hence average value of f(x) on 0≤x≤2
= 1/2 ∫f(x) with 0 and 2 as intervals
Since integration is basically the area under the curve we get
avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]
Since from 0 to 1, the figure is a triangle and beyond that a straight line we get
1/2[1/2 X 1 X 1 + 0]
= 1/4 sq units
b)
Similarly, the average value of g(x) on 0 ≤ x ≤ 2
1/2[area from 0 to 1 + area from 1 to 2]
= 1/2[0 + 1/2]
= 1/4 sq units
c) here we need to find the average of f(x) . g(x)
Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1
Hence we see that on multiplying the functions, the resultant has to be a 0 function.
Hence its average value will be 0.
d)
Average(f) . Average(g) = 1/4 X 1/4
= 1/16
Average of (f.g) = 0
Hence the statement is false
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Complete Question
The figure attached to the left is a graph of f(x), and below to the right is g(x).
The figure below to the left is a graph of f(x), a
(a) What is the average value of f(x) on 0≤x≤2? avg value = __________
(b) What is the average value of g(x) on 0≤x≤2? avg value = __________
(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________
(d) Is the following statement true?
Average(f) . Average(g)=Average(f.g)
A. Yes
B. No
1. a room has dimensions 15m by 9m by 12m the dimensions of its
scale model is 5m by
3m by 4m what is the ratio of the dimensions of the actual room to that of the scale
model
2. the ratio of the dimensions of the scale model to that of the
actual object s 1:16 the length and width of the actual object are
2.4m and 1.8m respectively
Answer: To find the ratio of the dimensions of the actual room to that of the scale model, we can divide the dimensions of the actual room by the dimensions of the scale model.
The dimensions of the actual room are 15m by 9m by 12m, and the dimensions of the scale model are 5m by 3m by 4m.
Therefore, the ratio of the dimensions of the actual room to that of the scale model is:
length: 15m / 5m = 3 : 1
width: 9m / 3m = 3 : 1
height: 12m / 4m = 3 : 1
So, the ratio of the dimensions of the actual room to that of the scale model is 3:1 for all dimensions (length, width, and height)
The ratio of the dimensions of the scale model to that of the actual object is 1:16
so to find the length and width of the actual object, you can use this relation
length = scale model length * 16 = 2.416 = 38.4m
width = scale model width * 16 = 1.816 = 28.8m
So the length and width of the actual object are 38.4m and 28.8m respectively.
Step-by-step explanation:
Please answer these questions! I will give brainliest
Answer:
2. k = -24
3. y = 50
4. m = -13
5. b = 8/7
6. x = -1/2
7. a = -4
8. k = 7.8
Step-by-step explanation:
2. -20 ÷ 5/6
3. 18 ÷ 0.36
4. -1/2 * 26
5. 6/7 + 2/7
6. 1/8 - 5/8
7. -2.3 - 1.7
8. 3.4 + 4.7
Those should be good. Good luck
Please help me asap!!
Answer:
its 28
Step-by-step explanation:
Answer:
The top second one :))
Step-by-step explanation:
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y = 0
NEED HELP ASAP
NO LINKS AND NO JUST SAYING HI, PLEASE ANSWER LEGITIMATELY! THANK YOU!!!! <3
Answer: It's 42
Since 48 + 90 = 138
And because every triangle equals 180 all you gotta do is add 42
Convert 12 m/s in
to km/h
By using the conversion factor: 1 km/h = 0.277778 m/s, we get 12 meter per second is equal to 43.2 km/h.
What is velocity?Velocity is a vector quantity that represents the rate of change of an object's position. It is defined as the displacement of an object divided by the time it takes for that displacement to occur. In other words, velocity tells you how fast an object is moving in a certain direction.
What is the unit and formula for velocity?The standard unit for velocity is meters per second (m/s) or kilometers per hour (km/h) in the International System of Units (SI). In imperial system of units, it is expressed in feet per second (ft/s) or miles per hour (mph).
The formula for velocity is:
velocity = displacement / time
To convert 12 m/s to km/h, you can multiply 12 by the conversion factor:
12 m/s * (1 km/h / 0.277778 m/s) = 43.2 km/h
So 12 meters per second is equal to 43.2 kilometers per hour.
Another way to do the conversion is by applying the formula :
Speed (km/h) = Speed (m/s) x 3.6
12 x 3.6 = 43.2
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please help: Can a triangle have side lengths with the given lengths? Explain. 8m, 10m, 19m
Answer:
no
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
8+10 is 18
which is less than 19
8t + 2 = 8(4) + 2
= 32 + 2
Please help me pleaseee
Given:
The quadratic function is:
[tex]f(x)=(x+2)^2+1[/tex]
To find:
The graph of the given quadratic function.
Solution:
The vertex form of a quadratic function is:
[tex]f(x)=a(x-h)^2+k[/tex] ...(i)
Where, a is a constant and (h,k) is the vertex of the graph of the quadratic function.
We have,
[tex]f(x)=(x+2)^2+1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=1[/tex]
[tex]h=-2[/tex]
[tex]k=1[/tex]
Now,
[tex](h,k)=(-2,1)[/tex]
It means the vertex of the graph of the given function is at point (-2,1).
Only in graph C, the vertex of the parabola is at (-2,1).
Therefore, the correct option is C.
TEKS 7.61 Nataly has 6 pink bows, 1 blue bow, and 3 purple bows in a box. She will randomly choose 1 bow from the box. What is the probability Nataly will choose a pink bow?
Given:
Number of pink bows = 6
Number of blue bows = 1
Number of purple bows = 3
Nataly will randomly choose 1 bow from the box.
To find:
The probability that the Nataly will choose a pink bow.
Solution:
The total number of bows is:
[tex]6+1+3=10[/tex]
The total number of bows is the total outcomes.
Total outcomes = 10
The number of pink bows is the favorable outcomes.
Favorable outcomes = 6
We know that, the probability that the Nataly will choose a pink bow is
[tex]\text{Probability}=\dfrac{\text{Number of pink bows}}{\text{Total number of bows}}[/tex]
[tex]\text{Probability}=\dfrac{6}{10}[/tex]
[tex]\text{Probability}=0.6[/tex]
Therefore, the probability that Nataly will choose a pink bow is 0.6.
AOC and BOD are diameter of a circle, centre O, prove that ABD and DCA are congruent by RHS
It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.
RHS congruency criteria:Triangles must have equal corresponding sides and equal corresponding angles in order to be congruent.
According to the RHS congruence theorem, two right-angled triangles are congruent if their respective hypotenuses and sides are the same as those of another right-angled triangle.
Here we have
AOC and BOD are diameters of a circle and have a center O.
It is given that AOC and BOD are diameters of a circle.
From the triangles Δ AOC and ΔBOD
⇒ BD = CA [ Diameters of the circle i.e Hypotenuse of triangles ]
⇒ ∠BAD = ∠CDA [ Right angles in a semicircle is 90°]
⇒ AD = AD [ Common in both triangles i.e sides of triangles ]
Thus, Using RHS congruence criteria
⇒ ΔABD ≅ ΔDCA
Hence,
It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.
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The two expressions below have the same value when rounded to the nearest hundredth
log5b log948
what is the approximate value of logb to the nearest hundredth
0.93
1.23
9.16
65.53
The approximate value of ㏒(b) to the nearest hundredth is 1.23.
Logarithms:The other method to write exponents in mathematics is using logarithms. A number's base-based logarithm is equal to some other number. A logarithm performs exponentiation's exact opposite function.
In Logarithms, ㏒ₐ(b) = ㏒(b)/ ㏒(a)
Given that
The two expressions below have the same value when rounded to the nearest hundredth
=> ㏒₅ (b) = ㏒₉ (48)
As we know ㏒ₐ(b) = ㏒(b)/ ㏒(a)
=> ㏒₅ (b) = ㏒(b)/㏒(5)
=> ㏒(b)/㏒(5) = ㏒₉ (48)
=> ㏒(b) = ㏒₉ (48) ㏒(5)
=> ㏒(b) = (1.7618)(0.6989)
=> ㏒(b) = 1.23132202
=> ㏒(b) = 1.23
Therefore,
The approximate value of ㏒(b) to the nearest hundredth is 1.23.
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What is 72 1/4 in a decimal
Answer:
I think it's 0.18 in decimal
Which is 536,900 in scientific notation
Answer:
5.369 x 105
Step-by-step explanation:
Answer:
5.369 x 105
Cause in scientific notation, the decimal point is always after the first number from the left.
Which equation should be used to find the volume of the figure?
Answer:
The first one
Step-by-step explanation:
The figure shown is a rectangular pyramid
The volume of a rectangular pyramid can be calculated using the formula
[tex]V=\frac{1}{3} lwh[/tex]
where l = length of base, w = width of base and h = height
We have a given length of 6 in, a given width of 4 in and a given height of 8 in
That being said, we plug in the given values into the formula
[tex]V=\frac{1}{3} (6)(4)(8)[/tex]
This equation matches A therefore A is the answer
28 = 4/5 x - 8 What value of x makes the equation true?
Answer:
x will have to be 45 to make this true
Step-by-step explanation:
A child plants flower seeds in her backyard in May. The flowers bloom in July. Is this an example of a
positive, negative, or no relationship between data
Combine like terms to simplify this expression:
8 + 7y + 2y + 4
Answer: The resulting expression is 8+9y+4, which simplifies to 12+9y.
Step-by-step explanation: To combine like terms, we add the coefficients of the terms that are the same. In this expression, the like terms are 2y and 7y. Their coefficients are 2 and 7, respectively, so when we add them we get 2+7=9. The resulting expression is 8+9y+4, which simplifies to 12+9y.