In the circle below, AB is parallel to CD, AD is a diameter of the circle, and AD = 36.What is the length of AB? Express your answer in terms of pi.
We get the length of AB as 7.37 pi units
We are given that:
AB || CD
AD = 36 cm
AD is the diameter of the circle.
So, we get that
1 / 2 AD = Radius (r)
r = 36 / 2 cm = 18 cm
Now, we are also given that:
∠ BAD = 50°
Since AD is a diameter, we get that:
ABD will form a right triangle with ∠ ABD = 90°
∠ ADB = 40° ( Angle sum property)
AB will be:
sin (40) = AB / 36
AB = 36 * sin (40) = 23.140353948732
AB ≈ 7.37 pi units
Therefore, we get the length of AB as 7.37 pi units
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a rectangular persian carpet has a perimeter of 232 inches. the length of the carpet is 30 inches more than the width. what are the dimensions of the carpet?
The dimensions of the carpet are 73 x 43. = 3139.
What is dimension explained?In mathematics, a dimension is a way to quantify the size or separation of an area, an object, or a space inside one direction. In simpler terms, It is just the measurements of an object's length, width, and height.
What is a geometric figure?Geometric figures can be created using any configuration of points, lines, or planes. Depending on their dimensions, geometric figures can be categorized as either a space figure, a surface figure, a line, another line segment, a ray, or a point.
According to the given data:The perimeter of the carpets = is 232.
The length of the carpet = 30 in.
In a rectangle, the edge is P = 2W + 2L
In this case 232 = 2W + 2L
Also, the 2nd sentence says L = W + 30
This length variable can be changed in the perimeter formula:
232 = 2W + 2(W+30)
232 = 2W + 2W + 60
232 = 4W + 60
172 = 4W
43 = W
Then, since L = W+30
L = 43+30 = 73
So the dimensions of the carpet are 73 x 43. = 3139.
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A bakery sold 120 chocolate cupcakes in a day,
which was 24% of the total number of cupcakes
sold that day. How many total cupcakes did the
bakery sell that day?
The correct answer is 28.8.
Everything is stated as though it were a fraction of a hundred in terms of quantity. The ratio can be expressed as a quarter of one hundred. The word "percent" denotes a percentage of 100. It is represented by the '%' symbol.
120 cupcakes were sold by a bakery in a single day, with 45% of them having a chocolate flavour.
The total quantity of chocolate-flavoured cupcakes served on that particular day will then be
Let x represent how many chocolate-flavoured cupcakes were sold on that particular day.
x = 24% of 120
x = 0.24 × 120
x = 28.8
Consequently, the quantity of chocolate-flavoured cupcakes sold that day will be 28.8.
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0.1-(-31/50)
it’s Math
So please help
Answer:
0.72 or 18/25
Step-by-step explanation:
Multiply -(-31/50)
0.1 + 31/50
To write 0.1 as a fraction with a common denominator, multiply by 50/50.
0.1*50/50+31/50
Combine 0.1 and 50/50.
0.1+50/50 + 31/50
Combine the numerators over the common denominator.
0.1*50+30/50
Simplify the numerator.
36/50
Cancel the common factor of 36 and 50.
Results are 18/25 and 0.72.
Hope this helps.
randy presses on his calculator twice to obtain two random numbers between and . let be the probability that these two numbers and form the sides of an obtuse triangle. find .
We are to calculate the value of 4p. The value of 4p will be π / 4.
Let's give the numbers we get from the calculator the names x and y. Independent random variables with a uniform[0,1] distribution are x and y.
Let's take notice that since x and y are both between 0 and 1, 1 is the triangle's longest side.
Let's start by interpreting geometry. If the triangle were a rectangle, the side with length 1 would be the hypotenuse, and x and y would then need to meet the following criteria:
x²+y² = 1
Keep in mind that we are supposing the triangle to be a rectangle in this instance. However, the task requires us to create an acute triangle.
To do that, we must widen the angle formed by the sides of length x and y. We can do that by 'growing' the triangle, but if we do so while maintaining the x and y values, the length of side 1 should rise, which is not what we want.
Therefore, if we enlarge the triangle, we should likewise decrease the value of x and/or y so that the length of the first side may be maintained. This insight allowed us to conclude that
x²+y² < 1
Let's now employ a more mathematical strategy. The Cosine Theorem states that a triangle with three sides of length a, b, and c is satisfying.
A2 is equal to b2+c2 - 2bc* cos(), where is the angle formed by the lengths of b and c's sides.
The result of applying this formula to our triangle is that
[tex]1+x^{2} +y^{2} - 2bc * cos\alpha[/tex] , where aplha is the angle between x and y.
Let's call the figures we obtain from the calculator x and y. X and Y are independent random variables with uniform[0,1] distribution.
Consequently, we must ascertain P(x2+y2 1). This likelihood may be calculated using integration. You need polar coordinates.
(X, Y) = (r*cos, r*sen), where r is an integer between 0 and 1, and (that way, the numbers are positive).
Because the Jacobian matrix has determinant r, X2 + Y2 = 1.
On integrating, we get out answer as π / 4
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The sum of three consecutive even integers is 48. Find the value of the middle of the
three.
Answer:
16
Step-by-step explanation:
You want the middle of three consecutive even integers that have a sum of 48.
Consecutive even integersWe can let x represent the middle of the three integers. Then the other two are (x -2) and (x +2), and their sum is ...
(x -2) +x +(x +2) = 48
3x = 48 . . . . . simplify
x = 16 . . . . . . divide by 3
The middle integer of the three is 16.
__
Additional comment
As we see here, the average of the three integers is their sum divided by their number: 48/3 = 16. The middle of an odd number of consecutive integers will be equal to their average value. Hence, the middle integer must be 16.
√2x³. √10x
Help please
You can write as [tex]2 \sqrt{5} {x}^{2}[/tex] or [tex]\boxed{2 {x}^{2} \sqrt{5}} [/tex]
Step-by-step explanation:
Find product of the groups,
[tex] \sqrt{2 {x}^{3} \: . \: 10x}[/tex]
Regrouping,
[tex] \sqrt{2{x}^{3 + 1} \: . \: 10 } [/tex]
Multiplying,
[tex] \sqrt{20 {x}^{3 + 1} } [/tex]
Add constants,
[tex] \sqrt{20 {x}^{4} } [/tex]
Rewrite 20 as 4 • 5,
[tex] \sqrt{4 \: . \: 5 {x}^{4} } [/tex]
Rewrite 4 as 2² ,
[tex] \sqrt{ {2}^{2} \: . \: 5 {x}^{4} } [/tex]
Using radical rules,
[tex] \sqrt{ {2}^{2} } \sqrt{x} \sqrt{5} [/tex]
Reduce root and power,
→ [tex] \underline {2 {x}^{2} \sqrt{5}} [/tex]
WILL GIVE BRAINLIEST IF ANSWERED WELL!!!
Answer:
S / 2πh
Explanation:
2πrh are all multiplied together to make S, so in order to isolate the r, we need to divide (the opposite operation of multiplication) 2πh from both sides.
Cara's bi-weekly gross pay is $735.18. She sees that $13.97 was deducted for Medicare tax. What percent of Cara's
gross pay has been withheld for Medicare tax? Round to the nearest tenth.
a. 0.19%
b. 1.9%
c. 2.1%
d. 3.5%
Answer:
b
Step-by-step explanation:
To find the percent of Cara's gross pay, divide what was deducted for Medicare tax by what her bi-weekly gross pay is.
So,
13.97 ÷ 735.18 = 0.019
Which means 1.9%
David requires at least $250 to hold his birthday party. If David can save $43 by the end of each month, how many months will he need to save to be able to afford his birthday party?
a. Write an inequality that describes this situation.
b. Solve the inequality. Show all your work.
c. Write your answer in a complete sentence.
Answer: 250/43
Step-by-step explanation
Answer:
he would need seven weeks, i believe.
7.
If twenty-one more than a fifth of a number is equal to two times the quantity of
three less than that number, what is the number?
Answer:
The number is 15.
Step-by-step explanation:
Let n be the number.
[tex] \frac{1}{5} n + 21 = 2(n - 3)[/tex]
[tex]n + 105 = 10(n - 3)[/tex]
[tex]n + 105 = 10n - 30[/tex]
[tex]9n = 135[/tex]
[tex]n = 15[/tex]
Rewrite 120 + 400 using the GCF and factoring.
12(10 + 40)
20(10 + 2)
40(3 + 400)
40(3 + 10)
Pls help asap
What is the cos A?
i need help bad
According to given triangle the value of cos A = 3/5
We know that cos theta = Adjacent Side / Hypotenuse Side
According to the question given that Adjacent side = 3
And Hypotenuse Side = 5
Then cos A = 3/5
Hence, option 3 is correct
Each geometrical shape has unique side and angle characteristics that enable us to recognize it. The following is a list of a triangle's key characteristics.
Three vertices, three internal angles, and three sides make up a triangle.
According to the triangle's "angle sum property," a triangle's three inner angles can never add up to more than 180 degrees. Take note of the triangle PQR shown above, where the angles P, Q, and R all add up to 180 degrees.
A closed triangle has three vertices, three sides, and three angles. The symbol for a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signboards in the shape of triangles are the most prevalent triangle-shaped objects.
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In the picture there is a triangle with ABC angles. Sides AB=5, BC=3, CA=4. The ratio of CosA=4/5.
Given that,
In the picture there is a triangle with ABC angles.
Sides AB=5, BC=3, CA=4
Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.
The right triangle's three sides are as follows:
Hypotenuse (the longest side)
Perpendicular (opposite side to the angle)
Base (Adjacent side to the angle)
According to the cos theta formula, the cos of an angle in a right-angled triangle is equal to the ratio of the Adjacent side to the hypotenuse.
Cos A = Adjacent side / hypotenuse
CosA=4/5
Therefore, CosA=4/5.
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HELP, I NEED ONE PERSON TO HELP WITH THE NEXT THREE QUESTIONS THAT INVOLVE COMBINING FUNCTIONSTHAT MODEL A REAL WORLD SITUATION
question picture below
C=??
Answer:
if (23)n=(1111)2find the base n
GH has a midpoint at M(3, 6). Point G is at (2, 6). Find the coordinates of point H.
Write the coordinates as decimals or integers.
Thus coordiante of point H is(4,6)
The Midpoint Formula: The midpoint of two points,
(x1,y1) and (x2,y2) is the point
M=(x1+x2)/2 and (y1+y2)/2
(2+x2)/2=3
(6+y2)/2=6
solving above equation
x2=4
y2=6
Thus coordiante of point H is(4,6)
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12. Classify the statement below as a descriptive or inferential statistic and explain why.
Because of the SG distance learners, Robin expects to serve 12% less meals this year than last year.
The given statement is a descriptive statistic.
What is descriptive statistics?Descriptive statistics are relatively short informational coefficients that summarize a given data set, which can be a representation of the entire population or a sample of a population. Descriptive statistics are divided into measurements of central tendency and measures of variability (spread). Descriptive statistics are used to describe or summarize the data in meaningful and useful ways. It would be useful to know, for example, that each of the participants in with us example wore blue shoes. Even so, it'd be useful to know how evenly distributed their anxiety ratings were.So, the statement "Robin expects to serve 12% fewer meals this year than last year" is a descriptive statistic.
Therefore, the given statement is a descriptive statistic.
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setenta y uno por tres dividido 43
Answer:
4.95
Step-by-step explanation:
espero que te ayude
measure the length of a ordinary sheet of 8x11 paper in metric units (if you do not have a metric measuring device, you can measure in us units and use a free online conversion tool to change to metric units). what is the area of the sheet of paper in correct metric units?
The area of the sheet of paper in correct metric units is 602.6c[tex]m^{2}[/tex].
What is an area?A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina. Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).
Calculations:
The length of a 8 X 11 paper in metric unit is 27.9 cm and width of 8 X 11 paper in metric unit is 21.6 cm.
Area of sheet of paper=length*width
=27.9*21.6
=602.6 c[tex]m^{2}[/tex]
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can someone help me really quick
Answer:
Step-by-step explanation:
The last option
This is because we are going to multiply in order. The -6 is only in parenthesis because its a negative number. this means we are multiplying 2 x 4 , then multiplying that answer by -6.
Hope this helps! ^^
Answer:
The answer to your question is (A) hope this helpsStep-by-step explanation:
please can someone solve this
you need to figure out what x is
y=5/2a √6x
Answer:
y = 5/2 √6x
Solution.
Rewrite
y = 5/2a√6x
y = 5a√6x
----------
2
Cross multiply
2y = 5a√6x
Swap both sides
√6x = 2y
-----
5a
Take the square of both sides
6x = 2y²
------
5a²
Divide both sides by 6
x = 2y² 6
----- ÷ -----
5a². 1
x = 2y² 1
---- × ----
5a². 6
x = 2y²
-----
75a²
y <= 1/2x - 5
y >= 3x - 20
In the xy-plane, a point with coordinates (h, k) lies in the solution set of the system of inequalities above. What is the maximum possible value of h?
The maximum possible value for 'h' = 6 for the given set of system of inequalities.
What do you mean by system of inequalities?A collection of two or so more inequalities for one or more variables is referred to as a system of inequalities. When a problem necessitates a variety of solutions and those solutions are constrained by more than one constraint, a system of inequalities is used. Inequalities systems are frequently used to describe the constraints on such a solution.For the given set of inequalities;
y ≤ 1/2x - 5
y ≥ 3x - 20
Equation both equation;
(1/2)x - 5 = 3x - 20
x - 10 = 6x - 40
Further simplifying;
-5x = -30
x = 6
Thus, the maximum possible value for 'h' is same as the value find for the x = 6; as h also represents the point on the x-axis.
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Find X
3x + 16
5x-10
3x + 8 = -10 I don’t know what this is and I need to solve it fast
Answer:
x = -6
Step-by-step explanation:
3x + 8 = -10
3x = -10-8
3x=-18
divide both sides by the coefficient of x which is 3
3x/3 = -18/3
x = -6.
A submarine descends to 1/6 of its maximum depth. Then it descends another 2/3 of its maximum depth. If it is now at 650 feet below sea level, what is its maximum depth.
The submarine can descend to a maximum depth of 780 feet.
What do we mean by depth?The distance is measured downward and perpendicularly from a point to a chosen reference surface.Let x be the maximum depth.
It descends to one-sixth of the maximum depth = (1/6)xIt descends another two-thirds of the maximum depth = (2/3)xIt is now 650 feet below sea level after descending the depths above.
Thus;
(1/6)x + (2/3)x = 650x(1/6 + ⅔) = 650x(5/6) = 650x = 6 × 650/5x = 780 ftTherefore, the submarine can descend to a maximum depth of 780 feet.
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the mathcounts international airport had 738,114 departures in 2001. if these were distributed uniformly throughout each 24-hour period, what is the mean number of seconds between each departure time? express your answer to the nearest whole number.
The MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.
For given question,
In 2001 there were 738,114 departures.
As we can see, 2001 was not a leap year.
So, the number of days in 2001 = 365
We find the number of departures per day in 2001.
738,114 / 365 = 2,022.23
So, approximately 2,022 departures per day.
Now we find the number of departures in an hour.
2,022 / 24 = 84.25
This means, approximately 84 departures per hour
We know that, 1 hour = 3,600 seconds
Now we find the mean number of seconds between departure time.
3,600 / 84 = 42.8
≈ 43 seconds
Therefore, the MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.
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Lawana is making cone-shaped hats 4 inches in diameter, 6.5 inches tall, with a slant height of 6.8 inches for party favors. Find each measure to the nearest tenth.
a. the volume of candy that will fill each cone
Given hats are forming a conical shape and the volume of the cone will be 27.28 inches³.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Given that,
4 inches in diameter, 6.5 inches tall, slant height of 6.8 inches
So,
D = 4 inches
Now radius r = D/2
r = 4/2 = 2 inches.
Height h = 6.5 inches.
The volume of the conical bar is given as ;
(1/3)πr²h
So,
Volume = (1/3)π(2)²6.5
Volume = 27.28 inches³
Hence "The volume of the given conical-shaped hat will be 27.28 inches³".
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the sequence obtained by starting with 10 and obtaining each term by subtracting 3 from the previous term
Answer:
A=10. D=_3
Step-by-step explanation:
Start from 10 and make minus 3 every time
At the ice cream shop there are 14 shakes so for every six months record the ratio is below.whats malts to total?
Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
How much interest will Rich accrue during the 4.5-year non-payment period?
Rich has to pay an interest of $1525.10 during the 4.5 year non payment period.
In the question
it is given that the Amount of loan taken by Rich = $7900
non payment time period = 4.5years
Interest charged during the non payment time = 4.29%
Interest charge for the first year = 4.29% of 7900
= 0.0429 * 7900 ...(as 4.29% = 0.0429)
= 338.91
So , the interest charge for first non payment year = $338.91
to find the interest for 4.5 years , multiply the first year interest by 4.5.
So the interest charge for 4.5 years = 4.5*338.91
=1525.095
≅1525.10
Therefore , Rich has to pay an interest of $1525.10 during the 4.5 year non payment period.
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A design for a library has a scale of 1/3in=1 foot. The height of the library in the drawing is 12 inches.What is the actual height of the library
The actual height of the library is 36 feet.
Given a scale of 1/3 inch = 1 foot
therefore, 1 inch = 3 feet
then, 12 inches = 12 × 3
36 inches.
therefore the actual height of the library is:
12 × 36
= 432 inches
= 36 feet.
It is obvious which dimension is intended when a rectangle is drawn with both horizontal and vertical sides when the term height is used; height designates how high (or how tall) the rectangle is. As a result, using the word width to describe the other dimension—the width of the rectangle from side to side—is simple. As long as there is no ambiguity, it is also appropriate to refer to the side-to-side measurement as the rectangle's length if it is bigger than its height.
hence we get the height of the library as 36 feet.
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