The correct answer is option a. 0.37.
Given that [tex]cos(2\theta) = 0.73[/tex], find a possible value of sin(theta).
It is known that:
[tex]cos(2\theta) = 1-2sin^2(\theta)[/tex].
Substituting the given value:
[tex]0.73 = 1-2sin^2(\theta)[/tex]
Rearrange to solve for sin²(theta):
[tex]2sin^2(\theta)=1-0.73[/tex]
[tex]2sin^2(\theta)=0.27[/tex]
[tex]sin^2(\theta)=0.135[/tex]
So, [tex]sin(\theta) = \sqrt{0.135}\ or\ sin(\theta) = -\sqrt{0.135}[/tex].
Since we are looking for a possible value, we take the positive root:
[tex]sin(\theta) \approx 0.367[/tex]
Considering the options given, the closest possible value is 0.37.
Geometry :)))))))))))))))))))))))))))))))
The measures are:
(a) BC = 20 mm
(b) GF = 10 mm
(c) CD = 10 mm
(d) KM = 10 mm
To find the measures you're looking for in the given diagram, we'll use properties of midsegments in triangles and trapezoids.
First, let's establish some properties:
In triangle ABC, FG is the midsegment, so FG is parallel to BC and half the length of BC.
In trapezoid CDEF, KM is the midsegment, so KM is parallel to EF and half the length of EF.
EF is parallel to KM and also parallel to DC.
Now, let's find the measures:
(a) BC:
Since FG is the midsegment of triangle ABC, FG is parallel to BC, and FG is half the length of BC. Therefore, BC = 2 * FG.
(b) GF:
GF is the midsegment of triangle ABC, so it's half the length of BC. Thus, GF = BC / 2.
(c) CD:
Since EF is parallel to DC and KM is the midsegment of trapezoid CDEF, CD is also half the length of EF. Therefore, CD = EF / 2.
(d) KM:
KM is the midsegment of trapezoid CDEF, so it's half the length of EF. Thus, KM = EF / 2.
Now, let's find the specific values using the information given:
Given values:
BC = 20 mm (from the diagram).
EF = 20 mm (since BC is parallel to EF in the same trapezoid).
(a) BC:
BC = 2 * FG
BC = 2 * GF (since GF is half the length of BC)
BC = 2 * (BC / 2) (substituting the given value for BC)
BC = BC
(b) GF:
GF = BC / 2
GF = 20 mm / 2
GF = 10 mm
(c) CD:
CD = EF / 2
CD = 20 mm / 2
CD = 10 mm
(d) KM:
KM = EF / 2
KM = 20 mm / 2
KM = 10 mm
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A basketball coach is purchasing 12 shirts for her team, each with a different number. At the checkout counter, the clerk places 5 of the shirts in the first bag. How many different ways can a group of 5 shirts be placed in that first bag? A. 19,008
B. 60
C. 792
D. 95,040
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Total number of shirts purchased for her team = 12
Number of shirts places in the first bag = 5
We need to find the number of ways a group of 5 shirts be placed in that first bag.
We will use "Combination" to find the number of different ways :
As we know the formula for Combination.
[tex]^nC_r=\frac{n!}{r!\times (n-r)!}\\\\here, n=12\\\\r=5\\\\So,\ it\ becomes,\\\\^{12}C_5=\frac{12!}{5!\times 7!}\\\\=\frac{12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2}\\\\=792[/tex]
Hence, there are 792 ways to do so.
Therefore, Option 'C' is correct.
a forest ranger spots a fire on a 28 foot tower,the angle of depression from the tower to the fire is 11 degrees to the nearest foot how far is the fire from the base of the tower show the steps you use to find the solution
running short on time to turn this answer in plz help
solve for 9(p-4)=-18
To solve the equation 9(p-4)=-18, distribute the 9, then add 36 to both sides, and finally, divide by 9 to isolate p, resulting in p = 2.
To solve the equation 9(p-4)=-18, we need to isolate the variable p. Here's a step-by-step solution:
First, let's distribute the 9 to both terms inside the parentheses: 9 times p - 9 times 4 = -18, which simplifies to 9p - 36 = -18.Next, we'll add 36 to both sides of the equation to move the constant term to the right side: 9p - 36 + 36 = -18 + 36, resulting in 9p = 18.Lastly, we'll divide both sides by 9 to get p by itself: 9p / 9 = 18 / 9, which gives us p = 2.The solution to the equation 9(p-4)=-18 is p = 2.
Delaney gave her hair stylist a $4.60 tip. The tip was 5% of the cost of the haircut. Write an equation to find b, the cost of the haircut.
The total cost of haircut is $92.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
We have,
Delaney gave her hair stylist a $4.60 tip.
The tip was 5% of the cost of the haircut.
let the cost of haircut be b.
So, 5% of b = 4.60
5/100 b = 4.6
b= 460 / 5
b = $92.
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Find the volume of the composite space figure to the nearest whole number.
The volume of the composite solid is approximately 438 mm³.
Given is a composite solid, composed of a half cylinder [cut vertically] as a roof and a rectangular prism of dimension 5 mm, 11 mm, 6 mm, as base.
We need to find the volume of the solid.
So, to find the volume of the whole solid we will just add the volume of the half cylinder and the rectangular prism.
Volume of a rectangular prism = length × width × height
Here, Length = 11 mm, Height = 6 mm and Width = 5 mm.
Volume of cylinder = π × radius² × height
Since here the cylinder is half so the volume = [π × radius² × height] ÷ 2
The diameter of the cylinder is the width of the prism, height is length of the prism,
Now, let calculate the volume,
Volume = [5 × 11 × 6] + [(3.14 × 2.5² × 11) ÷ 2]
Volume = 330 + 108
Volume = 438 mm³
Hence the volume of the composite solid is approximately 438 mm³.
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please help!! Assume the given triangular prism and rectangular prism have equal cross sections. Also assume the length and width of the rectangular prism's cross section are equal. If the volume of the triangular prism is V = 50h, then what is the length of the rectangular prism?
Answer:
5 square root 2
Step-by-step explanation:
Find the SUM of the first 40 terms of the arithmetic series:
17 + 24 + 31 + 38 + ...
Hints:
1) find the 40th term using formula
2) find the sum of all 40 terms using formula
297
6147
6280
6140
For which intervals is the function positive?
If sin^2(x) - 2sin(x) = 2, then sin(x) = _____.
In ΔPQR, find the measure of ∡ P. (4 points)
Triangle PQR where angle Q is a right angle. PQ measures 33 point 8. PR measures 57 point 6. Measure of angle P is unknown
In a right triangle, use the Pythagorean theorem and the cosine function to find the measure of angle P.
Explanation:In triangle PQR, where angle Q is a right angle, we can use the Pythagorean theorem to find the measure of angle P. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, PR is the hypotenuse and PQ and QR are the other two sides.
Using the given measurements, PQ = 33.8 and PR = 57.6. To find the measure of angle P, we can use the cosine function. Cosine is the ratio of the adjacent side to the hypotenuse, so we have cos P = PQ / PR.
Plugging in the given values, we have cos P = 33.8 / 57.6. Using a calculator, we find that cos P ≈ 0.586. To find the measure of angle P, we can take the inverse cosine of this value, which is approximately 54.3 degrees.
BRAINLIESTTTTT ASAP!!!
Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.
(x − 4)^2 = 3
(x − 3)^2 = 2
(x − 2)^2 = 1
(x − 1)^2 = 4
Can you help me for question 8??? I really confused
1.) A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone? A.) 2cm B.) 3cm C.) 4cm D.) 5cm
2.) A cylinder with a radius of 1cm and a height of 21cm has the same volume as a cone with a height of 7cm. What is the radius of the cone? A.) 3cm B.) 5cm C.) 7cm D.) 9cm
1. Find all the real square roots of 0.0064. (1 point)
0.25298 and –0.25298
0.0253 and –0.0253
0.08 and –0.08
0.0032 and –0.0032
2. Find the real-number root.
(1 point)
–0.605
1.1
–1.1
no real number root
how many liters will a quart (dry measure) hold?
Answer:
0.94635 Liters in a Quart
Step-by-step explanation:
The front row in a movie theater has 23 seats. If you were asked to sit in the seat the occupied the median position, in which seat would you have to sit?
PLEASE HELP!! I do not understand this. And can you explain it for me when I use it again?
1. A rectangular prism is defined as the drawing shows. Note B at (0, 5, 0) and F (0, 0, 4). The prism is reflected over the xz-plane. The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
a.) Show the results of your calculations for points A, B, C and D from the reflection.
b.) Show the results of your calculations for points A, B, C and D from the translation.
Here is the image- https://us-static.z-dn.net/files/d78/3d779b3d254fe859e35a544af4257d2f.png
I need to know how to do this, plz explain-Which function grows at the fastest rate for increasing values of x?
h(x)=2x
f(x)=4x2+9x
g(x)=18x
Answer: f(x)=4x2+9x
Step-by-step explanation:
Find the AGI and taxable income:
Gross Income $30,856
Adjustments $750
1 Exemption $8200
Deduction $2,300
$31,200 and $20,601
$30106 and $19,606
$29,586 and $18,505
$28,863 and $17,636
1 points
QUESTION 5
Find the AGI and taxable income.
Gross Income $67,890
Adjustments $0
3 Exemptions $24,600
Deduction $1469
$69,440 and $45,300
$68,990 and $42,831
$67,890 and $41,821
$65,551 and $44,821
1 points
QUESTION 6
Find the AGI and taxable income.
Gross income $19,723
Adjustments $255
1 Exemption $8200
Deduction $1430
$19,4
This explanation provides a step-by-step process for figuring out adjusted gross income (AGI) and taxable income, based on given values for gross income, adjustments, exemptions, and deductions in three examples.
Explanation:In context of tax calculations, your adjusted gross income (AGI) is calculated by taking your gross income and subtracting any adjustments. Taxable income is calculated by subtracting exemptions and deductions from your AGI.
Example 1:Gross Income: $30,856 minus Adjustments: $750 equals AGI: $30,106. Then, AGI: $30,106 minus Exemptions: $8,200 minus Deductions: $2,300 equals Taxable Income: $19,606.Example 2:Gross Income: $67,890 has no Adjustments. Hence, its AGI is $67,890. Then, AGI: $67,890 minus Exemptions: $24,600 minus Deductions: $1,469 equals Taxable Income: $41,821.Example 3:Gross Income: $19,723 minus Adjustments: $255 equals AGI: $19,468. Then, AGI: $19,468 minus Exemptions: $8,200 minus Deductions: $1,430 equals Taxable Income: $9,838. Learn more about Tax Calculation here:https://brainly.com/question/34140086
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DE has endpoints D 0, 3 and E 0, 12 find the length of DE to the nearest tenth
Answer: The length of side DE is 9 units.
Step-by-step explanation: Given that the co-ordinates of the end-points of DE are D(0, 3) and E(0, 12).
We are to find the length RT of the polygon.
We know that
the length of a line segment with endpoints P(a, b) and Q(c, d) is equal to the distance between the points P and Q.
By distance formula, the distance between P(a, b) and Q(c, d) is
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
So, the distance between D(0, 3) and E(0, 12) is given by
[tex]DE=\sqrt{(0-0)^2+(12-3)^2}=\sqrt{9^2}=9.[/tex]
Thus, the required length of DE is 9 units.
The base of a soup can has an area of 9π in
2
and a height of 10
in. Find the area for the label needed to wrap around the can with
no overlaps.
soup can is in the shape of cylinder
given, base area = 9 pi
base area = area of circle = pi * r^2 = 9 * pi
r = 3
total surface area of cylinder = 2 *pi*r(h+r)
= 2*3(10+3) pi= 78 pi
area for the label needed to wrap around the can with
no overlaps 78 pi inches^2
What is the range of f(x) = (3/4)^x – 4?
Answer:
answer is A bud
Step-by-step explanation:
i just took the test lol
Use the rules of significant figures to answer the following question: 43.5694•22.07
Answer:
961.6
Step-by-step explanation:
43.5694 22.07 = 961.6
How many roations does a wheel make if diameter is 5 feet after 600 feet?
Create a function with roots x = 3 and x = 2 and x = -3
The average of their maximum speed was 260 KM per hour if double Malcolm’s maximum speed would be 80 KM per hour more than Robbins maximum speed what were Malcolm and Robbie’s maximum speed
The area of a rectangle is 96 square feet. The ratio of the width to the length is 2:3. The width of the rectangle is ______ feet.
The width of a rectangle with an area of 96 square feet and a width to length ratio of 2:3 is 8 feet.
Explanation:In this mathematics problem, we are given the area of a rectangle (96 square feet) and the ratio between its width and length (2:3). The equation representing the area of a rectangle is Length x Width. Given that the area of the rectangle is 96 sq ft, and the ratio of width to length is 2:3. Let's assign the width to be 2x and the length to be 3x. Then, you would multiply these two together and set it equal to the area: (2x) * (3x) = 96 square feet. Simplifying this gives 6x2 = 96. Dividing both sides by 6 gives you x2 = 16. Taking the square root of both sides gives x = 4. Therefore, the width of the rectangle, which is 2x, is 2 * 4 = 8 feet.
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Help!! So confused!
Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series 3 + 10 + 17 + 24 + ...
a. Use summation notation to write the series. Explain what the numbers in the summation notation represent in this situation and how you found the expression used in the summation.
b. Find the total number of beads in the necklace. Explain your method for finding the total number of beads.
What is the value of x in the proportion StartFraction 2 x plus 7 over 3 x minus 4 EndFraction equals 11 over 2?
A. 2
B. 58
C. eleven-twenty-ninths
D. two-fifths