i) The length of the arc is approximately 73.148 meters.
ii) The area of the sector is approximately 85.584 square meters.
(i) The length of an arc can be calculated using the formula:
Arc Length = (θ/360) × 2πr
where;
θ = central angle in degrees
r = radius of the circle
π = mathematical constant approximately equal to 3.14159.
Given that the central angle is 85° and the radius is 7 meters, we can substitute these values into the formula:
Arc Length = (85/360) × 2π × 7
= (17/72) × 2 × 3.14159 × 7
≈ 1.7454 × 6.28318 × 7
≈ 73.148 meters (rounded to three decimal places.
(ii) The area of a sector can be calculated using the formula:
Sector Area = (θ/360) × πr²
Given that the central angle is 85° and the radius is 7 meters, we can substitute these values into the formula:
Sector Area = (85/360) × π × 7²
= (17/72) × 3.14159 × 7²
≈ 1.7454 × 3.14159 × 49
≈ 85.584 square meters (rounded to three decimal places)
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The correct question is:
Find:
(i) the length of an arc
(ii) the area of a sector in a circle of radius 7 meters subtended by the central angle of 85°.
Find the sine, cosine, and the tangent of the acute angle A of the triangle. Express each answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
sina=12/20=0.6
cosa=16/20=0.8
tana=0.6/0.8=0.75
The rule is x->y=3x. Copy and fill in the table with atleast 4 points
Our table looks like this:
x | y
--|--
1 | 3
2 | 6
-2 | -6
0 | 0
The rule given is x -> y = 3x, which means that the value of y is three times the value of x. To fill in the table with at least 4 points, we can choose any four values of x and calculate their corresponding values of y using the rule.
Let's start with x = 1. Plugging this value into the rule, we get y = 3(1) = 3. So the first point in our table is (1, 3).
Next, let's try x = 2. Using the rule, we get y = 3(2) = 6. So the second point in our table is (2, 6).
Moving on, let's choose x = -2. Using the rule, we get y = 3(-2) = -6. So the third point in our table is (-2, -6).
Lastly, let's try x = 0. Using the rule, we get y = 3(0) = 0. So the fourth point in our table is (0, 0).
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The volume of a suitcase is 8,556 Cubic
inches. It is 32 inches long and 15.5
inches high. Write an equation to
represent the width. Then find the width
of the suitcase.
To find the width of the suitcase, we need to use the formula for the volume of a rectangular prism:
Volume = Length × Width × Height
Given the volume of the suitcase as 8,556 cubic inches, the length as 32 inches, and the height as 15.5 inches, we can write the equation:
8556 = 32 × w × 15.5
Simplifying this equation, we can divide both sides by the product of 32 and 15.5:
8556 ÷ (32 × 15.5) = w
Solving for w, we get:
w ≈ 16.50 inches
Therefore, the width of the suitcase is approximately 16.50 inches.
What type of transformation is modeled?
The type of transformation modeled in the graph is Reflection across y-axis.
How many different coordinate transformations are there?The three different kinds of coordinate transformation are listed below. The motor's three-phase current and voltage are transformed by the Clark transformation from their original natural coordinates to two-phase static coordinates determined with reference to the stator.
What is the transformational rule?Because the domain or range values of the function f(x) have changed, rules of transformations assist in changing f(x) to a new function f'(x). With the use of these transformational rules, the function can be stretched or compressed as well as transformed vertically or horizontally.
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Write the word form of the number in standard decimal form for: three and fifty-four thousandths
Answer: 350.214
Step-by-step explanation:
I been trying to figure this out but im bad with squares even though it sounds easy.
Answer:
13in :)
Step-by-step explanation:
KJASJDAJK its oki! The formula for the area of a square is Side x Side= Area, meaning you can just square root the area (since its a square all sides should be the same length) sqrt of 169 would give you 13!
A cube has shaded shapes on three of its faces. Here is a net of the cube. Draw in the two missing shaded shapes.
The appropriate diagram to illustrate the cube is given.
What is a cube?A cube is a three-dimensional shape featureing six equal square faces, with its edges and vertices being of congruent length. It counts as one of the five platonic solids distinguished by all of its features having matching sizes.
The cube can be perceived as a special instance of a rectangular parallelepiped where all six are perfectly square in shape. In order to calculate the volume of such an ordinary cube, the number of its edge needs to be multiplied by itself thrice (V = a³).
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What is the area of the shaded part of the figure if =14
ft?
Use 3.14
to approximate π
The area of the shaded part is 42.14 ft² .
How to find the area of the shaded part of the figure?Area of the shaded part of the figure = area of square - area of quarter circle
Area of shaded part of the figure = s² - 1/4πr²
Where s = 14 ft and r = 14 ft
Substitute into the formula:
Area of shaded part = 14² - 1/4(3.14)(14²)
= 42.14 ft²
Therefore, the area of the shaded part is: 42.14 ft² .
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Complete Question
Check image
Give the formulas for the following:
the partial sum of a geometric sequence where a₁ is the first term, n is the number of
the terms in the sum, and r is the common ratio.
the infinite sum of a geometric sequence where |r | < 1.
The formula for the partial sum of a geometric sequence with first term a₁, common ratio r, and n terms is given by:
Sₙ = a₁(1 - rⁿ)/(1 - r)
How to explain the formulaA geometric sequence is a non-zero numerical sequence in which each term after the first is found by multiplying the preceding one by a fixed, non-zero quantity known as the common ratio.
In the formula, Sₙ is the sum of the first n terms of the sequence.
Alternatively, the formula can be expressed as:
Sₙ = (a₁(rⁿ - 1))/(r - 1)
Both of these formulas give the same result and can be used to calculate the partial sum of a geometric sequence.
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The trinomial: x² - 5x +11 is not factorable. Explain why this is.
Answer:
Step-by-step explanation:
I cannot find 2 numbers that multiply to the last term (+11) and add to middle term (-5)
So it can't be factored that way.
After further inspection. i try to plug it into b²-4ac from the quadratic formula.
b=-5
c=11
(-5)²-4(1)(11)
= -19 you can never get a negative under the square root. so this quadratic will produce 2 imaginary solutions. so it is not factorable.
if you help I would be so thankful
Answer:
I put the answer on the attachment please look
Solve for X. *
-48-x=-39
Answer:
x = - 9
Step-by-step explanation:
-48 - x = -39
Add 48 on both sides
-x = 9
Divided both sides by -1
x = - 9
So, the answer is x = - 9
Find f(g(1)) and g(f(1))
F(x)=x^2+2;g(x)=2x-5
Answer:
Step-by-step explanation:
Given the functions f(x) = x^2 + 2 and g(x) = 2x - 5, we can find f(g(1)) and g(f(1)) by evaluating the inner function first and then using its result as the input for the outer function.
First, let’s find f(g(1)). We start by evaluating the inner function g(1):
g(1) = 2 * 1 - 5 = -3
Now we can use this result as the input for the outer function f(-3):
f(g(1)) = f(-3) = (-3)^2 + 2 = 9 + 2 = 11
Next, let’s find g(f(1)). We start by evaluating the inner function f(1):
f(1) = 1^2 + 2 = 3
Now we can use this result as the input for the outer function g(3):
g(f(1)) = g(3) = 2 * 3 - 5 = 6 - 5 = 1
So, f(g(1)) = 11 and g(f(1)) = 1.
Find the measure of EB
The measure of angle subtended by the arc EB is 96 ⁰.
What is the measure of arc angle EB?The measure of angle subtended by the arc EB is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, the theory states that, the angle formed by the intersection of two chords at the circumference of a circle is equal to half of the difference between the arc angles of the two chords.
We will have the following equation;
m∠ECB = ¹/₂( 7x + 6 - (4x + 16))
25 x 2 = 7x + 6 - 4x - 16
50 = 3x - 10
60 = 3x
x = 60/3
x = 20
The measure of arc angle EB is calculated as follows;
m∠EB = 4x + 16
m∠EB = 4(20) + 16
m∠EB = 96 ⁰
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Solve for x. Round to the nearest tenth, if necessary.
Answer:
160
Step-by-step explanation:
The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp)
Adjacent = 80
Hypotenuse = x
therefore, cos(60) = 80/x
1/2 = 80/x
x = 80 x 2 = 160
Can someone help me thx
a group of students were asked if they are in the math club and if they are in the literature club. Partial results are shown in the table. What is the value of x+y?
Hence Option A. 22 is correct.
How to solveOf the students in the maths club , 67% are not in the literature club.
So the number of students in Maths club =
[ ( Number of students in maths club but not in the literature club) / 67 ] * 100 % = [ 16 / 67 ] * 100% = 24 (Rounded)
Hence, Number of students in maths club and in the literature club =
x = Total Number of students in Maths club - Number of students in maths club but not in the literature club
x = 24 - 16 = 8
Of the students not in the maths club , 78% are not in the in the literature club.
So, Of the students not in the maths club , 100% - 78% = 22% are in the literature club.
So the number of students not in the Maths club =
[ ( Number of students not in the maths club and in the literature club) / 22 ] * 100 %
= [ 4 / 22 ] * 100% = 18.18 = 18 (Rounded)
Hence, Number of students not in the maths club and not in the literature club =
y = Total Number of students not in the Maths club - Number of students not in the maths club and in the literature club
y = 18 - 4 = 14
So, x + y = 8 + 14 = 22.
Hence Option A. 22 is correct.
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18 m
Bookwork code: N93
Tyler wants to cover this prism in glitter.
If 80 g of glitter is needed to cover each m², how much glitter will he
need to cover the prism completely?
23 m
allowed
10 m
3,517 XP
25 m
Allie Eggleton MENU
14m
Tyler will need a amount of 79,200 grams (or 79.2 kilograms) of glitter to cover the prism completely.
To calculate the amount of glitter needed to cover the prism completely, we first need to find the total surface area of the prism.
The prism consists of five faces: two rectangular faces with dimensions 18 m x 10 m, two triangular faces with base 18 m and height 10 m, and one rectangular face with dimensions 18 m x 25 m.
The total surface area of the prism can be calculated by adding the areas of all the faces together:
Total Surface Area = 2(18 m x 10 m) + 2(0.5 x 18 m x 10 m) + 18 m x 25 m
Total Surface Area = 360 m² + 180 m² + 450 m²
Total Surface Area = 990 m²
Given that 80 g of glitter is needed to cover each m², we can now calculate the total amount of glitter needed:
Total Glitter = Total Surface Area x Glitter per m²
Total Glitter = 990 m² x 80 g/m²
Total Glitter = 79,200 g
Therefore, Tyler will need 79,200 grams (or 79.2 kilograms) of glitter to cover the prism completely.
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The table represents the quadratic functions f(x) and g(x).
x f(x) g(x)
−8 16 4
−4 4 1
0 0 0
4 4 1
8 16 4
What transformation of f(x) will produce g(x)?
g of x equals one fourth times f of x
g of x equals f of the quantity of one fourth times x end quantity
g(x) = 4f(x)
g(x) = f(4x)
The transformation of f(x) that will produce g(x) is given as follows:
g(x) = f(x)/4.
How to obtain the function g(x)?If we observe at the table, we have that each value of g(x) is one fourth of the value of the function f(x).
Hence the transformation of f(x) that will produce g(x) is given as follows:
g(x) = f(x)/4.
The transformation means that the function g(x) is a vertical compression by a factor of 4 of the function f(x).
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q
5cm
X =
X
8cm
4cm
cm
Answer:
2.5 cm
Step-by-step explanation:
The small arrow is 1/2 the side of the large arrow. 1/2 of 5 is 2.5 or 2 1/2.
Helping in the name of Jesus.
Which one of the following is a rule of multiplication?
A.The order in which you multiply two whole numbers
changes the product.
B.The product of a whole number and 1 is never the
same whole number.
C.The product of a whole number and zero is the same
whole number.
D.The way you group numbers in a series of
multiplication problems doesn't change the final
product.
Answer:
D.The way you group numbers in a series of
multiplication problems doesn't change the final
product.
Assume that the speed of automobiles on an expressway during rush hour is normally distributed with mean of 62 mph and a standard deviation of 5 mph.
What percent of cars are traveling slower than 55 mph?
About 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.
To solve this problemUsing the provided mean and standard deviation, we must standardize the value of 55 mph before determining the equivalent area under the standard normal distribution curve.
The standardized value, or z-score, is calculated as:
z = (x - μ) / σ
Where
x is the value we want to standardize (in this case, 55 mph) μ is the mean (62 mph)σ is the standard deviation (5 mph)Plugging in the values, we get:
z = (55 - 62) / 5 = -1.4
The area under the usual normal distribution curve to the left of z = -1.4 must now be determined. Using a common normal distribution table, we can determine that this area is roughly 0.0808.
Therefore, about 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.
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What is 0.08% written as a decimal?
Verify the given linear approximation at a = 0. Then use a graphing calculator or computer to determine the values of x for which the linear approximation is accurate to within 0.1. (Round your answers to three decimal places. Enter your answer using interval notation.)
sin−1(x) ≈ x
Therefore, the linear approximation sin⁻¹(x) ≈ x is accurate to within 0.1 when x is in the interval [-0.099, 0.099].
What is function?In mathematics, a function is a relationship between two sets, called the domain and range, such that for each element in the domain there is exactly one element in the range. In other words, a function assigns a unique output value to each input value. Functions are typically denoted using a rule or formula that describes how to calculate the output value based on the input value.
Here,
The linear approximation of sin⁻¹(x) at a = 0 is given by:
sin⁻¹(x) ≈ x
To verify this, we can take the derivative of sin⁻¹(x) and evaluate it at x = 0:
d/dx(sin⁻¹(x)) = 1/√(1-x²)
d/dx(sin⁻¹(x))|x=0 = 1
Since the derivative of sin⁻¹(x) evaluated at x = 0 is equal to 1, we can use the linear approximation sin⁻¹(x) ≈ x near x = 0.
To determine the values of x for which the linear approximation is accurate to within 0.1, we can use a graphing calculator or computer to plot the graphs of sin⁻¹(x) and x, and find the intervals where the difference between the two functions is less than or equal to 0.1.
Using a graphing calculator, we can plot the two functions and find the intervals where the difference is less than or equal to 0.1. The result is:
-0.099 ≤ x ≤ 0.099
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The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
7
7
22
The scale factor for this right triangles is equal to 5/4.
What is a scale factor?In Mathematics, the scale factor of any geometric figure can be determined by dividing the dimension or side length of the new figure (image) by the dimension or side length of the original figure (pre-image):
Scale factor = Dimension of new figure (image)/Dimension of original figure (pre-image)
By substituting the given dimensions into the formula for scale factor, we have;
Scale factor = image dimension/pre-image dimension
Scale factor = 15/12 = (25/4)/5
Scale factor = 5/4.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The number of times 100 groups took a selfie is as follows
find the probability a group will take their selfie exactly 5 times
Answer: 0.12
Step-by-step explanation:
just divide whatever is under 5 with the total amount of frequency
so then you do 12/100 which is 0.12
Boyd's board shop grt a shipment of 92 new skateboards wheels. Boyd assembles the skateboards and puts 4 of the new wheels on each board. You can use a function to describe the number of new wheels Boyd has left after assembling x skateboards
The function to describe the number of new wheels Boyd has left is f(x) = 92 - 4x
From the question, we have the following parameters that can be used in our computation:
Shipment of 92 new skateboards wheels. 4 of the new wheels on each board.After assembling x skateboards, we have
f(x) = Shipmnet - Rate * x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 92 - 4 * x
Evaluate
f(x) = 92 - 4x
Hence, the function is f(x) = 92 - 4x
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A child at a day care can choose one type of writing tool and one type of paper for an art project. The chart shows
the types of writing tools and paper that are available.
Art Project
Type of Writing Tool Type of Paper
Crayon
Marker
Pencil
Construction
Newsprint
Which list shows all the combinations of one type of writing tool and one type of paper that can be used for the art
project?
The list that shows all the combinations is given as follows:
{Crayon, Construction}, {Marker, Construction}, {Pencil, Construction}, {Crayon, Newsprint}, {Marker, Newsprint}, {Pencil, Newsprint}.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.
This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The options are given as follows:
Writing Tool: Crayon, Marker and Pencil. -> 3 options.Type of Paper: Construction and Newsprint -> 2 options.The total number of options is given as follows:
3 x 2 = 6.
Hence the list is:
{Crayon, Construction}, {Marker, Construction}, {Pencil, Construction}, {Crayon, Newsprint}, {Marker, Newsprint}, {Pencil, Newsprint}.
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A researcher is interested in hamster wheel-running activity during the summer versus the winter. She suspects that either the hamsters will run less during the winter to conserve energy, or they will run more to keep warm. She records the activity of n = 30 hamsters during June, July, and August and compares their running-wheel revolutions per hour to the activity of the same hamsters during December, January, and February.
The data are collected, and the results show an average difference score of = 5. 7 and a sum of squares of SS = 2,851.44.
What is the value for degrees of freedom for this repeated-measures t test?
There are 29 degrees of freedom for this repeated-measures t-test.
Understanding the degree of freedomThe degrees of freedom (df) for a repeated-measures t-test is calculated as (n-1), where n is the number of paired observations.
In this case, each hamster's activity was measured during both summer and winter, resulting in a paired sample design. Therefore, the number of paired observations is equal to the number of hamsters, which is n = 30.
Hence, the degrees of freedom for this repeated-measures t-test is:
df = n - 1 = 30 - 1 = 29
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Please help me i am so confused
The interval that will have the highest frequency will be: C. 11 - 15.
Which interval will have the highest frequency?The interval that will have the highest frequency will be 11 - 15. This interval will have the highest frequency because there are a total of 6 sales within this range.
The other intervals have sales that are 5 and below. So, since this interval has up to 6 sales, it can be regarded as the interval with the highest frequency. Frequency refers to how often something occurs. When an outcome happens several times, then we can refer to it as the highest frequency.
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