The probability that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.
What is the probability?The probability is determined using the normal approximation to the binomial distribution.
Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:
μ = n * p
μ = 200 * 0.15
μ = 30
σ = √(n * p * (1 - p))
σ = √(200 * 0.15 * (1 - 0.15))
σ ≈ 4.29
Then, the z-score corresponding to the proportion of 0.21 is:
z = (x - μ) / σ
z = (0.21 - 0.15) / 4.29
z ≈ 0.014
Using a calculator, the probability of a z-score of 0.014 is approximately 0.504.
Hence, the probability of obtaining a proportion at least 0.21, is:
Probability = 1 - 0.504
Probability ≈ 0.496
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A circle C has center at the origin and radius 5 . Another circle K has a diameter with one end at the origin and the other end at the point (0,15) . The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,θ) be the polar coordinates of P , chosen so that r is positive and 0≤θ≤2 . Find r and θ .
The value of R and θ is 6.18 and 53.13 degrees, under the condition that a circle C has center at the origin and radius 5 .
In order to evaluate the equation of the circle K. The diameter of K has endpoints at the origin and (0,15). Then, the center of K is at (0,7.5) and its radius is 7.5. Therefore, the evaluated equation of K is
x² + (y-7.5)² = 56.25.
The equation of circle C is x² + y² = 25.
The two circles intersect at two points. Now we have to evaluate the coordinates of these points.
Staging y = 5 - x² in the equation of K,
we get
x² + (5-x²-7.5)² = 56.25.
Applying simplification on this equation
x⁴ - 10x² + 31.25 = 0.
Calculating this quadratic equation gives us
x² = 5 ± √(10)/2.
If P lies in the first quadrant,
we choose x² = 5 + √(10)/2 and y = √(25-x²) to get P in Cartesian coordinates.
Converting P to polar coordinates gives us
r = √(x²+y²) and θ = arctan(y/x).
Staging x = √(5+√(10)/2) and y = √(25-x²) in these equations gives us
r ≈ 6.18 and θ ≈ 0.93 radians.
Using this formula to convert into degree
Rad × 180/π
= 0.93 × 180/π
≈ 53.13 degrees
Therefore, r ≈ 6.18 and θ ≈ 53.13 degrees.
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Gramma Gert's Granola is Noah's favorite brand of granola bars. They come in regular-size
bars or snack-size bars. Both sizes are shaped like rectangular prisms. The regular-size bar is
1 inches wide, of an inch tall, and has a volume of 4 cubic inches. The snack-size bar
has the same width and height, but it has a volume of 3 cubic inches.
How much longer is the regular-size granola bar than the snack-size granola bar?
Write your answer as a whole number, proper fraction, or mixed number.
inches
The regular-size granola bar is 1 1/3 inches longer than the snack-size granola bar.
The regular-size granola bar has a volume of 4 cubic inches, while the snack-size bar has a volume of 3 cubic inches.
Since both bars have the same width and height, we can use the formula for the volume of a rectangular prism to find the length of each bar:
Regular-size bar: V = lwh = 4 cubic inches, w = 1 inch, h = 3/4 inch
l = V/wh = 4/(1 × 3/4) = 16/3 inches
Snack-size bar: V = lwh = 3 cubic inches, w = 1 inch, h = 3/4 inch
l = V/wh = 3/(1 × 3/4) = 4 inches
Therefore, the regular-size granola bar is (16/3 - 4) = 4/3 inches longer than the snack-size granola bar.
This can also be written as the mixed number 1 1/3 inches.
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what is the equation that contains the point M(1,10,3), N(4,10,6) and P(7,10,9)?
The equation of the line is: x = 1 + 3t,, y = 10, z = 3 + 3t.
How to determine the equation of the lineTo determine the equation of the line passing through points M(1, 10, 3), N(4, 10, 6), and P(7, 10, 9), we need to find the direction vector of the line.
Let's denote the direction vector as D = (a, b, c). The line can be represented by the parametric equations:
x = 1 + at,
y = 10 + bt,
z = 3 + ct,
To find the direction vector, we can use two points on the line, for example, M and N. The direction vector can be obtained by subtracting the coordinates of M from the coordinates of N:
D = N - M = (4 - 1, 10 - 10, 6 - 3) = (3, 0, 3).
So, the equation of the line passing through M(1, 10, 3) and having the direction vector D = (3, 0, 3) is:
x = 1 + 3t,
y = 10 + 0t = 10,
z = 3 + 3t.
Therefore, the equation of the line is:
x = 1 + 3t,
y = 10,
z = 3 + 3t.
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UNIT ISCALING
SCALE DRAWING OF A SCHOOL BUS HAS A SCALE OF 1/2 INCH TO 5 FEET. IF THE
ENGTHS OF THE SCHOOL BUS IS 4 1/2 INCHES ON THE SCALE DRAWING, WHAT IS THE
ACTUAL LENGTH OF THE BUS? EXPLAIN OR SHOW YOUR REASONING
The actual length of the bus is given as follows:
45 feet.
How to obtain the actual length of the bus?The actual length of the bus is obtained applying the proportions in the context of the problem.
The scale drawing is of 0.5 inches to 5 feet, hence the length represented by each inch of drawing is given as follows:
5/0.5 = 10 feet.
The length of the drawing is given as follows:
4.5 inches.
Hence the actual length of the bus is given as follows:
4.5 x 10 = 45 feet.
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Find g(0), g(-1), g(2), and g(2/3)
for g(x) =x/ square root 1-x^2
Given statement solution is :- Outputs and values g(2/3) = 2/3.
To summarize:
g(0) = 0
g(-1) = undefined
g(2) = undefined
g(2/3) = 2/3
To find the values of g(x) for the given inputs, we substitute each input into the function g(x) = x / √([tex]1 - x^2[/tex]). Let's calculate the values:
g(0):
Substitute x = 0 into the function:
g(0) = 0 / √([tex]1 - 0^2[/tex])
= 0 / √(1 - 0)
= 0 / √1
= 0
Therefore, g(0) = 0.
g(-1):
Substitute x = -1 into the function:
g(-1) = (-1) / √(1 - [tex](-1)^2[/tex])
= (-1) / √(1 - 1)
= (-1) / √0
Since the square root of 0 is undefined, g(-1) is undefined.
g(2):
Substitute x = 2 into the function:
g(2) = 2 / √([tex]1 - 2^2[/tex])
= 2 / √(1 - 4)
= 2 / √(-3)
Since the square root of a negative number is undefined in the real number system, g(2) is undefined.
g(2/3):
Substitute x = 2/3 into the function:
g(2/3) = (2/3) / √(1 - [tex](2/3)^2[/tex])
= (2/3) / √(1 - 4/9)
= (2/3) / √(5/9)
= (2/3) / (√5/√9)
= (2/3) / (√5/3)
= (2/3) * (3/√5)
= 2√5 / 3√5
= 2/3
Therefore, outputs and values g(2/3) = 2/3.
To summarize:
g(0) = 0
g(-1) = undefined
g(2) = undefined
g(2/3) = 2/3
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The scatter plot shows the number of apples Aniyah picked from her apple trees each year. The equation of the line of fit is:
y = 15.2x + 111
What is the predicted number of apples picked in year 5? Explain your answer.
Answer: 187 apples
Step-by-step explanation:
Substitute "year 5" into the equation. y = 15.2(5) +111.
y = 76 + 111
y = 187
100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!
Answer:
[tex] \sin(x) + \sin(2x) = 0[/tex]
[tex] \sin(x) + 2 \sin(x) \cos(x) = 0[/tex]
[tex]( \sin(x) )(1 + 2 \cos(x) ) = 0[/tex]
sin(x) = 0 or 1 + 2cos(x) = 0
2cos(x) = -1
cos(x) = -1/2
x = kπ or x = 2π/3 + 2kπ or
x = 4π/3 + 2kπ
(k is an integer)
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
We have to given that;
All expressions are,
2 + x = 5
x + 1 = 4
9 + x = 6
x + (-4) = 7
-5 + x = -2
Now, We can simplify all the expressions as;
⇒ 2 + x = 5
⇒ x = 5 - 2
⇒ x = 3
⇒ x + 1 = 4
⇒ x = 4 - 1
⇒ x = 3
⇒ 9 + x = 6
⇒ x = 6 - 9
⇒ x = - 3
⇒ x + (-4) = 7
⇒ x = 7 + 4
⇒ x = 11
⇒ -5 + x = -2
⇒x = - 2 + 5
⇒ x = 3
Thus, All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
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Here is a right-angled triangle.
8.2 cm
y cm
12.3 cm
Work out the value of y.
Give your answer correct to 1 decimal place.
The value of y from the given right angled triangle is 9.2 cm.
Given that, a right angled triangle has 8.2 cm, y cm and 12.3 cm.
Let, hypotenuse = 12.3 cm, perpendicular = 8.2 cm and base = y cm.
By using Pythagoras theorem, we get
8.2²+y²=12.3²
67.24+y²=151.29
y²=151.29-67.24
y²=84.05
y=9.2 cm
Therefore, the value of y from the given right angled triangle is 9.2 cm.
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A certain manufacturing concern has total cost function C = 15+9x-6x²+x? Find x, when the total
Answer:
Step-by-step explanation:
Total cost function, C = 15+9x-6x²+x
By differentiation,
dc/dx= 9-12x²+1
but
dc/dx= 0
9-12x²+1 = 0
-12x = -10
x=10/12
x=5/6
An advertising executive thinks that the proportion of consumers who have seen his company advertisement in newspaper is around 0.65. The executive want to estimate the customer proportion to within ± 0.05 and have a 98% confidence in the estimate. How large a sample should be taken?
Answer:
To determine the sample size required to estimate the proportion of consumers who have seen the company's advertisement in the newspaper, we can use the formula for sample size calculation for proportions. The formula is as follows:
n = (Z^2 * p * q) / E^2
Where:
n = required sample size
Z = Z-score corresponding to the desired confidence level (in this case, 98% confidence corresponds to a Z-score of approximately 2.33)
p = estimated proportion (0.65)
q = 1 - p (the complement of the estimated proportion)
E = maximum error tolerance (+/- 0.05)
Let's plug in the values and calculate the sample size:
n = (2.33^2 * 0.65 * 0.35) / (0.05^2)
n = 339.28
Rounding up to the nearest whole number, the required sample size is 340.
Which side measures will not make a triangle
With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.
a. 3, 4, 8 - will not make a triangle
3 + 4 = 7 > 8 = false
3 + 8 = 11 > 4 = true
4 + 8 = 12 > 3 = true
b. 7, 6, 12 - will make a triangle
7 + 6 = 13 > 12 = true
7 + 12 = 19 > 6 = true
6 + 12 = 18 > 7 = true
c. 5, 11, 13 - will make a triangle
5 + 11 = 16 > 13 = true
5 + 13 = 18 > 11 = true
11 + 13 = 24 > 5 = true
d. 4, 6, 12 - will not make a triangle
4 + 6 = 10 > 12 = false
4 + 12 = 16 > 6 = true
6 + 12 = 18 > 4 = true
e. 4, 6, 10 - will not make a triangle
4 + 6 = 10 > 10 = false
4 + 10 = 14 > 6 = true
6 + 10 = 16 > 4 = true
Hope this helps!
factor the expression w^2(w+8)-5(w+8)
Answer:
Step-by-step explanation:
Let's factor the expression w^2(w+8)-5(w+8):
First, we can see that (w+8) is a common factor in both terms of the expression.
So, we can factor out (w+8) from both terms:
(w+8)(w^2 - 5)
Now, the expression is factored as (w+8)(w^2 - 5).
At the neighborhood block party, Joel served 1/6 of a gallon of hot chocolate and 1/12 of a
gallon of apple cider. How much more hot chocolate than apple cider did Joel serve?
Write your answer as a fraction or as a whole or mixed number.
gallons
Answer:
1/12 gallons
Step-by-step explanation:
We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.
Step 1: Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2
(1/6) * (2/2) = 2/12
Step 2: Now we can subtract 1/12 from 2/12:
2/12 - 1/12 = 1/12
Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.
The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. What is the rate of change?
Snowfall Amount
Length of Snowfall
(hours)
Amount of Snow on the Ground
(inches)
0
3.3
0.5
4.5
1.0
5.7
1.5
6.9
2.0
8.1
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
The average rate of change for this problem is given as follows:
2.4 inches per hour.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
The change in the output is given as follows:
8.1 - 3.3 = 4.8.
The change in the input is given as follows:
2 - 0 = 2.
Hence the average rate of change is given as follows:
4.8/2 = 2.4 inches per hour.
Missing InformationThe table is given by the image presented at the end of the answer.
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Help me please!!!!! .
Answer:
The angle in the first problem measures 67°.
x=16, y=40
Step-by-step explanation:
1st problem: draw the line r in figure (red) parallel to the two given one and containing the vertex of the angle. The two green angles are congruent since alternate angles from the two parallels t and r when crossed with the upper side of the angle. Same with the two blue angles created by the parallels r and b. The measure of the angle you need is the sum of the two, or 36+31= 67°.
Second problem. The two angles in red are congruent since corresponding angles generated by the parallels m and b and the transversal r. we can then write [tex]4x-5=3x+11\\[/tex]. Solving for x we find x= 16. Now the two angles marked in blue are conjugates when looking at the parallels l and r cut by the transversal m, thus they add up to 180° We know how much the angle with double marks measures (since we found x earlier) so we can write
[tex](3y+1) + (4\times16-5) = 180\\3y+ 1 + 59 = 180\\3y=120 \implies y=40[/tex]
please fast if could
Answer:9/41
SOH = opposite over hypotenuse
Step-by-step explanation:
Help
please
please
please
Answer: x=25 degrees
Step-by-step explanation:
25 degrees (blue) and x degrees (orange) are vertical angles. Vertical angles always equal each other.
(80 degrees {green} is just there to throw you off)
The lengths of the legs of a 45°-45°-90° triangle can be described by the expressions 3x − 10 and x + 2. What is the length of the legs of the triangle?
Answer:
8
Step-by-step explanation:
3x - 10 = x + 2
2x = 12
x = 6
3x - 10 = 3(6) - 10 = 8
The length of each leg of the triangle is 8.
Is 34.05 greater than 34.59
No, 34.05 is not greater than 34.59.
When comparing two numbers, we look at their digits from left to right.
In this case, both numbers start with 34, which means they have the same value in the tens place.
However, when we move to the decimal part, 0.05 is smaller than 0.59.
Therefore, 34.05 is smaller than 34.59.
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Gina Wilson Unit 10: Circles Homework 9: Standard Form of a Circle
The standard form (SF), center (C) and radius (R) are given as follow: (13) SF: (x + 4)² + (y - 3)² = 50, Center: (-4, 3), R: √50 (14) SF: (x - 2)² + (y - 6)² = 169, C: (2, 6), R: 13 (15) SF: (x + 7)² + (y + 5)² = 1, C: (-7, -5), R: 1 (16) SF: (x - 8)² + y² = 225, C: (8,0), R: 15 (17) SF: (x - 12)² + (y - 2)² = 63, C: (12, 2), R: √63 (18) SF: (x - 5)² + (y + 4)² = 100 , C: (5, -4), R: 10
Understanding Equation of CircleThe general form of a circle is given as:
(x - h)² + (y - k)² = r²
where:
(h, k) represents the center of the circle
r represents the radius.
Now we can use the above information to solve the following questions:
13. x² + y² + 8x - 6y - 25 = 0
Rearranging the equation:
x² + 8x + y² - 6y = 25
Completing the square for x terms:
(x² + 8x + 16) + y² - 6y = 25 + 16
Simplifying:
(x + 4)² + (y² - 6y) = 41
(x + 4)² + (y² - 6y + 9) = 41 + 9
(x + 4)² + (y - 3)² = 50
Center: (-4, 3)
Radius: √50
14. x² + y² - 4x - 12y - 129 = 0
Rearranging the equation:
x² - 4x + y² - 12y = 129
Completing the square for x terms:
(x² - 4x + 4) + y² - 12y = 129 + 4
Simplifying:
(x - 2)² + (y² - 12y) = 133
(x - 2)² + (y² - 12y + 36) = 133 + 36
(x - 2)² + (y - 6)² = 169
Center: (2, 6)
Radius: 13
15. x² + y² + 14x + 10y + 73 = 0
Rearranging the equation:
x² + 14x + y² + 10y = -73
Completing the square for x terms:
(x² + 14x + 49) + y² + 10y = -73 + 49
Simplifying:
(x + 7)² + (y² + 10y) = -24
(x + 7)² + (y² + 10y + 25) = -24 + 25
(x + 7)² + (y + 5)² = 1
Center: (-7, -5)
Radius: 1
16. x² + y² - 16x - 161 = 0
Rearranging the equation:
x² - 16x + y² = 161
Completing the square for x terms:
(x² - 16x + 64) + y² = 161 + 64
Simplifying:
(x - 8)² + y² = 225
Center: (8, 0)
Radius: 15
17. x² + y² = 24x + 4y - 85
Rearranging the equation:
x² - 24x + y² - 4y = -85
Completing the square for x and y terms:
(x² - 24x + 144) + (y² - 4y + 4) = -85 + 144 + 4
Simplifying:
(x - 12)² + (y - 2)² = 63
Center: (12, 2)
Radius: √63
18. x² + y² - 9x + 2y = x - 6y + 59
Rearranging the equation:
x² - 9x - x + y² + 2y + 6y = 59
Combining like terms:
x² - 10x + y² + 8y = 59
Completing the square for x and y terms:
(x² - 10x + 25) + (y² + 8y + 16) = 59 + 25 + 16
Simplifying:
(x - 5)² + (y + 4)² = 100
Center: (5, -4)
Radius: 10
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We are given the random variable X that follow an exponential distribution such as:
X ~ Exp(1/9.848)
1) Find the expected value
2) Find the standard deviation
3) Find P(X<12)
4) Find P(8 < X < 12)
I have already found the answers:
They are:
1) 9.848
2) 9.848
3) 0.7043
4) 0.2025
The required solution of the random variable X that follows an exponential distribution is shown below.
To find the expected value, standard deviation, and probabilities associated with the exponential distribution, we'll use the given parameter λ = 1/9.848.
Expected Value (Mean):
The expected value of an exponential distribution is equal to the reciprocal of the rate parameter λ. Therefore, the expected value is given by:
E(X) = 1 / λ
E(X) = 1 / (1/9.848)
E(X) = 9.848
So, the expected value of the random variable X is 9.848.
Standard Deviation:
The standard deviation of an exponential distribution is equal to the reciprocal of the rate parameter λ. Therefore, the standard deviation is given by:
σ = 1 / λ
σ = 1 / (1/9.848)
σ = 9.848
So, the standard deviation of the random variable X is also 9.848.
P(X < 12):
To find the probability that X is less than 12, we can use the cumulative distribution function (CDF) of the exponential distribution. The CDF is given by:
[tex]F(x) = 1 - e^{(-\lambda x)}[/tex]
Substituting the given λ = 1/9.848 and x = 12, we have:
[tex]P(X < 12) = F(12) = 1 - e^{-(1/9.848) * 12)}[/tex]
Calculating this expression, we find:
P(X < 12) ≈ 0.7043
Therefore, the probability that X is less than 12 is approximately 0.7737.
P(8 < X < 12):
To find the probability that X lies between 8 and 12, we subtract the cumulative probability at 8 from the cumulative probability at 12:
P(8 < X < 12) = F(12) - F(8)
= [tex]1 - e^{(-(1/9.848) * 12)]} - [1 - e^{(-(1/9.848) * 8)]}[/tex]
Calculating this expression, we find:
P(8 < X < 12) ≈ 0.2025
Therefore, the probability that X lies between 8 and 12 is approximately 0.2025.
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Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
We have that Linda's net and expression incorrect
With the Expression of the surface area of attic
45 (40 + 25 + 25) + 1/2 (40 x 15)
Hence, Surface area is,
X = 4050 + 600
X = 4650 feet²
Hence, The answer is No, Because Her expression for the triangles are incorrect;
1/2(40 x 15)
Instead of,
1/2 x 40 x 15
Hence, Linda's net and expression incorrect,
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Complete question is,Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
She needs to find the approximate surface area of the attic, including the walls, floor, and
ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes
the expression below to represent the surface area of the attic. Are Linda's net and
expression correct?
2 A car dealer, at a year-end clearance, reduces the price of last year's models by a certain amount. If a certain four-door model has been sold at a discounted price of Birr 51,000, with a discount of Birr 9,000, what is the percentage of discount?
For calculating the percentage of discount, we can use the formula:
Percentage of discount = (Discount amount / Original price) * 100
We have given that the discounted price is Birr 51,000 and the discount amount is Birr 9,000,we need to find the original price.
Original price = Discounted price + Discount amount
Original price = 51,000 + 9,000 = 60,000 Birr
Now, we can calculate the percentage of discount:
Percentage of discount = (9,000 / 60,000) * 100 = 15%
Hence, the percentage of discount for the four-door model is 15%.
Complete the equations. 95 × 1 0^3 =? 95 × 1 0^4=? 95×10^5 =?
Answer:
95 × 10^3 = 95000
95 × 10^4 = 950000
95 × 10^5 = 9500000
Find the area of the following figure. Round to the nearest hundred if necessary.
11 cm
A= type your answer...
The area of the semicircle is 47.5 square centimeters
We have to find the area of the semi circle
The diameter of the semicircle is 11 cm
Radius is half of the diameter
Radius = 5.5 cm
Let us find the area of semicircle by formula 1/2(πr²)
Radius = 1/2×3.14×(5.5)²
= 1/2×3.14×30.25
=47.4925 square centimeters
Hence, the area of the semicircle is 47.5 square centimeters
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i need the answer for this asap Please!
[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]
is the equation of the given system.
Equation of the line using the coordinates (-3, 0) and (0, 3), we get:
slope = (3 - 0) / (0 - (-3)) = 1
Now we have the slope of the line. Next, we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Using the point (-3, 0) and the slope we just found (which is also the slope of the line passing through the point (0, 3)), we get:
y - 0 = 1(x - (-3))
Simplifying, we get:
y = x + 3
Therefore, the equation of the line passing through (-3, 0) and (0, 3) is y=x+3.
Similarly, the equation of the line passing through (1, -1) and (0, -4) is y = -3x + 2.
Thus, from the graph the equation of the system is,
[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]
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Mary is building a fence around her triangular garden. How much fencing, in feet, does she
need? Round to the nearest foot.
AC=13 ft
C=40°
B=49°
The length of fencing needed around her triangular garden is 41 feet.
What is a triangle?A given shape which has three sides and three measures of internal angles which add up to 180^o is said to be a triangle.
For Mary to build a fence around her triangular garden, the amount of fencing needed can be determined by adding the length of each side of the garden.
So that;
A + B + C = 180^o
A + 49 + 40 = 180
A = 180 - 89
= 91
A = 91^o
Applying the sine rule, we have;
a/Sin A = b/Sin B = c/Sin C
a/Sin A = b/Sin B
a/Sin 91 = 13/ Sin 49
aSin 49 = 13*Sin 91
= 12.998
a = 12.998/ 0.7547
= 17.22
a = 17 ft
Also,
b/Sin B = c/Sin C
13/Sin 49 = c/ Sin 40
cSin 49 = 13*Sin 40
= 8.3562
c = 8.3562/ 0.7547
= 11.0722
c = 11 feet
Thus the amount of fencing required = 13 + 17 + 11
= 41
The fencing required is 41 feet length.
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In triangle ABC, find a if b = 2, c = 6,
and A = 35°
a. 20.3
b. 7.7
c. 5.5
d. 4.5
The value of a in the triangle, given that in the triangle ABC, b = 2, c = 6, and A = 35° is 7.7 (option A)
How do i determine the value of a?We can obtain the value of a in the triangle ABC as shown in the attached photo by using the cosine rule as illustrated below:
Side b = 2Side c = 6 Angle A = 35°Value of a =?Cosine rule states as follow:
a² = b² + c² + 2bc Cos A
Inputting the given parameters, we can obtain the value of a as follow:
a² = 2² + 6² + (2 × 2 × 6 × Cos 35)
Clear the bracket
a² = 4 + 36 + 19.66
a² = 59.66
Take the square root of both sides
a = √59.66
a = 7.7
Thus, we can conclude from the above calculation that the value of a is 7.7 (option A)
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Please help with picture below
The complete statement should be If 3m = 7n, then m/n = 7/3. The proportion was obtained by solving for m, and then using the converse of the cross products property. Option B
What does the converse of the cross product property say?The converse of the cross products property states that if two ratios are equal, then the product of the means is equal to the product of the extremes.
To justify the answer, you solve for m/n in the original equation by dividing each side by 3n, which gives you m/n = 7/3.
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