Answer:
The probability that the number chosen is not even = 4/8
Sally owns a restaurant in Wooville. The city is trying to get a minor league team to move there in 2021, either to location A (near her restaurant) or location B. The team might stay in location C in another city. The probability of these events, and her estimated annual profit in 2021 are shown in the table below.
The standard deviation of the restaurant profits in 2021 is given by $71181.
Restaurant profit for outcome 'move to A' = $ 260000
Restaurant profit for outcome 'move to B' = $ 120000
Restaurant profit for outcome 'stay in C' = $ 100000
The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.
Standard deviation of the restaurant profits in 2021 is given by
= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)
= $ √(((100000)² + (40000)² + (60000)²)/3)
= $ √(15200000000/3)
= $ √5066666667
= $ 71181 (rounded to the nearest dollar)
Hence standard deviation of the restaurant profits in 2021 is given by $71181.
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The question is incomplete. The complete question will be -
For the demand function d(x) and supply function s(x), complete the following.
d(x) = 600 − 0.8x, s(x) = 0.4x
(a) Find the market demand (the positive value of x at which the demand function intersects the supply function).
x =
Answer: The market demand is x = 750.
Step-by-step explanation:
Answer: The market demand is x = 750.
Explanation:
To find the market demand, we need to set the demand function equal to the supply function and solve for x:
d(x) = s(x)
600 − 0.8x = 0.4x
Combining like terms, we get:
600 = 1.2x
Dividing both sides by 1.2, we get:
x = 500
However, we need to find the positive value of x. Since x represents the quantity demanded, it cannot be negative.
Substituting x = 500 into both the demand and supply functions, we find that:
d(500) = 600 - 0.8(500) = 200
s(500) = 0.4(500) = 200
Since d(500) = s(500), x = 500 is not the market demand.
Substituting x = 750 into both the demand and supply functions, we find that:
d(750) = 600 - 0.8(750) = 0
s(750) = 0.4(750) = 300
Since d(750) = s(750), x = 750 is the market demand.
Therefore, the market demand is x = 750.
What is the circumference of a circle (to the nearest whole number) whose diameter is 12?
Answer: 3.14 is all ways the circumference
Step-by-step explanation:
what are the answers to these 4? thank you.
The area of the different types of polygon with given dimensions are,
Area of octagon= 391.07 cm²
Area of pentagon = 232m²
Area of triangle = 21.22in²
Area of hexagon = 11.24square units.
Polygon name = octagon,
Side length = 9cm
Degree of central angle = 360° /8
= 45°
To find Apothem ,
draw right triangle .
base is half of the side length = 4.5
Top angle of the right triangle = (1/2) × 45°
= 22.5°
Using tangent ratio considering top angle as α
tanα = 4.5/ Apothem length
⇒Apothem length = 4.5 / tan22.5°
⇒Apothem length = 4.5 / (√2 - 1 )
⇒Apothem length = 4.5 / 0.414
⇒Apothem length = 10.86cm.
Area of octagon = 2 ( 1 + √2 ) × (side length)²
= 2 × 2.414 × 9²
= 391.07 cm²
Polygon name = Pentagon,
Apothem= 8m
Degree of central angle = 360° /5
= 72°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle = (1/2) × 72°
= 36°
Using tangent ratio considering top angle as α
tanα = half of side length /Apothem length
⇒(1/2) side length = 8 × tan36°
⇒ side length = 16 × (0.7265)
⇒ side length= 11.62m
Area of pentagon
= 5/2 × side length × distance from the center of sides to the center of pentagon
= 5/2 × 11.6 × 8
= 232m²
Polygon name = triangle,
Apothem= 2in
Degree of central angle = 60°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle =60°
Using tangent ratio considering top angle as α
tanα = half of side length / Apothem length
⇒(1/2) side length = 2 × tan60°
⇒ side length = 4 (√3)
⇒ side length= 6.928in
≈ 7 in
Area of triangle = √3/4 × 7²
= 21.22in²
Polygon name = hexagon,
Apothem= 5
Degree of central angle = 60°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle =30°
Using tangent ratio considering top angle as α
sinα = half of side length / Apothem length
⇒(1/2) side length = 5 × sin30°
⇒ side length = 10 (0.5)
⇒ side length= 5
distance from center of sides to the center of hexagon
= √5² - 2.5²
=4.33
Area = (3√3)/2 × distance from center of sides to the center of hexagon
= (3√3)/2 × 4.33
= 11.24square units.
Therefore, the area of the given polygon are octagon = 391.07 cm² , pentagon = 232m² , triangle = 21.22in² , and hexagon = 11.24square units.
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A construction company is planning to bid on a building contract. The bid costs the company $1100. The probability that the bid is accepted is 1/10
. If the bid is accepted, the company will make $96,000 minus the cost of the bid.
What is the expected value in this situation?
Choose the statement below that best describes what this value means.
A.
In the long run, the construction company would expect to earn this amount on average per bid.
B.
In the long run, the construction company would expect to break even on average.
C.
In the long run, the construction company would expect to lose this amount on average per bid.
D.
None of the above
Answer:
The expected value in this situation can be calculated as follows:
E(X) = P(X) * V(X), where X is the random variable representing the profit of the construction company, P(X) is the probability of X, and V(X) is the value of X.
In this case, the profit of the construction company if the bid is accepted is $96,000 - $1,100 = $94,900, and the probability of the bid being accepted is 1/10. Therefore, we have:
E(X) = (1/10) * $94,900 = $9,490
The expected value of $9,490 means that in the long run, the construction company would expect to earn this amount on average per bid. Therefore, the correct answer is option A: "In the long run, the construction company would expect to earn this amount on average per bid."
For f(x) = x2 -4 and g(x) = 2x + 3, what is the domain of f - g?
A) (-90, ∞0)
B) (-2, 2)
C) (2, ∞)
D) [0, %)
Answer:
To determine the domain of f - g, we need to first find the expression for f - g.
f - g = (x^2 - 4) - (2x + 3)
f - g = x^2 - 2x - 7
The domain of f - g is the set of all real numbers for which the expression x^2 - 2x - 7 is defined.
We know that a quadratic expression of the form ax^2 + bx + c is defined for all real numbers x, so long as the expression under the square root in the quadratic formula (b^2 - 4ac) is non-negative.
In this case, a = 1, b = -2, and c = -7, so the expression under the square root is:
b^2 - 4ac = (-2)^2 - 4(1)(-7) = 4 + 28 = 32
Since 32 is positive, we know that the expression x^2 - 2x - 7 is defined for all real numbers x, and therefore the domain of f - g is all real numbers.
So the answer is not among the choices given.
marcus deposits $500 in an account that pays 6.8% simple annual interest. if he keeps the money in the account for 5 years how much interest will he earn
Marcus will earn $170 in interest after keeping his $500 in the account for 5 years.
To calculate the interest Marcus will earn, we can use the formula:
I = P * r * t
where I is the interest earned, P is the principal amount deposited, r is the annual interest rate as a decimal, and t is the time period in years.
In this case, Marcus deposited $500 and the annual interest rate is 6.8%, which is 0.068 as a decimal. He kept the money in the account for 5 years.
So we can plug in these values into the formula:
I = 500 * 0.068 * 5
I = $170
This is simple interest, which means that the interest is only earned on the original principal amount and not on any accumulated interest.
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Pls help help its urgent!
The comparison of the function A(t) to the function H(t) is given as follows:
It is vertically stretched by a factor of 1.2.It is horizontally compressed by a factor of 3.How to interpret the transformations?The function A(t) in the context of this problem is given as follows:
A(t) = 1.2H(3t).
The transformations, compared to the function H(t), are then listed and explained as follows:
It is vertically stretched by a factor of 1.2, due to the multiplication by 1.2 on the range.It is horizontally compressed by a factor of 3, due to the multiplication by 3 on the domain.(multiplication by a value greater than 1 on the range stretches, on the domain it compresses).
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If (2x, x + 17, x + 21, ....) is an arithmetic sequence find the value of x ?
Answer:
Since (2x, x + 17, x + 21, ...) is an arithmetic sequence, we know that the common difference between consecutive terms is constant.
The common difference can be found by subtracting any two consecutive terms in the sequence. Let's subtract the second term (x + 17) from the first term (2x):
2x - (x + 17) = x - 17
Now let's subtract the third term (x + 21) from the second term (x + 17):
(x + 17) - (x + 21) = -4
Since the common difference is constant, we can set the two expressions for the common difference equal to each other:
x - 17 = -4
Solving for x, we get:
x = 13
Therefore, the value of x that makes the sequence (2x, x + 17, x + 21, ...) an arithmetic sequence is x = 13.
1.6 Solve the following equation using
7x-8y+5z=5
-4x+5y-3z=-3
x-y+z = 0
a. Crammer's rule
b. Inverse Method
[10]
[10]
Answer:
Step-by-step explanation:
a. Using Cramer's Rule:The system of equations can be written in matrix form as:Copy code| 7 -8 5 | | x | | 5 | | -4 5 -3 | x | y | = |-3 | | 1 -1 1 | | z | | 0 |The determinant of the coefficients matrix is:scssCopy code| 7 -8 5 | | -4 5 -3 | | 1 -1 1 | = 7(5)(1) + (-8)(-3)(1) + 5(-4)(-1) - 1(-3)(7) - 1(5)(-8) - (-1)(-3)(5) = 70To find x, we replace the x-coefficients with the constants and solve for x:scssCopy code| 5 -8 5 | | -3 5 -3 | | 0 -1 1 | x = | 7 -8 5 | | -4 5 -3 | | 1 -1 1 | = (5(5)(1) + (-8)(-3)(1) + 5(-3)(-1) - 1(-3)(5) - 1(5)(-8) - 0(-1)(-4))/70 = 9/14To find y, we replace the y-coefficients with the constants and solve for y:scssCopy code| 7 5 5 | | -4 -3 -3 | | 1 0 1 | y = | 7 -8 5 | | -4 5 -3 | | 1 -1 1 | = (7(-3)(1) + (-8)(-3)(1) + 5(0)(-1) - 1(5)(-3) - 0(-8)(-4) - 1(-1)(-4))/70 = -1/14To find z, we replace the z-coefficients with the constants and solve for z:scssCopy code| 7 -8 5 | | -4 5 -3 | | 5 -1 0 | z = | 7 -8 5 | | -4 5 -3 | | 1 -1 1 | = (7(5)(0) + (-8)(-3)(1) + 5(-1)(-1) - (-1)(5)(5) - 1(5)(-8) - 0(-1)(-4))/70 = -12/35Therefore, the solution to the system of equations is x = 9/14, y = -1/14, z = -12/35.b. Using Inverse Method:The system of equations can be written in matrix form as:Copy code| 7 -8 5 | | x | | 5 | | -4 5 -3 | x | y | = |-3 | | 1 -1 1 | | z | | 0 |The coefficients matrix is:Copy code| 7 -8 5 | | -4 5 -3 | | 1 -1 1
I need help asap!!!!!!!!!!!!
The falls that make up Niagara Falls are eroding backwards, thus migrating upstream.
They have migrated back 100 feet in the past 50 years. What is the rate of erosion along the falls?
( )Feet per year
The rate of erosion along the falls is given as follows:
2 feet per year.
How to obtain the rate of erosion?The rate of erosion of Niagara Falls is obtained applying the proportions in the context of the problem.
The falls have migrated back 100 feet in the past 50 years, hence the rate of erosion in feet per year is given as follows:
100/50 = 2 feet per year.
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Which one of these tables are proportional? Show your work.
Answer:
Table B is proportional since y = 1.5x:
4.5 ÷ 3 = 1.5
7.5 ÷ 5 = 1.5
10.5 ÷ 7 = 1.5
Question 3 of 5
What is the median of the data set?
7, 9, 11, 14, 18, 20, 30, 35
Answer:
16
Step-by-step explanation:
To find the median, we find the middle of the data set.
7, 9, 11, 14, 18, 20, 30, 35
There are 8 values
7, 9, 11, 14, 18, 20, 30, 35
The median is between the 4th and 5th numbers
We need to find the mean of the middle two numbers
(14+18)/2 =32/2= 16
Answer:
16
Step-by-step explanation:
Median means the middle term in a data set.Remember that, you have to arrange the data points from smallest to largest to find the median of a data set.The formula to find the median of a data set is:[tex]\sf (\frac{n+1}{2}\:)^ t^h \:data[/tex]
Here,
n ⇒ number of terms
Let us find it now.
7, 9, 11, 14, 18, 20, 30, 35
[tex]\sf Median=\sf (\frac{n+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf (\frac{8+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf 4.5^ t^h \:data[/tex]
In this case, add 4th and 5th data and divide it by 2.
[tex]\sf Median = \frac{14+18}{2}\\\\ \sf Median = \frac{32}{2}\\\\\sf Median = 16[/tex]
Point A is located at (1, 2). Point B is located at (4, 6). Use this information to determine the length of the line, rounded to the nearest whole number.
If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.
To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.
Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:
d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5
Rounded to the nearest whole number, the length of the line is also 5 units.
In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.
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solve the diagram for x
Answer:
Step-by-step explanation:
b. the length of the adjacent side :11
c. you want to know the x which is hypotenuse
d. SOH CAH TOA, you know a and wants to know h, so should use cos function
Explain how you might show that 3 points lie on the same line using coordinate geometry.
If the determinant of the matrix formed by the coordinates of the three points is zero, then they are collinear
Given data ,
To show that three points lie on the same line using coordinate geometry, we need to check if they satisfy the equation of a line.
Let the coordinates of the three points be (x1, y1), (x2, y2), and (x3, y3).
To check if these three points are collinear, we can calculate the slope of the line passing through the first two points using the formula
m = (y2 - y1) / (x2 - x1)
Then, we can check if the slope of the line passing through the second and third points is equal to the slope we calculated above. If they are equal, then all three points lie on the same line
m' = (y3 - y2) / (x3 - x2)
If m = m', then the three points are collinear
Alternatively, we can use the determinant method to check if the three points lie on the same line. If the determinant of the matrix formed by the coordinates of the three points is zero, then they are collinear
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Arrange the steps in order to simplify the expression
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
The circumference of a circle is 20 � π cm. Find its radius, in centimeters.
The required radius of the circle is 10 cm.
The formula for the circumference C of a circle in terms of its radius r is given by:
C = 2πr
We are given that the circumference of the circle is 20π cm. So we can set this expression equal to 20π and solve for r:
20π = 2πr
Dividing both sides by 2π, we get:
r = 10
Therefore, the radius of the circle is 10 cm.
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What is the relation between the variables in the equation
varies inversely as y
varies directly as y
a.
b.
Please select the best answer from the choices provided
OA
* B
OC
OD
y
-7?
c. y varies directly as ¹
y varies inversely as ¹
d.
The best answer to the given question is B.
When a variable "varies inversely as y," it means that as y increases, the variable decreases, and vice versa. This relationship is expressed mathematically as:
variable = k/y
where k is a constant.
When a variable "varies directly as y," it means that as y increases, the variable also increases, and vice versa. This relationship is expressed mathematically as:
variable = k*y
where k is a constant.
Option (a) does not provide any information about the relationship between variables. Option (c) and (d) provide incomplete information as they do not specify the variable that varies with y. Option (b) correctly explains the two types of relationships between variables and their mathematical expressions.
Option B is the best answer.
Find the measure of each angle indicated.
P
U
160°
W
95° ?
V
Answer:
? = 65°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ PUV is an exterior angle of the triangle , then
? + 95° = 160° ( subtract 95° from both sides )
? = 65°
What is the value of x?
X
30°
24
Express your answer in radical form.
Enter your answer in the box.
Answer:
x = 12
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{x}{24}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 24 ( divide both sides by 2 )
x = 12
Use the long division method to find the result when 4x^3+15x^2+17x+6 is divide by 4x+3
The result when 4x³ + 15x² + 17x + 6 is divide by 4x + 3 using long dividion method will be x² + 3x + 2.
Given that:
Dividend, 4x³ + 15x² + 17x + 6
Divisor, 4x + 3
The division of the polynomial is given below.
4x + 3 ) 4x³ + 15x² + 17x + 6 ( x² + 3x + 2
- (4x³ + 3x²)
12x² + 17x
- (12x² + 9x)
8x + 6
- (8x + 6)
0 0
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CAN SOMEONE HELP WITH THIS QUESTION?
Part(A),
The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and right endpoints is approximately 0.231 square units.
Part(B),
The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.
To estimate the area under the graph of f(x) = 1/(x²+1) over the interval [3, 5] using four rectangles and right endpoints, we can use the following formula:
[tex]R_n = \dfrac{(b-a)}{n} \times [f(x_1) + f(x_2) + ... + f(x_n)],[/tex]
where a = 3, b = 5, n = 4, and xi = a + i(b-a)/n for i = 0, 1, 2, ..., n.
Using this formula with the right endpoints, we get:
[tex]R_4 = \dfrac{(5-3)}{4 }\times [f(3.5) + f(4) + f(4.5) + f(5)][/tex]
R₄ = (1/2) x [0.361 + 0.250 + 0.178 + 0.132]
R₄ = 0.231
Hence, the estimated area under the f(x) graph utilizing four rectangles and the right endpoints over the range [3, 5] is about 0.231 square units.
To repeat the approximation using left endpoints, we can use the following formula:
[tex]L_n = \dfrac{(b-a)}{n} \times [f(x_0) + f(x_1) + ... + f(x_{n-1)],[/tex]
where [tex]x_i = a + i\dfrac{(b-a)}{n}[/tex] for i = 0, 1, 2, ..., n-1.
Using this formula with left endpoints, we get:
[tex]L_4 = \dfrac{(5-3)}{4} \times [f(3) + f(3.5) + f(4) + f(4.5)][/tex]
L₄ = (1/2) x [0.250 + 0.361 + 0.250 + 0.178]
L₄ = 0.2405
Therefore, the estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.
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Select the correct answer.
Credit cards and charge cards differ in two important ways. One is the method of payment. What is the other difference?
A. You can get a credit card from your bank but not a charge card.
в.
You have to pay interest on charge cards but not on credit cards.
C.
You have to pay interest on credit cards but not on charge cards.
Slope of secant line pre calc
For the function f(x) = -2x² + 5x + 7 the slope of the secant line between x = -3 and x = 5 is -4
Consider the function f(x) = -2x² + 5x + 7
We need to find the slope of the secant line between x = -3 and x = 5
We know that the slope of secant line for the function f(x) on the interval [a, b] is given by the formula,
m = [f(b) - f(a)] / (b - a)
Let [a, b] = [-3, 5]
For x = -3 the value of the function would be,
f(-3) = -2(-3)² + 5(-3) + 7
= -2(9) - 15 + 7
= -18 - 15 + 7
= -26
And the value of the function for x = 5 would be,
f(5) = -2(5)² + 5(5) + 7
= -2(25) - 25 + 7
= -50 - 15 + 7
= -58
Using above formula the slope would be,
m = [f(5) - f(-3)] / (5 - (-3))
m = [-58 - (-26)] / 8
m = (-58 + 26) / 8
m = -4
Thus, the required slope is -4
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Answer:
Slope = 1
Step-by-step explanation:
A secant line is a straight line that intersects a curve at two or more points.
Given a curve represented by a function f(x), a secant line is determined by choosing two distinct points on the curve, (x₁, f(x₁)) and (x₂, f(x₂)).
The secant line passes through these two points and can be represented by a linear equation in the form y = mx + b, where m is the slope of the secant line and b is the y-intercept.
The slope of the secant line between the points (x₁, f(x₁)) and (x₂, f(x₂)) is given by the formula:
[tex]m = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]
To find the slope of the secant line between x = -3 and x = 5 for the function f(x) = -2x² + 5x + 7, first find f(-3) and f(5).
[tex]\begin{aligned}f(-3)&=-2(-3)^2+5(-3)+7\\&=-2(9)-15+7\\&=-18-15+7\\&=-26\end{aligned}[/tex]
[tex]\begin{aligned}f(5)&=-2(5)^2+5(5)+7\\&=-2(25)+25+7\\&=-50+25+7\\&=-18\end{aligned}[/tex]
Input the values into the slope formula:
[tex]m = \dfrac{f(5) - f(-3)}{5 - (-3)}=\dfrac{-18-(-26)}{5+3}=\dfrac{8}{8}=1[/tex]
Therefore, the slope of the secant line between x = -3 and x = 5 is 1.
Find the probability that a point chosen at random would lie in the shaded area of the figure. Round to the nearest tenth of a percent.
with the steps and explanation
Answer:
Okay, let's solve this step-by-step:
The figure shows a rectangle partitioned into 6 smaller rectangles
4 of these rectangles are shaded
To find the probability a randomly chosen point lies in a shaded area, we calculate:
Probability = (Number of shaded squares) / (Total number of squares)
There are 6 smaller rectangles
4 of these are shaded
So Number of shaded squares = 4
And Total number of squares = 6
Plugging this in:
Probability = (4) / (6)
= 2/3
Converting to a percent:
2/3 = 66.7%
Rounded to the nearest tenth: 67%
So the final answer is:
The probability that a point chosen at random would lie in the shaded area of the figure is 67% (rounded to the nearest tenth of a percent).
Let me know if this helps explain the steps and solution. I can provide more details if needed.
Good luck!
Step-by-step explanation:
what is the angle of depression on top of a 15 foot tall tree to a lake exactly at 30 feet from the top of the tree? what is the angle of elevation for someone on a boat that is 35 feet from shore looking up at the top of the tree?
Answer: We can use basic trigonometry to solve both of these problems:
Angle of depression from the top of the tree to the lake:
Let's draw a diagram of the situation:
A (top of tree)
|\
| \
30 | \ 15 ft
| \
| \
| \
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|__________\
B (lake)
In this diagram, A represents the top of the tree, B represents the lake, and the lines connecting them form a right triangle. We want to find the angle of depression, which is the angle between the horizontal line (from the top of the tree to the lake) and the line of sight from the top of the tree to the lake. This is angle θ in the diagram.
We know that the opposite side of this right triangle is 30 feet (the horizontal distance from the top of the tree to the lake) and the adjacent side is 15 feet (the height of the tree). Therefore:
tan(θ) = opposite/adjacent = 30/15 = 2
Taking the arctangent of both sides gives us:
θ = arctan(2) ≈ 63.4 degrees
Therefore, the angle of depression from the top of the tree to the lake is approximately 63.4 degrees.
Angle of elevation from the boat to the top of the tree:
Let's draw a diagram of the situation:
C (person on boat)
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35 | \
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|__________\
A (top of tree)
In this diagram, C represents the person on the boat, A represents the top of the tree, and the lines connecting them form a right triangle. We want to find the angle of elevation, which is the angle between the horizontal line (from the person on the boat to the shore) and the line of sight from the person on the boat to the top of the tree. This is also angle θ in the diagram.
We know that the opposite side of this right triangle is 15 feet (the height of the tree) and the adjacent side is 35 feet (the horizontal distance from the person on the boat to the tree). Therefore:
tan(θ) = opposite/adjacent = 15/35
Taking the arctangent of both sides gives us:
θ = arctan(15/35) ≈ 23.1 degrees
Therefore, the angle of elevation from the boat to the top of the tree is approximately 23.1 degrees.
[tex](x+7)x^{2} -(x-3)x^{2} =(x+35)x^{2} -(x+34)x^{2}[/tex]
The equation (x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2 has no solution for x
Evaluating the equationFrom the question, we have the following parameters that can be used in our computation:
(x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2
Divide through the equation by x^2
so, we have the following representation
(x+7) -(x-3) = (x+35) -(x+34)
When the brackets are removed and the like terms are evaluated, we have
2x + 10 = 2x - 1
Evaluate the like terms again
So, we have
10 = -1
The above equation is false
Hence, the equation has no solution for x
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Expand and evaluate the series.
∑6n=13n
{
,
,
,
,
,
}
S6=
Answer:
The series ∑6n=1 3n is a sum of the first 6 terms of the sequence 3n, which starts with n = 1 and increases by 3 for each successive term. Therefore, the first 6 terms of the sequence are:
3(1), 3(2), 3(3), 3(4), 3(5), 3(6)
which simplify to:
3, 6, 9, 12, 15, 18
The sum of these terms is:
∑6n=1 3n = 3 + 6 + 9 + 12 + 15 + 18 = 63
Therefore, S6, the sum of the first 6 terms of the series, is 63.
if anyone could help me please? :)
The characteristics that shows that the graph is a proportional relationship is: D. The line connecting the points passes through the origin.
What is a graph of a proportional relationship?A graph of a proportional relationship is a straight line that passes through the origin (0, 0) on a coordinate plane, where the points on the line represent pairs of values that are in direct proportion to each other.
From the graph shown above, if we connect the points together, the line will pass through the origin, therefore, the correct answer is: D. The line connecting the points passes through the origin.
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The characteristics that tell you that the graph shows a proportional relationship are: A straight line can be drawn through the points and The line connecting the points passes through the origin. Option B and D are the correct answer.
A proportional relationship is a relationship between two variables where the ratio of their values is constant. This means that if we multiply one of the values by a constant, the other value also gets multiplied by the same constant.
The graph of a proportional relationship is a straight line that passes through the origin. This is because the ratio of the x- and y-values is constant, so the points can be plotted as a straight line.
The ordered pairs all have the same x- and y-values means that the two variables are perfectly correlated. This is not necessary for a proportional relationship, but it is a common characteristic.
The line connecting the points does not need to pass through the origin for the relationship to be proportional. However, if the line does pass through the origin, then the two variables are directly proportional. Option B and D are the correct answer.
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