The angles of depression of two ships from the top of the light house are 45° and 30° towards east. If the ships are 200 m apart, find the height of the lighthouse.
please answer with figure.
Answers
Answer:
273 meters
Step-by-step explanation:
See image attached for the diagram I used to represent this scenario.
The distance between the ships, at angles 30 and 45, is 200 meters. The distance between the left ship and the lighthouse is x meters.
We can use trigonometric ratios to solve this problem. We can use the tangent ratio \(\big{(} \frac{\text{opposite}}{\text{adjacent}} \big{)}\) to create an equation with the two angles.
\(\displaystyle \text{tan(45)} = \frac{h}{x}\) \(\displaystyle \text{tan(30)} = \frac{h}{x+200} }\)Let's take these two equations and solve for x in both of them.
\(\textbf{Equation I}\)\(\displaystyle \text{tan(45)} = \frac{h}{x}\)tan(45) = 1, so we can rewrite this equation.
\(\displaystyle 1=\frac{h}{x}\)Multiply x to both sides of the equation.
\(\displaystyle x = h\) \(\textbf{Equation II}\)\(\displaystyle \text{tan(30)} = \frac{h}{x+200} }\)Multiply x + 200 to both sides and divide h by tan(30).
\(\displaystyle \text{x + 200} = \frac{h}{\text{tan (30)}}\)Subtract 200 from both sides of the equation.
\(\displaystyle \text{x} = \frac{h}{\text{tan (30)}} - 200\)Simplify h/tan(30).
\(x=\sqrt{3}h - 200\) \(\textbf{Equation I = Equation II}\)Take Equation I and Equation II and set them equal to each other.
\(h=\sqrt{3}h-200\)Subtract √3 h from both sides of the equation.
\(h-\sqrt{3}h=-200\)Factor h from the left side of the equation.
\(h(1-\sqrt{3}) =-200\)Divide both sides of the equation by 1 - √3.
\(\displaystyle h=\frac{-200}{1-\sqrt{3} }\)Rationalize the denominator by multiplying the numerator and denominator by the conjugate.
\(\displaystyle h=\frac{-200}{1-\sqrt{3} } \big{(} \frac{1+\sqrt{3} }{1+\sqrt{3}} \big{)}\) \(\displaystyle h=\frac{-200+200\sqrt{3} }{1-3}\) \(\displaystyle h =\frac{-200+200\sqrt{3} }{-2}\)Simplify this equation.
\(\displaystyle h=100+100\sqrt{3}\) \(h=273.20508075\)The height of the lighthouse is about 273 meters.
Answer:
\(h\approx 273.21 \text{ meters}\)
Step-by-step explanation:
Please refer to the attachment.
In the attachment, h is the height of the lighthouse and x is the distance from the lighthouse to Ship A.
Since the angle of depression from the top of the lighthouse to Ship A is 45°, this means that the angle of elevation from Ship A to the top of the lighthouse is 45°.
Likewise, the angle of elevation from Ship B to the top of the lighthouse is 30°.
So, we will form two right triangles: the smaller, 45-45-90 triangle, and the larger 30-60-90 triangle.
Remember that in 45-45-90 triangles, the two legs are congruent.
Therefore, we can write that:
\(h=x\)
Next, in 30-60-90 triangles, the longer leg is always √3 times the shorter leg.
In our 30-60-90 triangle, the shorter leg is given by:
\(\text{Shorter leg}=h\)
And the longer leg is given by:
\(\text{Longer leg}=x+200\)
So, the relationship between the shorter leg and longer leg is:
\(\sqrt3h = (x+200)\)
And since we know that h is equivalent to x, we can write:
\(\sqrt3h=(h+200)\)
Now, we just have to solve for h. We can subtract h from both sides:
\(\sqrt3h-h=200\)
Factoring out the h yields:
\(h(\sqrt3-1)=200\)
Therefore:
\(\displaystyle h=\frac{200}{\sqrt3-1}\)
Approximate. So, the height of the lighthouse is approximately:
\(h \approx 273.2050 \text{ meters}\)
Related Questions
Josh buys 6 pencils at the bookstore. Each pencil costs $0.20. How can Josh use the number
line to find the total cost of the pencils?
Answers
Answer:
0.20×6
1.2
Step-by-step explanation:
boom
bam
pow
baba beep bum
P O W
what is the value of x in the equation, 5x - 7 = y, if y=8?
Answers
Answer:
The value of x is 3.
Step-by-step explanation:
5x-7=y
5x-7=8
5x=8+7
5x=15
x=15/5
x=3
Hey there!
5x - 7 = y
5x - 7 = 8
ADD 7 to BOTH SIDES
5x - 7 + 7 = 8 + 7
CANCEL out: -7 + 7 because it give you 0
KEEP: 8 + 7 because it help solve for the x-value
NEW EQUATION: 5x = 8 + 7
SIMPLIFY IT!
5x = 15
DIVIDE 5 to BOTH SIDES
5x/5 = 15/5
CANCEL out: 5/5 because it give you 1
KEEPs 15/5 because it give you the x-value
NEW EQUATION: x = 15/5
SIMPLIFY IT!
x = 3
Therefore, your answer is: x = 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Help please, I'm desperate!
Answers
Because, 4-1.2=2.8
Answer:
Step-by-step explanation:
For bubble answers:
1. A
2. B
3. B
4. C
5. A
6. B
7. C
8. B
9. B
One or two may be wrong sorry
How many square feet of outdoor carpet will
we need for this hole?
ft?
Answers
Answer:
39 sqare feet
Step-by-step explanation:
Break the shape into two rectangles and find the area for each. First, find the area of the small rectangle jutting out from the bottom of the shape. Multiply the length (3) by the width (2) to get 6 square feet. Then, do the big rectangle following the same process to get 33 square feet. Adding these values together gives you the total area, which is 39 square feet.
which statement is true?
A. 6n+16=6(n+10)
B. 6n+16=4(2n+4)
C. 6n+16=5n+12+n+4
D. 6n+16=8n+14-2n+2-n
Answers
Answer:
i think the correct answer is the third one
have a nice day! (^o^)
type the Integra that makes the type the integral that makes the following multiplication sentence true * 7 equal -4
Answers
In order to determine the integer that makes true the given expression:
______ x 7 = -14
consider that such integer must be equal to the quotient between -14 and 7:
-14/7 = -2
In fact, you have:
-2 x 7 = -14
Hence, the integer is -2
solve for missing side of the right triangle, round to the nearest tenth .
Answers
a^2 + b^2 = c^2
Let’s say a = 6 and b = 11
6^2 + 11^2 = c^2
36 + 121 = c^2
c^2 = 157
C = squareroot of 157
C = 12.5
Solution: 12.5 m
In ΔEFG, g = 34 inches, e = 72 inches and ∠F=21°. Find the area of ΔEFG, to the nearest square inch.
Answers
The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.
To find the area of triangle EFG, we can use the formula:
\(Area = (1/2) \times base \times height\)
In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.
First, let's find the length of FG. We can use the law of cosines:
FG² = EF² + EG² - 2 * EF * EG * cos(∠F)
EF = 72 inches
EG = 34 inches
∠F = 21°
Plugging these values into the equation:
FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)
Solving for FG, we get:
FG ≈ 83.02 inches
Next, we need to find the height. We can use the formula:
height = \(EF \times sin( \angle F)\)
Plugging in the values:
height = 72 * sin(21°)
height ≈ 25.52 inches
Now we can calculate the area:
\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)
Area ≈ 1060.78 square inches
For more such questions on triangle
https://brainly.com/question/1058720
#SPJ8
Find the particular antiderivative of the following derivative that satisfies the given condition. C''(x)=4x2-3x ; C(0)=2000
Answers
The particular antiderivative that satisfies the given condition is: C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000
To find the particular antiderivative (or integral) of the given derivative \(C''(x) = 4x^2 - 3x\) that satisfies the condition C(0) = 2000, we need to integrate the given function twice.
First, we integrate C''(x) to find C'(x):
\(C'(x) = ∫ (4x^2 - 3x) dx\)
To find the antiderivative of \(4x^2\), we use the power rule for integration: the power of x increases by 1 and is divided by the new power. Similarly, the antiderivative of -3x is \(-(3/2)x^2\).
\(C'(x) = ∫ (4x^2 - 3x) dx = (4/3)x^3 - (3/2)x^2 + K1\)
Here, K1 is the constant of integration. Next, we integrate C'(x) to find C(x):
\(C(x) = ∫ (C'(x)) dx = ∫ ((4/3)x^3 - (3/2)x^2 + K1) dx\)
To find the antiderivative of \((4/3)x^3\), we again use the power rule for integration. Similarly, the antiderivative of \(-(3/2)x^2\) is \(-(3/2)(1/3)x^3\).
The constant of integration K1 will also be integrated with respect to x, resulting in another constant of integration, K2.
\(C(x) = (1/3)(4/3)x^4 - (1/2)(3/2)x^3 + K1x + K2\)
Simplifying further, we have:
\(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + K2\)
Now, we can apply the initial condition C(0) = 2000 to find the particular solution for K2:
\(C(0) = (4/9)(0)^4 - (9/8)(0)^3 + K1(0) + K2 = 2000\)
Since all the terms involving x become zero when x = 0, we have:
K2 = 2000
Therefore, the particular antiderivative that satisfies the given condition is: \(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000\)
To know more about antiderivative refer here:
https://brainly.com/question/33243567
#SPJ11
What is the solution of equations 8x 3y 5 3x 2y 5 *?
Answers
The solution of the given system of equations 8x+3y=5 and 3x-2y=5 is x = 1 and y = -1
In this question we have been given a system of equations.
8x+3y=5 ..........(1)
and 3x-2y=5 ..........(2)
We need to find the solution of the given system of equations.
As right hane side of both equations is equal, we equate LHS of both equations.
so, we get,
8x + 3y = 3x - 2y
⇒ 8x - 3x = - 2y - 3y
⇒ 5x = - 5y
⇒ x = - y .............(3)
By substituting x = - y in equation (1), we get,
8 ( - y ) + 3y = 5
⇒ - 8y + 3y = 5
⇒ - 5y = 5
⇒ y = - 1
Substitute above value of y in equation (3)
⇒ x = - (- 1)
⇒ x = 1
Therefore, x = 1 and y = -1 is solution of given equations.
Learn more about an equation here:
https://brainly.com/question/649785
#SPJ4
Solve the right triangle. See image below.
Answers
Hi there! You still remember the Pythagorean Theorem, right? It's useful when it comes to finding a missing leg or side of a right triangle. If you forget then here it is:
\( \large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }\)
Define c = hypotenuse while a and b can be both adjacent and opposite (because a²+b²=b²+a² via addition property)
Since we are missing the adjacent side. Thus,
We define a = 6 and c = 14.
\( \large{ {6}^{2} + {b}^{2} = {14}^{2} } \\ \large{36 + {b}^{2} = 196} \\ \large{ {b}^{2} = 196 - 36} \\ \large{ {b}^{2} = 160} \\ \large{ b = \sqrt{160} \longrightarrow \boxed{b = 4 \sqrt{10} }}\)
Put the value of b in a calculator then round to the nearest tenth and get 12.6
Thus, the value of b ≈ 12.6
Next we are going to find the angle in degree. We now know that b ≈ 12.6 or 4sqrt(10)
We can find the value of angle A by using tan or sin but I will use sin instead. Recall the sine ratio which is opposite to hypotenuse. Thus,
\( \large{sinA = \frac{6}{14} }\)
Use arcsin(6/14) and put it in calculator.
Then put the decimal value of arcsin in sin and convert in degree form which we should get 24. 555°. Round to the nearest whole number and we get 25°
Thus, the angle A is 25°
Next is we are finding the value of angle B. We aren't going to use any formula or equation. Recall that three angles add up to 180°.
Thus, 25° + 90° + x = 180°
90° comes from a right angle.
115+x = 180
x = 180-115
x = 65°
Thus, the angle B is 65°
Answer
b ≈ 12.6 or 4sqrt(10)angle A = 25°angle B = 65°The school store sells pencils and erasers.
• For 3 pencils and 2 erasers, the cost is $0.76.
• For 2 pencils and 4 erasers, the cost is $1.04.
How much more does 1 eraser cost than 1 pencil?
Answers
Answer:
$0.18
Step-by-step explanation:
we need to set up two simultaneous equations
using variables, pencils = p and erasers = e
3 pencils and 2 erasers, the cost is $0.76
3p + 2e = $0.76
2 pencils and 4 erasers, the cost is $1.04.
2p + 4e = $1.04
we now have
3p + 2e = $0.76
2p + 4e = $1.04
to make the number of erasers the same, multiply the first equation by 2 to give 4e
2(3p + 2e = $0.76)
6p + 4e = $1.52
now we have the same number of erasers for both equations
6p + 4e = $1.52
2p + 4e = $1.04
subtract across: 6p - 2p = 4p, 4e - 4e = 0, $1.52 - $1.04 = $0.48
we are left with 4p = $0.48
divide both sides by 4
p = $0.12
1 pencil = $0.12
go back to the start of both equations and use one of them to find 1 eraser. I'll use 3p + 2e = $0.76
input $0.12 in p
3($0.12) + 2e = $0.76
$0.36 + 2e = $0.76
subtract $0.36 on both sides
2e = $0.76 - $0.36
2e = $0.40
divide 2 on both sides
e = $0.20
1 eraser = $0.20
How much more does 1 eraser cost than 1 pencil?
we now know 1 pencil = $0.12 and 1 eraser = $0.20
find the difference between them
$0.20 - $0.12 = $0.18
final answer= $0.18
help pls
i will be friend
Answers
Answer:
brainliest pls
Step-by-step explanation:
(co 6) a university wants to plan how many classes to run next semester. to do this, it needs to estimate on average how many students register each semester. which statistical method would be best to use in this situation? g
Answers
The statistical method that would be best to use in this situation is b) Regression analysis.
Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.
Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.
Hence the answer is Regression analysis.
Learn more about Regression analysis click;
https://brainly.com/question/31873297
#SPJ12
In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30 - 34 group while Mary competed in the Women, Ages 25 - 29 group. Leo completed the race in 1:22:28 (4948 seconds), while Mary completed the race in 1:31:53 (5513 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performance of their groups:
The finishing times of the Men, Ages 30 - 34 group has a mean of 4313 seconds with a standard deviation of 583 seconds.
The finishing times of the Women, Ages 25 - 29 group has a mean of 5261 seconds with a standard deviation of 807 seconds.
The distributions of finishing times for both groups are approximately Normal. Remember: a better performance corresponds to a faster finish.
(a) Write down the short-hand for these two normal distributions.
(b) What are the Z scores for Leo�s and Mary�s finishing times? What do these Z scores tell you?
(c) Did Leo or Mary rank better in their respective groups? Explain your reasoning.
(d) What percent of the triathletes did Leo finish faster than in his group?
(e) What percent of the triathletes did Mary finish faster than in her group?
(f) If the distributions of finishing times are not nearly normal, would your answers to parts (b) - (e) change? Explain your reasoning
Answers
Therefore , the solution of the given problem of standard deviation comes out to be Mary beat about 62.44% of the other triathletes in her division, finishing first.
what does standard deviation mean?Statistics uses variance as a gauge of variation. The photograph of that figure is used to compute the average deviation between what was collected and the mean. In contrast with numerous other valid measures of variability, it includes those data points on their own by comparing each value to the mean. Variations may be brought on by willful mistakes, irrational expectations, or shifting economic or business conditions.
Here,
a) Men, 30-34 years old group: N(4313, 5832) Women, 25-29 years old group: N(5261, 8072)
(b)
=> Z score = (4948 - 4313) / 583 = 1.09 for Leo.
Mary's Z score is
=> (5513 - 5261) / 807 = 0.31.
(c) We must compare their Z scores in order to evaluate their rankings. Leo ended ahead of his group's mean, according to his Z score of 1.09, while Mary came in below it, according to her Z score of 0.31.
(d) . With the aid of a table or computer,
we determine that this region is roughly 0.8621 or 86.21%.
Leo outperformed about 86.21% of the triathletes in his division, finishing first.
(e) A table or calculator helps us determine that this region is roughly 62.44%.
Mary beat about 62.44% of the other triathletes in her division, finishing first.
(f) Our responses to sections (b) through (e) could change if the distributions of finishing times are not virtually normal.
Z ratings only have significance when the distribution is normal or roughly normal.
To know more about standard deviation visit :-
brainly.com/question/13673183
#SPJ1
what are the steps to induction nsls
Answers
These steps are often referred to as the principle of mathematical induction or PMI.
The steps for mathematical induction are:
Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.
Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.
Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.
Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.
These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.
Learn more about mathematical induction here
https://brainly.com/question/29503103
#SPJ11
Alonso brings \$21$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost \$2.50$2.50dollar sign, 2, point, 50. Then, he notices that the store only sells avocados in bags of 333 for \$5$5dollar sign, 5. He wants to buy as many avocados as he can with his remaining money.
How do u get 3 bags of avacodes or 9 avacadoes ??
Answers
Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
EquationAmount Alonso brings to the market = $21Cost of an egg = $2.50Cost of avocados in bags of 3 = $5Number of avocados bought = x21 = 2.50 + 5x
21 - 2.50 = 5x
18.50 = 5x
x = 18.50 / 5
x = 3.7 bags of avocados
To get 3 bags of avocados or 9 avocados
= $5 × 3
= $15
Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
Learn more about equation:
https://brainly.com/question/2972832
#SPJ1
what's the probability you don't roll doubles on your first roll, then roll doubles on your second roll?
Answers
We have a 1/6 chance of rolling doubles on the first roll. The odds of rolling a double on the second turn but not the first are (5/6) x (1/6) = 5/36.
So we have a total of 36 outcomes over here. So we have 36 possibilities, and if we simplify this, 6/36 is 1/6. So the chance of rolling doubles on two six-sided dice numbered 1 to 6 is 1/6.
The odds of rolling a double on the second turn but not the first are (5/6) x (1/6) = 5/36.
We'll now look at the chances of getting out of jail by rolling doubles. Because there are more possibilities to examine, this probability is significantly more complex to compute.
Learn more about to probability visit here;
https://brainly.com/question/11234923
#SPJ4
The answer to this question?
Answers
Answer: 0.429
Step-by-step explanation: Use a calculator and put the fraction and hit enter to get it in decimal form. You should get a number like 0.42857142857 but the problem asks us to round to the nearest thousandth. Since there is a 5 in the ten-thousandth place, we must round up. Therefore, the final answer will be 0.429.
Write (9m)⁴ without exponents.
Answers
we can multiply 6561m⁴ by 1 to get the final answer of 6561m⁴.
How to solve the problem?
In mathematics, an exponent refers to a numerical representation of repeated multiplication. An exponent is usually written as a small number that appears to the right and above a larger number, called the base. The exponent indicates how many times the base should be multiplied by itself. For example, in the expression 3², the base is 3, and the exponent is 2. This means that 3 should be multiplied by itself 2 times, resulting in 3 multiplied by 3, which equals 9.
Exponents are a shorthand way of representing repeated multiplication and can be used to simplify complicated expressions. They are widely used in algebra, calculus, and other branches of mathematics. Exponents can be positive, negative, or zero, and they can be fractions or irrational numbers. The rules of exponents, such as the product rule and power rule, allow for easy manipulation of expressions involving exponents.
To write (9m)⁴ without exponents, we need to perform the multiplication four times.
First, we can multiply 9m by 9m to get 81m².
Next, we can multiply 81m² by 9m to get 729m³.
Then, we can multiply 729m³ by 9m to get 6561m⁴.
Finally, we can multiply 6561m⁴ by 1 to get the final answer of 6561m⁴.
In summary, (9m)⁴ can be written as 6561m⁴ by performing multiplication four times using the distributive property of multiplication. It is important to note that exponents are a shorthand way of writing repeated multiplication, but the same result can always be obtained by performing the multiplication explicitly. This process may become more cumbersome for larger exponents, which is why exponents are a useful notation for expressing repeated multiplication in a more concise way.
To know more about exponent visit :-
https://brainly.com/question/13669161
#SPJ1
When the equation is f(x+h), what is the translation?
Answers
Answer:
a shift of h units left
Step-by-step explanation:
given f(x) then f(x± h) is a horizontal translation of h units
• if + h then a shift left of h units
• if - h then a shift right of h units
then
f(x + h) is a shift of h units to the left
If h is positive, the graph of f(x) is shifted horizontally to the left by |h| units. This means that every point on the graph will move to the left, making the function appear "delayed" or "shifted to the left."
If h is negative, the graph of f(x) is shifted horizontally to the right by |h| units. In this case, every point on the graph will move to the right, causing the function to appear "advanced" or "shifted to the right."
In summary, the equation f(x+h) represents a horizontal translation of the function f(x), with the value of h determining the direction and distance of the shift.
Paul brought $24.50 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1 3 as much as the sketchbook, and the sketchbook cost 1 2 the cost of the paint set. Paul had $2.00 left over after buying these items. What was the cost of each item
Answers
Answer:
so do
24.50-13=11.50
11.50-12.00= answer
Step-by-step explanation:
I think so
The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.
Answers
The sine, cosine, cosecant, and secant functions have period 2π; the tangent and cotangent functions have period π.
Definition for Period of a Trigonometric Function :
The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.
If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. Period is the interval between two occurrences of the wave.
Learn more about period here:
brainly.com/question/16061498
#SPJ1
Given the function f(x)=2x²+3, what is the average rate of change of f on the interval [2,2+h]?
Answers
Answer:
5.2
Step-by-step explanation:
find the sum (12p+9) + (4p-3) please help me
Answers
16p + 6
Step-by-step explanation:
(12p + 9) + (4p - 3)
12p + 4p = 16p
9 + (-3) = 6
Answer: 16p + 6
A restaurant’s goal is to serve 600 customers in 8 hours and 900 customers in 12 hours. Write an equation in point-slope form that represents the number of customers served per hour
Answers
y = 75x - 450 represents the number of customers served per hour where y is the number of customers served and x is the number of hours.
The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
To find the equation representing the number of customers served per hour, we can first find the slope of the line by using the information given. The slope of a line is the change in y over the change in x.
In 8 hours, the restaurant serves 600 customers and in 12 hours, 900 customers. Therefore, the change in y is 900 - 600 = 300 and the change in x is 12 - 8 = 4. The slope of the line is 300/4 = 75.
We also know that the restaurant serves 600 customers in 8 hours. This means that when x = 8, y = 600.
Using this information, we can write the equation in point-slope form:
y - 600 = 75(x - 8)
So the equation of the line representing the number of customers served per hour is:
y = 75x - 450
Where y is the number of customers served and x is the number of hours.
To learn more about point-slope form
visit; brainly.com/question/29054476
#SPJ4
reduce these to the simplest terms
Answers
Answer:
16. 1/2
17. 3/4
18. 1/3
19. 1/4
20. 2/3
21. 1/7
22. 1/4
23. 1/7
Answer:
16. 1/2 or 1 over 2
17. 3/4 or 3 over 4
18. 1/3 or 1 over 3
19. 1/4 of 1 over 4
20. 2/3 or 2 over 3
21. 1/7 or 1 over 7
22. 1/4 or 1 over 4
23. 1/7 or 1 over 7
Please Brainliest would be much appreciated
Company XYZ know that replacement times for the portable MP3 players it produces are normally distributed with a mean of 3 years and a standard deviation of 0. 9 years. Find the probability that a randomly selected portable MP3 player will have a replacement time less than 1. 3 years? PlX < 1. 3 years) =. 0294 Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or Z-scores rounded to 3 decimal places are accepted. If the company wants to provide a warranty so that only 2. 6% of the portable MP3 players will be replaced before the warranty expires, what is the time length of the warranty? warranty = years Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z- scores rounded to 3 decimal places are accepted
Answers
The company needs to provide a warranty of 1.3 years so that only 2.6% of the portable MP3 players will be replaced before the warranty expires.
To find the probability that a randomly selected portable MP3 player will have a replacement time less than 1.3 years, we need to standardize the value using the z-score formula:
z = (X - μ) / σ
where X is the replacement time we're interested in, μ is the mean replacement time of 3 years, and σ is the standard deviation of 0.9 years.
Plugging in the values, we get:
z = (1.3 - 3) / 0.9 = -1.7778
Using a standard normal distribution table or calculator, we can find that the probability corresponding to this z-score is 0.0384. Round this to 4 decimal places, we get 0.0384.
Therefore, the probability that a randomly selected portable MP3 player will have a replacement time less than 1.3 years is approximately 0.0384.
Now, let's find the time length of the warranty that the company needs to provide so that only 2.6% of the portable MP3 players will be replaced before the warranty expires. We need to find the replacement time X such that the area to the left of X under the standard normal curve is 0.026.
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to this area is -1.96 (rounded to 2 decimal places).
So we have:
-1.96 = (X - 3) / 0.9
Solving for X, we get:
X = -1.96 * 0.9 + 3 = 1.2664
Rounding this to 1 decimal place, we get the warranty time to be 1.3 years.
Therefore, the company needs to provide a warranty of 1.3 years so that only 2.6% of the portable MP3 players will be replaced before the warranty expires.
Learn more abou warranty here:
https://brainly.com/question/9575286
#SPJ11
Lef f(x,y) be a function of two variables with f
x
(2−,10)=f
y
(20,10)=0. Suppose f
xx
(20,10)=−2,f
yy
(20,10)=−5 and f
xy
(20,10)=3. Find out if the point (20,10) is a critical point and if so classify it. Clearly show how you got your answer. (5)
Answers
Given a function f(x,y) of two variables with the point (20,10) is a critical point, but it is not a local extremum.
According to the given information:
f(x = 20,y = 10)Let f_x(x,y) and f_y(x,y) be the partial derivatives of f(x,y) with respect to x and y, respectively.
\(f_x(x,y) = f(x,y)\\dx/dt|_y=yf_y(x,y) \\\= f(x,y)dy/dt|_x=xAt (x=20,y=10), f_x(20,10) = 0, \\f_y(20,10) = 0.\)
Thus, (20,10) is a critical point of f(x,y) or stationary point. Now, let f_xx, f_yy, and f_xy be the second-order partial derivatives of f(x,y) at (x,y).f_xx(x,y) = d^2f/dx^2|_y=yf_yy(x,y) = d^2f/dy^2|_x=xf_xy(x,y) = d^2f/dxdy|_x=xf_xx(20,10) = -2, f_yy(20,10) = -5 and f_xy(20,10) = 3. The Hessian matrix of f at (20,10) is given by:
Hessian(f)(20,10) = \([f_xx(20,10) f_xy(20,10); f_xy(20,10) f_yy(20,10)] = [-2 3; 3 -5]\)
The discriminant of the Hessian matrix is given by \(D = f_xx(x,y)f_yy(x,y) - f_xy(x,y)^2\)
Here, D = (-2)(-5) - (3)^2 = 4 > 0Since D > 0 and f_xx(20,10) < 0, the point (20,10) is a saddle point. Therefore, the point (20,10) is a critical point but it is not a local extremum.
Hence, the answer is: Yes, the point (20,10) is a critical point, but it is not a local extremum.
To know more about critical points, visit:
https://brainly.com/question/32077588
#SPJ11
Pls help fast stuck on the last question and it’s due soon:(
