The slope formula to calculate the slope of the ocean floor would be
[tex]slope = \frac{y}{x}[/tex].
What is slope?
The slope of a line characterizes its direction.
To find the slope of the ocean floor, we need to calculate the rise (change in depth) and the run (distance along the ocean floor) between the edge of the continental shelf and the beginning of the oceanic crust.
Let's call the depth of the water at the edge of the continental shelf "d1" and the depth of the water at the beginning of the oceanic crust "d2". Then, the rise is:
rise = d2 - d1
We don't have the actual values for d1 and d2, so let's call the rise "y" and the run "x". Then, the slope of the ocean floor is given by:
[tex]slope =\frac{rise}{run} \\\\slope = \frac{y}{x}[/tex]
So, we can use the slope formula to calculate the slope of the ocean floor.
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The diagram shows a circle with centre O.
A, B & C lie on the circumference of this circle.
Given that AC is a diameter of the circle and ∠BCA = 5 × ∠BAC, find the size of ∠BCA as highlighted in the diagram.
Answer:
∠ BCA = 75°
Step-by-step explanation:
∠ ABC = 90° ( angle in a semicircle )
then the 2 remaining angles in Δ ABC = 90° , that is
∠ BAC + ∠ BCA = 90° ( ∠ BCA = 5 × ∠ BAC )
∠ BAC + 5 ∠ BAC = 90°
6 ∠ BAC = 90° ( divide both sides by 6 )
∠ BAC = 15°
Then
∠ BCA = 90° - 15° = 75°
What is the geometric number between 16 and 64.
Hi there, here's your answer:
Geometric mean between 2 numbers a and b: [tex]\sqrt{ab}[/tex]
Therefore, the geometric mean between 16 and 64 will be
[tex]\sqrt{16*64}[/tex] = [tex]\sqrt{1024}[/tex] = 32.
Hope it helps!
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A system of equations has a solution (4, −1). One equation in the system is y=14x−2 . Which could be the second equation for the system?
The required equation in a system of equations that has a solution (4, −1) is given as y = -1/4x.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let's assume that the equation passing through the origin and (4, -1)
The equation is given as,
(y₂ - y₁) / (x₂ - x₁)
y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)
y - 0 = -1 - 0 / 4 - 0 [x - 0]
y = -1/4x
Thus, the required other equation in a system of equations has a solution (4, −1) is given as y = -1/4x.
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Evaluate each expression if a = 9, b = 3
15b + a^2
Answer:
126
Step-by-step explanation:
a=9
b=3
we have
15b+a^2
just substitute the value
15*3+9*9
45+81
126
Answer:
126 is your answer!
Step-by-step explanation:
15 x 3=45
9^2=81
45+81=126
A particle is moving along a spiral path defined by the equation r = a * e^(b * θ), where a and b are constants. Determine the velocity of the particle at a given value of θ.
Step-by-step explanation:
The velocity of the particle at a given value of θ can be found by taking the derivative of the position vector with respect to time:
v(θ) = dr/dt = dr/dθ * dθ/dt = dr/dθ * ω
where ω is the angular velocity and dr/dθ is the derivative of the position vector with respect to θ.
The position vector r = a * e^(b * θ) * i + a * b * e^(b * θ) * j
Taking the derivative with respect to θ:
dr/dθ = a * b * e^(b * θ) * i + a * b^2 * e^(b * θ) * j
So the velocity of the particle is given by:
v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * j
Answer:
Step-by-step explanation:
v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * jj
when looking to invest money in a company by purchasing stock why is it important to look at many companies to invest
Evaluating multiple companies before making an investment decision helps to make informed decisions, diversify your portfolio, and maximize returns.
It is critical to consider multiple companies before investing because:
Diversification reduces the risk of loss because the performance of one company does not determine the overall performance of your portfolio.
Opportunity Cost: Comparing and selecting the best investment options allows you to avoid missing out on potential higher returns by evaluating multiple companies.
Due Diligence: Investing in a company necessitates extensive research and due diligence. When you look at multiple companies, you can compare financial statements, management, products, and other factors that can affect stock performance.
Finally, evaluating multiple companies prior to making an investment decision allows you to make informed decisions, diversify your portfolio, and maximize returns.
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Drag each expression to show whether the expression is equivalent to 24x−48 24 x - 48 , 36x+12 36 x + 12 , or neither.
The equivalent expression 36x + 12 is the same as 24x - 48. Because the statement is identical to itself, the label 24x - 48 fits it.
This equation denotes the result of multiplying 24 by x and then subtracting 48.
The phrase is referred to as "36x + 12" since it is a duplicate of itself. This formula denotes the result of multiplying 36 by x and then adding 12.
The formulations in the two scenarios cannot be compared since they use different coefficients for x and different constant terms. The word "neither" does not apply to either phrase because they are both equal to one another.
Therefore, 36x + 12 is equal to the formula 24x - 48.
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if the divining rod is completely useless for locating water, what is the probability that the expert will correctly identify (by guessing) both of the cans containing water?
a) The sample space for this experiment:
S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }
b) The probability that the expert will correctly identify (by guessing) both of the cans containing water is: 1/6
Probability :Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Now, According to the information:
Let E1 and E2 represent the empty cans and W1 and W2 be the cans filled with water.
S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }
By merely guessing, the events are equally likely. Since there are 6 possible outcomes,
The probability that the expert will correctly identify (by guessing) both of the cans containing water is:
Since there are 6 possible outcomes,
probability = 1/6
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The given question is incomplete, complete question is:
According to Webster’s New Collegiate Dictionary, a divining rod is "a forked rod believed to indicate [divine] the presence of water or minerals by dipping downward when held over a vein." To test the claims of a divining rod expert, skeptics bury four cans in the ground, two empty and two filled with water. The expert is led to the four cans and told that two contain water. He uses the divining rod to test each of the four cans and decide which two contain water. a List the sample space for this experiment. b If the divining rod is completely useless for locating water, what is the probability that the expert will correctly identify (by guessing) both of the cans containing water?
Solve for x
80°
45°
11x
Given two parallel lines. Solve for x.
The value of x, given the parallel lines and the angles involved, can be found to be 12. 3 .
How to find the value of x ?The angles on the parallel lines are drawn such that 11 x and 45 degrees are supplementary angles .
This means that they add up to 180 degrees .
The value of x can therefore be found to be :
11 x + 45 = 180
11 x = 180 - 45
11 x = 135
x = 135 / 11
x = 12. 3
In conclusion, the value of x is 12. 3 .
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The linear equations graphed in the coordinate plane below intersect.
Which coordinate point is the solution?
(0, –7)
(1, 8)
(7, 0)
(8, 1)
The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equations are given below.
y = - 2x + 17 ...1
y = x - 7 ...2
From equations 1 and 2, then we have
x - 7 = - 2x + 17
3x = 24
x = 8
Then the value of 'y' is given as,
y = 8 - 7
y = 1
The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.
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suppose that you randomly draw one card from a standard deck of 52 cards. after writing down which card was drawn, you replace the card, and draw another card. you repeat this process until you have drawn 15 cards in all. what is the probability of drawing at least 7 clubs?
The probability of drawing at least 7 clubs in 15 draws from a standard deck of 52 cards is approximately 0.496.
The number of ways to draw 7 or more clubs in 15 draws can be found by using the cumulative distribution function for the binomial distribution. This distribution models the number of successful outcomes (clubs) in n independent trials (card draws), each with the same probability of success (drawing a club). The cumulative distribution function gives the probability of getting a certain number of successful outcomes or fewer.
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Pathagorean theorum, solve and steps pleaseee
Answer:
14
Step-by-step explanation:
formula
SQURED A+B=C
10+b =18
100+b=324
100-100 324-100
=224
squre root of 224
is 14
Answer this question with work included.
Answer:
12/8 = 1.5 °C per hour
Step-by-step explanation:
basically write the change over time in a formula, calculate it and find the answer, using the answer u can say that:
over the course of 8 hrs, the temperature has been reducing by a rate of 1.5°C/hr. (link it to the context as well)
Let the variable s represent the amount of videos streamed and let the variable c represent the cost.
For how many video streams will the cost be the same for both companies?
Which system of equations can be used to solve this problem?
A. c=40+2*8
c=24*8
B. c=42*8
c=24*
C. c=40*8+2
c=20*8+4
D. c=40*8- 2
c=20-4*8
The system of equations for cost of company A and B is c = 40 + 2s and c = 40 + 4s respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The amount of videos streamed is = s
The cost of streaming each video is = c
The amount of money charged by company A as membership fee is = $40.
The amount of money charged by company A per video stream is = $2.
The equation for cost of company A will be -
c = 40 + 2s
The amount of money charged by company B as membership fee is = $40.
The amount of money charged by company B per video stream is = $4.
The equation for cost of company A will be -
c = 40 + 4s
Therefore, the equations are c = 40 + 2s and c = 40 + 4s.
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Video streaming company A charges a one-time $40 membership fee and $2 per video stream
Video streaming company B charges a one-time $20 membership fee and $4 per video stream.
Let the variable s represent the amount of videos streamed and let the variable c represent the cost
For how many video streams will the cost be the same for both companies?
Which system of equations can be used to solve this problem?
what is the inverse of the function f (x) = 1/3x-5
Identify the figure shown in the front, top, and side views.
Answer: it's C
Step-by-step explanation:
Answer:D
Step-by-step explanation:
Part A
Which account will have a greater value after 10 years?
Account information for two accounts. Account A has principal 16 thousand dollars, annual interest 3 percent, compounded quarterly for number of years equals 10. Account B has principal 16 thousand dollars, annual interest 3 percent, compounded monthly for number of years equals 10.
A. Account A
B. Account B
What will the value of that account be after 10 years?
$
Part B
What type of growth do both accounts model?
A. linear
B. exponential
C. neither
Answer:
Both models are exponential
A: $21,573.58
B: $21,589.58
Step-by-step explanation:
A
f(x) = 16,000[tex](1 + .03/4)^{4(10)}[/tex]
f(x) = (16000)[tex]1.0075^{40}[/tex]
f(x) = $21,573.58 Rounded to the nearest cent.
B
f(x) = 16000[tex](1+ .03/12)^{12(10)}[/tex]
f(x) = (16000)[tex]1.0025^{120}[/tex]
f(x) = $21,589.66 Rounded to the nearest cent
The points (-1, 10) and (-4, 4) fall on a particular line. What is its equation in point-slope
Answer: (−10)=2(+1)
Step-by-step explanation:
How do I solve this, thx!
Answer:
Step-by-step explanation: y=22.5
Using the credit card from question 13,(you have a credit card that has a balance of $3,589.90 and a credit limit of $5,000.) if you have a good credit rating, how much must you pay at the end of the month to get the balance to the acceptable debt ratio percentage
You must pay $2,089.90 at the end of the month to bring the balance to the acceptable debt ratio percentage.
How to determine the amount to payFrom the question, we have the following parameters that can be used in our computation:
Balance = $3589.90
Credit limit = $5000
To determine the acceptable debt ratio percentage, we make use of 30% minimum credit utilization rate.
So, the acceptable balance on the credit card is:
Balance = $5,000 * 30% = $1,500.
Since the current balance is $3,589.90, we have
Payment = $3,589.90 - $1,500
Payment = $2089.9
So, you must pay $2,089.90
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What expression represents the value of y?
Answer:
Second choice:
[tex]\mbox{\large y = \sqrt{wz}}[/tex]
Step-by-step explanation:
Consider the right triangle ABC
By the Pythagorean theorem,
AB² = BC² + AC²
BC = x, AC = (w + x) and AB = v
Plug in above values
(w + z)² = v² + x² (1)
In right triangle BCD,
BC² = BD² + CD²
Plugging in values we get
x² = w² + y² (2)
In right triangle ABD
AB² = BD² + AD²
v² = y² + z² (3)
Plug in values of x² from eq (2) and v² from eq 3 into equation (1) to get
(w + z)² = y² + z² +w² + y²
Left side (w + z)² = w² + 2wz + z²
==> w² + 2wz + z² = y² + z² +w² + y²
w² and z² cancel out since they are on both sides of the equation with same sign
=> 2wz = y²+y²
2wz = 2y²
Divide by 2:
wz = y²
Switch sides:
y² = wz
[tex]\mbox{\large y = \sqrt{wz}}[/tex]
A survey organization conducted telephone interviews in December 2008 in which 1,009 randomly selected adults in the United States responded to the following question: At the present time, do you think television commercials are an effective way to promote a new product?
Yes, television commercials are an effective way to promote a new product.
The survey organization conducted a telephone survey in December 2008 to gauge the effectiveness of television commercials in promoting new products among a sample of 1,009 randomly selected adults in the United States.
The survey asked the respondents whether they believed that television commercials were an effective way to promote a new product at the time of the survey. The results of the survey can provide insights into the public's perception of television commercials as a tool for promoting new products, as well as how this perception may have changed over time.
The findings can also be useful for marketers and advertisers who want to understand consumer attitudes toward television commercials and use this information to guide their advertising strategies. However, it's important to note that the results of this survey are limited to the specific time and population studied and may not be generalizable to other populations or time periods.
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Resolve ax/a+x into an infinite series. Write the first 5 terms. Consider x as the variable. Then, use summation notation to create a formula for the infinite series
The infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.
The infinite series for ax/a+x can be represented as a geometric series. The first five terms can be expressed as:
[tex]Term 1: ax/(a+x)\\Term 2: (ax)^2/(a+x)^2\\Term 3: (ax)^3/(a+x)^3\\Term 4: (ax)^4/(a+x)^4\\Term 5: (ax)^5/(a+x)^5[/tex]
The infinite series can be expressed using summation notation as:
[tex]∑_(n=1)^∞ (ax)^n / (a+x)^n[/tex]
Using the formula for a geometric series, the sum of the infinite series can be calculated as:
[tex]S = ax/(a+x) * 1/(1-ax/(a+x)) \\ = ax/(a+x) * (a+x)/(a-ax) \\ = ax/(a-ax) \\ = a/a-x[/tex]
Therefore, the infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.
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A map has a scale of 1:250 000. How many centimeters on the map is a journey of 40 km?
Answer: I believe its 4.16 centimeters
Step-by-step explanation:
I do not have an explanation, but I hope the answer is correct.
the line through (4, 2) and (1,
7)
Answer:y=-5/3x+26/3
Step-by-step explanation:
2-7/4-1=-5/3
(4,2)
y-2=-5/3(x-4)
y-2=-5/3x+20/3
+2 +2
y=-5/3x+26/3
[tex]y=-\frac{5}{3}x+\frac{26}{3}[/tex]
It passes through the points
A film show lasted for 3 3/2 hours. Out of this ,1 1/3 hours were spent on advertisements. What was the actual duration of the film
3 3/2 hours as a decimal= 4.5
1 1/3 hours as a decimal = 1.3
Duration of the film show = 4.5 hours
Hours spent on advertisements = 1.3 hours
Actual duration of the film = 4.5 - 1.3 hours
= 3.2 hours
3.2 hours as a fraction = 3 1/5 hours.
Therefore, the actual duration of the film was 3 1/5 hours.
Movie lasted 3 hours and 10 minutes
You have to convert 3 3/2 and 1 1/3 to a fraction.You have to multiply 9/2 by 3 and 4/3 by 2 to get the least common multiple of those two numbers.Subtract 8/6 from 27/6 and you get 19/6.Convert 19/6 into a mixed number and you get 3 1/6 which is 3 hours and 10 minutes because the clock has 60 minutes so 1/6 is ten minutes.[tex]3\frac{3}{2} - 1 \frac{1}{3} = \frac{9}{2} - \frac{4}{3} = \frac{27 - 8}{6} = \frac{19}{6} = 3 \: \frac{1}{6} [/tex]
Car X travels 174 miles in 3 hours.
a. Write the equation of the line that describes the relationship between distance and time. Use x for the time in hours and y for the distance in miles.
b. What is the graph that represents the relationship between distance and time for Car X? Explain.
Answer:
Step-by-step explanation:
a. The equation of the line that describes the relationship between distance and time for Car X can be found by using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula: m = (change in y) / (change in x) = (distance traveled) / (time elapsed) = 174 miles / 3 hours = 58 miles per hour.
Since the car starts at time x = 0 and has traveled 174 miles at time x = 3, the y-intercept (b) can be found by setting x = 0 and solving for y: y = 58x + b, and y = 174 when x = 3, so b = 174 - 58(3) = -160.
Putting it all together, we get the equation: y = 58x - 160.
b. The graph that represents the relationship between distance and time for Car X is a line that passes through the point (0, -160) and has a slope of 58. This line represents the linear relationship between the distance traveled and the time elapsed for Car X.
The y-intercept of -160 represents the distance traveled when time is equal to 0. The slope of 58 represents the rate of change of the distance traveled with respect to time. This means that for every hour that passes, Car X travels 58 miles.
solve the equation 3.6=12n
The equivalent value of the equation is n = 0.3
Given data ,
Let the equation be represented as A
Now , the value of A is
3.6 = 12n be equation (1)
On simplifying , we get
Divide by 12 on both sides , we get
n = 3.6 / 12
On further simplification , we get
n = 0.3
Hence , the expression is n = 0.3
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suppose that the length of a certain rectangle is two centimeters more than three times its width. if the area of the rectangle is 33 square centimeters, find its length and width.
The rectangle measures 6 centimetres in width and 18 centimetres in length.
The rectangle's length is two millimetres longer than its width. As a result, the length (L) is equal to 3(W) + 2, where W is the rectangle's width. Additionally, we are aware that the rectangle (A) has a 33 square centimetre area. In order to find W, we can apply the formula A = L x W. 33 = 3W2 + 2W because it is (3(W) + 2) x W. The quadratic equation can be used to find W, which equals 6. This indicates that the rectangle has a width of 6 centimetres and a length of 3(6)+2=18 cm.
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The equation $y=0.5x+3$ represents the cost $y$ (in dollars) of riding in a taxi $x$ miles.
a. Use a graph to estimate how much it costs to ride 5.25 miles in a taxi.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -0.9 to 10.4 with ticks spaced every 1 unit(s).
The vertical axis goes from -0.9 to 10.4 with ticks spaced every 1 unit(s).
Created graph shapes
Line passing through (2, 4) and (0, 3).
MilesCost to ride in taxi (dollars)
Question 2
It costs about $
.
Question 3
b. Use the equation to find exactly how much it costs to ride 5.25 miles in a taxi.
It costs exactly $
.
The cost to ride 5.25 miles in a taxi is, $5.63.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
The equation represents the cost y (in dollars) of riding in a taxi x miles is,
⇒ y = 0.5x + 3
Hence, The cost to ride 5.25 miles in a taxi is,
⇒ y = 0.5x + 3
Substitute x = 5.25 in above equation,
⇒ y = 0.5 × 5.25 + 3
⇒ y = 2.63 + 3
⇒ y = $5.63
Thus, The cost to ride 5.25 miles in a taxi is, $5.63.
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