Solve each inequality and graph the solution on a number line.
a. x² - 2x 15 < 0
b. |3x-2| ≥ 10
The solution of the given inequalities is given below:
a. x < 5 or x < -3
b. x ≥ 4
What is the solution of an inequality?The solution of an inequality is the value that will make the inequality true.
The solution of the given inequalities is determined as follows:
a. x² - 2x - 15 < 0
x² - 5x + 3x - 15 < 0
x(x - 5) + 3(x - 5) < 0
x - 5 < 0
x < 5
or
x + 3 < 0
x < -3
b. |3x-2| ≥ 10
3x - 2 ≥ 10
3x ≥ 10 + 2
3x ≥ 12
x ≥ 4
The solutions are shown in the number lines attached.
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the weight of football players is normally distributed with a mean of 220 pounds and a standard deviation of 15 pounds. what is the minimum weight of the middle 95% of the players?
The minimum weight of the middle 95% of the players are 151 pounds.
The question is asking for the lower bound of the 95% two tailed Confidence interval of the normally distributed population.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
95% of C.I. is given by 220 + or - 1.96(15)
= 200 + or - 29 = (191)
Two standard deviations is =2×15=30 pounds
Minimum Weight =220−29 = 191 pounds
Therefore, the minimum weight of the middle 95% of players is 191 pounds.
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a bagel factory produced 90 bags of bagels. there were 10 bagels in each bag. how many bagels did the factory produce?
Answer:
900
Step-by-step explanation:
90 x 10
if thieves were to steal platinum from a bank using a small truck with a maximum payload capacity of 700 lb , how many 1 l bars of the metal could they take?
The thieves could take approximately 1555 bars of platinum.
Pt stands for platinum, an atomic number 78 chemical element. It is a thick, malleable, ductile, very inert, silvery-white-colored transition metal. Its name comes from the Spanish diminutive platina, meaning "silver"
One 1 lb bar of platinum has a volume of approximately 0.11 cubic feet. Assuming the density of platinum to be approximately 21 g/cm^3, the weight of 1 lb bar of platinum is approximately 0.45 kg. The maximum payload capacity of the small truck is approximately 317 kg. Hence, the thieves could take approximately 700 / 0.45 = 1555 bars of platinum.
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Part of the population of 6,000 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 7 of them are infected. How many elk are likely to be infected?
Answer: The number of elk that are likely to be infected can be estimated using the sample proportion of infected elk. The sample proportion is the ratio of the number of infected elk in the sample to the total number of elk in the sample.
In this case, the sample proportion is:
7/50 = 0.14
This proportion can be used to estimate the proportion of the entire population of elk that is infected. To do this, we can multiply the sample proportion by the total population of elk and round to the nearest whole number.
0.14 * 6,000 = 840
So, it's likely that 840 elk are infected.
Please note that this is an estimate and the actual number of infected elk could be different. Additionally, this estimation is based on a random sample, so it can have a margin of error.
Step-by-step explanation:
1
2
2
y=1/30
y=3(4)
d
(3) *
LO
Which function is graphed below?
5
6
6
.CO...
8
X
7
8
9
10
TIME REMAIN
45:49
In a connection that is represented by an exponential function, the independent variable's proportional change is unchanged with a constant change in the independent variable.
Explain about the exponential function?Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.
When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.
After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The fundamental exponential function generally has the shape,
y = nakx-------
(0,3) is the function's y intercept.
This location has to satisfy the equation (1). So let's substitute in order to get,
3 = na k(0)
⇒ 3 = n x a 0
⇒ 3 = n x 1
⇒ n = 3
Our equation 1 now changes.
y = nakx-------
Noting that the graph crosses through,(1 ,1) it must also satisfy its equation because it does so. Equation (2) can be solved by substituting this point, giving us
1 = 3ak (1)
⇒ 1/3 = ak
Now let's enter the value of ak = 1/3 into equation (3) to get,
y = 3(1/3)x
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Derek wants to withdraw $10,418. 00 from his account 3. 00 years from today and $12,440. 00 from his account 13. 00
years from today. He currently has $2,040. 00 in the account. How much must he deposit each year for the next 13. 0
years? Assume a 6. 05% interest rate. His account must equal zero by year 13. 0 but may be negative prior to that.
As per the concept of compounding interest, the amount he deposited on each year is $471.55
Compounding interest in math is the term defined as the interest on a deposit calculated based on both the initial principal and the accumulated interest from previous periods.
Here we know that the final amount is 12,400.00 and the time period is 13 years and interest rate is 6.05%.
Here we have identified that the compounding frequency is monthly basis.
Then the amount is calculated by using the compound interest formula
A = P(1 + r/n)ⁿˣ
Here we have to convert R as a percent to r as a decimal
r = R/100
r = 6.05/100
r = 0.0605 per year,
Now we have to solve the equation for P
P = A / (1 + r/n)ⁿˣ
P = 12,400.00 / (1 + 0.0605/12)⁽¹²ˣ¹³⁾
P = 12,400.00 / (1 + 0.0050416666666667)¹⁵⁶
P = $5,658.58
Here we know that the principal amount for one year for each month the amount is calculated as,
=> 5,658.58/12 = 471.55
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s) x²-2xy; (Formula)
Factor out x from the expression
answer : x×(x-2y)
a phlebotomist draws the blood of a random sample would this data be considered qualitative or quanitative
This data will be considered as Qualitative sample.
Qualitative data is the data that is not represented by numbers, On the other hand, the quantitative data is represented by numbers and it is classified as discrete and continuous.
Qualitative sample
In qualitative research, only a sample of a population is selected for any given study. The study's research objectives and the characteristics of the study population determine which and how many people to select.
Quantitative sample
The quantitative research sampling method is the process of selecting representable units from a large population. Quantitative research refers to the analysis wherein mathematical, statistical, or computational method is used for studying the measurable or quantifiable dataset.
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Was told to solve in pairs, not much information was given.
The solution to the first system of equations is given as follows:
(0, -0.6).
The solution to the second system of equations is given as follows:
(0.64, 1.18).
How to solve the system of equations?The first system of equations is given as follows:
7x - 10y = 6.14x - 5y = 3.Multiplying the first equation by -2, the system is given as follows:
-14x + 20y = -12.14x - 5y = 3.Adding the two equations, the solution for y is given as follows:
15y = -9
y = -9/15
y = -0.6.
Hence the solution for x is of:
7x - 10(-0.6) = 6
7x + 6 = 6
x = 0.
The second system of equations is given as follows:
2x + 6y = 9.-3x + 5y = 4.Multiplying the first equation by 3 and the second by 2, we have that:
6x + 12y = 18.-6x + 10y = 8.Adding them, the solution for y is obtained as follows:
22y = 26
y = 26/22
y = 1.18.
The solution for x is of:
6x + 12(1.18) = 18
x = (18 - 12 x 1.18)/6
x = 0.64.
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1. Cindy is doing a 30-day jumping jack challenge. On the first day she does 5 jumping jacks. On the second
day, she does 10 jumping jacks. On the third day, she does 15 jumping jacks. This pattern continues.
a. Let j(n) represent the number of jumping jacks Cindy does on the nth day of the challenge. Is j(n)
a linear function, a quadratic function, or neither? Explain.
Timear because w goes up by 5 each day.
b. Let t(n) represent the total number of jumping jacks Cindy has done by the nth day of the
challenge. Is t(n) a linear function, a quadratic function, or neither? Explain.
Answer:
a) linear function
b) quadratic function
Step-by-step explanation:
a) j(n) is a linear function since 5 is added everyday.
b) t(n) would be a quadratic function because the total amount of jumping jacks wouldn't have the same number that is beiung added.
day 1 = 5
day 2 = 15
day 3 = 30
day 4 = 50
day 5 = 75
This is showing that at first 10 jumping jacks are added but then for day 2 15 are added, for day 3 20 are added and so on.
A house on the market was valued at $274,000. After several years, the value decreased by 17%. By how much did the house's value decrease in dollars? What
is the current value of the house?
Answer:
The house's value decreased by $46580
The current value of the house is $227420
Step-by-step explanation:
How much did the house's value decrease in dollars?
17% = 0.17
$274,000 x 0.17 = $46580
So, the house's value decreased by $46580
What is the current value of the house?
$274,000 - $46580 = $227420
So, the current value of the house is $227420
simplify the expression 4^2(3-1/2)-121
Answer: its -81
hope this helps
a water system of 2 in. (inside diameter) pipe, having a length of 1 4 mile, is to be flushed with a volume of water equal to twice that contained in the system. how much water (gallons) must be flushed through the system?
To flush twice the volume of water contained in the system, you would need to flush 18.2 gallons x 2 = 36.4 gallons of water through the system.
Calculate the volume of waterTo calculate the volume of water contained in the system, you would use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the pipe (half the diameter), h is the length of the pipe, and π is approximately 3.14.
In this case, the radius of the pipe is 2 inches / 2 = 1 inch, and the length of the pipe is 1/4 mile = 1320 feet (since there are 5280 feet in a mile).So the volume of the pipe is: V = πr^2h = 3.14 x (1 inch)^2 x 1320 feet = 4201.6 cubic inches.Since there are 231 cubic inches in a gallon, the number of gallons of water in the pipe is: 4201.6 cubic inches / 231 cubic inches/gallon = 18.2 gallons.To flush twice the volume of water contained in the system, you would need to flush 18.2 gallons x 2 = 36.4 gallons of water through the system.Learn more about the volume of water here:
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When Damian runs the 400 meter dash, his finishing times are normally distributed
with a mean of 60 seconds and a standard deviation of 1 second. Using the empirical
rule, determine the interval of times that represents the middle 99. 7% of his finishing
times in the 400 meter race.
The interval of times that represents the middle 99. 7% of his finishing
times in the 400 meter race = (57, 63)
We know that the empirical rule or 68-95-99.7 rule states that for a normal distribution, 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
Here, mean (μ) = 60 seconds, standard deviation (σ) = 1 second
To determine the interval of times that represents the middle 99. 7% of his finishing times in the 400 meter race.
the 99.7% are within three standard deviations would be,
μ ± 3σ
= (60 - 3(1), 60 + 3(1))
= (57, 63)
The required interval is: (57, 63)
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how do i graph y<6, dont understand it at allllllll
Answer: Image attached below
Simply draw a dashed line at 6 and shade below the line
Inequalities are relationships between numbers or expressions that show whether a value is greater, less, or equal to another value.
Graph of y = 6
The first step of graphing any inequality is to graph it as though it were an equation. So, first graph the line y = 6. This line is a horizontal line at the y-value 6.
Then, go back to the inequality. The inequality states that y is less than 6. Since there is no "or equal to" sign, the line should be dotted. If there were an "or equal to" sign, then the line should have been solid. This is because the solutions to the inequality do not include 6.
Shading
Whenever you graph an inequality, the portion of the graph that satisfies the inequality should be shaded. In this case, the inequality is looking for all y-values less than 6. So, the portion of the graph under the line should be shaded in.
1. Consider the surface area of the following pyramid. (a) Calculate the total surface area of the pyramid. Show your work. (b) Calculate the lateral surface area of the pyramid. Show your work. Answer:
(a) The Total Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height + Base area
(b) The Lateral Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height
A pyramid's surface area is a measurement of the entire area occupied by all of its faces. Check out the pyramid shown below to view all of its faces as well as its peak, altitude, slant height, and base.
The whole area of a pyramid's faces makes up its surface area. There are two different types of surface areas in a pyramid: the total surface area(TSA) and the lateral surface area (LSA).
(a) The total surface area of the pyramid is measured as:
The Total Surface Area of a pyramid = lateral surface area of pyramid + Base area
The Total Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height + Base area
(b) The lateral surface area of the pyramid is measured as:
The Lateral Surface Area of a pyramid = The total area of the pyramid's side faces (triangles)
The Lateral Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height
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Translate the following statement to a symbolic representation. Papa Smurf is green or the Snorks use clams as money
The symbolic representation is pUq
Symbolic representation is defined as the representation of a principal, a nation for example, through a symbol, such as a flag, that evokes particular meanings and emotions about the nation
Papa Smurf is green or the Snorks use clams as money
let's suppose p = Papa Smurf is green
or q = Snorks use clams as money
here and logic is used in between Papa Smurf being green or the Snorks using clams as money
Or logic is represented by "U".
pUq will be the correct answer.
NOTE- a symbolic representation of Or is U.
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Select ALL of the expressions that are equivalent to
3. 5 - (4. 7).
(Select all that apply. )
4. 7 - (3. 5)
-4. 7 + 3. 5
3. 5 +4. 7
3. 5 - (-4. 7)
3. 5+ (-4. 7)
The All the expressions that are equivalent to "3.5 - (4.7)" are (b) -4.7 + 3.5 and (e) 3.5+ (-4.7) .
to find the equivalent expressions , we solve the expressions :
the main expression is 3.5 - (4.7) = -1.2 ;
Simplifying the expressions :
(a) 4.7 - (3.5) = 1.2 False
(b) -4.7 + 3.5 = -1.2 True
(c) 3.5 + 4.7 = 8.2 False
(d) 3.5 - (-4.7) = 3.5 + 4.7 = 8.2 False
(e) 3.5 +(-4.7) = 3.5 - 4.7 = -1.2 True
So , the only value of the expressions that matches with the main expressions are (b) -4.7 + 3.5 and (e) 3.5+ (-4.7) .
The given question is incomplete , the complete question is
Select ALL of the expressions that are equivalent to "3. 5 - (4. 7)"
(Select all that apply. )
(a) 4.7 - (3.5)
(b) -4.7 + 3.5
(c) 3.5 +4.7
(d) 3.5 - (-4.7)
(e) 3.5 + (-4.7)
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In circle T with m \angle STU= 94m∠STU=94 and ST=17ST=17 units, find the length of arc SU. Round to the nearest hundredth.
The length of the arc SU is given by 1.63978 units.
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: The angle ∠STU=94 and ST=17
Thus ST forms the radius of the circle.
Now we know the angle subtended by the arc is given by
SU=2πr×94°/360
=2×3.14×0.2611
=1.63978 units
Hence, The length of the arc SU is given by 1.63978 units.
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Which mechanic will charge less for a 50-hour repair?
The mechanic that would charge less for a 50-hour repair is Mechanic A.
What is the point-slope form?Mathematically, the point-slope form of any straight line can be modeled by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the points.For the table for Mechanic B, an equation which represent its data points is given by:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 300 = (600 - 300)/(20 - 10)(x - 10)
y - 300 = 300/10(x - 10)
y = 30x - 300 + 300
y = 30x.
When x = 50 hours, the charges for Mechanic A is given by:
y = 25x + 100
y = 25(50) + 100
y = $1,350
When x = 50 hours, the charges for Mechanic B is given by:
y = 30x
y = 30(50)
y = $1,500
In conclusion, we can logically deduce that Mechanic B charges a higher fee than Mechanic A.
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Find the measure of each angle indicated.
Answer:
The answer is
[tex]48[/tex]
Step-by-step explanation:
Greetings!!
N.B
Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Thus,
[tex]50 + 82 + x = 180 \\ 132 + z= 180 \\x = 180 - 13 \\ x = 48[/tex]
Hope it helps!!!
A sofa is on sale for 60% off. The sale price is $184.
What is the regular price?
Answer:
$460
Step-by-step explanation:
Let the regular price of the sofa be $PWe are given that the sales discount is 60% Convert 60% to decimal => 60/100 = 0.6So discount in $ terms = P x 0.60 = 0.6PSale price = Regular price - Discount = P(1 - 0.6P) = P(0.4) = 0.4PTherefore the regular price of the sofa is $460
bryce and alejandro hiked miles. In one day, dominic hiked times as far as bryce and alejandro hiked. How far did he hike?
We can write the expression as →
{z} = n{x + y}
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Bryce, Alejandro and Dominic went for hiking.
Assume that Bryce and Alejandro travelled {x} and {y} miles respectively.
Assume that Dominic hiked {z} miles and {n} times as far as Bryce and
Alejandro hiked.
We can write the expression as -
z = n{x + y}
Therefore, we can write the expression as →
{z} = n{x + y}
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A miner is working 184 feet below the surface of the earth. He climbs 53 feet to get a tool and then descends 168 feet. Write his current elevation as an integer, relative to the earth's surface.
Answer:
-299 ft
Step-by-step explanation:
Start: -184 ft
Climb: + 53 ft
Descent: - 168 ft
-184 ft + 53 ft - 168 ft = -299 ft
Answer: -299 ft
given a closed box, where the length is twice the height, the width is 10 meters less than the length, and the surface area is 10 times the width times the height, what are the dimensions?
So the dimensions of the box are:
Length: 20m
Width: 10m
Height: 10m
We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.
From the problem, we know:
L = 2H (the length is twice the height)
W = L - 10 (the width is 10 meters less than the length)
2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)
We can substitute the first and second equations into the third one to obtain:
2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)
Solving this equation we get H = 10m
With this value we can solve for the other dimensions:
L = 2H = 2 * 10 = 20m
W = L - 10 = 20 - 10 = 10m
So the dimensions of the box are:
Length: 20m
Width: 10m
Height: 10m
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So the dimensions of the box are:
Length: 20m
Width: 10m
Height: 10m
We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.
From the problem, we know:
L = 2H (the length is twice the height)
W = L - 10 (the width is 10 meters less than the length)
2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)
We can substitute the first and second equations into the third one to obtain:
2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)
Solving this equation we get H = 10m
With this value we can solve for the other dimensions:
L = 2H = 2 * 10 = 20m
W = L - 10 = 20 - 10 = 10m
So the dimensions of the box are:
Length: 20m
Width: 10m
Height: 10m
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a particular person's height oscillates throughout the day with a period of 24 hours. their average height is 170 cm, and their maximum height is 173 cm. at 4 am, their height is 170 cm and increasing. (a) find a possible formula for h(t), their height (in cm) t hours after midnight. (b) find a time when their height equals 169 cm.
The time when h(t) = 169 is 4.13am.
For (a), one possible formula for h(t) is the sinusoidal function, h(t) = Asin(Bt + C) + D, where A is the amplitude (maximum height - minimum height), B is the angular frequency (2 pi/period), C is the phase (starting point), and D is the minimum height. In this case, A = 3, B = 2pi/24, C = 0, and D = 170. Therefore, the formula for h(t) is h(t) = 3sin(2pit/24) + 170.
For (b), we need to solve for t when h(t) = 169. We can rearrange the equation to 3sin(2pit/24) = -1 and solve for t. Using a calculator, we can find that t = 8.21 hours. As 8.21 hours after midnight is 4.13am, the time when h(t) = 169 is 4.13am.
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The _____-coordinates of the endpoints are the same.?
The x-coordinates of the endpoints are the same.
What are the coordinates?
Coordinates are a set of numbers that are used to specify the position of a point on a graph or a coordinate plane. The most common type of coordinate system is the Cartesian coordinate system, which uses two perpendicular number lines called the x-axis and the y-axis to define the position of a point.
When talking about coordinates, there are two types of coordinates: x-coordinates and y-coordinates. The x-coordinate refers to the horizontal position of a point on a graph or a coordinate plane, while the y-coordinate refers to the vertical position of the point.
In the statement "The x-coordinates of the endpoints are the same," it means that the horizontal position of the two endpoints is the same. These endpoints could be the two points that define a line segment, a geometric figure, or a graph. The x-coordinates of both of these points are the same, while the y-coordinates could be different.
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The graph of a system of inequalities is shown.
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 6, negative 1) and (0, negative 4). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 2, negative 4) and (0, 0). Everything to the left of the line is shaded.
Which system is represented by the graph?
Answer:
graphing on a graph
Step-by-step explanation:
An iceberg is situated off the coast of Newfoundland at map coordinates (40,10). A cruise ship is
travelling along the line y=x+40 past the iceberg. Assuming that the cruise ship stays on
course and the iceberg does not drift, how close will the ship get to the iceberg?
The cruise ship will be 70 units (could be nautical miles, kilometers or any other unit) away from the iceberg.
What is the slope intercept?
The slope-intercept form of a linear equation is y = mx + b, where x and y are the coordinates of a point on the line, m is the slope of the line (the steepness of the line), and b is the y-intercept (the point where the line crosses the y-axis).
To determine how close the cruise ship will get to the iceberg, we need to find the point of intersection between the ship's path (y = x + 40) and the location of the iceberg (x = 40, y = 10).
Substituting x = 40 into y = x + 40, we get:
y = 40 + 40
y = 80
So the point of intersection is at (40, 80).
We can then use the distance formula to find the distance between the point of intersection and the location of the iceberg:
d = √((40 - 40)^2 + (80 - 10)^2)
d = √((0)^2 + (70)^2)
d = 70
So the cruise ship will be 70 units (could be nautical miles, kilometers or any other unit) away from the iceberg.
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