The possible outcomes for each of the given events are:
A --> {1, 3, 5}
B --> {4, 5, 6}
How to find the outcomes for each event?For a regular number cube, the sample space (possible outcomes) is:
S = {1, 2, 3, 4, 5, 6}
Now we have two events.
A = rolling an odd number
Here the outcomes can be any of the odd numbers in the sample space, so the possible outcomes are:
A --> {1, 3, 5}
The second event is:
B = the number rolled is greater than 3. Again, the outcomes are thevalues in the sample space that are larger than 3, these are:
B --> {4, 5, 6}
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my bike tire has a radius of 12 inches how much distance will i cover after 50 rotations
Therefore , the solution of the given problem of unitary method comes out to be 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).
What is a unitary method?The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.
Here,
The circumference of the circle the bike tyre forms is equal to the distance travelled in one rotation of the tyre. The following formula determines a circle's circumference:
=> C = 2πr
where the mathematical constant is roughly equivalent to 3.14159 and r is the circle's radius.
Your bicycle tyre's radius in this instance is 12 inches. The tyre's circumference is as follows:
=> C = 2π(12) = 24π inches
You may easily calculate how far you will travel after 50 spins by multiplying the tyre's circumference by the number of turns:
=> Covered distance: 50 × 24π ≈ 376.99 inches
As a result, after 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).
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nueve números son escritos en orden ascendente, el número de en medio es el promedio de todos los números, el promedio de los cinco números más grande es 68 y el promedio de los cinco más pequeños es 44 ¿Cuál es la suma de todos los números?
a) 112
b) 504
c) 144
d) 560
e) 122
The sum of all the number is found to be 630 which is not given in the options.
Let the middle number be x. Then the five numbers smaller than x have an average of 44, so their sum is 544 = 220. Similarly, the five numbers larger than x have an average of 68, so their sum is 568 = 340.
The total of all the numbers is 9x since x is the median and average of all the numbers. The total of all the numbers equals 9x since we know that x is the average of all the numbers.
Therefore, we have,
9x = 220 + x + 340
Simplifying and solving for x, we get,
8x = 560
x = 70
Therefore, the sum of all the numbers is 9x = 970 = 630.
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Complete question - Nine numbers are written in ascending order, the middle number is the average of all the numbers, the average of the five largest numbers is 68, and the average of the five smallest is 44. What is the sum of all the numbers? ?
a) 112
b) 504
c) 144
d) 560
d) 122
Ned has 55 marbles in his collection. He has twice as many white marbles as red marbles. He has five more blue marbles than white marbles. How many white marbles does Ned have?
Answer:
Ned has 20 white marbles.
Step-by-step explanation:
Let's call the number of red marbles "r".
We know that Ned has twice as many white marbles as red marbles, so the number of white marbles would be 2r.
We also know that he has five more blue marbles than white marbles, so the number of blue marbles would be 2r + 5.
The total number of marbles in Ned's collection is 55, so:
r + 2r + (2r + 5) = 55
Simplifying this equation, we get:
5r + 5 = 55
Subtracting 5 from both sides:
5r = 50
Dividing by 5:
r = 10
So Ned has 10 red marbles.
We can use this to find the number of white marbles:
2r = 2(10) = 20
So Ned has 20 white marbles.
The average speed of a volleyball serve is 58 miles per hour. Natalie practiced a new technique to improve her serving speed. Her coach recorded the speed of 41 random serves during practice and found that her average speed using the new technique was 59 miles per hour, with a standard deviation of 2.7 miles per hour.
Part A: State the correct hypotheses if Natalie is trying to prove the new technique is an improvement over the old technique. (2 points)
Part B: Identify the correct test and check the appropriate conditions. (4 points) .
Part C: Carry out the test and determine if there is sufficient evidence at the 0.05 level that Natalie's technique has improved her serve speed. (4 points)
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 16.2
Step-by-step explanation:
Using trig functions:
cos theta = adjacent side/ hypotenuse
cos 72 = 5/x
Solving for x
x = 5 /cos 72
x=16.18033
Rounding to the nearest tenth
x = 16.2
Answer: x = 16.2 units
Step-by-step explanation:
We are given an angle (72°), the adjacent side (5), and the hypotenuse (x). We will use the cosine function to solve.
cos(θ) = [tex]\frac{adjacent}{hypotenuse }[/tex]
cos(72°) = [tex]\frac{5}{x }[/tex]
xcos(72°) = 5
x = [tex]\frac{5}{cos(72\°)}[/tex]
x = 16.1803398 ≈ 16.2
The approximate number of zombies in a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Hours Since Zombies First Spotted, x
1
2
3
4
Approximate Number of Zombies, f(x)
24
56
88
122
function would best fit the data because as x increases, the y values change
. Rounded to the nearest .5, the
of this function is approximately
A linear function would be the best fit for the given data because as x increase the y-values change linearly.
Rounded to the .5 the slope of the function is approximately 32.5
Which type of function models the population?A linear relation means that any increase of 1 unit in the independent variable (x) has always the same impact in the other variable (y).
In this particular case, the increases in the y-value are:
56 - 24 = 32
88 - 56 = 32
122 - 88 = 34
The mean of that, rounded to .5, is (32 + 32 + 34)/3 = 32.5
So the change is almost the same one, then this seems to be a linear relation.
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Ellie and her older brother, Shawn, just got new phones! Both phones are shaped like rectangular prisms that are 3/4 of a centimeter tall. Ellie went with the smaller model that is 12 centimeters long and 6 centimeters wide, while Shawn went with the larger model that is 15 centimeters long and 8 centimeters wide. How many cubic centimeters larger is Shawn's phone than Ellie's?
Shawn's phone is 36 cubic cm larger than Ellie's phone.
How many cubic cm larger is Shawn's phone?To get difference in volume between the two phones, we must calculate volume of each phone and subtract the volume of Ellie's phone from the volume of Shawn's phone.
The volume of a rectangular prism is: length*width* height. The height of both phones is 3/4 centimeters.
The volume of Ellie's phone is:
= length x width x height
= 12 cm x 6 cm x (3/4) cm
= 54 cubic centimeters
The volume of Shawn's phone is:
= length x width x height
= 15 cm x 8 cm x (3/4) cm
= 90 cubic centimeters
The difference in volume is:
= Volume of Shawn's phone - Volume of Ellie's phone
= 90 cubic centimeters - 54 cubic centimeters
= 36 cubic centimeters
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in the diagram below A, B, C are points in the same horizontal plane with AC =BC=22.3 meters.AD is a vertical tower which is anchored at B and C.The angle of elevation of D from B is 25.4. BDC=58.6 and ACB= 50.8.
The length of AB is 27.3m and AD is 113 m.
Using Trigonometry in Triangle ABC
tan 50. 8 = P / B
tan 50.8 = AB / 22.3
1.2261 = AB/ 22.3
AB = 27.34 m
Now, again using Trigonometry
tan 25.4 = P / B
tan 50.8 = AD / 27.34
0.474 = AD/ 27.34
AD = 12.95916 m
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
A. Using the formula for area of rectangle, the length of the rectangular space is: 2x - 3
B. The expression to prove this is: (2x - 3) * 4x = 8x² - 12x
What is the Area of a Rectangle?To find the area of a rectangle, multiply the width and the length together. This means: Area = length * width.
Part A: We are given that area of the rectangular space is expressed as 8x² - 12x, if the width is 4x, then:
Length of the rectangular space = (8x² - 12x) / 4x = 4x(2x - 3)/4x
Length = 2x - 3
Part B: To prove this, we have:
length * width = 8x² - 12x
Substitute:
(2x - 3) * 4x = 8x² - 12x
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Solve and check: 3/4h+11=20 helpp!
Answer: 12
Step-by-step explanation:
We have to find h so the first step is to subtract the 11 from the 20
3/4h=9
Then to move the 3/4 over to the other side, you must multiply it by it's reciprocal, 4/3.
h= 4/3 x 9
This equals 12.
ACTIVITY 1: Find f−1 in each of the following.
The [tex]f^{-1}[/tex] inverse of f of each
1) (x + 1)/2
2) [tex]\sqrt{\frac{x+1}{4} } \\[/tex]
3) 3 - 4x
4) [tex](x+5)^{1/3}[/tex]
5) [tex]\sqrt{x + 4}[/tex]
1) function f(x) = 3x + 1
let f(x) = y
y = 3x + 1
y - 1 = 3x
(y - 1)/3 = x
x obtained is [tex]f^{-1}[/tex]
and y will be x
[tex]f^{-1}[/tex] = (x-1)/3
2) equation f(x) = 4x² - 1
let f(x) = y
y = 4x² - 1
y + 1 = 4x²
(y + 1 )/4 = x²
x = [tex]\sqrt{\frac{x + 1}{4} }[/tex]
x obtained is [tex]f^{-1}[/tex]
and y will be x
[tex]f^{-1}[/tex] = [tex]\sqrt{\frac{x + 1}{4} }[/tex]
similarly,
3) f(x) = 3-x/4
y = 3-x/4
4y = 3 - x
x = 3 - 4x
[tex]f^{-1}[/tex] = 3- 4x
4) y = x³ - 5
y + 5 = x³
x = [tex](y + 5)^{1/3}[/tex]
[tex]f^{-1}[/tex] = [tex](x+5)^{1/3}[/tex]
5) y = x² - 4
y + 4 = x²
x = √y + 4
[tex]f^{-1} = \sqrt{x + 4}[/tex]
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Suppose that you were 24 inches long at birth and 4 feet tall on your tenth birthday. Based on these two data points, create a linear equation for the function that describes how height varies with age. Use the equation to predict the height at age 9 and 31
An equation for this linear function that describes how height varies with age is y = 1/5(x) + 2.
The predicted height at 9 is 3.8 feet.
The predicted height at 31 is 8.2 feet.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Conversion:
1 feet = 12 inches
24 inches = 24/12 = 2 feet.
Next, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 2)/(10 - 0)
Slope (m) = 2/10
Slope (m) = 1/5
At data point (0, 2) and a slope of 1/5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 1/5(x - 0)
y = 1/5(x) + 2
When x = 9, the predicted height is given by;
y = 1/5(9) + 2
y = 3.8 feet.
When x = 31, the predicted height is given by;
y = 1/5(31) + 2
y = 8.2 feet.
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A sum of money raised in a show was distributed to Charities A, B and C. Charity A received of the total amount Charities B and C received. Charity C received of the otal amount Charities A and B received. a) What fraction of the total amount of money did Charity B receive? p) Charity B received $88 000. How much money was raised in the show? a)
The total money raised is (15/7) * $88,000 = $188,571.43.
How to solvea) Let x be the total amount raised.
Charity A received (1/3)(x - A), Charity C received (1/4)(x - C). We have A = (1/3)(B+C) and C = (1/4)(A+B).
Solving these equations, we find B's share to be 7/15 of the total amount.
p) Since Charity B received $88,000, which is 7/15 of the total amount, the total money raised is (15/7) * $88,000 = $188,571.43.
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Can someone help pleaseeee
The result of the row 1 multiplication by 1/4 is determined as [¹/₂ 0 ].
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [2 0]
To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;
[2 0] x 1/4 = 1/4(2 0)
= [¹/₂ 0 ]
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that is 2, and 0 by 1/4.
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At 9 15 , a van left Blossom Village for River Town at an average speed of 50 Km/h. Half an
hour later, a car passed Blossom Village heading towards River Town along the same route
at an average speed of 60 Km/h.
A) At what time would the car catch up with the van?
B) If the car reached River Town at 15 45, what was the distance between the two towns?
Answer: A) Let's first calculate how far the van would have traveled in the half hour before the car started. The van's speed is 50 km/h, which means in half an hour it would have traveled 50/2 = 25 km.
Now let's consider the time it takes for the car to catch up to the van. We can represent this using the formula:
distance = rate × time
Let's call the time it takes for the car to catch up "t". We know that during this time, the van is also traveling. In fact, it has been traveling for t + 0.5 hours (the half hour before the car started plus the time it takes for the car to catch up). So the distance the van has traveled is:
distance van = 50 × (t + 0.5)
The distance the car has traveled is:
distance car = 60t
When the car catches up to the van, they will have traveled the same distance. So we can set the two distances equal to each other:
50(t + 0.5) = 60t
Simplifying this equation:
50t + 25 = 60t
Subtracting 50t from both sides:
25 = 10t
So t = 2.5 hours.
But we're not done yet! We need to add the 0.5 hours that the van traveled before the car started to get the total time it took for the car to catch up:
t + 0.5 = 2.5 + 0.5 = 3 hours
So the car catches up to the van 3 hours after the van started, or at 12:15 pm.
B) We can use the formula:
distance = rate × time
to find the distance between the two towns. We know the car traveled for 6 hours (from 9:45 am to 3:45 pm) and its speed was 60 km/h. So the distance it traveled is:
distance car = 60 × 6 = 360 km
We also know that the van traveled for 6.5 hours (from 9:15 am to 3:45 pm) and its speed was 50 km/h. So the distance it traveled is:
distance van = 50 × 6.5 = 325 km
The distance between the two towns is the difference between these two distances:
distance = distance car - distance van = 360 - 325 = 35 km
So the distance between the two towns is 35 km.
The value of x in the following equation 4x-5=7 is .........
Answer:
Step-by-step explanation:
4x - 5 = 7
4x = 7 + 5
4x = 12
x = 12/4
x = 3
According to the graph, what is the maximum number of passengers he can transport What is the maximum amount he can collect? Use the graph to determine the amount he charges a single passenger.
I can't see the chart...
Please help me out with this
Answesar:
Step-by-step explanation:
SA = 10(5)² = 250cm²
Volume² = 2 (5)³ = 250cm³
They are not equal.
Surface area is in square cm and volume is in cm³.
HELP ASAP PLEASE 20 POINTS!!
The calculated value of the surface area of the cylinder is 138π square inches
Calculating the surface area of the cylinderFrom the question, we have the following parameters that can be used in our computation:
Height, h = 5 1/2 inches
Diameter, d = 12 inches
Using the above as a guide, we have the following:
SA = 2πr(r + h)
Where
Radius, r = d/2
r = 12/2
r = 6
Substitute the known values in the above equation, so, we have the following representation
SA = 2 * π * 6(6 + 5 1/2)
Evaluate
SA = 138π
Hence, the surface area of the cylinder is 138π square inches
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Write the linear equation that gives the rule for this table.
X
4
5
6
7
Y
24
30
36
42
Write your answer as an equation with y first, followed by an equals sign.
The equation of the line passing through the given points is y = 6x
Given that are the values of x and y coordinates we need to find the equation of the line using them,
So, considering the points (4, 24) and (5, 30),
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (4, 24) and (5, 30),
Therefore, the required equation is =
y-24 = 30-24/5-4 (x-4)
y-24 = 6(x-4)
y-24 = 6x-24
y = 6x
Hence, the equation of the line passing through the given points is y = 6x
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What is the equation through the points: (-7, -3), (1, 2)
ASAP please
The equation of the line passing through the points (-7, -3) and (1, 2) is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
First, we determine the slope of the line.
Given the two points are (-7, -3) and (1, 2)
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values, we get:
m = (2 - (-3)) / (1 - (-7))
m = 5/8
Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.
Let's use the point (-7, -3:
y - y₁ = m(x - x₁)
[tex]y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}[/tex]
Therefore, the equation of the line is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].
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A system of equations is shown.
{ x= = 10
3x + 5y = 20
What is the solution x of the system of equations?
Answer:
(r, y)=(10,-2)
Step-by-step explanation: Hope this helps :)
3 problems for 1 final answer. fairly easy 8th grade math.
When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)
How do i determine the value of A/5 + √(B - C)?
First, we shall determine the value of A. Details below:
A = Product of roots in x² - 11x + 30Value of A =?Quadratic equation is expressed as:
x² - (sum of root)x + product of root
Comparing the above with x² - 11x + 30, we have
x² - 11x + 30 = x² - (sumof root)x + product of root
Product of roots = 30
Thus,
A = 30
Next, we shall determine the value of B. details below:
f(x) = x² + 5Value of B = f(2) =?f(x) = x² + 5
f(2) = 2² + 5
f(2) = 9
Thus,
B = 9
Next, we shall determine the value of C. Details below:
(x² - 2x - 24) / (x + 4)Value of C = Remainder =?Let
x + 4 = 0
Thus,
x = -4
Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:
Remainder = x² - 2x - 24
Remainder = (-4)² - 2(-4) - 24
Remainder = 0
Thus,
C = 0
Finally, we shall determine value of A/5 + √(B - C). Details below:
A = 30B = 9C = 0Value of A/5 + √(B - C) =?A/5 + √(B - C) = 30/5 + √(9 - 0)
A/5 + √(B - C) = 6 + √(9
A/5 + √(B - C) = 6 + 3
A/5 + √(B - C) = 9
Thus, the value of A/5 + √(B - C) is 9 (option B)
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Can someone help me with this please
Answer:
36 °
Step-by-step explanation:
The markings imply equal sides*
So both of the angles are 27° there
To find angle a we do 180 - (27+27) and obtain 126°
Then to find angle y, we do 180-angle a which is 180-126 and we get 54°
We now have reached the triangle where you're supposed to find x right?
So x is equal to 180 - both other angles, which is 180 - (90 and angle y) = 180- (90+54) = 180 - 144 = 36 which is your final answer
A student wants to know which type of pizza the students at his high school prefer. Which
option would give a unbiased, representative sample:
Average
Answer:
Step-by-step explanation:
In November 1998, former professional wrestler Jesse “The Body” Ventura was elected governor of Minnesota. Up until right before the election, most polls showed he had little chance of winning. There were several contributing factors to the polls not reflecting the actual intent of the electorate:
Ventura was running on a third-party ticket and most polling methods are better suited to a two-candidate race.
Many respondents to polls may have been embarrassed to tell pollsters that they were planning to vote for a professional wrestler.
The mere fact that the polls showed Ventura had little chance of winning might have prompted some people to vote for him in protest to send a message to the major-party candidates.
But one of the major contributing factors was that Ventura recruited a substantial amount of support from young people, particularly college students, who had never voted before and who registered specifically to vote in the gubernatorial election. The polls did not deem these young people likely voters (since in most cases young people have a lower rate of voter registration and a turnout rate for elections) and so the polling samples were subject to sampling bias: they omitted a portion of the electorate that was weighted in favor of the winning candidate.
SAMPLING BIAS
A sampling method is biased if every member of the population doesn’t have equal likelihood of being in the sample.
So even identifying the population can be a difficult job, but once we have identified the population, how do we choose an appropriate sample? Remember, although we would prefer to survey all members of the population, this is usually impractical unless the population is very small, so we choose a sample. There are many ways to sample a population, but there is one goal we need to keep in mind: we would like the sample to be representative of the population.
Returning to our hypothetical job as a political pollster, we would not anticipate very accurate results if we drew all of our samples from among the customers at a Starbucks, nor would we expect that a sample drawn entirely from the membership list of the local Elks club would provide a useful picture of district-wide support for our candidate.
One way to ensure that the sample has a reasonable chance of mirroring the population is to employ randomness. The most basic random method is simple random sampling.
Ted made $56 in interest by placing $700 in a savings account with simple interest for 1 year. What was the interest rate?
The interest rate if Ted made $56 in interest for 1 year on a principle of $700 will be 8%.
Given, the interest amount is $56.
The principal amount is $700.
The time period of investment is 1 year.
Now, we have to find the interest rate.
The formula to find the simple interest is,
S.I = PTR/100.
Now, we need to substitute the values in the above formula.
S.I = PTR/100
56 = 700×1×R / 100
56 = 700R/100
5600 = 700R
R = 5600/700
R = 8
Therefore, the interest rate is 8%.
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Can someone please help with this question and break it down so I can learn a better way to do it.
Using trigonometry and the Pythagorean theorem, the length of the hypotenuse AC is found to be 3.5 cm, and using the Pythagorean theorem again, the length of BC is found to be approximately 1.75 cm.
Using trigonometry and the given angle and side length information, we can solve for the length of side BC (x).
We know that
sin(A) = opposite/hypotenuse
sin(30) = AC/7
AC = 7 × sin(30)
AC = 3.5 cm
Using the Pythagorean theorem, we have
BC² = AC² - AB²
BC² = (3.5)² - (7)² sin²(30)
BC² = 3.0625
BC = √3.0625
BC = 1.75 cm (rounded to two decimal places)
Therefore, the value of x is approximately 1.75 cm.
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Suppose that the local government of Corpus Christi decides to institute a tax on soda consumers. Before the tax, 30 million liters of soda were sold every month at a price of $11 per liter. After the tax, 25 million liters of soda are sold every month; consumers pay $14 per liter (including the tax), and producers receive $6 per liter.
The amount of the tax on a liter of soda isper liter. Of this amount, the burden that falls on consumers isper liter, and the burden that falls on producers isper liter.
True or False: The effect of the tax on the quantity sold would have been larger if the tax had been levied on producers.
True
False
False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.
What is Algebraic expression ?
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.
The tax incidence (the division of the burden of a tax between buyers and sellers) does not depend on which side of the market the tax is levied on, but rather on the relative elasticities of supply and demand. In this case, we don't have information about the elasticities of supply and demand, so we cannot determine the tax incidence. However, we can infer that the tax on consumers did reduce the quantity sold (from 30 million liters to 25 million liters), so it's unlikely that a tax on producers would have had a larger effect.
Therefore, False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.
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What is an equation of the line that passes through the point (5,-5)(5,−5) and is parallel to the line x+5y=20?
Answer:
[tex]y = -x/5 -4.[/tex]
Step-by-step explanation:
To simplify the line x + 5y = 20 into y = mx + b form:
x + 5y = 20.
5y = -x + 20.
y = -x/5 + 4.
The line parallel to the line y = -x/5 + 4 will have the same slope of -1/5.
We get the equation:
y = -x/5 + b.
To find b, we plug in the point (5, -5).
-5 = -5/5 + b.
-5 = -1 + b.
b = -4.
[tex]y = -x/5 -4.[/tex]
A turtle lives in a garden and a hedgehog lives in the woods. They leave their homes at the same time, walk toward each other, and meet in 5 hours. The turtle walks 10 meters per hour slower than the hedgehog. It the turtle had left home 4.5 hours earlier than the hedgehog, the two have me 150/ from the hedgehog's house. Find the distance between the garden and the woods.
If a turtle lives in a garden and a hedgehog lives in the woods. The distance between the garden and the woods is 450m.
How to find the distance?Let d represent the distance between the turtle's garden and the hedgehog's wood
Let h represent the speed of the hedgehog
Let the turtle's speed = h-10
Le the time it takes for the hedgehog to walk from the woods to the meeting point= t
Set up two equations
d = (h-10)(t+4.5) + ht (Equation 1)
d - 150 = ht (Equation 2)
Solve for d by substituting equation 2 into equation 1:
ht + (h-10)(t+4.5) = ht + 150
(h-10)t + 45h = 150
t = (150 - 45h) / (h-10)
Substitute t into equation 2:
d = ht + 150 - (h-10)(t+4.5)
d = h(150 - 45h)/(h-10) + 150 - (h-10)(45h/(h-10) + 4.5)
d = 2250/(h-10) (distance between the garden and the woods)
Since the turtle and hedgehog meet in 5 hours
Thus,
d = ( h-10 ) (5) + h( 5- 4.5 )
d = 5h - 25
Substitute
5h - 25 = 2250/(h-10)
Multiplying both sides by h-10
5h² - 75h + 250 = 0
Dividing both sides by 5
h²- 15h + 50 = 0
Using the quadratic formula
h = (15 ± sqrt(15^2 - 4(1)(50))) / (2*1)
h = (15 ± 5) / 2
So,
h = 10 or h = 5
Distance between the garden and the woods :
d = 2250/(h-10)
d= 2250/(5-10)
= 450 meters
Therefore the distance is 450m.
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