Using a standard normal distribution table or a z-table gives us
P(¯Z≤0.8181)≈0.20662
Let us write down some of the parameters and statistics that are given in the question.
Population mean thickness
μ=4mm.
Population standard deviation
σ=1.1mm.
Random sample size
n=100.
Let the random normal variable
¯X denote the average thickness of the sample.
Then according to the Central Limit Theorem,
¯X
follows a normal distribution with mean
μ¯X=μ=4
and standard deviation
σ¯X=σ√n=1.1√100=1.110=0.11.
Then we can convert ¯X
into its standard normal form ¯Z
using the following transformation:
¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)
Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need
P(¯X<3.91).
Using (2) we get
P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)
Using a standard normal distribution table or a z-table gives us
P(¯Z≤0.8181)≈0.20662
which is our answer.
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Using a standard normal distribution table or a z-table gives us
P(¯Z≤0.8181)≈0.20662
Let us write down some of the parameters and statistics that are given in the question.
Population mean thickness
μ=4mm.
Population standard deviation
σ=1.1mm.
Random sample size
n=100.
Let the random normal variable
¯X denotes the average thickness of the sample.
Then according to the Central Limit Theorem,
¯X
follows a normal distribution with mean
μ¯X=μ=4
and standard deviation
σ¯X=σ√n=1.1√100=1.110=0.11.
Then we can convert ¯X
into its standard normal form ¯Z
using the following transformation:
¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)
Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need
P(¯X<3.91).
Using (2) we get
P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)
Using a standard normal distribution table or a z-table gives us
P(¯Z≤0.8181)≈0.20662
which is our answer.
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Find the derivative of y with respect to x if y=e^-14x
Given that the function of ex is ex, the derivative of y with respect to x is -14e-14x.
The rate of a function's change with regard to one of its variables is known as the derivative. The derivative of y with respect to x in the case of y=e-14x is the rate at which y varies as x changes. The derivative is the derivative of ex, which is ex because derivative the function is e-14x. Simply multiplying ex by the coefficient of x, which is -14, yields the derivative of y with respect to x. Consequently, derivative -14e-14x is the derivative of y with respect to x. Accordingly, y will drop by 14e-14x units for every unit increase in x.
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let f (x) = |x3 64| find the area a of the region between the graph of f and the x axis on the interval [-8, 0]
The area between the graph of f and the x-axis on the interval [-8, 0] is 4608 square units.
How big is the region between the graph?The two-dimensional region enclosed by the function's graph and the x-axis is referred to as the region between the graph and the x-axis. Calculating the definite integral of the function over the specified interval and deducting the area below the x-axis, if any, will yield the area of this region.
There are two sections to the graph of f(x) = |x3 - 64|: a parabolic section and a linear section. The area between the graph of f and the x-axis is just the absolute value of the definite integral of f(x) over [-8, 0] because the graph of f(x) on the interval [-8, 0] is below the x-axis and contains negative values.
We must first get the antiderivative of f(x) before we can determine the definite integral, which may be accomplished by utilising partial fraction decomposition.
The antiderivative of f(x) = x⁴ - 64 is:
F(x) = (x⁴)/4 + 64x
The definite integral of f(x) over [-8, 0] is:
Area = F(0) - F(-8) = (0⁴)/4 + 64(0) - ((-8)⁴)/4 - 64(-8) = (8⁴)/4 + 64(8) = 4096 + 512 = 4608
Hence, the area between the graph of f and the x-axis on the interval [-8, 0] is 4608 square units.
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A taxi driver uses this formula to work out fares, Fare = £2. 50 + £0. 90 x miles
Use the formula to work out:
a. The fare for a 9-mile journey.
give your answer in pounds
ASAP PLEASE
The fare for a 9-mile journey can be calculated using the formula Fare = £2.50 + £0.90 x miles. To find the fare for a 9-mile journey, we just need to substitute 9 for miles in the formula:
Fare = £2.50 + £0.90 x 9
Fare = £2.50 + £8.10
Fare = £10.60
So, the fare for a 9-mile journey would be £10.60.
It's important to understand how the formula works in order to correctly use it. The first part of the formula, £2.50, is a fixed cost that is added to the fare regardless of the distance traveled. This could represent things like the cost of hiring the taxi, the driver's time, and any other fixed expenses that the taxi company incurs.
The second part of the formula, £0.90 x miles, is the variable cost that is added to the fare depending on the distance traveled. This could represent things like the cost of fuel, wear and tear on the vehicle, and any other expenses that the taxi company incurs as a result of traveling a certain distance. By multiplying the distance traveled by the cost per mile, £0.90, the formula calculates the total variable cost for the journey.
When these two costs are added together, the formula gives the total fare for the journey. In this case, for a 9-mile journey, the total fare would be £10.60.
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the average rate of change over π 2,π is enter your response here.
The average rate of change is defined as the change in the dependent variable (y) divided by the change in the independent variable (x), or (y2 - y1) / (x2 - x1).
The average rate of change over the interval [π/2, π] cannot be determined without knowing the specific function. The average rate of change is defined as the change in the dependent variable (y) divided by the change in the independent variable (x), or (y2 - y1) / (x2 - x1). To find the average rate of change, you need to know the values of y at the start and end of the interval, as well as the corresponding x values.
Thus, The average rate of change over the interval [π/2, π] cannot be determined.
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Let C R2 be the circle with radius 6 centered at the origin. Let F : R2 → R2 be the vector field defined by F(x, y) = (7x, 1 1). Find the flux of F coming out of the circle through the curve C.
The flux of F coming out of the circle C is 126π.
The flux of a vector field, F, out of a surface, S, is given by the formula
Flux = ∮F • n ds,
where n is a unit normal vector to the surface S.
In this case, the surface S is the circle C with radius 6 centered at the origin and the vector field F is given by F(x, y) = (7x, 11). We can use Green's Theorem to find the flux from the circle C. The equation for the circle is x2 + y2 = 36. Differentiating this equation with respect to x and y gives us the unit normal vector, n = (x/6, y/6).
Plugging these values into the flux formula, we get
Flux = ∮F • n ds = ∮ (7x, 11) • (x/6, y/6) ds
= ∮ 7x2/6 + 11y/6 ds
= (7/6) ∮ (x2 + y2) ds
= (7/6) * Area of C
= (7/6) * π * 36
= 126π.
Therefore, the flux of F coming out of the circle C is 126π.
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2 WXYZ is translated 6 units to the left and
then reflected in the x-axis to create
W'X'Y'Z'.
Write an ordered pair to show the location
of each vertex of the transformed figure.
The coordinates of each vertex after the translation and reflection can be written as an ordered pair. The coordinates for W' are (6, 0), for X' are (0, 3), for Y' are (6, 6), and for Z' are (0, 9).
This means that point W' has been moved 6 units to the left, X' has been moved 6 units to the left and 3 units down, Y' has been moved 6 units to the left and 6 units down, and Z' has been moved 6 units to the left and 9 units down, and then all the points have been reflected across the x-axis. This transformation results in a figure that is the same size and shape as the original figure, but shifted and reflected across the x-axis.
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I donut shop sold 40 donuts of which 15% of the donuts were jelly and 35% of the donuts were glazed using products,to find:
(A) The number of donuts that were jelly
(B) The number of donuts that were glazed
(A) The number of doughnuts that were jelly = 6
(B) The number of doughnuts that were glazed = 14
As per the data given in the question,
We have,
Total number of doughnuts sold = 40
Percentage of jelly doughnuts = 15%
Percentage of doughnuts that's were glazed = 35%
A) The number of doughnuts that were jelly can be found by multiplying the total number of doughnuts by the percentage that was jelly:
40 x 15% = 6 donuts
So there were 6 doughnuts that were jelly.
B) The number of doughnuts that were glazed can be found by multiplying the total number of doughnuts by the percentage that was glazed:
40 x 35% = 14 donuts
So there were 14 doughnuts that were glazed.
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A tower stands on top of a hill. From a point on the ground that is 148 meters directly east of a point directly under the tower, the angle of elevation to the bottom of the tower is 18 degrees. From the same point, the angle of elevation to the top of the tower is 34 degrees. Find the height of the tower.
Answer:
62.2 m
Step-by-step explanation:
From 148m away at ground level, the angel of elevation to the tower base is 18 degrees. Imagining this as a right angled triangle, if considering the angle of 18 degrees, 148m is the adjacent and the opposite is the height of the hill:
tanA=opposite/adjacent
tan18=opposite/148
opposite = 57.8357059295m
From 148m away at ground level, the angel of elevation to the tower top is 34 degrees. Imagining this as a right angled triangle, if considering the angle of 34 degrees, 148m is the adjacent and the opposite is the height of the hill+the tower:
tanA=opposite/adjacent
tan34=opposite/148
opposite = 120.062515998m
Knowing the height of the hill and tower is 120.062515998m and the height of the hill is 57.8357059295m, we can say the height of the tower is the difference:
120.062515998 - 57.8357059295 = 62.2268100685 m
Express the ratio below in its simplest form. 5 : 2 1 /2
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.
To find out what the simplest form is of the ratio 5: 2[tex]\frac{1}{2}[/tex], we can divide both sides by 2[tex]\frac{1}{2}[/tex].
5 ÷ 2[tex]\frac{1}{2}[/tex] = 22[tex]\frac{1}{2}[/tex] ÷ 2[tex]\frac{1}{2}[/tex] = 1The ratio simplified is 2: 1.
To determine the simplest form of the ration 5 : [tex]2\frac{1}{2}[/tex] , we can first simplify the mixed fraction [tex]2\frac{1}{2\\}[/tex]
So, [tex]2\frac{1}{2\\}[/tex] = [tex]\frac{5}{2}[/tex]
∴ 5 : [tex]2\frac{1}{2\\}[/tex] = 5 : [tex]\frac{5}{2}[/tex]
= ( 5 x 2 ) : ( [tex]\frac{5}{2\\}[/tex] x 2 )
= 10 : 5
= [tex]\frac{10}{5}[/tex] x [tex]\frac{5}{5}[/tex]
= 2 : 1
Hence, the simplest form of the ratio given is 2 : 1
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determine if 4y=16x-24 is linear, why?
Which learning preference category best describes a High School Fine Arts student who prefers a studio lesson that involves modeling with clay over a virtual field trip to the Louvre? Question 1 options: auditory learner kinesthetic learner visual learner
The learning preference category that best describes a high school fine arts student who prefers a studio lesson that involves modeling with clay over a virtual field trip to the Louvre is a kinesthetic learner.
Kinesthetic learners are individuals who learn best through hands-on, physical experiences and activities. They tend to be active and enjoy engaging their bodies in learning, such as manipulating objects or performing movements. For this student, modeling with clay provides a hands-on, physical experience that allows them to learn through touch and movement. They can feel the texture and weight of the clay, and manipulate it to create their desired form. This type of learning experience is much more engaging and effective for a kinesthetic learner compared to a virtual field trip to the Louvre, which is primarily a visual learning experience.
In conclusion, a kinesthetic learning preference involves hands-on, physical activities and experiences, and this preference is evident in the student's preference for a studio lesson that involves modeling with clay over a virtual field trip to the Louvre.
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Which type of transformation is described by (x,y) → (-x, y)?
a reflection across the y-axis
a rotation of 90° about the origin
a dilation of scale factor - 1
a rotation of 180° about the origin
Answer:
Reflection across the x-axis.
Step-by-step explanation:
Use squared paper and plot some coordinate points.
For example: (2,3) and (−3,−2) and reflect them in the x-axis. You should obtain the following results.
(2,−3) and (−3,2) respectively.
(Note that the x-coordinate remains unchanged, while the y-coordinate is the negative of the original point.In general this can be expressed as: Under reflection in the x-axis (x,y)→(x,−y))
1 - 8p= -6p - 7
tthanks
Answer: 7/15
Step-by-step explanation:
8p + 7 = -6p
15p = 7
p = 7/15
[tex] \: [/tex]
[tex]\large \frak{- 8p + 6p = - 7 - 1}[/tex][tex] \: [/tex]
[tex]\large \frak{- 2p = - 8}[/tex][tex] \: [/tex]
[tex] \large \frak{p = \cancel \frac { - 8}{ - 2} }[/tex][tex] \: [/tex]
[tex] \boxed{\underline{\large {\frak{\red{ \: p = 4 \: }}}}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
POINTS UP FOR GRABS!!!
The compound inequality for the graph shown above include the following:
x < -4.
x ≤ 5.
What is a number line?In Mathematics, a number line is a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.
Since the first point is at -4 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.
Additionally, the second point is located at 5 and the arrow points to the left of the number line with a shaded circle, it represents the greater than (>) inequality symbol and should be written as x ≤ 5.
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todd misread the recipe and added 3/5 of a teaspoon of salt to the bread dough the recipe called for 1/2 of a teaspoon how much extra salt was added
Please help I need to do this before I’m late lol
the answer which equal to the 1 1/4 are 8 3/4 - 7 1/2 and 9 5/12 - 8 1/6.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
a) 5 2/8 - 4 1/4 = 42/8 - 17/4 = 42-34/8 = 8/8 =1
b) 8 3/4 - 7 1/2 = 35/4 - 15/2 = 35-30/4 = 1 1/4
c) 2 1/8 - 1 7/8 = 17/8 - 15/8 = 2/8
d) 9 5/12 - 8 1/6 = 113 - 98/ 12 = 15/12 = 1 3/12 =1 1/4
So the answer which equal the 1 1/4 is 8 3/4 - 7 1/2 and 9 5/12 - 8 1/6.
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the probility of alvins mother will server rice with dinner is 0.78 the probilty that she will server carrots is with dinner is 0.30
The probability of both rice and carrots being served with dinner is 23.4%.
The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.
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Charlotte works in a department store selling clothing. She makes a guaranteed salary of $500 per week, but is paid a commission on top of her base salary equal to 30% of her total sales for the week. How much would Charlotte make in a week in which she made $1575 in sales? How much would Charlotte make in a week if she made
x
x dollars in sales?
Charlotte makes 500 pounds per week
30 % of 500 she has to pay to the commission per week
if she made 1575 one week how much would she get?
1575 divided by 30%=472.5
472.5 rounded = 473
x=473 or 472.5
Charlotte would make $972.50 in a week in which she made $1575 in sales and if Charlotte made x dollars in sales, she would make $500 + 0.3x in total earnings for the week.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To calculate how much Charlotte would make in a week in which she made $1575 in sales
we first need to calculate her commission:
Commission = 30% × $1575
= $472.50
Total earnings = Guaranteed salary + Commission
= $500 + $472.50
= $972.50
Therefore, Charlotte would make $972.50 in a week in which she made $1575 in sales.
To calculate how much Charlotte would make in a week if she made x dollars in sales, we can use the same method.
Her commission would be:
Commission = 30% ×x
And her total earnings would be:
Total earnings = Guaranteed salary + Commission
= $500 + 0.3x
So, if Charlotte made x dollars in sales, she would make $500 + 0.3x in total earnings for the week.
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Please help! Solve for x
The value of the variable 'x' will be 40.50. Then the correct option is D.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ΔPQS is similar to the triangle ΔRQS. Then the equation is given as,
x / 45 = 18 / 20
x / 45 = 0.90
x = 40.5
The value of the variable 'x' will be 40.50. Then the correct option is D.
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your cat gives birth to six kittens. three are black, two are grey and one is white. what percentage of the kittens are black?
50% of the kittens are black in colour.
Total number of kittens = 6
Out of these, 3 are black, 2 are grey, and 1 is white.
The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Now, percentage of kittens that are black:
(Total number of Black Kittens/Total number of kittens) x 100 %
= 3/6 x 100 % = 50%
Therefore, 50% of the kittens are black in colour.
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Name all chords that are drawn in Circle C
The name of all the chords that are drawn in Circle C are; SU, UV and TW.
How to Identify Circle Chords?The chord of a circle is a term that is defined as the line segment joining any two points on the circumference of the circle.
Looking at the image and comparing with the definition of chords above, we can say that the chords will be SU, UV and TW. This is because they join two points on the circumference of the given circle with center C
We further see that the segment CV is only the radius of the circle.
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yy x cos y da, d is bounded by y 0, y x 2, x 1
First, we need to set up the bounds for the integral. The lower and upper limits of the integral are x = 1 and y = x2, respectively. The integral ∫x1 [cos(x2)dx] is equal to -2/3.
Next, we can substitute the upper limit of the integral into the integrand to get:
∫x1 [cos(x2)dx]
Then, we can use integration by parts to solve the integral. We let u = cos(x2) and dv = dx. This gives us:
du = -2x sin(x2) dx
and
v = x
This gives us:
∫x1 [cos(x2)dx] = x cos(x2) - ∫x1 [-2x sin(x2)dx]
Now, we can solve the second integral. We let u = x2 and dv = -2 sin(x2)dx. This gives us:
du = 2x dx
and
v = -cos(x2)
This gives us:
∫x1 [-2x sin(x2)dx] = -x2 cos(x2) - ∫x1 [2x dx]
Finally, we can solve the last integral. We let u = x and dv = 2 dx. This gives us:
du = dx
and
v = x2
This gives us:
∫x1 [2x dx] = x3 + c
where c is the constant of integration.
Putting it all together, we get that
∫x1 [cos(x2)dx] = x cos(x2) - x2 cos(x2) - x3 - c
Substituting in the limits of the integral, we get that
∫x1 [cos(x2)dx] = 1 - x2 - x3 - c
Since the lower limit of the integral is x = 1, we have that
∫x1 [cos(x2)dx] = -x2 - x3 - c
Substituting in the upper limit of the integral, we get that
∫x1 [cos(x2)dx] = -1 - x2 - x
The integral ∫x1 [cos(x2)dx] is equal to -2/3.
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which is different? responses construct a quadrilateral with opposite sides congruent. construct a quadrilateral with opposite sides congruent. construct a quadrilateral with one pair of parallel sides. construct a quadrilateral with one pair of parallel sides. construct a quadrilateral with opposite angles congruent. construct a quadrilateral with opposite angles congruent. construct a quadrilateral with one pair of opposite sides congruent and parallel.
The difference between the given statements is that opposite sides are congruent means that all four sides of the quadrilateral are equal in length.
While one pair of parallel sides means that two sides of the quadrilateral are parallel and have the same length, the other two sides may or may not have the same length.
These two conditions define different types of quadrilaterals like a rectangle and a parallelogram, respectively.
So the answer is "construct a quadrilateral with one pair of opposite sides congruent and parallel."
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help pls asap due in 1 hour pls
Answer:
Subtract the amount of £1 coins from 50p coins:
256-172 = 84
84/3 coins = 28 people paid with 3 coins.
172 people paid using £1 coins
172 + 28 = 200 total people
percent who used 3 coins = 28/200 = 0.13 x 100 = 14% so the answer is 14%
identify the property of 3x·-4=1
The addition property and division properties are used to solve the expression.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 3x - 4 = 1
Now, We can solve as;
⇒ 3x - 4 = 1
Add 4 both side,
⇒ 3x - 4 + 4 = 1 + 4
⇒ 3x = 5
Divide by 3;
⇒ x = 5/3
Thus, The addition property and division properties are used to solve the expression.
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Binomial Distribution - Algebra 2B
A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?
So the probability that at least 3 customers out of the first 6 will buy bread is 0.7929 or about 79.29%.
To determine the appropriate probability, we may utilise the binomial distribution's cumulative distribution function (CDF). The likelihood that the number of successful occurrences in a specified number of independent trials is less than or equal to a specific value is given by the binomial distribution's CDF.
Let X represent the proportion of the first 6 clients who purchase bread. Then, X has a binomial distribution with n = 6 and p = 0.65 as its parameters. One less than the likelihood that fewer than three consumers will purchase bread results in the chance that at least three will:
P(X >= 3) = 1 - P(X < 3)
Using a cumulative distribution function of the binomial distribution, we can calculate P(X < 3) as:
P(X < 3) = CDF(2, n=6, p=0.65)
Using a binomial calculator or a programming library that implements the CDF of the binomial distribution, we find that P(X < 3) = 0.2071. Therefore, the desired probability is:
P(X >= 3) = 1 - P(X < 3) = 1 - 0.2071 = 0.7929
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we have 15 voters and four alternatives, and the individual preference lists are as follows: voters 1-3: a d b c voters 4-5: b d a c voters 6-7: c d a b voters 8-9: a d c b voters 10-11: b d c a voters 12-13: c d b a voters 14-15: d b a c what choice or choices result from the plurality voting procedure?
The complete question is:
We have 15 voters and four alternatives, and the individual preference lists are as follows:
Voters 1-3: a d b c
Voters 4-5: b d a c
Voters 6-7: c d a b
Voters 8-9: a d c b
Voters 10-11: b d c a
Voters 12-13: c d b a
Voters 14-15: d b a c
1) The plurality voting procedure? - Voters 1-3: a d b c
2) The Condorcet procedure? - Voters 8-9: a d c b
3) The Hare (instant runoff) system? - Voters 4-5: b d a c
4) The Borda count procedure? - Voters 8-9: a d c b
5) Sequential pairwise voting with agenda bdac? - Voters 8-9: a d c b
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x represents a positive quantity; y represents a negative quantity.
x^4=116
y^2= 11
Evaluate (x − y)(x+y)(x² + y²)
The value of the expression (x − y)(x+y)(x² + y²) will be 183.
How to illustrate the expressionIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case, when x⁴ = 116, x will be 3.5
Also y² = 11, y will be 3.3
The value of (x − y)(x+y)(x² + y²) will be:
= (3.5 - 3.3) (3.5 + 3.3)(3.5² + 3.3²)
= 0.2 × 6.8 × 134.75
= 183
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A car traveled a ditance of 600. 15 km in 7. 5 hour. How many kilometer did the car travel per hour on the average?
The car traveled 80.02 kilometer per hour on the average
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this problem is:
v= x/t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 600.15 kmt = 7.5 hv = ?Applying the velocity formula we have:
v = x/t
v = 600.15 km / 7.5 h
v = 80.02 km/h
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Sam and Tyrone are running on a trail. Sam reaches the 4th mile marker at the same time that Tyrone reaches the 1st mile marker. From the 4th mile marker, Sam runs another mile every 10 minutes. From the 1st mile marker, Tyrone runs another mile every 6 minutes. After how many minutes will Sam and Tyrone meet?
If Sam runs another mile every 10 minutes, From the 1st mile marker, Tyrone runs another mile every 6 minutes. Sam and Tyrone meets after 45 minutes
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
Given that,
Sam and Tyrone are running on a trail,
Sam reaches the 4th mile marker at the same time that Tyrone reaches the 1st mile marker
From the 4th mile marker,
Sam runs another mile every 10 minutes,
Speed = distance/time = 1/10 mile/minute
Tyrone runs another mile every 6 minutes,
Speed = distance/time = 1/6 mile/minute
Time when Sam and Tyrone meet = ?
Suppose,
When x distance covered by Sam then they will meet,
So, That time distance covered by Tyrone will be, (4-1) + x
And time taken for it will be, t
Now it can be written as,
Time for Sam after 4th mile = Time for Tyrone after 1st mile
x/(1/10) = (3 + x)/(1/6)
10x = 6(3 + x)
10x = 18 + 6x
4x = 18
x = 9/2
Time t =x/(1/10) = (3 + x)/(1/6)
t = (9/2)/(1/10)
t = 45 minute
Hence, After 45 minutes they will meet
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