A long distance runner started on a course running at an average speed of 6mph. half an hour later, a second runner began the same course at an average speed of 7mph. how long after the second runner started will the second runner overtake the first runner?
Answers
9 hours long after the second runner started will the second runner overtake the first runner.
What does it mean to do speed?
Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector.Runner I = 6 mph
Runner II = 7 mph
Difference in time= 90 minutes
Train A will have covered 9 miles before Runner II starts
catch up distance= 9 miles
catch up speed = 7-6 mph
catch up speed = 1 mph
Catchup time = catchup distance/catch up speed
catch up time= 9/1
catch up time= 9 hours
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Related Questions
A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 4 bags of potato chips for $14.50. Another customer buys 2 hot dogs and 2 bags of potato chips for $8.50. Find the cost of each item.
Answers
The cost of each hot dog is $2.00, and the cost of each bag of potato chips is $2.50.
To find the cost of each item, we can set up a system of equations using the given information. Let's assume the cost of each hot dog is x dollars, and the cost of each bag of potato chips is y dollars.
From the first customer's purchase, we know that 3x + 4y = $14.50.
From the second customer's purchase, we know that 2x + 2y = $8.50.
We can solve this system of equations using either substitution or elimination method. Let's use the elimination method to eliminate the variable x.
Multiplying the second equation by 1.5, we get 3x + 3y = $12.75.
Subtracting this equation from the first equation, we get:
(3x + 4y) - (3x + 3y) = $14.50 - $12.75
y = $1.75
Now, substituting the value of y into the second equation, we can solve for x:
2x + 2($1.75) = $8.50
2x + $3.50 = $8.50
2x = $8.50 - $3.50
2x = $5
x = $5 / 2
x = $2.50
Therefore, the cost of each hot dog is $2.50, and the cost of each bag of potato chips is $1.75.
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The area of a square floor on a scale drawing is 49 square centimeters, and the scale drawing is 1 centimeter:3 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?
Answers
Answer:
the area of the actual floor is 784 ft² and the ratio is (1 cm²) ÷ (16 ft²). The same would be relevant
Step-by-step explanation:
The computation of the area and the ratio of the area is shown below:
The ratio of the drawing area to the actual area is
= ((1 cm) ÷ (4 ft))²
= (1 cm²) ÷ (16 ft²)
Now the actual floor area is
(16 ft²) ÷ (1 cm²) = actual area ÷ (49 cm²)
= (16 ft²) × 49 ÷ 1
= 784 ft²
hence, the area of the actual floor is 784 ft² and the ratio is (1 cm²) ÷ (16 ft²). The same would be relevant
For the model 1/y = 0.80 + 4.7x, find y when x = 2. Round to two decimal places. a. y = 0.10 b. y = 10.20 c. y = -8.60 d. y = 0.09 e. y = -0.12
Answers
For the model 1/y = 0.80 + 4.7x, the value of y when x = 2 is option (a) y = 0.10
To find the value of y when x = 2 in the equation 1/y = 0.80 + 4.7x, we need to first solve for y.
We can start by isolating y on one side of the equation. To do this, we can take the reciprocal of both sides of the equation to get:
y = 1/(0.80 + 4.7x)
Now, we can substitute x = 2 into the equation and solve for y:
y = 1/(0.80 + 4.7(2))
y = 1/(0.80 + 9.4)
y = 1/10.20
y = 0.098
Rounding to two decimal places gives us y = 0.10,
Therefore, the correct option is (a) y = 0.10.
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Where does the line y=-4+9 cross the y-axis?
1. At y=9
2.At x=9
3.At y=-4
4.at x=-4
Answers
What term is defined by the formula?
Answers
Which is the most accurate measurement for the line segment?
Answers
Answer:
Step-by-step explanation:
So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length. The length of a line segment can be measured either in metric units such as millimeters, centimeters, or customary units like feet or inches.
A pair of pants that Jessica wants are usually $39. If the store is having a 33% off sale, how much will the pants cost
Answers
Answer: $12.87
Step-by-step explanation:
You need to set up your equation. We are trying to find x.
Step 1: \(\frac{x}{39} = \frac{33}{100}\)
Step 2: Multiply across: 39 x 33 divided by 100.
39 x 33 = 1287
1287 divided by 100 = $12.87
Answer: $12.87
Use the matrix of transition probabilities P and initial state matrix X_0 to find the state matrices X_1, X_2, and X_3. P = [0.6 0.2 0.1 0.3 0.7 0.1 0.1 0.1 0.8], X_0 = [0.1 0.2 0.7] X_1 = [] X_2 = [] X_1 = []
Answers
To find the state matrices X_1, X_2, and X_3, we can use the transition probability matrix P and the initial state matrix X_0.
P = [0.6 0.2 0.1
0.3 0.7 0.1
0.1 0.1 0.8]
X_0 = [0.1 0.2 0.7]
To calculate X_1, we multiply the transition probability matrix P with the initial state matrix X_0:
X_1 = P * X_0
To calculate X_2, we multiply P with X_1:
X_2 = P * X_1
Similarly, to calculate X_3, we multiply P with X_2:
X_3 = P * X_2
Performing these matrix multiplications will give us the state matrices X_1, X_2, and X_3.
Note: Since the provided matrix P has a dimension of 3x3 and the initial state matrix X_0 has a dimension of 1x3, the resulting state matrices X_1, X_2, and X_3 will also have a dimension of 1x3.
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To find the state matrices X₁, X₂, and X₃ given the transition probabilities matrix P and the initial state matrix X₀, we can apply matrix multiplication repeatedly.
P = [0.6 0.2 0.1
0.3 0.7 0.1
0.1 0.1 0.8]
X₀ = [0.1
0.2
0.7]
To find X₁, we multiply P with X₀:
X₁ = P * X₀
To find X₂, we multiply P with X₁:
X₂ = P * X₁ = P * (P * X₀)
To find X₃, we multiply P with X₂:
X₃ = P * X₂ = P * (P * (P * X₀))
Performing the matrix multiplications, we get:
X₁ = [0.6 0.2 0.1] * [0.1
0.2
0.7] = [0.06 + 0.04 + 0.07
0.03 + 0.14 + 0.07
0.01 + 0.02 + 0.56]
X₁ = [0.17
0.24
0.59]
X₂ = [0.6 0.2 0.1] * [0.17
0.24
0.59] = [0.048 + 0.048 + 0.059
0.023 + 0.168 + 0.059
0.007 + 0.048 + 0.472]
X₂ = [0.155
0.25
0.527]
X₃ = [0.6 0.2 0.1] * [0.155
0.25
0.527] = [0.042 + 0.031 + 0.053
0.021 + 0.175 + 0.053
0.006 + 0.05 + 0.422]
X₃ = [0.126
0.249
0.478]
Therefore, the state matrices are:
X₁ = [0.17
0.24
0.59]
X₂ = [0.155
0.25
0.527]
X₃ = [0.126
0.249
0.478]
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Someone help me with this pls
Answers
Sodium-24 has a half-life of approximately 15 hours. If only one-eighth of the sodium-24 remains, about how much time has passed?.
Answers
The half-life of sodium-24 is around 15 hours. If just 1/8 of the sodium-24 is left, it has been eliminated in 60 hours.
What is the decay and half-life law?The half-life is the amount of time needed for half of the initial population of radioactive atoms to decay. T1/2 = 0.693/λ is the equation that describes the connection between the half-life, T1, and the decay constant. The rate of radioactive atoms decaying at any given instant is precisely proportional to the quantity of atoms present at that time, as stated by the radioactive decay law.
dtd N ∝ N
dtd N = λ N
where, N is number of integrated nucleus present in the sample at any time t and λ is decay constant.
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The U.S. Open Women's Singles Championship begins with 128 players. The players compete in this single-elimination tournament until there is 1 winner. How many rounds of matches must be scheduled in order to complete the tournament
Answers
Using a geometric sequence, it is found that 7 rounds must be scheduled in order to complete the tournament.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term.
In this problem, the first round has 128 players, and each round, the players who lose a game go home, hence the common ratio is of q = 0.5.
Then, the geometric sequence for the number of players after n rounds is given by:
\(a_n = 128(0.5)^n\)
In the final round, there is one player, hence:
\(1 = 128(0.5)^n\)
\((0.5)^n = \frac{1}{128}\)
\((0.5)^n = \left(\frac{1}{2}\right)^7\)
n = 7
7 rounds must be scheduled in order to complete the tournament.
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whoever answers correct i’ll mark brainliest
Answers
Answer:
37% between 1989and 2009
Step-by-step explanation:
20%+17%=37%
Which products result in a perfect square trinomial? Select three options
Answers
Answer:
Options (2), (3) and (5)
Step-by-step explanation:
This question is incomplete; here is the complete question.
Which products result in a perfect square trinomial? Select three options.
1). (-x + 9)(-x - 9)
2). (xy + x)(xy + x)
3). (2x - 3)(-3 + 2x)
4). (16 - x²)(x²+ 16)
5). (4y² + 25)(25 + 4y²)
Option (1),
(-x + 9)(-x - 9) = -(-x + 9)(x + 9)
Therefore, product is not a perfect square.
Option (2)
(xy + x)(xy + x) = (xy + x)²
So the product is a perfect square trinomial.
Option (3)
(2x - 3)(-3 + 2x) = (2x - 3)²
Therefore, product is a perfect square trinomial.
Option (4)
(16 - x²)(x²+ 16) = (-x⁴+ 256)
Therefore, product is not a trinomial.
Option (5)
(4y² + 25)(25 + 4y²) = (4y² + 25)²
= 16y⁴ + 200y² + 625
Therefore, product is a perfect square trinomial.
Options (2), (3) and (5) are the correct options.
Answer:
Options (2), (3) and (5) are the correct options.
Bok
Match the key aspect of a function's graph with its meaning.
x-intercept
1x)<0
y-intercept
Matching the Meaning of Key Features of a Graph
140
4) Intro
location on graph where output is
zero
location on graph where input is zero
intervals of the domain where the
graph is below the x-axis
intervals of the domain where the
graph is above the x-axis
Answers
The x-intercept represents the intervals of the domain where the graph is below the x-axis.
The y-intercept represents the location on the graph where the output (or function value) is zero.
Here's the matching of the key aspects of a function's graph with their respective meanings:
x-intercept:
4) Intervals of the domain where the graph is below the x-axis.
This refers to the points on the graph where the function intersects or crosses the x-axis, meaning the y-coordinate of those points is zero.
y-intercept:
Location on the graph where the output is zero.
This refers to the point on the graph where the function intersects or crosses the y-axis, meaning the x-coordinate of that point is zero.
In summary:
The intervals of the domain where the graph is below the x-axis are represented by the x-intercept.
The graph's location where the output (or function value) is 0 is shown by the y-intercept.
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Suppose triangle ABC will be dilated using the rule D Subscript Q, two-thirds.
Point Q is the center of dilation. Triangle A B C is 6 units away from point Q. The length of A B is 3, the length of B C is 7, and the length of A C is 8.
What will be the distance from the center of dilation, Q, to the image of vertex A?
2 units
3 units
4 units
6 units
Answers
The distance from the center of dilation, Q, to the image of vertex A will be 4 units.
According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.
Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.
By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x 3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.
Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.
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A map of Pennsylvania has a scale of ¾ inch to 25 miles. If Pittsburgh and Philadelphia are 9 inches apart on the map, how many miles apart are the two cities?
Answers
Answer: 225
Step-by-step explanation:
0.75 inch : 1 mile
Times either side by 12
9 inch : 225
In a 2 x 2 between-subjects factorial experiment, there are a total of ____ treatment conditions in the experiment, and each participant serves in ____ condition(s).
Answers
In a 2 x 2 between-subjects factorial experiment, there are a total of four treatment conditions in the experiment, and each participant serves in one condition(s).
In a 2 x 2 between-subjects factorial experiment, there are a total of four treatment conditions in the experiment, and each participant serves in one condition. The four conditions in a 2 x 2 between-subjects factorial experiment are created by manipulating two independent variables, each with two levels.
The levels of these independent variables are crossed together to create four unique conditions.The factorial experiment design is used to analyze the effect of multiple independent variables on a dependent variable. When the levels of each independent variable are combined in a factorial design, this results in treatment conditions.
Each participant serves in one condition in a between-subjects design. Because each condition represents a distinct treatment in a factorial design, each participant serves in one treatment condition only. Therefore, in a 2 x 2 between-subjects factorial experiment, each participant serves in one of the four treatment conditions.
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2.
On each level, there are 12 spots close to the 3 elevators reserved for drivers
with disabilities. How many parking spots are reserved for drivers with disabilities
altogether?
Answers
Answer:
9
Step-by-step explanation:
When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, a one-way ANOVA is appropriate.a. It is also appropriate in this situation, however, to compare two means at a time using multiple independent two sample t-tests. b. It is appropriate to compare two means at a time with independent two sample t-tests but it might be time-consuming.c. It is not appropriate to compare two means at a time in the way described. This would inflate the overall Type I Error and is a 'Multiple Testing' problem. The one-way ANOVA controls for the Type I Error and should be used instead.
Answers
According one-way ANOVA, the test is false.
We learn about one-way ANOVA
"One-Way ANOVA, also known as "analysis of variance," examines the refers to two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."
According to the given information, it is inappropriate to compare two means at a time using multiple independent two sample t-tests. It will create multiple testing problem and error.
So using one way ANOVA test when comparing three or more populations refers to within a set of quantitative data that is categorized according to one factor/treatment and compare two means at a time using multiple independent two sample t-tests is false.
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Pippin owns 2 cats, 3 dogs, and a lizard as pets. What is the ratio of the number of cats to the total number of pets Pippin owns?
Choose 1 answer:
is it
A 1/6
B 1/3
C 2/5
D 1/2
or E 2/3
Answers
Answer: B) 1/3
2 cats/6 total animals
simplified is 1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
plz make me brainliest
What is the degree of the polynomial below?
4x2+3x2 +6x+5
A. 3
B. 0
C. 1
O D. 2
Answers
Step-by-step explanation:
What is the total magnification if we using objective lens 4x and our eyepiece (ocular) lens is 10x
40x
100x
400x
1000x
Answer:
Simplify: (4x2 - 2x) - (-5x2 - 8x).
Solution:
(4x2 - 2x) - (-5x2 - 8x)
= 4x2 - 2x + 5x2 + 8x.
= 4x2 + 5x2 - 2x + 8x.
= 9x2 + 6x.
= 3x(3x + 2).
Answer: 3x(3x + 2)
Step-by-step explanation:
Hope it help
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what is the focus of the parabola? y= 1/4^2-x-1 Enter your answer in the boxes (__,__)
Answers
The focus of the parabola y = 1/4(2 - x) is (0, -2).
The given equation is in the standard form of a parabolic equation
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.
Comparing the given equation with the standard form, we have
a = -1/4, h = 0, k = -1
Therefore, the vertex of the parabola is at (0, -1).
Since the parabola opens downwards (the coefficient of x² is negative), the focus is located below the vertex, at a distance of |1/(4a)| from the vertex.
Plugging in the values of a, we get
|1/(4a)| = |1/(-4/1)| = 1
So, the focus of the parabola is one unit below the vertex, at (0, -2).
Therefore, the focus of the parabola is at (0, -2).
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As seen in the diagram below, Madelyn is building a walkway with a width of a feet to
go around a swimming pool that measures 12 feet by 7 feet. If the total area of the
pool and the walkway will be 300 square feet, how wide should the walkway be?
Answers
Applying the area of a rectangle, the width of the walkway (x) is: 4 feet.
What is the Area of a Rectangle?Area of a rectangle = (length)(width)
Total area of the pool and walkway = 300 sq. ft
Length of the pool and walkway = 12 + 2x
Width of the pool and walkway = 7 + 2x
Thus, we will have the equation of the total area as:
(12 + 2x)(7 + 2x) = 300
4x² + 38x + 84 = 300
4x² + 38x + 84 - 300 = 0
4x² + 38x - 216 = 0
Factorize
(x - 4)(2x + 27) = 0
x = 4
or
x = -27/2
The width, x, cannot be negative, so, the width of the walkway (x) would be 4 feet.
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Determined three ways have a total cost of six dollars each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.
Answers
The cost of the apples is 2.9 dollars.
The cost of the bananas is 5.7 dollars.
How to find the number of fruits bought?The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.
Therefore,
let
x = number of apples
y = 2x
where
y = number of bananasTherefore, using equations,
1.5(x) + y(0.30) = 6
Hence,
where
y = 2x
1.5(x) + 2x(0.30) = 6
1.5x + 0.6x = 6
2.1x = 6
divide both sides by 2.1
x = 6 / 2.1
x = 2.9 dollars
y = 2(2.9) = 5.7 dollars
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I need help and I will give five stars and a big thank you comrades
Answers
Answer:
A.
Step-by-step explanation:
A way to find the equation of the graph is to find the solutions.
On the graph, the solutions are where the function intersects the x-axis. That would be where x = -2, x = 1, and x = 3.
In the equations, you will need to find factors when the x is inputted, the factor equals 0. For example, one of the factors is (x + 2). This is because x + 2 = 0, so x = 0 - 2, so x = -2. So, the three factors are (x + 2), (x - 1), and (x - 3).
The correct equation is A.
Hope this helps!
the half-life of radon (rn-222) is 3.82 days. how much (what fraction) of a sample remains after 11.46 days?
Answers
Radon-222 was initially present in a sample of 3.82 mg. Only 0.375 mg of the radon-222 in the sample were still present after 11.46 days, after which three half-lives had gone.
As per the data given in the above question are as bellow,
A material has a half-life when it takes a particular length of time for half of it to disappear or change.
11.46 days have 3 half lives because 11.46 x 3.82 Equals 3.
We thus split the 3 mg sample in half three times.
3 ÷ 2 = 1.5
1.5 ÷ 2 = 0.75
0.75 ÷ 2 = 0.375
After 11.46 days, there will only be 0.375mg of radon-222 left.
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The plots in A-D all show ____________ correlation.
Answers
Answer:
Positive corralation
Step-by-step explanation: Algebra 1A-B
Simplify
1-(cos^2)theta/(sin^2 )theta
A. 1
B. sin^2 theta
C. cos^2 theta
D. tan^2 theta
Answers
A) 1
Explination:
So 1-cos^2 = sin^2
Which means you now have sin^2 theta/sin^2 theta
Which =1
what is an algebraic expression for 2+5p
Answers
Answer:
two plus 5 times p or two more than the product of 5 and p.
Step-by-step explanation:
Can someone help me in this question
Answers
Answer:
The average speed of the athlete for the entire competition is approximately 21.23 km/hr
Step-by-step explanation:
The given parameters of the athlete performance in the triathlon are;
The length the athlete swims = 750 m = 0.75 km
The time the athletes spends swimming = 15 minutes = 0.25 hours
The speed with which the athlete cycles = 40 km/hr.
The time the athletes spends while cycling = 30 minutes = 0.5 hours
The distance the athlete ran = 5 km
The average speed with which the athlete ran = 3 m/s = 10.8 km/hr.
The formula for average speed, s is Average speed = Total distance/(Total time)
The distance, ∑d, the athlete covered in the entire competition is given as follows;
∑d = 0.75 km + 0.5 hr. × 40 km/hr. + 5 km = 0.75 km + 20 km + 5 km = 25.75 km
The distance, ∑t, the athlete spends in the entire competition is given as follows;
∑t = 0.25 hr. + 0.5 hr. + 5 km/(10.8 km/hr.) = 0.25 hr. + 0.5 hr. + 0.463 hr. ≈ 1.213 hr.;
Therefore;
The average speed of the athlete for the entire competition, s = ∑d/∑t = 25.75 km/(1.213 hr.) ≈ 21.23 km/hr.