The appropriate range for John's distance in miles (d) during the marathon is A. [tex]$0 \leq d \leq 26.2$[/tex].
In a marathon, the distance (d) John covers depends on the time (t) he spends running. The distance is fixed at 26.2 miles, so we need to find the appropriate range for the time (t) he spends running.
Let's calculate John's average speed (v) during the marathon. We know that speed is given by:
[tex]\[ v = \frac{d}{t} \][/tex]
Where:
- v = average speed (miles per hour)
- d = distance covered (miles)
- t = time spent running (hours)
Given that John's distance is 26.2 miles, and the marathon covers this distance, we have:
[tex]\[ 26.2 = \frac{26.2}{t} \][/tex]
Solving for t:
[tex]\[ t = \frac{26.2}{26.2} = 1 \][/tex]
So, John takes 1 hour to cover the 26.2 miles.
Now, let's consider the maximum and minimum possible times for John to complete the marathon:
- Minimum time: John completes the marathon in the fastest time possible. Let's say this is 0. This implies he runs the marathon in 0 hours.
- Maximum time: John takes his time and completes the marathon at the slowest pace possible. Let's use the average time for a marathon, which is around 4.5 hours.
Thus, the appropriate range for the time (t) is:
[tex]\[ 0 \leq t \leq 4.5 \][/tex]
This corresponds to option C: [tex]$0 \leq t \leq 4.5$[/tex].
Complete Question:
John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours) Which is an appropriate range for this situation?
A. [tex]$0 \leq d \leq 26.2$[/tex]
B. [tex]$0 \leq d \leq 4.5$[/tex]
c. [tex]$0 \leq t \leq 4.5$[/tex]
D. [tex]$0 \leq t \leq 26.2$[/tex]
Quadrilateral ABCD is a parallelogram with diagonals that intersect at point E. If /,/, /, and /, solve for x.
A.
x = 2
B.
x = 4
C.
x = 6
D.
x = 8
The average wind speeds for one year at 44 climatic data centers around the United States are as follows:
9.0, 6.9, 9.1, 9.2, 10.2, 12.5, 12.0, 11.2, 12.9, 10.3, 10.6, 10.9, 8.7, 10.3, 10.6, 10.9, 8.7, 10.3, 11.0, 7.7, 11.4, 7.9, 9.6, 8.0, 10.7, 9.3, 7.9, 6.2, 8.3, 8.9, 9.3, 11.6, 10.6, 9.0, 8.2, 9.4, 10.6, 9.5, 6.3, 9.1, 7.9, 9.7, 8.8, 6.9, 8.7, 9.0, 8.9, 9.3
a) Make a stem plot of the average wind speeds data. The frequency in the stem for 9 to 9.9 is?
b) The first quartile for the wind speed data set is?
HELP might fail class
Need help with math problem
Multiply
(3x – 7)(3x – 5)
A.
9x 2 + 6x + 35
B.
9x 2 + 36x + 35
C.
9x 2 – 36x – 35
D.
9x 2 – 36x + 35
in how many ways can a judge award first, second, and third place in a contest with 10 entries
720. just multiply 10 9 and 8 because first, second, and third, that is means three and that's how many numbers you multiply from 10,so it equals 720.
hope this helps
cheers!
One side of triangle is half the longest side. the third side is 7 feet less than the longest side. the perimeter is 43. find all three sides.
In a survey, the planning value for the population proportion is p*=.35. how large a sample should be taken to provide a 95% confidence interval with a margin of error of .05 (to the nearest whole number)?
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 + 4x + 3 = 0
In which of the following quadrilaterals are consecutive angles always congruent? Check all that apply.
Answer:
Rectangle and Square.
Step-by-step explanation:
To know if the angles of a quadrilateral is congruent you must overlap these angles one over the other, if all elements of the angles coincide, the angles are congruent; if the elements do not match, the angles are not congruent. In quadrilateral rectangle and square consecutive angles are always congruent.
In other words, two or more angles are said congruent if and only if they have the same measurement.
Harry Hoodeen made $24,567.00 net pay last year. His monthly expenses averaged $1,980.00. How much was left over for savings for the year?
What is i^16 simplified
the sum of 3 numbers is 26. the second number is twice the first and the third number is 6 more than the second. find the number
Answer:
the numbers are 4, 8, 14
Step-by-step explanation:
If we subtract 6 from the third number and from the total, we find that we now have 5 times the first number for a total of 20.
The first number is 4.
The second number is 2×4 = 8.
The third number is 8 + 6 = 14.
Simplify.
Square root of 121m^8n^4
A. 11mn
B. 11m^2n^2
C. 11m^4n^2
Answer:
B
Step-by-step explanation:
no
Need help geometry ^^^
Write a conditional that multiplies the value of the variable pay by one-and-a-half
Explain how you would use trig ratios to find the height of the tree if you know you are standing 30 feet from the base of the tree when you measure the 37-degree angle.
From use of trigonometric ratios, it is seen that the height of the tree is; 22.61 feet
How to work with trigonometric ratios?We are told that you are standing 30 ft from the base of a tree.
Now, the distance from where you are standing to the top of the tree will be the hypotenuse of the triangle formed by you and the tree.
Thus, if the height of the tree is h and the angle the hypotenuse makes with the 30 ft base is 37°, then we have;
h/30 = tan 37
h = = 30 * tan 37
h = 22.61 ft
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The equation of the straight line of slope 3 passing through the point (2, 5) may be written as
How can you tell whether a rational expression is in simplest form? Include an example with your explanation.
Rational numbers are numbers that are written as a ratio of two integers.
Let a and b be integers, hence a rational expression can be expressed as a/bIn order to tell whether a rational expression is in its simplest form, we need to ensure no integer can go in both the numerator and the denominator.
For instance, given the rational number 10/15, the simplest form of the rational number will be expressed as (5*2)/(5*3) = 2/3
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HELP ME PLEASE!
Peter walks 30 feet away from his house and places a mirror on the ground. He backs 6 feet away from the mirror so that he can see the tip of the roof. Peter's eyes are 5 feet above the ground. Peter and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Peter's eyes, the mirror, and the ground are congruent as shown in the image below:
Image depicts a mirror on the ground between a person and a house. The mirror is 6 feet away from the person and 30 feet away from the house.
What is the height of the house?
By setting up a proportion based on the similar triangles formed by Peter's line of sight and the analogous line from the top of the house to the mirror, we find that the house is 25 feet tall.
According to the Law of Reflection and the information provided, we have two similar triangles: one formed by Peter's eyes, the mirror, and the point on the ground directly below his eyes, and the other formed by the top of the house, the mirror, and the point on the ground directly below the top of the house.
The first triangle has a height of 5 feet (Peter's eye level) and a base of 6 feet (the distance from Peter to the mirror). The second triangle's height is what we are trying to find (height of the house), and its base is 30 feet (distance from the house to the mirror).
Because the triangles are similar, the ratios of their corresponding sides are equal. So, we can set up the following proportion:
Height of Peter's eyes / Distance to mirror = Height of the house / Distance to mirror from house
5 feet / 6 feet = Height of the house / 30 feet
Now, cross-multiply to solve for the height of the house:
5 feet * 30 feet = Height of the house * 6 feet
Height of the house = (5 * 30) / 6
Height of the house = 150 / 6
Height of the house = 25 feet
Therefore, the height of the house is 25 feet.
1. Given f(x)=3x+8f(x)=3x+8 and g(x)=6x+6g(x)=6x+6 then what is (f+g)(−1))(f+g)(−1)) ?
2. Given f(x)=6x+4f(x)=6x+4 and g(x)=3x+7g(x)=3x+7 then what is (f−g)(1)) ?
Sandy can assemble a particular type of light fixture in 3/8 hour. it takes her 2/3 hour to hang the fixture and another 1/6 hour to wire the fixture once it is hung. how many fixtures could sandy install in 29 hours?
Sandy can install a maximum of 24 fixtures in 29 hours.
Explanation:To calculate the number of fixtures Sandy can install in 29 hours, we need to determine the amount of time it takes for Sandy to complete one installation process (excluding assembly time).
Sandy takes 2/3 hour to hang the fixture and another 1/6 hour to wire it, totaling
2/3 + 1/6 = 7/6 hour.
Therefore, Sandy takes 7/6 hour per fixture.
Next, we can calculate the number of fixtures by dividing the total time available (29 hours) by the time it takes for one installation process.
Number of fixtures = Total time available / Time per fixture
Number of fixtures = 29 / (7/6) = 29 * (6/7) = 174/7 = 24.86
Since we can't have a fraction of a fixture, Sandy can install a maximum of 24 fixtures in 29 hours.
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On his birthday newton was 14 years old and his father was 41 newton noticed that his age was his fathers age with the digits reversed how many years later with their ages next have their digits reversed
When the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.
It is given that when Newton was 14 years old , his fathers age was 41 yrs.
We have to find out that at what age of Newton his fathers age will be reversed again ?
Solve for the value of x ; 10 x - 14 = 12x - 28 ?
The value of x will be 7.
Let's assume the tens place as x and one's place as y.
The actual number will be ; 10 x + y.
Reverse numbers pairs can be written as (10x+y) and (10y+x).
As the age of Newton's father is 41 yrs when he is 14 yrs old , so we have ;
(10x+y) - (10y+x) = 41–14 = 27
Hence , we can say that the age difference between Newton and his father is 27 years. This age difference will be same forever.
So ;
(10x+y) - (10y+x) = 27
and we have to find all values of x and y that will satisfy this equation.
⇒ (10x+y) - (10y+x) = 27
⇒ 9x - 9y = 27
⇒ x - y = 3
For all x’s and y’s who have their difference as 3 will answer the question. For example , (4,1) (5,2) (6,3) (7,4) (8,5) …. and so on.
Since Newton's father age today is 41 yrs.
The next age to satisfy the condition is 52 yrs.
This makes Newton’s age to be 52 - 27 = 25 which is the reverse of 52.
So , the answer of the question is that Newton should be of 25yrs , for his age to be the reverse of his father’s age.
Thus , when the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.
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1. What is 3/8x < -6 or 5x>2 solved and graphed?
2. What is 2<10 -4d< 6 solved and graphed?
I appreciate your help!
WILL GIVE A BRAINLIEST PLEASE HELP!!!
Use the formula below to find the 6th term in the geometric sequence.
a(n)=(5)x(3/2)n-1
A.
5
B.
15/2
C.
1,215/32
D.
3,645/64
How much dirt is there in a hole 3 feet deep, 6 ft long and 4 ft wide?
the volume of the hole would be 3 * 6 * 4 =72 cubic feet.
However, since it is a hole, there would be no dirt in it.
In 1980, the United States' national debt exceeded $9 billion dollars. Express the exact dollar amount in scientific notation.
Helpppppppppp me!!!!!!!!!
A) w/9=6
w=9*6
w=54
B) 5q=15
q=15/5
q=3
C)2s-3s=20
-1s=20
s=20/-1 = -20
s=-20
D)4-a=-12
a= 4+12 = 16
a=16
How do I do this someone please explain I need help
Directions: Describe the transformation. (x,y) -> (5x,5y)
The transformation (x, y) -> (5x, 5y) is a scaling transformation that dilates a point by a factor of 5 in both the x and y directions, making the entire figure five times larger while preserving its shape.
Explanation:The transformation described by (x, y) -> (5x, 5y) is a scaling transformation or dilation in both the x and y directions by a factor of 5. What this means is that any point on the plane, when subjected to this transformation, will move five times further away from the origin along both axes. For example, if you begin with the point (1, 1), applying this transformation will result in the point (5, 5). This dilation affects all points equally, meaning that the relative distances between points are preserved, but the entire figure is made larger by a factor of 5. Therefore, if you have a figure with dimensions of length and width, after the transformation, both dimensions will be increased by five times their original measure.
Final answer:
The transformation (x, y) -> (5x, 5y) represents a dilation, enlarging a figure by a factor of 5 along both the x-axis and y-axis, which alters size but not shape.
Explanation:
The transformation described by the rule (x, y) -> (5x, 5y) is a geometric transformation known as a dilation or scaling. This type of transformation alters the size of a figure without changing its shape. Specifically, the coordinates of each point in the figure are multiplied by 5, which means that the figure is enlarged by a factor of 5 in both the x-axis (east-west direction) and the y-axis (north-south direction). If, for example, we apply this transformation to a point (1, 2), the resulting coordinates will be (5, 10), and similarly, applying it to (3, 7) would yield (15, 35). This illustrates the dependence of y on x as each x-coordinate and y-coordinate are scaled by the same factor, maintaining the shape but increasing the size.
What is the slope of the line below