2.4kg.,
..
hope it helps
On average, mary has noticed that 18 trains pass by her house daily (24 hours) on the nearby train tracks. what is the probability that exactly 1 train will pass her house in a 3 hour time period?
The probability that exactly 1 train will pass Mary's house is 0.00889.
According to the given question.
On average, 18 trains pass by Mary's house daily i.e. in 24 hours.
As, we know that "Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event".
Therefore,
The probability that exactly one train will pass Mary's house in a 3 hour period
= [tex]\frac{^{18C_{1} } }{^{24} C_{3} }[/tex]
[tex]= \frac{\frac{18!}{1!\times17!} }{\frac{24!}{3!\times 21!} }[/tex]
[tex]= \frac{18}{\frac{24\times23\times22}{3\times2\times1} }[/tex]
[tex]=\frac{18}{8\times23\times\ 11}[/tex]
= 18/2024
= 0.00889
Hence, the probability that exactly 1 train will pass Mary's house is 0.00889.
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A student is trying to solve the system of two equations given below: equation p: y z = 6 equation q: 3y 4z = 1 which of these is a possible step used in eliminating the y-term? (y z = 6) ⋅ 4 (3y 4z = 1) ⋅ 4 (y z = 6) ⋅ −3 (3y 4z = 1) ⋅ 3
Option C is correct (y + z = 6) ⋅ −3
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.As per the statement -
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6 ....[1]
Equation Q: 3y + 4z = 1 ....[2]
Multiply the equation [1] by -3 to both sides we have;
-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)
Add equation [2] and [3] to eliminate the y-term;
z = -17
Therefore, the possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3
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The complete question is -
A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?
(y + z = 6) ⋅ 4
(3y + 4z = 1) ⋅ 4
(y + z = 6) ⋅ −3
(3y + 4z = 1) ⋅ 3
Brianna walks around a triangular park, daily. The longest side of the park measures 75 yards
and the shortest side measures 45 yards. If she walks 3 full laps around the park, how far does she
walk in one day?
She walks 540 yards for 3 full laps around the park per day.
How to determine the distanceFrom the information given;
The longest part of the triangular park = 75 yards
The shortest part = 45 yards
Let's find the other part, using Pythagorean theorem;
a² = b² + c²
75² = 45² + c²
c² = 75² - 45²
Find the squares
c² = 5625 - 2025
c² = 3600
Make 'c' the subject
c = √3600
c = 60 yards
If she walks
75 + 60 + 45 yards per lap
180 yards per lap
For three laps, she walks
= 3 × 180
= 540 yards
Thus, she walks 540 yards for 3 full laps around the park per day.
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Convert the cartesian coordinate (-6,-1) to polar coordinates, 0 ≤ θ < 2 π , r > 0 0≤θ<2π, r>0
The polar coordinate of given cartesian coordinate (-6, -1) is
(6.08, 0.0523π)
In this question,
We have been given the cartesian coordinate (-6, -1)
We need to convert given cartesian coordinate to polar coordinates.
We know that the polar coordinates is of the form (r, θ)
where, r is the magnitude with r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]
and θ is the angle associated with the coordinates which is given by θ = [tex]tan^{-1}(\frac{y}{x} )[/tex]
The magnitude of the given polar coordinate is,
⇒ r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]
⇒ r = [tex]\sqrt{(-6)^{2}+ (-1)^{2} }[/tex]
⇒ r = [tex]\sqrt{36+ 1}[/tex]
⇒ r = [tex]\sqrt{37}[/tex]
⇒ r = 6.08
And the angle associated with the coordinate is,
⇒ θ = [tex]tan^{-1}(\frac{-1}{-6} )[/tex]
⇒ θ = [tex]tan^{-1}(0.167 )[/tex]
⇒ θ = 9.48°
⇒ θ = 0.0523π
So, the polar coordinate is (6.08, 0.0523π)
Therefore, the polar coordinate of given cartesian coordinate (-6, -1) is
(6.08, 0.0523π)
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Is there any number in base 10 (positive or negative) that can be written in multiple
ways in base −4? Can you prove it? If yes, provide the number and the base −4
representations, and if no, show why.
The true statement is that no number in base 10 can be written in multiple ways in base 4
How to determine the true statement?The base of the numbers are given as:
Base 10 and base 4
Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers
There is only one equivalent of each number in each base.
This means that (for instance)
357 in base 10 is 11211 in base 4
The above number does not have any other representation in base 4 and it can not be written in another way.
This is the same for other numbers in base 10
Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4
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Jake volunteers to help out his younger brother's basketball team in his free time. One of his tasks is to ensure that all the basketballs have enough air in them. Given that a properly inflated basketball measures 8.8 inches across, what is the total volume of air inside six of Jake’s basketballs? Assume that the wall of each ball is infinitely thin.
Using the volume of a sphere, the total volume of air inside six of Jake's basketballs is of 2140.8 cubic inches.
What is the volume of a sphere?The volume of a sphere of radius r is given as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
From the problem, since the properly inflated basketball measures 8.8 inches across, the diameter is of 8.8 inches, hence the radius is:
r = 8.8/2 = 4.4 inches.
Then the volume in cubic inches of a single ball is:
V = 4 x pi x (4.4)³/3 = 2140.8 cubic inches.
For the six balls:
6 x 356.8 = 2140.8 cubic inches.
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corresponding angles are congruent =. which angle corresponds with 3
The angle that corresponds to 3 is angle 5
How to determine the angle that corresponds to 3?Corresponding angles are angles that are at the same relative position between parallel lines and transversal
These angles are congruent
From the figure, we have:
Angle 3 and Angle 5 are in the same relative position
Hence, the angle that corresponds to 3 is angle 5
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Choose the definition for the function.
(-x+ 2 x < 1
x ≥ 1
a. y = x + 1
(-x+ 2
x + 1
b.y = {-x+ 2 x≤1
1
x >
c. y = {-x-
C.
x≤ 1 d. y = { x + 1
(-x+ 2
x > 1
x ≤ 1
x ≥ 1
x < 1
Enter
Answer:
A
Step-by-step explanation:
The answer is negative so that eliminates one
and the greater sign is opposite of b so that makes the answer A!
A three-digit number has one more ten than it has hundreds, and it also has one more than twice as many units as tens. The sum of the number and that number reversed is 31 less than 10 cubed. Find the reverse number.
15 pts
The reverse number of the three-digit number is 732
How to determine the reverse of the number?Let the three-digit number be xyz.
So, the reverse is zyx
This means that
Number = 100x + 10y + z
Reverse = 100z + 10y + x
From the question, we have the following parameters:
y = x + 1
z = 1 + 2y
The sum is represented as:
100x + 10y + z + 100z + 10y + x = 10^3 - 31
100x + 10y + z + 100z + 10y + x = 969
Evaluate the like terms
101x + 101z + 20y = 969
Substitute y = x + 1
101x + 101z + 20(x + 1) = 969
101x + 101z + 20x + 20 = 969
Evaluate the like terms
101x + 101z + 20x = 949
121x + 101z = 949
Substitute y = x + 1 in z = 1 + 2y
z = 1 + 2(x + 1)
This gives
z = 2x + 3
So, we have:
121x + 101z = 949
121x + 101* (2x + 3) = 949
This gives
121x + 202x + 303 = 949
Evaluate the sum
323x = 646
Divide by 323
x = 2
Substitute x = 2 in z = 2x + 3 and y = x + 1
z = 2*2 + 3 = 7
y = 2 + 1 = 3
So, we have
x = 2
y = 3
z = 7
Recall that
Reverse = 100z + 10y + x
This gives
Reverse = 100*7 + 10*3 + 2
Evaluate
Reverse = 732
Hence, the reverse number of the three-digit number is 732
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1)give your answer in terms of π
2) give your answer using 3.14 for π
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
Volume of a cylinderA cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes
The volume of the composite cylinder is expressed as shown below;
V = πr²h
where
r is the radius
h is the height
According to the given diagram;
V = Vl - Vs
V = π(10)²*15 - π(5)²*15
V = 1500π - 375π
V = 1125π cubic inches
If the value of π is 3.14, hence;
V = 1125(3.14) cubic inches
V = 3532.5 cubic inches
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
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The length of a spring with no applied force acting on it is 10.00 centimeters. Juanita applied different forces to the spring and recorded the new lengths of the spring in a table. She also graphed a scatterplot from the results in the table. Based on the scatterplot, which equation BEST represents these data?
Answer:
the second option L = 0.05F + 10
Step-by-step explanation:
the first one
F = 0.05L + 10
does not make any sense, as for length = 10 the force has to be 0. but this function here gives us
0.05×10 + 10 = 0.5 + 10 = 10.5
which is clearly not 0. so, this is wrong.
the second one is correct.
L = 0.05F + 10
it is not perfect, but it is the only one describing the first data points well. like, when F = 0, then L = 10.
the third
L = 0.05F
fails already at the beginning F = 0, as it gives us L = 0 instead of 10. this is wrong.
the fourth
F = 0.05L
fails also already at the beginning. for L = 10 we need to have F = 0. but instead we get F = 0.5. this is wrong.
Verify whether the given differential equation is exact or not. if exact, solve. cosx y/x dx dy
The differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
For given question,
we have been given a differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex]
We have to determine given differential equation is exact or not.
Compare it with M dx + N dy = 0
⇒ M = cos(x) and N = y/x
Find the derivative of M with respect to y.
[tex]\Rightarrow M_y=-sin(x)[/tex]
Now, find the derivative of N with respect to x.
[tex]\Rightarrow N_x=\frac{-y}{x^{2} }[/tex]
Since [tex]M_y \neq N_x[/tex], given differential equation is not exact.
Therefore, the differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
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Which equation represents the relationship shown in the
graph?
gradient = rise/run
= 2/1
= 2
So,it's the first option, y=2x
Hope this helps!
Hodaya is drawing a map of the trails in the canyon near her house. she knows that the distance from the first creek crossing to the second creek crossing is 1.8 miles. if every 3 inches on the map represents 0.75 of a mile, how far apart will the two creek crossings be on the map, to the nearest tenth of an inch? 2.3 4.1 5.4 7.2
The correct answer is 7.2 inch.
What is meant by distance?The length of the path joining two points determines their distance from one another.The entire journey that an object has taken can be used to define distance. An illustration. If an automobile drives 5 km east, then turns and drives 8 km further north, the total distance driven by the car is 13 km.'Distance' can be a verb or a noun, as was said above. He set himself apart from the remarks made by several of his coworkers. Thirty miles separate Peterborough from the nearest point. He had pledged to complete this duty but fell short of his commitment.The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance between two points can be computed by measuring the length of the line segment connecting the two points.The nearest tenth of a 7inch.
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Consider a function that goes through the two points (0, 5) and (1, 20). Find the formula for the function if(a) the function is linear (of the formf(x) =mx b)
The formula for the linear function which is passing the points (0, 5) and (1, 20) is f(x) = 15x + 5.
According to the given question.
The linear form of the function is
f(x) = mx + b
Also, the function is passing through the points (0, 5) and (1, 20).
So, the given points (0, 5) and (1, 20) must satisfy f(x) = mx + b.
Now,
At (0, 5)
f(0) = m(0) + b
⇒ 5 = 0 + b
⇒ b = 5 ..(i)
Also,
at (1, 20)
f(1) = m(1) + b
⇒ 20 = m + 5 (from i)
⇒ m = 20 - 5
⇒ m = 15
Therefore, the formula for the linear function which is passing the points (0, 5) and (1, 20) is given by
f(x) = 15(x) + 5 (on substituting the vale of m and b in f(x) = mx + b).
⇒ f(x) = 15x + 5
Hemce, the formula of the function is f(x) = 15x + 5.
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Solve for d.
5+d > 5−d
Answer:
d>0
Step by Step Explanation:
Let's solve your inequality step-by-step.
5+d>5−d
Step 1: Simplify both sides of the inequality.
d+5>−d+5
Step 2: Add d to both sides.
d+5+d>−d+5+d
2d+5>5
Step 3: Subtract 5 from both sides.
2d+5−5>5−5
2d>0
Step 4: Divide both sides by 2.
2d/2>0/2
d>0
Answer:
3
Step-by-step explanation:
You could put 3 because 5+3 is greater than 5-3.
A sampling method is _________ when the individuals selected for one sample are used to determine the individuals in the second sample.
a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample
What is sampling?Sampling can be defined as a technique of selecting a subset of the population or individual members in order to make statistical inferences from them and estimate the entire characteristics of the whole population.
Sampling methods are used by researchers in market research to reduce the workload and also to research the entire population
It is time-friendly, cost-effective method and forms the basis of research design.
Some sampling methods are;
Simple random samplingSystematic samplingStratified samplingClustered samplingQuota samplingPurposive samplingIt can be said to be dependent when selecting from one sample affects another sample.
Thus, a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample.
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Find u special 4 A. 22‾√ 2 2 B. 4 C. 2 D. 2‾√
The value of u in the special triangle is 2√3
How to solve for u in the special triangle?The complete question is added as an attachment
From the attached figure, the value of u can be calculated using the following sine trigonometry ratio
sin(x) = Opposite/Hypotenuse
Where
x = 30
Opposite = u
Hypotenuse = 4√3
Substitute the known values in the above equation
sin(30) = u/4√3
Multiply both sides of the equation by 4√3
u = 4√3 * sin(30)
Evaluate the trigonometry expression sin(30)
u = 4√3 * 1/2
Evaluate the product
u = 2√3
Hence, the value of u in the special triangle is 2√3
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Given that a randomly chosen flight arrives in los angeles (lax), what is the probability that the carrier is american airlines (aa)?
Using concepts of probability, it exists found that there exists a 4.7% probability that it arrives at American airlines (aa).
What is probability?A probability exists given by the number of expected outcomes divided by the number of total outcomes.
Over a large number of trials, a percentage can also define the probability of a single event.
In this question, analyzing the problem on the internet, we have that over a considerable number of flights, of those which came on time, 4.7% of them were in American airlines.
There exists a 4.7% probability that it arrives on American airlines(aa).
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Answer: 2316/16924 = 0.137 = 13.7%
Step-by-step explanation:
What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?
Answer:
[tex]y=-\frac{1}{3}x+7[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is -1/3.
Substituting into point-slope form and converting to slope-intercept form,
[tex]y-5=-\frac{1}{3}(x-6) \\ \\ y-5=-\frac{1}{3}x+2 \\ \\ y=-\frac{1}{3}x+7[/tex]
What is the slope of the line that passes through the points (9, 2) and
(9,27)? Write your answer in simplest form.
Answer:
Slope (m) = infinity
Step-by-step explanation:
Given points:
⇒ (9, 2) and (9, 27)
In order to find the slope of these points, we must use the slope formula.
So the formula is ⇒ y₂ - y₁ / x₂ - x₁
Plug in the given points:
⇒ 27 - 2 / 9 - 9
Solve both the top and bottom (numerator and denominator):
⇒ 25 / 0
Divide:
⇒ Undefined.
(Anything divided by zero is undefined).
what is the answer for x+$4.30 =$15.00
Answer:
x = 10.7
Step-by-step explanation:
Which is the graph of the equation y- 1 = (x − 3)?
Answer:
the graph is a linear function
root (2,0) vertical intercept (0,2)
Step-by-step explanation:
Please help im not the brightest with math
Answer:
12 square in
Step-by-step explanation:
In the diagram, the diameter is 4 in. Radius is half the length of diameter, so the radius of the yellow circle is 2 in. Using the given formula, A = pi*r*r, we can calculate the approximate area of the circle.
A = pi*r*r = 3*2*2 = 12 square in
Answer:
12 in^2
Step-by-step explanation:
Since the formula to find the area of a circle is already up, we can use that to solve the question.
In the image, we can see that the diameter of the circle is 4inches. Since two radii equal one diameter, one radius is 2 inches.
--> The reason why we found the radius is because the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.
Now, we can just replace r with 2.
--> A = 4[tex]\pi[/tex]
Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.
--> A = 4 x 3
--> A = 12
We can conclude that the area of the circle is 12 in^2.
what are the minimum and maximum temperatures in the house ?
Answer:
I mean, I think it varies by house and by location but a general range would be:
Min: 64 *F
Max: 74 *F
Ken can run m miles at a
pace of 6.30 minutes per
mile. He ran slower for 10
minutes to warm up.
Write an equation that
represents the total time,
t, Ken spent running.
Equation that represents the total time t (in minutes) Ken spent running is = 10 + m/6.30.
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Total time t (in minutes) =Initial Time + distance/speed
Given :-
Distance = mSpeed = 6.30 miles per hourInitial Time = 10 minThus,
t = 10 + m/6.30.
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can someone please help me(20 points will give brainliest!!!)
Answer:
g(2) = 16; g(-2) = 4; g(a) = 3a + 10; 3(a+2) = 3a + 16
Step-by-step explanation:
We want to substitute the value in the parentheses on the left-hand side for the value of x on the right-hand side
Thus, g(2) = 3(2) + 10 = 6 + 10 = 16
g(-2) = 3(-2) + 10 = -6 + 10 = 4
g(a) = 3(a) + 10 = 3a + 10
g(a + 2) = 3(a + 2) + 10 = 3a + 6 + 10 = 3a + 16
one end of a tent is a triangle. the height of the triangle is 1.5 m and the base is 2.5 m. what is the area of the triangle?
Answer:
1.5×2.5/2=1.875.
Step-by-step explanation:
We all know that area of triangle is base into hight upon 2.
construct a quadrilateral
AB=6cm , BC = 5cm, AD = 4CM CD =7cm and BD = 6cm
If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.
What is quadrilateral?
If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.
Given: AB = 6cm , BC = 5cm, AD = 4cm, CD = 7cm and BD = 6cm
Draw a line AB with 6cm with A as the center draw an arc of radius 4 cm. And draw another arc of 6cm to cut the previous arc at D with B as the center draw an arc of radius 5cm. And with D draw another arc of 7cm to cut the previous arc at C. Join the lines of the quadrilateral.
Now ABCD exists as a required quadrilateral.
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give the volume of the cylinder below
Answer:
B. 126 [tex]\pi[/tex]
Step-by-step explanation:
The volume for a cylinder is: Area of the base x Height
The base is a circle with a diameter of 6cm.
The formula to find the area of the base is: radius x radius x pi
In this case, the radius is 3 (6/2) so the area will be 9pi.
Now that we know that area of the base, all we need to do is multiply the height, which is 14cm.
9 pi x 14 = 126 pi
So B. 126 pi is the correct answer!
Answer:
126π
option B is the correct answer
