The instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s
To estimate the instantaneous velocity of the train at t = 9 seconds, we can consider the average velocities over several small intervals of time that include the point t = 9. This is an approximation of the slope of the tangent line to the curve s(t) at t = 9, which is the instantaneous velocity.
We can calculate the average velocity over each interval by dividing the change in displacement by the change in time:
Average velocity from [8.5, 9] = (s(9) - s(8.5)) / (9 - 8.5) = (8√9 + 1 - 8√8.5 + 1) / 0.5 = 6.34 m/s (approx.)
Similarly, we can calculate the average velocities over the other intervals:
[8.7, 9]: 6.48 m/s (approx.)
[8.9, 9]: 6.60 m/s (approx.)
[8.99, 9]: 6.66 m/s (approx.)
[9, 9.01]: 6.67 m/s (approx.)
[9, 9.1]: 6.74 m/s (approx.)
[9, 9.3]: 6.87 m/s (approx.)
[9, 9.5]: 7.00 m/s (approx.)
As we consider smaller intervals closer to t = 9, the average velocities approach a limit, which is the instantaneous velocity at t = 9. In this case, we see that the average velocities are increasing as we approach t = 9, indicating that the instantaneous velocity at t = 9 is also increasing.
Based on these calculations, we can estimate that the instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s (averaging the average velocities from [8.99, 9] to [9, 9.5]).
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A sleep study was given to 20 randomly selected people between the ages of 1 and 16. The graph shows the relationship between the age of the person and the number of hours they slept.
Which of the following describes the pattern of association between the variables, based on the graph?
There is a positive linear association.
There is a positive nonlinear association.
There is a negative linear association.
There is a negative nonlinear association.
Greatest common factor of 32
What is the total perimeter of this figure?
34.71 ft
31.71 ft
39.42 ft
36.42 ft
The rectangle's circumference is 27+ (3/2) fee and one of its sides is a semicircle.
We can start by finding the perimeter of the rectangle, which is simply the sum of the lengths of all four sides:
Perimeter of rectangle = 2(length + width) = 2(12 + 3) = 30 feet
Next, we need to find the perimeter of the semicircle.
The diameter of the semicircle is equal to the width of the rectangle, which is 3 feet. The formula for the perimeter of a semicircle is:
Perimeter of semicircle = (π/2) x diameter + diameter
Plugging in the values, we get:
Perimeter of semicircle = (π/2) x 3 + 3 = (3/2)π + 3
Now, we can add the perimeter of the semicircle to the perimeter of the rectangle to get the total perimeter:
Total perimeter = Perimeter of rectangle + Perimeter of the semicircle- 2*diameter of the semicircle
= 30 + (3/2)π + 3 - 3*2
= 27+ (3/2)π
Therefore, the perimeter of the rectangle with a semicircle on one side is 27+ (3/2)π feet, or approximately 31.71 feet (rounded to two decimal places).
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Help meeeeeeeewwwwwwerr
1. The table below shows different make of cars owned by teachers in a certain school. Work out the angles and percentages then illustrate the information using a pie chart.
Make of cars Frequency
Toyota
Nissan
Datsun
Volvo
Peugeot 12
8
8
2
10
The angles and percentages have been calculated as shown below.
A pie chart for the information about the different make of cars is shown below.
How to determine the angles and percentage?For the total number of car makes, we have the following:
Total make of cars = 12 + 8 + 8 + 2 + 10
Total make of cars = 40.
Next, we would determine the angles and percentage as follows;
Toyota
12/40 × 360 = 108°
12/40 × 100 = 30%.
Nissan
8/40 × 360 = 72°
8/40 × 100 = 20%.
Datsun
8/40 × 360 = 72°
8/40 × 100 = 20%.
Volvo
2/40 × 360 = 18°
2/40 × 100 = 5%.
Peugeot
10/40 × 360 = 90°
10/40 × 100 = 25%.
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help pleaseeeeeeeeee
What’s the distance between 15,-17 and -20, -5
The distance will be in the decimal form is :41.34
Pythagoras Theorem Formula:Consider the triangle :
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
[tex]Hypotenuse^2 = Perpendicular^2 + Base^2[/tex]
[tex]c^2 = a^2 + b^2[/tex]
We have the points are:
15,-17 and -20, -5
To find the distance between them.
The distance of x- axis is:
15 - (-20)
= 15 + 20
= 35
The distance of y- axis is:
|17 - 5| = |-22| = 22
We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle:
[tex]x^2+y^2=(distance)^2[/tex]
[tex]35^2+22^2=distance^2[/tex]
[tex]1709= distance^2\\Distance = \sqrt{1709}[/tex]
In decimal form the distance would be around 41.34.
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what is the base what is the length of the base in the Triangle below
Answer:
Step-by-step explanation:
4
Twelve of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select a DVR that is not defective?
Step-by-step explanation:
a probability is always the ratio
"desired" cases / totally possible cases
the totally possible cases here are 100.
now, the question focuses on non-defective units.
how many out of the 100 are non-defective ?
well, 100 - 12 = 88 units.
so, the probability to select a non-defective (= working) unit is
88/100 = 22/25 = 0.88
in other words, as a mean and expected value, in 88 of 100 attempts, or in 22 of 25 attempts you will select a non-defective unit.
There are 100 DVRs in the inventory, and 12 of them are defective. Therefore, the number of non-defective DVRs is:
100 - 12 = 88
The probability of selecting a non-defective DVR can be found by dividing the number of non-defective DVRs by the total number of DVRs:
P(non-defective DVR) = number of non-defective DVRs / total number of DVRs
= 88 / 100
= 0.88
Therefore, the probability of randomly selecting a DVR that is not defective is 0.88, or 88%.
need help pls quick.. algebra here is screenshot right answer only
The value that would help Charlie find out how long it takes his basketball to reach the highest point is "x at the vertex". The correct option is A.
When the basketball reaches the highest point, its vertical velocity is zero. The time taken to reach this point can be found using the equation:
t = -b / (2a)
where a is the acceleration due to gravity (-9.8 m/s²) and b is the initial vertical velocity of the basketball.
The vertex of the parabolic path that the basketball follows is the point where the basketball reaches its maximum height. This point occurs at the halfway point of the ball's total flight time. The horizontal distance the basketball travels during this time is called "Ox at the vertex".
Therefore, by finding the "x at the vertex", Charlie can calculate the total flight time of the basketball, and then use the equation above to find the time it takes to reach the highest point.
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Simplify fraction numerator 6 minus x over denominator x squared minus 8 x plus 12 end fraction
The simplified form of the fraction is A = -1 / (x - 2)
Given data ,
Let the fraction be represented as A
Now , the value of A is
A = (6 - x) / (x² - 8x + 12)
On factorizing the denominator , we get
(x² - 8x + 12) = ( x - 6 ) ( x - 2 )
So , the new fraction is
A = ( 6 - x ) / ( x - 6 ) ( x - 2 )
A = - ( x - 6 ) / ( x - 6 ) ( x - 2 )
Taking the common factor out , we get
A = -1/ ( x - 2 )
Hence , the fraction is A = -1/ ( x - 2 )
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A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 time
the smaller number. Which equations represent the situation?
O 2x-y--6 and 3x-y--5
O 2x-y--3 and 3x-y--5
O 2x-y--6 and x-3y-5
O 2x-y--3 and x-3y-5
Mark this and return
Save and Exit
Next
Submit
Answer:
So the smaller number is x = 1 and the larger number is y = 8.
Step-by-step explanation:
substitute y = 3x + 5 into the first equation and solve for x.
y = 2(x + 3) 3x + 5 = 2(x + 3) Expand the parentheses 3x + 5 = 2x + 6 Subtract 2x from both sides x + 5 = 6 Subtract 5 from both sides x = 1
Now we can plug x = 1 into either equation to find y.
y = 2(x + 3) y = 2(1 + 3) y = 2(4) y = 8
Need help in Question no: 8.
With workings please.
Thank you.
The possible values for t for the points A and B with gradient 2 are t = -1 or t = 3/2.
How to evaluate for the possible values of tGiven the gradient 2 for the point A and B, we have that;
gradient = (y₂ - y₁)/(x₂ - x₁)
so;
2 = (2t² + 7 - t)/(7 - 2)
2 = (2t² + 7 - t)/5
10 = 2t² + 7 - t {cross multiplication}
2t² + 7 - t - 10 = 0
2t² - t - 3 = 0
2t² + 2t - 3t - 3 = 0 {we rewrite the middle term}
2t(t + 1) -3(t + 1) = 0
(2t - 3)(t + 1) = 0 {factorization}
2t - 3 = 0 or t + 1 = 0
t = 3/2 or t = -1
Therefore, the possible values for t for the points A and B with gradient 2 are t = -1 or t = 3/2.
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please write the answer in minutes.
Thank you.
My life depends on you
Note that the estimated time it will take to cause hearing loss at 106 decibels is 0.0625 hours or 3 minutes, 75 seconds.
How did we arrive at this conclusion?The formula used is:
Exposure Time = 8/ 2^((dBA-85)/3)
Since the decibel (dBA) given is 106
Exposure Time = 8/ 2^((106-85)/3)
= 8/2^1
= 8/ 128
= 0.0625 hours or 3 minutes, 75 seconds.
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Which of the numbers is not equal to the other?
Comparing all the numbers, we can see that (d) 21/2500 is not equal to the other numbers, since it is a fraction and all the other numbers are decimals. Therefore, (d) is the answer.
To determine which of the numbers is not equal to the other, we can convert all the numbers to the same form and compare them.
a) 0.84% can be written as 0.0084 in decimal form.
b) (0.21)(0.04) equals 0.0084.
c) 8.4 x 10⁻² can be written as 0.084 in decimal form.
d) 21/2500 can be simplified by dividing both the numerator and denominator by 21 to give 1/119.
e) 21/2500 x 10⁻² can be simplified by dividing both the numerator and denominator by 21 and multiplying by 100 to give 0.084.
In conclusion, to determine which number is not equal to the other, we need to convert all the numbers to the same form and compare them. In this case, we converted all the numbers to decimal form except for (d), which is a fraction. By comparing the numbers, we found that (d) is not equal to the other numbers.
Therefore, (d) is the answer.
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Find the total surface area of this cylinder. Give your answer to 1 decimal place. 18 cm 24 cm
The total surface area of the cylinder is 2260.8 cm².
How to find the total surface area of a cylinder?The height of the cylinder is 18 centimetres and the diameter of the cylinder is 24 centimetres.
Therefore, the total surface area of the cylinder can be calculated as follows:
total surface area = 2πr(r + h)
where
r = radiush = heightTherefore,
r = 24 / 2 = 12 cm
h = 18 cm
total surface area = 2 × 3.14 × 12(12 + 18)
total surface area = 75.36(30)
total surface area = 2260.8 cm²
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I’ll give brainliest Write an inequality that represents this situation below.
Your suitcase for vacation will fit at most 11 outfits you already have 5 packed
Answer: 6 ≤ x ≤ 11
Step-by-step explanation:
Let x be the number of additional outfits that can be packed in the suitcase.
The suitcase will fit at most 11 outfits, which means that x cannot be greater than 11 outfits.
On the other hand, 5 outfits have already been packed, so the number of additional outfits that can be packed is at least 6.
Therefore, the inequality that represents this situation is 6 ≤ x ≤ 11.
A hair stylist is creating a price list for his services. As he prices services for hair coloring, he must take into account the cost of the products that he uses for the process along with the time he spends applying the product. He charges $25 per hour for his time and the process takes an hour and 15 minutes. The products he uses cost him $32. He also wants to add 20% to the total amount for profit. What is the total he should charge for the coloring service? Show your work and/of explain your answer.
A child’s pool is in the shape of a rectangular prism with a height of 2 ft and a base that is 4 ft wide by 5 ft long. During the course of the summer, the child’s pool needed to be filled 3 times. How many cubic feet of water were needed to fill the pool during the summer? Responses 40 ft³ 40 ft³ 80 ft³ 80 ft³ 120 ft³ 120 ft³ 160 ft³ 160 ft³
The requried, 120 ft³ of water was needed to fill the pool during the summer.
The volume of the child's pool is given by multiplying its length, width, and height.
The volume of the pool = Length x Width x Height
= 5 ft x 4 ft x 2 ft
= 40 cubic feet
Since the pool was filled 3 times during the summer, the total amount of water needed is:
The total volume of water = Volume of pool x Number of times filled
= 40 ft³ x 3
= 120 ft³
Therefore, 120 ft³ of water was needed to fill the pool during the summer.
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Find the sum of the first 9 terms of the arithmetic sequence 1, 3, 5,....
The sum of the first 9 terms of the arithmetic sequence is 81.
What is an arithmetic sequence?An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.
To calculate the sum of the first 9 terms of the arithmetic sequence, we use the formula below
Formula:
S₉ = n/2[2a+( n-1)d]........................... Equation 1Where:
S₉ = Sum of the first 9 termsa = First term of the sequencen = Number of termsd = Common differenceFrom the question,
Given:
a = 1d = (3-1) = 2n = 9Substitute these values into equation 1
S₉ = 9/2[(2×1)+(9-1)2]S₉ = 9/2(2+16)S₉ = 9(18)/2S₉ = 81Learn more about Arithmetic sequence here: https://brainly.com/question/28369191
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Which of the
�
nn-values satisfy the following inequality?
3
�
−
7
<
26
3n−7<263, n, minus, 7, is less than, 26
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
�
=
10
n=10n, equals, 10
A
�
=
10
n=10n, equals, 10
(Choice B)
�
=
11
n=11n, equals, 11
B
�
=
11
n=11n, equals, 11
(Choice C)
�
=
12
n=12n, equals, 12
C
�
=
12
n=12n, equals, 12
All values of n must be smaller than 11 in order to meet the inequality. The answer may be expressed as follows in interval notation: n (-∞, 10)
To solve the inequality 3n - 7 < 26, you can follow these steps:
Add 7 to both sides of the inequality to isolate the n variable on one side:
3n - 7 + 7 < 26 + 7
3n < 33
Divide both sides of the inequality by 3 to get n by itself:
3n/3 < 33/3
n < 11
Therefore, the values of n that satisfy the inequality are all values less than 11. In interval notation, you can write the solution as:
n ∈ (-∞, 10)
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Someone pls help me with this
The value of the angle a is 38⁰
The value of the angle b is 52⁰
The value of the angle c is 104⁰
The value of the angle d is 90⁰
What are the value of the angles?The value of the angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
a = ¹/₂ x arc 76⁰
a = 38⁰
Since the chord passed through the center, arc c is calculated as;
arc c = 180 - 76 (sum of angles of a semicircle)
arc c = 104⁰
b = ¹/₂ x 104⁰
b = 52⁰
d = 180 - (a + b) (sum of angles in a triangle)
d = 180 - (38 + 52)
d = 90⁰
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Determine, to the nearest tenth of a meter, the radius of a sphere with a volume of 10000 cubic meters.
The radius of a sphere with a volume of 10000 cubic meters is 13.36 meters
We know that the formula for the volume of sphere is :
V = 4/3 × π × r³
where r is the radius of the sphere
Here, a volume of the sphere is 10000 cubic meters.
V = 10000 cubic meters
we need to find the radius 'r'
V = 4/3 × π × r³
10000 = 4/3 × π × r³
r³ = 10000 × 3/4 × 1/π
r³ = 30000/4π
r³ = 2387.32
taking cube root,
r = 13.36 meters
Therefore, the radius is 13.36 meters.
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Please help 100 points
The surface area of the triangular prism is 184 metres².
How to find the surface area of a triangular prism?The surface area of the triangular base prism can be found as follows:
surface area of the prism = (s₁ + s₂ + s₃)l + bh
where
b =base
h = height
l = height of the prism
s₁, s₂ and s₃ are side length of the prism.
Therefore,
b = 6 units
h = 4 units
s₁ = 5 units
s₂ = 5 units
s₃ = 6 units
l = 10 units
Hence,
surface area of the prism = (5 + 5 + 6)10 + 6(4)
surface area of the prism = 160 + 24
Therefore,
surface area of the prism = 184 metres²
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Which of the following coordinates represents a point that is collinear with the given points.
(4, -10) and (-2, 0)
The coordinates that represents a point that is collinear with the given points: (4, -10) and (-2, 0) is (0, 10/3). So the correct answer is option C.
We must check to see if a point is on the straight line that connects two other points in order to determine if they are collinear.
Using the point-slope form of a line we can find the equation of the straight line passing through the points (4,-10) and (-2,0):
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
where (x1, y1) = (4, -10) and (x2, y2) = (-2, 0).
Substituting the values, we get:
(y + 10)/(x - 4) = (0 + 10)/(-2 - 4)
Simplifying, we get:
(y + 10)/(x - 4) = -5/3
Multiplying both sides by (x - 4), we get:
y + 10 = (-5/3)(x - 4)
Simplifying, we get:
y = (-5/3)x + (10 + 20/3)
y = (-5/3)x + (50/3)
So, any point that satisfies this equation is collinear with the given points.
Now checking all the three points whether they satisfy the equation:
(a) (2, -6)
Substituting the values in the equation, we get:
-6 = (-5/3)(2) + (50/3)
-6 = -10/3 + 50/3
-6 = 40/3, which is not true.
Therefore, the point (2, -6) is not collinear with the given points.
(b) (3, -3)
Substituting the values in the equation, we get:
-3 = (-5/3)(3) + (50/3)
-3 = -15/3 + 50/3
-3 = 35/3, which is not true.
Therefore, the point (3, -3) is not collinear with the given points.
(c) (0, 10/3)
Substituting the values in the equation, we get:
10/3 = (-5/3)(0) + (50/3)
10/3 = 50/3, which is true.
Therefore, the point (0, 10/3) is collinear with the given points.
Hence, the answer is (c) (0, 10/3).
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Correct Question
Which of the following coordinates represents a point that is collinear with the given points.
(4, -10) and (-2, 0)
(a) (2, -6)
(b) (3, -3)
(c) (0, 10/3)
The picture below shows a large square with side lengths equal to 1 yd. The
square is divided into smaller squares that are all of equal size. Some of the
smaller squares are shaded, forming a shaded rectangular region.
Step-by-step explanation:
so, the 1 yard is split into 6 equal parts.
each small square has therefore an area of 1/6 × 1/6 yard² = 1/36 yard²
the shaded area is 4×3 = 12 small squares large.
is area is therefore
12 × 1/36 = 1/3 yard²
since 1 yard = 3 ft, 1 × 1 = 1 yard² = 3 × 3 ft² = 9 ft².
and 1/3 yard² = 1/3 × 9 ft² = 3 ft²
so, whatever dimension you need.
the area is
1/3 yard² = 3 ft²
Number 22. The local toy store sells a package of 7 different shaped erasers for 4.20 $ what is the unit cost of each eraser in the package
Answer:
$4.20 / 7 erasers = $0.60 per eraser
So each eraser in the package costs $0.60.
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth
ft²
10 ft
6 ft
1990
The lateral surface area of the cylinder is 376.8 sq ft
Finding the lateral surface area of the cylinder.From the question, we have the following parameters that can be used in our computation:
Radius, r = 10 ft
Height, h = 6 ft
The lateral surface area of the cylinder is calculated as
Lateral area = 2 * 3.14 * rh
Substitute the known values in the above equation, so, we have the following representation
Lateral area = 2 * 3.14 * 6 * 10
Evaluate the products
So, we have
Lateral area = 376.8
Rounding the answer to the nearest tenth, we have
Lateral area = 376.8
Hence, the Lateral area is 376.8 sq ft
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Which of the following are solutions to the equation sinx cosx = -1/4? Check all
that apply.
A. 7pi/12 + npi
B. 7pi/12 + npi/2
C. 7pi/6 + npi
D. 11pi/12 + npi
Answer: A, D
Step-by-step explanation:
We have sinx cosx = -1/4. This means that either sinx = -1/2 and cosx = 1/2 or sinx = 1/2 and cosx = -1/2. In the first case, we get x = 7pi/6 + 2npi or x = 11pi/6 + 2npi. In the second case, we get x = 7pi/12 + 2npi or x = 17pi/12 + 2npi. Therefore, the solutions are x = 7pi/12 + npi and x = 11pi/12 + npi. So, options A and D are correct. Options B and C are not solutions to the given equation.
which of the following functions represent the graph g(x) above
The function represented by the graph given is equivalent to -
g(x) = (x - 4)².
The function plotted represents a quadratic equation. A quadratic equation has a degree of 2. The given function is shifted to the left by 4 units. This means that the following transformation will take place on the x - coordinate of each and every point lying on the graph -
f(x, y) → f(x - 4, y)
So, we can write the function as -
g(x) = (x - 4)²
So, the function represented by the graph given is equivalent to -
g(x) = (x - 4)²
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