The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.
In this case, the ratio of the corresponding sides of the two triangles are:
AB/DE = 3/18 = 1/6
BC/EF = 7/42 = 1/6
Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.
A nursery owner buys 5 panes of glass to fix some damage to her greenhouse. The panes cost $13.25. Unfortunately, she breaks 2 more panes while repairing the damage. What is the cost of another 2
panes of glass?
Answer:
The cost of the other two panes should be $5.70.
Step-by-step explanation:
Given that,
There are 5 panes of glass that should be bought.The 5 panes cost should be 14.25.Now based on the above information, the calculation is as follows:
= 14.25 x 2 ÷ 5
= $5.70
Therefore we can conclude that the cost of the other two panes should be
$5.70.
4. For data at the interval level, you cannot calculate meaningful differences between data entries.
For data at the interval level, we cannot calculate meaningful differences between data entries. The statement is false.
Interval:
The interval of a numerical value generally represents the maximum and minimum value between which the numerical value belongs, it is the amount of time that has passed between the beginning and end of the event which is also known as elapsed time.
The various ways of showing intervals are Inequalities, interval notations, and number lines, the amount of time between two given times is known as the time interval.
Data at the ordinal level can be qualitative or quantitative. A true statement is "For data at the interval level, you can calculate meaningful differences between data entries."
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On January 1, 2010, Lucita bought a car for $25,000. If the car depreciates at a rate of 15% per year, which equation can be used to find the value of the car on January 1, 2018?
A. A term in an arithmetic sequence
B. The partial sum of an arithmetic series
C. A term in a geometric sequence
D. The partial sum of a geometric series
The equation can be used to find the value of the car on January 1, 2018, which is A term in an arithmetic sequence and A= 25000*(1-0.15)^8
The given data is:
Price of car = $ 25,000
Rate of depreciation = 15 %
Formula used:
A= P(1-r)^n-----(1)
where p= price of the car
A= new price of a car after depreciation
r = rate of depreciation i.e. 15/100 = 0.15
n= time in years 2018 - 2010 = 8 years
Putting values in formula:
A= 25000*(1-0.15)^8
A= 25000*(0.85)^8
A= $6812.263
So, the Equation that can find the value of the car on January 1, 2018, is:
A= 25000*(1-0.15)^8 and the value of the car after 8 years is $6812.263
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pls hurry this is urgent
Answer:
Step-by-step explanation:
5
12+24x+? complete the square
The missing c-value that makes 12x² + 24x a perfect square trinomial is 12.
What is the perfect square trinomial of the expression?Given the expression in the question;
12x² + 24x + c
To determine the perfect square trinomial, first factor out 12 from the expression and find the value of c ;
12x² + 24x
12( x² + 2x )
To find c, divide the coefficient of x by and square the result.
(b/2)² = ( 2/2)² = 1
Now, add 1 to get the perfect trinomial.
12( x² + 2x + 1 )
Simplify using distributive property.
12×x² + 12×2x + 12×1 )
12x² + 24x + 12
Therefore, the perfect square trinomial is 12x² + 24x + 12.
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A farmer has a cylindrical silo he uses to store corn. The silo has a height of 50 feet and a radius of 12 feet. How many cubic feet of corn can the silo hold? Use 3. 14 for pi
Answer:
The silo holds 22608 ft³ of the corn
Step-by-step explanation:
Assume the cylindrical silo is a perfect cylinder.
Volume of cylinder = πr²h
Volume = 3.14 × (12)² × 50
Volume = 22608 cubic feet
On January 22 in 1943, the town of Spearfish, South Dakota, set the record for the world’s fastest temperature change. At 7:30 a.m., the temperature was `-4`°F. By 7:32 a.m., the temperature was `45`°F. By 9:00 a.m. the same day, the temperature was `54`°F. By 9:27 a.m., the temperature was `-4`°F. How many degrees did the temperature change each minute from 9:00 to 9:27? Make sure to show whether the change was positive or negative.
From 9:00 a.m. to 9:27 a.m., the temperature changed from 54°F to -4°F, a change of 58°F. This change took 27 minutes.
The temperature change per minute was 58°F / 27 minutes = 2.15°F per minute.
The change was negative, because the temperature decreased from 54°F to -4°F.
What are the values of x and y*
The values of x and y are given as follows:
x = 3.[tex]y = 3\sqrt{2}[/tex]What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
In this problem, we have that the right angle is bisected, and thus it is divided into two angles of 45º.
As the angle of 45º has the same value for the sine and the cosine, the sides of the triangle BDC have the same length, hence the value of x is given as follows:
x = 3.
Applying the Pythagorean Theorem, the value of y will be given as follows:
y² = 3² + 3²
y² = 2 x 9
[tex]y = 3\sqrt{2}[/tex]
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Answer:
[tex]x=\dfrac{9}{4}=2.25[/tex]
[tex]y=\dfrac{15}{4}=3.75[/tex]
Step-by-step explanation:
Geometric Mean Theorem - Altitude RuleThe altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.
[tex]\boxed{\sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}}[/tex]
From inspection of the given right triangle:
altitude = BDsegment 1 = CDsegment 2 = ADTherefore:
[tex]\implies \dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]
[tex]\implies \dfrac{3}{x}=\dfrac{4}{3}[/tex]
[tex]\implies 3 \cdot 3 = 4 \cdot x[/tex]
[tex]\implies9 = 4x[/tex]
[tex]\implies x=\dfrac{9}{4}[/tex]
Geometric Mean Theorem - Leg RuleThe altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment segment directly opposite the leg.
[tex]\boxed{\sf \dfrac{hypotenuse}{leg\:1}=\dfrac{leg\:1}{segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{hypotenuse}{leg\:2}=\dfrac{leg\:2}{segment\;2}}[/tex]
From inspection of the given right triangle:
hypotenuse = ACleg 1 = BCsegment 1 = CDTherefore:
[tex]\implies \dfrac{AC}{BC}=\dfrac{BC}{CD}[/tex]
[tex]\implies \dfrac{4+x}{y}=\dfrac{y}{x}[/tex]
[tex]\implies x(4+x)=y^2[/tex]
Substitute the found value of x:
[tex]\implies \dfrac{9}{4}\left(4+\dfrac{9}{4}\right)=y^2[/tex]
[tex]\implies y^2=\dfrac{225}{16}[/tex]
[tex]\implies y=\sqrt{\dfrac{225}{16}}[/tex]
[tex]\implies y=\dfrac{\sqrt{225}}{\sqrt{16}}[/tex]
[tex]\implies y=\dfrac{15}{4}[/tex]
Meters and feet are two different scales for measuring distance. Five meters is approximately 16. 41 ft, and 12 m is approximately 39. 37 ft. Write an equation that shows the approximate distance in feet as a function of the distance in meters. Show your work
The approximate distance in feet as a function of the distance in meters is 3.28x + 0.01.
What is an equation that shows the approximate distance?Meters and feet are two different scales for measuring distance. Five meters is approximately 16. 41 ft, and 12 m is approximately 39. 37 ft.
Suppose the approximate distance in feet is y,
and the distance in meters is x
Suppose the function is y = ax + b
Given the information, we can know
S*r_{1} = 5; y_{1} = 16.41
x_{2} = 12
y_{2} = 39.37
S_{0} $ 16.41= 5a +b0 { Substitute }
39.37 = 12a + b*Theta
7a = 22.96
a = 3.28
So 16.41 = 5 * 3.28 + b {Substitute} b = 0.01
So the function is y = 3.28x + 0.01
The approximate distance in feet as a function of the distance in meters is 3.28x + 0.01
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Mary bought eight cups of coffee for her coworkers for $20. 64. How much did she pay for one cup of coffee?.
Mary paid $2.58 for one cup of coffee is the correct answer.
How much did she pay for one cup of coffee?.To find out how much Mary paid for one cup of coffee, we need to divide the total amount she spent by the number of cups she bought.Step 1: Divide the total amount by the number of cups.$20.64 ÷ 8 = $2.58 per cupStep 2: Round the answer to the nearest cent.$2.58 per cupSo, Mary paid $2.58 for one cup of coffee.To learn more about division refer:
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whats the origin of the number zero (pls give me interesting info its for a math project)
Answer:
Hindus from India invented zero to represent the idea of the power of the cosmos and universe as they expand into infinity. They called this the sunya which means empty in Sanskrit. The book Brahma Sphuta Siddhanta was published in c. 628 by Brahmagupta which defines zero as the subtraction of a number by itself, e.g. 5-5 =0.
Prove algebraically that the sum of the squares of any two consecutive even numbers is always a multiple of 4.
It is established that there is always a multiple of 4 between squares of consecutive even numbers.
What is consecutive even numbers?Take two consecutive even integers into consideration.
If n is an integer, then
The first even number would then be 2n.
Let 2(n+1) be the next consecutive even number.
The following even numbers would follow:
2n, 2(n+1)
Each succeeding even number's square would be:
(2n)² = 2n ×2n = 4n²
[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)
stretching out the brackets
= 4n² +4n +4n+4
[2(n+1)]² = 4n²+8n+4
We would choose values for n and calculate the difference between the squares of each consecutive even number in order to ascertain whether it is always a multiple of 4.
Let n = 1, 2, 3
For n= 1
4n² = 4(1)² = 4×1 = 4
4n²+8n+4 = 4(1)² + 8(1) + 4
= 4+8+4 = 16
The difference between consecutive even numbers' squares is equal to 16/4, or 12.
For n= 2
4n² = 4(2)² = 4×4 = 16
4n²+8n+4 = 4(2)² + 8(2) + 4
= 16+16+4 = 36
36-16 = 20 is the difference between the squares of two consecutive even numbers.
For n= 3
4n² = 4(3)² = 4×9 = 36
4n²+8n+4 = 4(3)² + 8(3) + 4
= 36+24+4 = 64
64-36 = 28 is the difference between the squares of two consecutive even numbers.
12 = 4×3
20 = 4×5
28= 4×7
We can see from the outcomes above that the numbers 12, 20, and 28 are multiples of 4.
As a result, a multiple of four always separates squares of succeeding even integers.
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Find the percent error in this situation:
Experimental value: 16. 5 sec
Theoretical value: 17. 1 sec
3. 64%
3. 51%
0. 0364%
0. 0351%
Find the percent error in this situation:
Estimated value: 231
Actual value: 215
0. 069%
6. 9%
7. 4%
0. 74%
1) The percent error in the situation of this:
- Experimental value: 16. 5 sec
- Theoretical value: 17. 1 sec
are : 3.51 %
2) The percent error in this situation:
- Estimated value: 231
- Actual value: 215
are: 7.4 %
Percent Error Calculation1) The steps to find the percent error in the situation where the experimental value is 16.5 sec and the theoretical value is 17.1 sec are:
Subtract the experimental value from the theoretical value:
17.1 - 16.5 = 0.6
Divide the difference by the theoretical value and multiply by 100 to get the percentage:
percent error = (0.6 / 17.1) * 100 = 3.51%
2) The steps to find 7.4% in the situation where the estimated value is 231 and the actual value is 215 are:
Subtract the estimated value from the actual value:
215 - 231 = -16
Divide the difference by the actual value and multiply by 100 to get the percentage:
percent error = (-16 / 215) * 100 = 7.4%
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heeeeeeeeellppppp pleeaasseeeeee
Answer:
Ez ahh question, the answer for A is $2125 and B $2000 (better give me brainliest)
Step-by-step explanation:
A. Suppose the price $X
- to make a profit of 25%
$1700 x (1 + 25%) = $x
1700 x 1.25 = $2125
B. Suppose the price $y
$y x (1+25%) = $2500
$y = $2500 divided by 1.25
= $2000
Question 3 of 5
The top of the table can be modeled with a cylinder, and the legs can be
modeled with rectangular prisms.
36 in
6 in
20 in
FITN
2 in
3 in
Estimate the amount of paint needed to cover all parts of the table, to t
nearest square inch.
A total of 3703 square inches of paint will be required to cover the table completely.
What is meant by Geometry?It deals with the dimensions, regions, and densities of the various 2D and 3D shapes.
A cylinder can be used to represent the table's top, and rectangular prisms can be used to represent the table's legs.
The surface area of the cylinder will be
SA of cylinder = 2πr² + 2πrh
substitute the values in the above equation, we get
SA of cylinder = 2π (18² + 18 × 3)
simplifying the equation, we get
SA of cylinder = 2375 square inches
The surface area of the prism will be
SA of prism = 4 [WL + 2(WH + LH)]
substitute the values in the above equation, we get
SA of prism = 4 [2 x 6 + 2 (2 x 20 + 6 x 20)]
simplifying the equation, we get
SA of prism = 4 [12 + 2 x 160]
SA of prism = 4 [12 + 320]
SA of prism = 1328 square inches
The total surface area of the table will be
Total surface area = SA of prism + SA of cylinder
simplifying the equation, we get
Total surface area = 1328 + 2375
Total surface area = 3703 square inches
In order to completely cover the table, 3703 square inches of paint will be required.
Therefore, the correct answer is option B. 3,703.
The complete question is:
The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.
Estimate the amount of paint needed to cover all parts of the table, to the nearest square inch.
A.2,375
B.3,703
C.2,707
D.4,014
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The amount of paint needed to cover all parts of the table will be 3703 square inches.
What is surface area?For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.
There are numerous shapes and dimensions in geometry, including sphere, cube, cuboid, cone, cylinder, etc. Each form has its own volume and surface area. However, we can only measure the area that two-dimensional shapes like squares, circles, rectangles, triangles, etc. cover; there is no volume available.
The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.
The table is shown below.
The surface area of the cylinder will be
SA of cylinder = 2πr² + 2πrh
SA of cylinder = 2π (18² + 18 × 3)
SA of cylinder = 2375 square inches
Then the surface area of the prism will be
SA of prism = 4 [WL + 2(WH + LH)]
SA of prism = 4 [2 x 6 + 2 (2 x 20 + 6 x 20)]
SA of prism = 4 [12 + 2 x 160]
SA of prism = 4 [12 + 320]
SA of prism = 1328 square inches
Then the total surface area of the table will be
Total surface area = SA of prism + SA of cylinder
Total surface area = 1328 + 2375
Total surface area = 3703 square inches
Thus, the amount of paint needed to cover all parts of the table will be 3703 square inches.
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a wheel has a radius of 0.25m which is moving initially at
The circumference of the wheel is 0.5π m
The radius is an important factor in determining the wheel's motion and speed.
In your question, the wheel has a radius of 0.25m and is initially moving at a certain speed.
The distance traveled by a point on the circumference of the wheel is equal to the circumference of the wheel.
The circumference of a wheel can be calculated using the formula,
=> circumference = 2πr
where r is the radius of the wheel.
Thus, the speed of a wheel can be calculated by multiplying the circumference by the number of rotations in a given time.
As the radius of the wheel is 0.25m,
the circumference will be 0.5π m,
and the speed will depend on the number of rotations in a given time.
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CAN SOMEONE HELP ME PLEASEEEEEEE
Answer:
Step-by-step explanation:
Because all of the other sides are equal so it makes that equal
using a formula for the variance of a sample, what is the denominator?
The number of observations in the sample, minus one, serves as the denominator in the formula for a sample's variance.
The formula for a sample's variance is the sum of the squared variances between each observation and the mean, divided by the sample's observation count, minus one. This is referred to as the sample size minus one (n-1). Rather than relying on the sample size The denominator in the formula for a sample's variance is equal to the number of observations in the sample, minus one. The denominator facilitates the calculation of a population variance, which is used to determine a sample variance (n). This is true because the population variance is a fair approximation of the population variance and the denominator helps with bias correction.
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A retailer buy ome bread toater from a manufacturer at $20 each. In addition to that, he need to pay a value added tax of 15%. If he ell a bread toater to a cutomer for $26,find the amount of profit he make
Answer:
he makes $6 profit
pleaseee and thankyou!!!
Answer:
fx=19 and fx-4= -1
Step-by-step explanation:
Add and divide those 2 problems and subtract.
Is 100 ml equal to 1 liter?
The unit 100 ml is not equal to 1 liter.
What is unit of measurements?
A quantifiable language that expresses the magnitude of the amount is referred to as a standard unit of measurement. Understanding how the measurement relates to the thing is helpful.
Here the given is 100 milliliters
we know that to convert milliliters into liter we need to divide them by 1000. Then,
=> 100 ml
=> [tex]\frac{100}{1000} = \frac{1}{10}[/tex]
=> 0.1 liters ≠ 1 liter.
Hence the unit 100 ml is not equal to 1 liter.
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A builder has some red and grey bricks. The red bricks weigh 9 kilograms each, and the grey bricks weigh 8 kilograms each. If the total weight of all 35 bricks is 298 kilograms, how many of each type of brick does Paul have?
The builder has 17 grey bricks and 18 red bricks. The total weight of the bricks is 298 kilograms.
What is the system of equations?
Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A solution is not assured even then.
Assume that the builder has x number of red bricks and y number of gray bricks.
The weight of 1 red brick is 9 kilograms.
The weight of x red bricks is 9x kilograms.
The weight of 1 gray brick is 8 kilograms.
The weight of y red bricks is 8y kilograms.
The weight of x red bricks and y red bricks is 9x + 8y kilogram.
The total number of bricks is 35 whose weight is 298 kilograms.
According to the question,
x+y = 35 ......(i)
9x + 8y = 298 .....(ii)
Solve the equations by using the elimination method:
Multiply 9 with equation (i) and subtract equation (ii) from it:
9x+9y = 315
9x + 8y = 298
(-) (-) (-)
_______________
y = 17
Putting y = 17 in equation (i)
x+17 = 35
x = 18
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What numbers come out the most in New York lottery?
The numbers 61 (78 times), 32 (77 times), 21, 63 (73 times), 69 (71 times), and 23 are those that appear the most frequently in the New York lottery (70 times).
Which six lottery numbers are picked the most frequently?For instance, reports indicate that the most popular Powerball lottery numbers are 32, 41, 16, 22, 23, and 29. These are the top six MegaMillions numbers: 15, 24, 33, 1, 46, and 39.
According to data, the Powerball numbers that appeared the most frequently over the past seven years were 61 (78 times), 32 (77 times), 21, 63, 69, and 23.
The New York lottery's most frequent numbers are 61 (78 times), 32 (77 times), 21, and 63 (73 times).
The numbers 61 (78 times), 32 (77 times), 21, 63 (73 times), 69 (71 times), and 23 are those that appear the most frequently in the New York lottery (70 times).
Since 2005, a consultant at Ernst & Young has examined the Mega Millions lottery's chosen numbers. The outcomes:
most often winning combinations
14 On 48 winning tickets — 11.6%
36 On 48 winning tickets — 11.6%
48 On 47 winning tickets — 11.4%
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A child learning to ave money inveted a capital of $ 250 at a nominal rate of 0. 0825 (per annum) with imple interet. If he earned $ 11. 98 at the maturity date, how many day wa the term of the depoit?
The term of the deposit that the child did was 7 months
What is simple interest?It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.
The formula for simple interest and procedure we will use to solve this exercise is:
T = (100 * S.I) / (P * R)
Where:
P = principalR = rate of interest in % per annumT = timeInformation about the problem:
P = $250R = 0. 0825S.I. = $11.98T = ?Applying the simple interest formula and isolating the time we get:
T = (100 * S.I) / (P * R)
T = (100 * 11.98) / (250* 8.25)
T = 1198/ 2062.5
T = 0.58 years
Converting the years to month we have:
0.58 years * 12 months/ 1 year = 7 months
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Correctly written question:
A child learning to have money invested a capital of $ 250 at a nominal rate of 0. 0825 (per annum) with simple interest. If he earned $ 11. 98 at the maturity date, how many day was the term of the deposit?
Natasha wants to plant a square garden and enclose it with a fence. She has 120 feet of fencing available and she wants the sides of her garden to be at least 6 feet long. Write and solve the inequality that describes the side lengths that are possible
Answer:omak sus
Step-by-step explanation:
The solution is, the side lengths that are possible are from 6 to 30. as, The inequality is, 6 ≤ x ≤ 30.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
given that,
Natasha wants to plant a square garden and enclose it with a fence.
She has 120 feet of fencing available
and she wants the sides of her garden to be at least 6 feet long.
now, we have to Write and solve the inequality that describes the side lengths that are possible,
so, we have,
the garden is square, so, perimeter = 4 * side length
now. let, the length of side = x
we get,
perimeter = 4x = y
so, we get,
x ≥ 6 ......(1)
and, y ≤ 120
i.e. 4x ≤ 120
or, x ≤ 30 .....(2)
so, from 1 & 2 we get,
The inequality is, 6 ≤ x ≤ 30
Hence, The solution is, the side lengths that are possible are from 6 to 30. as, The inequality is, 6 ≤ x ≤ 30.
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15. The sides of a triangle are 5, 12, and n. Write an inequality that expresses the interval of values (1 point) that n may have.15. The sides of a triangle are 5, 12, and n. Write an inequality that expresses the interval of values (1 point) that n may have.
An inequality that expresses the interval of values that n may have is 7 < n < 17.
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < n < b + c
Where:
n, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:
b - c < n < b + c
12 - 5 < n < 12 + 5
7 < n < 17.
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Write an equation for the quadratic function with the roots at x= 0, x = 5
The equation for the quadratic function with the roots at x= 0 and x = 5 will be y = x² - 5x.
How to get polynomials with zeroes?Let a, b, c, and d be the zeroes of the polynomial.
Then the polynomial is given as,
⇒ (x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
The zeroes of the quadratic equation are 0 and 5, then the quadratic equation is given as,
y = (x - 0)(x - 5)
y = x (x - 5)
y = x² - 5x
The equation for the quadratic function with the roots at x= 0 and x = 5 will be y = x² - 5x.
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Question 12 (1 point) Find T(v) using the following properties assuming T is a linear transformation. T:P, → Pz; T(22) = x3, T(x + 1) = 0, T(x - 1) = x; ; v=x2 +2
The equation is T(v) = x5 + 2x. The linearity property states that for any two vectors u, v and scalar c, then T(u + cv) = T(u) + cT(v).
Since T is a linear transformation, we can use the linearity property of linear transformations. The linearity property states that for any two vectors u, v and scalar c, then T(u + cv) = T(u) + cT(v).
We can use the linearity property to find T(v) by rewriting v equation as v = u + cv, with u = x2 and c = 2.
So, T(v) = T(u + cv) = T(x2) + 2T(x2) = x3 + 2x3 = x5 + 2x.
The equation is T(v) = x5 + 2x
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He data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. Construct (a) a relative frequency distribution (b) a frequency histogram, and (c) a relative frequency histogram. What percentage of players had a top speed between 1818 and 21. 921. 9 km/h? what percentage of players had a top speed less than 13. 913. 9 km/h? speed (km/hr) number of players 10 dash 13. 910–13. 9 44 14 dash 17. 914–17. 9 77 18 dash 21. 918–21. 9 1414 22 dash 25. 922–25. 9 5959 26 dash 29. 926–29. 9 324324 30 dash 33. 930–33. 9 181181 (a) construct a relative frequency distribution. Speed (km/hr) relative frequency 10 dash 13. 910–13. 9 nothing 14 dash 17. 914–17. 9 nothing 18 dash 21. 918–21. 9 nothing 22 dash 25. 922–25. 9 nothing 26 dash 29. 926–29. 9 nothing 30 dash 33. 930–33. 9 nothing (round to four decimal places as needed. )
a) The relative frequency distribution is 0.3212
b) The percentage of players that had a top speed less than 13.9 km/h = 0.007259 x 100 = 0.7259%
Given that,
Speed (km/hour) Number of players Relative frequency:
10 – 13.9
14 - 17.9
18 – 21.9
22 – 25.9
26 – 29.9
30 – 33.9
4
8
18
76
268
177 4/551=0.007259
8/551=0.01451
18/551=0.03266
76/ 551=0.1379
268/551 = 0.486
177/551=0.3212
Thus, The relative frequency distribution is 0.3212.
The percentage of players who had top speed between 14 and 17.9 km/h was = 0.01451 x100 = 1.451%
The percentage of players that had a top speed less than 13.9 km/h = 0.007259 x 100 = 0.7259%
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(a) Relative frequency distribution:
Speed (km/hr) Number of players Relative frequency
10-13.9 44 0.114
14-17.9 77 0.199
18-21.9 1414 0.368
22-25.9 5959 0.153
26-29.9 324324 0.084
30-33.9 181181 0.046
(b) Frequency histogram:
|
|
| X
| X
| X X
| X X
_______|__X__X
10 14 18 22 26 30
(c) Relative frequency histogram:
|
|
| X
| X
| X X
| X X
_______|___X___X
0.1 0.2 0.3 0.4 0.5 0.6 0.7
(d) Percentage of players with a top speed between 18 and 21.9 km/h:
0.368 * 100 = 36.8%
(e) Percentage of players with a top speed less than 13.9 km/h:
0.114 * 100 = 11.4%
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how to find the composition of a mixture using calibration curve?
To find the composition of a mixture using a calibration curve, a sample of the mixture must first be prepared. The sample should be of a known concentration or dilution. Then, the sample's absorbance must be measured at a known wavelength.
This measured absorbance should then be plotted on the calibration curve. The calibration curve is a graph that shows the relationship between the absorbance of a sample and its concentration. If a linear relationship exists between absorbance and concentration, the calibration curve can be used to determine the concentration of the sample. The concentration of the sample can then be used to calculate the amount of each component in the mixture.
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