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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Natalie has $300 in a savings account that earns 15% interest per year. How much interest will she earn in 4 years?
Answer:
Below
Step-by-step explanation:
Interest = p r t p = principle = 300 r = decimal interest = .14 t = years = 4
Interest = 300 * .15 * 4 = 180 dollars
9.prices in dollars of smartphones:311,309,312,314,399,312
The five-number summary for the given data include the following:
Minimum = 312.First quartile = 310.5.Median = 309.Third quartile = 335.25.Maximum = 399.What is a box-and-whisker plot?In Mathematics, a box-and-whisker plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided above, the five-number summary for the given data set include the following:
Minimum = 312.First quartile = 310.5.Median = 309.Third quartile = 335.25.Maximum = 399.By critically observing the box-and-whisker plots or boxplot (see attachment), we can logically deduce that it has a median of 309 with an interquartile range (IQR) as follows;
Interquartile range (IQR) = Q₃ - Q₁
Interquartile range (IQR) = 335.25 - 310.5
Interquartile range (IQR) = 24.75
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Complete Question:
Determine the five-number summary for the given data. Prices in dollars of smartphones:
311, 309, 312, 314, 399, 312
Simplify the following expression.
m²n³+ 18m³n² + 10m²n
2m²n
A.
B.
C.
O D.
m²n² + 9mn + 5
mn³ + 18m³n² + 8m²n
m²n² + 9mn + 5
2
²² + 16mn + 8
2
The simplification of the expression m²n³+ 18m³n² + 10m²n+2m²n is m²n ( n²+18mn+ 12)
What is simplifying expression?Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
m²n³+ 18m³n² + 10m²n+2m²n = m²n³ + 18m³n² +12m²n
Therefore we factorize the common factors out, they are m²n
= m²n ( n²+18mn+ 12)
therefore the simplification of the expression m²n³+ 18m³n² + 10m²n+2m²n is m²n ( n²+18mn+ 12)
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find the distance between the pair of points (-22,20) and (-23,-1)
[tex]\huge\begin{array}{ccc}d=\sqrt{442}=11\sqrt2\end{array}[/tex]
A distance between two points.
The formula:
[tex]A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]
SOLUTION:
We have:
[tex]A(-22,\ 20),\ B(-23,-1)[/tex]
Substitute:
[tex]|AB|=\sqrt{(-23-(-22))^2+(-1-20)^2}=\sqrt{(-1)^2+(-21)^2}\\\\=\sqrt{1+441}=\sqrt{442}=\sqrt{121\cdot2}=\sqrt{121}\cdot\sqrt2=\boxed{11\sqrt2}[/tex]
the sum of 2 and y aleks
The sum of the expression 2 and y is (2+ y).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
The sum of 2 and y.
As, the sum is shows by the addition whose symbol is "+"
So, the sum of 2 and y is
= (2 + y).
Hence, the expression is ( 2+ y).
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i'll pick you as brainily please quick formula for finding the distance between two points
[tex]Let \: the \: two \: points \: be \: \underline{\underline{A( x_{1} ,y_{1})}} \: and \: \underline{\underline{B \: ( x_{2}, y_{2})}}[/tex]
Then ,
[tex]\boxed{d(AB) = \sqrt{ {( x_{2} - x_{1}) }^{2} + {( y_{2} - y_{1}) }^{2} } }\\ [/tex]
where , d(AB) is the distance between the two points A and B.
hope helpful! :)
Answer:
the Distance Between the two points a and b
Step-by-step explanation:
Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
A farmer sells 6.9 kilograms of apples and pears at the farmer's market.
1/4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answer:
1.725
Step-by-step explanation:
1/4 or .25 multiplied by the total of 6.9
Geometry
There are 30 students in a class. They were asked if they have a cat or dog as a pet. 10 kids said they have a cat, 12 kids said they have a dog the rest said they don't have either. Of the kids that said they have a cat or dog, 3 kids said they have both pets.
(Please answer in fraction, decimal, and percent form)
a. How many students do not have either pet?
b. If a student is selected at random what is the probability that they have both pets?
c. If a student is selected at random, what is the probability that they have a cat or dog?
Answer:
a. 8
b. 1/10
c. 19/30
Step-by-step explanation:
a. 12 + 10 = 22 30 - 22 = 8
b. 3 students have both, 3/30 simplified is 1/10
not 100% sure about c. but is my best bet
how close to −2 do we have to take x so that the following is satisfied? (give the largest possible value.) 1 (x + 2)6 >
The largest value of x that satisfies the inequality is approximately -1.8639.
To find the largest possible value of x that satisfies the inequality 1/(x + 2)⁶ > 1,000,000, we can start by rearranging the inequality:
1/(x + 2)⁶ > 1,000,000
Taking the reciprocal of both sides:
(x + 2)⁶ < 1/1,000,000
Now, let's take the sixth root of both sides:
x + 2 < (1/1,000,000)[tex]}^{1/6[/tex]
Calculating the right side:
x + 2 < 0.1361
Subtracting 2 from both sides:
x < 0.1361 - 2
x < -1.8639
Therefore, the largest value of x that satisfies the inequality is approximately -1.8639.
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g(x) = x°-27x (a) Determine whether g is even, odd, or neither (b) There is a local minimum of -54 at 3. Determine the local maximum (a) Determine whether g is even, odd, or neither O Neither O Odd O Even (b) There is a local minimum of - 54 at 3. Determine the local maximum.
The local maximum is x = 13.5 with a value of g(13.5) = (13.5)^2 - 27 * 13.5 = g(13.5) = 125.375.
(a) To determine whether a function is even, odd, or neither, we need to check if g(x) = g(-x) for all x (even), g(x) = -g(-x) for all x (odd), or neither.
g(x) = x^2 - 27x is neither even nor odd because it does not satisfy either of the two conditions for even or odd functions.
(b) To determine the local maximum, we need to find the critical points (points where the derivative is equal to zero or undefined) and then determine if they are local maxima, local minima, or neither.
g'(x) = 2x - 27, which has critical points at x = 13.5 and x = 0. Since g'(x) > 0 for x < 0 and g'(x) < 0 for x > 0, x = 0 is a local minimum. Since g'(x) < 0 for x < 13.5 and g'(x) > 0 for x > 13.5, x = 13.5 is a local maximum.
Therefore, the local maximum is x = 13.5 with a value of g(13.5) = (13.5)^2 - 27 * 13.5 = g(13.5) = 125.375.
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A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. (1) What is the area of the glass? (ii) How much of tape is needed for all the 12 edges?
The area of the small indoor greenhouse (herbarium) is equal to 4,250 cm².
The length of tape needed for all the 12 edges is equal to 320 cm.
How to calculate the area of the glass?Mathematically, the total surface area (TSA) of this glass panes (including base) can be calculated by using this mathematical expression:
Total surface area (TSA) = 2[lb + lh + bh]
Where:
l represent the length of the glass panes.b represent the breadth of the glass panes.h represent the height of the glass panes.Total surface area (TSA) = 2[(30 × 25) + (30 × 25) + (25 × 25)]
Total surface area (TSA) = 2[750 + 750 + 625]
Total surface area (TSA) = 2[2,125]
Total surface area (TSA) = 4,250 cm².
Next, we would determine the length of tape needed for all the 12 edges by using this mathematical expression:
Total length = 4(l + b + h)
Total length = 4(30 + 25 + 25)
Total length = 4(80)
Total length = 320 cm.
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Bonsoir es ce que quelqu'un pourrait m'aider pour cette exercice plus précisément la question 2 et 3.
Merci d'avance
Answer:
2) 1885 km
3) 795 h 46 m 29 s
Step-by-step explanation:
2)
C = 2πr
C = 2 × 3.14159 × 300 km
C = 1885 km
3)
(1000000 km)/ (1885 km/tour) = 530.16477 tours
1 tour = 1 h 30 m = 1.5 h
530.16477 tours = 530.16477 × 1.5 h = 795.7747155 h = 795 h 46 m 29 s
A linear function is shown on the graph
What is the Romain of the function?
Check the picture below.
Find the value of x
x + x + (2x + 5) + (2x + 7)
Trigonometry Finding side length
Please help!!
The value of x for each given right angled triangle are:
x = 5.6x = 4.52x = 4√3x = 6.26x = 5.87Please remember that these answers are calculated using calculator.
Remember that a triangle has the sum of angles 180°; then since we have a right angled triangle, then the sum of the non-right angles in the triangle should be equal to 90°.
We use Θ as the note for the unknown non-right angle.
1. 36° + Θ = 90°
Θ = 54°
Under the Sinus Law:
x / sin 54 = 7 / sin 90
x / 0.8 = 7 / 1
x = 5.6
2. 41° + Θ = 90°
Θ = 49°
Under the Sinus Law:
x / sin 49 = 6 / sin 90
x / 0.75 = 6 / 1
x = 4.52
3. 30° + Θ = 90°
Θ = 60°
Under the Sinus Law:
x / sin 90 = 6 / sin 60
x / 1 = 6 / (√3/2)
x = 4√3
4. 37° + Θ = 90°
Θ = 53°
Under the Sinus Law:
5 / sin 53 = x / sin 90
x = 5 / 0.79
x = 6.26
5. 33° + Θ = 90°
Θ = 57°
Under the Sinus Law:
7 / sin 90 = x / sin 57
7 / 1 = x / 0.84
x = 5.87
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24) Find the quotient and write the answer in standard form.
(3.6×10 to the power of 10) divided by 5
Answer: Quotient is 3.6*10^10/5 and the standard form is 7.2*10^9
Step-by-step explanation:
Answer:
Step-by-step explanation:
3.6×10∧10÷5=0.72×10∧10
standard form=7.2×10∧9
What is the simplest form of (4x3 + 6x – 7) + (3x3 – 5x2 – 5x)
Answer:
4x-4 that's what I gottt
The function h(x) = -x +34 models the height of the roof of a house, where x is the horizontal distance from the center of the house. If a raindrop
falls from the end of the roof, how far from the center of the base does it land? Explain your solution.
The distance from the base's center at that time is 18 feet.
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.
A function is typically represented as y = f. (x).
h(x) = 16 ft x is the distance from the base when
h(x) = 16 h(x) = -IxI + 34
when a raindrop falls from the end of the roof.
16 = -IxI + 34
IxI = 34 – 16 = 18
It might land on the roof's opposite end.
The distance from the base's center at that time is 18 feet.
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Deepa invests money in an account paying a simple interest of 1% per year. If no money will be added or removed from the investment, what should she multiply her current balance by to find her total balance in a year in one step?
For Deepa to find his yearly balance in a single step, he must multiply his money by 1.01
Comparing basic and compound interest ?Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period. Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
The following calculation must be done in order to determine what Deepa should multiply his current balance by in order to find his total balance in a year in one step if no money will be added to or removed from the investment. Deepa invests money in an account that pays a simple interest rate of 1% per year.
Current balance = X
Interest = 1% = 1/100 = 0.01
Interest + principal = 1.01
1.01X = Total balance in a year
Deepa must therefore multiply her money by 1.01 in order to determine it in a single step.
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A person is watching a boat from the top of a lighthouse. The angle of depression from the person to the boat is 28°. The lighthouse is 200 feet tall. How far away is the boat? Round to the nearest foot
The boat is approximately 515 feet away from the lighthouse.
To find the distance from the boat to the lighthouse, we can use trigonometry. The angle of depression from the person to the boat is 28°, and the height of the lighthouse is 200 feet. Let's call the distance from the boat to the lighthouse x. Using the tangent function, we have
tan 28° = 200 / x.Solving for x, we have x = 200 / tan 28°. Approximating this value using a calculator, we have x ≈ 514.7 feet. Rounding to the nearest foot, the boat is approximately 515 feet away from the lighthouse.
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he first three terms of a sequence are given. round to the nearest thousandth (if necessary). 2,5,8,...2,5,8,... find the 41st term.find the 41st term.
The first three terms of the sequence are 2, 5, and 8.The 41st term of this sequence is 122.
What is the 41st term of the sequence?To find the 41st term of this sequence, you can use the common difference method.Step 1: Determine the common difference by subtracting the second term from the first term, and then subtracting the third term from the second term.The common difference is:5 - 2 = 3and8 - 5 = 3Step 2: Since the common difference is the same for each pair of consecutive terms, we can conclude that this sequence is an arithmetic sequence.Step 3: To find the 41st term, you can use the formula for the nth term of an arithmetic sequence:an = a1 + (n - 1)dwhere a1 is the first term, n is the term you're looking for, and d is the common difference.Substituting in the values:an = 2 + (41 - 1)3 = 2 + (40)3 = 2 + 120 = 122So the 41st term of this sequence is 122.
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Amanda invests 5000 in a CD at an annual rate of 2%. What will her investment be worth at the end of three years?
I got $5,300. But probably wrong.
after driving to a riverfront parking lot, bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. after running 3.25 miles south, he decides to run for only 50 minutes more. if bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?
A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra.
What is meant by equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Mathematical equations with two expressions on either side of the "equal to" sign are referred to as simple equations.
Let the distance he walks till turning back be 'd',
The total distance while returning back = d + 3.25 miles
Time per unit mile = 8 minutes,
Total distance he walks after already completing 3.25 miles
= 2d+3.25 miles
Therefore, total time for this distance [tex]$=(2 \mathrm{~d}+3.25) * 8=16 \mathrm{~d}+26$[/tex] minutes,
Given that it will take 50 minutes to get to the car after traveling 3.25 miles south,
Let the equation be
[tex]$$\begin{aligned}& 16 d+26=50 \\& 16 d=24 \\& d=\frac{24}{16}=1.5 \text { miles; }\end{aligned}$$[/tex]
Therefore, the required answer exists be 1.5 miles.
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What is the Formula of Sum of Cubes of n Natural Numbers?
The formula for the sum of cubes of the first n natural numbers is:
(1^3 + 2^3 + 3^3 + ... + n^3) = (1 + 2 + 3 + ... + n)^2
What is the formula of sum of cubes?The sum of cubes of the first n natural numbers is the sum of cubes of the numbers 1, 2, 3, ..., n.To find the formula, we can start by using the formula for the sum of the first n natural numbers: (1 + 2 + 3 + ... + n) = n(n+1)/2.We can then cube this expression: (n(n+1)/2)^3 = n^3(n+1)^3/8.Expanding the cube on the right side, we get: n^3(n+1)^3/8 = n^3(n^3 + 3n^2 + 3n + 1)/8.Combining like terms and simplifying, we get the final result: (1^3 + 2^3 + 3^3 + ... + n^3) = (1 + 2 + 3 + ... + n)^2.This formula can be used to efficiently calculate the sum of cubes of any set of natural numbers, without having to sum the cubes individually.To learn more about natural numbers refer:
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Ramon took a math tet and got 35 correct anwer and 15 incorrect anwer what i the percentage of the correct anwer
The percentage of correct answers=70
what i the percentage of the correct answer?
Number of correct answers=35
number of incorrect answers=15
total number of questions=number of correct answers + number of total incorrect answers
=35+15
=50
Percentage of correct answers = number of correct answers×100/Total i number of question
=35×100/50
= 3500/50
=70
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a website requires that passwords only contain alphabetic characters. for each character in checkstr that is not an alphabetic character, replace the character with 'x'.
After the loop has finished executing, the 'newstr' variable should contain 'abcdxxxxxXXXXX'. The newstr variable is set to an empty string and alphabetic, numerical, and symbol characters are replaced with 'x'.
newstr = "abcdxxxxxXXXXXX
1. Initialize a new string variable called 'newstr' set to an empty string.
2. Loop through each character in the 'checkstr' variable.
3. If the character is an alphabetic character, add it to the 'newstr' string.
4. If the character is not an alphabetic character, replace it with 'x' and add it to the 'newstr' string.
5. After the loop has finished executing, the 'newstr' variable should contain 'abcdxxxxxXXXXX'.
The newstr variable is set to an empty string and alphabetic, numerical, and symbol characters are replaced with 'x'.
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What are the coordinates of the point?
Responses
(6, −3)
(−3, 6)
(3, 6)
(−3, −6)
Answer: (-3,6)
Step-by-step explanation:
The point is 3 spaces to the left in the second quadrant on the x-axis which is negative
Then it is 6 spaces up on the y-axis which is positive
The response to a question has three alternatives: A,B , and C. A sample of 120 responses provides 54 A ,24 B, and 42C . Show the frequency and relative frequency distributions (use 2 decimal for the relative frequency column)
Class Frequency Relative Frequency
A
B
C
As a result, we obtain the frequency and relative frequency distributions:
Data Relative Frequency
A 0.5
B 0.19
C 0.31
What is relative frequency?The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.
Here,
Here we have a total sample as: 120
Also, the frequency corresponding to A is: 60
Corresponding to B is: 23
and corresponding to C is: 37
Hence, the Frequency table is as follows:
Data Frequency
A 60
B 23
C 37
The relative frequency table is given by:
Data Relative Frequency
A 60/120=0.5
B 23/120=0.19
C 37/120=0.31
Hence, we get the frequency and relative frequency distributions:
Data Relative Frequency
A 0.5
B 0.19
C 0.31
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What is the range of the function f(x) = 2x + 4 when the domain is {-2, 0, 3}?
A. {0, 4, 10}
B. All real numbers
O C. {4. 25, 5, 12}
D. {4. 25, 4, 12}
The range of the function is {0, 4, 10}. Option A. {0, 4, 10}
The concept used in finding the range of a function is called functional mapping, which maps the elements in the domain of the function to the corresponding elements in the range.
In this problem, we took a set of values in the domain of the function (which was {-2, 0, 3}) and evaluated the function for each of those values to find the corresponding outputs in the range of the function, which was {0, 4, 10}.
To find the range of the function f(x) = 2x + 4 for the domain {-2, 0, 3}, we need to calculate the output of the function for each of the values in the domain:
For x = -2: f(-2) = 2 * -2 + 4 = -4 + 4 = 0
For x = 0: f(0) = 2 * 0 + 4 = 4
For x = 3: f(3) = 2 * 3 + 4 = 10
Therefore, the range of the function is {0, 4, 10}. Option A. {0, 4, 10}
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The range of the function f(x) = 2x+4 when the domain is {-2,0,3} is {0,4,10} .
The range for this function would be {0,4,10}.
Given, Function f(x) = 2x+4
Domain = {-2,0,3}
After putting the value of x= -2 in the function f(x) =2x+4 ,
f(-2) = 2×-2+4 = -4+4= 0
After putting the value of x= 0 in the function f(x) = 2x+4
f(0)= 2×0+4 =0+4=4
After putting the value of x= 3 in the function f(x) = 2x+4
f(3) =2×3+4= 6+4= 10
Here, after putting values in function the domain will become {0,4,10}.
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A univerity tudent completed coure were three credit, and ome coure worth four credit. The tudent earned a total of 54 credit after completing 15 coure. How many coure or four credit did the tudent complete?
The student completed 9 courses of four credits each.
Let x = number of four-credit courses the student completed
If the student completed a total of 15 courses, then the expression for the number of three-credit courses the student completed is:
"15 - x"
If the student earned a total of 54 credits after completing 15 courses, then the equation to show this will be:
4x + 3(15 - x) = 54
Simplify the equation and solve for the value of x.
4x + 45 - 3x = 54
x = 9
Hence, the number of four-credit courses the student completed is 9 course.
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