The media of the following data is 525. Find the value of x and y, if the total frequency is 100.
Class interval Frequency (fᵢ)
0 - 100 2
100 - 200 5
200 - 300 x
300 - 400 12
400 - 500 17
500 - 600 20
600 - 700 y
700 - 800 9
800 - 900 7
900 - 100 4
Answers
Step-by-step explanation:
\(\large\underline{\sf{Solution-}}\)
The frequency distribution table is as follow
\(\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c}\sf Class\: interval&\sf Frequency\: (f)&\sf \: cumulative \: frequency\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}\\\sf 0 - 100&\sf 2&\sf2\\\\\sf 100 - 200 &\sf 5&\sf7\\\\\sf 200-300 &\sf x&\sf7 + x\\\\\sf 300-400 &\sf 12&\sf19 + x\\\\\sf 400-500 &\sf 17&\sf36 + x\\\\\sf 500-600 &\sf 20&\sf56 + x\\\\\sf 600-700 &\sf y&\sf56 + x + y\\\\\sf 700 - 800&\sf 9&\sf65 + x + y\\\\\sf 800-900&\sf 7&\sf72 + x + y\\\\\sf 900-1000&\sf 4&\sf76 + x + y\\\frac{\qquad}{}&\frac{\qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}\)
Given that,
Sum of all frequencies = 100So,
\(\rm :\longmapsto\: \sum \: f \: = \: 100\)
\(\rm :\longmapsto\: 76 + x + y \: = \: 100\)
\(\rm :\longmapsto\: x + y \: = \: 100 - 76\)
\(\rm\implies \:\boxed{ \: \tt{ x + y = 24 \: }} - - - (1)\)
Further given that,
Median of the series, M = 525We know, Median is evaluated by using the formula,
\(\rm :\longmapsto\:\boxed{ \sf Median, \: M= l + \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} - cf \bigg)}{f} \Bigg \}}\)
Here,
l denotes lower limit of median class h denotes width of median class f denotes frequency of median class cf denotes cumulative frequency of the class preceding the median class N denotes sum of frequencyAccording to the given distribution table,
We have
Median class is 500 - 600So, we have
l = 500, h = 100, f = 20, cf = 36 + xN = 100By substituting all the given values in the formula,
\(\dashrightarrow\sf M= l + \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} - cf \bigg)}{f} \Bigg \}\)
\(\dashrightarrow\sf 525= 500 + \Bigg \{100 \times \dfrac{ \bigg( \dfrac{100}{2} - (36 + x) \bigg)}{20} \Bigg \}\)
\(\dashrightarrow\sf 525 - 500 = 5(50 - 36 - x)\)
\(\dashrightarrow\sf 25 = 5(14 - x)\)
\(\dashrightarrow\sf 5 =14 - x\)
\(\bf\implies \:x = 9\)
On substituting the value of x in equation (1), we get
\(\rm :\longmapsto\:9 + y = 24\)
\(\bf\implies \:y = 15\)
Hence,
\(\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\bf{x = 9} \\ \\ &\bf{y = 15} \end{cases}\end{gathered}\end{gathered}\)
Related Questions
During a 90 school play the main character was on stage 80% of the time
Answers
Answer:7,200
Step-by-step explanation:
you have to do 90*80.0=7,200
Solve the following proportions
Answers
Answer:
x = 6 , y = 1.5
Step-by-step explanation:
1
\(\frac{3}{4}\) = \(\frac{x}{8}\) ( cross- multiply )
4x = 3 × 8 = 24 ( divide both sides by 4 )
x = 6
2
\(\frac{5}{y}\) = \(\frac{10}{3}\) ( cross- multiply )
10y = 5 × 3 = 15 ( divide both sides by 10 )
y = 1.5
what is 16.20 as a percent
Answers
Answer:
Step-by-step explanation:
so if you want to mind 16.20 as a percent you put it over 100 like this 16.20/100
and now make it a percent
16.2%
Answer:
Step-by-step explanation:
so if you want to mind 16.20 as a percent you put it over 100 like this 16.20/100
and now make it a percent
16.2%
Please answer correctly !!!!!!!!! Will mark brianliest answer !!!!!!!!!!!!
Answers
Answer:
9x^2 +12x
Step-by-step explanation:
To find the area of a rectangle you need to multiply the length by the width. So,
3 by 3x^2 = 9x^2
3 by 4x = 12x
So the area of the entire rectangle is: 9x^2 + 12x
Find the measure of angle b
A=108 degrees
C=72 degrees
D=81 degrees
Answers
Answer:
the anwser is c plz give brainlist
Shelly has $300 to shop for jeans and sweaters.
Each pair of jeans cost $65, each sweater costs $34,
and she buys 7 items. Determine the number of
pairs of jeans and sweaters Shelly bought.
Answers
65x3=195
34x3=102
Shelly bought three pairs of jeans and sweaters.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
Shelly is given $300 to spend on jeans and sweaters.
Each pair of pants is $65, each sweater is $34, and she purchases seven pieces.
As per the given question, the required solution would be as:
She could buy three pairs of jeans and three sweaters since any more would be insufficient because three pairs of jeans and three sweaters would equal $297.
65 x 3 = 195
34 x 3 = 102
Therefore, Shelly bought three pairs of jeans and sweaters.
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If two fair dice are rolled, what is the probability that the total showing is either even or less than five? 5.
these are the choices:
a. 5/9
b. 17/36
c. 19/36
d. 11/18
Answers
If two fair dice are rolled, the probability that the total showing is either even or less than five is 17/36. The correct answer is B.
There are 36 possible outcomes when rolling two dice, since each die has 6 possible outcomes.
To find the probability that the total showing is either even or less than five, we can first find the probability that the total showing is even, and then add to that the probability that the total showing is less than five, excluding the outcomes where the total showing is even.
To find the probability that the total showing is even, we can consider the following possibilities:
both dice show even numbers (probability 1/4)
both dice show odd numbers (probability 1/4)
So the probability of rolling an even total is 1/4 + 1/4 = 1/2.
To find the probability that the total showing is less than five, excluding the outcomes where the total showing is even, we can consider the following possibilities:
the two dice show 1 and 1 (probability 1/36)the two dice show 1 and 2 (probability 1/18)the two dice show 2 and 1 (probability 1/18)the two dice show 1 and 3 (probability 1/12)the two dice show 3 and 1 (probability 1/12)the two dice show 2 and 2 (probability 1/9)the two dice show 1 and 4 (probability 1/9)the two dice show 4 and 1 (probability 1/9)the two dice show 3 and 2 (probability 1/6)the two dice show 2 and 3 (probability 1/6)the two dice show 1 and 5 (probability 1/6)the two dice show 5 and 1 (probability 1/6)the two dice show 4 and 2 (probability 1/6)the two dice show 2 and 4 (probability 1/6)So the probability of rolling a total less than five, excluding the outcomes where the total showing is even, is 1/36 + 1/18 + 1/18 + 1/12 + 1/12 + 1/9 + 1/9 + 1/9 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 11/36.
Therefore, the probability that the total showing is either even or less than five is 1/2 + 11/36 = 17/36.
So the correct answer is (b) 17/36.
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Find the sum of the first 14 terms: 2 + 6 + 18 + 54 +
Answers
Step-by-step explanation:
First term (a) = 2
Common ratio (r) = 6 /2 = 3
Now
sum of first 14 terms (S14)
\( = \frac{a( {r}^{n} - 1) }{r \: - 1} \\ = \frac{2( {3}^{14} - 1) }{3 - 1} \\ = \frac{4782968}{2} \\ = 2391484\)
Hope it will help :)❤
2+3+18+54+162+486+1458+4374+13122+39366+118098+354294+1062882+3188646=4782965
1/5 divied by 2 as a fraction
Answers
The simplified form of the expression 1/5 divied by 2 as a fraction is 1/10.
What is 1/5 divied by 2 ?Given the expression in the question;
1/5 divied by 2
1/5 ÷ 2
To simplify, multiply 1/2 by the reciprocal of 2
1/5 ÷ 2
1/5 × 1/2
Simplify
( 1 × 1 ) / ( 5 × 2 )
( 1 ) / ( 5 × 2 )
Multiply 5 and 2
( 1 ) / ( 10 )
1/10
Therefore, the simplified form is 1/10.
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Simplify.
6‾√+36‾√
Responses
182‾√
18 2
436‾‾‾√
4 36
18
18
46‾√
Answers
Based on the information illustrated, it should be noted that 6 × ✓3 .will be 36.
How to calculate the value?It should be noted that the information that's illustrated has to do with the square root of numbers. It should be noted that a square root simply means a number that when multiplied by itself will be able to give the original number that's given in the question.
Based on the information, the numbers will be illustrated thus:
6 × ✓36
It should be noted that ✓36 = 6
Therefore, 6 × ✓36
= 6 × 6
= 36
Therefore, the correct option is 36.
Note that the options aren't well written.
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I need help on math ------- Please help as soon as possible
Answers
Answer:
How should I answering the math
An artist plans to sell $300 of prints online each week. This month, she is within $22 of her goal.
Part A: Define a variable and write an absolute value equation to represent the scenario.
Part B: Solve the equation, showing all steps.
Part C: What are the minimum and maximum amounts that the artist received for her products?
Answers
Answer:
A) |x - 1200| = 22
B) x = 1222, x = 1178
C) Minimum = $1,178
Maximum = $1,222
Step-by-step explanation:
Part ADefine the variable:
Let x = revenue from prints sold this month.Given information:
The artist plans to sell $300 of prints each week.This month, she is within $22 of her goal.If the artist plans to sell $300 of prints each week, then she plans to sell approx $1200 of prints each month, since there are approximately 4 weeks in each month.
If she is within $22 of her goal, this month then:
⇒ |x - 1200| = 22
Part BTo solve an equation containing an absolute value, set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations:
Equation 1
⇒ x - 1200 = 22
⇒ x - 1200 + 1200 = 22 + 1200
⇒ x = 1222
Equation 2
⇒ x - 1200 = -22
⇒ x - 1200 + 1200 = -22 + 1200
⇒ x = 1178
Part CTherefore:
Minimum amount the artist received = $1,178Maximum amount the artist received = $1,222change 10 inches per second to miles per second
Answers
Answer:
I don’t even know, what was the question?
Step-by-step explanation:
the diameters of ball bearings are distributed normally. the mean diameter is 58 millimeters and the standard deviation is 6 millimeters. find the probability that the diameter of a selected bearing is greater than 52 millimeters. round your answer to four decimal places.
Answers
The probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413. This can be calculated using the formula for probability of a normal distribution:
P(x > 52) = 1 - P(x ≤ 52)
P(x ≤ 52) = (52 - 58) / 6 = -1
P(x > 52) = 1 - P(-1) = 1 - 0.1587 = 0.8413.
Therefore, the probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413.
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which graph best represents a logarithmic function
Answers
In 7 years' time the combined age of my sister and her three
children will be 92. What will it be in 4 years' time?
Answers
Answer:
not sure maybe 112 or 115 ???
Step-by-step explanation:
im not that sure sorry
50+15+14+13= 92
In 4years time:
47+12+11+10= 80
Find all exact solutions on the interval 0≤θ≤2π. (Enter the answers as a comma-separated list.)tan(θ)=−1.
Answers
The exact solutions for the equation tan(θ) = -1 in the interval 0≤θ≤2π are θ = (3π)/4 and θ = (7π)/4.
To find all exact solutions on the interval 0≤θ≤2π for the equation tan(θ) = -1, follow these steps:
Step 1: Identify the principal angles where tan(θ) = -1.
The tangent function is negative in the second and fourth quadrants.
Recall that tan(θ) = sin(θ) / cos(θ). In the second quadrant, sin(θ) is positive and cos(θ) is negative. In the fourth quadrant, sin(θ) is negative and cos(θ) is positive.
The principal angles where tan(θ) = -1 are θ = (3π)/4 and θ = (7π)/4, as these angles have equal magnitude for sin(θ) and cos(θ) but opposite signs.
Step 2: Check if the principal angles are within the given interval.
Both (3π)/4 and (7π)/4 lie within the interval 0≤θ≤2π.
Step 3: List the exact solutions.
The exact solutions for the equation tan(θ) = -1 in the interval 0≤θ≤2π are θ = (3π)/4 and θ = (7π)/4.
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The points C(−6,−1), D(−4,5), and E(2,3) form a triangle. Plot the points then click the "Graph Triangle" button.
Answers
The slope of CD = 0.6.
The slope of DE = -1/3.
The slope of EC = 0.5.
The length of CD = √136 units.
The length of DE = √40 units.
The length of EC = √80 units.
Triangle CDE is a scalene triangle.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) CD = (5 + 1)/(4 + 6)
Slope (m) CD = 6/10
Slope (m) CD = 0.6.
Slope (m) DE = (3 - 5)/(2 + 4)
Slope (m) DE = -2/6
Slope (m) DE = -1/3.
Slope (m) EC = (3 + 1)/(2 + 6)
Slope (m) EC = 4/8
Slope (m) EC = 0.5.
Next, we would determine the length of each sides of triangle CDE as follows;
Distance CD = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance CD = √[(4 + 6)² + (5 + 1)²]
Distance CD = √136 units.
Distance DE = √[(2 + 4)² + (3 - 5)²]
Distance DE = √40 units.
Distance EC = √[(2 + 6)² + (3 + 1)²]
Distance EC = √80 units.
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Given f(x)=-2x-1, what is the value of f(5)
Answers
Answer:
x=-11 this is right
In a lab experiment, 830 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 28 hours. How many bacteria would there be after 13 years, to the nearest whole number?
Answers
Answer:
1145
Step-by-step explanation:
830(2) 28/13
^ do that ok??????? plug it in!!!!!!!!
then do u know what u will get? u will get this !!!!!! y = 1145.09631989
round 2 da whole numba and den boom shakalaka B ) i got my question wrong so that i could put the right answer here. bye yall
The number of bacteria doubling every 28 hours will be 1145 after 13 hours.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is y = y₀.e^(kt).
The formula for exponential decay is y = y₀.e^(-kt).
In the case of doubling the growth of bacteria, we can use the formula,
\(y_f = y_0\times2^{\frac{t_r}{t}\), where \(y_f\) represents the final population, \(y_0\) is the initial population, \(t_r\) is the time we are required to determine, and \(t\) represents the time rate growth.
Therefore from the given information, the number of bacteria after 13 hours will be,
\(y_f = 830\times2^{\frac{13}{28}\).
\(y_f = 830\times1.38\).
\(y_f = 1144.86\) or 1145 bacterias.
Q. In a lab experiment, 830 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 28 hours. How many bacteria would there be after 13 hours, to the nearest whole number?
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4. There are major chords built on what three notes (with all white notes and no accidentals)? O CFG O ABC GEB OCDE
Answers
The three major chords built on white notes without accidentals are:
1. C major chord (C, E, G)
2. F major chord (F, A, C)
3. G major chord (G, B, D)
These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.
Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.
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Kira needs 3,000 milligrams of zinc for a science experiment.
Which expression can be used to determine how many grams of zinc she needs?
A.
1000
÷
3000
B.
1000
×
3000
C.
3000
÷
1000
D.
3000
×
100
Answers
Answer:
3 grams
Explanation: To solve you have to divide the mass value by 1000.
3000/1000=3 Grams
I hope this helps :)
K H D U D C M
From mG to G it is three hops, so 3000 divided by 1000
The answer is C.
Which triangle pairs are similar polygons?
Answers
Triangle pairs are similar polygons if they have the same shape but not necessarily the same size. In order for two triangles to be similar, they must satisfy the following conditions:
They must have the same angles. This means that the measures of the angles in one triangle must be the same as the measures of the corresponding angles in the other triangle.
The lengths of the sides must be in the same ratio. This means that if you divide the lengths of the corresponding sides of one triangle by the lengths of the corresponding sides of the other triangle, you must get the same ratio for all pairs of sides.
For example, if triangle ABC is similar to triangle DEF, the ratios of AB/DE, AC/DF, and BC/EF must all be the same.
To determine if two triangles are similar, you can use one of several theorems and postulates, such as the Side-Side-Side (SSS) Similarity Theorem, the Side-Angle-Side (SAS) Similarity Theorem, or the Angle-Angle (AA) Similarity Postulate. These theorems and postulates provide different sets of conditions that must be satisfied in order for two triangles to be similar.
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A parabola has a vertex at (1,6) and passes through(3,-18). Write the equation in vertex form. Formula: f(x)=a(x-h)^(2)+k
Answers
The total price of four oranges and five pears is $32 while the total price of three oranges and two pears is $17. How much is a pear?
Answers
Answer:
A pear is 3.4
Step-by-step explanation:
Answer: A pear cost $4.
Step-by-step explanation:
If the total price of four oranges and five pears is $32 then we could represent it by the equation 4x + 5y = 32 where x is cost of one orange and y is the cost of one pear.
The same way we could represent the second statement by the equation
3x + 2y = 17
We know have the two systems of equations:
4x + 5y = 32
3x + 2y = 17 Solve using the elimination method
Multiply the top equation by -3 and the down equation by 4 to eliminate x.
-3(4x + 5y) = -3(32) = -12x - 15y = -96
4(3x +2y) = 4(17) = 12x + 8y = 68
We now have the two new equations:
-12x -15y = -96 Add both equations
12x + 8y = 68
- 7y = -28
y= 4
Which means the cost of one pear is $4.
Find the area of this triangle. PLS HELPP!!
Answers
Answer: 152ft squared
Step-by-step explanation:
When solving the area of a triangle you multiply by 1/2 so your equation would be 1/2*16*19 = 152ft squared. (Do not forget your units in other problems!!!)
use the formula:
A = 1/2bh
substitute:
A= 1/2 x 16 x 19
= 152
Other ways you can put it into your calculator:
• 0.5 x 16 x 19
• 8 x 19 (half the 16)
The lions won 16 games last year. This year the lions won 20 games. What is the percentage increase in the number of games the lions won from last year to this year?
Answers
Answer:
25%
Step-by-step explanation:
20/16=1.25
With the ".25" in the answer being the percentage increase
The average product at L = 2 and L = 8 are and respectively. A 2; 1.13 B 0.5; 0.89 C 8; 72 D 1.5. 0.5
Answers
The average products are 1.5 and 0.5.
The term "average product" refers to the average amount of product produced per unit of labor (L). At L = 2, the average product is 1.5, meaning that, on average, each unit of labor produces 1.5 products. At L = 8, the average product is 0.5, meaning that each unit of labor produces only 0.5 products on average.
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May 03, 2023
i) y = -1/2x² + 6x + 5
2
Answers
Step-by-step explanation:
To evaluate y when x = 2 in the equation y = -1/2x² + 6x + 5, we simply substitute x = 2 into the equation and solve for y:
y = -1/2(2)² + 6(2) + 5
y = -1/2(4) + 12 + 5
y = -2 + 12 + 5
y = 15
Therefore, when x = 2, y = 15 in the equation y = -1/2x² + 6x + 5.
x²+12x+43=0 Perfect Square Trinomals
Answers
Answer:
The equation x²+12x+43=0 is a quadratic equation that can be solved by factoring or using the quadratic formula.
Factoring the equation:
x²+12x+43=(x+7)(x+6)=0
x+7=0 or x+6=0
x=-7 and x=-6
Therefore, the solutions for the equation are x=-7 and x=-6.
Alternatively, you can use the quadratic formula:
x = (-b± √(b²-4ac))/2a
Where a=1, b=12, c=43
x = (-12± √(12²-4143))/2*1
x = (-12± √(144-172))/2
x = (-12± √(-28))/2
x = (-12± i*√28)/2
x = (-12+ i2√7)/2 or x = (-12- i2√7)/2
These solutions are complex numbers, x = (-6+2i√7) or x = (-6-2i√7)