The class width is 5 for the given frequency distribution.
What are class boundaries?
The values used to demarcate classes are called class borders. The difference between a class's upper-class limit and its lower-class limit indicates the extent of the gap between classes.(a) Class width is the same for all the classes. It is the difference between the lower class limit of two consecutive classes
Therefore Lower limit of 50 - 54 = 50
Lower limit of 55 - 59 = 55
Class width = 55 - 50
Class width = 5
If calculated all have the same class width.
(b) Midpoint is the average of the sum of lower and upper-class limits of the class.
Temp Freq Midpoint
50-54 1 52
55-59 3 57
60-64 5 62
65-69 11 67
70-74 7 72
75-79 7 77
80-84 1 82
(c) Class boundaries are to make the classes continuous mostly. We can find this by first calculating the difference between the upper-class limit and the lower-class limit of the next class and taking its average.
Add this average to the upper limit and subtract this average from the lower limit
Lower boundary for 50 - 54 = 50 - 0.5 = 49.5
Upper boundary for 50 - 54 = 54 + 0.5 = 54.5
Temp Freq Class Boundaries
50-54 1 49.5-54.5
55-59 3 54.5-59.5
60-64 5 59.5-64.5
65-69 11 64.5-69.5
70-74 7 69.5-74.5
75-79 7 74.5-79.5
80-84 1 79.5-84.5
The class width is 5 for the given frequency distribution.
Complete question: Use the given frequency distribution to find the
(a) class width.
(b) class midpoints.
(c) class boundaries.
Temperature (°F) Frequency
32-36 1
37-41 3
42-46 5
47-51 11
52-56 7
57-61 7
62-66 1
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List the partial products of 242 and 28.
The partial products of 242 × 28 are 4,000, 1,600, 840 and 336 and the value of 242 × 28 exists 6,776.
What is meant by partial product?To estimate the partial product of two numbers, first, we write both numbers as the sum of the place values of the digits. Multiply each place value of the first number by the place value of the second number.
Given: 242 × 28
(200 + 42) × (20 + 8)
(200 × 20) + (200 × 8) + (42 × 20) + (42 × 8)
simplifying the above equation, we get
200 × 20 = 4,000
200 × 8 = 1,600
42 × 20 = 840
42 × 8 = 336
The above values are the partial product.
4,000 + 1,600 + 840 + 336 = 6,776
Therefore, the partial products of 242 × 28 are 4,000, 1,600, 840 and 336 and the value of 242 × 28 exists 6,776.
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Solve using Substitution
9x+10y=1
y=-8
(?,?)
Answer:
x=9,y=8
Step-by-step explanation:
Step 1: Substitute y=-8 into equation 1
9x+10(-8)=1
9x+(-80)=1
9x=1+80
9x=81
Step 2: Divide both sides by the coefficient of x which is 9 then,
x=9
Step 3: Also substitute x=9 into equation 1
9(9)+10y=1
81+10y=1
10y=1-81
10y=-80
Step 4:Divide both sides by 10 then,
y=-8
What is the equation of this line?
The equation of the given line in the diagram above is expressed as: b. y = 2/3x.
How to Find the Equation of a Line?For a line that passes through the origin (0, 0) of a graph, the equation that represents the line can be written in slope-intercept form as y = mx, where the slope of the line is represented as m.
The y-intercept of this type of line is zero, that is why we have the equation expressed as y = mx. Where the y-intercept is not equal to zero, the equation of the line would be expressed as y = mx + b, where b is the y-intercept and m is the slope of the line.
Find the slope of the line using two points on the line, (0, 0) and (3, 2):
Slope of the line (m) = (2 - 0)/(3 - 0)
Slope of the line (m) = 2/3.
To write the equation of the line, substitute m = 2/3 into y = mx:
y = 2/3x.
The equation is: B. y = 2/3x.
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A data set has these values: 6, 8, 8, 10, 10, 10, 10, 12, 12, 14. The histogram of
the distribution is shown.
Frequency
5
4
3
21
0
11
Data values
5 7 9
13 15
Which statement does not describe the data set?
The statement that does not describe the data set 6, 8, 8, 10, 10, 10, 10, 12, 12, 14 is:
(C) The range of the data set is 15.
Consider the data set,
6, 8, 8, 10, 10, 10, 10, 12, 12, 14
The mean of the data set will be:
mean = ( 6 + 8 + 8 + 10 + 10 + 10 + 10 + 12 + 12 + 14 )/ 10
mean = 100/10
mean = 10
The data set in ascending order are:
6, 8, 8, 10, 10, 10, 10, 12, 12, 14
As the number of terms is even. Therefore, the median will be the sum of two middle numbers divided by 2.
So,
Median = ( 10 + 10 )/2 = 20/2 = 10
The mode of a data set is the maximum number of times a number appears in the data set.
Therefore, the mode of the data set is 10.
The range of the data set is the difference between the highest and the lowest number in the data set.
Range = 14 - 6 = 12
The data set is a symmetric distribution if the mean, median, and mode all fall at the same point.
As the mean, median, and mode are 10, 10, and 10 respectively. Hence, the data set is symmetric.
Hence, statements (A), (B), and (D) are true.
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Write the equation of a line that forms a 45 degree angle with the positive x- axis and passes through the origin?.
Answer:
y = x
Step-by-step explanation:
an equation that an equation that forms an angle of 45 ° and passes through the origin of the axes is the bisector, and its equation is y = x.
For the equation |2-2x| = 14, find all values of x which makes the equation true
Answer:
x=-6,8
Step-by-step explanation:
First, let's observe our equation, there is an absolute value (|x|) that means 'x' will have two answers most likely positive and negative.
First we will take off the lines.
now we have
2-2x=14
next minus 2 out of both side of the equation
2 - 2 -2x = 14- 2
-2x =12
now we will divide -2 from both side of the equation
[tex] \frac{ - 2x = 12}{ - 2} [/tex]
we will cancel out - 2
[tex]\frac{x = - 6}{1} [/tex]
x= -6
We aren't done yet since this is an absolute value we have to convert the sum of the equation ( 14) to negatives now which will be in this case (-14)
your new equation will look like this
2-2x= -14
next minus 2 out of both side of the equation
2 - 2 -2x = -14- 2
-2x = - 16
now we will divide -2 from both side of the equation
[tex] \frac{ - 2x = - 16}{ - 2} [/tex]
we will cancel out - 2
[tex] \frac{x = 8}{1} [/tex]
x = 8
Check:x = -6
2 - 2x = 14
2 - 2(-6) = 14.
2 + 12 = 14✓.
x= 8
2 - 2x = -14
2 - 2 (8) = -14
2 - 16 = -14✓
hope this helped happy learning
Given the equation: a+2b=5
Which equation below is correctly solved for a?
Answer:
E. [tex] a = 5-2b [/tex]
Step-by-step explanation:
how to find the value of a, we need to subtract 2b from both side to single out the variable
a + 2b = 5
subtract 2b from both sides
a + 2b - 2b = 5 - 2b
a = 5 - 2b
Therefore, Option E is the correct answer
I did not really understand can some one help
Answer:
62 pages in each notebook
Step-by-step explanation:
she filled 372 pages in 6 notebooks , then
372 ÷ 6 = 62
there are 62 pages in each notebook
solve |2x-6|<0 not urgent. But its for a test
The inequality expression given as |2x - 6 | < 0 has a solution of x > 3
How to solve the inequality?From the question, the inequality is given as
|2x-6|<0
This gives
|2x - 6 | < 0
Remove the absolute bracket
So, we have the following representation
2x - 6 > 0
Add 6 to all sides of the inequality
So, we have
2x - 6 + 6 > 0 + 6
Evaluate the like terms
So, we have
2x > 6
Divide through by 2
x > 3
Hence, the solution to the expression is x > 3
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according to a recent student poll, \frac{5}{7} of the 21 members of the finance club are interested in a career in investment banking. if two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
The probability that at least one of them is not interested in investment banking is 13/14.
What is a probability?It is a branch of mathematics. The possibility of the outcome of any random event is termed as probability. The range of the probability must be between o to 1. Here o indicates impossibility of an event and 1 indicates certainty. Probability can be expressed in proportions. Probability deals in finding the occurrence of an event.
Probability of the first person who is not interested in investment banking is 6/21
Probability of the second person who is not interested in investment banking and also first person was not interested then it is taken as 5/20.
probability that at least one is not interested in investment banking
=1- The probability that neither one of them is not interested in investment banking
=1-((6/21)×(5/20)
=13/14
Therefore, the probability that at least one of them is not interested in investment banking is 13/14.
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Calculate the volume of the cuboid shown
below.
Give your answer in cm³.
If your answer is a decimal, then round it
to 1 d.p.
11 cm
16 cm
21 cm
Answer: 3696cm³
Step-by-step explanation:
The formula for a Cuboid's volume is LxWxH = V
so plug the numbers in
11cm x 16cm x 21cm = V
3696cm³ = V
Dada una sucesión aritmética, el 75° término, a75 es igual a 556, y el 8° término, a8 es igual a 87. Hallar el valor del 36° término, a36
The value of the 36th term of the arithmetic sequence is 283.
How to calculate the value?It should be noted that an arithmetic sequence illustrate the common difference between the terms.
The following can be deduced from the information:
75th term = a + 74d = 556
8th term = a + 7d = 87
Subtract the equations
(74d - 7d) = 556 - 87
67d = 469
Divide
d = 469/67
d = 7
The first term(a) will be:
a + 7d = 87
Recall d = 7
a + 7(7) = 87
a + 49 = 87
a = 87 - 49
a = 38
Therefore, the 36th term will be:
a + 35d.
a = first term
d = common difference
38 + 35(7)
= 38 + 245
= 283
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12. The tallest platform for Olympic diving is
33 feet above the water. After a diver
completes a dive, they reach 14 feet below
the water. What is the distance between the
height of the platform and the depth of the
diver? (Example 3)
The distance between the height of the platform and the depth below water is 47ft . The concept of depth describes how far something extends.
How to calculate depth ?A deep area in a body of water is what the word "DEPTH" means.
Ocean depth is most frequently and quickly measured using sound. Sonar, which stands for sound navigation and range, is a technique that allows ships to map the topography of the ocean below. The instrument uses sound waves to send to the ocean's bottom and time how long it takes for an echo to come back.
Water depth is the distance in feet between the ocean's surface and bottom, as determined by mean lower low water.
Use the following formula for measuring ocean depth.
D = V Times 1/2 T D
Depth (in meters) T= Time (in seconds) V = 1507 m/s (speed of sound in water)
In the question we have,
Platform to surface of water = 33ft
Platform to depth below water = 33+14 = 47ft
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please help me it's due soon please PLEASE HELP i love you
Answer: -1/3
Step-by-step explanation:
Pretty sure it's -1/3, one unit down from a point, and then 3 units right.
The answer is -1/3. Hope this helps.
explain how to expand (x + 3)7 using the binomial theorem.
According to the binomial theorem, the binomial (x + 3)⁷ is equal to the septimic polynomial x⁷ + 21 · x⁶ + 189 · x⁵ + 945 · x⁴ + 2835 · x³ + 5103 · x² + 5103 · x + 2187.
How to expand the power of a binomial by using binomials theorem
Binomial theorem offers a brief form to expand the power of a binomial, that is, an algebraic expression of the form (a + b)ⁿ, where n is a natural number. The complete formula is shown below:
(a + b)ⁿ = Σ {n! / [k! · (n - k)!]} · [tex]a^{n-k}[/tex] · [tex]b^{k}[/tex], for k ∈ {0, 1, 2, ..., n - 1, n}
If we know that a = x, b = 3 and 7, then the expanded form of the power of the binomial is:
(x + 3)⁷ = [7! / (0! · 7!)] · x⁷ · 3⁰ + [7! / (1! · 6!)] · x⁶ · 3 + [7! / (2! · 5!)] · x⁵ · 3² + [7! / (3! · 4!)] · x⁴ · 3³ + [7! / (4! · 3!)] · x³ · 3⁴ + [7! / (5! · 2!)] · x² · 3⁵ + [7! / (6! · 1!)] · x · 3⁶ + [7! / (7! · 0!)] · x⁰ · 3⁷
(x + 3)⁷ = x⁷ + 7 · x⁶ · 3 + 21 · x⁵ · 3² + 35 · x⁴ · 3³ + 35 · x³ · 3⁴ + 21 · x² · 3⁵ + 7 · x · 3⁶ + 3⁷
(x + 3)⁷ = x⁷ + 21 · x⁶ + 189 · x⁵ + 945 · x⁴ + 2835 · x³ + 5103 · x² + 5103 · x + 2187
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Answer:
To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.Simplify by evaluating the coefficients and powers of 3.
2) Roni donates 10% of her paycheck to a local charity and puts 15% of her
paycheck in a savings account. If Roni's paycheck is $2,020.00, which of the
following is the amount which will go to charity and savings?
A. $505
B. $909
C. $202
D. $303
Step-by-step explanation:
amt. means amount
explaination in my workings
hope this helps!!
Find the slope of the line that passes through the following points:
(3, -4)
(-1, 0)
Considering the expression of a line, the slope of the line that passes through the pair of points (3, -4) and (-2,0) is -1.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Equation in this caseIn this case, being (x₁, y₁)= (3, -4) and (x₂, y₂)= (-1, 0), the slope m can be calculated as:
m= (0 - (-4))÷ (-1 -3)
m= (0 +4)÷ (-1 -3)
m= 4÷ (-4)
m= -1
Finally, the slope of the line is -1.
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What is the volume of a metal box if the density is 5.4 g/cm³ and a mass of 75 grams
Answer: 0.072 cm^3
Step-by-step explanation:
density=mass*volume
Volume=gensity/mass
5.4/75=0.72
270x-3x^2-3x^3=0
solve by factoring
9 feet=___ yards please and thank you for your help
the ratio of feet to yards is:
[tex]\frac{3feet}{1yard}[/tex]Now, the proportion to find the equivalent yards for 9 feet is:
[tex]\frac{3feet}{1yard}=\frac{9feet}{x\text{ yards}}[/tex]Let's solve for x:
[tex]\begin{gathered} x=\frac{9ft\times1yard}{3ft} \\ x=3\text{yards} \end{gathered}[/tex]Therefore, 9 feet=3 yards.
hi help please thanks
In linear equation, x = 9 is the value of Maggie that she made.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.4x + 2 = 7x - 25
7x - 4x = 2 + 25
3x = 27
x = 27/3
x = 9
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Tiana and vince are practicing their trying skill in computer science class the both typed the same number of words but tiana took less time they are practicing in a trying competition next week in the competition they will have the same amount of time to type who will likely type more during the competition
Tiana is more likely to win the competition as she took less time to type the same number of words, She will type more during the competition as her typing speed is more.
Since the upcoming match is next week, it is very important to practice before the actual match, hence, both participants were practicing to their best.
It is more likely that the person who does their best while practicing is more likely to perform better in the actual competition.
The competition will have the same amount of time to type, hence who will take less time to type more words will ultimately win the match.
Since Triana took less time while practicing the same amount of words, hence, it is more likely that she will type more during the competition.
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Which graphs are correct?
Answer:
11 = A
12 = B
Step-by-step explanation:
I'd advice you take some extra lessons in this because this is sort of basic math
Sample response: I set up an equation to show that the number of bracelets multiplied by the cost of each bracelet minus the commission is equal to the total, 6(x – 1.25) = 16.50. I divided each side by 6, then added 1.25 to each side with a result of x = 4. Hyo-Jim sold each bracelet for $4.
Each bracelet price is $4 if Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The equation is in the word:
With the commission of $1.25 for each bracelet sold, Hyo-Jin made a total of $16.50.
Let x be the cost of each bracelet:
Total earning = 16.50 + 7.50
Total earning = 24
Each bracelet price x = 24/6 = $4
Thus, each bracelet price is $4 if Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets.
The question is incomplete.
The complete question is:
Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets. After paying the website a commission of $1.25 for each bracelet sold, Hyo-Jin made a total of $16.50. How much does each bracelet sell for on the website? Explain the steps you followed to get your answer.
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Radicales simples ……….
The expressions with radicals which are variables and numbers raised to a fractional indices are simplified as follows.
13. √(9·x) = 3·√x
14. √(4·y) = 2·√y
15. √(8·x²) = 2·x·√2
16. √(9·x²) = 3·x
17. √(3·x²) = x·√3
18. √(5·y²) = y·√5
19. √(13·x²) = x·√(13)
20. √(29·y²) = y·√(29)
21. √(64·y²) = 8·y
22. √(125·a²) = 5·a·√5
23. ∛(16) = 2·∛2
24. √(50·a²·b) = 5·a·√(2·b)
What are radicals expressions?
A radical expression is one that contains the radical (square root or nth root) sign, √.
13. √(9·x)
√(9·x) = √(3²·x) = 3·√x
√(9·x) = 3·√x14. √(4·y)
√(4·y) = √(2²·y) = 2·√y
√(4·y) = 2·√y15. √(8·x²)
√(8·x²) = √(4 × 2·x²) = √(2² × 2·x²)
√(2² × 2·x²) = √(2²·x² × 2) = 2·x·√2
√(8·x²) = 2·x·√216. √(9·x²)
√(9·x²) = √(3²·x²) = 3·x
√(9·x²) = 3·x17. √(3·x²)
√(3·x²) = x·√318. √(5·y²)
√5 × √(y²) = √5 × y = y·√5
√(5·y²) = y·√519. √(13·x²)
√(13·x²) = √(13) × √x² = √(13) × x = x·√(13)
√(13·x²) = x·√(13)20. √(29·y²)
√(29·y²) = √(29) × √(y²) = √(29) × y = y·√(29)
√(29·y²) = y·√(29)21. √(64·y²)
√(64·y²) = √(8²·y²) = √(8²) × √(y²) = 8 × y = 8·y
√(64·y²) = 8·y22. √(125·a²)
√(125·a²) = √(25 × 5 × a²) = √(25) × √5 × √(a²) = 5 × √5 × a
5 × √5 × a = 5·a·√5
√(125·a²) = 5·a·√523. ∛(16)
∛(16) = ∛(16) = ∛(8 × 2) = ∛(2³ × 2) = 2·∛2
∛(16) = 2·∛224. √(50·a²·b)
√(50·a²·b) = √(25 × 2 × a² × b) = √(5² × 2 × a² × b) = √(5² × a² × 2 × b)
√((5² × a²) × 2 × b) = 5·a·√(2·b)
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Suppose Jessica's route from her house to school consists of two straight legs: First, she drives straight for 5 miles, and then she makes a right turn of 45 degrees and drives another 9 miles. What is the distance (as the crow fl ies) from Jessica's school to her house in miles? (Round your answer to the nearest hundredth.
The distance from Jessica's school to her house is 7.48 miles.
Consider following diagram.
In right triangle ABC, vertex B is the Jessica's house vertex A be her school.
The route from her house to school consists of two straight legs.
She drives straight for 5 miles, and then she makes a right turn of 45 degrees and drives another 9 miles.
⇒ BC = 5 miles and AC = 9 miles
We need to find the distance from Jessica's school to her house in miles.
i.e., we need to find AB
Using Pythagoras theorem,
AC² = AB² + BC²
9² = AB² + 5²
AB = √(81 - 25)
AB = 7.48
Therefore, the distance from Jessica's school to her house is 7.48 miles.
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Given the equation 4x + 12 = 64: part a: write a short word problem about a purchase made to illustrate the equation. (6 points) part b: solve the equation showing all work. (4 points) part c: explain what the value of the variable represents. (2 points)
From the equation 4x + 12 = 64, we have that:
a. The problem is: An amount was quadrupled then added by 12, resulting in a final amount of 64.
b. The solution to the equation is x = 13.
c. The solution of x = 13 represents the initial amount.
Context of the equation 4x + 12 = 64The amount x is unknown, hence the problem begins with the unknown amount x.
4x means that the amount was quadrupled.4x + 12 means that 12 was added to the amount.4x + 12 = 64 means that the final amount has a value of 64.Which means that the problem can be summarized as:
An amount was quadrupled then added by 12, resulting in a final amount of 64.
The equation can be solved isolating x as follows:
4x + 12 = 64
4x = 64 - 12
4x = 52
x = 52/4
x = 13.
Meaning that the initial amount was of 13.
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True or False:
A compound logic statement made up of two statements joined with the word "and" is a conjunction.
Answer:
False that is a conjunction
Step-by-step explanation:
hope this helps
At the beginning of the week, Naveen has 87 trading cards. On Monday, he gets 9 more. On Tuesday, he gives 16 away. On Wednesday, he is given 3 by a friend. On Thursday, he sells all of his cards to a collector. The collector pays him a rate of c for every card that Naveen has. If Naveen earns $124.50 from the sale, what is c, the rate that the collector pays for each card?
a. $1.08
b. $1.50
c. $41.50
d. $83.00
The graph shows Ms. Padilla's monthly cell phone cost, where x is the number of minutes she uses the phone during the month.
Graph of a line on a coordinate plane. The horizontal x axis labeled Seconds ranges from negative 50 to 300 in increments of 25. The vertical y axis labeled Meters. ranges from negative 600 to 100 in increments of 10. A line passes through the points begin ordered pair 0 comma negative 580 end ordered pair and begin ordered pair 175 comma negative 200 end ordered pair.
Which statements are true? Select each correct answer.
Question options:
The x-intercept is meaningless here.
Ms. Padilla is charged $5/min.
Ms. Padilla is charged $0.04/min.
Ms. Padilla pays $16 for months she makes 0 min of calls.
Answer: the X intercept mean this here
Ms.
Padilla is charged $0.04/min.
Ms. Padilla pays $16 for months she makes 0 min of calls
Step-by-step explanation:
