Step-by-step explanation:
1.
200 - 7/21 = (200×21 - 7)/21 = (4200 - 7)/21 =
= 4193/21 = 599/3 = (199×3 + 2)/3 =
= 199 2/3
we could have seen that 7/21 = 1/3.
so, then this problem was
200 - 1/3 = (200×3 - 1)/3 = 599/3 = 199 2/3
(see above)
2.
50 - 4/7 = (50×7 - 4)/7 = (350 - 4)/7 =
= 346/7 = (49×7 + 3)/7 = 49 3/7
3.
24 1/4 - 20 3/5 = (24×4 + 1)/4 - (20×5 + 3)/5 =
= 97/4 - 103/5
to calculate this we need to bring both fractions to the save denominator. the LCM (lowest common multiple) of 4 and 5 is 20.
so,
97/4 - 103/5 = (97×5)/(4×5) - (103×4)/(5×4) =
= 485/20 - 412/20 = 73/20 =
= (3×20 + 13)/20 = 3 13/20
4.
10 5/8 - 6 4/9 = (10×8 + 5)/8 - (6×9 + 4)/9 =
= 85/8 - 58/9
the LCM of 8 and 9 is 72.
85/8 - 58/9 = (85×9)/(8×9) - (58×8)/(9×8) =
= 765/72 - 464/72 = 301/72 =
= (4×72 + 13)/72 = 4 13/72
5.
6 1/2 - 5 3/4 = (6×2 + 1)/2 - (5×4 + 3)/4 =
= 13/2 - 23/4
the LCM of 2 and 4 is 4.
13/2 - 23/4 = (13×2)/(2×2) - 23/4 =
= 26/4 - 23/4 = 3/4
You estimate that you can do 30 math problems in 45 min. How many minutes should it take you to do 40 math problems
Simplify the expression:
3s + -9s - s + −4s + −s
Submit
Answer:
s=0
Step-by-step explanation:
1. Simplify the expression
[tex]3\mathrm{s}-9\mathrm{s}-1\mathrm{s}-4\mathrm{s}-1\mathrm{s}=0[/tex]
2. Simplify the arithmetic
[tex]-12\mathrm{s}=0[/tex]
Answer: I believe the answer is 3s + -13
Step-by-step explanation:
3s + -9s - s + -4s + -s
3s + -9 + -4
3s + -13
100 PONITSS HELPPPPPPPPP
Mrs. Sparks is a 9th grade Algebra 1 teacher. She teaches three
Algebra 1 courses and all the classes recently took a chapter exam.
Below are the scores.
Class 1
45
68
77
90
90
95
100
100
86
90
50
55
Class 2
64
65
70
40
100
87
84
88
90
90
95
80
Class 3
70
75
75
90
100
80
55
65
76
80
88
99
a. Find the mean, median, mode and range of Class 1.
b. Find the mean, median, mode and range of Class 2.
c. Find the mean, median, mode and range of Class 3.
d. Find the standard deviation of Class 1.
e. Find the standard deviation of Class 2.
f. Find the standard deviation of Class 3.
g. Which class had a higher standard deviation and what does that mean?
h. In your opinion, which class did better on the exam? Explain your answer.
The values of the descriptive statistics of the given data on the scores of the classes in the Algebra class are;
a. Mean; 78.83, Median; 88, Mode; 90, Range; 55
b. Mean; 79.52, Median; 85.5, Mode; 90, Range; 60
c. Mean; 79.52, Median; 78, Mode; 75, Range; 45
d. 19.66
e. 16.87
f. 13.27
g. Class 1
h. Class 3
What is a descriptive statistic?A descriptive statistic is one that provides an idea of contents of a dataset by outlining the pattern found within the dataset
Mean
The mean of the dataset is given by the formula;
[tex] \displaystyle{Mean = \frac{Sum \: of \: data}{Number \: of \: data}} [/tex]
Median
The median of a dataset is the middle term of a dataset when the data are arranged in increasing order
Mode
The mode of a dataset is the value that occurs most frequently
Range
The range is given by the difference between the maximum and minimum values of the dataset
a. The mean of Class 1 obtained from an application is 78.83
The median = 88
The mode = 90
The range = 55
b. The mean of Class 2 obtained from an application is 79.42
The median = 85.5
The mode = 90
The range = 60
c. The mean of Class 3 obtained from an application is 79.42
The median = 78
The mode = 75
The range = 45
d. The standard deviation is given by the formula;
[tex] \displaystyle{\sigma = \sqrt{\frac{\sum (x_i -\bar x)^2} {N}}}[/tex]
Where;
[tex] \displaystyle{ x_1}[/tex] = The ith data
[tex] \displaystyle{\bar x}[/tex] = The mean
N = The number of data
Solving using a spreadsheet application, we have;
The standard deviation for class 1 = 19.65
e. The standard deviation of class 2 found using a spreadsheet application is 16.87
f. For class 3, the standard deviation is 13.27
g. From the above calculations, the class that has the highest standard deviation is class 1, with a standard deviation of 19.65
The high standard deviation means that there is a lot of variability or variation in the scores of class 1
h. The class that did better is class 3, that has the lowest standard deviation and range as well as one of the highest mean
Learn more about descriptive statistics data here:
https://brainly.com/question/6990681
#SPJ1
Please help IXL due at midnight!
When the inequality expression 1 > |b - 5| is evaluated, the value of the expression is 4 < b < 6
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine the solution to the inequality?The absolute value inequality is given as
1 > |b - 5|
Remove the absolute value inequality symbol
So, we have the following expression
-1 < b - 5 < 1
Add 5 to all sides of the inequality expression
So, we have the following expression
5 -1 < b - 5 + 5 < 1 + 5
Evaluate the sum and the difference in the above inequality expression
So, we have the following expression
4 < b < 6
Hence, the solution to the inequality expression 1 > |b - 5| is 4 < b < 6
Read more about inequality expression at
https://brainly.com/question/25275758
#SPJ1
1. Using the numbers 8, 6, 4, and 2, write an expression that equals 6.
Answer:
4+2=6
8-2=6
You can use any one of these
A line passes through the point (9, 7)and has a slope of 4/3
Write an equation in slope-intercept form for this line.
[tex]\displaystyle\\Answer:\ y=\frac{4}{3}x-5[/tex]
Step-by-step explanation:
[tex]y=mx+b\\[/tex]
[tex]\displaystyle\\The\ slope\ m=\frac{4}{3} \\\Rightarrow\ y=\frac{4}{3}x+b[/tex]
A line passes through the point (9, 7)
Thus,
[tex]\displaystyle\\x=9\ \ \ \ y=7\\\\7=\frac{4}{3} (9)+b\\\\7=\frac{4(9)}{3} +b\\\\7=\frac{36}{3} +b\\\\7=\frac{3(12)}{3} +b\\\\7=12+b\\7-12=12+b-12\\-5=b\\So,\ y=\frac{4}{3}x-5[/tex]
sion of the question. Make sure you start new workings.
Chris is taking part in a 20 kilometres (km) running race
and has completed 5/8 of the course.
How many metres (m) does he have left to run?
Answer:
7500 or 7.5 or 10³ ..... .............
9 + 3x = 2x + 4y
What's x and what's y? I'll give the Brainly thingy for a right answer, Scout's honor
I'm not a scout but ykwim
Answer:
There are probably multiple answers to this question, but the answer I got was x = 7, and y = 4.
Step-by-step explanation:
First Equation: 9 + 3x. (Below)
3 x 7 = 21
21 + 9 = 30
Second equation: 2x + 4y.
2 x 7 = 14
4x4 = 16
16 + 14 = 30.
———————
Since they both have the same solution it leads me to believe it’s the answer,
Is an Isoceles triangle With a vertex angle of 50° unique ?
Answer:f
Step-by-step explanation:
Select the algebraic expression for the verbal expression 7 divided by the product of 9 and x.
The algebraic expression for the verbal expression 7 divided by the product of 9 and x is 7/9x.
What are algebraic expressions?When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression. The variables in the algebraic expressions, which have numerous multiples, are used to depict a real-world event. Calculations are made easier by expressing a real-world situation as an expression.Given verbal expression is 7 divided by the product of 9 and x.
Hence, the required algebraic expression for given verbal expression is 7/9x.
To know more about algebraic expressions visit:
https://brainly.com/question/553729
#SPJ9
in 2010, $1.00 u.s. bought 8.24 chinese yuan and in 2012 it bought 6.64 chinese yuan. how many u.s. dollars could 1 chinese yuan purchase in 2010 and 2012?
1 Chinese yuan could purchase $0.12 and $0.15 in the year 2010 and 2012 respectively.
For the year 2010; we can calculate as follows;
1 US dollar = 8.24 Chinese yuan
x US dollar = 1 Chinese Yuan
using cross multiplication to find x;
8.24x = 1 ×1
8.24x = 1
x = 1 / 8.24
x = $0.12
For the year 2012; we can calculate as follows;
1 US dollar = 6.64 Chinese Yuan
x US dollar = 1 Chinese Yuan
Using cross multiplication to find x;
6.64x = 1
x = 1 / 6.64
x = $0.15
Therefore, one Chinese yuan could purchase $0.12 in 2010 and $0.15 in the year 2012.
To learn more about cross multiplication; click here:
https://brainly.com/question/23064464
#SPJ4
The length of a colorado brook trout is normally distribute. what is the probability that a brook trout's length exceeds the mean? (round your answer to 2 decimal places.) the likelihood of a value greater than the mean is .50 because the whole area under the curve is 1 and the mean is the midway point.
The probability that a brook trout's length exceeds the mean is 0.50.
How to find the probability in normal distribution?One of the benefits of normal distributions is that we can find probabilities without being given the parameters of the distribution. This is achieved provided that we know the number of standard deviations from the mean the value of the random variable that delimits the indicated interval is.
We are given;
Distribution of length of a Colorado brook trout; Normal Distribution
Now, we want to find the likelihood of a value greater than the mean is 0.50.
We also know that if it is seen that the shape of the data is almost like a bell shape, then the data will be considered to have a normal distribution.
Thus, by the property of a normal distribution, the probability is 0.50.
Read more about probability in normal distribution at; https://brainly.com/question/4079902
#SPJ1
on a scaled drawing a building measers 4.5 cm tall if the scale drawing is 25 meters per 2 cm how tall is the actual building?
The actual building is tall 56.3 meters
How to calculate the height of the actual building ?
On a scaled drawing a building measures 4.5 cm tall
The scale drawing is 25 meters per 2 cm
The first step is to calculate the equivalent of 1 cm in meters
2 centimetres= 25 meters
1 centimetre= x
cross multiply both sides
2x= 25
x= 25/2
x= 12.5
1 centimetre is 12.5 metres
4.5 centimetres in metres is
= 4.5 × 12.5
= 56.3
Hence the height of the actual building is 56.3 meters
Read more on meters here
https://brainly.com/question/11911800
#SPJ1
identify the independent variable and the dependent variable. a cabinet shop wants to determine the effect of adhesive brands on the bonding of veneer to cabinets. the independent variable is . the dependent variable is
The dependent variable is "Bonding of veneer to cabinets" and the independent variable is "a cabinet shop".
What is a Dependent variable?In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule. A test score, for instance, could be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were.So, in the given sentence, the dependent variable is "Bonding of veneer to cabinets" and the independent variable is "a cabinet shop".
Therefore, the dependent variable is "Bonding of veneer to cabinets" and the independent variable is "a cabinet shop".
Know more about Dependent variables here:
https://brainly.com/question/25223322
#SPJ9
Latanya has 37 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (the fourth side of the enclosure would be the river.) the area of the land is 143 square meters. list each set of possible dimensions (length and width) of the field.
The set of possible dimensions (length and width) of the field are {13.5, 10, 5.5, and 26}.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
The perimeter = 2W+ L
37 = 2W + L
L = 37 - 2W
Hence,
area = W(37 - 2W)
143 = 37W - 2W²
-2W² + 37W - 143 = 0
W² - 18.5 W + 71.5 = 0
W = 13.5, 5.5
Take the value of W = 13.5
Then,
L = 37 - 2W
L = 37 - 2(13.5)
L = 10 meters
Take the value of W = 5.5
Then,
L = 37 - 2W
L = 37 - 2(5.5)
L = 26 meters
Therefore, the set of possible dimensions (length and width) of the field are {13.5, 10, 5.5, and 26}.
Learn more about the Perimeter of the rectangle here:
brainly.com/question/15287805
#SPJ1
hello so i got stuck on this problem thanks to whoever answers this!!!
The machine can make 25 soda bottles each minute.
What is the slope of a graph?The ratio between the change in the values of the y variables and the change in the values of the x variables is known as the slope. It shows how much the y-value changes for every unit change in the x-value.
Given:
The graph shows a relationship between the time and the number of soda bottles a machine can make.
Points are (3,75) and (7,175).
We have to calculate the number of soda bottles the machine can make each minute i.e. rate of the machine.
To determine the rate of the machine which is equal to the slope of the graph,
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] = [tex]\frac{175-75}{7-3}[/tex] = [tex]\frac{100}{4} =25[/tex]
Therefore, the machine can make 25 soda bottles each minute.
To learn more about slope visit:
https://brainly.com/question/14548961
#SPJ9
help me lead with don’t know how to do this
Answer: line mn = 4
Step-by-step explanation:
Note: There's a chance i might be wrong.
Due to de=12, and ef=10, it seems as though a pattern is clear and that ef was -2 the size of de. Since lm is 6, de got divided by 2, 12/2=6
Therefore, subtract 2 from 6, and you get 4.
Hope this helps
at 1:00 pm, the temperature was 18 degrees. It rose 7 degrees during the afternoon and then dropped 30 degrees by midnight. What was the temperature at midnight
Answer:
-5
Step-by-step explanation:
(18+7)-30
25-30=
-5
Janie is designing a flyer for her business. she needs twice the width of the flier to be within 4 inches of 20 inches. complete the sentence to identify the minimum and maximum width of the flier.
Using proportions, it is found that:
The minimum width of the flier is of 8 inches. The maximum width of the flier is of 12 inches.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures using operations such as multiplication and division to find the unknown variables.
In the context of this problem, we have that:
Twice the width of the flier is of 2w.Measures within 4 inches of 20 inches are measures between 16 inches and 24 inches.Hence the minimum width of the flier is found as follows:
2w = 16
w = 16/2
w = 8 inches.
The maximum width of the flier is found as follows:
2w = 24
w = 24/2
w = 12 inches.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
If this trapezoid is moved through the
translation (x+3, y-2), what will the
coordinates of B' be?
A
B
C
5
B' = ([?], [ 1)
4
3
2
1
-7 -6 -5 -4 -3 -2 -1 0
-1
-2
D
1
2
3
PLEASE HELP ASAP
Answer:
(-2, 2)
Step-by-step explanation:
[tex]B(-5,4) \longrightarrow B'(-5+3, 4-2)=B'(-2, 2)[/tex]
You are a clerk at a local convenience store. You make $10.20/hour. They will only give you 20 hours a week. Calculate your gross pay.
Answer:
$204
Step-by-step explanation:
Salary per hour = $10.20
Therefore salary for 20 hours = 10.20 X 20
= $204
I hope you understood the answer and it has helped you!!!
given g(x)=2x-4 , find g(2)
Answer:
g(2) = 0
Step-by-step explanation:
g(2) is the value of x.
So, we would place g(2) with x:
g(2) = 2(2) - 4
g(2) = 4 - 4
g(2) = 0
If the given function is g(x)=2x-4, the value of g(2) will be 0.
What is a function?The function is described as a particular kind of relationship, and each value in the domain is associated with exactly one value in the range according to the function. They have a predefined domain and range.
It is given that the function is, g(x)=2x-4
We have to find g(2).
In order to find the g(2), substitute 2 as the place of x as,
g(x)=2x-4
g(2)=2×2-4
g(2)=4-4
g(2)=0
Thus, for the given function g(x)=2x-4, the value of g(2) will be 0.
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
Tom is in charge of the track and field games at his school. He was given two boxes of prizes. He has given out 7/5 boxes. He estimates he will give out another 4/5 box. Does he have enough? If he does not have enough, how much more does he need?
Answer:
he needs 0.2 more
Step-by-step explanation:
2-7/5=0.6 that means he still has 0.6 left of the boxes.
minus the 4/5= -0.2
so Tom needs 0.2 more to give out that amount.
Answer:
11/10
he needs one more
Step-by-step explanation:
Nicholas has some cans at home to donate to the soup kitchen, but he decides to start a can drive at his school to see if other students will help. The table represents the number of cans donated, y, which is dependent on the number of days cans are collected, x.
A 2-column table with 3 rows. Column 1 is labeled x with entries 4, 7, 10. Column 2 is labeled y with entries 955, 1660, 2365.
Find the linear equation that represents the scenario.
y = 235x + 15
y = 4x + 955
y = 15x + 235
y = 3x + 705
The linear equation that represents the scenario is: y = 235x + 15.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (1660 - 955)/7 - 4)
Slope = 705/3
Slope = 235.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁) or y = mx + c
Where:
m represents the slope.x and y are the points.By critically observing the graph (see attachment) which models the data in the given table, we can reasonably infer and logically deduce that the linear function is given by: y = 235x + 15.
Read more on slope here: https://brainly.com/question/25239789
#SPJ1
On Gabriela’s first birthday, her parents gave her a $50 savings account. On every birthday after that her parents added to the account, increasing the amount they deposited by $25 each year. Complete the recursive definition for the sequence that represents this situation by finding the values for a1 and d.
We will see that the first term is $50, and the common difference is $25, then the recursive formula is:
aₙ = aₙ₋₁ + $25.
How to get the recursive formula?Here we will have something like an arithmetic sequence, such that the recursive sequence is something like:
aₙ = aₙ₋₁ + d
Where d is the common difference.
We know that the first value (the first amount that she has in her savings account) is $50, so we can write the first term as:
a₁ = $50
Now, each new year (the subindex "n" represents the number of the year) $25 are added to that savings account, then we will have:
a₂ = $50 + $25 = $75
a₃ = $50 + $25 + $25 = $100
And so on..
So the common difference is d = $25, then the recursive relation is:
aₙ = aₙ₋₁ + $25.
Learn more about recursive formulas.
https://brainly.com/question/1275192
#SPJ1
Nth term question picture attached
The nth term in the sequence is 30 and the sequence becomes like this: 0, 2, 6, 12, 20, 30
What is a sequence?A sequence is an enumerated group of objects in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of elements. Sequence (countable and uncountable, plural sequences) (countable and uncountable, plural sequences) A series is a group of items arranged in a row next to one another. (Uncountable) The act of following or being successive; succession.So, the n term that comes next in the sequence is:
The sequence is: 0, 2, 6, 12, 20We can notice the hidden sequence, that is:
0 + 0 = 00 + 2 = 22 + 4 = 66 + 6 = 1212 + 8 = 2020 + 10 = 30Therefore, the nth term in the sequence is 30 and the sequence becomes like this: 0, 2, 6, 12, 20, 30
Know more about sequence here:
https://brainly.com/question/6561461
#SPJ13
Emiliano buys two coffees for $8.98. He tips the barista 20% of the bill. How much did Emiliano tip? Round your answer to the nearest cent.
Please help!
The amount for Emiliano tip is $1.8.
How to calculate the value?From the information, Emiliano buys two coffees for $8.98 and he tips the barista 20% of the bill.
The value of the tip will be:
= Percentage × Value of coffee
= 20% × $8.98
= 0.2 × $8.98
= $1.796
= $1.8 to the nearest cent.
This illustrates the concept of multiplication.
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
3 4 + 2 . 5 = (input whole numbers only)
Numerical answers expected
Answer:
37 is the correct answer
Solve the quadratic equations by factoring.
1. 5x^2 = 3x + 2
2. x^2 - 4x + 3 = 0
Help on these two problems above would be very appreciated, thanks!
Solving by factoring in steps shown below
Question 15x² = 3x + 25x² - 3x - 2 = 05x² - 5x + 2x - 2 = 05x(x - 1) + 2(x - 1) = 0(5x + 2)(x - 1) = 05x + 2 = 0 and x - 1 = 05x = - 2 and x = 1x = - 2/5 and x = 1Question 2x² - 4x + 3 = 0x² - x - 3x + 3 = 0x(x - 1) - 3(x - 1) = 0(x - 3)(x - 1) = 0x - 3 = 0 and x - 1 = 0x = 3 and x = 1Answer:
[tex]\textsf{1. \quad $x=1, \quad x=-\dfrac{2}{5}$}[/tex]
[tex]\textsf{2. \quad $x=1, \quad x=3$}[/tex]
Step-by-step explanation:
Solving quadratic equations by factoring
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] , find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], and rewrite [tex]b[/tex] as the sum of these two numbers.Factor the first two terms and the last two terms separately.Factor out the common term.Solve for x by applying the zero-product property.Question 1Given equation:
[tex]5x^2=3x+2[/tex]
Subtract (3x + 2) from both sides:
[tex]\implies 5x^2-(3x+2)=3x+2-(3x+2)[/tex]
[tex]\implies 5x^2-3x-2=0[/tex]
Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], and rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies ac=5 \cdot -2=-10[/tex]
[tex]\implies b=-3[/tex]
Therefore, the two numbers are -5 and 2.
Rewrite [tex]b[/tex] as the sum of the two numbers:
[tex]\implies 5x^2-5x+2x-2=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 5x(x-1)+2(x-1)=0[/tex]
Factor out the common term (x - 1):
[tex]\implies (5x+2)(x-1)=0[/tex]
Apply the zero-product property:
[tex]\implies 5x+2=0 \implies x=-\dfrac{2}{5}[/tex]
[tex]\implies x-1=0 \implies x=1[/tex]
Therefore, the solutions are:
[tex]\boxed{x=1, \quad x=-\dfrac{2}{5}}[/tex]
Question 2Given equation:
[tex]\implies x^2-4x+3=0[/tex]
Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], and rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies ac=1 \cdot 3=3[/tex]
[tex]\implies b=-4[/tex]
Therefore, the two numbers are -3 and -1.
Rewrite [tex]b[/tex] as the sum of the two numbers:
[tex]\implies x^2-3x-x+3=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-3)-1(x-3)=0[/tex]
Factor out the common term (x - 3):
[tex]\implies (x-1)(x-3)=0[/tex]
Apply the zero-product property:
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies x-3=0 \implies x=3[/tex]
Therefore, the solutions are:
[tex]\boxed{x=1, \quad x=3}[/tex]
B. Between which two consecutive integers does the square root lie?
Answer:
The square root of what number?