Find the sum of 4 1/8 and -1 1/2
Answers
Answer:
\(\frac{21}{8}=2\frac{5}{8}\)
Decimal result:
\(2.625\)
Step-by-step explanation:
Method: Operations with fractions
1. Simplify the expression
\(33/8+-3/2\)
Find the lowest common denominator:
\(\frac{33}{8}+\frac{\left(-3\cdot 4\right)}{\left(2\cdot 4\right)}\)
Multiply the denominators:
\(\frac{33}{8}+\frac{\left(-3\cdot 4\right)}{8}\)
Multiply the numerators:
\(\frac{33}{8}+\frac{-12}{8}\)
Combine the fractions:
\(\frac{\left(33+-12\right)}{8}\)
Combine the numerators:
\(\frac{21}{8}\)
21/8 in mixed number form is equal to 2 5/8.
_____________
Why learn this:
Let's say you invite ten friends over for movie night and order four pizzas to split. How do you divide the pizza evenly so everyone gets the same amount of pizza? If each section of the couch can fit 1+1/5 people, how many sections would there need to be to accommodate all of your friends? The whole world is made up of little bits and pieces that are part of something larger, and the key to understanding them is fractions.
Fractions are the mathematical representation of any whole thing that is made up of multiple parts. Knowing how to manipulate them using operations like addition, subtraction, multiplication, and division is one of the most widely applicable math skills in everyday situations and provides an important foundation for other math concepts you will encounter.
_________________
Terms and topics
Operations with fractionsA fraction represents a smaller part of a whole and is usually written as a numerator, which represents the smaller part, written over a denominator, which represents the whole. To express the fraction as a single number, the quotient, we divide the numerator by the denominator.
There are three main kinds of fractions:
Proper fractions
The numerator is smaller than the denominator.Improper fractions
The numerator is larger than the denominator.Mixed fractions
A whole number combined with a proper fractionIt is important to note that improper fractions and mixed fractions can be used to express the same values.
When doing operations with fractions, it is usually easier to first convert any integers and/or mixed fractions into improper fractions:
To convert an integer into an improper fraction, simply place the integer over 1.
To convert a mixed fraction into an improper fraction, multiply the denominator (bottom number) by the whole number (number in front or to the left of the fraction), add the product to the numerator (top number), and write the sum over the original numerator.
Adding and subtracting fractions
The general rule for adding fractions is: \(\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{bc}{bd}=\frac{ad+bc}{bd}\)
The general rule for subtracting fractions is: \(\frac{a}{b}-\frac{c}{d}=\frac{ad}{bd}-\frac{bc}{bd}=\frac{ad-bc}{bd}\)
There are 4 steps to adding and subtracting fractions:
1. Simplify the fractions by reducing them, if possible. Divide the numerator (top number) and the denominator (bottom number) by their greatest common factor (gcf). The gcf of a set of numbers is the highest number that can divide evenly into all numbers in the set with no remainder.
2. Find the fractions' common denominator. There are two ways to find the common denominator:
1. Multiply the top and bottom of each fraction by the denominator of the other fraction.
2. Find the least common denominator. To do this, we find the least common multiple (lcm) of the denominators and use it as the common denominator. There are two ways to find the lcm: listing numbers' multiples (solver coming soon!) and by prime factorization.
3.Add or subtract the numerators. At this point, the fractions should have the same denominator, meaning we can simply add or subtract the numerators and write the result over the denominator we found in the previous steps.
Simplify the resulting fraction by reducing, if possible, as described above in step 1.
Multiplying fractions
The general rule for multiplying fractions is: \(\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}\)
There are 4 steps to multiplying fractions:
1. Simplify the fractions by reducing them, if possible. Divide the numerator (top number) and the denominator (bottom number) by their greatest common factor (gcf). The gcf of a set of numbers is the highest number that can divide evenly into all numbers in the set with no remainder.
2. Multiply the numerators (top numbers).
3. Multiply the denominators (bottom numbers).
4. Simplify the resulting fraction by reducing, if possible, as described above in step 1.
_______________________________________
#SPJ2
Related Questions
Will give BRAINLEST please look at photo attached
Answers
Answer:
Step-by-step explanation:
if you set (x+5)(x-1) to equal zeros, you would get x+5=0 and x-1=0. then you would subtract 5 and 1 to get x=-5 and x=1
If a pound of turkey costs $0.82, how much will n pounds cost?
Answers
CAN SOMEONE HELP WITH THIS QUESTION?
Answers
The value of the given summation is:
\(\sum (29a_i - 13b_i) ]= -30\)
How to find the sum?Here we know that the sums are:
\(\sum a_i = -10\\\\\sum b_i = -20\)
And we want to find the value of the sum:
\(\sum (29a_i - 13b_i)\)
First we can distribute the sum to get:
\(\sum 29a_i + \sum - 13b_i\)
And take the coefficients out of the sum:
\(29\sum a_i -13\sum b_i\)
Now replace the known values:
\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)
Learn more about sums at:
https://brainly.com/question/30518693
#SPJ1
Find the length of the unknown segment (x) in each figure. Use theorem of secant segment and
external secant segment.
Answers
Answer:
1. x = 6 2. x = 9 3. x = 3
Step-by-step explanation:
Use Intersecting Secants Theorem:
If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
1. AC and AD are secants that intersect at point A
So, AB x AC = AE x AD
\(x\) x 15 = 6 x (6 + 9)
15\(x\) = 90
\(x\) = 6
2. KM and KN are secants that intersect at point K
So, KL x KM = KO x KN
10 x (10 + 8) = \(x\) x 20
180 = 20\(x\)
\(x\) = 9
3. IG and IF are secants that intersect at point I
So, IH x IG = IJ x IF
\(x\) x 39 = 9 x (9 + 4)
39\(x\) = 117
\(x\) = 3
The following table (Table C2.1) is a partial listing of the sales transactions for the Watson Distributing Company for the year ended December 31, 200X. Select the first three sample items from the population using the following techniques. a. The systematic selection technique with a random starting point of 13 and a sampling interval of 30. b. The probability-proportional-to-size sampling selection technique with a random starting dollar of $17,240 and a sampling interval of $220,000. c. The random-number table selection technique using Figure 2.1 on pp. 24-25. Using the last four digits of the invoice number, begin at row (0004) and column (01), continuing across the row and then down to the beginning of the next row.
Answers
The three methods are used to select a sample from a larger population in order to make inferences about the population as a whole.
Probability-proportional-to-size sampling is a method where the probability of an item being selected is proportional to its size. In this case, the size is represented by the dollar amount of the sale.
Systematic selection involves selecting items at regular intervals. In this case, the starting point is 13 and the interval is 30. Every 30th item is selected, starting from the 13th item.
The starting dollar is $17,240 and the interval is $220,000. Every item with a sales amount that falls within the interval is selected with a probability proportional to its size.
The random-number table selection technique involves using a random number table to select items. The last four digits of the invoice number are used to determine which item is selected.
The selection process starts at row (0004) and column (01) and continues across the row and then down to the next row.
The probability of an item being selected in each method differs and is important in ensuring a representative sample is obtained.
To know more about Probability here.
https://brainly.com/question/11234923
#SPJ4
please help me with math the last answer choice is 8/15
Answers
Answer:
This answer would be 1/8
Step-by-step explanation:
All of the colors are equal and there are 4 colors and 3 numbers if you try putting it together then yes it does equal 1/8 because it is equal and it fits just right for both spinners.
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
For similar question on probability.
https://brainly.com/question/7965468
#SPJ8
There are 1000 students at a college. In January, æ of these students had passed
their driving test.
Between January and April, the number of students who had passed their driving
test increased by 20%, and the number of students who had not passed
decreased by 5%. No one left or joined the college during this time.
a) Explain why the number of students who had not passed their driving test yet
was 0.95(1000 - x) in April.
b) Hence explain why 1.2x +0.95(1000-x) = 1000.
c) How many students had passed their driving test in January?
Answers
a) In April, the number of students who had not passed their driving test decreased by 5%.
b) The equation is 1.2x + 0.95(1000 - x) = 1000.
c) 200 students passed their driving test in January.
a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).
In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).
b)
The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).
The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).
Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.
c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.
Expanding the equation, we get:
1.2x + 950 - 0.95x = 1000
0.25x = 50
x = 200
Therefore, 200 students passed their driving test in January.
Learn more about the equations here:
brainly.com/question/10413253
#SPJ1
the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone
Answers
Answer:
Step-by-step explanation:
V = 3.9V
I = 0.12A
Ohm's Law, V = IR
Rearranging Ohm's Law, R = V/I
R = 3.9/0.12 = 32.5Ω
given f(x) =-7x+9 and h(x)=-5f(x) what are the slope an y intercept of the graph of function h?slope=y-intercept =
Answers
First step let us multiply f(x) by -5
\(\begin{gathered} h(x)=-5\lbrack-7x+9\rbrack \\ h(x)=(-5)(-7x)+(-5)(9) \\ h(x)=35x+(-45) \\ h(x)=35x-45 \end{gathered}\)The general form of the linear equation is f(x) = mx + b, where
m is the slope
b is the y-intercept
Since h(x) = 35 x - 45, then
m = 35
b = -45
So:
The slope = 35
y-intercept = -45
What is the vertex of the quadratic function give below.#5
Answers
Given the Quadratic Function:
\(f\mleft(x\mright)=5\mleft(x+1\mright)^2-3\)You can identify that is written in Vertex Form.
By definition, the Vertex Form of a Quadratic Function is:
\(f(x)=a(x-h)^2+k\)Where the vertex of the parabola is:
\((h,k)\)In this case, you can identify that:
\(\begin{gathered} h=-1 \\ k=-3 \end{gathered}\)Therefore, the answer is:
\((-1,-3)\)find the domain of the function f/g(x) given f(x)=x^2+2x-8 and g(x)=x^2-16
Answers
Answer:
C) \(\{x|x\neq-4 \:or \:4\}\)
Step-by-step explanation:
\(\frac{x^2+2x-8}{x^2-16}\\ \\\frac{(x+4)(x-2)}{(x+4)(x-4)}\\ \\x\neq-4 \:or \:4\)
Here, \(x\neq-4\) is a hole on the graph since \(x+4\) exists in both the numerator and denominator.
2) 8x +9y = 82
2x + 2y = 20
Answers
According to a study done by a university student, the probability a randomiy selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and
obsorve people's habits as they sneeze.
What is the probability that among 10 randomly observed individuals fewer than 5 do not cover their mouth when sneezing?
Answers
Answer:
the total number of random sample n 10
probability of is 0.267
Please answer this correctly
Answers
Answer:
41-50 ⇒ 4
Step-by-step explanation:
Numbers 42,43,45 and 48 in the range of 41-50 so there are 4 numbers in the range
Answer:
41-50: 4
Step-by-step explanation:
If you look at the stem and leaf plot, we get the data:
40, 40, 42, 43, 45, 48
Only 4 of those are greater than 40 and less than 50.
For accounting purposes, the value of assets (land, buildings, equipment) in a business are depreciated at a set rate per year. The value, V(t) of $537,000 worth of assets after t years, that depreciate at 17% per year, is given by the formula V(t) = Vo(b)t. What is the value of Vo and b, and when rounded to the nearest cent, what are the assets valued at after 9 years?
a
Vo = $537,000, b = 0.17, and the value after 9 years is $0.45
b
Vo = $537,000, b = 0.83, and the value after 9 years is $100,386.92
c
Vo = $537,000, b = 1.17, and the value after 9 years is $98,291.76
d
Vo = $537,000, b = 0.83, and the value after 9 years is $91,290.00
Answers
Answer:
I think it is D
Step-by-step explanation:
Two pedestrians simultaneously left two villages 27 km apart and walked toward each other, meeting after 3 hours. The first pedestrian walked at a speed of 4 km per hour. At what speed (in km per h) did the second pedestrian walk?
Answers
The speed of the second pedestrian is 5 kilometers per hour.
At what speed did the second pedestrian walk?Let's say that the speed of the second pedestrian is S.
We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:
(4km/h + S)*3h = 27km
It says that both pedestrians work, together, a total of 27km in 3 hours.
Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.
4km/h + S = 27km/3h = 9 km/h
S = 9km/h - 4km/h = 5km/h
The speed of the second pedestrian is 5 kilometers per hour.
If you want to learn more about speed:
https://brainly.com/question/4931057
#SPJ1
how do you solve a two step equation in algebra
Answers
1) Begin by adding or subtracting the same amount on both sides of the linear equation.
2) Next, divide or multiply both sides of the linear equation by the same integer.
3)Always multiply both sides of the equation by the reciprocal of the variable's coefficient, instead of step #2.
PLEASE HELP THIS IS DUE IN 30 MINUTES I'LL BLESS YOUR FIRSTBORN
Complete a two-column algebraic proof solving your equation.
Post your equation and two-column proof
Answers
Answer:
Step-by-step explanation:
1. Find the system for 2x+3y=5 and 3x+y=6 using substition.
I will solve your system by substitution.
(You can also solve this system by elimination.)
3x+y=6;2x+3y=5
Step: Solve3x+y=6for y:
3x+y+−3x=6+−3x(Add -3x to both sides)
y=−3x+6
Step: Substitute−3x+6foryin2x+3y=5:
2x+3y=5
2x+3(−3x+6)=5
−7x+18=5(Simplify both sides of the equation)
−7x+18+−18=5+−18(Add -18 to both sides)
−7x=−13 (Divide both sides by -7)
x=\(\frac{13}{7}\)
Step: Substitute \(\frac{13}{7}\) forxiny=−3x+6
y=−3x+6
y=−3(\(\frac{13}{7}\))+6
y=\(\frac{3}{7}\)
2. Let's solve your system by elimination.
3x+y=6;2x+3y=5
Multiply the first equation by -3,and multiply the second equation by 1.
−3(3x+y=6)
1(2x+3y=5)
Becomes:
−9x−3y=−18
2x+3y=5
Add these equations to eliminate y:
−7x=−13
Then solve−7x=−13for x:
−7x=−13 (Divide both sides by -7)
x=\(\frac{13}{7}\)
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
3x+y=6
Substitute\(\frac{13}{7}\) forxin3x+y=6
3(\(\frac{13}{7}\))=6 (Simplify both sides of the equation)
y+39/7+−39/7=6+−39/7 (Add (-39)/7 to both sides)
y=\(\frac{3}{7}\)
A line which passes through the point (0,4) has gradient 5.
Write down the equation of the line.
Answers
A(0;4); x=0, y=4; m=5
General equation of linear function is \(y=mx+b\) ⇒
\(4=0\times x+b\\b=4\)
Answer: \(y=5x+4\)
One of the two key assumptions for confidence intervals is that the researcher has used _____ ____ ____. (Hint: 3 words). simple random sampling.
Answers
One of the two key assumptions for confidence intervals is that the researcher has used is simple random sampling
The confidence intervals is defined as the the probability that the population parameter will be between the set of values. We can also say that the mean of the estimate plus or minus variation in the estimate
The simple random sampling is defined as the choosing a sample randomly from the population, the probability of choosing any sample in the population will be same
Here, one of the two key assumptions for confidence intervals, so the researches used simple random sampling
Therefore, the method is simple is random sampling
Learn more about confidence interval here
brainly.com/question/24131141
#SPJ4
A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 15 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 75 bolts. The sample mean bolt length was 15.07 centimeters. The population standard deviation is known to be a = 0.26 centimeters. What is the test statistic z? Ex: 1.23 What is the p-value? Ex. 0.123 Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of a 0.01?
Answers
The test statistic z is 2.33, the p-value corresponding to the test statistic z value is 0.0099.
What is Probability?Probability is the measure of the likeliness of happening of an event.
The mean of the data is 15.07 centimeters
The standard deviation of the data is 0.26 centimeters.
n = 75
Significance Level ∝ = 0.01
According to the null and alternative hypothesis
Hₐ : \(\rm \mu\) ≤15 vs H₁ : \(\rm \mu\) >15
The test statistic z is given by
\(\rm Z = \dfrac{(X-\mu)}{\sigma/\sqrt{n}}\)
Z = ( 15.07 -15)/(0.26/√75)
Z = 2.33
The p-value corresponding to z value is 0.0099
as p-value < significance level, therefore the H₁ : \(\rm \mu\) >15 is acceptable.
No, significant evidence is not present to tell that the length of bolts is actually greater than the mean value at a significance level of 0.01.
To know more about Probability
https://brainly.com/question/11234923
#SPJ2
Part A
Select the correct choices to complete the sentence.
Identify the figure with the vertices
A(3,5),B(3,1),and C(0,1).
Part B
Fill in the blank question.
Find the perimeter and area of the figure
Answers
The figure with three verticies A(3,5), B(3,1), and C(0,1) is a triangle it has a perimeter of 12 units and its area is 6 units.
What is semiperimeter?The semiperimeter is half of the perimeter.
We know a rectangle has four verticies and a triangle has three verticies Given are 3 verticies they are A(3,5), B(3,1) and C(0,1).
We know the perimeter of any 2D figure except circle is the sum of the lengths of all the sides.
Now to obtain lenghts of the sides of the triangle we have to find the distance between the points by distance formula which is,
D = \(\sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}\).
∴ The length of the side AB is,
= \(\sqrt{(3-3)^2 + (1 -5)^2\).
= \(\sqrt{(-4)^2\).
= \(\sqrt{16}\).
= 4 units.
Length of the side BC is,
= \(\sqrt{( 0 - 3)^2 + (1 - 1)^2}\).
= 3 units.
Length of the side AC is,
= \(\sqrt{(0 -3)^2 + (1 - 5)^2}\).
= 5 units.
As the length of all the sides are different this is a scalene triangle and perimeter is,
= ( 3 + 4 + 5) units.
= 12 units.
We know area of a scalene triangle is \(\sqrt{(s(s-a)(s-b)(s-c)\) where s is the semiperimeter which is of 6 units.
∴ The are of the triangle is \(\sqrt{6(6-3)(6-4)(6-5)\).
= \(\sqrt{6(3)(2)(1)\) units.
= \(\sqrt{36}\) units.
= 6 units.
learn more about scalene triangle here :
https://brainly.com/question/6987787
#SPJ1
Given the following system of equations, identify the type of system.
x + y = 6
2x - y = -4
A. Consistent
B. Inconsistent
C. Equivalent
Answers
Step-by-step explanation:
I think is b i hope this works
Mary has a bowl She puts
7 nickels into the bowl
Jack sees the bowl and
takes 2 nickels. How much
money (in cents) is left in
the bowl?
Answers
Answer:
25 cents
Step-by-step explanation:
7 nickles is equivalent to 35 cents.
2 nickels is equivalent to 10.
35-10 = 25
There is 25 cents remaining.
There is a ratio of 5 apples to 3 pears in a basket. There are 24 pears in the basket. How many apples are in the basker?
Answers
Answer:
There are 40 apples in the basket.
This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.
I hope this helped you, have an amazing day! :)
PLEASE HELP MEEE IM SO STRESSED!
Answers
Answer:
(a) -2-(-9)=-2+9
=7
(b) -2-9=-11
(c) -2-(-9)-(-2)=-2+9+2
=9
Write the following ratios in their simplest form.
27:30
Answers
Answer:
9/10
Step-by-step explanation:
Answer:
9:10
Step-by-step explanation:
27:30 = 9:10
BRAINLIEST PLEASE
10 celcius equals ____ farenheight
Answers
Answer:
50
Step-by-step explanation:
\(\frac{9}{5}(10)+32=50\)
Determine the probability of randomly selecting two individuals who are issued exactly two credit cards. [Hint: Are the events independent?] Interpret this result.
Answers
Answer:
They are dependent because we have to select from people who are given cards.
Step By Step Explanation:
So we'll take away people not given cards first den find the probability of selecting people with cards over the total number of people present .
Probability we'll be equal to = number of people with card(C) two persons/total number of people
Where C represent combination