Answer:
convert the mixed fractions to improper fractions (where the numerator is greater than or equal to the denominator): multiply the whole number part by the fraction's denominator, add that to the numerator, write the result on top of the denominator.if the denominators are not the same, work out the common denominator and rewrite the fractions with the same denominatorssubtract by subtracting the numerators and writing the result over the denominatorconvert back to mixed fractions by dividing the numerator by the denominator, write down the whole number answer, write down the remainder above the denominator.
Example
[tex]3\frac23-1\frac45[/tex]
convert to improper fractions:
[tex]\dfrac{3 \times 3+2}{3}-\dfrac{1 \times 5+4}{5}=\dfrac{11}{3}-\dfrac{9}{5}[/tex]
common denominator = 3 × 5 = 15, so:
[tex]\dfrac{11}{3}-\dfrac{9}{5}=\dfrac{11\times 5}{3\times 5}-\dfrac{9\times 3}{5\times 3}=\dfrac{55}{15}-\dfrac{27}{15}[/tex]
subtract:
[tex]\dfrac{55}{15}-\dfrac{27}{15}=\dfrac{55-27}{15}=\dfrac{28}{15}[/tex]
convert back to mixed fractions:
[tex]28 \div 15=1 \textsf{ remainder }13=1 \frac{13}{15}[/tex]
To subtract mixed fractions, we must follow the steps:
Convert the mixed fraction to improper fraction.2. Multiply the denominator and the numerator by the LCM of the denominators to make the denominators same. P.S: (If the denominators are the same, you can skip this step).
3. Simplify the fractions. (The denominators do not change).
4. (Optional) Convert the fractions to mixed fraction.
Solving an example:Let's take an example.
⇒ [tex]4 \frac{2}{5} - 3 \frac{3}{8}[/tex]Step-1: Convert the fractions to improper fraction:
⇒ [tex]4 \frac{2}{5} - 3 \frac{3}{8}[/tex]⇒ [tex]\frac{(4)(5) + 2}{5} - \frac{(3)(8) + 3}{8}[/tex]⇒ [tex]\frac{20 + 2}{5} - \frac{24+ 3}{8}[/tex]⇒ [tex]\frac{22}{5} - \frac{27}{8}[/tex]Step-2: Make the denominators same:
⇒ [tex]\frac{22}{5} - \frac{27}{8}[/tex]⇒ [tex]\frac{(22)(8)}{(5)(8)} - \frac{(27)(5)}{(8)(5)}[/tex]⇒ [tex]\frac{176}{40} - \frac{135}{40}[/tex]Step-3: Subtract:
⇒ [tex]\frac{176}{40} - \frac{135}{40}[/tex]⇒ [tex]\frac{41}{40}[/tex]Step-4: Convert the fraction to mixed fraction:
⇒ [tex]\frac{41}{40}[/tex]⇒ [tex]\frac{40}{40} + \frac{1}{40}[/tex]⇒ [tex]1 + \frac{1}{40}[/tex]⇒ [tex]1\frac{1}{40}[/tex]Radioactive isotope Carbon-14 decays at a rate proportional to the amount present. If the decay rate is 12.10% per thousand years and the current mass is 135.2 mg, what will the mass be 2.2 thousand years from now?
Using an exponential function, it is found that the mass 2.2 thousand years from now will be of 103.6 mg.
What is an exponential function?It is modeled by:
[tex]A(t) = A(0)e^{-k\frac{t}{n}}[/tex]
In which:
A(0) is the initial value.k is the decay rate per n years.In this problem:
The decay rate is 12.10% per thousand years, hence k = 0.121, n = 1000.The current mass is 135.2 mg, hence A(0) = 135.2.Then:
[tex]A(t) = A(0)e^{-k\frac{t}{n}}[/tex]
[tex]A(t) = 135.2e^{-0.121\frac{t}{1000}}[/tex]
The mass 2.2 thousand years from now will be given by:
[tex]A(2200) = 135.2e^{-0.121\frac{2200}{1000}} = 103.6[/tex]
The mass 2.2 thousand years from now will be of 103.6 mg.
More can be learned about exponential functions at https://brainly.com/question/25537936
I WILL GIVE BRAINLEST! PLEASE HELP!
On your graph paper, create a coordinate plane with axes and label the origin as O.
Place your compass on the origin, and open the compass to a radius that is equal to your favorite number. Construct a circle. You can add shading detail to start to make the circle appear like a sphere if you would like.
Label the radius value.
Using this radius value, calculate the volume of your sphere using the formula
Radius = _________
Work Space: Show all work and include the final volume. Volume = 4/3 π r3
Answer:
radius 2.7
Step-by-step explanation:
2.7 on the axes
Answer:
Step-by-step explanation:
Radius = 5
Volume = 4/3 π r3
= 4/3 (3.14) 5^3
= 523.33
Please help!!
Combinations
For f(x) = 5x and g(x) = x + 1,
find the following functions.
a. (fog)(x)=
b. (gof)(x)=
c. (fog)(3)=
d. (gof)(3)=
a. (fog)(x)=
(Simplify your answer.)
Answer 1:
[tex]f\left(x\right)o\left(x\right)=5x^2+5x[/tex]
Answer 2:
[tex]g\left(x\right)o\left(x\right)=x^2+2x+1[/tex]
Answer 3:
[tex]f\left(3\right)o\left(3\right)=60[/tex]
Answer 4:
[tex]g\left(3\right)o\left(3\right)=16[/tex]
I hope this helps you
:)
10. Multi-Step The paleontologist measures the fossils again and finds two errors. Two fossils with a length of 7.9 centimeters instead measure 8.1 and 8.2 centimeters. Which two numbers will have the same number of dots? A) 7.8 and 7.9 (В 8.0 and 8.2 © 7.8 and 8.1 D 7.9 and 8.1
The two numbers on the dot plot that will have the same number of dots would be: B. 8.0 and 8.2.
What is a Dot Plot?A dot plot can be described as a simple form of data visualization that shows the frequency at which each data points in the data set occurs, which are plotted as dots.
The data set of the measures of the fossils taken by the paleontologist include the following data points and the frequency at which they occur and how they are represented on a dot plot:
7.8 - 5 times (5 dots)7.9 - 6 times (6 dots)8.0 - 0 times (0 dot)8.1 - 3 times (3 dots)8.2 - 1 times (1 dot)We are told that the paleontologist found two errors, where a length of two fossils that measure 7.9 are recorded as 8.1 and 8.2.
Therefore, if the correct measures are used to draft a new dot plot, we would have the following data points and number of dots representing the correct frequency of each measures:
7.8 - 5 times (5 dots)7.9 - 8 times (8 dots)8.0 - 0 times (0 dot)8.1 - 2 times (2 dots)8.2 - 0 times (0 dot)Therefore, the two numbers on the dot plot that will have the same number of dots would be: B. 8.0 and 8.2.
Learn more about dot plot on:
https://brainly.com/question/24309209
A home decor store donated a percent of every sale to hospitals. The total sales were $8,300 so they store donated "$322." What percent of $8,300 was donated to hospitals?
Answer:
I believe they donated 4% to the hospitals
Wool Inc. also sells wool so that crafters can use their signature wool to create their own products at home. Wool Inc. produces three joint products from raw wool. At the split-off point, three basic products emerge: red wool, blue wool, and yellow wool. Each of these products can be either sold at the split-off point or processed further. If they are processed further, the resulting products can be sold to high-end crafters as a premium product. Cost and revenue information is as follows. Sales Value and Additional Costs If Proce ssed Further Pounds Produced Sales Value at Split-Off Final Sales Value Additional Further Processing Cost Red Wool 10,000 $110,000 $200,000 $50,000 Blue Wool 5,000 100,000 180,000 60,000 Yellow Wool 3,000 90,000 110,000 21,000 Required: a. Which products should Wool Inc. process beyond the split-off point? b. At what price per pound would it be advantageous for Wool Inc. to sell blue wool at the split-off point rather than process it further?
a. Wool Inc. should process further Red Wool and Blue Wool.
b. Wool Inc. can sell Blue Wool at the split-off point at $24 per unit ($120,000/5,000) without further processing, instead of selling at $36 per unit ($180,000/5,000) after further processing.
What is the split-off point?The split-off point is the processing point when joint products can be further processed separately.
At the split-off point, the costs of the joint products can be identified separately.
Data and Calculations:Sales Value and Additional Costs If Processed Further:
Pounds Sales Value Final Sales Further Profit from
Produced at Split-Off Value Processing Further
Cost Processing
Red Wool 10,000 $110,000 $200,000 $50,000 $40,000
Blue Wool 5,000 100,000 180,000 60,000 20,000
Yellow Wool 3,000 90,000 110,000 21,000 -1,000
Thus, the profits from further processing are computed as the Final Sales Value minus Further Processing Cost minus Sales Value at the Split-off point.
Learn more about joint products at https://brainly.com/question/25408525
Helppp meeee !!
!!
!!
Answer:
no
Step-by-step explanation:
3^3=27
so 3^3+3^3+3^3=27+27+27=81
3^9=19683
Answer:
No it's not same because we cannot add degrees. 3^9 is much greater than 3^3+3^3+3^3.
27+27+27≠ 19, 683
81≠19,683
Pls mark me brainliest
Step-by-step explanation:
pls answer this all pls ASAP
What is the multiplicative inverse of 1/4
Answer:
4
Step-by-step explanation:
To make a unit fraction, say 1⁄4 to 1, we need to add it 4 times. Or in other words, multiply 1⁄4 by 4. Thus, the multiplicative inverse of 1⁄4 is 4.
Hope this helps
Answer:
4
Step-by-step explanation:
To make a unit fraction, say 1⁄4 to 1, we need to add it 4 times. Or in other words, multiply 1⁄4 by 4. Thus, the multiplicative inverse of 1⁄4 is 4.
How many arrangements can be formed using the letters in the word FILIBUSTER?
Maya works mowing lawns and babysitting. She earns $8.60 an hour for mowing and $7.80 an hour for babysitting.
for 1 hour of mowing and 5 hours of babysitting
Answer:
total of 46.6 dollars
Step-by-step explanation:
8.60x1= 8.60
5x7.80= 39
Find the median of the data in the box plot below.
problems
Number of math problems
assigned by Ms. O'Brien
HH
0 2 4 6 8
HHHHH
14 16
20
10
12
18.
What is the median?
Answer:
median = 11
Step-by-step explanation:
The median is represented by the vertical line inside the boxplot
That is the median = 11
Answer:
11
Step-by-step explanation:
Where the line is ,it's at 11.
Also i got it correct on khan
Which lines or segments are parallel? Justify your answer.
Answer:
CA || HR
CM || HA
Step-by-step explanation:
the triangles are the same
The sum of two consecutive numbers is
thirty-five, what are the numbers?
Answer:
17 and 18
Step-by-step explanation:
divide 35 by 2 and u get 17.5, this is in between 17 and 18 so that's why they are they consecutive numbers.
(-3)*(2a+b)-4(b+a) help plez
Answer:
-10a - 7b
Step-by-step explanation:
Solving
[tex](-3)(2a)+(-3)(b)+(-4)(b)+(-4)(a)[/tex] [tex]-6a-3b-4b-4a[/tex] [tex](-6a-4a)+(-3b-4b)[/tex] [tex]-10a-7b[/tex]Have a lovely rest of your day/night, and good luck with your assignments! ♡
What is the solution for the equation?
a+8/3=2/3
1.a=-10/3
2.a=-2
3.a=2
4.a=10/3
Answer:
2 is the answer of the question
hi please help im giving full points and brainliest:) Let y = 2(x – 3)2 – 6.
Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine a possible restriction on the domain such that the relation is one-to-one. (5 points)
Part B: Determine y–1. Show all necessary calculations. (5 points)
Part C: Prove algebraically that y and y–1 are inverse functions. (5 points)
Answer/Step-by-step explanation:
Part A:
Yes, the given relation is a function
No, the given is not one-to-one.
The given relation is a function: True
The given one-to-one function: False
For the domain (3, + ∝) or the domain (- ∝,3)
the relation is one-to-one.
Part B:
[tex]y=2(x-3)^2-6[/tex]
[tex]y+6=2(x-3)[/tex]
[tex](x-2)^1=\frac{y}{2}+3[/tex]
[tex]x-2=[/tex] ±[tex]\sqrt{\frac{y}{2}+3}[/tex]
[tex]x=[/tex] ± [tex]\sqrt{\frac{y}{2}+2+2}[/tex]
So, [tex]y^-^1=[/tex] ± [tex]\sqrt{\frac{x}{2}+3}+3[/tex]
Part C:
[tex]y(y^-^1)=2([/tex]±[tex]\sqrt{\frac{x}{1}+3+3-3)^2-6}[/tex]
[tex]=2(\frac{x}{2}+3)-6[/tex]
[tex]x+6-6=x[/tex]
So y and y^-^1 are inverse function.
[RevyBreeze]
Can someone help me I need help
Answer:
thanks
Step-by-step explanation:
for 5 poinvf67t4
If the farmer has 164 feet of fencing, what is the largest area the farmer can enclose?
Answer:
it is 41 because you would divide 164 by 4 and get 41
The area which will cover the 164 feet of fencing in form of a square is 1681 square feet.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
If we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.
Length of fencing = 164 feet
Let's suppose this fencing is covered outside of a square with side "a".
The perimeter of the square = 4a
4a = 164
a = 41
Now the area of the square is a².
Therefore,41² = 1681 square feet.
Hence "The area which will cover the 164 feet of fencing in form of a square is 1681 square feet".
To learn more about surface area,
https://brainly.com/question/2835293
#SPJ5
Question
If
f(x) = ax + 6,
where a is a constant, and f(2) = 8, calculate a.
Provide your answer below:
Answer:
1
Step-by-step explanation:
f(x) = a(2) + 6 = 2a + 6
Given f(2) = 8
so 2a + 6 = 8
2a = 8 - 6 = 2
so a = 1
John is making a friendship bracelet with 6 different colors of thread. He uses 22 inches of each color. How many feet of thread does he use in all?
Answer:
132 inches of string in total
Step-by-step explanation:
since he uses 22 inches of each color and he has 6 colors what you have to do is multiply 22 by 6 and you get 132
find the value of x 22,27
please help me i need it i will give brainliest
Answer: 3m + 1 - m
plzz mark brainliest ;)
Find the reference angle for a rotation of 347°
The Refernce angle is 13
Step-by-step explanation:
For example imange a coordinate plane lets say we want to draw an angle thats 144° We start on the right side of the x-axis, where three o’clock is on a clock. We rotate counterclockwise, which starts by moving up. We keep going past the 90° point (the top part of the y-axis) until we get to 144°. hope this helps!
What is y when x = 40?
about 120
about 150
about 190
about 210
Answer:
About 190
Step-by-step explanation:
Hope that helps!
Answer:
Step-by-step explanation:
I took the quiz :)
PLZ HELP ty :) ur kind person ty
Answer:
True
Step-by-step explanation:
is 40 000 less than 43 987
Answer:
Of course.
Step-by-step explanation:
Hope it helps you:)
(-3x) – (-5) = (-2) + (-2x)
=
Draw a picture.
Explain the step.
Write the equation.
Answer:
Easy to solve.
X=7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
у = 3х – 8
(6х + Зу = -9
y = 3x - 8 ---- i
6x + 3y = -9
=>6x +3 (3x-8) = -9 (substituting y= 3x-8)
=> 6x + 9x - 24 = -9
=> 15x = 24 -9
=> 15x = 15
=> [tex]\red{\bold{\large{ x= 1}}}[/tex]
Now substituting x = 1 in equation i,
y = 3 × 1 -8
=> y = 3 -8
=> [tex]\red{\bold{\large{ y= -5}}}[/tex]
Lashonda runs 12 miles in 92 minutes.
How many miles does she run per minute?