Step-by-step explanation:
For Adding and Subtraction:
1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator).
1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.
1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them).
1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them). 4. combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed.
1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them). 4. combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed. 5. simplify the numerator by distributing and combining like terms.
1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them). 4. combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed. 5. simplify the numerator by distributing and combining like terms. 6. Factor the numerator if can and replace the letters "LCD" with the actual LCD.
1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them). 4. combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed. 5. simplify the numerator by distributing and combining like terms. 6. Factor the numerator if can and replace the letters "LCD" with the actual LCD. 7. simplify or reduce the rational expression of you can. Remember, to reduce rational expressions, the factors must be exactly the same in both the numerator and the denominator.
To Multiply:
first determine the GCF of the numerator and denominator. Then, regrouping the fractions to make fractions equal to One. Then, multiply any remaining factors.To Divide:
First, rewriting the division as multiplication by the reciprocal of the denominator. The remaining steps are the same for multiplication.9514 1404 393
Answer:
necessary: addition and subtractionnot necessary: multiplication and divisionStep-by-step explanation:
For multiplication and division, the denominator of the result is developed as part of the algorithm for performing these operations on rational expressions. For example, ...
(a/b)(c/d) = (ac)/(bd)
(a/b)/(c/d) = (ad)/(bc)
It is not necessary to make the operands of these operations have a common denominator before the operations are performed. That being said, in some cases, the division operation can be simplified if the operands do have a common denominator or a common numerator:
(a/b)/(c/b) = a/c
(a/b)/(a/c) = c/b
__
If the result of addition or subtraction is to be expressed using a single denominator, then the operands must have a common denominator before they can be combined. That denominator can be developed "on the fly" using a suitable formula for the sum or difference, but it is required, nonetheless.
(a/b) ± (c/d) = (ad ± bc)/(bd)
This formula is equivalent to converting each operand to a common denominator prior to addition/subtraction:
[tex]\dfrac{a}{b}\pm\dfrac{c}{d}=\dfrac{ad}{bd}\pm\dfrac{bc}{bd}=\dfrac{ad\pm bc}{bd}[/tex]
Note that the denominator 'bd' in this case will not be the "least common denominator" if 'b' and 'd' have common factors. Even use of the "least common denominator" is no guarantee that the resulting rational expression will not have factors common to the numerator and denominator.
For example, ...
5/6 - 1/3 = 5/6 -2/6 = 3/6 = 1/2
The least common denominator is 6, but the difference 3/6 can still be reduced to lower terms.
If we were to use the above difference formula, we would get ...
5/6 -1/3 = (15 -6)/18 = 9/18 = 1/2
∑_(n=1)^∞▒〖( 1/2 )〗^2n
Answer:
The series converges to [tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
It seems to be this series:
[tex]$ \sum_{n=1}^{\infty} \left(\dfrac{1}{2} \right)^{2n}$[/tex]
We have
[tex]$ \sum_{n=1}^{\infty} \left(\dfrac{1}{2} \right)^{2n} = \sum_{n=1}^{\infty} \left(\dfrac{1}{4} \right)^{n}$[/tex]
Using the Root test we can see that this series converges once
[tex]$ \lim_{n \to \infty} \sqrt[n]{|a_n|} < 1 \implies \sum_{n=1}^{\infty} a_n \text{ is convergent}$[/tex]
Then, [tex]$\lim_{n \to \infty} \sqrt[n]{\left(\dfrac{1}{4} \right)^{n}} = \lim_{n \to \infty} \dfrac{1}{4} = \dfrac{1}{4} < 1$[/tex]
The series is convergent.
Once the series is geometric, the first term is [tex]\dfrac{1}{4}[/tex] and the ratio is also [tex]\dfrac{1}{4}[/tex] in this case.
The sum of infinite geometric series is [tex]S = \dfrac{a_1}{1-r}[/tex] such that [tex]r < 1[/tex]
[tex]\therefore S = \dfrac{\frac{1}{4} }{1-\frac{1}{4}} = \dfrac{1}{3}[/tex]
A student uses the ratio of 4 oranges to 6 fluid ounces to
find the number of oranges needed to make 24 fluid
ounces of juice. The student writes this proportion:
4 24
616
Explain the error in the student's work.
A student uses the ratio of 4 oranges to 6 fluid ounces to find the number of oranges needed to make 24 fluid ounces of juice. The student writes the proportion:4/6=24/16
You are ordering a new home theater system that consists of a TV, surround sound system, and DVD player. You can choose from 66 different TVs, 1212 types of surround sound systems, and 1818 types of DVD players. How many different home theater systems can you build
Answer:
You can build 1296 different home theater systems.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
There are:
6 different TVs
12 types of surround sound systems.
18 types of DVD players.
How many different home theater systems can you build?
The components are independent, so, by the fundamental counting principle:
6*12*18 = 1296
You can build 1296 different home theater systems.
at sunrise, the outside temperature was 3 below zero by lunchtime the temperature rose by 27 and fell by 10 by night what was the temperature at the end of the day?
Answer:11 degrees at sunrisde the temp was -1 degree
Step-by-step explanation:
Can someone please help me?
Answer:
The Answer for your question is B
Answer:
78%
Step-by-step explanation:
They are asking for spotted animals and dogs so
Spotted animals=40%
Dogs=38%
So just add them to get 78%
(Don’t get confused by the 12% spotted dogs those are from the 38%)
What is sin(C)? Please explain.
Answer:
sin(C) = opposite side / hypotenuse
= 15/17
Answer:
[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]
Step-by-step explanation:
[tex] \small \sf \: Sin ( C ) = \frac {Opposite \: side }{Hypotenuse} \\ [/tex]
Where we have given :-
Opposite side = 15Hypotenuse = 17substitute the values, we get
[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]
Fill in the y values of the t–table for the function y = RootIndex 3 StartRoot x EndRoot
x y
−8
−1
0
1
8
Answer:
the answer will - 16
Step-by-step explanation:
because 8 minus 1 is 7 and plus 0 is also 7 then you have add 1 means you have to plus 1 and then their will be 8 and then plus another 8 and the answer will be minus 16
The y values of the table for the function will be -2, -1, 0, 1, and 2.
How to depict the values?The given function is y = 3✓x. Therefore, for x = -8, y = 3✓-8 = -2. For x = -2, y will be = 3✓-1 = -1.
For x = 0, y = 3✓0 = 0. When x = 1, y = 3✓1 = 1 and lastly when x = 8, y = 3✓8 = 2.
In conclusion, the y values of the table for the function will be -2, -1, 0, 1, and 2.
Learn more about t tables on:
https://brainly.com/question/12488423
The graph of the function f(x) = 4 over 5 square root x is shown. What is the domain of the function?
Answer:
all real numbers greater than or equal to 0
Step-by-step explanation:
The domain of the function is whatever the input (in this case, x) can be. As you cannot take the square root of a negative number, x cannot be negative. Because you can take the square root of 0 (which is 0), x can be anything postive or 0, meaning anything greather than or equal to 0. The domain is all real numbers greater than or equal to 0.
Kenneth did of 1/3 of his laundry on Sunday and 7/15 of his laundry on monday. what fraction of laundry did kenneth do in total?
1.What are the coordinates of the vertices of ABC? Use the coordinates to find the lengths of AC and AB .
2.Use the distance formula to find BC. Show your work.
Answer/Step-by-step explanation:
1.
✔️Coordinates of vertices ABC:
A(2, 2)
B(6, 2)
C(2, -1)
✔️AC = |2 - (-1)| = 3 units
AB = |2 - 6| = 4 units
2. Distance formula => [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Distance between B(6, 2) and C(2, -1):
[tex] BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Where,
[tex] B(6, 2) = (x_1, y_1) [/tex]
[tex] C(2, -1) = (x_2, y_2) [/tex]
[tex] BC = \sqrt{(2 - 6)^2 + (-1 - 2)^2} [/tex]
[tex] BC = \sqrt{(-4)^2 + (-3)^2} [/tex]
[tex] BC = \sqrt{16 + 9} = \sqrt{25} [/tex]
[tex] BC = 5 units [/tex]
Answer:
The person above me has the correct answer and solves it in the correct way.
Step-by-step explanation:
This is what I used as my answer though.
Distance Formula: d = √(x2-x1)^2 + (y2-y1)^2
BC = √(x2-x1)^2 + (y2-y1)^2
B = (6,2)
C = (2,-1)
BC = √(2-6)^2 + (-1-2)^2
BC = √(-4)^2 + (-3)^2
BC = √16+9
BC = √25
BC = 5
Which angels are corresponding angles? Check all that apply
Answer:
Only A and B.
Step-by-step explanation:
Corresponding angles are angles in the same position and are the same size. The others are wrong as they are not the same sizes or are not the same
The volume of a right cylinder is 277 cubic centimeters, and the
height is 3 centimeters (cm). What is the radius of the cylinder?
Answer:
3cm
use the formula for the volume of a cylinder
and substitute
What is the quotient of the fractions below? 2/3÷5/4
answer:
2/3÷5/4 is equal to 8/15
Help me please with this math problem
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
[tex](5x-14)+(8x+12)=180[/tex]
These two angles on the line is 180°
Solve the equation:
[tex]5x-14+8x+12=180[/tex]
[tex]5x+-14+8x+12=180[/tex]
[tex](5x+8x)+(-14+12)=180[/tex] {combine the like terms}
[tex]13x-2=180[/tex]
[tex]13x=180+2[/tex]
[tex]13x=182[/tex]
[tex]x=182/13[/tex]
[tex]x=14[/tex]
PROOF:
{substitute 14 in the place of x}
[tex](5(14)-14)+(8(14)+12)=180[/tex]
[tex]56+124=180[/tex]
[tex]180=180[/tex]
hope this helps....
PLS HELP ASAP.!
THANK YOU, WILL MARK BRAINLIEST
Answer:
Explanation:
The volume of the triangular prism:
The base area of the prism = 1/2 x 4 x 6 = 12 ft2
Height = 6 ft
The volume of the triangular prism = 12 x 6 = 72 ft3
The volume of the rectangular prism:
The base area of the prism = 4 x 6 = 24 ft2
Height = 12 ft
The volume of the triangular prism = 12 x 24 = 288 ft3
Volume of the composite figure = (288 + 72)ft3 = 360 ft3
Step-by-step explanation:
Linda is doing car wash with her teammates to collect money for their trip. They can
get $12 for the car that they wash. In order to start their work, they spent $155 to buy
supplies needed for the work.
Part A:
Create a function f(c) to represent the profit that they make for washing c cars.
f(c) =
(b)
Part B:
Use the function rule that you created on Part A to find the value of f '(145)
f-? (145)
9514 1404 393
Answer:
(a) f(c) = 12c -155
(b) f⁻¹(145) = 25
Step-by-step explanation:
(a) Profit is the difference between revenue (12c) and cost (155). The profit function is ...
f(c) = 12c -155
__
(b) The number of cars Linda's team must wash to achieve a profit of $145 is found from ...
145 = 12c -155
300 = 12c . . . . . . add 155
25 = c . . . . . . . . . divide by 12
f⁻¹(145) = 25 . . . . the team must wash 25 cars for a profit of $145
Consider the following sets of sample data:
A: 20,347, 20,327, 22,117, 21,762, 20,864, 20,102, 21,684, 20,063, 21,728, 21,580, 21,720, 20,920, 21,442, 20,766
B: 3.38, 4.64, 4.09, 3.93, 4.25, 4.63, 4.78, 4.25, 4.46, 2.93, 3.64
Required:
For each of the above sets of sample data, calculate the coefficient of variation, CV.
Answer:
3.319%
14.13%
Step-by-step explanation:
A: 20347, 20327, 22117, 21762, 20864, 20102, 21684, 20063, 21728, 21580, 21720, 20920, 21442, 20766
B: 3.38, 4.64, 4.09, 3.93, 4.25, 4.63, 4.78, 4.25, 4.46, 2.93, 3.64
Given the data:
The mean, m = Σx / n
The standard deviation, s = √Σ(x - m)²/ (n-1))
The coefficient of variation is, CV = s / mean
Using calculator to save computation time :
A: 20,347, 20,327, 22,117, 21,762, 20,864, 20,102, 21,684, 20,063, 21,728, 21,580, 21,720, 20,920, 21,442, 20,766
Data A :
Mean, m = 21101.5714
Standard deviation, s = 700.28925
CV = s / m * 100% = 700.28925 / 21101.5714 * 100% = 3.319%
Data B:
Mean = 4.089
Standard deviation, s = 0.5776
CV = 0.5776 / 4.089 * 100% = 14.13%
Choose the correct Set-builder form for the following set written in Roster form: { − 2 , − 1 , 0 , 1 , 2 }
Step-by-step explanation:
{x:x is an integer where x>-3 and x<3}
HELP I NEED TO PASS!!!!!
A. g(x) = 2x-1
B. g(x) = 2x + 1
C. g(x) = 2x –1
D. g(x) = 2x+1
Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 At 95% confidence, the null hypothesis _____. a. should not be rejected b. should be revised c. should be rejected d. None of these answers are correct
Answer:
Option C
Step-by-step explanation:
n = 81
s2 = 625
H0: σ2 = 500
Ha: σ2 ≠ 500
Test Statistics X^2 = (n-1)s^2/ σ2 = (81-1)*625/500
X^2 = 100
P value = 0.0646 for degree of freedom = 81-1 = 80
And X^2 = 100
At 95% confidence interval
Alpha = 0.05 , p value = 0.0646
p < alpha, we will reject the null hypothesis
At 95% confidence, the null hypothesis
(x-2)(-5x^2+x)=(x)(-5x^2)+(x)(x)+(-2)(-5x^2)+(-2)(x) is an exsample of
this is an example of linear equations is one variable
pls help me i will mark brainliest if you are right !
Answer:
second option
Step-by-step explanation:
diameter= 22 cm
radius = diameter/2
=22/2
11 cm
volume of a sphere = [tex]\frac{4}{3}*pie* r^3[/tex]
=[tex]\frac{4}{3} * 3.14 *11^3[/tex]
=4.186666 * 1331
=5572 . 5 cubic centimeters (cm^3)
Can someone answer with steps and explanation? Thanks.
Answer:
[tex]BC=9\sqrt{3}\approx15.59\text{ units}[/tex]
Step-by-step explanation:
Since Segment BOA is a diameter:
[tex]m\angle ACB=90[/tex]
Arc Ac and Arc CB are in a ratio of two to four. Since Segment BOA is a diameter, Arc ACB measures 180°. Letting the unknown value be x, we can write that:
[tex]2x+4x=180[/tex]
Hence:
[tex]x=30[/tex]
Thus, Arc CB = 120°. By the Inscribed Angle Theorem:
[tex]\displaystyle m\angle A=\frac{1}{2}\left(\stackrel{\frown}{CB}\right)=\frac{1}{2}\left(120)=60[/tex]
Therefore, ΔABC is a 30-60-90 triangle. Its sides are in the ratios shown in the image below.
Since AC is opposite from the 30° triangle, let AC = a.
We are given that AC = 9. Hence, a = 9.
BC is opposite from the 60° angle and it is given by a√3. Therefore:
[tex]BC=9\sqrt{3}\approx15.59\text{ units}[/tex]
GIVING OUT BRAINLIEST HELP PLEASE ❤️
Answer:
C
Step-by-step explanation:
Miguel borrowed $1,800 for 2 years and ended up paying $180 in simple interest what was the interest rate
Answer: 103.534%
I used a calculator and everything
if 4,1,2 in middle is 21
if 2,1,4 in middle is 16
then 1,4,2 what is number in middle?
Answer:
5
Step-by-step explanation:
21-16=5
hope it helps!!
is this an Olympiad qn?
Divide 259875 by the smallest number so that the quotient is a perfect cube. Also find the cube root of the quotient
Answer: The smallest number by which 259875 should be divided to make it a perfect cube is 77.
Step-by-step explanation:
Let's expand the number 259875 into prime factors:
259875 = 3³ ∙ 5³ ∙ 7 ∙ 11
Since in the factorization, 7 and 11 appears only one time, we must divide the number 259875 by 7 · 11 = 77, then the quotient is a perfect cube.
259875 ÷ 77 = 3375
[tex]\sqrt[3]{3375} =\sqrt[3]{3^{3} \cdot 5^{3} } =3 \cdot 5 = 15[/tex]
Find the value of
[tex]3 \frac{1}{5} \div \frac{8}{20} [/tex]
Answer:
[tex]{ \bf{3 \frac{1}{5} \div \frac{8}{20} }} \\ = \frac{16}{5} \div \frac{8}{20} \\ { \boxed{ \tt{reciprocal \: of \: \frac{8}{20} = \frac{20}{8} }}} \\ \therefore \: = \frac{16}{5} \times \frac{20}{8} \\ = \frac{320}{40} \\ { \bf{ answer : 8}} \\ \\ {\underline{\tt {\blue{becker \: jnr}}}}
[/tex]
HELP QUICK! WILL GIVE BRAINLIEST ANSWER!!
Answer:
x = 22 degree
Step-by-step explanation:
40 + 5x + 30 = 180 degree (being linear pair)
5x + 70 = 180
5x = 180 - 70
x = 110/5
x = 22 degree
−12 as a ratio of two integers.
Answer:
-12 can be written as the ratio of -24 and 2, for example.
Step-by-step explanation:
Ratio of a to b:
The ratio of a to b is given by the division of a by b, that is:
[tex]r = \frac{a}{b}[/tex]
−12 as a ratio of two integers.
Here, we want any division in which the result is -12. One example is:
[tex]-12 = \frac{-24}{2}[/tex]
-12 can be written as the ratio of -24 and 2, for example.
