What is the value of 1/6 + 1/12 + 2/6
Answer:
7/12
Step-by-step explanation:
1/6 +1/12+2/6
=1×2/6×2 +1/12+2×2/6×2
=2/12+1/12+4/12
final answer is
= 7/12
1/6 + 1/12 + 2/6
= 2/12 + 1/12 + 4/12
= (2 + 1 + 4)/12
= 7/12
Ahmad Conan deposited 60 quarters, 53 dimes, 44 nickels, and 50 pennies into his checking account. The total of the checks he deposited equaled $17 less than twice his total deposit. If Ahmad received 2 twenty-dollar bills in cash, what was his total deposit?
Answer:
40 $
Step-by-step explanation:
He first deposited 60 quarters=15$, 53 dimes=5.3$, 44 nickels=2.2$, and 50 pennies=0.5$ Total 23$
23$+17$=2*(total deposit)
so total deposit = 20
"If Ahmad received 2 twenty-dollar bills in cash" - does not mean that he deposited those 40$
so total deposit = 20$
Part III- Percentage Problems
1. You currently have $4,500 saved in your bank account. You have decided to use $2700.
What percentage of your savings did you use? Show all your work to justify your answer.
2. An organization raises money for students who attend Berkeley College every year.
Currently, they have raised $11,250 which represents 45% of the money they raise.
Determine the amount of money the organization will raise in total. Show all your work
to justify your answer.
The percentage of your savings that I use is 60%
This shows that the amount of money the organization will raise in total is $25,000.
1) Given
Total amount saved = $4500
Amount used = $2,700
Percentage of money used = Amount used/Total amount saved × 100%
[tex]Percentage \ of \ money \ used = \frac{2700}{4500} \times 100\\Percentage \ of \ money = \frac{27}{45} \times 100\\Percentage \ of \ money \ used = \frac{2700}{45} \\Percentage \ of \ money \ used = 60 \%[/tex]
Hence the percentage of your savings that I use is 60%
2) Let the amount of money the organization will raise in total be x
Since the 45% of the money they raise represents $11,250, hence:
[tex]45\% \ of \ x = \$11,250\\0.45x = 11,250\\x = \frac{11250}{0.45}\\ x = 25,000[/tex]
This shows that the amount of money the organization will raise in total is $25,000
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A 7ft board is to be cut into three pieces, two equal length ones and the third 6 inches shorter than each of the other two. If the cutting does not result in any length being lost, how long are the pieces?
Answer:
The two boards of equal length are 30 inches long, and the third board is 24 inches long
Step-by-step explanation:
First, convert the length of the board to inches. There are 12 inches in a foot, so multiply 7 by 12:
7(12)
= 84
Let x represent the length of the two boards of equal length. The length of the third board can be represented by x - 6, since it is 6 inches shorter than the other two.
Create an equation to represent this and solve for x:
(x) + (x) + (x - 6) = 84
3x - 6 = 84
3x = 90
x = 30
So, the two boards of equal length are 30 inches long.
Subtract 6 from this to find the length of the third board:
30 - 6
= 24
The two boards of equal length are 30 inches long, and the third board is 24 inches long.
Question 2b only! Evaluate using the definition of the definite integral(that means using the limit of a Riemann sum
Answer:
Hello,
Step-by-step explanation:
We divide the interval [a b] in n equal parts.
[tex]\Delta x=\dfrac{b-a}{n} \\\\x_i=a+\Delta x *i \ for\ i=1\ to\ n\\\\y_i=x_i^2=(a+\Delta x *i)^2=a^2+(\Delta x *i)^2+2*a*\Delta x *i\\\\\\Area\ of\ i^{th} \ rectangle=R(x_i)=\Delta x * y_i\\[/tex]
[tex]\displaystyle \sum_{i=1}^{n} R(x_i)=\dfrac{b-a}{n}*\sum_{i=1}^{n}\ (a^2 +(\dfrac{b-a}{n})^2*i^2+2*a*\dfrac{b-a}{n}*i)\\[/tex]
[tex]=(b-a)^2*a^2+(\dfrac{b-a}{n})^3*\dfrac{n(n+1)(2n+1)}{6} +2*a*(\dfrac{b-a}{n})^2*\dfrac{n (n+1)} {2} \\\\\displaystyle \int\limits^a_b {x^2} \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} R(x_i)\\\\=(b-a)*a^2+\dfrac{(b-a)^3 }{3} +a(b-a)^2\\\\=a^2b-a^3+\dfrac{1}{3} (b^3-3ab^2+3a^2b-a^3)+a^3+ab^2-2a^2b\\\\=\dfrac{b^3}{3}-ab^2+ab^2+a^2b+a^2b-2a^2b-\dfrac{a^3}{3} \\\\\\\boxed{\int\limits^a_b {x^2} \, dx =\dfrac{b^3}{3} -\dfrac{a^3}{3}}\\[/tex]
What is the end behavior of the function f(x)=54x2?
9514 1404 393
Answer:
as x → ±∞, f(x) → ∞
Step-by-step explanation:
The function is of even degree, so the end behavior is the same for x → ±∞. The leading coefficient is positive, so the end behavior is f(x) → +∞.
Based on what we have learned, how can we ensure that we choose a sample of students that is representative of all 8:00 AM classes that take place on a given morning
Sampling technique is a way of selecting a sample from a given population. The best way to get a sample of students that represents all 8:00 AM classes is by using a stratified sampling technique.
From the complete question, we can summarize the given data as follows:
[tex]Buildings = 3[/tex] ----3 buildings in the college
[tex]Lecture\ Halls =2[/tex] ---- 2 lecture halls in each building
[tex]Capacity = 100[/tex] --- 100 students in each lecture hall
Because the students' lecture halls are not in the same building, the best way to get a sample is as follows:
Divide the students into groups (In this case, the students will be grouped by the buildings of their lecture halls)The number of students in each building is:
[tex]Students = Capacity \times Lecture\ Halls[/tex]
[tex]Students = 100 \times 2[/tex]
[tex]Students = 200[/tex]
There are 200 students in each building
Then select at random an equal proportion of student from each building (say 30 students in each building)The above method is referred to as a stratified sampling technique because the population of the students are divided into groups, before being randomly selected.
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Let two events A and B be independent. Knowing P(A)=0.8 and P(A+B)=0.93. Calculate the probability P(B).
Answer:
Hello,
P(B)=0.65
Step-by-step explanation:
If P(A+B) means P(A∪B)=0.93 then you may read below.
Let's say x=P(B)
A and B being independent, P(A∩B)=P(A)*P(B)=0.8*x
Since P(A∪B)=P(A)+P(x)-P(A∩B) ,
0.93=0.8+x-0.8*x
0.2*x=0.13
x=0.65
fridays high temp was -1. the low temp was -5. what was the difference between the high and low temps
Answer:
4
Step-by-step explanation:
count up from -5 to -1
so -5,-4,-3,-2,-1 and there are four numbers excluding-5
URGENT!! (Picture included)
Answer:
-85
Step-by-step explanation:
You can use calculator for this question
Two cars started from the same place at the same time but travelled in opposite directions. After 9 hours they were 910 kilometers apart. If the speed of one car is 10 kilometers per hour slower than the other what were their speeds per hour
Answer:
55.55 and 45.55
Step-by-step explanation:
Let the car 1 speed be x km/hr and car 2 speed be x-10 km/hr.
Their relative velocity is 2x-10.
Distance covered in 9 hrs=9(2x-10).
18x-90=910, x=55.55 km/hr, x-10=45.55km/hr
Which of the following phrases are expressions?
6-1>L,
-6k = -8,
1/4<3/8,
3 + 5
Answer:
-6k = -8 is an expression
A and C are inequalities
D is arithmetic
find two expressions whose difference is 3x + 4
Answer:
(7x+4) and (4x)
Step-by-step explanation:
The expression are (7x+4) and (4x)
The two expressions are (4x+4) and x whose difference is 3x + 4.
What is expression?Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
Let two expressions are (4x+4) and x
So, difference of two expressions as :
⇒ (4x+4) - x
⇒ 3x + 4
Hence, the two expressions are (4x+4) and x whose difference is 3x + 4.
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#SPJ2
Write the degree of [tex] {x}^{2} + 2x + 3 {x}^{5} + 4 {x}^{3} + 9[/tex].
Answer:-
5
Explanation:-The highest degree included in the polynomial is known as degree of polynomial
[tex]\sf \checkmark[/tex] Polynomial with degree 1=monomial
[tex]\sf \checkmark[/tex] Polynomial with degree 2 =binomial
[tex]\sf \checkmark[/tex] Polynomial with degree 3=Trinomial
What is the length of the hypothenuse of the triangle?
Answer:
26ft
Step-by-step explanation:
10^2 +24^2 =AB^2
AB=26
Answer: 26 ft
Step-by-step explanation:
a^2+b^2=c^2
10^2+24^2 = c^2
100+576=c^2
Sqrt 676 = c
C = 26
describe the translation. y = (x-5)squared +5 - y = (x-))squared +0
In functions; translations are used to move lines, points or shapes across the graph (i.e. up, down, right or left).
The translation from [tex]y = (x - 5)^2 +5[/tex] to [tex]y = (x - 0)^2 +0[/tex] is to shift [tex]y = (x - 5)^2 +5[/tex] to the left by 5 units and then downward by 5 units
The given parameters are:
[tex]y = (x - 5)^2 +5[/tex]
[tex]y = (x - 0)^2 +0[/tex]
Assume the first point is: [tex]y = (x - 5)^2 +5[/tex]
While the second is: [tex]y = (x - 0)^2 +0[/tex]
The first point is first shifted left by 5 units
The rule to this translation is: [tex](x,y) \to (x + 5,y)[/tex]
So, we have:
[tex]y' = (x - 5 + 5)^2 + 5[/tex]
[tex]y' = (x - 0)^2 + 5[/tex]
Next, the resulting function is shifted down by 5 units.
The rule to this translation is: [tex](x,y) \to (x,y- 5)[/tex]
So, we have:
[tex]y" = y' - 5[/tex]
This gives:
[tex]y" = (x - 0)^2 + 5 - 5[/tex]
[tex]y" = (x - 0)^2 + 0[/tex]
Hence, the translation from [tex]y = (x - 5)^2 +5[/tex] to [tex]y = (x - 0)^2 +0[/tex] is to shift [tex]y = (x - 5)^2 +5[/tex] to the left by 5 units and then downward by 5 units
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in chemistry class, 9 Liters of a 40% silver iodine solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?
9 L of 40% silver iodine solution contains 0.40 (9 L) = 3.6 L of silver iodine.
x L of a 10% solution contains 0.10 (x L) = 0.1x L of silver iodine.
Mixing these two solutions results in another solution of volume (x + 9) L and containing (0.1x + 3.6) L of silver iodine, which gives it a concentration of 6%.
But this is impossible! Let a < b. You cannot mix two solutions at concentrations of a and b and magically end up with a mixture whose concentration is smaller than a or larger than b, it has to fall somewhere in the middle.
We can still try solving for x to demonstrate this:
(0.1x + 3.6)/(x + 9) = 0.06
0.1x + 3.6 = 0.06 (x + 9)
0.1x + 3.6 = 0.06x + 0.54
0.04x = -3.06
x = -76.5
Nonsense.
Perhaps you meant the target concentration to be 16%? In that case, there is a valid solution:
(0.1x + 3.6)/(x + 9) = 0.16
0.1x + 3.6 = 0.16 (x + 9)
0.1x + 3.6 = 0.16x + 1.44
0.06x = 2.16
x = 36
14 80 tiles of side 30cm were used to cover a counter top. Calculate the area of the counter top in square metres.
Answer:
Step-by-step explanation:
1,480 is a lot of tiles. Did you mean 80 tiles?
30 cm = 0.3 m
Area of one tile = 0.3² m² = 0.09 m²
Multiply the number of tiles by 0.09 m².
WORTH 30 POINTS PLEASE HELP!!!!! WILL GIVE POINTS
Answer:
2/3 and 4/6
Step-by-step explanation:
For the partially complete factorization, find the other binomial which will complete the factorization n^2-8n-20=(n+2)(_____)
Answer:
(n-10)
Step-by-step explanation:
Jdjdjdhbejdudjkdff
What is the area of the right triangle with sides 10,26 and 24
Answer:
[tex]\boxed {\boxed {\sf 120 \ units^2}}[/tex]
Step-by-step explanation:
We are asked to find the area of a triangle. The formula for calculating this is:
[tex]a= \frac{1}{2} bh[/tex]
This is a right triangle, so the base and height are the legs of the triangle. The 2 smallest sides are the legs because the longest side is the hypotenuse. Since the side lengths are 10, 26, and 24, the base and height must be 10 units and 24 units.
b= 10 unitsh= 24 unitsSubstitute these values into the formula.
[tex]a= \frac{ 1}{2} ( 10 \ units)(24 \ units)[/tex]
Multiply the numbers in parentheses.
[tex]a= \frac{1}{2}(240 \ units^2)[/tex]
Multiply by 1/2 or divide by 2.
[tex]a= 120 \ units^2[/tex]
The area of the triangle is 120 units squared.
We have that 2a+1=1 and b-a=1. What is the value of b?
Answer:
b=1
Step-by-step explanation:
2a+1 =1
Subtract 1 from each side
2a+1-1 = 1-1
2a=0
a=0
Now find b from the second equation
b-a =1
b-0=1
b=1
Answer:
Equation: 2a+1=1
Subtract 1 from both sides: 2a=0
Divide by 2: a=0
Equation: b-a=1
Substitute: b-0=1
Combine: b=1
So, b=1.
Let me know if this helps.
Choose the expression that is equivalent to -4 - (-9).
A 4 + 9
B 4 - 9
C -4 + 9
D -4 + (-9)
Answer:
d
Step-by-step explanation:
[tex]\\ \sf\longmapsto -4-(-9)[/tex]
[tex]\\ \sf\longmapsto -4+9[/tex]
Option C is correct .
Note:-
(-)(-)=(+)(+)(-)=(-)(-)(-)=(+)(+)(+)=(+)Use logarithmic differentiation to find dy/dx
Answer:
Hello,
Step-by-step explanation:
Let's say:
[tex]y=x^{cotg(x)}\\\\ln(y)=cotg(x)*ln(x)\\\\\\\dfrac{y'}{y}=\dfrac{-1}{sin^2(x)} *ln(x)+\dfrac{cotg(x)}{x} \\\\\\y'=-\dfrac{x^{cotg(x)}*ln(x)}{sin^2(x)} +cotg(x)*x^{cotg(x)-1}\\[/tex]
look the image below
Answer:
Does the answer help you?
Does the answer help you?Please choose my answer as a brainliest answer and please rate.
Does the answer help you?Please choose my answer as a brainliest answer and please rate.It take a few mins to solve your question.
Answer:
V≈696.91
Step-by-step explanation:
V=4
3πr3=4
3·π·5.53≈696.90997
9/10 - 4/10 = _
PLEASE ANSWER!! :)
Answer:
5/10
Step-by-step explanation:
Answer:0.5
Step-by-step explanatiolos divides ambos y después restarlos 0
8. Add.
445,976 + 37,415 =
Consider the following three expressions. To be the same what would P, Q, and R have to be
Step-by-step explanation:
Px^2+6x+1=x^2+x^2+Qx+1
P=2 and Q=6
Next, 3x^2-5-(x^2-6x+R/2)=2x^2+6x+1
2x^2-5-R/2+6x=x^2+6x+1
-5-R/2=6, R=-22
If 30 percent of the people surveyed use both of the methods "exercise near home or work" and "exercise outdoors", what percent of people surveyed use at least one of the two methods?
A 26%
B 52%
C 56%
D 74%
E 86%
A. 26%
There are 30% people who use both methods, Exercise near home or work and Exercise outdoor.
There are 46% people who prefer exercise near home or office rather than outdoor.
There are 40% people who prefer exercise outdoor rather than near home or office.
Then there are 30% people among them who use both methods. The remaining 26% people use one of the method.
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Find the sum of ∑4/k=1 (-4k)
Answer:
Hello,
Answer C: -40
Step-by-step explanation:
[tex]\displaystyle \sum_{k=1}^4\ (-4k)\\\\=-4*\sum_{k=1}^4\ k\\\\=-4*4*\dfrac{1+4}{2} \\\\=-4*5*2\\\\=-40\\[/tex]
