If the three postal workers sort the mail together or work in parallel, it will take them 15 minutes.
What is parallel working?Parallel working refers to the system that can process a common task simultaneously by many workers communicating with one another.
When workers perform the same task together, they tend to achieve greater speed, unlike when they work individually without communicating.
Data and Calculations:Time to sort a stack of mail by A = 45 minutes or 1/45
Time to sort a stack of mail by B = 25 minutes or 1/25
Time to sort a stack of mail by C = 1/225
Time for the three workers to sort the stack together = 1/45 + 1/25 + 1/225
= 15 minutes (5 + 9 + 1)
Thus, if the three postal workers sort the mail together or work in parallel, it will take them 15 minutes.
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b) A different sequence has this expression for the nth term: 1 (n + 1)² Work out the first four terms in the sequence. b ) A different sequence has this expression for the nth term : 1 ( n + 1 ) ² Work out the first four terms in the sequence.
The first four terms in the sequence are 4, 9, 16 and 25.
Given that, the nth term of the sequence is 1 (n + 1)².
We need to find the first four terms in the sequence.
What is the sequence?In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
To find the first four terms of the sequence, replace n=1, 2, 3 and 4.
Now, when n=1
1(1+1)²=1×4=4
When n=2
1(1+2)²=1×9=9
When n=3
1(1+3)²=1×16=16
When n=4
1(1+4)²=1×25=25
Therefore, the first four terms in the sequence are 4, 9, 16 and 25.
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The next number in the series 7, 9, 13, 29, is:
Answer:
67
Step-by-step explanation:
7 + 2 =9
9 + 4 = 13
13 + 16 = 29
29 + 38 = 67
Are the two smaller triangles similar? If so, write the similarity statement and identify which theorem or postulate is used
to prove the two triangles similar.
A. Yes, AABC-ACBD by the AA similarity postulate.
B. Yes, AABC-ADBC by the SSS similarity theorem.
C. Yes, AABC-ACBD by the SAS similarity theorem.
D. No, these triangles are not similar.
Answer:
C. Yes, △ABC~△CBD by the SAS similarity theorem
Step-by-step explanation:
i think
Answer:
C- SAS similarity theorem
Explantion:
Two sides and one 90 degree angle
What is the value of the function when x = 1 in the
piecewise function
g(x) =
{
3x
-2x
when x>1
when x≤1
Answer:
-2
Step-by-step explanation:
3x isnt used because it stated when x>1.
so -2(1) is -2, because x =< 1 is true
Assume that the halting language [tex]H_T_M[/tex] is reducible to
some language B ([tex]H_T_M[/tex] [tex]$\leq$[/tex] [tex]_m[/tex] B). Is it possible that is decidable? Answer true/false and explain. Please help me this answer?
H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.
How to Interpret Machine Language?A language is referred to as Decidable or Recursive if there is a Turing machine that accepts and halts on every input string w. This tells us that every decidable language is Turing-Acceptable.
Now, we are told that the halting language is reducible to some language B. This means that it is an undecidability via reduction.
Now, Using the idea that “ If A is undecidable and reducible to B, then B is undecidable.” Suppose R decides HALT_TM, we will construct S to decide ATM .
S = “On input (M, B)
This means that H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.
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The principal represents an amount of money deposited in a savings account subject to
compound interest at the given rate.
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
Click the icon to view some finance formulas.
A. The amount of money in the account after 5 years is $
(Round to the nearest hundredth as needed.)
Principal
$11,000
Rate
5%
Compounded
annually
Time
5 years
Step-by-step explanation:
So the general formula for compound interest is [tex]A = P(1+\frac{r}{n})^{nt}[/tex] where t is typically time in years, and n is how many times it's compounded per year. But in this case it's only compounded 1 time per year so the equation is just [tex]A = P(1+r)^t[/tex]. in this case P is the principal amount, r is the interest, and A is the final amount. So the 5% interest rate becomes 0.05 by dividing by 100 to convert it into decimal form and the principle amount of 11,000. This gives you the formula [tex]A = 11000(1.05)^t[/tex]. This is the answer to the first question where t is the time in years. When it says "Find interest earned" I'm a bit confused, is it giving you x amount of years where you have to calculate the interest earned or does it want a general equation? Because the general equation would be the final amount - the principle amount which calculates the difference. So the equation for interest earned would be [tex]11000(1.05)^t-11000[/tex]. To calculate the amount of money after 5 years you simply plug in 5 as t. this gives you the equation [tex]11000(1.05)^5 \approx 11000(1.276) \approx 14,039.10[/tex]
MATH: GRAPHS AND FUNCTIONS 3. HELP! 12 PTS (HARD)
Answer:
Step-by-step explanation:
Determine the composition of transformations that would map figure ABCD to figure A''B'C''D'
The composition of transformations that would map figure ABCD to figure A''B'C''D' is 180° degree rotation about point C.
What is transformation?It should be noted that transformation simply means the manipulation of a shape or geometric figure.
In this case, the composition of transformations that would map figure ABCD to figure A''B'C''D' is 180° degree rotation about point C.
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which table represents a linear function? y=3,7,11,15 y=3,8,15,21 y=3,9,3,9 y=3,9,27,81?
The table that represents a linear function is y=3,7,11,15
How to determine the table?For a table to represent a linear function, the table must have a constant rate of change i.e. a common difference
From the list of options, we have:
y=3,7,11,15
The difference between each y value is 4
i.e. 7 - 3 = 11 - 7 = 15 - 11 = 4
Hence, the table that represents a linear function is y=3,7,11,15
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For the system of inequalities below, which ordered pair is a solution?
3x-y<2
3y<9x-6
The solution to the given pair of inequalities is at any point on the line
System of inequalitiesInequalities are expressions that are not separated by an equal sign. Given the system of inequalities as shown:
3x-y<2
3y<9x-6
The solution of the system of inequality is the point of intersection of the lines. From the graphed line below, you can see that the point of intersection is at any point on the line since the lines are the same
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please help ..
Use the function f(x) = 2x2 − x − 10 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
I have part a and b
The end behavior is that as the value of x increases the value of function increases.
How to get the graph of a function?A) We want to completely factor; f(x) = 2x² - x - 10
⇒ f(x) = 2x² - 5x + 4x - 10
⇒ 2x(x + 2) - 5(x + 2)
⇒ (2x - 5)(x + 2)
B) The x-intercept occurs at y = 0. Thus;
(2x - 5)(x + 2) = 0
x =5/2 and x = -2
C) f(x) = 2x² - x - 10
Thus, the end behavior is that as the value of x increases the value of function increases.
D) The graph steps has been attached
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A cookware consultant sells two types of pizza stones. The circular(e) stone sells for $26 and the rectangular (r) one sells for $34. In one month she sold 37 stones. If she made a total of $1138 from the sale of the pizza stones, how many of each size did she sell?
Answer:
Step-by-step explanation:
Conditions
Let the circular stones = x
Let the rectangular stones = y
Equations
x + y = 37 Subtract x from both sides of this equation.
y = 37 - x Notice that x is on the right side of the equation
Solution
26x + 34y = 1138 Substitute for y
26x + 34(37 - x) = 1138 Remove the brackets
26x + 1258 -34x= 1138 Combine
-8x + 1258 = 1138 Subtract 1258 from both sides
-8x +1258-1258 = 1138-1258 Combine.
-8x = -120 Divide both sides by -8
-8x/-8 = -120/-8
x = 15 Two minuses make a plus (last step)
x+ y = 37
15 + y = 37 Subtract 15 from both sides
15-15 +y = 37-15 Combine
y = 22
Answer
x = 15 Circular pizza dishes
y = 22 square pizza dishes
The consultant sold 15 circular pizza stones and 22 rectangular pizza stones.
How to determine how many of each size did she sell?Let's assume the number of circular pizza stones sold is "c" and the number of rectangular pizza stones sold is "r."
We are given two pieces of information:
1. The total number of stones sold: c + r = 37
2. The total amount earned from the sale of the stones: 26c + 34r = 1138
Now, we can use these two equations to solve for the values of "c" and "r."
First, let's use the first equation to express "c" in terms of "r":
c = 37 - r
Now, substitute this value of "c" into the second equation:
26c + 34r = 1138
26(37 - r) + 34r = 1138
962 - 26r + 34r = 1138
Combine the "r" terms:
8r = 1138 - 962
8r = 176
Now, divide by 8 to find the value of "r":
r = 176 / 8
r = 22
Now that we have the value of "r," we can find the value of "c" using the first equation:
c = 37 - r
c = 37 - 22
c = 15
So, the consultant sold 15 circular pizza stones and 22 rectangular pizza stones.
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Use a graphing calculator to find the value of the correlation coefficient r and determine if there is a strong correlation among the data. (12, 28), (15, 50), (18, 14), (21, 28), (24, 36)Group of answer choicesweak positive correlationstrong negative correlationstrong positive correlationweak negative correlation
The value of the correlation is -0.0721 and it is a weak negative correlation
How to determine the correlation coefficient?
The points are given as:
(12, 28), (15, 50), (18, 14), (21, 28), (24, 36)
Enter the above points in a graphing calculator.
From the graphing calculator, we have the following summary:
X Values
Sum X = 90Mean = 18∑(X - Mx)^2 = SSx = 90Y Values
Sum Y = 156Mean = 31.2∑(Y - My)^2 = SSy = 692.8X and Y Combined
N = 5∑(X - Mx)(Y - My) = -18R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
This gives
r = -18 / √((90)(692.8)) = -0.0721
So, the correlation coefficient is -0.0721
The above is a negative correlation because it is less than 0 and it is a weak correlation because it is closer to 0 than -1
Hence, the correlation is a weak negative correlation
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If a, b and c are integers, which of the following statements is/are TRUE?
If a, b and c are integers then the correction option in the above case is that both equation 1 and 2 are correct.
What is the proves?Note that:
If a|(bc), then a|b is true If ab|bc, then b|c is trueBecause:
Suppose one say a|b. Then one can see that an integer do exist which is n such that b = an.
Hence:
bc = (an)c = a(nc), so a|(bc) (the reverse is still the case or still applies)
Therefore, If a, b and c are integers then the correction option in the above case is that both equation 1 and 2 are correct.
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graph g(x) = 5|x-6| + 2
Answer + Step-by-step explanation:
[tex]f(x) = 5|x-6|+2 = \begin{cases}5\left( x-6\right) +2&if\ x\geq 6\\ 5\left( 6-x\right) +2 &if\ x\leq 6\end{cases}[/tex]
[tex]\Longrightarrow f(x) = \begin{cases}5x-30+2&if\ x\geq 6\\ 30-5x +2 &if\ x\leq 6\end{cases}[/tex]
[tex]\Longrightarrow f(x) = \begin{cases}5x-28&if\ x\geq 6\\ -5x +32 &if\ x\leq 6\end{cases}[/tex]
case 1: x ≥ 6 → f(x) = 5x - 28
5(6) - 28 = 30 - 28 = 2
Then
the point A(6 ,2) lie on the graph (line) of f
5(7) - 28 = 35 - 28 = 7
Then
the point B(7 ,7) lie on the graph (line) of f
Graphing :
When x ≥ 6 ,the graph of f is the ray [AB) (just connect the points A and B)
case 2: x ≤ 6 → f(x) = -5x + 32
-5(6) +32 = -30 + 32 = 2
Then
the point A(6 ,2) lie on the graph (line) of f
-5(5) +32 = -25 + 32 = 7
Then
the point C(5 ,7) lie on the graph (line) of f
Graphing :
When x ≤ 6 ,the graph of f is the ray [AC) (just connect the points A and C)
don’t understand the question would be a pleasure if someone were to explain and answer the questions! thank you
Use the function below to find F(3).
Answer:
D
Step-by-step explanation:
Answer:
D. 1/125
Step-by-step explanation:
[tex]f(3)=(\frac{1}{5} )^{3} =\frac{1^{3} }{5^{3} } =\frac{1}{125}[/tex]
Hope this helps
Which expression is equivalent to √-80
O 4√5
O -4√√51
4√√51
O 4√√5
Answer: [tex]4i\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{-80}\\\\=\sqrt{-1} \sqrt{80}\\\\=\sqrt{-1} \sqrt{16} \sqrt{5}\\\\=4i\sqrt{5}[/tex]
None of the provided options is equivalent to √-80.
We have,
To simplify the expression √-80, we need to determine the square root of -80.
However, since -80 is a negative number, its square root is not a real number.
The square root of a negative number is usually expressed using the imaginary unit "i," where i = √(-1).
In this case, we can rewrite the expression as:
√(-1 * 80) = √(-1) * √(80) = i * √(80).
Therefore,
None of the provided options is equivalent to √-80.
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How can the following expression be written so that no negative exponents appear?
(a5)³a-6
Q-2
Answer:
a^11
Step-by-step explanation:
1) Simplify the numerator. Use the laws: (x^a)^y = x^ay, x^a × x^b = x^a+b.
= a¹⁵ × a^-6 / a^-2
= a⁹ / a^-2
2) Divide them. Use the law: x^a / x^b = x^a - b.
= a^9 - (-2) / 1
= a^9 + 2 / 1
= a^11
Whats the correct answer answer asap for brainlist
Answer:
Id say A but it's tricky.
Israel is in the Eurasian plate. Go ahead with A for the correct one
Find the diffrence between 6/7 and 2/3 In lowest terms
Answer:
4/7
Step-by-step explanation: Multiply 2/3 x 6/7 Put your answer in lowest terms a. 4/7
Answer:
Difference: 4/21
Step-by-step explanation:
the difference between two quantities is the result of a subtraction
[tex]\frac{6}{7} -\frac{2}{3} =\frac{(6)(3)-(7)(2)}{(7)(3)} =\frac{18-14}{21} =\frac{4}{21}[/tex]
The fraction can no longer be reduced
Hope this helps
determine the slope of a line that is parrallel to the equation 3x + 6y =18
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Determine the slope of a line that is parallel to the equation [tex]\bf{3x+6y=18}[/tex].
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
First we should divide the whole equation by 6,
[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}}[/tex] | simplify
[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x
[tex]\bf{y=-\dfrac{1}{2}x+3[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope-\dfrac{1}{2}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
3x - 6y = 8 then x - 2y
Equations are written by equating two expressionsThe value of x - 2y is 8/3
Equations are written by equating two expressions. Given the following equation
3x - 6y = 8
Divide through by 3 to have:
3x/3 - 6y/3 = 8/3
x - 2y = 8/3
Hence the value of x - 2y is 8/3
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please help I will report if wrong... Brainlyest for the first right answer
Answer:
first three expressions are polynomials and last three are not.
Step-by-step explanation:
last three expression has negative powers of X and some powers of Xs are not integers.
For each of the transformed square root functions, state the transformations and use them to plot the
transformed function on the same graph with the parent function.
Step-by-step explanation:
so, if I understand this correctly, the original function (shown in the graph) is
f(x) = sqrt(x)
the following transformations were done going from f(x) to h(x) :
x -> x + 4 as variable term moved the whole curve 4 units to the left. because now a specific functional value is calculated for a smaller x (by 4 units) than for the original f(x). e. g. let's call g(x) = sqrt(x + 4). then g(-4) = f(0). as mentioned, everything moved over to the left by 4 units.
sqrt(x) -> 3×sqrt(x) increased the range of the function (the generated y values) by the factor 3. was the functional result for a x value = 1, then it is now 3 for the same x value.
sqrt(x) -> sqrt(x) - 1 moved the whole curve down by 1 unit.
in summary, the whole original curve was moved 4 units to the left, then stretched upwards by the factor 3, and then that result was moved down by 1 unit.
so, e.g.
h(-4) = 3×f(0) - 1 = -1 point (-4, -1) corresponds to old (0, 0)
h(-3) = 3×f(1) - 1 = 2 point (-3, 2) corresponds to old (1, 1)
h(0) = 3×f(4) - 1 = 5 point (0, 5) corresponds to old (4, 2)
Find f^-1(x) and it’s domain.
Answer: A
Step-by-step explanation:
Letting [tex]f(y)=x[/tex],
[tex]x=\sqrt{y}-5\\\\x+5=\sqrt{y}\\\\y=(x+5)^{2}[/tex]
Also, the domain of an inverse is the same as the range of the original function, so the range is [tex]x \geq 0[/tex]
Hi, need help please to get my HS diploma...did not graduate :(
Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
Answer:
The answer is A Find the point-slope form.
y+3= −7/5 ⋅ (x+2)
Step-by-step explanation:
Suppose that f(n)=f(n/5)+3n when n is a positive integer divisible by 5, and f(1)=4.
By means of recurrence formulas and a given initial value, we find the following three results: f(5) = 19, f(125) = 469, f(3125) = 11719.
How to find the value the elements of a sequence by recurrence formula
Sequences are sets of values defined by at least one condition. In this case, we have three conditions to generate the required values:
f(n) = f(n/5) + 3 · n
f(1) = 4
[tex]n \in \mathbb{N}[/tex]
Now we proceed to find the elements by recurrence:
f(5) = f(1) + 3 · 5
f(5) = 4 + 15
f(5) = 19
f(25) = f(5) + 3 · 25
f(25) = 19 + 75
f(25) = 94
f(125) = f(25) + 3 · 125
f(125) = 94 + 375
f(125) = 469
f(625) = f(125) + 3 · 625
f(625) = 469 + 3 · 625
f(625) = 469 + 1875
f(625) = 2344
f(3125) = f(625) + 3 · 3125
f(3125) = 2344 + 9375
f(3125) = 11719
By means of recurrence formulas and a given initial value, we find the following three results: f(5) = 19, f(125) = 469, f(3125) = 11719.
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Chuck's birthday is 2 days before Linus's.
Lucy's birthday is 3 days after Marcy's.
Patty's birthday is 4 days before Lucy's. If
Marcy's birthday is March 10, when is
Patty's birthday?
Answer:
march 9
Step-by-step explanation:
10+3-4
=9
I think that's the answer
Set up an algebraic equation and then solve.
One integer is 4 times another. If the product of the two integers is 256, then find t
integers.
One possible set of answers is:
Another possible set of answers is :
The first set of integers are: 8 and 32
The second set of integers are: -8 and -32
What is an Integer?An integer is a whole number.
It is also the ratio of any real number and 1.
It does not have a decimal part or the decimal part of the integer is zero.
Analysis:
Let the two inters be x and 4x
product of integers = 4x(x) = 256
4[tex]x^{2}[/tex] = 256
[tex]x^{2}[/tex] = 256/4
[tex]x^{2}[/tex] = 64
x = ±[tex]\sqrt{64}[/tex]
x = -8 0r 8
The other integer = 4 x -8 = -32 or 32
In conclusion the two integers are -8 and -32 or 8 and 32
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