: Practice & Problem Solving
Part 1 of 2
Marsha deposited $9,000 into a savings account 3 years ago. The simple interest rate is 5%. How much money did Marsha earn in interest?
Substitute the values into the equation.
Answer:
Marsha earn $1350.
Step-by-step explanation:
Given;P = $9000T = 3 yearsR = 5%To Find;InterestSo,
9000 × 5 × 3 ÷ 100
135000/100
$1350
Thus, Marsha earn $1350.
What is the solution for -3x ≥ 36?
Answer:
x ≤ -12
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesStep-by-step explanation:
Step 1: Define inequality
-3x ≥ 36
Step 2: Solve for x
Divide both sides by -3: x ≤ -12Here we see that any number smaller than or equal to -12 would work as a solution.
PLEASE HELP GIVING POINTS!!!!!
Answer:
its c
Step-by-step explanation:
Mark has some money in his wallet. He was paid $8 for for working for an hour and then had a total of $15. How much money did he have in his wallet before working?
show your work
a supervisor of a manufacturing plant is interested in relating the average number of defects produced per day to two factors: the operator working the machine and the machine itself. the supervisor randomly assigns each operator to use each machine for three days and records the number of defects produced per day. is there sufficient evidence to conclude that there is a significant difference among the average number of defects produced per day for the different operators? number of defects produced per day operator a operator b machine a 0 0 7 7 3 3 8 8 0 0 4 4 3 3 0 0 machine b 6 6 2 2 8 8 3 3 8 8 1 1 3 3 0 0 machine c 2 2 6 6 2 2 4 4 2 2 0 0 5 5 4 4 anova source of variation ss ss df df ms ms machine 3.0000 3.0000 2 2 1.5000 1.5000 operator 0.3750 0.3750 1 1 0.3750 0.3750 interaction 67.0000 67.0000 2 2 33.5000 33.5000 within 95.2500 95.2500 18 18 5.2917 5.2917 total 165.6250 165.6250 23 23 step 1 of 2 : find the value of the test statistic for testing the difference among the average number of defects produced per day for the different operators. round your answer to two decimal places, if necessary.
The test statistic (F-ratio) for testing the difference among the average number of defects produced per day for different operators is approximately 0.07 (rounded to two decimal places).
To find the test statistic for testing the difference among the average number of defects produced per day for different operators, we need to perform a two-way ANOVA (Analysis of Variance) test. The information provided gives us the necessary values for this calculation.
Step 1: Identify the mean square values for the operators and within variation.
From the provided ANOVA table:
- Mean square for operators (MS_operator) = 0.3750
- Mean square within variation (MS_within) = 5.2917
Step 2: Calculate the test statistic, which is the F-ratio.
F-ratio = MS_operator / MS_within
Using the provided values:
F-ratio = 0.3750 / 5.2917 ≈ 0.0709
The value of the test statistic is F = 0.0709.
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As we’ve reviewed as part of the learning plan this week, there are different approaches to multiplication and division beyond having to manually complete all the calculations. Efficiency especially with these core fundamental calculations are key for optimal processing. Research to identify at least 3 techniques or methods that can be applied at a low level. Compare and contrast each of the approaches and explain the advantages and disadvantages of each. Review this article "Faster Integer Multiplication" by Furer looks at a fast integer multiplication technique for algorithms.
Three techniques for efficient multiplication and division at a low level include the Karatsuba algorithm, the Schönhage-Strassen algorithm, and the Toom-Cook algorithm.
The Karatsuba algorithm is a divide-and-conquer technique that reduces the number of multiplication operations required by recursively breaking down the operands into smaller parts. It has a time complexity of O(n^log2(3)), which is an improvement over the traditional O(n^2) complexity. However, it requires additional memory to store intermediate results.
The Schönhage-Strassen algorithm is based on the Fast Fourier Transform (FFT) and uses number theoretic techniques. It has a time complexity of O(n log n log log n) and is particularly efficient for large numbers. However, it requires complex arithmetic operations and is more suitable for specialized applications.
The Toom-Cook algorithm is an extension of the Karatsuba algorithm and allows for even larger operands. It breaks down the operands into multiple parts and performs intermediate computations using polynomial interpolation. It has a time complexity of O(n^log2(5)) and strikes a balance between the Karatsuba and Schönhage-Strassen algorithms.
In conclusion, these three techniques provide efficient alternatives to traditional multiplication and division methods. The Karatsuba algorithm is suitable for general-purpose applications, while the Schönhage-Strassen algorithm is more specialized for large numbers. The Toom-Cook algorithm offers a balance between efficiency and applicability to a wider range of operand sizes.
Understanding the advantages and disadvantages of each technique allows for selecting the most appropriate approach based on specific requirements and constraints. The article "Faster Integer Multiplication" by Furer provides further insights into a fast integer multiplication technique, likely discussing one or more of these algorithms in detail and presenting additional optimizations.
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Identify the domain and range for the relation: (-4, -2), (-6, -3), (-8, -4), (-10,-5)
Answer:
Domain: {-10, -8, -6, -4}
Range: {-5, -4, -3, -2}
Step-by-step explanation:
The domain is a set of all the x's. Here you were given points and the first number in the parenthesis is the x in (x, y). Sometimes they will give you a table or a graph. But domain is all the x's gathered together. I put them in order from small to big to be neat. There aren't any repeats here, but if there ever are repeats you don't have to list them multiple times, just once.
The range is all the y's in the points (x, y) its the second number. Gather all the y's in a set, that is the range.
what is the circumference of the circle ?
Answer: 2π x radius
Step-by-step explanation:
The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line then the length of that line will be the circle's circumference.
marh section 2.3 help
Answer:
-0.07
Step-by-step explanation:
Given the parent function f(x) = 2x, which graph shows f(x) − 1? Group of answer choices exponential function going through point 0, 2 and ending up on the right exponential function going through point 0, 0 and ending down on the right exponential function going through point 0, 0 and ending up on the right exponential function going through point 0, 1.5 and ending up on the right
Answer:exponential function going through point 0, 0 and ending up on the right
Help i only have a day. 5% of what number is 12? Round your answer to the nearest tenth place if necessary. (Use any method to solve this question, but you must show work)
Answer:
240
Step-by-step explanation:
So here’s the step by step (for the show your work thingy)
so we can write an equation
0.05x=12
We use 0.05 becuase 5 percent is basically 5/100 and the x is used becuase we don’t know what the number is and the =12 is for the number that came out as a final result
ow we can solve the equation
x=12/0/05
x=240
Final answer is 240
URGENT i need the answer for number 23 tyyyy
Answer:
The y-intercept should be -3 since it is 4x-3 so no your friend is not right
Step-by-step explanation:
Hey i am a student of Grade 10 . due to online classes i havent studied for 2 years and i have no idea about maths. what order do i got to recap everything . some one please help! (CBSE)
Answer:
Khan academy could really help it has videos and lessons so start there.
Step-by-step explanation:
hey, can somebody help me please and thank you. :)
The weight of a honeybee is 1.2\cdot10^{-1}\text{ g}1.2⋅10 −1 g1, point, 2, dot, 10, start superscript, minus, 1, end superscript, start text, space, g, end text. The weight of the pollen collected by the bee on one trip is 6.0 \cdot 10^{-2} \text{ g}6.0⋅10 −2 g6, point, 0, dot, 10, start superscript, minus, 2, end superscript, start text, space, g, end text.
Answer:1.8*10^-1
Step-by-step explanation:
Answer: 1.8 x 10^−1
Step-by-step explanation:
What is the value of x in the triangle at the right?
Answer:
x=20
Step-by-step explanation:
To find x use the fact that all triangle's angles sum to 180. This means that if you add all of the angles together, they will always equal 180 degrees. So, create an equation to represent this.
The equation looks like this:2x+65+75=180
Then, combine the like terms2x+140=180
Next, subtract 140 from both sides2x=40
Finally, divide both sides by 2x=20
This means that the missing angle is 40 degrees.
Which of the following is a solution to the inequality y<−4(x+1)2−3?
It takes your equipment 3 minutes to travel 264 feet. what speed is the equipment traveling?
Answer:
To determine the speed, we can use the formula:
speed = distance / time
where distance is measured in feet and time is measured in minutes.
In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:
speed = 264 feet / 3 minutes
simplifying, we get:
speed = 88 feet/minute
Therefore, the equipment is traveling at a speed of 88 feet per minute.
Fast as possible, 100 point
Write an expression for the Product of (x+5)(x-3)
Answer:
I think this could be the answer- x^ +2x-15
Help fast I will do anything
Mercy participates in a bowling league on a team with her friends. The cost of
ordering team shirts can be represented by f(x) = 12.75x + 3.50, where the total
cost is a function of x, the number of shirts ordered Mercy's team must have a
minimum of 6 players and a maximum of 10 players. Which is a reasonable
range for the situation?
a. All real numbers
b. 80 SXS 131
C. {80, 92.75, 105.5, 118.25, 131}
d. y > 80
suppose f is holomorphic in the unit disk. prove that there exists zn in the disk with |zn| → 1 that f(z) is bounded
There exists a sequence of points zn in the unit disk with |zn| → 1 such that f(z) is bounded.
Let's assume the contrary, that f(z) is unbounded in the unit disk. Then, for each positive integer n, there exists a point zn in the unit disk such that |f(zn)| > n. Consider the sequence zn in the unit disk. Since the unit disk is bounded, this sequence must have a limit point z ∈ ¯D (closure of the unit disk).By the maximum modulus principle, f(z) cannot attain its maximum within ¯D unless f is a constant function. But f is holomorphic, so it must have a maximum on the boundary of the unit disk, i.e., |f(zn)| ≤ M for some positive constant M and all n. This contradicts our initial assumption that |f(zn)| > n for all n. Therefore, the assumption that f(z) is unbounded must be false.
Hence, there exists a sequence of points zn in the unit disk with |zn| → 1 such that f(z) is bounded.
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Find 4ab when (a+b)=15 and (a-b)=12
Answer:
81
Step-by-step explanation:
here,
(a+b)=15 -------(1)
(a-b)=12 -------(2)
Equating the equation (1) and (2)
a + b = 15
a - b = 12
(b gets cancelled having opposite signs)
or, 2a = 27
or, a = 27÷2
a = 13.5
then, putting value of a in equation (1)
a+b=15
or, 13.5 + b=15
or, b=15-13.5
b=1.5
lastly,
4ab = 4×13.5×1.5
= 81
hope it helps!!
Ana is going to a craft fair where she'll sell her handmade scarfs. She has six scarf designs, and she's made 15 of each. She's paid $128 for the booth, and each scarf costs $9.80 to make. How much should she charge for each scarf if she wants to break even after selling a third of her scarves?
Answer:
$33.6667
Step-by-step explanation:
Given the following :
Number of Scarf designs = 6
Number of each made = 15
Total scarfs = (15 * 6) = 90
Cost:
Booth = $128
Production cost per scarf = $9.80
Total production cost = $9.80 * 90 = $882
Total cost = $128 + $882 = $1010
Break even = profit - loss = 0
One third of scarves = 1/3 * 90 = 30
This means he must cover for the total cost of $1010 after selling 30 scarves
Hence price per scarf will be :
$1010 / 30
= $33.6667
X + 24 + 4 + 63 = 180
Answer:
x=89
Step-by-step explanation:
180-91=89
Answer:
x = 89
Step-by-step explanation:
x + 24 + 4 + 63 = 180
x + 91 = 180
x = 89
Suppose you know the measures of all three angles of a triangle. Can you use the Law of Sines to find the lengths of the sides? Explain.
Answer:
No
Step-by-step explanation:
Without any side lengths, the most three angles can determine is similarity, not congruency. This means you can determine the ratio of the lengths of the sides, but not any of the sides individually.
Find the distance between the points 10,2 and 5,-10
can anyone help me with this problem with a full explanation?? thank you
Answer:
1, 3, 5
Step-by-step explanation:
let the 3 consecutive odd numbers be n , n + 2 , n + 4 , then
5(n + 2) = 2(n + n + 4) + 3 ( 5 times 2nd = twice sum of 1st and 3rd + 3 )
5n + 10 = 2(2n + 4) + 3
5n + 10 = 4n + 8 + 3
5n + 10 = 4n + 11 ( subtract 4n from both sides )
n + 10 = 11 ( subtract 10 from both sides )
n = 1
n + 2 = 1 + 2 = 3
n + 4 = 1 + 4 = 5
The 3 consecutive odd numbers are 1, 3, 5
Step-by-step explanation:
let the three consecutive odd number be x + 1 , x + 3 , x + 5
a/q
5 times the middle number = 5(x + 3) is
3 more than twice the sum of 1st and 3rd number = 3 + 2(x+1 + x + 5 )
so,
= 5 ( x + 3 ) = 3 + 2 ( x + 1 + x + 5 )
= 5x + 15 = 3 + 4x + 12
= 5x + 15 = 4x + 15
= -4x + 5x = 15 - 15 = 0
= x = 0
so, the 3 consecutive odd numbers are,
x + 1 = 1
x + 3 = 3
x + 5 = 5
and also a/q
5 times the middle number = 5×3 = 15
is equal to 3 more than twice the sum of 1st and 3rd number = 3 + 2(1+5) = 12 + 3 = 15
LHS = RHS
hope this answer helps you dear...take care and may u have a great day ahead!
What is the solution to the system of equations y =- 3x 2 5x 2y 15?
The solution of the given system of equation is (-19, 55).
In the given question we have to find the solution to the system of equations:
y = -3x-2 and 5x + 2y = 15
We can solve the system of equation using the substitution method.
In substitution method we have to put the the value of one variable from one equation to the other equation.
We have to equations:
y = -3x-2...................................(1)
5x + 2y = 15.............................(2)
Now putting the value of y from the equation 1 in equation 2
5x + 2(-3x-2) = 15
Now solving the equation using the distribution method.
5x - 6x - 4 = 15
Simplifying
-x - 4 = 15
Add 4 on both side we get
-x = 19
Now the value of x is -19.
Now putting the value of x in equation 1
y = (-3)*(-19)-2
y = 57-2
y = 55
Hence, the solution of the given system of equation is (-19, 55).
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The right question is:
What is the solution to the system of equations y = -3x-2, 5x+2y=15?
Last year, Mrs. Sclair's annual salary was $88,441. This year she
received a raise and now earns $96,402 annually. She is paid weekly.
a. What was her weekly salary last year?
b. What is Mrs. Sclair's weekly salary this year?
c. On a weekly basis, how much more does Mrs. Sclair earn as a result
of her raise?
Answer:
A. she made $1,694.92 weekly last year
B.she makes $1,847.49 weekly this year
C. she makes $152.57 more weekly this year than ast year.
Step-by-step explanation:
a ) Her weekly salary last year is $1842
b ) Mrs Sinclair's weekly salary this year is $2008.375
c ) On a weekly basis, Mrs Sclair's earn as a result of her raise is $158.37
What is the salary?The amount of money paid by any company to their employees on a weekly or monthly basis is called a salary.
Given that:
Last year, Mrs Sclair's annual salary was $88,441. This year sheReceived a raise and now earn $96,402 annually.a ) Her weekly salary last year is $1842
Annual salary = $88441
Weekly salary = 88441 / 48 = $1842
b ) Mrs Sinclair's weekly salary this year is $2008.375
Annual salary = $ 96,402
Weekly salary = 96,402 / 48 = $2008.137
c ) On a weekly basis, Mrs Sclair's earn as a result of her raise is $158.37
= 2008.137 - 1842
= $158.37
Therefore Her weekly salary last year is $1842, Mrs Sinclair's weekly salary this year is $2008.375, On a weekly basis, Mrs Sclair's earn as a result of her raise is $158.37
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Yo! Please quickly help me solve this! Select the equivalent expression (2^5/x^2)^4
( Would give more points if I had more, but THANK YOU!! )
Answer:
(2⁵/x²)⁴
(32/X²)
32⁴+x⁶
1,048,576 + X⁶
Step-by-step explanation:
i don't know if this is right. this is all I know