Answer:
The options are: A, C and D
Step-by-step explanation:
The sine wave has a general form : y = A sin (BX)
Where A is the amplitude and B = 2π/period
So, we will check which of the options will be a harmonic on a string that is 10 cm long.
A.) y=2sin(pi/5 x)
B = π/5 ⇒ period = 2π/B = 2π ÷ π/5 = 2π * 5/π = 10
So, one cycle of y=2sin(pi/5 x) will be a harmonic on a string that is 10 cm long.
B.) y=2sin(2pi/7 x)
B = 2π/7 ⇒ period = 2π/B = 2π ÷ 2π/7 = 7
C.) y=2sin(pi/10 x)
B = π/10 ⇒ period = 2π/B = 2π ÷ π/10 = 20 = 2 * 10
So, half a cycle of y=2sin(pi/10 x) will be a harmonic on a string that is 10 cm long.
D.) y=2sin(10pi x)
B = 10π ⇒ period = 2π/B = 2π ÷ 10π = 1/5 = 10/50
So, 50 cycles of y=2sin(10pi x) will be a harmonic on a string that is 10 cm long.
E.) y=2sin (5/2pi x)
B = 5/2π ⇒ period = 2π/B = 2π ÷ (5/2π) = 4π²/5
So, options A, C and D can be a harmonic on a string that is 10 cm long.
Answer:
A. y=2sin(pi/5x)
C. y=2sin(pi/10x)
D. y=2sin(10pix)
Step-by-step explanation:
Which expression is equivalent to (x - 2)(x + 4) ?
(x + 1)2 – 9
(x - 1)² – 9
(x + 1)² – 7
(x - 1)² – 7
Answer:
Step-by-step explanation:
hello :
(x + 1)2 – 9 is equivalent to (x - 2)(x + 4)
because (x + 1)2 – 9 =(x + 1)2 – 3²
= (x+1-3)(x+1+3) =(x-2)(x+4)
Answer:
(x + 1)² - 9
Step-by-step explanation:
Expand each of the factors using FOIL
(x - 2)(x + 4)
= x² + 4x - 2x - 8 ← collect like terms
= x² + 2x - 8
Now consider the expansions of
(x + 1)² - 9
= x² + 2x + 1 - 9
= x² + 2x - 8 ← equivalent to (x - 2)(x + 4)
--------------------------------------------------------------
(x - 1)² - 9
= x² - 2x + 1 - 9
= x² - 2x - 8 ← not equivalent to (x - 2)(x + 4)
-----------------------------------------------------------------
(x + 1)² - 7
= x² + 2x + 1 - 7
= x² + 2x - 6 ← not equivalent to (x - 2)(x + 4)
--------------------------------------------------------------------
(x - 1)² - 7
= x² - 2x + 1 - 7
= x² - 2x - 6 ← not equivalent to (x - 2)(x + 4)
Caitlin is at the grocery store, and she’s trying to finthe unit price on a 6-pack of drinks on sale for $2.99.
Her younger brother says that at that
would cost just over $1.00. Is he correct, and how do
you know? If he were incorrect, how would Caitlin’s
brother find the correct price?
Well, first off, any ameteur who read the question once would know he is INCORRECT, this is because you can easily see he's dividing it by 3 not 6 like you should be, so 2.99 divided by 6 is 0.498333 ( continuing ) so since this must be rounded to the nearest hundredth, so, 50 cents per bottle.
So question 1: No, because he divided with the incorrect numbers.
Question 2:( I actually don't understand this question, cause we just established he was wrong ) so since I don't understand this one, imma say no, or meh.
CORRECT unit rate: 50 cents per bottle.
Hope this helps, if not, comment below please!!!!
Pre-image point N(6,-3) was dilated to point N'(2, -1). What was the scale factor used?
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Consider the ratio of the x and y- coordinates, image to original, that is
scale factor = [tex]\frac{2}{6}[/tex] = [tex]\frac{-1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
How much is 1+1x3x6+2x20-100/3x20
Answer:
-41/60
Step-by-step explanation:
Type the whole thing into a calculator.
Answer:
The answer is -41/60
Step-by-step explanation:
19.4mm what the lower bound correct to 1dp
Answer:
The lower bound of 19.4 is 19.35
The table shows the mean monthly temperatures in Alcudia for the last 2 years in degrees Celsius. °C Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Last Year 9 10 11 14 19 22 27 29 21 18 11 6 2 Years Ago 7 11 10 13 17 23 25 25 20 18 12 9. What was the modal temperature last year?
Answer:
The modal temperature last year is 11 (March and November)
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
A year ago Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
9 10 11 14 19 22 27 29 21 18 11 6
2 years ago Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
7 11 10 13 17 23 25 25 20 18 12 9
2. What was the modal temperature last year?
Let's recall the mode of a data set is the number that occurs most frequently in the set. The number that occurs the most in the average temperatures last year is 11 (March and November) and 2 years ago is 25 (July and August)
Round 86 to the nearest 10
Answer:
90
Step-by-step explanation:
"The answer is 90.
To round 86 to the nearest ten, one must look at the digit in the ones place, which is 6 in this case. Since 6 is greater than or equal to 5, the number in the tens place is increased by one. The digit in the tens place is 8, so when it is increased by one, it becomes 9. Therefore, 86 rounded to the nearest ten is 90."
Eighteen less than the quotient of twelve and a number
Eighteen less than the quotient of twelve and a number is written as:
[tex]\frac{12}{x} - 18[/tex]
Solution:
Given statement is:
Eighteen less than the quotient of twelve and a number
We have to translate the given sentence into algebraic expression
Let "x" be the number
Therefore,
Eighteen less than the quotient of twelve and "x"
Quotient means result of division
Therefore,
[tex]\frac{12}{x} - 18[/tex]
Which means, 18 less than quotient of 12 and x
Thus the given sentence is translated into algebraic expression
The phrase 'eighteen less than the quotient of twelve and a number' is mathematically expressed as 12/n - 18, where n represents the unknown number.
The expression 'eighteen less than the quotient of twelve and a number' translates to a mathematical operation. First, we find the quotient of twelve and a number, which is the result of dividing twelve by that number (let's call it n). Then, we subtract eighteen from that quotient. The algebraic representation of this expression is 12/n - 18.
It's important to follow mathematical rules and order of operations correctly when performing such calculations, similarly to how the rules of arithmetic must be applied correctly regardless of the context, as is described in the example of counting goats or students. Mathematics provides various methods to arrive at the correct answer, and in this case, simplifying the operation is straightforward. It is a demonstration of understanding the correct usage of mathematical operations as well as number fluency.
Tell if the slope is positive, negative, zero, or no slope.
Answer:
I think the slope is zero
Answer:
The slope is 0.
Step-by-step explanation:
If the slope line is straight with the x-axis, its 0.
If the slope isnt going straight on x nor y-axis, it had a slope of anything greater or less than 0, but not 0.
720 = N + 315 + 240 what is it
Answer:
Note: N is represented by n instead.
Step-by-step explanation:
[tex]720 = n + 315 + 240[/tex]
Add the numbers
[tex]720 = n + 555[/tex]
Move the variable to the left-hand side and change its sign
[tex] - n + 720 = 555[/tex]
Collect like terms
[tex] - n = 555 - 720[/tex]
Calculate the difference
-N= - 165
N= 165
Hope this helps
Whats the square root of 4?
Answer:
2
Step-by-step explanation:
Answer: 2
Step-by-step explanation: The square root of 4 is 2.
4 is a perfect square which means that a whole number which in this case is 2 can be multiplied by itself to give us 4.
It's also on our perfect square list which I have attached below.
If an asset declines in value from $5,000 to $4,100 over 9 years, what is the mean annual growth rate in the asset’s value over these 9 years? Enter your answer as a percentage. If needed, round your answer to 2 digit decimals.
Answer:
2.4 %
Step-by-step explanation:
annual growth is the changes in the value of asset
STEP 1: annual growth rate
= (current value - old value)/old value
= (4100 - 5000)/ 4100
= -0.2195 // 21.95%
Step 2: Mean of x
mean of x= average of x
= total of x / count of x ( x here is the annual growth rate)
= annual growth rate / no of years
= -0.2195/ 9
= -0.02 // 2.4 %
What percent of the 2019 world population lives in Canada? Round the percentage to three decimal places.
Population in Millions
World: 7,691
Canada: 37.4
0.486 % of world population lives in canada
Solution:
From given,
World population = 7691 million
Canada population = 37.4 million
We have to find the percent of world population lives in canada
Let "x" be the percent of world population lives in canada
Therefore, from question,
x % of world population = canada population
x % of 7691 = 37.4
Solve the above equation for "x"
[tex]x \% \times 7691 = 37.4\\\\\frac{x}{100} \times 7691 = 37.4\\\\7691x = 3740\\\\Divide\ both\ sides\ by\ 7691\\\\x = \frac{3740}{7691}\\\\x = 0.486[/tex]
Thus 0.486 % of world population lives in canada
The length of CD is 12 units C’D’ is the image of CD under a dilation with a scale factor of n.Which of these are true?
Answer: FIrst option, Fourth option and Fifth option.
Step-by-step explanation:
First it is important to know the definition of "Dilation".
A Dilation is defined as a transformation in which the Image (which is the figure obtained after the transformation) and the Pre-Image (this is the original figure, before the transformations) have the same shape, but their sizes are different.
If the length of CD is dilated with a scale factor of "n" and it is centered at the origin, the length C'D' will be:
[tex]C'D'=nCD=(n)(12\ units)[/tex]
Therefore, knowing this, you can determine that:
1. If [tex]n=\frac{3}{2}[/tex] , you get:
[tex]C'D'=(\frac{3}{2})(12\ units)=18\ units[/tex]
2. If [tex]n=4[/tex], then the length of C'D' is:
[tex]C'D'=(4)(12\ units)=48\ units[/tex]
3. If [tex]n=8[/tex], then:
[tex]C'D'=(8)(12\ units)=96\ units[/tex]
4. If [tex]n=2[/tex], then, you get that the lenght of C'D' is:
[tex]C'D'=(2)(12\ units)=24\ units[/tex]
5. If [tex]n=\frac{3}{4}[/tex], the length of C'D' is the following:
[tex]C'D'=(\frac{3}{4})(12\ units)=9\ units[/tex]
The lawn is 30 yd long and 16 yd wide how much shorter is your walk if you walk diagonally
Check the picture below.
1. If I have a car that cost 30,000 and every year it loses value at 20% a year, then what would the value of
the car be after 5 years?
Growth
rate
Answer:
$9,830.40
Step-by-step explanation:
1st year--$30,000.00 x .20=$6,000.00= $30,000.00 - $6,000.00 =$24,000.00
2nd year--$24,000.00 x .20=$4 800.00=$24,000.00 -$4,800.00=$19 200.00
3rd year---$19,200.00 x .20 =$3,840.00= $19,200.00 - $3,840.00 = $15,360.00
4th year---$15,360.00 x .20=$3,072.00=$15,360.00 - $3,072.00=$12,288.00
5th year $12,288.00 x .20=$2,457.60=$12,288.00 - $2,457.60 =$9,830.40
Conditional Probability
Yo sup??
P(A|B)=P(A∩B)/P(B)
P(A∩B)=probability of finding a girl and is sophomore
P(B)=probability of finding a sophomore
P(A|B)=9/10
Hope this helps.
Answer:
Step-by-step explanation:
Total number of persons = 37
Number of girl and sophomore= 9
Prob(girl/sophomore) = 9/37
Explain the error in the work shown. Find the
correct answer.
1/64 = 16^2a 4^-3=(2^4)^2a 4^-3=2^8a -3=8a
-3/8 = a
Answer:
[tex]a = - \frac{3}{4}[/tex]
Step-by-step explanation:
The correct solution of the given equation is as follows :
We have,
[tex]\frac{1}{64} = 16^{2a}[/tex]
⇒ [tex]4^{- 3} = (2^{4} )^{2a}[/tex]
⇒ [tex]2^{(2 \times (-3))} = 2^{8a}[/tex]
⇒ [tex]2^{- 6} = 2^{8a}[/tex]
Comparing the power of equal base, we get
- 6 = 8a
⇒ [tex]a = - \frac{6}{8}[/tex]
⇒ [tex]a = - \frac{3}{4}[/tex]
Therefore, before equating the powers of two terms the base of the terms should be equal and here this is the error. (Answer)
Answer:
The bases were not the same when the exponents were set equal to each other.
16 should have been written as 4 squared.
The exponent on the right should be 4a instead of 8a.
The correct solution is a = -3/4
Step-by-step explanation:
correct on edge
Suppose that 21 inches of wire costs 63 cents. At the same rate, how much (in cents) will 14 inches of wire costs?
See picture for solution and answer.
SOMEONE PLEASE HELP ME PLEASE
Answer
23. 180
24. congruent
25. transversal line
please help me...... I need help
First, let us find out how many miles the hikers travel per day.
They walk at a rate of two mph for eight hours each day which means that they travel 16 miles per day (8x2).
Because the total distance of the great wall is 3948 miles to find out the amount of time needed...
3948/16 = 246.75 days (which is greater than 3 months)
answer: They can't cover the entire distance in three months.
Ise the terms 4, 12a, 6, 2a, and 24 to make equivalent expressions
Answer:
12a + 24 = 6(2a + 4) is the equivalent expressions
Step-by-step explanation:
Given the terms ; 4, 12a, 6, 2a, and 24
There are two terms with unknown = 12a and 2a
but 12a = 2a x 6 .........(1)
from the last term = 24 = 6 x 4 ...........(2)
add both equation 1 and 2 = 12a + 24
12a + 24 = 6(2a + 4) is the equivalent expressions .
to VERIFY; Use a = 2
substitute into the expression ; LHS = RHS
= 12(2) + 24 = 24 + 24 = 48 (LHS)
FOR RHS = 6(2a+4) = 6(2x2 + 4)
= 6(4+4) = 48
Hence LHS = RHS
A rectangular table has a border of same-sized square tiles. The rectangle has 10 tiles along the length and 6 tiles along the width for a total of 28 total tiles. Notice that 10 + 10 + 6 + 6 ≠ 28. If the rectangular table has L tiles along the length and W tiles along the width, which of the following expressions represents the total number of tiles in the border?
l. 2l + 2w
II. 2l + 2w + 4
III. 2l + 2w - 4
IV. 2(1-2) + 2(w-2)+4
A. I only B. II and IV only C. III only D. III and IV only
Answer:
IV. 2(1-2) + 2(w-2)+4
Step-by-step explanation:
III. 2l + 2w - 4
Tell whether the statement is true or false. If A is 45% of B, then the ratio A:B is 9:20.
Answer:
True
Step-by-step explanation:
A ratio is a numerical comparison broken down to its most simplest form. Theoretically, a ratio can be the same as a percentage.
45% is the same as 45/100. It can be simplified by dividing 5 from it to get 9/20...
which is the same as the 9:20 ratio.
Hope this helps!
Hope this
Final answer:
The statement is true; A being 45% of B is the same as the ratio A:B being 9:20, since 45% can be expressed as the fraction 9/20.
Explanation:
The statement that if A is 45% of B, then the ratio A:B is 9:20 is true. To understand this, we consider that 45% can be written as a fraction, which is 45/100 or simplified to 9/20.
Using the definition of percentage as a ratio that compares numbers with a denominator of 100, we can translate 45% into a fraction or ratio. This makes A/B = 9/20. Hence, expressing A as a percentage of B (A is 45% of B) is the same as writing the ratio of A to B as 9 to 20.
A practical example can illustrate this further. If B were $100, then 45% of $100 is $45, meaning A would be $45. Thus, A:B would be $45:$100, which simplifies down to 9:20 when considering their fractional equivalents.
Write 2 numbers that cannot be divided evenly by 8 or 9. Write 1 number that can be divided evenly by both 8 and 9.
Answer:
17 and 26 (cannot be divided evenly by 8 and 9)
72 (LCM for 8 and 9)
Step-by-step explanation:
The value of 2 numbers that cannot be divided evenly by 8 or 9 are 17 and 19.
And, The value of 1 number that can be divided evenly by both 8 and 9 is 72.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The value of 2 numbers that cannot be divided evenly by 8 or 9 are,
⇒ 17 and 19
Cleary. Both number cannot divide by 8 or 9.
And, The value of 1 number that can be divided evenly by both 8 and 9 is,
⇒ LCM of {8, 9}
⇒ 72
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Help ASAP!!! 3/8 of the seventh grade students were taking Advanced math at the beginning of the year, but Seven dropped out by the end of the year. If there were 140 students taking advanced math at the end of the year, how many total seventh grade students are there?
Answer:
There are 392 students in the seventh grade.
Step-by-step explanation:
Let us assume that there are x number of students in the seventh grade.
Now, 3/8 of the seventh grade students were taking Advanced math at the beginning of the year, but seven dropped out by the end of the year.
So, after the end of the year there were [tex](\frac{3}{8}x - 7)[/tex] number of students taking advanced math.
So, as per given condition, [tex](\frac{3}{8}x - 7) = 140[/tex]
⇒ [tex]\frac{3}{8}x = 147[/tex]
⇒ x = 392
Therefore, there are 392 students in the seventh grade. (Answer)
The product of a number m and 6 is no less than 30.
Answer:
x= anything less than 5
Step-by-step explanation:
We know that 5*6 is 30, so x would have to be anything less than five.
Answer:m+6<30
Step-by-step explanation:
I need help on this please
Answer:
B. R/3
Step-by-step explanation:
Marcus and Phillip are in the Robotics Club. They are both saving money to buy materials to build a new robot. They plan to save the same amount of money.
Marcus decides to open a new bank account. He deposits $25 that he won in a robotics competition. He also plans on depositing $15 each week that he earns from
tutoring. Phillip also opens an account. He deposits $40 he has saved from mowing lawns over the summer. He plans to save $10 a week from his allowance. After
how many weeks will they have the same amount of money saved?
3 weeks
4 weeks
5 weeks
6 weeks
Answer:
Step-by-step explanation:
marcus : deposits 25 + 15 each week(w)
25 + 15w
Philip : deposits 40 + 10 each week(w)
40 + 10w
when will they be equal.....set them equal and solve for w, the number of weeks
25 + 15w = 40 + 10w
15w - 10w = 40 - 25
5w = 15
w = 15/5
w = 3 <==== they will be equal at 3 weeks
The number of weeks for both Marcus and Phillip to have the same amount of money saved is 3 weeks
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of weeks be = A
The amount Marcus deposits in the bank account = $25
The amount Marcus deposits each week = $15
So ,
After A weeks , Marcus will deposit = $ 15A
And , Total deposit in the bank for Marcus =
Amount Marcus deposits in the bank account + Amount Marcus deposits for A weeks
Total deposit in the bank for Marcus = 25 + 15A
And ,
The amount Phillip deposits in the bank account = $40
The amount Phillip deposits each week = $10
So ,
After A weeks , Phillip will deposit = $ 10A
And , Total deposit in the bank for Phillip =
Amount Phillip deposits in the bank account + Amount Phillip deposits for A weeks
Total deposit in the bank for Phillip = 40 + 10A
Now , for both Marcus and Phillip to have the same amount after A weeks ,
Total deposit in the bank for Marcus = Total deposit in the bank for Phillip
Substituting the values , we get
25 + 15A = 40 + 10A
Subtracting 10A on both sides , we get
5A + 25 = 40
Subtracting 25 on both sides , we get
5A = 15
Divide by 5 on both sides , we get
A = 3 weeks
Hence , The number of weeks for both Marcus and Phillip to have the same amount of money saved is 3 weeks
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Terry shared an apartment with three other people. Each person paid an equal share of the rent. Together they paid $1495.00 per month. How much did Terry pay per month?
Answer:$493.33
Step-by-step explanation:
$373.75 Terry paid per month.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Terry shared an apartment with three other people. .
The total number of people is 4.
Each person paid an equal share of the rent. Together they paid $1495.00 per month.
We have to find the Terry pay per month.
To find this we have to divide $1495.00/4
$373.75
Hence, $373.75 Terry paid per month.
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