The ratio of black and white keys of piano give correct values of A, B, C as 9, 52, 130.
The ratio of black to white keys of Piano of different sizes are as follow,
Black A 36 63 90
White 13 B 91 C
From the table of black and white keys relation of proportionality is equal to,
( A / 13 ) = ( 36 / B ) = ( 63 / 91 ) = ( 90 / C )
This implies ,
( A / 13 ) = ( 63 / 91 )
⇒ A = ( 63 / 91 ) × 13
⇒ A = ( 9 / 13 ) × 13
⇒ A = 9
Similarly,
( 36 / B ) = ( 63 / 91 )
⇒ B = 36 × ( 91 / 63 )
⇒ B = 36 × ( 13 / 9 )
⇒ B = 52
And
( 63 / 91 ) = ( 90 / C )
⇒ C = 90 × ( 91 / 63 )
⇒ B = 90 × ( 13 / 9 )
⇒ B = 130
Therefore, the correct values of A , B, C using the ratio of black and white keys of the piano is equal to 9, 52, 130.
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The above question is incomplete, the complete question is:
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
a solid metal prism has a rectangular base with sides of 4 inches and a height of 6 inches. a hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism.
What is the approximate volume of the remaining solid, in cubic inches?
a. 19 cubic inches b. 77 cubic inches c. 96 cubic inches d. 93 cubic inches
The approximate volume of the remaining solid is option (b) 77 cubic inches
The volume of the rectangular prism is given by
V_rectangular prism = base area x height = 4 x 4 x 6 = 96 cubic inches
The volume of the cylinder is given by
V_cylinder = π x r^2 x h = π x 1^2 x 6 = 6π cubic inches
To find the volume of the remaining solid, we need to subtract the volume of the cylinder from the volume of the rectangular prism
V_remaining solid = V_rectangular prism - V_cylinder = 96 - 6π ≈ 77 cubic inches (rounded to the nearest whole number)
Therefore, the correct option is (b) 77 cubic inches
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cubic feet. The box has a length of
(x + 8) feet, a width of x feet, and a height of (x − 2) feet. Find the dimensions of the box.
Answer:
Step-by-step explanation:
To find the dimensions of the box, we need to solve for the value of x in the expressions given for its length, width, and height.
The volume of a box is given by multiplying its length, width, and height, so we can write:
V = (x+8) * x * (x-2)
Expanding the expression, we get:
V = (x^3 + 6x^2 - 16x)
We know that the volume of the box is measured in cubic feet, so we can assume that V is a positive value. Therefore, we can set V equal to some positive number, such as 1000 or 2000, and solve for x using algebraic techniques such as factoring or the quadratic formula.
For example, if we set V = 1000, we can write:
1000 = x^3 + 6x^2 - 16x
Simplifying and rearranging the terms, we get:
x^3 + 6x^2 - 16x - 1000 = 0
Using a graphing calculator or other mathematical software, we can find that the real solution to this equation is approximately x = 10.5.
Therefore, the dimensions of the box are:
- Length: x+8 = 18.5 feet
- Width: x = 10.5 feet
- Height: x-2 = 8.5 feet
the probability that a randomly selected case will have a score beyond either +1.00 or -1.00 standard deviation of the mean is select one a 6826
b 5000 c 3174 d 1/2 of the area of 1 standard deviation
Correct option is (c) 3174
The probability that a randomly selected case will have a score beyond either +1.00 or -1.00 standard deviation of the mean depends on the type of distribution and the area under the curve beyond these values.
Assuming a normal distribution, approximately 68% of the cases fall within one standard deviation from the mean, and approximately 32% of the cases fall beyond either +1.00 or -1.00 standard deviation of the mean.
To calculate the probability of a randomly selected case falling beyond either +1.00 or -1.00 standard deviation of the mean, we need to calculate the area under the curve beyond these values. Since the distribution is symmetric, we can calculate the area on one side of the mean and multiply it by 2.
Using a standard normal distribution table or calculator, we can find the area under the curve beyond +1.00 standard deviation from the mean as 0.1587 and the area under the curve beyond -1.00 standard deviation from the mean as 0.1587.
Therefore, the total probability of a randomly selected case falling beyond either +1.00 or -1.00 standard deviation of the mean is 0.1587 + 0.1587 = 0.3174, which is approximately 32%.
Hence, the correct option is (c) 3174.
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14
6.66 points
Identify the factors of 9x² + 49y²
(3x + 7y)(3x - 7y)
O prime
(3x-7y)(3x - 7y)
O (3x + 7y)f3x + 7y)
Answer:
Step-by-step explanation:
Hi ,
9x² - 49y² + 3x + 7y
= [ (3x)² - ( 7y )² ] + ( 3x + 7y )
= ( 3x + 7y ) ( 3x - 7y ) + 1( 3x + 7y )
= ( 3x + 7y ) ( 3x - 7y + 1 )
I hope this helps you.
:)
use half angle identity. help
pls
Required value of the given expression is (1+√2)
Given expression is [tex]tan \frac{11\pi}{8} [/tex]
We want to solve it.
Now,
[tex] \tan( \frac{11\pi}{8} ) = \tan( \frac{3\pi}{8} + \frac{8\pi}{8} ) \\ = \tan( \frac{3\pi}{8} + \pi ) \\ = \tan( \frac{3\pi}{8} ) [/tex]
Finding [tex] \tan( \frac{3\pi}{4} ) [/tex]
Let,
[tex] \tan(2t) = \tan( \frac{3\pi}{4} ) = - 1[/tex]
Use half angle identity,
[tex] \tan(2t) = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ - 1 = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ {tan}^{2} t - 2tant - 1 = 0[/tex]
Let,[tex]x = tant[/tex]
So,[tex] {x}^{2} - 2x - 1 = 0[/tex]
Now, [tex]x = 1 \pm \sqrt{2} [/tex]
So,
[tex]tant = tan \frac{3\pi}{8} = 1 \pm \sqrt{2} [/tex]
[tex]tan \frac{3\pi}{8} [/tex] is positive,then required value is 1+√2.
So, option D is the correct answer.
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a line that passes through (3,5) and (4,13)
Answer:
y = 8x-19
Step-by-step explanation:
The first step is to find the slope.
m= ( y2-y1)/(x2-x1)
= ( 13-5)/(4-3)
= 8/1
= 8
Then we can use the slope intercept formula.
y = mx+b
y = 8x+b
Substitute a point to find the intercept.
5 = 8*3+b
5 = 24+b
-19 = b
The formula is
y = 8x-19
Answer:
y = 8x - 19
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 5 ) and (x₂, y₂ ) = (4, 13 )
m = [tex]\frac{13-5}{4-3}[/tex] = [tex]\frac{8}{1}[/tex] = 8 , then
y = 8x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 5 )
5 = 8(3) + c = 24 + c ( subtract 24 from both sides )
- 19 = c
y = 8x - 19 ← equation of line
Grace wants to buy carpet to cover her whole living room, except for the tiled floor. The tiled
floor is 6ft by 3-ft. Find the area the carpet needs to cover.
Therefore, the area that the carpet needs to cover is: LW - 18 square feet.
What is area?Area is a mathematical term that refers to the amount of space occupied by a two-dimensional object or shape. It is typically measured in square units such as square feet, square meters, or square inches.
Here,
If the tiled floor is excluded from the area that needs to be covered by the carpet, then we need to find the area of the living room without the tiled floor and add the tiled floor's area to it.
Let's assume that the living room is a rectangular shape with length L and width W.
The area of the living room without the tiled floor is:
Area = L x W - (6 x 3) (since the tiled floor has an area of 6 ft x 3 ft)
Area = LW - 18 square feet
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use laplace transforms to solve the initial value problem where primes indicate derivatives with respect to t.
To use Laplace transforms to solve the initial value problem where primes indicate derivatives with respect to t, follow these steps.
Write down the given differential equation and initial conditions. Apply the Laplace transform to both sides of the differential equation, using the properties of Laplace transforms for derivatives. Substitute the initial conditions into the transformed equation to get a new equation with no derivatives.Solve this new equation for the Laplace transform of the desired solution function. Apply the inverse Laplace transform to find the solution function in the time domain.Remember to be accurate and concise while solving the problem.
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John and his family are going on vacation. They travel 137.5 miles in 2.5 hours. What is the average miles per hour that they travel?
The average miles per hour that John and his family travel is 55 mph.
What is the average annual mileage?American drivers now log a total of 14,263 miles in a single year on average. Around 1,200 miles are driven per month on average, according to this information.
We must divide the whole distance travelled by the total time taken by John and his family in order to determine their average miles per hour:
Total distance x Total time equals average speed.
In this instance, their total journey distance was 137.5 miles, and their total travel duration was 2.5 hours. Hence, we can enter the following values into the formula:
Average speed = 137.5 miles / 2.5 hours
137.5 divided by 2.5 results in:
Average speed is 55 miles per hour.
John and his family therefore travel at an average speed of 55 mph.
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if y varies directly as x, and y=7 when x=3, find when x=7
By definition, direct variation takes the following form:
y=kx
Where k is the proportionality constant.
You can find k given the information in the problem:
7=3k
k=3/7
You can now find y when x=7 as follows:
y=(7*3)
Values can be substituted. Then:
y=(7*7)/3
y=49/3
If y varies directly from x, then the value of y = 49/3 when x = 7.
If y varies directly from x, we can write its relationship in the form of the equation below :
y = m*x
Where m is the slope of the line on the graph.
From the given data:
y=7
x=3,
We can substitute these values in the above equation and find m :
7 = m*3
m = 7/3
So, the equation can also be written as follow:
y = 7/3 x
Finding y when x=7, then substituting the x value in the above equation we get:
y = (7/3)*(7)
y = 49/3
Therefore the value of the y = 49/3.
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To make balloon animals at birthday parties, Ani charges $3 for each balloon animal plus $8 to cover travel costs. If she made $53 at a party, how many balloon animals did she make?
Without the travelling cost being $8, Ani made a total of $45 and she made 15 animal balloons.
We know that the total cost Ani charges for travelling is $53
and the total amount Ani made at the party = $53
therefore, first to find the number of balloons she made we need to subtract the travelling cost from the total amount she made:
= 53 - 8 = 45
therefore, now we know that Ani made a total amount $45 from balloons alone:
also, we know that each balloon costs $3 each therefore we need to divide $45 by 3, we get 15,
hence, we can say that Ani made a total of 15 animal balloons for the party.
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daisy has the following production possibilities frontier per week. her resource is 5 lbs of flour. note: you will use this ppf to answer the next several questions. given daisy's ppf, the following production combo, 9 pies and 8 tarts is
The following question is incomplete.
Please complete the question so it can be answered.
Without the actual Production possibility frontier table or chart we cannot determine the exact quantities.
However, based on the information provided, we can determine that the production combo of 9 pies and 8 tarts is a point on Daisy's PPF.
This means that Daisy can produce 9 pies and 8 tarts per week using her available resources of 5 lbs of flour.
To fully analyze production possibilities of Daisy, we would need to see her complete PPF, which would show all possible combinations of pies and tarts that she could produce with her resources.
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Valerie is a member of a movie club. She pays a fixed fee of $40 annually. She must pay $6 for every movie she rents. She rented 14 movies this year. What is the total amount that she paid this year
Valerie paid a total amount of $124 this year for her movie club membership and the 14 movies she rented.
What is total amount?In math, the total amount typically refers to the final sum or result of a calculation involving multiple numbers or quantities.
Valerie pays a fixed fee of $40 annually, and she rented 14 movies at a cost of $6 each. Thus, the total amount she paid this year can be calculated as follows:
Total cost of movie rentals = 14 x $6 = $84
Adding the fixed annual fee to the rental costs:
Total amount paid by Valerie this year = $40 + $84 = $124
Therefore, Valerie paid a total of $124 this year for her movie club membership and the 14 movies she rented.
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ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
? Round to the nearest hundredth. Enter your answer in the box.
Answer:9.22
Step-by-step explanation:
You dont need the left side of this triangle to figure out the answer. You can use the fact that the remaining side to find is of a right triangle and use pythagorean theorem to solve.
Since 11 is the hypotenuse, and the pythagorean theorem states that a^2 +b^2 = c^2, the hypotenuse being c, you can reverse the equation like this:
11^2-6^2=rt^2
if you plug this in, you get that rt is exactly equal to 9.21954445729
Since you asked for it rounded to the nearest hundredth, you can round it to 9.22
factor the expression 6x^3 + 5x
Answer:
x(6x^2 + 5)
Step-by-step explanation:
To factor the expression 6x^3 + 5x, we can first factor out the greatest common factor of the two terms, which is x. This gives:
x(6x^2 + 5)
We can see that 6x^2 + 5 cannot be factored any further using integer coefficients, so the final factored form of the expression is:
x(6x^2 + 5)
a random telephone survey of 1,051 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. the survey results showed that 664 of those surveyed planned to file their taxes electronically. (round your answers to the nearest whole number.)
The percentage of adults who planned to file their taxes electronically is approximately 63%.
A random telephone survey of 1,051 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. The survey results showed that 664 of those surveyed planned to file their taxes electronically.
Total number of adults surveyed = 1,051
Number of adults who planned to file their taxes electronically = 664
Percentage of adults who planned to file their taxes electronically is;
= (Number of adults who planned to file their taxes electronically / Total number of adults surveyed) x 100%
=(664/1051) x 100%
= 63.16 %
Therefore, the percentage of adults who planned to file their taxes electronically is approximately 63%.
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The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. Is the relation a function? Explain. Yes, because for each input there is exactly one output Yes, because for each output there is exactly one input No, because for each input there is not exactly one output No, because for each output there is not exactly one input
Answer:No
Step-by-step explanation:
Because each X is an input, this means that Y is obviously the output.
In order for a set of data, there must ALWAYS be one output for every input, no more, no less. Because this particular set of data has multiple Y values with respect to different X values, this is not a function. Your correct answer is "No, because for each input there is not exactly one output."
A miniature golf course recently provided a number of customers with golf balls, including 2 red golf balls and 6 other golf balls. Based on experimental probability, how many of the next 12 golf balls handed out should you expect to be red golf balls?
Answer:
1.5 or about 1 or 2 maybe
hope this helpd
Consider the expression (x2−9)(x+4). Select all the values of x for which (x2−9)(x+4)=0
Answer:
X= 567890
Step-by-step explanation:
Answer:
See below, please.
Step-by-step explanation:
Using the zero product property, we can set each factor equal to zero and solve for x:
(x² - 9)(x + 4) = 0
(x² - 9) = 0 or (x + 4) = 0
For the first factor, we can factor it further as the difference of squares:
(x + 3)(x - 3) = 0
So, either (x + 3) = 0 or (x - 3) = 0, giving us:
x = -3, x = 3, or x = -4
Therefore, the values of x for which (x² - 9)(x + 4) = 0 are -3, 3, and -4.
(8x - 12) = (3x + 5)
Answer:
x = [tex]\frac{17}{5}[/tex]
Step-by-step explanation:
(8x - 12) = (3x + 5) ← remove parenthesis
8x - 12 = 3x + 5 ( subtract 3x from both sides )
5x - 12 = 5 ( add 12 to both sides )
5x = 17 ( divide both sides by 5 )
x = [tex]\frac{17}{5}[/tex]
or x = 3.4 ( in decimal form )
Please answer my question by the way the number 4 and 5 is FOIL.
Using FOIL method for the multiplication, we have:
1: 3x (5x - 4) = 15x² - 12x
2: x²(5x² + 3y + 1) = 5x⁴ + 3x²y + x²
3: (4x + 3)(4x -5) = 16x² - 8x - 15
4: (7x - 3)(4x - 5) = 28x² - 47x + 15
How to carry out multiplication using FOIL?
FOIL is an acronym that stands for "First, Outer, Inner, Last". It is a mnemonic device that is commonly used to remember the process of multiplying two binomials.
No. 1
3x (5x - 4) = 3x*5x + 3x*(-4)
= 15x² - 12x
No. 2
x²(5x² + 3y + 1) = x²*5x² + x²*3y + x²*1
= 5x⁴ + 3x²y + x²
No. 3
(4x + 3)(4x -5) = 4x(4x-5) + 3(4x-5)
= 4x*4x + 4x*(-5) + 3*4x + 3*(-5)
= 16x² - 20x + 12x - 15
= 16x² - 8x - 15
No. 4
(7x - 3)(4x - 5) = 7x(4x - 5) - 3(4x - 5)
= 7x*4x + 7x*(-5) - 3*4x - 3*(-5)
= 28x² - 35x -12x + 15
= 28x² - 47x + 15
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Polygon B is a scaled copy of Polygon A using scale factor of 5. How many time as lagre is the area of Polygon B compared to the area of Polygon A?
please help!! this stuff is very confusing to me!
the combined area of the garden and the walkway when the width of the walkway is 4 feet is LW + 8L + 8W + 64 square feet.
why it is?
Let's assume that the length of the rectangular garden is L and the width is W. Let the width of the walkway be x.
a. The area of the rectangular garden is L x W. The combined area of the garden and the walkway is the area of the larger rectangle formed by the outer boundary of the walkway. The length of this larger rectangle is (L + 2x) and the width is (W + 2x). Therefore, the polynomial that represents the combined area of the garden and the walkway is:
(L + 2x)(W + 2x)
Expanding this expression, we get:
LW + 2Lx + 2Wx + 4x²2
So, the polynomial that represents the combined area of the garden and the walkway is LW + 2Lx + 2Wx + 4x²2.
b. If the width of the walkway is 4 feet, then x = 4. Substituting this value in the polynomial we obtained in part (a), we get:
LW + 2L(4) + 2W(4) + 4(4)²2
Simplifying this expression, we get:
LW + 8L + 8W + 64
Therefore, the combined area of the garden and the walkway when the width of the walkway is 4 feet is LW + 8L + 8W + 64 square feet.
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Kelly is flying a kite to which the angle of elevation is 70 degrees. The string on the kite is 65 meters long. How far is the kite above the ground?
If Kelly is flying a kite to which the angle of elevation is 70 degrees. The string on the kite is 65 meters long. The kite is about 61 meters above the ground.
How to find the height?We can use trigonometry to solve the problem. Let's call the height of the kite above the ground "h".
Using trigonometry, we can write:
sin (70) = h / 65
Solving for h, we get:
h = 65 * sin(70)
h= 65 * 0.9397
h ≈ 61 meters
Therefore, the kite is about 61 meters above the ground.
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a 35 foot ladder leans against the top of a building. the ladder's base is 9.7 feet from the building. find the angle of elevation between the ladder and the ground.
As a result, there is a about 74.53 degree elevation difference between the ladder and the ground.
what is angle ?A geometric shape known as an angle is created when two rays or line segments come together at a location known as the vertex. The sides of the angle are the rays or line segments. Angles are used to define the amount of rotation or inclination between two lines or planes and are commonly measured in degrees or radians. The most popular unit of measurement for angles is the degree, which is derived from the 360 equal divisions of a circle. Angles are measured in degrees using a protractor, and each component is referred to as a degree.
given
We may resolve this issue using trigonometric functions. The elevation angle between the ladder and the ground will be denoted by the symbol. Next, we have
opposite/hypotenuse of sin()
adjacent/hypotenuse = cos()
The building's height in this instance serves as the opposing side, and the length of the ladder serves as the hypotenuse. We thus have:
height/35 cos() = 9.7/35 sin()
By rearranging the first equation, we can find the height:
height equals 35*sin()
The second equation can then be changed to include the following expression:
cos(θ) = 9.7/35
cos(θ) = 0.2771
By taking the inverse cosine of both sides, we can now solve for :
θ = cos^(-1)(0.2771) (0.2771)
7.453 degrees
As a result, there is a about 74.53 degree elevation difference between the ladder and the ground.
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By the 46th day, there are 400 water lilies in the pond. the estimate you made:____.a. close to 46 (or exactly right) because it was estimated well.b. too low because the quick exponential growth was not accounted for. c. too high because the exponential growth was overestimated.
By the 46th day, there are 400 water lilies in the pond. the estimate you made: a). close to 46 (or exactly right) because it was estimated well.
We know that the regression equation is: y = 3.915(1.106)ˣ and that the pond can hold 400 water lilies.
y = 3.915(1.106)ˣ
Here, y is equal to the number of water lilies the pond can hold.
So, y = 400
And, x is the required time taken.
So,
400 = 3.915(1.106)ˣ
⇒ (1.106)ˣ = 400/3.915
⇒ (1.106)ˣ = 102.17
Taking logarithm on both sides, we get
log (1.106)ˣ = log (102.17)
⇒ x log (1.106) = log (102.17) .............. [log aˣ = x loga]
⇒ x = [log (102.17)/log (1.106)]
⇒ x = 45.92
x ≅ 46
So, the pond will take 46 days to become full.
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Complete question:
Regression equation: y = 3.915(1.106)ˣ . The pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day.
Answer:
b
Step-by-step explanation:
just did it
No idea how to use this app tbh
Answer:
-10
Step-by-step explanation:
I added a photo of my solution
Answer:
Answer is -10
Step-by-step explanation:
Given f (x) = x2 + 10x + 28 in standard form, convert to vertex form using completing the square. Show work to receive credit. (20 points)
Answer:
f(x) = (x + 5)² + 3
Step-by-step explanation:
f(x) = x² + 10x + 28
to complete the square
add/subtract ( half the coefficient of the x- term )² to x² + 10x
f(x) = x² + 2(5)x + 25 - 25 + 28
= (x + 5)² + 3 ← in vertex form
is tderiv one-to-one? explain the significance of this result in terms of the derivative on polynomials.
The total derivative of a function is not necessarily one-to-one. The total derivative represents the change in a function with respect to all of its input variables.
If a function has multiple input variables, the total derivative is a matrix, called the Jacobian matrix, whose entries represent the partial derivatives of the function with respect to each input variable.
A function with a non-invertible Jacobian matrix is not one-to-one, since multiple input values can result in the same output value. For example, consider the function f(x,y) = (x^2, y^2). The total derivative of f is given by the Jacobian matrix:
| 2x 0 |
| 0 2y|
This matrix is non-invertible when x=0 or y=0, since it has a determinant of zero. Thus, the function f is not one-to-one when x=0 or y=0.
In terms of polynomials, the total derivative is important for determining whether a polynomial has multiple roots. A root of a polynomial is a value of the input variable that causes the polynomial to equal zero. If a polynomial has multiple roots, it is not one-to-one, since different input values can result in the same output value.
The total derivative of a polynomial can be computed using the power rule of differentiation. For example, consider the polynomial p(x) = x^3 - 6x^2 + 11x - 6. The total derivative of p with respect to x is:
p'(x) = 3x^2 - 12x + 11
If p'(x) has multiple roots, then p(x) has multiple roots as well. In this case, p'(x) has roots at x=1 and x=11/3, so p(x) has multiple roots at x=1 and x=3. Thus, the total derivative is useful for identifying when a polynomial is not one-to-one.
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Is total derivative is one-to-one? explain the significance of this result in terms of the derivative on polynomials.
help please i’ll give brainliest!!!
Answer:
Apparently it's 4800 according to desmos.
Step-by-step explanation:
Step-by-step explanation:
x y
-3 150
-2 300
-1 600
0 4800
As you can see, for negative values of x, the area burned becomes smaller and smaller as x becomes more negative. This is because the equation y = 4800(2)^x has a base of 2, which means that as x becomes more negative, 2^x becomes smaller and smaller, causing y to become smaller and smaller as well.