how many eighth notes are in a sixteenth note

Answer:

24

Step-by-step explanation:

Answer:

the remainder is 81

Step-by-step explanation:

so , equate x +3 to 0 , as in x + 3 = 0 then x = -3

so now we know the value of x so just replace it in the expression to get the remainder

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Let's say that F(y) = P(Y <= y), then F(F^-1(x)) = P(F^-1(X) <= F^-1(x)) = P(X <= x), which means F(F^-1(x)) = x, since X is uniformly distributed on [0,1].

In mathematics, a uniformly distributed function is a function whose values are randomly distributed over a defined interval or set, such that any value within the interval or set has equal probability of being selected. A uniform distribution is a type of probability distribution where all values in the range have equal probability of occurring

Therefore, the c.d.f. of Y = F^-1(X) is F.

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By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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Using a line of best fit, the predicted tsunami speed for the following depths is given by:

a. 1151 km/h.

b. 572 km/h.

c. 130 km/h.

d. 122 km/h.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (depth, velocity) are given by:

(7000, 943), (4000, 713), (2000, 504), (200, 159), (50, 79), (10,36)

Inserting these points in the calculator, the velocity in function of the depth is:

v(d) = 0.12879d + 121.03448

Hence, the velocities are given as follows:

a. v(8000) = 0.12879 x 8000 + 121.03448 = 1151 km/h.

b. v(3500) = 0.12879 x 3500 + 121.03448 = 572 km/h.

c. v(70) = 0.12879 x 70 + 121.03448 = 130 km/h.

d. v(5) = 0.12879 x 5 + 121.03448 = 122 km/h.

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Answer:

x = 139

Step-by-step explanation:

Isosceles triangle.

Let the equal angles = y

y + y + 98 = 180   {Sum of all the angles of triangles}

  2y + 98 = 180

          2y = 180 - 98

          2y = 82

           y = 82/2

          y = 41

x = 41 + 98     { exterior angles equals the sum of interior opposite angles}

x = 139

The decibel measurement for the quiet room is 54 dB.

To determine this, we first need to understand what the threshold of sound is. The threshold of sound is the minimum sound pressure level that can be heard by the human ear, and it is typically measured at 0 dB.

Next, we can use the formula for decibel measurement:

dB = 10 log (I/I0)

where I is the intensity of the sound in the quiet room, and I0 is the threshold of sound.

Since the noise in the quiet room is 500 times as intense as the threshold of sound, we can plug in the values into the formula:

dB = 10 log (500/1)

dB = 10 log (500)

dB = 10 * 2.7

dB = 27

Therefore, the decibel measurement for the quiet room is 27 dB. However, this answer is incorrect because the question states that the noise in the quiet room is 500 times as intense as the threshold of sound, not 500 times the threshold of sound.

To correct this mistake, we need to use the formula for decibel measurement with the correct values:

dB = 10 log (500 * I0/I0)

dB = 10 log (500)

dB = 10 * 2.7

dB = 27

Therefore, the decibel measurement for the quiet room is 27 dB + 27 dB = 54 dB.

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Step-by-step explanation:

Because straight lines (that are not the 'same line') can have at most, only one point of intersection...the unique solution.

Answer:

no it not have a unique solution.

Answer:

Answer is 3% more peat and 9% more vermiculite.

Step-by-step explanation:

The weight of the initial potting mixture is not given, but the percentage amounts of peat moss & vermiculite are given.

The weight of the new potting mixture is 100lb.

For the new mixture to have 15% peat and 15% vermiculite,

The amount of peat that must be added is 3% of the peat in the initial mixture.

Hint: subtract 12 from 15. Retain the percentage sign.

The amount of vermiculite that must be added is 9% of the vermiculite in the initial mixture.

Hint: subtract 6 from 15. Retain the percentage sign, as that is the scale of measurement here.

Answer:

Step-by-step explanation:

The scale is

Then

Cross multiplication

Answer:

1:3

Step-by-step explanation:

because you would get 1 of 3 flavours

The required it will take 2 hours for the friends to put 7 km between them.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the number of hours it takes the friends to be "x". During that time, Rae will have traveled 2x km. And Dana will have traveled 3(x-1) km (since she left an hour later).

We can now set up an equation:

2x + 3(x-1) = 7

Expanding the second term:

2x + 3x - 3 = 7

Combining like terms:

5x - 3 = 7

Adding 3 to both sides:

5x = 10

Finally, dividing both sides by 5:

x = 2

So it will take 2 hours for the friends to put 7 km between them.

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The required simplified expression is given as  -12h² + 5g - 4. Option C is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expressions
y = –10g – 4h²  + 15g – 8h²  – 4
y = -4h²  - 8h²  -10g + 15g - 4
y = -12h² +5g -4

Thus, the required simplified expression is given as  -12h² + 5g - 4. Option C is correct.

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One solution to the system of equations is (2, -2). However, there are infinitely many other solutions that satisfy the system of equations.So the correct answer is "Infinite Solutions".

The system of equations by elimination, we need to add the two equations together to eliminate one of the variables. In this case, we can add the first equation and the second equation to eliminate y:

(-4x - 4y) + (4x + 4y) = 0 + 0

Simplifying the left side, we get:0x + 0y = 0

This equation is always true, regardless of the value of x or y. This means that the system of equations has infinitely many solutions, because any values of x and y that satisfy one of the equations will also satisfy the other equation.

To find one solution to the system of equations, we can choose any value of x or y and plug it into one of the equations to solve for the other variable. For example, let's choose x = 2. Then, we can use the first equation to solve for y:

-4x - 4y = 0

-4(2) - 4y = 0

-8 - 4y = 0

-4y = 8

y = -2

Therefore, one solution to the system of equations is (2, -2). However, there are infinitely many other solutions that satisfy the system of equations.So the correct answer is "Infinite Solutions".

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Answer:

\(\dfrac{1}{102}\)

Step-by-step explanation:

Average rate of change of function \(f(x)\) over the interval \(a \leq x \leq b\) is:

\(\dfrac{f(b)-f(a)}{b-a}\)

Given function:

\(f(x)=\dfrac{2x-2}{5x-6}\)

Given interval \(0\leq x\leq 8\) :

when \(x=0\):

\(f(0)=\dfrac{2(0)-2}{5(0)-6}=\dfrac13\)

when \(x=8\):

\(f(8)=\dfrac{2(8)-2}{5(8)-6}=\dfrac{7}{17}\)

Therefore, average rate of change:

\(\dfrac{f(8)-f(0)}{8-0}=\dfrac{\frac{7}{17}-\frac13}{8}=\dfrac{1}{102}\)

Answer:

$200 each.

Step-by-step explanation:

You are sharing the $600 bonus with 2 of your kids, meaning that the money will be evenly divided between 3 people. Divide the total amount of money with the total amount of people:

$600/3 persons = $200/person

Each person obtains $200.

~

Therefore, the total mass of all bags of beads is 19.27 grams

Given masses of three bags of beads as

Mass of beads in bag1 = 10.3 grams

Mass of beads in bag2 = 5.23 grams

Mass of beads in bag3 = 3.74 grams

We have to calculate the total mass of all the beads as below

The total mass of all bags of beads = mass of bag1 + mass of bag2 + mass of bag3

                                                           = 10.3 + 5.23 + 3.74

                                                           = 19.27 grams

Therefore, the total mass of all bags of beads is 19.27 grams

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Answer: x=14 and y=8

*Note: x and y are used as variables to solve the problem. Just know that the sides for one square is 14 and the other, 8.

Step-by-step explanation:

For this problem, we can use system of equations to solve. Let's use x for one side of a square and y for the other.

Equation 1:

x²+y²=260

We get this equation from the sum of the areas. The x² and y² are from the area. Since all sides of a square are equal lengths, we can directly square them.

Equation 2:

4x-4y=24

This equation comes from the difference of the perimeters. 4x and 4y are perimeters because perimeter is adding all sides of the square together. There are 4 sides to a square, therefore we get 4x and 4y.

We can use substitution method to solve.

4x-4y=24                                   [add both sides by 4y]

4x=24+4y                                  [divide both sides by 4]

x=6+y

Now that we have x, we can plug it into any equation and solve.

(6+y)²+y²=260                            [expand]

y²+12y+36+y²=260                    [combine like terms]

2y²+12y+36=260                       [subtract both sides by 36]

2y²+12y=224                              [factor out 2]

2(y²+6y)=224                             [divide both sides by 2]

y²+6y=112                                   [subtract both sides by 112]

y²+6y-112=0                                [factor equation]

(y-8)(y+14)=0                              [set each factor equal to 0 to solve]

y=8 and y=-14

We know that y=8 because (y+14)=0 gives you y=-14, but a length or area can NEVER be negative, only positive.

Now that we have y, we can plug it into any equation to find x.

4x-4(8)=24                                 [combine like terms]

4x-32=24                                   [add both sides by 32]

4x=56                                         [divide both sides by 4]

x=14

Now, we have x and y. x=14 and y=8.

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer:

The minimum exam score to be awarded an A is about 8.52.

Step-by-step explanation:

Let X represent the scores on a common final exam.

It is provided that X follows a normal distribution with mean, μ = 71 and standard deviation, σ = 9.

It is provided that according to the department policy is that the top 10% of students receive an A.

That is, P (X > x) = 0.10.

⇒ P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The corresponding z-score is:

z = 1.28

Compute the value of x as follows:

\(z=\frac{x-\mu}{\sigma}\\\\1.28=\frac{x-71}{9}\\\\x=71+(1.28\times 9)\\\\x=82.52\)

Thus, the minimum exam score to be awarded an A is about 8.52.

Step 1

Collinear points are a set of three or more points that exist on the same straight line. Collinear points may exist on different planes but not on different lines.

Step 2

Graph the points; (-5,2),(0,6),(6,4)

Step 3

Conclude based on step 2

Since the points are not a straight line, we can conclude that the 3 points are not collinear.

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

From the question, we have the following parameters that can be used in our computation:

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

1.3859

Step-by-step explanation:

The formula for Margin of Error is given as:

Margin of Error = Critical value × Standard Error

Critical value = z score

In the question, we are given a confidence interval of 95%.

Z score for a 95% confidence level is given as: 1.96

Hence, critical value = 1.96

Standard Error = σ / √n

Where n = number of samples = 98 chicken eggs

σ = Standard deviation = 7 milligrams

Standard Error = 7/√98

Standard Error = 0.7071067812

Hence, Margin of Error = Critical value × Standard Error

Margin of Error = 1.96 × 0.7071067812

Margin of Error = 1.3859292911

Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859

Answer:

Option 2: A=1, B=3, C=4

Step-by-step explanation:

Answer:

x=2 4/5

Step-by-step explanation:

3x-7=x/2

Multiply each side by 2

2(3x-7)=x

6x-14=x

Add 14 to each side

6x=x+14

Subtract 1x from each side

5x=14

Divide each side by 5

X=14/5 or 2 4/5

Answer:

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means  chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

Step-by-step explanation:

We formulate our null and alternative hypotheses as

H0 u≤ 6 ug     Ha : u > 6 ug

The significance level ∝ = 0.05

The test statistic used is

t = X` - u / s/ √n

which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.

The critical region t > t (0.05,11) = 1.796

We compute the t value from the data

Xi               Xi²

8.92         79.5664

6.99          48.8601

5.54          30.6916

5.73           32.8329

6.38           40.7044

5.51            30.3601

6.45           41.6025

7.50           56.25

8.48           71.9104

5.56          30.9136

6.90          47.61

6.46          41.7316          

80.42         553.0336      

Now x` = ∑x/ n = 80.42/12 = 6.70

S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)

= 1/11 (553.034-538.948) = 1.2805

s= 1.1316

Putting the values in the test statistics

t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12

= 2.1698

The critical region t > t (0.05,11) = 1.796

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means  chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.

To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given points into the formula, we get:

m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2

Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.

y = mx + b

3 = (-1/2)(4) + b

3 = -2 + b

b = 5

Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:

y = -x/2 + 5

So, correct option is A.

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Complete question is:

What is the equation of the line that passes through (4, 3) and (-4, -1)?

Choices:

y = -x/2 + 5

y=2x+7

y=x/2 +1

y= -x/2 +7