Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

A) A above middle C with a frequency of 440 cycles per second is 49 notes up the piano keyboard.

B) frequency of the pitch that is 73 notes up the keyboard is 1760 cycles per second.

A. To find how many notes up the piano keyboard the pitch with a frequency of 440 cycles per second is, solve the formula

n = 1 + 12 × log₂(f/27.5) for n,

where f = frequency of the pitch to find and n = number of notes up the keyboard.

Substituting f = 440:

n = 1 + 12 × log_2(440/27.5)

n = 1 + 12 × log_2(16)

n = 1 + 12 × 4

n = 49

Therefore, the A above middle C with a frequency of 440 cycles per second is 49 notes up the piano keyboard.

B. Using the same formula, n = 1 + 12 × log₂(f/27.5), to find the frequency of the pitch that is 73 notes up the keyboard. Solving for f:

73 = 1 + 12 × log₂(f/27.5)

72 = 12 × log₂(f/27.5)

6 = log₂(f/27.5)

2⁶ = f/27.5

f = 27.5 x 2⁶

Therefore, the frequency of the pitch that is 73 notes up the keyboard is:

f = 27.5 x 2⁶ = 1760 cycles per second.

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The length of the arc are

Arc MN =  72 degrees

Arc NQR = 180 degrees

Arc NQ = 108 degrees

Arc MRP =  193 degrees

Arc QR = 72 degrees

Arc QMR = 288 degrees

Arc PQ = 13 degrees

Arc PRN = 265 degrees

Arc MQN = 288 degrees

The relationship between central angle and intercepted arc is that they are equal. This is used in solving the length of arcs

hence we have that

angle ROQ = angle NOM =  72 degrees (vertical angles)

Arc MN = angle NOM =  72 degrees

Arc NQR = 180 degrees (semicircle)

Arc NQ

angle POQ = 180 - 72 - 95

angle POQ = 13

Arc NQ = 95 + 13 = 108 degrees

Arc MRP = 180 + 13 = 193 degrees

Arc QR = 72 degrees

Arc QMR = 360 - 72 = 288 degrees

Arc PQ = 13 degrees

Arc PRN = 360 - 95 = 265 degrees

Arc MQN = 360 - 72 = 288 degrees

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The future value of 35,000 at 6% semi annually for 12 years is 1,33,700.

Present value = 35000

Rate (r) = 6% = 0.06

Time (n) = 12 years semi annually = 23

Future Value = ?

∴ Future Value = PV(1 + r)ⁿ

Future Value = 35000(1 + 0.06)∧23

                       = 35000(1.06)∧23

                       = 35000(3.820)

Future Value = 1,33,700

Therefore, the future value of 35,000 at 6% semi annually for 12 years is 1,33,700.

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Answer:

Try the desmos graphing calculator:

Step-by-step explanation:

The observed frequency = 42, and the expected is 22.5.

option A.

The observed and expected frequencies for the boys participating in soccer is calculated as follows;

Total boys = 18 + 42 + 12 = 72

Total girls = 30 + 15 + 18 = 63

Total number of the students = 72 + 63 = 135

Ratio of boys = 72/135 = 0.533

Ratio of girls = 63 / 135 = 0.467

The observed and expected frequencies for the boys participating in soccer is calculated as follows;

Expected frequency = 0.534 x 42

= 22.4

Thus, the observed frequency = 42, and the expected is 22.5.

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Answer:

Observed: 42

Expected: 24

Step-by-step explanation:

If we simply go to the chart then we can directly see the observed frequency for boys participating in soccer is 42.

To find the expected frequency, we need to find the number of occurrences if the null hypothesis is true, which in this case, was that the three options are equally likely, or if the three options were all evenly distributed.

First, add up all the options in the boys column:

18 plus 42 plus 12 equals 72

If each of these three options were evenly distributed among the 72 boys, we would need to divide the total evenly between the three options:

72 divided by 3 equals 24

This means we would expect 24 boys to choose tennis, 24 boys to choose soccer, and 24 boys to choose swimming.

Answer:

C. y = 1/3x + 4

Step-by-step explanation:

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

y = mx + b

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

To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line. We can choose the points (x1,y1) = (-3,3) and (x2,y2) = (6,6) from the table.

m = (6 - 3) / (6 - (-3)) = 3/9 = 1/3

Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept:

y - y1 = m(x - x1)

where (x1,y1) is any point on the line. We can choose the point (x1,y1) = (3,5) from the table.

y - 5 = (1/3)(x - 3)

Now we can solve for y to get the equation in slope-intercept form:

y = (1/3)x + (5 - 1/3*3)

y = (1/3)x + 4

Therefore, the equation of the line that passes through the given points is C) y= 1/3x + 4.

Lance needs to jog for an additional 316.08-25.5 = 290.58  minutes to burn 380 Calories.          

The information given in the table to  produce a direct equation that relates the number of Calories burned to the time spent jogging. Let's use the  pitch- intercept form y =  mx b, where y represents the number of Calories burned( in hundreds), x represents the time spent jogging( in  twinkles), m represents the rate of Calories burned( in hundreds per  nanosecond), and b represents the  original Calories burned( in hundreds).  To find m, we can use the points( 10, 13) and( 15, 19), which represent two ordered  dyads on the line. We can find the  pitch of the line using the  pitch formula  

m = ( y2- y1)/( x2- x1)  m = ( 19- 13)/( 15- 10)  

m = 1.2  So the equation for the line is  y = 1.2 x b.

 To find b, we can use the point

( 10, 13)  = 1.2( 10) b  b = 0.7

 So the complete equation for the line is  y = 1.2 x0.7  Now we can use this equation to  break for x, the number of  twinkles Lance needs to jog to burn 380 Calories.  

380 = 1.2 x0.7  = 1.2 x  x = 316.08

So Lance needs to jog for an additional 316.08-25.5 = 290.58  minutes to burn 380 Calories.

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Answer:

20π in.

Step-by-step explanation:

The central angle of minor arc SV is θ = 5π/6 radians, which is 150 degrees. The length of a minor arc is given by the formula s = rθ, where r is the radius of the circle. Substituting r = 24 in. and θ = 5π/6, we get:

s = 24 × 5π/6 = 20π in.

Therefore, the length of minor arc SV is 20π in.

Answer:

she used 8 bags of mulch altogether.

Step-by-step explanation:

if this isn't correct, you may want to reword or specify the question.

Answer:

-7

Step-by-step explanation:

you divide -8 on both sides

the two -8 on your left will cancel each other

and 56 divided by-8=-7

Answer:

P(A or B) = 1 - P(neither A nor B)

= 1 - 18/66 = 48/66 = 8/11

= .727 = 72.7%

For the given function the value of limits are

[tex]\lim _{x\to 0^-}\left(f\left(x\right)\right)[/tex] is 5

[tex]\lim _{x\to 0^+}\left(f\left(x\right)\right)[/tex] is 0

[tex]\lim _{x\to 0}\left x^2+5[/tex]is 5

The given function is f(x)= x²+5, when x≤0

f(x)=2x when x>0

[tex]\lim _{x\to 0^-}\left(f\left(x\right)\right)[/tex]

Which is [tex]\lim _{x\to 0^-}\left x^2+5[/tex]

The given limit is a left hand limit as there is minus in the limits

When we apply x as 0 we get the value 5

Now [tex]\lim _{x\to 0^+}\left(f\left(x\right)\right)[/tex]

So [tex]\lim _{x\to 0^+}\left 2x[/tex]

The given limit is a right hand limit as there is positive in the limits

When we apply x as 0 we get 0

Now [tex]\lim _{x\to 0}\left(f\left(x\right)\right)[/tex]

Which is [tex]\lim _{x\to 0}\left x^2+5[/tex]

We get 5

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The length of side SW is greater than the length of side PW.

Side SW has the shortest length of the three sides.

A triangle is a two-dimensional geometric shape that is defined by three straight sides and three angles. It is the simplest polygon with three sides and three vertices.

We know that the magnitude x is gotten from;

x² - 11x + 146 + 39 - 3x +44 = 180 (Sum of angles in a triangle)

x²- 11x - 3x + 146 + 39  +44 = 180

x²- 14x + 229= 180

x²- 14x = 180 - 229

x²- 14x = -49

Hence;

x²- 14x + 49 = 0

x = 7

Thus;

<P = 7^2 - 11(7) + 146 = 49 - 77 + 146 = 118

<W = 3(7) + 44 = 65

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The y- intercept represents the anticipated number of gloves  vended on a day when the low temperature is 0 degrees.    

The terms you mentioned are  formerly included in the problem description.  The y- intercept of the equation is the value of y when x =  0. In the given line of fit equation,

y = -1.2 x 122, the y- intercept is 122.  The y- intercept represents the anticipated number of gloves  vended on a day when the low temperature is 0 degrees. In this case, when the low temperature is 0,

the store is  prognosticated to  vend 122 gloves. Keep in mind that this is an estimate grounded on the line of fit and may not be an exact value.

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Answer:

66.666%

Step-by-step explanation:

the numbers on the dice would be 1,2,3,4,5,6

1,2,3,5 are all prime numbers.

4/6 =2/3 =66.666%

The inverse of function f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.So, the correct option is D.

To find the inverse of a function, we switch the x and y variables and solve for y. So, if f(x) = -2, we have:
x = -2
y = f(x) = -2
Switching x and y, we get:
x = f¯¹(y)
y = -2
Solving for f¯¹(y), we get:
f¯¹(y) = 2y + 3
Therefore, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
To find the inverse of a function, we need to swap the input (x) and output (f(x)), and then solve for the new input. Given f(x) = -2, let's find the inverse:
1. Swap the input and output: x = -2
2. Solve for the new input: Since the function f(x) is a constant function and doesn't involve x, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
Therefore, Option D is the correct inverse of f(x).

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The predicted weight of a 12-week-old puppy is 25.5 pounds.

To predict the weight of a 12-week-old puppy using the line of fit equation y = 2x + 1.5, follow these steps:
1. Identify the value of x: In this case, x represents the puppy's age in weeks, so x = 12.
2. Plug the value of x into the equation: y = 2(12) + 1.5.
3. Solve the equation: y = 24 + 1.5.
4. Calculate the result: y = 25.5.
So, the predicted weight of a 12-week-old puppy is 25.5 pounds.

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Using the best of fit equation given , the predicted weight of a 12 - weeks old puppy would be 25.5lb

The line of fit is used to establish a mathematical relationship between two variables. A good line of fit would give a good mathematical relationship between related variables.

In the question above; our line of fit equation is y = 2x + 1.5

x = puppy's age ; y = weight

To obtain the value of y for any value of x ; we substitute either of the given value .

For x = 12

y = 2(12 ) + 1.5

y = 24 + 1.5

y = 25.5

Hence, weight of puppy after 12 weeks will be 25.5lbs

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A description that best compare the graph of the functions is: B. the line for function A is steeper.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of function B;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 + 2)/(3 - 0)

Slope (m) B = 1/3.

At data point (0, -1) and a slope of 1/3, function B can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 1 = 1/3(x - 0)

y = 1/3(x) - 1

In conclusion, the line for function A is steeper because it has a greater slope than function B i.e 3 > 1/3.

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Answer:

29658

Step-by-step explanation:

N =  A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

N = 28337 (1 + 0.0153)^3

= 28337 (1.0153)^3

= 29658 to nearest number

Answer:

The domain of a function is the set of all real numbers for which the function is defined. In this case, the function is defined when the denominator is not equal to zero. The denominator is equal to zero when x=1. Therefore, the domain of the function is all real numbers except for x=1.

In interval notation, the domain is written as

(-∞,1) ∪ (1,∞)

Step-by-step explanation:

The probability of flipping heads twice followed by tails three times is 1/32 or approximately 0.031.

Each coin flip is an independent event, meaning the outcome of one flip does not affect the outcome of any other flip. Therefore, the probability of getting heads on any one flip is always 1/2, regardless of previous outcomes.

Using this information, we can calculate the probability of flipping heads twice followed by tails three times as:

P(heads) = 1/2

P(tails) = 1/2

P(heads on first flip) = 1/2

P(heads on second flip) = 1/2

P(tails on third flip) = 1/2

P(tails on fourth flip) = 1/2

P(tails on fifth flip) = 1/2

P(heads twice followed by tails three times)

= P(heads on first flip) x P(heads on second flip) x P(tails on third flip) x P(tails on fourth flip) x P(tails on fifth flip)

= (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

= 1/32

Therefore, the probability of flipping heads twice followed by tails three times is 1/32 or approximately 0.031.

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Answer:  11,000 now = 12,697.52$, The interest earned was 1,697.52$

20,000 now = 23086.41$ the interest earned was 3,086$.

Step-by-step explanation: 11,000(1.049)^3 solve the equation and voila.

Q.#2 20,000(1.049)^3

The point at coordinate 3 represents the weighted average.

Point E measures (-1) and has weight 2x weight of F

point F has a measure of 2 and no particular stated weight

point G measures 6 and has a weight of 3x weight of F

Since we can assign a weight to point F and the other weights will be based on that, let's just keep it simple and give point F a weight of 1.

That gives E a weight of 2, and G a weight of 3.

So, E value times E weight is   (-1)   x   2 = -2

F value times F weight is      2   x   1 =   2

G value times G weight is   6   x   3 = 18

Sum of (value x weight)  =  18

Sum of the weights = 2 + 1 + 3 = 6

we get the weighted average by taking the sum of (value x weight) products (18) and then dividing by the sum of the weights (6).

18/6 = 3, the weighted average

Hence, the point at coordinate 3 represents the weighted average.

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points E,F and G are plotted on a number line at -1, 2 and 6 respectively. Find the coordinate o f the point that represents the weighted average of E, F and G, if point E weighs twice as much as point F and point G weighs three times as much as point F.

a The slope of line £ is 3/4.

b The equation for £ is y = 3/4x + 3.

c The radius of OC is 5.

d The distance from £ to OC along the y-axis is 3.

The slope of a line is the change in y over the change in x. In this case, the change in y is 3 and the change in x is 4. So, the slope of line £ is 3/4.

The equation for a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 3/4 and the y-intercept is 3. So, the equation for £ is y = 3/4x + 3.

The radius of a circle is the distance from the center to any point on the circle. In this case, the center of the circle is at the origin, which is at (0, 0). The point on the circle is at (-4, 3). So, the radius of the circle is the distance from (0, 0) to (-4, 3).

This distance can be found using the Pythagorean theorem:

r² = 4² + 3²

r² = 25

r = 5.

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The surface area of the triangular prism is 84 ft/2

The surface area of a triangular prism is found with: Area = bh + (s1 + s2 + s3)L.

Given a 4ft base, 3ft height, 5ft slant height, and 2ft length, we substitute to get:

Area = (4ft3ft) + 3(5ft*2ft) =

[tex]12ft^2 + 30ft^2 = 42ft^2.[/tex]

In the specified format, the surface area of the triangular prism is 84 ft/2.

This is because the format given is blank ft/2

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Could you provide the formula to calculate the surface area of a triangular prism, given dimensions of 4ft, 3ft, 2ft, and 5ft? The surface area should be presented as (blank ft/2).

The value of area of rectangle is,

⇒ Area = x² + 10x + 21

We have to given that;

Lenght = (x + 7)

Width = (x + 3)

Hence, We can formulate;

The value of area of rectangle is,

⇒ Area = Lenght x width

⇒ Area = (x + 7) (x + 3)

⇒ Area = x² + 7x + 3x + 21

⇒ Area = x² + 10x + 21

Thus, The value of area of rectangle is,

⇒ Area = x² + 10x + 21

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Answer:

Step-by-step explanation:

5(x - 3) ? x + 13

if x = 6

5(6 - 3) ? 6 + 13

15 ? 19

15 ≠ 19

Step-by-step explanation:

When substituting 6 for x, the equation becomes:

5(6 - 3) ?= 6 + 13

Now, we can solve both sides of the equation:

5(3) ?= 6 + 13

15 ?= 19

Since these are not equal, the equation is not true for x = 6.

The answer to all parts is shown below.

1. The diameter of a donut is 3 inches.

so the circumference is πd = 3π ≈ 9.42 inches.

2. 2.5 square feet is equal to 2.5 x 144 = 360 square inches.

3. The minimum length, width, and height of the box are equal to the diameter and height of the donut, which is 3 inches and 1.5 inches, respectively.

Adding 1/2 inch to each dimension gives a length of 4 inches, a width of 4 inches, and a height of 2 inches.

4. The area of the bottom of the new box is length x width

= 4 x 4 = 16 square inches.

The length and width of the new box meet Dave's requirements because they are each greater than or equal to the minimum length and width of 3.5 inches (3 inches + 1/2 inch).

5. The surface area of the new box can be calculated as follows:

Top and bottom: 2 x (length x width) = 2 x (4 x 4) = 32 square inches

Front and back: 2 x (height x length) = 2 x (2 x 4) = 16 square inches

Sides: 2 x (height x width) = 2 x (2 x 4) = 16 square inches

Total surface area = 32 + 16 + 16 = 64 square inches.

6. The surface area of one original box is equal to the sum of the areas of the top, bottom, and four sides.

Each side has dimensions of 3 inches by 1.5 inches,

so the area of each side is 3 x 1.5 = 4.5 square inches.

The area of the top and bottom is 3 x 3 = 9 square inches.

Therefore, the surface area of one original box is:

Top and bottom: 2 x 9 = 18 square inches

Sides: 4 x 4.5 = 18 square inches

Total surface area = 18 + 18 = 36 square inches.

The surface area of the new box is 64 square inches, so the total cardboard needed for one box is:

64 square inches / 144 square inches per square foot = 0.44 square feet

The cost of cardboard for one box is:

0.44 square feet x $0.20 per square foot = $0.088

To find the cost of 35 new boxes, we multiply the cost per box by the number of boxes:

35 boxes x $0.088 per box = $3.08

Therefore, the new box costs less than the original box, which costs $21.00 for 35 boxes.

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Answer:

-----------------------------

To find sin theta, we can use the identity:

We know cos θ, so we can solve for sin θ:

Since tan θ is positive and cos θ is negative, sin θ must be negative as:

Therefore, the answer is:

The inequality for this problem is defined as follows:

y ≤ 2x - 6.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The function in this problem crosses the y-axis at y = -6, hence the intercept b is given as follows:

b = -6.

When x increases by 3, y increases by 6, hence the slope m is given as follows:

m = 6/3

m = 2.

Hence the function is:

y = 2x - 6.

The inequality is composed by the values to the left of the solid line, hence it is given as follows:

y ≤ 2x - 6.

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