What is the amplitude, period, and phase shift of f(x) = −3 cos(4x + π) + 6?

A. Amplitude = 3; period = pi over two; phase shift: x = negative pi over four
B. Amplitude = −3; period = pi over two; phase shift: x = pi over four
C. Amplitude = −3; period = negative pi over two; phase shift: x = negative pi over four
D. Amplitude = 3; period = 2π; phase shift: x = negative pi over four

Answer:

272 cm²

Step-by-step explanation:

Step 1

We have to find the scale factor

When given the volume of two solids, the formula for the scale factor is

V1/V2 = (Scale factor)³

The volume of Pyramid A is 704 cm³ and the volume of Pyramid B is 297 cm³

V1 = Pyramid A

V2 = Pyramid B

704/297 = (scale factor)³

We simplify the left hand side to simplest fraction

The greatest common factor of 704 and 297 = 11

704÷11/297÷11 = (scale factor)³

64/27 = (scale factor)³

We cube root both sides

cube root(scale factor)³ = cube root (64/27)

scale factor = (4/3)

Step 2

(Scale factor)² = S1/S2

S1 = Surface area of Pyramid A =?

S2 = Surface area of Pyramid B = 153 cm²

Hence,

(4/3)² = S1/153

16/9 = S1/153

Cross Multiply

S1 × 9 = 16 × 153

S1 = 16 × 153/9

S1 = 272 cm²

Therefore, the Surface Area of Pyramid A = 272 cm²

Answer:

Try A.

Step-by-step explanation:

I just took the test and it says that A is the answer.

The graph given is of exponential function f(x) = 3·(1.7)ˣ

An exponential function is a mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Given is graph, we need to determine its exponential function,

Since, the given graph is of increasing nature.

Therefore, the base of the exponential will be greater than 1.

Also, at x=0 the value of y=3

At x=0, y=3 for option 3 which satisfies the graph.

f(x) = 3·(1.7)ˣ

Hence, the graph given is of exponential function f(x) = 3·(1.7)ˣ

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Answer: 700

Step-by-step explanation:

Answer:

700

Step-by-step explanation:

copy and paste

Answer:

Variables : C , S

Equations : C + S = 11

                  3C + 4S = 35

Step-by-step explanation:

Chocolate cookies be = C

Sugar Cookies be = S

Total number of cookies : C + S = 11

Total Spent on the cookies : 3C + 4S = 35

[tex]C + S = 11\\C = 11 - S\\3C + 4S = 35\\3(11 - S ) + 4S = 35\\33 -3S +4S = 35\\-3S + 4S = 35 - 33\\S = 2\\\\C + S = 11\\C + 2 = 11\\C = 9[/tex]

[tex]60\% = 180\\1\%=\frac{180}{60} = 3[/tex]

[tex]100\% - 60\% = 40\%\\40\% = 3*40=120[/tex]

Answer: 120 cans.

Answer:

C. 0.6ft

Step-by-step explanation:

Given data

Volume of sphere= 1 cubic foot

DIameter= ????

The expression for the volume of a sphere is given as

Volume= 4/3πr^3

Substitute

1= 4/3*3.142*r^3

1= 4.189r^3

r^3= 1/4.189

r^3= 0.2387

Cube root both side

r= ∛0.2387

r= 0.62

r=0.6ft approx

Answer:

[tex]cos32° = \frac{x}{23} [/tex]

cos32°=Adjacent / hypotenuse

Answer:

x

Step-by-step explanation:

cos32° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{23}[/tex]

Answer:

8 pizzas

Step-by-step explanation:

every 4 students ate a pizza

so 32/4 = 8

Answer:

8 Whole pizza's.

Step-by-step explanation:

32/x=1/4

x= 32/4

x=8

Answer:

Simple random sampling is the most straightforward approach to getting a random sample. It involves picking the desired sample size and selecting observations from a population in such a way that each observation has an equal chance of selection until the desired sample size is achieved.

[tex] 7.9 \\ 11.94 \\ 12.58 \\ - - - - - \\ 32.04[/tex]

u gotta add them since they asked about their cost in all

Answer:

Perpindicular is when two lines cross to form a 90 degree angle

Step-by-step explanation:

Answer:

566

Step-by-step explanation:

785-219=566

Answer:

Step-by-step explanation:

Brooks Middle School ordered 7 1/2 pizzas on Monday for lunch. The teachers ate 1/3 of the pizzas for lunch. How many pizzas did the staff eat on Monday?

This is calculated as: 1/3 of 7 1/2

= 1/3 × 7 1/2 pizzas

Write a number sentence to support your answer

Answer:

35

Step-by-step explanation:

B

Answer:

to fine the volume of a cone, you do [tex]\pi r^2*h/3[/tex], r is 3 and h is 4, so [tex]9\pi *4/3[/tex], the cylinder formula is [tex]\pi r^2*h[/tex], r=3 and h=12, so [tex]9\pi *12[/tex], so 12[tex]\pi[/tex]+108[tex]\pi[/tex], this gives a answer of 120[tex]\pi[/tex] or 376.991118431.... GL :)

Step-by-step explanation:

Answer:

Alternate Exterior Angles

Step-by-step explanation:

Alternate exterior angles are two angles on the opposite outer sides of two parallel lines cut by a transversal.  

The two angles given, 2 and 7, are alternate exterior angles.

Hope it helps! :)

Answer:

6.4

Step-by-step explanation:

5^2 + 4^2 = c^2 (pythagoras)

c^2 = 41

c = 6.4

Answer:

Step-by-step explanation:

6^7/6^3

=6^7-3

=6^4

The truncation error for S4 is 4.6875

Truncation error is defined as the difference between the true (analytical) derivative of a function and its derivative obtained by numerical approximation.

In the given Truncation error formula put n= 4

On substitution n value from 1 to 4

5/16 +5/8 + 5/4 + 5/2 = 4.6875

Thus the truncation error for S4 is 4.6875.

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Answer:

A

Step-by-step explanation:

edg 2023

We have the given equation:

9e - 7 = 7e - 11

Our goal is to isolate the variable, e.

9e - 7 = 7e - 11

     +7          +7

____________

9e = 7e - 4

-7e  -7e

____________

2e = -4

/2     /2

____________

e = -2

Answer:

A) 45

Step-by-step explanation:

P(green) = 6/20

6/20 = x/150

20x = 900

x = 45

Answer:

The coordinates of H’ is (-1,-6)

Step-by-step explanation:

Here, we want go get clockwise rotation about the origin

mathematically, if we had this kind of rotation, it would be that

(x,y) will turn to (y,-x)

So we have it that (6,-1 becomes)

(-1,-6)

Answer:

[tex]\frac{5}{1}[/tex] or 5

Step-by-step explanation:

Using the data provided we would create the following equation to calculate Grace's bank account using the variable x to represent the number of weeks.

f(x) = 5x + 15

The slope of a function in such a function would be the value of that is being multiplied by x. The numerator would be the numberof units it is rising in a graph while the denominator represents the number of units it is moving to the right. Since in this scenario, the number is a whole number (5) the denominator is automatically 1. Meaning that the slope is 5 units up for every 1 unit to the right.

The z-score of the value P ( x < 92 ) is given by z = -1 with standard deviation of 6 is P ( x < 92 ) = 0.16

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the distribution be a normal distribution where

The mean of the data is μ = 98

The standard deviation is σ = 6

Now , the Z-score is determined by z = (x - μ)/σ

On simplifying , we get

when x = 92

P ( x < 92 ) is

z = ( 92 - 96 ) / 6

z = -1

So , the p value of P ( x < 92 ) is 0.1587

On rounding to the nearest value , we get

P ( x < 92 ) = 0.16

Hence , the z-score is solved

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Answer:

V = 1250π/3 mm³

V = 1309 mm³

Step-by-step explanation:

The composite figure is made up of a cylinder with radius 5 mm and two hemispheres of radius 5 mm. The height of the cylinder is

20 mm - 5 mm - 5 mm = 10 mm

The two hemispheres make up a full sphere of radius 5 mm.

V = πr²h + (4/3)πr³

V = π(5 mm)²(10 mm) + (4/3)π(5 mm)³

V = [(25 mm²)(10 mm) + (4/3)(125 mm)³]π

V = [250 mm³ + 500/3 mm³]π

V = 1250π/3 mm³

V = 1309 mm³

Answer: They would be A.

Step-by-step explanation: Don't take my word for it 100%

The missing frequencies for G# and D# in the given equal temperament octave is 311.1 and 415.3 respectively. The ratios of frequencies between G# and D# is 1.33.

The equal tempered scale is the common musical scale used at present, used for the tuning of pianos and other instruments of relatively fixed scale. It divides the octave into 12 equal semitones. The ratio between successive notes is constant and it is 1.0595.

With reference to the image attached in the question,

Since we know that ratio between successive notes is 1.0595.

This implies,

[tex]\frac{C\#}{C} = \frac{277.2}{261.6} = 1.0595\\\\[/tex]

Or we can say that, C# = 1.0595C

Similarly,

D# = 1.0595D = 1.0595 * 293.6 = 311.1

G# = 1.0595G = 1.0595 * 392 = 415.3

The ratios of frequencies between G# and D# = [tex]\frac{G\#}{D\#} = \frac{415.3}{311.1} = 1.33 = \frac{4}{3}[/tex]

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