Tammy is testing the cellphone service in a certain area for a cellphone company. The signal during the test can be modeled by sin t+3 where t is the time in seconds. Focusing on the domain 0 < t < 3 π/2, at what time is the signal the strongest?

Answer:

-15y^6z^{10}+35y^4z^6

Step-by-step explanation:

used an equation calculator

Rational exponents are quite simple really.  For instance, 2 to the power of 1/2 is the square root of two.  You take the numerator of the fraction and use that as the exponent and take the denominator and use it to root the number.  I know that sounds confusing, so I'll give a bunch of examples

2 to the power of 1/3

is the cube root of 2

2 to the power of 2/3

is the cube root of 2 to the power of 2, or the cube root of 4

2 to the power of 3/4

Is the 4th root of 2 to the power of 3, or the fourth root of 8

Hope it helps <3, if you have any questions just comment.

The required answer for the number of questions has been listed in the answer section.

Given that,
A number of questions are given

The function which is in format f(x) = a^x   where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).  

Part A
What operation does the power 1/2 represent?
The power 1/2 represents the square root of the value i.e. x^{1/2} = √x

Part B
What operations that other fractional powers represent, such as 1/3, 1/4, and 2/3?
Power 1/3 represents the cube root i.e. x^{1/3} = ∛x
Similarly
Power 1 / 4 represents the fourth root.
Power 2 / 3 represents cube root of square i.e. (x²)^{2 / 3} = ∛x²

Thus, the solution to the question is mentioned above.

Learn more about exponential function here:

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Answer:

3

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (2, - 4) , thus

y = a(x - 2)² - 4

To find a substitute (3, - 1 ) into the equation

- 1 = a(3 - 2)² - 4 ( add 4 to both sides )

3 = a

Thus

y = 3(x - 2)2 - 4 ← equation in vertex form

   = 3(x² - 4x + 4) + 4

    = 3x² - 12x + 12 + 4

     = 3x² - 12x + 16 ← equation in standard form

with coefficient of x² term = 3

Answer:

The answer is B. 30 seconds

Step-by-step explanation:

just simplify the above equation and substitute in the second one.

Answer:

Step-by-step explanation:

2x+3y=6 -----1

3x-5y=2-----2

solving by elimination method,

multiply eq1 with3

multiply eq2 with2

you will get,

6x+9y=18----3

6x-10y=4----4

eq3-eq4=

19y=14

y=14/19------5

substitute eq 5 in eq 1

you will get,

x=50/19...

hope it helps...pls mark brainliest if it does...

Answer:

Area = πr²

= π * 2²

= 3.14 * 4

= 12.6

Answer:

[tex] \boxed{\sf Area = 12.6 \: {cm}^{2}} [/tex]

Given:

Radius of circle (r) = 2 cm

To Find:

Area of circle

Step-by-step explanation:

[tex] \sf Area \: of \: circle = \pi {r}^{2} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times {2}^{2} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3.14 \times 4 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =12.56 \: {cm}^{2} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \approx 12.6 \: {cm}^{2} [/tex]

Answer: ∠ABD =  [tex]\bold{\frac{1}{2}}[/tex]∠C

Step-by-step explanation:

[tex]\angle A + \angle B + \angle C = 180^o\\\\\dfrac{1}{2}\angle A+\dfrac{1}{2}\angle B+\angle D=180^o\\\\\\\text{Solve the system by multiplying the second equation by -2}\\\angle A + \angle B + \angle C = 180^o\\\underline{-\angle A - \angle B - 2\angle D = -180^o}\\.\qquad \qquad \quad \angle C-2\angle D=0\\.\qquad \qquad \qquad \qquad \angle C=2\angle D\\.\qquad \qquad \qquad \quad \dfrac{1}{2}\angle C=\quad \angle D\\[/tex]

Answer:

{ x ≠ ±6 ∪ x ≠ ± 6}

Step-by-step explanation:

x cannot be zero even though x can be cancelled in this expression.  Furthermore, x^2 - 36 cannot be zero, and thus x ≠ ±6.

Domain is { x ≠ ±6 ∪ x ≠ ± 6}

Answer:

The correct answer is:

[tex]g(x) = x+1[/tex]

Step-by-step explanation:

Given that:

[tex]h(x) = f\circ g(x)= \sqrt[3]{x+3}[/tex]

[tex]f(x) = \sqrt[3]{x+2}[/tex]

To find:

[tex]g(x) = ?[/tex]

Solution:

Let [tex]g(x) = m[/tex]

We have

[tex]f\circ g(x)= \sqrt[3]{x+3}\\OR\\f( g(x))= \sqrt[3]{x+3}[/tex]...... (1)

Now, we have let:

[tex]g(x) = m\\\therefore f(g(x)) = f(m)[/tex]

Putting x = in f(x), we get

[tex]f(x) = \sqrt[3]{x+2}\\\Rightarrow f(m) = \sqrt[3]{m+2}[/tex]....... (2)

Comparing equation (1) and (2):

[tex]\sqrt[3]{x+3} =\sqrt[3]{m+2}[/tex]

Taking cubes both sides:

[tex]x+3=m+2\\\Rightarrow m = x+3-2\\\Rightarrow m = x+1[/tex]

[tex]\therefore g(x) = x+1[/tex]

Hence,

The correct answer is:

[tex]g(x) = x+1[/tex]

Answer:

f, g, and h only

Step-by-step explanation:

The letters are the variables.

Answer:

[tex]1.\ 10+x+ 8 = 18+ x[/tex]

[tex]2.\ 9(3x) = 27x[/tex]

[tex]3.\ \frac{1}{2}(10x) + 7 - 3 = 5x + 4[/tex]

[tex]4.\ -5(4x) = -20x[/tex]

[tex]5.\ 10 - 2 (8x) - 3 = 7 - 16x[/tex]

[tex]6.\ 3(7x) + 3 (-5) = 21x -15[/tex]

Step-by-step explanation:

Required

Solve each expression

[tex]1.\ 10+x+ 8[/tex]

Start by collecting like terms

[tex]10+ 8+x[/tex]

Add like terms

[tex]18+x[/tex]

The expression can't be solved further

Hence; [tex]10+x+ 8 = 18+ x[/tex]

[tex]2.\ 9(3x)[/tex]

Open the bracket

[tex]9 * 3x[/tex]

[tex]27x[/tex]

The expression can't be solved further

Hence, [tex]9(3x) = 27x[/tex]

[tex]3.\ \frac{1}{2}(10x) + 7 - 3[/tex]

Open bracket

[tex]\frac{1}{2} * 10x + 7 - 3[/tex]

[tex]5x + 7 - 3[/tex]

[tex]5x + 4[/tex]

The expression can't be solved further;

Hence, [tex]\frac{1}{2}(10x) + 7 - 3 = 5x + 4[/tex]

[tex]4.\ -5(4x)[/tex]

Open the bracket

[tex]-5 * 4x[/tex]

[tex]-20x[/tex]

The expression can't be solved further

Hence, [tex]-5(4x) = -20x[/tex]

[tex]5.\ 10 - 2 (8x) - 3[/tex]

Open Bracket

[tex]10 - 2 *8x - 3[/tex]

[tex]10 - 16x - 3[/tex]

Collect like terms

[tex]10 - 3 - 16x[/tex]

[tex]7 - 16x[/tex]

The expression can't be solved further

Hence, [tex]10 - 2 (8x) - 3 = 7 - 16x[/tex]

[tex]6.\ 3(7x) + 3 (-5)[/tex]

Open both brackets

[tex]3*7x + 3 * -5[/tex]

[tex]21x -15[/tex]

The expression can't be solved further

Hence, [tex]3(7x) + 3 (-5) = 21x -15[/tex]

Answer:25

Step-by-step explanation:

Answer: C)  [tex](-\dfrac{1}{2},\dfrac{3}{2})[/tex]

Step-by-step explanation:

The given system of equations :

[tex]2(y-x) = 5+2x\ \ ...(i)\\\\ 2(y+x)=5-2y\ \ ..(ii)[/tex]

Simplify left side, we get

[tex]2y-2x=5+2x\Rightarrow\ 2y-4x=5\ \ ...(iii)\\\\ 2y+2x=5-2y\Rightarrow\ 4y+2x=5\ \ ...(iv)[/tex]

Multiplying 2 on equation (iii), we get

[tex]4y-8x=10\ \ ...(v)[/tex]

Subtracting (v) from (iv) , we get

[tex]2x-(-8x)=5-10\\\\\Rightarrow\ 2x+8x=-5\\\\\Rightarrow\ 10x=-5\\\\\Rightarrow\ x=-\dfrac{5}{10}=-\dfrac{1}{2}[/tex]

Put value of [tex]x=-\dfrac{1}{2}[/tex] in (v), we get

[tex]4y-8(-\dfrac{1}{2})=10\\\\\Rightarrow \ 4y+4=10\\\\\Rightarrow\ 4y=10-4=6\\\\\Rightarrow\ y=\dfrac{6}{4}=\dfrac{3}{2}[/tex]

hence, the solution to the system is [tex](x,y)=(-\dfrac{1}{2},\dfrac{3}{2})[/tex]

The range of the data is 10.

Box plot, which is also known as box and whisker plot, is a method of graphically representing the measures like minimum, maximum and the quartiles of the data set.

Given is a box plot.

Range of a data set is the difference between the highest and the lowest point.

The highest and lowest point of the data set is the points where the whiskers of the box plot extends to.

Here, whiskers extends from 5 to 15.

Range = Maximum - Minimum

          = 15 - 5

          = 10

Hence the range of the data set is 10.

Learn more about Box Plots here :

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Answer:

3000

Step-by-step explanation:

First find the 4 digit numbers that have all odd digits

Possible Odd digits  =5(1,3,5,7,9)  

So, total number of 4 digit numbers with odd digits can be calculated as  =5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the first digit as either 2,4,6,8 ( 0 would make it a 3 digit number)

The first digit can be 2,4,6,8

=4×5×5×5=500

Now find all the 4 digits numbers with at least 3 odd digits and the second digit as either 0,2,4,6,8

=5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the third digit as either 0,2,4,6,8

Now find all the 4 digits numbers with at least 3 odd digits and the second digit as either 0,2,4,6,8

=5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the fourth digit as either 0,2,4,6,8

=5×5×5×5=625

Add them together

625+500+625+625+625=3000

Answer:

3000

Step-by-step explanation:

4*5*5*5+5*5*5*5+5*5*5*5+5*5*5*5+5*5*5*5 = 3000

one pump, let's call it A, fills the reservoir by 1/60 every hour. Now, B fills it by 1/80 every hour. C empties it by 1/90 every hour. All three are on, so now we combine them into one function: t(1/60 + 1/80 - 1/90) = 1, where t = the time it takes to fill it, and 1 is just our "reservoir finally filled" marker.

isolate t onto one side and we see t = 720/13 exactly, or approximately 55.38 hours. let me know if this is the wrong answer but I'm pretty sure it is correct!

Answer:

1/time needed = 1/time of 1st pump + 1/time of 2nd pump - 1/time of 3rd pump

1/t = 1/t1 + 1/t2 - 1/t3

1/t = 1/60 + 1/80 - 1/90

1/t = 12/720 + 9/720 - 8/720

1/t = 13/720

t = 720/13 hours = 55.38 hours = 55 hours 23 minutes

Answer:

70

Step-by-step explanation:

Answer:

y - 7 = (1/10)(x - 5)

Step-by-step explanation:

Next time please share the possible answers.  Thank you.

Any line perpendicular to y = -10x + 1 has the slope +1/10, which is the negative reciprocal of -10.

Using the point-slope formula, we get:

y - 7 = (1/10)(x - 5)

Answer:

Solution,

Hypotenuse(h)= 25

Base(b)= 20

perpendicular (p)= X

Now,

Using Pythagorean theorem:

[tex] {p}^{2} = {h}^{2} - {b}^{2} \\ {x}^{2} = {25}^{2} - {20}^{2} \\ {x}^{2} = 625 - 400 \\ {x}^{2} = 225 \\ x = \sqrt{225} \\ x = \sqrt{ {15}^{2} } \\ x = 15 [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

x = 15

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 20² = 25² , that is

x² + 400 = 625 ( subtract 400 from both sides )

x² = 225 ( take the square root of both sides )

x = [tex]\sqrt{225}[/tex] = 15

Answer:

x - 2y + 6 = 0  

Step-by-step explanation:

Going from (-2, 2) to (4, 5), we see that x (the 'run') increases by 6 and that y (the 'rise') increases by 3.  Thus, the slope of the line through these two points is m = rise / run = 3/6, or m = 1/2.

Starting with the slope-intercept formula y = mx + b, and using the x and y values from the point (-2, 2), we get

2 = (1/2)(-2) + b, or 4 = -2 + 2b, or 6 = 2b, or b = 3.  Then the slope-intercept form of the desired equation is y = (1/2)x + 3.  To obtain the standard form, we multiply all three terms of this result by 2, obtaining 2y = x + 6, or

x - 2y + 6 = 0                                                                        

Answer:

? = 21

Step-by-step explanation:

Parallel lines cut off proportional segments on transversals.

27/? = 18/14

18 * ? = 27 * 14

2 * ? = 3 * 14

? = 3 * 7

? = 21

Answer:

21

Step-by-step explanation:

Answer:

[tex]-4(a + b = 6)[/tex]

Step-by-step explanation:

Given

[tex]a + b = 6[/tex]

[tex]4a + 2b = 19[/tex]

Required

Eliminate a

Multiply the first equation by -4

[tex]-4(a + b = 6)[/tex]

Add to the second equation

[tex]-4(a + b = 6) + (4a + 2b = 19)[/tex]

Solve brackets

[tex](-4a -4b = -24) + (4a + 2b = 19)[/tex]

Open bracket

[tex]-4a + 4a -4b + 2b = -24 + 19[/tex]

[tex]-4b + 2b = -24 + 19[/tex]

At this point, a has been eliminated;

From the list of given options, the option that answers the question is [tex]-4(a + b = 6)[/tex]

Answer:

road side cabins

Step-by-step explanation:

Answer:

Option a

Step-by-step explanation:

This is a nice simple problem!

Given that the function f( x ) is equivalent to 3x + 400, respectively g( x ) = 5x + 200, all we are being asked to do is find their difference. Substitute the given values as such -

h( x ) = f( x ) - g( x )

⇒ h( x ) = ( 3x + 400 ) - ( 5x + 200 ) - Distribute negative sign, taking out ( )

⇒ h( x ) = 3x + 400 - 5x + 200 - Combine like elements

⇒ h( x ) = - 2x + 200

And there you have it! Our solution should be option a ( h( x ) = - 2x + 200 )

If you would like, there is a graph of the function in the attachment below.

Answer:

It's B on edge!

Hey there! :)

Answer:

y = 0, also known as the x-axis.

Step-by-step explanation:

The equation [tex]f(x) = \frac{2}{3} ^{x}[/tex] is an exponential function.

There is an asymptote at y = 0, or the x-axis because:

[tex]\frac{2}{3} ^{x}\neq 0[/tex]

An exponential function, unless containing a vertical shift, can never cross the x-axis resulting in an asymptote at y = 0.

Answer: c) 27:8

Step-by-step explanation:

As volume of cube is side^3

volume of cube with side 2a is 8.a^3

volume of cube with side  3a is 27.a^3

ration of volumes is 27:8

Answer:

The answer is solution D.

Step-by-step explanation:

130 + 12.50p ≤ 1500

The 130 is the setup fee

The 12.50 is the amount to pay per person

p means the number of people

The symbol ≤ means smaller than or equal to so it could be either of those

The 1500 is the max amount of money that they could spend for the party.

Answer:

1, 2, 4, 8, 16...

Step-by-step explanation:

To be a geometric sequence there must be a common ratio which basically means the number you multiply a term by to get the next one, and the common ratio must be the same between all terms. The only sequence that follows this is the first one.

Answer:

Step-by-step explanation:

Each term of a geometric sequence is a multiple of the previous term.  For example, if the first term is 2 and the common ratio is 3, then the next term is 6; the next term is 18.  And so on.

1,2,4,8,16.... fits this pattern.  The first term is 1 and each succeeding term is 2 times the previous term:  1*2 = 2; 2*2 = 4; 4*2 = 8, and so on.