which of the following is equal to 5^-3?

Answer:

A. –f(x)

Step-by-step explanation:

The transformation of a reflection about the x-axis is

f(x) -> -f(x).

So the answer is

A. –f(x)

Answer:

because this is equal to the given matrix, the given matrix is symmetric.

Step-by-step explanation:

A symmetric matrix is a square matrix which has same number of rows and columns. Square matrix is equal to transpose. Equal matrices have equal dimensions. The given matrix is symmetric because the rows and columns are equally distributed.

Answer:

[tex]Mean = 53.25[/tex]

Step-by-step explanation:

Given

Low Temperature : 40−44 || 45−49 ||  50−54 || 55−59 || 60−64

Frequency: --------------- 3 -----------6----------- 1-----------3--- -----7

Required

Determine the mean

The first step is to determine the midpoints of the given temperatures

40 - 44:

[tex]Midpoint = \frac{40+44}{2}[/tex]

[tex]Midpoint = \frac{84}{2}[/tex]

[tex]Midpoint = 42[/tex]

45 - 49

[tex]Midpoint = \frac{45+49}{2}[/tex]

[tex]Midpoint = \frac{94}{2}[/tex]

[tex]Midpoint = 47[/tex]

50 - 54:

[tex]Midpoint = \frac{50+54}{2}[/tex]

[tex]Midpoint = \frac{104}{2}[/tex]

[tex]Midpoint = 52[/tex]

55- 59

[tex]Midpoint = \frac{55+59}{2}[/tex]

[tex]Midpoint = \frac{114}{2}[/tex]

[tex]Midpoint = 57[/tex]

60 - 64:

[tex]Midpoint = \frac{60+64}{2}[/tex]

[tex]Midpoint = \frac{124}{2}[/tex]

[tex]Midpoint = 62[/tex]

So, the new frequency table is as thus:

Low Temperature : 42 || 47 ||  52 || 57 || 62

Frequency: ----------- 3 --||- -6-||- 1-||- --3- ||--7

Next, is to calculate mean by

[tex]Mean = \frac{\sum fx}{\sum x}[/tex]

[tex]Mean = \frac{42 * 3 + 47 * 6 + 52 * 1 + 57 * 3 + 62 * 7}{3+6+1+3+7}[/tex]

[tex]Mean = \frac{1065}{20}[/tex]

[tex]Mean = 53.25[/tex]

The computed mean is greater than the actual mean

Answer:

Step-by-step explanation:

Given that:

[tex]x = 5 + In (t)[/tex]

[tex]y = t^2+2[/tex]

At point (5,3)

To find an equation of the tangent to the curve at the given point,

By without eliminating the parameter

[tex]\dfrac{dx}{dt}= \dfrac{1}{t}[/tex]

[tex]\dfrac{dy}{dt}= 2t[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{ \dfrac{dy}{dt} }{\dfrac{dx}{dt} }[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{ 2t }{\dfrac{1}{t} }[/tex]

[tex]\dfrac{dy}{dx}= 2t^2[/tex]

[tex]\dfrac{dy}{dx}_{ (5,3)}= 2t^2_{ (5,3)}[/tex]

t²  + 5 = 4

t² = 4 - 5

t² = - 1

Then;

[tex]\dfrac{dy}{dx}_{ (5,3)}= -2[/tex]

The equation of the tangent  is:

[tex]y -y_1 = m(x-x_1)[/tex]

[tex](y-3 )= -2(x - 5)[/tex]

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

By eliminating the parameter

x = 5 + In(t)

In(t)  = 5 - x

[tex]t =e^{x-5}[/tex]

[tex]y = (e^{x-5})^2+5[/tex][tex]y = (e^{2x-10})+5[/tex]

[tex]\dfrac{dy}{dx} = 2e^{2x-10}[/tex]

[tex]\dfrac{dy}{dx}_{(5,3)} = 2e^{10-10}[/tex]

[tex]\dfrac{dy}{dx}_{(5,3)} = 2[/tex]

The equation of the tangent  is:

[tex]y -y_1 = m(x-x_1)[/tex]

[tex](y-3 )= -2(x - 5)[/tex]

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

Answer:

C. 42 square units

Step-by-step explanation:

This is a rectangle and to calculate the area of a rectangle we multiply length and width

The length of this rectangle is 7 units and the width is 6 units

6 × 7 = 42 square units

Answer:

12 , 19 , 26 , 33

Here, n+7

12+7=19

19+7=26

So,

26+7=33

Hope you understand ❣

Step-by-step explanation:

12 , 19 , 26 , ?

Given

___________

a1= 12

a2= 19

a3 = 26

d= ?

a4 = ?

––——————

we can solve this by using formula from Ap .

But for this we have to find d

As we know that

common difference(d) = a2-a1 = 19 -12

= 7

so difference after every no is 7 so

a4 = a3 + d

= 26 +7

= 33

So 33 is ur answer mate

Hope it helps

Answer:

60% discount given in total, so only 40% is paid.

Step-by-step explanation:

Answer:

3.19 seconds

Step-by-step explanation:

Given:

Phone gets dropped from a Height = 150 ft

To find:

Time taken for the phone to reach the ground = ?

Solution:

First of all, let us learn about the formula of distance in terms of Initial speed u; Time t and Acceleration a:

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

Here the phone is dropped from a height so a = g m/[tex]s^2[/tex] i.e. acceleration due to gravity.

g = 9.8 m/[tex]s^2[/tex]

s = 150 ft

Initial velocity, u = 0

Putting all the values in the formula:

[tex]150=0 t+\dfrac{1}{2}gt^2\\\Rightarrow 50=\dfrac{1}{2}\times 9.8 \times t^2\\\Rightarrow t^2=\dfrac{50}{4.9 }\\\Rightarrow t^2=10.20\\\Rightarrow t = 3.19\ sec[/tex]

So, the time taken is 3.19 seconds.

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

Answer:

Median = 14

Step-by-step explanation:

2, 5, 14, 15, 21, 18, 15, 9, 2

First, order the numbers:

2, 2, 5, 9, 14, 15, 15, 18, 21

Then, cancel out the numbers, starting the first and last number, going outwards in. If there is 1 number left, it is your median. If there are 2 left, add the 2 numbers together and divide them by two:

2, 2, 5, 9, 14, 15, 15, 18, 21

2, 5, 9, 14, 15, 15, 18

5, 9, 14, 15, 15

9, 14, 15

14

The median is 14.

Please tell me if I was wrong! I hope this helps you!

Answer: The median is 14

Step-by-step explanation: The median is the number that is halfway into the data set. To find the median, the data should be arranged in order from least to greatest. For this example.  2,2,5,9,14,15,15,18,21. Find the number that is halfway. which is 14

Answer:

14.5°

Step-by-step explanation:

The sketch results in an angle of depression problem.

In this case, the opposite side of the triangle formed is 5 ft

The hypotenuse side is 20 ft

The adjacent side is the [tex]5\sqrt{15}[/tex] ft

Using tangent θ = opp/adj

tangent θ = 5/[tex]5\sqrt{15}[/tex] = [tex]\frac{1}{\sqrt{15} }[/tex] = 0.258

θ = [tex]tangent^{-1}[/tex] 0.258 = 14.5°

Answer:

Step-by-step explanation:

To find the ratio first find the diameter of the larger circle

Diameter of first circle = 6 inches

Diameter of second circle = 4 × diameter of the first circle

Which is

Diameter of second circle

= 4 × 6 = 24 inches

Area of a circle = πr²

r is the radius

Area of smaller circle

Diameter = 6 inches

Radius = 6 / 2 = 3 inches

Area = (3)² π = 9π in²

Area of larger circle

Diameter = 24 inches

Radius = 24 / 2 = 12 inches

Area = (12)²π = 144π in²

The ratio of the smaller circle to the larger circle is

[tex] \frac{9\pi}{144\pi} [/tex]

Reduce the fraction by 9π

That's

[tex] \frac{1}{16} [/tex]

We have the final answer as

Hope this helps you

Answer:

C. 1:16

Step-by-step explanation:

Area of a circle is:

[tex]\pi \times {r}^{2} [/tex]

Small circle Area:

radius = diameter/2

radius = 6/2 = 3

[tex]area \: of \: a \: circle \: = \pi {3}^{2} [/tex]

a = 28.27

Large circle 4 times larger diameter

6*4 = 24

diameter = 24

r = 24/2

r = 12

[tex]a \: = \pi {12}^{2} [/tex]

a = 452.39

area of large circle/ area of small circle

452.39/28.27 = 16.00

ratio is 1:16

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

For these kind of problems, simply take the denominator and compare it to zero. Then solve the equation.

[tex]x+2=0\\\\\Rightarrow x=-2[/tex]       By subtracting 2 from both sides!

Best Regards!

Answer:

(a) Minimum red blood cells 5.744 million cells per micro liter

(b) Maximum red blood cells 5.068 million cells per micro liter.

Step-by-step explanation:

Z-score formula is = [tex]\frac{x-u}{Standard deviation}[/tex]

Z-score = [tex]\frac{x-5.5}{0.4}[/tex]

The value of z-score is 0.61 so then x will be;

x = 5.744

The minimum red blood cells count that can in top is 27% of count which is 5.744 million cells per micro liter.

Z-score = [tex]\frac{x-5.5}{0.4}[/tex]

The value of z-score is 0.14 so then x will be;

x = 5.068

The maximum red blood cells count that can be in top is 14% of count which is 5.068 million cells per micro liter.

Answer: You are correct. The answer is choice C.

The sum of the vectors is the resultant vector, which is where the net force is directed.

An example would be if you had a ball rolling on a table and you bumped the ball perpendicular to its initial velocity, then the ball would move at a diagonal angle rather than move straight in the direction where you bumped it.

Acceleration is the change in velocity over time, so the acceleration vector tells us how the velocity's direction is changing.

The direction of the acceleration on a body upon which multiple forces are applied depends on the direction of the netforce acting on the body.

Therefore, acceleration will be due in the direction of the netforce.

Learn more :https://brainly.com/question/17858024?referrer=searchResults

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

[tex]6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]

( 2 ) [tex]\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}[/tex]

These two identities makes sin(π / 10) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and cos(π / 10) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex].

Therefore cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]. Substitute,

[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex]

And now simplify this expression to receive our answer,

[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex] = [tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i[/tex],

[tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}[/tex] = [tex]-2.01749\dots[/tex] and [tex]\:\frac{3\sqrt{3-\sqrt{5}}}{4}[/tex] = [tex]0.65552\dots[/tex]

= [tex]-2.01749+0.65552i[/tex]

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex], cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

[tex]6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}[/tex]

We know that [tex]6\sqrt{5+\sqrt{5}} = 16.13996\dots[/tex] and [tex]-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots[/tex] . Therefore,

Solution : [tex]16.13996 - 5.24419i[/tex]

Which rounds to about option b.

Answer:

Step-by-step explanation:

The answer is b

120.01 grams

Answer:

the answer is going to be 2/4

False.

2x10^6 you move the decimal point 6 places to the right. ( add 6 zeros after the 2)

2x 10^6 = 2,000,000

Answer:

Here is the answer i got-

Step-by-step explanation:

325823-250823=75000

325823’s 244367250percent is 75000

Hey there! I'm happy to help!

We want to isolate y on one side of the equation to see what it equals. To do this, we use inverse operations to cancel out numbers on the y side and find the correct value.

1/3y+4=16

We subtract 4 from both sides, canceling out the +4 on the right but keeping the same y-value by doing the same to the other side.

1/3y=12

We divide both sides by 1/3 (which is multiplying both sides by 3) which will cancel out the 1/3 and tell us what y is equal to.

y=36

Now you know how to solve basic equations! Have a wonderful day! :D

Answer:

x = 4

Step-by-step explanation:

6x + 3 = 2x + 19  ------ subtract 3 both sides

6x + 3 - 3 = 2x + 19 - 3   simplify

6x = 2x + 16         ------ subtract 2x both sides

6x - 2x = 2x + 16 - 2x      simplify

4x = 16

x = 16 / 4

x = 4

Answer: x = 4

Step-by-step explanation: If the variable appears on both sides of the equation, we put the variables together on one side of the equation and the numbers together on the other side of the equation.

So let's put our variables on the left side by first subtracting

2x from both sides of the equation to get 4x + 3 = 19.

Next, we subtract 3 from both sides to get 4x = 16.

Finally, we divide both sides by 4 to get x = 4.

Answer:

12 - 6 x (0 + 15) = 34

How I got my answer

First, how i got my answer was that I had to solve the equation first, ignoring the answer. I got 0 x 6 = 0, then I did 124 - 0 = 124, then I did 124 - 15 = 109, which clearly isn't 34. I figured that we have to put the parentheses around the zero because if we don't, we are going have to multiply something by zero, which always gets zero. After that, I decided that I should put the parentheses around either the 6, or the 15. I did both, and saw which one was correct. If we put it around the 6, we get, 124 - (6 x 0) + 15 = 124 - 0 - 15 = 124 - 15 = 109, which isn't 34. Then I checked 124 - 6 x (0 + 15) = 124 - 6 x 15 = 124 - 90 = 34, and we just got the answer.

P.S. Sorry if it was confusing, I didn't really know how to explain it

Answer:

Example: solve √(2x−5) − √(x−1) = 1

isolate one of the square roots:√(2x−5) = 1 + √(x−1) square both sides:2x−5 = (1 + √(x−1))2 ...

expand right hand side:2x−5 = 1 + 2√(x−1) + (x−1) ...

isolate the square root:√(x−1) = (x−5)/2. ...

Expand right hand side:x−1 = (x2 − 10x + 25)/4. ...

Multiply by 4 to remove division:4x−4 = x2 − 10x + 25.

Answer:

Step-by-step explanation:

ewrerewrwrwerrwer

Answer:

21

Step-by-step explanation:

√1500 ≈ 38.7

round that up to 39 and square it:

39² = 1521

Answer:

Interval Level of Measurement

Step-by-step explanation:

The Interval level of measurement highlights the distances between two measurements. These distances are meaningful and could be rated as low intervals or high intervals. Intervals also indicate class and order between measurements. The inauguration of the United States President is an event that occurs 72 to 78 days after the presidential election. It is usually done as a private and public oath-taking ceremony on January 20, four years after the last presidential election. So, even if the president is on a second term, this event must be held.

The last U.S presidential election occurred on January 20, 2017, and the next one will be held on January 21, 2021. So there is an interval of four years between the last and next U.S presidential inauguration ceremony.

Answer:

P = 3x - 4

Step-by-step explanation:

Side 1 = x - 3

Side 2 = x

Side 3 = 2 + (Side 1) = 2 + x - 3 = x - 1

Perimeter = 20 in

Perimeter = Side 1 + Side 2 + Side 3

Perimeter = (x - 3) + (x) + (x - 1)

Perimeter = x - 3 + x + x - 1

Perimeter = 3x - 3 - 1

Perimeter = 3x - 3 - 1

Perimeter = 3x - 4

P = 3x - 4

Answer:

Option B.

Step-by-step explanation:

Let as consider the given equation:

[tex]2\ln e^{\ln 2x}-\ln e^{\ln 10x}=\ln 30[/tex]

It can be written as

[tex]2(\ln 2x)-(\ln 10x)=\ln 30[/tex]         [tex][\because \ln e^a=a][/tex]

[tex]\ln (2x)^2-(\ln 10x)=\ln 30[/tex]        [tex][\because \ln a^b=b\ln a][/tex]

[tex]\ln \dfrac{4x^2}{10x}=\ln 30[/tex]        [tex][\because \ln \dfrac{a}{b}=\ln a-\ln b][/tex]

[tex]\ln \dfrac{2x}{5}=\ln 30[/tex]

On comparing both sides, we get

[tex]\dfrac{2x}{5}=30[/tex]

Multiply both sides by 5.

[tex]2x=150[/tex]

Divide both sides by 2.

[tex]x=75[/tex]

Therefore, the correct option is B.

Answer:

b x=75

Step-by-step explanation:

Answer:

Its commutative property..

Step-by-step explanation:

Commutative property says A×B=B×A

Explanation is attached below.

Answer:

15.7 in  

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826  

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]

It checks.