A right triangle has legs of 5 ft and 6 ft. What is the length of the hypotenuse? _____ ft. A. 7.8 B. 3.3 C. 11.0 D. 1.0

Answer:

The answer is 9 (D).

Step-by-step explanation:

Hope this helps!

Answer:

[tex]\frac{9}{a - b}[/tex].

Step-by-step explanation:

a^2 - b^2 = 9

(a + b)(a - b) = 9

a + b = [tex]\frac{9}{a - b}[/tex].

ab = 3

a = 3/b

3/b + b = [tex]\frac{9}{\frac{3}{b} -b}[/tex]

3 + b^2 = [tex]\frac{9b}{\frac{3}{b}-\frac{b^2}{b} }[/tex]

3 + b^2 = [tex]\frac{9b}{\frac{3-b^2}{b} }[/tex]

3 + b^2 = [tex]9b * \frac{b}{-b^2 + 3}[/tex]

3 + b^2 = [tex]\frac{9b^2}{-b^2 + 3}[/tex]

(b^2 + 3)(-b^2 + 3) = 9b^2

-b^4 + 9 = 9b^2

b^4 + 9b^2 - 9 = 0

Let's say that b^2 = x

x^2 + 9x - 9 = 0

Hope this [somewhat] helps!

Answer:

Step-by-step explanation:

a²-b²=9

ab=3 then a=3/b

a²-b²=9

(a+b)(a-b)=9 ( the values has to b (3*3) or (9*1)

but since ab=3. so the value has to be (3*3)

(a+b)(a-b)=9

3*3=9

a+b=3

ab=3

Answer:

The sampling method used is a stratified sampling method

Step-by-step explanation:

sampling is the selection of a predetermined representative subpopulation from a larger population, to estimate the characteristics of the whole population.

Stratified sampling: Here, the total population are divided into subcategories (strata) before sampling is done. The strata are formed based on some common characteristics. In our example, the times of the day (morning, afternoon and evening) has widely varying atmospheric conditions which will add biases to the measurement of air quality. For example, the air in the morning if compared to the afternoon in an industrial area may be purer because of minimal industrial activity, hence effective comparison will be made by stratification.

Answer:

a. Area = 1.94m²

b. Area = (p² + 0.5)m²

c. Height = 1.5m

Step-by-step explanation:

Given

Let H represents Height and A represents Area

From the first and second statements, we have that:

[tex]A = H^2 + 0.5[/tex]

a. Calculating Area When Height = 1.2

[tex]A = H^2 + 0.5[/tex]

Substitute 1.2 for H

[tex]A = 1.2^2 + 0.5[/tex]

[tex]A = 1.44 + 0.5[/tex]

[tex]A = 1.94[/tex]

Hence, the area is 1.94m²

b. Calculating Area When Height = p

[tex]A = H^2 + 0.5[/tex]

Substitute p for H

[tex]A = p^2 + 0.5[/tex]

Hence, the area is (p² + 0.5)m²

c. Calculating Height When Area = 2.75m²

[tex]A = H^2 + 0.5[/tex]

Substitute 2.75 for A

[tex]2.75 = H^2 + 0.5[/tex]

Subtract 0.5 from both sides

[tex]2.75 - 0.5 = H^2 + 0.5 - 0.5[/tex]

[tex]2.75 - 0.5 = H^2[/tex]

[tex]2.25 = H^2[/tex]

Take Square Root of both sides

[tex]\sqrt{2.25} = \sqrt{H^2}[/tex]

[tex]\sqrt{2.25} = H[/tex]

[tex]1.5 = H[/tex]

[tex]H = 1.5[/tex]

Hence, the height is 1.5m

Answer:

9 years i think

Step-by-step explanation:

Answer:

in day 44 it covered half the area.

Step-by-step explanation:

A bacterial culture doubles every two days, so if today it covers [tex]3 cm^2[/tex], in two days it will cover [tex]6cm^2[/tex]. In other words, if today it covered x space, two days ago it covered half the space [tex](\frac{x}{2})[/tex].

Now, following that reasoning, we have that after 46 days the bacterial culture covered the entire surface area in the Petri dish, therefore, two days ago it covered half the area and we can conclude that in day 44 it covered half the area.

Answer:

Step-by-step explanation:

The box encloses data between the two quartiles, namely at least half of the data.  If there are 40 schools, then half of them would be in the box, between 1 and 6.

see attached plot.

Answer:

really hard to tell what the box plot is like without an attachment so im gonna help u find it out anyway

Step-by-step explanation:

basically when u look at a  box plot and the range the line in the middle is the median  and then the max the lowest range the lower quartile and then the higher quartile you can find ur anser, simply find the median first, find where the lower quartile is and then the lowest number in the group thats in betweeen 1 and 6

Answer: 90 degrees clockwise rotation

Step-by-step explanation:

Common rotations about Origin :

90° clockwise    (x,y)→(y,-x)

90° counterclockwise    (x,y)→(-y,x)

180°       (x,y)→ (-x,-y)

270°  clockwise     (x,y)→(-y,x)

Given:  Julio’s rotation maps point K(–6, 9) to K’(9, 6).

Rotation corresponding to this is (x,y) → (y,-x) since K(–6, 9) → K’(9, -(-6)) = K(9,6).

Therefore, Julio’s rotates 90° clockwise to map point K(–6, 9) to K’(9, 6).

so , correct answer is "90 degrees clockwise rotation".

Answer:

90 degrees clockwise

Step-by-step explanation:

EDGE2020

Answer:

a) The mirror is concave

b) The focal length of the mirror = -1.25m or -5/4 m

Step-by-step explanation:

a) Determine whether the mirror is convex or concave?

A concave mirror is a spherical mirror that it's magnification is equal to, less than or more than 1 while a convex mirror is a mirror whereby it magnification is always less than one.

From the above question we are told that the spherical mirror is magnified 5 times.

Hence, because the spherical mirror is magnified 5, it is a concave mirror.

b) Magnification = - image distance/ object distance

Magnification = 5

Image distance = 5m

Object distance = ???

5 = -5/Object distance

Object distance = -5/5

= -1m

Formula for focal length =

1/f = 1/v + 1/u

v = image distance = 5

u = object distance = -1

1/f = 1/5 +1/-1

1/f = 1/5 - 1

1/f = -4/5

f = -5/4

f = -1.25m

The focal length of the mirror = -1.25m

Answer: 16,384

Step-by-step explanation:

The seven marbles have different colours, so we can differentiate them.

Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.

For the first marble, we have 4 options ( we have 4 jars)

For the second marble, we have 4 options.

Same for the third, for the fourth, etc.

Now, the total number of combinations is equal to the product of the number of options for each selection.

We have 7 selections and 4 options for each selection, then the total number of combinations is:

C = 4^7 = 16,384

Answer:

the answer is 16384

Step-by-step explanation:

have a nice day.

Answer:

The cosine function to model the height of a water particle above and below the mean water line is h = 2·cos((π/30)·t)

Step-by-step explanation:

The cosine function equation is given as follows h = d + a·cos(b(x - c))

Where:

[tex]\left | a \right |[/tex] = Amplitude

2·π/b = The period

c = The phase shift

d = The vertical shift

h = Height of the function

x = The time duration of motion of the wave, t

The given data are;

The amplitude [tex]\left | a \right |[/tex] = 2 feet

Time for the wave to pass the dock

The number of times the wave passes a point in each cycle = 2 times

Therefore;

The time for each complete cycle = 2 × 30 seconds  = 60 seconds

The time for each complete cycle = Period = 2·π/b = 60

b = π/30 =

Taking the phase shift as zero, (moving wave) and the vertical shift as zero (movement about the mean water line), we have

h = 0 + 2·cos(π/30(t - 0)) = 2·cos((π/30)·t)

The cosine function is h = 2·cos((π/30)·t).

Answer:

Length of arc = 5 cm (Approx)

Step-by-step explanation:

Given:

Radius of circle = 20 cm

Angle = 1/4 radian

Find:

Length of arc

Computation:

Angle in degree = 1/4 radian × 180°π

Angle in degree = 1/4 × 180°  / 22/7

Angle in degree = 14.31° Approx

Length of arc = (Ф / 360)2πr

Length of arc = (14.31 /360)2(22/7)(20)

Length of arc = 4.997 cm

Length of arc = 5 cm (Approx)

Answer:

g=5

Step-by-step explanation:

32g+8g-10g=150

30g=150

g=5

Answer:

Step-by-step explanation:

Hello!

a)

You have three triangles and you have to find the ratio of the adjacent sides to the angle 23.1º

Remember, considering a specific angle ∠, "the adjacent sides" are those that make contact with the angle and the "opponent side" is the one that is in the opposite side of the angle and the hypotenuse is the longest side of the right triangle, always opposed to the right angle.

First triangle, the adjacent sides, are

JL= 20.17m (hypotenuse)

JK= 18.55m

Ratio: [tex]\frac{JK}{JL}= \frac{18.55}{20.17}= 0.9196= 0.92[/tex]

Second triangle, adjacent sides:

PR= 141.19m (hypotenuse)

PQ= 129.85m

Ratio: [tex]\frac{PQ}{PR} = \frac{129.85}{141.19}= 0.9196= 0.92[/tex]

Third triangle, adjacent sides:

XZ= 181.53m (hypotenuse)

XY= 166.95m

Ratio: [tex]\frac{XY}{XZ} = \frac{166.95}{181.53} = 0.9196= 0.92[/tex]

b)

Using the calculator you have to calculate the trigonometric ratios of 23.1º:

sin(23.1º)= 0.392= 0.39

cos(23.1º)= 0.9198= 0.92

tan(23.1º)= 0.426= 0.43

c)

To calculate the trigonometrical ratios manually you have to do as follows:

Consider the angle A

[tex]sinA= \frac{opposite}{hypotenuse}[/tex]

[tex]cosA= \frac{adjacent}{hypotenuse}[/tex]

[tex]tanA= \frac{opposite}{adjacent}[/tex]

In item a) you calculated the ratios of the adjacent sides of the angle by the hypotenuse, this is equal to the cosine of the given angle.

I hope this helps!

Answer:

Hello! The answer to your question will be below.

Step-by-step explanation:

The answer would be clockwise.

So point k was rotated 90 degrees clockwise.....

Review.....

Question:

Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.

THE DIRECTION OF THE ROTATION WAS CLOCKWISE.

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer:

clockwise.

So point k was rotated 90 degrees clockwise.....

Review.....

Question:

Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.

Step-by-step explanation:

Answer:

149=19/9 (10) +b

130=19/9(1)+b

Step-by-step explanation:

for Loren to find a line passes through two points:(1,130), (10.149)

1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9

m=19/9

to find b in the equation y=mx+b for point (1,130)

y=130, x=1, m=19/9

130=19/9(1)+b

for point (10,149)

149=19/9 (10) +b

you have two options

The solution is, the equations of line passes through two points:(1,130), (10.149) is:

149=19/9 (10) +b

130=19/9(1)+b

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

for Loren to find a line passes through two points:(1,130), (10.149)

1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9

m=19/9

to find b in the equation y=mx+b for point (1,130)

y=130, x=1, m=19/9

130=19/9(1)+b

for point (10,149)

149=19/9 (10) +b

you have two options

Hence, The solution is, the equations of line passes through two points:(1,130), (10.149) is:

149=19/9 (10) +b

130=19/9(1)+b

To learn more on Equation 0f Straight-Line click:

brainly.com/question/11116168

#SPJ6

Greetings from Brasil...

With the recursive formula, lets build the sequence:

A1 = 4

A2 = A1 - 7

A3 = A2 - 7

A4 = A3 - 7

A5 = A4 - 7

(...)

But pay attention to A3....

A3 = A2 - 7   but  A2 = A1 - 7 , so rewriting A3

A3 = (A1 - 7) - 7 ⇒ A3 = A1 + 2.(- 7)

A4 = A3 - 7 ⇒ A4 = [(A1 - 7) - 7] - 7 = A1 + 3.(- 7)

A5 =  {[(A1 - 7) - 7] - 7} - 7 = A5 + 4.(- 7)  

so

Answer:

Step-by-step explanation:

To use the regression function on your calculator, first hit STAT then choose 1:Edit by pressing ENTER. Then a table pops up. If it's not clear, arrow up to L1, hit CLEAR then ENTER and the table empties. Do the same with L2. Arrow left and right as needed to get from one column to the other. Then in L1 enter the x values one at a time, hitting ENTER after each. When all the x values are in, arrow over to L2 and enter the y values in the same way.

Next, hit STAT again, then right arrow over to CALC. Choose 6:CubicReg by either arrowing down to it or by pressing 6. If you have a TI 83+, the equation comes right up for you; if you have a TI 84+ or 84+CE, you have to arrow down to CALCULATE and hit ENTER to get your equation. The equation is

[tex]-2x^3+2x^2-4x+3[/tex] with a coefficient correlation (r-squared) value of 1 which means this is a perfect equation for this data and all the points you entered into the table fall perfectly on this curve.

Answer:

2 CDs and 6 movies

Step-by-step explanation:

Let the number of CD you bought be x, and the number of movies you bought be y.

Since you bought 8 items in total,

x + y = 8 ______(1)

The sum of money spent is 78, so

9x + 10y = 78 ________(2)

From equation (1),

x = 8 - y ________(3)

Substitute (3) into (2),

9 (8-y) + 10y = 78

72 - 9y + 10y = 78

- 9y + 10y = 78-72

y = 6

Now substitute y=6 into (3).

x = 8 - y

x = 8-6

x = 2

Therefore, you bought 2 CDs and 6 movies.

Answer:

B = Blue

Y = Yellow

G = Green

P = Pink

The info that we have is:

3*B = Y

(1/2)Y = G

P = (3 + 1/4) gal

P = G + 3/4 gal.

So we have 4 equations. The first step is replacing the third equation into the fourth equation, and get:

G + 3/4 gal = (3 + 1/4) gal

G = (3 + 1/4) gal - 3/4 gal = (2 + 2/4) gal

Now we can replace this into the second equation ((1/2)*Y = G) to find the value of Y.

(1/2)Y = (2 + 2/4) gal

Y = 2*(2 + 2/4) gal = (4 + 1)gal = 5 gal.

Now we can replace this into the first equation and get:

3*B = 5gal

B = 5/3 gal = (1 + 2/3)gal

So the total amount of paint used is:

T = P + G + Y + B = (3 + 1/4) gal +  (2 + 2/4) gal + 5gal + (1 + 2/3)gal

T = (11 + 3/4 + 2/3)gal

T = (11 + 9/12 + 8/12)gal = (11 + 17/12)gal = (11 + 1 + 5/12)gal = (12 + 5/12) gal.

Answer:

A. 8 3/4 degrees

Step-by-step explanation:

Alaska temperature dropped from 3 degrees Fahrenheit to twelve and a quarter degrees Fahrenheit below zero

12 1/4°F - 3°F

=8 3/4°F

The temperature dropped by 8 3/4°F

Answer:

A. 243

Step-by-step explanation:

just multiply the next number by 3

81*3= 243

Answer:

[tex]\boxed{243}[/tex]

Step-by-step explanation:

The ratio can be found by dividing a term in the sequence by the previous term.

[tex]\frac{27}{9} =3[/tex]

Each term gets multiplied by 3 to get the next term.

[tex]81 \times 3 = 243[/tex]

Answer:

[tex]\dfrac{1}{x^{48}y^{36}z^{6}}[/tex]

Step-by-step explanation:

[tex] (\dfrac{(x^2y^3)^{-2}}{(x^6y^3z)^{2}})^3 = [/tex]

[tex] = (\dfrac{1}{(x^6y^3z)^{2}(x^2y^3)^{2}})^3 [/tex]

[tex] = (\dfrac{1}{x^{12}y^6z^{2}x^4y^6})^3 [/tex]

[tex]= (\dfrac{1}{x^{16}y^{12}z^{2}})^3[/tex]

[tex]= \dfrac{1}{x^{48}y^{36}z^{6}}[/tex]

Answer:

[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]

Step-by-step explanation:

[tex]\displaystyle[\frac{(x^2 y^3)^{-2}}{(x^6 y^3 z)^2 } ]^3[/tex]

[tex]\displaystyle \frac{(x^2 y^3)^{-6}}{(x^6 y^3 z)^6 }[/tex]

[tex]\displaystyle \frac{(x^{-12} y^{-18})}{(x^{36} y^{18}z^6 ) }[/tex]

[tex]\displaystyle \frac{x^{-48} y^{-36}}{z^6 }[/tex]

[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]

Solution: C

Explanation:

Use the cosine rule

A^2=B^2+C^2-2BCcos a

5^2=8^2+8^2-2×8×8cos a

cos a=(25-64-64)÷(-2×64)

a=36.419°

approx = 36

Answer:  [tex]\sum\limits_{i=1}^{n} n^2[/tex] , where n is a natural number.

Step-by-step explanation:

A series can be represented in a summation or sigma notation.

Greek capital letter, ∑ (sigma), is used to represent the sum.

For example: [tex]\sum\limits_{n=1}^{\infty} n=1+2+3+4+5+...[/tex], where n is a natural number.

The given series : 1,4,9,16 which can be written as [tex]1^2, 2^2, 3^2,...[/tex] .

So , we can write it as

[tex]\sum\limits_{n=1}^{\infty} n^2[/tex] , where n is a natural number.

Answer:

B=6

C=n^2

Just did the test

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

x + 8 = -3

x + 8 - 8 = -3 - 8

x = - 11

Answer:

A. x= -11

Step-by-step explanation:

We want to solve for x. Therefore, we must get x by itself on one side of the equation.

x+8= -3

8 is being added to x. The inverse of addition is subtraction. So, subtract 8 from both sides of the equation.

x+8-8=-3-8

x= -3-8

x= -11

Now let’s check our solution. Plug -11 in for x in the original equation.

x+8=-3

-11+8=-3

-3=-3

This checks out, so we know our solution is correct and A. x= -11 is the correct choice.

Answer:

60 cents or $0.60

Step-by-step explanation:

9.00/15 = 0.6

Answer:

$.60

Step-by-step explanation:

This is just 9 divided by 15 which is $.60

Answer:

825 or 500

Step-by-step explanation:

Depends, if it is talking about just an up-down, it is 500, but if it is just distance in general, it would be 825 because 325+500=825

Hope this will help

Answer:

[tex]5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex].

Step-by-step explanation:

The given expression is

[tex]\sqrt[3]{5xy^2}[/tex]

We need to find the expression in rational exponent form.

It can be written as

[tex](5xy^2)^{\frac{1}{3}}[/tex]           [tex][\because \sqrt[n]{x}=x^{\frac{1}{n}}][/tex]

[tex]=(5)^{\frac{1}{3}}(x)^{\frac{1}{3}}(y^2)^{\frac{1}{3}}[/tex]           [tex][\because (ab)^m=a^mb^m][/tex]

[tex]=5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex]           [tex][\because (a^m)^n=a^{mn}][/tex]

Therefore, the required expression is  [tex]5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex].

Answer:

Probability of selecting none of the correct six integers:

a) 0.350

b) 0.427

c) 0.489

d) 0.540

Step-by-step explanation:

a) 40

Given:

Number of integers in a lottery  6

Order in which these integers are selected does not matter

To find:

Probability of selecting none of the correct six integers

Solution:

When the order of selection does not matter then we use Combinations.

Given integers = 40

Number of ways to choose 6 from 40.

Let A be the sample space of choosing digits 6 from 40.

Then using Combinations:

(n,k) = n! / r! (n-r)!

n = 40

r = 6

40C6

=(40,6) = 40! / 6! ( 40 - 6)!

           = 40! / 6!34!

           = 40*39*38*37*36*35*34! / 6!34!

           = 2763633600 / 720

          = 3838380

Let E be the event of selecting none of the correct six integers.

So using combinations we can find the total number of ways of selecting none of 6 integers from 40

n = 40 - 6 = 34

r = 6

34C6

=(34,6) = 34! / 6! ( 34 - 6)!

           = 34! / 6! 28!

           = 34 * 33 * 32 * 31 * 30 * 29 * 28! / 6! 28!

           =968330880 / 720

           = 1344904

Probability of selecting none of the correct six integers:

P(E) = E / A

       = 1344904 / 3838380

        = 0.350

Probability of selecting none of the correct six integers is 0.350

b) 48

Following the method used in part a)

(n,k) = n! / r! (n-r)!

n = 48

r = 6

48C6

=(48,6) = 48! / 6! ( 48 - 6)!

            = 48! / 6! ( 42 )!

            = 48*47*46*45*44*43*42! / 6!42!

            = 8835488640 / 720

            = 12271512

Let E be the event of selecting none of the correct six integers.

So using combinations we can find the total number of ways of selecting none of 6 integers from 48

n = 48 - 6 = 42

r = 6

42C6

= (42,6) = 42! / 6! ( 42 - 6)!

              = 42! / 6! 36!

              = 3776965920

              = 5245786

P(E) = E / A

       = 5245786/12271512

       = 0.427

c) 56

(n,k) = n! / r! (n-r)!

n = 56

r = 6

56C6

=(56,6) = 56! / 6! ( 56- 6)!

            = 56! / 6! ( 50 )!

            = 56*55*54*53*52*51*50! / 6! 50!

            = 23377273920/6

            = 32468436

Let E be the event of selecting none of the correct six integers.

So using combinations we can find the total number of ways of selecting none of 6 integers from 56

n = 56 - 6 = 50

(50,6) = 50! / 6! ( 50- 6)!

           = 50*49*48*47*46*45*44! / 44! 6!

           = 11441304000 / 6

           = 15890700

P(E) = E / A

       = 15890700 / 32468436

      = 0.489

d) 64

(n,k) = n! / r! (n-r)!

n = 64

r = 6

64C6

=(64,6) = 64! / 6! ( 64 - 6)!

            = 64! / 6! ( 58 )!

            = 64*63*62*61*60*59*58! / 6! 58!

            = 53981544960 / 720

            = 74974368

Let E be the event of selecting none of the correct six integers.

So using combinations we can find the total number of ways of selecting none of 6 integers from 64

n = 64 - 6 = 58

(58,6) = 58! / 6! ( 58- 6)!

           = 58*57*56*55*54*53*52! / 52! 6!

           = 29142257760/ 6

           = 40475358

P(E) = E / A

       = 40475358/ 74974368

      = 0.540

The probability of selecting none of the correct six integers in a lottery is, 0.350.

Number of integers given = 40

So, Total outcomes for choosing 6 from 40 integers.

         Number of arrangements [tex]=_{6}^{40}\textrm{C}[/tex]

                                                    [tex]=\frac{40!}{6!*34!} =3838380[/tex]

Since, we have to find probability of selecting none of the correct six integers in a lottery.

Remaining integer = 40 - 6 =34

Let favourable outcomes is selecting none of the correct six integers.

So, number of arrangements, = [tex]=_{6}^{34}\textrm{C}[/tex]

                                                 = [tex]\frac{34!}{6!*28!}=1344904[/tex]

Probability is defined as, divide favourable outcomes by total outcomes.

So, The probability of selecting none of the correct six integers in a lottery,

                            [tex]P=\frac{1344904}{3838380}=0.35[/tex]

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