Which expression is equivalent to
4^sqrt 6 / 3^sqrt2

Answer:

  36 tablets

Step-by-step explanation:

We are asked to find the number of tablets of a particular mass that are required to give a specific mass-to-volume ratio for a given volume of solution. The units used are all SI (metric) units.

__

The International System of units (abbreviated SI in all languages) defines seven base units and a number of derived units. The base unit for length is the meter. For mass, the base unit is the kilogram. The derived unit for volume is the liter, which is 1/1000 of a cubic meter.

Currently, there are 20 prefixes defined that signify powers of 10 ranging from 10^-24 to 10^24. These are used in front of the abbreviations for units. Useful here are the prefixes kilo- and milli-, standing for 10^3 and 10^-3, respectively. The relevant abbreviations are ...

In this problem, the volume of syrup used is 180 ml, or 180×10^-3 liters. The mass of medicine in one tablet is 10 mg, or 10×10^-3 grams.

__

We desire a solution with a concentration of 2 mg/ml. We want 180 ml of the solution, so the mass of medicine that needs to be incorporated is ...

  (180 ml)×(2 mg/ml) = 360 mg

number of tablets

Each tablet supplies 10 mg of medicine. To get 360 mg of medicine, we need n tablets, such that ...

  n(10 mg) = 360 mg

  n = (360 mg)/(10 mg) = 36 . . . . tablets

36 tablets of 10 mg each are needed to mix with 180 ml of syrup to give 2 mg/ml.

Step-by-step explanation:

the median is the value, where half of the other values is smaller (or equal), and the other half bigger (or equal).

with an even number of data points that is not directly possible to find.

in this case the 2 middle values are taken and their mean value is the median.

in our case, the 2 middle values are 12 and 14.

their mean value is

(12+14)/2 = 26/2 = 13

so,

13 is the median (even though if is not a data point itself).

Answer:

y = 40 degrees

Step-by-step explanation:

All three interior angles of a triangle sum to 180 degrees.

2y   + y+10  + 50 = 180

3y + 60 = 180

3y = 120

y = 40  

Answer:

[tex]2( \frac{2}{5} x + 2) = \frac{4}{5} x + 4[/tex]

Step-by-step explanation:

Use the distributive property.

2y=x+10

3y=3x+15

2y-10=x

3y=3(2y-10)+15

2y-10=x

3y=6y-30+15

2y-10=x

0=3y+15

2y-10=x

3y=15

x=2y-10

y=5

2y=x+10

2×5=x+10

x=0

x=0, y=5

Answer:

3.61cm^2

Step-by-step explanation:

1.9 * 1.9 = 3.61

Hi student, let me help you out! :)

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We are asked to find the slope of (-4, -7) and (-2, -19).

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's the slope formula:

[tex]\star~\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]

Where

y2 and y1 are y-coordinates

x2 and x1 are x-coordinates

Input the values, which are:

-19: y2

-2: x2

-7: y1

-4: x1

[tex]\star~\mathrm{\cfrac{-19-(-7)}{-2-(-4)}}[/tex]

[tex]\star~\mathrm{\cfrac{-19+7}{-2+4}}[/tex]

Simplify!

[tex]\star~\mathrm{\cfrac{-12}{2}}[/tex]

[tex]\star~\mathrm{-6}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students out :)

Answer:

4. x = 9 and y = 18

Step-by-step explanation:

Hello there!

When given such a problem we have to methods to handle this:

On this problem, let's limit ourself to substitution method;

x + y = 27 ..................... eq.1

y = 2x ........................ eq.2

Eq.2 is already manipulated. Substitute it into eq.1

x + y = 27

=> x + 2x = 27

3x = 27

x = 9

Substitute x into eq.2

y = 2 (9)

= 18

In terms of x and y;

(x, y) => (9, 18)

I hope this helps you.

Have a nice time and nice studies.

Answer:

4x ÷ 7

Step-by-step explanation:

the product of 4 and a number (x)

would be 4x. Then you would divide by 7.

Answer:

(-4,1)

Step-by-step explanation:

Factoring, Guess and check.

To factorize a polynomial you need to find the zeros, and then you can write the polynomial as a product of bynomials.

For a polynomial of the form:

[tex]p(x) = A_n*x^n + A_{n-1}*x^{n-1} + ... + A_1*x + A_0[/tex]

We define the zeros as the values of x such that:

p(x) = 0.

On the above case, the degree of the polynomial is n (the maximum exponent). Then the number of zeros of the polynomial is n (same as the degree).

Once we know the n zeros, we can factorize the polynomial as:

[tex]p(x) = A_n*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]

For example, for the polynomial:

[tex]p(x) = 2x^2 - 8[/tex]

The two zeros are x = 2 and x = -2, then it can be rewriten as:

[tex]p(x) = 2*(x + 2)*(x - 2)[/tex]

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Answer:

see explanation

Step-by-step explanation:

a translation of 3 squares right means add 3 to the x- coordinate

a translation of 3 squares up means add 3 to the y- coordinate

then

(1, 1 ) → (1 + 3, 1 + 3 ) → (4, 4 )

(3, 1 ) → (3 + 3, 1 + 3 ) → (6, 4 )

(1, 4 ) → (1 + 3, 4 + 3 ) → (4, 7 )

Answer:

[tex](5x+3)(2x+1)[/tex]

Step-by-step explanation:

- Sum-product method

For a polynomial of the form [tex]ax^2+bx+c[/tex]

We rewrite the middle term as a sum of two terms whose product is

[tex]a*c = 10*3 = 30[/tex] and whose sum is [tex]b = 11[/tex]

[tex]10x^2 + 11x + 3[/tex]

[tex]10x^2 + 6x + 5x + 3 -- > (3*10 = 6*5), (6+5 = 11)[/tex]

- Factor using the greatest common factors (GCF)

[tex]2x(5x + 3) + 1(5x + 3)[/tex]

- Final Answer

[tex]= (5x+3)(2x+1)[/tex]

The probability that can be chosen by Jake will be 33.5%.

The area of the whole dartboard will be:

= πr²

where r will be:

= 3 + (4 × 4)

= 3 + 16

= 19

Area = π(19)² = 361π²

The area of 30, 40, and 50 points will be:

= π × [3 + (2 × 4)]²

= 121π²

The probability will be:

= (361π - 121π) × 100

= 33.5%

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The amount of iced tea left in quartz is  3 quartz

The coach makes 9 quarts of iced tea.

she fills 12 bottles with 2 cups of iced tea each to share with her team.

1 quartz = 4 cups

Therefore, she shared the following amount of tea in cups:

amount shared = 12 × 2 = 24 cups

Then, let's convert to quartz,

4 cups = 1 quartz

24 cups = ?

amount shared in quartz = 24 / 4 = 6 quarts

Therefore,

the amount of ice tea left = 9 - 6 = 3 quartz

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Answer:

15

Step-by-step explanation:

Let 2n+1 be the first odd integer.

Therefore, the consecutive odd integers will be 2n+3 and 2n+5

If the sum of the consecutive odd integers is 51 then:

⇒ 2n + 1 + 2n + 3 + 2n + 5 = 51

⇒ 6n + 9 = 51

⇒ 6n = 42

⇒ n = 7

To find the values of the integers, substitute the found value of n into the expressions:

Therefore, the three consecutive odd integers that sum to 51 are 15, 17 and 19.  The smallest of which is 15.

Answer:

1 / 1024

Step-by-step explanation:

Each flipping has 1/2 chance

In ten flippings:

[tex](\frac{1}{2} )^{10} =\frac{1^{10} }{2^{10} } =\frac{1}{1024}[/tex]

Hope this helps

Answer:

the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal

Answer:

I was taught like this.

Corresponding has emphasis on the word pond

Fish live in a pond

Therefore, it has to be an angle F

Answer:

X=70

Step-by-step explanation:

aw we can for a triangle, where the 2 angles are complementary from the outer ones, so the 2 angles are 50, and 60

so the third one will be 70

The formula for calculating the height is h = 3V/πr²

The formula given is the formula for calculating the volume of a cone

V = 1/3πr²h

where

h is the height

r is the radius

Make h the subject of the formula

Cross multiply

3V = πr²h

Divide both sides by πr²

3V/πr² = πr²h/πr²

h = 3V/πr²

Hence the formula for calculating the height is h = 3V/πr²

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Answer:

  x ≈ 8.99

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.

__

The tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(angle of elevation) = (tower height)/(length of shadow)

Solving for the length of shadow, we have ...

  length of shadow = (tower height)/tan(angle of elevation)

The difference in shadow lengths is 2x for the two different angles, so we have ...

  2x = 24.57/tan(30°) -24.57/tan(45°)

__

Dividing by 2 and factoring out the tower height, we have ...

  x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)

  x ≈ 8.993244

The value of x is about 8.99.

The area of the triangle DEF is 2 square units

The given parameters are:

D(9,-8), E(8,-3), and F(2,-5),

The area of the triangle is calculated using:

Area = 0.5|x1 * (y2 -y3) + x2 * (y1 -y3) + x3 * (y2 -y1) |

This gives

Area = 0.5|9 * (-3 + 5) + 8 * (-8 + 5) + 2 * (-3 + 8) |

Evaluate

Area = 0.5|4|

Expand

Area = 2

Hence, the area of the triangle DEF is 2 square units

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Answer:

z=98 degrees

x=64 degrees

y=18 degrees

Step-by-step explanation:

y is congruent to 18 since theyre opposite of eachother, same with x and 64. find z by using the straight 180 line. (180=64+18+z, so z=98)

Answer:

-66

Step-by-step explanation:

add the numbers

-26 -37 = -66

[tex] - 26 - 37 = - 63[/tex]

Whenever the sign of the numbers is same , add them but don't forget the negative sign.

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Considering the given function, we have that:

a) D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.

b) D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.

The distance that the family is from home, after t hours of driving, is given by:

D(t) = 3260 - 55t.

Then, after 12 hours, the distance is given by D(12), that is:

D(12) = 3260 - 55 x 12 = 2600.

D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.

D(t)=2490, hence:

3260 - 55t = 2490

55t = 770

t = 770/55

t = 14

D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.

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