9. If ATLY ~ ACHK, find the value of x.

Answer:

[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex]

[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex]

[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex]

Step-by-step explanation:

Given

[tex]x^\frac{3}{5}[/tex]

Required

The equivalent expressions

We have:

[tex]x^\frac{3}{5}[/tex]

Expand the exponent

[tex]x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}[/tex]

So, we have:

[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex] ----- this is equivalent

Express 1/5 as roots (law of indices)

[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex] ------ this is equivalent

The above can be rewritten as:

[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex] ------ this is equivalent

Answer:

x = 1/5

Step-by-step explanation:

5(3x + 4) = 23

Distribute

15x+20 = 23

Subtract 20 from each side

15x+20-20 = 23-20

15x = 3

Divide by 15

15x/15 = 3/15

x = 1/5

Answer:

[tex]x = 0.2[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]5(3x + 4) = 23[/tex]

[tex](5 * 3x) + (5 * 4) = 23[/tex]

[tex](15x) + 20 = 23[/tex]

Step 2:  Subtract 20 from both sides

[tex](15x) + 20 - 20 = 23 - 20[/tex]

[tex]15x = 3[/tex]

Step 3:  Divide both sides by 15

[tex]\frac{15x}{15} = \frac{3}{15}[/tex]

[tex]x = \frac{1}{5}[/tex]

[tex]x = 0.2[/tex]

Answer:  [tex]x = 0.2[/tex]

Step-by-step explanation:

6a. Both the x and y coordinates are negative so this means isn't must be in the Third Quadrant.

6b. The measure of this using the unt circle is

[tex] \cos(x) - \frac{1}{2} [/tex]

[tex] \sin(x) = - \frac{ \sqrt{3} }{2} [/tex]

In the unit circle, this occurs about

an angle of 240 degrees. We can find coterminal angles within the interval of 2 pi to -2 pi. Just subtract 260 from theta.( which is 240)

[tex]240 - 360 = - 120[/tex]

So the angles in the interval is

240, -120.

6c. pi/2 is the same as 90 degrees so this means that

[tex](240 + 90) = 330[/tex]

In the unit circle, we know that at 330 degrees,

[tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]

[tex] \sin(330) = \frac{1}{2} [/tex]

So the coordinates are

(sqr root of 3/2, 1/2).

6d. pi is the same as 180 degrees so this means that

[tex](240 - 180) = 60[/tex]

In the unit circle, we know that 60 degrees,

[tex] \cos(60) = \frac{1}{2} [/tex]

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

So the coordinates are

(1/2, sqr root of 3/2)

9514 1404 393

Answer:

  x = 14 cm

Step-by-step explanation:

We can only solve for x if the triangles are similar. The arrows on the left and right legs say those are parallel. Since alternate interior angles at each of the transversals are congruent, the triangles are AA similar.

ΔABC ~ ΔDEC, so we have ...

  EC/ED = BC/BA

  x/(18 cm) = (35 cm)/(45 cm)

  x = (18 cm)(7/9) = 14 cm

Answer:

there are infinite solutions

Step-by-step explanation:

if you add y-3 to both sides of the first equation, you will see that it is equal to the second equation, so they are the same line. Therefore, there are infinite solutions to this system

Answer:

17 units

Step-by-step explanation:

Use the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Plug in the points and simplify:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(-8 - 7)^2 + (0-8)^2}[/tex]

[tex]d = \sqrt{(-15)^2 + (-8)^2}[/tex]

[tex]d = \sqrt{225 + 64[/tex]

[tex]d = \sqrt{289[/tex]

[tex]d = 17[/tex]

So, the distance between the points is 17 units

Answer:

17.637 ounces

Step-by-step explanation:

35.274 ounces is 1 kilogram so divide 35.274 by 2

Answer:

[tex]35.36,44.64[/tex]

Step-by-step explanation:

Sample size [tex]n=40[/tex]

Mean weight [tex]\=x =67[/tex]

Standard deviation [tex]\sigma=11.4[/tex]

Confidence Interval [tex]CI=0.99[/tex]

\alpha==0.01

Therefore

[tex]Z_{\frac{\alpha}{2}}=Z_[0.005][/tex]

From table

[tex]Z_{\frac{\alpha}{2}}=2.576[/tex]

Generally, the equation for Margin of error is mathematically given by

[tex]M.E=Z_{\frac{\alpha}{2}}*(\frac{\sigma}{sqrt{n}}[/tex]

[tex]M.E=2.576*(\frac{11.4}{\sqrt{40}}[/tex]

[tex]M.E=4.64[/tex]

Therefore Estimated mean is

[tex]\=x-M.E<\mu <\=x +E[/tex]

[tex]40-4.64<\mu< 40+4.64[/tex]

[tex]35.36<\mu < 44.64[/tex]

[tex]35.36,44.64[/tex]

Answer:

0.0625

Step-by-step explanation:

Given that :

Number of toppings = 4 (ground beef, black beans, refried beans, and sour cream)

The probability of choosing any particular topping at random from the four is :

Probability = required / total possible outcomes

Hence, P = 1 / 4 = 0.25

Hence, the probability of choosing : getting refried bean and sour cream :

P(refried bean) = 1/4

P(sour cream) = 1/4

P(refried bean and sour cream) = 1/4 * 1/4 = 1/16 =

0.0625

Answer:

D

Step-by-step explanation:

8 and 3/5 = 8.2 and 8.2 is between 8 and 9 so the answer is D.

Answer:

Step-by-step explanation:

a) categorical

b) add all of the numbers and divide by how many numbers there were.

c) outliers means any that were far away from the rest of the data

d) not entirely, you can make an estimate based on it, but nat an exact answer.

Answer:

C

Step-by-step explanation:

Answer:

C) $2,762.07

you can use a compound interest calculator to find the answer

Step-by-step explanation:

Area ABC=1/2ab×sin C

=1/2 ×20×10 ×Sin C

Sin C =100

Answer:

162.4 miles

Step-by-step explanation:

We can write a ratio to solve

116 miles            x miles

----------------- = ------------

5 gallons           7 gallons

Using cross products

116*7 = 5x

Divide by 5

812 /5 = 5x/5

162.4 =x

162.4 miles

Answer:

The zeroes of the function are: 3 and 4

Step-by-step explanation:

Answer:

The initial value of the laser printers was $1,900, and the value decreases by 18% each year.

Step-by-step explanation:

Here ya go bestie <3

Answer:

x = - 10

Step-by-step explanation:

(6x -5x) / 10 = - 1

x = - 10

Answer:

1250 supermarkets

Step-by-step explanation:

Given

[tex]\frac{dN}{dt} = N(1 - 0.0008N)[/tex]

[tex]N(0) = 1[/tex]

Required

Number of supermarkets over a long period of time

To do this, we simply set

[tex]\frac{dN}{dt} = 0[/tex]

So, we have:

[tex]N(1 - 0.0008N) = 0[/tex]

Split

[tex]N = 0\ or\ 1 - 0.0008N = 0[/tex]

Solve: [tex]1 - 0.0008N = 0[/tex]

Collect like terms

[tex]0.0008N = 1[/tex]

Make N the subject

[tex]N = \frac{1}{0.0008}[/tex]

[tex]N = 1250[/tex]

So:

[tex]\lim_{t \to \infty} N(t) = 1250[/tex]

Answer:

how many times should u use the metal rod ??

Answer:

isosceles acute

Step-by-step explanation:

We have two sides that are equal so the triangle is isosceles

None of the angles are larger than 90 degrees so non of the angles are obtuse,  and none of the angles are 90 degrees, so the triangle is acute ( which means the angles are all less than 90 degrees)

= 2025

When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)

For this, you divide the given lengths using the numbers that divides all through.

I have added an image to this answer. Go through it for more explanation

Answer:

c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.

Step-by-step explanation:

Given :

Groups:

x1 = 69 ; s1 = 19 ; n1 = 38

x2 = 32 ; s2 = 14 ; n2 = 37

1 - α = 1 - 0.95 = 0.05

Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :

The confidence interval obtained is :

(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between

(24.32 ; 39.68) .

Answer:

B. The question may not be directly stated.

Answer:

obtuse                    

aniuhafjhnfajfnha

Answer:

absolutely yes, because pythagorean theorem is used in a right triangle

and when we match a line from the tee to the hole, we have a right triangle

Step-by-step explanation:

Answer:

The rate at which the distance between the two cars is increasing is 30 mi/h

Step-by-step explanation:

Given;

speed of the first car, v₁ = 24 mi/h

speed of the second car, v₂ = 18 mi/h

Two hours later, the position of the cars is calculated as;

position of the first car, d₁ = 24 mi/h  x 2 h  = 48 mi

position of the second car, d₂ = 18 mi/h  x 2 h = 36 mi

The displacement of the two car is calculated as;

displacement, d² = 48² + 36²

                        d² = 3600

                        d = √3600

                        d = 60 mi

The rate at which this displacement is changing = (60 mi) / (2h)

                                                                                 = 30 mi/h