write the expression and fully simplify

Answer:

1/6 (simplified)

Step-by-step explanation:

It's 3/18, but in most cases you should simplify unless it says to not.

Given:

z be inversely proportional to the cube root of y.

When y =0.064, then z =3.

To find:

a) The constant of proportionality k.

b) The value of z when y = 0.125.​

Solution:

a) It is given that, z be inversely proportional to the cube root of y.

[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]

[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex]              ...(i)

Where, k is the constant of proportionality.

We have, z=3 when y=0.064. Putting these values in (i), we get

[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]

[tex]3=k\dfrac{1}{0.4}[/tex]

[tex]3\times 0.4=k[/tex]

[tex]1.2=k[/tex]

Therefore, the constant of proportionality is [tex]k=1.2[/tex].

b) From part (a), we have [tex]k=1.2[/tex].

Substituting [tex]k=1.2[/tex] in (i), we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]

We need to find the value of z when y = 0.125.​ Putting y=0.125, we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]

[tex]z=\dfrac{1.2}{0.5}[/tex]

[tex]z=2.4[/tex]

Therefore, the value of z when y = 0.125 is 2.4.

Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n}[/tex]

or

[tex]n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For the given case, it is given that:

[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]

Let the constant of proportionality be k, then we have:

[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]

It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:

[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]

Thus,  the constant of proportionality k is 1.2. And the relation between z and y is:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]

Putting value y = 0.0125, we get:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]

Thus, for the given relation between y and z, we have:

Learn more about proportionality here:

https://brainly.com/question/13082482

Answer:

angle KPN=95 degree

Step-by-step explanation:

angle KPN = angle JPO (because they are vertically opposite angles)

Now,

angle JPO+angle LOP=180 degree(being co interior angles)

angle JPO + 85 =180

angle JPO =180-85

angle JPO =95

since angle JPO is equal to KPN ,angle KPN is 95 degree

Answer: [tex]\dfrac{49}{50}[/tex]

Step-by-step explanation:

Given

Length of the stick is [tex]2y\ m[/tex]

A piece of [tex]4y\ cm[/tex] is cut

We know, 1 m=100 cm

So, [tex]2y\ m[/tex] in cm is [tex]200y\ cm[/tex]

Remaining length after cut is

[tex]\Rightarrow 200y-4y=196y[/tex]

Fraction of length that is left after the cut is

[tex]\Rightarrow \dfrac{196y}{200y}\\\\\Rightarrow \dfrac{49}{50}[/tex]

Thus, [tex]\frac{49}{50}[/tex] fraction of original stick remains after cut

Answer:

D. 1.6

Step-by-step explanation:

magic

Answer:

D) 1.6

Step-by-step explanation:

Hope this helps!

Answer:

aef true and bcd false

hope u get well in your exams

Step-by-step explanation:

Answer:

Peter needs to get 36 problems correct to get 12 stars

Step-by-step explanation:

for every 3 correct answers, Peter gets 1 star

1/3

if he wants 12 stars he will have to get 'x' amount of questions correctly

considering this is constant, 1/3 will have to equal 12/x

[tex]\frac{1}{3} = \frac{12}{x} \\\\1x = 36\\[/tex]

1x = x, so you don't need to do anything to 36

therefore the answer is that you need to get 36 problems correct to get 12 stars

Answer:

x = -5 ±4sqrt(2)

Step-by-step explanation:

(x+5)²=32

Take the square root of each side

Sqrt((x+5)²)=±sqrt(32)

x+5 = ±sqrt(16*2)

x+5 = ±4sqrt(2)

Subtract 5 from each side

x+5-5 = -5 ±4sqrt(2)

x = -5 ±4sqrt(2)

Answer:

[tex]\bar x = 260.1615[/tex]

[tex]\sigma = 70.69[/tex]

The confidence interval of standard deviation is: [tex]53.76[/tex] to [tex]103.25[/tex]

Step-by-step explanation:

Given

[tex]n =20[/tex]

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}[/tex]

[tex]\bar x = \frac{5203.23}{20}[/tex]

[tex]\bar x = 260.1615[/tex]

[tex]\bar x = 260.16[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

[tex]\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}[/tex][tex]\sigma = \sqrt{\frac{94938.80}{19}}[/tex]

[tex]\sigma = \sqrt{4996.78}[/tex]

[tex]\sigma = 70.69[/tex] --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

[tex]c =0.95[/tex]

So:

[tex]\alpha = 1 -c[/tex]

[tex]\alpha = 1 -0.95[/tex]

[tex]\alpha = 0.05[/tex]

Calculate the degree of freedom (df)

[tex]df = n -1[/tex]

[tex]df = 20 -1[/tex]

[tex]df = 19[/tex]

Determine the critical value at row [tex]df = 19[/tex] and columns [tex]\frac{\alpha}{2}[/tex] and [tex]1 -\frac{\alpha}{2}[/tex]

So, we have:

[tex]X^2_{0.025} = 32.852[/tex] ---- at [tex]\frac{\alpha}{2}[/tex]

[tex]X^2_{0.975} = 8.907[/tex] --- at [tex]1 -\frac{\alpha}{2}[/tex]

So, the confidence interval of the standard deviation is:

[tex]\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }[/tex] to [tex]\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }[/tex]

[tex]70.69 * \sqrt{\frac{20 - 1}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{20 - 1}{8.907}[/tex]

[tex]70.69 * \sqrt{\frac{19}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{19}{8.907}[/tex]

[tex]53.76[/tex] to [tex]103.25[/tex]

Answer

x<12

Explanation

5(x+5)<85

5x+25<85

5x<85-25

5x<60

x<60/5

x<12

Answer:

[tex]x^2 = 2y[/tex] --- equation

[tex](x,y) = (0,\frac{1}{2})[/tex] --- focus

[tex]y = -\frac{1}{2}[/tex] --- directrix

[tex]Width = 2[/tex] ---- focal width

Step-by-step explanation:

Given

[tex]depth = 2[/tex]

[tex]diameter = 4[/tex]

Required

The equation of parabola

The depth represents the y-axis. So:

[tex]y = 2[/tex]

The diameter represents how the parabola is evenly distributed across the x-axis.

We have:

[tex]diameter = 4[/tex]

-2 to 2 is 4 units.

So:

[tex]x = [-2,2][/tex]

So, the coordinates of the parabola is:

[tex](-2,2)\ and\ (2,2)[/tex]

The equation of the parabola is calculated using:

[tex]x^2 = 4py[/tex]

Substitute (-2,2) for (x,y)

[tex](-2)^2 = 4p*2[/tex]

[tex]4 = 8p[/tex]

Divide by 8

[tex]p = \frac{4}{8}[/tex]

[tex]p = \frac{1}{2}[/tex]

So, the equation is:

[tex]x^2 = 4py[/tex]

[tex]x^2 = 4 * \frac{1}{2} * y[/tex]

[tex]x^2 = 2y[/tex]

The defining features

(a) Focus

The focus is located at:

[tex](x,y) = (0,p)[/tex]

[tex](x,y) = (0,\frac{1}{2})[/tex]

(b) Directrix (y)

[tex]y = -p[/tex]

[tex]y = -\frac{1}{2}[/tex]

(c) Focal width

[tex]Width = 4p[/tex]

[tex]Width = 4*\frac{1}{2}[/tex]

[tex]Width = 2[/tex]

Answer:

Base = 7

Height = 10

Area = 35

Step-by-step explanation:

Area is 35.

7 * 10 = 70

70/2 = 35

Base = 7 (Given)

Height = 10 (Given)

Answer:

base: 7 (yd)

height: 10 (yd)

area: 35 (yd²)

Step-by-step explanation:

To find the area of a triangle, multiply the base and height, then, divide the product by 2. The quotient is the area of the triangle.

[tex]7*10=70.[/tex]

[tex]70/2=35.[/tex]

I, therefore, believe the area of this triangle is 35 yd.

Answer:

Step-by-step explanation:

The area of 1 face is s^2

The area of 6 faces is 6s^2

6s^2 = 433.5                 Divide by 6

s^2 = 433.5 / 6

s^2 = 72.25                   Take the square root of both sides

sqrt(s^2) = sqrt(72.25)

s = 8.5

Normally you would find the volume of parallelepiped by using L * W * H

Since L W and H are all equal in a cube, the volume = s^3

S^3 = 8.5^3 = 614.125

Answer:$181.81

Step-by-step explanation:300/198

=1.5151515….multiple by 120

=181.818181

Answer:

[tex] {x}^{2} + 2x + 1 = 17 \\ {x}^{2} + 2x - 16 = 0 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} \\ x = \frac{ - 2± \sqrt{68} }{2} \\ x = \frac{ - 2±2 \sqrt{17} }{2 } \\ x = - 1± \sqrt{17} [/tex]

Answer:

20 carros

Step-by-step explanation:

Dado que un automóvil tiene cuatro neumáticos, multipliqué la C por 4

M es para motocicletas. ya que las motos tienen 2 neumáticos. Multipliqué M por 2

de hecho, la respuesta está en la imagen de arriba

Answer:

272 cups

Step-by-step explanation:

so you need 34 cups for one batch if you need to make 8 batches then you would need to multiple them to find the answer.

34*8=272

Answer:

Pedro vendió = 320 calendarios

Katrina vendió = 200 calendarios

Step-by-step explanation:

Dejemos que el número de calendarios

Pedro vendió = x

Katrina vendió = y

Pedro y su compañera Karina vendieron 520 calendarios en diciembre.

x + y = 520 .... Ecuación 1

Pedro vendió 120 calendarios más que su socio.

x = y + 120

Sustituimos y + 120 por x

y + 120 + y = 520

2 años = 520 - 120

2 años = 400

y = 400/2

y = 200 calendarios

Resolviendo para x

x = y + 120

x = 200 + 120

x = 320 calendarios

Por lo tanto,

Pedro vendió = 320 calendarios

Katrina vendió = 200 calendarios

Answer:

yes angle measures 84°as they are alternate angles

Answer:

[tex]secA = \frac{65}{63}[/tex]

Step-by-step explanation:

[tex]cosec A = \frac{65}{16}\\\\sin A = \frac{1}{cosecA} = \frac{16}{65}\\\\cos^2 A = 1 - sin^2 A[/tex]

        [tex]= 1 - (\frac{16}{65})^2\\\\=\frac{4225-256}{4225}\\\\=\frac{3969}{4225}\\[/tex]

[tex]cos A = \sqrt{\frac{3696}{4225}} = \frac{63}{65}[/tex]

[tex]secA = \frac{1}{cosA} = \frac{65}{63}[/tex]

Answer:

$389.73 in change

Step-by-step explanation

500-( (18.95 x 3)+(26.71 x 2) )=

500-(56.85+53.42)=

500-110.27=

389.73

Answer:

It is x=908.

Might be wrong tho so dont jump me

Answer: 908

Step-by-step explanation:

x/4 = 89 + 138

x/4 = 227

x = 227 x 4

x = 908

Answer:

Option 3 : ∠BAC = 60°

Step-by-step explanation:

Exterior angle = sum of interior opposite angles.

That is ,

            2x + 3x = 150°

              5x = 150°

                  x = 30

∠BAC = 2x = 2 × 30 = 60°

Answer:

The measure of <BAC is 60

Answer:

-1049

Step-by-step explanation:

Let's assume it's a arithmetic sequence

a_1 = -26

d = a_2-a_1 = -11

==> a_94 = a_1+93*d = -1049

Answer:

-1071

Step-by-step explanation:

Let the common difference be 'd'.

d is 11

Find the difference from a (first term) and 11

Then use (n-1)

Answer: Each fraction is greater than the previous fraction.

Step-by-step explanation:

The fractions given are:

2/3, 4/6, 8/12, 16/24

Note that

2/3 = 4/6 = 8/12 = 16/32

The Fractions are all equal. Each fraction is equivalent to 2/3

The pattern used here is:

2/3 × 2/2 = 4/6

4/6 × 2/2 = 8/12

8/12 × 2/2 = 16/24

16/24 × 2/2 = 32/48

Each fraction is equal to the previous fraction in the pattern multiplied by 2/2

Also, the next fraction in the pattern is 32/48.

The statement that "Each fraction is greater than the previous fraction" is incorrect. The fractions are all equal.

Answer:

2

Step-by-step explanation:

she will have 2 arangments of one rose and two daisies.

Answer:

2

Step-by-step explanation:

group off the daisies and rose

2 Rose's

4 raises

in order to make it identical

group 1 consist of ( 1 rose and 2 daisies)

group 2 consist of (1 rose and 2 daises)

only 2 bouquets

Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2 , then

y = 2x + c ← is the partial equation

To find c substitute (3, 5) into the partial equation

5 = 6 + c ⇒ c = 5 - 6 = - 1

y = 2x - 1 ← equation of line