In the following table y is proportional to x.



What is the constant of proportionality?


A. 5/14


B. 5/7


C. 7/5


D.20/7

(a) 67900

(b) 291700

(a) 25 x 679 x 4

Rearrange the terms starting with the smallest

4 x 25 x 679

The property used here is the commutative property of multiplication which states that the order in which these numbers are multiplied does not matter.

Now solve

4 x 25 x 679 = 67900

(b) 2917 x 102 - 2917 x 2

Factor out the common terms

2917(102 - 2)

Using the distributive property which states that when a number is multiplied by the sum or difference of two numbers, the result is the same as multiplying each of the two numbers by the number and then adding or subtracting the products.

Now solve

2917(102 - 2) = 2917(100)

= 291700

Answer:

4ft

Step-by-step explanation:

The bottom of the ladder will be 16.25 feet from the bottom of the building.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

As per the situation, we create a right triangle as shown.

Let x be the distance from the bottom of the building to the bottom of the ladder.

Using Pythagoras's theorem, then, we have:

x² + 31² = 35²

Simplifying this equation, we get:

x² = 35² - 31²

x² = 264

x = 16.25 (rounded to the nearest tenth of a foot).

Therefore, the bottom of the ladder will be 16.25 feet from the bottom of the building.

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Answer:

[tex]v=<\sqrt{32}cos(319.11^{\circ}),\sqrt{32}sin(319.11^{\circ})>[/tex] or [tex]v=\sqrt{32}cos(319.11^{\circ})i+\sqrt{32}sin(319.11^{\circ})j[/tex]

Step-by-step explanation:

Find the magnitude of [tex]<2\sqrt{6},-2\sqrt{2}>[/tex]:

[tex]||v||=\sqrt{(2\sqrt{6})^2+(-2\sqrt{2})^2}[/tex]

[tex]||v||=\sqrt{24+8}[/tex]

[tex]||v||=\sqrt{32}[/tex]

Find the direction angle of [tex]<2\sqrt{6},-2\sqrt{2}>[/tex]:

[tex]\alpha=tan^{-1}|\frac{-2\sqrt{2}}{2\sqrt{6}}|[/tex]

[tex]\alpha=tan^{-1}|-\frac{\sqrt{3}}{2}|[/tex]

[tex]\alpha=tan^{-1}(\frac{\sqrt{3}}{2})[/tex]

[tex]\alpha=40.89^{\circ}[/tex]

Since [tex]\alpha=40.89^{\circ}[/tex] is our reference angle, we determine our direction angle [tex]\theta[/tex] by verifying our angle is in Quadrant IV, which is where the vector is located. Therefore, [tex]\theta=360^{\circ}-\alpha=360^{\circ}-40.89^{\circ}=319.11^{\circ}[/tex]

To represent a vector's magnitude and direction in trigonometric form, we use the form [tex]v=<||v||cos\theta,||v||sin\theta>[/tex] or [tex]v=||v||cos\theta i+||v||sin\theta j[/tex].

In conclusion, the trigonometric form of the vector is:

[tex]v=<\sqrt{32}cos(319.11^{\circ}),\sqrt{32}sin(319.11^{\circ})>[/tex] or

[tex]v=\sqrt{32}cos(319.11^{\circ})i+\sqrt{32}sin(319.11^{\circ})j[/tex]

Answer:

x = 18

mZT = 71º

Step-by-step explanation:

Complementary angles total 90º

(3x + 17) + 19 = 90

Subtract 19 from both sides

3x + 17 = 71

mZT = 71º

Subtract 17 from both sides

3x = 54

Divide both sides by 3

x = 18

Answer:

12

Step-by-step explanation:

y = 3 so

4 × 3 = 12

The value of 4y at y=3 is 12.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Expression : 4y

Now, we have to put y= 3

So, 4y

= 4(3)

= 12

Hence, the value of 4y at y=3 is 12

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Answer:

[tex]y = 10x[/tex]

Step-by-step explanation:

Given

The attached plot

Required

The line of the best fit using [tex](8,80)[/tex] and [tex](2,20)[/tex]

We have:

[tex](x_1,y_1) = (8,80)[/tex]

[tex](x_2,y_2) = (2,20)[/tex]

Calculate slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{20 - 80}{2- 8}[/tex]

[tex]m = \frac{-60}{-6}[/tex]

[tex]m = 10[/tex]

The equation is then calculated using:

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

[tex]y = 10(x - 8) + 80[/tex]

Expand

[tex]y = 10x - 80 + 80[/tex]

[tex]y = 10x[/tex]

Multipuly po ba (15;000 7%)

Answer:

b

Step-by-step explanation:

make g by itself -> inequality becomes g>-1. Answer choice b fits the criteria

Answer:

8

Step-by-step explanation:

all numbers must be positive when you have the lines on the side

Answer:

8

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Well the answer is 3,375

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

C. The number of hours she babysits

Step-by-step explanation:

In this situation, the number of hours she babysits is the independent variable.

This is because it will directly influence the amount of money that she earns, which is the dependent variable.

For example, working for 1 hour will earn her $15.

So, the correct answer is C. The number of hours she babysits

Answer:

aaaaa

Step-by-step explanation:

Answer:

I think it’s A

Step-by-step explanation:

the probability is 7/15

Step-by-step explanation:

because there are 7 girls and 8 boys

Complete Question

A two-state system is in an environment at temperature 500 K. The energy of state 1 is[tex]E_1=4.1e-20 J[/tex], and the energy of state 2 is [tex]E_2= 5.7e-20 J[/tex]. Let P(1) be the probability of finding the system in state 1, and be the probability of finding the system in state 2. What is the ratio P(2)/P(1)

Answer:

 [tex]X=0.0984[/tex]

Step-by-step explanation:

From the question we are told that:

Temperature T=500 K

Energy of state 1 [tex]E_1=4.1e-20 J[/tex],

Energy of state 2 is [tex]E_2= 5.7e-20 J[/tex]

Generally the equation for Probability of finding the system in state is mathematically given by

 [tex]P(1)=e ^{\frac{-E_1}{KT}}[/tex]

Therefore

For Probability of finding the system in state 1 [tex]P(1)[/tex]

 [tex]P(1)=e ^{\frac{-E_1}{KT}}[/tex]

Where

   K is Boltzmann constant

   [tex]K=1.38*10^{-23}[/tex]

 [tex]P(1)=e ^{\frac{-(4.1e-20 J)}{1.38*10^{-23}*500}}[/tex]

For Probability of finding the system in state 1 [tex]P(2)[/tex]

 [tex]P(2)=e ^{\frac{-(5.7e-20 J)}{1.38*10^{-23}*500}}[/tex]

Generally the equation for The Ratio of [tex]P(2)[/tex] and [tex]P(2)[/tex] is mathematically given by

 [tex]X=\frac{P(2)}{p(1)}[/tex]

 [tex]X=e ^{\frac{E_1-E_2}{KT}}[/tex]

 [tex]X=e ^{\frac{-(4.1-5.7)e-20 J)}{1.38*10^{-23}*500}}[/tex]

 [tex]X=0.0984[/tex]

Answer:

Option b is correct answer

Step-by-step explanation:

The complete question is attached herewith

Solution

The equation of a line in given by

y=a +bx where

a is the Y- intercept and

b is the  slope

From the given piece of information, we can derive that

coefficient of intercept = 10.1  

coefficient of fertilizer= 1.150

Substituting the given values in above equation, we get -

y=10.1+1.150x

Option b is correct answer

19,683

Hope this Helped!

Answer:

3.333 hours

Step-by-step explanation:

Given the total distance is 30 miles, and boat 1 travels at 3 mph and boat 2 travels at 6 mph, and the time for both is the same. Distance is speed S times time T so

30 = D(boat 1) + D(boat 2)

30 = (S1 * T) + (S2 * T)

30 = 3T + 6T

30 = 9T

3.333 = T

Answer:

How many thirds are equal to 2/6?

1/3 = 1/3

2/6 = 1/3

3/9 = 1/3

4/12 = 1/3

Step-by-step explanation:

I hope that this answer helps you to understand your question more thoroughly. If you have any other questions, please put them below.  

Have a great rest of your day/night!

1 thirds

divide 2/6 by 2 and you get 1/3. or multiply 1/3 by two and you get 2/6.

Answer:

Step-by-step explanation:

1.C. circumference

2.D. 25.12 decimeters

Solution

C=2πr=2·π·4≈25.13274

3.B. 28.26 meters

Using the formulas

C=2πr

d=2r

Solving for C

C=πd=π·9≈28.27433m

4.B. 25.12 meters

Using the formulas

C=2πr

d=2r

Solving for C

C=πd=π·8≈25.13274m

5.B. 21.98 meters

Using the formulas

C=2πr

d=2r

Solving for C

C=πd=π·7≈21.99115m

Answer:

D 34

Step-by-step explanation:

i hope you understand

Answer: hello! have a good day! :)))

P = 2

Answer:

2,144.66 miles³

Step-by-step explanation:

v = (4/3)πr³

v = (4/3)π(8³)

v = 2,144.6605848506

Rounded

2,144.66 miles³

Answer:

11+y > -33

Step-by-step explanation:

Answer:

You wrote

"Which of the following" Meaning there's should be options present.

But Going with the statement...

The sum of 11 and y is greater than -33

I'd say

11 + y > -33.

Answer:

20 × 9= 180

...............................

Hi there!

[tex]\large\boxed{180 u^2}[/tex]

Use the following formula to solve for the area:

A = b × h

Plug in the given numbers:

A = 20 ×  9 = 180 units²

Answer:

[tex]154m^{2}[/tex]

Step-by-step explanation:

8 · 7 = 56m (horizontal rectangle shape) the width was given by subtracting the total of the width (23m) minus (16m).

5 · 8 = 40m (square shape) Subtract 8m - 3m = 5m.

6 · 8 = 48m (square shape to the left of the polygon)

2 · 5 = 10m  (small rectangle shape bottom left) 8 - 6 = 2 for the length and 5 for the width by 8 - 3 = 5

56m + 40m + 48m + 10m = 154 [tex]m^{2}[/tex]

Answer:

Jeffery because the other dude go the 2 numbers wrong (he put the x coordinates on y and y on x)

Answer:

7 socks were sold

Step-by-step explanation:

7*8=56

11-7=4

4×11=44

56+44=100

This proves the answer of 7 to be correct