Which expressions are equivalent to the one below? Check all that apply.

16^x/4^x

Answer:

The proportion that can be used to estimate the height of the tree is option;

A. [tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex]

Step-by-step explanation:

The given parameters in the question are;

The medium through which the person looks at the top of the tree = A mirror

The angle formed by the person and the tree with the ground = Right angles = 90°

The distance of the person from the mirror, d₁ = 5 ft.

The height of the person, h₁ = 6 ft.

The distance of the tree from the mirror, d₂ = 12 ft.

The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂

Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;

TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar

The corresponding legs are;

The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively

The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively

∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR

The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB

Given that θ₁ = θ₂, we have;

tan(θ₁) = tan(θ₂)

∴ tan(∠TMR) = tan(∠AMB)

[tex]tan\angle X = \dfrac{Opposite \ leg \ length \ to \ reference \ angle}{Adjacent \ leg \ length \ to \ reference \ angle}[/tex]

[tex]tan(\angle TMR) = \dfrac{TR}{MR} = \dfrac{h}{12}[/tex]

[tex]tan(\angle AMB) = \dfrac{AB}{BM} = \dfrac{6}{5}[/tex]

From tan(∠TMR) = tan(∠AMB), we have;

[tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex]

[tex]\therefore h = \dfrac{6 \, ft.}{5 \, ft.} \times 12 \, ft. = 14.4 \, ft.[/tex]

The height of the tree, h = 14.4 ft.

Therefore, from the proportion [tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex] the height of the tree can be estimated.

Answer:

The evidence does not support the math chairperson's claim that the percentage is no longer 40%

Step-by-step explanation:

The known population percentage of research in mathematics published by US authors = 40%

The proportion, p = 0.40

Therefore, q = 1 - p = 1 - 0.4 = 0.6

The number of articles in the sample = 130

The number of articles by US authors in the sample = 62

Therefore, the proportion of US authors in the sample, [tex]\hat p[/tex] = (62/130) × 100 =

[tex]0.4\overline{769230}[/tex]

∴ The percentage of US authors in the sample ≈ 47.7%

The null hypothesis, H₀; p = 0.4

The alternative hypothesis, Hₐ; p ≠ 0.4

The z-test is given as follows;

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p\cdot q}{n}}}[/tex]

[tex]z=\dfrac{0.477-0.40}{\sqrt{\dfrac{0.4\times 0.6}{130}}} \approx 1.792[/tex]

The p-value P(Z > 1.79) = 2 × (1 - 0.96327) = 0.07346

Therefore, given that the p-value is larger than 0.05 there is significant evidence in favor of the null hypothesis and we reject the alternative hypothesis

Therefore, also, there is not enough statistical evidence to support the math chairperson's claim that the percentage is no longer 40%.

Answer:

Jason is training for a triathlon and needs to swim a certain distance for ... If he swims at the rec center pool, he will complete a 200-yard warmup and then swim laps in a lane that is 20 yards long. If Jason swims at the indoor pool at his gym, he will complete a ... How long will Jason's workout be in total? 1.

Step-by-step explanation:

Answer:

11 sweatshirts and 17 t shirts

Step-by-step explanation:

[tex]t + s = 28\\12t = 20s = 424[/tex]

Step one: cancel out one variable. In this one, t.

[tex]-12(t + s = 28)\\-12t -12s =-336[/tex]

Now that we have that, subtract that from the other expression.

[tex]12t + 20s = 424\\-12t -12s = 336[/tex]

You should get:

[tex]8s = 88\\ s = 11[/tex]

Plug s in any expression

[tex]t + 11 = 28[/tex]

You should know where to go from there, I'm lazy :p

Then t = 17

GOod Luck!!!!

Answer:

Step-by-step explanation:

[tex](x*-7)+13 = 62[/tex]

[tex](x*-7) = 62 - 13[/tex]

[tex]x*-7 = 49[/tex]

[tex]x = 49 / -7[/tex]

[tex]x = -7[/tex]

check work

[tex]((-7)*-7)+13 = 62[/tex]

[tex](49)+13 = 62[/tex]

[tex]62 = 62[/tex]

Answer:

6 cifras.

Step-by-step explanation:

Siempre que tengamos un numero que termina en "mil", entonces la primer parte la escribimos y luego ira una coma:

por ejemplo, en "ciento once mil trecientos catorce"

lo separamos en:

"ciento once mil" y "trecientos catorce"

y lo escribimos como:

"ciento once" , "trecientos catorce"

111,314

Ahora que definimos esto, vamos a nuestro problema.

Tenemos el numero "quinientos cincuenta y cinco mil"

El cual podemos escribir como:

555,000

Ahora simplemente podemos contar las cifras, tenemos 6.

las cuales son:

Cientos de miles = CM = 5

Decenas de miles = DM = 5

Un miles = UM = 5

Cientos = C = 0

Decenas = D = 0

Unidades = U = 0

Answer:

That is the simplest form.

Step-by-step explanation:

[tex]3x^2+13x+4[/tex] = (3x+1)(x+4)

Answer:

The equation is already simplified!

Step-by-step explanation:

credits to the user jlinnartz for pointing out my mistake! kudos to the explanation above!!! :)

x = −12/5 and y = −58/15

Step-by-step explanation:

x+3y=−14

4x−3y=2

Add these equations to eliminate y:

5x = −12

Then solve 5x = −12 for x:

5x = −12

5x/5 = −12/5 (Divide both sides by 5)

x = −12/5

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

x + 3y = −14

Substitute −12/5 for x in x + 3y = −14:

−12/5 + 3y = −14

3y + −12/5 = −14

(Simplify both sides of the equation)

3y + −12/5 + 12/5 = −14 + 12/5

(Add 12/5 to both sides)

3y = −58/5

3y/3 = −58/5/3

(Divide both sides by 3)

y = −58/15

Answer:

A = 28.27

Step-by-step explanation:

Answer:

9pi meters^2

Step-by-step explanation:

The area of a circle is pi * r^2. Basically, pi is simplified to 3.14 but for an exact answer, you'd leave it as a symbol. the "r" stands for the radius which is given(3). we square 3 to get 9. so the answer should be 9 pi or about 28.26.

Answer:

I believe one flash drive would cost $16.50.

Step-by-step explanation:

55=2x+22

-22       -22

33=2x

/2    /2

16.50=x

Hope this helps! Have an Amazing day!!

MARK ME AS BRAINLIEST OK FRIEND

Family is a group of people who want as well as choose to be together embraced by a bond so powerful and strong that not even the slightest test of trials and troubles can breach.Family means nobody gets left behind or forgotten.

Answer:

Hello There!!

Step-by-step explanation:

Family consists of parents and their children.

hope this helps,have a great day!!

~Pinky~

Answer:

Mrs.Royal's ticket costs $800.

Step-by-step explanation:

Child's Ticket= x

Adult's Ticket= 4x

4x-x=600

3x=600

x=200

200*4=800

Answer:

The binomial 14[tex]x^{2}[/tex] - 35x can be factored as 7x(2x+5)

Step-by-step explanation:

When factoring, you want to factor each constant or variable by their greatest common factor (or GCF). Since [tex]14x^{2}[/tex] and [tex]35x[/tex] has a greatest common factor of 7x, factor each term by 7x and you'll get [tex]7x(2x+5)[/tex].

Answer:

30.1 ft²

Step-by-step explanation:

The area of a triangle with an included angle and two sides cam be found using the formula, A = ½*ab*sin(C)

a = 7 ft

b = 9 ft

C = 73°

Plug in the values

Area = ½*7*9*sin(73)

Area = 30.1235998 ≈ 30.1 ft² (nearest tenth)

Answer:[tex]-12x^{2} + 8x - 30[/tex]

Step-by-step explanation:

Simplify the expression.

Answer:

Below in bold.

Step-by-step explanation:

2x + 18 + 3x + 12 = 180  (property of a cyclic quadrilateral).

5x = 180 - 18 -12

5x = 150

x = 30

So m < A = 2(30)+18

= 78 degrees.

Answer:

16.3

Step-by-step explanation:

The height of the building to the nearest tenth is 16. 3 ft

The situation forms a right triangle.

The length of the ladder is the hypotenuse of the triangle formed.

The distance from the foot of the ladder to the bottom of the building is the adjacent sides.

Therefore,

c² = a² + b²

where

c = hypotenuse

a and b are the other two legs.

b² = 29² - 24²

b² = 841 - 576

b = √265

b = 16.2788205961

b = 16.3 ft

learn more on right angle here: https://brainly.com/question/23919428?referrer=searchResults

Answer: number of adults = 3, number of children = 5

Step-by-step explanation:

let the number of adults be x, and the number of children be y.

x + y = 8 , 15x + 8y = 85

1st equation x 8 = 8x + 8y = 64

[tex]8x+8y-15x-8y = 64 - 85\\-7x = -21\\x=3[/tex]

substitute x=3

[tex]3+y=8\\y=5[/tex]

Answer: It snowed 0.665 meters

hope this helps! :)

Answer:

Step-by-step explanation:

61.5cm= (6.15/100)m = .615m

Answer:

121.92

Step-by-step explanation:

There's 121.92 centimeters in 4 feet.

Hope this helps! :^)

Answer:

B) 155 sq. cm.

Step-by-step explanation:

225 - 70 = 155 sq. cm.

Answer:

i believe its B.

hope this helps.

its a benchmark, so do your best :)!

Answer:

hope it helps

Step-by-step explanation:

Answer:

No, the Science Club will only make $480. On the graph, the point  (,)                                       is below the line, so it is not a solution of the inequality.

Step-by-step explanation:

just answered this, and this was the correct answer :) !

Answer:

I'm pretty sure it's D

Step-by-step explanation:

I could be wrong tho

Answer:

According to the model, in 2025 the world population will be 8,493,750,000

Step-by-step explanation:

Rate at which population was growing per year = 0.09125 billion

Initial population figure in 1990 = 5.3 billion

World population prediction in 2010 ;

Predicted population figure :

Initial population + (population growth value per year * number of years)

number of years = (2025 - 1990) = 35 years

Predicted population figure in 2025 :

5.3 + (0.09125 * 35)

5.3 + 3.19375

= 8.49375 billion.

8,493,750,000 by 2025

Answer:

b

Step-by-step explanation:

edge 2021

Answer:

x = √72 and yes, it forms a Pythagorean triple

Step-by-step explanation:

a^2 + b^2 = c^2,

3 is a, x is b, anf 9 is c

3^2 + x^2 = 9^2

9 + x^2 = 81

Subtract 9 from both sides

x^2 = 72

x = √72

a Pythagorean triple is a^2 + b^2 = c^2, and this has it

Answer:

X = 9.4

Step-by-step explanation:

Pythagorean Theorem:

Formula: a² + b² = c²

- A Pythagorean triple consists of any three positive integers.

Answer:

1. C  2.H  3.G  4.E  5.B  6.D  7.A

Step-by-step explanation:

1. C  

2.H  

3.G  

4.E  

5.B  

6.D  

7.A

Leave a like if this answered your question.

Answer:

y = 4 root 3, x = 8

Step-by-step explanation: