The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank?

Answers

Answer 1

Answer: $S-Sam's\ age\nH-Hank's\ age\n\n \left\{\begin{array}{ccc}(S)/(H)=(5)/(3)\nS+H=24&\to S=24-H\end{array}\right\n\nsubstitute\ S=24-H\ to\ (S)/(H)=(5)/(3)\n\n(24-H)/(H)=(5)/(3)\n\ncross\ multiply\n\n5H=3(24-H)\n5H=72-3H\n5H+3H=72\n8H=72\ \ \ /:8\nH=9\n\nAnswer:Hank\ is\ 9\ years\ old.$

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The gap is selling shirts for 30% off the original price. The shirts are on sale for $22.40. What was the original price of the shirt?

Answers

If you would like to know what was the original price of the shirt, you can calculate this using the following steps:

30% + 100% = 130%

130% of $22.40 = 130% * 22.40 = 130/100 * 22.40 = $29.12

The original price of the shirt was $29.12.

"From the graph of g, state the intervals on which g is continuous. Select all that apply.(-INFINITY, -4]
(-INFINITY, -4)
[-4,-2]
[-4,-2)
[-2,2]
(-2,2)
[2,4]
[2,4)
[4,6]
(4,6)
[6,8]
(6,8)
[8,INFINITY)
(8,INFINITY)"

Answers

Final answer:

Without seeing the graph, it's not possible to give specific intervals where the function g is continuous. However, based on interval notation, round brackets indicate the end points are not included, while square brackets show they are included. Therefore, the function is continuous where the graph does not have gaps, jumps or holes.

Explanation:

Without seeing the exact graph, it's impossible to accurately determine the intervals on which g is continuous. However, in general, a function is said to be continuous over an interval if the graph is unbroken over this interval, without any gaps, jumps, or holes. To determine this from the choices provided, generally you'll need to look at the graph and see where there is an uninterrupted line.

A key thing to note is how the intervals are represented. For instance, an interval like (-Infinity, -4] means that the function is continuous from negative infinity up to and including -4. The round bracket, '( )', means that the end points are not included in the interval, while the square brackets, '[ ]', indicate that they are included.

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If f(x)=log2(x+4), what is f^-1(3)?

Answers

$f\left( x \right) =\log _( 2 ){ \left( x+4 \right) } \n \n \log _( 2 ){ \left( x+4 \right) } =y\n \n { 2 }^( y )=x+4$

$\n \n x={ 2 }^( y )-4\n \n \therefore \quad { f }^( -1 )\left( x \right) ={ 2 }^( x )-4\n \n \therefore \quad { f }^( -1 )\left( 3 \right) ={ 2 }^( 3 )-4=4$

The value of f^-1(3) is 4

What are inverse functions?

The inverse of a function f(x) is the opposite of the function

How to determine the inverse function?

The functionf(x)is given as:

$f(x) = log_2(x + 4)$

Express f(x) as y

$y = log_2(x + 4)$

Swap the positionsof x and y

$x = log_2(y + 4)$

Express as exponents

$2^x = y + 4$

Make y the subject

$y = 2^x - 4$

Express the equationsas an inverse function

$f^(-1)(x) = 2^x - 4$

Substitute 3 for x in the above equation

$f^(-1)(3) = 2^3 - 4$

Evaluate

$f^(-1)(3) = 4$

Hence, the value of f^-1(3) is 4

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What is the area of the figure?

Answers

First solve for 16x20. 16*20= 320 inches. Now subtract the area that is removed, the 8x8 square. 8*8=64. 320-64=256. Our answer is 256in^2.

Which radical expression is equivalent to 3^3/4

Answers

The numerator of the fraction is the power of the number and the denominator is the root of the number. This is expressed as follows:

⁴√(3)³

Answer:27

Step-by-step explanation:

SAVE ME. Please Answer my Questions Clevers. Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:
A. Prime numbers,
B. Composite numbers,
C. Divisible by three,
D. Square of 2.

Q2. The opposite angle of acyclic quadrilaterals is in the ratio of 2:3. Find the degree measure of each opposite angle?

Q3. what is the solution set of
9x-4<13x-7 (domain, xez) ?

Q4. if three fourth of a number is one tenths, what is the number?

Q5. which one is the equation of the line passing through the origin and having a slope 4?

A. Y= -0.4x
B. Y= 4x
C. Y= -4x
D. Y= 0.4x

Answers

Answer:

See below

Step-by-step explanation:

Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:

Counting numbers are Natural numbers: $\mathbb{N}$

Also, we have Whole numbers. Despite not having an official symbol, I usually denote the set as $\mathbb{Z}_(\ge 0)$

Whole numbers less than or equal to 20: $A\leq 20, A \subset \mathbb{Z}_(\ge 0) \n\implies A=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}$