What is the recursive formula for this sequence?

14, 18, 22, 26, 30, …

Answer:

(goh) (4) = 7

Step-by-step explanation:

g(x) =5x-3 and h(x) = sqrt x

[tex]g(x)= 5x-3[/tex] and [tex]h(x)= \sqrt{x}[/tex]

WE need to find (g o h)(4)

[tex](g o h)(x) = g( h(x))[/tex]

Plug in h(x) in g(x)

we know  [tex]h(x)= \sqrt{x}[/tex]

Plug it in g(x)

[tex](g o h)(x) = g( h(x))=g(\sqrt{x})[/tex]

Now plug in sqrt(x) in g(x)

[tex](g o h)(x) = g( h(x))=g(\sqrt{x})= 5\sqrt{x} - 3[/tex]

To find (g o h)(4), plug in 4 for x

[tex](g o h)(4) = g( h(4))=g(\sqrt{4})= 5\sqrt{4} - 3= 5(2)-3= 7[/tex]

(goh) (4) = 7

Answer:

d. Antonio could reduce his monthly entertainment expenses by $75 and his food expenses by $50 to pay the monthly rent. He could take $200 out of savings once for the deposit.

Step-by-step explanation:

As you can see, Antonio´s expenses add up to a total of $1,125 a month

Expenses:

Food                    $250

Cellphone            $175

Savings                $200

Entertainment      $200

Car                        $300

Total:                     $1175

So he has $375 each month free to pay for the rent, he is $125 short of making it to the $500 monthly rent, so he only has to cut expenses for $125 dollars, by reducing his food expenses $75 and his entertainment expenses $50 he makes the $125 that he is lacking and is able to afford the $500 monthly rent.

Answer-

The rule (x, y) → (-y, x) would rotate the figure 270° clockwise and after rotation the coordinate of A will be (4, 0)

Solution-

ABCD is a trapezoid with vertex A at (0, -4)

The trapezoid ABCD is rotated 270°.

While rotating a point with coordinate (x, y) 270° clockwise, its new coordinate will be (-y, x)

So applying the rule, new coordinate of A will be (4, 0)

Therefore, the rule (x, y) → (-y, x) would rotate the figure 270° clockwise and after rotation the coordinate of A will be (4, 0)

Dominic's total earnings for the week are calculated by adding his fixed salary of $285 to his commission, which is 8% of his sales. The commission on $4,213 worth of sales is $337.04, resulting in total earnings of $622.04.

The question requires us to calculate Dominic's total earnings for the week based on his fixed salary and the commission he makes from sales. Dominic earns a fixed amount of $285 per week plus an 8% commission from his sales. To find his total earnings, we need to calculate his commission from the $4,213 worth of merchandise he sells.

Firstly, we convert the 8% commission rate into decimal form by dividing by 100, which gives us 0.08. Then, we multiply the total sales amount by this decimal to find the commission amount:

Next, we add the commission to Dominic's fixed salary to get his total earnings for the week:

Therefore, Dominic's total earnings for the week will be $622.04.

When you cut 20 sandwiches into thirds, you will end up having 60 pieces of sandwiches.

The question you're asking requires a simple multiplication. Given that you have 20 sandwiches and you're cutting each sandwich into thirds, you need to multiply the number of sandwiches (20) by the number of cuts (3). The equation is 20 sandwiches * 3 pieces/sandwich.

So, when you multiply 20 by 3, you end up with a total of 60 pieces of sandwich. Therefore, after cutting all the sandwiches into thirds, you should have 60 pieces of sandwich for the party.

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Answer:

[tex]C=0.2RA+0.3A[/tex]

Step-by-step explanation:

To solve the equation [tex]R=5(\frac{C}{A}-0.3)[/tex] for [tex]C[/tex] you must:

[tex]\mathrm{Switch\:sides}\\\\5\left(\frac{C}{A}-0.3\right)=R[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5\left(\frac{C}{A}-0.3\right)}{5}=\frac{R}{5}[/tex]

[tex]\mathrm{Simplify}\\\\\frac{C}{A}-0.3=\frac{R}{5}[/tex]

[tex]\mathrm{Add\:}0.3\mathrm{\:to\:both\:sides}\\\\\frac{C}{A}-0.3+0.3=\frac{R}{5}+0.3[/tex]

[tex]\mathrm{Simplify}\\\\\frac{C}{A}=0.2R+0.3[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}A\\\\\frac{CA}{A}=0.2RA+0.3A[/tex]

[tex]\mathrm{Simplify}\\\\C=0.2RA+0.3A[/tex]

The correct answer is A. (0,5)

Answer:

(C)

Step-by-step explanation:

The given expression is :

[tex]0.00055[/tex]

which on simplifying, we get

[tex]\frac{55}{100000}=55{\times}10^{-5}[/tex]

The given expression can be easily rewritten as:

[tex]5.5{\times}10^{-4}[/tex] and [tex]0.55{\times}10^{-3}[/tex]

but [tex]5.5{\times}10^{4}=55000{\neq}0.00055[/tex]

Thus, Option (C) is the expression which is not equal to the given expression.

The number of t-shirts given to men is 29867 and the number of t-shirts given to women is 16928.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given that,

Each male finisher has given a t-shirt

So,

Number of men finishers = number of t shirt

Since,

number of t-shirts given to man = 29867

Similarly,

Each women's finisher has given a t-shirt

So,

Number of women's finishers = number of t-shirts

So,

number of t-shirts given to women = 16928

Hence "The number of t-shirts given to men is 29867 and the number of t-shirts given to women is 16928".

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Matrix-chain-multiply is a recursive algorithm used to find the optimal matrix multiplication for a chain of matrices.

Matrix chain multiplication is a dynamic programming problem that aims to find the most efficient way to multiply a chain of matrices. We can solve this problem using a recursive algorithm called matrix-chain-multiply.

The algorithm takes four parameters: the matrix chain a, an array s to store the optimal split points, and indices i and j that determine the subchain to be multiplied. The base case of the recursive algorithm is when i and j are equal, in which case we simply return a[i].

For any other case, we iterate through all possible split points and recursively calculate the number of scalar multiplications required. We then select the split point that minimizes the required scalar multiplications. The overall complexity of the algorithm is O(n^3), where n is the number of matrices in the chain.

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Final answer:

The difference in height between the bird's nest and the mole's den is 132 inches.

Explanation:

To find the difference in height between the bird's nest and the mole's den, we need to convert the measurements to the same units. The nest is 12 feet above the ground, which is equivalent to 12 x 12 = 144 inches above the ground. The mole's den is 12 inches below the ground. To find the difference, we subtract the depth of the mole's den from the height of the bird's nest: 144 - 12 = 132 inches.

Final answer:

To find the difference in height between the bird's nest and the mole's den, convert the measurements to the same unit and calculate the total difference.

Explanation:

To find the difference in height between the bird's nest and the mole's den, we need to convert the measurements to the same unit. Since the bird's nest is 12 feet above the ground and the mole's den is 12 inches below the ground, we can convert both measurements to inches. There are 12 inches in a foot, so the bird's nest is 12 x 12 = 144 inches above the ground. The difference in height is then 144 inches + 12 inches (negative sign since it's below the ground) = 156 inches.

Answer:-2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 78x from both sides.

Step 3: Add 30 to both sides.

Step 4: Divide both sides by -30.

x=−2

The expression as 8/9(54x−36)+2=−34(−40+16x)+90x gives the value of x is -2.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

Given ;

8/9(54x−36)+2=−34(−40+16x)+90x

First we need to use the distributive property

48x-32+2=30-12x+90

Now then add or subtract like terms,

48x-30=30+78x

Then subtract 48x

-30=30 +30x

Now, then -30

-60=30x

then multiply by 30

We get the value of x

x=−2

Therefore, the expression as 8/9(54x−36)+2=−34(−40+16x)+90x gives the value of x is -2.

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Final answer:

To express [tex]1.230 \times 10^3[/tex] as a decimal, you move the decimal point three places to the right, resulting in the number 1230.

Explanation:

The question asks how the number [tex]1.230 \times 10^3[/tex] should be properly expressed as a decimal. To convert from scientific notation to decimal form, we multiply the numerical part of the expression by 10 raised to the power indicated by the exponent. In this case, 1.230 is multiplied by  [tex]10^3,[/tex] which means 1.230 needs to be multiplied by 1000 (because 103 = 1000). Therefore, we move the decimal point three places to the right (since the exponent is positive), transforming  [tex]1.230 \times 10^3[/tex] into 1230.

The question requires us to simplify 8(y + 12) using the distributive property, which results in 8y + 96. So, correct answer is D: 8y + 96.

The question is asking us to simplify the expression 8( y + 12)

using the distributive property. The distributive property states that multiplication distributes over addition. In simpler terms, it means that if you have a multiplication operation involving a sum (or difference), you can 'distribute' the multiplier to each term inside the parenthesis.

Applying the distributive property to 8( y + 12) gives us:

8 * y + 8 * 12

This simplifies to:

8y + 96

So the correct answer is D : 8y + 96.

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