distributive property of (9×3)+(9×8)

To simplify 3 5/2 in radical form, convert the mixed number to an improper fraction and express it as √(13/2).

To express 3 5/2 in simplified radical form, we need to convert the mixed number to an improper fraction. 3 5/2 is equivalent to 13/2. Therefore, the expression can be written as √(13/2).

Final answer:

To equal the mass of an elephant weighing 8 metric tons, it takes approximately 2 billion ants, each weighing 4×10^-3 grams.

Explanation:

The question asks how many ants would equal the mass of an elephant when the mass of an ant is approximately 4×10^-3 grams and the mass of an elephant is about 8 metric tons. First, we need to convert the mass of the ant into the same units as the elephant's mass. Since there are 1,000 grams in a kilogram and 1,000 kilograms in a metric ton, we can calculate the mass of the ant in metric tons as 4×10^-3 grams × (1 kilogram / 1,000 grams) × (1 metric ton / 1,000 kilograms), which simplifies to 4×10^-9 metric tons. To find the number of ants needed to equal the mass of an elephant, we divide the elephant's mass by the mass of one ant: 8 metric tons / 4×10^-9 metric tons per ant = 2×10^9 ants. Therefore, it takes approximately 2 billion ants to have the same mass as an 8 metric ton elephant.

Regular price of sofa is $ 350.

Selling price is defined as the price that a customer pays to purchase a product.

Selling price of Sofa is $259

Let the regular price is x

So, sale price is 26% lower than regular price =

x * (100 - 26)/100 = 0.74x

So, 0.74x = 259

Or, x = 259/0.74 = $ 350

Hence, regular price of sofa is $ 350.

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 let x = number of apple pies you would make

let y= the number of apple cobblers you make

 4 cups of apples for a pie 2 cups for cobbler with 16 cups

so we have: 4x+2y<=16

3 cups of flour for both pies and cobbler we get: 3x+3y<=15.

solve the system of inequalities to get (3,2)

check: 4(3) +2(2) = 12+4 = 14, this is less than 16 so this is true

3(3) + 3(2) = 9 +6 = 15 does equal 15 so this is true

 Now profit equation is 3x +2y = profit

3(3) +2(2) = 9+4 = 13

You can make 3 apple pies and 2 apple cobblers for maximum profit

In this exercise we have to have knowledge about finances, in order to be able to calculate and write a function that corresponds to profits, so:

[tex]3x +2y = profit[/tex]

Then using the information given in the text we can write that:

So writing the function we have that corresponds to:

[tex] 4x+2y\leq 6[/tex]

So writing the second function that corresponds to 3 cups of flour, we have:

[tex]3x+3y\leq 15[/tex]

So solving these systems we find:

[tex] 4(3) +2(2) = 12+4 = 14\\ 3(3) + 3(2) = 9 +6 = 15\\ 3x +2y = profit[/tex]

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Final answer:

The 40-m rope cut in a 3:5 ratio gives a 15 m piece and a 25 m piece. Doubling the rope length to 80 m with the same ratio yields a 30 m piece and a 50 m piece.

Explanation:

To find the length of each piece of a 40-m rope cut in the ratio 3:5, we need to work out the parts of the rope that each ratio value represents. First, we add the parts of the ratio together: 3 + 5 = 8 parts in total. Then, we find the length of each part by dividing the total length of the rope by the total number of parts: 40 m ÷ 8 = 5 m per part. Furthermore, to find the length of the smaller piece, we multiply the size of one part by 3, and for the longer piece, we multiply by 5.

Answer:

$16

Step-by-step explanation:

We find that p+q = 17.

To find p+q, we need to solve the given equation step by step:

(q+4)(p+3) - (q+2)(p+1) = 44

Expanding both products, we get:

qp + 3q + 4p + 12 - qp - q - 2p - 2 = 44

We notice here that the 'qp' terms cancel each other out. Simplifying, we are left with:

2q + 2p + 10 = 44

Subtracting 10 from both sides gives:

2q + 2p = 34

Divide by 2:

q + p = 17

Therefore, p+q = 17.

60 x 3.9x10-3 = 234x10e3ml/minute/plane

You have 5.1x10e3 planes in the air

(234 x 5.1) (10e6) ---you add the two exponents together for this one

1193.4 x 10e6...which turns into 1.2 x 10e9

Sandra's unit rate is 0.178 miles per minute, which is lower than Terrance's rate of 0.2 miles per minute and higher than Jessie's rate of 0.133 miles per minute.

To compare the unit rates of Sandra, Terrance, and Jessie, we need to determine how many miles they can run in one minute.

Comparing the unit rates, Terrance has the highest rate at 0.2 miles per minute, followed by Sandra at 0.178 miles per minute, and Jessie at 0.133 miles per minute.

Complete question:

Sandra Runs at a rate of 8 miles in 45 minutes. how does her unit rate compare to Terrance and Jessie (Terrance 6 miles per half an hour jesse 2 miles every 15 minutes).

The linear equation of the line will be y = -x + 6.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. A2 nd the third parameter is the slope of the line which represents the elevation of the line.

Given that a line passes through the points (−1, 7) and (2, 4). The equation of the line will be calculated by finding the slope of the line.

y = mx + c

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 2 - ( -1 ) / ( 4 - 7)

m = ( 3 / -3 )

m = -1

y = mx + c

( 7 ) = ( -1 )( -1 ) + x

c = 6

The equation will be written as:-

y = mx + c

y = -x + 6

Therefore, the linear equation of the line will be y = -x + 6.

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1 piece cuts into 2, 2 pieces cuts into 4, 4 pieces get cut into 8, so there is a multiple of 2 involved so the equation needs a multiple of 2 in it.

 The correct answer is a) p(1) = 1; p(n) = 2p(n-1), for n is greater than or equal to 2

If we want to simplify this expression:

10h+6-5h+3

We have to join each term with h and each term with no variable (no h) :

10h-5h+6+3

Sum each h-term and each variable:

5h+9   This the simplified result

Answer:

Step-by-step26+8 = 34{SUM}

(26+8)/2

(13+4){GCF} explanation: