A certain computer can perform 10 to the 5th power calculations per second. How many calculations can it perform in 10 seconds?

Answer:

$16

Step-by-step explanation:

We are required to find the cost of 1 pound of salmon and 1 pound of swordfish

The cost of 1 pound of salmon and 1 pound of swordfish is $16.60

let

cost of a pound swordfish = x

cost of a pound salmon = y

x = y - 0.20. (1)

2.5y + 1.25x = 31.25. (2)

Substitute x = y - 0.20 into (2)

2.5y + 1.25x = 31.25

2.5y + 1.25(y - 0.20) = 31.25

2.5y + 1.25y - 0.25 = 31.25

2.5y + 1.25y = 31.25 + 0.25

3.75y = 31.5

y = 31.5 / 3.75

y = 8.4

Recall,

x = y - 0.20. (1)

x = 8.4 - 0.20

x = 8.2

Therefore, the cost of a pound swordfish, x is $8.2 and cost of a pound salmon, y is $8.4

Total cost of 1 pound of salmon and 1 pound of swordfish = $8.4 + $8.2

= $16.6

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If Mr.Ramirez divides 12 frogs equally into 6 groups for students each group will have 2 frogs.

Unitary method is a mathematical technique for first obtaining the value of a single unit then deriving the required units by multiplying it with the single unit.

This type of question can be solved using the unitary method where we can obtain how many frogs each group gets.

Given, Mr.Ramirez divides 12 frogs equally into 6 groups for students to study.

∴ Each group will have the total number of frogs upon the total number of groups which is,

= (12/6).

= 2 frogs.

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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

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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 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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The equation representing the Manuel's situation is -

y = 10x + 5

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following problem -

Manuel builds and sells wooden crates. He made this table to show how much his crates cost in dollars -

Number of crates (n)    2       4       6       8

Cost ($)                       $25   $45   $65   $85

We can write the equation as -

y = mx + c

y = {(45 - 25)/(4 - 2)}x + c

y = 10x + c

c = 25 - 10 x 2

c = 5

Therefore, the equation representing the Manuel's situation is -

y = 10x + 5

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Final answer:

With the remaining 3/4 pound of turkey, after converting to ounces, Luis can make 3 additional 1/4 pound burgers.

Explanation:

Luis has 3 pounds of ground turkey and makes 6 burgers using 3/8 pound of turkey per burger. To find out how much turkey he used, we multiply the number of burgers by the weight of turkey per burger:

6 burgers × 3/8 pound/burger = 18/8 pounds = 2 1/4 pounds

Now, subtract the amount used from the initial amount to find the remaining turkey:

3 pounds - 2 1/4 pounds = 3/4 pound remaining

To convert pounds to ounces (as there are 16 ounces in a pound), multiply 3/4 pound by 16:

(3/4) × 16 = 12 ounces remaining

To determine how many 1/4 pound burgers Luis can make, we convert the quarter pounds to ounces, which is 4 ounces per burger, and then divide the remaining ounces by 4:

12 ounces / 4 ounces/burger = 3 burgers

Therefore, Luis can make 3 more 1/4 pound burgers with the remaining turkey.

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).

To find out how long Marsha and Sílvio practiced, we set up the equation x + 2x = 90, where x is the time Sílvio practiced. Solving the equation, we found that Sílvio practiced for 30 minutes and Marsha for 60 minutes.

The question asks us to solve for the amount of time Marsha and Sílvio each practiced their instruments given that Marsha practiced for twice the time that Sílvio did and together they practiced for a total of 90 minutes.

Let's denote the time Sílvio practiced as x minutes. This means Marsha practiced for 2x minutes. We know that the sum of their practice times is 90 minutes, which gives us the equation:

x + 2x = 90

Combining like terms, we have:

3x = 90

Dividing both sides by 3 to solve for x gives:

x = 30

Therefore, Sílvio practiced for 30 minutes and Marsha practiced for 60 minutes (double the time of Sílvio).

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.

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:

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

To find the number of bowling pins equal in mass to one bowling ball, divide the mass of the ball by the mass of one pin. Approximately 4 pins are equal in mass to a 5.54 kg bowling ball.

To find how many bowling pins are equal in mass to one bowling ball, we divide the mass of the bowling ball by the mass of a single pin. This gives us the number of pins that would have a combined mass equal to the mass of the ball.

Mass of bowling ball = 5.54 kg
Mass of one pin = 1.58 kg

We calculate the number of pins as follows:

Number of pins = Mass of bowling ball / Mass of one pin
Number of pins = 5.54 kg / 1.58 kg
Number of pins ≈ 3.51

Since the number of pins must be a whole number, we would say that approximately 4 pins are equal in mass to one bowling ball.

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.