The ratio of boys to girls in a certain school is 5:6. If there are 420 girls, how many boys are there?(put solution)​

Answers

Answer 1
Answer:

Answer:

I'm not completely sure but I think it's 350

Step-by-step explanation:

5/6 is .8333 then you multiply .8333 by 420 and you get 350


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There are 9 applicants for 3 jobs: software engineer, computer programmer, and systems manager. Which statement best describes this situation?A.
There are 9P3 = 504 ways the positions can be filled because the order in which the applicants are chosen doesn’t matter.
B.
There are 9C3 = 84 ways the positions can be filled because the order in which the applicants are chosen doesn’t matter.
C.
There are 9P3 = 504 ways the positions can be filled because the order in which the applicants are chosen matters.
D.
There are 9C3 = 84 ways the positions can be filled because the order in which the applicants are chosen matters.

Answers

The situation which is best described there is 9P3 = 504 ways the positions can be filled with order matters so option (C) will be correct.

What are permutation and combination?

Combination and permutation are two alternative strategies in mathematics to break up a collection of components into groups. This subset's components can be listed in any order when concatenated. The components of the subgroup are listed in a permutation in a particular order.

npr = factorial n/ factorial (n -r)

Given that,

Number of applicants = 9

Number of jobs = 3

Since the jobs are certain to the applicant so the order will matter.

Numberof ways to choose 3 people among 9 jobs

9p3 = factorial 9/factorial (9 -3)

9p3 = 9 × 8 × 7 × factorial 6/factorial 6

9p3 = 504

So there will be a total of 504 ways to feel the position such that order will also matter.

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Answer:

the correct answer is C

Step-by-step explanation:

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A large tank is filled to capacity with 600 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is pumped out at a rate of 12 gallons/min. Find the number A(t) of pounds of salt in the tank at time t. A(t)

Answers

Salt flows into the tank at a rate of

(5 lb/gal) * (6 gal/min) = 30 lb/min

The volume of solution in the tank after t min is

600 gal + (6 gal/min - 12 gal/min)*(t min) = 600 - 6t gal

which means salt flows out at a rate of

(A(t)/(600 - 6t) lb/gal) * (12 gal/min) = 2 A(t)/(100 - t) lb/min

Then the net rate of change of the salt content is modeled by the linear differential equation,

A'(t)=30-(2A(t))/(100-t)

Solve for A:

A'+(2A)/(100-t)=30

Multiply both sides by the integrating factor, \frac1{(100-t)^2}:

(A')/((100-t)^2)+(2A)/((100-t)^3)=(30)/((100-t)^2)

\left(\frac A{(100-t)^2}\right)'=(30)/((100-t)^2)

Integrate both sides:

\frac A{(100-t)^2}=(30)/(100-t)+C

\implies A(t)=30(100-t)+C(100-t)^2

The tank starts with no salt, so A(0) = 0 lb. This means

0=30(100)+C(100)^2\implies C=-\frac3{10}

and the particular solution to the ODE is

A(t)=30(100-t)-\frac3{10}(100-t)^2=\frac3{10}t(100-t)

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Answers

Answer:

ADMC

Step-by-step explanation:

The secant of a circle is a line that cuts the cuts two points of the circumference with one end point external to the circle;

Fro the given diagram, the two lines that cuts the circumference of the circle at two points are AEB and ADMC

Hence the one that contains diameter with point M is line ADMC

The owner of a grocery store wants to mix two kinds of candy together to make 15 lb that he can sell for $5.00 per lb. He wants to use chocolate candies that he sells for $7.00 per lb and sugar candies that he sells for $2.00 per lb. How many pounds of each should the owner use?_ pounds of chocolate candies
_ pounds of sugar candies
=OWO=

Answers

Answer: 9 pounds of chocolate and 6 pounds of sugar candies

Let's define the variables:

C = pounds of chocolate candies used.

S = pounds of sugar candies used.

We know that he wants to make a total of 15lb, then:

C + S = 15

We also want that the price per pound to be equal to 5$.

This means that the price of the 15 pounds will be the same as the price of the un-mixed candies.

C*$7.00 + $2.00*S = $5.00*15

Then we have a system of equations:

C + S = 15

C*$7.00 + $2.00*S = $5.00*15

To solve this system, we need to start by isolating one of the variables, i will isolate C in the first equation:

C = 15 - S

now we can replace that in the other equation:

(15 - S)*$7.00 + $2.00*S = $5.00*15

Now we can solve this for S.

$105 - $5.00*S = $75

$105 - $75 = $5.00*S

$30 = $5.00*S

$30/$5 = S = 6

Then there are 6 pounds of sugar candy, and we can use the equation:

C + S = 15

C + 6 = 15

C = 15 - 6 = 9

There are 9 pounds of chocolate candy in the mix.

Step-by-step explanation:

Final answer:

To find the pounds of chocolate and sugar candies the owner should use, set up and solve equations based on the given information.

Explanation:

Let's assume that the owner uses x pounds of chocolate candies and y pounds of sugar candies.

According to the problem, the total weight of the candies should be 15 pounds.

So, we can set up the equation:

  1. x + y = 15

The owner wants to sell the candies for $5.00 per pound. We can set up another equation to represent the total value of the candies:

  1. 7x + 2y = 5 * 15

Now we can solve these equations to find the values of x and y.
By solving the equations, we find that x = 9 and y = 6.

Therefore, the owner should use 9 pounds of chocolate candies and 6 pounds of sugar candies.

How to solve this?
4cos(4x)sin(10x)

Answers

Answer:

2/5 or 0.4

Step-by-step explanation:

Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.

Answers

Answer: 258 yard^(2)

Step-by-step explanation: To find the surface area you add the area of all the sides. And the unit for a surface area is unit (yards) squared.

Front: 5 • 9 = 45

Back: 5 • 9 = 45

Left: 6 • 5 = 30

Right: 6 • 5 = 30

Top: 9 • 6 = 54

Bottom: 9 • 6 = 54

45 + 45 + 30 + 30 + 54 + 54 = 258.

Final answer:

To calculate the surface area of a rectangular prism, you use the formula 2ab + 2bc + 2ac where a, b, and c represent the length, width, and height of the prism respectively. You compute the surface area in square units.

Explanation:

To find the surface area of a rectangular prism, you need to find the area of all faces and add them up. If the length a, width b, and height c, of the rectangular prism are given, the formula for the surface area is 2ab + 2bc + 2ac square units. Let's take an example: if length (a) is 3 units, width (b) is 4 units, and height (c) is 2 units, then, by using the formula, the surface area would be 2*3*4 + 2*4*2 + 2*3*2 = 24 + 16 + 12 = 52 square units.

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