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daser333 [38]
3 years ago
7

A certain solution of salt water is 10% salt and weighs 50 pounds. more salt must be added to produce a solution that is 25% sal

t. if x represents the pounds of salt to be added, which of the following expressions represents the number of pounds of salt in the 25% solution?
a) 0.25 (x+50)
b) 0.25x
c) 1.25 (x+50)
Mathematics
1 answer:
Semenov [28]3 years ago
8 0

Answer

7.5 pounds

Step-by-step explanation:

Since adding x grams of salt will bring th percentage of the salt to 25

Hence. 10% of the 50 gram gives. 5 gram initial salt before it is added.

5+ x/ 50 * 100= 25/

5+x /50 = 0.25

5+x = 12.5

X= 12.5- 5

X= 7.5pounds

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Here is a triangular pyramid and its net.
bazaltina [42]

Answer:

a) Area of the base of the pyramid = 15.6\ mm^{2}

b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

d) Total Surface Area = 87.6\ mm^{2}

Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. \text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\

{\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\  mm^{2}

Hence,

a) Area of the base of the pyramid = 15.6\ mm^{2}

b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

d) Total Surface Area = 87.6\ mm^{2}

3 0
3 years ago
Toby buys a new MP3 player for a price of $45.50. What is the total amount his credit card is
Fittoniya [83]

Answer:

$48.69

Step-by-step explanation:

45.50 + (45.50 * 0.07) = 48.69

hope this helps!

5 0
3 years ago
HELP!
wel

Answer:

1. 6w+6=48

2. n = 9

3. 2x+2 = 5.64

4. 2x-3 = 7.80

5. 2x+6 = 30

6. 3x+3 = 153

7. 2x - 6 = 14

8. 3x + 6 = 54

9. 1424 = 356*t

Step-by-step explanation:

1.

Let the width be w, then twice the width is 2w. But our length is 3 more than twice the width, implying that our length will be 2w+3.

The perimeter of a rectangle is given by the formula;

p = 2(length + width)

2(2w+3+w) = 48

6w+6=48 is our required equation.

2.

Fifteen more than four times a number is 6 more than five times the number. Use "n" for the number.

We first evaluate, Fifteen more than four times a number;

since our number is n, the above statement can be written mathematically as,

4n + 15

The next step we evaluate; five times the number,

5n

In the final step we compare these two expression and solve for n;

we have been told that; Fifteen more than four times a number is 6 more than five times the number. This implies;

4n + 15 - 5n = 6

-n = -9

n = 9

3.

Let the amount paid by Martha be x. Therefore, the amount paid by Sally would be x+2 since she paid 2 more than Martha. The total amount paid by both is;

x+x+2 = 2x+2

The required equation is thus;

2x+2 = 5.64

4.

We let the amount spent by Tim be x. This would mean that Bob spent x-3 since we are told that Bob paid $3 less than Tim. Therefore, the total amount spent by Bob and Tim in terms of x is;

x+x-3 = 2x-3

Therefore, the required equation would be;

2x-3 = 7.80

5.

We let the number of men be x, then the number of women would be x+6 since we are told that there were six more women on the committee than men. The total number of people on the committee in terms of x is thus;

x+x+6 = 2x+6

Therefore, our required equation would be;

2x+6 = 30

6.

Three consecutive integers have the sum of 153.

We let the three consecutive integers be;

x, x+1, and x+2

The difference between consecutive integers is usually 1.

The sum of the above integers in terms of x would be;

x+x+1+x+2 = 3x+3

Therefore, our required equation would be;

3x+3 = 153

7. Five times the first of three consecutive even integers is fourteen more than three times the second.  

We let the first even integer be x. The second even integer would be x+2 while the third one would be x+4. The difference between two consecutive even integers is always 2. Now Five times the first of three consecutive even integers would be;

5*x = 5x

On the other hand, three times the second even integer would be;

3*(x+2) = 3x + 6

Now, we are told that 5x exceeds 3x + 6 by 14. Therefore, we can write;

5x - (3x +6) = 14

2x - 6 = 14

Which is the required equation

8. The sum of three consecutive even integers is fifty-four.

We let the first even integer be x. The second even integer would be x+2 while the third one would be x+4. The difference between two consecutive even integers is always 2. The sum of the three consecutive even integers in terms of x would be;

x+x+2+x+4 = 3x+6

The required equation would thus be;

3x + 6 = 54

9. An airplane flies at a rate of 356 km/h. The plane travels a total distance of 1424 km. (Use Distance = Rate * Time for your equation.)

The distance traveled by the plane is given as 1424 while its      rate or speed is 356. We let t denote the time it took the plane to travel the given distance at the given rate. Using the equation Distance = Rate * Time, we can write the following equation in t;

1424 = 356*t

Which is our required equation.

3 0
3 years ago
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