11. Sam has to pay a 15% tax on a boat that cost him $500. He believes he can determine the tax

There are a total of 15 dimes and quarters in a covered cup. The value of all 15 coins totals 2.85

QveST [7]

Answer:

There are 6 dimes and 9 quarters.

Step-by-step explanation:

Represent the number of dimes and the number of quarters by d and q.

Then d + q = 15, or q = 15 - d.

Also, ($0.25)q + ($0.10)d = $2.85, or 5q + 2d = 57.

Substituding 15 - d for q, we get 5(15 - d) + 2d = 57, or

75 - 5d + 2d = 57, or

75 - 3d = 57, or

3d = 18. Thus, there are 6 dimes. Since q = 15 - d, q = 15 - 6 = 9.

There are 6 dimes and 9 quarters.

6 0

3 years ago

Rene is going to the lake to visit some friends. If the lake is 60 miles away, and Rene is driving at 40 miles per hour the enti

Tpy6a [65]

One hour and twenty minutes????

6 0

3 years ago

The perimeter of a triangle is 17x-5 units. One side is 3.x + 5 units and another is 8x-3 units. How many units long is the thir

Ivahew [28]

Answer:

C = 6x - 7 units

Step-by-step explanation:

Let the three sides of the triangle = A, B, and C respectively.

<u>Given the following data;</u>

Perimeter of triangle, P = 17x-5 units

Side A = 3x+5 units

Side B = 8x-3 units

To find side C?

The perimeter of a triangle is given by the addition of all its three (3) sides.

Mathematically, the perimeter of a triangle is given by the formula;

P = A + B + C

Making "C" the subject of formula, we have;

C = P - A - B

Substituting into the equation, we have

C = 17x - 5 - (3x + 5) - (8x - 3)

C = 17x - 5 - 3x - 5 - 8x + 3

Collecting the like terms, we have;

C = 17x - 3x - 8x - 5 - 5 + 3

C = 6x - 7 units

Therefore, the third side is 6x - 7 units long.

5 0

3 years ago

Each morning, Hungry Harry eats some eggs. On any given morning, the number of eggs he eats is equally likely to be 1, 2, 3, 4,

mamaluj [8]

Answer:

Mean = 35

Variance = 291.7

Step-by-step explanation:

Data provided in the question:

X : 1, 2, 3, 4, 5, 6

All the data are independent

Thus,

The mean for this case will be given as:

Mean, E[X] = $\frac{\textup{Sum of all the observations}}{\textup{Total number of observations}}$

or

E[X] = $\frac{\textup{1+2+3+4+5+6}}{\textup{6}}$

or

E[X] = 3.5

For 10 days, Mean = 3.5 × 10 = 35

And,

variance = E[X²] - ( E[X] )²

Now, for this case of independent value,

E[X²] = $\frac{1^2+2^2+3^2+4^2+5^2+6^2}{\textup{6}}$

or

E[X²] = $\frac{1+4+9+16+25+36}{\textup{6}}$

or

E[X²] = $\frac{91}{\textup{6}}$

or

E[X²] = 15.167

Therefore,

variance = E[X²] - ( E[X] )²

or

variance = 15.167 - 3.5²

or

Variance = 2.917

For 10 days = Variance × Days²

= 2.917 × 10²

= 291.7

3 0

3 years ago

For (x)=3x+1 and g(x)=x^2 -6, find (f+g)(x)

julsineya [31]

Answer:

Step-by-step explanation:

$(f+g)(x)=f(x)+g(x)\\\\f(x)=3x+1;\ g(x)=x^2-6\\\\(f+g)(x)=(3x+1)+(x^2-6)=x^2+3x+1-6=x^2+3x-5$

4 0

3 years ago