What is the exact volume of the cone?

Caroline has some dimes and some quarters. She has a maximum of 15 coins worth at least $2.85 combined. If Caroline has 3 dimes,

gayaneshka [121]

Answer:

11, 12.

Step-by-step explanation:

Let q represent number of quarters.

We have been given that Caroline has a maximum of 15 coins worth at least $2.85 combined. We are also told that Caroline has 3 dimes. This means that total coins are less than or equal to 15.

We can represent this information in an inequality as:

$q+3\leq 15...(1)$

We are also told that the coins worth at least $2.85 combined. This means that the worth of all coins is greater than or equal to 2.85.

We know that each dime is worth $0.10 and each quarter is worth $0.25.

$0.25q+3(0.10)\geq 2.85...(2)$

Now, let us solve our system of inequalities.

From 1st inequality, we will get:

$q+3-3\leq 15-3$

$q\leq 12$

From 2nd inequality, we will get:

$0.25q+0.30\geq 2.85$

$0.25q+0.30-0.30\geq 2.85-0.30$

$0.25q\geq 2.55$

$\frac{0.25q}{0.25}\geq \frac{2.55}{0.25}$

$q\geq 10.2$

Upon combining our both inequalities, we will get:

$10.2\leq q\leq 12$

This means that numbers of quarters would be greater than or equal to 10.2 and less than or equal to 12.

Since we cannot have 0.2 of a coin, therefore, Caroline could have 11 or 12 quarters.

6 0

3 years ago

Can you help with did pretty please I'm stuck help just a, c ,d thanks luv.

Misha Larkins [42]

Answer:

a) The slope of the function is 3.

c) The equation is represented by $n(t) = 3\cdot t + 35$ .

d) The y-intercept of the function is 35.

Step-by-step explanation:

a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:

$n(t) = m\cdot t + n_{o}$ (1)

Where:

$m$ - Slope, measured in number of pieces per minute.

$t$ - Time, measured in minutes.

$n_{o}$ - Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.

$n$ - Current number of pieces of mail that must be hand-sorted, measured in pieces.

From Geometry, we know that a line can be formed by know two distinct points. If we know that $n(15\,min) = 80\,p$ and $n(45\,min) = 170\,p$ , then the following system of linear equations is formed:

$15\cdot m + n_{o} = 80$ (2)

$45\cdot m + n_{o} = 170$ (3)

The solution of the system of equations is:

$m = 3$ and $n_{o} = 35$

The slope of the function is 3.

c) By (1) and using results from a) we conclude that the equation function is:

$n(t) = 3\cdot t + 35$ (4)

d) The y-intercept of the function is 35.

5 0

3 years ago

Monica is a lawyer who earns $8,322.65 every month. She spends $830.98 on rent, $210.36 on food, and $120.45 on gas every month.

Step2247 [10]

She would have $7160.86 left over in cash here's why.....
she starts off with $8,322.65 and spends $830.98 on rent $8,322.65-$830.98= $7,491.67
then spends $210.36 on food and another $120.45 on gas
$7,491.67-$210.36= $7,281.31 - $120.45= $7,160.86 <---- Left over $

7 0

3 years ago

Ayudaaaaaa es para hoy

murzikaleks [220]

Answer:

Step-by-step explanation:

a (2³)² = 2³ˣ² = 2⁶

b (7⁰)¹ = 7⁰ˣ¹ = 7⁰ = 1

c (5⁶)³ = 5⁶ˣ³ = 5¹⁸

d (6²)⁴ = 6²ˣ⁴ = 6⁸

e (8³)⁴ = 8³ˣ⁴ = 8¹²

f (4³)² = 4³ˣ² = 4⁶

g (9¹)² = 9¹ˣ² = 9² = 81

h (3⁷)² = 3⁷ˣ² = 3¹⁴

i (10²)³ = 10²ˣ³ = 10⁶

j (11²)⁴ = 11²ˣ⁴ = 11⁸

8 0

3 years ago

A recipe for fruit punch calls for every 9 cups of grapefruit juice for every 4 cups of OJ. If 60 cups of OJ are used, then how

vampirchik [111]

Answer:

15 cups

Step-by-step explanation:

60/4=15

3 0

3 years ago