What is the slope of the line that passes through points (26,7) and (-29,12)

Valerie is making identical quilts for herself and her sister. For each quilt she buys 5 yards of solid fabric and w yards of pr

Nadusha1986 [10]

Valerie bought 18yrds of fabric. If she used 9yrds of fabric on her quilt, she will use another 9yrds on her sister's. The total is 18yrds.

8 0

3 years ago

Find the volume of the cone. Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and round yo

NeTakaya

Answer:

Volume of the cone = 130.83 cubic units

Step-by-step explanation:

The question us incomplete without the diagram of the cone and it's dimensions as this would enable us get the exact answer.

Find attached the diagram used in solving the solution.

Volume of cone = ⅓ πr²h

Radius = r = 5 unit

Height = h = 5 unit

π = 3.14

By inserting the values of each variables, we have:

Volume of cone = ⅓ × 3.14× (5)² × 5

= ⅓ × 3.14× 25×5 = ⅓ × 3.14×125

Volume of cone = (392.5)/3

Volume of cone = 130.8333

Volume of cone = 130.83 cubic units (to the nearest hundredth)

Volume of cone = 130.83 unit³

8 0

3 years ago

A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.

Vlada [557]

Answer:

a) $y=12000(2)^{\frac{t}{50}}$

b) Approx. 27,569 bacteria

c) About 103 minutes

Step-by-step explanation:

a)

This will follow exponential modelling with form of equation shown below:

$y=Ab^{\frac{t}{n}}$

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

$y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}$

b)

To get number of bacteria after 1 hour, we have to plug in the time into "t" of the formula we wrote earlier.

Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

$y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76$

The number of bacteria after 1 hour would approximate be 27,569 bacteria

c)

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

$y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103$