HELP ME I VERY STRESSED(⓿

A state requires that all boat licenses consist of the letter A or M followed by any five digits. What is the number of groups o

torisob [31]

Answer:

200000

Step-by-step explanation:

The boat licenses are strings of six elements. Let's count the number of ways of constructing such string with the given conditions.

There are 2 ways of choosing the first character of the string (A or M). The second character can be any digit, so there are 10 possible choices. The third character is also any digit, so it can be chosen in 10 ways. Similarly, the fourth character can be chosen in 10 ways, and the fifth character can be chosen in 10 ways.

By the product rule there are 2×10×10×10×10×10=2×10^5=200000 ways to choose all the characters. Every choice of characters becomes a unique string (boat license) thus the number of avaliable boat licenses is 200000.s

7 0

3 years ago

A conical hole is made in a cylinder. The axis of symmetry of a cone is the same as that of the cylinder. The cylinder has a rad

zlopas [31]

Answer:

C.O.G is 2.71 cm from the base

Step-by-step explanation:

Mark brainliest please

7 0

3 years ago

PLEASE HELP!!! WILL MARK BRAINLIEST!! THX! A golfer hits a ball with an initial velocity of 32.7 m/s from the ground. Find the f

OLEGan [10]

Answer:

See below

Step-by-step explanation:

First Problem

The ball hits the ground when $h(t)=0$ , therefore:

$h(t)=-4.9t^2+v_0t+h_0$

$0=-4.9t^2+32.7t$

$0=t(-4.9t+32.7)$

$t=0$ and $t=\frac{32.7}{4.9}\approx6.67$

Since the ball is in the air before it hits the ground, $t=6.67$ (seconds) is the more appropriate choice.

Second Problem

The maximum height of the ball is determined when $t=-\frac{b}{2a}$ , therefore:

$t=-\frac{b}{2a}$

$t=-\frac{32.7}{2(-4.9)}$

$t=-\frac{32.7}{-9.8}$

$t\approx3.34$

This means that the height of the ball is at its maximum after 3.34 seconds:

$h(t)=-4.9t^2+32.7t$

$h(3.34)=-4.9(3.34)^2+32.7(3.34)$

$h(3.34)\approx54.55$

Thus, the answer is 54.55 (meters).

Third Problem

Refer to the second problem

Fourth Problem

$h(t)=-4.9t^2+32.7t$

$h(4.3)=-4.9(4.3)^2+32.7(4.3)$

$h(4.3)\approx50.01$

Therefore, the height of the ball after 4.3 seconds is 50.01 (meters).

Fifth Problem

The ball will be 24 meters off the ground when $h(t)=24$ , therefore:

$h(t)=-4.9t^2+32.7t$

$24=-4.9t^2+32.7t$

$0=-4.9t^2+32.7t-24$

$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$t=\frac{-32.7\pm\sqrt{(32.7)^2-4(-4.9)(-24)}}{2(-4.9)}$

$t_1\approx0.84$

$t_2\approx5.83$

Therefore, the ball will be 24 meters off the ground after 0.84 (seconds) and 5.83 (seconds)

5 0

2 years ago

Are the lines y = –x + 8 and 4x + 4y = 12 perpendicular? Explain.

melamori03 [73]

We have that
y = –x + 8
and
4x + 4y = 12

we know that
if two lines are perpendicular
so
m1*m2=-1

step 1
find the slope of the lines
y = –x + 8 -------> m1=-1

4x + 4y = 12-----> x+y=3 (divided by 4 all expression)
y=3-x
m2=-1

therefore
m1=m2
the lines are parallel

the answer is
No; their slopes are not opposite reciprocals.

see the attached figure

5 0

3 years ago

Why is the metric system used instead of the us customary system

Softa [21]

Answer:

The metric system if used because it's a standard unit of measurement used internationally. In contrast the us customary system is used only in certain regions. The use of the metric system allows data to be quantifiable in a way that's understood by everyone everywhere.

6 0

3 years ago

HELP ME I VERY STRESSED(⓿_⓿)