How much is in a pound?

Solve the following inequality. 3x - 4 > 11

vampirchik [111]

3x - 4 > 11

15 it’s not that hard

3 0

1 year ago

Suppose someone tells you that she has a triangle with sides having lengths 2.6, 8.1, and 8.6. Is this a right triangle? Why or

Elodia [21]

First you check for Pythagoras' Theorem.

Is 8.6² = 8.1² + 2.6² ?

8.1² + 2.6² = 65.61 + 6.76 = 72.37
8.6² = 73.96

8.1² + 2.6² ≠ 8.6²

Since Pythagoras' Theorem is not satisfied it is not a right angled triangle.

The longest side is 8.6, let's find the angle facing the longest side 8.6.

By cosine formula CosA = (b² + c² - a²) / (2bc)

CosA = (2.6² + 8.1² - 8.6²) / (2*2.6*8.1) = -1.59/42.12 = -0.0377

A = Cos inverse (-0.0377) = 92.1 degrees

So there is an angle is greater than 90 degrees.

8 0

3 years ago

According to a 2013 study by the Pew Research Center, 15% of adults in the United States do not use the Internet (Pew Research C

Ivahew [28]

Answer:

a) $P(X=0)=(10C0) (0.15)^0 (1-0.15)^{10-0}= 0.1969$

b) $P(X=3)=(10C3) (0.15)^3 (1-0.15)^{10-3}= 0.1298$

c) $P(X \geq 1) = 1- P(X$

$P(X=0)=(10C0) (0.15)^0 (1-0.15)^{10-0}= 0.1969$

So then we have:

$P(X \geq 1) = 1- P(X$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.15)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

For this case we want this probability:

$P(X=0)=(10C0) (0.15)^0 (1-0.15)^{10-0}= 0.1969$

Part b

For this case we want this probability:

$P(X=3)$

And using the probability mass function we got:

$P(X=3)=(10C3) (0.15)^3 (1-0.15)^{10-3}= 0.1298$

Part c

For this case we want this probability:

$P(X \geq 1)$

And we can use the complenet rule and we got:

$P(X \geq 1) = 1- P(X$

$P(X=0)=(10C0) (0.15)^0 (1-0.15)^{10-0}= 0.1969$

So then we have:

$P(X \geq 1) = 1- P(X$

3 0

2 years ago

Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)

dolphi86 [110]

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = $\int_a^b \delta\left|r^{\prime}(t)\right| d t$

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

$\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}$

Further simplifying;

$\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}$

Now, use integration to find the mass of the wire;

$\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}$

Therefore, the mass of the wire is estimated as 40π√2 units.

To know more about density function, here

brainly.com/question/27846146

#SPJ4

The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

5 0

1 year ago

Use the information given to enter an equation in standard form.

grin007 [14]

Answer:

6x - 5y = -5

Step-by-step explanation:

Your FIRST goal is to fill out y = mx + b with the values of m (your slope) and b (your y-intercept). First, find m by dividing the change in y in the two points given by their change in x. (43 - 31)/(35-25) = 12/10 = 6/5. Plug this in immediately for a "placeholder equation" of y = 6/5x + b, which you can plug either of your points into and solve for b.

43 = 6/5(35) + b

43 = 42 + b

1 = b

Your SLOPE-INTERCEPT equation is y = 6/5x + 1. However, you were asked for standard form. This means you must convert into ax + by = c, where a b and c are all whole numbers, and a is positive.

y = 6/5x + 1

-6/5x + y = 1

6/5x - y = -1

6x - 5y = -5, and this is your final answer.

Let me know if you need a more in-depth explanation on any part of this!

6 0

3 years ago