Bob recorded the number of hours each person watched TV in a week. He then organized the information in a frequency table.

What is the area of the triangle formed from (0,-1), (0.4), and (4,-1)?

Rufina [12.5K]

Answer:

10 squared units

Step-by-step explanation:

This triangle is pretty easy since it creates a right triangle. So the base length and height length are pretty easy to identify.

The area of a triangle is .5*base*height.

The base length after drawing the points is a horizontal so just count it or do 4-0=4.

The height length after drawing the points is a vertical so just count it or do 4-(-1)=4+1=5.

So the area of the triangle is .5*4*5=.5(20)=10 units squared.

Now if you didn't fill like drawing it and you knew how to find the determinant.

You just compute

.5 times det| 0 -1 1 |

| 0 4 1 |

| 4 -1 1 |

.5[ 0 det| 4 1 | - -1 det| 0 1 | + 1 det | 0 4 | ]

| -1 1 | | 4 1 | | 4 -1 |

.5[ 0 - -1(0-4) + 1(0-16)]

.5[ 0 -4 -16]

.5[-20]

-10

And if you get a negative just take the absolute value of it giving you 10.

3 0

2 years ago

If P(E) = 0.25, what are the odds against E?

FinnZ [79.3K]

Answer:

Explanation:

Probability is the ratio of *favorable* outcomes to *total* outcomes. Odds can be expressed as odds in favor or odds against.

<em>hope this helps~</em>

3 0

2 years ago

How do you factor 6x^2+14x+4

Taya2010 [7]

(3x+1) (2x+4)

When the first number has multiple factors (like 6) it often times seems to be the factors that are closest together (3×2 instead of 6×1) So I usually use that as a starting point and play with the numbers until you find your answer. The more you do it, the easier it gets. And remember to always check your answer!

3 0

2 years ago

P and q are integers that are multiple of 5. Which of this

zhuklara [117]

Answer:

we conclude that the only option (a) is true.

Step-by-step explanation:

As we know that the multiples of 5 are the numbers which we get when we multiply by 5.

i.e.

5×1=5

5×2=10

Here, 5 and 10 are multiples of 5.

Let p and q are integers that are multiples of 5.

Let us consider

p=5

q=10

so

p+q=5+10

= 15

A number is divisible by 5 if it ends in 5 or 0.

i.e. 15/5 = 3

so p+q is divisible by 3 as there is no remainder left.

Therefore, option (a) is true.

Checking the other options:

(b) P –q is divisible by 10

As

p=5

q=10

so

p-q=5-10

= -5

Numbers that are divisible by 10 need to be even or divisible by 2 and divisible by 5.

As -5 is not divisible by 2.

So, option b is NOT true.

(c) P +q is divisible by 20

As

p=5

q=10

so

p-q=5+10

= 15

Divisibility rule of 20 implies that the last two digits of the number are either 00 or divisible by 20 .

Therefore, P + q= 20 is not divisible by 20 as we don't get the whole number.

(d) P + q is divisible by 25

As

p=5

q=10

so

p-q=5+10

= 15

p+q=15 is not divisible by 25 as it does not end with 00, 25, 50, or 75.

so, option d is NOT correct.

Therefore, we conclude that the only option (a) is true.

5 0

2 years ago

Calc 3 iiiiiiiiiiiiiiiiiiiiiiiiiiii

Lilit [14]

Take the Laplace transform of both sides:

L[y'' - 4y' + 8y] = L[δ(t - 1)]

I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :

(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]

s²Y - 4sY + 8Y = exp(-s)

(s² - 4s + 8) Y = exp(-s)

Y = exp(-s) / (s² - 4s + 8)

and complete the square in the denominator,

Y = exp(-s) / ((s - 2)^2 + 4)

Recall that

L⁻¹[F(s - c)] = exp(ct) f(t)

In order to apply this property, we multiply Y by exp(2)/exp(2), so that

Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)

Then taking the inverse transform, we have

L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]

L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]

L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]

Next, we recall another property,

L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)

where F is the Laplace transform of f, and u(t) is the unit step function

$u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}$

To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is

L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)

Then we find

L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))

and so we end up with

y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)

7 0

2 years ago

Bob recorded the number of hours each person watched TV in a week. He then organized the information in a frequency table.​

Bob recorded the number of hours each person watched TV in a week. He then organized the information in a frequency table.