Y= -9x+5
The slope intercept formula is y=mx +b, where m is the slope and b is the y-intercept. We know that m is -9 because that’s the slope and b is 5 because the y-intercept is at (0, 5), meaning that’s where the line crosses the y-axis.
The measure of the exterior angle at vertex D is: D. 54°
<em><u>Recall:</u></em>
- The exterior angle theorem of a triangle states that the measure of an exterior angle equals the sum of the measures of two opposite interior angles of the triangle.
<em><u>Thus:</u></em>
In ΔDEF, (8x−2)º is an exterior angle at vertex D.
m∠E = (3x−8)° (interior angle)
m∠F = (4x+13)° (interior angle)
<em>Therefore:</em>
(8x−2)º = (3x−8)° + (4x+13)°
8x - 2 = 3x - 8 + 4x + 13
8x - 2 = 7x + 5
8x - 7x = 2 + 5
x = 7
Exterior angle at vertex D = (8x−2)º
= 8(7) - 2
= 54º (option D)
Learn more about exterior angle theorem on:
brainly.com/question/24756010
We are going to take out the dividends step by step:
Dell:
(66) * (1.79) = 118.14 $
Coca Cola:
(95) * (2.62) = 248.9 $
Nike:
(180) * (1.18) = 212.4 $
Adding the three dividends we have:
118.14 + 248.9 + 212.4 = 579.44 $
Answer:
Manuel does receive 579.44 $ in dividends every year
According to the probabilities given, it is found that the correct option regarding the independence of the events is given by:
No, P(carry cash) != P(carry cash|have children).
<h3>What is the probability of independent events?</h3>
If two events, A and B, are independent, we have that:
Which also means that:
In this problem, we have that:
- 62% carry cash on a regular basis, hence P(cash) = 0.62.
- 46% has children, hence P(children) = 0.46.
- Of the 46% who have children, 85% carry cash on a regular basis, hence P(cash|children) = 0.85.
Since P(carry cash) != P(carry cash|have children), they are not independent.
More can be learned about the probability of independent events at brainly.com/question/25715148
Answer:
Step-by-step explanation:
Let f(x) = x^7 - 4e^x
.
Then f '(x) = 7x^6 - 4e^x, and
f "(x) = 42x^5 - 4e^x, and so:
f '(-1) = 7(-1)^6 - 4e^(-1) = 7 + 4/e
and
f "(x) = 42(-1)^5 - 4e^(-1) = -42 + 4/e
