Answer:
The values of x and y are x = 6 and y = 9
Step-by-step explanation:
MNOP is a parallelogram its diagonal MO and PN intersected at point A
In any parallelogram diagonals:
- Bisect each other
- Meet each other at their mid-point
In parallelogram MNOP
∵ MO and NP are its diagonal
∵ MO intersect NP at point A
- Point A is the mid-point pf them
∴ MO and NP bisect each other
∴ MA = AO
∴ PA = AN
∵ MA = x + 5
∵ AO = y + 2
- Equate them
∴ x + 5 = y + 2 ⇒ (1)
∵ PA = 3x
∵ AN = 2y
- Equate them
∴ 2y = 3x
- Divide both sides by 2
∴ y = 1.5x ⇒ (2)
Now we have a system of equations to solve it
Substitute y in equation (1) by equation (2)
∴ x + 5 = 1.5x + 2
- Subtract 1.5x from both sides
∴ - 0.5x + 5 = 2
- Subtract 5 from both sides
∴ - 0.5x = -3
- Divide both sides by - 0.5
∴ x = 6
- Substitute the value of x in equation (2) to find y
∵ y = 1.5(6)
∴ y = 9
The values of x and y are x = 6 and y = 9
Answer:
Sophia gets 7,150
Step-by-step explanation:
The slope-intercept form<span> is simply the way of writing the equation of a line so that the </span>slope<span> </span><span>Often, this </span>form<span> is called y = mx + b
</span>form<span>.</span>
9.4 because the number after the firs decimal point is higher than 5
Answer:
We can reject the hypothesis at the 0.05 significance level.
Step-by-step explanation:
given that an urn contains a very large number of marbles of four different colors: red, orange, yellow, and green. A sample of 12 marbles drawn at random from the urn revealed 2 red, 5 orange, 4 yellow, and 1 green marble.
H0: All colours are equally likely
Ha: atleast two colours are not equally likely
(Two tailed chi square test at 5% significance level)
color Red Orange Yellow Green total
Observed O 2 5 4 1 12
Expected E 3 3 3 3 12
(O-E)^2/E 0.3333 5.3333 0.3333 5.3333 11.3333
chi square = 11.3333
df =3
p value = 0.010055
Since p < 0.05 we reject H0
We can reject the hypothesis at the 0.05 significance level.