Answer:
<u>Marge's</u> present age = 14 ; <u>Dan's</u> present age = 29
Step-by-step explanation:
Let Marge's present age be = M
Dan's present age [D] : 14 years elder than Marge = M + 14
Marge Age = M - 8
Dan's Age = D - 8 = (M + 14) - 8 = M + 6
{Given} : Dan's age = 3 times Marge's age
M + 6 = 3 (M - 8)
M + 6 = 3M - 24
6 + 24 = 3M - M
30 = 2M
M = 30/2
M = 15 [Marge's present age]
Dan's present age [D] = M + 14 = 29
Step 1 (simplify):
3+5x(2-1)
8 x 1
Step 2 (solve):
8 x 1 = 8
8 is your answer. Hope this helps :)
Answer:
15 degrees
Step-by-step explanation:
Draw a horizontal segment approximately 4 inches long. Label the right endpoint A and the left endpoint C. Label the length of AC 4.2 meters. That is the horizontal distance between the eye and the blackboard.
At the right endpoint, A, draw a vertical segment going up, approximately 1 inch tall. Label the upper point E, for eye. Label segment EA 1 meter since the eye is 1 meter above ground.
At the left endpoint of the horizontal segment, point C, draw a vertical segment going up approximately 2 inches. Label the upper point B for blackboard. Connect points E and B. Draw one more segment. From point E, draw a horizontal segment to the left until it intersects the vertical segment BC. Label the point of intersection D.
The angle of elevation you want is angle BED.
The length of segment BC is 2.1 meters. The length of segment CD is 1 meter. That means that the length of segment BD is 1.1 meters.
To find the measure of angle BED, we can use the opposite leg and the adjacent leg and the inverse tangent function.
BD = 1.1 m
DE = 4.2 m
tan <BED = opp/adj
tan <BED = 1.1/4.2
m<BED = tan^-1 (1.1/4.2)
m<BED = 15
Answer: 15 degrees
Answer:
0.7673
Step-by-step explanation:
We have the following:
The null and alternative hypothesis is,
H0: m = 290
Ha: m> 290
x = 285.2
m = 290
sd = 59.3
n = 82
is m the mean, sd the standard deviation and n the population size
Now we calculate the value of z like this:
z = (x - m) / sd / (n ^ (1/2))
z = (285.2 - 290) / 59.3 / (82 ^ (1/2))
z = -0.73
now
P (z> -0.73) = 1 - P (z <-0.73)
we look at the normal distribution table
P = 1 - 0.2327 = 0.7673
Therefore the value of p is equal to 0.7673
Answer:
a. ∫ xSinx dx
iii. integration by parts
u =x and dv= sinx
b. ∫ x⁴/(1+x³). dx
ii. neither
Long division is an option here before integration is done
c. ∫ x⁴. e^x³. dx
i. substitution
where u = x⁵
d. ∫x⁴ cos(x⁵). dx
i. substitution
where u = x⁵
e. ∫1/√9x+1 .dx
i. substitution
where u = 9x+1
