Answer:
The probability they have one boy and one girl = 0.50 = 50 %
Step-by-step explanation:
Here the family has two children, we need to find what is the probability they have one boy and one girl.
Probability for babies are boys = 51.3% = 0.513
Probability for babies are girls = 1 - 0.513 = 0.487
The probability they have one boy and one girl = 1 - probability that they have two boys - probability that they have two girls
The probability they have one boy and one girl = 1 - 0.513² - 0.487² = 0.499 = 0.50
The probability they have one boy and one girl = 0.50 = 50%
Alex finally had $(x+110) amount of money in his account i.e. He had $100 more then before!
<u>Step-by-step explanation:</u>
Alex wrote checks on Tuesday for $30 and $40. He also made a deposit in his checking account of $180. Let's solve it step by step :
<u>Alex wrote checks on Tuesday for $30 and $40:</u>
Let's suppose Alex initially had x amount of money out of which $30 & $40 is deducted! so left amount of money is $(x-70) .
<u>He also made a deposit in his checking account of $180:</u>
Out of left money $(x-70) , Alex deposited $180 in account so new money = $(x-70) + $180 = $(x+110)
Therefore, Alex finally had $(x+110) amount of money in his account i.e. He had $100 more then before!
Answer (x,y) (3, -2)
Explanation:
using the
substitution method
y
=
x
−
5
→
(
1
)
y
=
−
2
x
+
4
→
(
2
)
since both equations are expressed in terms of x we
can equate them
⇒
x
−
5
=
−
2
x
+
4
add 2x to both sides
2
x
+
x
−
5
=
−
2
x
+
2
x
+
4
⇒
3
x
−
5
=
4
add 5 from both sides
3
x
+
5
−
5
=
4
+
5
⇒
3
x
=
9
divide both sides by 3
3
x
3
=
9
3
⇒
x
=
3
substitute this value in
(
1
)
y
=
3
−
5
=
−
2
As a check
substitute these values into
(
2
)
right
=
−
6
+
4
=
−
2
=
left
⇒
point of intersection
=
(
3
,
−
2
)
Answer:
42.25 feet
Step-by-step explanation:
The height function is a parabola. The maximum value of a negative parabola is at the vertex, which can be found with:
x = -b/2a
where a and b are the coefficients in y = ax² + bx + c.
Here, we have y = -16t² + 52t. So a = -16 and b = 52. The vertex is at:
t = -52 / (2×-16)
t = 13/8
Evaluating the function:
h(13/8) = -16(13/8)² + 52(13/8)
h(13/8) = -169/4 + 169/2
h(13/8) = 169/4
h(13/8) = 42.25
