ANSWER
93 and 70
EXPLANATION
We have that one number is 23 more than another.
Let the first number be x.
Let the second number be y.
This means that:
x = 23 + y ____(1)
The sum of the two numbers is 163. This means that:
x + y = 163 ____(2)
Put (1) in (2):
23 + y + y = 163
23 + 2y = 163
2y = 163 - 23
2y = 140
y = 140 / 2
y = 70
From (1):
x = 23 + 70
x = 93
The two numbers are 93 and 70.
Answer:
a) 229 and 305 days
b) 229 days or less
c) 305 days or more
Step-by-step explanation:
The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 267
Standard deviation = 19
(a) Between what values do the lengths of the middle 95% of all pregnancies fall?_____________and___________days
By the Empirical rule, 95% of all pregnancies fall within 2 standard deviations of the mean.
So
267 - 2*19 = 229 days
to
267 + 2*19 = 305 days
(b) How short are the shortest 2.5% of all pregnancies?______days or less
95% of all pregnancies fall within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. Since the distribution is symmetric, 2.5% is more than 2 standard deviations below the mean(shortest 2.5%) and 2.5% is more than 2 standard deviations above the mean(longest 2.5%). So
267 - 2*19 = 229 days
c) How long do the longest 2.5% of pregnancies last?________days or more
Explanation in b)
267 + 2*19 = 305 days
Answer:
k = 4/5
Step-by-step explanation:
First, rewrite 5/6k as (5/6)k; this is "five sixths of the variable k."
Next, identify the LCD. It is 6. Then the given equation becomes
5k + 4 = 8
Consolidate the constant terms:
5k = 4
Solve for k: k = 4/5
Answer:
<h2>y=8</h2>
Step-by-step explanation:
4y-4=28
4y=28+4
4y=32
y=32/4
y=8
now plug in 8 for y and check the equation true:
4y-4=28
4*(8)-4=28
32-4=28
28=28
So, y is equal to eight 8
Answer:
option 3, 45
Step-by-step explanation:
3x - 9° + 30° + 24° = 180° (angle sum property of a triangle)
3x - 9° + 54° = 180°
3x + 45° = 180°
3x = 180° - 45°
3x = 135°
x = 135/3
x = 45°
therefore, option 3 is the correct option
