Answer:
Step-by-step explanation:
product of slopes of perpendicular lines=-1
(t-5)/(3+4)×(2-3)/(-4-1)=-1
(t-5)/7×(-1/-5)=-1
(t-5)/35=-1
t-5=-1×35=-35
t=-35+5
t=-30
2.
slopes of parallel lines are equal.
(-2+3)/(t-4)=(-1-4)/(4+2)
1/(t-4)=-5/6
t-4=-6/5
t=4-6/5=(20-6)/5=14/5
3.
x>0,y<0
so P lies in4th quadrant.
except cos and sec all are negative.
so only cos and sec are positive.
Answer:
Twelve less three times a number is at least nine.
Twelve minus the product of three and a number is no smaller than nine.
Step-by-step explanation:
complete question is:
Twelve less than three times a number is greater than or equal to nine.
Twelve less than three times a number is at least nine.
Twelve less three times a number is at least nine.
Twelve minus the product of three and a number is no more than nine.
Twelve minus the product of three and a number is no smaller than nine.
ANSWER:
<u>Twelve less three times a number is at least nine.</u>
The phrase "twelve less three..." means that the "three times a number" is being subtracted from twelve. So, it has to be at least nine.
<u>Twelve minus the product of three and a number is no smaller than nine.</u>
Even the least number you suppose is 1 we'll get 9
e.g: 12-3(1)=9. Therefore, this statement also represent the inequality
Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
For this problem, the parameters are given as follows:
The probability is the <u>p-value of Z when X = 16 subtracted by the p-value of Z when X = 15</u>, hence:
X = 16:
By the Central Limit Theorem
Z = 2.11
Z = 2.11 has a p-value of 0.9826.
X = 15:
Z = 0
Z = 0 has a p-value of 0.5.
0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.
More can be learned about the normal distribution at brainly.com/question/15181104
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9514 1404 393
Answer:
3a by 4a
Step-by-step explanation:
For dimensions L and W, the area and perimeter are ...
A = LW = 12a^2
P = 2(L+W) = 14a
Using the second equation, we can find L:
L +W = 7a . . . . . divide by 2
L = 7a -W
Substituting into the area formula gives the quadratic ...
(7a -W)(W) = 12a^2
W^2 -7aW +12a^2 = 0 . . . . arrange in standard form
(W -3a)(W -4a) = 0 . . . . . . . factor (find factors of 12 that total 7)
Then we have the two solutions ...
W = 3a, L = 4a
W = 4a, L = 3a
The rectangle dimensions are 3a by 4a.
