Answer:
a = 5
Remainder when p(x) is divided by x+2 = 62
Step-by-step explanation:
Given:
P(x) = x⁴-2x³+3x²-ax+3a-7
When x+1 divides the polynomial p(x) the ramainder is 19.
Applying remainder theorem,
x = -1
p(-1) = 19
Substitute the x = -1 into the polynomial expression
p(-1) = (-1)⁴-2(-1)³+3(-1)²-a(-1)+3a-7 = 19
1+2+3+a+3a-7 = 19
6-7+4a = 19
4a-1 = 19
4a = 19+1
4a = 20
a = 20/4
a = 5.
Hence, a = 5
p(x) = x⁴-2x³+3x²-5x+8
If p(x) is divided by x+2,
Then the remainder is p(-2)
p(-2) = (-2)⁴-2(-2)³+3(-2)²-5(-2)+8
p(-2) = 16+16+12+10+8
p(-2) = 62
Hence the remaider when p(x) is divided by x+2 is 62
The equivalent form of the compound inequality <span>−44 > −2x − 8 ≥ −8 is
</span>D. <span>D. −2x − 8 < −44 and −2x − 8 ≥ −8. In this case, we just have to divide the inequality into two parts such that two separate expressions are distinguished. This is a bit tricky among the choices.</span>
Answer:
The 95% confidence interval is
Step-by-step explanation:
From the question we are told that
The population standard deviation is ![\sigma =7 \ inches](https://tex.z-dn.net/?f=%5Csigma%20%20%3D7%20%5C%20%20inches)
The sample size is n = 20
The sample mean is ![\= x = 20](https://tex.z-dn.net/?f=%5C%3D%20x%20%20%3D%2020)
From the question we are told the confidence level is 95% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of
is
Generally the margin of error is mathematically represented as
=>
=>
Generally 95% confidence interval is mathematically represented as
=>
=>
400150000 is the answer pal
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Answer:
Step-by-step explanation:
<u>Use the law of cosines:</u>
- cos C = (25² + 27² - 28²)/(2*25*27)
- cos C = 0.4222
- m∠C = arccos 0.4222
- m∠C = 65°