Answer:
P = (18a+10b+13) cm
Step-by-step explanation:
Given that,
A triangle has the lengths of (10a+9) cm, (8a—3) cm and (10b+7) cm.
We need to find an expression that represents the perimeter of the triangle.
Perimeter = sum of all sides
P = (10a+9) + (8a-3) + (10b+7)
Taking like terms together,
P = (10a+8a)+10b+(9-3+7)
= 18a+10b+13
Hence, the epresssion for the perimeter is (18a+10b+13) cm.
Answer:
2m² (2m)
Step-by-step explanation:
Answer:
0.015 radians per second.
Step-by-step explanation:
They tell us that at the moment the speed would be 6 ft / s, that is, dx / dt = 6 and those who ask us is dθ / dt.
Which we can calculate in the following way:
θ = arc sin 100/200 = pi / 6
Then we have the following equation of the attached image:
x / 100 = cot θ
we derive and we are left:
(1/100) * dx / dt = - (csc ^ 2) * θ * dθ / dt
dθ / dt = 0.01 * dx / dt / (- csc ^ 2 θ)
dθ / dt = 0.01 * 6 / (- csc ^ 2 pi / 6)
dθ / dt = 0.06 / (-2) ^ 2
dθ / dt = -0.015
So there is a decreasing at 0.015 radians per second.
Trying to factor by splitting the middle term
Factoring <span> b2-4b+4</span>
The first term is, <span> <span>b2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -4b </span> its coefficient is <span> -4 </span>.
The last term, "the constant", is <span> +4 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> 1 • 4 = 4</span>
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is <span> -4 </span>.
<span><span> </span></span>
<span><span>-4 + -1 = -5</span><span> -2 + -2 = -4 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -2
<span>b2 - 2b</span> - 2b - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
b • (b-2)
Add up the last 2 terms, pulling out common factors :
2 • (b-2)
Step-5 : Add up the four terms of step 4 :
(b-2) • (b-2)
Which is the desired factorization
Answer: (a). 99 percent of the sample proportions results in a 99% confidence interval that includes the population proportion.
(b). 1 percent of the sample proportions results in a 99% confidence interval that does not include the population proportion.
Step-by-step explanation:
(a). 99 percent of the sample proportions results in a 99% confidence interval that includes the population proportion.
Explanation: If multiple samples were drawn from the same population and a 99% CI calculated for each sample, we would expect the population proportion to be found within 99% of these confidence intervals.
(b). 1 percent of the sample proportions results in a 99% confidence interval that does not include the population proportion.
Explanation: The 99% of the confidence intervals includes the population proportion value, it means, the remaining (100% – 99%) 1% of the intervals does not includes the population proportion.
If multiple samples were drawn from the same population and a 99% CI calculated for each sample, we would expect the population proportion to be found within 99% of these confidence intervals and 1 percent of the sample proportions results in a 99% confidence interval that does not include the population proportion.
