<span>We write the equation in the standard form which is:
ax^2 + bx + c = 0
(x + 15)(x) = 100
x^2 + 15x - 100 = 0
(x + 20) (x-5) = 0
The solutions are
x = -20 and x = 5
Therefore, the correct answer is option B. </span><span>The solution x = 5 should be kept, but x = –20 is unreasonable.</span><span>
</span>
Answer:5.6
Step-by-step explanation:multiply 2×2 and then 3.6×2 and then add them 2 and ÷ by 2
Answer:
12:00 am midnight
Step-by-step explanation:
Given;
I can read a 336-page book in 6 hours.
My rate r1 = 336/6 pages per hour = 56 pages per hour
Jayne can read a 144-page book in 3 hours.
Jayne rate r2 = 144/3 = 48 pages per hour
If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM
Taking 10 am as the reference time.
Let x represent the time from 10 am at which they would both be on the same page.
For me;
Since i started by noon; 2 hours after 10 am
Time t1 = x-2
For Jayne;
She started by 10 am
Time t2 = x
For them to be on the same page they must have read the same number of pages;
Number of pages read = rate × time
r1(t1) = r2(t2)
Substituting the values;
56(x-2) = 48(x)
56x - 112 = 48x
x(56-48) = 112
x = 112/(56-48)
x = 14 hours
Since 10 am is the reference, the time would be;
=10 am + x = 10 am + 14 hours
= 24:00
= 12:00 am midnight
Answer:
The population standard deviation is not known.
90% Confidence interval by T₁₀-distribution: (38.3, 53.7).
Step-by-step explanation:
The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus 
.
Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,
- The area to the left of the lower end of the interval shall be
. - The area to the left of the upper end of the interval shall be
.
Look up the t-score of the upper end on an inverse t-table. Focus on the entry with
- a degree of freedom of 10, and
- a cumulative probability of 0.95.
.
This value can also be found with technology.
The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:
,
where
is the t-score at the upper end of the interval, 
is the unbiased estimate for the standard deviation, and
is the sample size.
For this confidence interval:
Hence the width of the 90% confidence interval is
.
The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:
.
W=2L
P=300=2(L+W)
so
300=2(L+W)
divide by 2
150=L+W
W=2L
subsitute
150=L+2L
150=3L
divide by 3
50=L
sub back
W=2L
W=2(50)
W=100
the field is 100yd wide by 50yd long
, and
.