Answer:
Length = 16 or -5 feet.
Width = 5 or -16 feet.
Step-by-step explanation:
Let the length of the concrete pad = l
Let the width of the concrete pad = w
Given the following data;
Area of concrete pad, a = 80ft²
Translating the word problem into an algebraic equation, we have;
[tex] l = 11 + w[/tex]
We know that, the area of rectangle, A = length * width
[tex] A = l*w[/tex]
Substituting the values into the equation, we have;
[tex] 80 = (11 + w)w[/tex]
Expanding the bracket, we have;
[tex] 80 = 11w + w^{2}[/tex]
[tex] w^{2} + 11w - 80 = 0[/tex]
*Solving the quadratic equation by using factorization method*
[tex] w^{2} + 16w - 5w - 80 = 0[/tex]
[tex] w(w + 16) - 5(w + 16) = 0[/tex]
[tex] (w - 5)(w + 16) = 0 [/tex]
Width, w = 5 feet or w = -16 feet.
Therefore, the width of the concrete pad is 5 feet or -16 feet.
To find its length, l;
[tex] l = 11 + w[/tex]
When w = 5 feet
[tex] l = 11 + 5[/tex]
Length, l = 16 feet
When w = - 16 feet
[tex] l = 11 + (-16)[/tex]
[tex] l = 11 - 16[/tex]
Length, l = -5 feet.
Hence, the dimensions of the concrete pad is 16 by 5 feet or -5 by -16 feet.
what is parallel to y=3x+1
you can only use the numbers 3,-2,1,4,-1,0,2,5 and put it in y= x +
Answer:
y=3x+1
Step-by-step explanation:
A parallel line has the same slope as the other line.
y=mx+b, m is the slope
Thus in y=3x+1, m =3
y = 3x + b
plug in points (1, 4) to determine b
4 = 3(1) + b
4 = 3 + b
subtract 3 on both sides
4 - 3 = b
b = 1
y = 3x + 1
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The lifetime of LCD TV sets follows an exponential distribution with a mean of 100,000 hours. Compute the probability a television set:
a. Fails in less than 10,000 hours.
b. Lasts more than 120,000 hours.
c. Fails between 60,000 and 100,000 hours of use.
d. Find the 90th percentile. So 10 percent of the TV sets last more than what length of time?
Answer:
0.9
0.3012
0.1809
230258.5
Step-by-step explanation:
Given that:
μ = 100,000
λ = 1/μ = 1 / 100000 = 0.00001
a. Fails in less than 10,000 hours.
P(X < 10,000) = 1 - e^-λx
x = 10,000
P(X < 10,000) = 1 - e^-(0.00001 * 10000)
= 1 - e^-0.1
= 1 - 0.1
= 0.9
b. Lasts more than 120,000 hours.
X more than 120000
P(X > 120,000) = e^-λx
P(X > 120,000) = e^-(0.00001 * 120000)
P(X > 120,000) = e^-1.2
= 0.3011942 = 0.3012
c. Fails between 60,000 and 100,000 hours of use.
P(X < 60000) = 1 - e^-λx
x = 60000
P(X < 60,000) = 1 - e^-(0.00001 * 60000)
= 1 - e-^-0.6
= 1 - 0.5488116
= 0.4511883
P(X < 100000) = 1 - e^-λx
x = 100000
P(X < 60,000) = 1 - e^-(0.00001 * 100000)
= 1 - e^-1
= 1 - 0.3678794
= 0.6321205
Hence,
0.6321205 - 0.4511883 = 0.1809322
d. Find the 90th percentile. So 10 percent of the TV sets last more than what length of time?
P(x > x) = 10% = 0.1
P(x > x) = e^-λx
0.1 = e^-0.00001 * x
Take the In
−2.302585 = - 0.00001x
2.302585 / 0.00001
= 230258.5
Using the exponential distribution, it is found that:
a) There is a 0.0952 = 9.52% probability that a television set fails in less than 10,000 hours.
b) There is a 0.3012 = 30.12% probability that a television set lasts more than 120,000 hours.
c) There is a 0.1809 = 18.09% probability that a television set fails between 60,000 and 100,000 hours of use.
d) The 90th percentile is of 230,259 hours.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In this problem:
Mean of 100,000 hours, hence, they decay parameter is [tex]\mu = \frac{1}{100000}[/tex]
Item a:
[tex]P(X \leq 10000) = 1 - e^{-\frac{10000}{100000}} = 1 - e^{-0.1} = 0.0952[/tex]
0.0952 = 9.52% probability that a television set fails in less than 10,000 hours.
Item b:
[tex]P(X > 120000) = e^{-\frac{120000}{100000}} = e^{-1.2} = 0.3012[/tex]
0.3012 = 30.12% probability that a television set lasts more than 120,000 hours.
Item c:
[tex]P(X \leq 60000) = 1 - e^{-\frac{60000}{100000}} = 1 - e^{-0.6} = 0.4512[/tex]
[tex]P(X \leq 100000) = 1 - e^{-\frac{100000}{100000}} = 1 - e^{-0.6} = 0.6321[/tex]
[tex]P(60000 \leq X \leq 100000) = P(X \leq 100000) - P(X \leq 60000) = 0.6321 - 0.4512 = 0.1809[/tex]
0.1809 = 18.09% probability that a television set fails between 60,000 and 100,000 hours of use.
Item d:
This is x for which:
[tex]P(X > x) = 0.1[/tex]
Hence:
[tex]e^{-\mu x} = 0.1[/tex]
[tex]e^{-0.00001 x} = 0.1[/tex]
[tex]\ln{e^{-0.00001 x}} = \ln{0.1}[/tex]
[tex]-0.00001 x = \ln{0.1}[/tex]
[tex]x = -\frac{\ln{0.1}}{0.00001}[/tex]
[tex]x = 230259[/tex]
The 90th percentile is of 230,259 hours.
A similar problem is given at https://brainly.com/question/25645425
A line passes through (-2, 10) and (8.-9). Write an equation for the line in point-slope
form AND rewrite the equation in standard form using integers.
Merry Christmas and Happy Holidays!!! <3
Answer:
The Standard Form of the equation of a line is: Ax+By=C
Converting that, once and forevermore, into slope-intercept form, and remembering the result,
the slope m=(-A/B).
If the given slope is 8, the equation of the line is 8x-y=C and we a point to determine C. Use (2,10)
8(2)-10=C
6 = C
The equation of the line, in Standard Form, is: 8x - y = 6
The zoo needs to hire b staff members for each exhibit. Write the expression for
the number of staff members they need to hire for 20 exhibits.
Answer:
feed them to the lions
Step-by-step explanation:
rawr
Which of the following statements are true? Select all that apply.
HELP PLEASE!
x^3*x^?=x^17 I don't know what the is.
Answer:
14Step-by-step explanation:
x^3*x^?=x^17x^(3 + ?) = x^173 + ? = 17? = 14Answer:
First write the given equation[tex]{:}\xrightarrow{ }\tt x^3×x^?=x^17 [/tex]
Simplify[tex]{:}\longrightarrow\tt x^{(3+?)}=x^17[/tex]
[tex]{:}\longrightarrow\tt 3+?=17 [/tex]
Interchange sides[tex]{:}\longrightarrow\tt ?=17-3 [/tex]
[tex]{:}\longrightarrow\tt ?=14 [/tex]
Explore more:-Formulas of exponents:-[tex]\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}[/tex]
Demarcus' workout playlist consists of classic rock songs and rap songs.
His playlist contains a total of 47 songs,
Which of the following statements represent the number of classic rock
and rap songs on Demarcus' playlist? Select all that apply.
x+y = 47
24 and 24
43 and 4
x = y + 47
y=-x+ 47
13 and 34
A farmer divided his piece of land into 2 equivalent groups and the quality of the soil is the same in both of these groups. He used fertilizers for the first group of land. He did not use fertilizers for the second group of land. At the end of the season, he measured the yield of the crops in these 2 groups. Is the study observational or experimental
Answer:
Observational would mean that he (farmer) has no direct impact or change on the statistical study.Experiment would mean that he imposed a certain treatment up a group in this case it would be the land.Hence we can determine that the the study was an experimental one.Solve. Please show your work
Answer:
128
Step-by-step explanation:
8^2√2^2
64√2^2 rewrite √2^2 as 2
64*2
=128
In a Create of 30 eggs
only 60 % is good how many
are bad?
Answer:
In my point of view 40% are bad
2. If a certain disease is found in 1 out of 12,000 people, what is the probability that there will be at least one person with that disease in a town of 24,000 people
Answer:
0.865
Step-by-step explanation:
Given that:
Disease is found in 1 out of 12000 people ; probability that disease is found in atleast one out of 24000 people
Using the binomial probability formula :
P(x = x) = nCx * p^x * (1 - p)^(n-x)
p = 1/ 12000 = 0.0000833333
n = 24000
P(x ≥ 1) = p(x = 1) + p(x =2) + ... + p(x = 24000)
In other to save computation time, we can employ the use of an online binomial probability calculator or a Ti-89 calculator :
The result is thus : 0.86467588659
P(x ≥ 1) = 0.865
Wall-mart had a laptop for $500. Best Buy was selling the same laptop for 15% more. What is price of the laptop at Best Buy?
Answer:
575
Step-by-step explanation:
15% of 500 = 75
500 + 75 = 575
Answer:
$425
Step-by-step explanation:
500*0.15=75
500-75=524
Indicate the answer choice that best completes the statement or answers the question.
The table shows the cost of long distance calls as a function of the number of minutes used. Is the cost a linear or nonlinear function of the
number of minutes used? Explain.
Number of Minutes 40 |80 120 160 1200
Cost (S)
14.00 8.00 12.00 16.00 120.00
Answer: hold on you didn’t give enough info for this to make sense
Step-by-step explanation:
Find x =
Please help I’ll give brainiest answer
Answer:
The Answer is 6
-3/7 × - 1 2/3
what is the answer
Answer:
[tex]\boxed{\frac{5}{7} }[/tex]
Step-by-step explanation:
[tex]-\frac{3}{7} \times (- 1 \frac{2}{3} )[/tex]
[tex]= -\frac{3}{7} \times (- \frac{5}{3} )[/tex]
[tex]= \frac{5}{7}[/tex]
Answer:
5/7
Step-by-step explanation:
do you get the answer?
Which graph shows a line with a slope of 3?
Answer:
The first graph shows a slope of 3.
Step-by-step explanation:
If the slope is 3, it's actually 3/1 because of rise/run. So you find any point on the graph that's directly between two lines, like (-1,-5). Since the line is positive, you would go right one and up three. Then you see if that point is directly between two lines. The next point is (0, -2). If you did the same on the second graph, it wouldn't match up.
Jamie scored an 85% on a test that had 20 questions on it. How many question did she get right? How many questions did she get wrong? PLS ANSWER FASTTT!! :)
Answer:i think it is like 17
Step-by-step explanation:
One week, Madelyn earned $265.60 at her job when she worked for 16 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $199.20?
Answer:
12 hours
Step-by-step explanation:
1. Start by dividing $265.60 by 16 hours to calculate the amount earned per hour.
$265.60 / 16 hours = $16.60/hr
2. Now, divide the new amount earned by her hourly wages (16.60)
199.20/16.60 = 12 hours
The number of visits to public libraries increased from 1.3 billion in 1994 to 1.6 billion in 1999. Find the average rate of change in the number of public library visits from 1994 to 1999.
Answer: 60 million per year
Step-by-step explanation:
The average rate of change in the number of public library visits from 1994 to 1999 will be calculated thus:
Average rate of change = change in number of vists in billions / number of years passed
= (1.6 billion - 1.3 billion) / 1999 - 1994
= 0.3 billion/5
= 60,000,000
= 60 million per year
HELP QUICK! 20 POINTS PLEASE GET IT CORRECT
What is the volume of a cylinder with a radius of 2 cm and a height of 8 cm?
Answer:
V = 100.531 cm³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Cylinder: V = πr²hStep-by-step explanation:
Step 1: Define Variables
r = 2 cm
h = 8 cm
Step 2: Find Volume
Substitute [Volume]: V = π(2 cm)²(8 cm)Exponents: V = π(4 cm²)(8 cm)Multiply: V = π(32 cm³)Multiply: V = 100.531 cm³what is -5x + 3y= 12 in slope intercept form?
Answer:
y = (5/3)x + 4
Step-by-step explanation:
-5x + 3y = 12 (What you start with)
3y = 12 + 5x (Adding 5x to both sides)
y = (5/3)x + 4 (Dividing the equation by 3)
The earth travels one full rotation around the sun in approximately 365.25 days. How many minutes does it take for the earth to travel one full rotation around the sun? Show your work. Make sure to include units in your answer.
Using proportions, it is found that it takes 525,960 minutes for the earth to travel one full rotation around the sun.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
One day has 24 hours of 60 minutes, hence the number of minutes in a single day is given by:
Md = 24 x 60 = 1440 minutes.
Hence, the number of minutes in 365.25 days is given by:
My = 1440 x 365.25 = 525,960 minutes
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
HELP PLS!!!!!!!!!!!!!!!!!!!!!!!!!!!! I WILL GIVE BRAINLIEST
Answer:
[tex]n=\frac{5\ln \left(\frac{q}{r}\right)}{\ln \left(q\right)}-2[/tex]
Step-by-step explanation:
Answer:
n = 3
Step-by-step explanation:
I guess you want the value of n
-----------------------------------------------------------
Since n is the index of q, you can simply
ignore all p and r stuff and make it
[tex]q^{2}[/tex]×[tex]q^{n}[/tex] = [tex]q^{5}[/tex]
[tex]q^{2+n}[/tex] = [tex]q^{5}[/tex]
2 + n = 5
n = 3
Please Help!!! :( I don't understand
Answer:
Step-by-step explanation:
You would do
4×18.5 =74
2×6.75 =13.5
14×7/8 =12.25
Add all that up and it equals 99.75lbs/pounds
10. What is the area of a triangle with base 4cm and
height 8cm?
A. 6cm2 B. 9cm2 C. 14cm D. 16 cm
Step-by-step explanation:
Area of triangle = 0.5(4)(8) = 16cm² (D).
Please answer I will give branliest
Answer:
Step-by-step explanation:
assuming that weekends are only sat and sunday
24 students
or
if were assuming that friday is included
30 students
hope this helps <3
Answer:
24 students prefer weekend days C:
Step-by-step explanation:
uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer: so 5 out of 5 is like if it said 100 out of 100
soooo the answer is 100% ;)
Step-by-step explanation:
PLEASE HELP!
Given that m∠NMP=(5y+11)∘ and m∠OMP=(8y−13)∘, identify m∠NMO.
Answer: 102
Step by Step Explanation:
5y+11=8y-13
-8 -8y
-3y+11=-13
-11 -11
3y = -24 = 8 y=8
3y 3y
5(8)+11=51
Multiple 51 times 2 and you're answer will be the following.
please i really really need help BRAIBLIST ASAP