Answers
9514 1404 393
Answer:
c. y = (x +2)² -5
Step-by-step explanation:
If you replace the squared term with zero, you are choosing the minimum of the remaining values. (A squared term cannot have a negative value.)
a) 3
b) 4
c) -5 . . . . the graph with the least possible y-value
d) 0
Related Questions
Engineers are designing a large elevator that will accommodate 44 people. The maximum weight the elevator can hold safely is 8228 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 186 pounds and standard deviation 60 pounds, and the weights of adult U.S. women have mean 157 pounds and standard deviation 69 pounds.
a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?
b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
Answers
Answer:
a) Their average weight is of 187 pounds.
b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.
c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?
8228/44 = 187
Their average weight is of 187 pounds.
b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
For men, we have that [tex]\mu = 186, \sigma = 60[/tex]
Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]
This probability is 1 subtracted by the p-value of Z when X = 187. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a p-value of 0.5438.
1 - 0.5438 = 0.4562
0.4562 = 45.62% probability that the maximum safe weight will be exceeded.
c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
For women, we have that [tex]\mu = 157, \sigma = 69[/tex]
Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]
[tex]Z = 2.88[/tex]
[tex]Z = 2.88[/tex] has a p-value of 0.998.
1 - 0.998 = 0.002.
0.002 = 0.2% probability that the maximum safe weight will be exceeded
Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days. (Round your answers to two decimal places.) (a) What is the half-life (in days) of this substance
Answers
Answer:
The half-life of this substance is of 569.27 days.
Step-by-step explanation:
Amount of a substance after t days:
The amount of a substance after t days is given by:
[tex]P(t) = P(0)e^{-kt}[/tex]
In which P(0) is the initial amount and k is the decay rate, as a decimal.
Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days.
This means that [tex]P(300) = 0.694P(0)[/tex]. We use this to find k.
[tex]P(t) = P(0)e^{-kt}[/tex]
[tex]0.694 = P(0)e^{-300k}[/tex]
[tex]e^{-300k} = 0.694[/tex]
[tex]\ln{e^{-300k}} = \ln{0.694}[/tex]
[tex]-300k = \ln{0.694}[/tex]
[tex]k = -\frac{\ln{0.694}}{300}[/tex]
[tex]k = 0.0012[/tex]
So
[tex]P(t) = P(0)e^{-0.0012t}[/tex]
What is the half-life (in days) of this substance?
This is t for which P(t) = 0.5P(0). So
[tex]0.5P(0) = P(0)e^{-0.0012t}[/tex]
[tex]e^{-0.0012t} = 0.5[/tex]
[tex]\ln{e^{-0.0012t}} = \ln{0.5}[/tex]
[tex]-0.0012t = \ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.0012}[/tex]
[tex]t = 569.27[/tex]
The half-life of this substance is of 569.27 days.
please solve this fast
Answers
Step-by-step explanation:
1.
[tex]qr - pr \: + qs - ps[/tex]
[tex]r(q - p) + s(q - p)[/tex]
[tex](r + s)(q - p)[/tex]
2.
[tex] {x}^{2} + y - xy - x[/tex]
[tex] {x}^{2} - x - xy + y[/tex]
[tex]x(x - 1) - y(x - 1)[/tex]
3.
[tex]6xy + 6 - 9y - 4x[/tex]
[tex] - 4x + 6 + 6xy - 9y[/tex]
[tex]2( - 2x + 3) - 3y( - 2x + 3)[/tex]
[tex](2 - 3y)( - 2x + 3)[/tex]
4.
[tex] {x}^{2} - 2ax - 2ab + bx[/tex]
[tex]x(x - 2a) - b(x - 2a)[/tex]
[tex]-(x +b)(2a-x)[/tex]
5.
[tex]axy + bcxy - az - bcz[/tex]
[tex]xy(a + bc) - z(a + bc)[/tex]
[tex](xy - z)(a + bc)[/tex]
Kayla, Devon and Maggie are working on translating verbal expressions into algebraic
expressions. The question on their assignment asks them to translate "seven less than four
times the square root of x".
Answers
9514 1404 393
Answer:
4√x -7
Step-by-step explanation:
Four times the square root of x is written 4√x. Seven less than that is found by subtracting 7:
[tex]4\sqrt{x}-7[/tex]
help plzz! find the value of x
Answers
Answer: 12°
Hope this helps!
What is the vertex of the parabola graphed
below?
-4-2 o
2 4
(2,0)
(2,-4)
0 (-4,0)
(4,0)
Other:
Answers
Answer:
Step-by-step explanation:
The vertex is either the highest point on the parabola or the lowest point. We have a positive parabola, so the vertex is a low point. It sits at (2, -4). Locate that point and see what I mean by the lowest point on the parabola.
I need to know the answer and the work it asks for
Answers
Answer:
b 25x6 = 150
25 decreases every month so
150 decreses every 6 month
800-150
650 are the bees remaining after 6 month
F(x) = 4x^3 + 7x^2-2x-1
G(x) = 4x-2
Find (f-g)(x)
Answers
I really need help please
Answers
Answer:
first question is D
second question is D .875
Step-by-step explanation:
35*2.5= 87.5
7 divided by 8= .875
Answer:
D 87.5 miles
D 0.875 = 7/8 so it is a decimal that terminates after 3 dp.
Step-by-step explanation:
We write;
Scale Inch x Miles
2.5 x 35 = 87.5 miles
Why??
87.5 miles is found when we use the scale of 35 miles = 1inch
Answer = D 87.5 miles
The second one we can either multiply by 7/8 or divide by 1-7/8 = 1/8 to show that;
1/ 1/8 = 0.125
1-0.125 = 0.875
1. In a group, there were 115 people whose proofs of identity were being verified. Some hadpassport, some had voter id and some had both. If 65 had passport and 30 had both, how many had voter id only and not passport? .
Answers
Answer: 65 have passport and 30 have passport and voter ID so the remainder of people with voter ID only would be 20
Step-by-step explanation
Marta's bedroom floor is rectangular is 18 feet long and 15 feet wide. The height of the ceiling is 8 feet. She has 3 rectangular windows that are each 6 feet long and 4 feet wide. She will paint the entire room except the floor and the window. What is the area that Marta will paint?
Answers
9514 1404 393
Answer:
726 ft²
Step-by-step explanation:
The perimeter of the room is ...
P = 2(L+W) = 2(18 +15) = 66 . . . . ft
Then the gross wall area (including windows) is ...
A = LH = (66 ft)(8 ft) = 528 ft² . . . . gross wall area
The area of the 3 windows is ...
A = 3×LW = 3×(6 ft)(4 ft) = 72 ft² . . . . window area
The area of the ceiling is ...
A = LW = (18 ft)(15 ft) = 270 ft² . . . . ceiling area
__
Then the net area to be painted is ...
gross wall area + ceiling area - window area
= 528 ft² +270 ft² -72 ft² = 726 ft²
The area that Marta will paint is 726 ft².
make x the subject of the relaton3x-ax=2x+5
Answers
Answer:
x =5/ (1-a)
Step-by-step explanation:
3x-ax=2x+5
Subtract 2x from each side
3x -ax-2x = 2x+5-2x
3x -ax -2x = 5
combine like terms
x-ax = 5
Factor out x
x(1-a) =5
Divide each side by 1-a
x =5/ (1-a)
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]3x-ax=2x+5\\\\3x-ax-2x=5\\\\(3-2)x-ax=5\\\\x-ax=5\\\\x(1-a)=5\\\\\dashrightarrow x=\dfrac{5}{1-a}[/tex]
Anthony steps on a bathroom scale that records his weight at 195 pounds. He immediately steps back onto the same scale, which records his weight at 205 pounds. It is MOST accurate to describe these scales as:
Answers
Answer:
Moving upwards with an acceleration.
Step-by-step explanation:
weight of the person = 195 pounds
Apparent weight = 205 pounds
As the weight increases so the scale is moving upwards with some acceleration.
The scale is in elevator which is moving upwards.
The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
Answers
Answer:
Step-by-step explanation:
Part A
The x-intercept are the values of the variable "x" for which the value of the function, f(x) is zero (f(x) = 0)
The given parameters are;
The values of the function, f(x) = The company's profit
The values of the independent variable, "x" = The price of erasers
Therefore, at the x-intercept, where the values of the variable "x" are 0 and 8, the profit of the company, (f(x)) is 0 (the company does not make any profit)
2) The maximum value, which is the highest point of the graph with coordinate (4, 270), gives the company's maximum profit, f(x) = $270, and the price of the eraser, x-value, at which the company makes maximum profit which is at the price of an eraser, x = $4
3) The intervals where the function is increasing is 0 ≤ x ≤ 4
At the interval where the function is increasing, the sale price is increasing and the profits are increasing
The intervals where the function is decreasing is 4 ≤ x ≤ 8
At the interval where the function is decreasing, the sale price is increasing and the profits are decreasing
Part B
The appropriate average rate of change of the graph from x = 1 to x = 4 where f(x) = 120 and 270 respectively is given as follows
Rate of change of the graph from x = 1 to x = 4 is (270 -120)/(4 - 1) = 50
The average rate of change of the graph represents that the as the price of the eraser increases by $1.00 the profits increases by $50.00
THIS WAS NOT MY OWN ANSWER, PLEASE LET oeerivona TAKE THE POINTS!!
In a quiz , positive marks are given for correct answers and negative marks are given dor incorrect answers. If Jack's scores in five successive rounds were 25,-5,-10, 15 and 10 , what was the total at the end.
I need it fast
Answers
Given:
Jack's scores in five successive rounds were 25,-5,-10, 15 and 10.
To find:
The total score at the end.
Solution:
It is given that the scores in five successive rounds were 25,-5,-10, 15 and 10. So, the sum of the scores at the end is:
[tex]Sum=25+(-5)+(-10)+15+10[/tex]
[tex]Sum=(25+15+10)+(-5-10)[/tex]
[tex]Sum=50+(-15)[/tex]
[tex]Sum=50-15[/tex]
[tex]Sum=35[/tex]
Therefore, the total score at the end. is 35.
Help...I will give brainlist...but answer must be right
A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and 1. How many solutions are possible for this situation?
a) Infinitely many solutions exist because the two situations describe the same line.
b)Exactly one solution exists because the situation describes two lines that have different slopes and different y-intercepts.
c)No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
d)Exactly one solution exists because the situation describes two lines with different slopes and the same y-intercept.
Answers
Answer:
The answer is C, no solution.
Step-by-step explanation:
if f(x)=√x-x and g(x)=2x^3-√x-x find f(x)-g(x)
Answers
Answer:
2sqrt(x)-2x^3
Step-by-step explanation:
f(x) - g(x) = sqrt(x)-x-(2x^3)+sqrt(x)+x=2sqrt(x)-2x^3
The difference of the two functions f(x) and g(x) is -
f(x) - g(x) = [tex]-2x^{3} + 2\sqrt{x}[/tex]
We have - two functions of [tex]x[/tex] :
[tex]f(x)=\sqrt{x} -x\\g(x) = 2x^{3} - \sqrt{x} -x[/tex]
We have to find -
[tex]f(x)-g(x)[/tex]
What do you understand by the term - [tex]y=f(x)\\[/tex] ?The term [tex]y=f(x)[/tex] indicates that [tex]y[/tex] is expressed as a function of [tex]x[/tex], where [tex]x[/tex] is a independent variable and [tex]y[/tex] is a dependent variable which depends on [tex]x[/tex].
According to question -
[tex]f(x)-g(x)=\sqrt{x} -x - (2x^{3} - \sqrt{x} -x)\\f(x)-g(x)=\sqrt{x} -x-2x^{3} + \sqrt{x} +x\\f(x)-g(x)=-2x^{3} + 2\sqrt{x}[/tex]
Hence, f(x) - g(x) = [tex]-2x^{3} + 2\sqrt{x}[/tex]
To solve more questions on operations of functions, visit the link below-
https://brainly.com/question/12688480
#SPJ2
.
Bob wants to install a
solar panel on his roof to
heat water for his family. The
power company advertises a
35% savings to electric bills
with the installation of a solar
panel. If Bob's average
electric bill is $132.50 how
much could he save if he had
a solar panel?
a. $35.00
b. $46.38
c. $62.14
d. $100.35
Answers
Answer:
46.38
Step-by-step explanation:
all the answer are not same but buy calculating its the right answer
tell me the ans of e
Answers
The distance from the origin is a.
Step-by-step explanation:
If the point is located at the coordinate [tex](a\cos \alpha, a\sin \alpha)[/tex], then its distance from the origin is given by
[tex]r = \sqrt{x^2 + y^2} = \sqrt{(a\cos \alpha)^2 + (a\sin \alpha)^2}[/tex]
[tex]\:\:\:\:=\sqrt{a^2(\cos^2\alpha + \sin^2 \alpha)}[/tex]
[tex]\:\:\:\:= a[/tex]
Write the equation 5x – 2y = 10 in the form y = mx + b.
Answers
-2y=10-5x
-2y/-2=(10-5x)/-2
Y=5/2x-2
Matthew Travels 42/50 Meters In 26/30 Minutes. Find The Speed of Mathew In Meters Per Second.
Answers
Answer:
Matthew travels 0.0161 meters per second.
Step-by-step explanation:
Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:
42/50 = 0.84
26/30 = 0.86
0.86 x 60 = 52
0.84 meters in 52 seconds
0.84 / 52 = 0.01615
Therefore, Matthew travels 0.0161 meters per second.
Find the arc length of the semicircle. Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Answers
Answer:
9.42
Step-by-step explanation:
The circumference of a circle is calculated using the following formula:
C=2πr (C: circumference, r : radius)
radius here is 6 and π is given as 3.14
2*(3.14)*6 = 18.84 now divide this by 2 to find the length of semicircle
18.84/2 = 9.42
Answer:
6π
Step-by-step explanation:
Find the length of the missing side. triangle with an 8 inch side and 12 inch side with a right angle 8.9 in. 104 in. 4 in 14.4 in
Answers
Given:
In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.
To find:
The length of the missing side.
Solution:
In a right angle triangle,
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.
Substituting Perpendicular = 8 inches and Base = 12 inches, we get
[tex]Hypotenuse^2=8^2+12^2[/tex]
[tex]Hypotenuse^2=64+144[/tex]
[tex]Hypotenuse^2=208[/tex]
Taking square root on both sides, we get
[tex]Hypotenuse=\sqrt{208}[/tex]
[tex]Hypotenuse=14.422205[/tex]
[tex]Hypotenuse\approx 14.4[/tex]
The length of the missing side is 14.4 inches. Therefore, the correct option is D.
Find the missing side. Round your answer to the nearest tenth
Answers
Answer: Around 37.3
Step-by-step explanation:
[tex]tan(63)=\frac{x}{19} \\\\x=19*tan(63)=37.2895996...[/tex]
Answer:
37.3
Step-by-step explanation:
tan (63)=x/19
x=19×tan(63)=37.3
HELP ASAP!!!!!!!PLEASE SHOW WORK!!!!!!
Answers
Answer:
Area = 72.62 m²
Step-by-step explanation:
Area of a triangle with the given three sides is given by,
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Here, s = [tex]\frac{a+b+c}{2}[/tex]
And a, b, c are the sides of the triangle.
From the question,
a = 20 m, b = 10 m and c = 15 m
s = [tex]\frac{20+10+15}{2}[/tex]
s = 22.5
Substitute these values in the formula,
Area = [tex]\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)}[/tex]
= [tex]\sqrt{22.5(2.5)(12.5)(7.5)}[/tex]
= [tex]\sqrt{5273.4375}[/tex]
= 72.62 m²
2 times the sum of a number Plus 8 is 26 what is the number
Answers
Answer:
x = 5
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
2(x + 8) = 26
Step 2: Solve for x
[Division Property of Equality] Divide 2 on both sides: x + 8 = 13[Subtraction Property of Equality] Subtract 8 on both sides: x = 5From a random sample of 20 bars selected at random from those produced, calculations gave a mean weight of = 52.46 grams and standard deviation of s = 0.42 grams. Assuming t distribution is followed, construct a 90% confidence interval for the mean weight of bars produced, giving the limits to two decimal places.
Answers
Answer:
(52.30 ; 52.62)
Step-by-step explanation:
Given :
Sample size, n = 20
Mean, xbar = 52.46
Standard deviation, s = 0.42
We assume a t - distribution
The 90% confidence interval
The confidence interval relation :
C.I = xbar ± Tcritical * s/√n
To obtain the Tcritical value :
Degree of freedom, df = n - 1 ; 20 - 1 = 19 ; α = (1 - 0.90) /2 = 0.1/2 = 0.05
Using the T-distribution table, Tcritical = 1.729
We now have :
C.I = 52.46 ± (1.729 * 0.42/√20)
C. I = 52.46 ± 0.1624
C.I = (52.30 ; 52.62)
Below, the two-way table is given for a
class of students.
Freshmen Sophomore
Juniors
Seniors
Total
Male
4
6
2
2
Female 3
4
6
3
Total
If a student is selected at random, find the
probability the student is a male given that it's
a sophomore. Round to the nearest whole
percent.
[?]%
Answers
Answer:
20%
Step-by-step explanation:
The total number of students is: 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 (students)
The probability is: 6/30 = 1/5 = 0.2 = 20%
The probability that the student is a male given that he's a sophomore is approximately 60%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The probability that the student is a male given that it's a sophomore can be calculated using the formula:
P(male | sophomore) = P(male and sophomore) / P(sophomore)
The number of male sophomores is 6, and the total number of sophomores is 6+4=10.
So, the probability of selecting a sophomore is:
P(sophomore)
= (number of sophomores) / (total number of students)
= 10 / 23
The number of male sophomores is 6.
So,
The probability of selecting a male sophomore is:
P(male and sophomore) = 6 / 23
Therefore,
The probability that the student is a male given that it's a sophomore is:
P(male | sophomore)
= (6 / 23) / (10 / 23)
= 6 / 10
= 3 / 5
Rounding to the nearest whole percent, we get:
P(male | sophomore) ≈ 60%
Thus,
The probability that the student is a male given that he's a sophomore is approximately 60%.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ7
I need help.
You are interested in finding a 95% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 12 randomly selected non-residential college students. Round answers to 3 decimal places where possible.
Answers
Answer:
(11.847 ; 15.813)
Step-by-step explanation:
We are given 12 samples which are :
8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25
We use a T-distribution to find the confidence interval since the sample size. is small, n < 30
Using a calculator :
The sample mean, xbar = 13.83
Sample standard deviation, s = 6.87
The confidence interval, C.I
C.I = xbar ± Tcritical * s/√n)
Tcritical at 95%, df = n - 1, 12 - 1 = 11
Tcritical(0.05, 11) = 2.20
Hence,
C.I = 13.83 ± 2.20(6.87/√12)
C.I = 13.83 ± 1.9831981
C. I = (13.83 - 1.983 ; 13.83 + 1.983)
C. I = (11.847 ; 15.813)
Given m = 1/2 and the point (3, 2), which of the following is the point-slope form of the equation?
Answers
Answer:
The point-slope form is y - 2 = 1/2 (x - 3)
Step-by-step explanation:
The point-slope form is y - y1 = m (slope) (x - x1). All I did was plug the numbers in the correct locations to get my answer.
