If one of the vertices on the x-axis is (x, 0), then the other vertex on the same axis is (-x, 0), so that the rectangle has base 2x. The other two vertices on the parabola are the points (x, 6 - x²) and (-x, 6 - x²), so the height of the rectangle is 6 - x².
Then the area of the rectangle is given by the function
[tex]A(x)=2x(6-x^2)=12x-2x^3[/tex]
Compute the critical points of A:
[tex]A'(x)=12-6x^2=0\implies x=\pm\sqrt2[/tex]
So the maximum area is obtained when the vertices are the points (-√2, 0), (√2, 0), (√2, 4), and (-√2, 4). This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.
The maximum area is obtained when the vertices are the points
(-√2, 0), (√2, 0), (√2, 4), and (-√2, 4).
This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.
The area of a rectangle is expressed as shown:
A = xy
x is the length of the rectangle
y is the width
Given that y = 6 - x²
If its other two vertices above the x-axis and lying on the parabola, hence
the length of the rectangle will be 2x
The area of the rectangle will be A = 2x(6-x²)
If the dimension of the rectangle is at the maximum, hence dA/dx=0
A = 12x - 2x³
dA/dx = 12 - 6x²
0 = 12 - 6x²
6x² = 12
x² = 12/6
x² = 2
x = ±√2
Hence the maximum area is obtained when the vertices are the points
(-√2, 0), (√2, 0), (√2, 4), and (-√2, 4).
This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.
Learn more here: https://brainly.com/question/16925800
The mean family income for a random sample of 600 suburban households in Loganville shows that a 95 percent confidence interval is ($43,100, $59,710). Alma is conducting a test of the null hypothesis H0: µ = 42,000 against the alternative hypothesis Ha: µ ≠ 42,000 at the α = 0.05 level of significance. Does Alma have enough information to conduct a test of the null hypothesis against the alternative?
Answer:
[tex] 43100 \leq \mu \leq 59710[/tex]
And for this case we want to test the following hypothesis:
Null hypothesis: [tex] \mu =42000[/tex]
Alternative hypothesis: [tex] \mu \neq 42000[/tex]
For this case since the lower value of the confidence interval is higher than 42000 we have enough evidence to reject the null hypothesis at the 55 of significance and we can conclude that the true mean is significantly different from 42000
Step-by-step explanation:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And for this case the 95% confidence interval is already calculated as:
[tex] 43100 \leq \mu \leq 59710[/tex]
And for this case we want to test the following hypothesis:
Null hypothesis: [tex] \mu =42000[/tex]
Alternative hypothesis: [tex] \mu \neq 42000[/tex]
For this case since the lower value of the confidence interval is higher than 42000 we have enough evidence to reject the null hypothesis at the 55 of significance and we can conclude that the true mean is significantly different from 42000
Answer: Yes, because $42,000 is not contained in the 95% confidence interval, the null hypothesis would be rejected in favor of the alternative, and it could be concluded that the mean family income is significantly different from $42,000 at the α = 0.05 level
Step-by-step explanation:
took the test
(Please hurry)
Explain how to find the value of x
Answer:
96
Step-by-step explanation:
Exterior angles add up to 360
360 - 134-130 = 96
x = 96
3.
QR
find the arc length
02.83
021.99
O 12.57
0 34.56
How do I set up this problem. I'm lost
Answer:
the answer is 64 .
Step-by-step explanation:
basically i just divided 48 by 2.4 and got 20 .. so that means that 20 has to be the multiplied factor so i just multiplied 3.2 by 20 and got 64.
(Geometry) PLZ HELP ASAP
Answer:
121 square feet
Step-by-step explanation:
The area of a triangle is the height multiplied by the base divided by 2. Since this is a right triangle, you can simply use the two legs for this. The area of this triangle is therefore:
[tex]\dfrac{24.2\cdot 10}{2}=\dfrac{242}{2}=121[/tex]
Hope this helps!
Answer:
Area: 121 feet²
Step-by-step explanation:
The formula for the area of any triangle is [tex]\frac{1}{2} *b*h[/tex]
This triangle's base is 10 feet
This triangle's height is 24.2 feet
[tex]\frac{1}{2} *10*24.2=\\5*24.2=\\121[/tex]
The area of the triangle is 121 square feet or 121 ft²
18$ for 24 ounces. rate or ratio and in simplest form
Answer:
$3/4 ounces
.75 per ounce
Step-by-step explanation:
Take the dollar amount and divide by the number of ounces
18/24
$3/4 ounces
.75 per ounce
In the triangles below, m B = MZP and mZT = m J.
What is the length of PQ?
6
3
5
12
I can't solve it because it didn't have enough information
A customer visiting the suit department of a certain store will purchase a suit with probability 0.22, a shirt with probability 0.30, and a tile with probability 0.28. The customer will purchase both a suit and a shirt with probability 0.11, both a suit and a tie with probability 0.14, and both a shirt and a tie with probability 0.10. A customer will purchase all 3 items with probability 0.06. What’s the probability that a customer purchase: (a) none of these items? (b) exactly 1 of these items?
Answer:
a. The probability that a customer purchase none of these items is 0.49
b. The probability that a customer purchase exactly 1 of these items would be of 0.28
Step-by-step explanation:
a. In order to calculate the probability that a customer purchase none of these items we would have to make the following:
let A represents suit
B represents shirt
C represents tie
P(A) = 0.22
P(B) = 0.30
P(C) = 0.28
P(A∩B) = 0.11
P(C∩B) = 0.10
P(A∩C) = 0.14
P(A∩B∩C) = 0.06
Therefore, the probability that a customer purchase none of these items we would have to calculate the following:
1 - P(A∪B∪C)
P(A∪B∪C) =P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C)
= 0.22+0.28+0.30-0.11-0.10-0.14+0.06
= 0.51
Hence, 1 - P(A∪B∪C) = 1-0.51 = 0.49
The probability that a customer purchase none of these items is 0.49
b.To calculate the probability that a customer purchase exactly 1 of these items we would have to make the following calculation:
= P(A∪B∪C) - ( P(A∩B) +P(C∩B) +P(A∩C) - 2 P(A ∩ B ∩ C))
=0.51 -0.23 = 0.28
The probability that a customer purchase exactly 1 of these items would be of 0.28
A container holds less than 4 gallons of paint. Which inequality represents q, the number of quarts of paint it can hold? Recall that 4 quarts equal 1 gallon. A. q 1 C q 16
Answer:
q<16
Step-by-step explanation:
Multiply four quarts by four gallons. This gives us 16. Now, since it says less than, and not less than or equal to, we use < symbol. q<16
Answer:
q<16
Step-by-step explanation:
If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
There are two complex roots.
There are two real roots.
There is one real root.
There is one complex root.
Answer:
There are two complex roots.
Step-by-step explanation:
When the discriminant is a negative number, the parabola will not intersect the x-axis. This means that there are no solutions/two complex solutions.
148 is 37% of what amount
Answer:
400
Step-by-step explanation:
Answer: 148 is 37% of What Number? 37% of 400 is 148. 100% of 400 is 400, therefore 37 percent of 400 equals 148.
Brainlest would be appreciated.
If a triangle has sides that are 21 and 6 what is the range for third side x?
Enter your answer without spaces in range format.
Example: 1<x<3
Answer:
15<x<27
Step-by-step explanation:
Rule for the sides of a triangle:
The sum of the two smallest sides of a triangle must be greater than the biggest side.
In this question:
Sides of 6, 21 and x. We have to find the range for x.
If 21 is the largest side:
Two smallest are 6 and x.
x + 6 > 21
x > 21 - 6
x > 15
If x is the largest side:
Two smallest and 6 and 21. So
21 + 6 > x
27 > x
x < 27
Then
x has to be greater than 15 and smaller than 27. So the answer is:
15<x<27
Nam owns a used car lot. He checked the odometers of the cars and recorded how far they had driven. He
then created both a histogram and a box plot to display this same data (both diagrams are shown below).
Which display can be used to find how many vehicles had driven more than 200,000 km (kilometers)?
Choose 1 answer:
Answer:
a histogram
Step-by-step explanation:
You can count easily from hiistogram how many vehicles had driven more than 200,000 km (kilometers) and that's not the case with the box plot
If a variable has a distribution that is bell-shaped with mean 16 and standard deviation 6, then according to the Empirical Rule, 99.7% of the data will lie between which values? g
Answer:
99,7 % of all values will be in the interval ( -2 ; 34)
Step-by-step explanation:
Empirical Rule for the normal distribution with mean X, implies that the intervals :
X ± σ will contain 68 % of all values
X ± 2σ will contain 95 % of all values
X ± 3σ will contain 99,7 % of all values
Therefore in the interval X - 3σ ; X + 3σ
X - 3*6 = X -18 = 16 - 18 = -2
And
X + 3*6 = X + 18 = 16 + 18 = 34
99,7 % of all values will be in the interval ( -2 ; 34)
What is the solution to the equation a+5-2/3=9
Answer:
a= [tex]\frac{14}{3}[/tex]
a≈4.6
Step-by-step explanation:
a+5- [tex]\frac{2}{3}[/tex] =9
a+ [tex]\frac{15}{3} -\frac{2}{3}[/tex] =9
a+ [tex]\frac{13}{3}[/tex] =9
Subtract [tex]\frac{13}{3}[/tex] from both sides
a=[tex]\frac{14}{3}[/tex]
a≈4.6
Answer:
a
Step-by-step explanation:
Expansion Numerically Impractical. Show that the computation of an nth-order determinant by expansion involves multiplications, which if a multiplication takes sec would take these times:
n 10 15 20 25
Time 0.004 sec 22 min 77 years 0.5.109years
Answer:
number of multiplies is n!n=10, 3.6 msn=15, 21.8 minn=20, 77.09 yrn=25, 4.9×10^8 yrStep-by-step explanation:
Expansion of a 2×2 determinant requires 2 multiplications. Expansion of an n×n determinant multiplies each of the n elements of a row or column by its (n-1)×(n-1) cofactor determinant. Then the number of multiplies is ...
mpy[n] = n·mp[n-1]
mpy[2] = 2
So, ...
mpy[n] = n! . . . n ≥ 2
__
If each multiplication takes 1 nanosecond, then a 10×10 matrix requires ...
10! × 10^-9 s ≈ 0.0036288 s ≈ 0.004 s . . . for 10×10
Then the larger matrices take ...
n=15, 15! × 10^-9 ≈ 1307.67 s ≈ 21.8 min
n=20, 20! × 10^-9 ≈ 2.4329×10^9 s ≈ 77.09 years
n=25, 25! × 10^-9 ≈ 1.55112×10^16 s ≈ 4.915×10^8 years
_____
For the shorter time periods (less than 100 years), we use 365.25 days per year.
For the longer time periods (more than 400 years), we use 365.2425 days per year.
Consider the system:
y = 3x + 5
y = ax + b
What values for a and b make the system
inconsistent? What values for a and b make the
system consistent and dependent? Explain.
Answer:
Step-by-step explanation:
In this problem, we have the following linear equations:
y=3x+5
y=ax+b
We know that a linear equation is an equation for a line. In a system of linear equations, two or more equations work together.
1. What values for a and b make the system inconsistent?
A system is inconsistent if and only if the lines are parallel in which case the system has no solution. This is illustrated in the first Figure bellow. Two lines are parallel if they share the same slope. So, the system is inconsistent for:
a=3
for any value of b
2. What values for a and b make the system consistent and dependent?
A system is consistent if and only if the lines are the same in which case the system has infinitely many solutions. This is illustrated in the second Figure bellow. So, the system is consistent and dependent for:
a=3 and b=5
Answer:
When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.
Step-by-step explanation:
What’s the correct answer for this question?
Answer: choice D 1/2
Step-by-step explanation:
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.
so
1/6=1/3*p(A)
p(A)=1/2
if you’re good with permutations in math 30 help out with this easy question
In how many ways can five boys and three girls sit in a row such that all boys sit together?
a) 4800
b) 5760
c) 2880
d) 1440
Answer:
2880
Step-by-step explanation:
Consider the 5 boys to be 1 group. The boys and 3 girls can be arranged in 4! ways.
Within the group, the boys can be arranged 5! ways.
The total number of permutations is therefore:
4! × 5! = 2880
Solve X squared minus 8X +3 equals zero by completing the square which equation is used in the process?
Answer:
x = 4 ± √13
Step-by-step explanation:
x² − 8x + 3 = 0
Complete the square. (-8/2)² = 16.
x² − 8x + 16 − 13 = 0
(x − 4)² − 13 = 0
(x − 4)² = 13
x − 4 = ±√13
x = 4 ± √13
please hurry I’ll make brainiest
A marble is thrown off of a balcony, towards the ground, from a height
of 18 feet above ground level, with a velocity of 4.5 feet per second.
Which function could be used to model the height of the marble, after
t seconds?
Answer:
Option (3)
Step-by-step explanation:
A stone has been thrown off towards the ground from a height [tex]h_{0}[/tex] = 18 feet
Initial speed of the stone 'u' = 4.5 feet per second
Since height 'h' of a projectile at any moment 't' will be represented by the function,
h(t) = ut - [tex]\frac{1}{2}(g)(t)^2[/tex] + [tex]h_{0}[/tex]
h(t) = 4.5t - [tex]\frac{1}{2}(32)t^2[/tex]+ 18 [ g = 32 feet per second square]
h(t) = 4.5t - 16t² + 18
h(t) =-16t² + 4.5t + 18
Therefore, Option (3) will be the answer.
The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages ( x ) in the city has the following probability distribution.xf (x)00.8010.1520.0430.01The mean and the standard deviation for the number of electrical outages (respectively) are _____.
Answer:
Therefore, the mean and the standard deviation for the number of electrical outages (respectively) are 0.26 and 0.5765 respectively.
Step-by-step explanation:
Given the probability distribution table below:
[tex]\left|\begin{array}{c|cccc}x&0&1&2&3\\P(x)&0.8&0.15&0.04&0.01\end{array}\right|[/tex]
(a)Mean
Expected Value, [tex]\mu =\sum x_iP(x_i)[/tex]
=(0*0.8)+(1*0.15)+(2*0.04)+(3*0.01)
=0+0.15+0.08+0.03
Mean=0.26
(b)Standard Deviation
[tex](x-\mu)^2\\(0-0.26)^2=0.0676\\(1-0.26)^2=0.5476\\(2-0.26)^2=3.0276\\(3-0.26)^2=7.5076[/tex]
Standard Deviation [tex]=\sqrt{\sum (x-\mu)^2P(x)}[/tex]
[tex]=\sqrt{0.0676*0.8+0.5476*0.15+3.0276*0.04+7.5076*0.01}\\=\sqrt{0.3324}\\=0.5765[/tex]
Therefore, the mean and the standard deviation for the number of electrical outages (respectively) are 0.26 and 0.5765 respectively.
18. The servicing of a machine requires two separate steps, with the time needed for the
first step being an exponential random variable with mean 0.2 hour and the time for the
second step being an independent exponential random variable with mean 0.3 hour. If a
repair person has 20 machines to service, what is approximately the probability that all the
work can be completed in 8 hours?
Answer:
Step-by-step explanation:
Let X denote the first step
Let Y denote the second step
Then
E(X) = 0.2
E (Y) = 0.3
V (X) = 0.04
V (Y) = 0.09
Now,
E(X,Y) = E[X] + E{Y}
0.2 + 0.3 = 0.5
And since X and Y are independent
Therefore,
V(X , Y) = V(X) + V(Y)
= 0.04 + 0.09
= 0.13
Now required probability is
[tex]P\{ \sum X_i+\sum Y_i<8 \}=P\{ \frac{\sum X_i + \sum Y_i-nE[X+Y]}{\sqrt{Var(X+Y)n} } <\frac{8-20\times0.5}{\sqrt{0.13\times20} } \}\\\\=P\{Z_n<\frac{8-10}{\sqrt{2.6} } \}\\\\=P\{Z_n<-1.24\}[/tex]
= Φ(-1.24)
= 1 - Φ (1.24)
= 1 - 0.8925
= 0.1075
The random variable x is the number of vehicles that pass through an intersection in a 30-minute interval. It can be assumed that the probability of an occurrence is the same in any two time intervals of an equal length. It is known that the mean number of occurrences in 30 minutes is 9. What is the expected value of the random variable x?
Answer:
9 is the correct answer to the given question .
Step-by-step explanation:
AS mention in the question the random variable x is the number of vehicles that passing through the intersection in the 30-minute .So we concluded that it is normal distribution because in the normal distribution the variable values are divided .
In the Normal distribution
[tex]Mean \ number\ =\ Expected\ value\ \\Here Mean number\ =\ 9[/tex]
Therefore the Expected value =9.
What is the solution to the question
82.24 =-8.48 + 4x
Answer:
22.68
Step-by-step explanation:
82.24 =-8.48 + 4x
82.24+8.48 = 4x
90.72=4x
90.72/4=x
22.68=x
If (-2, y) lies on the graph of y=3x, then y=
1/9
0-6
hi
if reduce equation of line is y = 3x
and if x = -2 so y = 3*-2 = -6
Please answer this question for me thank you !! 20 Points !! Will give brainliest !!
Answer:
b
Step-by-step explanation:
In a parralel graph, the slopes would always be the same. The intercept in the answer is 2, showing that the coordinate points are (0,2)
Hope this helps!:)
Answer:
B) y = 2x + 2
Step-by-step explanation:
Firstly, you have to know that parallel lines have congruent slopes. That means that the slope of this line will be 2.
Next, make a point slope form of the equation:
y - y1 = m(x - x1)
y - 2 = 2(x - 0)
y - 2 = 2x - 0
Now, we can make it into slope intercept form.
y - 2 = 2x
y = 2x + 2
Hope this helps :)
Which triangle’s area would be calculated using the trigonometric area formula?
Triangle E F D is shown. The length of E F is 10, the length of D F is 7, and the length of D E is 12.
Triangle Q R P is shown. The length of Q R is 5 and the length of R P is 6. Angle Q R P is 40 degrees.
Triangle A B C is shown. The length of A B is 4 and the length of B C is 5. Angle B C A is 25 degrees.
Triangle X Y Z is shown. The length of Y Z is 4. Angle Z X Y is 29 degrees and angle X Y Z is 110 degrees.
Answer:
Triangle Q R P is shown. The length of Q R is 5 and the length of R P is 6. Angle Q R P is 40 degrees.
Step-by-step explanation:
The trigonometric formula refers the two sides length of the triangle and it also consists of included angle to find out the area
A = [tex]\frac{1}{2}[/tex] ab sin C
QPR contains two sides and the included angle
XYZ has one side and the two angles
DEF has only three sides
And, the ABC contains two sides but does not have the included angle
Based on the explanation above, the correct option is B
Answer: the second option aka B
Step-by-step explanation: The other person explained it and I'm just here to tell you they gave the correct and answer for edge 2020.
Please answer this correctly
Answer:
Stem | Leaf
13 | 4 9 9
16 | 0 2 3 6
Step-by-step explanation:
134, 139, 139
160, 162, 163, 166
I NEED HELP WITH THIS PLEASE HELP ME
Answer:
156 minutes
Step-by-step explanation:
So we need to create an equation to represent how Frank's phone company bills him
I will denote "y" as the total for his billI will denote "x" as the number of minutes Frank usesSo the phone company charges an $8 monthly fee, so this value remains constant and will be our "y-intercept"
They then charge $0.06 for every minute he talks, this will be our "slope"
Combining everything into an equation, we have: y = 0.06x + 8
Now since we were given Franks phone bill total and want to figure out how many minutes he used, we just need to solve the equation for x and plug in our known y value
y = 0.06x + 8 → y - 8 = 0.06x → [tex]x=\frac{y-8}{0.06}[/tex] Then plugging in our y value we get [tex]x=\frac{17.36-8}{0.06}=\frac{9.36}{0.06}= 156[/tex]Frank used up a total of 156 minutes