Answer:
[tex]x=4[/tex]
Step-by-step explanation:
We have the quadratic function:
[tex]\displaystyle y=0.3(x-4)^2-2.5[/tex]
And we want to determine its axis of symmetry.
Notice that this is in vertex form:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex of the parabola.
From our function, we can see that h = 4 and k = -2.5. Hence, our vertex is the point (4, -2.5).
The axis of symmetry is equivalent to the x-coordinate of the vertex.
The x-coordinate of the vertex is 4.
Therefore, the axis of symmetry is x = 4.
HELPPP PLEASEEE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start either now. Thank you for your time.
The mean per capita consumption of milk per year is 131 liters with a variance of 841. If a sample of 132 people is randomly selected, what is the probability that the sample mean would be less than 133.5 liters
Answer:
0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.
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.
The mean per capita consumption of milk per year is 131 liters with a variance of 841.
This means that [tex]\mu = 131, \sigma = \sqrt{841} = 29[/tex]
Sample of 132 people
This means that [tex]n = 132, s = \frac{29}{\sqrt{132}}[/tex]
What is the probability that the sample mean would be less than 133.5 liters?
This is the p-value of Z when X = 133.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{133.5 - 131}{\frac{29}{\sqrt{132}}}[/tex]
[tex]Z = 0.99[/tex]
[tex]Z = 0.99[/tex] has a p-value of 0.8389
0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.
Which value of X makes the quotient of (5x^5+90x^2-135x)/(x+3) undefined
A -2
B -3
C -4
D -1
Answer:
b) - 3
Step-by-step explanation:
If x = -3 , then
x + 3 = -3 + 3 = 0
So, denominator would become 0. So , anything divided by 0 is undefined
if f(x)=x+8 and g(x)=-4x-3 find (f+g)(x)
Answer:
for this case we have the following functions:
f (x) = x + 8
g (x) = -4x - 3
Subtracting the functions we have:
(f - g) (x) = f (x) - g (x)
(f - g) (x) = (x + 8) - (-4x - 3)
Rewriting:
(f - g) (x) = x + 8 + 4x + 3
(f - g) (x) = 5x + 11
Answer:
D. (f - g) (x) = 5x + 11
3x7 I need help with this i do not know the answer pls help.
Answer:
21
Step-by-step explanation:
7+7+7=21
Find the area of the regular pentagon. 4.1 cm 6 cm Area = [?] cm? Enter your answer to the nearest tenth.
Answer:
Area of the given regular pentagon is 61.5 cm².
Step-by-step explanation:
Area of a regular polygon is given by,
Area = [tex]\frac{1}{2}aP[/tex]
Here, a = Apothem of the polygon
P = Perimeter of the polygon
Apothem of the regular pentagon given as 4.1 cm.
Side of the pentagon = 6 cm
Perimeter of the pentagon = 5(6)
= 30 cm
Substituting these values in the formula,
Area = [tex]\frac{1}{2}(4.1)(30)[/tex]
= 61.5 cm²
Therefore, area of the given regular pentagon is 61.5 cm².
Write an addition or a subtraction equation (your choice!) to describe the diagram. Pls help
Answer:
Addition equation = -4-0) + [(-13)-(-4)]
Answer = -13
Step-by-step explanation:
For the small arrow in the diagram, the expression is (-4 - 0)
For the bog arrow, the expression will be -13 - (-4)
Adding both expressions
Addition = (-4-0) + [(-13)-(-4)]
Addition = (-4) + (-13+4)
Addition = -4 + (-9)
Addition = -4-9
Addition = -13
What is the mean?
9.12.34.6.8.9.
Answer:
13
Step-by-step explanation:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Answer:
The mean (average) of these numbers is equal to 13.
Step-by-step explanation:
Another word for the "mean" of numbers is the "average" of numbers. You can find the average by adding all the numbers together and then dividing the sum you got by the number of values you added together, so in our case, there are 6 values given, therefore we will find the sum of all these numbers and then divide it by 6...
[tex]\frac{9 + 12 + 34 + 6 + 8 + 9}{6} = \frac{78}{6} = 13[/tex]
Therefore, the mean (average) of this number is equal to 13.
Sorry to ask so many questions but I need help in MATH
PLZZZ HELPPP
Answer:
24 26 27 94 is the answer 45
Answer:
the correct answer is 45
I need to find a but I don’t know how to, could you please explain
Answer:
87
Step-by-step explanation:
Given is a figure of cyclic quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
Therefore,
z° + 93° = 180°
z° = 180° - 93°
z° = 87°
z = 87
The graphs below have the same shape the equation of the bluegrass is f(x)=x^3 what is the equation of the red graph
Answer:
g(x) = x^3 - 2
Step-by-step explanation:
As you can see on the graph, the line has been translated down 2 units.
If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2
g(x) = x^3 - 2
Hope this helps!!
Area of composite shapes ?
Answer: 58
Step-by-step explanation: you add them all together
Its 108 the other answer is the perimeter not the area.
what is the distance in the image below?
The distance is:
5 + 3 = 8 units
Since the segment is completely horizontal we need not to use formula for computing the length of a segment in 2D euclidean space.
Instead we can simplify the problem to a single dimension, only considering the x-coordinates of the endpoints of the segment.
The x-coordinates are -5 and 3.
Subtracting and applying absolute value yields the answer,
[tex]\mathrm{abs}(-5-3)=\boxed{8}[/tex].
Hope this helps.
This is the graph of y = -x2 - 2x + 8.
What is the range of this function?
Hi there!
[tex]\large\boxed{(-\infty, 9)}[/tex]
We can find the range using completing the square:
y = -x² - 2x + 8
Factor out a -1:
y = -(x² + 2x) + 8
Use the first two terms. Take the second term's coefficient, divide by 2, and square:
y = -(x² + 2x + 1) + 8
Remember to add by 1 because we cannot randomly add an additional number into the equation:
y = -(x² + 2x + 1) + 8 + 1
Simplify:
y = -(x + 1)² + 9
Since the graph opens downward (negative coefficient), the range is (-∞, 9)
factor the GCF out of the polynomial
Answer:
1. Find the GCF of all the terms in the polynomial.
2. Express each term as a product of the GCF and another factor.
3. Use the distributive property to factor out the GCF.
BRAINLIEST HELP ME!!!
Which graph shows the solution to this system of linear Inequalities?
ys2x-3
A. Graph
B. Graph B
C. Graph A
D. Graph D
21. Which of the following statements is true?
(1) -18 > -5
(2) -5 > -0.5
(3) -5> 0
(4) -5 > 52
(5) -5 > -18
Answer: (5) -5 > -18
Step-by-step explanation:
The farther the negative number is from 0, the smaller it becomes.Negative numbers will be smaller than positive numbers, since they're smaller than 0.-5 is 5 away from zero, making it larger than -18 since it's closer to 0, while -18 is 18 away from zero.
A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is correct. State the null and alternative hypotheses.
Answer:
The answer is:
[tex]H_0: p=0.83\\\\H_a: p \neq 0.83[/tex]
Step-by-step explanation:
Now, we're going to test if sociologists claim to be have visited a region of 0.83 by a person picked randomly on Time In New York City.
Therefore, null or other hypotheses are:
[tex]H_0: p=0.83\\\\H_a: p \neq 0.83[/tex]
After heating a fixed volume of gas at 50 psia from 300° R to 600°R, its pressure will be:
Answer:
100 psia
Step-by-step explanation:
Applying,
Pressure law,
P/T = P'/T'................. Equation 1
Where P = initial pressure, P' = Final pressure, T = initial temperature, P' = Final temperature.
make P' the subject of the equation
P' = PT'/T............ Equation 2
From the question,
Given: P = 50 psia, T = 300°R = (300×5/9)K = 166.66 K, T' = 600°R = (600×5/9)K = 333.33 K
Substitute these values into equation 2
P' = (50×333.33)/166.66
P' ≈ 100 psia
P ≈ 100 psia
Please hlep x^2+6x+1=0
Answer:
Substitute into the quadratic formula
-6 ± √32 / 2
= -3 ± √16
= 1 and -1 are the answer
Answer:
x = - 3 ± 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
x² + 6x + 1 = 0 ( subtract 1 from both sides )
x² + 6x = - 1
Using the method of completing the square
add/ subtract ( half the coefficient of the x- term)² to both sides
x² + 2(3)x + 9 = - 1 + 9
(x + 3)² = 8 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( subtract 3 from both sides )
x = - 3 ± 2[tex]\sqrt{2}[/tex]
Then
x = - 3 - 2[tex]\sqrt{2}[/tex] , x = - 3 + 2[tex]\sqrt{2}[/tex]
Let f(x)
2x + 8, g(x) = x2 + 2x – 8, and h(x) = 3x – 6.
Perform the indicated operation. (Simplify as far as possible.)
(h · f)(3) =
Answer:
36
Step-by-step explanation:
(h · f)(x) = h(f(x))
h(f(x)) = h(2x+8)
h(f(x))= 3(2x+8) - 6
h(f(x)) = 6x + 24 - 6
h(f(x))= 6x + 18
If x = 3
h(f(x))= 6(3) + 18
h(f(x))= 18 + 18
h(f(x))= 36
Hence (h · f)(3) = 36
If 128x is a perfect square number what is the least value of x
Please answer the question fast
Answer:
in a square all sides are equal so x has to equal
128
Hope This Helps!!!
find the missing length. the triangles are similar.
Answer:
? = 130
Step-by-step explanation:
I'm letting ? be x
Since the triangles are similar, larger outer and smaller inner, then the ratios of corresponding sides are equal.
If x is the length of side of larger then x - 70 is corresponding length of smaller.
Then
[tex]\frac{x}{x-70}[/tex] = [tex]\frac{78}{36}[/tex] ( cross- multiply )
78(x - 70) = 36x ← distribute left side
78x - 5460 = 36x ( subtract 36x from both sides )
42x - 5460 = 0 ( add 5460 to both sides )
42x = 5460 ( divide both sides by 42 )
x = 130
Sita and Ram divided Rs. 250 into 2:3 ratio. Find their shares.
Answer:
Rs. 100 and Rs. 150
Step-by-step explanation:
the ratio = 2:3 => the sum = 2+3=5
Sita gets = 2/5 × 250 = 100
Ram gets = 3/5 × 250 = 150
A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 15 ft3/min, how fast is the water level rising when the water is 8 inches deep
Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
The x-value(s) for which f(x)g(x) is/are ___
9514 1404 393
Answer:
x = -1, 1, 9
Step-by-step explanation:
You want x such that f(x) = g(x). Subtracting g(x) from both sides of this equation lets us rewrite it as ...
f(x) -g(x) = 0
x³ -9x² -(x -9) = 0
x²(x -9) -1(x -9) = 0 . . . factor the first pair of terms
(x² -1)(x -9) = 0 . . . . . . use the distributive property
(x -1)(x +1)(x -9) = 0 . . . . factor the difference of squares
Values of x that make these factors zero will make f(x) = g(x):
x = -1, 1, 9 for f(x) = g(x)
Two linear equations are shown in the graph.
#Brainliest award
What are the coordinates of the point where the two lines intersect?
A. (–2, 3)
B. (3, 3)
C. (3, 0)
D. (–3, 3)
Answer:
I am taking this graph because this question looked similar to this one.
Step-by-step explanation:
Answer should be B.
The intersection point is (3,3)
A Line passes through the .4 -6 and has a slope of -3 and four which is the equation of the line
Answer:
(in the image)
Step-by-step explanation:
I'm not sure I understood your question completely but I hope this helps.
Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the y-intercept is 4. How much more is the rate of change of function A than the rate of change of function B?
2
3
6
9
Answer:
[tex]{ \tt{rate \: of \: change \: in \: A = 9}}[/tex]
Rate of change in function A is two times than that in function B
Find the mean of 2,2,2,2 and 2
Answer:
2
Step-by-step explanation:
mean = sum of data / no of data
=2+2+2+2+2/5
=10/5
=2