What is the minimum of y=1/3 x^2 + 2x + 5

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.

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.

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.

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

Answer: 58

Step-by-step explanation: you add them all together

Its 108 the other answer is the perimeter not the area.

Answer:

-3

Step-by-step explanation:

12x + 1 - 2(y + 2)

=> 12x + 1 - 2y - 4

=> 12x - 3 - 2y

Answer:

-3

Step-by-step explanation:

12x+1-2y-4

12x+1-2y-4

12x-2y-3

Answer: (5) -5 > -18​

Step-by-step explanation:

-5 is 5 away from zero, making it larger than -18 since it's closer to 0, while -18 is 18 away from zero.

Answer:

54 cm is the perimeter I think

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

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)

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)

Answer:

m(m – 3) = 108

The correct equation can be used to solve for m, the greater integer is,

⇒ m (m - 3) = 108

We have to given that,

Two positive integers are 3 units apart on a number line.

And, Their product is 108.

Let us assume that,

In a number line, first point is m

Then, Second point is, m - 3

So, We get;

The correct equation can be used to solve for m, the greater integer is,

⇒ m (m - 3) = 108

Learn more about the equation visit:

brainly.com/question/28871326

#SPJ7

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!!

Answer:

a) See step by Step explanation

b) z(s) = 48.88

c) We reject H₀. The sample is not representative of American Adult Population

Step-by-step explanation:

From sample

sample mean .    x = 49.28

sample standard deviationn   s = 17.21

sample size  n₁  = 4857

Population mean according to Census data

μ  = 37.2

a) Test Hypothesis

Null Hypothesis .                  H₀ .                    x =  μ  = 37.2

Alternative Hypothesis        Hₐ .                    x ≠ μ

b) We have sample size (4857) we can use normal distribution

z (c) for    α = 0.01   α/2 . = 0.005  is from z-table . z(c) = 2.575

To calculate  z(s) =  ( x  - μ ) / s /√n

z(s) =  12.08 * √4857 / 17.21

z(s) = 12.08* 69.64 / 17.21

z(s) = 48.88

z(s) > z(c)

We should reject H₀. The sample is not representative of American Adult population

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

Answer:

[tex]{ \tt{rate \: of \: change \: in \: A = 9}}[/tex]

Rate of change in function A is two times than that in function B

Answer:

(in the image)

Step-by-step explanation:

I'm not sure I understood your question completely but I hope this helps.

Answer:

Quadratic formula

Step-by-step explanation:

The function is quadratic because it is a parabola. Exponential functions shoot either upwards or downwards rapidly, and it is clearly not linear due to it's curve. It also isn't piecewise because the function never stops or starts irregularly.

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]

Answer:

firstly we have to identify the problems, understand carefully and chose the best way to solve problems.

Answer:

2

Step-by-step explanation:

mean = sum of data / no of data

=2+2+2+2+2/5

=10/5

=2

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

Answer:

21

Step-by-step explanation:

7+7+7=21

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

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.

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.

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

Answer:

24 26 27 94 is the answer 45

Answer:

the correct answer is 45