What graph represents the inequality? Whoever answers first gets brainliest!

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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1. The total change in the members is 61.

2. The average or mean vhange over the four months is 15.25.

1. The total change in the members based on the information will be the addition of the values given. This will be:

= (-13 + 89) (-28 + 12) + (-67 + 54) + (-3 + 17)

= 76 -16 - 13 + 14

= 61

The change is 61.

2. The average change over the four months will be the addition of the values divided by 4. This will be:

= Total change / 4

= 61 / 4

= 15.25

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9514 1404 393

Explanation:

The quadrilateral will be a parallelogram if the diagonals bisect each other. That will be the case if the sums of their end-point coordinates are the same.

  A + C = (-3, 6) +(9, -9) = (6, -3)

  B + D = (6, 0) +(0, -3) = (6, -3)

Both diagonals have their midpoint at (3, -1.5), so the diagonals are mutual bisectors. The figure ABCD must be a parallelogram.

___

The midpoint of AC is (A+C)/2 = (6, -3)/2 = (3, -1.5).

According to the question The probability that the sample proportion of disapproval is greater than 0.55 is approximately 0.259.

In a random sample of 205 marketing professionals, 117 expressed disapproval of using ultraviolet ink on a mail survey. We want to determine the probability that the sample proportion of disapproval is greater than 0.55.

Assuming random sampling, independence, and a sufficiently large sample size, we calculate the sample proportion as 0.57. By computing the z-score and referring to a standard normal distribution table, we find that the probability of obtaining a z-score greater than 0.644 is approximately 0.259.

Hence, the probability that the sample proportion of disapproval is greater than 0.55 is approximately 0.259.

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Answer:

G = $612.50 when H = 46hours

Step-by-step explanation:

Given:

G = 18.75(H-40) + 500

Where,

G =Gross pay in dollars

H = Number of hours worked

If her gross pay one week was $612.50, what was the

total number of hours she worked that week?

G = $612.50 when H = ?

G = 18.75(H-40) + 500

612.50 = 18.75H - 750 + 500

612.50 = 18.75H - 250

Add 250 to both sides

612.50 + 250 = 18.75H

862.5 = 18.75H

Divide both sides by 18.75

862.5 / 18.75 = 18.75H / 18.75

46 = H

H = 46

If her gross pay one week was $612.50, her total hours worked = 46hours

Answer:

9 cups

Step-by-step explanation:

you would take half of 18 because that how much it takes

Answer:

Domain = x > 2 , Range = {R}

Step-by-step explanation:

The given function to us is ,

\(\implies f(x) = log_{10} ( x - 2 ) + 1 \)

Since logarithm are defined only for positive numbers therefore ,

=> (x - 2) > 0

=> x > 2

Therefore the domain of the function is x > 2 and it can have all positive real numbers .

Answer:

\( \sqrt{3 \times 2 {?}^{2} } = \sqrt{12} = 3.46\)

Answer:

60 baskets per hour

Step-by-step explanation:

given that every 2.5 hours, the machine produces 150 baskets

Goal: to express this production rate in number of baskets the machine can produce in 1 hour (i.e obtain the unit rate)

2.5 hours -------> machine produces 150 baskets

1 hour --------> machine produces 150 ÷ 2.5 = 60 baskets

hence the unit rate  of production is 60 baskets per hour

Answer:

60 baskets per hour

Step-by-step explanation:

given that every 2.5 hours, the machine produces 150 baskets

Goal: to express this production rate in number of baskets the machine can produce in 1 hour (i.e obtain the unit rate)

2.5 hours -------> machine produces 150 baskets

1 hour --------> machine produces 150 ÷ 2.5 = 60 baskets

hence the unit rate  of production is 60 baskets per hour

The correct value of  cost of equity for Rosana's Grill is 9%.

To calculate the average expected cost of equity for Rosana's Grill, we can use the dividend discount model (DDM) formula. The DDM formula is as follows:

Cost of Equity = Dividend / Stock Price + Dividend Growth Rate

Given the information provided:

Dividend = $1.30

Stock Price = $26

Dividend Growth Rate = 4%

Let's calculate the cost of equity using these values:

Cost of Equity = $1.30 / $26 + 4% = $0.05 + 0.04 = 0.09 or 9%

The cost of equity for Rosana's Grill is 9%.

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Answer:

After the decimal point (left to right) are the tenths, hundredths, thousandths, ten-thousandths, and so on. The value of the 9 would be 9 hundredths.

:)

Answer:

452.39

Step-by-step explanation:

Hope this is right

Answer:

30 hectares

Step-by-step explanation:

Answer:

Step-by-step explanation:

Land area James inherited = 19.5 hectares

The area of the land he inherited is 65% of the total land his father owned.

Let

x = Total land his father owned

Land area James inherited = 65% of the total land his father owned

19.5 = 65% of x

19.5 = 65/100 * x

19.5 = 0.65 * x

19.5 = 0.65x

x = 19.5 / 0.65

x = 30

x = Total land his father owned = 30 hectares

Step-by-step explanation:

1)  Total rectangle area =  W x H = 12 x 8 = 96 cm^2

 area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2

              Nonshaded portion = 96 - 28 cm^2 = 68 cm^2

          ratio shaded:nonshaded is then   28 : 68 = 7:17

2)   Look at the two middle triangles :  Height of each = 8 cm

       then reading across the diagram  height + base + height = 21 cm

            so base = 5 cm

   area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2

        total area for FOUR of them  = 80 cm^2

Answer: I have two days to get this class done on Plato I need more points

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

I think it will be D, because you will be decreasing 0.25x and increasing 0.75x, you will add 0.25x to -0.25x to get rid of 0.25x. Then you will need to do the same thing to the other side. You will add 0.25x to 0.75x so you will be increasing 0.75 since you will be adding to it.

Step-by-step explanation:

X – 0.25x = 0.75x

X-0.25x+0.25x=0.75x+0.25x

X= 1.00x

All you need to do is add 0.25x to both -0.25x and positive 0.75x. That way it will be equal.

So, I believe it will be D

The Taylor series for the function 1/x about the point 1 is 1 - (x - 1) + (x - 1)^2/2 - (x - 1)^3/6 + ...

To find the Taylor series for the function 1/x about the point 1, we can use the formula for the Taylor series expansion of a function.

The Taylor series expansion of a function f(x) about a point a can be expressed as:

f(x) = f(a) + f'(a)(x - a) + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...

Let's calculate the Taylor series expansion of 1/x about the point 1:

First, we find the derivatives of 1/x:

f'(x) = -1/x^2

f''(x) = 2/x^3

f'''(x) = -6/x^4

...

Evaluate the derivatives at x = 1:

f(1) = 1/1 = 1

f'(1) = -1/1^2 = -1

f''(1) = 2/1^3 = 2

f'''(1) = -6/1^4 = -6

...

Now we can write the Taylor series expansion:

1/x = f(1) + f'(1)(x - 1) + f''(1)(x - 1)^2/2! + f'''(1)(x - 1)^3/3! + ...

Plugging in the values, we have:

1/x = 1 - 1(x - 1) + 2(x - 1)^2/2! - 6(x - 1)^3/3! + ...

Simplifying the terms:

1/x = 1 - (x - 1) + (x - 1)^2/2 - (x - 1)^3/3 + ...

Therefore, the Taylor series for 1/x about the point 1 is 1 - (x - 1) + (x - 1)^2/2 - (x - 1)^3/3 + ...

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Answer:

I think x equals 7.5

Step-by-step explanation:

Please let me know if this was correct or what you were looking for. Thanks!

\( \\ \sf \longmapsto \: HT=√15^2+8^2\)

\( \\ \sf \longmapsto \: HT=√225+64\)

\( \\ \sf \longmapsto \: HT=√289\)

\( \\ \sf \longmapsto \: HT=17cm\)

Angle T=15x

Let others be 8x and 17x

\( \\ \sf \longmapsto \: 8x+17x+15x=180\)

\( \\ \sf \longmapsto \: 40x=180\)

\( \\ \sf \longmapsto \: x=\dfrac{180}{40}\)

\( \\ \sf \longmapsto \: x=4.5\)

\( \\ \sf \longmapsto \: 15x=15(4.5)\)

\( \\ \sf \longmapsto \: \angle T=67.5°\)

\( \\ \sf \longmapsto \: \angle H=8x\)

\( \\ \sf \longmapsto \: \angle H=32.5°\)

The domain and the range of the function in interval notation are [-5, 5) and [-4, 3] respectively

The domain of the function is the set of input values of the graph while the range of a function is the set of output values of the graph.

The graph represents the given parameter

Based on the definition above, the range of a function is the set of y values of the graph while the domain is the set of x values of the graph

On the graph, we can see that:

The x values start from -5 and ends at 5

This means that the domain is [-5, 5)

On the graph, we can see that:

The y values start from -4 and ends at 3

This means that the range is [-4, 3]

Hence, the domain and the range of the function in interval notation are [-5, 5) and [-4, 3] respectively

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Answer:

x = 24

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ x/12 = 2

Then the value of x will be,

→ x/12 = 2

→ x = 2 × 12

→ [ x = 24 ]

Hence, the value of x is 24.

\(\huge\text{Hey there!}\)

\(\mathsf{\dfrac{x}{12} = 2}\)

\(\mathsf{\dfrac{1}{12}x = 2}\)

\(\large\text{MULTIPLY 12 to BOTH SIDES}\)

\(\mathsf{\dfrac{1}{12}x\times 12 = 2 \times 12}\)

\(\large\text{Simplify it}\)

\(\mathsf{x = 12\times 2}\)

\(\mathsf{x = 24}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{x = 24}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

17.138

Step-by-step explanation:

area of segment = area of minor sector of the circle -area of triangle TSR

NOTE : AM using area of triangle as

1/2absinC

(48/360 ×22/7 ×19 ) - (1/2 × 19 ×19 × sin 48)

= 151.276 - 134.134

= 17.138

Question 37:  The following is a solution to the differential equation y = t - 1. d.

Question 38:  The tea temperature be after a very long time is dT/dt = k(S - T); T ≈ 20 degrees after a very long time. a.

To determine the solution to the given differential equation: t²(d²y/dt²) - 6t(dy/dt) + 12 = 0, we can solve the equation by assuming a solution in the form of y = tⁿ, where n is a constant.

By differentiating y with respect to t, we can substitute the derivatives into the differential equation to determine the value of n.

Let's differentiate y = tⁿ with respect to t:

dy/dt = n × tⁿ⁻¹

d²y/dt² = n(n-1) × tⁿ⁻²

Substituting these derivatives into the differential equation:

t²(n(n-1)tⁿ⁻²) - 6t(ntⁿ⁻¹) + 12 = 0

Simplifying the equation:

n(n-1)tⁿ - 6ntⁿ + 12 = 0

n(n-1)tⁿ - 6ntⁿ = -12

Since this equation must hold for all values of t, the coefficients of the tⁿ terms on both sides of the equation must be equal.

We can equate the coefficients:

n(n-1) = 0

n = 0 or n = 1

The general solution to the differential equation is y = c₁ + c₂ × t, where c₁ and c₂ are constants.

According to Newton's law of cooling, the rate of change of the temperature T of an object is proportional to the temperature difference between the object's temperature T and the surroundings' temperature S.

We can write the differential equation as follows:

dT/dt = k(S - T)

dT/dt represents the rate of change of temperature, k is the proportionality constant, and (S - T) represents the temperature difference between the object and the surroundings.

The cup of tea starts at 100 degrees and cools to 50 degrees in 3 minutes, with the room temperature at 20 degrees.

We can assume that the temperature of the tea will tend toward the room temperature as time goes to infinity.

This option correctly represents that as time goes to infinity, the temperature T of the tea will approach the temperature S of the surroundings, which is approximately 20 degrees.

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To translate the sentence into an equation, we can let c represent the value we want to find. The difference between c and 25 is 75, so we can write this as:

c - 25 = 75

To solve the equation, we can add 25 to both sides:

c - 25 + 25 = 75 + 25

c = 100

So the value of c is 100.

  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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The interior of S is empty, which means that S is a closed set. The boundary of S is equal to R², which means that it contains all real numbers.

The interior of S is the set of points that lie inside the set S. Therefore, it is the set of all elements that can be obtained by choosing a point in S and then taking an open ball around that point that is completely contained within S. Here,

S = {(x, y): x and y are rational numbers}.

Hence, the interior of S is empty as there is no open ball around any point that lies completely within S. Therefore, S is closed.

The boundary of S is the set of points that are neither in the interior of S nor in the exterior of S. Hence, it is the set of all points that lie on the boundary of S.

Here, S = {(x, y): x and y are rational numbers}.

Therefore, the boundary of S is the set of all points that lie on the border of the set S. The set S is dense in the real plane. Therefore, the boundary of S is the set of all real numbers.

Hence, the boundary of S is equal to R².

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