Calculate the expected value of X, E(X), for the given probability distribution. E(X):_________

x 0 1 2 3
P(x) 0.5 0.1 0.1 0.3

Answer:

All of the figures have 4 sides  and 4  vertices

They have opposite sides parallel and congruent.

They have four right angles.

They also have perpendicular line segments.

Step-by-step explanation:

Hope this helps!!!

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

Answer:

B? - Hopes it helps

Step-by-step explanation:

Happy early valentines Day! - p.s mark me brainly and another bessing comes ur way!

Answer:

Hello,

Step-by-step explanation:

\(\dfrac{P_1*V_1}{T_1} =\dfrac{P_2*V_2}{T_2} (\' equation\ des\ gaz\ parfaits\ PV = nRT)\\\\\\\boxed{T2=\dfrac{P_2*V_2*T_1}{P_1*V_1} }\)

The ordered pair(y,x) that is a solution to the equation is (1, 0)

The equation of the function is given as

-x + 6y = 6

The ordered pair is given as

(y, x)

This means that x is a function of y

So, we make x the subject in -x + 6y = 6

This gives

x = 6y - 6

Next, we assume a value for y and solve for x

Assume y= 1

so, we have

x = 6(1) - 6

Evaluate

x = 0

So, we have

(y, x) = (1, 0)

Hence, the ordered pair is (1, 0)

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Step-by-step explanation:

Since y= -7x you will want to substitute the y in the other equation.

2x -(-7x) = -9

2x + 7x = -9

9x = -9

so x will be -1

y= -7(-1)

x= -1

y= 7

Answer:

x = -1 , y =7      (-1,7)

Step-by-step explanation:

\(y=-7x\\2x-y = -9\\\)

\(2x+7x = -9\)

\(2x+7x = 9x\\\)

\(9x = -9\\\)

\(\frac{9x}{9} =\frac{-9}{9}\)

\(x = -1\\\)

\(y = -7(-1)\\y = 7\)

Answer:

  -5/7

Step-by-step explanation:

The slope of a line is given by

m = (y2-y1)/(x2-x1)

   = ( -1 -4)/(5 - -2)

   = (-1-4)/(5+2)

   -5/7

Slope formula: y2-y1/x2-x1

= -1-4/5-(-2)

= -5/7

Best of Luck!

Answer:

the domain is: ( − ∞ , 0 ) ∪ ( 0 , ∞ ) , { x | x ≠ 0 }

Step-by-step explanation:

Answer:

48°

Step-by-step explanation:

Given that GK is the diameter of the circle ;

Then GK which is the half of the circle is 360/2 = 180 (Angle at a Point = 360°)

Diameter =half of the entire circle = 360 /2 = 180

GK = 180°

GK =GR + KR = 180

KR = 132°

180 = GR + 132

GR = 180 - 132

GR = 48°

Answer:

lollll.

Step-by-step explanation:

Answer: B = 7

Step-by-step explanation:

2*6+2*7 = 26

26 =26

Answer:

no solution

Step-by-step explanation:

on opening the braces , we get

7x - 14 - 4 = 7x - 11

solving further 7x gets canceled being common on both sides of the equality and we're left with an absurd thing

-18 = - 11

and it's not true, so the given equation has no solution

Answer:

Step-by-step explanation:

7(x - 2) - 4= 7x-11

(7x - 14) - 4 = 7x - 11

7x - 10 = 7x - 11

7x - 7x = -11 + 10

no solution :/

Answer:

----------------------

See attached graph to help with answer choices.

Given function:

Answer choices:

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:

The values of ∠B, a and c in the triangle are 68°, 8.1 and 13

triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle. A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.

The sum of he interior angles of the triangle is 180°

so that, ∠A + ∠B + ∠C =180

37  +  ∠B  + 75 = 180

∠B  = 180 - 112

∠B  = 68°

Using sine rule to find a and c

a/sinA = b/sinB = c/sinC

tto find a

a/SinA = b/sinB

substitute A, B and b o fin a

a/sin37 = 12/sin68

cross multiply

a sin68 = 12 sin 37

a sin68 = 12(0.6018)

a(0.9271) = 7.221

a = 7.221/0.9271

a = 8.4

to  find c

b/sin B = c / sin C

12/sin68 = c/sin75

cross multiply we have

c sin 68 = 12sin(75)

c(0.9271) = 12(0.9659)

c = 12.5

In conclusion the values of A, a and c are 68°, 8.4 and C 12.5

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The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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Therefore , the solution of the given problem of function comes out to be  $3,556 this is the total startup expense.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected limit. The relationship between a group of inputs, which each have a corresponding upper bound, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input.

Here,

Because the launch expense exceeds $50,000, any startup expenses that cannot be deducted may be prorated over a 180-month period beginning with the start of business.

The startup costs are divided by the entire number of months authorized for amortization, and the result is then calculated by the number of months that were traded throughout the year.

The Root bark Corporation has been conducting business in the case at hand for 10 months, from March to December 2019.

Amount that can be amortized: ($64,000 / 180 months) * 10 months.

=>  $3,556 this is the total startup expense that may be deducted.

Therefore , the solution of the given problem of function comes out to be  $3,556 this is the total startup expense.

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a) The mean rainfall from seeded clouds exceeds 25 acre-feet is 1.99

b) As per the normal distribution, with the significance level 0.05 the rainfall is normally distributed.

c) The power of the test if the true mean rainfall is 27 acre-feet is 23.5%

d) The sample size would be required to detect a true mean rainfall of 27.5 acre-feet if we wanted the power of the test to be at least 0.9 is 28 clouds

e) The upper bound is greater than 25 acre-feet, we can support the claim that the mean rainfall from seeded clouds exceeds 25 acre-feet with a level of confidence of 99%.

a) To support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet, we can perform a one-tailed hypothesis test with a significance level of α = 0.01.

Substituting the values, we get:

t = (25.96 - 25) / (4.48 / √20) = 1.99

b) To test if the rainfall is normally distributed, we can perform a normal probability plot and a Shapiro-Wilk test.

Using software, we can create a normal probability plot and perform the Shapiro-Wilk test.

The Shapiro-Wilk test also does not reject the null hypothesis that the data is normally distributed at a significance level of α = 0.05, we can assume that the rainfall data is normally distributed.

c) To compute the power of the test if the true mean rainfall is 27 acre-feet, we can perform a one-tailed hypothesis test with a significance level of α = 0.01. The null hypothesis H0 is that the mean rainfall is less than or equal to 25 acre-feet, and the alternative hypothesis Ha is that the mean rainfall is greater than 25 acre-feet.

Substituting the values, we get:

t = (25.96 - 27) / (4.48 / √20) = -1.43

Using software or a t-distribution table, we find that the probability of rejecting the null hypothesis when the true mean is 27 acre-feet is 0.235. Therefore, the power of the test is 0.235 or 23.5%.

d) To determine the sample size required to detect a true mean rainfall of 27.5 acre-feet with a power of at least 0.9, we can use power analysis.

Substituting the values, we get:

d = (27.5 - 25) / 4.48 = 0.56

Therefore, a sample size of at least 28 clouds would be required to detect a true mean rainfall of 27.5 acre-feet with a power of at least 0.9.

e) To answer the question in part (a) by constructing a one-sided confidence bound on the mean diameter, we can use a one-sided confidence interval with a level of confidence of 99%.

Substituting the values, we get:

x + tα,df * (s / √n) = 25.96 + 2.861 * (4.48 / √20) = 27.23

This means that we can be 99% confident that the true population mean rainfall from seeded clouds is greater than 27.23 acre-feet.

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The significance level is set at 5% and the probability of the result is 3.6% which is less than the significance level. The result is statistically significant

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true

The probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more will be:

= (26 + 8 + 2)/1000

= 36/1000

= 0.036

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The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)

we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Answer:

2.5 pints of fruit juice

Answer:

2.5

Step-by-step explanation:

Answer:

2, 3

Step-by-step explanation:

The prime factorization of 6 is 2(3), so one possibility is 2 and 3.

The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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Answer:

1. The sum of the residuals is always close to zero.

2.The coefficient of determination measures how much of the variation in the y-values is explained by the regression line.

3. In the equation of the least-squares regression line, y hat is a predicted value when x is known

Step-by-step explanation:

The least square regression line is a line that makes distance from data points to the regression line to be as minimal as possible. This line is a best fit for the data points. Let's say we have a collection of numbers and a scatter plot, this line is a line that exists and best fits the data.

Therefore, the least square regression line minimizes sum of squared error to be close to zero. R² measures the extent to which variations in the value of y is explained by the regression line. In the equation of this line, y hat is a predicted value when x is known.

The least square regression line minimizes the sum of squared error such that the sum of the residual is zero or very close to 0. Hence, the true statements from the options given are :

The least square regression Line is used to create a Linear model in the form y = bx + c

The Coefficient of determination R² gives the proportion of the variation explained by the regression line.

The predicted value of y is obtained using the model of the Least Square Regression Line for a given value of x.

Outlier values often affects the performance and accuracy of the Least Square Regression Line.

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