If the population proportions are not equal, one would expect a sample difference proportion greater than the one observed in about 1 out of 100 repetitions of this experiment.

Answer:

a pyramidal prism is 1/3 the volume of a similar rectangular prism of same base and height

so V=(1/3)bh

V=36

H=6

find area of base

36=(1/3)b6

36=2b

divide both sides by 2

18=b

the area of the base is 18 square units

Step-by-step explanation:

the answer is : V= B.h

Answer:

94

Step-by-step explanation:

all angles add up to 180

56+30 = 86

180-86=94

By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25

The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1

Let us solve this problem by applying the Kuhn-Tucker theorem.

Let us first write down the Lagrangian function:

L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)

Then, we find the first order conditions for a maximum:

Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0

Ly = x - 8λ₁y - 2λ₁x = 0

Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0

Lλ₂ = 2x - y + 1 = 0

The complementary slackness conditions are:

λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0

λ₂(2x - y + 1) = 0

Now, we solve for the above equations one by one:

From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1

Substitute this in equation (1), we get:

8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0

Simplifying, we get:

10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)

From equation (2), we can write x = 8λ₁y + 2λ₁x

Substitute this in equation (1), we get:

8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0

Simplifying, we get:

-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)

Solving equations (4) and (5) for λ₁ and λ₂, we get:

λ₁ = 1/20 and λ₂ = 9/100

Then, substituting these values in the first order conditions, we get:

x = 2/5 and y = 9/5

Therefore, the maximum value of xy is:

2/5 x 9/5 = 18/25

Hence, the required answer is 18/25.

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Answer:

-4x + 19

Step-by-step explanation:

3 + 2(4x + 7) - 12x + 2

3 + 8x + 14 - 12x + 2

-4x + 19

I hope this helps!

Answer:

11x² - x + 10

Step-by-step explanation:

Given

(5x² + 2x + 1) + (6x² - 3x + 9 ) ← remove both parenthesis

= 5x² + 2x + 1 + 6x² - 3x + 9 ← collect like terms

= 11x² - x + 10

Answer:

x=2, y=5

Step-by-step explanation:

the triangle that x is in is a right triangle (don't remember the theorem sorry)

use pythagorean theorem (a^2 + b^2 = c^2)

x is the hypotenuse(c)

1 squared plus /3 squared =c squared

1+3= c squared

4= c squared

c=2

x=2

find y using pythagorean theorem as well

/12 squared plus 2 squared = y squared

y is the hypotenuse

12+4=y squared

16= y squared

4=y

add one to account for that extra little piece

y=5

... I don't see z

Answer:

y= if it is the hypoteneuse for the whole triangle it √16 or 4, if it is the side of the smaller triangle it is 3

x=√4 which is 2

z= I don't think ther's a z

Answer:

D. y = -3/7 + 2

Step-by-step explanation:

Slope intercept form: y = mx + b

m = slope

b = intercept

Answer:

16 < n < 40

Step-by-step explanation:

use triangle inequality theorem:

n = length of third side

12 + 28 > n;    n > 40

12 + n > 28;    n > 16

n + 28 > 12  (this inequality can be discounted because it results in a negative)

The volume increase when the radius changes from 7 to 7.1 ft is 62.45 ft³ i.e. 4.34%. of the previous volume.

We know that the volume of the sphere is 4/3πr³.

So, here the radius of the sphere is 7 ft,

Therefore the volume of the sphere will be = 4/3π(7)³.

so, V1 = 4/3*3.14*(7)³.

V1 = 1436.76  ft³.

When the radius of the sphere will increase tp 7.1 feet then the volume will also increase which will be :

V2 = 4/3*3.14*(7.1)³.

V2 = 1499.21 ft³.

Now the increase in volume is V2- V1 .

which is , 1499.21 ft³ -  1436.76  ft³

i.e. 62.45 ft³ is the increase of the volume of the sphere.

This increased volume is the 4.34% of the previous volume of the sphere.

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To determine the significance of each independent variable, we need to apply the decision rule at the 0.05 significance level.

In statistical hypothesis testing, the decision rule is used to determine whether to reject or fail to reject the null hypothesis based on the test statistic and the level of significance. In this case, we are interested in testing the significance of each independent variable in a regression model at the 0.05 level of significance. To do this, we can use the t-test for each independent variable by calculating the t-statistic and comparing it to the critical value of the t-distribution with n-k-1 degrees of freedom, where n is the sample size and k is the number of independent variables in the model. If the absolute value of the t-statistic is greater than the critical value, then we reject the null hypothesis and conclude that the independent variable is statistically significant at the 0.05 level. Otherwise, we fail to reject the null hypothesis and conclude that the independent variable is not statistically significant at the 0.05 level.

Alternatively, we can also use the p-value approach to determine the significance of each independent variable. We calculate the p-value for each variable and compare it to the level of significance. If the p-value is less than or equal to 0.05, then we reject the null hypothesis and conclude that the independent variable is statistically significant at the 0.05 level. Otherwise, we fail to reject the null hypothesis and conclude that the independent variable is not statistically significant at the 0.05 level.

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In some base \(B\), we have

\(abab_B \equiv 555_{10}\)

so that

\(aB^3 + bB^2 + aB + b = 555\)

Factorize the left side.

\(aB (B^2 + 1) + b (B^2 + 1) = 555\)

\((aB + b) (B^2 + 1) = 555\)

Now, \(B\) is a positive integer greater than 1, and \(a,b\) are positive integers taken from \(\{0,1,2,\ldots,B-1\}\). So consider the prime factorization of 555 on the right side.

\((aB + b) (B^2 + 1) = 3\times5\times37\)

which we can write as

\((aB + b) (B^2 + 1) = 15\times(6^2 + 1) = (2\times6 + 3) \times (6^2+1)\)

and so the base is 6, and the number in question is 2323₆.

Answer:

$15

Step-by-step explanation:

Since there are 10 cards and a total possible prize of 30 dollars, the probability for each one is 30/10=3 dollars. And since 5 out of the 10 are even, you can multiply the individual amount by 5 to get a total estimated payout of $15. Hope this helps!

Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

a. For solving homogeneous equation x²y' - xy = x² + y² substitute v = y/x

then y = vx and y' = v'x + v

b. The linear differential equation obtained after substitution is x³v' - (1 + v²)x² + x²v² = 0

c. The general solution to the original differential equation is,

y = x(ln|x| + C)

To solve the homogeneous equation x²y' - xy = x² + y²,

use the substitution v = y/x.

a. First, let's write y and y' in terms of x, v, and v',

Given v = y/x, rearrange the equation to solve for y,

y = vx

To find y', differentiate both sides of the equation with respect to x,

y' = v'x + v

b. Now, let's substitute y and y' in the original equation,

x²y' - xy = x² + y²

⇒x²(v'x + v) - x(vx) = x² + (vx)²

⇒x³v' - x²v + x²v² = x² + v²x²

⇒x³v' - x²v + x²v² - x² - v²x² = 0

⇒x³v' - (1 + v²)x² + x²v² = 0

c. The resulting equation after substitution is,

x³v' - (1 + v²)x² + x²v² = 0

To solve this linear differential equation, rewrite it as,

x³v' - x² - v²x² = x²(1 - v²) - x²v' = 0

Dividing both sides by x²(1 - v²), we get,

v' = (1 - v²)/(x(1 - v²))

This is a separable differential equation.

separate the variables and integrate to find v.

∫(1 - v²)/(1 - v²) dv = ∫1/x dx

⇒∫dv = ∫1/x dx

⇒v + C₁ = ln|x| + C₂

where C₁ and C₂ are arbitrary constants.

Therefore, the solution for v is v = ln|x| + C

Now, substituting back v = y/x, we have

y/x = ln|x| + C

⇒y = x(ln|x| + C)

where C is an arbitrary constant.

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The above question is incomplete, the complete question is:

Find the general solution of the homogeneous equation x²y ′- xy=x² +y²

a. To solve this, we should use the substitution v= _____help (formulas) or, writing y and y ′ in terms of x, v and v ′ ,

we have y= ___

y ′ = _____ help (formulas)

b. After the substitution from the previous part, we obtain the following linear differential equation in x, v, v ′ _______. help (equations)

c. The general solution to the original differential equation is (use C for the arbitrary constant): y= ________help (equations)

The formula for calculating the height is h = 3V/πr²

The formula given is the formula for calculating the volume of a cone

V = 1/3πr²h

where

h is the height

r is the radius

Make h the subject of the formula

Cross multiply

3V = πr²h

Divide both sides by πr²

3V/πr² = πr²h/πr²

h = 3V/πr²

Hence the formula for calculating the height is h = 3V/πr²

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Answer:

Just do 812-78 that equals 734.

Answer:

734 pennies

Step-by-step explanation:

10 +68 =78 pennies that she gave to her sister and her brother

812 - 78 =734 pennies has

The 4 (four) quadrants in order are: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV.

A coordinate plane is divided into four sections called quadrants. These quadrants are numbered I, II, III, and IV in a counterclockwise direction, starting with the top right.

Quadrant I is the top right section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are positive.

Quadrant II is the top left section of the coordinate plane, and it contains all the points where the x-coordinate is negative and the y-coordinate is positive.

Quadrant III is the bottom left section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are negative.

Quadrant IV is the bottom right section of the coordinate plane, and it contains all the points where the x-coordinate is positive and the y-coordinate is negative.

Understanding this concept is important for solving mathematical problems, especially in algebra and geometry.

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Answer:

Etu

Step-by-step explanation:

Answer:

Etu painted more

Step-by-step explanation:

There are multiple ways to do find out how, here are some of the ways:

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

1. Convert the fractions into a decimal,

\(\frac{1}2}\) = 50%

\(\frac{1}{3}\) = 33%

Therefore, \(\frac{1}2}\)  is larger since 50% is bigger than 33%.

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

2. Convert the fractions to the Lowest Common Denominator (LCD)

The LCD is 6

So:

\(\frac{1}2}\) = \(\frac{3}{6}\)

\(\frac{1}{3}\) = \(\frac{2}{6}\)

\(\frac{1}2}\)  is larger

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

Have a good day :)

The slope of the regression line is  b=61.02 and y-intercept is a=3.12

Regression analysis is a set of statistical processes used to estimate the relationships between a dependent variable and one or more independent variables. Linear regression is the most popular type of regression analysis, in which one finds the line (or a more sophisticated linear combination) that best fits the data according to a certain mathematical criterion. The ordinary least squares method, for example, finds the unique line (or hyperplane) that minimizes the sum of squared discrepancies between the genuine data and that line (or hyperplane). This enables the researcher to estimate the

Given,

The regression line is y=3.12+61.02 s

Here the slope is b=61.02

The slope indicates that the distance is increased by 61.02 yards for every one mile per hour of the speed.

And the y-intercept is a=3.12

It is the distance estimated by this model if the speed is zero miles per hour.

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Answer:

Value of the function will be 2742.06

Step-by-step explanation:

Given function is,

f(x) = 1500(1.09)ˣ

By substituting the value of x we can find the value of the given function.

For x = 7,

f(7) = 1500(1.09)⁷

     = 1500(1.828)

     = 2742.0587

     ≈ 2742.06

Value of the function will be 2742.06

The equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4 will be y=2x-11.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

It is given that,  

y=2x-4

We have to write an equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4.

The slope of the given equation,

y=2x-4

m=2

The slope of the parallel lines is equal,

m=2

The equation of a line that passes through the point (5,-1) with slope 2 is,

y-y₁=m(x-x₁)

y-(-1)=2(x-5)

y+1=2(x-5)

y+1=2x-10

y=2x-11

Thus, the equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4 will be y=2x-11.

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Answer:

So, to do this we must do distrubition so 2 times x = 2x -3 times 2 = -6 and 4x times 2 equals 6x and subtract the 6x from 6 which equals x so therefore 2 and 2 cancels out so you're left with x=x and there is ur answer and remember to subtract have a good day^_^

Step-by-step explanation:

Step-by-step explanation:

What you are dealing with is what we call special right triangles. There are two types of right triangles.

30-60-90 triangle- A special

right triangle with side length ratio as

\((a)(a \sqrt{3} )(2a)\)

, where a is any positve number

45-45-90- a special right triangle which side length ratios are

\((a)(a)(a \sqrt{2)} \)

where a is any positve number.

45 45 90 triangles is indicated by two congruent side measures( if the legs are congruent and it has a right angle, it is a 45-45-90.

30-60-90 triangles is indicated by a having at least two of the following angles given (30,60, and 90).

Shortcuts:

For a 45 45 triangle,

the legs are equal while the hypotenuse is the sqr root of 2 times than the legs.

Example, look at 1. The legs side length is 12 so our hypotenuse side length will be

\(12 \sqrt{2} \)

For a 30-60-90 triangle, the side that is adjacent to the 30 and 90 degree measure sqr root of 3 times more than the horizontal leg.

the slanted side or the side which is adjacent to the 30 and 60 degree angle is twice the length of the horizontal leg or the side that is adjacent to the 60 and 90 degree.

Example, look at 3. We need to find x but we are given the horizontal side so just multiply sqr root of 3 to 12.

\(x = 12 \sqrt{3} \)

\(1.12 \sqrt{2} \)

2.Both equal

\(2.8 \sqrt{2} \)

\(3.12 \sqrt{3} \)

4. a=13

\(4.13 \sqrt{3} \)

\(5.9 \sqrt{4} \)

Answer:

where is the drawing l don't understand the measurements

Answer:

7 11/12

Step-by-step explanation:

3 2/3 + 4 1/4 = 3 8/12 + 4 3/12 = 7 11/12