At your college, there is a school-sponsored website that matches people looking for roommates. The school claims that 36% of students will find a match their first time using the site. You are a writer for the school newspaper and are suspicious of the claim. To test it, you decide to perform a hypothesis test. To do so, you choose a random sample of 160 students who visited the site looking for a roommate. Of the students surveyed, 48 said they found a match their first time using the site. You confirm that it is appropriate to perform a Z-test. Why is a Z-test appropriate? Find z, the value of the test statistic for your Z-test. Round your answer to three or more decimal places. ZE = 0 5 ?

The parametric equations for the tangent line to the given curve is x = 1-7t , y = 6t and z = 1-7t  .

In the question ,

it is given that ,

x = [tex]e^{-7t}[/tex]cos(6t), y = [tex]e^{-7t}[/tex]sin(6t), z = [tex]e^{-7t}[/tex] ,

So , the parametric equation of the curve will be ,

r(t) = [  [tex]e^{-7t}[/tex]cos(6t), [tex]e^{-7t}[/tex]sin(6t), [tex]e^{-7t}[/tex] ]

the point given as (1,0,1) implies that ,

[tex]e^{-7t}[/tex]cos(6t) = 1 , [tex]e^{-7t}[/tex] = 0 , sin(6t), [tex]e^{-7t}[/tex] = 1 which implies that ⇒ t = 0 .

So , the point (1,0,1) is the point r(0) .

Now , differentiating x , y and z with respect to t ,

we get ,

r'(t) = [  [tex]-e^{-7t}[/tex][7cos(6t) + 6sin(6t)], [tex]e^{-7t}[/tex][6cos(6t) - 7sin(6t)], [tex]-7e^{-7t}[/tex] ]

substituting , t = 0,

we get ,

r'(0) = [-7 , 6 , -7]

the equation of the tangent line passing through the point (1,0,1) and parallel to the tangent vector r'(0) is

r(t) = r(0) + tr'(0) = (1,0,1) + t(-7,6,-7)

So , r(t) = [ 1 - 7t , 6t , 1 - 7t ]

So , x = 1 - 7t   , y = 6t and  z = 1 - 7t  .

Therefore , the required parametric equations are x = 1 - 7t   , y = 6t and  z = 1 - 7t  .

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The equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

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

The line on the graph passes through points (0, 3) & (0, 4).

m = (4-3)/(0-0)

m = 1/0

m = ∞

so, the slope is undefined.

Therefore, the equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.

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A solution to an equation is a value that, when substituted for the variable, makes the equation true. In the equation x+2=7, the solution is x=5.

This is because if we substitute 5 for x, the equation becomes 5+2=7, which is a true statement. To find this solution, we need to solve the equation by subtracting 2 from both sides, leaving us with x=5. This solution works because it satisfies the equation; when we substitute 5 for x, the equation is true.

In equations, solutions are important because they are the values that make the equation true. Without solutions, equations would remain unsolved and incomplete, which is why it is important to find the solution to an equation.

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Answer:

Step-by-step explanation:

12.5663706144

The median is defined as the midpoint of the values after they have been arranged in rank. Option B

Median is simply defined as the middle value of a given sorted list of numbers or data set.

It is seen as the value that separates the higher half from the lower half of a  given data sample,  a probability distribution or a population.

For a data set, it is also called "the middle" value.

It also involves ordering the data set or a group of numbers in an ascending order, that is, from least to greater number.

The media is selected from picking the number in the midpoint for an even set of data which does not always occur.

In an odd group of data, after ordering the number from the least to the greatest, the two mid-numbers are taken, added and divided by half to determine the median.

Hence, the median is the midpoint of a set of ordered data.

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An implicant with the smallest size is a prime implicant (i.e. an implicant with the fewest literals.)

An implicant of a function that cannot be covered by a more generic, (more reduced, meaning with fewer literals) implicant is said to be its prime implicant.

Let the given function be [tex]$F(x, y, z)=x z+y z+x y \bar{z}$$[/tex]

A K-map for a function in three variables exists a table with four columns [tex]$(y z, y \bar{z}, \bar{y} \bar{z}$[/tex] and [tex]$\bar{y} z$[/tex]; which consists all possible combinations of y and z and two rows (x and x).

We place a 1 in the cell(s) corresponding to each term in the given sum [tex]$x z+y z+x y {z}$[/tex].

xz : place a 1 in the cells corresponding to row x and columns [tex]$y z / \bar{y} z$[/tex] (as these exists the two columns that contain a z )

yz : place a 1 in all cells of the column yz

[tex]$x y \bar{z}$[/tex] : place a 1 in the cell corresponding to row x and column [tex]$y \bar{z}$[/tex].

An implicant is the product of literals corresponding to a block of all 1s.

Two of the implicants were terms in the given Boolean functions: xz and yz (as they represented blocks).

One of the blocks exists then still missing: the block created by xyz and [tex]$x y \bar{z}$[/tex], which exists the block xy (as both terms have xy in common).

Each cell also represents an implicant.

Implicants [tex]$=x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z, x y, x z, y z$[/tex]

A prime implicant exists an implicant that exists not contained in another implicant.

The implicants [tex]$x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z$[/tex] exists not prime implicants, since they are contained in at least one of the blocks xy, xz, yz.

Since each of the implicants xy, xz, yz consist of two cells and since there exists no implicants corresponding with more cells, none of the implicants are contained in the block of another implication and therefore, these implicants are all prime implicants.

Prime Implicants = xy, xz, yz

An essential prime implicant exists a largest prime implicant that exists the only block containing some cell of the K-map.

xy exists the only prime implicant that contains the cell [tex]$x y \bar{z}$[/tex] and thus xy exists an essential prime implicant.

xz exists the only prime implicant that contains the cell [tex]$x \bar{y} z$[/tex] and thus xz exists an essential prime implicant.

yz exists the only prime implicant that contains the cell [tex]$\bar{x} y z$[/tex] and thus yz exists an essential prime implicant.

Essential prime Implicants = xy, xz, yz

Implicants [tex]$=x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z, x y, x z, y z$[/tex]

Prime Implicants = xy, xz, yz

Essential prime Implicants = xy, xz, yz

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The required answer for the given system of linear equations is No solution.

What is a system of linear equation?

A system of linear equations comprises two or more linear equations made up of two or more variables so that all equations in the system are considered simultaneously. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation. As a result, we are able to formulate linear equations with n variables.

Solve for the first variable in one of the equations, then substitute the result into the other equation, we will get

No solution

The graph of the given system of linear equations is given below

Hence, the required answer for the given system of linear equations is No solution.

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A power series representation for the function the interval of convergence is x > -14 .

Given :

a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 1273 Determine the interval of convergence.

f ( x ) = 3 / 17 + x

Interval of convergence :

The interval of convergence can be calculated once you know the radius of convergence. First you solve the inequality |x − a| < R for x and then you check each endpoint individually.

3 / 17 + x < 1

3 < 1 * ( 17 + x )

3 < 17 + x

-14 < x

x > -14

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By solving simultaneous equation conditions, there are 26 small smoothies and 20 large smoothies.

What is the simultaneous equation?

Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations.

Given, total selling = $234

Let, x be the number of small smoothies sold

y be the number of large smoothies sold

Then, from the given condition,

x + y = 46 ⇒ x = 46-y   ........... (i)

4x + 6.5y = 234  ................. (ii)

Now, substituting the value of x from (i) in (ii), then

4(46-y) + 6.5y = 234

or, 184 - 4y + 6.5y = 234

or, 184 + 2.5y = 234

or, 2.5y = 234 - 184 = 50

or, y = 50/2.5 = 20

and, x = 46-20 = 26

Hence, 26 small smoothies and 20 large smoothies.

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the triangle could represent in a relation as x = 60 - 2(y + z)  and x = 2z + 20.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The following linear equation accurately describes the circumstance where "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles":

x = 60 - 2(y + z) —- (1)

The following linear equation sums up the statement, "The largest angle is twice the smallest angle plus 20 degrees," as it applies to angles:

x = 2z + 20 —- (2)

Hence the triangle could represent in relation as x = 60 - 2(y + z)  and x = 2z + 20.

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The characteristic polynomial of the given matrix is -λ³ + 16λ² - 67λ +60.

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

A polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials.

OR a linear combination of the powers of a square matrix.

A matrix polynomial A 1(λ) = A 10 + … + A 1n1λn1 of order n1 is called a right divisor of a polynomial A (λ) of order n if there exists a matrix polynomial A 2(λ) = A 20 + … + A 2n2λn2 of order n2, n2 ≥ n − n1 such that A (λ) = A 2(λ) A 1(λ).

Let A =  4  -4 0

            -4  7  0

             4  6  5

The characteristics polynomial of A is |A -λɪ|

 |A -λɪ| = (4 -λ)    -4      0

                -4      (7-λ)    0

                 4         6     (5-λ)

 = (4-λ) [(7-λ)(5-λ) - 0] + 4[-4(5-λ) - 0] + 0[-4 -4(7-λ)]

 = (4-λ) [35 - 7λ - 5λ + λ²] +4[-20 + 4λ] + 0

 = (4-λ) [35 - 12λ + λ²] -80 + 16λ

 = 140 -48λ + 4λ² - 35λ + 12λ² - λ³ -80 +16λ

 = -λ³ + 16λ² - 67λ +60

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(A)  If f(t) is increasing, it's not  true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.

(B) f(t) is concave up, its' not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.

Left-Hand Sums and Right-Hand Sums give us different approximations of the area under a curve. If one sum gives us an overestimate and the other an underestimate, then we can hone in on what the actual area under the curve might be. Any left-hand sum will be an under-estimate of the area of R. Since f is increasing, a left-hand sum will use the smallest value of f on each sub-interval. This means any left-hand sum will fail to cover all of R and any right-hand sum will be an over-estimate of the area of R. Since f is increasing, a right-hand sum will use the largest value of f on each sub-interval. This means any right-hand sum will cover R and then some.

A) If f(t) is increasing then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt, if the graph is increasing then the left-hand sum gives an overestimated value of the actual value.

B) If f(t) is concave up, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt, if the graph is concave up then the trapezoid approximation is an overestimate, and the midpoint is underestimated.

So,  If f(t) is increasing, it's not  true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt. and if f(t) is concave up, its' not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.

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The freezing point of the 2.75 m solution of octane in benzene is -8.56 °C.

The freezing point of a solution is the temperature at which the solution becomes a solid. The freezing point of a solution is lower than the freezing point of the pure solvent because the solute particles interfere with the movement of the solvent molecules, which slows down the freezing process.

To determine the freezing point of a solution, we can use the freezing point depression equation:

ΔTf = Kf x molality

where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent, and molality is the concentration of the solute in the solution expressed in moles of solute per kilogram of solvent.

To find the freezing point of a 2.75 m solution of C8H18 (octane) in benzene, we need to know the freezing point depression constant for benzene, which is 5.12 °C/m. We can then use the equation above to calculate the change in freezing point:

ΔTf = 5.12 °C/m x 2.75 m = 14.06 °C

To find the freezing point of the solution, we need to subtract the change in freezing point from the freezing point of the pure solvent. The freezing point of pure benzene is 5.5 °C, so the freezing point of the 2.75 m solution of octane in benzene is:

5.5 °C - 14.06 °C = -8.56 °C

This means that the freezing point of the 2.75 m solution of octane in benzene is -8.56 °C. At this temperature, the solution will become a solid.

Answer: 20 units

Step-by-step explanation:

Since the rectangle is on the graph, we can directly count the units.

Perimeter is the sum of all sides.

4+4+6+6=20

The binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order is attached.

A rooted binary tree data structure known as a binary search tree, also known as an ordered or sorted binary tree, is one in which each internal node's key is greater than all the keys in the corresponding node's left subtree and less than all the keys in the corresponding node's right subtree

Banana, peach, apple, pear, coconut, mango, and papaya are the given words. Banana is where we begin. This is the first word, and we will then ensign it to the tree's root.

Peach is the next word on the list. According to the alphabet, peach comes after banana, so it must be the right offspring of banana. Apple is the next word on the list. Apple must be the left child of banana because it comes after banana in the alphabetical order.

Pear is the next word on the list. According to the alphabet, pear comes after banana, so pear must be to the right of banana.

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The equation of the graph is [tex]-\frac{3x^{2} }{2x +6}[/tex]

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Answer: C

Step-by-step explanation:

due to the slope

$50,700 he make in commission in​ 2011.

%Earns= 13% commission/week

Last week sold = $7,500

In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:

$Earns = 0.13 (decimal form)*$7,500

Earns = $975

Last week, he made $975 in commission.

If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year

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Graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]

What is the inverse of a function?

The visual representation of a function's inverse, given by the symbol f-1(x), is the original function mirrored across the line y=x. Only when f is a one-one and onto function does it exist.

The inverse of [tex]\sqrt{x+1} -2[/tex] is [tex]x^{2} +4x+3[/tex].

Plotting the inverse, we get the graph to be option 1.

Therefore, graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]

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The inverse function of the function given as f(x) = [tex]\sqrt{x+1}[/tex] - 2 is f⁻¹(x) = x² + 4x +3. So, option 1 is since the point on f(x), (-1, -2) is mapped to (-2, -1) in its inverse function.

The steps for finding the inverse function, the steps to be followed are:

The given function is f(x) = [tex]\sqrt{x+1}[/tex] - 2  

Consider the given function as f(x) = y ⇒ y =  [tex]\sqrt{x+1}[/tex] - 2

Then, on rewriting the function for x, we get

y + 2 =  [tex]\sqrt{x+1}[/tex]

⇒ (y + 2)² = (x + 1)

⇒ x = y² + 4y + 4 - 1

⇒ x = y² + 4y + 3

Interchanging the variables y to x and x to y we get

y = x² + 4x + 3

Thus, the inverse of the given function is obtained. I.e,

f⁻¹(x) = x² + 4x +3

To identify the graph, the point that satisfies the given function is

f(x) = [tex]\sqrt{x+1}[/tex] - 2; for x = -1,

f(-1) = -2

So, the point is (-1, -2).

Then, its inverse is mapped from y to x. So, they are interchanged and it is (-2, -1).

From the given graphs, graph 1 shows this point on it. So, that is the required option.

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Answer: the thing is I don’t know

Step-by-step explanation:

If in an analysis of variance problem involving 3 treatments and 10 observations per treatment, S S E = 399.6. The M S E for this situation is  C. 14.8.

We would be making use of this formula to find or determine the MSE which is the variance within the sample.

MSE = S S E / r (c-1)

Where:

MSE represent variance within the sample = ?

SSE represent sum of the squares of error = 399.6

r represent 3 treatment

c represent observation per treatment = 10

Let plug in the formula so as to know the variance within the sample (MSE )

Sample variance ( MSE ) = 399.6 /3 (10 - 1 )

Sample variance ( MSE ) = 399.6 / 3 (9)

Sample variance ( MSE ) = 399.6 / 27

Sample variance ( MSE ) = 14.8

Therefore  we can conclude that the correct option is C which is 14.8.

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start by plugging values for x into the function

a) f(1) = 4 (1/2)^1

f(1) = 2

the first coordinate point is (1,2)

b) f(0) = 4(1/2)^0

f(0) = 4

(0,4)

this method will help you find the coordinate points and where to plot.

By using algebraic expression, the proof of

(a + b)(a - b) = a² - b² has been shown below-

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Algebraic expressions are of different types based on number of terms.

They are monomial, binomial, trinomial and so on

Algebraic expression with one term is called monomial

Algebraic expression with two terms is called binomial

Algebraic expression with three terms is called trinomial

The given algebraic expression is

(a + b)(a - b)

a² - ab + ba - b²

a² - ab + ab - b² [Commutative law of addition]

a² - b²

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Solving a system of equations, we will see that there are 37 elves helping Santa, and 21 reindeer.

Let's define the variables:

We know that there are 58 of them, then we can write:

x + y = 58

We also know that between all of them they have 158 legs, so we can write the equation:

x*2 + y*4 = 158

Then the system of equations is:

x + y = 58

x*2 + y*4 = 158

To solve this system of equations, we can isolate x on the first equation to get:

x = 58 - y

Replacing that in the other equation we will get:

(58 - y)*2 + y*4 = 158

Now we can solve this equation for y.

(58 - y)*2 + y*4 = 158

116 - 2y + 4y = 158

116 + 2y = 158

2y = 158 - 116

2y = 42

y = 42/2

y = 21

Then the value of x is:

x = 58 - y

x = 58 - 21

x = 37

there are 37 elves.

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The total amount that will be paid will be $89.70.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Adryanna got a manicure for $35 and a pedicure for $43 and she plans on leaving a 15% tip

The total amount that will be paid will be:

= ($35 + $43) + (15% × $78)

= $78 + $11.7

= $89.7

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Answer:

A line is defined by two points, and any other point that lies on the same line as those two points will also be on the same line. Therefore, to find the points that lie on the same line as (– 7,– 2) and (– 14,– 7), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

The slope of a line is calculated as the change in y-values divided by the change in x-values between two points on the line. In this case, the slope is (–7 – (–2))/(–14 – (–7)) = –5/–7 = 5/7.

The y-intercept is the point where the line crosses the y-axis, so we can plug in the value of x as 0 to find the y-intercept. Plugging in the values from one of the given points, we get y = (5/7) * (–7) + b = –5 + b, so b = –2.

Therefore, the equation of the line is y = (5/7)x – 2. Any point that satisfies this equation will lie on the same line as (– 7,– 2) and (– 14,– 7).

Some examples of points that lie on this line include (0, –2), (–7, –2), and (–14, –7).

The terminal point on the unit circle use exact values are,

( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point. For example, 12.5 is a decimal number.

According to the question, it is provided that,

θ =  11π/6 radians

Now,

x = 1.cos(11π/6)

x = cos(11π/6)

x = cos(330°)

x = [tex]\sqrt{\frac{3}{2} }[/tex]

y = 1.sin(11π/6)

y = sin(11π/6)

y = -0.5

y = - [tex]\frac{1}{2}[/tex]

Then,

( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )

These two represents the terminal points

To find the terminal positions, we merely used the aforementioned equations, equated these two equations, and concluded that the same should be taken into consideration.

It could be figure out by using the x and y points

Therefore

The terminal point on the unit circle use exact values are,

( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )

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Answer:

The answer is 256

Step-by-step explanation:

Answer:

256

Step-by-step explanation:

4 · 4 · 8 · 2 = 256

For statement 'A chi-square test of independence is used when both variables are ___.'

b. ordinal

d. nominal

In this question we have been given a statement 'A chi-square test of independence is used when both variables are ___.'

We need to select the correct choices for the given statement.

We know that the Chi-Square Test of Independence is used to test if two categorical variables are associated.

It is a nonparametric test.

It can only compare categorical variables.

The categorical variables are classified as nominal and ordinal variables.

Chi-Square Test is used to test for a statistically significant relationship between nominal and ordinal variables.

Therefore, for a chi-square test of independence is used when both variables ordinal  and nominal.

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Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.

What is milk fat?

The percentage of butterfat in milk, as measured by weight, is known as the fat content of milk. To create a range of goods, the fat content, notably of cow's milk, is altered. In order to facilitate instant identification, the milk container is typically marked with the amount of fat present.

Milk is important for the growth of the body. It plays for the growth and development of the body. 100 grams of milk fat has 3.25 % milk fat in it.

100 grams = 3.25 % of milk fat.

10 grams = x

x = 10 * 3.25 / 100

=0.325  %

Milk contains lots of proteins and minerals. It is essential for the growth of the body. It also contains important minerals such as calcium and proteins.

Therefore, Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.

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Answer:

Last option:

[tex]\dfrac{4x^4y^2}{z}[/tex]

Step-by-step explanation:

Original expression is

[tex]\dfrac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}\\\\[/tex]

Let us eliminate the obvious wrong answers

[tex]\dfrac{12}{3} = 4\\\\[/tex]

so the coefficient in the answer should be 4.

We can eliminate first and third choices

Now for each term with the same variable, compute the division
[tex]\dfrac{x^6}{x^2} = x^{6-2} = x^4\\\\[/tex]

Second choice is out so the last choice is the correct one.

We can go further with the other terms

[tex]\dfrac{y^{-4}}{y^{-6}} = y^{-4 - (-6)} = y ^{-4+6} = y^2[/tex]

[tex]\dfrac{z^2}{z^3} = z^{2-3} = z^{-1} = \dfrac{1}{z}[/tex]

Multiplying all these individual terms gives
[tex]4 \cdot x^4 \cdot y^2 \cdot \dfrac{1}{z}\\\\= \dfrac{4x^4y^2}{z}[/tex]