Question 4


According to a survey of 1,362 adult college students, the mean number of alcoholic beverages consumed


per week is 15, with a standard deviation of 3 beverages. What test statistic is calcuated for this scenario?

The slope-intercept form of a linear equation is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Given that the slope of the line is 1 and it passes through the point (8, –1), we can use the point-slope form of a linear equation to write the equation in slope-intercept form. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Substituting the values given in the problem into the point-slope form, we get:

y - (-1) = 1(x - 8)

Expanding the right side and rearranging the terms, we get:

y + 1 = x - 8

y = x - 9

This is the equation of the line in slope-intercept form. The y-intercept is (-9, 0), which is the point at which the line crosses the y-axis.

(Option D. Incentre) The incentre of a triangle is the point equidistant from all three of the triangle's vertices. This means that its distance from each vertex is the same.

The incentre of a triangle is an important point of reference for geometry. It is located at the center of the triangle's inscribed circle, which is the circle that touches each of the triangle's three vertices. This is why the incentre is also known as the triangle's inner center or center of the triangle's inscribed circle. As it is equidistant from all three of the triangle's vertices, the incentre is useful for finding the angles of the triangle and for finding the lengths of the triangle's sides. It can also be used to calculate the area of the triangle.

Learn more about the Triangles: https://brainly.com/question/17335144

#SPJ4

The value of x or we can say that the value of side DF will be equal to 5.29.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

The sides of the right triangle are,

DE, h = 8

FE, b = 6

DF, p = x

Then, use Pythagoras' theorem,

h² = x² + b²

8² = x² + 6²

x² = 64 - 36

x = √28

x = 5.29  

To know more about equation:

https://brainly.com/question/29657983

#SPJ1

According to the provided data, to be one of the top 7% earners a manager needs to earn $48,360.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.

The formulas are given below:

[tex]\mu = \frac {\sum x}{N}[/tex]      (Mean)

[tex]\sigma = \sqrt {\frac {\sum (X- \mu ) ^ {2}} {N}[/tex]    (Standard Deviation)

Mean = $48,000

Standard Deviation = $4,000

According to this data, Max Earning made = $48,000 + $4,000

=$52,000

7% of $52,000 = $3,640

To be top 7% earner, A manager must earn = $52,000 - $3,640

=$48,360

To learn more about mean and standard deviation visit:

https://brainly.com/question/11822836

#SPJ4

Answer:$53,903

Step-by-step explanation:

Here, the mean, μ, is 48,000 and the standard deviation, σ, is 4,000. Let x be the cutoff salary for teachers in the top 7%. The area to the right of x is 7%=0.07. So, the area to the left of x is 1−0.07=0.93.

Open Excel. Click on an empty cell. Type =NORM.INV(0.93,48000,4000) and press ENTER.

Round the answer to the nearest dollar, is x≈53,903. Therefore, the cutoff salary for managers in the top 7% is $53,903.

The given series diverges.

Given:

aₙ = n²/√n³+7n

using series divergence test

If limₙ→∞ aₙ ≠0, then ∑  aₙ diverges .

limₙ→∞ (n²/√n³+7n) = limₙ→∞ (n²/√n³(1+7/n²)

= limₙ→∞ (n²/n³/²√1+7/n²)

= limₙ→∞ (√n/√1+7/n²)

= (∞/√1+0)

= ∞

Therefore the series diverges.

Learn more about Divergence here:

brainly.com/question/17177764

#SPJ4

Answer:

Yes

Step-by-step explanation:

y-8= -8(x-2)  ==> solve for y

y = -8(x - 2) + 8  ==> add 8 on both sides to isolate y

y = (-8 * x - 2(-8)) + 8  ==> distribute -8 to x and -2 using the distribution

                                         property

y = (-8x - (-16)) + 8 ==> simplify

y = (-8x + 16) + 8  ==> subtracting by a negative number is equivalent to

                               adding by a positive number.

y = -8x + 16 + 8

y = -8x + 24  ==> Degree of x in the equation is 1, so the function is linear

The table of values represents a quadratic function. And a quadratic function is y = x² / 10.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function.

Linear functions have constant first differences.

Here,  if a and b is the first and second term.

Then the first difference is b-a.

Quadratic functions have constant second differences.

Let the first differences are:

b-a = m, c-b = n

Then the second difference is n-m.

Exponential functions have a constant ratio.

The ratio of first term and second term is b/a.

Here, from the table;

y₂-y₁ = 0.4 - 0.9 = -0.5 = m₁

y₃-y₂ = 0.1 - 0.4 = -0.3 = m₂

y₄-y₃ = 0 - 0.1 = -0.1 = m₃

y₅-y₄ = 0.1 - 0 = 0.1 = m₄

y₆-y₅ = 0.4 - 0.1 = 0.3 = m₅

From the first differences, we have no idea about the function property.

So, the second differences:

m₂ -  m₁ = -0.3 + 0.5 = 0.2

m₃ - m₂ = -0.1 + 0.3 = 0.2

m₄ - m₃ = 0.1 + 0.1 = 0.2

m₅ - m₄ = 0.3 - 0.1 = 0.2

Here, the second differences are constant 0.2.

And the common ratio is varying.

So, quadratic functions have constant second differences.

And the quadratic function is y = x² / 10.

Therefore, the given function is a quadratic function.

To learn more about the quadratic function;

https://brainly.com/question/29775037

#SPJ1

From a group of 15 randomly selected residents , the probability that at least thirteen of them shop at Walmart is 0.0271  .

6 out of 10 Niceville residents shop at Walmart

So, the probability of shopping at Walmart (p) is = 6/10 = 0.6

The probability of not shopping at Walmart is (q) = 1 - 0.6 = 0.4 .

The number of members in the group is(n) = 15 ;

We have to find the probability that, at least thirteen of them shop at Walmart

By the Binomial Probability Distribution,

we know that ; P(x = a) = ⁿCₐ×pᵃ×qⁿ⁻ᵃ

So , P(x ≥ 13) = P(x=13) + P(x=14) + P(x=15)

Substituting the values of a , n and p and q ,

We get ;

= ¹⁵C₁₃p¹³q² + ¹⁵C₁₄p¹⁴q¹ + ¹⁵C₁₅p¹⁵q⁰

= ¹⁵C₁₃(0.6)¹³(0.4)² + ¹⁵C₁₄(0.6)¹⁴(0.4)¹ + ¹⁵C₁₅(0.6)¹⁵(0.4)⁰

= 0.0219 + 0.0047 + 0.0004

= 0.0271

Therefore, the required probability is 0.0271

Learn more about Binomial Probability Distribution here

https://brainly.com/question/26077592

#SPJ4

The average daily inventory is 253 cases

In this question, we have been given we have been given the number of cases of zippers on inventory t days after the shipment arrives is

N(t) = 630 − 30√18t

We need to find the average daily inventory.

We use the definite integral to compute for the average value over that interval from a to b.

(∫[a_b] f(x) dx )/ (b - a)

Here, a = 1 and b = 18

so, the average daily inventory would be,

∫[18_1] N(t)dt / (18 - 1)

= ∫[18_1] (630 − 30√18t) dt / 17

= 4314.85 / 17

= 253.81

= 253

Therefore,  the average daily inventory = 253 cases

Learn more about the definite integral here:

https://brainly.com/question/29685762

#SPJ4

The complete question is:

the dog days clothing company receives 630 cases of imported zippers every 18 days. the number of cases of zippers on inventory t days after the shipment arrives is  N(t) = 630 − 30√18t. Find the average daily inventory.

The answer is (76.42 ; 78.17)

Given that:

A botanist is attempting to determine how many seeds are typically present in a particular fruit. She collects 65 samples and counts how many seeds are present in each. Using her sample data, the mean is 77.3 and the SD is 5.5.

Sample size, n = 65

Mean, xbar = 77.3

Standard deviation, s = 5.5

Confidence level, Zcritical at 80% = 1.28

Confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Margin of Error = 1.28 * 5.5/sqrt(65)

Margin of Error =0.873

Lower boundary = 77.3 - 0.873 =76.42

Upper boundary = 77.3  + 0.873 = 78.17

Therefore, the answer is (76.42 ; 78.17)

To learn more about Standard deviation click here:

brainly.com/question/16555520

#SPJ4

Answer: No, i dont think so.

Step-by-step explanation:

AC = BC is not listed as given.

Answer:The only rational root of x3−3x2+4x−12=0 is 3.

Step-by-step explanation:

{1,−1,2,−2,3,−3,4,−4,−6,12,−12} , if at least one root is rational.

hope this helps

The flux of the given sphere as calculated from the data is, flux= 5πa³/6.

We can use spherical coordinates for this sphere with radius r=ar =a.

The surface can then be described using the parametric equation as

r(θ,Ф)= acosθsinФi + asinθsinФj + acossθk

The partial derivatives of this parametric function with respect to its parameters are,

r ϕ​=acosθcosϕi+asinθcosϕj−asinϕk

r θ=−asinθsinϕi+acosθsinϕj

​

Therefore,

the cross product will be ,

ndσ=a²[cosθsin²ϕi+sinθsin²ϕj+sinϕcosϕk]dϕd

In these coordinates

F = 5zk = 5acosФk

therefore on integrating we get ,

flux= 5πa³/6

Flux is a physics term that refers to the number of electric or magnetic field lines that pass through a surface in a given amount of time. Field lines provide a visual representation of the magnitude and direction of the field being measured.

To learn more about flux

brainly.com/question/17052775

#SPJ4

​

The function is increasing for all real values of x where

x < –1 and where x > 4.

What is increasing and decreasing functions?

Calculus uses a function's derivative to determine whether a function is increasing or decreasing at various intervals in a specific domain. For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

Given function is

f(x) = (x - 4)(x + 1)

If f(x) = 0,  x=4 & x=-1

f'(x) = 0, x=3/2

So, we will check the behavior of the function in the neighborhood of  x=4,-1, 3/2.

What is the increasing and decreasing function?

A function is said to be an increasing function if its slope is continuously increasing in a given interval.

A function is said to be a decreasing function if its slope is continuously decreasing in a given interval.

If x>4

Let us check at x=5

f(5) =6(+ve)

f(x) >0 for x>4

So, the function is increasing in x>4

Similarly, If x <-1

f(x) >0 for  x <-1

So, function is increasing in x <-1

If -1<x<3/2

f(x)<0 for -1<x<3/2

So, function is decreasing in -1<x<4

If 3/2<x<4

f(x)>0 for 3/2<x<4

So, the function is increasing in 3/2<x<4

From the graph too, we can see the behavior of the given function

by observing the slope.

We can see that for x<-1 and x>4, the slope is continuously increasing

So, the function is increasing in x<-1 and x>4.

Therefore, the function is increasing for all real values of x where

x < –1 and where x > 4.

Learn more about increasing and decreasing functions link below?

brainly.com/question/11861192

#SPJ1

Answer:

y - 2.5 = 2(x - 1)

Step-by-step explanation:

Here given slope is 2 and the point through which the straight line passes is (1, 2.5)

Let the equation be y = mx + c where m and c represent slope and y intercept respectively.

We know the slope, so we input that in our equation

y = 2x + c ------- i

This straight line also passes through (1, 2.5)

Putting the values in place of x and y we get,

2.5 = (2X1) + c

⇒ 2.5 = 2 + c

⇒ c = 2.5 - 2

⇒ c = 0.5

Now, putting value of c in i, we get

y = 2x + 0.5 -------- ii

It can also be written as y - 2.5 = 2(x - 1) ------- iii

this equation and ii are same and you can verify that by simplifying iii, by multiplying 2 and then shifting the -2.5 from LHS to RHS

Equations are not equivalent because the values are found to be different.

What is an expression?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Expressions are:

(9a - 27) - 4 = 9a  - 31 -------(I)

and -3(- 4 - 3) = -3(-7) = 21 -----(II)

From (I) and (II), expressions are not equivalent.

Hence, equations are not equivalent because the values are found to be different.

To learn more about expression, visit:

https://brainly.com/question/1859113

#SPJ1

The value of the expression (f * g) by using two ways that is by direct integral and by Laplace transform is equal to (1/2)e^t/(1-t) - (1/2)e^t/(1+t) + C.

To compute the convolution of f(t) and g(t) by directly evaluating the integral in the definition of the convolution, we have:

(f * g)(t) = ∫f(w)g(t-w)dw

Substituting in the expressions for f(t) and g(t), we have:

(f * g)(t) = ∫e^w*e^(-6)(t-w)dw

This integral can be evaluated as follows:

(f * g)(t) = ∫e^(-5w)dw

(f * g)(t) = (-1/5)e^(-5w) + C

(f * g)(t) = (-1/5)e^(-5w) + C

To compute the convolution of f(t) and g(t) by computing the inverse Laplace transform of the product of the Laplace transforms of f(t) and g(t), we have:

F(s) = L{f(t)} = ∫f(t)e^(-st)dt = ∫e^t*e^(-st)dt = 1/(s-1)

G(s) = L{g(t)} = ∫g(t)e^(-st)dt = ∫e^(-6t)*e^(-st)dt = 1/(s+6)

Therefore,

F(s)G(s) = (1/(s-1))(1/(s+6)) = 1/(s^2-1)

To find the inverse Laplace transform of F(s)G(s), we use the following formula:

L^-1{F(s)G(s)} = ∫F(s)G(s)e^st ds

Substituting in the expression for F(s)G(s), we have:

L^-1{F(s)G(s)} = ∫(1/(s^2-1))e^st ds

This integral can be evaluated as follows:

L^-1{F(s)G(s)} = (1/2)e^st/(s-1) - (1/2)e^st/(s+1) + C

L^-1{F(s)G(s)} = (1/2)e^st/(s-1) - (1/2)e^st/(s+1) + C

Thus, the convolution of f(t) and g(t) can be computed either by directly evaluating the integral in the definition of the convolution or by computing the inverse Laplace transform of the product of the Laplace transforms of f(t) and g(t). In both cases, the result is:

(f * g)(t) = (1/2)e^t/(1-t) - (1/2)e^t/(1+t) + C

Learn more about Laplace transform at:

brainly.com/question/29583725

#SPJ4

The issue with this model is that purchases with a cost of $30 appear to be negative, which is impractical in real-world situations.

This is due to the model's linear best fit line's potential for being inaccurate for the end points.

A linear probability model:

Purchasei = 1.7-0.06×pricei

For an increase in $20 in price,

Change in purchase = -0.06 × 20

change in purchase = -1.2

There would be 1.2 less purchase.

Purchase at price of $10 is:

Purchase 10= 1.7 ×0.06 × 10

Purchase 10 = 1.1

Purchase at price of $30 is:

Purchase 30 = 1.7 × 0.06 × 30

Purchase 30 = -0.1

This is the problem with this model that the purchases at price of $30 is coming as negative which is not possible in practical situation.

It is because that the linear best fit line of the model which might not be accurate for the end points.

Hence we get the required estimates here:

Learn more about Estimate here:

brainly.com/question/28416295

#SPJ4

Answer:

The answer is 13.2

Step-by-step explanation:

d = 10

e = 3.2

d + e = 10 + 3.2 = 13.2

Thus, The answer is 13.2

Answer:

c. between 4&5 and -1&0

Step-by-step explanation:

The statement of triangle is that it has three corresponding sides and three corresponding angles.

There are at least 3 theorems about triangles, those are: the total of the three interior angles in any triangle is 180 degrees; when a triangle side is constructed, the exterior angle formed is equal to the sum of the interior opposite angles; and, the base angles of an isosceles triangle are equivalent.

Scalene, isosceles and equilateral triangle are the types of triangles which differ from each other based on their side-length. If all the three sides are different in length, then its scalene triangle. If any two sides are equal in length, then it is an isosceles triangle.

Learn more about triangles at: https://brainly.com/question/2773823

#SPJ4

fn is an integrable function on [a, b]. further, assume that the sequence (fn) converges uniformly to f on [a, b]. f is integrable on integral [a, b].

Let ε > 0. Since (fn) converges uniformly to f on [a, b], there exists an N such that |fn(x) - f(x)| < ε for all x ∈ [a, b] and all n ≥ N.

Since fn is integrable on [a, b], it follows that

∫a b|fn(x)|dx < ∞ for all n ≥ N.

We have

∫a b|f(x)|dx ≤ ∫a b|fn(x)|dx + ∫a b|fn(x) - f(x)|dx

Since |fn(x) - f(x)| < ε, it follows that

∫a b|f(x)|dx ≤ ∫a b|fn(x)|dx + ε(b - a)

Since the right hand side is finite, it follows that ∫a b|f(x)|dx is finite. Hence, f is integrable on integral [a, b].

Learn more about integral here

https://brainly.com/question/18125359

#SPJ4

The expected mean of the sampling distribution and the standard deviation of the sampling distribution is $29.50.

Standard deviation

In statistics, standard deviation refers  the square root of variance by determining each data point's deviation relative to the mean.

Given,

Here we know that a statistics student is trying to decide whether she should take a gamble and play bingo. And the average bingo player earns $9 per game, distributed normally, with a population standard deviation of $8.

And we need to find if a sample of 25 bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.

0; = $0.32 0; = $8 O = $1.60 Mi = $9 Hi = $1.80

Here the standard deviation of the sample distribution is calculated as,

=> σₓ = √1.80 = 1.34

Here we know that the distribution is normal then the mean of the sampling distribution is equal to the mean of the population, based on this theory, the resulting value is $29.50.

To know more about Standard deviation here.

https://brainly.com/question/16555520

#SPJ4

The equation that can be used to model the total time y for number of chimes is y = 2x.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, it takes Ernest's grandfather clock 2 seconds to chime.

Therefore, the equation that can be used to model the total time y for number of chimes x will be:

y = 2 × x

y = 2x.

The equation is y = 2x.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

The value of y is 4.

Generally, To find the value of y in the expression [0 (3z-9) (y-1)], we need to isolate y. To do this, we can start by combining like terms:

[-1(4x-2) -5] [-1 2 -5] [0 (3z-9) (y-1)] [0 3 2]

Becomes:

[-4x + 2 - 5] [0 3 2]

Then we can rearrange the terms to get:

[-4x - 5 + 2] [0 2 + 3]

This simplifies to:

[-4x - 3] [5]

Finally, we can isolate y by dividing both sides by 2:

[-4x - 3] / 2 = 5 / 2

This gives us:

y = (5/2) + 3/2

Simplifying, we find that y = 4.

Therefore, the value of y in the expression [0 (3z-9) (y-1)] is 4.

Read more about expression

https://brainly.com/question/14083225

#SPJ1

The graph of the linear equation y = 9/7x - 9 is attached below

A linear graph is the graphical representation of a straight line. It showcases a linear equation in two variables and shows the linear association between two quantities. A linear function often have a straight line with a slope and y-intercept.

To solve this, we can simply write an equation of the linear equation which is often given as

y = mx + c

Let's substitute the values and find the equation;

y = 9/7x - 9

Kindly find the attached image below;

Learn more on graph of a linear equation here;

https://brainly.com/question/14323743

#SPJ1

Correct option is A

Independent variable

Independent variable is manipulated by the researcher to determine the effect of its change relative to a change in dependent variable.

Independent Variables

An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable.

In an experiment the independent variable is the variable that is varied or manipulated by the researcher. The dependent variable is the response that is measured. One way to think about it is that the dependent variable depends on the change in the independent variable.

Qualitative research consist in observing some variables and obtaining information. Usually the qualitative research does not involve the manipulation of independent variables, these types of researches focuses more in collecting answers in groups of people, and making statistics with those answers or information. So the variables are not manipulated.

Correct option is A

To learn more about Independent Variables visit:

brainly.com/question/29430246

#SPJ4

Answer:

warmth

Step-by-step explanation:

they migrate to stay warm I hope you do good (:

Answer:

To find a warmer place for nesting grounds or migration.

Step-by-step explanation:

The equation will be t = 3s where t is total cost and s is number of snow cones. this can be find out be relationship of number of snow cones and total cost in table .

In given table :

Number of snow cones               Total cost

2                                                      6

6                                                      12

5                                                      15

From above table, we can relate

1st case :
number of snow cones = 2 and total cost = 6

i.e. 3 times of number of cones.

2nd case:

number of cones = 4 and total cost = 12

i.e. 3 times the number of cones.

3rd case :

number of cones = 5 and total cost = 15

i.e. 3 times the number of cones.

So, we see same pattern is repeated in all.

Then equation will be t = 3s where t = total cost , s = number of snow cones.

Learn more about equation using link :

https://brainly.com/question/25976025

#SPJ1

The additional jump in inches that John must make to beat the record is

5 1/4 inches

The problem is solved by converting the given dimensions in ft to  inches

conversion to inches is solved using

12 inches = 1 ft

The record jump is

= 23 feet 1 3/4 in

= 23 * 12 + 1 3/4 in

= 276 + 1 3/4

= 277.75 in

John's best long jump

= 22 ft 8 1/2 in

= 22 * 12 + 8 1/2 in

= 264 + 8 1/2

= 272.5 in

John's additional jump

= record jump - John's best long jump

= 277.75 - 272.5

= 5.25 in

= 5 1/4 in

Learn more about conversion of  units at:

https://brainly.com/question/141163

#SPJ1