THIS IS NOT A TEST OR ASSESSMENT!! NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE EXPLAIN!! Chapter 13


1. What is a conic ? How would you be able to model different conic sections at home(how would you slice a 3D shape to create the conic sections)?



2. How does the equation for the ellipse compare to the equation for a hyperbola? How can you determine the difference?


3. What is the difference between a vertex, a focus, and a directrix?

Answers

Answer 1

9514 1404 393

Explanation:

1.

A cone is a 3-dimensional object created by revolving a line about an axis that intersects that line. This figure is a "double-napped" cone. The point where the revolved line and the axis meet is the a.pex, or vertex, of the cone. Typically, we're concerned with a finite portion of the cone, from the vertex to a base that is a circle in a plane perpendicular to the axis.

A "conic" is a 2-dimensional figure that results from the intersection of a plane and a cone. There are four general categories, named according to the angle the plane makes with the axis and/or the side of the cone. These are illustrated in the attachment.

a circle - the plane of intersection is perpendicular to the axisan ellipse - the plane of intersection is at an angle between 90° and the angle of the side relative to the axis. Both an ellipse and a circle are closed figures.a parabola - the plane of intersection is at the same angle as the side of the cone. A parabola is a one-sided open figure.a hyperbola - The plane of intersection is at an angle between that of the side of the cone and the axis of the cone. The plane will intersect both parts of a double-napped cone producing a double-sided open figure.

Producing these at home can be an interesting project. A circle can be made using a compass.

An ellipse can be drawn using a pair of pins and a loop of string. The pins would be placed at the foci of the ellipse, and the string would constrain the drawing instrument (pen or pencil) to have a constant total distance to the two foci.

A parabola can be drawn on graph paper using coordinates derived from an equation for it. It can also be drawn using a compass and a set square by plotting points that are equidistant from the focus and a line that is called the directrix. If you have a physical cone-shaped object, you can cut it at an angle that will produce a parabola.

A hyperbola can be drawn on graph paper from an equation. It can also be drawn using a compass by plotting points that have a constant difference in their distance to the two foci, or by plotting points whose ratio of distance to focus and directrix is a constant. A physical cone-shaped object can be cut to produce a hyperbola.

__

2.

The general form equation for a conic is ...

  Ax² +Bxy +Cy² +Dx +Ey +F = 0

Usually, we're concerned with conics that have axes parallel to the coordinate axes, so B=0. The equation of an ellipse has A and C with the same sign. The equation of a hyperbola has A and C with opposite signs,

In standard form, the equations for figures centered at the origin are ...

ellipse: x²/a +y²/b = 1hyperbola: x²/a -y²/b = 1 (opens horizontally)hyperbola: y²/a -x²/b = 1 (opens vertically)

__

3.

The vertex of a conic is an extreme point on the (major) axis of the conic. The focus is a point used in the definition of the conic. The focus is "inside" the curve, on the axis of symmetry. The directrix is a line used in the definition of the conic. The directrix is "outside" the curve, perpendicular to the axis. The second attachment shows these for a parabola.

THIS IS NOT A TEST OR ASSESSMENT!! NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE EXPLAIN!!
THIS IS NOT A TEST OR ASSESSMENT!! NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE EXPLAIN!!

Related Questions

If a normally distributed population has a mean (mu) that equals 100 with a standard deviation (sigma) of 18, what will be the computed z-score with a sample mean (x-bar) of 106 from a sample size of 9?

Answers

Answer:

Z = 1

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean (mu) that equals 100 with a standard deviation (sigma) of 18

[tex]\mu = 100, \sigma = 18[/tex]

Sample of 9:

This means that [tex]n = 9, s = \frac{18}{\sqrt{9}} = 6[/tex]

What will be the computed z-score with a sample mean (x-bar) of 106?

This is Z when X = 106. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{106 - 100}{6}[/tex]

[tex]Z = 1[/tex]

So Z = 1 is the answer.

What is the solution of log3x + 4 4096 = 4?

Answers

Step-by-step explanation:

X= - 1

X=0

X=4/3

X=3

We solve for x by simplifying both sides of the equation, then isolate the variable.

Answer :

C (x=4/3)

round 12.5478 to the nearest hundredths

Answers

Answer:

12.04

Step-by-step explanation:

Find the number in the hundredth place  4  and look one place to the right for the rounding digit  1 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

Hey guys can help me please

Answers

Answer:

Can you select multiple answers to this question? then option A, B and C all three applies, if only one the go for option C, since that's the major change happens to the parent function

A newsstand spends $600 a month on rent and electricity, and it spends $2
for each magazine that it sells. The newsstand charges $5 for each
magazine. If n is the number of magazines, which equation represents the
profit function of the newsstand?
O A. p = 2n + 600
B. p = 3n-600
O c. p = 600n + 3
O D. p = 5n-600

Answers

Answer: B. p = 3n-600

Step-by-step explanation:

Cost = 2n + 600Earned = 5n

Profit(p) = Earned - Cost

p = 5n - (2n + 600) = 5n - 2n - 600 = 3n - 600

The equation representing the profit function of the newsstand is

p = 3n - 600

Option B is the correct answer.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The revenue generated by selling n magazines is 5n dollars.

The cost of selling n magazines is the sum of the cost of purchasing n magazines and the fixed cost of rent and electricity, which is $2n + $600.

Now,

The profit function can be represented by:

p = revenue - cost

= 5n - (2n + 600)

= 3n - 600

Thus,

The equation representing the profit function of the newsstand is

p = 3n - 600

Learn more about functions here:

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Michael is 4 times as old as Brandon and is also 27 years older than Brandon.
How old is Brandon?

Answers

Answer:

9

Step-by-step explanation:

b = Brandon

4b=b+27

-b   -b

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

3b = 27

----   ----

3      3

b = 9

Brandon is 9 years old.

A bank wishes to estimate the mean balances owed by customers holding Mastercard. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?
A. 76
B. 85
C. 86
D. 77

Answers

Answer:

D. 77

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The population standard deviation is estimated to be $300

This means that [tex]\sigma = 300[/tex]

If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?

This is n for which M = 80. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]80 = 2.327\frac{300}{\sqrt{n}}[/tex]

[tex]80\sqrt{n} = 2.327*300[/tex]

[tex]\sqrt{n} = \frac{2.327*300}{80}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327*300}{80})^2[/tex]

[tex]n = 76.15[/tex]

Rounding up:

77 cardholders should be sampled, and the correct answer is given by option d.

How do you Find the acute Angle A when sinA=0.616?

Answers

Answer:

arcsin0.616

Step-by-step explanation:

arcsino.616

PLEASE HELP URGENT!!!
Janine determines that the total resistance in her circuit is 80 ohms. Using the inverse equation modeling this situation, find the resistance of the second lightbulb.

The resistance of the second lightbulb is ohms.

A. 120
B. 240
C. 300
D. 40

Answers

The sum of resistors arranged in parallel is the inverse of the sum of the inverses of the magnitudes of the individual resistances

The correct option for the resistance of the second light bulb in ohms (Ω) is option B;

B. 240

The reason why option B is the correct answer is s follows:

Known parameters:

Based on a online search, the question appears to have some parts missing which can be as follows;

The resistance of the first light bulb = 120 Ω

Janine's model of the total resistance of the circuit, [tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]

Where;

r = The resistance of the second light bulb

The unknown parameter:

Resistance of the second light bulb

Method:

Find r using Janine's  model of the total resistance, which is the equation of total resistances in parallel arrangement

The inverse relationship modelling the sum, t, of resistances, r, and 120, arranged in parallel, presented as follows;

[tex]\mathbf {\dfrac{1}{t} } =\dfrac{1}{120} + \dfrac{1}{r}[/tex]

∴ [tex]\mathbf {\dfrac{1}{t}} = \dfrac{r + 120 }{120 \cdot r}[/tex]

Therefore, by finding the inverse of both sides of the above equation, we get Janine's model as follows;

[tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]

The above equation is the inverse equation modelling the total resistance of the parallel arrangement of the resistances in the lightbulb

The question details include:

The total resistance in her circuit, t = 80 Ω

Solution:

Plugging in t = 80 in [tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex], gives;

[tex]80 = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]

Therefore, we get;

80·(r + 120) = 120·r

80·r + 80 × 120 = 120·r

∴ 120·r - 80·r = 80 × 120 = 9,600

120·r - 80·r = 40·r

∴ 40·r = 9,600

r = 9,600/40 = 240

The resistance of the second light bulb, r = 240 Ω

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Answer:240

Step-by-step explanation:

i watched the walk through

To almirahs are purchased for 7,800.
200 was spent on the transportation. One of them is sold at a profit of 40% and the other one at a loss of 40% If the selling price was same in both the cases, and the cost price of each almirah​

Answers

Answer:

The Cost Price of the Almirah Is 4000

A gardener makes a new circular flower bed. The bed is ten feet in diameter.Calculate the circumference and the area of the circular flower bed

Answers

Answer:

It will be 31.4 cm rounded off for circumference

It will be 78.53 cm2 rounded off for area

Step-by-step explanation:

Diameter = 10 cm

Radius = 10/2 cm = 5 cm

Circumference = 2×pi×radius

= 2pi×5

= 31.4 cm

Area = pi × r square

= 25 pi

= 78.53cm2

A study was done to determine the proportion of voters that feel that their local government is doing an adequate job. Of the 220 voters surveyed, 175 feel that their local government is doing an adequate job. Calculate the 95% confidence interval for the true proportion of voters that feel that their government is doing an adequate job.

Answers

Answer:

( 0.742, 0.849 )

Step-by-step explanation:

sample size = 220

number of voters with positive response ( i.e. number of voters who believe the government is doing right )  = 175

Calculate the 95% confidence interval

P = 175 / 220 = 0.796

the 95% confidence interval = ( 0.796 ± 0.054 )

attached below is the detailed solution

Maria reads 3/5 chapters in 5/6 hours whats the unit rate?

Answers

Answer: 18/25 chapters / hour

Step-by-step explanation:

Concept:

Here, we need to know the idea of unit rate.

A unit rate is a rate with 1 in the denominator.

In simple words, the unit rate is something per one thing. For example, when you go to a store, you bought a book that is priced at $10. In actually meaning, it is $10 per book, or $10/book.

Solve:

Given formula

Unit rate = Number of chapters / Hours

Substitute the value into the formula

Unit rate = (3/5) / (5/6)

Convert to multiplication by taking the reciprocal of the divisor

Unit rate = (3/5) · (6/5)

Numerator times numerator / denominator times denominator

Unit rate = (3 × 6) / (5 × 5)

Unit rate = 18 / 25 chapter / hour

Hope this helps!! :)

Please let me know if you have any questions

The unit rate is 18/25 chapters per hour. This means Maria is reading at a rate of 18/25 chapters in one hour.

How to determine the unit rate

To calculate the unit rate, we're trying to find out how much of something (in this case, chapters) happens in a single unit of another thing (time, in hours).

In this scenario, Maria reads 3 out of 5 chapters in 5 out of 6 hours. To find the unit rate, we divide the chapters read (3/5) by the time taken (5/6 hours):

Unit Rate = Chapters Read / Time Taken

= (3/5) / (5/6)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

Unit Rate = (3/5) * (6/5)

= (3 * 6) / (5 * 5)

= 18 / 25

So, the unit rate is 18/25 chapters per hour. This means Maria is reading at a rate of 18/25 chapters in one hour.

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b) An achievement test was administered to a class of 20,000 students. The mean score was 80 and the standard deviation was 11. If Lingard scored 72 in the test, how many students did better than him

Answers

Answer: 15328

Step-by-step explanation:

The following can be deduced from the information given:

N = 20000

μ = 80

σ = 11

P(X>72) = 1 - P (X<72)

= 1 - P(Z < 72-80/11)

= 1 - P(Z < -8/11)

= 1 - P(Z < 0.7272)

= 1 - 0.2336 = 0.7664

Therefore, the number of students that were better than Lingard n(X > 72) will be:

= 20000 × 0.7664

= 15328

The scatterplot shows the average miles per gallon versus the age, in years, of a car.


A graph titled Fuel efficiency has age (years) on the x-axis, and miles per gallon on the y-axis. Points are at (1, 25), (2, 32), (3, 26), (4, 23), (5, 19), (6, 16), (7, 17), (8, 14), (9, 13), (10, 10).


If age was on the vertical axis and miles per gallon on the horizontal axis, how would the correlation change? Select all statements that would apply to the new correlation coefficient.


The sign would be the opposite.

The sign would remain the same.

It would have the same value.

It would become closer to 0.

It would become closer to 1.

(2 and 3) B,C

Answers

Answer:

The sign would remain the same.

It would have the same value.

ED2021

Answer: b&c

The sign would remain the same.

It would have the same value.

Solve 2x^2+5x+5=0 round solutions to the nearest hundredth.

Answers

Answer:

-0.56

Step-by-step explanation:

Fill in the blank with a number to make the expression a perfect square.
u^2- 18u +

Answers

Answer:

u^2- 18u +81 = (u-9)^2

Step-by-step explanation:

u^2- 18u +

Take the u coefficient

-18

Divide by 2

-18/2 = -9

Square it

(-9)^2 = 81

u^2- 18u +81 = (u-9)^2

Answer:

The blank should contain 81

Step-by-step explanation:

E = u^2 - 18u + (-18/2)^2

E = (u^2 - 18u + 9^2)

E = (u - 9)^2

To be perfectly correct what you have there is a perfect square, but you need to subtract out (9/2)^2 to make it a valid statement.

E = (u - 9)^2 - 81

write 342 to 1 significant figure​

Answers

Answer:

300

Step-by-step explanation:

A significant figure is the most important (largest) number you can round it to.

As it wants 1 significant figure, you count 1 to the left and round the 4 down.

Hope this helps :)

Help please and thank you!!!!!

Answers

9514 1404 393

Answer:

a) 2 and 4; b) 1&2, 2&3, 3&4x = 16

Step-by-step explanation:

1a. Vertical angles share a vertex and are composed of opposite rays. Here, angles 2 and 4 are vertical angles.

1b. Consecutively numbered angles are adjacent, as are angles 1 and 5. The pairs of interest can be chosen from ...

  1&2, 2&3, 3&4, 4&5, 5&1

__

2. Angles 1 and 3 have the same measure, because they are vertical angles. Then we have ...

  78° = (5x -2)°

  80 = 5x . . . . . . . divide by °, add 2

  16 = x . . . . . . . divide by 5

Solve the triangle. round your answer to the nearest tenth

Answers

Answer:

∡A =41°

~~~~~~~~~~~~

BC=21

~~~~~~~~~~~~~~

sin(24)/AC=sin(41)/21

AC=13

~~~~~~~~~~~~~~

sin(115)/AB=sin(41)/21

AB=29

Step-by-step explanation:

Erica’s family is moving away from California. They decided to have a moving sale and sell each item for 70% off the price they originally paid for it. The sofa had an original price of $799, and the love seat had an original price of $549. What is the total cost of both items after the discount?

Answers

Find the sale price by multiplying the original price by 70% then add the two prices together to get the total.

799 x 0.70 = 559.30

549 x 0.70 = 384.30

Total: 559.30 + 384.30 = $943.60

Which facts are true for the graph of the function below? Check all that apply.
F(x)-(3/7)^x

Answers

Answer:

Step-by-step explanation:

Drag each label to the correct location on the table. Each label can be used more than once. Match the attributes to the quadratic functions. x-intercept (-2,0) 1 y-intercept: 0,-8) minimum value: -1 axis of symmetry: 1 x-intercept: 2,0) y-intercept: (0,8) f(x) = x2 - 2x - 8 g(x) = x2 + 6x + 8 h(x) = -x2 + 2x​

Answers

9514 1404 393

Answer:

f: x-intercept (-2, 0), y-intercept (0, -8), axis of symmetry x = 1g: x-intercept (-2, 0), y-intercept (0, 8), minimum value -1h: axis of symmetry x = 1

Step-by-step explanation:

The equations can be written in factored form and vertex form to see the x-intercepts, axis of symmetry, and extreme value.

The y-intercept is the constant in the equation in standard form.

The axis of symmetry is the vertical line through the vertex.

__

f(x)

f(x) = x² -2x -8 = (x -4)(x +2) = (x -1)² -9

  x-intercept (-2, 0), y-intercept (0, -8), axis of symmetry x = 1

__

g(x)

g(x) = x² +6x +8 = (x +2)(x +4) = (x +3)² -1

  x-intercept (-2, 0), y-intercept (0, 8), minimum value -1

__

h(x)

h(x) = -x² +2x = -(x)(x -2) = -(x -1)² +1

  axis of symmetry x = 1

_____

Additional comment

We have only listed the intercepts, axis, and extreme where the values match a label.

if f(x)=x+7 and 9(x)=1/x-13 what is the domain of (f•g)(x)

Answers

Answer:

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Step-by-step explanation:

Set up the expression.

[tex](x+7)*(\frac{1}{x}-13)[/tex]

Multiply using FOIL.

[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]

[tex]1-13x+\frac{7}{x}-91[/tex]

[tex]-13x+\frac{7}{x}-91[/tex]

Find the Domain.

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Decompose -6x/(x+2)(x+8) into partial fractions.

Answers

The partial fraction expansion takes the form

-6x/((x + 2) (x + 8)) = a/(x + 2) + b/(x + 8)

Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.

Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:

-6x = a (x + 8) + b (x + 2)

Expand the right side and collect terms by powers of x :

-6x = (a + b) x + (8a + 2b)

It follows that

a + b = -6   and   8a + 2b = 0

==>   a = -2   and   b = 8

So we end up with

-6x/((x + 2) (x + 8)) = -2/(x + 2) + 8/(x + 8)

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) 1/((1 + 9x)^4) ≈ 1 − 36x

Answers

Answer:

Part 1)

See Below.

Part 2)

[tex]\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)[/tex]

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

[tex]\displaystyle L \approx f'(a)(x-a) + f(a)[/tex]

We want to verify that the expression:

[tex]1-36x[/tex]

Is the linear approximation for the function:

[tex]\displaystyle f(x) = \frac{1}{(1+9x)^4}[/tex]

At x = 0.

So, find f'(x). We can use the chain rule:

[tex]\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)[/tex]

Simplify. Hence:

[tex]\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}[/tex]

Then the slope of the linear approximation at x = 0 will be:

[tex]\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36[/tex]

And the value of the function at x = 0 is:

[tex]\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1[/tex]

Thus, the linear approximation will be:

[tex]\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x[/tex]

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

[tex]\displaystyle \left| f(x) - L(x) \right | \leq 0.1[/tex]

By definition:

[tex]\displaystyle -0.1\leq f(x) - L(x) \leq 0.1[/tex]

Therefore:

[tex]\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1[/tex]

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

[tex]\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)[/tex]

Write the sum using summation notation, assuming the suggested pattern continues.

100 + 121 + 144 + 169 + ... + n2 + ...

Answers

100 = 10², so the sum you're considering is the sum of squared integers starting with 10.

[tex]\displaystyle 100+121+144+168+\cdots+n^2+\cdots = \boxed{\sum_{k=10}^\infty k^2}[/tex]

Help me please and thank you

Answers

Answer:

Option C is correct

Step-by-step explanation:

[tex]log( {10}^{3} )[/tex]

Use logarithm rules to move 3 out of the exponent.

[tex]3 \: log \: (10)[/tex]

Logarithm base 10 of 10 is 1.

[tex]3×1[/tex]

Multiply 3 by 1.

[tex]3[/tex]

Hope it is helpful....
C is the correct answer

In the parallelogram below, solve for x.
D (9x + 5)
E
G
F (13 - 43y

Answers

Answer:

[tex]x = 12[/tex]

Step-by-step explanation:

Given

[tex]\angle D = 9x + 5[/tex]

[tex]\angle F = 13x -43[/tex]

Required

Find x

To find x, we make use of:

[tex]\angle D =\angle F[/tex] --- opposite angles of a parallelogram

So, we have:

[tex]9x + 5 =13x -43[/tex]

Collect like terms

[tex]9x - 13x = -5-43[/tex]

[tex]-4x = -48[/tex]

Divide by -4

[tex]x = 12[/tex]

A study was conducted in order to estimate ?, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3.6 hours.
A similar study conducted a year earlier estimated that ?, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.
Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:
a. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
b. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
c. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
e. None of the above. The only way to reach a conclusion is by finding the p-value of the test.

Answers

Answer:

d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.

Step-by-step explanation:

Mean was of 8 hours, test if it has changed:

At the null hypothesis, we test if it has not changed, that is, the mean is still of 8, so:

[tex]H_0: \mu = 8[/tex]

At the alternative hypothesis, we test if it has changed, that is, the mean is different of 8, so:

[tex]H_1: \mu \neq 8[/tex]

Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:

8 is part of the confidence interval, which means that the study does not provide evidence that the mean has changed, and the correct answer is given by option d.

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