Quart cartons of milk should contain at least 32 ounces. A sample of 22 cartons was taken and amount of milk in ounces was recorded. We would like to determine if there is sufficient evidence exist to conclude the mean amount of milk in cartons is less than 32 ounces? a) Two sample t testb) One sample t testc) Two sample p testd) Matched pairs

The problem requires finding the ratio of $5 bills to $10 bills given certain conditions. It involves solving two equations and is typically encountered in a high school Mathematics course.

The SUBJECT

of Maryam's question involves the field of

Mathematics

, more specifically it belongs to the area of

ratios and proportions

. The problem presents a scenario where she has a combination of $5 and $10 bills in her wallet. Then, given are two conditions - (1) 'The

ratio

of the number of bills to the total dollar value is 1/9.' and (2) 'The total dollar value of the bills is $360.' We are asked to determine the ratio of $5 bills to $10 bills.

Represent $5 bills as 'x' and $10 bills as 'y'. Firstly, considering condition (1), we know that the total number of bills (x + y) divided by the total value (5x + 10y) is 1/9. Secondly, from condition (2), we have that the total dollar value, i.e., 5x + 10y equals $360. By solving these two equations, the values of 'x' and 'y' can be found, and thus, the required ratio will be x:y.

However, the problem requires solving two equations which is a skill typically taught and applied in high school Mathematics courses.

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Answer: eyyyyyy my name is Jan what a coincidence

Step-by-step explanation:

Answer:

A company declares a​ 5% stock dividend.

The debit to retained earnings is an amount equal to - the market value of the shares, that are to be issued.

We can say that a retained earnings balance is increased when we are using a credit and this is decreased when we make a debit.

A retained earnings is the total amount of money left, after all the expenses and dividends are paid by the company.

A 5% stock dividend represents a distribution of extra shares, 5% of existing ones, to shareholders. The debit to retained earnings is equal to 5% of the total market value of the previously existing shares.

When a company declares a 5% stock dividend, this means that the company is distributing additional shares of its stock to the existing shareholders. The quantity of these additional shares is equal to 5% of the shares that each shareholder currently owns. The debit to retained earnings is an amount equal to the total market value of these additional shares, which is determined by multiplying the declared dividend rate (5%) by the total market value of circulating shares prior to the issuance of dividend.

For instance, if a company has 1000 shares with a market value of $10 each, it would issue additional 50 shares (5% of 1000 shares). Therefore, the debit to retained earnings would be $500 (50 shares * $10/share).

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Answer:

Isosceles

Step-by-step explanation:

In order to figure what type of triangle this is out, we need to start by plotting the given points. That will help us visualize the triangle better and see if our conclusions make sense. (See attached picture).

Once we got the triangle, the strategy to follow is to use the distance between two points formula to see what the measurement of each side of the triangle is. This will help us determine if 2, 3 or none of the sides of the tirangle are the same.

The distance formula is the following:

[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

so now we can find the desired distances, let's start with the distance between P and Q:

[tex]|PQ|=\sqrt{(-4-0)^{2}+(9-8)^{2}}[/tex]

which yields:

[tex]|PQ|=\sqrt{17}[/tex]

next, let's find the distance between P and R:

[tex]|PR|=\sqrt{(-4-(-3))^{2}+(9-5)^{2}}[/tex]

which yields:

[tex]|PR|=\sqrt{17}[/tex]

and finally the distance between Q and R:

[tex]|QR|=\sqrt{(0-(-3))^{2}+(8-5)^{2}}[/tex]

which yields:

[tex]|QR|=3\sqrt{2}[/tex]

As you  may see from the result, only two of the three sides are the same, |PQ| and |PR|, so this will be an Isosceles triangle.

Answer:

 h  =   1,743

Step-by-step explanation:

Volume of a box is

V(h) =  ( A  -  2h) *  ( B  -  2h)* h              A  =  7     B  =  12

We have

V(h) = ( 7  -  2h)  *  ( 12  -  2h ) * h

V(h)  = ( 84  -  14*h  -  24*h  + 4*h² )  * h

V(h)  =  ( 84 -  38*h  + 4 *h² ) * h     ⇒  V(h)  =  84h - 38h² + 4h³

Taking derivatives both sides of the equation

V´(h)    =  84 - 76h + 12x²

V´(h)    =  0              84 - 76h + 12x² = 0     42 - 38h + 6x²

3x² - 19h   + 24  = 0

Solving for h          h1  = [  ( 19 + √(19)² - 288  ]/ 6    h1  = [ (19 + √73)/6]

h₁  =  4,59   we dismiss this value since 9,18  (4,59*2)  > A

h₂  = [ 19 - √73)/6]          h₂  =   1,743

h  =  1.743 is h value to maximizes V

Answer: Our required probability is 45.05%.

Step-by-step explanation:

Since we have given that

                         Males                  Females               total

Left handed       6.3                         4.95                     11.25%

Right handed     43.7                       45.05                  88.75%

Total                   50%                        50%                   100%

Since 12.6% of 50% are males are left handed = 6.3%

So, 9.9% of 50% are females are left handed = 4.95%

So, Females who are right handed would be

[tex]50\%-4.95\%\\\\=45.05\%[/tex]

Hence, our required probability is 45.05%.

To calculate the probability that the selected person is a female, given the person is right-handed, we need to use conditional probability. The exact probability cannot be calculated without the percentage of females in the population. However, it is known that the probability is less than or equal to 11.25%.

To find the probability that the selected person is a female, given that the person is right-handed, we need to use conditional probability. Let's denote the events A and B as follows: A: Selected person is a female, B: Selected person is right-handed.

The probability of event A (P(A)) can be calculated as the product of the probability of event B given event A (P(B|A)) and the probability of event A without any condition (P(A)) divided by the probability of event B (P(B)).

In this case, P(A) refers to the probability of selecting a female, P(B|A) refers to the probability of being right-handed given the person is female, and P(B) refers to the probability of being right-handed.

First, let's calculate the probability of being right-handed (P(B)). Since 90% of people are right-handed, P(B) = 0.9.

Next, let's calculate the probability of being right-handed given the person is female (P(B|A)). Since 9.9% of females are left-handed, the probability of being right-handed is 1 - 0.099 = 0.901.

Finally, let's calculate the probability of selecting a female (P(A)). Since the percentage of females in the population is not provided, we cannot calculate the exact probability. We can only say that it is less than or equal to the total percentage of left-handed people, which is 11.25%.

Therefore, the probability that the selected person is a female, given that the person is right-handed, can be defined as: P(A|B) = (P(B|A) * P(A)) / P(B) = (0.901 * P(A)) / 0.9 = 0.901 * P(A).

Since we don't have the exact value of P(A), we cannot calculate the exact probability. However, we know that it is less than or equal to 11.25%.

Answer:

  30 miles

Step-by-step explanation:

Let d represent the distance to the island. The relation between time, speed, and distance is ...

  time = distance/speed

so the total time for the round trip is ...

  d/15 +d/10 = 5

Multiplying by 30, we get

  2d +3d = 150

  d = 150/5 = 30

The island was 30 miles from the harbor.

To solve this problem we use the equation Speed = Distance/Time for both legs of the trip to form an equation and solve for the distance. Through these calculations, we find the distance from the harbor to the island to be 30 miles.

This problem can be solved by understanding the relationship of speed, distance, and time, often expressed as Speed = Distance/Time. First, let's define the time it took to go to the island and back. From the problem, we know that the total time was 5 hours but the speeds were different, so the time spent on each leg of the trip was different. We'll define the time it took to get to the island as two hours. Therefore, the return trip took 5-t hours. Solving for Distance To calculate the distance, we use the speed of each leg of the trip multiplied by the time of that leg. So, Distance = 15t = 10(5-t). We can solve this equation for t, finding that t equals to 2 hours. Inserting t back into Distance = 15t gives us a distance of 30mph to the island. This means it is 30 miles from the harbor to the island.

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Answer:

124.8 %

Step-by-step explanation:

Given,

Initial percentage of working students = 14.1%,

Final percentage of working students = 31.7%,

Thus, the percentage increase = [tex]\frac{\text{Final percentage-initial percentage}}{\text{Initial percentage}}\times 100[/tex]

[tex]=\frac{31.7 - 14.1}{14.1}\times 100[/tex]

[tex]=\frac{17.6}{14.1}\times 100[/tex]

[tex]=\frac{1760}{14.1}[/tex]

≈ 124.8 %

Final answer:

To find the original percentage of working students before an increase of 14.1%, subtract 14.1% from the new percentage of 31.7%, which gives us 17.6% as the original percentage.

Explanation:

The student is asking to find the original percentage of working students before a 14.1% increase resulted in a new percentage of 31.7%. To determine the original percentage, we need to subtract the increase from the final percentage. Here's the calculation:

Final percentage = Original percentage + Increase

31.7% = Original percentage + 14.1%

To find the original percentage, we subtract 14.1% from 31.7%:

Original percentage = 31.7% - 14.1% = 17.6%

Rounded to the nearest tenth of a percent, the original percentage of working students was 17.6%.

Answer: The correct option is C

Step-by-step explanation:

You begin a job with an annual salary of $32,900

Each year you are assured of a 5.5%. If you get the same amount each year, that is a 100% payment. It is neither reducing nor increasing. But with an increase of 5.5% each year, it means you are getting (100+5.5)% each year. This equals 105.5%. So for each year, you get 105.5% of the previous year.

This is a geometric progression. To determine the total amount that you can earn in 15 years, we will find the sum of 15 terms, S15 of the series. The formula for sum of the nth term of a geometric progression is expressed as

Sn = [a(r^n - 1)] / r - 1

Where

Sn = sum of the nth terms of the series

a = the first term(salary of the first year

r = common ratio

n = number of years.

From the question,

a = 32900

n = 15

r = 105.5/100 = 1.055

S15 = [32900(1.055^15 - 1)] / 1.055 - 1

S15 = [32900(2.23247649224 - 1)] / 0.055

S15 = [32900 × 1.23247649224] / 0.055

S15 = $737245

Answer:

ok with whuth do you need help with

Answer:

The right answer for question 1 is b)  -14

Step-by-step explanation:

Since it's a decline, the amount will be negative.

your second question is not clear in the image

3.5 per day for 4 days so multiply 3.5 by 4, which equals: $14

so the overall change is -$14.00

Approximately 81.5% of the daily light bulb replacement requests in the state university's physical plant can be expected to number between 63 and 75.

The question is asking for the percentage of daily light bulb replacement requests numbering between 63 and 75 at a state university's physical plant. This can be answered using the 68-95-99.7 rule, also known as the Empirical Rule, which applies to a bell-shaped distribution.

Firstly, identify that a request count of 75 is two standard deviations above the mean (63 + 6*2 = 75), because the standard deviation here is 6. According to the Empirical Rule, approximately 95% of the data lies within two standard deviations of the mean.

However, we are only interested until the upper limit of 75 and not the lower limit (63 - 6*2 = 51). Therefore, we consider half of this 95%, which gives us 47.5%. However, don't forget to include the 34% that lies within the first standard deviation (from 63 to 69). Therefore, approximately 81.5% of the light bulb replacement requests should number between 63 and 75.

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the approximate percentage of light bulb replacement requests numbering between 63 and 75 is 47.5%.

Using the Empirical Rule:

Answer:

4.18 hours

Step-by-step explanation:

Since the plane needs 2 hours to cover the las 990 miles at the end of the flight, and in the last half hour it flies with a speed of 190mph, meaning it covers a distance of 190 / 2 = 95 miles in this last half hours.

That means for the other 1.5 hours, its cruising speed is

[tex] v_c = \frac{990 - 95}{1.5} = 596.7 mph[/tex]

Beside the first and last half hour of the trip (which covers 190 miles), the cruising distance must be

d = 2090 - 190 = 1900 miles

The cruising time is therefore

[tex]t_c = \frac{d}{v_c} = \frac{1900}{596.7} = 3.18 hours[/tex]

Hence the total time for the entire flight is

3.18 + 1 = 4.18 hours

In 4.18 hours is the entire flight.

Given

A plane flies at 190 mph for the first and last half hours of a flight.

It flies at a higher constant speed for the rest of the flight.

The route is 2090 miles.

The plane is 990 miles from the destination 2 hours before the end of the flight.

The plane needs 2 hours to cover the last 990 miles at the end of the flight, and in the last half hour it flies with a speed of 190mph,

Then,

The distance covered by plane in last half hour is;

[tex]\rm Distance=\dfrac{190}{2}\\\\Distance=95 \ miles[/tex]

The velocity is;

[tex]\rm Velocity = \dfrac{Distance }{Time}\\\\Velocity=\dfrac{900-95}{1.5}\\\\Velocity=\dfrac{805}{1.5}\\\\Velocity=596.7[/tex]

The first and last half hour of the trip (which covers 190 miles), the cruising distance must be;

Distance = 2090 - 190 = 1900 miles

Therefore,

The cruising time is;

[tex]\rm Time =\dfrac{Distance}{Velocity}\\\\Time=\dfrac{1900}{596.7}\\\\Time=3.18 \ hours[/tex]

The total time for the entire flight is

= 3.18 + 1 = 4.18 hours

Hence, in 4.18 hours is the entire flight.

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Answer:

x intercept = 15 # of cars to detail if no SUVs

y intercept =  10 # of SUVs to detail if no cars

Hope this helps!

The x-intercept and the y-intercept for the equation 30x + 45y = 450 are 15 and 10 respectively, The x-intercept denotes the number of cars if there is no SUV serviced and the y-intercept represents the number of SUVs if there is no car.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

Awesome autos car detail charges $30 for a full-service detail on SUVs,

The equation 30x + 45y = 450 represents the amount that must be earned each hour to cover expenses,

From this equation, we can determine that the autos car detail charges $45 for a full-service detail on car,

Find the x-intercept as shown below,

30x + 45 × 0 = 450   (For x-intercept y = 0)

30x = 450

x = 450 / 30

x = 15

Find the y-intercept as shown below

30 × 0 + 45y = 450   (For y-intercept x = 0)

45y = 450

y = 10

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Answer:

D. There is a significant difference among the reading speeds somewhere.

Hope this helps!

Answer:

Step-by-step explanation:

Nelson grows tomatoes and sells them at a nearby farmers roadside stand.

Let x = number of tomatoes sold

Let m = amount of money made for selling x tomatoes.

He sells them for $2.50 each. This means that he sells x tomatoes for 2.5×x = $2.5x

The farmer charges him $15 a day to use the stand. This means that he pays a constant amount of $15 each day.

Amount of money that Nelson will make will be total amount made in selling x tomatoes minus the constant amount being paid for rent. It becomes

m = 2.5x - 15 This is the general form. In the factored form, it will be

m = 2.5(x+6)

Final answer:

To find the original selling price of the ski set, work backward from the sale price by adding the markdowns back to it. Start by assigning a variable to represent the original selling price and use the given markdown amounts to calculate the original price. The original selling price of the ski set is $387.50.

Explanation:

A sporting goods store manager was selling a ski set for a certain price. The manager offered markdowns, making the one-day sale price of the ski set $325. To find the original selling price of the ski set, we will work backwards from the sale price by adding the markdowns back to it.

Step-by-step process:

Let x be the original selling price.

Given markdowns, if the sale price after markdowns is $325, then x - $30 - $20 - $12.50 = $325.

Solving for x, we get x = $387.50.

Answer:

a) y </= 8 is not sufficient

b) y >/= 4 is sufficient (y is not less than 3.5)

Step-by-step explanation:

Number of Red marbles = 8

Number of white marbles = y

Total number of marbles in the jar = 8+ y

Let Pr(R) be the probability of picking red marbles

Let Pr(W) be the probability picking white marbles

Pr(R) = 8/ (8+y)

Pr(W) = 7/(7+y)

Pr(RR) = Pr(R1) * Pr( R2)

= 8/(8+y) * 7/(7+y)

Pr(RW) = Pr(R1) * Pr(W2) + Pr(W1) * Pr(R2)

= 2[Pr(R1) * Pr(W2)

= 2[8/(8+y) * y/(7+y)]

The probability of having 2 red is greater than one marble of each color.

Pr(RR) > Pr( RW)

8/(8+y) * 7/(7+y) > 2[8/(8+y) * y/(7+y)]

7/(7+y) > 2(y/(7+y)

7/y > 2

7/2 > y

3.5 > y

y < 3.5

Therefore;

a) y </= 8 is not sufficient

b) y >/= 4 is sufficient (y is not less than 3.5)

Answer: c. H0: p = 0.16; Ha: p ≠ 0.16

Step-by-step explanation:

We know that ,

Null hypothesis is a statement about the population parameter([tex]\mu , p, \sigma....[/tex]) and contains equality (=),≤ or  ≥ signs.

Alternative hypothesis is also statement about the population parameter([tex]\mu , p, \sigma....[/tex]) but against null hypothesis and contains signs < , > or ≠.

In the given situation , the parameter is p (population proportion).

A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16.

i.e. the point estimate of the population proportion(p) of the young adults who reported smoking at least twice a week or more is 0.16.

Now, the hypotheses to be tested for this study would be :

[tex]H_0: p=0.16\\\\ H_a: p\neq0.16[/tex]

Hence, the correct answer is  c. H0: p = 0.16; Ha: p ≠ 0.16

Answer: The speed of the current is 3 miles per hour.

The speed of the boat in still water is 10 miles per hour

Step-by-step explanation:

Let the speed of the boat be x miles per hour

Let the speed of the current be y miles per hour

Speed = distance / time

If the boat moves 39 miles downstream in 3 hours, then, the speed is

39/3= 13 miles per hour

Let us assume that it moved it moved in the same direction with the current hence, it moved in still water

The total speed would be x + y. Therefore

x + y = 13 - - - - - - -1

If the boat moves 21 miles upstream in 3 hours, the the speed is

21/ 3 = 7 miles per hour

It is assumed that it moved in the opposite direction to the current.

The total speed would be x - y. Therefore

x - y = 7 - - - - - - -2

Adding equation 1 and equation 2, it becomes

2x = 20

x = 20/2 = 10 miles per hour

y = 13 - x

y = 13 - 10 = 3 miles per hour

Answer:

1.5 hours

Step-by-step explanation:

Since Joe painted 2/3 section (2 out of 3 sections) of each section, we can break up the sections into parts of "3".

So 8 sections would have total subsections of 8 * 3 = 24 subsections

He painted 2 subsections of each of the 8 sections, so number of subsections painted would be:

8 * 2 = 16 subsections

There are more 24 - 16 = 8 more subsections to paint

If 1 hour means 16 subsections,

1/16 hour = 1 subjection

Thus,

8 remaining subsections would take:

8 * 1/16 = 8/16 = 1/2 hour

So

Initially 1 hour, then 1/2 hour, so total of 1 + 1/2 = 1.5 hours

So, to paint all sections, he took 1.5 hours

Answer:

Part 1) The perimeter of triangle ABC is 24 units

Part 2) [tex]y=97\°[/tex]

Step-by-step explanation:

Part 1)

we know that

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

The perimeter of triangle ABC is equal to

[tex]P=AB+BC+AC[/tex]

Applying the Midpoint Theorem

Find the measure of AB

[tex]AB=\frac{XZ}{2}[/tex]

substitute given value

[tex]AB=\frac{18}{2}=9\ units[/tex]

Find the measure of BC

[tex]BC=\frac{XY}{2}[/tex]

[tex]XY=2AY[/tex]

substitute given value

[tex]XY=2(7)=14\ units[/tex]

[tex]BC=\frac{14}{2}=7\ units[/tex]

Find the measure of AC

[tex]AC=\frac{YZ}{2}[/tex]

[tex]YZ=2BZ[/tex]

substitute given value

[tex]YZ=2(8)=16\ units[/tex]

[tex]AC=\frac{16}{2}=8\ units[/tex]

Find the perimeter  of triangle ABC

[tex]P=9+7+8=24\ units[/tex]

Part 2)

step 1

Find the measure of angle z

Remember that the sum of the interior angles in a triangle must be equal to 180 degrees

[tex]55\°+42\°+z=180\°\\97\°+z=180\°\\z=180\°-97\°\\z=83\°[/tex]

step 2

Find the measure of angle y

we know that

[tex]y+z=180\°[/tex] ----> by supplementary angles (form a linear pair)

substitute the value of z

[tex]y+83\°=180\°[/tex]

[tex]y=180\°-83\°=97\°[/tex]

Answer:

53/72

Step-by-step explanation:

5/8 = x - 1/9

+1/9       +1/9

5/8 + 1/9 = x

9(5/8)  + 8(1/9)

45/72 + 8/72

x= 53/72

Answer:

The answer is3

Step-by-step explanation:

because there is three colors

Answer:

22.

Step-by-step explanation:

You might take 10 red balls  out in the first  10 picks. Now you are left with 11 blue and 23 green and you might take out the 11 blue in 11 picks. The next pick must be green.

So the answer is 10 + 11 + 1 = 22 balls.

Answer:

75 square feet

Step-by-step explanation:

The aquarium is designed to hold 62.5cubic feet

Since the aquarium has a square base, assume the aquaruim is a square prism

Let X be the lenght

Let y be the height

x^2.y = 62.5

y = 62.5x^2

The area of each side of the aquarium is xy. Since there are four sides, the total area of the side= 4xy

The area of the bottom of the aquarium = x^2

Total surface area = 4xy + x^2

Put y = 62.5/x^2 into the total surface area equation

A = 4x(62.5/x^2) + x^2

A= 250/x + x^2

Differentiate A with respect to x

dA/dx = -250(x^-2) + 2x

dA/dx = 0

0 = 2x - 250x^-2

2x = 250x^-2

2x =250/ x^2

2x^3 = 250

x^3 = 250/2

x^3 = 125

x = cbrt (125)

x = 5

Put x= 5 into A = x^2 + 250x^-1

A= 5^2 + 250(5^-1)

A= 25 + 250/5

A = 25 + 50

A = 75 square feet

The surface area of a solid object can be determine by measuring the total area that surface of the object cover.

The minimum possible exterior surface area of the aquarium is [tex]75 \:\rm feet^2[/tex].

Given:

The aquarium designed hold [tex]62.5 \:\rm feet^3[/tex].

Let assume the aquarium is square prism.

Let [tex]x[/tex] is height and [tex]y[/tex] is length.

The aquarium designed hold [tex]62.5 \:\rm feet^3[/tex]. Write the system equation.

[tex]x^2y=62.5\\y=\frac{62.5}{x^2}[/tex]

The area of four side of aquarium is as follows,

[tex]\rm A_1=4xy[/tex]

The bottom area of aquarium is as follows,

[tex]A_2=x^2[/tex]

The total area is as follows,

[tex]A=A_1+A_2\\A=4xy+x^2[/tex]

Put [tex]y=\frac{62.5}{x^2}[/tex] in above expression.

[tex]A=4x(\frac{65.2}{x^2} )+x^2\\A=\frac{250}{x}+x^2[/tex]

Differentiate [tex]A[/tex] with respect to [tex]x[/tex].

[tex]\frac{dA}{dx}=-250(x^{-2})+2x[/tex]

For the minimum possible exterior surface area [tex]\frac{dA}{dx} =0[/tex].

[tex]0=2x-250x^{-2}\\2x=250x^{-2}\\2x^3=250\\x^3=\frac{250}{2}\\x^3=125\\x=5[/tex]

Substitute [tex]x=5[/tex] to find the area.

[tex]A=5^2+250\times 5^{-1}\\A=25+\frac{250}{5}\\A=75\:\rm feet^2[/tex]

Thus, the minimum possible exterior surface area of the aquarium is [tex]75 \:\rm feet^2[/tex].

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2012

Step-by-step explanation:

cuz 16 years mande the increase so much the years are making money go worthless faster and faster

Using the given exponential function model for Consumer Price Index (CPI), one can conclude that the costs were approximately 90% higher than 1990 in country A in the year 2018.

This question is related to

exponential functions

in Mathematics. The formula given, a(t) = 100e^0.023t, is an exponential function representing the Consumer Price Index (CPI) of country A. In this context, a 90% increase from 1990 corresponds to a cost of $190, as 90% of $100 is $90, and this added onto the initial $100 gives us $190. So, you are looking for the year (t) when a(t) = 190.

This requires simplifying the equation 190 = 100e^0.023t. First, divide by 100 to get 1.9 = e^0.023t. Then take the natural log of each side to get ln(1.9) = 0.023t. Now solve for t by dividing ln(1.9) by 0.023 which gives you approximately 28.71 years. As the question measures years after 1990, add this to 1990 to determine the year costs were 90% higher. This gives us the year 2018 (since we cannot have a fraction of a year) that the goods will cost 90% more than in 1990.

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Answer: [tex]H_0:\mu=0.44\ ,H_a:\mu<0.44[/tex]

Step-by-step explanation:

Since we have given that

A very large study showed that aspirin reduced the rate of heart attacks by 44%.

we claim that they have a drug that will be more effective than aspirin.

so, our hypothesis would be

[tex]H_0:\mu=0.44\\\\H_a:\mu<0.44[/tex]

So, it will be one tail test.

Hence, [tex]H_0:\mu=0.44\\\\H_a:\mu<0.44[/tex]

The null hypothesis (H0) for this clinical trial would state that the new drug is no more effective than aspirin at reducing heart attacks (reduction rate is 44% or less). The alternative hypothesis (Ha) would claim that the new drug is more effective than aspirin (reduction rate greater than 44%).

In this context, the null hypothesis (H0) and the alternative hypothesis (Ha) are representations of scenarios that the researchers are trying to investigate through their study. The null hypothesis is typically a statement of no effect or no difference while the alternative hypothesis represents the scenario where there is an effect or difference.

For this case, we could state:

Alternative Hypthesis (Ha): The new drug is more effective at reducing heart attacks than aspirin (i.e., the reduction rate is greater than 44%).

These hypotheses set the stage for the pharmaceutical company to analyze the study's data and determine which hypothesis is most supported by the evidence presented.

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Answer: Our required probability is 0.91.

Step-by-step explanation:

Since we have given that

n = 85

mean = 100 points

standard deviation = 11

We need to find the probability that the sample mean will not differ from the population mean by more than 2 points.

so, it becomes,

[tex]P(100-2<\bar{x}<100+2)\\\\=P(98<\bar{x}<102)\\\\=P(\dfrac{98-100}{\dfrac{11}{\sqrt{85}}}<Z<\dfrac{102-100}{\dfrac{11}{\sqrt{85}}})\\\\=P(-1.68<Z<1.68)\\\\=P(z<1.68)-P(z<-1.68)\\\\=0.9535-0.0465\\\\=0.9070\\\\\approx 0.91[/tex]

Hence, our required probability is 0.91.

Answer:

d) Good, the interval is related to the variable of interest and the population mean analyzed.

Step-by-step explanation:

1) Data given

[tex]\bar x = 23[/tex] represent the mean

[tex]ME=2[/tex] represent the margin of error

[tex]confidence=95\%=0.05[/tex]

The confidence interval for the mean is given by the following formula:

[tex]\bar x \pm ME = 23\pm 3=(21,25)[/tex]

Where the margin of error is given by [tex]ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

Based on the interval obtained we can say that "we have 95% of confidence that the mean winter snowfall would be between 21 and 25"

2) Analyze the possible options

a) Wrong, we are not analyzing the individual winters, the interval is related to the population mean.

b) Wrong, the confidence interval can't be interpreted as a chance that are not related to the population mean of interest.

c) Wrong, the confidence interval is not related to the individual days of winter.

d) Good, the interval is related to the variable of interest and the population mean analyzed.

e) Wrong, the confidence interval is not related to specific events, is related to the population mean.

Viewers should interpret the news by considering the confidence interval and understanding the statements.

The viewers should interpret this news as follows:

a. The statement that during 95 of the past 100 winters, the region got between 21" and 25" of snow is valid.

This is because the average winter snowfall of 23" falls within this range with a margin of error of 2".

b. The statement that there's a 95% chance the region will get between 21" and 25" of snow this winter is not correct.

The confidence interval (21" to 25") represents the range of values in which the true average snowfall is likely to fall, not the probability of the upcoming winter's snowfall falling within that range.

c. The statement that there will be between 21" and 25" of snow on the ground for 95% of the winter days is not supported by the given information.

The confidence interval pertains to the average winter snowfall, not individual daily observations.

d. The statement that residents can be 95% sure that the area's average snowfall is between 21" and 25" is valid.

The confidence interval provides a range of values within which the true average is likely to fall.

e. The statement that residents can be 95% confident that the average snowfall during the past century was between 21" and 25" per winter is valid.

The confidence interval represents the range of likely values for the true average.

Learn more about confidence intervals here:

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Answer:

inverse of f(x) is g(x)

Step-by-step explanation:

f(x) = (x+9)/4

g(x) = 4x-9

f^-1(x) = g(x)

Let y = (x+9)/4

4y = x + 9 (make x the subject)

x = 4y - 9

f^-1(x) = 4x - 9

= g(x) (shown)

Answer:

Below.

Step-by-step explanation:

If f(x) is the inverse then f(g(x)) = x.

f(g(x)) =  ((4x - 9) + 9) / 4

= 4x/4

= x.

So it is true.

It can also be shown that g(f(x)) = x.