A bottled water distributor wants to determine whether the mean amount of water contained inâ 1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water is 0.008 gallon. You select a random sample of 50 bottles, and the mean amount of water perâ 1-gallon bottle is 0.995 gallon.

Required:
a. Is there evidence that the mean amount is different from 1.0 gallon?
b. What is the test statistic?
c. Compute theâ p-value and interpret its meaning.
d. Construct a 95% confidence interval estimate of the population mean amount of water perâ 1-gallon bottle.

Answer:

9000

Step-by-step explanation:

Hello

To solve this question, we should understand we just have to find the difference in time between the two scenarios

The difference in time between 10 - 15 minutes is

The difference in time between 11 - 12 minutes is

The probability here would be

The probability here is equal to 1/5 or 0.2 or 20%

Answer:

Final answer -

\(number \: of \: 50 \: paise \: coins \: in \: the \: bag = 4x \\ \dashrightarrow{4 \times 12 = 48 \: coins}\)

hope helpful :D

The number of 50 paise coins that we have in the bag with the respective other coins is; 48 coins

Since the respective coins are in ratio of 1:2:4. Then, we can deduce the following;

Let number of 2 rupees coins in the bag = 1x

Let number of 1 rupees coins in the bag = 2x

Let number of 50 paise coins in the bag = 4x

Total amount of money = 72 rupees. Thus;

(2 * 1x) + (1 * 2x) + (0.5 * 4x) = 72

2x + 2x + 2x = 72

6x = 72

x = 72/6

x = 12

Thus, number of 50 paise coins = 4x = 4 * 12 = 48 coins

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Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

Meaning of probability :

Probability is calculation of how likely some event will happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are going to happen.

The analysis of events governed by probability is called statistics.

According to the given information :

Red section = \(\frac{2}{5}\)

multiply numerator and denominator by \(2\) we get

Red section = \(\frac{4}{10}\)

 Blue section = \(\frac{1}{2}\)

 multiply numerator and denominator by \(5\) we get

 Blue section = \(\frac{5}{10}\)

 Green section = \(1\)- Red section - Blue section

 Green section =\(1-\frac{4}{10} -\frac{5}{10}\)

  Green section = \(\frac{1}{10}\)

Therefore Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

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Answer:

Step-by-step explanation:

Cube

Solve for edge

a= 2

V Volume 8

Step-by-step explanation:

Hey there!

The points are;(4,-3) and (8,-2).

Use slope formula.

\(slope(m) = \frac{y2 - y1}{x2 - x1} \)

Put all values.

\(m = \frac{ - 2 + 3}{8 - 4} \)

\(m = \frac{1}{4} \)

Therefore, the slope is 1/2.

Hope it helps...

The exact values of the six trigonometric functions for angle θ are:

sinθ = -0.6

cosθ = -0.8

tanθ = 0.75

cscθ = -1.67

secθ = -1.25

cotθ = 1.33

We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the terminal side of angle θ and the x and y axes:

h² = (-12)² + (-9)²

h² = 144 + 81

h² = 225

h = 15

Let us use the definitions of the six trigonometric functions to find their respective values of sine, cosine and tan functions

sinθ = opposite/hypotenuse = (-9)/15 = -0.6

cosθ = adjacent/hypotenuse = (-12)/15 = -0.8

tanθ = opposite/adjacent = (-9)/(-12) = 0.75

cscθ = 1/sinθ = -1.67

secθ = 1/cosθ = -1.25

cotθ = 1/tanθ = 1.33

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Answer:

dont cheat

Step-by-step explanation:

Answer:

\(a.\ \dfrac{3}{5}\)

Step-by-step explanation:

We can see the fractions \(\frac{5}{4}\) and \(\frac{3}{4}\) of cups.

It can be seen that denominator has 4 i.e. the fraction \(\frac{1}{4}\).

Let us suppose, a unit is equal to \(\frac{1}4\) of a cup.

Susan was supposed to use \(\frac{5}{4}\) of a cup.

i.e. 5 units of butter was to be used.

But, actual recipe has only 3 units of butter.

\(\text{Fraction of butter used} = \dfrac{\text{Units of butter used}}{\text{Unit of butter Susan was supposed to use}}\)

a. \(\text{Fraction of butter used} = \dfrac{3}{5}\)

Alternatively, we could have directly divided the given fractions:

\(\dfrac{\dfrac{3}{4}}{\dfrac{5}{4}} = \dfrac{3}{5}\)

The fraction of the butter that she should have used did Susan actually use is :

Fractions =5/4 and 3/4 of cups.

Denominator = 4 i.e. the fraction 1/4

Let us suppose,

A unit is equal to 1/4 of a cup.

Susan was supposed to use 5/4 of a cup.

5 units of butter was to be used.

But, actual recipe has only 3 units of butter.

Fraction of butter used=unit of butter used/unit of butter                        

                                                                 that was supposed to      

                                                                         be use

                                        =3/4/5/4

                                        =3/5

The fraction of the butter that she should have been used is 3/5.

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Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.

The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

a.) 1/2

b.) 1/8

c.) 5/8

d.) 1/2

Step-by-step explanation:

for A it is asking for probability of 1 and is 1/2 of the circle

for B it is asking for  probability of 3 and it is 1/2 of and 1/4 of the circle so 1/8

for C it is asking for probability of the odd numbers and there is tow odd numbers 1 and 3 the probability of 1 is 1/2 and the probability of 3 is 1/8 adding them up will give you 5/8

for d it asks for the probability of at least 2 so therefor 2, 3, and 4 and they are 1/8 + 1/8 + for 1/4 = 1/2

Answer:

1.  dividing

2.  faster than

Step-by-step explanation:

Edge 2020

Answer:

The speed of a turtle can be found by distance by time.

   adding

   subtracting

   multiplying

✔ dividing

The speed of the winning turtle was the speed of the other two turtles.

   slower than

   the same speed as

✔ faster than

Answer:

More than likely no full answer key however there might be answers for each individual question.

The complete statement is "The set is -6 < x ≤ -7"

The set notation for the intersection of two sets is "n".

So in this case, we are looking for the set of elements that belong to both (-9,-6) and [-7,6].

To find this set, we can compare the elements of each set and only keep the ones that are present in both sets.

We can see that the only common elements in both sets are [-6,-7]

Therefore, the set (-9,-6) n [-7,6] = [-6, -7]

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The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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Answer: Yes, Yukio is correct.

Step-by-step explanation:

Assuming that Triangle DEF and ABC have the same angles (they do because they are right-angled), we can take the length from the larger triangle (DEF) and divide it by the length of the smaller triangle (ABC).

Length of DEF = 6cm

Length of ABC = 2cm

= 6/2

= 3

Proves that scale of DEF to ABC is 3:1

For a game, Bob has a total of 60 adventure cards. The distribution of cards, c, to players, p, is shown in the table. c = 60 ÷ p

Probability defines the possibility of occurrence of an event. Probability is the unit of measurement for an event's likelihood. It represents the proportion of positive results to all results. For instance: Receiving the numbers 3 and 5 while rolling the dice, as well as getting both an even and an odd number.

The equation would read: c = 60 / 2, which implies c = 30 if p=2. The equation would read 12 = 60 / p, p = 5, 20 = 60 / 3, etc. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.

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Answer:

1 mm Hg per year

Explanation:

Here equation : y = x + 95

Comparing with slope intercept formula: y = mx + b

                                    where m is slope and b is y-intercept

Slope determines the increase per year.

Equation given

Comapre to slope intercept form y=mx+b

Rate of change=Slope=1mm HG /year

The expression that represents "3 more than twice a number" is 2n + 3.

The expression "3 more than twice a number" can be translated into an algebraic expression as 2n + 3, where "n" represents the number in question. To understand this expression, we first need to know the order of operations. In this case, "twice a number" means "2n", and "3 more than" means adding 3 to that result. Therefore, the entire expression becomes "2n + 3". It's important to remember that expressions like this are not equations, but rather just a way to represent a mathematical relationship. This type of expression is commonly used in algebraic problem-solving and can be manipulated to solve for different variables.

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Complete question:

Which expression represents "3 more than twice a number"? Choices:

2n−3

3−2n

2n+3

2+n+3

The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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Therefore , the solution of the given problem of  probability comes out to be the right response is thus: "Drawing a red card or a Queen from a regular deck of cards is an overlapping occurrence."

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

Because the Queen of Hearts and Jack of Spades are not face cards or nines,

the occurrences "Drawing a Queen of Hearts or Jack of Spades from a standard deck of cards" and "Drawing a face card or a 9 from the a standard deck of cards" do not overlap.

A Queen of Hearts is both a red card and a queen, and a diamond is a type of red card and a club is a type of card, so the occurrences "Drawing a Diamond or a Club from a Standard Deck of Cards" and "Drawing a Red Card or a Queen from a Standard Deck of Cards" overlap.

The right response is thus: "Drawing a red card or a Queen from a regular deck of cards is an overlapping occurrence."

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The Sample space, a clear set of possible outcomes for choosing one card from the set.

The sample space for choosing one card from a set of 10 labeled cards, where each card is labeled with an expression, would consist of all the possible outcomes of this selection process.

Since there are 10 cards in the set, the sample space would consist of the individual expressions labeled on each card. Let's assume the expressions on the cards are labeled as follows:

Card 1: Expression 1

Card 2: Expression 2

Card 3: Expression 3

...

Card 10: Expression 10

{Expression 1, Expression 2, Expression 3, ..., Expression 10}

This sample space represents all the possible outcomes when selecting one card from the set. Each outcome corresponds to one specific expression labeled on a card.

the sample space only includes the individual expressions and not any particular order or arrangement of the cards. The order of the expressions does not matter in this case, as the focus is solely on the expressions themselves.

the sample space, we establish a clear set of possible outcomes for choosing one card from the set.

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