Question 7: The line passing through (1, p) and (5, 1) has a gradient of 0.75
Find p.

The woman at the dinner party consumed 24 fluid ounces of wine containing approximately 4.8 standard drinks assuming the wine had an alcohol content of 12%. She exceeded the recommended limit for moderate drinking on that day.

Assuming each glass of wine contained 8 fluid ounces, the woman consumed a total of 24 fluid ounces of wine throughout the evening.

To determine the number of standard drinks ingested, we need to know the alcohol content of the wine. In the United States, a standard drink is defined as containing 0.6 fluid ounces or 14 grams of pure alcohol.

Assuming the wine had an alcohol content of 12% (which is a typical percentage for table wine), we can calculate the number of standard drinks ingested by using the following formula:

Number of standard drinks = (Volume of alcohol consumed in ounces x % alcohol by volume) / (0.6 ounces of alcohol per standard drink)

Number of standard drinks = (24 fl oz x 0.12) / 0.6 fl oz

Number of standard drinks = 4.8

Therefore, the woman consumed approximately 4.8 standard drinks.

To determine if she drank alcohol in moderation, we need to consider the recommended limits for moderate drinking. According to the National Institute on Alcohol Abuse and Alcoholism, moderate drinking is defined as up to one drink per day for women.

Since the woman consumed 4.8 standard drinks in one evening, she exceeded the recommended limit for moderate drinking for that day.

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If a man loses 10 percent by selling his watch for 450 then the cost price of the watch would be 500.

Let's assume the cost price of a watch is 100.

So, after selling at a loss of 10 percent, the selling price of the watch is 90.

By comparing the assumed selling price of the watch with the original selling price, 450/90 = 5.

So, the original selling price is 5 times the assumed selling price.

Thus original cost price should also be 5 times of assumed cost price, so  the original cost price × 5 = 100 × 5 = 500.

Hence the original cost price of the watch is 500.

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The percentage change in the visit of total number of customers in the second week as compare to first week is equal to 16.67%.

Total number of customers visited the store in the first week = 360

Total number of customers visited the store in the second week = 300

Percentage Change = (|First week - second week / First week) x 100%

Substitute the value of the number of customers in different weeks in the formula we get,

Percentage Change

= (|300 - 360| / 360) x 100

= (60 / 360) x 100

=( 100 / 6 )

= 16.66666%

= 16.67%

Therefore, the percentage change in the number of customers that visited the store from the first week to the second week is a decrease of 16.67%.

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The above question is incomplete, the complete question is:

Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store.

What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?

By permutation and combination, Maximum 171 number of different  2 - person teams are possible.

Provide an example of permutation and combination?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are organized in a linear or sequential order.

                       As an illustration, set A=1,6 has the permutation 2, which is 1,6,1. Permutations include the arrangement of individuals, digits, numbers, alphabets, letters, and colors. Combinations include things like choosing a menu, cuisine, clothing, a subject, and a team.

Total number of ways to choose different 2 person out of 19 person.

                     = ¹⁹C₂

              = 19!/2! (19 - 2)!

              =  19!/2!   17!

             = 19 * 18 * 17!/2 * 1 * 17!

            = 19 * 7

              = 171

Hence, maximum 171 number of different  2 - person teams are possible.

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The measure of the angle x of the polygon is 100 degrees if the polygon has 5 sides. The interior angle measures are 117°, 104°, 113°, 106°.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight line segments are joined and to end to form a closed shape. The vertices also known as corners, are the points where two lines segments meet and form an angle.

We know that the sum of the interior angles in a polygon is given by:-

180(n-2) here, n is 5.

therefore, 180(5-2) = 540° .

117°+104°+106°+x= 540°.

440°+x= 540°

x= 540°-440°

x= 100° .

Thus, the measure of the angle x is 100° .

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Answer:

it is a triangle bc it has angles of points

Step-by-step explanation:

In the given triangle, the value of x = 5.

What is a triangle's definition?

A triangle is a geometrical shape that is defined as a polygon with three sides and three angles. It is a closed figure with three line segments as its sides, and these sides intersect at three points, which are called vertices. When we add all the angles of a triangle then the result will always be 180°.

Now,

As we know the property of a triangle that

sum of all angles of triangle=180°

given angles are (9x-1)°, 74° and 62°

then,

        9x-1+74+62=180°

9x+135=180

9x=45

x=5

Hence,

           the value of x is 5.

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The value of q according to the given triangle measures is 3 cm.

What is Sine Rule for Traingles?

For any general triangle ABC with 3 angles A, B, and C and 3 sides a, b, and c corresponding to their opposite angle, the formula of sine is always fulfilled :

               [tex]\frac{a}{sin A} = \frac{b}{sin B} =\frac{c}{sin C}[/tex]

Here, we are given that :

s i.e. Side QR = 3.1 cm

Angle Q = 62 degree

Angle R = 114 degree

Firstly we need to find the third angle S using the sum of triangle angles property :

                   [tex]AngleQ + AngleR + AngleS = 180\\[/tex]

                   [tex]Angle S = 180 - 114 - 62[/tex]

                                [tex]= 180 - 176[/tex]

                                [tex]= 4[/tex]

Now, we apply the sine formula for angles Q and S :

                    [tex]\frac{q}{sinQ} = \frac{s}{sinS}[/tex]

                      [tex]q = (sinQ) * s / (sinS)[/tex]

                          [tex]= ( 3.1 * sin(62)) / sin(4)[/tex]

                          [tex]= ( 3.1 * (-0.739)) / (-0.756)[/tex]

                           [tex]= 3.03[/tex]

Hence, the length of side RS i.e. q to its nearest 10th is 3 cm.

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Answer:

the length of the hypotenuse is approximately 21.1 inches, rounded to the nearest tenth.

Step-by-step explanation:

Rosy will receive 12 chocolates and Fathima will receive 18 chocolates.

To divide 30 chocolates between Rosy and Fathima in the ratio 2:3.

We need to divide the total into 2 + 3 = 5 equal parts (each representing one part of the ratio).

Each part will be equal to:

30 chocolates ÷ 5 = 6 chocolates

Now,

Rosy will receive 2 parts which is:

2 × 6 chocolates

= 12 chocolates.

Fathima will receive 3 parts, which is:

3 × 6 chocolates

= 18 chocolates.

Therefore, the share of Rosy and Fatima are 12 and 18 chocolates respectively.

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Answer:

Step-by-step explanation:

If the dartboard has a diameter of 14 inches, then the radius is 7 inches. The area of the dartboard is given by the formula for the area of a circle: A = pi x r^2, where pi is approximately 3.14 and r is the radius.

A = 3.14 x 7^2 = 153.86 square inches (rounded to two decimal places)

Each number occupies 1/20 of the board, so we need to divide the total area by 20 to get the area occupied by a single number:

153.86 / 20 = 7.69 square inches (rounded to two decimal places)

Therefore, a single number occupies approximately 7.69 square inches of space on the dartboard.

Answer:

To solve this expression, we need to follow the order of operations: parentheses, exponents, multiplication and division (performed left to right), and addition and subtraction (performed left to right).

There are no parentheses or exponents, so we can simplify multiplication and division first:

-2/8 × 2/8 + 2/8 - 2/8 × 2/8 = (-2 × 2)/(8 × 8) + 2/8 - (2 × 2)/(8 × 8)

= -4/64 + 2/8 - 4/64

= (-4 + 16 - 4)/64

= 8/64

= 1/8

Therefore, -2/8 × 2/8 + 2/8 - 2/8 × 2/8 = 1/8.

Answer:

x = -32

Step-by-step explanation:

Given: (2x + 4) + 112 + 132 = 180

First, write it down:

(2x + 4) + 112 + 132 = 180

Then collect like terms:

2x = 180 - 112 - 132

Then calculate:

2x = -64  (Divide both sides by 2)

x = -32

163.79 students were surveyed.

The survey asked randomly selected students whether they preferred vanilla ice cream or chocolate ice cream. 58% of the students said they preferred vanilla ice cream, with a 5% margin of error. To calculate the total number of students surveyed, we can use the following formula:

Number of Students Surveyed = (100 - Margin of Error) ÷ (Percentage that Prefer Vanilla/100)

In this case, we get:

Number of Students Surveyed = (100 - 5) ÷ (58/100)

Number of Students Surveyed = 95 ÷ 0.58

Number of Students Surveyed = 163.79

Therefore, 163.79 students were surveyed.

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Answer: the answer would be 122

Step-by-step explanation:

To find the surface area you need to find the area of each face and add them together

2 (W L+H L+H W) = surface area  

2·(4·7+3·7+3·4)=122

Answer:

Step-by-step explanation:

Given dimensions of the rectangular prism ,

4"×3"×7"

We know, Total surface area of a cuboid= 2(lb+bh+hl)

where, l=length of the cuboid

 b= breadth " " "

 h= height " " "

Since, a rectangular prism holds the shape of a cuboid, therefore it's surface area should also be 2(lb+bh+hl)

Now, surface area of the rectangular prism = 2(4×3+3×7+7×4)

 =2(12+21+28)

 =2×61

 =122 square inches.

According to the bureau of justice statistics, 10% of persons age 16 or older had been victims of identity theft during the prior 12 months in 2016. 200 is the minimal sample size of a random sample of persons age 16 or older to generate a normal distribution approximation.

In order to generate a normal distribution approximation from a sample of persons aged 16 or older, a minimum sample size of 200 individuals would be necessary. This number is based on the assumption that 10% of persons aged 16 or older had been victims of identity theft in 2016, according to the Bureau of Justice Statistics.

The normal distribution approximation of a population is determined by obtaining a random sample of the population, and using it to approximate the probability distribution of a given variable. The larger the sample size, the more accurate the approximation will be, so a sample size of 200 individuals is the minimum required to generate a normal distribution approximation.

In order to obtain a random sample, the population must be divided into subgroups and a certain number of individuals from each group should be selected. A larger sample size will be more representative of the population and will improve the accuracy of the approximation.
In conclusion, a minimum sample size of 200 individuals would be necessary in order to generate a normal distribution approximation of persons aged 16 or older in 2016, based on the Bureau of Justice Statistics finding that 10% of persons aged 16 or older had been victims of identity theft during the prior 12 months in 2016.

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The measure of angle A is 25°, where the value of x = 12.

Three vertices, three sides, and three angles make up a clοsed triangle.

PQR serves as the symbοl fοr a triangle with the vertices P, Q, and R. Triangle-shaped items are mοst cοmmοnly fοund in sandwiches and signbοards.

A triangle cοnsists οf numerοus parts. There are 3 angles, 3 vertices, and 3 sides tο it.

A triangle has three sides, three internal angles, and three vertices.

The three inner angles οf a triangle can never add up tο mοre than 180 degrees, which is knοwn as the "angle sum prοperty" οf triangles.

Take nοte οf the triangle PQR in the illustratiοn abοve, where the sum οf the angles P, Q, and R is 180 degrees i.e.

90° + (2x + 1)° + (5x + 5)° = 180°

Solving for x

⇒ (2x + 1)° + (5x + 5)° = 180° - 90°

⇒  (2x + 1)° + (5x + 5)° = 90°

⇒ 7x + 6 = 90

⇒ 7x = 90 - 6

⇒ 7x = 84

⇒ x = 84/7

⇒ x = 12

Now, m∠A = (2x + 1)°

m∠A = (2(12) + 1)°

m∠A = 24 + 1

m∠A = 25°

Thus, The measure of angle A is 25°.

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Answer:

n-2x180

Step-by-step explanation:

to be abke to find it wouldnt you use n-2x180

a) 32nd unit will take approximately 20.4 hours to produce b) T2 = 59.4 and graph of curve can be plotted similarly for T4, T8, T16

a) Using the learning curve formula, we can estimate how long it will take to make the 32nd unit:

[tex]Tn = T1 * n^k[/tex]

where n: total number of units created, Tn: time it takes to produce the nth unit, T1 is the time it takes to make the first unit, and k is the rate of learning.

T1 is assumed to be 72 hours, and k is specified to be [tex]log(0.85)/log(2)-0.278[/tex].

With the use of these numbers, we may determine T32 as follows:

[tex]T32 = T1 * 32^k \sT32 = 72 * 32^(-0.278) (-0.278)[/tex]

20.4 hours in T32

Hence, it will take about 20.4 hours to generate the 32nd unit.

b) The time it takes to create each unit for a variety of values of n can be determined using the same technique as previously in order to illustrate the learning curve. Therefore, using n as the x-axis and Tn as the y-axis, we may plot these numbers on a graph.

As an illustration, we can compute T2 as follows:

[tex]T2 = T1 * 2^k \sT2 = 72 * 2^(-0.278) (-0.278)[/tex]

59.4 hours in T2.

Similar calculations can be made for T4, T8, T16, and so forth. Then, we may graph these numbers to get a learning curve.

The resulting learning curve will demonstrate how, as production volume grows, each unit's production time gets smaller until it approaches an asymptote. The learning rate will determine how steep the curve is. A steeper curve indicates a faster rate of improvement, and a higher learning rate will produce it. In contrast, a flatter curve indicates a slower rate of improvement than a higher learning rate.

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A stadiometer can be used to measure height, age, and shoe size of learners. It is a simple device consisting of a ruler mounted on a vertical board, and the measurements can be taken in the Frankfort Plane position.

An instrument that can be used to measure height, age, and shoe size of learners is a stadiometer. A stadiometer is a device designed to measure the height of an individual, typically from the floor to the crown of the head. It consists of a ruler, graduated in metric or imperial units, mounted on a vertical board. To measure a person's height, they must stand against the board with their feet together and their head in the Frankfort Plane. The Frankfort Plane is an imaginary line running from the top of the ears to the bottom of the eyes. Once the person is standing in this position, the height is read off the ruler and recorded.

In addition to height measurement, a stadiometer can also be used to measure age and shoe size of learners. To measure age, the stadiometer must be calibrated with the average height of the population by age. Then, when the person is standing in the Frankfort Plane position, their age can be read off the ruler. To measure shoe size, the stadiometer must be calibrated with the average height of a person with a certain shoe size. Once the person is standing in the Frankfort Plane position, their shoe size can be read off the ruler.

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Answer: 2+2

Step-by-step explanation: easy math

Answer:

Neither of the statements are true.

i. A large p-value indicates weak evidence against the null hypothesis. A small p-value (typically less than 0.05) is strong evidence against the null hypothesis.

ii. We cannot set a higher standard of proof by choosing a lower significance level (alpha) because doing so would increase the likelihood of making a Type II error, which is failing to reject a false null hypothesis. The level of significance should be chosen based on the goals of the study and the consequences of making a Type I or Type II error.

When individuals are classified into qualitatively different categories, this is an example of nominal level of measurement.

Nominal level of measurement is the lowest level of measurement in which variables are measured by naming, labeling or categorizing them into different groups without any inherent order or ranking.

Nominal data involves variables that are categorical in nature and cannot be numerically ranked. Examples of nominal variables include gender, race, ethnicity, hair color, eye color, and so on. These variables can be classified into different categories, but they cannot be arranged in any meaningful order or assigned numerical values.

Nominal data is important in many fields, including social sciences, health research, and market research. It allows for the classification of data into different categories or groups based on certain characteristics, which can then be used to analyze patterns and trends.

However, because nominal data cannot be measured in numerical terms, certain statistical analyses, such as mean and standard deviation, are not applicable. Instead, nominal data is often analyzed using measures of frequency, such as percentages and proportions.

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Answer:

No

Step-by-step explanation:

No. So if the number next to the "x" we're the same, it would have been. But they are different (one is -3 and one is 1/3)

Answer:

96 hours.

Step-by-step explanation:

There are 24 hours in a day, so multiply 24 hours x 4 days.
24x4=96.

Answer:

27 cubic units

Step-by-step explanation:

Since each small cube is a unit cube, then each small cube has side length 1 unit. Each side of the Rubik's cube has length 3 units.

V = s³ = 3³ = 27

Answer: 27 cubic units

Answer:

4.68 dollars.

Step-by-step explanation:

We are looking for how much money Sam spent on grapes. We know that each pound is 90 cents. We also know that Sam bought 5.2 pounds of grapes. We need to find how much he spent.

Our equation would be like this:

0.9 * 5.2 = x

To find X, we multiply 0.9 and 5.2.

4.68 = x

We now know that Sam spent 4.68 dollars on grapes.

The equation that can be used to find the sale price, s, of the pizza is S = 0.8(15).

It is the final amount paid for a product or service and is often lower than the original asking price.

This equation uses the percentage discount of 20%, which can be represented as 0.8, to find the sale price.

To calculate the sale price, the equation multiplies the regular price of $15 by the discount, 0.8.

0.8*15 =12

Therefore, the sale price of the pizza is $12.

The other equations are not correct because they do not take into account the percentage discount of 20%.

S = 0.1(15) does not consider the discount of 20%, as it is multiplying the regular price of $15 by 0.1, which is equivalent to 10%, not 20%.

Similarly, S = 0.115 is incorrect because it is multiplying the regular price of $15 by 1.15, which is equivalent to 115%, not 20%.

Lastly, S=0.8 15 is incorrect because it is not multiplying the regular price of $15 by the discount of 20%, which is 0.8.

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Answer:

153

Step-by-step explanation:

The relationship in the row is below

4³ +2³ +1³ =64 + 8 +1 = 72

1³ + 2³ +6³= 1 + 8 + 216

3³ + 1³ + 5³ = 27 +1 +125 = 153

All numbers below the first level are raised to power 3 and added together

The probability that a librarian chooses a fiction book, then a nonfiction book, then a fiction book is approximately 0.305.

The solution to this problem is a probability calculation.

To calculate the probability of selecting a fiction book, then a nonfiction book, then a fiction book from a selection of 10 nonfiction books and eight fiction books, we need to use the multiplication rule of probability.

The multiplication rule states that the probability of two or more independent events happening together is equal to the product of their individual probabilities.

To apply this rule, we'll break down the question into three events:

Probability of choosing a fiction book = 8/18 = 4/9

Probability of choosing a nonfiction book (after selecting a fiction book) = 10/17

Probability of choosing a fiction book (after selecting a nonfiction book) = 8/16 = 1/2

Now we can use the multiplication rule:4/9 * 10/17 * 1/2 = 0.305 (rounded to three decimal places)

Therefore, the approximate probability that the librarian will choose a fiction book, then a nonfiction book, then a fiction book is 0.305.

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