The same type of dinner plate is sold in two different packs. Small pack contents 3 plates £5. 25. Large pack contents 12 plates £21. 24 which size packet is the better value for money?​

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~2 - (-3)~~)^2 + (~~3 - (-2)~~)^2} \implies d=\sqrt{(2 +3)^2 + (3 +2)^2} \\\\\\ d=\sqrt{( 5 )^2 + ( 5 )^2} \implies d=\sqrt{ 25 + 25 } \implies d=\sqrt{ 50 }[/tex]

32 rows are needed in the truth table that we would use to evaluate a logical statement in five variables

As per the given data:

If we have a logical statement in five variables then we have to determine how many rows we need in the truth table that you would use to evaluate it.

It is calculated by both from truth table and by using the formula.

A table with rows and columns is created for a compound statement, and the number of rows depends on the number of statements.

As we know that the formula for number of rows need in the truth table.

Number of rows = [tex]2^{n}[/tex]

Where n = Number of variables

Here given number of variables are 5.

n = 5

  [tex]2^{n}[/tex] = [tex]2^{5}[/tex]

= 32

Therefore 32 rows are needed in the truth table.

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Time in Line to Buy Groceries is Quantitative-Discrete type of data. So the option C is correct.

We can observe data in a straightforward integer format or monitor quantitative discrete data in a real line at regular intervals.

We need to utilize an integer time point, which cannot be a decimal, to keep track of time while standing in line for groceries. It cannot be delivered in 2.45 days because a grocery store is unable to provide a delivery schedule in fractions.

The correct solution is therefore quantitative discrete.

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The complete question is:

Identify the type of data that would be used to describe a response.

Time in Line to Buy Groceries

A. Qualitative (Categorical)

B. Quantitative - Continuous

C. Quantitative - Discrete

Answer:

Step-by-step explanation:

Let the 3 angles be x , 2x , and 3x

notice x:2x:3x = 1:2:3

we know x+2x+3x = 180

6x = 180

x = 30

so the largest angle is 3(30) or 90 degrees

Answer: b ≤ 17/10

Step-by-step explanation:

7/2 ≥ b + 9/5

7/2 - 9/5 ≥ b

17/10 ≥ b

b ≤ 17/10

Answer:

Refer to the step-by-step

Step-by-step explanation:

Since ∠1 and ∠2 are alternate exterior angles, m∠2=108°

Angle EBI and angle BCJ are congruent is proved as follow.

To prove that corresponding angles are congruent, we can use the transformation that takes angle EBI to angle BCJ.

Therefore, we can conclude that corresponding angles are congruent.

Alternatively, we can use the fact that if two lines are parallel, then the alternate interior angles are congruent and corresponding angles are congruent. Since AI and GJ are parallel, angle EBI and angle BCJ are congruent.

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The ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed as 3:2, 3:4, or 4:3. This means that there are two sedans for every three sports coupes, or three sedans for every two sports coupes, etc.

The ratio of sedans to sports coupes on the lot can be expressed as a fraction, which is the number of sedans divided by the number of sports coupes. In this case, there are 24 sedans and 18 sports coupes, which can be written as 24/18. This fraction can be simplified to 2/3, which is equivalent to the ratio 2:3. This ratio can also be expressed as 3:2, 3:4, or 4:3, which means that there are two sedans for every three sports coupes, three sedans for every two sports coupes, three sedans for every four sports coupes, or four sedans for every three sports coupes. In summary, the ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed in several other ways.

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The probability that the student will be a student who lives on campus is 0.24

In math the term probability is referred as the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

Here we have given that one full-time student who is a freshman or sophomore is selected at random.

Here we need to find the probability that the student will be a student who lives on campus.

Here we know that the probability that a student is a sophomore is calculated as,

=> P(S) = 19/42 = 0.45.

Whereas the probability that a student has a freshman is calculated as,

=>P(H)=25/42=0.6.

Then the probability that the student will be a student who lives on campus is calculated as,

=> P(H∩S)=P(S)+P(H)−P(S∪H)

Apply the values then simplify this one then we get,

=> 0.45+0.6−(42−8)/42=0.24

Complete Question:

Suppose that a certain college class contains 42 students and then if one full-time student who is a freshman or sophomore is selected at random, what is the probability that the student will be a student who lives on campus?

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Answer:They use the process of photosynthesis to transform water, sunlight, and carbon dioxide into oxygen, and simple sugars that the plant uses as fuel. These primary producers form the base of an ecosystem and fuel the next trophic levels

Step-by-step explanation:

The value of x is 3. Option B

It is important to note that the given shape is a parallelogram.

The properties of a parallelogram are;

Now, let's equate the sides, we have;

4x - 1 = 6x - 5

collect like terms

4x - 6x = -5 -1

Subtract like terms

-2x = -6

Make 'x' the subject of formula

x = -6/-2

x = 3

Hence, the value is 3

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Answer:

First question: 452.2

Second question: 267.9

Step-by-step explanation:

Not a hundred percent sure on second ques

Five repetitions should be done for each exercise in the preparation drill.

Preparation drills are an important part of any fitness routine, as they allow the muscles and joints to be prepared for the workout ahead. Doing the correct number of repetitions for each exercise in the preparation drill is key to getting the most out of the workout. Generally, five repetitions is recommended for each exercise. This should give the body just enough time to get used to the exercise while still providing enough of a challenge. Doing too many repetitions may lead to fatigue or overstretching, leading to injury. Doing too few repetitions may not be enough to prepare the body and prevent injury. Five repetitions is the ideal number for most preparation drills.

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Answer:

rate = 7%

Step-by-step explanation:

From the question

Principal = $1,800

Time = 7 years

simple interest = $882

Rate = ?

rate = 100 × ST

P × T

rate = 100 × $882

$1,800 × 7

rate = $88200

12,600

rate = 7%

The vector u can be expressed as a sum of n and p when n= (-33/10, 11/10) and p= (-7/10, -21/10).

To find the vector p that is parallel to v, we need to project u onto v. We can use the formula for projection:

p = (u . v) / (||v||^2) * v

where . represents dot product and ||v|| represents the magnitude of v.

First, we need to find the dot product of u and v:

(-4,-1) . (1,3) = -4*1 + -1*3 = -4 + -3 = -7

Next, we need to find the magnitude of v:

||v|| = sqrt(1^2 + 3^2) = sqrt(1 + 9) = sqrt(10)

Then, we can plug these values into the projection formula:

p = (-7) / (sqrt(10))^2 * (1,3) = (-7/10) * (1,3) = (-7/10, -21/10)

So the vector p that is parallel to v is (-7/10, -21/10)

To find the vector n that is orthogonal to v, we can subtract p from u:

n = u - p = (-4,-1) - (-7/10, -21/10) = (-4 + 7/10, -1 + 21/10) = (-33/10, 11/10)

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The majority of human physical, mental, and personality factors have a mean in the middle of the distribution, where there are also the most cases. For example, in baseball, the rookie of the year often has a poor second season.

Correct answer is b) regression to the mean.

Regression to the mean is the propensity of outcomes that are extreme by chance on the first measurement to move closer to the average when tested a second time. Results that are susceptible to regression to the mean are those that are vulnerable to some degree of chance. When exceptional scores are the result of chance or a fluke, it's improbable that those extreme scores will be obtained again.

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a. Each shoebox has a volume of 288 cubic inches.

b. Each crate has a volume of about 5,760 cubic inches.

c. If the crate could hold 27 shoeboxes, the total volume would be of about 7,776 cubic inches.

The volume of a rectangular prism is obtained by the multiplication of the dimensions of the prism.

Hence the volume of the box in this problem is of:

6 x 4 x 12 = 288 cubic inches.

For the crates, we have that:

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Answer:

A.288

B.5,760

C.27 shoeboxes

Step-by-step explanation:

They needed a total of 8 weeks to save the same amount of money, and after 8 weeks, everyone would have $200.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Harper and Joe want to buy season passes for Disneyland but neither of them has the $1,300 needed to purchase a pass.

Since Harper decides to get a job that pays $25 a week. She has nothing saved right now. Joe already has $80 and plans to save $15 of her weekly allowance.

To save up for the season pass:

Harper needs = 1300$

Since, She earns 25$ a week

Harper needs total weeks = 1300/25

Harper needs total weeks = 52 weeks

joe also needs 1300 $

Since, joe already has $80 and plans to save $15 of her weekly allowance.

Joe needs total weeks = (1300 -80)/15

Joe needs total weeks = 81.33

To have the same amount of money saved up:

Let "x" be the weeks they required to save the equal money:

25 *x = 80 + 15*x

10*x = 80

x = 8

Everyone will have = 25 * 8

Everyone will have = 200$

Therefore, they required total of 8 weeks to have the same amount of money saved up and everyone will have 200$ after 8 weeks.

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In parallelogram lmno measure of angle m m∠M = 80°

In a parallelogram, opposite sides and opposite angles are congruent to each other.

⇒ m∠N = m∠L and m∠M = m∠O ..........(1)

Also, the sum of any two consecutive angles of a parallelogram is supplementary that is 180°

⇒ m∠M + m∠L = 180°  ...........(2)

Now, using equation (1)

m∠N = m∠L

⇒ 5x = 3x + 40

⇒ 5x - 3x = 40

⇒ 2x = 40

⇒ x = 20

⇒ m∠N = m∠L = 5x = 100°

Now, from equation (2)

m∠M + m∠L = 180°

⇒ m∠M + 100 = 180

⇒ m∠M = 80°

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The association between the two sets of data in the scatterplot is; Positive.

A scatter plot is a graph that shows the association that exists between two variables. A scatter plot matrix shows all the pairwise scatter plots for a lot of  variables.

Now, If the variables tend to increase and decrease together, the association is said to be positive. However, If one variable tends to increase as the other decreases, then the association is said to be negative. Finally, If there is no pattern, then the association is said to be zero.

When a straight line is used to describe the relationship between the variables, then the association is said to be linear. When a constantly increasing or decreasing nonlinear function describes the relationship, the association is monotonic.

The scatterplot given shows us that the association is positive as increasing x values lead to increasing y values.

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For making of 60 biscuits the quantity and packs of butter required by Helen is :

a. The exact amount of butter is 480 grams to make 60 biscuits.

b. Number of packs of butter Helen needs to buy is 2 packs.

Amount of sugar need to make 15 biscuits = 60 grams

Flour is three time of sugar to make 15 biscuits = 60 × 3

                                                                               = 180 grams

Amount of flour to make 60 biscuits = 180 × 4

                                                            = 720 grams

Butter is two times as sugar  to make 15 biscuits= 60 × 2

                                                                                = 120grams

a. Exact amount of butter to make 60 biscuits is:

Butter required to make 60 biscuits = 120 × 4

                                                            = 480 grams

b. One pack is of 250 grams

Number of packs of butter she need to buy = 480 / 250

                                                                         = 1,92

                                                                         ≈ 2packs

Therefore, the quantity of butter and number of packs of butter is given by :

a. The exact amount of butter required to make 60 biscuits is 480 grams.

b. The number of packs she needs to purchase is 2 packs.

The above question is incomplete, the complete question is :

Helen has to buy all the butter she needs to make 60 biscuits. She buys the butter in 250g packs.

(i) What is the exact amount of butter she needs?

(ii) How many packs of butter will she have to buy?

Figure is attached.

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A population is a person or object that is a member of the sample being studied while a sample is the entire group that is being studied.

In a research study, a sample is a relatively small group of people from whom data is collected. The population is the bigger group to whom the information is then generalized.

All citizens, whether they are living there permanently or are only visiting, are referred to as the "people."

This indicator shows the average population density of a given area. The annual population fluctuations brought on by births, deaths, and net migration are known as growth rates.

A population is any large group that has at least one attribute in common. Not all populations are made up of people.

Populations can include, but are not limited to, people, animals, groups, organizations, buildings, houses, trucks, farms, and things.

Of the 7.8 billion people on the planet, 1%, or around 78 million individuals, would be there. One percent of the 7.8 billion people on the planet, or 78 million people, live there.

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Complete question -

A person or object that is a member of the group being studied is called ______.

Using the information in the issue and the formulas for the total surface area and volume of a rectangular solid, we can determine the volume of the rectangle solid in detail.

First, we calculate the rectangular solid's overall surface area using the following formula:

2(lw + lh + wh) = 972

Where the rectangular solid's dimensions are l for length, w for width, and h for height.

We can describe the three sides in terms of x, so that l = 10x, w = 4x, and h = x, since the ratio of the length to the breadth to the height is 10:4:1.

Now, we change the variables in the equation for the total surface area to match these values:

The formula is 2(lw + lh + wh) = 2(10x * 4x + 10x * x + 4x * x) = 972.

The equation will become more precise and give us:

80x^2 = 972

x^2 = 12.15

x = 3.5

Now that we have one side's value (height), we can use the following formula to get the solid's volume:

V = lwh

V = (10x)(4x)(x)

V = 40x^3

V = 40 * (3.5)^3

V = 40 * 42.875

V = 1715 cubic units

As a result, the rectangular solid has a volume of 1715 cubic units.

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Answer: The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 0.845^2 = 0.7146. This tells us that 71.46% of the variation in the data is explained by the regression line, while 28.54% is unexplained.

The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 1^2 = 1. This tells us that 100% of the variation in the data is explained by the regression line, and 0% is unexplained.

The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = -2.5x, so we can use this equation to find the predicted values and then calculate the SSE and SEE.

The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = 1.523x + 6.343, so we can use this equation to find the predicted values and then calculate the SSE and SEE by using the given data.

Answer:

3

Step-by-step explanation:

Experimental probability is based on the actual outcomes of an experiment (gathered by experimenting repeatedly).  

Theoretical probability is based on the possible outcomes (expected outcomes).

Probability formula

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

Theoretical probability of flipping a head

A coin has two sides: one side is a "head", the other side is a "tail".

The number of ways flipping a head can occur is 1.

The total number of possible outcomes is 2.

Therefore, the theoretical probability of flipping a head is 1/2.

Theoretical probability of rolling a number less than 3

The cube has six sides labelled 1, 2, 3, 4, 5 and 6.

The number of ways that rolling less than 3 can occur is 2 (rolling 1 or 2).

The total number of possible outcomes is 6.

Therefore, the theoretical probability of rolling a number less than 3 is 2/6 = 1/3.

Therefore, the theoretical probability of flipping a head and rolling a number less than 3 is:

[tex]\sf P(head)\; and\; P(X < 3)=\dfrac{1}{2} \times \dfrac{1}{3}=\dfrac{1}{6}[/tex]

To calculate the number of actual outcomes and expected outcomes after 90 trials, multiply the number of trials by the probability for each outcome:

[tex]\textsf{Number of actual outcomes}=90 \times \dfrac{2}{15}=12[/tex]

[tex]\textsf{Number of expected outcomes}=90 \times \dfrac{1}{6}=15[/tex]

Therefore, the difference between the number of expected outcomes and the number of actual outcomes is:

[tex]\implies 15-12=3[/tex]

Note: If Olivia continued to flip the coin and roll the number cube, as the number of trials increased, we would expect the experimental probability of 2/15 to get nearer to the theoretical probability of 1/6 and so the difference between the number of actual and expected outcomes would become smaller.

Answer:

SEE ATTACHED

Step-by-step explanation: