6 Anton is buying supplies for a charity event.
A pack of 50 paper cups costs £1.89.
A pack of 10 paper plates costs 49p.
Anton has £15 to spend.
Anton buys 250 paper cups and spends the rest on paper plates.
How many paper plates can he buy?

Correct this group constitutes a sample of all students in the class.

What are some instances of intuitive reasoning?

As an illustration, when we enter a coffee shop, we immediately recognize a cup as one that we have seen many times before.

                           We also immediately recognize that it will probably be hot and spill quickly over an uneven surface.

What is the intuitional method?

Intuition is the earliest means of knowing. When we use our intuition, we are putting our trust in our feelings, emotions, and/or instincts to lead the way.

                          When using intuition, one believes what seems true rather than looking at the facts or using reason.

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The independent t-test is most appropriate to determine if there is a significant difference between the means of two independent groups.

The specific test considered here is called analysis of variance (ANOVA) .

The independent t-test, also called the two sample t-test, independent-samples t-test or student's t-test, is an inferential statistical test that determines whether there is a statistically significant difference between the means in two unrelated groups.

The specific test considered here is called analysis of variance (ANOVA) and is a test of hypothesis that is appropriate to compare means of a continuous variable in two or more independent comparison groups.

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(A) A normal distribution centered at 1/3 with a standard deviation of about 0.0351.

Normal Distribution:

The normal distribution, also known as the Gaussian distribution, is a probability distribution symmetrical about the mean, indicating that data near the mean occurs more frequently than data far from the mean. The normal distribution model is important in statistics and is the key to the central limit theorem (CLT). The theory states that means computed from independent, identically distributed random variables have an approximately normal distribution, regardless of the type of distribution from which the variable is sampled (provided it has finite variance). Mean (average value), median (center), and mode (most frequent observation) are all equal. Moreover, these values ​​all represent the peak or highest point of the distribution.

Standard Deviation:

The standard deviation (or σ) is a measure of the distribution of data from the mean. A low standard deviation means the data is clustered around the mean, and a high standard deviation means the data is more scattered. A standard deviation close to zero indicates that the data points are close to the mean, while a high or low standard deviation indicates that the data points are above or below the mean, respectively.  The top curve is more spread out and therefore has a higher standard deviation, while the bottom curve is more concentrated around the mean and therefore has a lower standard deviation.

Complete Question:

A successful waffle-man has recently developed a new recipe for waffles. To test the popularity of this new waffle compared to two other tried-and-true types of waffles, our friend the waffle-man randomly selected 180 lucky customers to vote on which of the three waffle types they liked best. Exactly 35% of these customers (or 63 in total) voted in favor of the new waffle. If all waffles were equally tasty, then the waffle-man knows to expect that each waffle would receive around 1/3 of the votes (so around 60 votes per waffle).

Are 63 votes for the new waffle enough to conclude that significantly more customers like it compared to the others? Luckily, our friend the waffle-man triple-majored in waffles, statistics, and clinical neurophysiology and knows how to objectively answer this question. He conducts a hypothesis test for proportions,

H0:p=1/3 H0:p=1/3, Ha :p>1/3 Ha: p>1/3

with a sample proportion of 63/180.

In carrying out this test, what null distribution for p^p^ should he use? In other words, what is the distribution of the sample statistic assuming the null hypothesis is true? (Be sure to use at least four decimal places in your calculations.)

Select one:

a)A normal distribution centered at 1/3 with a standard deviation of about 0.0351

b)A normal distribution centered at 1/3 with standard deviation of about 0.0356

c)A normal distribution centered at 0.35 with standard deviation of about 0.0356.

d)A normal distribution centered at 0.35 with standard deviation of about 0.0351.

e)We cannot use a null distribution in this problem because the population is not normally distributed.

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Understanding a set’s nature or properties is made easier by its closure property

The set is closed if it has the closure property. This means that any operation performed on an element within a set will provide a result that belongs to that element’s set.

Why Closure Property is important?

Understanding a set’s nature or properties is made easier by its closure property. Mathematical applications of closure are numerous. Any operation that adheres to this condition is said to be “closed” or to have “fulfilled the operation’s closure property.”

Example – The set of even number is closed under subtraction

                   Even – Even = Even

                   6 – 4 = 2

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Answer:

A ≈ 418.9 cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × \(\frac{120}{360}\) ( r is the radius )

 = π × 20² × \(\frac{1}{3}\)

 = \(\frac{400\pi }{3}\)

 ≈ 418.9 cm² ( to the nearest tenth )

The minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.

In this target game, Malia needs to have the lowest mean distance of all throws to win. The mean distance is calculated by adding up all the distances and dividing by the number of throws.

First, we need to calculate the mean distance of Malia's first 7 throws.

Mean distance = (2 + 3 + 4 + 2 + 5 + 3 + 4) / 7 = 3.14

Now, we know that Malia's mean distance must be less than 3.14 to win the game. Let's call the distance of her last throw x.

The mean distance of all 8 throws will be: (2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8

To find the minimum distance that Malia needs on her last throw to win the game, we can set up an inequality:

(2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8 < 3.14

Multiplying both sides by 8 gives us:

2 + 3 + 4 + 2 + 5 + 3 + 4 + x < 25.12

Simplifying gives us:

x < 25.12 - 23

x < 2.12

Therefore, the minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.

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Use 1/8*(whatever amount of days until fractions match)

it will take road x 44 days to repair (1/8*44)

road y will take 70 days to repair (1/8*70)

it will take road y 26 days longer to repair

(a) The marginal pmf of X: fX(1) = 9/32, fX(2) = 11/32

(b) The marginal pmf of Y: fY(1) = 7/64, fY(2) = 9/64, fY(3) = 11/64 fY(4) = 13/64

(c) P(X > Y) = 11/32

(d) P(Y = 2X) = 1/16

(e) P(X + Y = 3) = 1/8

(f) P(X ≤ 3 - Y) = 11/64

(g) X and Y are dependent.

(h) Mean of X (μX) = 41/32, Mean of Y (μY) = 205/64, Variance of X (σX²) = 113/1024 and Variance of Y (σY²) = 8199/8192

(a) To find fX(x), the marginal pmf of X, we sum the joint probabilities for each value of x:

fX(1) = f(1,1) + f(1,2) + f(1,3) + f(1,4) = 3 + 4 + 5 + 6 = 18

fX(2) = f(2,1) + f(2,2) + f(2,3) + f(2,4) = 4 + 5 + 6 + 7 = 22

Therefore, the marginal pmf of X is:

fX(1) = 18/64 = 9/32

fX(2) = 22/64 = 11/32

(b) To find fY(y), the marginal pmf of Y, we sum the joint probabilities for each value of y:

fY(1) = f(1,1) + f(2,1) = 3 + 4 = 7

fY(2) = f(1,2) + f(2,2) = 4 + 5 = 9

fY(3) = f(1,3) + f(2,3) = 5 + 6 = 11

fY(4) = f(1,4) + f(2,4) = 6 + 7 = 13

Therefore, the marginal pmf of Y is:

fY(1) = 7/64, fY(2) = 9/64, fY(3) = 11/64, fY(4) = 13/64

(c) P(X > Y) can be found by summing the joint probabilities where X is greater than Y:

P(X > Y) = f(2,1) + f(2,2) + f(2,3) + f(2,4) = 4 + 5 + 6 + 7 = 22/64 = 11/32

(d) P(Y = 2X) can be found by summing the joint probabilities where Y is twice the value of X:

P(Y = 2X) = f(1,2) = 4/64 = 1/16

(e) P(X + Y = 3) can be found by summing the joint probabilities where X + Y equals 3:

P(X + Y = 3) = f(1,2) + f(2,1) = 4 + 4 = 8/64 = 1/8

(f) P(X ≤ 3 - Y) can be found by summing the joint probabilities where X is less than or equal to 3 - Y:

P(X ≤ 3 - Y) = f(1,1) + f(1,2) + f(2,1) = 3 + 4 + 4 = 11/64

(g) To determine if X and Y are independent or dependent, we compare the joint pmf with the product of the marginal pmfs:

f(x,y) = 32x+y

fX(x) × fY(y) = (9/32) × (7/64) = 63/2048

Since f(x,y) is not equal to fX(x)× fY(y), X and Y are dependent.

(h) To find the means and variances of X and Y, we use the formulas:

Mean of X (μX) = ∑(x × fX(x))

Mean of Y (μY) = ∑(y×fY(y))

Variance of X (σX²) = ∑((x - μX)² * fX(x))

Variance of Y (σY²) = ∑((y - μY)² × fY(y))

Calculating the means:

μX = (1 × (9/32)) + (2 × (11/32)) = 41/32

μY = (1 × (7/64)) + (2× (9/64)) + (3 × (11/64)) + (4 × (13/64)) = 205/64

Calculating the variances:

σX²= ((1 - 41/32)² × (9/32)) + ((2 - 41/32)² × (11/32)) = 113/1024

σY² = ((1 - 205/64)²× (7/64)) + ((2 - 205/64)²× (9/64)) + ((3 - 205/64)² × (11/64)) + ((4 - 205/64)² × (13/64)) = 8199/8192

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Answer:

12 batches

Step-by-step explanation:

Total cups of flour = 1 1/2

Flour used per batch = 1/8 cups

What is the maximum number of times (batches) Steve can complete the recipe?

Maximum batches Steve can make = Total cups of flour / Flour used per batch

= 1 1/2 ÷ 1/8

= 3/2 ÷ 1/8

= 3/2 × 8/1

= (3*8) / (2*1)

= 24 / 2

= 12 batches

Maximum batches Steve can make = 12 batches

The solution set of a homogeneous system of 18 linear equations in 20 variables lies in the null space of the coefficient matrix.

To know that every associated nonhomogeneous equation has a solution, we need to ensure that the homogeneous system has a nontrivial solution.

This means that we need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, i.e., whether there exist free variables.

If the rank is less than the number of variables, then there are infinitely many solutions to the homogeneous system, and thus every associated nonhomogeneous equation has a solution.

However,

We also need to ensure that the particular solution to the nonhomogeneous equation does not lie in the null space of the coefficient matrix.

This is equivalent to checking whether the null space of the coefficient matrix is orthogonal to the vector on the right-hand side of the nonhomogeneous equation.

If it is, then the nonhomogeneous equation has a solution.

So, in summary, to know that every associated nonhomogeneous equation has a solution.

We need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, and we need to check whether the particular solution lies in the null space of the coefficient matrix.

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Remember that the equation of a line in slope-intercept form, is:

Where m is the slope of the line and b is the y-intercept.

First, write the equation 3x-y=8 in slope-intercept form to find its slope:

Answer:

y = 17.5

It says y is proportional to x, and y = 35 when x = 140, but we don't know what y is when x = 70. So since y is proportional to x and x = 140 we have to find out how 140 gets to 70, and that is dividing by 2 because 70 is half of 140. So then you would just divide the previous y value, 35, by 2, and you would get 17.5. And there you go, you've got you're answer.

Answer:

The missing value is -9

Step-by-step explanation:

Given

\(-7 = _ -(-2)\)

Required

Determine the missing value

Represent _ with a variable

\(-7 = x -(-2)\)

Open the bracket

\(-7 = x -1*-2\)

\(-7 = x + 2\)

Subtract 2 from both sides

\(-7 - 2 = x + 2 - 2\)

\(-9 = x\)

Reorder

\(x = -9\)

Hence, the missing value is -9

Answer:

The answer is 4=−2+6

Step-by-step explanation:

I checked on khan

Answer:

x = −y+45

Step-by-step explanation:

Step 1: Add -2y to both sides.

Step 2: Add 8 to both sides.

Step 3: Divide both sides by 2.

Answer:

option 4

Step-by-step explanation:

put like terms on either side

9x + 2a = 3a - 4x

subtract both sides by 2a

9x = a - 4x

add both sides by 4x

13x = a

divide both sides by 13

x = a/13

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Answer:

4.) a/13

Step-by-step explanation:

9x + 2a = 3a - 4x

9x + 4x = 3a - 2a

13x = a

13x/13 = a/13

x = a/13

Venn diagram:

The percentage of students that studied mathematics = 25%
The percentage of students that studied electronics = 20%
The percentage of students that studied Communications = 55%
The percentage of students that studied both electronics and Communications subjects = 10%

P(studied Communications or electronics or both subjects)
= P(studied Communications) + P(studied electronics) - P(studied both electronics and Communications subjects)
= 55% + 20% - 10%
= 65%

Therefore, the probability that a student studied Communications or electronics or both subjects is 65%.

P(studied mathematics and Communications subjects)
= P(studied mathematics) × P(studied Communications)
= 25% × 55%
= 13.75%

Therefore, the probability that a student studied mathematics and Communications subjects is 13.75%.

Drawing a Venn diagram, we have 25% studying Mathematics (M), 20% studying Electronics (E), and 55% studying Communications (C).10% studied both Electronics and Communications.

Therefore, the percentages become as follows: M = 25% - 10% = 15% E = 20% - 10% = 10% C = 55%.

Part 2 - To obtain the probability that a student studied Communications or Electronics or both subjects

P(Communication or Electronics) = P(Communication) + P(Electronics) - P(Communication and Electronics) = 55% + 20% - 10% = 65%.

The probability that a student studied Communications or Electronics or both subjects is 65%.

Part 3 -To obtain the probability that a student studied Mathematics and Communications subjects,

P(Mathematics and Communications) = P(Mathematics) * P(Communications) = 25% * 55% = 13.75%.

The probability that a student studied Mathematics and Communications subjects is 13.75%.

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Answer:

100.03

Step-by-step explanation:

i think it is correct

x = number of hours

want to find probability (P) x >= 13

x is N(14,1) transform to N(0,1) using z = (x - mean) / standard deviation so can look up probability using standard normal probability table.

P(x >= 13) = P( z > (13 - 14)/1) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413

To convert that to percentage, multiply 100, to get 84.13%

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The function notation is: f(x) is a function can be expressed as f(x) = 3x + 1.

What is function notation?

Formal Notation. A function is frequently written as "f(x)" when it is expressed as an equation. This formula, "multiply by five and remove one," is used when constructing a table of values for an equation, such as

y = 5x - 1, to convert an input x value into the output y value.

Consider the given function;

F(a + 1) = 3(a + 1) + 1

Write a + 1 as x i. e  x = a + 1

So, the function becomes,

F(x) = 3x + 1.

where, x is the input variable and 3x + 1 is the output.

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Answer:

  18π cm² ≈ 56.5 cm²

Step-by-step explanation:

The area of the sector can be found using an appropriate area formula.

When the sector central angle is given in radians, the formula for the area of that sector is ...

  A = 1/2r²θ . . . . . . where θ is the central angle, and r is the radius

When the angle is in degrees, the formula will include a factor to convert it to radians:

  A = 1/2r²θ(π/180) . . . . where angle θ is in degrees

  A = (πθ/360)r² . . . . simplified slightly

The figure shows r=9 cm, and θ=80°. Using these values in the formula gives an area of ...

  A = π(80/360)(9 cm)² = 18π cm² ≈ 56.5 cm²

Answer: x=80

Step-by-step explanation: You add 14 to both sides of the equation. The left side of the equation cancels out leaving you with 80

Answer:

\(\boxed {x = 80}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(x - 14 = 66\)

-Add \(14\) on both sides:

\(x - 14 + 14 = 66 + 14\)

\(\boxed {x = 80}\)

So, the value of \(x\) is \(80\).

Answer:

x^2-16x+48

Step-by-step explanation:

Use foil,

x^2-12x-4x+48

x^2-16x+48

Answer:

blue

Step-by-step explanation:

The final values of the angles are:

C0 = A0 = 2

C1 = B1 = -7

theta1 = 0 degrees

C2 = B2 = -7

theta2 = 0 degrees

Here, we have,

To determine the values of C0, C1, theta1 (in degrees), C2, and theta2 (in degrees), we need to match the given expressions for x(t) with the given values for A0, A1, B1, A2, B2, and w.

Comparing the expressions:

x(t) = C0 + C1sin(wt+theta1) + C2sin(2wt+theta2)

x(t) = A0 + A1cos(wt) + B1sin(wt) + A2cos(2wt) + B2sin(2w*t)

We can match the constant terms:

C0 = A0 = 2

For the terms involving sin(wt):

C1sin(wt+theta1) = B1sin(w*t)

We can equate the coefficients:

C1 = B1 = -7

For the terms involving sin(2wt):

C2sin(2wt+theta2) = B2sin(2wt)

Again, equating the coefficients:

C2 = B2 = -7

Now let's determine the angles theta1 and theta2 in degrees.

For the term C1sin(wt+theta1), we know that C1 = -7. Comparing this with the given expression, we have:

C1sin(wt+theta1) = -7sin(wt)

Since the coefficients match, we can equate the arguments inside the sin functions:

wt + theta1 = wt

This implies that theta1 = 0.

Similarly, for the term C2sin(2wt+theta2), we have C2 = -7. Comparing this with the given expression, we have:

C2sin(2wt+theta2) = -7sin(2w*t)

Again, equating the arguments inside the sin functions:

2wt + theta2 = 2wt

This implies that theta2 = 0.

Therefore, the final values are:

C0 = A0 = 2

C1 = B1 = -7

theta1 = 0 degrees

C2 = B2 = -7

theta2 = 0 degrees

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Answer:

The nth term of the given sequence  tₙ = 3 n - 7

Step-by-step explanation:

Given sequence   - 4 , -1 , 2 , 5, 8 , .....

First term a = -4

The difference of two terms of a given sequence

d = -1 - (-4) = -1 +4 = 3

d = 2 - (-1) = 2 +1 = 3

d = 5 -2 = 3

d = 8 - 5 =3

The difference of two terms of a given sequence is equal

∴ The given sequence is in Arithmetic progression(AP)

     The nth term of given sequence

   \(t _{n} = a + ( n-1 ) d\)

  \(= -4 + (n -1 ) 3 \\= - 4 + 3n - 3 \\= 3 n - 7\)

Final answer:-

The nth term of the given sequence  tₙ = 3 n - 7

Chance is a term used to represent the percentage of time a specific result is expected to occur when the same basic procedure is repeated over and over again, where each repetition is independent.

Chance is a term that is used to describe the probability that a certain outcome will occur given a set of fundamental instructions repeated again with each repetition being independent.

Ultimately, this means the number of times a result of an event occurs when repeated over a number of times is chance.

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