When class 11Y1 found that their favourite teacher, Mr Musson, was leaving they decided to organise a party for him.
Lewis, one of the class members, wants to buy 34 cartons of juice. He can buy a single carton of juice for 45p.
He can buy a pack of 4 cartons for £1.51.
Lewis buys all the cartons he needs for the least possible amount of money. How much did he spend?

The inequality that shows the relationship between thier heights is g < r or r > g

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

Reese is taller than Gage.

Also, from the question; we have

Reeses's height = r

Gage's height = g

Because Reese is taller than Gage, then it means that

The value of r is greater  than the value of g

So, we have the following inequality expression

r > g

Also, we have

g < r

Hence, the inequality is g < r

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Answer:

---------------------------------------

First, solve the inequality:

This is option C (you have chosen it correctly).

Now, graph it:

Answer:

x < -11  or  x > 8

Step-by-step explanation:

Given absolute value inequality:

[tex]|2x+3| > 19[/tex]

[tex]\boxed{\begin{minipage}{7.1 cm}\underline{Absolute rule}\\\\If\;\;$|u| > a,\;a > 0$\;\;then\;\;$u < -a$\;\;or\;\;$u > a$\\ \end{minipage}}[/tex]

Apply the absolute rule:

[tex]\underline{\sf Case\;1}\\\begin{aligned}2x+3& < -19\\2x& < -22\\x& < -11\end{aligned}[/tex]            [tex]\underline{\sf Case\;2}\\\begin{aligned}2x+3& > 19\\2x& > 16\\x& > 8\end{aligned}[/tex]

To graph the solution:

The following are binomial random variable,

A)A Roll a fair die 5 times and X = the number of rolls that land showing a "4", is a binomial random variable.

B) Roll 5 fair dice at once and let Z = the number of dice that land showing an even value (2, 4, or 6), is a binomial random variable.

C) Roll 5 fair dice at once and let Y = the number of dice that land showing a "4" , is a binomial random variable.

A random binomial variable should satisfy the following conditions:

1. The number of trials are defined or fixed.

2. Each trial is independent of others.

3. The probability of success is same in all trials.

4. There should be only two outcomes in each trial.

Lets we evaluate the options based on the above conditions:

(A) Rolling fair dice 5 times have 5 trials, each rolling is independent, probability of 4 is 1/6 in all cases and the dice will either land 4 or will not land 4. So, X will have values from 0 to 5, 0 when dice doesn't land 4 even once in 5 rolls and 5 when dice land 4 in all rolls. This variable satisfies the condition to be a random binomial variable. So, X is a random binomial variable.

(B)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice with even number to all 5 dices with even number. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Z is a random binomial variable as it satisfies all the conditions.

(C)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice land with 4 to all 5 dices land with 4. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Y is a random binomial variable as it satisfies all the conditions.

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The function plotted in the graph is given by - g(x) = 3.5 sin(x)

        [tex]$\sin \theta=\frac{a}{h}[/tex]

      {θ} = angle theta

      {a} = length of opposite side a

      {h} = length of hypotenuse h

        [tex]${\displaystyle {\begin{aligned}\sin(x)&=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \;= \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}}[/tex]

        {sin(A) / a = sin(B) / b = sin(C) / c}

Given is a graph as shown in the image.

A sine function has its maximum value of [1] and the minimum value of [-1]. The given graph g(x), is a amplitude scaled version of the function f(x) given by -

f(x) = sin(x)

and

g(x) = Asin(x)

Here, [A] is equal to 3.5. So, the function g(x) is equal to -

g(x) = 3.5 sin(x)

Therefore, the function plotted in the graph is given by -

g(x) = 3.5 sin(x)

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Answer:

no melissa isn't correct she has made 3 mistakes

Step-by-step explanation:

You would need to deposit $2,500 in order to have $5,000.00 in the account in 1633 days.

1st method: This can be found by using the simple interest formula I=PRT. In this case, I=5000, P=2500, R=.42, and T=1633. Solving for I gives you the answer.

2nd Method: If you deposit $2,500 in an account now, you will have $5,000 in the account in 1633 days. $2,500 * 1.42 = $3,550 $3,550 + $2,500 = $6,050 $6,050 / 2 = $3,025

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The number or visits that Jim must make to make Plan A the cheaper option is more than 5 visits

An equation is the statement that illustrates the variables given. Jim has to choose between two gym membership plans.

For Plan A: $50 monthly membership fee and $10 per visit. This will be:

50 + 10v

Plan B: $25 one time membership fee and $15 per visit. This will be:

= 25 + 15v

Let v = number of visit

This will be illustrated as:

50 + 10v = 25 + 15v

Collect like terms

15v - 10v = 50 - 25

5v = 25

Divide

v = 25 / 5

v = 5

There will be more than 5 visits for a cheaper option.

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For the quiz score of 100, the time will be equal to 5.26 hours.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.

The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.

Given that the relationship can be represented by the equation y=7.6x+60. Here x is the time and y is the score of the quiz.

At the score of the quiz of 100, the value of x will be calculated as,

y = 7.6x+60

100 = 7.6x + 60

40 = 7.6x

x = 40 / 7.6

x = 5.26 hours

The meaning of the value of x = 5.26 hours is that for scoring 100 on the quiz the time will be 5.26 hours.

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Type I regions- ∫∫R f(x,y)dA = ∫b x=a ∫h(x) y=g(x) f(x,y) dy dx

Type II regions- ∫∫R f(x,y)dA = ∫d y=c ∫h(y) x=g(y) f(x,y) dx dy

Curves of type I can be described for yy in terms of xx and often "lay above and below" one another.

Type II curves, on the other hand, can be defined for xx in terms of yy and are more or less "left and right" of one another.

Type II regions can be divided into horizontal slices, but Type I regions can be divided into vertical slices.

When a location is simultaneously classified as Type I and Type II, you can choose to examine it in any manner.

Type I regions are regions that are bounded by vertical lines x=a and x=b, and curves y=g(x) and y=h(x), where we assume that g(x)<h(x) and a<b. Then we can integrate first over y and then over x:

∫∫R f(x,y)dA = ∫b x=a ∫h(x) y=g(x) f(x,y) dy dx

Type II regions are bounded by horizontal lines y=c and y=d, and curves x=g(y) and x=h(y), where we assume that g(y)<h(y) and c<d. Then we can integrate first over x and then over y:

∫∫R f(x,y)dA = ∫d y=c ∫h(y) x=g(y) f(x,y) dx dy

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The equation that matches the graph is 7x-30y=-275

We should know that an equation is a mathematical expression in which two sides are equal.

The equation of a line is the equation formed with the slope of the straight line

The slope of the of the is determined taking the points

[tex]M=\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]

Slope=(7-1)÷(35-5)

m=1/5

The equation of the line is

1/5 = (y-1)÷(x-35)

Cross multiplying the equation

7x-245=30y-30

Rearrange,

7x-30y=-30-245

7x-30y=-275

In conclusion the equation to match the graph is 7x-30y=-275

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Answer:

the first option

Step-by-step explanation:

in an "and" statement both parts need to be true, so that the overall condition is true.

is x = 6 a valid solution ?

no, it violates both, x <= -8 and x <= 4

is a value between -8 and 4 a valid solution like x = -2 ?

no, it violates x <= -8, even though it is true for x <= 4.

only values that are smaller or equal to -8 (like -9) are true for both.

and therefore the first answer option is correct.

The true statement regarding the probabilities on the spinner is given as follows:

The probability that the spinner will point to yellow is less than 1/4.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

Hence, for the spinner given in this problem, the probabilities are given by the fraction occupied by each area, as shown by the image given at the end of the answer.

From the text, these fractions, representing the probabilities, are given as follows:

The problem is given by the image shown at the end of the answer.

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Answer:Printmaking is the process of creating artworks by the process of printing. It can be done on paper, brick, wood, and even metal.A lithographic is a planetographic process where the design is drawn into a flat stone and is prepared by use of metal. As per the paintings shows the artwork shows us the rhinosaruers. The painting is made from water and oil.Hence the painting B shows us the use of lithography.

Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor.

To determine the total increase recorded in the Work in Process account related to direct labor, we need to first calculate the total standard cost of direct labor for the period and then compare it to the actual cost of direct labor.

According to the standard cost card, each unit of the product requires 2 hours of direct labor at a rate of $16.00 per hour.

This means that the total standard cost of direct labor for the period is 2 * $16.00 * 7,800 = $248,000.

Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor. Therefore, the total increase recorded in the Work in Process account related to direct labor would be $0.

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By means of trigonometric functions, the length of side BC is approximately equal to 11.6 centimeters.

In this problem we find a geometric system formed by two right triangles, from which we need to determine the exact measure of side BC. This can be done by means of trigonometric functions, that represents relationships between two sides of a right triangle:

sin θ = y / r

cos θ = x / r

tan θ = y / x

cot θ = x / y

sec θ = r / x

csc θ = r / y

Where:

First, obtain the length of side BD:

cos θ = BD / AB

BD = AB · cos θ

BD = 5 · cos 30°

BD = 5√3 / 2 cm

Second, calculate the length of side BC:

sin θ = BD / BC

BC = BD / sin θ

BC = 5√3 / 2 / sin 22°

BC ≈ 11.6 cm

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The discontinuity of our given function is at point (-6, -7).

The zero of our given function is, (1, 0).

What is discontinuity and zero of the function?

A discontinuous function is a graph function that is not connected to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first kind at x = a.

The x-intercept(s) of the function's graph represent the real zero of the function.

Consider the given function,

[tex]f(x) = \frac{x^2+5x-6}{x+6}[/tex]

We know that a function is discontinuous, when its denominator is equal to zero.

To find the discontinuity for our given function, we will equate denominator to 0 as:

x + 6 = 0

    x = -6

Now simplify the given function.

[tex]f(x) = \frac{x^2+5x - 6}{x+6}\\ f(x) = \frac{x^2 +6x - x - 6}{x+6}\\ f(x) = \frac{x(x+6)-1(x+6)}{x+6}\\ f(x) = \frac{(x-1)(x+6)}{x+6} \\f(x) = x-1[/tex]

Take  y = x - 1

Since the denominator term is cancelled out, so our give function has a removable discontinuity.

Now, we will find value of y by substituting  x = -6

⇒ y = -6 - 1

   y = -7

Therefore, the discontinuity of our given function is at point (-6, -7).

Now, we will find zero of our given function by substituting  f(x) = 0,as zero of the function is the point, where graph intersects x-axis and value of y is 0 at x-axis:

⇒  0 = x - 1

x - 1 = 0

    x = 1

Therefore, the zero of our given function is, (1, 0).

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The required butter she needed is given as 1.67 cups of butter.

As given in the question, Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels,

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,
Let the nutter need be x cups,
now,
Taking the ratio o butter to kernels
[1 / 2] / 3 = x / 10
x = 10 / 6
x = 1.67

Thus, As of the given proportion, she requires 1.67 cups of butter.

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The volume of the first and second designs are  2.7 m³ and 2.64 m³ so, the second design will hold more sand.

The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.

Given:

One design is 3 m by 3 m by 30 cm,

A second design is 3.25 m by 3.25 m by 25 cm,

Calculate the volume for the first design as shown below,

Volume of first design = 3 × 3  × 30/ 100   (1 m = 100 cm),

The volume of the first design = 270 / 100

The volume of the first design = 2.7 m³

Calculate the volume of the second design as shown below,

The volume of the second design = 3.25 × 3.25 × 25 / 100

The volume of the second design = 264.06 / 100

The volume of the second design = 2.64 m³

The difference in the volume of both designs = The volume of the first design - The volume of the second design

The difference in the volume of both designs = 2.7 - 2.64

The difference in the volume of both designs =0.06 m³

Thus, the first design will hold more volume of sand.

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Answer:

the price of one gallon of milk has increased by 25%.

Step-by-step explanation:

The price of one gallon of milk has increased from $3.24 to $4.05, which is an increase of $4.05 - $3.24 = $0.81. To find the percentage increase, we can divide the amount of the increase by the original price and multiply by 100%. This gives us:

(0.81 / 3.24) * 100% = 25%

Therefore, the price of one gallon of milk has increased by 25%.

The solution is 25 %

The percentage increase in the price of one gallon of milk is given by the equation P = 25 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the original price of the milk be A = $ 3.24

Let the increased price of the milk be B = $ 4.05

Let the percentage increase in the price be = P

Now , the equation will be

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Substituting the values in the equation , we get

Percentage increase P = [ ( 4.05 - 3.24 ) / 3.24 ] x 100

On simplifying the equation , we get

Percentage increase P = ( 0.81 / 3.24 ) x 100

Percentage increase P = 0.25 x 100

Percentage increase P = 25 %

Therefore , the value of P is 25 %

Hence , the percentage increase is 25 %

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Using confidence interval concepts, it is found that the correct options are:A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.

There is a 99% chance that the mean of the population is between 14.3 and 30.4.

The interpretation of a x% confidence interval is that we are x% sure that the population mean is in the interval.

In this problem, 99% confidence interval for widget width is between 14.3 and 30.4, hence we are 99% sure that the population mean, that is, the mean width of all widgets is between 14.3 and 30.4, hence options A and C are correct.

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The expression that represents the volume of the prism is

2 × 3 × 9 units³. That is option C.

Prism is defined as the type of polyhedron that has two polygonal faces lying in parallel planes and with the other faces parallelograms.

A prism can be of a regular shape or of an irregular shape. The volume of a regular shapes prism can be calculated using the formula stated below

volume of a prism = l × b × h

Length (l) = 9 units

Breath = 2 units

Height (h) = 3 units.

Therefore, the volume of the given prism can be calculated as 2 × 3 × 9 units³.

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The expected number of students that pick soda is 80

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

Ice cream = 40

Soda = 20

popsicle = 10

This means that the proportion of soda is

Soda = 20/(40 + 20 + 10)

Evaluate the sum

Soda = 20/70

So, we have

Soda = 2/7

For a group of 280 students, we have

Soda = 2/7 *280

Evaluate

Soda = 80

Hence, the number of students is 80

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The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

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In the factorization, the bottom triangular matrix L is the only one.

The exponent of a number indicates how many times it has been multiplied by itself.

Exponent-related issues can be solved using either exponent laws or exponent characteristics. When a number is repeated numerous times by itself, writing the product without the use of exponents becomes very difficult. Major exponentiation rules are also thought of as having these characteristics.

Given that A is a positively defined symmetric matrix with a Cholesky decomposition,

A = L[tex]L^{T}[/tex]  = [tex]R^{T} R[/tex]

Let A be our positive define symmetric matrix,

suppose A has Cholesky decomposition,

A = L₁L₂ = L₁L₂ , for L₁, L₂ lower triangular matrix with positive diagonal entries,

thus (A x ,x) = (Lx, Lx) = (Lx, Lx)

pick x = eₓ  the last coordinate vector,

then (Aₓ, x) = Axx = || L₁x||² = || L₂x||²

Given that L1, and L2 are lower triangular, which necessitates that their lower right entry be the same,

The Kth entry is currently the last row.

given by (L₁, eₓ, eₓ) = 1/√Axx (L₁eₓ, L₂eₓ) = 1/ Aₓ = (Aeₓ, eₓ)

so the last row of L₁, L₂ be the same,

we reduce our A to new (n - 1)x(n - 1) submatrix,

which will likewise be true, and then repeat the process to discover each row's unique value.

Thus, the inductive process shows that L1 = L2.

As a result, the factorization's bottom triangular matrix L is exclusive.

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Based on the given analysis where T(1) = 3, and T(n+1) = T(n) +5 for n>1, the first four terms of the sequence are 3, 7, 8, 9

First term, T(1) = 3

nth term, T(n+1) = T(n) +5 for n>1

Second term, T2 = T(n) +5

= 2 + 5

= 7

Third term, T3 = T(n) +5

= 3 + 5

= 8

Fourth term, T3 = T(n) +5

= 4 + 5

= 9

Therefore, the first four terms of the sequence are 3, 7, 8, 9

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Final conclusion would be that the difference between the means of the two samples is not statistically significant.

What is Null Hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

It is not possible to test the claim that the two samples come from populations with the same mean without more information about the samples themselves. In order to test this claim, you need to have the sample data, the sample sizes, and the standard deviations of the samples. You can then use a t-test for independent samples to determine whether the difference between the means of the two samples is statistically significant.

The t-test is a statistical test that is used to compare the means of two samples. The test statistic for the t-test is the difference between the means of the two samples divided by the standard error of the difference. The degree of freedom for the t-test is the sum of the sample sizes minus 2. The significance level, alpha, is the probability of making a type I error, which is the probability of rejecting the null hypothesis when it is true. The rejection region for the t-test is the set of values of the test statistic for which the null hypothesis is rejected.

If the test statistic does not fall in the rejection region, you cannot reject the null hypothesis, and you must conclude that the difference between the means of the two samples is not statistically significant.

Final conclusion would be that the difference between the means of the two samples is not statistically significant.

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Answer:

Step-by-step explanation:rate = minute/meter => 20/5

so, 5/1 for rate

so for 11 meter,  (5m/1min)(11)

The answer is 55 minutes

Answer:

R'>R

Step-by-step explanation:

To determine the range of the scores, we conduct a test of 100 students. After grading the test, we realized that the 10 students with the highest scores did exceptionally well. We decide to award these 10 students a bonus of 5 more points each. The range of the new score distribution will be greater than that of the original score distribution.

We know the range is defined by R

R = X(n) - X(1), where X(n) is the maximum value of the observed values, and X(1) is the minimum value of those observed values.

Here for this test study, we awarded 10 highest scorers extra 5 points each. Therefore our maximum observed value becomes X(n) + 5.  So, our range also becomes

R = X(n) + 5 - X(1)

So,  R'>R. Hence, the range of the new score will be greater than that of the original score distribution.

Therefore, the length of a rectangle is 13m and width is 8m

A region's size on a planar or curved surface is described mathematically as its area. In contrast to a plane region or plane's area, which refers to a form or planar lamina, a surface area is the size of an open surface or the edge of a three-dimensional object.

Here,

width=x

length=2x-3

Area =l x w

104=(2x-3)(x)

104=2x^2-3x

52=x^2-3/2(x)

52+9/16=x^2-3/2(x)+9/16

841/16=(x-3/4)^2

29/4=x-3/4

x=32/4

x= 8m

Thus width = 8m

length =  2(8)-3  = 13m

Therefore the length of a rectangle is 13m and width is 8m

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