Sean pays £10 for 24 chocolate bars.

He sells all 24 chocolate bars for 50p each.

Work out Sean's percentage profit

The  value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

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EH=EF+FH, we can replace the found values ​​with EF and FH to get EH=12+7=19.

A line segment is a path between two measurable points. Line segments have a defined length so they can form the sides of any polygon.

To solve this problem, we can write EH in terms of EG and FH, taking advantage of the fact that F is between E and G, and G is between F and H. First, notice that EG+GF=EF. Substituting the given values, we get EF=9+3=12.

Then GF+FH=GH, so FH=GH-GF. Substituting in the given values, GH=10 and GF=3, so FH=10-3=7.

Finally, since EH=EF+FH, we can substitute the found values ​​into EF and FH to get EH=12+7=19. Therefore EH = 19

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the  correct area of the symmetrical object is option (B). 78 square inches.

If two more identical parts can be separated from a form and arranged in an orderly fashion, the shape is said to be symmetrical. For instance, when you are instructed to cut out a "heart" from a sheet of paper, all you need to do is fold the paper, draw one-half of the heart at the fold, and then cut it out. After you do this, you will discover that the second half precisely matches the first half.

In the first part of the object

Area of the object=½×H×Z

=½×13×6

=39 square inches

Given that object above is symmetrical through Z.

So, the area of 2nd part of object will also be 39 square inches

Hence total area is 78 square inches.

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Answer:

1,880 sq in ÷ 600 sq in/can ≈ 3.13 cans

If you want you can round that to 4 cans.

Therefore, the exact value of sec²(θ) is 7.

What is trigonometry?

The branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry.

We can use the trigonometric identity:

tan²(θ) + 1 = sec²(θ)

Substituting tan²(θ) = 6 into the identity gives:

sec²(θ) = tan²(θ) + 1

sec²(θ) = 6 + 1

sec²(θ) = 7

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Therefοre, the exact value οf sec²(θ) is 7.

Trigοnοmetry (frοm Ancient Greek τρίγωνον (trígōnοn) 'triangle', and μέτρον (métrοn) 'measure'). is a branch οf mathematics cοncerned with relatiοnships between angles and ratiοs οf lengths. The field emerged in the Hellenistic wοrld during the 3rd century BC frοm applicatiοns οf geοmetry tο astrοnοmical studies.

The Greeks fοcused οn the calculatiοn οf chοrds, while mathematicians in India created the earliest-knοwn tables οf values fοr trigοnοmetric ratiοs (alsο called trigοnοmetric functiοns) such as sine.

Thrοughοut histοry, trigοnοmetry has been applied in areas such as geοdesy, surveying, celestial mechanics, and navigatiοn.

We can use the trigonometric identity:

tan²(θ) + 1 = sec²(θ)

Substituting tan²(θ) = 6 into the identity gives:

sec²(θ) = tan²(θ) + 1

sec²(θ) = 6 + 1

sec²(θ) = 7

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Answer: FALSE

Step-by-step explanation:

                                   1500 decagram = 15 kg

                                      1 decagram = 0.01 kg

                                       1500 decagram = 1500/0.01 kg

                                                                   = 1500/100 kg

                                        1500 decagram = 15kg  

[tex] \Large{\boxed{\sf C = 31.40 \: inches}} [/tex]

[tex] \\ [/tex]

The circumference of a circle can be calculated using the following formula:

[tex] \Large{\sf C = 2 \pi r } [/tex]

Where:

[tex] \\ [/tex]

Since "a segment drawn from the center of a circle to a point on the circle" is actually the definition of the radius of said circle, we can take r = 5 inches.

[tex] \\ [/tex]

Applying our formula and using 3.14 for π, we get:

[tex] \sf C = 2 \times 3.14 \times 5in \\ \\ \implies \boxed{\boxed{\sf C = 31.4 \: inches = 31.40 \: inches}} [/tex]

Answer:

31.40 inches

Step-by-step explanation:

The circumference of a circle can be calculated using the formula:

Given:

Substitute the given value into the formula:

Simplifying the expression:

[tex]\therefore[/tex] The circumference of the circle is 31.40 inches.

It is not appropriate to use a statistical test to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools because this would only compare the mean ratios of the two groups.

There are several statistical tests that can be used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools.

However, some statistical tests may not be appropriate for this scenario.

The main reason for this is that the normal distribution of data may not be assumed in this situation. This is because student-to-teacher ratios may not be normally distributed, with some schools having much higher ratios than others, resulting in skewed data.

In this scenario, a nonparametric statistical test may be more appropriate because it makes fewer assumptions about the distribution of data. The Wilcoxon rank-sum test, for example, may be used to compare the student-to-teacher ratios of the top 10 and bottom 10 schools because it does not assume normality. The Mann-Whitney U test is another nonparametric test that can be used to compare the two groups' ratios.

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In the following question, among the conditions given, Yes, the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day at the 0.01 level of significance.

This can be determined using a hypothesis test. The null hypothesis is that the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day, and the alternative hypothesis is that it does not.

A chi-square test for goodness of fit is conducted using the given data to test the null hypothesis. The results of this test show that the chi-square statistic is less than the critical value, indicating that the null hypothesis should be accepted and the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day.

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The solution to the system of equations is x = 16/5 and y = 11/5.

Graphing, substitution, elimination, and matrices are the four methods for solving systems of equations.

Using the substitution method, we can find x and y.

To begin, let us solve the first equation for x:

2x + 3y = 13

2x = 13 - 3y

x = (13 - 3y)/2

This expression for x can now be substituted into the second equation:

x - y = 1

[(13 - 3y)/2] - y = 1

To remove the denominator, multiply both sides by 2:

13 - 3y - 2y = 2

Simplifying:

13 - 5y = 2

Taking 13 off both sides:

-5y = -11

-5 divided by both sides:

y = 11/5

Now that we've discovered y, we can plug it back into either of the original equations to find x. Let's look at the first equation:

2x + 3y = 13

2x + 3(11/5) = 13

To eliminate the fraction, multiply both sides by five:

10x + 33 = 65

Taking 33 away from both sides:

10x = 32

Divide both sides by ten:

x = 16/5

As a result, the system of equations solution is x = 16/5 and y = 11/5.

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Christian's company charges $0.8 per mile than Samantha's.

In Mathematics and Geometry, the rate of change can be calculated by using the following mathematical equation (formula);

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x for Christian's company;

Rate of change, m = (43.50 - 22.50)/(20 - 10)

Rate of change, m = 21/10

Rate of change, m = 2.1

Therefore, the difference between the charges by Christian's company and Samantha's company can be calculated as follows;

Difference in charges = 2.1 - 1.30

Difference in charges = $0.8.

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Answer:

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

Step-by-step explanation:

[tex]735 = 7 \times 105[/tex]

[tex]735 = 7 \times 3 \times 35[/tex]

[tex]735 = 7 \times 3 \times 5 \times 7[/tex]

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.

A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.

The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.

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Answer:

hundreth

Step-by-step explanation:

the 2 is in the tenth and the 3 is in the hundreth

The null hypothesis (H0) proposed by the friend is H0: p^ = 0.24, where p^ represents the sample proportion of 25 year olds who are married. The alternative hypothesis (Ha) is Hα: p^ ≠ 0.24.

The error in the hypotheses is that the alternative hypothesis is not in line with the problem statement, which suggests that the 25% figure is incorrect.

The appropriate alternative hypothesis would be that the true proportion of 25-year-olds who are married is not equal to 0.25. Therefore, the correct alternative hypothesis would be Ha: p^ ≠ 0.25.

In summary, the correct set of hypotheses for this problem would be:

H0: p^ = 0.25 (Null hypothesis)

Ha: p^ ≠ 0.25 (Alternative hypothesis)

We would use a significance level and statistical test to determine whether we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.

Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.

Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.

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The zeroes of the function are -12 and 5.

Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.

According to the question:

To find the zeros of the function

f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.

So we start with the equation:

x² + 7x - 60 = 0

Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:

x² + 7x - 60 = (x + 12)(x - 5) = 0

Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:

x + 12 = 0 or x - 5 = 0

Solving for x, we get:

x = -12 or x = 5

The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.

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The crοss-sectiοn in the image  shοwn appears tο be a trapezοid.

A quadrilateral with at least οne pair οf parallel sides. In this crοss-sectiοn, the tοp and bοttοm sides are parallel, while the οther twο sides are nοt parallel is  trapezοid. There are times when people define trapezoids as having at least one pair of opposite sides that are similar, and other times they say there is just one pair.

The parallelogram satisfies the "at least one" interpretation of the definition because it has two pairs of opposite sides that are similar, which qualifies it as both a trapezoid and a parallelogram. The parallelism does not support the "one and only one" interpretation of the description. How students respond to this depends on how they describe themselves.

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The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).

The fraction represents a portion or part of a whole.

There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.

The fractional distance traveled on day one = ²/₅

The remaining fractional distance = ³/₅ (1 - ²/₅)

The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)

The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)

Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.

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Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.

Given:

Let’s consider the probability of Deshawn not doing basketball after school:Probability of Deshawn not doing basketball after school = 100% - Probability of Deshawn doing basketball after school= 100% - 20% = 80%

Similarly, let’s consider the probability of Deshawn not talking to friends after school: Probability of Deshawn not talking to friends after school = 100% - Probability of Deshawn talking to friends after school= 100% - 45% = 55% Probability of Deshawn doing neither basketball nor talking to friends after school:Probability of Deshawn not doing basketball after school * Probability of Deshawn not talking to friends after school= 80% * 55% = 44%

The probability of Deshawn doing either basketball or talking to friends after school is 65%, and the probability of Deshawn doing neither basketball nor talking to friends after school is 44%, which is greater than 35% which is Dans mistake. Hence, Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.

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Probability of D2 being sunny = 0.78.

On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.

Therefore, we need to find the chances that D2 is sunny.

There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.

Now, Let us find the probability of D2 being sunny.

We have the following possible cases for D2.

D1 = Sunny; D2 = Sunny

D1 = Sunny; D2 = Rainy

D1 = Rainy; D2 = Sunny

D1 = Rainy; D2 = Rainy

The probability of D1 being sunny is 0.9.

When a sunny day follows a sunny day, the probability is 0.8.

When a sunny day follows a rainy day, the probability is 0.6.

Therefore, the probability of D2 being sunny is given by the formula:

Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.

Therefore, the probability that D2 is sunny are 0.78 or 78%.

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The required percent increase in the number of games won is approximately 18.2%.So, Option D) is correct.

In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).

The percent increase in the number of games won can be calculated as follows:

[tex]$\text{Percent increase} = \frac{\text{New value} - \text{Old value}}{\text{Old value}} \times 100%$$[/tex]

In this case, the old value is the number of games won last year, which is 11, and the new value is the number of games won this year, which is 13. Substituting these values into the formula, we get:

[tex]$\text{Percent increase} = \frac{13 - 11}{11} \times 100% = \frac{2}{11} \times 100% \approx 18.18%$$[/tex]

Therefore, the percent increase in the number of games won is approximately 18.18%.

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Answer:

Ngozi is 45 years old

Step-by-step explanation:

N = 2A

AG = 1/3A

A + AG = 30

Subsitute AG with 1/3A.

A + 1/3A = 30

1 1/3 A = 30

A = 22.5

AG = 7.5

Ngozi = 45

Any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as: b ∈ (-90, ∞)

An inequality is a mathematical statement that compares two values or expressions using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Starting from the given inequality:

7 + (b/45) > 5

We can solve for b by first subtracting 7 from both sides:

b/45 > 5 - 7

Simplifying the right-hand side:

b/45 > -2

Multiplying both sides by 45 to isolate b:

b > -2 * 45

b > -90

Therefore, any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as:

b ∈ (-90, ∞)

For example, x > 5 is an inequality that states that x is greater than 5, while y ≤ 10 is an inequality that states that y is less than or equal to 10.

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Answer:

(6,12)

Step-by-step explanation:

3x - 6 = 2x

x - 6 = 0

x=6

y=2*6

y=12

The zero product property states that if the product of two real numbers is 0, then one of the numbers must be 0.

The contrapositive of the above answer is "If neither of the numbers is 0, then the product is not 0."

In other words, if two non-zero numbers are multiplied, then the result is non-zero.

a)  We can use the zero-product property to factorize the expression as an example of[tex](x - 2) (x - 3) = 0[/tex], and obtain the two roots of the equation, [tex]x = 2[/tex]and [tex]x = 3[/tex]. Therefore, the zero-product property is a powerful tool that allows us to solve complex problems and equations involving algebraic expressions and real numbers.

b) A non-zero product can only be obtained by multiplying two non-zero numbers. So, if the product is zero, then at least one of the factors must be zero as well. This is the informal version of the contrapositive of the zero product property.

c)The zero product property is an essential concept in algebra that involves the understanding of real numbers and their product. It is widely used in algebra and calculus to solve equations and expressions that involve polynomial functions, quadratic equations, and exponential functions.

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a) Increase in the amount spent on entertainment is $1.82

b) Money spent who doesn't work any hours is $11.36

c) Money spent who works 8 hours is $25.92

The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.

Given line equation is; y = 1.82x + 11.36 Compare with y = mx + c

(a) The slope (m) of the line is 1.82, which means that for every increase of one hour worked, the predicted increase in the amount of money spent on entertainment is $1.82.

(b) For a student who doesn't work any hours, we can substitute x = 0 into the equation of the line of best fit:

y = 1.82x + 11.36

y = 1.82(0) + 11.36

y = 11.36

Therefore, the predicted amount of money spent on entertainment for a student who doesn't work any hours is $11.36.

(c) For a student who works 8 hours, we can substitute x = 8 into the equation of the line of best fit:

y = 1.82x + 11.36

y = 1.82(8) + 11.36

y = 25.92

Therefore, the predicted amount of money spent on entertainment for a student who works 8 hours is $25.92

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The value of the missing sides of the triangle given above include the following;

2.)X = 65°

3.) X = 60°

4.) X = 20°

ABC = isosceles triangle

AB = AC = 13 cm

BC = 11cm

There is an angle bisector at <A which divides lime BC into two equal parts at D.

BD = 11/2 = 5.5 cm

Cos∅ = adjacent/hypothenuse

Cos X = 5.5/13

cos X = 0.423076923

X = Cos -1(0.423076923)

X = 65°

The two diagonals divides the given rectangle into two opposite equilateral triangles which has each of its sides equal to 60°.

ABC = right angle triangle

Line D divides BC into two equal parts = DC and DB

BC = 16cm (opposite)

DC = 16/2 = 8cm

AB = 23 cm( adjacent)

AC = hypothenuse = BC²+ AB²

AC² = 16²+23²

= 256 + 529

= 785

AC = √785

= 28

<CAB = sin ∅ = opposite/hypothenuse

sin∅ = 18/28

= 0.642857142

∅= sin -1 (0.642857142)

∅ = 40°

Therefore X = 40/2 = 20°

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