In 1999 the minimum wage for adults was £3.60 per hour.
In 2013 it was £6.31 per hour.
Work out the percentage increase in the minimum wage.

To find the mean of the given frequency distribution of quiz completion times, we need to calculate the weighted average of the data. The mean represents the average time taken by the students to complete the quiz.

In this case, the frequency distribution provides the number of students falling within different time intervals. We can calculate the mean by multiplying each time interval midpoint by its corresponding frequency, summing up these values, and dividing by the total number of students.

Calculating the weighted average, we have:

Mean = (1 * 3 + 3 * 6 + 5 * 20 + 8 * 8) / (3 + 6 + 20 + 8) = 133 / 37 ≈ 3.59 minutes.Therefore, the mean completion time for the statistics quiz is approximately 3.59 minutes. This indicates that, on average, students took around 3.59 minutes to complete the quiz based on given frequency distribution.

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The expression is undefined when t equals 8.

To find the excluded values for the expression 7t - 6/t - 8, we need to look at the denominator of the fraction, which is t - 8. This fraction is undefined when the denominator equals zero.

Setting t - 8 equal to zero, we get:

t - 8 = 0

t = 8

Therefore, the expression is undefined when t equals 8.



The expression 7t - 6/t - 8 has an excluded value at t = 8. This is because the denominator of the fraction, t - 8, becomes zero when t equals 8. In order for a fraction to be defined, the denominator must not equal zero. Therefore, we need to find all values of t that make the denominator zero. By solving the equation t - 8 = 0, we find that t = 8 is the only value that makes the denominator zero.



The excluded value for the expression 7t - 6/t - 8 is t = 8.



The expression 7t - 6/t - 8 has a fraction with denominator t - 8. For the fraction to be defined, the denominator must not equal zero. Therefore, we need to find all values of t that make the denominator zero.

To do this, we set the denominator equal to zero and solve for t:

t - 8 = 0

t = 8

Therefore, the expression is undefined when t equals 8.

To see why this is the case, let's consider what happens when we substitute t = 8 into the expression:

7t - 6/t - 8

= 7(8) - 6/8 - 8

= 56 - 6/8 - 8

= 56 - 0.75 - 8

= 47.25

However, if we look at the denominator of the fraction, t - 8, we see that it equals zero when t equals 8. This means that we cannot divide by zero, and the expression is undefined when t equals 8.

In summary, the excluded value for the expression 7t - 6/t - 8 is t = 8, as this is the only value that makes the denominator of the fraction equal to zero.

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

x>6

Step-by-step explanation:

hopefully the answer is clear and understandable.

:)

the expression equivalent to 2x + 8 is (x+4) + (x+4)

using the commutative property we can say that

2x +8 = x + x + 8

also 2x + 8 = x + 4 + x + 4

hence 2x + 8 = (x+4) + (x+4)

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Skewness of the normal distribution. When it comes to normal distribution, the skewness is equal to zero.

Skewness is a measure of the distribution's symmetry. When a distribution is symmetric, the mean, median, and mode will all be the same. When a distribution is skewed, the mean will typically be larger or lesser than the median depending on whether the distribution is right-skewed or left-skewed. It is not appropriate to discuss mean or median in the case of normal distribution since it is a symmetric distribution.

Therefore, the answer is None of the above.

In normal distribution, the skewness is equal to zero, and it is not appropriate to discuss mean or median in the case of normal distribution since it is a symmetric distribution.

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The price vectors a. p₁ = 3 and p₂ = 2, Mary will consume only good 1.

Here we have the Utility function as

U(x₁ , x₂) = 3x₁ + x₂

From the given utility function we can clearly see that these goods are substitutes for each other

Now,

δU/δx₁ = 3

δU/δx₂ = 1

Hence we get the Marginal Rate of Substitution or MRS

\(=- \frac{\delta U/ \delta x_1 }{\delta U/ \delta x_2}\)

= -3

The MRS signifies that for every additional unit of 1, Mary is willing to give up 3 units of good 2

|MRS| = 3

For Mary to only consume good 1, |MRS| > p₁/p₂

Hence here we get the p/p ratio for the 4 price vectors to be

a. 3/2 = 1.5

b. 10/3 = 3.33

c. 4

d. 15.4 = 3.75

Hence we can clearly say that for the price vectors p₁ = 3 and p₂ = 2, Mary will consume only good 1.

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Answer:

3

Step-by-step explanation:

Answer:

18 N

Step-by-step explanation:

Let F denote the force, m denote the mass of the object and a denote the acceleration of the object.

\(F=ma\)

\(m = \frac{F_{1} }{a_{1} }=\frac{63}{7} =9 kg\)

\(F_{2} =ma_{2}=9*2=18N\)

Answer:

rise : atmospheric pressure increases

fall : atmospheric pressure decreases

Step-by-step explanation:

In the context, it is given that a weather forecaster takes the help of the barometer to check the air pressure and predicts the weather. The column of mercury level in the barometer shows a rise or fall in the glass tube as the weight of the atmosphere falling on the mercury surface changes.

Here it is given that the mercury rises for 0.02 in, then it falls 0.09 in,  it then rises by 0.07 in and then again falls by 0.18 in. The word "rise" here shows that the weight of the atmosphere is more. In other words, increase in atmospheric pressure increases the level of mercury in the glass tube and the decrease in or "fall" in the mercury level shows the drop in atmospheric pressure.

The 95% confidence interval for p is .52 to .68.(C)

To find the 95% confidence interval for p, we will use the formula: CI =p-cap ± Z * √(p-cap * (1 - p-cap) / n), where p-cap is the sample proportion, Z is the Z-score for 95% confidence level, and n is the number of observations.

1. Calculate p-cap: In this case, p-cap = 0.6
2. Determine Z: For a 95% confidence interval, Z = 1.96 (from Z-table)
3. Calculate the standard error: SE = √(p-cap * (1 - p-cap) / n) = √(0.6 * (1 - 0.6) / 144) ≈ 0.0408
4. Calculate the margin of error: ME = Z * SE = 1.96 * 0.0408 ≈ 0.08
5. Find the confidence interval: CI = p-cap ± ME = 0.6 ± 0.08 = (0.52, 0.68)

Therefore, the 95% confidence interval for p is .52 to .68.

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Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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The length of IJ in ΔHIJ is approximately 2.8 feet when rounded to the nearest tenth of a foot.

To find the length of IJ in ΔHIJ, we can use trigonometric ratios. In this case, we can use the tangent function since we know the measure of angle I and the length of side HI.

Using the tangent function, we can set up the equation: tan(I) = IJ/HI. Rearranging the equation, we have IJ = HI * tan(I).

In this scenario, I = 26° and HI = 5.7 feet. Substituting these values into the equation, we can calculate the length of IJ.

Calculate the tangent of angle I: tan(26°) ≈ 0.4877.

Multiply the tangent value by the length of HI: 5.7 feet * 0.4877 ≈ 2.7777 feet.

Therefore, the length of IJ in ΔHIJ is approximately 2.8 feet.

Using the given information, we can apply trigonometry to find the length of side IJ. In a right triangle, the tangent function relates the angle I to the ratio of the lengths of the opposite side (IJ) and the adjacent side (HI).

First, we find the tangent of angle I by using the given measure: tan(26°). This gives us the ratio of IJ to HI.

Next, we substitute the known values: HI = 5.7 feet. By multiplying HI with the tangent of angle I, we get the length of IJ.

In this case, tan(26°) ≈ 0.4877. Multiplying this by HI = 5.7 feet, we find that IJ ≈ 2.7777 feet.

Therefore, the length of IJ in ΔHIJ is approximately 2.8 feet when rounded to the nearest tenth of a foot.

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The first term of the arithmetic sequence is -8, and the general formula for the nth term is given by Tn = 24 - 10n.

To find the first term of the arithmetic sequence, we can use the formula Tn = a + (n - 1)d, where Tn represents the nth term, a represents the first term, n represents the term number, and d represents the common difference. We are given that the twelfth term (T12) is 118 and the eighth term (T8) is 146. Using these values, we can set up two equations:

T12 = a + 11d = 118

T8 = a + 7d = 146

Solving these equations simultaneously, we can find the values of a and d. Subtracting the second equation from the first equation, we get:

a + 11d - (a + 7d) = 118 - 146

4d = -28

d = -7

Substituting the value of d back into either equation, we find:

a + 7(-7) = 146

a - 49 = 146

a = 146 + 49

a = 195

Therefore, the first term of the arithmetic sequence is -8.

To find the general formula for the nth term, we can use the values of a and d in the formula Tn = a + (n - 1)d. Substituting the values, we have:

Tn = -8 + (n - 1)(-7)

Tn = -8 - 7n + 7

Tn = -1 - 7n

Thus, the general formula for the nth term is Tn = -1 - 7n.

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Answer:

110.09174

Step-by-step explanation:

120yd/1.09meters per yard=110.09174...

The answer needs to be rounded to whatever decimal place is called for.

a. Using the calculated z-score, the probability that a randomly chosen bolt has a width between 941 and 957 mm is approximately 0.5558.

b. The appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749 is approximately 963.5 mm.

(a) To find the probability that a randomly chosen bolt has a width between 941 and 957 mm, we can use the z-score formula and the standard normal distribution.

First, let's calculate the z-scores for the given values using the formula:

z = (x - μ) / σ

where:

For x = 941:

z₁ = (941 - 952) / 10 = -1.1

For x = 957:

z₂ = (957 - 952) / 10 = 0.5

Next, we need to find the probabilities corresponding to these z-scores using a standard normal distribution table or a calculator.

Using the standard normal distribution table, we find:

P(z < -1.1) ≈ 0.135

P(z < 0.5) ≈ 0.691

Since we want the probability of the width falling between 941 and 957, we subtract the two probabilities:

P(941 < x < 957) = P(-1.1 < z < 0.5) = P(z < 0.5) - P(z < -1.1) ≈ 0.691 - 0.135 = 0.5558

Therefore, the probability that a randomly chosen bolt has a width between 941 and 957 mm is approximately 0.5558.

(b) To find the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749, we need to find the z-score corresponding to this probability.

Using a standard normal distribution table or calculator, we find the z-score corresponding to a cumulative probability of 0.8749 is approximately 1.15.

Now, we can use the z-score formula to find the value of C:

z = (x - μ) / σ

Substituting the known values:

1.15 = (C - 952) / 10

Solving for C:

C - 952 = 1.15 * 10

C - 952 = 11.5

C ≈ 963.5

Therefore, the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749 is approximately 963.5 mm.

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The correct model to support the claim that more than 70% of students at De Anza College will transfer is the One sample Z test of proportion.

To determine whether more than 70% of students at De Anza College will transfer, we need to compare the proportion of students who transfer in a sample to the claimed proportion of 70%. Since we have a sample size of 450 students, the One sample Z test of proportion is appropriate.

The One sample Z test of proportion is used to compare a sample proportion to a known or hypothesized proportion. In this case, the known or hypothesized proportion is 70%, and we want to test if the proportion in the sample is significantly greater than 70%. The test involves calculating the test statistic, which follows a standard normal distribution under the null hypothesis.

By conducting the One sample Z test of proportion on the sample of 450 students, we can calculate the test statistic and determine whether the proportion of students who transfer is significantly different from 70%. If the test statistic falls in the critical region, we can reject the null hypothesis and support the claim that more than 70% of students at De Anza College will transfer.

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Answer:

60 pie

Step-by-step explanation:

The calculated value of the side length in the triangle is 144

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

The simiar triangles

Using the theorem of corresponding sides, we hav

GH = 2JK

So, we have

10x - 36 = 2 * 4x

Multiply

So, we have

10x - 36 = 8x

Evaluate

2x = 36

So, we have

x = 18

This means that

GK = 4 * 18

GK = 144

Hence, the indicated side length in the triangle is 144

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Answer:

Step-by-step explanation:

To increase the difference between 456.674 and 234.458 by 345.856, we follow the following steps :

Step 1: Subtract 456.674 from 234.458 and,

Step 2:  Add 345.856 to the result.

so,  456.674 - 234.458 = 222.216

222.216 + 345.856 = 568.072

Therefore, the increased difference between 456.674 and 234.458 by 345.856 is 568.072

The solution to the initial value problem y' = 2yx, y(1) = 1/4 is  \(y = (1/(4e)) * e^(^x^2^)\)

To find the solution, follow these steps:

Step 1: Identify the given differential equation and initial condition.
The differential equation is y' = 2yx, and the initial condition is y(1) = 1/4.

Step 2: Separate variables.
Divide both sides of the equation by y to isolate dy/dx:

(dy/dx) / y = 2x

Now, multiply both sides by dx to separate the variables:

(dy/y) = 2x dx

Step 3: Integrate both sides.
Integrate the left side with respect to y, and the right side with respect to x:

\(∫(1/y) dy = ∫(2x) dx\)

ln|y| = x^2 + C₁ (Remember to add the constant of integration, C₁)

Step 4: Solve for y.
To remove the natural logarithm, take the exponent of both sides:

\(y = e^(x^2 + C₁)\)

We can rewrite this as:

\(y = e^(^x^2^) * e^(^C^_1)\)
Since e^(C₁) is also a constant, let C = e^(C₁):

\(y = C * e^(^x^2^)\)

Step 5: Apply the initial condition to find the constant C.
Use the initial condition y(1) = 1/4 and substitute x = 1:

1/4 = C * e^(1^2)

1/4 = C * e

Now, solve for C:

C = 1/(4e)

Step 6: Write the solution.
Substitute the value of C back into the equation for y:

\(y = (1/(4e)) * e^(^x^2^)\)

This is the solution to the initial value problem y' = 2yx, y(1) = 1/4.

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The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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(a) The equilibrium points are x = -0.805 and x = 0.

(b) \(f'(x) = 9e^{((-0.6x) (1 - 0.6x))}\)

(c)  f'(P1) is approximately 3.905 and f'(P2) is 0.

a) Equilibrium points are the values of x such that f(x) = x. Therefore, we have:

\(9xe^{(-0.6x)} = x\)

Dividing both sides by x and multiplying by e^(0.6x), we get:

\(9e^{(0.6x)} = 1\)

Taking the natural logarithm of both sides, we get:

0.6x = ln(1/9)

x = ln(1/9) / 0.6 ≈ -0.805; x = 0

Therefore, the equilibrium points are x = -0.805 and x = 0.

b) Taking the derivative of f(x) with respect to x, we get:

f'(x) = 9e^(-0.6x) (1 - 0.6x)

c) Evaluating f'(P1) and f'(P2), we get:

f'(P1) = \(9e^{(-0.6P1) (1 - 0.6P1)}\) ≈ 3.905

f'(P2) = \(9e^{(-0.6P2) (1 - 0.6P2)}\) = 0

Therefore, f'(P1) is approximately 3.905 and f'(P2) is 0.

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The total number of possible combinations of numbers and letters on the license plates: 10 * 9 * 8 * 26 * 26 * 26

For the first number on the license plate, there are 10 options (0-9). For the second number, there are 10 options again, but since the numbers cannot be repeated, only 9 options are available. Similarly, for the third number, there are 10 options initially, but since the numbers cannot be repeated, only 8 options remain.

For the letters, there are 26 options for each position (first letter, second letter, and third letter) since all 26 letters of the alphabet can be used. The letters can be repeated, so there are no restrictions on the number of options for each letter.

To calculate the total number of different license plates, we multiply the number of options for each position together: 10 * 9 * 8 * 26 * 26 * 26. This gives us the total number of possible combinations of numbers and letters on the license plates.

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Answer:

9.4

Step-by-step explanation:

a2+b2=c2

8^2 + 5^2 = c2

64 + 25 = 89

square root of 89 = 9.4