Ben is paid £9.60 per hour.
If he works for more than 7 hours in a day, he is paid overtime for the additional hours at a rate of 1.5 times his normal rate of pay.
Yesterday, Ben worked for 12 hours.
How much money did he earn

Normal curve A normal curve is a bell-shaped curve that represents the probability distribution of a random variable. It's symmetrical and centered around the mean. It's commonly used in statistics because many real-world phenomena follow this pattern.

Here is an example of a normal curve:b) Critical values and rejection regions for hypothesis tests using z-table or t-table:1. Right-tail test,\(n=20, σ=4.7, α=0.05\)First, we need to find the critical value for a right-tail test with \(α=0.05\)and 19 degrees of freedom (n-1) using the t-table. The critical value is 1.7291. Because it's a right-tail test, we only need to shade the rejection region in the right tail of the curve.

The critical value is \(±1.7109\). Because it's a two-tail test, we need to shade the rejection regions in both tails of the curve. The rejection regions are to the left of -1.7109 and to the right of 1.7109. Here is a graphical representation of the test

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

yes, Send me your questions

Answer: 15 DVDs

Step-by-step explanation:

C = 2D + 11

41 = 2D + 11

2D = 30

D = 15 DVDs

One-half of the dogs in each shelter are between the weights represented by the first and third quartiles, which are approximately 20-55 pounds for the first shelter and 25-65 pounds for the second shelter, respectively.

A box plot is a visual representation of a set of data that shows the median, quartiles, and outliers of the data. The box represents the middle 50% of the data, with the bottom and top edges of the box representing the first and third quartiles, respectively. The line inside the box represents the median, or the middle value of the data set. The "whiskers" extend from the edges of the box to the minimum and maximum values of the data set, but outliers beyond the whiskers are represented as individual points.

Now, let's look at the two box plots showing the weights of dogs in two different animal shelters. One-half of the dogs in each shelter are between the first and third quartiles, which are represented by the edges of the box in each plot.

If we take the first box plot, we can see that the first quartile is approximately 20 pounds and the third quartile is approximately 55 pounds. Therefore, one-half of the dogs in this shelter weigh between 20 and 55 pounds.

To know more about shelter visit:-

https://brainly.com/question/14394978

#SPJ11

Answer:

Geometric sequence

Step-by-step explanation:

Because this is not adding or subtraction, but multiplication, this would be a geometric sequence.

Answer:

x=8

Step-by-step explanation:

2x+7 = 23

2x=16

x=8

Answer:

4.69

Step-by-step explanation:

13.76/4 +1.25

The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

Learn more about Normal Distribution at https://brainly.com/question/27701525

#SPJ4

The statement is False" Some seventh graders" isn't a set.

we know, set is a well- defined collection of distinct objects, which are appertained to as rudiments or members of the set.

For illustration, consider the set A = { 1, 2, 3}. This set contains the rudiments 1, 2, and 3.

It's a expression that describes a group of individualities without furnishing a well- defined collection of rudiments.

A set is a well- defined collection of distinct objects.

To represent a set, we generally use curled braces and list the rudiments within the set.

For illustration,{ 1, 2, 3} is a set containing the rudiments 1, 2, and 3.

Learn more about Set here:

https://brainly.com/question/8053622

#SPJ1

Answer:

4) 10

Step-by-step explanation:

The number with x is slope and the other number is y-intercept so it's 10

The supply of loanable funds in the country is equal to national saving, government expenditures, domestic investment and net capital outflow added up and is 140 billion.

The supply of loanable funds in a country is the total amount of money available for lending. This is calculated by adding National Saving, Government Expenditures, Domestic Investment and subtracting Net Capital Outflow. In this case, National Saving is $80 billion, Government Expenditures are $40 billion, Domestic Investment is $50 billion and Net Capital Outflow is $30 billion. Thus, the Supply of Loanable Funds is equal to $140 billion. National Saving refers to the amount of income that is not spent by the people of a country and is saved instead. Government Expenditures are all the money that the government spends. Domestic Investment is the amount of money that is invested within a country. Finally, Net Capital Outflow is the difference between total capital inflows and total capital outflows from a country. Therefore, by adding National Saving, Government Expenditures, Domestic Investment and subtracting Net Capital Outflow, the Supply of Loanable Funds is equal to $140 billion.

Supply of loanable funds = National Saving + Government Expenditures + Domestic Investment - Net Capital Outflow

= 80 + 40 + 50 - 30

= 140 billion

Learn more about expenditureshere

https://brainly.com/question/18250434

#SPJ4

The highest temperature recorded was 415°F(maximum).

At its lowest, the temperature is 385°F(minimum).

The function of absolute value calculates the separation between a point and an origin.

A less-than-compound inequality is represented by:

\( |x| \leq a\)

then the solution is

\( - a \leq \: x \: \leq \: a\)

according to the question

Temperature T is set to 400°F with a tolerance of 15°F, meaning that the absolute difference between T and 400°F may not be greater than 15°F; in other words:

\( |T - 400| \leq \: 15\)

now apply the solution

\( - 15 \leq \: T - 400 \leq \:15\)

then simplify this

\(T - 400 \ge \: - 15 \\ T \geq \: - 15 + 400 \\ T \geq \: 385\)

\(T - 400 \leq \: 15 \\ T \leq \: 15 + 400 \\ T \leq \: 415\)

Hence, The highest temperature recorded was 415°F(maximum).

At its lowest, the temperature is 385°F(minimum).

Learn more about finding temperature from here:

https://brainly.com/question/25677592

#SPJ4

Answer:

(4t - 8/5) - (3 - 4/3t) = 16/3t - 23/5

5(2t + 1) + (-7t + 28)= 3t+33

(-9/2t +3) + (7/4t + 33) = -11/4c+56

3 (3t-4) - (2t + 10)= 7t -22

Sooo Sorry that it took soooo long! Hope this helps!!!

Happy holidays!!

The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

To know more about the factors affecting the demand for good X, refer here:

https://brainly.com/question/32566433#

#SPJ11

Answer:

0

Step-by-step explanation:

\(m=\frac{-21-(-21)}{-14-36}\)

Answer: slope = 0  

Step-by-step explanation:

slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0

It's a horizontal line

The selling price for the flat-screen TV for Thomas is $245.1. Here the total percentage of discount for him is 43%.

The formula for finding the selling price with a percentage of discount is

Selling price = Original price - original price × discount (in decimal)

It is given that,

Thomas receives a discount for flat screen tv on a sale = 33%

He also receives an additional discount on all merchandise at the store where he works = 10%

The original price of the TV is $430.

So, the total discount percentage = 33% + 10% = 43% = 0.43 (in decimal)

Then, the selling price of the tv for him is,

Selling price = Original price - original price × discount (in decimal)

                     = $430 - $430 × 0.43

                     = $430 - $184.9

                     = $245.1

Therefore, Thomas's selling price for the flat-screen tv is $245.1.

Learn more about calculating the selling price with a discount percentage here:

https://brainly.com/question/7459025

#SPJ1

9514 1404 393

Answer:

  y +6 = (-1/3)(x +6)

Step-by-step explanation:

Given a point and a slope, it is appropriate to use the point-slope form to represent the equation:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

For your point and slope, the equation is ...

  y -(-6) = -1/3(x -(-6))

  y +6 = -1/3(x +6)

__

Of course, this can be rearranged to whatever form you need.

  y = -1/3x -8 . . . . slope-intercept form

  x +3y = -24 . . . . standard form

In the n-Firm Cournot Model, where there are n≥2 firms, each firm determines the quantity it produces in a Cournot oligopoly. The aggregate production level, denoted as Q, is the sum of the quantities produced by all the firms (q1+⋯+qn).

To represent this game as a static game with complete information, we can use the normal-form representation. In the normal-form representation, we describe the strategies and payoffs of each firm.

Let's go through the steps to create the normal-form representation of this game:

1. Identify the players: In this case, the players are the n firms participating in the Cournot oligopoly.

2. Determine the strategies: Each firm chooses the quantity it will produce, denoted by qi, where i represents the firm number. The quantity produced by each firm is the strategy of that firm.

3. Define the payoff function: The payoff for each firm depends on the market price, which is determined by the aggregate production level Q. The market price, P(Q), is given by the demand function P(Q) = a - Q.

4. Calculate the payoff for each firm: The payoff for each firm depends on the quantity it produces and the market price determined by the aggregate production level. The payoff can be calculated using the formula πi = P(Q) * qi, where πi represents the payoff for firm i.

5. Construct the normal-form representation: The normal-form representation is typically presented as a matrix, where each row represents a strategy profile (combination of quantities produced by the firms) and each column represents a player's strategy (quantity produced by a single firm). The entries in the matrix represent the payoffs for each firm.

For example, let's consider a 3-firm Cournot oligopoly with demand function P(Q) = a - Q. Firm 1, 2, and 3 have the strategies q1, q2, and q3, respectively. The payoffs can be calculated as follows:

- Payoff for firm 1: π1 = (a - Q) * q1
- Payoff for firm 2: π2 = (a - Q) * q2
- Payoff for firm 3: π3 = (a - Q) * q3

The normal-form representation matrix would look like this:

| Firm 1\2\3 | q1     | q2     | q3     |
|------------|--------|--------|--------|
| q1         | π1,1   | π1,2   | π1,3   |
| q2         | π2,1   | π2,2   | π2,3   |
| q3         | π3,1   | π3,2   | π3,3   |

Each entry in the matrix represents the payoff for each firm based on the combination of quantities produced by the firms.

To know more about payoff function refer to:

https://brainly.com/question/32760850

#SPJ11

Answer:

# equel x to get 6 to get13

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

the partial derivatives are ∂p/∂u = 6 + (∂p/∂z), ∂r/∂u = 1, and ∂θ/∂u = 0 when p=1, r=1, and θ=0.

We have the following equations:

u = \(x^{3}\) + yz,

x = prcos(θ),

y = prsin(θ),

z = p + r.

To find ∂p/∂u, we apply the Chain Rule:

∂p/∂u = (∂p/∂x) × (∂x/∂u) + (∂p/∂y) × (∂y/∂u) + (∂p/∂z) × (∂z/∂u).

Substituting the given equations and evaluating the derivatives at p=1, r=1, and θ=0, we get:

∂p/∂u = (∂p/∂x) × (∂x/∂u) + (∂p/∂y) × (∂y/∂u) + (∂p/∂z) × (∂z/∂u)

= (3\(pr^{2}\)cos(θ)) × (∂x/∂u) + (3\(pr^{2}\)sin(θ)) ×(∂y/∂u) + (∂p/∂z) × (∂z/∂u)

= (3p) × (rcos(θ)) + (3p) × (rsin(θ)) + (∂p/∂z) × 1

= 3p + 3p + (∂p/∂z)  = 6p + (∂p/∂z).

Since p=1, the value of ∂p/∂u is 6(1) + (∂p/∂z).

Similarly, for ∂r/∂u and ∂θ/∂u, we can follow the same process of applying the Chain Rule and substituting the given equations. The resulting values at p=1, r=1, and θ=0 are ∂r/∂u = 1 and ∂θ/∂u = 0.

learn more about Chain Rule here:

https://brainly.com/question/30764359

#SPJ11

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

For such more questions on Power Sets Examples for Sets

https://brainly.com/question/33026825

#SPJ8

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

For more questions on population mean

https://brainly.com/question/26941429

#SPJ11

By evaluating the integrals and using the appropriate limits of integration, we can find the x and y coordinates of the centroid point.

To find the centroid for the area defined by the equations y=2x+4 and y=(2x−3)2+1, we need to calculate the coordinates of the centroid point. The centroid represents the center of mass of the area.

To find the centroid, we first need to determine the limits of integration by finding the points of intersection between the two curves. Setting the two equations equal to each other, we have:

2x + 4 = (2x - 3)^2 + 1

Simplifying the equation, we get:

(2x - 3)^2 - 2x - 3 = 0

Solving this quadratic equation, we find the two points of intersection, which are the limits of integration.

Once we have the limits of integration, we can proceed to calculate the centroid using the formulas:

x = (1/A) ∫[a,b] x f(x) dx

y = (1/A) ∫[a,b] (f(x))^2 dx

where A represents the area of the region, and x and f(x) are the coordinates of the points on the curves.

Learn more about quadratic equation here:

brainly.com/question/30098550

#SPJ11

Answer:

Yes, it is a proportional relation ship because 6 and 2 are equivalent to each other.

Step-by-step explanation

Answer:

the two equations you can use are

y = 2x - 3

y + x = 9

Answer:

4/5

Step-by-step explanation:

Convert 4y+5x=16 to slope intercept form

4y=-5x+16

y=-5/4+4

Perpendicular line has slope of 4/5

The probability that less than or equal to 5 of the 10 independent customers will take more than 3 minutes to check out their groceries is approximately 0.9245.

To calculate this probability, we can use the binomial probability formula. Let's denote X as the number of customers taking more than 3 minutes to check out. We want to find P(X ≤ 5) when n = 10 (number of trials) and p (probability of success) is not given explicitly.

Step 1: Determine the probability of success (p).

Since the probability of each customer taking more than 3 minutes is not provided, we need to make an assumption or use historical data. Let's assume that the probability of a customer taking more than 3 minutes is 0.2.

Step 2: Calculate the probability of X ≤ 5.

Using the binomial probability formula, we can calculate the cumulative probability:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X ≤ 5) = C(10, 0) * p^0 * (1 - p)^(10 - 0) + C(10, 1) * p^1 * (1 - p)^(10 - 1) + C(10, 2) * p^2 * (1 - p)^(10 - 2) + C(10, 3) * p^3 * (1 - p)^(10 - 3) + C(10, 4) * p^4 * (1 - p)^(10 - 4) + C(10, 5) * p^5 * (1 - p)^(10 - 5)

Substituting p = 0.2 into the formula and performing the calculations:

P(X ≤ 5) ≈ 0.1074 + 0.2686 + 0.3020 + 0.2013 + 0.0889 + 0.0246

P(X ≤ 5) ≈ 0.9928

Rounding this probability to the nearest hundredth/second decimal place, we get approximately 0.99. However, the question asks for the probability that less than or equal to 5 customers take more than 3 minutes, so we subtract the probability of all 10 customers taking more than 3 minutes from 1:

P(X ≤ 5) = 1 - P(X = 10)

P(X ≤ 5) ≈ 1 - 0.9928

P(X ≤ 5) ≈ 0.0072

Therefore, the probability that less than or equal to 5 customers out of 10 will take more than 3 minutes to check out their groceries is approximately 0.0072 or 0.72%.

For more questions like Probability click the link below:

https://brainly.com/question/11234923

#SPJ11

Answer:

f(x) -5x

g(x) -85x²

f(x) . g(x)

-90x

Answer:

36x³ + 25x² + 12x + 2

Step-by-step explanation:

f(x) × g(x)

= (- 4x - 1)(- 9x² - 4x - 2)

Each term in the second factor is multiplied by each term in the first factor

- 4x(- 9x² - 4x - 2) - 1 (- 9x² - 4x - 2) ← distribute parenthesis

= 36x³ + 16x² + 8x + 9x² + 4x + 2 ← collect like terms

= 36x³ + 25x² + 12x + 2