Ben went on holiday to Australia. He changed £350 into Australian dollars ($).
The exchange rate was £1 = $2.1
(a) Work out how many Australian dollars Ben should have received.
$.......

The probability that it is new is 0.0833.

The probability that it is overdue is 0.25.

To solve this problem, use conditional probability.

Let A be the event that the account is new, and B be the event that the account is overdue.

A) To find the probability that an account is new given that it is overdue, calculate:

P(New | Overdue) = P(New and Overdue) / P(Overdue)

P(New | Overdue) = 0.05 / (0.05 + 0.55) = 0.0833 or 8.33%

So the probability that the account is new, given that it is overdue, is 8.33%.

B) To find the probability that an account is overdue given that it is new, calculate:

P(Overdue | New) = P(Overdue and New) / P(New)

P(Overdue | New) = 0.05 / (0.05 + 0.15) = 0.25 or 25%

So the probability that the account is overdue, given that it is new, is 25%.

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The complete question is:

A firm has classified its customers in two ways: according to whether the account is overdue and whether the account is new (less than 12 months) or old. An analysis of the firm's records provided the input for the following table of joint probabilities: One account is selected at random. If the account is overdue, what is the probability that it is new? If the account is new, what is the probability that it is overdue?

Answer:

The answer would be 80.

Step-by-step explanation:

First you want to add 16 and 24.

Next you want to multiply that answer by 2.

Then you have your answer and I hope this helps

Answer:

6 $6 books

Step-by-step explanation:

Using the information, we can create a system of equations.

We can let x represent the total number of $6 Marci bought and y represent the total number of $8 books she bought.

Because the total number of books is 10, one equation we have is x + y = 10.

Because the total cost of both types of books is $68, our other equation is 6x + 8y = 68.

We can solve with substitution by isolating y in the first equation and plugging it into the second equation:

[tex]x+y=10\\y=-x+10\\\\6x+8(-x+10)=68\\6x-8x+80=68\\-2x+80=68\\-2x=-12\\x=6[/tex]

Thus, the total number of $6 books Marci bought was 6.

The expression are simplified to ;

7. 16 + 8g

8. 4h - 20g

9. -35 + 7n

10. 16m + 8

13. -56n + 7m

14. -36 - 6d

15. -8c - 4d

16. -6f + 10g

Algebraic expressions are defined as expressions that are usually made up of terms, variables, constants, factors and coefficients.

These expressions are identified with mathematical or arithmetic operations, such as;

From the information given, we need to expand the bracket to determine the expressions, we have;

a. -7(8n - m)

expand the bracket

-56n + 7m

b. (6+d)(-6)

expand the bracket

-36 - 6d

c. (4c + 2d) - 2

expand the bracket

-8c - 4d

d. -2(3f - 5g)

expand the bracket

-6f + 10g

e. (2 + g) 8

expand the bracket

16 + 8g

f. 4(h - 5g)

expand the bracket

4h - 20g

g. -7(5 - n)

expand the bracket

-35 + 7n

h. 8(2m + 1)

expand the bracket

16m + 8

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Step-by-step explanation:

13. -7(8n-m)= -56n+7m

14. (6+d)(-6)= -36-6d

15. (4c+2d)(-2)= -8c-4d

16. -2(3f-5g)= -6f+10g

7. (2+g)8= 16+8g

8. 4(h-5g)= 4h-20g

9. -7(5-n)= -35+7n

10. 8(2m+1)= 16m+8

Answer:

Below

Step-by-step explanation:

The interior angles of ANY triangle add up to 180 degrees

   you want to divide this 180 into   2 + 3 + 4 = 9  parts

       180 / 9 = 20 degrees for each part

           2 parts = 2 * 20 = 40 °

          4 parts = 4 * 20 = 80 °

The percent rate of change to the nearest tenth of a percent is approximately 30.0% for both forms.

Starting with [tex]Y=5e^{-0.7}[/tex]  we can rewrite it using the property that [tex]e^{In(x)} = x[/tex]:

[tex]y=5e^{0.7t} = 5e^{ine^{in-0.7t} } =5e^{ln(5)}e^{-0.7t}[/tex]

Using the property that e^(ln(x)) = x again, we can simplify further:

[tex]y = 5e^{(ln(5)} e^{-0.7t} = 5(5^{1/In(5)}e^{-0.7t})[/tex]

Let [tex]a = 5^{1/ln(5)}[/tex]and r = 0.7, then we have:

[tex]y = 5a(1 + r)^{-t} ; y = a(1 - r)^t[/tex]

Rounding r to the nearest thousandth, we have:

r ≈ 0.700

To find the percent rate of change, we can use the formula:

percent rate of change = (1 ± r) * 100%

For the first form, we have:

percent rate of change = (1 - 0.700) * 100% ≈ 30.0%

For the second form, we have:

percent rate of change = (1 - 0.700) * 100% ≈ 30.0%

Therefore, the percent rate of change to the nearest tenth of a percent is approximately 30.0% for both forms.

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The height of the parallelogram is 9 cm.

To find the height of a parallelogram with a given base and area, we can use the formula:

Area = base x height

In this case, we are given that the base of the parallelogram is 12 cm and the area is 108 sq. cm. Substituting these values into the formula, we get:

height = 108/12

Simplifying this expression, we get:

height = 9cm

A parallelogram is a four-sided polygon with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure, meaning that the adjacent angles are supplementary (their sum is 180 degrees).

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Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.The inequality that describes the situation is:250 - 179.85 ≤ x

where x represents the amount of money Mr. Donovan still needs to spend in order to meet the Angler's Club requirement.

To solve for x, we first subtract 179.85 from 250 to get:

70.15 ≤ x

Therefore, Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.

In summary, Mr. Donovan's spending so far this month is less than the minimum required by the Angler's Club, and he needs to spend at least $70.15 more to meet the requirement.

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The variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.

Variance is a measure of the spread or variability of a set of data. It is the average of the squared differences from the mean. The formula for variance is:

Variance = (sum of squared deviations from the mean) / (number of observations - 1)

where the squared deviation from the mean is the difference between each data point and the mean of the data set, squared. The variance is useful in statistical analysis and can provide information about the distribution of the data. A higher variance indicates that the data is more spread out, while a lower variance indicates that the data is clustered more closely around the mean.

In the given question,

To find the variance of the sample, we can use the formula:

Variance = [(sum of squared deviations from the mean)/ (number of observations - 1)]

First, we need to find the squared deviation of each observation from the mean, which is the difference between each observation and the mean, squared:

(3-5.4)² = 5.76

(5-5.4)² = 0.16

(12-5.4)² = 43.56

(3-5.4)²= 5.76

(2-5.4)²= 12.96

Next, we need to sum up these squared deviations:

5.76 + 0.16 + 43.56 + 5.76 + 12.96 = 68.2

Then, we divide the sum of squared deviations by the number of observations minus 1:

Variance = 68.2/(5-1) = 17.05

Therefore, the variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.

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Answer:

The first person to answer was correct, the answer is 301 m squared.

Step-by-step explanation:

I took the quiz so you don't have to! <3

28= (1+2x)(x)

28=x+2x²

2x²+x-28 = 0

2x²+8x-7x-28 =0

2x(x+4) -7(x+4) =0

(x+4)(2x-7) = 0

x = -4 and 7/2

dimensions can't be negative

length=1+2×7/2 =1+7 = 8ft

width= 7/2ft

Answer:

Step-by-step explanation:

Hi there I am able to help so when you do 8,552/16 it is best to reverse it then add the expression, what I mean by that is translating expressions. the answer would be 444.23 then you would want to add (480/16) no mental math how you would do this is the recalabric way, take 480/16 and put in an a fraction to make it work easier than the rest of your problems you would do the same things its simple, just repeat what I did to all the other problems,

regards, me

Answer:

If 28 students are divided into 7 groups, then each group will have 28/7 = 4 students.

To find out how many groups would be created if there were 32 students, we can use the same ratio:

32 students divided into groups of 4 students each would give us:

32/4 = 8 groups.

Therefore, if there were 32 students, they would be divided into 8 groups of the same size.

The purchase cost is $40. Question: What is the discount price of shoes if they were originally $80 and are currently on sale for 50% off.  % formula: Sale price equals 50% of $80.

The word puzzle asks you to determine the sale price of shoes that are being offered at a 50% discount. The percent equation, which asserts that the percent of the whole is equal to the part over the entire, or percent = part/whole, may be used to solve this problem. In this instance, the sale price is the component we are interested in, the initial price of $80 is the component as a whole, and 50% is the percentage. With these numbers as inputs, we can calculate the sale price as 50% of $80. When we solve for the sale price, we arrive at $40. Hence, the sneakers are $40 on sale.

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Write a word problem involving percents for which the percent is about one half and the whole is known. Write a percent equation for the problem and then use it to solve the problem. If a store has a sale on shoes for 50% off and the original price is $80, what is the sale price?

Answer: 3 mph

Step-by-step explanation:

I did it in mah brain

Answer:

10

Step-by-step explanation:

We can use the distance formula to find the distance between the two points:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates of A and B, we get:

Distance = √((-2 - 6)^2 + (-1 - 5)^2)

Distance = √((-8)^2 + (-6)^2)

Distance = √(64 + 36)

Distance = √100

Distance = 10

Therefore, the distance between A(6, 5) and B(−2, −1) is 10 units.

After addressing the issue at hand, we can state that  As a result, the square value of x to three significant figures is 5.03 cm.

According to Euclidean geometry, a square is an equilateral quadrilateral with four equal sides and four equal angles. It is also referred to as a rectangle with two neighbouring sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Furthermore, the diagonals of the square are evenly spaced and split at a 90-degree angle. a neighbouring rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

The Pythagorean theorem can be used to find the square's diagonal:

2x2 = diagonal2 = x2 + x2 = 2x2[tex]x * \sqrt = diagonal = sqrt(2x2) (2)[/tex]

Because the diagonal equals the circle's diameter, the radius is half of the diagonal:

x * \sqrt(2) / 2 = radius

We can now use the formula for the area of a circle to calculate x:

[tex]\pi * radius2 = area[/tex]

[tex]\Pi * (x * sqrt(2) / 2)2 = 56[/tex]

[tex]56 = pi * (x^2 / 2)[/tex]

[tex]x^2 = 112 / pi[/tex]

x = 5.027 (rounded to 3 significant figures) (rounded to 3 significant figures)

As a result, the value of x to three significant figures is 5.03 cm.

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Answer:

B

Step-by-step explanation:

He was accepted to UCLA's School of Management

The algebraic expression that represents the sentence "N increased by 25%" is 0.25N.

Hence the correct option is A.

This means that N is multiplied by 0.25 or 1/4. To find the result of N increased by 25%, you simply need to multiply N by 0.25 and add the result to the original value of N. The option A, 0.25N, represents this concept in a clear and concise manner.

The other options (B, C, and D) are either incomplete or incorrect. It is important to understand the concept of percentage increase and how it is represented algebraically, as it is a common operation in many mathematical and real-life scenarios, such as calculating interest rates, growth rates, and inflation rates.

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Therefore , the solution of the given problem of inequality comes out to be   y - 12 = -(3/4)(x - 2)².

Without the equal sign, an association or collection of numbers can be a disparity in mathematics. Equity always comes after equilibrium. When standards are still incompatible, inequality results. Fairness and disparity have different variable characteristics. Because parts aren't always similar or close to one another, we decided to select the most common symbol (). It is also possible to use disparities of any size to assess values.

Here,

We must recast the parabola's equation in this form in order to determine the inequality's standard form. The vertex version of a quadratic equation is as follows:

=> y = a(x - h)² + k

where (h, k) is the parabola's apex. Inputting the numbers provided yields:

=> y = a(x - 2)² + 12

We can use the information that the parabola passes through (-2, 0) and to determine the value of a. (6, 0). When we enter these values into the formula, we obtain:

=> 0 = a(-2 - 2)² + 12

=> 0 = 16a + 12

=>  a = -3/4

The parabola's solution is as follows:

=>  y = -(3/4)(x - 2)²

We need to separate y on one side in order to determine the inequality's standard form:

=> y - 12 = -(3/4)(x - 2)²

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The diameter of the wheel is approximately 1.918 meters.

We can use the formula:

distance traveled = circumference of wheel x number of rotations

The circumference of the wheel is equal to the distance traveled in one rotation, which is equal to the diameter of the wheel times pi (π). So we can rewrite the formula as:

distance traveled = (diameter of wheel x π) x number of rotations

where d is the diameter of the wheel.

We are given that the bicycle travels 30.09 meters and the wheel makes five rotations, so we can plug in these values:

30.09 = (d x π) x 5

Solving for d, we get:

d = 30.09 / (π x 5)

d ≈ 1.918 meters

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The cost of the plan for the limited talk and text is $50 with an additional cost of $22.99 for each gigabyte of data.

Generally, a mathematical function means a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables. It can take an input from many variables but will  always give the same output, unique to that function.

We are given that "H(g) = 22.99g + 50", where H represents the cost, in dollars, and g represents the number of gigabytes of data. The main answer is based on the given function where the constant term of 50 represents the cost of the plan for limited talk and text, and the coefficient of 22.99 represents the additional cost for each gigabyte of data used.

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The volume of the cheese is approximately 135 cubic centimeters.

To calculate the volume of the cheese, we can use the formula:

Volume = Mass / Density

Given that the mass of the cheese is 216 grams and the density is 1.6 g/cm³, we can plug these values into the formula:

Volume = 216 g / 1.6 g/cm³

Now, we need to convert the units so that they are consistent. Since density is given in grams per cubic centimeter (g/cm³), we need to convert the mass from grams to cubic centimeters.

1 gram is equal to 1 cubic centimeter, so:

Volume = 216 cm³ / 1.6 cm³

Now, divide:

Volume ≈ 135 cm³

The volume of the cheese is approximately 135 cubic centimeters.

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Part A: k = 8.4, to find the value of k, we must solve for k in the equation.

Part B: 193°F is the temperature of the water after 4.5 minutes.

Initial temperature is the temperature of a system before it undergoes a change. It can be calculated by subtracting the change in temperature from the final temperature.

Part A: k = 8.4

To find the value of k, we must solve for k in the equation.

We are given the temperature of the room (67°F) and the initial temperature of the water (208°F).

We are also given the temperature of the water after 3 minutes (193°F). We can plug these values into the equation and solve for k:

T-Ta = k(To-T)

193-67 = k(208-193)

126 = 15k

k = 126/15

k = 8.4

Part B: 193°F

To find the temperature of the cup of water after 4.5 minutes, we can plug the k-value we found in Part A into the equation, along with the given temperature of the room (67°F) and the initial temperature of the water (208°F).

T-Ta = k(To-T)

T = Ta + k(To-T)

T = 67 + 8.4(208-T)

T = 67 + 1747.2 - 8.4T

9.4T = 1814.2

T = 193

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Part A: k = 8.4, to find the value of k, we must solve for k in the equation.

Part B: 193°F is the temperature of the water after 4.5 minutes.

The temperature of a system at the start of a shift is called the initial temperature. You can figure it out by deducting the final temperature from the temperature difference.

Part A: k = 8.4

We must answer for k in the equation in order to determine its value.

We are informed of the room's temperature (67°F) and the water's starting temperature (208°F).

After three minutes, we are also told the water's temperature (193°F). We can solve for k by entering these numbers into the equation:

T-Ta = k(To-T)

193-67 = k(208-193)

126 = 15k

k = 126/15

k = 8.4

Part B: 193°F

We can enter the k-value we discovered in Part A, the given room temperature (67°F), and the starting temperature of the water (208°F) into the equation to determine the temperature of the cup of water after 4.5 minutes.

T-Ta = k(To-T)

T = Ta + k(To-T)

T = 67 + 8.4(208-T)

T = 67 + 1747.2 - 8.4T

9.4T = 1814.2

T = 193

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The complete question is,

EXIT TICKET

After heating up in a teapot, a cup of hot water is poured at a temperature of 208^0F . The cup sits to cool in a room at a temperature of 67^0 F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between temperature of the water and the temperature of the room, as given by the formula shown below.

Part A: If the cup of water reaches the temperature of 193^0 F after 3 minutes. Find the value of k, to the room, as given by the formula shown below. nearest thousandth.

Part B: Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.

Answer:

12996

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

14x - 2

To find the difference between (−5x+7) and (9x+5), we need to subtract the first expression from the second.

(9x+5) - (-5x+7)

= 9x + 5 + 5x - 7 [Distribute the negative sign to (-5x+7)]

= 14x - 2

Therefore, the difference between (−5x+7) and (9x+5) is 14x - 2.

Using expression 5⁷ x 9,  there are 59,049,125 ways to answer all 9 tests if you select one option per question and leave nothing blank.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a value or a quantity.

Expressions can be simple or complex, and they can contain one or more variables. For example, "2x + 3" is a simple expression that contains the variable x.

Now,

To solve this problem, we can use the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

For each of the 9 tests, there are 5 choices for each of the 7 questions. Therefore, there are 5 x 5 x 5 x 5 x 5 x 5 x 5 possible ways to answer the questions on each test. Using the multiplication principle, we can find the total number of ways to answer all 9 tests by multiplying the number of ways to answer each test together:

5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 5⁷ x 9 = 59,049,125

Therefore,

                 there are 59,049,125 possible ways ways to answer all 9 tests if you select one option per question and leave nothing blank.

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