if you roll two fair six-sided dice, what is the probability that the sum is 4 44 or higher?

9514 1404 393

Answer:

  45 yd²

Step-by-step explanation:

The area of a rectangle is the product of its length and width. If your given measures are the length and with of a rectangle, the area is found by multiplying them.

  A = LW

  A = (9 yd)(5 yd) = 9·5 yd·yd = 45 yd²

The area of a 9 yd by 5 yd rectangle is 45 square yards.

Answer:

25n

Step-by-step explanation:

product of n and 25

Product means multiply

25n

Answer: 13

Step-by-step explanation:

This equation holds true, which confirms that AB is indeed the hypotenuse of the right triangle.

If the Pythagorean equation holds for all right triangles and ∠C is a right angle, then we can use the Pythagorean theorem to show that side AB is indeed the hypotenuse of the triangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

So in this case, we have side AB as the hypotenuse, and sides AC and BC as the other two sides.

According to the Pythagorean theorem, we have:
AB^2 = AC^2 + BC^2

Since ∠C is a right angle, AC and BC are the legs of the triangle. By substituting these values into the equation, we get:
AB^2 = AC^2 + BC^2
AB^2 = AB^2

This equation holds true, which confirms that AB is indeed the hypotenuse of the right triangle.

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Answer:

212 meters

Step-by-step explanation:

The diagonal of a square is the square root of 2 times the length of the square. This can be rewritten as the square root of (2*area)

2 * 22500 = 45000

The square root of 45000 is about 212.13, which would round down to 212 meters.

The dairy farmer used the relative frequency method of probability to reach his conclusion.

Relative frequency is a method of calculating probability that is based on the observation of how often an event occurs in a sample. The farmer likely observed how often he gets between 12 and 14 gallons of milk in a day and used that data to calculate the probability of it happening.

In contrast, theoretical probability is based on the assumption that all possible outcomes are equally likely. It is calculated by dividing the number of desired outcomes by the total number of possible outcomes.

Therefore, the correct answer is relative frequency.

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Answer:

47x+42/2

Step-by-step explanation:

simplify 9/2

((19x+20)+(9/2×x))+1

(47x+40)/2+1

(47+42)/2

Answer:

The 3 possible values of x are;

6, 4 and 2

Step-by-step explanation:

If the triangle is isosceles, then two of the sides must be equal

So we equate the sides, 2 at a time to get the different values of x

3x + 4 = 2x + 10

3x-2x = 10-4

x = 6

3x + 4 = x + 12

3x-x = 12-4

2x = 8

x = 8/2 = 4

2x + 10 = x + 12

2x - x = 12-10

x = 2

Answer:

8. 5/6

9. 6.25 or 6 1/4

10. 14.4 Fish

Step-by-step explanation:

8. Reduce the fraction. (20/24) You can divide both the numerator and denominator by 4.

9. Divide 75 by 12

10. Divide 72 by 5

Answer:

m GHI = 82°

Step-by-step explanation:

59+39=98

180-98=82 <==== answer

180 is the total amount of degree

Answer:

uuuuhhhh . . . huh?

Step-by-step explanation:

Answer:

There will be 12 full teams and 7 extra people.

Step-by-step explanation:

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10 a. You pay a total of R703,125 if you increase your monthly payment by 25% and pay off your bond in 125 months.

10 b. you would save a total of R376,875 by increasing your monthly payment by 25% and paying off your bond in 125 months.

If you were to increase your monthly repayment by 25%, you would pay off your bond in 125 months. Let's calculate what you would pay (and save) in total:

First, we calculate the new monthly payment:

R4,500 × 1.25 = R5,625

Then, we multiply this new monthly payment by 125 months to get the total amount paid:

R5,625/month ×125 months = R703,125

So, you pay a total of R703,125 if you increase your monthly payment by 25% and pay off your bond in 125 months.

To calculate how much you save, we subtract this total from the total amount you would have paid over 20 years:

R1,080,000 - R703,125 = R376,875

The above answer is based on the full question

Your home loan is one of your most dramatic examples of the effect of compound interest over time. How much do you pay in total over 20 years for your R450 000 home if your monthly repayment stays at R4 500?

10.4 If you were to increase your monthly repayment by 25%, you would pay your bond off in 125 months. Calculate what you would pay (and save) in total:

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The smallest possible value of nullity(a) is 0, and the largest possible value of nullity(a) is 4. To determine the minimum and maximum possible values of nullity(a) for a 7 × 4 matrix, we need to consider the properties of a matrix and nullity.

Nullity(a) is defined as the dimension of the null space of the matrix 'a'. It is also equal to the number of linearly independent columns in the matrix that are not part of its column space.
Since the matrix is a 7 × 4 matrix, it has 4 columns. The rank-nullity theorem states that:
rank(a) + nullity(a) = number of columns in matrix 'a'
The minimum possible value of nullity(a) occurs when all columns are linearly independent, which would mean the rank of the matrix is at its maximum value. In this case, the maximum rank of a 7 × 4 matrix is 4. So, the smallest possible value of nullity(a) is: nullity(a) = number of columns - rank(a)
nullity(a) = 4 - 4 = 0
The maximum possible value of nullity(a) occurs when the rank of the matrix is at its minimum value. In this case, the minimum rank of a 7 × 4 matrix is 0. So, the largest possible value of nullity(a) is: nullity(a) = number of columns - rank(a)
nullity(a) = 4 - 0 = 4
To summarize, the smallest possible value of nullity(a) is 0, and the largest possible value of nullity(a) is 4.

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The derivative of a function represents the rate of change of the function with respect to its variable. This rate of change is described as the slope of the tangent line to the curve of the function at a specific point. The derivative of the cosine function can be found by applying the limit definition of the derivative to the cosine function.

\(f(x) = cos(x) then f'(x) = -sin(x)\).

Let's proceed with the proof.  Definition of the Derivative: The derivative of a function f(x) at x is defined as the limit as h approaches zero of the difference quotient \(f(x + h) - f(x) / h\) if this limit exists. Using this definition, we can find the derivative of the cosine function as follows:

\(f(x) = cos(x) f(x + h) = cos(x + h)\)

Now, we can substitute these expressions into the difference quotient: \(f'(x) = lim h→0 [cos(x + h) - cos(x)] / h\)

We can then simplify the expression by using the trigonometric identity for the difference of two angles:

\(cos(a - b) = cos(a)cos(b) + sin(a)sin(b)\)

Applying this identity to the numerator of the difference quotient, we obtain:

\(f'(x) = lim h→0 [cos(x)cos(h) - sin(x)sin(h) - cos(x)] / h\)

We can then factor out a cos(x) term from the numerator:

\(f'(x) = lim h→0 [cos(x)(cos(h) - 1) - sin(x)sin(h)] / h\)

We can then apply the limit laws to separate the limit into two limits:

\(f'(x) = lim h→0 cos(x) [lim h→0 (cos(h) - 1) / h] - lim h→0 sin(x) [lim h→0 sin(h) / h]\)

The first limit can be evaluated using L'Hopital's rule:

\(lim h→0 (cos(h) - 1) / h = lim h→0 -sin(h) / 1 = 0\)

Therefore, the first limit becomes zero:

\(f'(x) = lim h→0 - sin(x) [lim h→0 sin(h) / h]\)

Applying L'Hopital's rule to the second limit, we obtain:

\(lim h→0 sin(h) / h = lim h→0 cos(h) / 1 = 1\)

Therefore, the second limit becomes 1:

\(f'(x) = -sin(x)\)

Thus, we have proved that if \(f(x) = cos(x), then f'(x) = -sin(x)\).

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(a) To construct a 95% confidence interval for the proportion of all customers who fill up their cup more than 3 times, we can use the formula:

CI = p ± z*√((p(1-p))/n)

where pis the sample proportion, z is the z-score corresponding to the confidence level (95% corresponds to a z-score of 1.96), and n is the sample size.

In this case, we have p= 19/90 = 0.2111. Plugging in the values, we get:

CI = 0.2111 ± 1.96*√((0.2111(1-0.2111))/90)

CI = (0.1084, 0.3138)

Interpreting this interval, we can say that we are 95% confident that the true proportion of all customers who fill up their cup more than 3 times when ordering a drink and eating in the restaurant falls between 10.84% and 31.38%.

(b) To calculate the minimum number of times a customer must fill up their cup for the restaurant to start losing money on the drink, we need to know the cost per drink and the profit margin on each drink. Let's assume that the cost per drink is $0.25 and the profit margin is 75% (i.e., the restaurant makes $0.75 for every $1.00 in sales).

If a customer fills up their cup more than 3 times, they are essentially getting more than 4 drinks for the price of one. So, if the cost per drink is $0.25 and the customer pays $1.00 for the drink, the restaurant is losing $0.75 for every extra drink that the customer gets. Therefore, the minimum number of times a customer must fill up their cup for the restaurant to start losing money is:

$1.00 ÷ $0.75 = 1.33

In other words, if a customer fills up their cup more than 1.33 times, the restaurant is losing money on the drink.

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

It's the bottom one

Step-by-step explanation:

I got it wrong on the IXL, but the explanation says so. If someone can help me, please do because I have no idea how to do these

The limit of the sequence of terms of a series is zero, this test alone does not prove that the series converges, and further testing is needed to determine convergence or divergence.

The divergence test is a test used to determine if a series converges or diverges. It states that if the limit of the sequence of terms of a series is not zero, then the series diverges.

The series 3n/(2n + 1) can be simplified to

=3/2 - 3/4n + 3/4n+1.

As n approaches infinity, the terms in the series approach 3/4n, which approaches infinity as n approaches infinity.

Therefore, the limit of the sequence of terms of this series is not zero, and so the series diverges. Thus, the answer to the question is the series diverges.

A more general form of the divergence test states that if the limit of the sequence of terms of a series is not zero, then the series diverges. However, if the limit of the sequence of terms of a series is zero, this test alone does not prove that the series converges, and further testing is needed to determine convergence or divergence.

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Step-by-step explanation:

y = 200  - 3 *x  has slope = -3   this is downward sloping from L to R

Answer:downward sloping

Step-by-step explanation:

negative slope

a. This is a very low probability, indicating that the new system implemented by Kroger is effective in reducing waiting times.

b. The probability that a customer will have to wait between 2 and 4 seconds is approximately 0.5433.

c. The probability that a customer will have to wait more than 5 minutes (300 seconds) is approximately 0.000006, or 0.0006%.

a. The probability density function of waiting time applicable at Kroger is the exponential distribution function.

b. The probability of a customer having to wait between 2 and 4 seconds can be calculated as follows:

Let λ be the rate parameter of the exponential distribution, which represents the average number of customers served per second. Since the waiting times are exponentially distributed, the probability density function of the waiting time t is given by:

\(f(t) = \lambda \times e^{(-\lambda\times t)}\)

We want to find the probability that a customer will have to wait between 2 and 4 seconds. This can be calculated as the difference between the cumulative distribution functions (CDF) evaluated at 4 seconds and 2 seconds:

P(2 < t < 4) = F(4) - F(2)

where F(t) is the CDF of the exponential distribution:

\(F(t) = 1 - e^{(-\lambda \times t)}\)

Substituting the value of λ (which we need to estimate), we can solve for the probability:

\(P(2 < t < 4) = (1 - e^{(-\lambda4)}) - (1 - e^{(-\lambda2)})\\= e^{(-\lambda2)} - e^{(-\lambda4)}\)

To estimate λ, we can use the information given in the problem that the average waiting time is "just seconds". Let's assume that this means an average waiting time of 2 seconds. Then, the rate parameter λ can be estimated as:

λ = 1 / 2

Substituting this value in the equation above, we get:

\(P(2 < t < 4) = e^{(-1)} - e^{(-2)\)

≈ 0.5433

c. The probability of a customer having to wait more than 5 minutes (i.e., 300 seconds) can be calculated as follows:

P(t > 300) = 1 - F(300)

where F(t) is the CDF of the exponential distribution as given above. Substituting the value of λ estimated earlier, we get:

\(P(t > 300) = 1 - (1 - e^{(-\lambda300)})\\= e^(-\lambda300)\)

Substituting the value of λ, we get:

\(P(t > 300) = e^{(-150)}\)

≈ 0.000006

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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 cost of equity for Chelsea Fashions is approximately 9.86%. This is calculated using the dividend discount model, taking into account the expected dividend, the stock price, and the growth rate.

The cost of equity for Chelsea Fashions can be determined using the dividend discount model (DDM). The DDM formula is as follows: Cost of Equity = Dividend / Stock Price + Growth Rate.

Given that the expected dividend is $1.10 and the market price of the stock is $21.80, we can substitute these values into the formula: Cost of Equity = $1.10 / $21.80 + 4.5%.

First, we divide $1.10 by $21.80 to get 0.0505 (rounded to four decimal places). Then, we add the growth rate of 4.5% (expressed as a decimal, 0.045). Finally, we sum these values: Cost of Equity = 0.0505 + 0.045 = 0.0955.

Converting this decimal to a percentage, we find that the cost of equity for Chelsea Fashions is approximately 9.55%. Therefore, the firm's cost of equity is approximately 9.86% when rounded to two decimal places.

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From the given question above we can conclude that when 6x +16 += 2x+28 , then the value of x is 3.

What is Linear Equation?

A linear equation is a mathematical expression in which the highest power of the variable is 1. It can be written in the form of:

y = mx + b

where y and x are variables, m is the slope of the line, and b is the y-intercept of the line. This form is called the slope-intercept form of a linear equation.

To solve the equation 6x + 16 = 2x + 28:

Simplify both sides of the equation by combining like terms:

6x + 16 = 2x + 28

Subtract 2x from both sides:

4x + 16 = 28

Subtract 16 from both sides:

4x = 12

Solve for x by dividing both sides by 4:

4x = 12

x = 3

Therefore, the solution to the equation 6x + 16 = 2x + 28 is x = 3.

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Answer:

3

Step-by-step explanation:

Answer:

A proportional relationship is something like:

y = k*x

where k is the constant of proportionality.

Notice that in these relationships we will always have the pair (0, 0)

because if x = 0:

y = k*0 = 0

Then we always have x= 0, y = 0.

Notice that in the first two tables we have the points:

(2, 0) in the first one

(0, 1) in the second one.

then neither of these can be a proportional relationship.

The only option left is the third one.

To graph the relationship, we can just graph the four points in the table.

Then draw a line that passes through all the points, like in the image below.

And this line is written as:

y = 3*x

such that:

y(1) = 3*1 = 3 -----> (1, 3)

y(2) = 3*2 = 6 -----> (2, 6)

y(3) = 3*3 = 9 ------>  (3, 9)

The correct explicit formula for the geometric sequence {1/3, 1/9, 1/27, 1/81, ...} is D.

A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a constant factor called the common ratio (r). In this case, the common ratio is 1/3 because each term is obtained by dividing the previous term by 3.

The explicit formula for a geometric sequence is given by an = a1(r)^(n-1), where a1 is the first term and n is the term number.

Using this formula, we can find the explicit formula for the given sequence as follows:

a1 = 1/3 (the first term)

r = 1/3 (the common ratio)

So, the explicit formula is:

an = (1/3)(1/3)^(n-1) = 1/3^(n)

Therefore, option D, an = 1/3(1/3)^(n-1), is the correct formula for the given geometric sequence.

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Answer:

D

Step-by-step explanation:

Did the test