11. Ellen borrowed $110 from her brother. He is charging 10% interest per year.
How much interest will she owe him if she repays him after 3 months?

These values of h and k are specific to the given system of equations and may not apply to other systems.

(a) The system has no solution when h = 16.
(b) The system has a unique solution for any value of h ≠ 16.
(c) The system has many solutions when h = 16.

To determine the values of h and k that result in different solutions for the given system of equations, let's analyze the coefficient matrix of the system:
```
2   4
8   h
```
(a) To have no solution, the coefficient matrix must be inconsistent. This occurs when the determinant of the matrix is zero. In this case, the determinant is 2h - 32. So, to have no solution, we need 2h - 32 = 0. Solving this equation, we find h = 16. Therefore, the system has no solution when h = 16.

(b) To have a unique solution, the coefficient matrix must be consistent and have a non-zero determinant. This means that 2h - 32 ≠ 0. Since the determinant of the coefficient matrix is 2h - 32, we can conclude that the system has a unique solution for any value of h such that h ≠ 16.
(c) To have many solutions, the coefficient matrix must be consistent and have a determinant of zero. In this case, we need 2h - 32 = 0, which gives us h = 16. Therefore, the system has many solutions when h = 16.

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Answer:

22

Step-by-step explanation:

x-3=19

 +3 +3

     =22 so there for x=22

Answer:

x/y, the cost would be $13.75

Step-by-step explanation:

x would be the amount paid and y would be the number of shirts bought.

Answer:

13.75

Step-by-step explanation:

The required probability of the sample mean is less than 74 and between 74 and 76 are 0.1038 and 0.7924, respectively.

The Central Limit Theorem states that the sample distribution will follow a normal distribution if the sample size is large enough. In the given problem, the population's shape is unknown, and the sample size is large enough (n = 40), so we can use the normal distribution with mean `μ = 75` and standard deviation `σ = 5/√40 = 0.79` to find the probability of the sample mean.

(i) Probability that the sample mean is less than 74:`z = (x - μ) / (σ/√n) = (74 - 75) / (0.79) = -1.26`

P(z < -1.26) = 0.1038 (from z-table)

Therefore, the probability that the sample mean is less than 74 is 0.1038 or approximately 10.38%.

(ii) Probability that the sample mean is between 74 and 76:

`z1 = (x1 - μ) / (σ/√n) = (74 - 75) / (0.79) = -1.26``z2 = (x2 - μ) / (σ/√n) = (76 - 75) / (0.79) = 1.26`

P(-1.26 < z < 1.26) = P(z < 1.26) - P(z < -1.26) = 0.8962 - 0.1038 = 0.7924

Therefore, the probability that the sample mean is between 74 and 76 is 0.7924 or approximately 79.24%.

Hence, the required probability of the sample mean is less than 74 and between 74 and 76 are 0.1038 and 0.7924, respectively.

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Expecting that you're alluding to a triangle ABC with a flat side AB, and a bat hitting the triangle at a few points D over side AB, here's a reply:

The whole of the points in a triangle is continuously 180 degrees. Let's call the third point in triangle ABC "C". At that point, we have:

point A + point B + point C = 180 degrees

Since we know that point A and point B are both less than 90 degrees (since they're portion of a right triangle with side AB as the hypotenuse), we know that point C must be more prominent than degrees and less than 90 degrees. Subsequently, the conceivable measures of point C are any esteem between and 90 degrees, comprehensive.

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Step-by-step explanation:

hope it helps you

Answer:

Step-by-step explanation:

Comment

Either you know the answer to this or you don't. There is no point in eliminating the wrong answers until you get to the right one. It is better to get to the right one immediately.

A rhombus and its diagonals have many interesting properties.  This one is one of those properties. The diagonals are not the same length. The diagonals bisect each other at right angles.

Answer: B

Answer: The form of payment that Courtney can lose and not get back would be cash.

Step-by-step explanation:

The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.

Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated  verification process.

Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!

-From Certified 5th Grade Honors Student

Answer:

50.24

Step-by-step explanation:

4²=16

16×3.14=50.24

Firstly, we must use the equation to solving a circle which is \(A = \pi r^2\). Since we already know pi (3.14) and the radius (4), we must plug the numbers into the formula. Here is how it should look like with the plug-ins: \(A = 3.14 * 4^2\).

Next, we solve the formula. After solving, we get 50.24. The final answer to the problem is 50.24 inches squared.

Answer:

Step-by-step explanation:

translate

Newton's method formula is: xn+1 = xn - f(xn)/f'(xn).

Newton's method is an iterative numerical method used to find the root of a function. The formula for Newton's method is xn+1 = xn - f(xn)/f'(xn), where xn represents the current approximation, f(xn) is the function evaluated at xn, and f'(xn) is the derivative of the function evaluated at xn.

For the given function f(x) = x² - 4x - 45 and the initial approximation x0 = 7, we can apply Newton's method as follows:

Compute f(x0) = f(7) = 7² - 4(7) - 45 = -11.

Compute f'(x0) = 2x0 - 4 = 2(7) - 4 = 10.

Substitute the values into the Newton's method formula: x1 = x0 - f(x0)/f'(x0) = 7 - (-11)/10 = 8.1.

Repeat steps 1 to 3 with x1 as the new approximation to get x2, x3, and so on until the desired accuracy is achieved.

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Answer:

7×3

Step-by-step explanation:

option b

i hope it is helpful for you

Answer:  B. 7x3

This is because 7 times 3 = 21. The other answer choices do not multiply to 21.

Think of it like having 7 rows and 3 columns to give 21 squares overall to make this larger rectangle.

Answer:16'3

Step-by-step explanation:

The value shown on the number line is 3 8/10

The number line represents the given parameter

On the number line, we have the point located between 3 and 4

Such that the point is at 0.8 between 3 and 4

When the above expression is represented as a number, we have

Number = 3 + 0.8

Express the decimal as a fraction

So, we have

Number = 3 + 8/10

Evaluate

Number = 3 8/10

Hence, the solution is 3 8/10

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Answer: The second one

Step-by-step explanation:

Since A and B are mutually exclusive, the probability of A occurring given that B has already occurred is 0. This means that P(A | B) = 0.

P(A ∩ B) = 0, since the events are mutually exclusive.

P(A | B) = 0, since the probability of A given B is 0 when A and B are mutually exclusive.

Since A and B are mutually exclusive, they cannot both occur at the same time. This means that the probability of them both happening at the same time is 0. As a result, P(A ∩ B) = 0.

Since A and B are mutually exclusive, the probability of A occurring given that B has already occurred is 0. This means that P(A | B) = 0.

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The first differential equation has two stationary points, y = 0 and y = 1, with y = 0 being stable and y = 1 being unstable. The second differential equation has no stationary points, and therefore, no equilibrium points to analyze.

To draw the phase line for the first differential equation dy/dt = y^3(y - 1), we can locate the critical points by setting dy/dt = 0. This gives us two stationary points: y = 0 and y = 1. We can now analyze the dynamic stability of these points. For y = 0, we observe that when y < 0, dy/dt < 0, indicating that y = 0 is a stable equilibrium point. When y > 0, dy/dt > 0, indicating that y = 0 is an unstable equilibrium point. For y = 1, we find that dy/dt < 0 when y < 1 and dy/dt > 0 when y > 1, meaning that y = 1 is an unstable equilibrium point.

Moving to the second differential equation dy/dt = y^2 - 5x + 6, we notice that it is not in the standard form for a phase line analysis. We need to express it as dy/dt = f(y), where f(y) is a function of y only. By rearranging the equation, we have dy/dt = y^2 - 5x + 6 = y^2 + 6 - 5x. Since the term -5x is not a function of y, it does not affect the analysis of the equilibrium points. Thus, we can focus on the function f(y) = y^2 + 6. In this case, there are no stationary points since f(y) = y^2 + 6 is always positive. Hence, there are no equilibrium points to analyze for this differential equation.

In summary, the first differential equation has two stationary points, y = 0 and y = 1, with y = 0 being stable and y = 1 being unstable. The second differential equation has no stationary points, and therefore, no equilibrium points to analyze.

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The statement that "If the correlation between the growth of a stock and the growth of the economy as a whole is close to 1, then this would be a good stock to hold during a recession when the economy shrinks" is False.

If the correlation between the growth of a stock and the growth of the economy as a whole is close to 1, then this would not be a good stock to hold during a recession when the economy shrinks. The statement is false.

The correlation can be defined as the statistical relationship between two variables that shows the strength of their association.

A positive correlation is one where the two variables move in the same direction, while a negative correlation is one where the two variables move in opposite directions.

A correlation of +1 indicates a perfect positive correlation, while a correlation of -1 indicates a perfect negative correlation. A correlation of 0 indicates no correlation.

A correlation between 0 and +1 or 0 and -1 indicates a positive or negative correlation, but it is not perfect.

If a stock is positively correlated with the economy, it means that it is affected by the economy's performance. As a result, when the economy grows, the stock grows, and when the economy shrinks, the stock shrinks.

When the economy is in a recession, it is more likely that the stock will be negatively affected. As a result, holding such a stock during a recession when the economy shrinks is not recommended.

Therefore, if the correlation between the growth of a stock and the growth of the economy as a whole is close to 1, then this would not be a good stock to hold during a recession when the economy shrinks. The statement is false.

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Comparison or relational operations, such as <, >, =, allow for comparing numbers. They determine if a number is less than, greater than, equal to, or not equal to another number, enabling decision-making and comparisons within arithmetic and programming operations.

When comparing numbers, you can use various relational operators to determine the relationship between them. Here are the commonly used comparison operators:

Less than (<): This operator compares two numbers and returns true if the first number is smaller than the second number. For example, 5 < 10 is true.

Greater than (>): This operator compares two numbers and returns true if the first number is larger than the second number. For example, 10 > 5 is true.

Less than or equal to (<=): This operator compares two numbers and returns true if the first number is smaller than or equal to the second number. For example, 5 <= 5 is true.

Greater than or equal to (>=): This operator compares two numbers and returns true if the first number is larger than or equal to the second number. For example, 10 >= 10 is true.

Equal to (==): This operator compares two numbers and returns true if they are equal. For example, 5 == 5 is true.

Not equal to (!=): This operator compares two numbers and returns true if they are not equal. For example, 5 != 10 is true.

These comparison operators allow you to compare numbers and make decisions based on their relationships within arithmetic or programming operations.

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As per the unitary method, the amount of white beans are there than kidney beans are 30.

The term unitary method is known as a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.

Here we have given that in a jar containing dry beans, the ratio of white beans to kidney beans is 5:4.

And we also know that if 30 white beans were replaced with 30 kidney beans, the ratio would be 1:1.

Here we have consider that let the number of pinto beans be x and that is the number of white beans will be x + 30

In which means the total number of beans in the jar will be written as,

=> x + x + 30 = 2x + 30

Here we know that the Total ratio is calculated as,

=> 5 + 4  = 9

In order to find the number of pinto beans then it can be calculated as,

=> ratio of pinto beans / Total ratio  X Total number of beans

Which can be written as.

=>  (2x + 30) = x

When we simplify this one then we get the value of x as,

=> x = 30.

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Answer:  I believe the answer is 16 hope this helps

Step-by-step explanation:

Step-by-step explanation:

3 + 6 = 9

9 x 2 = 18

12/18 = 0.66 repeating

0.66 repeating >> simplified >> 2/3

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The probability of the shop purchasing is 5/9.

Let X be the number of non-defective engines purchased by the auto shop out of the 4 engines bought. We want to find P(X >= 3), the probability of getting at least 3 non-defective engines.

Using the hypergeometric distribution formula, we have:

P(X >= 3) = P(X = 3) + P(X = 4)

where

P(X = k) = (C(7, k) * C(2, 4-k)) / C(9, 4)

So, we have:

P(X = 3) = (C(7, 3) * C(2, 1)) / C(9, 4) = (35 * 2) / 126 = 5/18

P(X = 4) = (C(7, 4) * C(2, 0)) / C(9, 4) = (35 * 1) / 126 = 5/18

Therefore,

P(X >= 3) = 5/18 + 5/18 = 10/18 = 5/9

So the probability of the shop purchasing at least 3 non-defective engines is 5/9.

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Answer:

x=-45

Step-by-step explanation:

-x/3=15

-x=15×3

=45

Hence, x=-45.

Answer:

x = -45

Step-by-step explanation:

-x/3 = 15

Multiply each side by -3

-x /3 * -3 = 15 *-3

x = -45

The unit price of a mini action figures given the total cost as $18.96 is $4.74.

This is the price per each item of a particular good. We can get unit price by dividing the price of certain number of units of an item by the number of units to find the unit price of that item.

Unit price = Total price of items / total number of items.

Unit price of mini action figures = Total cost of items / Number of mini action figures

= $18.96 / 4

= $4.74

Therefore, the unit price of a mini action figures given the total cost as $18.96 is $4.74.

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Answer:

1:3

Step-by-step explanation:

3:12 is the amount of shaded circles to all circles, 8:2 is basically the same thing as 3:12 and 9:3 is the amount of shaded circles to the amount of non-shaded circles.  1:3 wouldn't work because it is not the right ratio.

Answer:

200

Step-by-step explanation:

Answer:

The y-intercept is 1/3

Step-by-step explanation:

The y-intercept of the function is 1/3 because if u put into form y=mx+b then the b is the y-intercept.

Answer:

1/3

Step-by-step explanation:

For this formula you look at the b value from the formula y = mx + b where in this case b = 1/3

Answer:

the answer for your question is 1200pi