As he heads to the store, after how many minutes was Hakeem 1 blocks from his house?

The given information tells us that Terry's wins-to-races ratio is 2:3, but we cannot determine the exact number of races he has won without additional information about the total number of races he has participated in.

If the ratio of the number of times Terry has won to the number of races he has swum in is 2:3, we can set up a proportion to determine the number of races he has won.

Let's denote the number of times Terry has won as x, and the total number of races he has swum in as y. According to the given ratio, we have:

x/y = 2/3

To find the value of x, we need to solve for x when y is known. Since y represents the total number of races, we don't have that information in the given problem. Therefore, we cannot determine the exact number of races Terry has won without knowing the total number of races he has participated in.

The ratio tells us the relationship between the number of wins and the total number of races, but without knowing the denominator (total races), we cannot find a specific value for the numerator (number of wins). We can only determine the ratio between the two quantities.

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Given statement solution is :- a) T = [tex]A^−1[/tex] b) T - 1.

For suitable values of s = -2 and t = 1, T = [tex]A^−1[/tex] and T - 1.

To show that for suitable values of s and t, T = [tex]A^−1[/tex], and T - 1, let's assume a matrix A and its inverse [tex]A^−1[/tex]. We'll find suitable values of s and t such that T = [tex]A^−1[/tex] and T - 1.

Consider the equation T = [tex]A^−1[/tex]. If T is the inverse of A, then we have A * [tex]A^−1[/tex] = I, where I is the identity matrix. Let's construct a specific matrix A and solve for [tex]A^−1[/tex] to find T.

Let's take the following matrix A:

A = [[1, 2],

[3, 4]]

To find the inverse of A, we can use the formula:

[tex]A^−1[/tex] = (1 / det(A)) * adj(A)

where det(A) represents the determinant of A, and adj(A) is the adjugate of A.

The determinant of A is calculated as follows:

det(A) = 1 * 4 - 2 * 3 = -2

Now, let's find the adjugate of A by interchanging the elements of the main diagonal and changing the sign of the other elements:

adj(A) = [[4, -2],

[-3, 1]]

Finally, we can compute [tex]A^−1[/tex] by multiplying the adjugate by the reciprocal of the determinant:

[tex]A^−1[/tex] = (1 / -2) * [[4, -2],

[-3, 1]]

= [[-2, 1],

[3/2, -1/2]]

Therefore, we have found the inverse of A. We can set T =[tex]A^−1[/tex]:

T = [[-2, 1],

[3/2, -1/2]]

Now, let's show that T - 1 using suitable values of s and t. To do that, we'll assume T - 1 = [tex]A^−1[/tex] and solve for s and t.

Let's set T - 1 =[tex]A^−1:[/tex]

T - 1 = [[-2, 1],

[3/2, -1/2]]

We can rewrite T - 1 as:

T - 1 = [[s, t],

[u, v]]

Comparing the corresponding elements, we have:

s = -2

t = 1

u = 3/2

v = -1/2

Therefore, for s = -2 and t = 1, we have T - 1 = [tex]A^−1.[/tex]

In conclusion, we have shown that for suitable values of s = -2 and t = 1, T = [tex]A^−1[/tex] and T - 1.

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The current yield of the corporate bond is 14.23%.

1. To calculate the current yield, we need to divide the annual coupon payment by the market price of the bond.

2. The annual coupon payment can be calculated by multiplying the coupon rate by the par value of the bond.

  Annual coupon payment = Coupon rate * Par value = 13.41% * $1,000 = $134.10

3. The market price of the bond is given as $943.01.

4. Now, divide the annual coupon payment by the market price of the bond and multiply by 100 to convert it to a percentage.

  Current yield = (Annual coupon payment / Market price of the bond) * 100

  Current yield = ($134.10 / $943.01) * 100

  Current yield ≈ 0.1423 * 100 ≈ 14.23%

5. Round off the current yield to two decimal points, and that gives us the final answer.

  The current yield of the corporate bond is 14.23%.

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The computer can occupy a maximum of 1200 bytes of memory.

To determine the maximum memory capacity of a computer that can execute 300 instructions, we need to consider the representation of integers and the storage requirements for instructions.

If each instruction is stored in the entire memory word, it implies that each instruction occupies one memory word. Therefore, the number of instructions executed (300) directly corresponds to the number of memory words required.

The memory capacity of a computer is typically measured in bytes. However, since we are assuming each instruction occupies one memory word, we can consider the memory capacity in terms of memory words.

Hence, the maximum memory capacity this computer can occupy would be 300 memory words.

To convert this capacity into bytes, we need to know the size of a memory word. If we assume the computer uses a 32-bit word size, which is common in many systems, each memory word would consist of 4 bytes (32 bits / 8 bits per byte). Therefore, the maximum memory capacity in bytes would be:

300 memory words * 4 bytes per word = 1200 bytes.

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The solution to the equation 4 |x + 7| + 8 = 32 is x = -1 and x = -13.So, the correct answer is: B. x = -1 and x = -13

To solve the equation 4 |x + 7| + 8 = 32, we can follow these steps:

1. Subtract 8 from both sides of the equation:

  4 |x + 7| = 24

2. Divide both sides by 4:

  |x + 7| = 6

Now we have two cases to consider, one for when x + 7 is positive and one for when x + 7 is negative.

Case 1: x + 7 ≥ 0

In this case, the absolute value simplifies to x + 7:

  x + 7 = 6

  Subtract 7 from both sides:

  x = -1

Case 2: x + 7 < 0

In this case, the absolute value simplifies to -(x + 7) since x + 7 is negative:

  -(x + 7) = 6

  Remove the negative sign:

  x + 7 = -6

  Subtract 7 from both sides:

  x = -13

Therefore, the solution to the equation 4 |x + 7| + 8 = 32 is x = -1 and x = -13.

So, the correct answer is:

B. x = -1 and x = -13

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Answer:

It will take approximately 9 years to take investment *o reach the value of $940

Answer:

y = 3 * 9^x

Step-by-step explanation:

To write an exponential function in the form y = ab that goes through the points (0, 3) and (2, 243), we need to find the values of a and b.

Let's start by using the point (0, 3). When x = 0, y = 3. Substituting these values into the exponential function equation, we get:

3 = ab^0

3 = a * 1

a = 3

Now, let's use the second point (2, 243). When x = 2, y = 243. Substituting these values into the exponential function equation, we get:

243 = 3b^2

To find the value of b, we can rewrite the equation as:

3b^2 = 243

Dividing both sides of the equation by 3, we have:

b^2 = 81

Taking the square root of both sides, we get:

b = ±9

Since we are looking for a positive value for b, we can take b = 9.

Therefore, the exponential function that goes through the points (0, 3) and (2, 243) is: y = 3 * 9^x

[tex]((x^3) * (x^2))^4[/tex] divided by [tex]3x^4[/tex]simplifies to[tex]x^{16/3[/tex]using the rules of exponents.

To simplify the expression[tex]((x^3) * (x^2))^4[/tex]divided by [tex]3x^4[/tex], we need to follow the rules of exponents.

First, let's simplify the numerator,[tex]((x^3) * (x^2))^4[/tex]. According to the exponent rule for multiplying powers with the same base, when we multiply two powers with the same base, we add their exponents. Applying this rule, we get[tex](x^{(3+2)})^4[/tex], which simplifies to [tex](x^5)^4.[/tex]

Next, we apply the exponent rule for raising a power to another power. When we raise a power to another power, we multiply the exponents. In this case, we have [tex](x^5)^4[/tex], which becomes [tex]x^{(5*4)[/tex] or [tex]x^{20.[/tex]

Now let's simplify the denominator, [tex]3x^4[/tex]. Since division is equivalent to multiplying by the reciprocal, we can rewrite the expression as [tex](x^{20})/(3x^4).[/tex]

To simplify this division, we use the exponent rule for dividing powers with the same base. According to this rule, when we divide two powers with the same base, we subtract their exponents. In this case, we have [tex]x^{20[/tex] divided by x^4, which gives us[tex]x^{(20-4)[/tex]or x^16.

Therefore, the simplified expression for [tex]((x^3) * (x^2))^4[/tex]divided by 3x^4 is[tex]x^{16/3.[/tex] This is the final answer, as the expression has been simplified as much as possible.

In summary,[tex]((x^3) * (x^2))^4[/tex]divided by 3x^4 simplifies to [tex]x^{16/3[/tex] using the rules of exponents.

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Answer:

-4 < x < 1/2

Step-by-step explanation:

Given the inequality:

[tex]\displaystyle{\dfrac{x+4}{2x-1} < 0}[/tex]

Where x can not equal 1/2 since it will result the undefined expression. Furthermore, by solving a rational inequality (fractional inequality) is different from solving a linear inequality.

If we assume that for the expression on the left side is always positive, we can say that:

[tex]\displaystyle{\dfrac{x+4}{2x-1} < 0}[/tex]

However, the expression can remain negative. If a denominator remains somewhat negative and you multiply both sides by the denominator, you'll end up from < to >, basically swap in inequality sign.

Thus. If we let x > 1/2, the interval where the expression is always positive, we can solve the inequality as:

[tex]\displaystyle{\dfrac{x+4}{2x-1} \cdot \left(2x-1\right) < 0 \cdot \left(2x-1\right)}\\\\\displaystyle{x+4 < 0}\\\\\displaystyle{x < -4}[/tex]

However, this inequality is false so we can say that there's no region where this expression is less than 0 at x > 1/2.

Now let's say that at x < 1/2, the expression will start to remain in negative (although there is an interval that the expression is positive at x < 1/2 but majority negative.) Therefore, let's say:

[tex]\displaystyle{-\dfrac{x+4}{2x-1} < 0}\\\\\displaystyle{\dfrac{x+4}{2x-1} > 0}[/tex]

When we solve for the inequality, we should have x + 4 > 0 which results in x > -4. When union x > -4 with x < 1/2, it fits perfectly. Thus, the solution is:

[tex]\displaystyle{-4 < x < \dfrac{1}{2}}[/tex]

The boat will arrive at the other port at 12:45 p.m.

To determine the time the boat arrives at the other port, we can use the formula:

Time = Distance / Speed

Given:

Distance = 80 km

Speed = 32 km/h

Calculate the time it takes for the boat to travel the given distance:

Time = Distance / Speed

Time = 80 km / 32 km/h

Time = 2.5 hours

Convert the time to minutes:

Since the time is given in hours, we need to convert it to minutes.

1 hour = 60 minutes

2.5 hours = 2.5 * 60 = 150 minutes

Add the calculated time to the departure time:

The boat leaves the port at 10:15 a.m. We need to add 150 minutes to this time to find the arrival time.

10:15 a.m. + 150 minutes = 12:45 p.m.

Therefore,​ the boat will arrive at the other port at 12:45 p.m.

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To identify the correct weight to the nearest 1/8 pound, you need to have a weight measurement that is divisible by 1/8 pound. If you have a weight that is not divisible by 1/8 pound, then you need to round it to the nearest 1/8 pound.

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By following this rounding method, you can determine the correct weight to the nearest 1/8 pound based on the specific weight measurement provided.

To identify the correct weight to the nearest 1/8 pound, we need a specific weight or measurement to work with.

Once we have that information, we can apply the rounding method.

When rounding to the nearest 1/8 pound, we look at the digit immediately after the 1/8 pound mark, which is 0.125 pounds.

If this digit is 4 or less, we round down, and if it is 5 or greater, we round up.

For example, let's say we have a weight of 15.6 pounds. The digit after the 1/8 pound mark is 6, which is greater than 4.

Therefore, we round up, and the weight to the nearest 1/8 pound is 15.75 pounds.

On the other hand, if we have a weight of 12.3 pounds, the digit after the 1/8 pound mark is 3, which is less than 4.

Thus, we round down, and the weight to the nearest 1/8 pound is 12.25 pounds.

Similarly, if the weight is 22.7 pounds, the digit in the thousandth place is 7. Since 7 is greater than 4, we round up.

The 1/8 pound measurement is 0.125 pounds, so rounding up gives us 22.875 pounds.

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