T/F : If A is a 5Ã4 matrix, and B is a 4Ã3 matrix, then the entry of AB in the 3rd row / 2nd column is obtained by multiplying the 3rd column of A by the 2nd row of B

We need a sample size of at least 665 drivers to estimate the proportion of all drivers exceeding the legal speed limit on the certain stretch of road between Los Angeles and Bakersfield with a margin of error of 0.04 and a 99% confidence level.

To estimate the proportion of all drivers exceeding the legal speed limit on a certain stretch of road between Los Angeles and Bakersfield with a margin of error of 0.04 and a 99% confidence level, we need to use the following formula:

[tex]n = (Z^2 * p * (1 - p)) / E^2[/tex]

where n is the sample size, Z is the Z-score for the desired confidence level (2.576 for 99% confidence level), p is the estimated proportion of drivers exceeding the speed limit (we don't have an estimate, so we'll use 0.5 for maximum variability), and E is the margin of error we want (0.04).

Plugging in the values, we get:

[tex]n = (2.576^2 * 0.5 * (1 - 0.5)) / 0.04^2[/tex]

n = 664.92

Therefore, we need a sample size of at least 665 drivers to estimate the proportion of all drivers exceeding the legal speed limit on the certain stretch of road between Los Angeles and Bakersfield with a margin of error of 0.04 and a 99% confidence level.

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The vectors u and v are not equal because they have different direction.

If the initial point is (x₁, y₁)  and terminal point is (x₂, y₂) then the vector is

Vector =(x₂-x₁)i+(y₂-y₁)j

Vector v with an initial point of (0, 0) and a terminal point of (50,120).

Vector v = 50i+120j..(1)

Vector u with an initial point of (50, 120) and a terminal point of (0,0).

Vector u = (0-50)i+(0-120)j

=-50i-120j..(2)

Hence, the vectors u and v are not equal because they have different direction.

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The gradient of the line is 2

[tex]Distance AB = \sqrt{[(5-(-3))^2 + (2-4)^2]}= \sqrt{68} \\Distance AC = \sqrt{[(-3-0)^2 + (4-(-3))^2]} = \sqrt{58} \\Distance BC = \sqrt{[(5-0)^2 + (2-(-3))^2]}= \sqrt{50}[/tex]

mAB = (2 - 4) / (5 - (-3)) = -1/2

This is the slope of AB

-1 / (-1/2) = 2

we have to find the point that is perpendicular to AB

(-3 + 5) / 2 = 1

(4 + 2) / 2 = 3

1 , 3 are  perpendicular to AB

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

There fore the gradient of the line is 2

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Answer:

87.3

Step-by-step explanation:

131 ÷ 1.5 = 87.3

The answer will be 87.3 repeat.

131 divided by 1.5 is equal to 8 with a remainder of 11, or 8.7333 (rounded to four decimal places).

We have,

To divide 131 by 1.5, we can perform the division operation as follows:

131 ÷ 1.5

To make the calculation easier, we can convert 1.5 to an equivalent fraction with a denominator of 10.

We can multiply both the numerator and denominator by 10 to get 15.

So, the division becomes:

131 ÷ 15

When we divide 131 by 15, we get a quotient of 8 with a remainder of 11.

Therefore,

131 divided by 1.5 is equal to 8 with a remainder of 11, or 8.7333 (rounded to four decimal places).

131 ÷ 1.5 is approximately equal to 8.7333.

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According to the given information, the noise level in a restaurant is normally distributed with an average of 30 decibels. To find the value below which 99% of the time the noise level is, we need to use the Z-table.

We know that 99% of the area under the normal curve is below a Z-score of 2.33 (found from the Z-table).

To find the corresponding noise level value, we use the formula:

Z-score = (X - μ) / σ

where X is the noise level value we want to find, μ is the average (30 decibels), and σ is the standard deviation (which is not given in this question).

However, we can use the empirical rule (68-95-99.7 rule) to estimate the standard deviation. According to the rule, 99.7% of the data falls within 3 standard deviations of the mean. So, if 99% of the time the noise level is below a Z-score of 2.33, then we can estimate that the standard deviation is approximately:

(2.33 x σ) = 3

Solving for σ, we get:

σ = 3 / 2.33 = 1.29 (approx.)

Now we can use the formula above to find the noise level value below which 99% of the time the noise level is:

2.33 = (X - 30) / 1.29

X - 30 = 2.33 x 1.29

X = 33.01

So, 99% of the time, the noise level in the restaurant is below 33.01 decibels (rounded to two decimal places).

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The probability that during a snowstorm the company will lose both sources of power is 2.7%.

To find the probability that during a snowstorm the company will lose both sources of power, we need to multiply the probabilities of each event happening. Since the two sources are independent, we can use the formula: P(A and B) = P(A) * P(B).

Let A be the event that there is a power failure during a snowstorm, with a probability of 0.30.

Let B be the event that the generator will stop working during a snowstorm, with a probability of 0.09.

Then, the probability of both events happening together is:

P(A and B) = P(A) * P(B)

P(A and B) = 0.30 * 0.09

P(A and B) = 0.027 or 2.7%

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Rounding up to the nearest whole number, we get a sample size of 314 students. Therefore, if we randomly select 314 students who are classified as high on their need for closure. we can be 99% confident that the sample mean score is within 1.5 points of the population mean score.

To determine the sample size needed, we can use the formula:

n = (z * σ / E)^2

Where:
z = the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence)
σ = the population standard deviation (8.35)
E = the maximum allowable error (1.5)

Plugging in these values, we get:

n = (2.576 * 8.35 / 1.5)^2
n = 313.15

To determine the required sample size for a 99% confidence interval within 1.5 points of the population mean score, follow these steps:

1. Identify the given information:
- Population standard deviation (σ) = 8.35
- Desired margin of error (E) = 1.5
- Confidence level (z-score) = 2.576 (for 99% confidence interval)

2. Use the formula for sample size calculation:
n = (Z * σ / E)^2

3. Plug in the values:
n = (2.576 * 8.35 / 1.5)^2

4. Calculate the result:
n ≈ 121.22

5. Round up to the nearest whole number:
n = 122 students

So, a sample size of 122 students is needed to be 99% confident that the sample mean score is within 1.5 points of the population mean score for students who are high on the need for closure.

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The 8th term of the geometric sequence [tex]4,-12, 36[/tex]  is  [tex]-8748[/tex].

We must find common ratio by dividing the term by its preceding term. By dividing second term (-12) by the first term (4), this gives us:

= -12 / 4

= -3

So, the common ratio is -3.

The formula for the nth term of geometric sequence to find the 8th term is : an = a1 * r^(n-1) where an = nth term, a1 =  first term, r =  common ratio and n = term number

a8 = 4 * (-3)^(8-1)

a8 = 4 * (-3)^7

a8 = 4 * (-2187)

a8 = -8748.

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29. The percentage of change is -39.66%.

30. The percentage of change is 35.29%

31. The percentage of change is 150.38%.

32. The percentage of change is -62.5%

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

The percentage of change is

= (-2300 / 5800) × 100

= -39.66%.

The percentage of change is:

= 6/17 × 100

= 35.29%

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The two number lines to represent these fractions are shown in the image attached below.

Marcus has more homework left to complete.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

For James, he has completed 3x/4 of his homework while Marcus has completed 2x/3 of his homework and as such, Marcus has more homework left to complete.

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The time taken by them to complete the work is 18 minutes.

Time taken by Sophie to peel all the potatoes = 45 minutes

Time taken by Simon to peel all the potatoes = 30 minutes

Amount of work done by Sophie in one minute = 1/45

Amount of work done by Simon in one minute = 1/30

Let the time taken by both of them to complete the work together be x.

So, the time taken by them to complete the work,

1/x = (1/45) + (1/30)

x = 1350/75

x = 18 minutes

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False. If Determinant  A is zero, it does not necessarily imply that two columns of A must be the same or that all elements in a row or column of A are zero.

If det A is zero, it does not necessarily imply that two columns of A must be the same or that all elements in a row or column of A are zero.

For example, consider the following 2x2 matrix:

A = [1 2]
   [2 4]

The determinant of A is det(A) = (1*4 - 2*2) = 0, but the columns of A are not the same, and not all elements in a row or column are zero.

However, it is true that if two columns of A are the same or all of the elements in a row or column of A are zero, then det A must be zero.

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The annual payment is $7,351.98 if the APR rate is 6.75% over a 20-year period.

Area of land =  275 acres

Price = $4,300/acre

Time = 20-year

APR rate =  6.75%

down payment  = 25% of the total cost

Total cost = 275 acres x $4,300/acre

Total cost  = $1,182,500

Down payment = 0.25 x $1,182,500

Down payment = $295,625

The remaining amount = Total cost - Down payment

The remaining amount  = $1,182,500 - $295,625

The remaining amount = $886,875

The present value of an annuity,

PMT = [tex](r * PV) / (1 - (1 + r)^{n} )[/tex]

The interest rate =  6.75% / 12 = 0.5625% per month

The total number of periods = 20 years x 12 months/year = 240 months.

PMT = [tex](0.005625 * $886875) / (1 - (1 +0.005625)^{240} )[/tex]

PMT  = $7,351.98

Therefore, we can conclude that the annual payment is approximately $7,351.98

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The sum of the numbers 3+6+9+12+....+150 is 3825. To find the sum of an arithmetic series, you can use the formula:

Sum = (n * (a1 + an)) / 2

where n is the number of integers, a1 is the first integer, and an is the last integer.

In this case, the series is 3, 6, 9, ..., 150, and it's an arithmetic series with a common difference of 3. To find the number of integers (n) in the series, use the formula:

n = ((an - a1) / common difference) + 1

n = ((150 - 3) / 3) + 1 = (147 / 3) + 1 = 49 + 1 = 50

Now, use the sum formula:

Sum = (n * (a1 + an)) / 2
Sum = (50 * (3 + 150)) / 2
Sum = (50 * 153) / 2
Sum = 7650 / 2
Sum = 3825

So the sum of the given series is 3825.

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The calclated length of segment OG is 8 units

From the question, we have the following parameters that can be used in our computation:

DG = 4√5

DO = 4.

The length OG is calculated as

OG^2 = DG^2 - DO^2

substitute the known values in the above equation, so, we have the following representation

OG^2 = (4√5)^2 - 4^2

Evaluate

OG^2 = 64

So, we have

OG = 8

Hence, the solution is 8

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The calculated volume of the prism is 104 cubic feet

From the question, we have the following parameters that can be used in our computation:

Volume of right pyramid = 312 cubic feet

The volume of the prism next to it is calculated as

Volume = 1/3 * Volume of right pyramid

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3 * 312 cubic feet

Evaluate

Volume = 104 cubic feet

Hence, the volume is 104 cubic feet

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The coefficient of the squared term in the parabola's equation is 1/25.

In this exercise, you are required to determine the factored form of the given quadratic function that passes through the points (2, -4) and (-3, -3).

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided above, we can determine the value of a as follows:

f(x) = a(x - h)² + k

-3 = a(-3 - 2)² - 4

-3 = 25a - 4

1 = 25a

a = 1/25

Therefore, the required quadratic function is given by:

f(x) = a(x - h)² + k

f(x) = y = 1/25(x - 2)² - 4

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The maximum monthly profit is $420.  To find the maximum monthly profit, we need to find the production level (X) that will maximize the profit.

We can do this by setting the marginal profit equation equal to zero and solving for X:

p'(x) = -0.4x + 20 = 0
0.4x = 20
x = 50

So, the production level that will maximize the profit is 50 widgets per month.

To find the maximum monthly profit, we need to calculate the total monthly revenue and subtract the fixed cost. The total monthly revenue can be calculated as the product of the price per unit and the number of units sold:

p(x) = -0.2x^2 + 20x
p(50) = -0.2(50)^2 + 20(50) = $500

So, the total monthly revenue is $500.

The maximum monthly profit can now be calculated as:

Profit = Total Revenue - Fixed Cost
Profit = $500 - $80
Profit = $420

Therefore, the maximum monthly profit is $420.

So, the answer is $420.

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The bird with the greater wingspan is the great egret

To determine the greater wingspan, we need to know the following conversion values, we have;

1 decimeter = 10 centimeters

1 decimeter = 100millimeters

1 centimeter = 10 millimeters

From the information given, we have;

The red-tailed hawk = 1,100 millimeters

The great egret = 180 centimeters

convert the millimeters to centimeters

if 1 centimeters = 10 millimeters

then, 180 centimeters = x

cross multiply

x = 1800 millimeters

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Therefore, the linearization of f(x) at a = -1 is L(x) = -10x - 6.

To find the linearization L(x) of the function f(x) = x⁴ + 3x² at a = -1, we need to use the formula:

L(x) = f(a) + f'(a)(x-a)

where f'(x) is the derivative of f(x) with respect to x.

First, we need to find f(-1) and f'(-1).

f(-1) = (-1)⁴ + 3(-1)²

= 1 + 3

= 4

f'(x) = 4x³ + 6x

f'(-1) = 4(-1)³ + 6(-1)

= -4 - 6

= -10

Now we can substitute these values into the linearization formula:

L(x) = f(-1) + f'(-1)(x - (-1))

L(x) = 4 - 10(x + 1)

L(x) = -10x - 6

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Based on fractional values, if Susan originally has 7 yards of fabric, after making 3 aprons consuming 5⁵/₈ yards, the quantity of fabric left is 1³/₈ yards.

Fractional values are the results of fractional computations.

Fractions may be proper, improper, and complex fractions, depending on the values of the denominators and the numerators.

Algebraic expressions that have fractions are stated as fractional values.

The original quantity of fabric that Susan has = 7 yards

The quantity of fabric used for the front of each apron = 1¹/₄ yards

The quantity of fabric used for the tie of each apron = ⁵/₈ yards

The total quantity of fabric used for each apron = 1⁷/₈ yards (1¹/₄ + ⁵/₈)

The total quantity of fabric used for the 3 aprons made = 5⁵/₈ yards (1⁷/₈ x 3)

Therefore, the remaining quantity of fabric that Susan has after making the 3 aprons = 1³/₈ yards (7 - 5⁵/₈).

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Susan first made 3 aprons using 1¹/₄ yards for the front and ⁵/₈ yards for the tie.

The area of the shaded region is 180 square feet.

The figiure in the image is a triangle inscribed in a rectangle.

To get area of the shaded region, we subtract the area of the triangle from the area of the rectangle.

For the triangle:

For the rectangle:

Hence:

Area of the shaded region = Area of rectangle - Area of triangle

Area of the shaded region = ( length × width ) - ( 1/2 × base × height )

Area of the shaded region = ( 18ft × 12ft ) - ( 1/2 × 8ft × 9ft )

Area of the shaded region = 216ft ²- 36ft²

Area of the shaded region = 180ft²

Therefore, the area is 180ft².

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The Domain of the function is Domain = {-1, -1, -2, -2, -3, -3, -4, -4}.

Yes the relation a function.

We have the set,

{(-1,1), (-1,-1),(-2,2), (-2,-2),(-3,3),(-3,-3),(-4,4), (-4,-4)}

We know that the domain is the input value or the x value.

So, Domain = {-1, -1, -2, -2, -3, -3, -4, -4}

and, the range is the output value or y value

So, Range = {1, -1, 2, -2, 3, -3, 4, -4}

As, each input value have distinct output s then the relation a function.

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The drive-thru is able to estimate their wait time more consistently will be;

⇒ A. Burger Quick, because it has a smaller IQR.

Since, The range of values in the middle of the scores is known as the interquartile range, or IQR.

The appropriate measure of variability is the interquartile range when a distribution is skewed and the median is used instead of the mean to show a central tendency.

Since, IQR is the difference between the third quartile and the first quartile, which is represented by the box in the box plot.

Now, In this case, the IQR for Burger Quick is,

15.5 - 8.5 = 7.0,

while the IQR for Fast Chicken is,

14.5 - 10 = 4.5.

Hence, A smaller IQR indicates that the data is more consistent and less spread out.

Thus, The correct option here is Burger Quick, because it has a smaller IQR (Interquartile Range).

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The length of side x based on the triangle given will be 26.2cm.

It should be noted that the image of the triangle is missing, so i have attached it.

In this case, to find the value of x, we will use cosine rule;

x² = 15² + 18² - 2(15 × 18)cos105

x² = 225 + 324 - 540(-0.2558)

x² = 549 + 138.132

x² = 687.132

x ≈ 26.2 cm

Therefore, length of side x based on the triangle given will be 26.2cm.

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If 15 people are each bringing 2 tables, then there will be a total of 30 tables at the family reunion.

Since there are the same amount of people sitting at each table, we can divide the total number of people (90) by the total number of tables (30).

90 ÷ 30 = 3

Therefore, there will be 3 people sitting at each table.

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In a double-elimination tournament with n players, the minimum number of matches that can be played is 2n - 3, and the maximum number of matches is 3n - 3.

In a double-elimination tournament with n players, we need to determine the minimum and maximum number of matches that can be played. Here's the step-by-step explanation:

1. the Minimum number of matches:
In a double-elimination tournament, each player is eliminated after their second loss. The minimum number of matches occurs when all players except the eventual winner lose twice in succession. In this case, there will be (n-1) matches in the winner's bracket and (n-2) matches in the loser's bracket.

Minimum number of matches = (n-1) + (n-2)
                                     = 2n - 3

2.The maximum number of matches:
In the maximum case scenario, each player has to be defeated twice except the eventual winner who will only have one defeat. This means there will be (n-1) matches in the winner's bracket and 2(n-1) matches in the loser's bracket.

Maximum number of matches = (n-1) + 2(n-1)
                                      = 3n - 3

So, in a double-elimination tournament with n players, the minimum number of matches that can be played is 2n - 3, and the maximum number of matches is 3n - 3.

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The given representation is a quadratic function.

The given table can be represented in the form of equation as,

y = x²

When x = 0, y = 0

When x = 1, y = 1

When x = 2, y = 2² = 4

When x = 3, y = 3² = 9

When x = 4, y = 4² = 16

This can be written as,

y = x² + 0x + 0

This is a quadratic function.

Hence the given representation is a quadratic function.

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To prove that the recursive algorithm for finding the reversal of a bit string is correct, let's consider the algorithm's key components: base case, recursive case, and the correctness of the algorithm

The recursive algorithm for finding the reversal of a bit string is as follows:

1. If the string is empty or has only one character, return the string as it is.
2. Otherwise, split the string into two parts: the first character (i.e., the leftmost character) and the rest of the string (i.e., all the other characters).
3. Recursively reverse the rest of the string.
4. Concatenate the reversed rest of the string with the first character.

To prove that this algorithm is correct, we need to show that it produces the correct output for any input string. We can do this by induction on the length of the string.

Base case: If the string is empty or has only one character, the algorithm returns the string as it is, which is the correct reversal.

Induction step: Suppose the algorithm correctly reverses any string of length n or less. We want to show that it also correctly reverses any string of length n+1. Let s be a string of length n+1, and let s' be the string obtained by removing the last character of s. Then we have s = s' + c, where c is the last character of s.

By the induction hypothesis, the algorithm correctly reverses s'. Let s'' be the reversed s'. Then s'' + c is the reversal of s, since the reversed s' is the reversed rest of the string, and c is the first character.

Therefore, the algorithm correctly reverses any string of length n+1, and by induction, it correctly reverses any string of any length.

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The mean value theorem states that if a function f(x) is continuous on the interval [a, b] and differentiable on (a, b), then there exists a value c in (a, b) such that:

f'(c) = (f(b) - f(a))/(b - a)

In this case, the interval is [2, 6]. So, we need to find the value(s) of c that satisfy:

f'(c) = (f(6) - f(2))/(6 - 2)

We can make an estimate based on the graph of the function.

If the graph of f(x) is a straight line between (2, f(2)) and (6, f(6)), then the derivative is constant over the interval [2, 6]. In this case, we can use the formula:

f'(c) = (f(6) - f(2))/(6 - 2) = (y2 - y1)/(x2 - x1)

where (x1, y1) = (2, f(2)) and (x2, y2) = (6, f(6)).

Solving for c, we get:

c = (x1 + x2)/2 = (2 + 6)/2 = 4

This is the only value of c that satisfies the conclusion of the mean value theorem in this case.

If the graph of f(x) is not a straight line, then we cannot make a simple estimate for c based on the graph alone.
To estimate the value(s) of c that satisfy the conclusion of the Mean Value Theorem (MVT) on the interval [2, 6], you need to follow these steps:

1. Identify the function, f(x), that you're working with.

2. Ensure the function is continuous on the interval [2, 6] and differentiable on the open interval (2, 6). This is required for MVT to be applicable.

3. Calculate the average rate of change (mean value) of the function over the interval [2, 6] by using the formula (f(6) - f(2)) / (6 - 2).

4. Take the derivative of the function, f'(x).

5. Set f'(x) equal to the mean value calculated in step 3 and solve for the value(s) of x, which will give you the value(s) of c that satisfy the MVT.

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