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711/6
sin
2
7π
tan
12
711/6
COS
2
? ] + [
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Carl made a mistake by multiplying the two values in the quotient rather than dividing them.

So, the result of 4 divided by 2 1/3 and an explanation of Carl's error:

Thus, if we divide 4 2/3 by 2 1/3, we get:

Carl made the error of assuming his quotient (2) was equal to the value of the terms it contained.

Therefore, Carl made a mistake by multiplying the two values in the quotient rather than dividing them.

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Answer:

I BELIEVE THE ANSWER WOULD BE C

Step-by-step explanation:

Hey there! :)

Answer:

15° Celsius.

Step-by-step explanation:

Begin by deriving an equation to represent the values in the table. Use the slope formula:

\(m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

Plug in values from the table into the formula:

\(m = \frac{27.0 - 22.2}{15-9}\)

Simplify:

\(m = \frac{4.8}{6}\)

Reduces to:

m = 0.8. This is the slope of the equation.

Use a point from the table and plug it into the equation y = mx + b, along with the slope to calculate the y-intercept:

27 = 0.8(15) + b

27 = 12 + b

27 - 12 = b

b = 15. This represents the value when x = 0, therefore:

The engine's temperature at rest is 15° Celsius.

Answer:

15

Step-by-step explanation:

Answer: Length = 43 ; Breadth = 21.5

Step-by-step explanation:

Let the width be 'x'

The length = 2x

The perimeter = 129

Formula of perimeter of rectangle = 2 ( length + breadth )

Substitute:

2 ( 2x + x ) = 129

2 ( 3x ) = 129

6x = 129

x = 21.5

Therefore, the width = 21.5

Length  = 2x = 2(21.5) = 43

To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

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ANSWER

7/15

EXPLANATION

We can see that there are 6 time slots. It is said that the first five are 50 minutes long and the 6th is 75 minutes long.

Gerald has a class on the 2nd slot, another on the 3rd slot and one more in the 6th slot. Therefore in total he's scheduled for:

175 minutes of class.

We have to see how many minutes there are between 8 AM and 2:15 PM. We can add first the hours: from 8am to 12pm there are 4 hours. Then from 12pm to 2 pm there are 2 more hours. In total that's 6 hours which in minutes is:

But we have to add the last 15 minutes:

In summary, between 8AM and 2:15 PM there are 375 minutes, from which 175 minutes are the one Gerald has classes. To find the fraction we have to put 175 in the numerator and 375 in the denominator:

And simplify:

So Gerald is scheduled for class 7/15 of the time between 8AM and 2:15 PM

If the company hires an expert at a cost of $75,000 to perform tests to predict the presence of oil in the field, the Expected Monetary Value (EMV) is $1,002,500.

To calculate the EMV if the company hires the expert, we need to consider the different scenarios and their probabilities.

Scenario 1: The test predicts oil on the field (with a probability of 0.55).

In this case, the probability of actually finding oil is 0.85.

The value if oil is found is $3,650,000.

Scenario 2: The test does not predict oil on the field (with a probability of 0.45).

In this case, the probability of actually finding oil is 0.2.

The value if oil is found is $3,650,000.

Using these probabilities and values, we can calculate the EMV:

EMV = (Probability of Scenario 1 * Value of Scenario 1) + (Probability of Scenario 2 * Value of Scenario 2) - Cost of Expert

EMV = (0.55 * 0.85 * $3,650,000) + (0.45 * 0.2 * $3,650,000) - $75,000

EMV = $1,002,500

Therefore, if the company hires the expert at a cost of $75,000, the EMV is $1,002,500. This indicates that hiring the expert is a favorable decision based on the expected monetary value.

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Answer:

31.8

Step-by-step explanation:

side AD : side EH

13 : 46

side BC : side FG

9 : x

these ratios work because these are similar quadrilaterals and their sides correlates when the figures are rotated to match the other figure's position.

13/46 = 9/x

x = 31.846

x = approx. 31.8

Answer:

FG = 31.8

Step-by-step explanation:

\(\frac{13}{46} = \frac{9}{x}\)

13x = 46 * 9

13x = 414

x = 31.8

There are 3,338,496 ways the ten people can be seated in a row so that a certain two of them are not next to each other.

There are two ways to approach this problem. The first approach uses the inclusion-exclusion principle, while the second uses permutations with restrictions. We will use the first approach because it is shorter and easier to follow.

First, We will count the number of ways the ten people can be seated in a row.

This is simply 10! = 3,628,800 because there are ten choices for the first seat, nine choices for the second seat, and so on, until there are only two choices for the last seat.

There are nine choices for the two people to sit together, and then 8! ways to arrange the other eight people and the pair.

Therefore, there are 9 × 8! = 290,304 ways the ten people can be seated in a row with the two specified people sitting next to each other.

Finally, we will subtract the number of ways the ten people can be seated in a row with the two specified people sitting next to each other from the total number of ways the ten people can be seated in a row.

This gives us:

= 10! − 9 × 8!

= 3,628,800 − 290,304

= 3,338,496

Therefore, there are 3,338,496 ways the ten people can be seated in a row so that a certain two of them are not next to each other.

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Answer: two units to the left, four units down and reflected across the y axis

The product of the two polynomials is (8x³)(4x⁷) = 32x¹⁰.

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Answer:

490,000 grams

Step-by-step explanation:

To convert from kilograms to grams - multiply the number of kilograms by 1000. (there are 1000 grams in a kilogram)

\(490 * 1000 = 490,000\)

Answer:

490000

Step-by-step explanation:

1 kg : 1000 gram

So,

490 kilograms : 490 ×1000 grams

: 490000 grams

A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

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Answer:

2 and half

Step-by-step explanation:

Knowing the roots first write the equation in factored form:

(X - 3/4)(x +5) = 0

Now use the FOIL method ( multiply each term in one set of parentheses by each term the other set:

X•x + x•5 -3/4•x -3/4•5

Simplify:

X^2 + 5x -3/4x -3 3/4

Combine like terms:

X^2+ 4 1/4x - 3 3/4

The four functions can be described as follows: a) rect(x/8) - rectangular pulse centered at the origin with a width of 8 units, b) Δ(ω/10) - Dirac delta function with a spike at ω = 0 and zero everywhere else, c) rect(t-3/4) - rectangular pulse centered at t = 3/4 with a width of 1 unit, d) sinc(t) * rect(t/4) - modulated sinc function by a rectangular pulse of width 4 units centered at the origin.

a) rect(x/8):

The function rect(x/8) represents a rectangle function with a width of 8 units centered at the origin. It has a value of 1 within the interval [-4, 4] and a value of 0 outside this interval. The graph of rect(x/8) will consist of a rectangular pulse centered at the origin with a width of 8 units.

b) Δ(ω/10):

The function Δ(ω/10) represents a Dirac delta function with an argument ω/10. The Dirac delta function is a mathematical construct that is zero everywhere except at the origin, where it is infinitely tall and its integral is equal to 1. The graph of Δ(ω/10) will be a spike at ω = 0. The value of Δ(ω/10) at ω ≠ 0 is zero.

c) rect(t-3/4):

The function rect(t-3/4) represents a rectangle function with a width of 1 centered at t = 3/4. It has a value of 1 within the interval [3/4 - 1/2, 3/4 + 1/2] = [1/4, 5/4] and a value of 0 outside this interval. The graph of rect(t-3/4) will consist of a rectangular pulse centered at t = 3/4 with a width of 1 unit.

d) sinc(t) * rect(t/4):

The function sinc(t) * rect(t/4) represents the product of the sinc function and a rectangle function. The sinc function is defined as sinc(t) = sin(t)/t. The rectangle function rect(t/4) has a width of 4 units centered at the origin. The graph of sinc(t) * rect(t/4) will be the multiplication of the two functions, resulting in a modulated sinc function where the rectangular pulse shapes the sinc function.

Therefore, the four functions can be described as follows:

a) rect(x/8) - rectangular pulse centered at the origin with a width of 8 units.

b) Δ(ω/10) - Dirac delta function with a spike at ω = 0 and zero everywhere else.

c) rect(t-3/4) - rectangular pulse centered at t = 3/4 with a width of 1 unit.

d) sinc(t) * rect(t/4) - modulated sinc function by a rectangular pulse of width 4 units centered at the origin.

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Answer:

C

Step-by-step explanation:

The 99% confidence interval for the true population proportion of people with kids is:

CI = (0.482, 0.578)

To construct a 99% confidence interval for the true population proportion of people with kids, we can use the following formula:

\(CI = p $\pm z $ \sqrt{(p(1-p)/n)}\)

where CI is the confidence interval, p is the sample proportion, z is the critical value from the standard normal distribution corresponding to the desired confidence level (in this case, 99% corresponds to a critical value of 2.576), and n is the sample size.

Substituting the given values into the formula, we get:

\(CI = 0.53 $\pm 2.576 $\sqrt{(0.53(1-0.53)/600)}\)

Simplifying this expression, we get:

CI = 0.53 ± 0.048

Therefore, the 99% confidence interval for the true population proportion of people with kids is:

CI = (0.482, 0.578)

This means that we can be 99% confident that the true proportion of people with kids in the population lies between 0.482 and 0.578.

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Answer: $47.28

Step-by-step explanation:

There are 126 inches of fabric.

You need to convert this to yard as that is the pricing unit.

1 yard = 36 inches

126 inches is:

= 126/32

= 3.94 yards

Cost is $12 per yard so Henry pays:

= 12 * 3.94

= $47.28

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Answer:

\(763 ft^3\) or 763 cubic feet.

Step-by-step explanation:

The tank is cylindrical and the volume of a cylinder is given as:

\(V = \pi r^2h\)

where r = radius and h = height

The radius, r, of the tank is 4.5 ft and the height, h, of the tank is 12 ft.

Therefore, the volume of the cylindrical water tank is:

\(V = \pi * 4.5^2 * 12\\V = 763.407 ft^3\)

Approximating to whole number, the volume of the tank is \(763 ft^3\) or 763 cubic feet.

The required answers are:

A. The city fuel economy of an automobile with an engine size of 5 L is 15 ml/gal

B. The city fuel economy of an automobile with an engine size of 2.8 L is 18ml/gal

C. The engine size of an automobile with a city fuel economy of 11ml/gal is 6L.

D. The engine size of an automobile with a city fuel economy of 28ml/gal is 2L.

Given that the line graph which gives the relationship between the engine size(L) and city fuel economy(ml/gal).

To find the values by looking in the graph with corresponding values.

Therefore, A. The city fuel economy of an automobile with an engine size of 5 L is 15 ml/gal

B. The city fuel economy of an automobile with an engine size of 2.8 L is 18ml/gal

C. The engine size of an automobile with a city fuel economy of 11ml/gal is 6L.

D. The engine size of an automobile with a city fuel economy of 28ml/gal is 2L.

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Answer:

4/15 was left over from is salary.

Step-by-step explanation:

Common denominator is 15. 5/15+6/15= 11/15.

15/15-11/15= 4/15.

If Mr Hassan spent 1/3 of his salary on food and 2/5 of the remainder on transport then 4/15  fraction of his salary was left.

A fraction represents a part of a whole.

Let us consider the salary of Hassan as 1.

Mr Hassan spent 1/3 of his salary on food

2/5 of the salary on transport.

We need to find the fraction of his salary left.

We need to subtract 1/3 and 2/5 from 1

1-1/3-2/5

LCM of 3 and 5 is 15

15-5-6/15

4/15

Hence, 4/15 is the fraction of Hassan salary was left

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The missing lengths  in the triangles are h = 3/2√2 and b = 4√3

Triangle a and b

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

A special right triangle

For a right triangle with an angle of 45 degrees

The measure of the leg is

h = Hypotenuse/√2

So, we have

h = 3/√2

Evaluate

h = 3/2√2

For the other triangle, we have

sin(60) = b/6

So, we have

b = 6/sin(60)

Evaluate

b = 4√3

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1) a) Overflow: Exponent greater than 7 b) Underflow: Exponent smaller than -7 2) (a) Overflow (b) No overflow (c) No overflow (d) No overflow (e)Underflow

To determine the overflow, underflow, and representable number regions of the given systems, as well as represent the quantities in the specified system, we'll consider the format and ranges provided for each system.

1) System: F(10.6, -7, 7)

a) Overflow: The exponent range is -7 to 7. Any number with an exponent greater than 7 will result in an overflow.

b) Underflow: The exponent range is -7 to 7. Any number with an exponent smaller than -7 will result in an underflow.

c) Representable Number Region: The representable number region includes all numbers that can be expressed within the given range and precision.

2) System: F(10, 6, -7, 7)

(a) 88888 / 3:

Step 1: Convert 88888 and 3 to binary:

88888 = 10101101101111000

3 = 11

Step 2: Normalize the binary representation:

88888 = 1.0101101101111000 * 2^16

3 = 1.1 * 2^1

Step 3: Determine the mantissa and exponent values:

Mantissa = 0101101101 (10 bits, including sign bit)

Exponent = 000101 (6 bits)

The representation of 88888 / 3 in the specified system is:

1.0101101101 * 2^000101

(b) −10^(-9) / 6:

Step 1: Convert -10^(-9) and 6 to binary:

-10^(-9) = -0.000000001

6 = 110

Step 2: Normalize the binary representation:

-10^(-9) = -1.0 * 2^(-29)

6 = 1.1 * 2^2

Step 3: Determine the mantissa and exponent values:

Mantissa = 1000000000 (10 bits, including sign bit)

Exponent = 000001 (6 bits)

The representation of -10^(-9) / 6 in the specified system is:

-1.0000000000 * 2^000001

(c) −10^(-9) / 153:

Step 1: Convert -10^(-9) and 153 to binary:

-10^(-9) = -0.000000001

153 = 10011001

Step 2: Normalize the binary representation:

-10^(-9) = -1.0 * 2^(-29)

153 = 1.0011001 * 2^7

Step 3: Determine the mantissa and exponent values:

Mantissa = 1000000000 (10 bits, including sign bit)

Exponent = 000111 (6 bits)

The representation of -10^(-9) / 153 in the specified system is:

-1.0000000000 * 2^000111

(d) 2 × 10^8 / 7:

Step 1: Convert 2 × 10^8 and 7 to binary:

2 × 10^8 = 1001100010010110100000000

7 = 111

Step 2: Normalize the binary representation:

2 × 10^8 = 1.001100010010110100000000 * 2^27

7 = 1.11 * 2^2

Step 3: Determine the mantissa and exponent values:

Mantissa = 0011000100 (10 bits, including sign bit)

Exponent = 000110 (6 bits)

The representation of

2 × 10^8 / 7 in the specified system is:

1.0011000100 * 2^000110

(e) 0.002:

Step 1: Convert 0.002 to binary:

0.002 = 0.00000000001000111101011100

Step 2: Normalize the binary representation:

0.002 = 1.000111101011100 * 2^(-10)

Step 3: Determine the mantissa and exponent values:

Mantissa = 0001111010 (10 bits, including sign bit)

Exponent = 111110 (6 bits)

The representation of 0.002 in the specified system is:

1.0001111010 * 2^111110

Note: Overflow and underflow situations can be determined by checking if the exponent exceeds the given range.

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The complete question is:

1) Indicate the overflow, underflow and representable number regions of the following systems

a) F (10.6, -7,7)

b) F(10.4, -3,3)

2) Let the system be F(10, 6, −7, 7). Represent the quantities below in this system (so normalized) or indicate whether there is overflow or underflow.

(a) 88888 / 3

(b) −10^(-9) / 6

(c) −10^(-9) / 153

(d) 2×10^(8) / 7

(e) 0.002