Suppose A = +54 and B = -3 (both in base 10).
Part 1: What is the lowest number of rounds theoretically to complete the integer division using the optimized division algorithm?
Part 2: What is the resulting number in binary representation if we use 8 bits to represent it?
Part 3: What is the resulting number in FP decimal representation if we use the IEEE 754 standard for single precision? (form of this result should be in sign, true exponent in binary, IEEE-754 Exponent in binary and IEEE-754 exponent in decimal (base 10 number) )

Answer:

62 cm²

Step-by-step explanation:

The surface area is the sum of the areas of the 6 faces

The opposite faces of the cuboid are congruent , then

SA = area of front/ back + area of top/ bottom + area of side faces

SA = 2(5 × 3) + 2(5 × 2) + 2(2 × 3)

    = 2(15) + 2(10) + 2(6)

    = 30 + 20 + 12

    = 62 cm²

The system of equations:

3x + y = 4

2y = -6x + 8

Has infinite solutions.

We have the equation:

3x + y = 4

Now we want to find an equation of a line such that if we make a system of equations, the system will have infinite solutions.

The system of equations will have infinite solutions only if both equations represent the same line, then we can rewrite our line like

3x + y = 4

If we multiply both sides by 2

2*(3x + y) = 2*4

6x + 2y = 8

And we can move some terms to get:

2y = -6x + 8

Then the system:

3x + y = 4

2y = -6x + 8

Has infinite solutions.

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Answer:

Answer:

y = 8*(9/4)^x

Point (1.5, 27)

Step-by-step explanation:

We can solve each unknown in separate steps. The first step is to take advantage of given point (0,8) to find the value of a. Since x is zero, b^x will just be 1, regardless of b. That makes it easy to solve for a, which is found to be 8.

Once a is known, we can use the next point (1,18) to solve for b. b is (9/4).

Once we have a and b, we have the full equation: y = 8*(9/4)^x

k is found by entering the x value and solving for y (which is k). k = 27

Answer:

The values of a and b are,

a = 5, b = 3

Step-by-step explanation:

We are given that (1,15) , and (4,405) are on the graph of the equation

y = ab^x

so,

15 = ab^(1)   (i)

405 = ab^(4)  (ii)

solving this system of equations,

dividing (ii) by (i),

405/15 = ab^(4)/ab

27 = b^(4-1)

27 = b^3

taking the cube root,

\(b = \sqrt[3]{27}\\ b = 3\)

b = 3

Putting this value in  (i),

15 = a(3)

a = 15/3

a = 5

Hence a = 5, b = 3

Answer:

Step-by-step explanation:

1

(x+3)+(x-1)+(x+1) = 90°

3x + 3 = 90°

3x = 90 - 3

3x = 87

x = 87/3

x = 29°

2

x + (x+104) = 180°

2x + 104 = 180°

2x = 180 - 104

2x = 76

x = 76/2

x = 38°

Answer:

We can determine what percent of 40 is 24 by dividing 40 from 24 which gives us 0.6.  We then multiply this number 100 to turn it into a percentage and that gives us 60%.

The solution is: 60% of 40 is 24.

Here, we have,

We can determine what percent of 40 is 24 by dividing 40 from 24

which gives us 0.6.  

We then multiply this number 100 to turn it into a percentage

and that gives us 60%.

i.e. we have,

24/40 = 0.6

and, then,

0.6 * 100

=60%

Hence, The solution is: 60% of 40 is 24.

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Answer:

x = 152.6

Step-by-step explanation:

180 - 27.4 there you go

Answer: 152.6

Step-by-step explanation:

Remember the interior and exterior angle add up to 180°.

180 - 27.4 = 152.6

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer:

option c

Step-by-step explanation:

Answer:

\(\textsf{b)} \quad \dfrac{(y+3)^2}{25}-\dfrac{(x-1)^2}{15}=1\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.4 cm}\underline{Standard equation of vertical hyperbola}\\\\$\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center. \\ \phantom{ww}$\bullet$ $(h, k\pm a)$ are the vertices. \\\phantom{ww}$\bullet$ $(h\pm b, k)$ are the co-vertices. \\\phantom{ww}$\bullet$ $(h, k\pm c)$ are the foci where $c^2=a^2-b^2$.\\\end{minipage}}\)

Given:

As the x-values of the given center, vertex and focus are the same, the hyperbola is vertical (opening up and down).

Given the center is (1, -3):

Use the vertices formula (h, k±a) to find a:

\(\begin{aligned} (h, k \pm a) = (1, -3 \pm a) &= (1, 2)\\\implies -3 \pm a &= 2\\a &= 5\end{aligned}\)

Use the foci formula (h, k±c) to find c:

\(\begin{aligned} (h, k \pm c) = (1, -3 \pm c)&=(1, -3 \pm 2\sqrt{10})\\c &= 2 \sqrt{10}\end{aligned}\)

Use the found values of a and c with Pythagoras Theorem to find b²:

\(\begin{aligned}c^2 &=a^2+b^2\\\implies (2 \sqrt{10})^2&=5^2+b^2\\40&=25+b^2\\b^2&=15\end{aligned}\)

Therefore:

Substitute the found values into the hyperbola formula to create an equation of the hyperbola with the given parameters:

\(\dfrac{(y+3)^2}{25}-\dfrac{(x-1)^2}{15}=1\)

Answer:

17. landmark

18. BANALITIES

Step-by-step explanation:

The size of an exterior angle of a regular hexagon is 60 degrees.

In a regular hexagon, all the interior angles are equal and are given by the formula:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

For a hexagon, n = 6, so the interior angle is:

Interior angle = (6-2) x 180 / 6 = 120 degrees

An exterior angle is the supplement of an interior angle, which means it is the angle that when added to the interior angle, will equal 180 degrees.

So, exterior angle = 180 - interior angle = 180 - 120 = 60 degrees.

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Answer:

The number in front of the x

Step-by-step explanation:

Once you have your formula set to y = , then whatever number is in front of the x is the slope. This is according to the formula y = mx + b, where m is the slope.

1. y = -x  slope: -1

2. y = x - 3   slope: 1

3. y = 3x    slope: 3

4. y = 1/2x    slope: 1/2

5. y = 2x     slope: 2

By forming and solving equations, we know that the speed of the runner is 4 miles per hour.

So, we need to form an equation to get the speed of the runner:

'x' is the speed of the runner. Now, solve for x as follows:

Therefore, by forming and solving equations, we know that the speed of the runner is 4 miles per hour.

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Answer:

Step-by-step explanation:

No, because they wouldn't contain the same amount of sugar per cookie  

for the first recipe - 24 cookies with 6 tablespoons  

thats 6/24 so 0.25 tablespoons of sugar per cookie  

for the second recipe - 36 cookies with 10 tablespoons  

thats 10/36 so 0.276 tablespoons per cookie  

the cookies in the second recipe would be slightly sweeter than the cookies in the first  

Answer:

One rational solution

Step-by-step explanation:

proof

5x2 - 2x - 3=0, the sum of coefficients is 5-2-3=0, so the equation has exactly two solutions, x=1, and x = -3/5 this last is the one rational solution

Answer:

-5

Step-by-step explanation:

4-5=-1

So therefore:

-5+4=-1

The definition and explanation of an equation are given below with an example.

in mathematics, an equation is defined as an expression that expresses equality between 2 quantities or expressions. We use equations quite a lot in our daily lives whenever we have to equate two quantities and find out how they are equal. These are used in all branches of science because of the huge purpose they serve.

in simple words it tells what we have on the Left-Hand Side of the "=" sign is the same as what we have on the right-hand side of the statement. Some examples of equations are-

E²=m²c⁴+p²c²

x²+3x-1=0

70 oranges= 7 oranges × 10 oranges

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The probability of having exactly one boy and 2 girls is 3/8 or 0.375.

What is probability?

The likelihood of an event happening is gauged by probability. Many things are impossible to forecast with absolute confidence. Probability can range from 0 to 1, with 0 indicating an impossibility and 1 indicating a certainty.

For each child, one can have either a boy or a girl.

There are 50% chances for each, so, in total, there are 8 possible outcomes because cube of 2 is 8.

In this, each one is equally likely.

The outcomes are as follows:

(BBB, BBG, BGB, BGG, GGG, GGB, GBB, GBG)

Now, for 1 boy and 2 girls, there are 3 possibilities i.e. BGG, GGB and GBG.  So, this means that there’s a 37.5% chance of this happening.

Hence, the probability of having exactly one boy and 2 girls is 3/8 or 0.375.

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Answer:850

Step-by-step explanation:

I hope it helps

Another possible vertex of the square is determined as (2, 1).

option B is the correct answer.

The vertex of a figure is the point of intersection of two sides of the shape.

The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;

P = 12 units

a side length = 12 units / 4 = 3 units

To determine another possible vertex of the square, the length between the points must be equal to 3.

Let's consider point A;

A = (1, 2)

given vertex = (-1, 1)

distance between the points = √ (-1 -1)² + (1 - 2)² = √5

Let's consider point B;

B = (2, 1)

given vertex = (-1, 1)

distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3

Thus, point B is another possible vertex of the square.

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Answer:

DC⊥EF as the 2 angles in smallest triangle are 30 and 60 degrees, so the last one is 90 making Line DC perpendicular to Line EF.

Step-by-step explanation:

DC⊥EF means that Line DC is perpendicular (90 degrees) to EF.

To prove this, we can use the two angles of the small triangle created by the intersection of the triangles AEF and DCB.

The remaining angle of triangle AEF is 60, as all angles of triangles add up to 180 (so 180 - 12 = 60). This angle at F is shared with the little triangle.

Now we will get the angle at D using the triangle DCB. Since we are given two angles 90 and 60, angle D has to be 30.

So of our little triangle, we have angles 30 and 60, meaning the last one is 90 degrees and hence, DC⊥EF

Answer:

800

Step-by-step explanation:

You do 2 to the 5 power, which equals 32. Then add 13 and 12 to get 25. Then multiply 32 and 25 to get 800

Answer:

− 3 a ^3 + 5 a ^2 − 3 a + 7

Step-by-step explanation:

Apply the distributive property.

a ^3 − 2 a + 5 − ( 4 a ^3 ) − ( − 5 a ^2 ) − a −  − 2

Simplify.

a ^3 − 2 a + 5 − 4 a ^3 + 5 a ^2 − a + 2

Simplify by adding terms.

Subtract  4 a ^3  from  a ^3 .

− 3 a ^3 − 2 a + 5 + 5 a ^2 − a + 2

Subtract  a  from  − 2 a .

− 3 a ^3 − 3 a + 5 + 5 a ^2 + 2

Simplify the expression.

Add  5  and  2 .

− 3 a^ 3 − 3 a + 5 a ^2 + 7

Move  − 3 a .

− 3 a ^3 + 5 a ^2 − 3 a + 7

I hope this helped. I am sorry if you get this wrong.

Answer:

$267.7

Step-by-step explanation:

The level of production that yields the maximum profit is 65 units, and the maximum profit is $3225. To get the level of production that yields maximum profit and the maximum profit for the commodity with the profit function p(x) = 130x - x^2 - 1000, follow these steps:

Step 1: Determine the derivative of the profit function with respect to x.
p'(x) = d(130x - x^2 - 1000)/dx = 130 - 2x
Step 2: Set the derivative equal to zero to find the critical points.
130 - 2x = 0
Step 3: Solve for x to find the level of production.
2x = 130
x = 65 units
Step 4: Evaluate the profit function at the critical point to find the maximum profit.
p(65) = 130(65) - 65^2 - 1000 = 8450 - 4225 - 1000 = $3225
The level of production that yields the maximum profit is 65 units, and the maximum profit is $3225.

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Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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The equation that describes a line passing through (4, -1) and perpendicular to y = 2x - 4 is y = 2x +6, y = 2x +6. The correct option is D.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Perpendicular lines have the same negative reciprocal slope as the line they are perpendicular to, which is important information to know.

This indicates that you may calculate the slope of the perpendicular line by taking the slope of the first line, adding a negative sign, and switching the numerator and denominator.

Therefore, the correct option is D. y = 2x +6, y = 2x +6.

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Answer:

hii

Step-by-step explanation:

follow me please gugs

Answer:

m = - 1

Step-by-step explanation:

Given

- 9m - 86 = - 75 + 2m ( subtract 2m from both sides )

- 11m - 86 = - 75 ( add 86 to both sides )

- 11m = 11 ( divide both sides by - 11 )

m = - 1