37. Perform the following binary multiplications, assuming unsigned integers: a) 1011 x 101

The value of b² is 125.44 units since b equals 11.2 units when c equals 13 units and an equals 6.6 units.

The Pythagorean theorem is a mathematical theorem that asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right-angled triangle is equal to the sum of the squares of the other two sides. It is mathematically stated as c2 = a2 + b2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Here,

c=13²

a=6.6²

a²+b²=c²

b=√(c²-a²)

=√(13²-6.6²)

b=11.2 units

b²=125.44 units

The value of b² is 125.44 units as b is equal to 11.2 units when c is 13 units and a is 6.6 units.

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Answer:

43

Step-by-step explanation:

The system of equation with the same solution with x + 2y = 3, 2x - y = 4 is  2x + 4y  = 6, 4x - 2y = 8 .

The system of equation can be solved using method such as elimination method and substitution method. Let's solve using elimination method.

Let's find the solution of  the system of equation

x + 2y = 3

2x - y = 4

multiply equation(1) by 2

2x + 4y = 6

2x - y = 4

subtract the equations

5y = 2

y = 2 / 5

x = 3 - 2(2 / 5)

x = 3 - 4 / 5

x =  15 - 4/ 5

x = 11 / 5

Therefore, the equation with same solution is 2x + 4y  = 6, 4x - 2y = 8

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When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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The only number that is 10 times as much as 72 is 720.

To find the numbers that are 10 times as much as 72 or 1/10 of 72, we can perform the following calculations:

10 times 72 = 720

1/10 of 72 = 7.2

So, the numbers that are 10 times as much as 72 are 720.

The number 67 is not 10 times as much as 72 or 1/10 of 72. Therefore, it is not one of the numbers we are looking for.

On the other hand, 1/10 of 72 is 7.2, which is not one of the numbers we are looking for either.

Therefore, the only number that is 10 times as much as 72 is 720.

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complete question

Select all the numbers that are 10 times as much as 72, 67, or 1/10 of 72.

- 67

-46

-720

-480

Answer:

a and f

Step-by-step explanation:

The transformation is 3 units up, which is concluded from the fact that there is a positive 3 meaning up. This also represents the y-intercept.

Hope this makes sense :)

The equation of the given line is:

Slope intercept form is: y = -x + 6

Point slope form is: (y - 6) = -1(x - 0)

Standard form is: x + y = 6

The formula for the linear equation between two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

The two coordinates are:

(0, 6) and (1, 5)

Thus:

(y - 6)/(x - 0) = (5 - 6)/(1 - 0)

This can be simplified as:

(y - 6) = -1(x - 0)

It can be further written as:

y - 6 = -x - 0

y = -x + 6

The formula for linear equation in standard form is:

Ax + By = C

Thus, we have: x + y = 6

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The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

25 pi

Step-by-step explanation:

area of circle = pi (r)^2

radius = 10/2 = 5

5×5 = 25

25 pi

Answer:

C

Step-by-step explanation:

The formula is pi(r＾2)

r=radius

=10/2

The number of miles he drove for a cost of $30.50 is 275 miles.

Using linear equation,

y = mx + b

where

Therefore,

9 cents = $0.09

y = 35.50 + 0.09x

where

x = number of miles drove

y = total cost

Therefore,

60.25 =  35.50 + 0.09x

60.25 - 35.50 = 0.09x

24.75 = 0.09x

x = 24.75 / 0.09

x = 275 miles

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The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius is given as,

r = 36 / 2

r = 18 inches

The area of the circle is given as,

A = π x (18)²

A = 3.14 x 324

A = 1,017.36 square inches

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

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The complete question is given below.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth is cut from the square?

(π = 3.14)

1,017.36 in2

1,489.24 in2

1,182.96 in2

1,276.00 in2

The tree is 34 feet tall.

Ratio of length of the stick to the length of the shadow = 6 : 4.5 = 4:3

Ratio of length of the tree to the length of its shadow   = x : 25 = 4:3

x / 25 = 4 / 3

x = 25 x 4 / 3 = 100/3 = 33.33

Therefore, the length of the tree to the nearest foot is 34 feet (approximately).

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Answer:

x = 27

Step-by-step explanation:

this problem is similar to a scale drawing where we can set up a proportion:

'x' is to 5 as 162 is to 30

x/5 = 162/30

cross-multiply:

30x = 810

x = 810/30

x = 27

Answer:

x=27

Step-by-step explanation:

The number of butterscotch bags is 2.75 and the number of chocolate bags is 5.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that you bought eight bags altogether chocolate chips cost three dollars and 50 Cent per bag and butterscotch chips cost $4.75 per bag and you spent $30.25 at the store how many bags of each time did you buy

The number of bags will be calculated as,

3.5C + 4.75B = 30.25

C + B = 8

Solve by elimination method,

3.5C + 4.75B = 30.25

3.5C + 3.5B = 28

________________

                 B = 2.75

The number of chocolate bags,

C + B = 8

C = 8 - 2.75

C = 5.25

Therefore, the number of butterscotch bags is 2.75 and the number of chocolate bags is 5.25.

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

Answer:

1680

Step-by-step explanation:

Answer:

I guess if she is Pays the money in three years, she will pay a capital of 1500/3 per year, which is 500$ per year. The Interest she pays the first year is: I=Debt*interest rate, so I=1500$*0.04, which is: I=60$. So without other information, i assume she pays 60$ each year, so in three years: I=60*3 --> 180$.

a) The sample space has a total of 52 * 6 = 312 outcomes.

b)  There are 26 * 3 = 78 outcomes where a red card is drawn with a roll of an even number.

c) The probability of winning this game is 1/4 or 0.25.

a. The sample space for this game consists of all possible outcomes of drawing a card and rolling a die. Since there are 52 cards in a deck and 6 sides on a die, the sample space has a total of 52 * 6 = 312 outcomes.

b. To identify the outcomes where a red card is drawn with a roll of an even number, we need to consider the cards and the numbers that satisfy this condition. There are 26 red cards in the deck and 3 even numbers on the die (2, 4, and 6).

Therefore, there are 26 * 3 = 78 outcomes where a red card is drawn with a roll of an even number.

c. To calculate the probability of winning the game, we need to determine the number of favorable outcomes (drawing a red card with a roll of an even number) and divide it by the total number of possible outcomes. From part b, we know that there are 78 favorable outcomes. The total number of possible outcomes is 312, as calculated in part a. Therefore, the probability of winning the game is 78/312, which simplifies to 1/4 or 0.25.

In summary, the probability of winning this game is 1/4 or 0.25.

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Answer:

k = 6

Step-by-step explanation:

Step 1: Find slope m

m = (4 - 8)/(-10 - 6)

m = -4/-16

m = 1/4

y = 1/4x + b

Step 2: Find b

4 = 1/4(-10) + b

4 = -5/2 + b

b = 13/2

Step 3: Rewrite equation

y = 1/4x + 13/2

Step 4: Find k

y = 1/4(-2) + 13/2

y = -1/2 + 13/2

y = 12/2

y = 6

Answer: 6

Step-by-step explanation:

As you move left to right on the x-coordinate, your y value is increasing. If you notice, the x values are increasing by eight at a time. So, if you take the value in between 4 and 8, you get your answer, which is 6.

The possibility are 1,716 possible ways to cast the roles of Larry, Curly, and Moe from a group of 13 actors.

There are 13 actors auditioning for the roles of Larry, Curly, and Moe, there are 13 choices for who can be cast in the first role, 12 choices left for who can be cast in the second role, and 11 choices left for who can be cast in the third role (assuming that no actor can play more than one role).

To determine the number of ways the roles of Larry, Curly, and Moe could be cast with 13 different actors auditioning, we can use the concept of permutations.

In this case, we have 13 actors and 3 roles to fill, so we calculate it as follows:

Permutations = 13 * 12 * 11 Permutations

= 1,716

So, there are 1,716 different ways the roles of Larry, Curly, and Moe could be cast from the 13 actors auditioning.

Therefore, the number of ways the roles can be cast is:

13 x 12 x 11 = 1,716

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P(not having a computer | not connected to the internet) = P(not having a computer and not connected to the internet) / P(not connected to the internet)

To solve the given question, we need to apply the probability formula. Probability can be defined as the number of favorable outcomes divided by the number of total outcomes. In this case, we have to determine the probability that the household does not have a computer since they are not connected to the internet.

Let's assume that the probability of a household not having a computer is P(not having a computer). Similarly, the probability of households not connected to the internet is denoted by P(not connected to the internet). We need to calculate the probability of not having a computer among households not connected to the internet, which can be represented as P(not having a computer | not connected to the internet).

The formula used to calculate conditional probability is P(A|B) = P(A and B) / P(B), where A and B represent two events. Here, A represents not having a computer, and B represents not being connected to the internet. Therefore, we can use the formula as follows:

P(not having a computer | not connected to the internet) = P(not having a computer and not connected to the internet) / P(not connected to the internet)

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Answer:

-5x + 1

Step-by-step explanation:

Hello!

We can find the quotient by factoring the numerator, and cancelling common factors.

The quotient is (-5x + 1).

\(\huge\text{Hey there!}\)

\(\huge\textbf{Equation:}\)

\(\mathbf{\dfrac{15x^2 - 3x}{-3x}}\)

\(\huge\textbf{Simplify the current equation:}\)

\(\mathbf{= \dfrac{-3x(-5x + 1)}{-3x}}\)

\(\huge\textbf{Cancel out \boxed{\bf -3x} \& simplify it:}\)

\(\mathbf{= \dfrac{-15x + 3}{3}}\)

\(\huge\textbf{Simplify that above:}\)

\(\mathbf{= -5x + 1}\)

\(\huge\textbf{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{-5x + 1 }}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

For the two lines to be parallel, the value of n must be 3

When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line. If the slopes are the same then the lines are parallel.

The slope of each line is calculated as (y2-y1)/x2-x1

for line AB, the slope = (6n-n)/10-4 = 5n/6

for line CD, the slope= 8n-(-6)/9-(-3)=( 8n+6)/12

for AB and CD to be parallel,

5n/6 = (8n+6)/12

multiply both sides by 12

10n= 8n+6

collect like terms

10n-8n= 6

2n= 6

n= 6/2= 3

therefore for the value of n= 3 line CD and AB are parallel.

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Jessica Bradley scored 806 points during the championship.

Let's assume Tina Harner scored x points during the championship. Since Jessica Bradley scored 81 more points than Tina Harner, her score can be represented as (x + 81).

According to the given information, the total points scored by both players combined is 1531. So we can set up the following equation:

x + (x + 81) = 1531

Combining like terms, we have:

2x + 81 = 1531

Subtracting 81 from both sides, we get:

2x = 1450

Dividing both sides by 2, we find:

x = 725

Therefore, Tina Harner scored 725 points during the championship.

To find Jessica Bradley's score, we can substitute the value of x back into the equation:

x + 81 = 725 + 81 = 806

So, Jessica Bradley scored 806 points during the championship.

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Ms. Schuster's class has approximately 107 students, and Ms. P's class has approximately 53 students

Sure, I'd be happy to help!

So, the problem states that Ms. P's class has half as many students as Ms. Schuster's. This means that if we let the number of students in Ms. Schuster's class be "x", then the number of students in Ms. P's class would be "x/2" (since Ms. P's class has half as many students).

Now, the problem doesn't give us any specific information about the number of students in either class, but it does tell us that there are a total of 160 students between the two classes. So, we can set up an equation based on this information:

x + x/2 = 160

To solve for "x" (the number of students in Ms. Schuster's class), we can first simplify the equation by multiplying both sides by 2:

2x + x = 320

Combining like terms, we get:

3x = 320

Finally, we can solve for "x" by dividing both sides by 3:

x = 106.67

Now, we can use this information to find the number of students in Ms. P's class by dividing "x" by 2:

x/2 = 53.33

However, since we can't have a fraction of a student, we'll need to round both of these answers to the nearest whole number:

I hope this helps! Let me know if you have any other questions.

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There are roughly 107 pupils in Ms. Schuster's class, and there are about 53 in Ms. P's class.

The issue is that Ms. P's class has half as many kids as Ms. Schuster's, according to the problem. The number of pupils in Ms. P's class would be "x/2"

The problem does not specifically state how many people are enrolled in either class, but it does indicate that there are a combined 160 pupils in the two sessions. Using the following data, we can construct the following equation:

x + x/2 = 160

We can first make the problem simpler by dividing both sides by 2, and then we can solve for "x"

2x + x = 320

Combining similar phrases, we obtain:

3x = 320

By multiplying both sides by 3, we can finally find the answer for "x":

x = 106.67

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Answer:

42

Step-by-step explanation:

i = prt

i = 300 × 0.07 × 2

i = 42

Answer:

i = 42

Step-by-step explanation:

I = PRT/100

where I = Simple interest

P = Principal

R = Rate (%)

T = Time (years)

I = (300 x 7 x 2) ÷ 100

I = 4200 ÷ 100

I = 42

Answer:

\( \huge{ \boxed{ \bold{ \tt{ - 5}}}}\)

☪\( \tt{Question} : \)

☥ \( \tt{Step - by - step \: explanation : }\)

☄\( \tt{Solution : }\)

\( \sf{Step \: 1} : \) Assign one of the ordered pairs to be ( x₁ , y₁ ) and another to be ( x₂ , y₂ )

\( \sf{Step \: 2} : \) Substitute values into the slope formula and then simplify :

\( \boxed{ \sf{slope = \frac{y2 - y1}{x2 - x1}}} \)

↦ \( \sf{ \frac{ - 8 - ( - 3)}{1 - 0}} \)

↦ \( \sf{ \frac{ - 8 + 3}{1} }\)

↦ \( \boxed{ \sf{ - 5}}\)

Hence , Our answer is \( \boxed{ \sf{ - 5}}\).

Hope I helped!

Have a wonderful day / night ツ

~TheAnimeGirl ♪

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

The answer is two base cases, using induction.

What is induction ?

Weak induction is when an inductive mathematical proof holds true for all integers in a set of countable proofs. Natural numbers typically use this. The base step and inductive step are used to prove a set, making it the simplest type of mathematical induction.

Two examples make up an induction proof. Without requiring any prior knowledge of other examples, the first, or base case, establishes the claim for n = 0. The induction process, which is used in the second case, demonstrates that if the assertion is true for any particular scenario where n = k, it must also be true for the subsequent case where n = k + 1.

If a statement true  for n= k, accordily to induction it have to hold good for n = k+1,

Hence, base cases does a proof by the weak form of the principle of mathematical induction requires 2 bases.

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This real-world problem has the limitations 75< x <110 and 0< y\(\leq\) 50, hence:

option (C) is the best choice.

The term "inequality" refers to a mathematical expression in which both sides have mathematical signs that are either less than or greater than one another, and the expression is one where the two sides are not on equal footing.

We have:

Your senior vacation is scheduled to include a class trip to a beach. Only when it's between 75 and 110 degrees do guests at the resort get access to the pool. 50 passengers can go with you.

Let y be the number of passengers and x be the temperature

75 to 110 degrees are the range of the temperature.

75 < x < 110

50 passengers can go with you.

0 < y ≤ 50

In order to illustrate this real-world issue, the limitations are 75 <x <110 and 0< y \(\leq\)50.

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