What is the volume of the prism?



Enter your answer, as a mixed number in simplest form, in the box.


cm³

Simplifying the linear equation 4a + 7 when a= 1/2 is 9

Linear equation is an equation in whi8ch the highest power of the variable is 1

From the linear equation, 4a + 7 when a = 1/2

By substituting for a in the equation

=4(1/2) + 7

By expanding the bracket

=(4x1/2) + 7

=4/2+7

=2+7

=9

Hence, The final answer to the linear equation 4a + 7 when a= 1/2 = 9

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Answer:

a/c = a/c

Step-by-step explanation:

That is, if a, b, and c are real numbers such that a = b and c ≠0, then

a/c = a/c

The property state that c≠0 because division by zero does not exist.

The Division Property of Equality says that for every real number a, b, and c, if a = b and c ≠ 0, then a/c = b/c.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

When "a" and "b" are divided, the outcome of the division is the amount of "a" that each of the "b" items will receive.

Therefore, if there are 20 pens and 5 students, the amount of mangoes that each student would receive is 20 ÷ 5 or 4, or 4 pens.

When a number is divided, it can be thought of as being divided equally into a total of x parts, where x is the number of parts into which the given number is divided.

The Division Property of Equality says that for every real number a, b, and c

if a = b and c ≠ 0, then a/c = b/c.

The property state that c ≠ 0 because division by zero does not exist.

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Comparing the articles I, II, and III of the constitution, in the descending order of length and detail, the articles are ranked as I, II, and III. Article I is the longest.

Article I of the constitution created the legislative branch, article II of the constitution created an executive branch, and article III of the constitution created a judicial constitution. Article I is the longest and more detailed part of the constitution as the powers and the duties of the legislative branch are much more varied than the executive branch. Additionally, the legislative branch is composed of more individuals than the executive branch.

Article 1 is the longest as founding fathers believed that a legislative branch is very important in a government that represents the citizens. Article 3 is the shortest part of the constitution as the founding fathers did not expect the judiciary to play a large role.

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Answer:

Rs.34,944

Step-by-step explanation:

(6006 km)/(66 km) = 91

The distance from his hometown to Delhi is 91 times 66 km.

He will need 91 times the amount of petrol.

91 * Rs.384 = Rs.34,944

ANSWER: THEY SCORED 32 POINTS FEWER THAN LAST YEAR

Answer:

32.

Step-by-step explanation:

If the bulls scored 210 points last season this season they scored 178 so first step is you subtract.

210-178

= 32

To get your answer and to find how many fewer points.

Answer:

D

Step-by-step explanation:

The next step of marshall should be divide both sides of the equation by 5.

Given:

Marshall is writing an equivalent equation to solve for x. what should be his next step.

5 + 4 y = 8.

5+4y-4y = 8-4y

5x = 8 - 4y

To solve for x:

The correct step is:

divide by 5 on both sides

5x/5 = 8-4y / 5

x = 8/5 - 4y/5

x = 1/5(8-4y).

Therefore The next step of marshall should be divide both sides of the equation by 5.

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Answer:

A data type is an attribute associated with a piece of data that tells a computer system how to interpret its value

Step-by-step explanation:

Data types categorize data and specify its nature, amount characteristics, and behavior. It decides how data is handled within a computer system in terms of storage and manipulation.

Data types categorize data and specify its nature, characteristics, and behavior. It is a crucial part of every data structure and computer language. Primitive data types and complex data types are the two basic divisions of data types. Basic types like numbers, characters, booleans, and strings are examples of primitive data types. Arrays, objects, and records are examples of sophisticated data types that are more complex. Data types specify how information is handled and stored by computer systems. Size, precision, and range are a few examples of the unique qualities that each data type possesses. The arithmetic, comparison, and logic operations that can be carried out on the data are also determined by the data types.

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Step-by-step explanation:

u= 4

...................

EXPLAIN:

Ex:  the line is:  y = ax + b

The line go through 2 points ( 0 ; -5 ) and ( 5 ; 0 )

So: \(\left \{ {{0=5a+b} \atop {-5=0a+b}} \right. =>\left \{ {{b=-5a} \atop {b=-5}} \right. =>\left \{ {{a=1} \atop {b=-5}} \right.\)

The line: y = x - 5 = (1)x + (-5)

ANSWER: y = (1)x + (-5)

ok done. Thank to me :>

In a case whereby letters in the word bubble are arranged in a row the number of unique arrangements that are there  in the letters is 120.

From the question we were given the word, bubble  which can be recognized as 6! arrangements  however we know that the  3 B’s are interchangeable, from the word which is to be arranged, and we can see that there are 6 letters all together in the word and can be arranged as;

6!/3!

= 720/6

= 120

Hence, we can conclude the arangement here is 120 unique wayas.

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Answer:

apples

Step-by-step explanation:

Answer:

you will have 8 baskets

because if you look at all the number you will see that they have one number in common which is eight. then you will need to find the division partner which would be:

4 sanwiches,5 granola bars,and 6 apples in one picnic basket. doing that you will get eight basket in total.

The answer is e. none of the above/can’t be determined with info given.

Based on the information given, we have:

P(A) = 0.46

P(B) = 0.17

P(A U B) = 0.63

Note that P(A U B) represents the probability of either event A or event B occurring, or both.

If events A and B are mutually exclusive, it means they cannot occur at the same time. In other words, if event A occurs, event B cannot occur, and vice versa. In this case, the probability of both events occurring would be zero.

On the other hand, if events A and B are collectively exhaustive, it means that together they account for all possible outcomes. In other words, either event A or event B (or both) must occur, and there are no other possibilities.

Using these definitions, we can see that events A and B are neither mutually exclusive nor collectively exhaustive. This is because the probability of both events occurring (i.e., the intersection of A and B) is not zero, which means they are not mutually exclusive. Additionally, the probability of either A or B occurring (i.e., the union of A and B) is not equal to one, which means they are not collectively exhaustive.

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The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.

Therefore the answer is (5, -6).

The graph f(x) = |x - 5| - 6 is symmetrical about the axis  x = 5.

A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is

(5, -6)

We can observe that was added 5 units to the x, that is, a negative translation through the horizontal axis. So, our function is located at x = -5, because a horizontal translation to the left is when we add to the x certain units.

Then, we observe that the function subtracted 6 units to the vertical variable, that is, the function is translated 6 units downside.

Therefore, our functions is locate in (-5;-6), it starts there, which is the vertex.

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = |x - 5| - 6?"

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The slopes 3 and -1/3 are the opposites of one another. So the line y = 3x - 7 is perpendicular to line 3x + 9y = 9.

In the given question, we have to explain the line y = 3x - 7 is either parallel or perpendicular to 3x + 9y = 9.

The given equation is y = 3x - 7.

y = mx+ c is the line's equation in the slope-intercept form.

By comparing this to the preceding equation, we can determine that this line's slope is 3 and its y-intercept is -7.

Lines with equal slopes are said to be parallel. Lines that are perpendicular will have a slope product of -1.

3x + 9y = 9

We can write this equation as

9y = -3x + 9

Divide by 9 on both side, we get

y = -3/9 x + 9/9

y = -1/3 x + 1

Now the slope is -1/3 and y-intercept is 1.

Hence, the slopes 3 and -1/3 are the opposites of one another. So the line y = 3x - 7 is perpendicular to line 3x + 9y = 9.

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The complete question is:

Is the line y = 3x - 7 parallel or perpendicular to 3x + 9y = 9? Explain your answer.

55% percentage  of the cupcakes had sprinkles.

A percentage is a number, οr ratiο, that expresses a fractiοn οut οf 100. Percentages are easy tο recοgnize because they are always fοllοwed by a percent sign (%). A percentage is an alternative way tο represent a fractiοn οut οf 100 instead οf using a traditiοnal fractiοn fοrmat. Fοr example, we can write ½ οr 50/100 tο represent a half fractiοn, using percentage we can alsο write 50%.

Add the total no. of cupcakes = 11 + 9 = 20 cupcakes

Out of 20 cupcakes only 11 cupcakes had sprinkles = 11/20

To find percentage multiply be 100 percent = 11/20 × 100

                                                                          = 55%

Thus, 55% percentage  of the cupcakes had sprinkles.

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Answer:

Help me with my Physics lol

Answer:

25.40134119

Step-by-step explanation:

1000/39.368

a.  The probability is approximately \(0.1847\).

b. The probability of exactly 2 times falling between 1 and 5 seconds is approximately \(0.3038\).

(a) To find the probability that between 1 and 5 seconds elapse between emits, we can use the Poisson distribution. Given a mean rate of 3 emits per second, the parameter \($\lambda$\) for the Poisson distribution is also 3.

Let \($X$\) be the random variable representing the waiting time between emits. We want to find \($P(1 \leq X \leq 5)$\).

Using the Poisson distribution formula, we can calculate this probability:

\($P(1 \leq X \leq 5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$\)

\(P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}\)

Substituting \($\lambda = 3$ and $k = 1, 2, 3, 4, 5$\), we have:

\($P(1 \leq X \leq 5) = \frac{e^{-3} 3^1}{1!} + \frac{e^{-3} 3^2}{2!} + \frac{e^{-3} 3^3}{3!} + \frac{e^{-3} 3^4}{4!} + \frac{e^{-3} 3^5}{5!}$\)

Calculating this expression, we find that the probability is approximately \(0.1847\).

(b) When selecting 10 times between emissions randomly, the number of times falling between 1 and 5 seconds follows a binomial distribution. The probability of exactly 2 times falling in this range can be calculated using the binomial distribution formula:

\($P(X = 2) = \binom{10}{2} \cdot (P(1 \leq X \leq 5))^2 \cdot (1 - P(1 \leq X \leq 5))^{(10 - 2)}$\)

Substituting the probability from part (a), we have:

\($P(X = 2) = \binom{10}{2} \cdot (0.1847)^2 \cdot (1 - 0.1847)^{(10 - 2)}$\)

Calculating this expression, we find that the probability of exactly 2 times falling between 1 and 5 seconds is approximately 0.3038.

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As per the given statement a.) The probability that between 1 and 5 seconds elapse between emits is 5.26%. b.) The probability that exactly 2 of the emissions are between 1 and 5 seconds is 27.05%.

a. To find the probability that between 1 and 5 seconds elapse between emits in a Poisson process with a mean rate of 3 per second, we can use the exponential distribution.

The exponential distribution is characterized by the parameter lambda \((\(\lambda\))\), which is equal to the mean rate of the process. In this case, \(\(\lambda = 3\).\) The probability density function (PDF) of the exponential distribution is given by:

\(\[ f(t) = \lambda e^{-\lambda t} \]\)

To find the probability that between 1 and 5 seconds elapse between emits, we need to calculate the integral of the PDF from 1 to 5 seconds:

\(\[ P(1 \leq t \leq 5) = \int_{1}^{5} \lambda e^{-\lambda t} dt \]\)

Integrating the PDF, we have:

\(\[ P(1 \leq t \leq 5) = \left[ -e^{-\lambda t} \right]_{1}^{5} \]\)

\(\[ P(1 \leq t \leq 5) = -e^{-3 \cdot 5} - (-e^{-3 \cdot 1}) \]\)

\(\[ P(1 \leq t \leq 5) = -e^{-15} + e^{-3} \]\)

\(\[ P(1 \leq t \leq 5) \approx 0.0526 \]\)

Therefore, the probability that between 1 and 5 seconds elapse between emits is approximately 0.0526, or 5.26%.

b. If we randomly select 10 times between emissions, and we assume they are independent, we can model the situation as a binomial distribution.

The probability of having exactly 2 times between emissions between 1 and 5 seconds can be calculated using the binomial probability formula:

\(\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]\)

where \(\( n \)\) is the number of trials (10), \(\( k \)\) is the number of successful trials (2), and \(\( p \)\) is the probability of success (probability that between 1 and 5 seconds elapse between emits).

From part a, we know that \(\( P(1 \leq t \leq 5) \approx 0.0526 \).\)

Plugging in these values into the formula:

\(\[ P(X = 2) = \binom{10}{2} (0.0526)^2 (1 - 0.0526)^{10 - 2} \]\)

\(\[ P(X = 2) = 45 \cdot (0.0526)^2 \cdot (0.9474)^8 \]\)

\(\[ P(X = 2) \approx 0.2705 \]\)

Therefore, the probability that exactly 2 of the times between emissions are between 1 and 5 seconds is approximately 0.2705, or 27.05%.

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Answer:42

Step-by-step explanation:

LCM OF 2 , 3 & 7 is 42

Answer:

Step-by-step explanation:

Answer:78 feet and 34 cubic feet

Step-by-step explanation:

Answer: Use a variable

w

to represent the width of the room.

From the given information find that

10

w

=

80

, hence

w

=

8

.

So the room is

8

meters by

32

meters.

Explanation:

Let

w

represent the width of the room in meters.

Then the length of the room is

4

w

.

So the perimeter of the room is

w

+

4

w

+

w

+

4

w

=

10

w

.

Given that the perimeter is

80

meters, that translates as:

10

w

=

80

Divide both sides by

10

to get

w

=

8

.

Hence the width of the room is

8

meters and the length is

4

w

=

32

meters.

Step-by-step explanation:

The dimensions of the room are 5 meters long and 5 meters wide.

The perimeter of a rectangular room is equal to twice the sum of its length and width. In this case, the perimeter of the rectangular room is equal to 2 x (length + width) =  10 meters.

Therefore, we can write:
2 x (L + W) = 10

To find the dimensions of the room, we need to solve the equation for L and W.
L + W = 5
L = 5 - W

Substitute this equation for L in the original equation:
2 x (5 - W + W) = 10
2 x (5) = 10
10 = 10

Therefore, L = 5 and W = 5, so the dimensions of the room are 5 meters long and 5 meters wide.

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Answer:

900 degrees

Step-by-step explanation:

Answer:

  2 × (14 – 9) – (17 – 14) = 7

Step-by-step explanation:

Evaluate the choices to see which is true.

(2 x 14) – 9 – (17 – 14) = 7   ⇒  28 -9 -3 ≠ 7

2 x (14 – 9) + (– 17 – 14) = 7   ⇒  2(5) +(-31) ≠ 7

(2 x 14) – (9 – 17) – 14 = 7   ⇒   28 -(-8) -14 ≠ 7

2 x (14 – 9) – (17 – 14) = 7   ⇒   2(5)- 3 = 7 . . . . true

The amplitude of y = -2 sin 3x is 2

What is amplitude?

The largest movement of a particle on the medium from its rest position is referred to as a wave's amplitude. The amplitude can be thought of as the distance from the rest to the crest. The amplitude can also be determined by measuring it from the rest position to the trough position.

Given,Use the form sin(bx - c)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift.a=−2b=3c=0d=0Find the amplitude |a|.

Amplitude: 2

Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The ending balance in accumulated other comprehensive income on December 31, 2019, is $10,200 (credit balance).

To determine the ending balance in accumulated other comprehensive income on December 31, 2019, we need to analyze the changes in comprehensive income and other comprehensive loss. The net income of $12,000 and other comprehensive loss of $3,000 (net of tax) for the year ended December 31, 2020, indicate that the comprehensive income for the year is $9,000 ($12,000 - $3,000).

The ending balance in accumulated other comprehensive income can be calculated by adding the comprehensive income for the year to the beginning balance in accumulated other comprehensive income. Given that the ending balance on December 31, 2020, is $6,800 (credit balance), we can derive the beginning balance in accumulated other comprehensive income on December 31, 2019, by subtracting the comprehensive income for the year ($9,000) from the ending balance on December 31, 2020. Therefore, the ending balance in accumulated other comprehensive income on December 31, 2019, is $10,200 (credit balance).

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Answer:

b = 2√3

a = 4

Step-by-step explanation:

Here taking 60 as reference angle

so

tan60 = p/b

\(\sqrt{3}\)    = p/2

so p = 2√3

so

b = 2√3

so

\(h^2 = p^2 + b^2\\h^2 = (2\sqrt{3})^2 + 2^2\\h^2 = 12 + 4\\h^2 = 16\\h = \sqrt{16} \\h = 4\)

a = 4