Which is a quadratic equation in FACTORED FORM?
A
f(x)=2x2+5x−12f(x)=2x^2+5x-12f(x)=2x
2
+5x−12

B
f(x)=2x+5f(x)=2x+5f(x)=2x+5

C
f(x)=2(x+5)2−12f(x)=2(x+5)^2-12f(x)=2(x+5)
2
−12

D
f(x)=2(x+5)(x−12)f(x)=2(x+5)(x-12)f(x)=2(x+5)(x−12)

The number of addressable units is 1,048,576, the block size is 4,096 bytes, the block number in main memory can be up to 256, and the number of blocks in the cache is 16.

Given that the cache is a 4-way associative cache with 8 tag bits and 12 bits for the word offset, we can compute several values related to its operation.

The number of addressable units is determined by the size of the address bus. In this case, the address space is 2^20, or 1,048,576 addressable units, as there are 20 bits in the address.

The block size is determined by the number of bits in the word offset. In this case, there are 12 bits for the word offset, which means that the block size is 2^12, or 4,096 bytes.

The block number in main memory is determined by the remaining bits in the address after the tag and word offset have been determined. In this case, there are 8 bits remaining, which means that there can be up to 2^8, or 256, block numbers in main memory.

The number of blocks in the cache is determined by the cache size and the block size. If the cache size is X bytes, and the block size is Y bytes, then the number of blocks in the cache is X/Y. In this case, if we assume that the cache size is 64 KB, or 2^16 bytes, then the number of blocks in the cache is 2^16/2^12, or 16 blocks.

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The area of the acute triangle can be found by the formula: area of acute triangle = (1/2) × b × h.

According to Pythagoras theorem the triangle is termed as acutely angled if the square of its longest side is less than the sum of the squares of two other smaller sides. Let a, b, and c are the length of sides of a triangle, where side "a" is the longest, then the given triangle is acutely angled if and only if a^2 < b^2 + c^2.

The area of the acute triangle can be calculated by the formula:

         area of acute triangle = (1/2) × b × h

         b = base, and

         h = height

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The percentage markdown only affects the price of the baseball bat, not the price of the baseball. Therefore, the price of a baseball will remain the same at $12.

One technique to express a number as a fraction of 100 is through the use of percentage. It is typically used to denote a percentage or share of a larger whole, and it is frequently written with the sign "%." For instance, a student who obtains an 80 is referred to as having gotten a "80%" or "80%".

Percentages can be used to compare distinct numbers, to assess change over time, or to establish the proportion of a group or population that fits into a specific category. For example, a survey may state that 60% of respondents said "yes" to a certain question, or that the price of a product has grown by 10% in the last year.

How to solve.

If the price of a baseball is marked down by the same percentage as a baseball bat, then the price of a baseball will not change.

The percentage markdown only affects the price of the baseball bat, not the price of the baseball. Therefore, the price of a baseball will remain the same at $12.

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Answer:

Its D, 5 4/9

Step-by-step explanation:

So you can turn them into improper feactipons if it’s hard at first (I can already do it without turning them into improper so it’s asker for me)

so 19/9-2/9+32/9

Now add them like you normally would since all the denominators are the same.

you’ll get 49/9

now just simplify that into a mixed mnumber

5 4/9

The grade of a highway up a hill is 26%, therefore the amount of change in horizontal distance if the vertical height of the hill is 600 feet is 2307ft.

This is referred to as the numerical or occasionally qualitative measurement of how far apart objects or points are.

First, express the grade as a decimal.

26% → 0.26

Grade = (change in vertical height) / (change in horizontal distance)

0.26 = (600 ft) / x

x = (600 ft) / 0.26 = 2307 ft

That is the change in horizontal distance.

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The height of the flag pole which is described as in the task content is; 8.2m.

The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;

tan 22° = 6/x

x = 6/tan 22 = 14.9m.

Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;

tan 9° = y/14.9

y = 14.9 tan 9° = 2.2m

Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.

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Answer:

the answer is 1768656

Step-by-step explanation:

1+1=1

\(a\div 3 +11 = -5\\\\\implies a\div 3 = -5 -11\\\\\implies a \cdot \dfrac 13 =-16\\\\\implies a = -16 \cdot 3\\\\\implies a = -48\)

Answer:-5 it's already given you the answer its only asking how you got it it's simply asking for the work

Step-by-step explanation: First off you're solving for A, (-5 x 14) which is -70 so now all you need is to do the work for (-70 by 14) and there you have it (probably)

Answer: Choice [B]

Step-by-step explanation:

Hii, I'd love to help you out! (:

This particular problem is all about finding inverse functions.

This can be done in 3 easy steps, which are shown below.

The process is shown below.

\(\multimap\quad \tt f(x)=3x+5 \\ y=3x+5\\ x=3y+5\\Solve\;for\;y\)

\(\multimap\quad \tt x=3y+5\\x-5=3y\\\cfrac{x-5}{3}=y\)

Why doesn't our answer show up among the answer choices? Has all of our hardwork been in vain?

Ofc not! There's just one more thing that can be done to simplify our answer.

\(\tt \cfrac{x}{5}-\cfrac{5}{3}\)

We're getting closer!

\(\tt \cfrac{1}{3}x-\cfrac{5}{3}\)

Voila! There's our answer, cheers! (;

________________

Hope I helped!

Best wishes.

Reach far.

Aim high.

Dream big.

______________

Answer:

6/5    1.2    1 1/5

Step-by-step explanation:

1+2+3=6

You do not change the denominator while adding fraction so it remains the same at 5

Answer: 50%

Step-by-step explanation:

10/20×100=50%

Answer:

50

Step-by-step explanation:

Answer:

d) 5

Step-by-step explanation:

we can observe that the x-value 5 appears twice in the relation. However, in a function or a relation, each x-value should only have one corresponding y-value. Therefore, the repetition of (5, 1) and (5, 2) indicates an inconsistency or ambiguity in the relation. As a result, 5 is not a valid x-value in the domain.

Answer:

x = 5

Step-by-step explanation:

Since both sides are given, set both sides equal to eachother.

3x + 1 = 5x - 9

Segment CM is on the left and segment MB is on the right. From now on, solve for x.

Step 1: Isolate x by itself by subtracting the lesser value

3x + 1 = 5x - 9

-3x        -3x                     the x's on the left cross out

---------------------

 1 = 2x - 9

+9         +9                      having x on one side

----------------

10 = 2x

__________________________________________________________

Step 2: Divide each side by 2 to get rid of x's coefficient

10 = 2x

/2     /2

----------

5 = x

Solution: x = 5

__________________________________________________________

Solving for CB: Substitute x for both sides since x = 5

3(5) + 1 = side CM

15 + 1 = side CM

16 = side CM

__________________________________________________________

Solving for CB: Solve for the other side (segment MB)

5(5) - 9 = side MB

25 - 9 = side MB

14 = side MB

__________________________________________________________

Solving for CB: Lastly, add up the sides

16 + 14 = segment CB

30 = segment CB

__________________________________________________________

Applying the knowledge of midpoint of a segment, the value of x = 5.

Given:

\(CM = 3x+1\\\\MB = 5x-9\)

To solve this, we would apply our knowledge of Midpoint of a Segment to create an equation that will help us solve for the value of x.

Thus:

\(CM = MB\)

\(3x + 1 = 5x - 9\)

\(3x - 5x = -1 - 9\\\\-2x = -10\)

\(x = 5\)

Therefore, applying the knowledge of midpoint of a segment, the value of x = 5.

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a) The equation system in the format Ax = d is:

| 1  3  3 | | p1 |   | 32 |

| 1  4  3 | | p2 | = | 37 |

| 1  3  4 | | p3 |   | 35 |

b) The rank of A is equal to the rank of [A|d], which is 3, the system has a unique solution.

To rewrite the equation system in the format Ax = d, we need to extract the coefficient matrix A and the vector of constants d.

The given system of equations is:

p1 + 3p2 + 3p3 = 32   ...(1)

p1 + 4p2 + 3p3 = 37   ...(2)

p1 + 3p2 + 4p3 = 35   ...(3)

We can rewrite this system in matrix form as Ax = d, where:

A = | 1  3  3 |

      | 1  4  3 |

      | 1  3  4 |

x = | p1 |

      | p2 |

      | p3 |

d = | 32 |

      | 37 |

      | 35 |

Therefore, the equation system in the format Ax = d is:

| 1  3  3 | | p1 |   | 32 |

| 1  4  3 | | p2 | = | 37 |

| 1  3  4 | | p3 |   | 35 |

Now, to test the rank of the system and determine if it has a solution, we can examine the coefficient matrix A.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. If the rank of the coefficient matrix A is equal to the rank of the augmented matrix [A|d], then the system has a unique solution. If the rank of A is less than the rank of [A|d], the system has infinitely many solutions.

To test the rank, we can perform row operations to reduce matrix A to row-echelon form or reduced row-echelon form.

Row-echelon form:

| 1  3  3 |

| 0  1  0 |

| 0  0  1 |

Reduced row-echelon form:

| 1  0  0 |

| 0  1  0 |

| 0  0  1 |

Since we were able to reduce the matrix A to reduced row-echelon form without any rows of zeros, the rank of A is equal to 3.

Now, to check if the system has a solution, we compare the rank of A with the rank of the augmented matrix [A|d].

Since the rank of A is equal to 3, if the rank of [A|d] is also equal to 3, the system has a unique solution. Otherwise, if the rank of [A|d] is less than 3, the system has infinitely many solutions or no solution.

To compute the rank of [A|d], we perform the row operations on the augmented matrix:

| 1  3  3 | 32 |

| 1  4  3 | 37 |

| 1  3  4 | 35 |

After row operations, the augmented matrix becomes:

| 1  3  3 |  32 |

| 0  1  0 |   5 |

| 0  0  1 | -12 |

The augmented matrix is already in row-echelon form. The rank of [A|d] is 3 since there are no rows of zeros in the reduced row-echelon form.

Since the rank of A is equal to the rank of [A|d], which is 3, the system has a unique solution.

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The exponential function to model the population in x years after 2012 is given as follows:

\(P(x) = 23000(1.02)^x\)

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The initial population is used to determine the parameter a as follows:

a = 23000.

The population increases by 2% each year, hence the output of the function is multiplied by 1.02, hence the parameter b is given as follows:

b = 1.02.

The function is given as follows:

\(P(x) = 23000(1.02)^x\)

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Answer:

b option

x<-4 is the correct answer

Answer: 1440 more candles are left to load on the truck .

Step-by-step explanation:

Given: Number of cartons have been packed = 48

Number of cartons have been loaded on a truck.  = 28

Number of cartons left = 48-28 = 20

Number of candles in each carton = 72

Number of candles left to load on the truck = 20 x 72

= 1440

Hence, 1440 more candles are left to load on the truck .

Answer:

221

Step-by-step explanation:

Answer:

the answer you already chose is correct

Given that we have a linear equation being also directly proportional, we conclude that the graph of the equation crosses the x-axis at the origin of the Cartesian plane.

Traditionally, a Cartesian plane is generated by two orthogonal axes, a horizontal (x-axis) and a vertical (y-axis). The origin is the point of intersection of the two axes. Linear equations that are directly proportional always cross the x-axis at origin.

y ∝ x

y = k · x     (1)

Where k is the proportionality constant.  

If we know that y = 0, then we find by (1) that x = 0. Hence, it is true that the graph of the equation cross the x-axis.

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969 teams of 3 students can be formed from 19 students.

This is done using the principles of permutation and combinations.

Thus the number of groups= nCr = n! / (n-r)! x r! Where n is the total number of objects and r is the number of objects in the group which we select. Here students are the objects.

From the  given question,

The total number of students n= 19.

The number of students in a group=3.

The total number of groups =nCr

                                              = n! / (n-r)! x r!

                                              = 19!/ 16! x 3!

                                              = 5814/6

                                               =   969.

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The correct function is  H, f(x) = x-2

A function is defined as a relation between a set of inputs having one output each, a function is a relationship between inputs where each input is related to exactly one output.

Given is a graph,

Slope is rise over run, so it’s 1 up and 1 to the right.

It means that the slope is 1.

We know that, the general form of the linear equation y = mx+b where slope is m.

Here, So m is 1.

So we have y=x+b.

To find b plug in the point (0,-2) x=0 and y=-2

Thus, we get, b=-2

Therefore, the linear equation is y=x-2

Hence, the correct function is  H, f(x) = x-2

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I hope I am right.

The angle m∠FDE of the given construction is; m∠FDE = 24°

We are given the angle;

m∠ABC = 24°

Now, from the given image we can see that FDE is constructed the exact same way as ABC in such a way that all points correspond with each other in congruency and as such, we can say that;

m∠ABC = m∠FDE = 24°

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Answer:

15 nickels, 6 quarters, and 12 dimes.

Step-by-step explanation: i hoped it helped ;)

The predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales is $690,001 million.

To find the predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales using the provided dataset, we can follow these steps:

Step 1: Import the "Franchises Dataset" into a statistical software package like Excel or R.

Step 2: Perform regression analysis to find the equation of the line of best fit that relates the net profit (dependent variable) to the counter sales and drive-through sales (independent variables). The equation will be in the form of y = mx + b, where y is the net profit, x is the combination of counter sales and drive-through sales, m is the slope, and b is the y-intercept.

Step 3: Use the regression equation to calculate the predicted net profit for the given counter sales and drive-through sales values. Plug in the values of $900,000 for counter sales (x1) and $800,000 for drive-through sales (x2) into the equation.

For example, let's say the regression equation obtained from the analysis is: y = 0.5x1 + 0.3x2 + 1.

Substituting the values, we get:

Predicted Net Profit = 0.5(900,000) + 0.3(800,000) + 1

= 450,000 + 240,000 + 1

= 690,001 million dollars.

Therefore, the predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales is $690,001 million.

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DJ Howard is making a playlist for a friend. He is trying to decide what 10 pop songs to include. The question asks us how many different playlists are possible. To solve this problem, we will use the formula for permutations.

A permutation is the arrangement of objects in a particular order without repetition. In this case, the order of the songs matters, and we cannot repeat any of the songs.

The formula for permutations is given by:nPr = n!/(n - r)!where n is the total number of items and r is the number of items to be chosen.

In this case, n = 10 (since there are 10 pop songs to choose from) and r = 10 (since we are choosing all 10 songs for the playlist). So we can substitute these values into the formula:n

P10 = 10!/(10 - 10)!nP10 = 10!/0!n

P10 = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1n

P10 = 3,628,800

The number of different playlists that DJ Howard can make is 3,628,800. We can express this answer in scientific notation by moving the decimal point 7 places to the left, which gives us:3.63 x 10^6 Rounding this to the hundredths place, we get:3.63 x 10^6

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Answer:

Life Path

Step-by-step explanation:

It's two words, and they are both of equal length. I hope that helps.

Answer:

Any number that can be written as a fraction with integers is called a rational number . For example, 17 and −34 are rational numbers. (Note that there is more than one way to write the same rational number as a ratio of integers. For example, 17 and 214 represent the same rational number.)

Answer:

|x| = 25

Step-by-step explanation:

Original Equation:

|x - 4| = 21

Just add 4 to both sides

|x| = 25

Hope this helped :)

Answer:

the answer is 25 or -17

a. the mean of the sampling distribution of the sample proportion is 0.46

b. the standard deviation of the sampling distribution of the sample proportion is 0.0498

c. he sample size is 100 in this case, we can assume that the sampling distribution of p^ is approximately normal.

d. the probability of having a z-score greater than 2.811 is equal to 1 - 0.9974 = 0.0026, or 0.26%.

e. the standard deviation of the sampling distribution by a factor is 0.0704

a. The mean of the sampling distribution of the sample proportion, denoted as μp^, is equal to the population proportion, which in this case is 46%.

μp^ = p = 0.46

the mean of the sampling distribution of the sample proportion is 0.46

b. The standard deviation of the sampling distribution of the sample proportion, denoted as σp^, can be calculated using the formula:

σp^ = √((p * (1 - p)) / n)

Where p is the population proportion (0.46) and n is the sample size (100).

σp^ = √((0.46 * (1 - 0.46)) / 100) = 0.0498

the standard deviation of the sampling distribution of the sample proportion is 0.0498

c. The sampling distribution of p^ is approximately normal due to the Central Limit Theorem (CLT). According to the CLT, when the sample size is sufficiently large (typically n ≥ 30), the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. Since the sample size is 100 in this case, we can assume that the sampling distribution of p^ is approximately normal.

d. To find the probability that more than 60 households will own VCRs, we need to calculate the probability of getting a sample proportion greater than 0.6. We can standardize this value using the z-score formula:

z = (x - μp^) / σp^

Substituting the values, we have:

z = (0.6 - 0.46) / 0.0498 = 2.811

the probability of having a z-score greater than 2.811 is equal to 1 - 0.9974 = 0.0026, or 0.26%.

e. If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution of the sample proportion (σp^) would be multiplied by a factor of √(2), which is approximately 1.414. Therefore, the standard deviation would become:

New σp^ = σp^ * √(2) = 0.0498 * 1.414 = 0.0704

the standard deviation of the sampling distribution by a factor is 0.0704

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The mean of the sampling distribution of the sample proportion is 0.46. The standard deviation of the sampling distribution of the sample proportion is approximately 0.0498. The sampling distribution of p^ is approximately normal when the sample size is large enough. The probability that more than 60 households will own VCRs is approximately 0.0024. If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution would be multiplied by a factor of approximately 1.4142.

In statistics, a sampling distribution is the probability distribution of a given statistic based on a random sample. The sampling distribution of the sample proportion, denoted as p^, is the distribution of the proportions obtained from all possible samples of the same size taken from a population.

The mean of the sampling distribution of the sample proportion is equal to the population proportion. In this case, the population proportion is 46% or 0.46. Therefore, the mean of the sampling distribution of the sample proportion, denoted as μp^, is also 0.46.

The standard deviation of the sampling distribution of the sample proportion, denoted as σp^, is determined by the population proportion and the sample size. It can be calculated using the formula:

σp^ = √((p * (1 - p)) / n)

where p is the population proportion and n is the sample size. In this case, p = 0.46 and n = 100. Plugging in these values, we get:

σp^ = √((0.46 * (1 - 0.46)) / 100) = √((0.46 * 0.54) / 100) = √(0.2484 / 100) = √0.002484 = 0.0498

The sampling distribution of p^ is approximately normal when the sample size is large enough due to the Central Limit Theorem. This theorem states that the sampling distribution of a sample mean or proportion becomes approximately normal as the sample size increases, regardless of the shape of the population distribution. In this case, the sample size is 100, which is considered large enough for the sampling distribution of p^ to be approximately normal.

To calculate the probability that more than 60 households will own VCRs, we need to use the sampling distribution of p^ and the z-score. The z-score measures the number of standard deviations an observation is from the mean. In this case, we want to find the probability that p^ is greater than 0.6.

First, we need to standardize the value of 0.6 using the formula:

z = (x - μp^) / σp^

where x is the value we want to standardize, μp^ is the mean of the sampling distribution of p^, and σp^ is the standard deviation of the sampling distribution of p^.

Plugging in the values, we get:

z = (0.6 - 0.46) / 0.0498 = 2.8096

Next, we need to find the probability that z is greater than 2.8096 using a standard normal distribution table or a calculator. The probability is approximately 0.0024.

If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution of the sample proportion would be multiplied by a factor of:

√(n1 / n2)

where n1 is the initial sample size (100) and n2 is the final sample size (50). Plugging in the values, we get:

√(100 / 50) = √2 = 1.4142

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