Grant is making muffins for a reunion. The recipe for blueberry muffins makes 12 muffins. The recipe for bran muffins makes 18 muffins. He wants to make the same number of each kind of muffin using only full recipes of each. Question 1 Part A What is the least number of each type of muffin Grant can make? Enter the correct answer in the box.

The given system is consistent for all the b₁, b₂, and b₃. And this system satisfies 7b₁+5b₂+b₃=0. So the correct statement is option A.

When the system of equations is written in standard form as a matrix using the constants and coefficients, the augmented matrix is formed.

Let us consider the value of \(X=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]\). Then, the system Ax=b is written as follows,

\(\left[\begin{array}{ccc}1&-3&2\\-2&5&-1\\3&-4&5\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]=\left[\begin{array}{ccc}b_1\\b_2\\b_3\end{array}\right]\)

Then, the augmented matrix is written as,

\(\left[\begin{array}{ccc|c}1&-3&2&b_1\\-2&5&-1&b_2\\3&-4&5&b_3\end{array}\right]\)

Now, we have to find the row-reduced echelon form of the above matrix. For this apply the formula, R₂→R₂+2R₁, and R₃→R₃-3R₁. And we get,

\(\left[\begin{array}{ccc|c}1&-3&2&b_1\\0&-1&3&b_2+2b_1\\0&5&-15&b_3-3b_1\end{array}\right]\)

Applying R₃→R₃+5R₂, we get,

\(\left[\begin{array}{ccc|c}1&-3&2&b_1\\0&-1&3&b_2+2b_1\\0&0&0&7b_1+5b_2+b_3\end{array}\right]\)

Therefore, the system is consistent if 7b₁+5b₂+b₃=0. So option A is the correct one.

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The complete question is -

Let \(A =\left[\begin{array}{ccc}1&-3&2\\-2&5&-1\\3&-4&5\end{array}\right]\) and \(b=\left[\begin{array}{ccc}b_1\\b_2\\b_3\end{array}\right]\).

Determine if the equation Ax = b is consistent for all possible b₁, b₂, and b₃. If the equation is not consistent for all possible b₁, b₂, and b₃, give a description of the set of all b for which the equation is consistent (i.e., a condition which must be satisfied by b₁, b₂, b₃). What can you use this system for?

A) Equation is consistent for all b₁, b₂, b₃. satisfying 7b₁ + 5b₂ + b₃ = 0.

B) Equation is consistent for all possible b₁, b₂, b₃.

C) Equation is consistent for all b₁, b₂, b₃ satisfying -b₁ + b₂ + b₃ = 0.

D) Equation is consistent for all b₁, b₂, b₃ satisfying -3b₁ + b₃ = 0

Answer:

6 , -6 , -9 , 9

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

Answer:

mom

Step-by-step explanation:

Let's begin by listing out the data given to us:

Tom has 5 action figures

Tyler gives him 4 more

Tom's total action figures = the sum of Tom's a5 + 4 = 9

In the given parallelogram ABCD, the equal vectors are AB and CD.

A parallelogram is a quadrilateral with opposite sides parallel to each other. In this case, the given parallelogram is ABCD, and point E is located at its center. The sides AB and CD are longer than the sides BC and AD.

When we consider the vectors in the parallelogram, we can observe that AB and CD are equal vectors. This is because in a parallelogram, opposite sides are parallel and have the same length. In this case, AB and CD are opposite sides of the parallelogram and therefore have the same magnitude and direction.

The vector AB represents the displacement from point A to point B, while the vector CD represents the displacement from point C to point D. Since AB and CD are opposite sides of the parallelogram, they are equal in magnitude and direction. This property holds true for all parallelograms, ensuring that opposite sides are congruent vectors.

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To complete the integer division using the optimized division algorithm, the lowest number of rounds theoretically required depends on the specific algorithm employed. In the given scenario, the specific algorithm is not mentioned. However, we can provide explanations based on common algorithms such as binary division. Additionally, the resulting number in binary representation can be determined by converting the quotient to binary using 8 bits. Lastly, the resulting number in floating-point decimal representation can be determined by converting the quotient to IEEE 754 single precision format.

Part 1: The lowest number of rounds theoretically required to complete the integer division using the optimized division algorithm depends on the algorithm itself.

One common algorithm is binary division, where the dividend is continuously divided by the divisor until the remainder becomes zero or reaches a terminating condition.

The exact number of rounds needed in this case would depend on the values of A (dividend) and B (divisor). Without knowing the specific algorithm being used, it is not possible to determine the exact number of rounds.

Part 2: To represent the resulting quotient in binary format using 8 bits, we need to convert the quotient of A divided by B to binary. In this case, A = +54 and B = -3.

Performing the division, we get a quotient of -18. Representing -18 in 8-bit binary format, we have: 10010010. The most significant bit (MSB) represents the sign, where 1 indicates a negative value.

Part 3: To represent the resulting quotient in FP decimal representation using the IEEE 754 single precision standard, we need to convert the quotient to binary and then apply the specified format. Considering the quotient of -18, in binary it is represented as 10010.

Using IEEE 754 single precision format, the sign bit would be 1 (negative), the true exponent would be biased by 127, and the fraction would be normalized. The IEEE-754 exponent in binary would be 10000101, and in decimal (base 10) it would be 133. The resulting representation in IEEE 754 single precision format would be: 1 10000101 10010000000000000000000.

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Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

28x - 1 = 27x + 1 (being alternate angles)

28x - 27x = 1 + 1

x = 2

Hope it will help :)

Answer:

The length of the short side was 12 and the length of the long side was 32

Step-by-step explanation:

We will say that the length is the shorter side, and be using l as the variable, and that width is the longer side, and be using w as the variable. The first two equations we have are:

w = l + 20

And

2(2l + 3w) = 240

We will start with the second equation, then substitute in the first equation for w. We have:

4l + 6w = 240

Divide both sides by 2:

2l + 3w = 120

Then, we substitute in l + 20 for w, giving us:

2l + 3l + 60 = 120

Subtract 60 from both sides and combine like terms:

5l = 60

l = 12

So, the original length was 12, now substituting this into our first equation gives us:

w = 12 + 20 = 32

So the original width was 32. So, the length of the short side was 12 and the length of the long side was 32.

Hope this helped!

Answer:

2, 2, 3, 5, 7 that is the farthest you can go

Step-by-step explanation:

2,2,3,5,7 prime factorization of 420 but impossible to get 9 factors

The length x of the right triangle is 18.8 units.

A right angle triangle is a triangle that has one of it angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Hence, let's use trigonometric ratios to find the side x of the right triangle.

Therefore,

tan 37 = opposite / adjacent

opposite side = x

adjacent side = 25

tan 37 = x / 25

cross multiply

x = 25 tan 37

x = 25 × 0.7535540501

x = 18.8388512526

x = 18.8 units

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In a case whereby a  journey to school takes a girl 53 minutes the time she arrive if she leaves home at 08:38 is 09:31.

Based on the question, we werr told that the time she will used to get to school is 53 minutes, and were told that she left home around 08:38, then we can calculate the time she will get there as

[08:38 + 00:53]

= 09:31

Then we can conclude that the time that she will she will arrive at school  can be expressed as  09:31 which could be in the morning or night since it was not stated.

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Answer: try 13

Step-by-step explanation:

I did the math in my head lol

The probability that the mean for this sample is less than $21.50 is approximately 0.2033.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means from a population with a known mean and standard deviation is approximately normal, as the sample size gets larger. In this case, we are given the population mean and standard deviation, so we can assume that the sample means are normally distributed.

The formula for the standard error of the mean is

SE = σ/√n

where σ is the population standard deviation, n is the sample size, and SE is the standard error of the mean.

Plugging in the given values, we get

SE = 6/√35 ≈ 1.013

Next, we need to standardize the sample mean using the z-score formula

z = (X - μ) / SE

where X is the sample mean, μ is the population mean, and SE is the standard error of the mean.

Plugging in the given values, we get

z = (21.5 - 22.34) / 1.013 ≈ -0.829

Now, we need to find the probability that a standard normal variable is less than -0.829. Using a standard normal distribution table or calculator, we find that this probability is approximately 0.2033

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If there are 5 finalists at a singing competition, in 120 ways they can be ordered, if they each take turns singing by applying basic counting principles.

There are 5 finalists at a singing competition and each of them takes turns singing.

We can calculate the number of ways the 5 finalists can take up turn by applying basic counting principles.

Therefore, they can be ordered in n factorial ways, that is n !, where n is the number of finalists who take turns to sing.

Thus, number of ways the finalists can be ordered is = 5!

= 5*4*3*2*1 ( ways )

= 120 ways

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Answer:

Step-by-step explanation:

You just have to substitute -3 into your function.

Therefore: 9 + 15 + 36 = 50

The value of the  f (−3) is 42 after plugging the value of x = -3 in the function f(x) = -x² - 5x + 36.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

f(x) = -x² - 5x + 36

Any function of the form \(\rm f(x) =ax^2+bx+c\)  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

Plug x = -3 in the above function:

f(-3) = -(-3)² - 5(-3) + 36

f(-3) = -9 + 15 + 36

f(-3) = 42

Thus, the value of the  f (−3) is 42 after plugging the value of x = -3 in the function f(x) = -x² - 5x + 36.

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Answer:

27,44,95

Step-by-step explanation:

These numbers are in order from least to greatest, hope this helped!

Answer:

27, 44, 95

Step-by-step explanation:

Since 27 is smaller than 44 and 95 it goes first and since 95 is bigger than 27 and 44 it goes at the end and 44 is in the middle

1) d - c is calculated as; -4

2) Simplifying ³/₄ - ²/₅ gives; 7/20

1) We are given;

c = 12 and d = 8. Thus;

d - c is calculated as;

8 - 12 = -4

2) We want to simplify ³/₄ - ²/₅

Factoring out 1/20 gives;

1/20(15 - 8) = 7/20

3) Number of pencils purchased = 888 pencils

Number of pencils in a box = 12

Thus;

Number of boxes purchased = 888/12 = 74 boxes

4) An integer is a whole number (not a fractional number) that can be positive, negative, or zero. The only one that is not an integer here is; 20/6

5) √64 = 8

6) (30 - 4 * 2)/(2 * 2²)

= (30 - 8)/8

= 22/8 = 11/4

7) 11 = x + 19

x = 11 - 19

x = -8

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Answer:

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Step-by-step explanation:

yeah

Answer:

Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

I don't know if you want an example?

The width of rectangle is 5 feet.

Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).

Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -

Perimeter = 2 × (length + width)

Keep the values in formula to find the value of width

26 = 2 × (x + x - 3)

Performing addition of variables inside the bracket

26 = 2 × (2x - 3)

Shifting 2 to other side of equation to find the value of x

2x - 3 = \(\frac{26}{2}\)

Performing division to find the value of x

2x - 3 = 13

Shifting 3 to other side of equation to find the value of x

2x = 13 + 3

Performing addition to find the value of x

2x = 16

Shifting 2 as denominator to other side of equation to find the value of x

x = \(\frac{16}{2}\)

Performing division to find the value of x

x = 8

So, length of rectangle is 8 feet

Width of rectangle = x - 3

Width of rectangle = 8 - 3

Width of rectangle = 5 feet

Hence, the width of rectangle is 5 feet.

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Answer:

a

Step-by-step explanation:

you have to multply

Answer:

A

Step-by-step explanation:

The sample size is 289.

Zα/2 = \(Z_{0.025}\)

= 1.96  

Sample size = n

n = [Zα/2* σ / E] 2

n = [1.96 * 26 / 3 ]2

n = 288.54

n = 289.

In records, the pattern size is the measure of the number of man or woman samples used in an experiment. As an example, if we are testing 50 samples of folks that watch tv in a town, then the sample length is 50.

An awesome sample length is normally 10% as long because it no longer exceeds a thousand. A very good sample length is commonly around 10% of the populace, as long as this doesn't exceed one thousand. for example, in a populace of 5000, 10% could be 500. In a populace of 200,000, 10% would be 20,000.

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Answer:

The quantity of the first model is 150 and the second model is 100 that maximize the profit.

Step-by-step explanation:

Let the quantity of first model = x

Let the quantity of second model = y

The cost of the first model = $100

The cost of the second model = $150

Total number of models = 250 units

Total amount to spend on units = $30000

Now form the equations.

x  +  y  = 250

100x + 150y = 30000

Now solve for the x and y.

x = 250 – y

Now insert this value in the 100x + 150y = 30000.

100(250 –y) + 150y = 30000

25000 – 100y + 150y = 30000

50y = 30000 – 25000

50y = 5000

Y = 100

Now insert the Y in x + y = 250

x = 250 – y

x = 250 – 100

x = 150

Therefore, the first model is 150 units and the second model is 100 units that maximize the profit.

Answer:

X=-10

Step-by-step explanation:

Collinear points are points on the same line.

Use the equation of gradient to find the gradient. Then use the gradient to find X

\(\frac{Y2-Y1}{X2-X1}=Gradient of a slope\)

\(\frac{2-(-4)}{3-0}=\frac{2+4}{3}=\frac{6}{3}=2\)

\(\frac{x+4}{-3-0}=2\)

Multiply both sides of the equation to get rid of the fraction.

\(\frac{x+4}{-3}*-3 =2*-3\)

x+4=-6

x=-6-4

x=-10

It is impossible to get an answer to this! For two different variables, you need at least two different equations before you can work something out! :)

The area of the parallelogram is \(\sqrt{132}\).

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.

Given that,

vertices k(1, 1, 3), l(1, 3, 5), m(6, 9, 5), and n(6, 7, 3)

Area of Parallelogram = |KL × KN|

KL = (1, 1, 3) - (1, 3, 5) = (0, 2, 2)

KN = (1, 2, 3) - (3, 7, 3) = (2, 5, 0)

Area of the parallelogram = cross product of two vectors, represented by the adjacent sides.

Area of Parallelogram = |(0, 2, 2) × (2, 5, 0)|

                                    = |i(2 × 0 - 5 × 2) - j(0 × 0 - 2 × 2) + k(0 × 5 - 2 × 2)|

                                    = |i(-10) - j(-4) + k(-4)|

                                    = |-10i + 4j - 4k|

                                    = \(\sqrt{(-10)^{2}+(4)^{2}+(-4)^{2} }\)

                                    = \(\sqrt{100+16+16}\)

                                    = \(\sqrt{132}\)

Hence, The area of the parallelogram is \(\sqrt{132}\).

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Answer:

it was a incomplete question

Answer:

w= 11/3

Step-by-step explanation:

Multiply:

w×3=11

Regroup terms:

3w=11

Dive both sides by 3:

3.666667

w= 11/3

Answer:

I think it’s 56

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ralph reads 7 pages. Lily reads 8 times as Ralph reads.

Lily reads 7*8=56 pages.