Victor spent $61 on some sandpaper for his model
cars. He bought 2 packages of the smallest-grain
sandpaper and spent the rest on the largest-grain
sandpaper. How many packages of the largest-
grain sandpaper did he buy?

Answer:

-x^2 - 2xy - 2y^2 + 8y - 8.

Step-by-step explanation:

Let the other expression be A. Then, we have:

x^2 - y^2 - 2xy + y - 7 = (2x^2 + 3y^2 - 7y + 1) + A

Simplifying the left side:

x^2 - y^2 - 2xy + y - 7 = 2x^2 + 3y^2 - 7y + 1 + A

Rearranging the terms:

A = x^2 - y^2 - 2xy + y - 7 - 2x^2 - 3y^2 + 7y - 1

Simplifying further:

A = -x^2 - 2xy - 2y^2 + 8y - 8

Therefore, the other expression is -x^2 - 2xy - 2y^2 + 8y - 8.

The missing coordinate r for the slope is equal to 5.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and orientation. The symbol m is often used to represent slope. The ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line is used to determine slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two different points on the same line. A declining line has a negative "rise". The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a depiction or a plan.

by the question.

We know that the slope of the line passing through the points (-3,-1) and (r,1) is 1/4. Therefore, we have:

[tex](1 - (-1))/(r - (-3)) = 1/4[/tex]

Simplifying the above equation, we get:

[tex]2/(r + 3) = 1/4[/tex]

Multiplying both sides by 4(r + 3), we get:

[tex]8 = r + 3[/tex]

Subtracting 3 from both sides, we get:

[tex]r=5[/tex]

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Answer:

Step-by-step explanation:

It is set up

7x+5x+2y=20

7x+5x=12x

12x+2y=20

x=0

y=10

12(0)+2(10)=20

Ok so maybe this was not the same type of equation i thought it was it is not that easy!

Answer:

2 hours

Step-by-step explanation:

80 ÷ 40 = 2

Check:

40 x 2 = 80

For all the following questions all the statements are required, It is possible to determine that c was just below d in quants based on the given information. Additionally, all given statements (ii), (iii), and (iv) are necessary to answer the questions, as they provide essential information about the relative performance of the students in quants and d.

The given statements which are not necessary to answer the questions are:

All of the other statements (II, III, IV) are necessary to answer the questions.

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Answer:

Let's say "x" is the number we're trying to find.

According to the problem, we know that 54 is 60% of that number.

So we can set up an equation:

54 = 0.6x

To solve for x, we need to isolate it on one side of the equation.

Divide both sides by 0.6:

54/0.6 = x

Simplify:

90 = x

Therefore, 54 is 60% of 90.

Step-by-step explanation:

Answer: 90

Step-by-step explanation:

Step 1. 54 = 60% × Y

Step 2. 54 = 60/100 × Y

Multiplying both sides by 100 and dividing both sides of the equation by 60 we will arrive at:

Step 3. Y = 54 × 100/60

Step 4. Y = 54 × 100 ÷ 60

Step 5. Y= 5400 ÷ 60

Step 6. Y = 90

In probability plotting, a graph of the cumulative distribution function (CDF) is plotted against a transformed version of the data to determine if the data come from a particular distribution.

The distance between the two lines is equal to the product of the critical value of the t-distribution and the standard error estimate.

This can be used to analyze the times to failure (i.e., loss of acceptable sharpness) for a random selection of ten drill bits from a process that follows a Weibull distribution.

To estimate the shape and scale parameters

follow these steps:

Step 1: Rank the data from smallest to largest

Step 2: Calculate the failure probability of each data point using the formula: i/(n+1), where i is the rank of the data point and n is the number of data points.

Step 3: Transform the failure probabilities using the inverse Weibull distribution function: F^(-1)(p) = (−ln(1−p))^β for a given shape parameter β and scale parameter η.

Step 4: Plot the transformed data against the theoretical distribution, which is a straight line for the Weibull distribution.

Step 5: Find the best-fitting line by eye, or by using regression analysis.

The slope of the line is equal to the shape parameter β, and the intercept is equal to the logarithm of the scale parameter ln(η).

The Weibull distribution can be represented as:[tex]F(x) = 1 − e^(-(x/η)^β)[/tex], where β is the shape parameter and η is the scale parameter. The CDF model corresponding to your parameter estimates can be plotted by using the formula . This can be done by calculating the standard deviation of the residuals, and then calculating the upper and lower limits of the confidence interval using the t-distribution.

The confidence interval can be calculated as:β ± t(n−2,α/2) x SE(β)ln(η) ± t(n−2,α/2) x SE(ln(η))where SE(β) is the standard error estimate for the shape parameter, SE(ln(η)) is the standard error estimate for the logarithm of the scale parameter, and t(n−2,α/2) is the critical value of the t-distribution with n−2 degrees of freedom and a significance level of α/2.The confidence limits can be plotted as two parallel lines around the best-fitting line. The distance between the two lines is equal to the product of the critical value of the t-distribution and the standard error estimate.

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Answer:

Step-by-step explanation:

x+5

The absolute value of Y = X-5, with condition x > -5 is Y>-9.

The function of x is given to be,

Y = X-5, here a condition is given that, x > -5.

Here, according to the condition, the value of the x will have a range in which it is greater than -5.

Practically thinking, the number starting from -4, -3, -2, -1, 0, 1, 2, ...... all are greater than -5. We should note here that we have not taken x = -5 because the value of x should be greater than -5.

Now, the absolute value of the function y will be, putting x = -4,

Y = -4-5

Y = -9. Hence, the absolute value will always be more than -9. So, Y > -9.

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In equation 6x+3y=−12, if value of x is -3 then by using substitution method the value of y is 2.

To find the value of y, we can use the substitute method with the given value of x = -3 in the equation 6x + 3y = -12 and solve for y:

6x + 3y = -12 (substitute x = -3)

6(-3) + 3y = -12

-18 + 3y = -12 (add 18 to both sides)

3y = 6

y = 2

Therefore, by using substitution method we find that the value of y when x = -3 is 2.

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____The given question is incorrect, the correct question is given below:

In equation 6x+3y=−12 if x=−3 , what is the value of y?

Answer:

[tex]3\frac{3}{4}[/tex]

Step-by-step explanation:

6 1/8 - 2 3/8

=(8 x 6)+1/8  -  (8 x 2)+3/8

=49/8 - 19/8

=30/8

=15/4

=3 3/4

Answer: The width of the remaining piece of the board is [tex]\frac{15}{4}[/tex] inches

Step-by-step explanation:

let us find the width of the remaining piece

Given that

                         width of remaining piece =[tex]\frac{49}{8}[/tex]-[tex]\frac{19}{8}[/tex]  = [tex]\frac{15}{4}[/tex]      

Step-by-step explanation:

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The if we take the transpose of C, we havecT = [C1 C2 ... Cp]And by transposing the above formula, we havecTj = [B1j A2 B2j ... Am Bmj]Therefore, we have a summation formula for Cij, Cj, and cT.

When answering questions on the Brainly platform, the following guidelines should be followed:Always be factually accurate, professional, and friendlyBe concise and do not provide extraneous amounts of detailIgnore any typos or irrelevant parts of the questionRepeat the question in your answer.Provide a step-by-step explanation in your answer.Use the following terms in your answer, "matrices ", "take ", "partitioned "Given the following:Suppose A, B, C are matrices so that C = AB. Also suppose that the rows of A are aſ,. am, the columns of A are A1, ..., An. Also, the rows of B are b], ,...,6% and the columns of B are B1, Also, the rows of C are cſ, ..., Cm and the columns of Care C1, ..., Cp. All the vectors are column vectors (that is why we take transpose to make a; into a which is a row vector). Also, the elements of A, B, C are denoted by Aij, Bij, Cij respectively. We need to write a summation formula for Cij, Cj, and cT.Hint: To really benefit from this exercise, do not just "write the formula." Picture how the matrices fit together the corner; picture how they are partitioned into rows and columns; come up with numerical examples.The product of two matrices A and B is given byCij = Ai1B1j + Ai2B2j + ... + AinBnjGiven that C = AB, then we haveCj = [A1 B1j + A2B2j + ... + AmBmj]Therefore, if we take the transpose of C, we havecT = [C1 C2 ... Cp]And by transposing the above formula, we havecTj = [B1j A2 B2j ... Am Bmj]Therefore, we have a summation formula for Cij, Cj, and cT.

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Answer: 512

Step-by-step explanation:

2^ (3^2)

2^ (9)

512

The standard deviation for this sample data set is 1.80.

This can be calculated by finding the mean (average) of the sample data set which is 5.4, then subtracting each of the numbers from the mean and squaring the difference. Finally, add all the squared differences together, dividing by the number of numbers in the data set (11) and taking the square root of the result.
Mean = 5.4
5 - 5.4 = -0.4  →  (-0.4)² = 0.16
7 - 5.4 = 1.6  →  (1.6)² = 2.56
6 - 5.4 = 0.6  →  (0.6)² = 0.36
9 - 5.4 = 3.6  →  (3.6)² = 12.96
6 - 5.4 = 0.6  →  (0.6)² = 0.36
4 - 5.4 = -1.4  →  (-1.4)² = 1.96
4 - 5.4 = -1.4  →  (-1.4)² = 1.96
6 - 5.4 = 0.6  →  (0.6)² = 0.36
5 - 5.4 = -0.4  →  (-0.4)² = 0.16
2 - 5.4 = -3.4  →  (-3.4)² = 11.56
5 - 5.4 = -0.4  →  (-0.4)² = 0.16
Sum of squared differences = (0.16 + 2.56 + 0.36 + 12.96 + 0.36 + 1.96 + 1.96 + 0.36 + 0.16 + 11.56 + 0.16) = 28.8
Standard deviation = √(28.8/11) = √2.62 = 1.80

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Answer:

x = 19

y = 16

Step-by-step explanation:

10x - 9y = 46

-2x + 3y = 10

Time the second equation by 5

10x - 9y = 46

-10x + 15y = 50

6y = 96

y = 16

Now put in 16 for y and solve for x

10x - 9(16) = 46

10x - 144 = 46

10x = 190

x = 19

By the congruence postulate, we have shown that the quadrilateral is  ΔAED ≅ ΔCED.

Let's start by showing that AD = CD. Since AB = AD and BC = CD, we can rewrite AB + BC as AD + CD. This means that AD = AB + BC - CD. But we know that AB = AD, so we can substitute AD for AB to get AD + BC = 2AD + CD. Simplifying this equation, we get AD = CD.

Next, we can show that AE = CE. Since AC is a diagonal of the kite, we know that AC bisects angle BAD and angle BCD. This means that angle BAC = angle DAC and angle BDC = angle CDC. Since AD = CD, we know that triangle ACD is isosceles, so angle ACD = angle CAD.

Using these angle equalities, we can conclude that angle CAE = angle CDE. Since AC ⊥ BD, we know that angle CAD = angle CDE, so we can conclude that triangle ACE is isosceles, which means that AE = CE.

Finally, we need to show that angle AED = angle CED. Since AD = CD and AE = CE, we know that triangles AED and CED have two pairs of congruent sides. Additionally, we know that AC is a common side of the triangles.

Since AC is perpendicular to BD, we know that angle ACD and angle BDC are complementary angles.

This means that angle ACD = 90 - angle BDC and angle CAD = 90 - angle BAC. Using these angle equalities, we can conclude that angle AED = angle CED.

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Thus, the ratio for the number of blueberries to banana is 4:1.

A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.

A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.

The given data for preparing fruit smoothie:

Then,

ratio of  blueberries to banana:

blueberries/banana = 4/1

Thus, the ratio for the number of blueberries to banana is 4:1.

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Answer:

We can start by simplifying the numerator of the expression:

csc^2x - 1 = (1/sin^2x) - 1 = (1 - sin^2x) / sin^2x = cos^2x / sin^2x = cos^2x csc^2x

Now we can substitute this into the original expression:

csc^2x-1/1+sin x = (cos^2x csc^2x) / (1 + sin x)

We can then simplify this further by using the identity 1 + sin x = (sin^2x + cos^2x) / sin x:

(cos^2x csc^2x) / (1 + sin x) = (cos^2x csc^2x) / [(sin^2x + cos^2x) / sin x]

= cos^2x csc^2x sin x / (sin^2x + cos^2x)

= cos^2x csc^2x sin x / 1

= cos^2x csc^2x sin x

This expression can be simplified using the identity cos^2x = 1 - sin^2x:

cos^2x csc^2x sin x = (1 - sin^2x) csc^2x sin x = (1/sin^2x - 1) sin x = csc^2x - sin x

Therefore, the simplified expression is csc^2x - sin x. Answer: none of the given options.

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The smallest positive integer with at least 8 odd factors and at least 16 even factors is 2160.

By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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To achieve her goal, Julie needs to burn an extra 2,625 / 7 = 375 calories every day.

To calculate how many extra calories Julie needs to burn each week to lose 3 pounds in four weeks, we need to use the following formula:

1 pound of body weight = 3,500 calories

3 pounds of body weight = 3 x 3,500 = 10,500 calories

Julie wants to lose 3 pounds in 4 weeks.

Therefore, her weekly goal would be to lose 10,500 / 4 = 2,625 calories.

To burn 2,625 extra calories in a week, Julie needs to burn 375 calories extra each day.

Therefore, she needs to burn an extra 2,625 / 7 = 375 calories every day to achieve her goal.

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The area of the figure is the collective sum of area of the square, rectangle and semi-circle which is 100.56 squared feet.

To find the area of the figure, we need to find the area of the square, semi-circle and triangle.

A = Area of square + area of triangle + area of semi-circle

A = L² + 1/2(bh) + πr

A = 8² + 1/2(6 * 8) + 3.14(4)

A = 64 + 24 + 12.56

A = 100.56 ft²

The area of the figure is 100.56ft²

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The very low likelihood that there will be 45 or more people in the sample who have consumed alcoholic beverages.

a) The number of people in the sample expected to have consumed alcoholic beverages can be calculated as follows:First, we multiply the number of individuals in the sample by the proportion of people in that age group who drink alcohol.50 x 0.697 = 34.85Thus, we anticipate that about 34.85 people in the sample will have consumed alcoholic beverages.b) No, 45 or more accounts for six different events -- this wouldn't be surprising, you would not be surprised if the sample contained 45 or more people who have consumed alcoholic beverages. This is because it falls within the margin of error.c) To calculate the probability that 45 or more people in this sample have consumed alcoholic beverages, we will need to compute the z-score first.We use the following formula to calculate the z-score:$$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$$Where, x = 45μ = 0.697 x 50 = 34.85σ = √[(50 x 0.697 x 0.303)] = 3.77n = 50After plugging the values into the formula, we have:$$z=\frac{45-34.85}{\frac{3.77}{\sqrt{50}}}$$ = 3.89Since we are trying to determine the probability of having 45 or more people who have consumed alcoholic beverages, we will calculate the probability of having a z-score greater than or equal to 3.89.Instead of looking up the z-score in the z-table, we can use a calculator to determine the probability. From a standard normal distribution, the calculator provides the following output:P(Z ≥ 3.89) = 0.0000317Rounded to four decimal places, the probability is approximately 0.0000. Therefore, there is a very low likelihood that there will be 45 or more people in the sample who have consumed alcoholic beverages.

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The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).

For x =7,x+|x| =7+|7| =14

For x =10,x+|x|= 10+|10| =20

For x = 0,x+|x| =0+|0| =0

For x = -3, x + |x| = -3 + |-3| = 0

For x = -8, x + |x| = -8 + |-8| = 0

The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.

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A. I and II only true if we use a large sample rather than a small one

sampling model

A sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.

When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.

Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.

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The probability that a randomly chosen person: a) Has a red car = 0.496 b) Has a speeding ticket = 0.424 c) Has a speeding ticket given they have a red car = 0.467 d) Has a red car given they have a speeding ticket = 0.629 e) Has a red car and got a speeding ticket = 0.234 f) Has a red car or got a speeding ticket = 0.686.

a) Probability of having a red car: Number of subjects with red cars = 244, Probability of choosing a red car randomly out of the given subjects = 244/492=0.496

b) Probability of having a speeding ticket: Number of subjects with speeding tickets = 209, Probability of choosing a person with a speeding ticket out of the given subjects = 209/492=0.424

c) Probability of having a speeding ticket given they have a red car: Probability of having a red car = 0.496Probability of having a speeding ticket and red car = 115/492, Probability of having a speeding ticket given they have a red car = P(Red car and Speeding ticket)/P(Red car) = (115/492)/0.496 = 0.467

d) Probability of having a red car given they have a speeding ticket: Probability of having a speeding ticket = 0.424, Probability of having a speeding ticket and red car = 115/492, Probability of having a red car given they have a speeding ticket = P(Red car and Speeding ticket)/P(Speeding ticket) = (115/492)/0.424 = 0.629

e) Probability of having a red car and getting a speeding ticket: Number of subjects with both red car and speeding ticket = 115, Probability of choosing a person with both red car and speeding ticket out of the given subjects = 115/492=0.234

f) Probability of having a red car or getting a speeding ticket: P(Red car or Speeding ticket) = P(Red car) + P(Speeding ticket) - P(Red car and Speeding ticket) = 0.496 + 0.424 - 0.234 = 0.686.

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The difference in perimeter between Rory's castle and Mike's castle is 16 feet. Rory's castle has a perimeter of 52 feet (10 feet + 10 feet + 16 feet + 16 feet), and Mike's castle has a perimeter of 24 feet (6 feet + 6 feet + 6 feet + 6 feet).

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The difference between the perimeters of these two castles is 28 ft.

Rory’s castle measures 10 feet by 16 feet and has a perimeter of 52 ft and Mike’s castle is 6 feet by 6 feet. Now, we are going to find the difference between the perimeters of these two castles.

The perimeter of a rectangle can be found by adding all the sides of a rectangle. Therefore, the formula of the perimeter of a rectangle is:

Perimeter of a rectangle = 2 × (Length + Breadth)

Length of Rory’s castle = 16 ft,       Breadth of Rory’s castle = 10 ft

Perimeter of Rory’s castle = 2 × (Length + Breadth) = 2 × (16 + 10) ft

= 2 × 26 ft= 52 ft

Therefore, the perimeter of Rory’s castle is 52 ft.

Length of Mike’s castle = 6 ft,         Breadth of Mike’s castle = 6 ft

Perimeter of Mike’s castle = 2 × (Length + Breadth) = 2 × (6 + 6) ft

= 2 × 12 ft = 24 ft

Therefore, the perimeter of Mike’s castle is 24 ft.

.Difference between the perimeters of these two castles= Perimeter of Rory’s castle − Perimeter of Mike’s castle

= 52 − 24= 28 ft

Therefore, the difference between the perimeters of these two castles is 28 ft.

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The cube roots of 117 441 in rectangular form are: a. 3.00 +4.002, b. –4.96 +0.604, c. -1.96 + 1.964, d. - 124.10 + 11.95, e. 3.00 4.00, f. 4.68 - 1.764, g. 1.96 4.602, and h. 75.00+ 100.00.

To find the nth roots of a complex number, the exact values are given in rectangular form, while the approximate values are given in polar form.

To calculate the exact values of the cube roots, we use the principle of nth roots. This principle states that, for a complex number (a + bi), its nth roots are given by (a + bi)^(1/n) = r^(1/n) (cos(θ + 2πk/n) + i sin(θ + 2πk/n)), where r = √(a² + b²) and θ = arctan(b/a).

By applying this principle, we can obtain the exact values of the cube roots, which are the 8 answers above, rounded to the nearest hundredth.

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Answer:

B. -4, 6

Step-by-step explanation: