Solve the following simultaneous equations algebraically
xy = 6
y-x=1

In response to the stated question, we may state that The rectangle with vertices A, B, C, and D is the form you just drew.

A rectangle in Euclidean geometry is a parallelogram with four small angles. It can also be defined as a fundamental rule hexagon or one with all angles equal.

A straight angle is another alternative for the parallelogram. Four vertices in a square are the same length. A quadrilateral with a rectangle-shaped cross-section has four 90° angle vertices and equal parallel sides.

€ As a result, it is also known as a "equirectangular rectangle" in some circles. A rectangle is sometimes referred to as a parallelogram, since its two sides have equal and parallel dimensions.

here's how to draw a rectangle with the vertices A(2,-2),B(2,3),C(5,3),D(5,-2):

Begin by sketching the x and y axes on graph paper and noting the origin (0,0).

Plot point A at (2,-2), B at (2,3), C at (5,3), and D at (5,3). (5,-2).

The rectangle with vertices A, B, C, and D is the form you just drew.

Here's an illustration of the rectangle:

     C (5,3)

     *

    /|

   / |

  /  |

 /   |

D (5,-2)|

 |   |

 |   |

 |   |

A (2,-2)|

 *---*---*B (2,3)

Therefore, draw a line segment between points A and B, then another between points B and C, and so on until you get a closed form.

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The production manager's claim that no more than 4,000 insulating washers are defective per day is likely to be true, based on the sample of 200 washers.

Proportion refers to the relationship between two quantities or numbers, indicating how they are related to each other in size or amount.

To determine whether the production manager's claim is likely to be true, we can use hypothesis testing. We can formulate the following hypotheses:

Null hypothesis (H0): The true proportion of defective insulating washers is equal to or less than 0.02 (4,000/225,000).

Alternative hypothesis (Ha): The true proportion of defective insulating washers is greater than 0.02.

We can use a significance level of 0.05, which means we are willing to accept a 5% chance of rejecting the null hypothesis when it is actually true.

To test these hypotheses, we need to calculate the test statistic and p-value. We can use the normal approximation to the binomial distribution, since the sample size (200) is large enough and the proportion of defective washers is relatively small (0.02).

The test statistic is calculated as:

z = (0.02 - 0.02) / √(0.02×(1-0.02)/200) = 0

The p-value is the probability of getting a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. Since we are testing the alternative hypothesis that the true proportion of defectives is greater than 0.02, we need to calculate the right-tailed p-value. We can use a standard normal distribution to calculate the p-value:

p-value = P(Z > z) = P(Z > 0) = 0.5

We are unable to reject the null hypothesis since the p-value is higher than the significance level of 0.05. This means we do not have sufficient evidence to conclude that the true proportion of defective insulating washers is greater than 0.02.

Therefore, the production manager's claim that no more than 4,000 insulating washers are defective per day is likely to be true, based on the sample of 200 washers.

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Answer:

If a polygon is dilated by a scale factor of k, then its area is multiplied by k².

a. When k = 4, the area of the image is 10 × 4² = 160 square units.

b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.

c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)

d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.

Step-by-step explanation:

Answer:

64sq cm

Step-by-step explanation:

To find area of net of square pyramid, you have to find area of the 4 triangles and area of square bottom.

Triangle Area = 1/2bh (times 4 because there are 4 triangles.

Square Area = lw

TA= 4(1/2bh)

4(1/2*4*6)

4(1/2*24)

4(12)

TA= 48 sq cm

SA= lw

4*4

SA= 16 sq cm

48 sq cm + 16 sq cm = 64 sq cm

The slope of the tangent line at the point (x,y) is -x/(2y). The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0).

The rate of change of a curve at a certain position is represented by the slope of a tangent line to the curve at that location. In other words, it indicates whether the curve is steep or shallow at that particular location. Calculating the derivative of a function in calculus also requires estimating the slope of a tangent line, which is a crucial step. We may determine the slope of the tangent line and subsequently the derivative of the function at a location by determining the limit of the slope of a secant line as the two points on the line approach closer and closer together.

The equation of the ellipse is x²)/16 +y²/4=1.

We take the derivative of the equation with respect to xto find the slope:

x²/16 + y²/4 = 1

(x²/16)' + (y²/4)' = 1'

2x/16 + 2y/4 * dy/dx = 0

dy/dx = -x/(2y)

When the denominator of 2y equals 0, there are some locations where the slope is not specified. The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0), and all locations on the x-axis between these two points when y = 0, which occurs.

Hence, the slope of the tangent line at the point (x,y) is -x/(2y). The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0).

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The probability that it will fail to detect an underfilled can for the first time when it encounters the 10th underfilled can is approximately 0.005.

Since the probability that an automated weight monitor detects underfilled cans of beverages is 0.98, the probability that it will not detect an underfilled can for the first time when it encounters the 10th underfilled can is given by:

(1 - 0.98)10-1(0.98)

Using the formula above, we will solve for the probability below:

(1 - 0.98)10-1(0.98)≈0.005

Thus, the probability that it will fail to detect an underfilled can for the first time when it encounters the 10th underfilled can is approximately 0.005.

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Answer:

Step-by-step explanation:

First Of all, Say the N-word, Now if she said the N-word, shell be given 27 dollars,Now I need to do my Homework, if i made you laugh, mark me the Brainliest

Step-by-step explanation:

From CalcWorkshop:

" Intersecting Chords Theorem. If two chords or secants intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord "

6 * 4 = 8 * x

x = 3

The dollar interval that would give a probability of 0.500 is X ± $8.47.

To determine the dollar interval that would give a probability of 0.500, we need to calculate the confidence interval using the formula:

Confidence interval = X ± Zα/2 × σ/√n

where:

X = sample mean

Zα/2 = Z-score for the desired level of confidence (in this case, 0.500 corresponds to a Z-score of 1.96)

σ = population standard deviation

n = sample size

Substituting the given values, we have:

Confidence interval = X ± 1.96 × 80/√64

Confidence interval = X ± 19.6

Since we want a probability of 0.500, we need to find the z-scores that correspond to the middle 50% of the normal distribution. Using a standard normal table, we can find that the z-scores are approximately -0.6745 and +0.6745.

Therefore, the confidence interval that will give a probability of 0.500 is:

X ± 0.6745 × 80/√64

X ± 8.47

So, when presenting the Q2 Sales Report to management, we would have to provide a dollar interval of X ± $8.47 to obtain a probability of 0.500.

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Answer:

-8x^2 - 10x + 7

Step-by-step explanation:

2x^2 - 10x^2 = -8x^2

-5x - 5x = -10x

3 - (- 4) = 7

-8x^2 - 10x + 7

Hope this helps!

The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.

The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.

A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.

If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.

Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.

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The inequality for the times when Valente is closer than Chiamaka to the university is - 170 + 110t < 149 + 95t

Distance of Chiamaka = 149km

Driving distance of Chiamaka = 95km

Distance of Valente = 170 km

Driving distance of Valente = 110 km

The graph of a linear function is always a straight line. A linear function has the form shown below. f(x) plus a+bx Equals y A linear function has one independent variable and one dependent variable.

Calculating the distances of Chiamaka -

C(t) = 149 + 95t

Calculating the distances of Valente -

V(t) = 170 + 110t

Now, Valente is closer when:

V(t) < C(t)

Figuring out the inequality -

170 + 110t < 149 + 95t

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Answer:

Proofs attached to answer

Step-by-step explanation:

Cant really graph since we don't have access, but here are some pointers.

Answer: 60?

Step-by-step explanation:

The reference angle is the acute angle formed between the terminal side of an angle in standard position and the x-axis. To find the reference angle of an angle, you can follow these steps:

Determine the quadrant in which the angle terminates. For -60 degrees, this would be the fourth quadrant.

Determine the corresponding angle in the first quadrant by finding the angle formed between the terminal side and the x-axis. In the fourth quadrant, this angle is equal to 360 degrees minus the original angle. So for -60 degrees, the corresponding angle in the first quadrant is 360 - 60 = 300 degrees.

Subtract this angle from 360 degrees to find the reference angle. For -60 degrees, the reference angle is 360 - 300 = 60 degrees.

Therefore, the reference angle of -60 degrees is 60 degrees.

cos(-180°) = -1

tan 8° = 0.1425

cos 690° = 0

sin (8-180°) = - sin 172° = - 0.9997

cos² (6-90°) = cos(-84°) = 0.4997

Therefore, the answer to the expression is -0.4997.

(x-11, y+14) = (-4-7, 7+7) = (-11,14) which matches the new coordinates T(-11,14).

In this sense, coordinates are the points where a grid system intersects. GPS coordinates are typically created by combining latitude and longitude. The distance of north and the south from the equator, which is 0 degrees iof north and south, is measured by lines of latitude.

8. T (-4,7)             7 units right, 7 units up                      (x-11, y+14)    

9. U (3,-4)               7 units left, 7 units up                         (x+7, y+7)      

10. V (-2,-10)           7 units right, 7 units down                  (x+7, y-7)  

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In given triangle, the value of t is 3.75 and the value of s is 10.4.

In a right triangle, the hypotenuse is the longest side, a "opposite" side is the one across from a given angle, and a "adjacent" side is close to a given angle. We use unique terminology to describe the sides of right triangles.

We can set up the following ratios because the two triangles in the illustration are comparable to one another:

t / 5 = 6 / 8 (using the smaller triangle)

s / 13 = 8 / 10 (using the larger triangle)

Simplifying these ratios, we get:

t / 5 = 3 / 4

s / 13 = 4 / 5

We may cross-multiply and simplify to find t and s:

t = 5(3/4) = 15/4 = 3.75

s = 13(4/5) = 10.4

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The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.

Answer:

a. Goron 224

b. Smith 96

Fishman 256

Step-by-step explanation:

a. For Goron: 640 x 0.35 = 224

b. For Smith: 640 x 0.15 = 96

   For Fishman: 640 x 0.40 = 256

For the blood analysis, there are a total of twelve possible experimental outcomes. The value of random variable  for each of the experimental outcome is zero.

Therefore it can be shown as:

a. The experimental outcomes associated with performing the blood analysis are:

List out all the possible outcomes that can occur during the blood analysis.

The outcomes are based on the number of steps required for each of the procedures, with the first procedure having either one or two steps, and the second procedure having either one, two, or three steps.

   (1) - First procedure requires one step, second procedure requires one step

   (2) - First procedure requires two steps, second procedure requires one step

   (3) - First procedure requires two steps, second procedure requires two steps

   (1,1) - First procedure requires one step, second procedure requires one step

   (1,2) - First procedure requires one step, second procedure requires two steps

   (1,3) - First procedure requires one step, second procedure requires three steps

   (2,1) - First procedure requires two steps, second procedure requires one step

   (2,2) - First procedure requires two steps, second procedure requires two steps

   (2,3) - First procedure requires two steps, second procedure requires three steps

b. Let z denote the total number of steps required to do the complete analysis. The value of the random variable for each of the experimental outcomes is:

It defines the value of the random variable, z, which denotes the total number of steps required to complete the analysis. It then provides the value of z for each of the experimental outcomes. For instance, outcome (1) requires one step in the first procedure and one step in the second procedure, so the value of z is 1+1=2. Similarly, for outcome (2), the value of z is 2+1=3.

   (1) - z = 1 + 1 = 2

   (2) - z = 2 + 1 = 3

   (3) - z = 2 + 2 = 4

   (1,1) - z = 1 + 1 = 2

   (1,2) - z = 1 + 2 = 3

   (1,3) - z = 1 + 3 = 4

   (2,1) - z = 2 + 1 = 3

   (2,2) - z = 2 + 2 = 4

   (2,3) - z = 2 + 3 = 5

   (3,1) - z = 2 + 1 = 3

   (3,2) - z = 2 + 2 = 4

   (3,3) - z = 2 + 3 = 5

If an outcome does not occur, the value of the random variable is 0.This is because the outcome did not happen, and there was no analysis to perform.

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Answer:

  $4.80

Step-by-step explanation:

You want to know the finance charge on a balance of $480 if the APR is 12%.

The monthly finance charge is the product of the monthly interest rate and the balance. The monthly interest rate is 1/12 of the annual rate.

  finance charge = (1/12 · 12%) · $480 = 0.01 · $480 = $4.80

The finance charge on the next monthly statement is $4.80.

In the following question, among the various parts to solve- a). DVD player functions for at least 10 hours is 0.0062. b)DVD player functions for at most 13 hours is 0.8944. c). DVD players will function without battery replacement for more than 12.83 hours.

(a) Probability that the DVD player functions for at least 10 hours. (Round your answer to four decimal places.)Given, mean (μ) = 12 hours and standard deviation (σ) = 0.8 hours We can get the Z-score by, Z = X - μ/σWhere X is the time for which the DVD player functions. Z = 10 - 12/0.8Z = -2.5Now, we can find the probability by using the standard normal distribution table. From the table, the probability corresponding to -2.5 is 0.0062. Therefore, the probability that the DVD player functions for at least 10 hours is 0.0062.

(b) Probability that the DVD player works for at most 13 hours. (Round your answer to four decimal places.)Z = X - μ/σWhere X is the time for which the DVD player functions. Z = 13 - 12/0.8Z = 1.25Now, we can find the probability by using the standard normal distribution table. From the table, the probability corresponding to 1.25 is 0.8944. Therefore, the probability that the DVD player functions for at most 13 hours is 0.8944.

(c) Find a number ** such that only 15% of all DVD players will function without battery replacement for more than x* hours. (Round your answer to two decimal places.)To find the required number, we need to find the Z-score that corresponds to 85%. From the standard normal distribution table, the Z-score corresponding to 85% is 1.0364. Therefore, the required number is = μ + ZσX = 12 + 1.0364 x 0.8X = 12.8291 ≈ 12.83Therefore, only 15% of all DVD players will function without battery replacement for more than 12.83 hours.

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Answer:

Step-by-step explanation:

Let's use the variable "s" to represent the number of slices in each pizza.

The drama club bought 999 large pizzas, and each pizza had s slices. So, the total number of pizza slices is given by the product of 999 and s, which can be written as:

999s = 727272

To solve for s, we can divide both sides of the equation by 999:

s = 727272/999

Using a calculator, we can simplify this fraction to:

s ≈ 728.73

Therefore, each pizza has approximately 728 slices. Note that this is an unusual number of slices for a pizza, so it's possible that the problem is not intended to be taken literally, but rather as a math puzzle or word problem.

Answer:

Each pizza has 729 slices.

Step-by-step explanation:

Answer:

x = 8500

y = 15000

Step-by-step explanation:

small vans: x

large vans: y

A: 5x + 2y = 72500

B: 2x + 6y = 107000

5x + 2y = 72500 => y = (72500 - 5x)/2

2x + 6(72500 - 5x)/2 = 107000

2x + 217500 - 15x = 107000

15x - 2x = 217500 - 107000

13x = 110500

x = 110500/13 = 8500

y = (72500 - 5x)/2 = y = (72500 - 5x8500)/2 = 15000

The rate of change of the distance between the cars at that instant is 5.46 meters/ second.

The first car's velocity = 7 meters per second

The second car's velocity = 3 meters per second.

Distance from the intersection of first car = 5m

Distance from the intersection of second car = 12m

The rate of change is used to numerically quantify the percentage change in value over a predetermined period of time. It is a measure of a variable's velocity.

Calculating the distance between both cars at the instant

= √(12² + 5²)

= √ 144 + 25

= √169

= 13

Calculating the rate of change of distance -

2d/dt

= d(x² + y²)/dt

= 2x dx/dt + 2ydy/dt

= 2×5×7 + 2×12×3

= 70 + 72

= 142

Therefore, total distance -

dd/dt

= 142/26

= 5.46

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The number of receptacles required in the classroom is 14.

To determine the number of receptacles required in a classroom, we need to consider the electrical code requirements for the room size and layout.

According to the National Electrical Code (NEC), there should be at least one duplex receptacle for every 12 linear feet of wall space in a classroom.

In addition, there should be at least one receptacle within 6 feet of each doorway and at least one receptacle on each wall space that is 2 feet or more in width.

Using this information and the dimensions provided, we can calculate the required number of receptacles as follows:

Calculate the perimeter of the room:

Perimeter = 2(Length + Width) = 2(36 + 24) = 120 feet

Calculate the total linear feet of wall space:

Total wall space = Perimeter - Width of door = 120 - 3 = 117 feet

Determine the number of receptacles required:

Number of receptacles = Total wall space / 12 + Number of doorways + Number of wall spaces wider than 2 feet

Number of doorways = 1 (as stated in the question)

Number of wall spaces wider than 2 feet = 2 (the two 24-foot-long walls)

Number of receptacles = (117 / 12) + 1 + 2 = 11 + 1 + 2 = 14

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Answer:

x = 94°

Step-by-step explanation:

ABCD is a cyclic quadrilateral , its 4 vertices lie on the circle.

the opposite angles of a cyclic quadrilateral sum to 180° , that is

x + 86° = 180° ( subtract 86° from both sides )

x = 94°

Rami collected 150 glass bottles in all over the 6 days of his recycling project.

Arithmetic operations are basic mathematical calculations that involve addition, subtraction, multiplication, and division.

Rami collected 24 glass bottles each day for 5 days, so the total number of bottles he collected during those 5 days is:

24 bottles/day × 5 days = 120 bottles

On the sixth day, Rami collected an additional 30 bottles.

To find out how many bottles Rami collected in total, we can add up the number of bottles he collected on each day:

Total bottles collected = 120 bottles + 30 bottles = 150 bottles

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The cost of sales for liquor, expressed as a percentage is 19.39%.

To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:

Cost of sales = (Cost of Goods Sold / Total Sales) × 100

where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)

Total Sales = Gross sales - Sales discounts - Sales returns and allowances

Let's compute for the COGS first:

COGS = Beginning Inventory + Purchases - Ending Inventory

= $0 + $2,500 - $0

= $2,500

Total Sales = Gross sales - Sales discounts - Sales returns and allowances

= $12,890 - $0 - $0

= $12,890

Cost of sales is obtained as follows:

Cost of sales = (Cost of Goods Sold / Total Sales) × 100

= ($2,500 / $12,890) × 100

= 19.39%.

Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.

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(a) Dataset with mean substantially less than median:

9, 10, 11, 12, 90

The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.

(b) Dataset with mean substantially more than median:

98, 99, 100, 101, 200

The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.

(c) Dataset with mean equal to median:

2, 3, 4, 4, 5

The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.

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