Which system of equations has exactly one solution?
O 2x - 4y = 8
X+ y = 7
o 3x+y=-1
6x+2y = -2
3x+3y = 3
-6x-6y=3
3x-2y = 4
-3x + 2y = 4

Answer:

8

Step-by-step explanation:

Deer = snow flake = 4

4 + 4 + 4 = 12

Dear - 3 = 1

Snowman = 1

Tree = 8

8 + 1 (snowman) + 8 = 17

1. Independent random samples arise when one random sample is split into groups differing by an observed feature is incorrect.

2. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

1. Independent random samples arise when individuals in a sample are randomly assigned to experimental groups, data is recorded repeatedly on a random sample of individuals, or random samples are selected separately. The statement that one random sample is split into groups differing by an observed feature does not accurately describe independent random samples.

2. The margin of error in a confidence interval represents the range of values within which the true population parameter is likely to fall. It is calculated by taking half of the width of the confidence interval. Therefore, the correct answer is that the margin of error is equal to half the width of the confidence interval.

In summary, the incorrect statement is that independent random samples arise when one random sample is split into groups differing by an observed feature. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

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Answer:

 answer is B,E and C

Step-by-step explanation:

U tell me

The formulated Linear Program aims to minimize the objective function, which is the sum of production and inventory costs minus the revenue from selling the end-of-period inventory at month 4.

In this problem, we need to determine the optimal production and inventory levels over the four-month period to minimize costs and maximize revenue. We can formulate this as a linear programming problem with the following decision variables:

Let x1, x2, x3, x4 represent the production quantities for months 1, 2, 3, and 4, respectively.

Let y1, y2, y3, y4 represent the end-of-month inventory levels for months 1, 2, 3, and 4, respectively.

The objective function we want to minimize is:

Minimize: (5x1 + 8x2 + 4x3 + 7x4) + (2y1 + 2y2 + 2y3) - (15y4)

Subject to the following constraints:

1. Initial inventory: y1 = 15 (given)

2. Production capacity constraints:

  x1 <= 90 (month 1 capacity)

  x2 <= 75 (month 2 capacity)

  x3 <= 80 (month 3 capacity)

  x4 <= 50 (month 4 capacity)

3. Inventory balance equations:

  y1 + x1 - 50 = y2 (month 1)

  y2 + x2 - 65 = y3 (month 2)

  y3 + x3 - 100 = y4 (month 3)

  y4 + x4 - 70 = 0 (month 4, no carryover inventory)

4. Non-negativity constraints:

  x1, x2, x3, x4, y1, y2, y3, y4 ≥ 0

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The coordinates of the center of the circle x^2 + 2x + y^2 - 4y = 12 are (-1, 2).

To determine the coordinates of the center of the circle defined by the equation x^2 + 2x + y^2 - 4y = 12, we need to complete the square for both the x and y terms.

Starting with the x terms, we can add (2/2)^2 = 1 to both sides of the equation to get:

x^2 + 2x + 1 + y^2 - 4y = 12 + 1

Simplifying:

(x + 1)^2 + (y - 2)^2 = 13

Comparing this to the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, we see that the center of the circle is (-1, 2) and the radius is sqrt(13).

Therefore, the coordinates of the center of the circle x^2 + 2x + y^2 - 4y = 12 are (-1, 2).

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The first scenario described is an example of a retrospective cohort study.  The second scenario suggests a retrospective cohort study as well. The third scenario represents a cross-sectional study, where researchers conduct a survey among high school students to assess the prevalence of obesity and diabetes.

1. In the first scenario, a retrospective cohort study is conducted by tracking individuals over a 20-year period. The study begins in 1960 and collects data on cigar smoking practices. After 20 years, the participants are followed up to determine if they developed any cancers. This type of study design allows researchers to examine the long-term effects of smoking Cuban cigars.

2. The second scenario involves a retrospective cohort study as well. The objective is to study the long-term neurological effects of a discontinued anesthetic agent. The researchers identify patients who received the drug before it was discontinued and then assess the occurrence of subsequent neurological disorders. This study design allows for the examination of the relationship between exposure to the anesthetic agent and the development of neurological disorders.

3. The third scenario represents a cross-sectional study. Researchers aim to assess the prevalence of obesity and diabetes among high school students during their junior year. They conduct a survey to gather information on the students' current weight, diabetes status, and other relevant factors. A cross-sectional study provides a snapshot of the population at a specific point in time, allowing researchers to examine the prevalence of certain conditions or characteristics.

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Answer:

x=-45/11

Step-by-step explanation:

2x/3-3/2=5x/2+6

2x/3=5x/2+7.5

11x/6=7.5

11x=45

x=-45/11

Answer:

The real solution is \(n=6\).

Step-by-step explanation:

\(\cos(\frac{\pi}{2})=0\) while \(\sin(\frac{\pi}{2})=1\)

So the equation becomes:

\(-64=(2(0)+2i(1))^n\)

\(-64=(0+2i)^n\)

\(-64=(2i)^n\)

We know that \(2^6=64\). So let's see what \(n=6\) gives us:

\((2i)^6=64i^6=64i^4i^2=64(1)(-1)=-64\).

\(-64\)  is the result we wanted.

\(n=6\) is therefore a solution.

From the given information, total surplus in a market is equal to the sum of consumer surplus and producer surplus.

Consumer surplus is the difference between the highest price a consumer is willing to pay for a good or service (the "reservation price") and the actual price they pay. Producer surplus is the difference between the lowest price a producer is willing to accept for goods or services and the actual price they receive.

When a market is in equilibrium, the price and quantity are such that the quantity demanded equals the quantity supplied. At this point, total surplus is maximized, since all trades that benefit both consumers and producers have taken place. The total surplus represents the net benefit to society from the production and consumption of the good or service in the market.

In other words, total surplus is the sum of the gains from trade that accrue to consumers and producers in the market, and it represents the difference between the value that buyers and sellers place on the good or service and the resources that were actually used to produce it.

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Answer:

1. 12x+7

2. x=7

Step-by-step explanation:

1. 4(5x-1)-8x+11=?

multiply 4(5x-1)

20x-4-8x+11

Subtract 8x from 20x which is 12x

then subtract 4 from 11 which is 7

12x+7

Answer:

Step-by-step explanation:

4(5x - 1) - 8x + 11

= 20x - 4 - 8x +11

= 12x + 7

-5(x + 1) + 3x = 6 - (4x - 3)

↔ -5x - 5 + 3x = 6 - 4x + 3

↔ -2x - 5 = 9 - 4x

↔ 2x = 14

↔ x = 7

Answer:

C. For each additional hour of service, the price of the dog walker increases by $10.

Step-by-step explanation:

Hope this helps!

:)

Answer:

1) 187.5ms^2

1) 187.5ms^22) 307.5m

Step-by-step explanation:

1) You can use the formula:

Force = Mass x Acceleration

750 = 4 x a

750 = 4a

750/4 = a

187.5ms^2

2)

For every one second it travels 12.3 meters therefore you can just do 12.3x25 = 307.5m

Answer:

x = 27

Step-by-step explanation:

Step 1: Write out equation

54 + 6x = 216

Step 2: Solve for x

6x = 162

x = 27

Answer:

x=27

Step-by-step explanation:

54+6x=216

Collect like terms:

6x=216-54

6x=162

Divide both sides by the coefficient of x

6x\6=162\6

x=27

Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.

To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.

P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.

P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.

To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.

The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.

Therefore, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= (2/3) * (6/13) + (5/9) * (7/13)

= 89/117

Now we can plug in all the values into Bayes' theorem to find P(A|B):

P(A|B) = P(B|A) * P(A) / P(B)

= (2/3) * (6/13) / (89/117)

= 52/89

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.

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The scale that Wyatt used is 1 inch represents 0.36 yards

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. The scale provides information on the proportional relationship between the scale of the drawing and the original image.

Scale of the drawing = original length / length of the drawing

84 / 231 = 0.36 yards

This means that 1 inch is represented by 0.36 yards

Alternatively, it can be written as 1 : 0.36 yards

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Answer:

Reorder  u  and  t .

S  =  t u  +  1 /2

Step-by-step explanation:

pretty sure that's correct

The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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Answer:

0.9357

Step-by-step explanation:

The change of base rule can be used if a and b are greater than 0 and not equal to 1, and x is greater than 0.

log a (x) = ( log b (x) / log b (a) )

Substitute in values for the variables in the change of base formula, using b=10.

log(7) / log(8)

The result can be shown in multiple forms.

Exact Form:

log(7) / log(8)

Hope this helped you out!

The total amount of money owned by Bhavin will be $3100. The percentage of the money will be 51%.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that Bhavin, Max and Imran share 6000 rupees in the ratios 2 : 3: 7 Imran then gives 3/5 of his share of the money to Bhavin.

Bhavin's share of the money will be calculated as,

2x + 3x +7x = 6000\x = 500

Bhavin's share = 2x = 2 x 500 = $1000

Imran's  share = 7x = 7 x 500 = $3500

Bhavin's total after = 1000 + (3500 x 3 / 5)

Bhavin's total after = 1000 + 2100 = $3100

The percentage of the money,

Percentage = 3100 / 6000 = 51%

Therefore, the total amount of money owned by Bhavin will be $3100. The percentage of the money will be 51%.

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Answer:

Angle C prime

Step-by-step explanation:

First design and sketch it:

Make a rectangle with corners C D E and F. 90 degrees each. Now rotate it 45 degrees to the left. Angle D is diagonally from Angle C.

I hope this helps! :)

The thief stole 22 oranges using algebraic equations.

To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.

According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.

We also know that the thief was left with only 9 oranges. So we can set up the equation:

x - [(1/2)x + 2] = 9

Simplifying this equation:

(1/2)x - 2 = 9
(1/2)x = 11
x = 22

Therefore, the thief stole 22 oranges.

The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.

To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.

In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.

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Answer:

3

Step-by-step explanation:

The slope is rise/run and for this case, it is 3/1 which equals 3!!!

There are 27 different ways for Sam to color the sides of the equilateral triangle, accounting for rotations and reflections.

We have,

To calculate the number of different ways Sam can color the sides of the equilateral triangle, we need to consider the symmetry of the triangle.

Since two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring, we need to account for these symmetries.

Let's analyze the possibilities:

- All three sides have the same color:

There is only one way to color the triangle in this case.

- Two sides have the same color, and the third side has a different color: Sam can choose the color for the two sides in 5 ways and the color for the remaining side in 4 ways (since it must be different from the other two colors).

However, we need to divide this by 3 to account for the different rotations of the equilateral triangle.

Thus, there are (5 x 4) / 3 = 20 / 3 = 6.67 (approx) ways to color the triangle in this case.

Since the number of colorings must be a whole number, we consider this as 6 ways.

- All three sides have different colors:

Sam can choose the color for the first side in 5 ways, the color for the second side in 4 ways (since it must be different from the first), and the color for the third side in 3 ways (since it must be different from the first two).

However, we need to divide this by 6 to account for the different rotations and reflections of the equilateral triangle.

Thus, there are (5 x 4 x 3) / 6 = 20 ways to color the triangle in this case.

In total, the number of different ways Sam can color the sides of the equilateral triangle is:

= 1 + 6 + 20

= 27.

Thus,

There are 27 different ways for Sam to color the sides of the equilateral triangle, accounting for rotations and reflections.

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The number of small ball bags she will need is 7 small bags, the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given that;

Need of flour for cakes= 17 2/5 pounds

Now,

There are 4 large bags, and each one has 4 pounds.

She buys all of the large bags, she already has;

4x4=16

16 pounds. So, she only needs

17 2/5 -16= 1 2/5

=5/5+2/5

=7/5

1 2/5 pounds more, this fraction is equals to 7/5 pounds.

The small bags only contains 1/5 pounds of flour so,

7/5/1/5

=7*5/1*5

=7

Therefore, by algebra the answer will be 7 bags

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The complete question is;

Erika has a baking company and needs to purchase 17 pounds of flour for her cakes. The Baking Goods Store sells two different-sized bags of flour. The table shows the amounts of flour in the bag, the number of bags at the store, and the cost per bag of flour. Size Pounds 1 Bags for Sale 75 Cost per Bag Small $0.84 5 Large 4 4 $16.80 If Erika buys all of the large bags, how many small bags will she need? A. 7 small bags B. 12 small bags C. 28 small bags D. 71 small bags

The directional derivative D_u f(0, π/3) is equal to (-9√3/10) + (6/5).

To get the directional derivative of the function f(x, y) = 3(e^x) sin y at the point (0, π/3) in the direction of the vector v = <-6, 8>, follow these steps:       Compute the gradient of the function:
∇f(x, y) = (df/dx, df/dy) = (3(e^x) sin y, 3(e^x) cos y)
Evaluate the gradient at the given point (0, π/3):
∇f(0, π/3) = (3(e^0) sin(π/3), 3(e^0) cos(π/3)) = (3(1)(√3/2), 3(1)(1/2)) = (3√3/2, 3/2)
Normalize the direction vector v:
||v|| = √((-6)^2 + 8^2) = √(36 + 64) = √100 = 10
u = v/||v|| = (-6/10, 8/10) = (-3/5, 4/5)
Compute the directional derivative D_u f(0, π/3) by taking the dot product of the gradient at the given point and the normalized direction vector:
D_u f(0, π/3) = ∇f(0, π/3) · u = (3√3/2, 3/2) · (-3/5, 4/5) = (-3/5)(3√3/2) + (4/5)(3/2) = (-9√3/10) + (6/5)
So, the directional derivative D_u f(0, π/3) is equal to (-9√3/10) + (6/5).

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Answer: A) 1888 B) 664.225 C)?

Step-by-step explanation:

A= 42+76(1/2) = 59

59(32)=1888

A=163/10(163/4)=664.225

The the parallelogram is like:

Where h is the height, The area of this parallelogram is calculated as:

A = 24*h

If the Area is equal t 18 square units, the height h is:

18 = 24*h

Solving for h, we get:

18/24 = h

0.75 units = h

Answer: a possible parallelogram's height is 0.75 units

Using the given information, the percent error is 52%

From the question, we are to calculate the percentage error

From the given information,

Prediction = 23 people

Actual = 48 people

Using the formula,

\(Percent \ error = \frac{|Prediction - Actual|}{|Actual|}\times 100\%\)

\(Percent \ error = \frac{|23 - 48|}{|48|}\times 100\%\)

\(Percent \ error = \frac{|-25|}{|48|}\times 100\%\)

\(Percent \ error = \frac{25}{48}\times 100\%\)

Percent error = 52.083%

Percent error ≈ 52%

Hence, the percent error is 52%

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