x-3y=5
-3x+6y=8

Elimination Style/Pls Show steps

Answer:

Here is the answer

Step-by-step explanation:

On paper

The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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To find the differential equation for a family of curves, we need to find an equation that relates the variables involved in the curves. For example, consider the family of curves given by:

y = mx + c

where m and c are constants. To find the differential equation for this family of curves, we can take the derivative of both sides with respect to x:

dy/dx = m

This is the differential equation for the family of curves.

To find the family of orthogonal trajectories, we need to find a new family of curves that intersect the original family of curves at right angles. We can use the fact that the product of the slopes of two perpendicular lines is -1. So, if the differential equation for the original family of curves is:

dy/dx = f(x, y)

then the differential equation for the family of orthogonal trajectories is:

dy/dx = -1/f(x, y)

To find a specific orthogonal trajectory, we need to solve this differential equation for y as a function of x.

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Answer:

sorry

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

Step-by-step explanation:

A higher confidence interval means less power which in turns means a smaller rejection religion.So our confidence interval would become wider.

Answer:

x = 22

Step-by-step explanation:

5x + 24 = 134

134 - 24 = 110

110 / 5 = 22

x = 22

Answer:

C: 180 degrees

Step-by-step explanation:

Note that it got flipped across the origin, so it is 180 degrees.

Answer:

180 degrees.........

A country with little land and few natural resources could make up for such deficits without depending on other countries and having a healthy economy by developing its Human Capital.

Examples of small countries with low natural resources and high GDP are:

It is to be noted that of all the factors of production, (Land, labor, Capital, and Entrepreneurship) Human Capital (Labor and Entrepreneurship) are the most valuable and yield the greatest return on investment.

The Democratic Republic of the Congo is commonly regarded as the world's richest country in terms of natural resources; its undiscovered stockpiles of raw minerals are estimated to be worth more than US $24 trillion.

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\(\frac{3}{1}\)Answer:

Step-by-step explanation:

3x-y = 2

2x+y =4

put them into slope intercept form

y=3x-2

y=-2x+4

Now, you can either graph it or use substitution

3x-2 = -2x+4

+2x +2x

5x -2 = 4

+2 +2

5x = 6

5x/5 = 6/5

x = 6/5

3x -2 = y

3(6/5) -2 = y

3 x 6 / 1 x 5 = 18/5

3 3/5 -2 = 1 3/5

Let me know if it's wrong.

Hope this helps

In this question, we are asked to determine the truth-values of two statements involving sets A and B. For each statement, we need to determine if it is true or false. If it is false, we need to provide specific counterexamples by choosing appropriate sets A and B.

a. (A\B) ⊆ A

The statement (A\B) ⊆ A is true for any sets A and B. This is because the set difference (A\B) contains elements that are in A but not in B. Therefore, by definition, every element in (A\B) is also an element of A. There are no counterexamples to this statement.

b. A^c ⊆ (AUB)

The statement\(A^c\) ⊆ (AUB) is true for any sets A and B. This is because the complement of A, denoted as \(A^c\), contains all elements that are not in A.

On the other hand, the union of A and B, denoted as (AUB), contains all elements that are in A or in B or in both.

Since the complement of A contains all elements not in A, it includes all elements in B that are not in A as well.

Therefore, \(A^c\) ⊆ (AUB) holds true for any sets A and B. There are no counterexamples to this statement.

In conclusion, both statements are true for any sets A and B, and there are no counterexamples.

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60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

According to the question,

We have the following information:

3 digits integers are to be made from 1,2,3,4 and 5

So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.

Now, we have:

Total number of digits = 5

Number of digits to be made = 3

So, we have:

\(^{5} P_{3}\)

Solving this expression:

5*4*3

60

Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

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The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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The probability hat house sales will increase and cost of lawn care will go up in the next 6 months is 0.185.

We know that if A and B are independent events then the probability i.e.

P(A and B) = P(A)*P(B)

Now let A be the event that house sales will go up in next 6 months.

Given P(A) = 0.25

and B be the event that the cost of lawn care will go up in the next 6 months.

Given, P(B) = 0.74

Since A and B are independent event.

Thus the probability that house sales will increase and cost of lawn care will go up in the next 6 months is,

P(A and B) = P(A)*P(B) = 0.25*0.74 = 0.185

Hence the probability hat house sales will increase and cost of lawn care will go up in the next 6 months is 0.185.

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We will see that the percentage of the 60 children who choose orange is 25%.

In this case, the 60 children are the 100%.

We want to find which percentage 15 (number of kids that like orange) represents.

Then we can write:

15 = x

60 = 100%

x = (15/60)*100% = 25%

So we conclude that 25% of the children choose orange.

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The possible outcomes when the coin toss is heads are {H,1}, {H,2}, {H,3}, {H,4}.

Sample space:

Sample space is defined as the set of all possible outcomes. Since Linda is going to flip the coin once and pick a card randomly from the box, so there are 8 possible outcomes.

These are given below:

{H,1}, {H,2}, {H,3}, {H,4}, {T,1}, {T,2}, {T,3}, {T,4}

Event: An event is defined as a subset of the sample space. If Linda gets a head as the result of the coin toss, then the possible outcomes will be:

{H,1}, {H,2}, {H,3}, {H,4}

Since, the coin has two possible outcomes and the card has four possible outcomes so the total number of possible outcomes is given by

2×4 = 8

Hence, the sample space has 8 elements.

The possible outcomes when the coin toss is heads are {H,1}, {H,2}, {H,3}, {H,4}.

Conclusion: The sample space of the experiment and the outcomes for the event that the coin toss is heads have been provided in the answer.

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All the possible outcomes for the event that the coin toss is heads.

The given terms are as follows:

Box has four cards numbered Linda will toss a coin once and record the toss as heads () or tails ().
Then she will randomly pick a card from the box and record the number chosen.

Sample space:

The sample space consists of all possible outcomes.

Here, the possible outcomes of tossing a coin and then picking a card from the box are:

\($$\{(\text{H}, 1), (\text{H}, 2), (\text{H}, 3), (\text{H}, 4), (\text{T}, 1), (\text{T}, 2), (\text{T}, 3), (\text{T}, 4)\}$$\)

The above table denotes all possible outcomes.

For example, \($(\text{H}, 1)$\) denotes that a head is tossed and the card picked has number 1.

Similarly, \($(\text{T}, 4)$\) denotes that a tail is tossed and the card picked has number 4.

Outcomes of the event that the coin toss is heads:

We are given that the coin toss is heads.

Therefore, the outcomes with heads can be listed as follows:\($$(\text{H}, 1), (\text{H}, 2), (\text{H}, 3), (\text{H}, 4)$$\)

The above are all the possible outcomes for the event that the coin toss is heads.

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(a) The curve defined by the parametric equations x = t^2, y = -1/4t (t > 0) represents a parabolic trajectory, the point of intersection between the curve and the hyperbola is (4∛2, -1/(4∛2)).

To find the points on the curve where the tangent line is parallel to the line y = x, we need to determine when the slope of the tangent line is equal to 1.

The slope of the tangent line is given by dy/dx. Using the chain rule, we can calculate dy/dt and dx/dt as follows:

dy/dt = d/dt(-1/4t) = -1/4

dx/dt = d/dt(\(t^2\)) = 2t

To find when the slope is equal to 1, we equate dy/dt and dx/dt:

-1/4 = 2t

t = -1/8

However, since t > 0 in this case, there are no points on the curve where the tangent line is parallel to y = x.

(b) To determine the points on the curve where it intersects the hyperbola xy = 1, we can substitute the parametric equations into the equation of the hyperbola:

\((t^2)(-1/4t) = 1 \\-1/4t^3 = 1\\t^3 = -4\\\)

Taking the cube root of both sides, we find that t = -∛4. Substituting this value back into the parametric equations, we get:

x = (-∛4)^2 = 4∛2

y = -1/(4∛2)

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Answer:

Yes

Step-by-step explanation:

The ratio of 5:21 is multiplied by 2 as 10:42 and therefore is correct.

The equation of the line which best fits the given data as represented in the table is; Choice D; y = -x.

It follows from the task content that the equation which best fits the data as represented in the given table be determined.

Since the given table is;

x : 5 4 3 2 1

y : -5 -4 -3 -2 -1

On this note, it filled from observation that the value of y in each for each input value x is simply; -x.

Therefore, the equation which correctly represents the y-intercept of the given data as represented in the table is; y = -x.

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Answer:

a = 1

Step-by-step explanation:

Original Equation:

-1 + 8 = 10 - 3a

Add 1 to both sides

8 = 11 - 3a

Subtract 11 from both sides

-3 = -3a

Divide both sides by -3

a = 1

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Answer:

a = 1

Step-by-step explanation:

-1 + 8 = 10 - 3a

   7 = 10 - 3a

 -10    -10

-3 = -3a

----   -----

-3     -3

1 = a

Answer:

7. Option B:40 is the correct answer.

8. Option D: y = 40x+75 is the correct answer.

Step-by-step explanation:

Given that:

Charges per hour = $40

Fee charged by repairman = $75

x = number of hours

y = total fee

According to given statement;

y = 40x+75

The standard equation is

y = mx + b

On comparing;

Slope of the line is given by m, therefore

Slope = m = 40

Hence,

7. Option B:40 is the correct answer.

8. Option D: y = 40x+75 is the correct answer.

Answer:

The answer would be -4/5

Step-by-step explanation:

When you add a negative to a negative, you first take out the plus sign and rewrite it as: -2/5 - 2/5.

Now you just simply subtract 2/5 from -2/5 to get -4/5.

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If you take the test and get a positive result, the probability that you have tetrachromacy is approximately 0.3571 or 35.71%.

To determine the probability that you have tetrachromacy given a positive test result, we can use Bayes' theorem. Let's define the following probabilities:

P(T) = Probability of having tetrachromacy (10% or 0.1)

P(¬T) = Probability of not having tetrachromacy (90% or 0.9)

P(Pos|T) = Probability of a positive test result given tetrachromacy (true positive rate, 70% or 0.7)

P(Pos|¬T) = Probability of a positive test result given no tetrachromacy (false positive rate, 14% or 0.14)

We want to find P(T|Pos), the probability of having tetrachromacy given a positive test result.

According to Bayes' theorem:

P(T|Pos) = (P(Pos|T) * P(T)) / P(Pos)

To find P(Pos), the probability of a positive test result, we can use the law of total probability:

P(Pos) = P(Pos|T) * P(T) + P(Pos|¬T) * P(¬T)

Plugging in the values:

P(Pos) = (0.7 * 0.1) + (0.14 * 0.9)

= 0.07 + 0.126

= 0.196

Now we can calculate P(T|Pos):

P(T|Pos) = (P(Pos|T) * P(T)) / P(Pos)

= (0.7 * 0.1) / 0.196

= 0.07 / 0.196

≈ 0.3571

Therefore, if you take the test and get a positive result, the probability that you have tetrachromacy is approximately 0.3571 or 35.71%.

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The correct answer is B) She is 95% confident that the true mean length of this species after five weeks of life is between 8.5 and 11.9 inches.

The 95% confidence interval (CI) is a range of values that we are 95% confident contains the true population parameter (in this case, the mean length of the fish species after five weeks of life). The supervisor cannot say with certainty that 95% of all fish of this species are between 8.5 and 11.9 inches long (A), as the CI only pertains to the mean length. She can also not say with certainty that 95% of all fish of this species that are five weeks mature are between 8.5 and 11.9 inches long (D), as the sample was randomly selected and may not represent the entire population.

The correct answer is B, as she is 95% confident that the true mean length of this species after five weeks of life is between 8.5 and 11.9 inches. This means that if she were to repeat the experiment many times and construct a CI for each sample, 95% of those intervals would contain the true population mean. Finally, option C is similar to option B and could also be considered correct.

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Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

Part A: Missing Numbers are 64 and 7 going downwards

Part B: Make a TABLE representing how much money they made for 5, 6, 8 hours which they made $64

Part C: ??

Step-by-step explanation:

The value of {x} is equivalent to 7.

Given is a triangle ΔXYW.

The median of a triangle is a bisector of the angle. Median is found to be joining the vertex of the triangle with the opposite side of the triangle. So, we can write -

m∠1 = m∠2

(2x + 9) = (4x - 5)

2x + 9 = 4x - 5

14 = 2x

x = 7

Therefore, the value of {x} is equivalent to 7.

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In the special case of two degrees of freedom, the chi-squared distribution does not coincide with the exponential distribution. The chi-squared distribution is a continuous probability distribution that arises in statistics and is used in hypothesis testing and confidence interval construction. It is defined by its degrees of freedom parameter, which determines its shape.

On the other hand, the exponential distribution is also a continuous probability distribution commonly used to model the time between events in a Poisson process. It is characterized by a single parameter, the rate parameter, which determines the distribution's shape.

While both distributions are continuous and frequently used in statistical analysis, they have distinct properties and do not coincide, even in the case of two degrees of freedom. The chi-squared distribution is skewed to the right and can take on non-negative values, while the exponential distribution is skewed to the right and only takes on positive values.

The chi-squared distribution is typically used in contexts such as goodness-of-fit tests, while the exponential distribution is used to model waiting times or durations until an event occurs. It is important to understand the specific characteristics and applications of each distribution to appropriately utilize them in statistical analyses.

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