Which of the following represent the distance formula? Select all that apply.
A. d=(x1−x2)2+(y1−y2)2−−−−−−−−−−−−−−−−−−−−−−−−−√
B. d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−−−−−−−−√
C. d=(x2+x1)2+(y2+y1)2−−−−−−−−−−−−−−−−−−−−−−−−−√
D. d=|x2−x1|2+|y2−y1|2−−−−−−−−−−−−−−−−−−−−−−−√

Answer:

76 passengers

Step-by-step explanation:

100-36 is 64 and that makes 64 + 36 =100-30 is 70% and we have 36 + 40 =76

There were 300 passengers.

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions.

Given:

Fraction of British = 2/5

Percent of British men = 30%

Number of British men = 36

let the British passenger be x

30 /100 * x= 36

x=120

and let the total passenger by y

2/5 of y = 120

y= 120 * 5/2

x= 300

Hence, there were 300 passengers.

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Answer: $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.

Explanation:

To find out the total cost of raising a child in a household with an annual income of $64,000, we can plug in x = 64,000 into the equation y = 1.55x + 110,419:

y = 1.55x + 110,419

y = 1.55 * 64,000 + 110,419

y = 101,600 + 110,419

y = $212,019

So, it would approximately cost $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.

The range of the given relation is:

R: {1, 2, 4, 5}

Thus the correct option is A.

A relation maps elements from one set, the set of the inputs called the domain, into elements from another set, the range.

A point in a relationship is written as (x, y), where y is on the range.

Here we have the relation given by the pairs:

(1, 2), (2, 4), (4, 5), (6, 1)

The range is the set given by the second values of each point, thus the range is:

R: {1, 2, 4, 5}

The the correct option is A.

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If you received a gift of $10,000 3 years ago and you want to spend it in 3 years with interest rate is 4%, it will be worth $12,653.19. Option b is correct.

To calculate the future value of a present sum after a specified period, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)ᴺ

In this case, the present value is $10,000, the interest rate is 4% or 0.04, and the number of periods is 6 years because you received the gift 3 years ago and want to spend it in 3 years.

Using the formula:

Future Value = \(\$10,000 * (1 + 0.04)^6\)

Future Value = \(\$10,000 * (1.04)^6\)

Future Value = $10,000 * 1.1265319

Future Value ≈ $12,653.19

Therefore, the amount will be approximately $12,653.19. Option b is correct.

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The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

We can use the formula for the area of a triangle, which is A = (1/2)bh, where b is the length of the base and h is the height. In this case, we know that the base has length 2a, so we need to find the height.

Let's call the third side of the triangle, which is not given, b. We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, so we have:

a + 2a > b

3a > b

We can rearrange this to solve for b:

b < 3a

Now, let's use the formula for the area of a triangle:

A = (1/2)bh

We want to maximize A, so we want to maximize h. We know that h is the height of the triangle, which is perpendicular to the base, so it forms a right angle. We can use the Pythagorean theorem to find h in terms of a and b:

\(h^2 = b^2 - a^2\)

We can substitute our inequality for b:

\(h^2 < (3a)^2 - a^2\)

\(h^2 < 8a^2\)

h < √(8\(a^2\))

h < 2 √(2)a

Now we can use the formula for the area of the triangle again:

A = (1/2)bh

A < (1/2)(2 √(2)a)(a)

A < \(a^2\) √(2)

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

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Answer:

10.44y - 12.32

Step-by-step explanation:

Use the distributive property.

4(2.61y − 3.08) =

= 10.44y - 12.32

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

The correct answer is option (D) "The graph shifts 7 units right and 8 units down".Explanation:To solve the given question, we need to use the rules for vertical and horizontal shifts, which are as follows:

Vertical Shift: y=f(x)+a moves the graph of f(x) upward if a > 0 and downward if a < 0.Horizontal Shift: y=f(x+a) moves the graph of f(x) left if a > 0 and right if a < 0.Now, let's transform the function f(x) into function g(x) and determine the shift required.The transformation of f(x) to g(x) is: g(x) = f(x - a) + bwhere a = horizontal shift and b = vertical shiftThe equation of the given functions is:f(x) = 1/(x − 2) and g(x) = 1/(x^(5/9))Let's set the equation of function f(x) in the standard form:y = 1/(x - 2)and the equation of function g(x) in the standard form:y = 1/(x^(5/9))

Now, we can observe that:To transform the graph of f(x) onto the graph of g(x), we need to shift the graph of f(x) right by 7 units and down by 8 units, which is given in option (D).Hence, the correct option is (D) "The graph shifts 7 units right and 8 units down".

The graph shifts 7 units right and 8 units down is the statement that describes the transformation of the graph of function f onto the graph of function g.Conclusion:Thus, we have determined the correct answer with an explanation and concluded that the correct option is (D) "The graph shifts 7 units right and 8 units down".

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(A) The British literature class is most likely larger, because the standard deviation is lower.

A high standard deviation suggests that the observed data is very variable around the mean. This suggests that the observed data is widely dispersed. Instead, a modest or low standard deviation would suggest that the majority of the observed data is closely packed around the mean.

The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed.

Hence, when standard deviation is lower the class is most likely to be larger in number.

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The standard normal distribution has the largest variance.

The variance of a normal distribution determines the spread or dispersion of the data.

A larger variance indicates a wider spread of values around the mean. The standard normal distribution is a specific case of the normal distribution with a mean of 0 and a variance of 1. Since the variance is fixed at 1 for the standard normal distribution, it has the largest variance compared to any other normal density with different variances.

The variance of a normal distribution measures how much the data values deviate from the mean.

It is calculated as the average of the squared differences between each data point and the mean. A higher variance implies a greater dispersion of values, indicating a wider range of possible outcomes.

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15 is area of Side of Square .

What is a square, exactly?

All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees away from each other or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle.

Length of diagonal of Square =15√2 cm-------------(1)

Let side of Square = a cm

So, Length of Diagonal

By Using Pythagorean Theorem

       = √a² + a²

        =  a√2        ........................(2)

  Equating (1) and (2)

    a√2   =  15√2

      a = 15

 cancelling root 2 from both sides.

     a = 15

Side of Square= 15 cm

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The complete question is -

Find the side of a square whose diagonal is of the given measure. Given = 15√2 cm.

The calculations will yield the values for the absolute permeability (ц) and relative permeability (\(\mu_r\)) of oxygen gas at 20°C.

To calculate the absolute permeability (\mu) and relative permeability (\(\mu_r\)) of oxygen gas at 20°C, we'll follow the steps outlined in the previous response:

Given:

Magnetic susceptibility (\(\chi\)) of oxygen gas at 20°C = 176 x 10⁻¹¹ H/m

Vacuum permeability (\(\mu_0\)) = 4π x 10⁻⁷ H/m

Step 1: Calculate the relative permeability (\(\mu_r\))

\(\mu_r = 1 + \chi\\\mu_r = 1 + 176 \times 10^{-11}\)

Step 2: Calculate the absolute permeability (\(\mu\))

\(\mu = \mu_0 \times \mu_r\\\mu = 4\pi \times 10^-7 H/m \times (1 + 176 \times 10^-11)\)

Performing the calculations will yield the values for the absolute permeability (\(\mu\)) and relative permeability (\(\mu_r\)) of oxygen gas at 20°C.

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Answer:

The correct option is;

C. The polynomial in standard form is 2·x⁵ + 6x³ + x² - 4

Step-by-step explanation:

The given polynomial is x² + 6x³ - 4 + 2·x⁵

Therefore, we have;

The highest power in the polynomial is 5, therefore, the degree of the polynomial is 5

The end behavior is f(x) → ∞ as x → ∞ and f(x) → - ∞ as x → -∞ which is not similar to f(x) = -x

The standard form is accomplished by arranging the polynomial in decreasing powers of x that is rom the biggest too lowest exponent as follows;

2·x⁵ + 6x³ + x² - 4

The polynomial decreases fox x < 0

Degree of polynomial is the highest power written in the equation

thus the correct answer is C for the question

Explanation

Thus we conclude that the answer to the above question C

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Answer:

x = -2

Step-by-step explanation:

Let the number be x

12 -2x = 8x +32

Add 2x to each side

12 -2x +2x = 8x+32+2x

12 = 10x+32

Subtract 32 from each side

12-32 = 10x+32-32

-20 =10x

Divide each side by 10

-20/10=10x/10

-2 =x

JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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The 95% confidence interval for the population mean weekday sleep time of all adult residents in the Midwestern town is approximately 6.00 to 6.80 hours.

Confidence Interval = x ± Z * (σ/√n)

Substituting the given values into the formula, we get:

Confidence Interval = 6.4 ± 1.96 * (1.8/√80)

Calculating the standard error (σ/√n):

Standard Error = 1.8/√80 ≈ 0.2015

Substituting the standard error into the formula, we have:

Confidence Interval = 6.4 ± 1.96 * 0.2015

Confidence Interval = 6.4 ± 0.3951

Lower limit = 6.4 - 0.3951 ≈ 6.00

Upper limit = 6.4 + 0.3951 ≈ 6.80

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A researcher in a small Midwestern town wants to estimate the mean weekday sleep time of its adult residents. He takes a random sample of 80 adult residents and records their weekday mean sleep time as 6.4 hours. Assume that the population standard deviation is fairly stable at 1.8 hours. (You may find it useful to reference the table.)

Calculate the 95% confidence interval for the population mean weekday sleep time of all adult residents of this Midwestern town. (Round final answers to 2 decimal places.)

Function aligns value from one set to another. The function will have a removable discontinuity at x = -3.

A function assigns the value of each element of one set to the other specific element of another set.

As the function is given to us,

\(F(x) = \dfrac{(x^2+12x+27)}{(x^2+4x+3)}\)

Now, factorizing the numerator and the denominator,

\(F(x)=\dfrac{(x+3)(x+9)}{(x+3)(x+1)}\)

Now, in order to find the point at which the function will be discontinued, we will equate the denominator with 0.

\((x+3)(x+1)=0\\\\\\(x+3)=0\\x =-3\\\\\\(x+1)=0\\x=-1\)

Now, As (x+3) is the factor of the numerator and the denominator, therefore, you will have a removable discontinuity, which appears as a hole in the graph.

Hence, the function will have a removable discontinuity at x = -3.

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Answer:

first one is (-3,-3)

second one is B (x=-1)

Step-by-step explanation:

We can expect 30 guests to receive free admission out of the 1500 guests expected this weekend.

To determine how many guests can be expected to receive free admission, we need to use the given information about the ratio of guests with coupons to guests without coupons. We can do this by setting up a proportion and solving for the unknown variable.

Let x be the number of guests we can expect to receive free admission.
1/50 = x/1500

Cross-multiplying gives us:
50x = 1500

Dividing both sides by 50 gives us:
x = 30

Therefore, we can expect 30 guests to receive free admission out of the 1500 guests expected this weekend.

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The MSE for the regression models developed in parts (b) and (d) is Ŷ = 5.10 + 0.83X

Let's assume that the dependent variable in both models is denoted by Y, and the independent variable is denoted by X. The regression model developed in part (b) is expressed as:

Y = 5.10 + 0.83X

The regression model developed in part (d) is expressed as:

Y = 4.90 + 0.89X + 0.012X²

To calculate the MSE for the model developed in part (b), we need to first calculate the predicted values of Y using the equation:

Ŷ = 5.10 + 0.83X

Then, we can calculate the squared difference between the predicted value Ŷ and the actual value Y for each data point, and take the average of these squared differences. This gives us the MSE for the model developed in part (b).

Similarly, to calculate the MSE for the model developed in part (d), we need to first calculate the predicted values of Y using the equation:

Ŷ = 4.90 + 0.89X + 0.012X^2

Then, we can calculate the squared difference between the predicted value Ŷ and the actual value Y for each data point, and take the average of these squared differences. This gives us the MSE for the model developed in part (d).

After calculating the MSE for both models, we can compare them to determine which model is more effective. A lower MSE indicates that the model is more accurate in predicting the dependent variable.

Therefore, the model developed in either part (b) or (d) with the lower MSE is considered to be more effective.

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ABDC is a quadrilateral with two non-parallel sides. It has two pairs of opposite sides which are parallel. It is also known as a trapezoid.

ABDC is a four-sided figure with two pairs of opposite sides that are parallel. This type of quadrilateral is also known as a trapezoid. A trapezoid has two non-parallel sides, while the other two sides are parallel to each other. In this case, the two parallel lines are L1 and L4, while L2 and L3 are the two non-parallel sides. We can see that the point C on L2 is a distance of 4cm from L1, and L4 is a line that is parallel to L1 and passes through C. Finally, L4 intersects L3 at the point D, which completes the trapezoid ABDC.

The length of AB can be determined by using the Pythagorean Theorem. We know that the length of L1 is 8 cm, so the length of AB is 3 cm.

example

AB = √(8^2 - 4^2) = √64 - 16 = √48 = 6 cm

The length of BD can also be determined by using the Pythagorean Theorem. We know that the length of L2 is 4 cm, so the length of BD is 3 cm.

BD = √(4^2 - 4^2) = √16 - 16 = 0 cm

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Answer:

X=8.7 (1dp)

Step-by-step explanation:

X=8.7

Please give Brainliest

Answer:

Hey there!

X+Y=0.

For example, two numbers that are equally far from the 0 on a number line are -2 and 2.

-2+2=0

Hope this helps :)

Answer:

x + y = 0

Step-by-step explanation:

Since the two values are the same distance from zero on the number line (i.e., they are equivalent in distance) and one is in the negative direction, and the other is in the positive direction, then the sum of both will be zero.

Since they are the same distance, just opposite in direction, it requires the same amount of "hops" for both values to reach zero, hence they will cancel each other out when added together.

Consider, -1 and 1.  Both are the same distance from 0; however, if you add them together (-1 + 1) you'll get the sum to be 0.

Cheers.

Answer:

x=-2

Step-by-step explanation:

7x-11=-19+3x

7x-3x=-19+11

4x=-8

4x/4=-8/4

x=-2

Yes, the given transformation is found to be  linear.

To determine if a transformation is linear, we need to check two conditions: preservation of addition and preservation of scalar multiplication.

For the preservation of addition, let's consider two arbitrary vectors u and v in R^2.

The transformation Lwt translates each vector up by 3 units.

Therefore,

Lwt(u+v) = (u+v) + (3,3)

= (u + (3,3)) + (v + (3,3))

= Lwt(u) + Lwt(v).

For the preservation of scalar multiplication, let's consider an arbitrary vector u in R^2 and a scalar c. The transformation Lwt translates the vector u up by 3 units.

Therefore,

Lwt(cu) = cu + (3,3)

= c(u + (3,3))

= cLwt(u).

Since both conditions hold true, the transformation Lwt is linear.

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Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

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Answer:

\(1.8 \text{ x } 10^5\)

Step-by-step explanation:

Hello!

To multiply terms, we multiply the like terms.

Like terms:

Like terms are terms with the same degree or base. In this example, 1 and 1.8 are like terms by degree, and 10² and 10³ are like by base.

Multiply:

That's your solution! 1.8 x 10^5