Writing equations of lines
Write the equation of each line with the given information

Answer:

3√3v/3x V

Step-by-step explanation:

d/dt[32/3π, sin (tim), 3√3v/3x, V]

The probability that 200 or fewer homes were purchased as investment properties is 0.937. This is calculated using the binomial distribution formula, where n = 600, p = 0.31, and x = 200.

1. The binomial distribution formula for calculating the probability of an event occurring is:

P(x) = nCx * p^x * q^(n-x)

where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1 - p).

2. In this problem, n = 600, p = 0.31, x = 200, and q = 1 - 0.31 = 0.69.

3. Plugging these values into the formula, we get:

P(x) = 600C200 * 0.31^200 * 0.69^400

4. Solving this equation, we get P(x) = 0.937.

5. Therefore, the probability that 200 or fewer homes were purchased as investment properties is 0.937.

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Rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given that the expression, y = [tex]\frac{5}{4}x+1[/tex].

To find the rate of change,

first we make the equation in standard form.

Slope intercept form ;

(y₂ - y₁) =m (x₂ -x₁) + c

Comparing the expression to the standard form;

Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)

Rate of change = (y₂ - y₁) / (x₂ -x₁)

Rate of change = 5/4

Therefore, rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

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The distributive property of 25+45 is 25+45 = 5(5+9).

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Say you wish to multiply 5 by the product of 10 plus 3.

When two terms are similar, we often sum the two amounts before multiplying by 5. 5(10 + 3) = 5(13) = 65.

So, the distributive property of 25+45:

25+45 = 5(5+9)

Therefore, the distributive property of 25+45 is 25+45 = 5(5+9).

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A base is a negative number and an exponent is also a negative number is explained in two ways:

(a) if the negative exponent is an even number, then the result will be a positive number.

(b) if the negative exponent is an odd number, then the result will be a negative number.

The required negative exponential formula is

a⁻ᵇ = 1/aᵇ or 1/a⁻ᵇ = aᵇ

Consider two negative numbers '-x' as the base and '-n' as the exponent.

So, the given statement in mathematical form is as below:

⇔ (-x)⁻ⁿ

Then, we can evaluate them in two ways by considering 'n' to be an even and an odd number.

(a) If 'n' is an even number:

from the exponent formula, a⁻ᵇ = 1/aᵇ, we can write

(-x)⁻ⁿ = 1/(-x)ⁿ

Since 'n' is an even number (-x)ⁿ = xⁿ

So, the result will be a positive rational or decimal number.

I.e., (-x)⁻ⁿ = 1/xⁿ

(b) If 'n' is an odd number:

from the exponent formula, a⁻ᵇ = 1/aᵇ, we can write

(-x)⁻ⁿ = 1/(-x)ⁿ

Since 'n' is an odd number (-x)ⁿ = -xⁿ

So, the result will be a negative rational or decimal number.

I.e., (-x)⁻ⁿ = -1/xⁿ

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The probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched:

No-hitters    probability

     0             0.5944

     1             0.3093

     2             0.0804

     3             0.0139

In this question, we have been given  the probability that a major league pitcher pitches a no-hitter in a game is about 1/1300.

We need to determine the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched.

Here, p = 1/1300

            = 0.0008

q = 1 - p

  = 1 - 1/1300

  = 1299/1300

  = 0.9992

And n = 650

We know that the binomial distribution formula.

P(x) = nCx * p^(x) * q^(n - x)

Using binomial distribution we find required probability.

For x = 0,

P(x = 0) = 650C0 * (1/1300)^0 * (1299/1300)^(650 - 0)

P(x = 0) = 1 * 1 * (0.9992)^650

P(x = 0) = 0.5944

For x = 1,

P(x = 1) = 650C1 * (1/1300)^1 * (1299/1300)^(650 - 1)

P(x = 1) = 650 * (0.0008) * (0.9992)^649

P(x = 1) = 0.52  * 0.5948

P(x = 1) = 0.3093

For x = 2,

P(x = 2) = 650C2 * (1/1300)^2 * (1299/1300)^(650 - 2)

P(x = 2) = 210925 * (0.0008)^2 * (0.9992)^648

P(x = 2) = 0.0804

For x = 3,

P(x = 3) = 650C3 * (1/1300)^3 * (1299/1300)^(650 - 3)

P(x = 3) = 45559800 * (0.0008)^3 * (0.9992)^647

P(x = 3) = 0.0139

Therefore, the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched are 0.5944, 0.3093, 0.0804, and 0.0139 respectively.

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The coordinate of T ' will be;

⇒ T ' = (- 31, - 23)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

This is a Dilation with a scale factor of 4 (D4).

Now,

Since, The Center of Dilation of this transformation is at the center. But the transformation is given by a scale factor of 4 and adding to (-3,1) as;

⇒ T ' = 4 (- 7, - 6) + (-3, 1)

        = (- 28, - 24) + (-3, 1)

        = (- 31, - 23)

Thus, The coordinate of T ' = (- 31, - 23)

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In the given diagram, the arc length of the given arc is 10.46.

From the question, we are to determine the length of the arc.

From the formula for calculating the length of an arc, we have that

Length of an arc = θ/360° × 2πr

Where θ is the angle subtended by arc at the center of the circle

and r is the radius of the circle

In the given diagram,

Angle subtended = π/3 = 60°

Radius, r = 10

Thus,

The length of the arc = 60/360 × 2πr

Length of the arc = 1/6 × 2×3.14×10

Length of the arc = 10.46

Hence, the length is 10.46

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WR Answer: 10.46

Step-by-step explanation:

he length of the arc = 60/360 × 2πr

Length of the arc = 1/6 × 2×3.14×10

Length of the arc = 10.46

Hence, the length is 10.46

As per the given line segments, the work done by the particle is 78N.

Line segments:

In meth, then bounded by two distinct points on a line is called as line segment.

Given,

Here we have a particle moves along line segments from the origin to the points (1, 0, 0), (1, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field below.

And we need to find the work done.

While we have the function in the given question as,

=> F(x,y,z) = z²i + 3xy j + 4y²k

Here we have consider that, If C is the path the particle follows, then work done is ∫ₓᵃ F dx.

Then according to the question the force F(x,y,z) = z²i + 3xy j + 4y²k and all four points are in the plane is written as,

z = 1/4 y

So, if S is the at surface with boundary C, so that S is the portion of the plane  over the rectangle is calculated as,

=> D=[0,2] x [0,4].

Then as per the stroke's theorem,

=> ∫∫[2z(0) + 3z(1/4) + 4y]

=> ∫∫3z/4 + 4y

=> [39]₀²

=> 78

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As reported by the Bureau of Labor Statistics, the inflation rate of CPI for Airfare from 2263 and 22264 is - 0.06198 ( disinflation).

We have given that,

The CPI for Airfare in 2263 = 579.6

The CPI for Airfare in 2262 = 617.9

Base year is 1914 ,

Following the formula which is used to calculate inflation rate of airfare from 2263 to 2263

Inflation= (CPI₂₂₆₃ - CPI₂₂₆₂)/CPI₂₂₆₂

= (579.6 - 617.9)/617.9

= - 153.8/617.9

= - 0.06198

= 6.198%

Since , the inflation is negative this means that the economy is experiencing disinflation of 6.198%.

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(a) The point estimate of the population variance is 400

(b) According to the 90% confidence interval, the population variance is 152 ≤ σ² ≤ 800

(c) According to the 90% confidence interval, the population standard deviation is 23.8 ≤ σ ≤  41.1

Standard deviation

in probability, standard deviation refers the measure of how dispersed the data is in relation to the mean.

Given,

Here we know that because of staffing decisions, managers of the a certain hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 25 days of operation shows a sample mean of 300 rooms occupied per day and a sample standard deviation of 20 rooms.

Here we need to find the following.

a)  Here the point estimate of the population variance is calculated as,

=> Square of S = S²

The value of S is 20

=> 20² = 400

b) As per the confidence interval, the population variance is calculated as,

n = 20

S² = 400

Then the variance is

=> (n-1)s²/0.05  ≤ σ² ≤  (n-1)s²/0.95

When we apply the values on the equation, then we get

=>  (20-1) x 400/0.05  ≤ σ² ≤  (20 - 1) x 400/0.95

Variation 152 ≤ σ² ≤ 800

c) Finally, the Standard Deviation is calculated as,

=> 23.8 ≤ σ ≤  41.1

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An algorithm is a collection of clear instructions for solving a specific issue in computer programming.

Step 1: Start

Step 2: Declare variables num1, num2 and sum.

Step 3: Read values num1 and num2.

Step 4: Add num1 and num2 and assign the result to sum.

       sum←num1+num2

Step 5: Display sum

Step 6: Stop

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If the domain of f(x) = x² - 4 is limited to {-1, 0, 1, 2} the greatest value of the range is 0

The range represents the output values

Using the given expression to solve it can be found that the output values are

for x = -1, f(x) = x² - 4 = -1² - 4 = -3

for x = 0,  f(x) = x² - 4 = 0² - 4 = -4

for x = 1, f(x) = x² - 4 = 1² - 4 = -3

for x = 2, f(x) = x² - 4 = 2² - 4 = 0

The greatest value of the range is 0

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Probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

If 60% of the population supports massive federal budget cuts.

We have to find the probability in that a survey of 250 people, at most 155 people support such cuts.

So, the probability is, 155 / 250 = 0.62

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

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An example of inverse variation is y = 3/x .

What is Inverse Variation ?

Unlike the direct variation, where one quantity varies directly as per changes in another quantity, in the case of inverse variation, the first quantity varies inversely as per another quantity. Hence, the first quantity is inversely proportional to the other.

Let us say, x and y are two variables, then as per inverse variation:

y = k/x

or

xy = k

For example :

If x and y are in an inverse variation and k/3 = 2, and k/x = 3, then find the value of x when y = 2.

Given, k/3 = 2

then, k = 3 x 2 = 6

k/x = 3

So, x = k/3 = 6/3 = 2

Hence, if y = 2, then ;

x = k/y = 6/2 = 3

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Answer:

6 2/3

Step-by-step explanation:

2 1/6 + 4 3/6

6 4/6

6 2/3

Answer:

6.64

Step-by-step explanation:

The nearest hundredth is the second digit after the decimal point.

6.6428571 rounded to the nearest hundredth is 6.64

Answer:

-7i

Step-by-step explanation:

Sqrt-49 = Sqrt49 *(- 1)

= Sqrt49 * sqrt-1

= ±7 * i

= ±7i

It will take 1 hour 12 minutes to clear the field together Ted and jacob when Ted can remove the trash from a football field in three hours.

Given that

Ted can remove the trash from a football field in three hours. The same field may be cleared by Jacob in two hours. The scenario can be represented by the equation when they cooperate, where t is the total number of hours needed to clear the field.

We have to find how long will it take ted and jacob to clear the field together.

We know that,

Let the number of hours = t

Ted can clear the field = t/3

Jacob can clear the field = t/2

Together they can clear the field = t/3 + t/2 = 1

3t+2t/6 = 6/6

2t + 3t = 6

5t = 6

t = 6/5

t = 1.2 hours.

Converting

1.2 hours = 1 hour 12 minutes.

Therefore, It will take 1 hour 12 minutes to clear the field together Ted and jacob when Ted can remove the trash from a football field in three hours.

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Yes ,induction can be used to prove the following is true for every nonnegitive integer n.

If P (n) is true, so is P (n + 1) because this argument holds true for any nonnegative integer n, it establishes the second fact required by the induction proof. As a result of the Induction Principle, the predicate P (m) is true for all nonnegative integers, m.

Mathematical induction is a technique for proving the truth of a statement, theorem, or formula for each and every natural number n. This is generalized as the 'Principle of Mathematical Induction,' which we would use to prove any mathematical statement.

For instance, 13 +23 + 33 +..... +n3 = (n(n+1) / 2)

The statement is assumed to be true for all natural number values in this case.

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Answer:

I'm sure its x>10

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+7>27

Subtract 7 from both sides

2x+7−7 27−7

2x>20

Divide both sides by 2

2x/2 > 20/2

= x>10

The joint probability for events A and B is:

P(A and B) = 0.2072

We know that if two events A and B, each with correspondent probabilities

P(A) and P(B) are independet, then the joint probability (this is the probability that both events happen at the same time) is given by the product between the individual probabilities.

In this particular case we know that:

P(A) = 0.28

P(B) = 0.74

Then the joint probability of A and B is:

P(A and B) = P(A)*P(B) =0.28*0.74

P(A and B) = 0.2072

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Using Pythagoras theorem, the length of AE in the square  2√2 unit

To find the length of side AE, we have to use use the dimension of BD given.

In the figure given, the length of all sides are equal to one another. This implies that the sides are equidistant to one another.

In a given square, all the sides are equal to one another, but the length of the diagonal is the square root of the sum of two sides

This can be further explained as

BD = AC

Using Pythagoras theorem

BD² = AD² + BA²

4² = x² + x²

16 = 2x²

x² = 8

x = √8

x = 2√2

However, we need to find the length of AE

AE is half the length size of AD

AE = 2√2 / 2

AE = √2

The distance AE = √2

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Answer:

k = -4

Step-by-step explanation:

Given system of linear equations:

[tex]\begin{cases}4x - 8y = -3\\2x + ky = 10\end{cases}[/tex]

Rewrite the given equations so that they are in slope-intercept form.

[tex]\begin{aligned}4x-8y&=-3\\4x&=8y-3\\4x+3&=8y\\\dfrac{4x+3}{8}&=y\\y&=\dfrac{1}{2}x+\dfrac{3}{8}\end{aligned}[/tex]

[tex]\begin{aligned}2x+ky&=10\\ky&=-2x+10\\y&=\dfrac{-2x+10}{k}\\y&=-\dfrac{2}{k}x+\dfrac{10}{k}\end{aligned}[/tex]

An inconsistent system of linear equations has no solutions and therefore the lines are parallel.  

Parallel lines have the same slope:

[tex]\implies \dfrac{1}{2}=-\dfrac{2}{k}[/tex]

[tex]\implies \dfrac{1}{2}k=-2[/tex]

[tex]\implies k=-2 \cdot 2[/tex]

[tex]\implies k=-4[/tex]

Answer:

--------------------------

Equation in the standard form ax + by = c  has:

Given system:

Compare the slopes of the two lines:

We need them to be equal:

Compare the y-intercepts of the two lines:

We need to confirm they are not same:

Confirmed, so k = -4 is our solution.

The 90 % confidence interval estimate for the population mean using the student's t-distribution is [ 87.137 , 92.863 ] .

Given :

Suppose that the times to complete an obstacle course are normally distributed with an unknown mean and standard deviation. A random sample of 33 course times is taken and gives a sample mean of 90 seconds and a sample standard deviation of 10 seconds.

a 90% confidence interval estimate for the population mean using the student's t-distribution.round the final answers to two decimal places.

Confidence interval :

CI = X ± Z * s / √n

= 90  ±  1.6449 * 10 / √33

= 90 ± 2.863

= [ 87.137 , 92.863 ]

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Full question:

is in the image uploaded.

In a rhombus, all sides are the same length, and the opposite angles are equal. The diagonals also bisect each other at 90 degrees.

We know that,

A rhombus has two congruent acute and two congruent obtuse angles.

Here we use the terms  x and y to represent the angles.

where x is the acute angle

The angles total 360 degrees.

So far, we have:

2(x+y) = 360

By dividing both sides by 2 , we get,

x + y = 180

We can assume y is 3 times larger than x,

That is y = 3x

As a result, the equation becomes,

x + 3y = 180

Calculate the total

4x = 180

As a result, the acute angle is 45 degrees.

Hence we proved that y is 3 times larger than x.

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The area of a trapezoid is 136[tex]cm^{2}[/tex].

we know that the area of a trapezoid is:

Area= 1/2 * (a+b) * h

where a and b are the lengths of the parallel sides of the trapezoid, and h is the height.

Now as per the question,

first parallel side, a = 12cm

second parallel side, b = 22cm

height, h =8cm

Area of a trapezoid = 1/2 * (12+22) *8 [tex]cm^{2}[/tex]

                                 = 136[tex]cm^{2}[/tex]

Therefore, the area of a trapezoid is 136[tex]cm^{2}[/tex].

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This means that the probability that a doll selected at random will blink and have moving limbs is 0.26.

There is a 50% chance that the outcome will be heads, thus 50 heads are to be expected. When we really attempt it, though, we might instead get 48 heads, 55 heads, or anything else at all, but in most situations, it will be a figure close to 50.

calculation

If B is a set of moveable arms and legs and A is the number of dolls that can blink, then P(A)=0.47, P(B)=0.56, P(A' and B')=0.23,

therefore P(A or B)=1-0.23=0.77, and

P(both blink and moveable limbs)=P(A and B)=0.47+0.56-0.77=0.26.

This means that the probability that a doll selected at random will blink and have moving limbs is 0.26.

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Answer:

All Correct! The corinates on the graph are all graphed in the correct position.

Answer:

Yes, you are correct.

Step-by-step explanation: