Calculate each stope between the given two points.
13. (5, 4) and (6, 1)
14. (2, 9) and (0,4)
15. (-6, 1) and (4.-2)
Only need the circled top 3

No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.

To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).

The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).

To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:

(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4

Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.

The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.

Learn more about dot product here:

https://brainly.com/question/29097076

#SPJ4

Answer:

if you have 270000

Step-by-step explanation:

if you spend money 261063 in 3 years

270000-261063

8937

Answer:

3/8

Step-by-step explanation:

He purchased 3/4 yard of fabric, then used 3/8 of it. You would need to subtract the 3/8 from 3/4 because the fabric is being used up.

The other root of the polynomial is 1 - √3.

The roots of a polynomial are the values of the independent variable at which the polynomial is zero.

If a polynomial has integral coefficients with 3 + i and 1 + √3  as roots, then what other roots must it have? To find the roots it has, we note that the root of a polynomial with a square root in the root also has the conjugate of the square root as a root.

So, since 1 + √3, the conjugate is also a root.

The conjugate is 1 - √3.

So, the other root is 1 - √3.

Learn more about root of a polynomial here:

https://brainly.com/question/2833285

#SPJ1

Answer:

4 \(\frac{3}{6}\)

Step-by-step explanation:

First rewrite the fractions to have a common denominator.

2/3 = 8/12 , 1/2 = 6/12 and 3/4 = 9/12

Now you have:

-7 8/12 + (-5 6/12) + 8 9/12

-7 8/12 + (-5 6/12) becomes -7 8/12 - 5 6/12 = -13 2/12

Now you have

-13 2/12 + 8 9/12 = -4 5/12

Answer: -4 5/12

Step-by-step explanation:

-7(⅔) + -5(½) + 8(¾)

-23/3 + (-11/2) + 35/4

-92 - 66 + 105/12

-154 + 105/12

-49/12

a) According to the central limit theorem, the mean is $142 and the standard deviation is $0.7488.

b) Nearly normal according to the central limit theorem.

c) 0.0901 = 9.01% probability that the average cable service paid by a sample of cable service customers exceeds $170 in the central limit theorem.

Normal probability distribution:

The normal probability distribution, discovered by Abraham De Moivre in 1733, approximates the binomial probability distribution when a particular experiment has a very large number of trials. In 1774 Laplace studied the mathematical properties of the normal probability distribution. By historical error, the discovery of the normal distribution was attributed to Gauss, first mentioned in his 1809 paper. In the 19th century, many scientists discovered that measurement errors in a particular experiment followed a pattern (usual error curve). ), which was very well approximated by this probability distribution.

Central Limit Theorem:

The central limit theorem is a statistical theory that for large sample sizes with finite variance, samples are normally distributed and the mean of the sample is approximately equal to the mean of the entire population.

According to the Question:

The average monthly charge is $142 with a standard deviation of $29.

This is μ = 142 and σ = 29

Part a:

The mean and standard deviation of the sampling distribution of x to show your research and support your argument:

1500 samples (over 30).

According to the Central Limit Theorem

The mean is 142 $

The standard deviation is s = \(\frac{29}{\sqrt{1500} }\) = 0.7488

Part b:

Shape of sampling distribution of X.

Due to the large sample size, the shape of the sample distribution is almost normal. According to the central limit theorem, which states that the sampling distribution converges to the normal distribution as the sample size increases. Mean ~ N(142, 0.749²)

Part C:

The probability that the average cable service paid by a sample of cable service customers exceeds $170.

Therefore, by the central limit theorem, the p-value of Z when X= 170

                         Z =  x - μ/ σ

By the Central Limit Theorem:

   Z = 170 - 142 / 0.7488

      = 28/ 0.7488

      = 37.34 exceeds 0.9099

Using the Z probability calculator :

P(Z > 1.335) = 0.09093

Complete Question:

The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. the distribution is not normal many people pay about $76 for basic cable and about $160 for premium service but some pay much more. a sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. let x hat be the mean amount paid.

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Part b: what is the shape of the sampling distribution of x hat justify your answer.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $170? show your work.

Learn more about Central Limit Theorem:

https://brainly.com/question/18403552

#SPJ4

Answer:

N = I ( 1 + 50% )^t

Step-by-step explanation:

Given that The population of Columbus in 2015 was 840,000 people. In 2018 (three years later), The population grew to 972,405 people.

Write an exponential equations that models this situation.

From the question, the following parameters are given :

Initial number of population = 840,000

The new number of population = 972,405

The number of years = 3

Let the initial population = I

The new population = N

And the number of years = t

Since the population is increasing, the exponential equation can be written as

N = I ( 1 + R% )^t

Where R% is the percentage increase.

Solve for R

972405 = 840,000 ( 1 + R% )^3

972405/840000 = ( 1 + R% )^3

1.157625 = ( 1 + R% )^3

( 1 + R% ) = 1.05

Make R% the subject of formula

R% = 1.05 - 1

R% = 0.5

R = 0.5 × 100

R = 50%

Therefore, the exponential equations that models this situation can be expressed as:

N = I ( 1 + 50% )^t

For the random variable x with CDF f(x) the answer of the following are,

a. The pdf should be non-zero only within the range 2 ≤ x < 4 that is

f(x) = 1/2, 2 ≤ x < 4

     = 0, elsewhere

b. P(2/3 < x < 3) = 7/6.

c. P(x > 3.5) =0.

d. 60th percentile = 3.2.

e. P(x = 3) = 0.5.

a. To find the probability density function (pdf) of x,

Differentiate the cumulative distribution function (CDF) with respect to x within the appropriate intervals,

For 2 ≤ x < 4

f(x)

= d/dx [(x - 2)/2]

= 1/2

For x ≥ 4

f(x)

= d/dx [1]

= 0

Since the pdf should be non-zero only within the range 2 ≤ x < 4, we have,

f(x)

= 1/2, 2 ≤ x < 4

= 0, elsewhere

b. To find P(2/3 < x < 3),  integrate the pdf within the given interval.

P(2/3 < x < 3) = \(\int_{2/3}^{3}\) f(x) dx

Since the pdf is constant 1/2 within the interval [2, 4], we have,

P(2/3 < x < 3) = \(\int_{2/3}^{3}\) (1/2) dx

= (1/2) \(\int_{2/3}^{3}\) dx

= (1/2) [x] evaluated from 2/3 to 3

= (1/2) [3 - (2/3)]

= (1/2) [9/3 - 2/3]

= (1/2) [7/3]

= 7/6

Therefore, P(2/3 < x < 3) is equal to 7/6.

c. To find P(x > 3.5), we integrate the pdf from the lower bound of 3.5 to positive infinity,

P(x > 3.5) = \(\int_{3.5}^{\infty}\) f(x) dx

Since the pdf is zero for x ≥ 4, we have:

P(x > 3.5) = \(\int_{3.5}^{\infty}\) f(x) dx

= \(\int_{3.5}^{4}\) 0 dx

= 0

Therefore, P(x > 3.5) is equal to 0.

d. The 60th percentile represents the value x for which the cumulative distribution function (CDF) is equal to 0.6.

0.6 = F(x)

From the given CDF,

0.6 = (x - 2)/2

x - 2 = 1.2

x = 3.2

Therefore, the 60th percentile is 3.2.

e. To find P(x = 3), we need to evaluate the CDF at x = 3,

P(x = 3) = F(3)

From the given CDF,

F(3)

= (3 - 2)/2

= 0.5

Therefore, P(x = 3) is equal to 0.5.

Learn more about CDF here

brainly.com/question/32194701

#SPJ4

The above question is incomplete, the complete question is:

let x be a random variable with cdf

f (x)=0, x< 2

     =(x - 2)/2 ,  2 ≤ x < 4

     =1, x ≥ 4

a. find the pdf of x.

b. find p x (2 / 3 < x < 3).

c. find p x( x > 3.5).

d. find the 60th percentile.

e. find p x( x = 3 ).

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

C (4,6) and D(-1, -1)

The coordinates of the midpoint is

We have the final answer as

Hope this helps you

(a) The interval on which f is increasing: (0, ∞)

The interval on which f is decreasing: (0, 1)

(b) Local minimum: At x = 1, f(x) has a local minimum value of -1.

There is no local maximum value.

(c) Inflection point: At x ≈ 0.293, f(x) has an inflection point.

The function f(x) = x^2 - x - ln(x) is a quadratic function combined with a logarithmic function.

To find the interval on which f is increasing, we need to determine where the derivative of f(x) is positive. Taking the derivative of f(x), we get f'(x) = 2x - 1 - 1/x. Setting f'(x) > 0, we solve the inequality 2x - 1 - 1/x > 0. Simplifying it further, we obtain x > 1. Therefore, the interval on which f is increasing is (0, ∞).

To find the interval on which f is decreasing, we need to determine where the derivative of f(x) is negative. Solving the inequality 2x - 1 - 1/x < 0, we get 0 < x < 1. Thus, the interval on which f is decreasing is (0, 1).

The local minimum is found by locating the critical point where f'(x) changes from negative to positive. In this case, it occurs at x = 1. Evaluating f(1), we find that the local minimum value is -1.

There is no local maximum in this function since the derivative does not change from positive to negative.

The inflection point is the point where the concavity of the function changes. To find it, we need to determine where the second derivative of f(x) changes sign. Taking the second derivative, we get f''(x) = 2 + 1/x^2. Setting f''(x) = 0, we find x = 0. Taking the sign of f''(x) for values less than and greater than x = 0, we observe that the concavity changes at x ≈ 0.293. Therefore, this is the inflection point of the function.

Visit here to learn more about Inflection point:

brainly.com/question/30763521

#SPJ11

Conference committees operate after the House and the Senate have passed different versions of a bill. Conference committees exist to draft a compromise bill that both houses can accept. Both houses of Congress must eventually pass identical legislation for the bill to be presented to the President.

Using the law of syllogism, the conclusion is given as follows:

c. if a quadrilateral is a square, then it is a rectangle.

The Law of Syllogism is a logic axiom which states that if the conditional statements p -> q and q -> r are true, the conditional statement p -> r is also true, basically applying the transitive property.

In the context of this problem, the statements are given as follows:

Hence the conclusion is:

p -> r

Read as:

If p then r.

Replacing the statements, we have that:

If a quadrilateral is a square, then it is a rectangle.

Which means that option c is correct.

More can be learned about the law of syllogism at brainly.com/question/20725710

#SPJ1

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

Learn more about ordered pairs here: https://brainly.com/question/30467126

#SPJ1

Answer:

Hi There!

Step-by-step explanation:

Your Answers Are:

Its hard to work w/o a ruler or a protractor, so these might be incorrect.

If this helps, though, please give me a thanks!! ^^

- abakugosimp

Answer: x = 2

Step-by-step explanation:

The rule for reflecting over  x = 2 is that y remains the same and you add how many units x = 2 is from the point.

x = 2 is has the coordinate of x = 2 and y = the y coordinate of the point.

A (-1, 1) Since the y coordinate of (-1, 1) is 1, x = 2 - (2, 1)

Add 3 units to 2, the x coordinate since -1, 1 is 3 units from 2, 1

2,1 --> 5, 1

I really didn't know how to explain but Im 100% sure Im right and I hoped this helped somehow.

C=pi*d

Where pi is 3.14 and d is the diameter, in this case is 14ft. Find the circumference

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

For similar question on amount.

https://brainly.com/question/25720319  

#SPJ8

The volume of the solid is found to be  3.33π.

None of the provided answers match

We apply  the method of cylindrical shells.

The volume of the solid is :

V = ∫(2π * x * f(x)) dx

x =  variable of integration.

In this case, f(x) = √x-4 and the interval of integration is [4, 7].

V = ∫(2π * x * (√x-4)) dx

= 2π ∫(x√x - 4x) dx

= 2π (∫\(x^(3/2)\) dx - ∫4x dx)

= 2π (2/5 * \(x^(5/2)\) - 2x^2) evaluated from x = 4 to x = 7

= 2π * [(2/5 *\(7^(5/2)\) - 27²) - (2/5 * \(4^(5/2)\) - 24²)]

= 2π * [(2/5 * \(7^(5/2)\) - 27²) - (2/5 * \(4^(5/2)\) - 24²)]

=  3.33π

IN conclusion, the volume of the solid is 3.33π.

Learn more about volume at: https://brainly.com/question/27710307

#SPJ1

Answer:

Increasing by 40%

Step-by-step explanation:

This is a exponentional function. The format for this type of function is a(b)^x. So "a" is your initial value, and "b" is the rate. Now let's think to ourselves what times what is still equal to the same thing? That is 1. But in our question, we have 1.4. So we are increasing by 0.4, or 40%.

Answer:

The answer is C

Step-by-step explanation:

HOPE it helps!!:))))

Answer:

g=28

Step-by-step explanation:

g+6=3=31

3+4=31

g+3-3=31-3

g=31-3

g=28

Answer:

28

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

answer:

10:03 am

explanation:

9:00 am + 1 hour (60 min) + 3 min = 10:03 am.

The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

Learn more about index here :-

https://brainly.com/question/32793068

#SPJ11

Answer:

6x-2

Step-by-step explanation:

The evaluation of the expression is 2, if the expression is x - y + z(x + w).

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

Given that x = 1, y = 1, w = 1, and z = 1

We have been given expression

⇒ x - y + z(x + w)

Substitute the values of x = 1, y = 1, w = 1, and z = 1 in the above expression,

⇒ 1 - 1 + 1(1 + 1)

⇒ 0 + 1(2)

⇒ 2

Hence, the evaluation of the expression is 2.

Learn more about the expressions here :

brainly.com/question/21751419

#SPJ4

Your question is incomplete, probably the missing part is:

Given x = 1, y = 1, w = 1, and z = 1 and this expression x - y + z(x + w): what is the evaluation of the logical expression?

Answer:

I think two is it.

Step-by-step explanation:

because 2 multiplys 10 you get 20

Jill collected 30 tokens, Sam collected 60 tokens and Nicki collected 45 tokens.

Let u represent the number of tokens collected by Jill, Sam, and Nicki as J, S & N

According given information:

The total number of tokens collected is:

J + S + N = 135

Substituting value of S from equ 1 into 3:

J + 2J + N = 135

3J + N = 135

Substituting value of J from equ 2 into equ 3:

3(2/3)N + N = 135

2N + N = 135

3N = 135

N = 45

Substituting value of N back to equa 2:

J = (2/3)(45)

J = 30

Substituting values of J and N to equ 1:

S = 2(30)

S = 60.

Read more about equation

brainly.com/question/29174899

#SPJ4

Answer:

B. 35.

Step-by-step explanation:

there are only two types of fruits in the basket....... that is, apples and oranges.

the ratio is 2:5

a : o

2 : 5.

there are 10 apples and in the ratio, 2 represents the number of apples.

so, 2a = 10.

to get the total number of fruits, we add the numbers in the ratio. so. 2 + 5 = 7

if 2 represents 10.

what will 7 represent?

2x = 10

7x = ??

cross multiply

7 × 10 ÷ 2 = 35 fruits.

Answer: do PEMDAS and the answer should be 17 I’m not 100%

Step-by-step explanation: