Which statement is true about a line and a point? (1 point) a A point and a line have length as a dimension to measure. b A point is a location, and a line has many points located on it. c A line and a point cannot lie on the same plane. d A line and a point cannot be collinear.

Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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Answer:

\((a)\ P(White) = \frac{1}{2}\)

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

\(White = 5\)

\(Black =3\)

\(Red = 2\)

Solving (a): P(White)

This is calculated as:

\(P(White) = \frac{White}{Total}\)

\(P(White) = \frac{5}{5+3+2}\)

\(P(White) = \frac{5}{10}\)

\(P(White) = \frac{1}{2}\)

Solving (b): Additional white balls, if \(P(White) = \frac{3}{4}\)

Let the additional white balls be x

So:

\(P(White) = \frac{White+x}{Total+x}\)

This gives:

\(\frac{3}{4} = \frac{5+x}{10+x}\)

Cross multiply

\(30+3x = 20 + 4x\)

Collect like terms

\(4x - 3x = 30 - 20\)

\(x = 10\)

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if \(P(White) = \frac{1}{4}\)

Let the additional black balls be x

So:

\(P(White) = \frac{White}{Total+x}\)

So, we have:

\(\frac{1}{4} = \frac{5}{10+x}\)

Cross multiply

\(10+x = 5 * 4\)

\(10+x = 20\)

Collect like terms

\(x = 20 -10\)

\(x = 10\)

Hence, 10 additional black balls must be added

The number of reserved seats and the number of general seats, if The cost for general admission = $3.50, The cost for a reserved seat = $7, is 382 and 622 respectively.

The equals sign is used in equations to indicate the equality of two expressions in a formula. Equation: A statement that two variable or integer expressions are equal.

Given:

The cost for general admission = $3.50,

The cost for a reserved seat = $7,

The total cost = $4851.00

The total seat = 1004

Write the equation as shown below,

x + y = 1004  (Here, y is the number of a reserved seat and x is the number of a general seat)

3.5x + 7y = 4851

Solve the equations by using the elimination method,

y = 382, x = 1004 - 382 = 622

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Answer:

121

Step-by-step explanation:

firstly you arrange the numbers in ascending order the number in the middle is considered to be the median

Answer:

421.4 miles

Step-by-step explanation:

Numner of miles= ($270.79-$17.95)/86 cents

= $252.84/$0.60

=421.4 miles

The t-test value for the given collected data of hours of studying and exam grade is equal to 10.45.

As given in the question,

n = 5

Mean of the data ( time ) μ₁ = ( 1+ 3 + 4 + 3+ 6)/ 5

                                           = 3.4

Mean of the exam grade μ₂  = ( 55 + 75 + 80 + 85 + 99) / 5

                                           = 78.8

Standard deviation of time σ₁ = 1.82

Standard deviation of exam grade σ₂ = 16.04

Standard error of time = σ₁/√n

                                   = 1.82 / √5

                                   =0.81

Standard error of time =σ₂/√n

                                   = 16.04/ √5

                                   =7.17

Difference in mean of time and exam grade  = 78.8 - 3.4

                                                                      = 75.4

Standard error of difference 'S.E'= √ (0.81)² + (7.17)²

                                            = 7.215

t - test for the given data

= | μ₁ -  μ₂| / S.E.

= | 3.4 - 78.8| / 7.215

= 75.4 / 7.215

= 10.45

P value and statistical significance:

Two-tailed P value is smaller than 0.0001

Therefore, the t-test value for the given collected data is equal to 10.45.

The above question is incomplete , the complete question is:

Researchers have collected data on the hours of studying in a week and the exam grade of a student. you are given the data below (10 points). hint: this questions is similar to q1 in hw7.

hours of studying                            exam grade

1                                                       55

3                                                      75

4                                                      80

3                                                      85

6                                                      99

Calculate the t -test and interpret the data?

student 3 i thin srry if im wrong

Answer:

student 3

Step-by-step explanation:

Answer: the GFC of 14 and 22 is 2

GCF of 14 and 22 by Listing Common Factors

Factors of 14: 1, 2, 7, 14

Factors of 22: 1, 2, 11, 22

There are 2 common factors of 14 and 22, that are 1 and 2. Therefore, the greatest common factor of 14 and 22 is 2.

Answer:

The greatest common factor of 14 and 22 is 2 .

I HOPE IT WILL HELP YOU.

Thank you.

Teddy lover

Answer:

8423

Step-by-step explanation:

The formula that defines the sequence is f(n) = f(n-1) + 4

The recursive function rule is expressed as;

f(n) = f(n-1)  + d

where

d is the common difference

Given the following sequence

2, 6, 10, 14, 18..

Determine the common difference

d = 6-2 = 10-6

d = 4

Substitute to have

f(n) = f(n-1)  + d

f(n) = f(n-1) + 4

Hence the formula that defines the sequence is f(n) = f(n-1) + 4

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The amount of fewer euros he would receive as a result of the delay is 20 E.

The percentage loss that was caused by the delay is -4%.

Exchange rate is the rate at which one unit of a currency can buy another currency. In this question, the value of Euros appreciated by Monday. This is because $1 buys less Euros on Mondays. On the hand, dollars depreciates in value.

Amount of fewer Euros received = value of euros if it were exchanged on Friday - value of euros if it was exchanged on Monday

Value of euros if it were exchanged on Friday = 1.25 x 400 = 500 E

Value of euros if it was exchanged on Monday = 1.20 x 400 = 480 E

Difference = 500 E - 480 E = 20 E

Percentage loss = (Euros received on Monday / Euros that would have been received on Friday) - 1

Percentage loss = (480 / 500) - 1 = -0.04 = -4%

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The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Answer:

1.2

Step-by-step explanation:

Just divide

Answer:

1.2

Step-by-step explanation:

Divide 18 by 15 and get the answer.

Answer:

25 million on some jewlery that you put on you head

Step-by-step explanation:

Answer:

$52.5

Step-by-step explanation:

given

P=$50  R=0.05  T=1

I=PRT

I=50×0.05×1

I=$2.5

50+2.5=$52.5

Using the quadratic formula, we solve for \(z^2\).

\(z^4 - 5(1+2i) z^2 + 24 - 10i = 0 \implies z^2 = \dfrac{5+10i \pm \sqrt{-171+140i}}2\)

Taking square roots on both sides, we end up with

\(z = \pm \sqrt{\dfrac{5+10i \pm \sqrt{-171+140i}}2}\)

Compute the square roots of -171 + 140i.

\(|-171+140i| = \sqrt{(-171)^2 + 140^2} = 221\)

\(\arg(-171+140i) = \pi - \tan^{-1}\left(\dfrac{140}{171}\right)\)

By de Moivre's theorem,

\(\sqrt{-171 + 140i} = \sqrt{221} \exp\left(i \left(\dfrac\pi2 - \dfrac12 \tan^{-1}\left(\dfrac{140}{171}\right)\right)\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= \sqrt{221} i \left(\dfrac{14}{\sqrt{221}} + \dfrac5{\sqrt{221}}i\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= 5+14i\)

and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find

\(t = \tan^{-1}\left(\dfrac{140}{171}\right) \implies \cos(t) = \dfrac{171}{221}\)

as well as the fact that

\(0<\tan(t)<1 \implies 0along with the half-angle identities to find

\(\cos\left(\dfrac t2\right) = \sqrt{\dfrac{1+\cos(t)}2} = \dfrac{14}{\sqrt{221}}\)

\(\sin\left(\dfrac t2\right) = \sqrt{\dfrac{1-\cos(t)}2} = \dfrac5{\sqrt{221}}\)

(whose signs are positive because of the domain of \(\frac t2\)).

This leaves us with

\(z = \pm \sqrt{\dfrac{5+10i \pm (5 + 14i)}2} \implies z = \pm \sqrt{5 + 12i} \text{ or } z = \pm \sqrt{-2i}\)

Compute the square roots of 5 + 12i.

\(|5 + 12i| = \sqrt{5^2 + 12^2} = 13\)

\(\arg(5+12i) = \tan^{-1}\left(\dfrac{12}5\right)\)

By de Moivre,

\(\sqrt{5 + 12i} = \sqrt{13} \exp\left(i \dfrac12 \tan^{-1}\left(\dfrac{12}5\right)\right) \\\\ ~~~~~~~~~~~~~= \sqrt{13} \left(\dfrac3{\sqrt{13}} + \dfrac2{\sqrt{13}}i\right) \\\\ ~~~~~~~~~~~~~= 3+2i\)

and its negative, -3 - 2i. We use similar reasoning as before:

\(t = \tan^{-1}\left(\dfrac{12}5\right) \implies \cos(t) = \dfrac5{13}\)

\(1 < \tan(t) < \infty \implies \dfrac\pi4 < t < \dfrac\pi2 \implies \dfrac\pi8 < \dfrac t2 < \dfrac\pi4\)

\(\cos\left(\dfrac t2\right) = \dfrac3{\sqrt{13}}\)

\(\sin\left(\dfrac t2\right) = \dfrac2{\sqrt{13}}\)

Lastly, compute the roots of -2i.

\(|-2i| = 2\)

\(\arg(-2i) = -\dfrac\pi2\)

\(\implies \sqrt{-2i} = \sqrt2 \, \exp\left(-i\dfrac\pi4\right) = \sqrt2 \left(\dfrac1{\sqrt2} - \dfrac1{\sqrt2}i\right) = 1 - i\)

as well as -1 + i.

So our simplified solutions to the quartic are

\(\boxed{z = 3+2i} \text{ or } \boxed{z = -3-2i} \text{ or } \boxed{z = 1-i} \text{ or } \boxed{z = -1+i}\)

Answer:

The probability that at most three used the emergency room for a sample of 10 people is 0.8791.

Step-by-step explanation:

The random  variable X can be defined as the number of people in a community using the emergency room.

The probability that a person uses the emergency room is, p = 0.20.

A sample of n = 10 people are selected.

A person using the emergency room is independent of others.

The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.20.

The probability mass function of X is provided as follows:

\(P(X=x)={10\choose x}\ (0.20)^{x}\ (1-0.20)^{10-x};\ x=0,1,2,3...\)

Compute the probability that at most three used the emergency room as follows:

P (X ≤ 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)

             \(=\sum\limits^{3}_{x=0}{{10\choose x}\ (0.20)^{x}\ (1-0.20)^{10-x}}\\\\=0.10737+0.26844+0.30199+0.20133\\\\=0.87913\\\\\approx 0.8791\)

Thus, the probability that at most three used the emergency room for a sample of 10 people is 0.8791.

Once we have this data, we can substitute the values into the formula to find the empirical probability that a person prefers apple pie given that they prefer whipped cream. Therefore, the missing probability is 1/12, and we know this because it is the value that makes the sum of all probabilities equal to 1.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. For example, if the probability of winning a coin toss is 1/2, this means that there is an equal chance of the coin landing heads or tails. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability approach. Another approach is empirical probability, where probabilities are calculated based on observed data or experiments. Lastly, subjective probability involves making an informed guess or estimate about the likelihood of an event occurring based on subjective factors such as experience, intuition, or expert opinion. Probability is a fundamental concept in statistics and is used in many application

Here,

1. The formula needed to calculate the empirical probability that a person prefers apple pie given that they prefer whipped cream is:

P(Apple Pie | Whipped Cream) = P(Apple Pie and Whipped Cream) / P(Whipped Cream)

where P(Apple Pie and Whipped Cream) is the probability that a person prefers both apple pie and whipped cream, and P(Whipped Cream) is the probability that a person prefers whipped cream.

This formula is used because it is a conditional probability, which is a measure of the probability of an event occurring given that another event has occurred. In this case, we want to find the probability that a person prefers apple pie given that they already prefer whipped cream.

To calculate P(Apple Pie and Whipped Cream), we would need to gather data on the number of people who prefer both apple pie and whipped cream. Similarly, to calculate P(Whipped Cream), we would need to gather data on the number of people who prefer whipped cream.

2. To find the missing probability, we need to use the fact that the sum of all probabilities in a probability distribution must be equal to 1. Therefore, we can set up an equation to solve for the missing probability:

1/6 + 1/3 + x + 5/12 = 1

Simplifying the equation by finding a common denominator gives:

2/12 + 4/12 + x + 5/12 = 1

Combining like terms gives:

11/12 + x = 1

Subtracting 11/12 from both sides gives:

x = 1 - 11/12

x = 1/12

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Where the above conditions are given, the value of the test statistic is 2.06.

To test the researchers' claim that the birth rate in Bonn, Germany is higher than the national average, we can use a two-sample z-test for the difference in proportions.

Let p1 be the proportion of births in Bonn and p2 be the proportion of births in the national population.

The null hypothesis is that the two proportions are equal, i.e. H0: p1 = p2. The alternative hypothesis is that the proportion of births in Bonn is higher than the national proportion, i.e. Ha: p1 > p2.

The test statistic for this hypothesis test is given by:

z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where p = (x1 + x2) / (n1 + n2) is the pooled proportion, x1 and x2 are the number of births in the Bonn sample and national sample respectively, and n1 and n2 are the sample sizes.

In this case, x1 = 15, x2 = 30, n1 = 1500, and n2 = 5000. Therefore:

p1 = x1 / n1 = 15 / 1500 = 0.01

p2 = x2 / n2 = 30 / 5000 = 0.006

p = (x1 + x2) / (n1 + n2) = (15 + 30) / (1500 + 5000) = 0.005

Substituting these values into the formula for the test statistic, we get:

z = (0.01 - 0.006) / sqrt(0.005 * 0.995 * (1/1500 + 1/5000)) = 2.06

Rounding the test statistic to two decimal places, we get z = 2.06.

Therefore, the value of the test statistic is 2.06.

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Answer:

Its perimeter is 23 units

Step-by-step explanation:

The perimeter of any figure is the sum of the lengths of its outline sides

The rule of the distance between two points is:

In the given figure ABCD:

Its perimeter = AB + BC + CD + DE + EA

→ Find the length of each side using the rule above

A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1), E = (2, -4)

→ Substitute them in the rule above to find the lengths of its sides

\(AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}\)

∴ AB = 5

\(BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}\)

∴ BC = 3

\(CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}\)

∴ CD = \(\sqrt{18}\)

\(DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}\)

∴ DE = \(\sqrt{18}\)

\(EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}\)

∴ EA = \(\sqrt{40}\)

→ Add them to find the perimeter of the figure ABCDE

∴ Its perimeter = 5 + 3 + \(\sqrt{18}\) + \(\sqrt{18}\) +\(\sqrt{40}\) ≅ 22.8098

→ Round it to the whole number

∴ Its perimeter = 23 units

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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Answer:

Mean = 52  MAD = 47.3

Step-by-step explanation:

mean  = 50 + 100+ 75 + 80 + 40 + 60+ 50+ 20 +25 +30 +42  / amount of data = 572 / 11 = 52    MAD = rearrange numbers = 100+ 80+75+ 60 + 50 + 50+ 42 + 40+30+ 25+20 = 25 + 5 +15+10+8+2+10+5+5 = 85  / amount of data = 85/9= 9.44 then distance on number line each way = 9.44/2 = 4.72  = MAD =52-4.72 = 47.28

The mean and the MAD (mean absolute deviation) of the given data are 52 and 19.4.

Mean is the average number of the given terms and can be calculated as the ratio of the sum of the terms to the total number of terms.

mean = sum of the terms / total number of terms

MAD refers to the Mean absolute deviation which is the average distance between each data and the mean.

MAD =  \(\frac{1}{n} \rm |X_{i} - X|\)

mean = sum of the terms / total number of terms

\(= \frac{50 + 100 + 75 + 80 + 40 + 60 + 50+ 20+ 25+ 30+ 42 }{11}\)

\(=\frac{572}{11}\)

= 52

Mean = 52

MAD =  \(\frac{1}{n} \rm |X_{i} - X|\)

         =  2+ 48 + 23 +28+ 12+8+2+32+27+22+10 / 11

         =  214 / 11

Mean absolute deviation = 19.45

Therefore, the mean and the MAD (mean absolute deviation) of the given data are 52 and 19.4.

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Answer:

0.44

Step-by-step explanation:

Given the estimated logistic regression model on risk of having squamous cell carcinoma

-4.84 + 4.6*(SMOKER)

SMOKER = 0 (non-smoker) ; 1 (SMOKER)

What is the predicted probability of a smoker having squamous cell carcinoma?

exp(-4.84 + 4.6*(SMOKER)) / 1 + exp(-4.84 + 4.6*(SMOKER))

SMOKER = 1

exp(-4.84 + 4.6) / 1 + exp(-4.84 + 4.6)

exp^(-0.24) / (1 + exp^(-0.24))

0.7866278 / 1.7866278

= 0.4402863

= 0.44

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Answer:

0.6-2.1=1.5

Step-by-step explanation:

0.6-2.1=-1.5

0.6-2.1= - I2.1-0.6I

2.1

-0.6

--------

1.5

Answer:

This answer is A

Step-by-step explanation:

Just believe me its the right answer