Which of the following are among the five basic postulates of Euclidean geometry? Check all that apply.

A. All circles have 360 degrees
B. A straight line segment can be drawn between any two points.
C. A straightedge and compass can be used to create a triangle.
D. Any straight line segment can be extended indefinitely.

The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

y - 2 = (1/2)(x - 4).

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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Given a point on the terminal side of an angle, (9, 12), we can find the exact value of the cosecant (csc) of the angle. The exact value of csc(θ) is 13/9.

To find the exact value of csc(θ), we need to use the given point (9, 12) on the terminal side of angle θ.

The cosecant function (csc) is defined as the reciprocal of the sine function (sin). Since the sine of an angle is given by the ratio of the opposite side to the hypotenuse in a right triangle, we can determine the value of csc(θ) by calculating the ratio of the hypotenuse to the opposite side.

In this case, the coordinates of the point (9, 12) represent the lengths of the sides of a right triangle. The opposite side is 12 and the hypotenuse is the length of the hypotenuse is the distance from the origin (0, 0) to the point (9, 12), which can be calculated using the Pythagorean theorem.

Using the Pythagorean theorem, we find that the hypotenuse is √(9^2 + 12^2) = √(81 + 144) = √225 = 15.

Therefore, the exact value of csc(θ) is the reciprocal of the sine of the angle θ, which is 13/9.

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Answer

4z+5=

4*7+5=33

33

Step-by-step explanation:

Answer:

(D) 112,800

Step-by-step explanation:

75%x150,400= 112,800

112,800 use the headache medicine.

Answer:

option D

Step-by-step explanation:

Out of 4 , 3 use headache medicine . So the fraction is 3/4 .

Total number of people in city = 150,400 .

So ,

⇒ n = 3/4 × Population

⇒ n = 3/4 × 150,400

⇒ n = 112,800

Answer:

Use pythagorean theorem.

Step-by-step explanation:

The length of the shorter sides are 1 & 4

1^2+4^2=c^2

1+16=c^2

17=c^2

So, the length, rounded to the nearest whole inch, would be 4.

To find the perimeter, you need to find the side lengths first.

The short sides are 6 & 7.

6^2+7^2=c^2

36+49=c^2

85=c^2

So the length for that would be 8, in the nearest whole number.

Add all of the side lengths together.

6+7+8= 21

The perimeter is 21.

Answer:

32

Step-by-step explanation:

The shapes are the same except for the direction so i think it would be 32

Answer:

32°

Step-by-step explanation:

quadrilateral ABCD is similar to quadrilateral WXYZ

Corresponding angles of similar polygons are congruent. We are told the two quadrilaterals are similar, so the pairs of corresponding angles are congruent.

You know angles are corresponding according to the statement of similarity is written.

quadrilateral ABCD is similar to quadrilateral WXYZ

The vertices are listed in the same order in both polygons showing which angles are corresponding.

<A corresponds to <W

m<W = m<A = 32°

Answer: 32°

In 4 days your family drive 5/7 of a trip. Your rate of travel is the same throughout the trip. The total trip is 1250 miles. How many more days until you reach your destination?

Find the amount traveled in one day by dividing

(5/7)/4 = 5/28 of the trip

How many days would it take to add up to 1

1/(5/28) = 5.6 days total

since we already traveled for 4 days, we have 1.6 more days to go

Answer:

25 and 135

Step-by-step explanation:

you see that the small square equals 90

Answer:

2:36

Step-by-step explanation:

i don't know for my answer

Answer:6

Step-by-step explanation:

Answer:

g(x) = x+5

Step-by-step explanation:

Given that,

[tex]f(x)=x^4+5x^3-3x-15[/tex]

[tex]q(x) = (x^3-3)[/tex]

We need to find the polynomial. We know that, Euclid division lemma states that

[tex]f(x)=q(x)\times g(x)+r(x)[/tex]

Where

f(x) is dividend

g(x) is the poynomial

q(x) is quotient

r(x) is remainder

So,

[tex]x^4+5x^3-3x-15=(x^3-3)\times g(x) +0\\\\g(x)=\dfrac{x^4+5x^3-3x-15}{(x^3-3)}\\\\g(x)=x+5[/tex]

So, the polynomial is (x+5).

Answer: its C

Step-by-step explanation: i just took the test

The correct answer is 0.4772.

Step-by-step explanation: We know that Z is a standard normal random variable.

The standard normal distribution has a mean of 0 and a standard deviation of 1. It is also symmetric around the mean with 50% of the area to the left and 50% to the right of the mean.

The area under the standard normal curve is always equal to 1.

Now, we need to calculate the probability of the interval (1.41 < z < 2.85).

We know that the total area under the standard normal curve is 1. Therefore, we can calculate the required probability by finding the area between the two given values on the standard normal curve.

Using a standard normal distribution table, we can find the area corresponding to each value as shown below: Z (from the table)1.41 0.41922.85 0.4978

The area between these two values can be calculated as follows: P(1.41 < z < 2.85) = P(z < 2.85) - P(z < 1.41) = 0.49784 - 0.4192 = 0.07864

So, P(1.41 < z < 2.85) equals 0.07864 or approximately 0.4772.

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Complete Question is:

Jamie was surveying students about their use of the new computer lab in a school. Which question in the survey is a STATISTICAL QUESTION?

A.) How qualified is the trainer at the computer lab?

B.) Where is the computer lab located in the school?

C.) What is the number of learning stations at the computer lab?

D.) How many class projects did you complete using the computer lab?

Answer:

D.) How many class projects did you complete using the computer lab?

The answer is D because the question is directly related to the use of their new computer lab and the number of projects the students have completed in the computer lab. This is directly related to the survey since it is carried out for the students using computer lab.

Answer:

1620 degrees.

Step-by-step explanation:

In a polygon the number of sides = the number of angles.

Each external angle = 360 / 11 = 32 8/11 degrees.

Each internal angle = 180 - 32 8/11 = 147 3/11 degrees

So sum = 147 3/11 * 11

= 1617 + 3

= 1620 degrees.

Answer:

It's 1620°

Hope it helps

Step-by-step explanation:

Hint:>

( The sum of the interior angle (S),

The the sides of the polygon (n).)

Then use this formula :

S=180°(n-2)

= 180°(11-2)

= 180°(9)

= 1620°

Answer:

Yes 2*35.625

Step-by-step explanation:

Just divide by two and now you have dimensions for a rug that has an area of 71.25

Yes, Is it possible for the rug to have an area of 71.25 square feet.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

A rug weaver wants to create a large rectangular rug.

Now, From the figure;

Area (S) = (8 + x) (9 - x)

            = - x² + x + 72

            = - (x² - x + 1/4) + 1/4 + 72

           = - (x - 1/2)² + 72.25

Hence,

S (max) = 72.25 square feet

And, 72.25 > 71.25

Thus, Is it possible for the rug to have an area of 71.25 square feet.

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Complete question is shown in figure.

The joint probability, Prob(V1 < 0.5, V2 < 0.3), of two uniformly distributed variables V1 and V2, modelled using a Gaussian copula with a correlation coefficient of ρ = 0.5.

Given that V1 and V2 are uniformly distributed between 0.2 and 0.8, we need to transform these variables to standard normal variables before calculating the joint probability. The Gaussian copula is commonly used for this purpose.

The transformation from the uniform distribution to the standard normal distribution can be achieved using the inverse of the cumulative distribution function (CDF) of the standard normal distribution. Let Φ denote the CDF of the standard normal distribution. The transformed variables, denoted as U1 and U2, can be calculated as follows:

U1 = Φ^(-1)(V1)

U2 = Φ^(-1)(V2)

Since the correlation coefficient between U1 and U2 is ρ = 0.5, we can calculate the joint probability using the bivariate normal distribution function with mean 0, standard deviation 1, and correlation coefficient 0.5. Let Φ2 denote the cumulative bivariate normal distribution function.

[tex]Prob(V1 < 0.5, V2 < 0.3) = Prob(U1 < Φ^(-1)(0.5), U2 < Φ^(-1)(0.3))[/tex]

[tex]= Φ2(Φ^(-1)(0.5), Φ^(-1)(0.3); ρ = 0.5)[/tex]

By evaluating the bivariate normal distribution function at the given values, we can obtain the joint probability.

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To write down the joint probability Prob(V1 < 0.5, V2 < 0.3) in terms of the cumulative bivariate normal distribution function, we need to utilize the properties of the Gaussian copula and the correlation coefficient.

False.  A graphical interpretation of the 2-point backward difference formula for approximating is not the slope of the line joining the points.

The 2-point backward difference formula is a method for approximating the derivative of a function at a specific point using two nearby points.

The backward difference formula is given by:

f'(x) ≈ (f(x) - f(x - h)) / h

Where f(x) is the given function, f(x - h) is the function evaluated at a point slightly to the left of x, and h is a small step size.

The formula calculates the approximate derivative by computing the difference between the function values at two points and dividing it by the step size. It does not involve the concept of connecting points with a line or calculating slopes.

Therefore, the statement is false. The graphical interpretation of the 2-point backward difference formula does not represent the slope of the line joining the points.

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Answer 2.05

Step-by-step explanation: hope this helps

We can see that the computed z value lies inside the non-rejection region. Hence, we cannot reject the null hypothesis based on the evidence on hand.Therefore, the correct option is B. Based on the evidence on hand that the computed z statistic - 0.91 lies outside the rejection region, we cannot reject the null hypothesis.

The given values for the problem are: n = 74, p = 5/74, Po = 10%.

The significance level is given by alpha = 0.05 (given in the problem).

The null hypothesis and alternate hypothesis are as follows:H0: p = 0.10 Ha: p < 0.10.

The formula to calculate the z-statistic is given by:z = [tex](p - Po) / √[(Po(1 - Po))/n].[/tex]

Substituting the given values,z = [tex](5/74 - 0.10) / √[(0.10(0.90))/74] = -0.9138.[/tex]

Using the standard normal distribution table, the critical value for z at alpha = 0.05 for a left-tailed test is -1.645.

The computed z value is -0.9138 and the critical value at alpha = 0.05 is -1.645.

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Answer:

10 times

Step-by-step explanation:

1km=1000m

3*1000=3000m

3000/300=10

you will need to run 10 times around the field

The correct answers are:

An assignment model with 3 tasks and 4 resources will have 12 constraints, assuming no special constraints and not including non-negativity.

Warehouses are not part of assignment models.

The statement "Each task only requires one resource. Each resource can only complete one task. There are 4 tasks and 6 resources" will lead to an infeasible solution.

Therefore, the correct options are:

12

Warehouses

The statement "Each task only requires one resource. Each resource can only complete one task. There are 4 tasks and 6 resources."

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The regression line is y = 8.42 - 0.27x and there is a corresponding decrease of 0.27 hours in sleep time.

Given below is the calculation of the mean, variance, and standard deviation of GAS scores.

X f fx x^2 3.2 1 3.2 10.24 3.4 1 3.4 11.56 3.7 1 3.7 13.69 4.1 1 4.1 16.81 5 1 5 25 5.4 1 5.4 29.16 5.6 1 5.6 31.36 5.8 1 5.8 33.64 6 1 6 36 6.3 1 6.3 39.69 6.6 2 13.2 43.56 7.1 1 7.1 50.41 7.4 1 7.4 54.76 8 1 8 64 8.1 2 16.2 65.61 8.6 1 8.6 73.96 8.7 1 8.7 75.69

Total 15 131.8

Mean = sum of x*f/sum of f = 131.8/15 = 8.78

To find the variance of the given data set, use the formula:

Variance (s²) = (Σx² / n) - (mean)²

Variance = (520.75 / 15) - 76.96 = 8.977

The standard deviation is the square root of the variance, so:

Sd = sqrt(8.977) = 2.996

For these data, GAS scores that are less than the mean of the GAS scores tend to be paired with sleep times that are more than the mean of the sleep times.

According to the regression equation, for an increase of one in GAS score, there is a corresponding decrease of 0.27 hours in sleep time.

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The expression COSX + Sinx - tanx can be simplified by combining trigonometric identities.

We can use the trigonometric identities to simplify each term in the expression:

COSX + Sinx:

We know that sin(x) = cos(π/2 - x). Therefore, we can rewrite Sinx as Cos(π/2 - x):

COSX + Cos(π/2 - x)

tanx:

We know that tanx = sinx / cosx. Therefore, we can rewrite tanx as sinx/cosx:

sinx / cosx

Now, let's combine the terms:

COSX + Cos(π/2 - x) - sinx / cosx

Using the sum-to-product formula for cosine (Cos(A + B) = CosA * CosB - SinA * SinB), we can rewrite the expression as:

CosX * Cos(π/2) - SinX * Sin(π/2) - sinx / cosx

Since Cos(π/2) = 0 and Sin(π/2) = 1, the expression simplifies to:

0 - 1 - sinx / cosx = -1 - sinx / cosx

Therefore, the simplified expression is -1 - sinx / cosx.

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Answer:9

Step-by-step explanation:

The area of the triangle with vertices: Q(2,-1,1), R(3,-2,-2), S(5,1,-1) is 6.5 square units.

To find the area of the triangle with vertices: Q(2,-1,1), R(3,-2,-2), S(5,1,-1), we can use the formula Area of triangle = 1/2 * |(x2-x1) (y3-y1)-(x3-x1)(y2-y1)|

where, x1, y1, x2, y2, x3 and y3 are the coordinates of the given triangle Q(2,-1,1)

corresponds to x1=2, y1=-1R(3,-2,-2)

corresponds to x2=3, y2=-2S(5,1,-1)

corresponds to x3=5, y3=1

We can substitute these values in the above formula to get Area of triangle = 1/2 * |(x2-x1) (y3-y1)-(x3-x1)(y2-y1)|= 1/2 * |(3-2)(1-(-1)) - (5-2)(-2-(-1))|    = 1/2 * |-4 - 9|    = 1/2 * 13    = 6.5

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Answer:

G. 32

Step-by-step explanation:

32 x 335 = 10720

16,100 - 10720 = 5380/190 = 28.3157894737

275 x 32 = 8800

18,800 - 8800 = 10,000/400 = 25 (This is the closer).

30 x 335 = 10,050

16,100 - 10,050 = 6050/190  = 31.8421052632

30 x 275 = 8250

18,800 - 8250 = 10550/400 = 26.375 (Same reason why it does't work)

25 x 335 = 8375

16,100 - 8375 = 7725/190 = 40.6578947368

25 x 275 = 6875

18,800 - 6875 = 11925/400 = 29.8125

24 x 335 = 8040

16,100 - 8040 = 8060/190 = 42.4210526316

24 x 275 = 6600

18,800 - 6600 = 12200/400 = 30.5

Scatter plot

Box plot

Dot plot

To compare bite strength to weight for different carnivores, scatter plot, box plot, and dot plot are appropriate representations.

Scatter plot: A scatter plot can show the relationship between bite strength and weight by plotting each carnivore as a data point. The x-axis can represent weight, the y-axis can represent bite strength, and each point on the plot represents a different carnivore. This allows for visualizing the overall trend or pattern between the two variables.

Box plot: A box plot can display the distribution of bite strength and weight for different carnivores. It provides information about the median, quartiles, and any outliers in the data. By comparing the box plots for different carnivores, we can assess the variations in bite strength relative to weight.

Histogram: A histogram is not appropriate in this case because it represents the distribution of a single variable, such as bite strength or weight, and does not directly compare the two variables.

Table: A table can present the bite strength and weight data for different carnivores, but it does not provide a visual comparison or representation of the relationship between the two variables.

Dot plot: A dot plot can show the individual data points of bite strength and weight for each carnivore. Each dot represents a carnivore, and by comparing the position and density of dots, we can observe the relationship between bite strength and weight.

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The equation y = (0.9)t - 4 can be rewritten in the form y = a(1 - r)t, where a = -4 and r = 0.1. This represents exponential decay.

In the equation y = (0.9)t - 4, the term (0.9)t represents the exponential part, where the base is 0.9. By rewriting it in the form y = a(1 - r)t, we can identify the values of "a" and "r" that correspond to the given equation.

In this case, "a" is the initial value, which is -4. The negative value indicates a downward shift or decrease from the initial value. The term (1 - r) represents the remaining portion after each time interval. By comparing the given equation to the general form, we find that r = 0.1, which signifies a decay rate of 10%.

Overall, the equation y = (0.9)t - 4 represents exponential decay because the value of "r" is less than 1 (0.1) and "a" is negative (-4). This indicates a decreasing trend as time (t) increases.

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