Consider the following statement. (Assume that all sets are subsets of a universal set U.)
For all sets A, B, and C, if A ⊆ B and B ∩ C = ∅ then A ∩ C = ∅.
Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set.
Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C.
Then (A ∩ C)c = U.
Hence x ∈ B ∩ C by definition of intersection.
Then by definition of intersection and complement A = U.
By definition of intersection x ∈ A and x ∈ C.
Therefore A ⊈ B.
Thus B ∩ C ≠ ∅ by definition of ∅.
Proof by contradiction:
Suppose that there exists sets A, B, and C such that A ⊆ B, and B ∩ C = ∅ and A ∩ C ≠ ∅. Then there exists an element x such that x ∈ A ∩ C.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠ ∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠ ∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠ ∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠ ∅ by definition of ∅.
But this contradicts the supposition. Hence the supposition is false, and so A ∩ C = ∅.

Answer:

256 miles

Step-by-step explanation:

1 cm = 8 miles

32 cm = x miles

32 * 8 = 256 miles

Answer: it should be 12.8 percent

Step-by-step explanation:

The value of the missing sides assuming both triangles are similar will be 18 inches.

Similar figures are those figures which are identical in shape, but not necessarily in size.

Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.

As per the given two triangle,

Suppose the length of missing side is x inches.

Suppoes both triangles are similar by AAA rule.

The ratio of corresponding sides will be same thus,

x/6 = 12/4

x = 3 x 6 = 18 inches

Hence "If both triangles are comparable, the value of the missing sides will be 18 inches".

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Answer:

(a) To find the range of the function f(x), we need to consider all possible values of x in the range -7 ≤ x ≤ 7 and x ≠ -5. For each value of x, we can evaluate the function to find the corresponding value of f(x). Then, we can find the minimum and maximum values of f(x) in this range to determine the range of the function.

For example, if x = -7, then the function will return a value of 2 - 12/(-7) + 5 = 2 + 2 + 5 = 9. If x = 7, then the function will return a value of 2 - 12/7 + 5 = 2 - 1 + 5 = 6.

We can see that the minimum value of the function is 6, which is achieved when x = 7, and the maximum value of the function is 9, which is achieved when x = -7. Therefore, the range of the function is {6, 9}.

(b) To find the inverse of the function f(x), we need to switch the x and y values in the function definition to obtain a new function g(y) such that g(f(x)) = x for all values of x in the domain of the original function.

In this case, the inverse of the function f(x) is given by g(y) = (2 - y + 5)/(-12). This inverse function is defined for all values of y in the range {6, 9}, which is the range of the original function.

To find the value of f^-1(0), we can plug in 0 for y in the inverse function g(y) to obtain g(0) = (2 - 0 + 5)/(-12) = -1/12. Therefore, f^-1(0) = -1/12.

The probability that exactly one other guest has the same birthday as you is 0.3483.

The number of possible outcomes is divided by the total number of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event by the probability that it won't.

The likelihood of success is a measure of probability. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We express P(heads) = 12.

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The point that the line estimate best fits is the point x = 6 with a residual of 0.18

We are given a table which displays the point and then their residual values are also added from the graph to get;

The table is as follows:

x      y       Residual      Absolute Residual value

1      10       0.4                         0.4

2      8        -1.125                    1.125

2.5   9.5      0.625                   0.625

4       8        -0.25                       0.25

5     8        0.2                             0.2

6    7.5       0.18                          0.18

7.2     7        0.19                          0.19

8.5     6       -0.25                        0.25

The residual value is negative if the point on the scatter plot lies below the regression line and it is positive if the point on the scatter plot lies above the regression line.

Formula for the residual value is;

Residual value = Actual y-value(i.e. on scatter plot) - Observed y-value

Now, the residual value is farthest from the line if the absolute value of the residual value is highest.

Hence, the highest absolute residual value is: 1.125

The point that it best fits is the lowest absolute value which is 0.18

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Answer:

61.9%

Step-by-step explanation:

percent = part/whole × 100%

part = 86

whole = 139

percent = 86/139 × 100%

percent = 61.9%

Answer:

The percent is:

61.87%

Step-by-step explanation:

86 / 139 = 0.6187

0.6187 * 100 = 61.87%

Therefore, the value of the scalar k for which the two vectors are orthogonal is k =1/5.

In physics and mathematics, the term "vector" is used to refer, informally, to certain quantities that cannot be described by a single number or to certain constituents of vector spaces.

Here,

When the dot product of two vectors is zero, those two vectors are said to be orthogonal.

Dot product:

Let's assume we have the two vectors a and b.

a = (1,2) (1,2)

b = (2,3) (2,3)

Their dot item is:

a.b = (1,2). (1,2).

(2,3) = 1*2 + 2*3 = 8

Regarding this issue:

u = (2,3) (2,3)

(k + 1, k - 1) = v

So

u.v = (2,3). (2,3).

(k + 1, k - 1) = 2k + 1, 3k - 1, or 2k + 2, 3k - 3, or 5k - 1

The vectors must be orthogonal for the dot product to equal 0.

So:

=> 5k -1 =0

=> 5k =1

=> k =1/5

Therefore , the value of the scalar k for which the two vectors are orthogonal is k =1/5.

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Answer:

No (not a proportional relationship)

Step-by-step explanation:

The cost of fountain drinks at Hot Dog Hut:

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Volume & \sf Cost \\\sf \sf (fluid\;ounces) & \sf(\$) \\\cline{1-2} \vphantom{\dfrac12}16& 1.49\\\cline{1-2} \vphantom{\dfrac12}20&1.59 \\\cline{1-2} \vphantom{\dfrac12}30& 1.89\\\cline{1-2} \end{array}[/tex]

A proportional relationship is one in which two quantities vary directly with each other.

Calculate the rate of change of the ordered pairs.

Rate of change between (30, 1.89) and (20, 1.59):

[tex]\implies \dfrac{1.89-1.59}{30-20}=\dfrac{0.3}{10}=0.03[/tex]

Rate of change between (20, 1.59) and (16, 1.49):

[tex]\implies \dfrac{1.59-1.49}{20-16}=\dfrac{0.1}{4}=0.025[/tex]

As the rates of change are different (not constant), the relationship is not proportional.

Note:  The graph of a proportional linear relationship is a line that passes through the origin (0, 0).

Answer:

[tex]92.05^{\circ}[/tex]

Step-by-step explanation:

By the exterior angle theorem, the answer is [tex]m\angle Y+m\angle Z=92.05^{\circ}[/tex].

Answer:

A

Step-by-step explanation:

exterior angle = sum of the other two angles

63.25 + 28.8

92.05°

Answer:

Step-by-step explanation:

let the distance be x miles

the difference in time taken  between two towns = 7 minutes

   44 - x = 49

x = 49 - 44

      x = 5 miles

Therefore , the distance between two towns is 5 miles .

3/5 of 595 students are 7th graders:

5/8 of them participated in the competition:

2/5 of the 595 students are 8th graders:

7/8 of them participated in the competition:

About how many total students participated?

Find the sum of participated students from parts A and B:

The t-statistic for this hypothesis test is 2.019 and the appropriate conclusion is that we fail to reject the null hypothesis.

To find the p-value, we can use the t-distribution calculator and enter in the degrees of freedom (df = 59), the t-statistic (t = 2.019), and the significance level (alpha = 0.01). The resulting p-value is 0.055, which is greater than the significance level of 0.01. Therefore, we are unable to reject the null hypothesis.

The formula for the t-statistic can be used to calculate the t-statistic for this hypothesis test:

t = (1151 - 1120) / (112 / √60)

t = 2.019

Therefore, the t-statistic for this hypothesis test is 2.019 and the appropriate conclusion is that we fail to reject the null hypothesis.

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0.9(315 000) * 30(0.0375)

= 283 500 * 1.125

= 318 937.5   (total amount of 30 year mortgage)

= 318 937.5 / 360

= $885.94   (monthly payment)

315 00 * 0.1 = 31 500   (amount of down)

315 000 - 31 500 = 283 500 (balance without interest)

283 500 * 30(0.0375) = 318 937.5  (balance with interest)

318 937.5 / 30(12) = 885.94

Therefore, the monthly payment will be $885.94

Answer:

Step-by-step explanation:

Graph A

Answer:

128/25

Step-by-step explanation:

(3 1/5) / (5/8) =

(3 + 1/5) / (5/8) =

(15/5 + 1/5) / (5/8) =

(15+1)/5 / (5/8) =

16/5 / (5/8) =

16/5 * 8/5 =   ==> dividing by a number is equaled to multiplying by its

                           reciprocal: the reciprocal of 5/8 is 8/5.

(16 * 8) / (5*5) = 128/25

Lets turn 3.85% into a decimal first. Multiply 0.0385 with 410,000 which gives you 15785. Add that to 410,000 which gives you 425785. Multiply 3.85 by 425785. Repeat that process 5 times until you get the amount of interest earned after 5 years.

On analyzing the data given in question we get to know that the sensitivity is negative.

Our function is 40 + 24 x 2.4 /1 + 4x  to the point.

For the time being, our first task is to determine the sensitivity, which is the derivative of our discovery. The quotient rule, whose derivative we shall be utilizing, says that the derivative of F org equals G f prime minus f g prime all over g squared.

The bottom function is one plus four times the top function's derivative, or 40.4 times. 40 has a derivative of zero.

When a light source is x cm away from a light probe, the light's intensity is measured as y microwatts per square cm. The outcomes are displayed as ordered pairs( x , y).

So we just need to multiply 24 x240.4.

Using the power rule, we can reduce the 0.4 point to 9.6 x to the minus 0.6.

We subtract one from the initial exponents minus the top function 40 + 24 x to the point for times the bottom function's derivative 10 So we have the derivative of four additional 40.4 by the power rule,

we bring down the 0.4 multiplied by four against 1.6 next to the minus 0.6, and we divide all of that by one plus four x to the 40.4 squared.

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Answer:

Infinite number of integers that satisfy the inequality |x|<4.

Step-by-step explanation:

The absolute value of a number indicates its distance from 0 on the number line. Therefore, the inequality |x|<4 indicates that x is less than 4 units away from 0 on the number line. Because there are an infinite number of integers on the number line, there are an infinite number of integers that satisfy the inequality |x|<4.

The equation of the hyperbola with given x and y axes will be x² + y² = 4 that is option D is correct.

The hyperbola x² + y² = 4 is a standard form of the equation for a hyperbola centered at the origin, which means that the hyperbola passes through the point (0,0). However, the given information states that the hyperbola passes through the point (2,2). This can be achieved by shifting the hyperbola to the right and up by 2 units, resulting in the equation (x-2)² + (y-2)² = 4.

The asymptotes of a hyperbola are the lines that the hyperbola approaches but never touches as it extends to infinity. The asymptotes of a hyperbola centered at the origin are the x-axis and y-axis. Since this hyperbola has been shifted to the right and up by 2 units, the asymptotes are the x-axis and y-axis shifted by 2 units in the same direction. Therefore, the x- and y-axes are the asymptotes of this hyperbola.

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Answer:

f(-4)=16

Step-by-step explanation:

since f(x)=8-2x and we are asked to find f(-4),

we plug -4 in for x and we get

[tex]f(-4)=8-2(-4)[/tex]

[tex]2*-4=-8[/tex]

[tex]8-(-8)=8+8[/tex]

[tex]8+8=16[/tex]

[tex]f(-4)=16[/tex]

The campers will be 40 miles from their car after 12 hours.

Given :

A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours .

We can pick two points on the line graphed and substitute the coordinates into this formula to find the slope:

slope m = y2 - y1 / x2 - x1

Choosing the points (0,4) and (2,10), we get:

m = 4 - 10 / 0 - 2

= -6 / -2

= 6 / 2

= 3

We can substitute the point (0,4) and the slope into y = mx + b and solve for "b":

4 = 3 * 0 + b

b = 4

Then, the equation of this line is:

y = 3x + 4

Since the distance in miles is represented on the y-axis and the time in hours is represented on the x-axis. we can rewrite the equation as:

d = 3h + 4

if h = 12

d = 3 * 12 + 4

= 36 + 4

= 40 miles

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Full question :

A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours.How many miles will the campers be from their car after 12 hours?

Answer:

Solutions: (0,2) and (3,1)

Not a solution (6,4)                                                                                            

Step-by-step explanation:

x + 3y = 6

0 + 3y = 6

3y = 6

y = 2

(0,2)

x + 3y = 6

3 + 3y = 6

3y = 3

y = 1

(3,1)  

x + 3y = 6

6 + 3(4) = 6

6 + 12 = 12

18≠12

(6,4)

Answer:

s= 2

Step-by-step explanation:

4s - 14 = -6  Add 14 to both sides

4s - 14 + 14 = -6 + 14  Simplify

4s = 8  Divide both sides by 4

s = 2

Check

4x - 14 = -6

4(2) - 14 = -6

8 - 14 = -6

-6 = -6

First, we should the leave the variable [tex]s[/tex] on the left side of the equation.

Divide both sides by [tex]4.[/tex]

Conclusion:

   Consequently, the element [tex]2[/tex] in the given set is the only real solution of this equation. What we need to do in such questions is to leave the unknown alone. Since the power of the variable [tex]s[/tex] of our unknown is [tex]1[/tex] we can only find [tex]1[/tex] root, respectively.

Answer: 5 hours

Step-by-step explanation:

1800cal/day

a= ants

50a= 1 cal

150 licks per minute, 2 ants per lick--- 2*150 = 300 ants per minute

6*50a= 1 cal*6

-- 300a = 6cal

The anteater can get a avg of 6 calories per minute.

6*60 = 360

We can make a equation:

x =calories

360x = 1800

360/360x = 1800/360

x = 5

It would take the anteater a total of 5 hours to withdraw 1800 calories from ants. This is 300*60*5 ants!

To check:

360(5)=1800

1800=1800

The correct answer would be C, 6.36246 × 1019

The statement that best reflects the grade is "The variances of anxiety scores were roughly the same in the different groups of musicians."

The term variances refers the mean squared difference between each data point and the center of the distribution measured by the mean

Here we have given that a music teacher had noticed that some students went to pieces during exams and he wanted to test whether this performance anxiety was different for people playing different instruments. While he took groups of guitarists. drummers and pianists (variable = 'Instru') and measured their anxiety (variable = 'Anxiety') during the exam. Here he also noted the type of exam they were performing (in the UK, musical instrument exams are known as 'grades' and range from 1 to 8 ).

Now, we need to find the statements best reflects what the effect of GRADE in the table tells us.

While we looking into he given question we have identified that this performance anxiety was different for people playing different instruments.

So, based on this concept the correct statement id option (c).

Because, here the variances of anxiety scores were roughly the same in the different groups of musicians where if Levine's test of equality of error variances is non-significant (sig > .05) then there is equality of variances.

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Answer:

Step-by-step explanation:

You want the graphs of the given lines, and the centroid of the triangle they form.

It works well to start by plotting the y-intercept of each equation, then using the slope to identify the "rise" and "run" to another point on the line. Then the line can be drawn through the points.

The graph shows you the points of intersection of the lines are ...

  (-4, 2), (4, 8), (0, -4) . . . . . . . . . the last is the y-intercepts of y1 and y3

The centroid coordinates are the average of the vertex coordinates, their sum divided by 3.

  centroid = ((-4, 2) +(4, 8) +(0, -4))/3 = (-4+4+0, 2+8-4)/3 = (0, 6)/3

  centroid = (0, 2)

__

Additional comment

The slope of each line is the x-coefficient in the equation. That slope is the ratio of "rise" (change in y) to "run" (change in x) for the line. It is often convenient to draw a graph by finding points on the line counting the grid squares for rise and run.

Answer:

D) 540

Step-by-step explanation:

he sum of the interior angles of a polygon can be found using the formula (n - 2) * 180 degrees, where n is the number of sides in the polygon. In this case, we are given that the polygon has 5 sides, so we can plug this into the formula to find the sum of its interior angles:

(5 - 2) * 180 degrees = 3 * 180 degrees = 540 degrees

Therefore, the sum of the interior angles of a regular polygon with 5 sides is 540 degrees.

[tex]r=\frac{5i\sqrt{2} }{4}, -\frac{5i\sqrt{2} }{4}[/tex] or simply just say ± [tex]\frac{5i\sqrt{2} }{4}[/tex].

Hope this helps!

Answer:

[tex]r=\dfrac{5\sqrt{2}}{4}}\:i\:,\quad \;\;r=-\dfrac{5\sqrt{2}}{4}}\:i[/tex]

Step-by-step explanation:

To solve the given equation, rearrange the equation to isolate r.

Given equation:

[tex]0=-16r^2-50[/tex]

Add 16r² to both sides of the equation:

[tex]0+16r^2=-16r^2-50+16r^2[/tex]

     [tex]16r^2=-50[/tex]

Divide both sides of the equation by 16:

[tex]\dfrac{16r^2}{16}=\dfrac{-50}{16}[/tex]

   [tex]r^2=-\dfrac{25}{8}[/tex]

[tex]\textsf{For\;\:}x^2=f\left(a\right)\textsf{\:the\:solutions\:are\:\:}x=\pm\sqrt{f\left(a\right)}[/tex]

[tex]r=\pm\sqrt{-\dfrac{25}{8}}[/tex]

[tex]\textsf{Apply\;the\:radical\:rule:}\;\:\sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]

[tex]r=\pm\sqrt{\dfrac{25}{8}}\sqrt{ -1}[/tex]

[tex]\textsf{Apply\;the\:imaginary\:number\:rule:}\;\:\sqrt{-1}=i[/tex]

[tex]r=\pm\sqrt{\dfrac{25}{8}}\:i[/tex]

[tex]\textsf{Apply\;the\:radical\:rule:}\:\:\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}},\:\quad \:a\ge 0,\:b\ge 0[/tex]

[tex]r=\pm\dfrac{\sqrt{25}}{\sqrt{8}}\:i[/tex]

Simplify the numerator and denominator of the fraction:

[tex]r=\pm\dfrac{5}{2\sqrt{2}}\:i[/tex]

Rationalise the denominator by multiply the numerator and denominator by √2:

[tex]r=\pm\dfrac{5\cdot\sqrt{2}}{2\sqrt{2}\cdot \sqrt{2}}\:i[/tex]

[tex]r=\pm\dfrac{5\sqrt{2}}{4}}\:i[/tex]

Therefore, the solutions to the given equation are:

[tex]r=\dfrac{5\sqrt{2}}{4}}\:i\:,\quad \;\;r=-\dfrac{5\sqrt{2}}{4}}\:i[/tex]