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<image>As shown in the figure, a square with side length $a$ is cut along the dotted lines into two squares and two rectangles. If the smaller square with side length $b$ is removed, and the remaining three pieces are rearranged to form a larger rectangle, then the length of the longer side of this rectangle is.
| $a+b$ |
|
<image>As shown in the figure, $$PA$$ and $$PB$$ are tangents to the circle $$\odot O$$ at points $$A$$ and $$B$$, respectively, and intersect the tangent of $$\odot O$$ at points $$C$$ and $$D$$. Given that $$PA = \quantity{7}{cm}$$, the perimeter of $$\triangle PCD$$ is ___.
| $$\quantity{14}{cm}$$ |
|
<image>As shown in the figure, the one that can infer this geometric solid might be a triangular frustum is ___ (fill in the sequence number). 1. $$A_{1}B_{1}=2$$, $$AB=3$$, $$B_{1}C_{1}=3$$, $$BC=4$$; 2. $$A_{1}B_{1}=1$$, $$AB=2$$, $$B_{1}C_{1}=1.5$$, $$BC=3$$, $$A_{1}C_{1}=2$$, $$AC=3$$; 3. $$A_{1}B_{1}=1$$, $$AB=2$$, $$B_{1}C_{1}=1.5$$, $$BC=3$$, $$A_{1}C_{1}=2$$, $$AC=4$$; 4. $$AB=A_{1}B_{1}$$, $$BC=B_{1}C_{1}$$, $$AC=A_{1}C_{1}$$.
| 3 |
|
<image>As shown in the figure, the right-angle vertex C of a right-angled triangle is placed on the line EF. If ∠ACE = 59°39′, then the size of ∠BCF is.
| $30{}^\circ 21\prime $ |
|
<image>As shown in the figure, if ∠1 = ∠2, and ∠ADC = 78°, then the measure of ∠BCD is.
| 102° |
|
<image>As shown in the figure, the vertices A and C of rectangle ABCD lie on the graph of the inverse proportion function y = k/x (k > 0, x > 0). If the coordinates of point A are (3, 4), AB = 2, and AD is parallel to the x-axis, then the coordinates of point C are.
| (6, 2) |
|
<image>As shown in the figure, the parallelogram $$ABCD$$ is folded so that point $$C$$ coincides with point $$A$$. At this time, point $$D$$ falls on $$D_{1}$$, and the fold line is $$EF$$. If $$\angle BAE=55^{\circ}$$, then $$\angle D_{1}AD=$$ ___.
| $$55^{\circ}$$ |
|
<image>The base diameter of a conical chimney cap is $80cm$, and the slant height is $50cm$. To make $100$ such chimney caps, at least how many square meters of iron sheet are needed (the result should be in terms of $\pi$)?
| $20\pi$ |
|
<image>As shown in the figure, in quadrilateral ABCD, ∠A = 60°, then ∠1 + ∠2 =.
| 240° |
|
<image>As shown in the figure, in $$\triangle ABC$$, $$\angle ACB > 90^{\circ}$$, $$AD \bot BC$$, $$BE \bot AC$$, $$CF \perp AB$$, with the feet of the perpendiculars being $$D$$, $$E$$, and $$F$$ respectively. Then the line segment ___ is the altitude from $$AC$$ in $$\triangle ABC$$.
| $$BE$$ |
|
<image>Execute the program flowchart. If P=0.7, then the output n=_____.
| 3 |
|
<image>Observe the following figure: The sum of the numbers in the nth row equals ${{2017}^{2}}$.
| 1009 |
|
<image>Among the following four car logos, the number of logos that are both centrally symmetric and axially symmetric is ______.
| $$1$$ |
|
<image>As shown in the figure, point A lies on the inverse proportional function $y=\frac{k}{x}$ (x < 0). Construct right triangle ABC, where point D is the midpoint of the hypotenuse AC. Connect DB and extend it to intersect the y-axis at point E. If the area of triangle BCE is 12, then the value of k is.
| 24 |
|
<image>In the figure shown, the radius of the upper arc is $$r_{上}$$, and the radius of the lower arc is $$r_{下}$$. Then $$r_{上}$$ ___ $$r_{下}$$ (fill in with "$$>$$", "$$=$$", or "$$<$$").
| $$<$$ |
|
<image>Run the program flowchart as shown in the figure. The number of curves with foci on the $$y$$-axis is ______.
| 3 |
|
<image>As shown in the figure, in the right triangle ABC, ∠ACB = 90°, AC = 3, BC = 4, AB = 5. Point P is a moving point on AB. The minimum value of CP is ______.
| 2.4 |
|
<image>Execute the following flowchart. If the output result is $$\dfrac{15}{16}$$, then the input integer $$a=$$___.
| $$4$$ |
|
<image>As shown in the figure, point O lies on line AB, OC is perpendicular to OD, OC and OF bisect ∠AOE and ∠BOD respectively. If ∠AOC = 20°, then the measure of ∠BOF is.
| 35° |
|
<image>As shown in the figure, a rectangular paper ABCD is folded along CE, and point B lands exactly on the edge AD, let this point be F. After unfolding, if AB:BC = 4:5, then ∠CFD ≈ (accurate to 0.01°)
| 53.13° |
|
<image>The figure on the right is a flowchart of an algorithm. The final output of $$W$$=______．
| 22 |
|
<image>A certain forage planting base planted 50 acres of three types of forage, A, B, and C, in 2019, with the planting ratio as shown in the figure. The base plans to expand the planting areas of varieties A and C in 2020, while keeping the planting area of variety B unchanged, which will reduce the planting area ratio of variety B to 10%. If the planting area ratio of variety C remains unchanged, what will be the planting area of variety C in 2020?
| 15 |
|
<image>Observe the figure on the right and fill in the table:___.
| $$3an+2a$$ |
|
<image>The number of people queuing to pay at a supermarket checkout and their frequencies are shown in the following table. If the frequencies are considered as probabilities, then the probability of at least 2 people queuing to pay is ______. (Answer with a number)
| 0.75 |
|
<image>As shown in the figure, in rhombus $ABCD$, diagonals $AC$ and $BD$ intersect at point $O$, and $OE \perp AB$ with the foot of the perpendicular at $E$. If $\angle ADC = 128{}^\circ$, then the measure of $\angle AOE$ is.
| 64° |
|
<image>Given that line a is parallel to line b, place the right-angle vertex B of a triangular board on line b, and the other two sides intersect line a at points A and C (as shown in the figure). If ∠1 = 35°, then the measure of ∠2 is.
| 55° |
|
<image>As shown in the figure, sunlight enters the classroom through the window. The shadow of the window frame AB on the ground is DE = 1.8 m, the distance from the bottom of the window to the ground is BC = 1 m, and EC = 1.2 m. What is the height of the window AB in meters?
| 1.5 |
|
<image>As shown in the figure, $$AB$$ is the diameter of circle $$⊙O$$, with $$AB=10$$. $$BC$$, $$CD$$, and $$DA$$ are chords of circle $$⊙O$$, and $$BC=CD=DA$$. If point $$P$$ is a moving point on diameter $$AB$$, then the minimum value of $$PD+PC$$ is ___.
| $$10$$ |
|
<image>Xiao Ming starts from point A and wants to reach point C, which is located at a direction of 60° north of east. He first walks 200 meters due east to point B, and then walks in a direction of 30° north of east to reach his destination, point C. What is the distance between points B and C?
| 200 meters |
|
<image>As shown in the figure, $$\triangle ABC \cong \triangle DEF$$, please write down $$x=$$ ___.
| $$9$$ |
|
<image>In triangle ABC, ∠A = 80°, and the angle bisectors of ∠ABC and ∠ACD intersect at point E. Find ∠E.
| 40° |
|
<image>As shown in the figure, in the right triangle $$\text{Rt}\triangle ABC$$, $$\angle ACB=90^{\circ}$$, $$AB=2AC$$. Point $$E$$ is on the median $$CD$$, and $$BE$$ bisects $$\angle ABC$$. What is the measure of $$\angle DEB$$?
| $$45^{\circ}$$ |
|
<image>A school conducted a random survey of 50 students to understand their extracurricular reading habits, collecting data on the time each student spent reading outside of class on a particular day. The results are represented in the bar chart shown. According to the bar chart, the average time spent on extracurricular reading by these 50 students on that day is ___ hours.
| 0.9 |
|
<image>On the opposite surfaces of a cube, the two numbers marked are opposite numbers. The figure is the unfolded surface of this cube. What is the value of $$x + y$$?
| $$ - 10$$ |
|
<image>As shown in the figure, $$P$$ is a point outside the plane of $$\triangle ABC$$, and $$E$$, $$F$$, $$G$$ are the midpoints of $$AB$$, $$BC$$, and $$PC$$, respectively. The number of lines in the figure that are parallel to the plane through $$E$$, $$F$$, and $$G$$ is ___.
| $$2$$ |
|
<image>In the figure, in parallelogram $ABCD$, diagonals $AC$ and $BD$ intersect at point $O$, and a line through point $O$ intersects $AB$ and $CD$ at points $M$ and $N$, respectively. If the area of $\Delta CON$ is 2 and the area of $\Delta BOM$ is 3, then the area of $\Delta ADB$ is
| 10 |
|
<image>As shown in the figure, there is an inscribed cylinder inside a sphere O with radius $$R$$. When the lateral surface area of the cylinder is maximized, the difference between the surface area of the sphere and the lateral surface area of the cylinder is ___.
| $$4 \pi R^{2}-2 \pi R^{2}=2 \pi R^{2}$$ |
|
<image>As shown in the figure, combine the following four shapes into a large rectangle, and then factorize the resulting polynomial.
| ${{x}^{2}}+3x+2=\left( x+1 \right)\left( x+2 \right).$ |
|
<image>In the rectangle ABCD, AB=4, AD=3. A circle with radius x is drawn with vertex D as the center, such that points A, B, and C are all outside the circle. The range of values for x is.
| 0＜x＜3 |
|
<image>From a region of $$\number{15000}$$ elderly people, $$500$$ people were randomly selected to investigate their ability to take care of themselves. The results are shown in the table below: In the region, the number of men who cannot take care of themselves is approximately ___ more than the number of women.
| $$60$$ |
|
<image>In the figure, in △ABC, ∠ACB = 90°, ∠A = 30°, AB = 4. If CD is the altitude, then BD =.
| 1 |
|
<image>As shown in the figure, quadrilateral $ABCD$ is a trapezoid with $AB//CD$, and $AB//$ plane $\alpha$. $AD$ and $BC$ intersect plane $\alpha$ at points $M$ and $N$, respectively, and point $M$ is the midpoint of $AD$. Given $AB=4$ and $CD=6$, then $MN=$.
| 5 |
|
<image>As shown in the figure, there is an animation program where the square $$ABCD$$ on the screen is a black area (including the square's boundary), with $$A(1,1)$$, $$B(2,1)$$, $$C(2,2)$$, and $$D(1,2)$$. A signal gun fires a signal along the line $$y=-2x+b$$. When the signal encounters the black area, the area turns white. The range of values for $$b$$ that can turn the black area white is ___.
| $$3 \leqslant b \leqslant 6$$ |
|
<image>As shown in the figure, $$AB \perp CD$$ at point $$C$$, $$CE \perp CF$$, then there are ___ pairs of complementary angles in the figure.
| $$4$$ |
|
<image>As shown in the figure, in $\vartriangle ABC$, $AC=6$cm, $AB=8$cm, $BC=10$cm, $DE$ is the perpendicular bisector of side $AB$. What is the perimeter of $\vartriangle ADC$ in cm?
| 16 |
|
<image>If the complex number is a pure imaginary number (i is the imaginary unit), then a =.
| 2 |
|
<image>As shown in the figure, a square is divided into two smaller squares and two congruent rectangles. Based on the figure, write a correct equation containing $$a$$ and $$b$$: ___.
| $$a^{2}+2ab+b^{2}=(a+b)^{2}$$ |
|
<image>As shown in the figure, the right triangle COD is rotated counterclockwise to coincide with triangle AOB. If ∠AOD = 125°, then the rotation angle is.
| 35° |
|
<image>As shown in the figure, segments OA and OB are intercepted on the two sides of ∠MON, such that OA = OB; arcs are drawn with A and B as centers and OA as the radius, intersecting at point C; AC, BC, AB, and OC are connected. If AB = 2 cm, and the area of quadrilateral OACB is 4 cm². What is the length of OC in cm?
| 4 |
|
<image>The contingency table for the categorical variables $$X$$ and $$Y$$ is as follows: 1. The smaller the value of $$ad-bc$$, the weaker the relationship between $$X$$ and $$Y$$; 2. The larger the value of $$ad-bc$$, the stronger the relationship between $$X$$ and $$Y$$; 3. The larger the value of $$(ad-bc)^{2}$$, the stronger the relationship between $$X$$ and $$Y$$; 4. The closer the value of $$(ad-bc)^{2}$$ is to $$0$$, the stronger the relationship between $$X$$ and $$Y$$.
| 3 |
|
<image>A class is randomly selected from the senior year of a certain school, and the vision status of 50 students in the class is statistically analyzed based on their college admission health examination forms. The frequency distribution histogram is shown in the figure: If a certain college program A requires a vision of 0.9 or above, then the number of students in the class who can apply for program A is
| 20 |
|
<image>As shown in the figure, points $$E$$ and $$F$$ are two points on side $$BC$$ of parallelogram $$ABCD$$, and point $$G$$ is a point on side $$AD$$. If the area of parallelogram $$ABCD$$ is $$20cm^{2}$$, then the sum of the areas of $$\triangle ABE$$, $$\triangle GEF$$, and $$\triangle DFC$$ is ___.
| $$10cm^{2}$$ |
|
<image>As shown in the figure, the graphs of the functions $$y=-2x$$ and $$y=kx+b$$ intersect at point $$A\left(m,3\right)$$. The solution set for the inequality $$kx+b+2x>0$$ with respect to $$x$$ is ___.
| $$x>-\dfrac {3}{2}$$ |
|
<image>In the isosceles triangle ABC, AB = AC, and ∠A = 20°. The perpendicular bisector of segment AB intersects AB at point D and AC at point E. Connect BE. Then ∠CBE =.
| 60° |
|
<image>A bamboo stick is 10 feet tall. After it breaks, the tip of the bamboo stick touches the ground 3 feet away from the base of the bamboo. The height of the break from the ground is ___ feet.
| $\frac{91}{20}$ |
|
<image>As shown in the figure, to measure the height of the Eiffel Tower in France, a baseline $$AB$$ is selected on the ground, where $$AB = 324\sqrt{4-\sqrt{3}}\ \unit{m}$$. At point $$A$$, the angle of elevation to the top of the tower $$P$$ is $$\angle OAP = 30^{\circ}$$, and at point $$B$$, the angle of elevation to the top of the tower $$P$$ is $$\angle OBP = 45^{\circ}$$. It is also measured that $$\angle AOB = 60^{\circ}$$. What is the height of the tower in meters?
| $$324$$ |
|
<image>As shown in the figure, in parallelogram ABCD, BE bisects ∠ABC, BC = 6, DE = 2, then the perimeter of parallelogram ABCD is ___.
| 20 |
|
<image>Write the result of the following program execution.
| $-3$ |
|
<image>Water resources in Beijing are very scarce. To promote water conservation among residents, a tiered water pricing system was implemented for Beijing residents starting from May 1, 2014, with the detailed implementation rules as shown in the table: A household used a total of 190 cubic meters of water from January 1, 2015, to April 30, 2015. The total water bill for these 4 months is ___ yuan.
| $$\number{970}$$ |
|
<image>As shown in the figure, after folding the four corners of rectangle ABCD inward, they precisely form a seamless and non-overlapping quadrilateral EFGH, where EH=12 cm and EF=16 cm. What is the length of side AD in cm?
| 20 |
|
<image>As shown in the figure, $$AB \parallel CD$$, $$CB$$ bisects $$\angle ACD$$. If $$\angle BCD=28^{ \circ }$$, then the measure of $$\angle A$$ is ___.
| $$124^{\circ}$$ |
|
<image>In the figure, rectangle ABCD has E as the midpoint of BC. When triangle ABE is folded along line AE, point B lands on point F. Connecting FC, if ∠DAF = 18°, then ∠DCF = ____ degrees.
| 36 |
|
<image>If the side length of a regular hexagon is 3, then the length of its longer diagonal is.
| 6 |
|
<image>As shown in the figure, in rectangle ABCD, the angle bisector of ∠ABC intersects AD at point E, and CE is connected. If BC = 7 and AE = 4, then CE =.
| 5 |
|
<image>"The Tortoise and the Hare" tells the story: the leading hare, seeing the tortoise slowly crawling, becomes proud and takes a nap. When it wakes up, it finds the tortoise is almost at the finish line, so it hurriedly chases, but it's too late, and the tortoise reaches the finish line first. Let $$s_{1}$$ and $$s_{2}$$ represent the distances traveled by the tortoise and the hare, respectively, and $$t$$ represent time. The graph that matches the story is ___. (Fill in the number)
| 2 |
|
<image>Scientists, to estimate the most suitable temperature for the growth of a rare plant, placed the plant in different temperature environments. After a certain period, they measured the increase in the plant's height. Some of the data are shown in the table: Scientists hypothesized that there is a quadratic function relationship between $$l$$ and $$t$$. Based on this, the most suitable temperature for the growth of this plant can be inferred to be ___$$\unit{\degreeCelsius }$$.
| $$-1$$ |
|
<image>The system of linear inequalities that can represent the shaded area in the figure is ___.
| $$\left\lbrace\begin{align}& x-y\geqslant 0,\cr& x+y-1\leqslant 0,\cr&y\geqslant -1\end{align}\right .$$ |
|
<image>In the figure, all quadrilaterals are squares. The area of the square represented by the letter B is ______.
| 144 |
|
<image>As shown in the figure, in the cube $$ABCD-A_{1}B_{1}C_{1}D_{1}$$, $$P$$ is a moving point on the face $$BB_{1}C_{1}C$$. If the distance from point $$P$$ to the line $$BC$$ is equal to the distance from point $$P$$ to the line $$C_{1}D_{1}$$, then the trajectory of the moving point $$P$$ is ___. 1. Line 2. Circle 3. Ellipse 4. Parabola
| 4 |
|
<image>As shown in the figure, hexagon ABCDEF and hexagon A'B'C'D'E'F' are similar figures with O as the center of similarity, and OA' : OA = 1 : 2, then B'C' : BC = .
| 1:2 |
|
<image>As shown in the figure, in rhombus $$ABCD$$, diagonals $$AC$$ and $$BD$$ intersect at point $$O$$. Without adding any auxiliary lines, please add one condition: ___, to make quadrilateral $$ABCD$$ a square (fill in one only).
| $$\angle BAD=90^{\circ}$$ |
|
<image>In the figure, $$x_{1}$$, $$x_{2}$$, and $$x_{3}$$ are the independent scores given by three different reviewers for the same question, and $$p$$ is the final score of the question. When $$x_{1}=6$$, $$x_{2}=9$$, and $$p=8.5$$, what is $$x_{3}$$?
| $$8$$ |
|
<image>A social survey organization investigated the monthly income of $$\number{10000}$$ people in a certain area and drew a frequency distribution histogram based on the data (as shown in the figure). To investigate the relationship between residents' income and factors such as age, education, and occupation, a stratified sampling method will be used to select $$100$$ people from these $$\number{10000}$$ for further investigation. How many people should be selected from the monthly income segment $$[\number{2500},\number{3000})$$ (yuan/month)?
| $$25$$ |
|
<image>In △ABC, CD is perpendicular to AB at point D, BE is perpendicular to AC at point E, F is the midpoint of BC, DE = 5, BC = 8, then the perimeter of △DEF is.
| 13 |
|
<image>As shown in the figure, given that the lines $$m \parallel n$$, and $$\angle 1 = 100^{\circ}$$, then the measure of $$\angle 2$$ is ___.
| $$80^{\circ}$$ |
|
<image>As shown in the figure, given that plane α is perpendicular to plane β, on the intersection line l of α and β, a line segment AB = 4 cm is taken. AC and BD are in planes α and β, respectively, and both are perpendicular to the intersection line AB, with AC = 3 cm and BD = 12 cm. Then CD = _____.
| 13cm |
|
<image>As shown in the figure, O is a point on the straight line l, ∠1 + ∠2 = 78°42′, then ∠AOB =.
| 101°18′ |
|
<image>As shown in the figure, $$P$$ is a point outside the circle $$ \odot O$$. Two tangents are drawn from $$P$$ to $$ \odot O$$, touching the circle at points $$A$$ and $$B$$. A secant line is drawn through the midpoint $$Q$$ of $$PA$$, intersecting $$ \odot O$$ at points $$C$$ and $$D$$. If $$QC=1$$ and $$CD=3$$, then $$PB=$$ ___.
| $$4$$ |
|
<image>As shown in the figure, in △ABC, ∠ABC = 45°, AC = 3, F is the intersection point of the altitudes AD and BE. What is the length of segment BF?
| 3 |
|
<image>As shown in the figure, the function relationship between the monthly fee y (yuan) charged by a city's internet service provider and the internet usage time x (hours) is given. When a customer uses the internet for 121 hours per month, they need to pay yuan.
| 99 |
|
<image>As shown in the figure, $\angle ACB=90{}^\circ $, $AC=BC$, $AD\bot CE$, $BE\bot CE$, with the feet of the perpendiculars being $D$ and $E$ respectively. Given $AD=10$ and $DE=6$, then $BE=$.
| 4 |
|
<image>As shown in the figure, the area of quadrilateral $$ABCD$$ is $$42$$ square meters, where the areas of the two smaller triangles are $$3$$ square meters and $$4$$ square meters, respectively. What is the area of the largest triangle in square meters?
| 35 |
|
<image>As shown in the figure, points A and B are both on the graph of the inverse proportion function y = $\frac{k}{x}$ in the second quadrant, and triangle OAB is an equilateral triangle. If AB = 6, then the value of k is.
| -9 |
|
<image>In the figure, in △ABC, ∠C＝90°, D is a point on CB, and DA＝DB＝4, ∠B＝15°, then the length of AC is.
| 2 |
|
<image>As shown in the figure, $AC$ and $BD$ intersect at point $O$. If point $O$ bisects $AC$ and $BD$, how many pairs of congruent triangles are there in the figure?
| 4 |
|
<image>As shown in the figure, AB = AC = 6, $\angle C = {{15}^{\circ }}$, BD is perpendicular to AC and intersects the extension of CA at point D, then BD =.
| 3 |
|
<image>The right figure has ______ line segments.
| 15 |
|
<image>To understand the amount of New Year's money that students can freely支配 this Spring Festival, a department randomly surveyed 10,000 students out of 150,000 junior high school third-year students in the city and created a frequency distribution histogram of the amount of New Year's money these students can freely支配. Estimate the number of third-year junior high school students in the city who can freely支配 200—300 yuan (including 200 yuan, excluding 300 yuan) of New Year's money.
| 30,000 |
|
<image>Among the following figures, the scatter plot that does not match the correlation coefficient $$r$$ is ___ (fill in the number).
| 2 |
|
<image>As shown in the figure, point $$E$$ is on side $$BC$$ of parallelogram $$ABCD$$, and $$AB=BE$$. Line segment $$AE$$ is extended to intersect the extension of $$DC$$ at point $$F$$, with $$\angle F=70^{ \circ }$$. Then, $$\angle D=$$ ___ degrees.
| $$40$$ |
|
<image>As shown in the figure, extend the two pairs of opposite sides of the cyclic quadrilateral $$ABCD$$ to intersect at points $$E$$ and $$F$$. If $$\angle E=30^{\circ}$$ and $$\angle F=50^{\circ}$$, then $$\angle A=$$ ___.
| $$50^{\circ}$$ |
|
<image>As shown in the figure, $\angle 1$, $\angle 2$, $\angle 3$, and $\angle 4$ are four exterior angles of pentagon $ABCDE$. If $\angle A = 120{}^\circ$, then $\angle 1 + \angle 2 + \angle 3 + \angle 4 = $°.
| $300$ |
|
<image>As shown in the figure, in $$\triangle ABC$$, points $$D$$ and $$E$$ are on sides $$AB$$ and $$AC$$ respectively, and $$DE \parallel BC$$. If $$S_{\triangle ADE}=3$$ and $$S_{\triangle CDE}=4$$, then $$AD:DB=$$ ___.
| $$3:4$$ |
|
<image>As shown in the figure, in square $$ABCD$$, an equilateral triangle $$\triangle ABE$$ is constructed inside the square with $$AB$$ as one of its sides. Connect $$DE$$ and $$CE$$. The measure of $$\angle CED$$ is ___.
| $$150^{\circ}$$ |
|
<image>As shown in the figure, in the parallelepiped $$ABCD-A_{1}B_{1}C_{1}D_{1}$$, the number of vectors equal to the vector $$\overrightarrow{AA_{1}}$$ is ___.
| $$3$$ |
|
<image>As shown in the figure, it is a shape similar to Pascal's Triangle. The first and last numbers of the $$n$$th row are ___.
| $$2n-1$$ |
|
<image>In the right triangle ABC, as shown in the figure, fold along ED so that point C lands on point B. Given that the perimeter of triangle ABE is 15, and BD = 6, what is the perimeter of triangle ABC?
| 27 |
|
<image>As shown in the figure, $$∠AOB=∠AOC$$, $$∠BOC=86^{\circ}$$, then $$∠AOB=$$ ___.
| $$137^{\circ}$$ |
|
<image>As shown in the figure, lines $$AB$$ and $$CD$$ intersect at point $$O$$, $$OE⊥AB$$, and $$∠BOD=20^{\circ}$$. Then $$∠COE$$ equals ___ degrees.
| $$70$$ |
|
<image>Assume there are two categorical variables $$X$$ and $$Y$$, with values $$\left \lbrace x_{1},x_{2}\right \rbrace $$ and $$\left \lbrace y_{1},y_{2}\right \rbrace $$, respectively. The $$2\times 2$$ contingency table is as follows: For the same sample, the data that most strongly suggests a relationship between $$X$$ and $$Y$$ is ___. (Fill in the number) 1. $$a=9$$, $$b=8$$, $$c=7$$, $$d=6$$; 2. $$a=9$$, $$b=7$$, $$c=8$$, $$d=6$$; 3. $$a=6$$, $$b=7$$, $$c=8$$, $$d=9$$; 4. $$a=7$$, $$b=6$$, $$c=8$$, $$d=9$$.
| 4 |
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