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chengyewang
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geo623
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/623.png
As shown in the figure, AD and BC intersect at point O, and AB is parallel to CD. If rac{AO}{OD}= rac{2}{3}, then the value of rac{AB}{CD} is ()
C
['\\frac{2}{5}', '\\frac{3}{2}', '\\frac{2}{3}', '\\frac{4}{9}']
multi_choice
geo626
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/626.png
As shown in the figure, the lines l_{1}∥l_{2}∥l_{3} are parallel, and they intersect lines a and b at points A, B, C, D, E, and F respectively. If AB=2, BC=3, and DE=1, then what is the length of EF?
B
['\\frac{2}{3}', '\\frac{3}{2}', '6', '\\frac{1}{6}']
multi_choice
geo645
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/645.png
As shown in the figure, a person starts from point A, moves forward 8 meters, then turns right 60°, moves forward another 8 meters, and then turns right 60° again. If he continues to walk in this manner, how far will he have walked when he first returns to the starting point A?
D
['24m', '32m', '40m', '48m']
multi_choice
geo655
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/655.png
As shown in the figure, in △ABC, ∠ACB=90°, ∠A=30°, BC=4cm, point D is the midpoint of AB, then CD=()
B
['3cm', '4cm', '5cm', '6cm']
multi_choice
geo657
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/657.png
As shown in the figure, ∠1 + ∠2 = 180°, ∠3 = 108°, then the degree of ∠4 is ()
A
['72°', '80°', '82°', '108°']
multi_choice
geo662
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/662.png
As shown in the figure, AB is the diameter of circle O, and CD is a chord of circle O. If ∠ACD = 30°, then what is ∠BAD?
C
['30°', '50°', '60°', '70°']
multi_choice
geo670
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/670.png
As shown in the figure, △ABE is translated 2 cm to the right to obtain △DCF. If the perimeter of △ABE is 16 cm, what is the perimeter of quadrilateral ABFD?
C
['16cm', '18cm', '20cm', '21cm']
multi_choice
geo683
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/683.png
As shown in the figure, PA, PB, and CD are tangent to circle O at points A, B, and E respectively. CD intersects PA and PB at points C and D. If ∠P = 40°, then the sum of ∠PAE and ∠PBE is () degrees.
D
['50°', '62°', '66°', '70°']
multi_choice
geo684
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/684.png
As shown in the figure, AE, AD, and BC are tangent to circle O at points E, D, and F respectively. If AD = 20, then the perimeter of triangle ABC is ()
C
['20', '30', '40', '50']
multi_choice
geo700
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/700.png
As shown in the figure, given that point C is on line segment AB, points M and N are the midpoints of AC and BC respectively, and AB = 8 cm, what is the length of MN in cm?
C
['2', '3', '4', '6']
multi_choice
geo715
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/715.png
As shown in the figure, the slope ratio of the upstream slope AB of the cross-section of the river dam is 3:4, and BC = 6m. What is the length of the slope AB?
C
['6m', '8m', '10m', '12m']
multi_choice
geo789
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/789.png
As shown in the figure, in △ABC, D is the midpoint of AB, and DE∥BC. If the area of △ADE is 3, then the area of △ABC is ()
12
NULL
free_form
geo792
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/792.png
As shown in the figure, in △ABC, points D and E are on AB and AC respectively, and DE∥BC. If AE:EC=2:3 and AD=6, then the length of AB is ()
15
NULL
free_form
geo831
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/831.png
As shown in the figure, in circle O, ∠AOC = 160°, then ∠ABC is equal to ()
80°
NULL
free_form
geo841
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/841.png
As shown in the figure, P is a point on the diagonal AC of the rhombus ABCD. PE is perpendicular to AB at point E, and PF is perpendicular to AD at point F. If PF = 3 cm, then the length of the distance from point P to AB, PE, is ()
3cm
NULL
free_form
geo869
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/869.png
As shown in the figure, in parallelogram ABCD, point M is the midpoint of CD, and DC = 2AD. What is the degree of the angle between AM and BM?
90°
NULL
free_form
geo896
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/896.png
As shown in the figure, ⊙O is the circumcircle of △ABC, and ∠BOC = 110°. What is the measure of ∠A?
55°
NULL
free_form
geo910
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/910.png
As shown in the figure, points A, B, and C are on the circle O, and ∠BOC = 60°. What is ∠BAC equal to?
30°
NULL
free_form
geo928
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/928.png
As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral in circle O. If ∠BOD = 90°, then the measure of ∠BCD is ()
135°
NULL
free_form
geo947
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/947.png
As shown in the figure, a∥b. Place the right-angle vertex of the triangle ruler on line a. If ∠1=40°, then ∠2=()
50°
NULL
free_form
geo960
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/960.png
As shown in the figure, lines a and b intersect at point O. If ∠1 = 30°, then ∠2 equals ()
150°
NULL
free_form
geo965
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/965.png
As shown in the figure, given that the area of square B is 144 and the area of square C is 169, what is the area of square A?
25
NULL
free_form
geo975
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/975.png
As shown in the figure, lines AB and CD intersect at point O, and OE bisects ∠AOD. If ∠COE = 140°, then ∠BOC = ()
80°
NULL
free_form
geo983
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/983.png
In triangle △ABC, ∠C=90°, BC=5, AB=13, what is the value of sinA?
\frac{5}{13}
NULL
free_form
geo1008
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1008.png
As shown in the figure, in circle A with a radius of 5, chords BC and ED correspond to central angles ∠BAC and ∠EAD, respectively. Given that DE = 6 and ∠BAC + ∠EAD = 180°, what is the distance from the center to chord BC?
3
NULL
free_form
geo78
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/78.png
Find x.
4.5
NULL
free_form
geo395
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/395.png
As shown in the figure, AB is the diameter of circle O, and chord CD is perpendicular to AB. If ∠CAB = 25°, then what is ∠BOD?
C
['70°', '65°', '50°', '45°']
multi_choice
geo654
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/654.png
As shown in the figure: AB ∥ CD, the line MN intersects AB at E, and a line HE is drawn through point E perpendicular to MN. Given that ∠1 = 130°, what is the value of ∠2?
B
['50°', '40°', '30°', '60°']
multi_choice
geo779
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/779.png
As shown in the figure, in △ABC, ∠C=90°, ∠A=60°, with A as the center and AC as the radius, draw an arc intersecting AB at D. If the area of the sector ACD (shaded part) is 6π cm², then the length of AB is ()
12cm
NULL
free_form
geo970
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/970.png
As shown in the figure, given that lines AB, CD, and EF intersect at point O, ∠1 = 95°, ∠2 = 53°, what is the measure of ∠BOE?
32°
NULL
free_form
geo11
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/11.png
Express the ratio of \cos A as a decimal to the nearest hundredth.
0.92
NULL
free_form
geo62
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/62.png
Find x so that the quadrilateral is a parallelogram.
41
NULL
free_form
geo94
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/94.png
Find the area of the regular polygon. Round to the nearest tenth.
C
['9.2', '27.7', '55.4', '110.9']
multi_choice
geo238
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/238.png
Find the perimeter of the \triangle W Z X, if \triangle W Z X \sim \triangle S R T, S T = 6, W X = 5, and the perimeter of \triangle S R T = 15.
B
['10.5', '12.5', '15', '17.5']
multi_choice
geo254
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/254.png
Find the area of the figure. Round to the nearest tenth if necessary.
C
['512', '562.3', '612.5', '713.1']
multi_choice
geo421
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/421.png
As shown in the figure, Xiaolan made a conical birthday hat using colored paper. If the radius of the base is 5 cm and the slant height is 10 cm, without considering the seam, what is the lateral surface area of this cone?
D
['250πcm^{2}', '125πcm^{2}', '100πcm^{2}', '50πcm^{2}']
multi_choice
geo425
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/425.png
As shown in the figure, the street lamp on the utility pole is 8 meters above the ground. Xiao Ming (AB), who is 1.6 meters tall, stands at point A, which is 20 meters away from the base of the utility pole (point O). What is the length of Xiao Ming's shadow AM?
B
['4米', '5米', '6米', '8米']
multi_choice
geo526
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/526.png
As shown in the figure, the diameter AB of circle O is 2. Points C and D are on circle O, and ∠ADC = 30°. What is the length of BC?
B
['√{2}', '√{3}', '2', '1']
multi_choice
geo532
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/532.png
As shown in the figure, the extensions of the two pairs of opposite sides of the inscribed quadrilateral ABCD in circle O intersect at points E and F, respectively. If ∠E = ∠F = 35°, what is the degree measure of ∠A?
B
['35°', '55°', '60°', '65°']
multi_choice
geo557
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/557.png
As shown in the figure, AB is the diameter of circle O with a radius of 4. P is an arbitrary point on the circle other than A and B. The bisector of ∠APB intersects circle O at point C. Connect AC and BC. The line containing the midline of △ABC intersects circle O at points E and F. What is the length of EF?
A
['4√{3}', '2√{3}', '6', '2√{5}']
multi_choice
geo590
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/590.png
As shown in the figure, the side length of the rhombus ABCD is 10. Circle O is tangent to AB and AD at points E and F, respectively, and is tangent to BG at point G. If AO = 5 and the radius of circle O is 3, what is the length of BG?
C
['4', '5', '6', '7']
multi_choice
geo602
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/602.png
As shown in the figure, AB is tangent to circle O at point B. The extension of AO intersects circle O at point C. Connect BC. If ∠ABC = 120° and OC = 2, then the length of chord BC is ()
C
['2', '√{3}', '2√{3}', '4']
multi_choice
geo636
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/636.png
As shown in the figure, given that AB ∥ CD, AD intersects BC at point P, AB = 4, CD = 6, AP = 5, then the length of AD is equal to ()
A
['12.5', '10', '9', '7.5']
multi_choice
geo638
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/638.png
As shown in the figure, △ABC is similar to △DEF with a similarity ratio of 1:2. If BC = 1, then the length of EF is ()
B
['1', '2', '3', '4']
multi_choice
geo694
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/694.png
As shown in the figure, in △ABC, the bisectors of ∠ABC and ∠ACB intersect at point O. If ∠BOC = 130°, then the measure of ∠A is ()
C
['100°', '90°', '80°', '70°']
multi_choice
geo695
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/695.png
As shown in the figure, AB is a chord of circle O, AB = 6, OD is perpendicular to AB at point D, and intersects at point C. If OB = 5, what is the length of CD?
B
['0.5', '1', '1.5', '2']
multi_choice
geo735
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/735.png
As shown in the figure, given that the area of parallelogram ABCD is 24 cm^2, point P is a moving point on side CD. What is the area of the shaded part in the figure?
12cm^2^
NULL
free_form
geo739
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/739.png
As shown in the figure, in the parallelogram ABCD, the diagonals AC and BD intersect at point O. The line segments MN, PQ, and EF pass through point O. Given that BC = 10 and the height from BC is 6, find the area of the shaded region.
30
NULL
free_form
geo760
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/760.png
As shown in the figure, in the right triangle ABC, ∠C=90°, ∠ABC=30°, and AB=16. The triangle ABC is translated to the right along CB to obtain triangle DEF. If the area of quadrilateral ABED is equal to 32, then the translation distance is equal to ()
4
NULL
free_form
geo803
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/803.png
As shown in the figure, it is a schematic diagram of the cross-section of a reservoir dam. Among them, AB and CD respectively represent the horizontal lines of the upper and lower surfaces of the reservoir. ∠ABC=120°, and the length of BC is 100m. What is the height h of the reservoir dam?
50√{3}m
NULL
free_form
geo818
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/818.png
As shown in the figure, in order to green the barren mountain, a certain place plans to lay water pipes from the well house at the foot of the mountain along the slope, and build a pumping station on the slope to spray the green area on the slope. It is now measured that the angle between the slope and the horizontal plane is 30°. To make the height of the water outlet 35m, how long should the water pipe be prepared?
70m
NULL
free_form
geo843
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/843.png
As shown in the figure, in rhombus ABCD, ∠DAC=25°, then ∠B=()
130°
NULL
free_form
geo873
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/873.png
Given: As shown in the figure, in the parallelogram ABCD, AB=4, AD=7, the bisector of ∠ABC intersects AD at point E. Find the length of ED.
3
NULL
free_form
geo876
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/876.png
As shown in the figure, in the parallelogram ABCD, ∠C = 108°, BE bisects ∠ABC, then ∠AEB equals ()
36°
NULL
free_form
geo969
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/969.png
As shown in the figure, place two vertices of a right triangle with a 45° angle on the opposite sides of a ruler. If ∠1 = 15°, then what is the degree of ∠2?
30°
NULL
free_form
geo977
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/977.png
Given that AB ∥ CD and ∠ACD = 55°, find ∠BAC.
55°
NULL
free_form
geo986
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/986.png
As shown in the figure, in △ABC, DE∥BC, rac{DE}{BC}= rac{1}{3}, AD=2. What is the value of BD?
4
NULL
free_form
geo1020
/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1020.png
As shown in the figure, in the plane rectangular coordinate system, circle A passes through the origin O and intersects the x-axis and y-axis at points B and C, respectively. Given B(8,0) and C(0,6), what is the radius of circle A?
5
NULL
free_form
stat1003
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1003.png
To improve the quality of life for urban residents, the government renovated supporting facilities, including four types: leisure facilities, children's facilities, entertainment facilities, and fitness facilities. After the renovation, the government conducted a public satisfaction survey on these facilities in two communities, A and B, with the results (unit: points, full score 100) shown in the table below: Leisure Facilities Children's Facilities Entertainment Facilities Fitness Facilities Community A 80 82 80 81 Community B 70 70 81 80 If the facilities are assessed with a weighting ratio of 1:1:2:2, which community has higher satisfaction (fill in 'A' or 'B')?
A
NULL
free_form
stat1006
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1006.png
The math interest group conducted a repeated experiment of 'randomly tossing a thumbtack.' After multiple trials, they obtained the following data: Number of repeated trials: 10, 50, 100, 500, 1000 Number of times the thumbtack landed tip-up: 5, 15, 36, 205, 403 Based on this, the probability of a thumbtack landing tip-up when tossed randomly can be estimated to be approximately ______. (Rounded to one decimal place)
0.4
NULL
free_form
stat101
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/101.png
During the online learning period to combat 'COVID-19', a school aimed to study the weekly physical exercise time of 1,000 ninth-grade students. The school randomly surveyed 50 ninth-grade students and created a bar chart based on the data. According to the chart data, the number of students among these 50 whose weekly physical exercise time is not less than 7 hours is ______ students.
20
NULL
free_form
stat1011
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1011.png
The germination test results of a batch of Tibetan barley seeds under the same conditions are shown in the table below: Number of seeds per test | 50 | 1000 | 3000 | 4000 | 6000 | 10000 Number of germinated seeds | 47 | 960 | 2840 | 3800 | 5710 | 9500 Estimate the probability of germination for this batch of Tibetan barley seeds. (Round the result to 0.01)
0.95
NULL
free_form
stat1012
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1012.png
In a science and innovation competition, the scores of all participating students are recorded in the following table: Scores (points): 80 85 90 95 100 Number of students: 11 14 12 9 5 The median score of the participating students is ______ points.
90
NULL
free_form
stat1013
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1013.png
In order to enrich campus life and enhance class cohesion, a certain school organized a fun sports event for seventh-grade students. The following table shows the scores (in points) of three groups from Class 1, Grade 7, in various competition events. If a group with better performance and strong overall capability is to be selected to represent the class in the whole grade competition, which group should be chosen? (Fill in 'One', 'Two', or 'Three')
Three
NULL
free_form
stat1016
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1016.png
A certain shooter records their shooting scores under the same conditions as follows: Based on the stability of frequency estimation, estimate the probability that the shooter hits a score of '9 or above' in a single shot. (Keep the result to two decimal places).
0.8
NULL
free_form
stat1018
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1018.png
The table below records the number of shots and the number of bullseyes by a certain shooter who can perform consistently. Based on this, estimate the probability of the athlete hitting the bullseye (accurate to 0.1) ________.
0.8
NULL
free_form
stat102
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/102.png
As shown in the figure, if two of the switches S1, S2, S3 are randomly closed, the probability of making both bulbs light up simultaneously is ________.
1/3
NULL
free_form
stat1020
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1020.png
To inspire students to care for plants and protect the ecological environment, a school organized a tree-planting activity. After the activity, the tree-planting statistics for each student in Class 8 (1) were recorded and summarized in the following table: Tree count 3 4 5 6 Number of students 15 10 15 5 It is known that the average number of trees planted per student in Class 8 (1) is 4. The median and mode of this data are ______.
4 and 3
NULL
free_form
stat1022
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1022.png
The germination results of a certain plant's seeds under identical conditions are as follows: Number of seeds in each batch: 50, 100, 300, 400, 500, 1000 Number of seeds germinated: 45, 96, 283, 380, 475, 948 The estimated probability of germination for these plant seeds is ________. (Answer to 0.01 precision)
0.95
NULL
free_form
stat1027
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1027.png
In order to determine whether the school has implemented the 'double reduction' policy and effectively reduced students' homework burden, Class 9(1) randomly surveyed 10 students about the duration of time they spend completing homework each day. The survey data is summarized in the table below: Duration (h) | 2.5 | 1.5 | 1 | 0.5 Number of Students | 1 | 2 | 4 | 3 Estimate the average time Class 9(1) students spend completing homework each day, approximately _______ h.
1.5
NULL
free_form
stat1029
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1029.png
In a ninth-grade mathematics simulation test at a certain school, the mathematics scores of six students are shown in the table below. The median of this dataset is ________.
96
NULL
free_form
stat1034
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1034.png
A class plans to go on an educational trip during the summer vacation and intends to customize a batch of backpacks of equal capacity. The activity organizer surveyed the preferences of all 40 students in the class and obtained the following data: Capacity/L 23 25 27 29 31 33 Number of Students/Persons 4 3 5 23 3 2 To meet the needs of the majority, the capacity of the backpacks to be customized is _______L.
29
NULL
free_form
stat104
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/104.png
As shown in the given chart, it shows the weights (in kg) of a certain fruit that Lily purchased 4 times. What is the median weight of the 4 instances?
4
NULL
free_form
stat1040
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1040.png
After studying the physics chapter "Current and Circuit," Xiao Liang designed the circuit diagram shown in the figure, where S1, S2, and S3 represent three switches that can be closed, ⨁ represents a light bulb, and “⊥” represents a battery. When two of the three switches (S1, S2, S3) are randomly closed, the probability of the light bulb lighting up is _______.
2/3
NULL
free_form
stat1042
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1042.png
An appliance store, in order to motivate its salespeople, has established a reward and penalty system: any salesperson exceeding the sales target will receive a bonus. The store compiled the sales figures of all salespeople from last month and organized the data in the following table: Last Month's Sales (in Ten Thousand Yuan) | 12 | 13 | 14 | 15 | 16 Number of People | 2 | 1 | 5 | 4 | 3 If the store manager wants approximately half of the salespeople to receive bonuses, then it would be appropriate to set this month's sales target as _______ ten thousand yuan.
14
NULL
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stat1052
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1052.png
A study group conducting an experiment on 'estimating probability using frequency' calculated the frequency of a particular outcome and created a table. The probability of this outcome occurring is approximately ________ (accurate to 0.1).
0.3
NULL
free_form
stat1055
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1055.png
As shown in the chart, it is a statistical table (in minutes) of sports activity time at school for classmate Xiao Ruan this week. What is the median of the sports activity time for Xiao Ruan over these five days?
70
NULL
free_form
stat1063
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1063.png
In an English test, the number of students and average scores for Grade 7 (Class 1) and Grade 7 (Class 2) are shown in the table below: Class Number of Students Average Score (in points) Grade 7 (Class 1) 48 80 Grade 7 (Class 2) 52 85 Calculate the average score of these two classes, which is __________ points.
82.6
NULL
free_form
stat1065
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1065.png
According to statistics, the community of mathematicians is a long-lived group. A research team randomly sampled the ages of several mathematicians aged 90 and above from the 'Biographical Dictionary of Mathematicians,' which contains records of approximately 2,200 mathematicians. The data was organized and analyzed, and the statistical frequencies (percentages) are provided below. Which of the following conclusions is incorrect ( )?
D
['The team has counted the ages of 100 mathematicians.', 'The value in the statistical table is 5.', 'The age group with the most long-lived mathematicians is 92-93 years old.', "The number of mathematicians aged 96-97 in the 'Mathematician Biography' is estimated to be 110."]
multi_choice
stat107
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/107.png
If the bar chart shows the unit price of apples for the first three purchases, and the unit price of apples for the fourth purchase is 8 yuan/kg, it is found that the median of these four unit prices is exactly the same as the mode, then a =
8
NULL
free_form
stat109
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/109.png
If a computer is used to simulate the results of tossing a beer bottle cap, as the number of trials increases, the frequency of 'convex side up' shows a certain stability. The probability of 'convex side up' can be estimated as ___ (accurate to 0.001).
0.440
NULL
free_form
stat11
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/11.png
The 'Zhao Shuang's diagram of a chord' is composed of four congruent right triangles and a smaller square in the middle, forming a larger square (as shown in the figure). Xiao Liang randomly throws a dart into the interior region of the larger square. If the lengths of the two legs of the right-angled triangle are 2 and 1, respectively, what is the probability that the dart lands in the smaller square (shaded region)? ______.
1/5
NULL
free_form
stat12
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/12.png
As shown in the figure, switches K1, K2, and K3 are in the open state. If two of the switches K1, K2, and K3 are closed randomly, what is the probability that the two lamps light up simultaneously?
1/3
NULL
free_form
stat131
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/131.png
A school's student participation in extracurricular interest groups is shown in the chart. If the Information Technology group has 40 people, how many people are in the Labor Practice group?
60
NULL
free_form
stat138
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/138.png
Xiao Hui drew a pie chart based on the output data of high-tech industries in the first quarter of 2023 released by the municipal statistics bureau. What is the central angle of the sector corresponding to 'New Materials'? _____________________
72°
NULL
free_form
stat140
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/140.png
As shown in the figure, the bar chart describes the number of parts processed daily by workers in a certain workshop. The median number of parts processed daily by these workers is __________.
6
NULL
free_form
stat148
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/148.png
As shown in the figure, Xiao Liang has drawn two incomplete statistical charts based on the number of students in the class who like four types of ball games (each student in the class chooses one of these four kinds of ball games). The number of students who like 'table tennis' is ____.
20
NULL
free_form
stat15
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/15.png
As shown in the figure, two concentric circles are divided into eight equal parts by four diameters. What is the probability of a dart landing in the black region?
1/2
NULL
free_form
stat150
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/150.png
As shown in the circuit diagram, the probability that the light bulb does not light up when two of the switches S1, S2, and S3 are randomly closed is _____.
1/3
NULL
free_form
stat154
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/154.png
The frequency distribution histogram of the housework time for Class 7(1) with 40 students last week is shown in the figure. Let the median of this data be mh, then m ________ 2.6 (fill with '>', '=', '<').
<
NULL
free_form
stat164
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/164.png
A dairy company plans to export a batch of milk powder with a specification of 500 grams per can. There are two suppliers, A and B, offering the goods. Their prices are the same, and the quality is also similar. The quality inspector randomly samples 15 cans from each supplier for testing. The measured average weight of both batches is 500 grams, and the weight data is displayed as a broken line statistics chart. Based on the chart, compare the variances of the weights of milk powder from suppliers A and B, denoted as S²_1 and S²_2 (fill in '>' or '=' or '<').
<
NULL
free_form
stat167
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/167.png
As shown in the figure, during a physical education class, six students A, B, C, D, E, and F stand at the six vertices of a regular hexagon (facing the interior of the hexagon) to play a passing game. The rule is: the ball cannot be passed to oneself or to the person on the immediate left or right. If the ball is currently with A, what is the probability that after two passes, the ball ends up back with A?
1/3
NULL
free_form
stat189
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/189.png
4. Two people, A and B, play a game. Each of them randomly picks a card. If the product of the two numbers is even, A wins; otherwise, B wins. Based on this rule, _______ has a higher chance of winning.
A
NULL
free_form
stat198
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/198.png
Company A and Company B have compiled the following line charts based on car sales over the past few years. From 2010 to 2014, which of these two companies experienced faster sales growth?
Company A
NULL
free_form
stat199
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/199.png
As shown in the figure, there are 9 blind boxes placed horizontally on the shelf, all with identical outer packaging. Each blind box contains one item. There are 5 blind boxes containing product A and 4 blind boxes containing product B. If one blind box is randomly selected, which product is more likely to be drawn? (Answer with 'A' or 'B')
A
NULL
free_form
stat202
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/202.png
As shown in the diagram, a Zhaoshang chord diagram is formed by four congruent right triangles and a small square. If a dart is randomly thrown onto the board, what is the probability that the dart lands in the shaded area?
1/4
NULL
free_form
stat203
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/203.png
As shown in the figure, the spinner is divided into four equal sectors. If the spinner is spun twice, what is the probability that the pointer lands in the gray region both times?
1/4
NULL
free_form
stat206
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/206.png
As shown in the figure, one of the switches S1 or S2 in the circuit diagram is randomly closed. What is the probability that the light bulb will light up?
1/2
NULL
free_form
stat21
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/21.png
As shown in the figure, a school conducted a survey on students' commuting methods and produced an incomplete pie chart. If the school has a total of 1500 students, estimate how many of them walk to school_______.
600
NULL
free_form
stat210
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/210.png
A forestry bureau has created a line chart to display the survival rate of a certain type of transplanted sapling. From the chart, estimate the survival probability of this transplanted sapling (accurate to 0.1).
0.8
NULL
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