Khan Academy SAT Math Practice 2

In a particular county, a sample of the population showed that 84% of the households lived in the same residence as they had the previous year. The estimate had a margin of error of 1.5% at the 90% confidence level. If the county has 50,000 households, which of the following best estimates the number of households that lived in the same residence as they had the previous year, at the 90%confidence level?

41250 to 42750

3/(2+i)

6−3i/5

A circle in the xy plane has a center at (-32.7, -9.08) and a radius of square root of 10. Which of the following is an equation of the circle?

(x+32.7)^2 + (y+9.08)^2 =10

Which of the following is the measure of the above angle in radians?

5pi/3

A circle in the xy plane has the equation shown above. How long is the radius of the circle? (x-17)^2 + (y-19)^2 = 49

7

A circle in the xy-plane has its center at [(-2/3),(-3/4] and radius 5. Which of the following is an equation of the circle?

[x + (2/3)]^2 + [y + (3/4)]^2

A circle in the xy-plane contains the points (-1,1), (1,1) and (-1,-1). Which of the following is an equation of the circle?

x^2 + y^2 − 2 = 0

−8(7i−3i^2)

−56i−24

(3−i)^3

18−26i

A circle in the xy-plane has the equation (x+17.5)^2 + (y-15.3)^2 = 18.1

Center: (-17.5,15.3) Radius: Square root of 18.1

A circle with its center at C passes through point P and is graphed in the xy-plane at left. Which of the following is an equation for the graph of the circle?

(x+2)^2 + (y+3)^2 = 26

A circle in the xy-plane has its center at (11,12). If the point (13,14) lies on the circle, which of the following is an equation of the circle?

x^2 + y^2 − 22x − 24y = −257

A circle in the xy place has its center at (-2.8, 6.1) and radius 4.2. Which of the following is an equation of the circle?

(x + 2.8)^2 + (y - 6.1)^2 = 17.64

2x 2 − 2 11 ​ x− 2 3 ​ =0space, 2, x, start superscript, 2, end superscript, minus, start fraction, 11, divided by, 2, end fraction, x, minus, start fraction, 3, divided by, 2, end fraction, equals, 0 What are the solutions to the equation above?

x = -1/4 and 3

x 2 −13x+30=0space, x, start superscript, 2, end superscript, minus, 13, x, plus, 30, equals, 0 What are the solutions to the equation above?

3,10

A contractor must build a wheelchair ramp with a recommended 8 degrees of elevation above the horizontal to reach a door on a wall, as shown above. If the elevation from the sidewalk to the bottom of the door is 3.8 feet ft how many feet from the wall must the ramp begin? (Round your answer to the nearest tenth of a foot.)

27

A circle with its center at M passes through point P and is graphed in the xy-plane at left. Which of the following is an equation for the graph of the circle?

x^2 + (y-1)^2 = 25

2x 2 +5x−k=0space, 2, x, start superscript, 2, end superscript, plus, 5, x, minus, k, equals, 0 In the equation above, kkk is a constant. For what value of kkk does the equation have exactly one distinct real solution?

-25/8

(x+20)^2 + (y-30)^2 = 225

30

Which of the following is an equation of the circle?

(x+8)^2 + y^2 = 100

(−3+2i)(1−i^3)

-5-i

A circle in the xy place has the equation 36x^2 + 36y^2 - 12x - 27y - 8 = 8

5/8

A circle with its center at C passes through point P and is graphed in the xy-plane at left. Which of the following is an equation for the graph of the circle?

(x - 3)^2 + (y - 1)^2 = 50

A circle in the xy-plane has its center at (44,-34) and radius of the square root of 3. Which of the following is an equation of the circle?

(x-44)^2 + (y+34)^2 = 3

8 p ​ −2 3 ​ = 3 ​ +3 p space, 8, square root of, p, end square root, minus, 2, square root of, 3, end square root, equals, square root of, 3, end square root, plus, 3, square root of, p, end square root What value of p is the solution to the above equation?

D 27/25

A circle in the xy-plane has the equation x^2 + y^2 - 14y - 51 = 0. What is the center of the circle?

(0,7)

1−i 1 ​ space, start fraction, 1, divided by, 1, minus, i, end fraction Which of the following is equivalent to the complex number shown above?

(1+i)/2

4p ^1/2 + 5p=0 What is the least value of p that is a solution to the above equation?

0

Li Qiang is listening to a symphony that has 222 movements. The first movement has 333 beats per measure and the second movement has 444 beats per measure. The symphony has 446 measures. In an attempt to count the beats, Li Qiang counts at least xxx of the beats in the first movement and exactly b beats in the second movement. Let aaa be the number of beats in the first movement and b be the number of beats in the second movement. Which of the following inequalities must be true?

x/3 + b/4 less than or equal to 446

i 11 +i 13 space, i, start superscript, 11, end superscript, plus, i, start superscript, 13, end superscript Which of the following is equivalent to the complex number shown above?

0

A circle in the xy-plane has its center at the point (0.4,−0.3). If the point (6,5) lies on the circle, what is the diameter of the circle? Round the answer to the nearest tenth.

15.4

(5−7i+i^2)+(8i^3+12)

16

(10−8i 3 )−(6+i)space, left parenthesis, 10, minus, 8, i, start superscript, 3, end superscript, right parenthesis, minus, left parenthesis, 6, plus, i, right parenthesis Which of the following is equivalent to the complex number shown above?

4 + 7i

A circle in the x y-plane has the equation: (y - 4/5)^2 + (x + 7/10)^2 - 30 = 0 What is the radius of the circle? Round the answer to the nearest tenth.

5.5

1−i 2 ​ space, start fraction, 2, divided by, 1, minus, i, end fraction Which of the following is equivalent to the complex number shown above?

3/4

In a poll of 14697 randomly selected adults in the United States, those polled spent an average of $95 per day in November of last year, as compared with $91 per day in November two years ago. The estimates had a margin of error of $4 at the 95% confidence level. Which of the following is a reasonable claim to make based on this sample?

It is plausible that average daily spending of adults in the United States remained the same in November of last year as it was in November two years ago.

A company sells candy in jars that each have a volume of 333 cups. Each jar is filled above a certain line, guaranteeing that it has more than 8, divided by, 3, cups of candy. Which of the following graphs shows the possible volumes of candy, ccc, in cups, a customer may have, given that they bought j jars of candy?

B

Anya has two different sized cylindrical coffee mugs. The larger mug has an internal height of 151515 centimeters (\text{cm})(cm)left parenthesis, c, m, right parenthesis, and the smaller mug has an internal height of 10\,\text{cm}10cm10, space, c, m. Both mugs have an internal diameter of 8\,\text{cm}8cm8, space, c, m. Which of the following is closest to the difference in cubic centimeters (\text{cm}^3)(cm 3 )left parenthesis, c, m, start superscript, 3, end superscript, right parenthesis between the internal volume of the larger mug and the internal volume of the smaller mug?

251 cm^3

A vegetable stand sells p pumpkins for $5.00$5.00dollar sign, 5, point, 00 each and s squashes for \$3.00$3.00dollar sign, 3, point, 00 each. On Monday, the stand sold 666 more squashes than pumpkins and made a total of \$98.00$98.00dollar sign, 98, point, 00. Which system of equations can be used to determine the number of pumpkins and squashes sold?

5p + 3s = 98 p = s + 6

A tent forms an equilateral triangular prism, with both triangular faces exposed. Each side of the triangular face has a length of 196 centimeters and the tent is 250 cm long. What is the height, in centimeters, of the tent?

98 times the squareroot of 3

Caleb is designing a conveyor belt that has to move manufactured products up an incline, as shown above. To avoid products sliding or toppling, he has determined an ideal angle above the horizontal of 0.19 radians. What distance, ddd, in meters, will the product be conveyed using Caleb's design? (Round your answer to the nearest tenth of a meter.)

16.3

Anouk is an engineer planning sound and lighting for a free concert in the park. The concert was advertised with a promise to use no more than 108108108 kilowatts \text{(kW)}(kW)left parenthesis, k, W, right parenthesis of power. It was determined that the main contributors to power usage, speakers and floodlights, use 1.8 \text{ kW}1.8 kW1, point, 8, space, k, W and 2.2 \text{ kW}2.2 kW2, point, 2, space, k, W, respectively. Anouk also must keep within her budget of \$3{,}300$3,300dollar sign, 3, comma, 300. The rental company is charging \$75$75dollar sign, 75 for each speaker and \$42$42dollar sign, 42 for each floodlight. Which of the following combinations meets Anouk's requirements?

26 speakers and 13 floodlights

A circle in the xy-plane has its center on the line y=1. If the point (2,-3) lies on the circle and the radius is 4, which of the following could be the center of the circle?

(2,1)

Prior to the 2014 elections, 1000 randomly selected Louisiana voters were surveyed about what single issue would most likely influence their vote. Of those surveyed,560 voters answered that the state of the economy would most influence their vote. Based on this information, which statement about all voters in Louisiana is most appropriate?

Approximately 56% of all Louisiana voters thought the state of the economy would most influence their voting.

A circle in the xy-plane has its center at the point (-6,1). If the point (7,12) lies on the circle, what is the radius of the circle? Round the answer to the nearest tenth.

17

A circle in the xy-plane has the equation: 3.5(x+2.2)^2 + 3.5(y-11.1)^2 - 21 = 0 What is the radius of the circle? Round the answer to the nearest tenth.

2.4

Julia mows lawns in the summer for $15 per lawn. It costs Julia between $2 and $4 to mow 1 lawn. If l represents the number of lawns Julia mows, which graph correctly shades the possible values of Julia's net earnings, d, in dollars?

B

2 times the (squareroot of 9x) - 6 = 10 -2 squareroot of x What value of xxx is the solution to the above equation?

4

If theta = pi/2 radians which of the following shows the measure of theta in degrees?

90 degrees

A circle in the xy-plane has the equation (x+18.5)^2+(y-3.1)^2=71 What is the center of the circle?

(-18.5,3.1)

Vijay needs to take a taxi, which costs a flat fee of 333 dollars, plus an additional 444 dollars per mile. If Vijay has aaa dollars with him, which inequality shows the number of miles, mmm, he can afford to travel in the taxi?

0 m . a/4 - 3/4

A circle has a circumference of 12pi ft. An arc x in this circle has a central angle of 45 degrees. What is the length of x?

3pi/2 ft

K=(4.14⋅10 −15 )ν−ϕ In night vision goggles, light rays cause electrons to be projected from a metal surface. The above equation relates the kinetic energy in electron volts \text{(eV)} (eV)left parenthesis, e, V, right parenthesis, KKK, of emitted electrons to the frequency in hertz, \nuν, of incident light rays and the work function, \phiϕ, in \text{eV} eVe, V, of the metallic surface. In a particular set of night vision goggles, the electrons emitted must have a kinetic energy of at least 2.46 \text{ eV} 2.46 eV2, point, 46, space, e, V. If the frequency of incoming light rays is less than 9.60 \cdot 10^{14} 9.60⋅10 14 9, point, 60, dot, 10, start superscript, 14, end superscript hertz , which of the following systems of inequalities best models the relationship between the work function, \phiϕ, and the light source frequency, \nuν ?

B

In order to keep a malfunctioning satellite from falling into the earth, space agency officials decide to use a powerful rocket. At the time the rocket is attached, the satellite will be traveling with an initial velocity, v_0v 0 ​ v, start subscript, 0, end subscript, and for every second that the rocket fires, it will add approximately 180 180180 meters per second\, \left ( \dfrac {\text{m}} {\text{s}} \right )( s m ​ )space, left parenthesis, start fraction, m, divided by, s, end fraction, right parenthesis to this velocity. In order to ensure safety on earth, the velocity must be increased to at least 3{,}800 \, \dfrac {\text{m}} {\text{s}} 3,800 s m ​ 3, comma, 800, space, start fraction, m, divided by, s, end fraction . Also, the rocket can fire for no more than 444 seconds. For the initial velocity of the satellite, v_0v 0 ​ v, start subscript, 0, end subscript, which of the following systems of inequalities best models this situation, where ttt is time, in seconds, after the rocket is first fired?

A v + 180t 3,800 t . 4

Which of the following is the value of sin(pi/2)

1

On a cloudy night, Madhu, an aviation meteorologist, places a bright light on the ground to shine up at the clouds above, and then he moves to a point exactly 50 feet away from the light. He then measures the angle of inclination to the spot of light on the base of the clouds above, as shown in the figure. If Madhu measures the the angle of inclination to be 36.5 at a height of 4 ft]above the ground, what is the height of the cloud base above the ground, h, to the nearest foot?

41

k= 10+3k ​ −4space, k, equals, square root of, 10, plus, 3, k, end square root, minus, 4 What are all the possible values of k that satisfy the equation above?

-2 and -3

1+3i 5 ​ space, start fraction, 5, divided by, 1, plus, 3, i, end fraction Which of the following is equivalent to the complex number shown above?

(1-3i) divided by 2

A circle in the xy-plane has its center on the line x = 3. If the point (4,5) lies on the circle and the radius is square root of 2, which of the following could be the center of the circle?

(3,4)

A circle with its center at C passes through point P and is graphed in the xy-plane at left. Which of the following is an equation for the graph of the circle?

(x + 1)^2 + y^2 = 64

A circle with its center at C passes through point P and is graphed in the xy-plane at left. Which of the following is an equation for the graph of the circle?

(x - 1)^2 + (y + 2)^2 = 50

2x 2 +5x−k=0space, 2, x, start superscript, 2, end superscript, plus, 5, x, minus, k, equals, 0 In the equation above, kkk is a constant. For what value of kkk does the equation have exactly one distinct real solution?

0

n+2= a−n ​ space, n, plus, 2, equals, square root of, a, minus, n, end square root For what value of the constant a does the above equation have n=1 as the only solution?

10

Researchers measured the heart rates of several randomly selected astronauts exercising on stationary bicycles during long-term space missions. The researchers found the mean heart rate of the astronauts was 155 beats per minute with a margin of error of 12 beats per minute at a 90 percent confidence level. Which of the following is the most plausible value for the mean heart rate of all astronauts exercising on stationary bicycles during long-term space missions?

160 beats per minute

The change machine at an arcade gives change in the form of 252525-cent coins (quarters) and one-dollar bills. The manager of the arcade would like at least \$50$50dollar sign, 50 worth of quarters and \$100$100dollar sign, 100 worth of one-dollar bills in the machine at all times. Also, the manager does not allow more than \$500$500dollar sign, 500 in the machine at any time. What is the maximum number of quarters the manager would allow in the change machine?

1600

In the circle C shown at left, a central angle of 150 degrees intercepts an arc 15pi cm in length. Which of the following best approximates the length of the radius of the circle

18 cm

A top is formed by fusing two identical right circular cones by their bases as shown at left. The height of the top, hhh, which is the distance between the two cone points, is 666 centimeters \text{(cm)}(cm)left parenthesis, c, m, right parenthesis. The diameter of the circular cone bases, ddd, is also 6\,\text{cm}6cm6, space, c, m. What is the volume of the top, in cubic centimeters?

18 pi

The approximate height and base diameter of a conical metal valve plug are shown in the diagram above in centimeters What is the distance, d, in centimeters, from the vertex to the outer edge of the circular base? (Round your answer to the nearest tenth of a centimeter.)

4.8

In a baseball game, a player must touch 444 bases to get a run. However, some players get "out" before reaching the 4th , in which case the bases don't contribute towards a run. Let b be the total number of bases a player touches in one game and r be the total number of runs he gets from those bases. Which of the following graphs shows the possible number of bases a player touches, given the number of runs he gets?

C

(x-16)^2 + (y+25)^2 = 36 A circle in the xy-plane has the equation shown above. Which of the following correctly describes the location of the center of the circle and the length of its radius?

Center: (16,-25) Radius: 6

In a study of 40 randomly selected captive Octopus vulgaris, researchers found that the octopi could learn to integrate visual and tactile information to find food after a mean of 119119119 trials. The estimate had a margin of error of 181818 trials at a 95% confidence level. Which of the following is the most reasonable conclusion about the number of trials it would take all captive Octopus vulgaris in general to learn to find the food?

The evidence suggests that the mean number of trials would be between 101 and 137 trials.

Priyanka's car gets a maximum of 353535 miles per gallon. According to a particular convention, the "wear" on a vehicle is at least times 15/4 the total number of miles driven plus the total number of gallons used. For Priyanka's car, let m be the total number of miles driven, let g be the total number of gallons used, and let www be the "wear". Which of the following systems of inequalities correctly represents these relationships?

w−g≥15/4m m≤35g

, start fraction, 2, divided by, 1, minus, i, end fraction Which of the following is equivalent to the complex number shown above?

1 + i

In order to bring his business to the next level, Christov wants to gain at least 2{,}0002,0002, comma, 000 followers on a popular social media platform. From his own personal account, he knows that each original post gains him approximately 333 new followers and every 555 reposts gains about 111. Which of the following inequalities represents the numbers of posts, PPP, and reposts, RRR, Christov needs to reach his goal of gaining at least 2{,}0002,0002, comma, 000 followers?

3p + 0.2r . 2,000

Prachi needs between 240240240 and 260260260 total feet of fence panels. The home improvement store has 242424 short (6(6left parenthesis, 6-foot))right parenthesis fence panels and 282828 long (8(8left parenthesis, 8-foot))right parenthesis fence panels in stock. Which of the following combinations of fence panels could she buy?

6 short fence panels and 26 long fence panels