Praxis core academic skills for educators: Mathematics Diagnostic Test

Parker spends eight hours a day in the office. if 5/12 of her workday is spent answering emails, how much time does she spend doing other things

1) 60 minutes are in an hour, multiply 8 by 60 to get a total of 480 minutes. to find 5/12 of 480, multiply 5/12 x 480=200. So parker spends 200 min, or 3 hours and 20 minutes, answering emails. 3 hours and 20 min subtracted from 8 hrs is 4 hrs and 40 minutes

Maddie's soccer team used three diff colors for their socks: maroon for tournaments, gold socks for away leagues, and white socks for home league games. Maddie owns two pairs of tournament socks, three pairs for away league games, and four pairs for home league games, , but she is terrible about matching or folding them and just stuffs them all into a drawer. If she grab a sock at random from her sock drawer, what is the probability that it will NOT be white?

1) Maddie has 9 pairs of socks total, there are 18 socks in her drawer. four pairs or 8 socks are white, which means that 10 socks are not white. the chance of her selecting a nonwhite sock at random is 10/18, which simplifies to 5/9

Petra earns $10.40 per hour for the first 8 hrs that she works each day, and she earns time and a half for each hour after that. If she works an average of 9.5 hours per day, how much does she earn in a five-day work week?

1) calculate earnings for one day: $10.40 x 8 hours per day is equal to $83.20. For any amt of time she worked over 8 hours, she earns time and a half, or 1.5 times her regular pay. This is equal to $10.40 x 1.5 = $15.60 per hour worked over time. because she worked 1 and a half hours overtime on average, this is equal to $15.60 x 1.5 = 23.40 overtime pay per day. Therefore her total pay per day is equal to $83.20 + $23.40 = $106.60. multiply this amount by 5 days per week to get her weekly pay: $106.60 x 5 =$533.00

In sunny side, a special lottery is held for the elementary student who will attend the country's invention contest. There are 100 5th graders, 150 fourth graders, and 200 third graders who qualified for the lottery. Each 5th graders name is placed in the lottery 3 times, each fourth graders name is placed twice, and each third graders name is placed once. if one name is picked at random, what is the probability that a fifth graders name will be chosen

1) determine the total number of fifth graders names that are in the lottery and divide this by the total number of names in the lottery. 2) each fifth graders name is placed in the lottery 3 times, there are 3 x 100 = 300 fifth grade names. likewise, there are 2 x 150= 300 fourth grade names and 1 x 200 =200 third grade names in the lottery. The probability that a 5th graders name is chosen is 300/300+300+200 = 300/800=3/8

a major city recently received a snowstorm that left a total of 8 inches of snow. if snowed constant at a constant rate of three inches every 2 hours, how much snow had fallen in the first five hours of the storm.

1) find the rate of snowfall per hour 2) it snowed at a constant rate of three inches per hour, so divide 3inches/2inches to get a rate of 1.5 inches per hour. 3)multiply 1.5 inches per hour x 5 - 7.5 inches

for $2, a person can throw 3 balls at a dunk tank target in an attempt to dunk whoever is sitting on the platform. all proceeds from the dunk tank to to the police department. of the 252 balls thrown at the target while bailey was on the platform, only 12 resulted in a dunking. on average, how much money was spent for each dunking.

252/3=84 shows how many $2 packages were purchased. because 84 chances were purchased at $s each, $168 was earned. to find the average amt of money spent for each dunking, divide $168 by 12 to get $14

Rowan wears black socks and white socks. the number of white socks rowan has is six less than three times the number of black socks he has. if b represents the number of black socks rowan has, which of the following expressions represents the number of white socks he has...write an expression representing the number of white socks he has

3b-6

factor this expression completely: 5x^3-20x^2-60x

5x(x-6)(x+4)

Kevin was half the age of his father 20 years ago. Kevin is 40. How old is Kevin's father

Kevin is 40 so 20 years ago he was 40-20=20 years old. At that time in the past, kevin's father was twice his age, so his father was 40 then. therefore, kevins father is 40+20= 60 years old now

in isoceles triangle VIC, <V is the vertex. If <V is three times as large as each of the base angles, then what is the sum of one of the base angles and the vertex?

The sum of the interior angles of a triangle is 180 degrees. Because the vertex is 3 times as large as the base angles, let the measure of the vertex angle be 3b and each of the base angles measure b. solve the equation 3b+b+b=180 degrees; 5b=180 degrees, b=36 degrees, therefore the base angles will each equal 36 degrees and the vertex will be 3x36 = 108 degrees. The sum of one base angle and vertex is 36 degrees + 108 degrees = 142 degrees

A pole that casts a 15 foot long shadow stands near an 8 foot high stop sign. If the shadow cast by the sign is 3 feet long, how tall is the pole

This problem is modeled with two similar right triangles. the smaller one has a height of 8 and a shadow of 3. the larger one has a height of h and a shadow of 15. setting up a proportion of height over shadow and then cross-multiplying gives , height/shadow=8/3=h/15 3h=120 h=40 feet

which of the following is equivalent to 150% of 0.032

To find 150% of a number, multiply it by 1.5:0.0032 multiplied by 1.5 is equal to 0.0048

during the spring bowling season, a bowler achieves the following scores: 116, 100, 104, 104, 114, 109, 109. the bowlers three best scores are averaged for her final score on the season. what is her final score

answer is 113. the bowler three best scores are the highest three scores. these are 116, 114, 109. to find the average, divide the sum of these three scores by 3:

If R is divisible by 4, S is divisible by %, and B is divisible by 3, then any multiple of RBS must be divisible by what..

any multiple of RBS must be divisible by 5x4x3=60. Any number that is divisible by 60 will also be divisible by 6, 10, 12, and 15, because these are all factors of 60.

A rectangular patio has one side that measures 15 feet and another side that is one third as long. what is the area of the patio?

area is found by multiplying the length times the width. Because the length is 15 feet and the width is 1/3 as long as the length, the width is 1/3x15=5 feet. multiplying the length by the width yields the area: 15 feet x 5 feet = 75 square feet.

approximately 375 incoming freshmen have never read a book longer than 1,000 pages. the ratio of those who have not read a book longer than 1,000 pages to those who have is 3:1. how many students are in the freshmen class.

because ratio is 3:1, find what portion of the class has read a book longer than 1,000 pages. that will be 1/3rd of 375, or 125; the sum of 375 and 125 is 500

a rectangular yard is 30 feet wide. the length of the yard is 4/3 the width. if Jeannie wants to hang a clothing line diagonally across the yard, how many feet of line will jeannie need

because the length is 4/3 as long as the width, the length will be 4/3 x 30-40 feet. a rectangular yard of 30 feet by 40 feet cut by a diagonal will give two congruent right triangles. use the Pythagorean theorem to get 50 feet

two trains are heading toward each other. one train travels due east at 35 miles per hours and the other train travels due west at 15 miles per hour. If the two trains start out at 2,100 miles apart, how long will it take them to meet

because they are traveling toward each other, the trains' combined rate of travel is 35 miles + 15 miles = 50 miles distance = rate x time, time =distance/rate. divide the rate of travel into the total distance that the trains need to go: 2,100 miles/50 miles = 42 hours.

which of the following numbers has the greatest value... 2/7 4/11 1/3 3/8 3/10

change each of the fractions to decimal form to the nearest hundredth to compare them

Each teacher at Main Street school teaches at least three classes at more five classes per day. Each of the classes is 40 minutes in length. write a true statement

each teacher has between 120 and 200 minutes of class time per day, inclusive The words at least and at most indicate that a teacher at this school teaches between 3 to 5 classes inclusively, but no more and no less. the actual number of teachers at the school is not known, so the avg number of classes and the avg time spent teaching cannot be determined it can only be determined that each teacher has from 3 to 5 classes at 40 min each, for a total class time between 120-200 minutes per day

During the semester break, Marcus can wax the floors of five classrooms in an hour. Josie can wax the floors of four classrooms in an hour. If marcus works for three hours and josie works for two hours, what percentage of the 50 classrooms will be waxed.

find the total number of floors they can wax in the specified time. multiply rate of work for each person by the amt of time spent working for each marcus waxes five floors an hour for 3 hrs, or 15 floors; josie waxes 4 floors an hour for 2 hours, or 8 floors together they wax 23 floors. because there are 50 classrooms total, the percentage of classrooms whose floors are waxed is 23/50=0.46, which is equal to 46%

after three days, a group of hikers on a biology field trip discovers that they have used 2/5 of their food supplies. they need enough food to make a round trip. at this rate, how many more days can they go forward before they have to turn around

first, find out how long the entire hike can be, based on the rate at which the hikers are using the total amt of their supplies: 2/5 divided by 3 = 1/x (1=total amt of supplies and x is the number of days for the whole hike. cross multiply to get 2/5x=3. multiply each side of the equation by 5/2 to get x=5/2 x 3 =15/2=7 and 1/2 days for the length of the entire hike, which includes the trip back. half of 7 and 1/2 is 3 and 3/4 or 3.75, the hikers could go forward for 3.75 day altogether... they already hiked for three days so 3.75-3 = 0.75 (days) is the amt of times they can go forward before they have to turn back

3.00509...what place value is the 9 in

hundred thousandth

3.09050...what place value is the 9 in

hundredths place

f(x) = -2x (squared) + 8x-4...indicate all that is true about this function

it is a quadratic function. the graph of f(x) opens downward and that may be intercepted by horizontal lines at two points. the graph of f(x) is not a one to one function.

an administrative assistant can file 26 forms per hour. If 5,600 forms must be filed in an eight hour work day, how many assistants must you hire for that day

multiply 26 forms x 8 hours = 208 forms per day per assistant. divide total number of forms by number of forms one assistant can file per day: 5,600/208 = 26.9...27 assistants

all prime numbers are real numbers. some number q is a real number....write a true statement concerning this question

some real numbers are prime numbers it is given that all prime numbers are real numbers can be inferred that at least some real numbers are also prime numbers cannot be assumed that all real numbers are also prime numbers

3.00590..what place value is the 9 in

ten thousandths

3.90050...what place value is the 9 in

tenths place

what is the greatest prime factor of 7

the factors of 77 are 1, 7, 11, and 77. 77 is a factor of 77 , but it is not prime. 11 and 7 are both factors of 77 and prime, and the greater of these is 11

The Huntington cottage grove inn charges $1.50 for the first minute of an outgoing call and 60 cents for every additional minute of the call. If terry makes a call for m minutes, what is an equation that accurately represents the cost of the call in terms of c dollars

the first minute is charged only the 1.50 fee and not the 60 cents fee m must be subtracted by one before multiplying it by the 60 cents per minute charge write 60 cents in decimal terms as 0.60 0.60(m-1) represents what terry will be charged for all his minutes after his first minute. since his first minute costs 1.50$, add this to 0.60(m-1) to get the total price, c

Four congruent squares are joined together to form one large square. If the perimeter of one of the original squares was 8x units, what is the perimeter of the new, large square?

the perimeter of each small square is 8x units; therefore, the length of one side of each small square is 8x/4=2x units. because the new large square is comprised of two sides from each of the four squares ( the remaining four sides are now within the large square), the perimeter of the new, large square is equal to 4(2x+2x)=4(4x) = 16x units

according to a recent statistics of a certain region of the US, 5,000,000 students who took an aptitude test scored less than a perfect score. what is the ratio of students who earned a perfect score to the students who did not earn a perfect score

the ratio is number of perfect scores:number of non perfect scores this unreduced ratio is 8,000:5,000,000 or 8:5,000 because 5,000 divided by 8 equals 625, this ratio then becomes 1:625

tables in a cafeteria are arranged in four rows that are spaced 4 feet apart. each table is 3 feet wide. if there is a distance of 4 feet from the wall to the rows of tables along the edges of the room, how wide is the cafeteria?

the width of the room can be determined by two factors: the width of each table and the number of tables across the width of the room, and the width of the spaces between the tables and the walls, and the number of these spaces because there are 4 tables that are each 3 feet wide, there is 4.3=12 feet to include for the width of the tables in addition, there are five spaces either between tables or between a table and the wall that measures 4 feet in width: 5x4=20feet. combine these two together: 12 +20 = 32 feet

Joe has exactly 720 hours before his vacation begins; how many days are there before his vacation begins

this is a conversion problem. there are 24 hours in one day convert from a smaller unit to a larger unit requires division: 720 hrs divided by 24 hours per day = 30 days

if three more than one fourth of a number is three less than the number, what is the value of the number

this question translates into the equation 1/4x+3=x-3. subtract, 1/4x from both sides of the equation multiply both sides by 4 combine like terms x=8

Jac was 1/3 as young as her grandmother 15 years ago. If the sum of their ages is now 110, how old is jac's grandmother

this uses two algebraic equations to solve for the age: Jac (J) and her grandmother (G) have a sum of ages of 110 years J+G=110 J was 1/3 as young as her G 15 yrs ago, so J-15=1/3(G-15). this simplifies to 95-G=1/3G-5. Add G and 5 to each side: 100=4/3G. multiply each side of the equatioin by 3/4 to get G=75

3.00950 ...what place value is the 9 in...

thousandths place

35)

three out of the four sections are close to 30% look for graph with three of the four sections about the same size and that together make up 90% of the circle, and the fourth section making up half the size of one of the others

In the US, the yearly average is 15 births every 1,000 people. write a proportion to determine x, the total number of births expected in one year if the population is 301,000,000

to set up a proportion, put the number of births in the numerator and the corresponding number of people in the denominator: births/total # of people = 15/1000=x/301,000,000