TACHS: Math and Ability - TACHS Math
Card 0 of 20
Solve:
Solve:
The lines on either side of the negative integer represent that we need to find its absolute value. The absolute value of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All absolute values are positive.
Therefore, the absolute value—or distance from zero—is the following:
The lines on either side of the negative integer represent that we need to find its absolute value. The absolute value of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All absolute values are positive.
Therefore, the absolute value—or distance from zero—is the following:
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Find the area of a circle with the following radius:
Find the area of a circle with the following radius:
The area of a circle can be calculated using the following formula:
In this formula the radius is denoted by the variable, 
.
Substitute in the known variables and solve for the circle's area.
The area of a circle can be calculated using the following formula:
In this formula the radius is denoted by the variable,
Substitute in the known variables and solve for the circle's area.
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Which is equal to the radius of a circle with area 
Which is equal to the radius of a circle with area
The formula for the area 
of a circle, given its radius 
, is 
. Replace 
with 
:
To find the radius 
, first, divide both sides by 
:
Now, find the square root of both sides. Since 
, 20 is the square root of 400, so
.
The radius of the given circle is 20.
The formula for the area
To find the radius
Now, find the square root of both sides. Since
The radius of the given circle is 20.
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To determine whether a machine on an assembly line is filling bottles with the correct amount of soda, twenty bottles are selected. The tenth bottle and every tenth bottle after that are taken off the line and examined.
This is an example of which kind of sampling?
To determine whether a machine on an assembly line is filling bottles with the correct amount of soda, twenty bottles are selected. The tenth bottle and every tenth bottle after that are taken off the line and examined.
This is an example of which kind of sampling?
The sample in this scenario is selected from the population by choosing obects that occur at regular intervals. That makes this an example of systematic sampling.
The sample in this scenario is selected from the population by choosing obects that occur at regular intervals. That makes this an example of systematic sampling.
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What is the area of a circle that has a diameter of 
?
What is the area of a circle that has a diameter of
Recall how to find the area of a circle:
To find the length of the radius, divide the diameter by two.
Now, plug it into the equation for the area of a circle.
Recall how to find the area of a circle:
To find the length of the radius, divide the diameter by two.
Now, plug it into the equation for the area of a circle.
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A square has perimeter 24 feet. Give its area.
A square has perimeter 24 feet. Give its area.
The perimeter of a figure is the sum of the lengths of its sides. A square comprises four sides of equal length, so, if the perimeter of the square is 24 feet, then each side has length
feet.
The area of the square is equal to the length of a side multiplied by itself, so the area of this square is
square feet.
The perimeter of a figure is the sum of the lengths of its sides. A square comprises four sides of equal length, so, if the perimeter of the square is 24 feet, then each side has length
The area of the square is equal to the length of a side multiplied by itself, so the area of this square is
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Jennifer wants to wallpaper her room which is made up for four rectangular walls each measuring at 
feet by 
feet. If each roll of wallpaper covers 
square feet of space, how many rolls of wallpaper will Jennifer need?
Jennifer wants to wallpaper her room which is made up for four rectangular walls each measuring at
Start by finding out the total square footage of wallpaper needed.
Find the area of one wall. Recall that in order to find the area of a rectangle, you must multiply the length by the width.
Since we have four identical walls,
Now divide this by the amount of square feet covered by each roll of wallpaper to find how many rolls are needed.
Start by finding out the total square footage of wallpaper needed.
Find the area of one wall. Recall that in order to find the area of a rectangle, you must multiply the length by the width.
Since we have four identical walls,
Now divide this by the amount of square feet covered by each roll of wallpaper to find how many rolls are needed.
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Find the circumference of a circle with the following radius:
Find the circumference of a circle with the following radius:
In order to find the circumference of a circle we will use the following formula:
In this equation, the variable, 
, represent's the circle's radius.
Substitute in for the circle's radius.
Simplify and solve.
In order to find the circumference of a circle we will use the following formula:
In this equation, the variable,
Substitute in for the circle's radius.
Simplify and solve.
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Add.
Add.
In order to solve this problem we need to line up the decimal places and add.
In order to solve this problem we need to line up the decimal places and add.
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Square 0.44.
Square 0.44.
To square a number means to multiply it by itself, so we seek to compute
To multiply two decimal fractions, first multiply, ignoring the decimal points:
Move the (implied) decimal point the number of spaces right equal to the total number of digits right of the decimal points in the factors; this can be seen to be four:
The square of 0.44 is 0.1936.
To square a number means to multiply it by itself, so we seek to compute
To multiply two decimal fractions, first multiply, ignoring the decimal points:
Move the (implied) decimal point the number of spaces right equal to the total number of digits right of the decimal points in the factors; this can be seen to be four:
The square of 0.44 is 0.1936.
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Tiffany earns 
each week. If Mark earns 
less than Tiffany, what is the sum of their salaries each week?
Tiffany earns
Start by finding out how much Mark makes. Since he makes 
less than Tiffany, we can write the following to find Mark's weekly salary:
Mark must make 
each week. Now, add together their salaries to find the sum.
Start by finding out how much Mark makes. Since he makes
Mark must make
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Rachel earns 
an hour as an assistant in a science lab. How many 
hour work weeks will she need to work in order to pay for a car that costs 
?
Rachel earns
Start by figuring out how much Rachel can earn in each week by multiplying her hourly rate by the number of hours worked each week.
Now, divide the amount she needs to earn by the amount earned each week to find how many weeks she will need to work to earn that amount.
Rachel must work for 
weeks in order to earn enough for the car.
Start by figuring out how much Rachel can earn in each week by multiplying her hourly rate by the number of hours worked each week.
Now, divide the amount she needs to earn by the amount earned each week to find how many weeks she will need to work to earn that amount.
Rachel must work for
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Which of the following is equivalent to 
?
Which of the following is equivalent to
Recall that when a number is raised to an exponent, that means we will need to multiply the number the number of times that is equal to the exponent.
Thus, with 
, this means we will need to multiply 
by itself four times:
Recall that when a number is raised to an exponent, that means we will need to multiply the number the number of times that is equal to the exponent.
Thus, with
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What is the value of 
?
What is the value of
Start with finding the value of 
.
In order to add fractions with different denominators, we will need to change one or both denominators first. Notice that 
is a factor of 
, which means we can multiply the numerator and the denominator of 
by 
to get 
.
Now, add the two fractions together as they have the same denominator.
Next, solve 
.
The least common multiple of 
and 
is 
.
Thus, 
Start with finding the value of
In order to add fractions with different denominators, we will need to change one or both denominators first. Notice that
Now, add the two fractions together as they have the same denominator.
Next, solve
The least common multiple of
Thus,
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Janice's car can travel 
miles on one gallon of gas. Her car can normally hold 
gallons of gas, but it is only 
full. How many miles can Janice travel before the tank is empty?
Janice's car can travel
Start by finding out how many gallons is currently in Janice's tank.
Since it is only 
full,
.
The tank only has 
gallons in it right now. Multiply this by the number of miles traveled per gallon to find how far Janice can travel before the tank is empty.
Start by finding out how many gallons is currently in Janice's tank.
Since it is only
The tank only has
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Paul can type 
words per minute. If Josie can type 
faster than Paul can, how many words can Josie type in 
minutes?
Paul can type
Start by finding out Josie's typing rate.
Since she types 
faster, we can find her rate with the following equation:
Since Josie types at 
words per minute, we can multiply by the total number of given minutes to find out how many words she can type in the given time frame.
Start by finding out Josie's typing rate.
Since she types
Since Josie types at
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What is the product of 
and 
?
What is the product of
Since the question asks for the product, you will need to multiply the two fractions. Recall that in multiplying two fractions, you will multiply the numerators together and then multiply the denominators together.
Next, reduce the fraction.
Since the question asks for the product, you will need to multiply the two fractions. Recall that in multiplying two fractions, you will multiply the numerators together and then multiply the denominators together.
Next, reduce the fraction.
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What is the difference between 
and 
?
What is the difference between
Since the question asks you to find the difference, you will need to subtract the two fractions:
Start by making both denominators the same. Multiply the numerator and denominator of 
by 
to get 
.
Now, subtract.
Make sure to simplify the answer.
Since the question asks you to find the difference, you will need to subtract the two fractions:
Start by making both denominators the same. Multiply the numerator and denominator of
Now, subtract.
Make sure to simplify the answer.
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What is the greatest common factor of 
and 
?
What is the greatest common factor of
Start by listing out the factors of 
.
Next, list out the factors of 
.
Now, find the largest factor that the two numbers share. In this case, the greatest common factor is 
.
Start by listing out the factors of
Next, list out the factors of
Now, find the largest factor that the two numbers share. In this case, the greatest common factor is
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Solve the following inequality:
Solve the following inequality:
In algebra an inequality is a relationship that holds through different values of a variable. An inequality is considered to be solved when the variable is isolated to one side of the inequality. We will do this by performing the reverse of the operations that were done to the variable. It is important to note that what is done to one side of the inequality needs to be done on the other.
Let's start by writing the inequality.
Subtract 
from both sides of the inequality.
Divide each side of the inequality by 
.
Solve.
The variable is greater than four.
In algebra an inequality is a relationship that holds through different values of a variable. An inequality is considered to be solved when the variable is isolated to one side of the inequality. We will do this by performing the reverse of the operations that were done to the variable. It is important to note that what is done to one side of the inequality needs to be done on the other.
Let's start by writing the inequality.
Subtract
Divide each side of the inequality by
Solve.
The variable is greater than four.
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