Simplify the expression below. Which of the following is correct?
A
B
C
D
Correct Answer : D
We use the properties of exponent with the same base to solve for above expression.
Multiplication of exponents with same base, we add the exponents
Division of exponents with same base, we subtract the exponents
Using these two properties, we can solve the expression:
Now we use the following properties:
y0 =1, and , thus
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Correct Answer is B
Explanation
from the provided table, the first option represents the amount of gas in gallons while the second column shows the distance in miles. Thus, (6, 144) will denote that the car can 144 miles by consuming 6 gallons of a gas.
Correct Answer is A
Explanation
A whole pizza is equivalent to 1. Then
One friend eats half of the pizza=1/2 of 1=1/2*1=1/2
Remaining amount of pizza to be shared=1-1/2=2/2-1/2=1/2
Now, three friends share ½ equally and each friend will get,
          Â
Thus, the three friends each share 1/6.
Correct Answer is A
Explanation
Here we collect like terms together and solve for the unknown value of x.
7x-6=3x-26
Add 6 to both sides of the equation
7x-6+6=3x-26+6
7x=3x-20
Subtract 3x from both sides of the equation
7x-3x=-20
4x=-20
Divide both sides by 4
4x/-4=-20/4
x = -5
The value of x = -5
Correct Answer is B
Explanation
The best way to display the frequency of each day of the week when students get up after 8 a.m. is by using a bar graph. Bar graphs are well-suited for representing categorical data, where each day of the week is a separate category, and the height of each bar corresponds to the count or frequency of students waking up late on that specific day.
Note: Histograms, on the other hand, are more appropriate for visualizing continuous or numerical data and are not ideal for categorical data like days of the week.Histograms are useful for understanding the distribution of data, identifying patterns, and assessing the shape of the data distribution, such as whether it's normally distributed, skewed, or has multiple modes.
As you can see below, the Histogram is used to depict a pattern/continuous data. While a bar graph does just fine even with discrete data.
Correct Answer is A
Explanation
all products represent 100%. Then, the portion of defect products is:
0.0025 of 100%
‘of’ means multiply
0.0025 *100%=0.25%
Correct Answer is D
Explanation
We can interpret ‘cannot exceed” as less than ‘<’. Therefore, in our inequality, the symbol < must be included. Now let’s convert the word problem into a mathematical inequality.
Money spent on supplies=s
Money spent on textbooks=t
Total money spent=money spent on supplies + money spent on textbooks
Total money spent = s+t
But the money spent cannot exceed $12,000. Then,
s+t <$12,000.
However the money spent can still be equal to $12000, as it has not exceeded it.
Therefore, therequired inequality is s + t <= $12,000.
Correct Answer is B
Explanation
Here we are required to find the area of the square of sides 3.1 m. The square is a four-sided figure with each side equal and opposite sides making 90 degrees.
Area of the square =side*side
Side=3.1 m
Area of the square =3.1 m *3.1 m=9.61 m2
Note: 3.1 + 3.1 = 6.2 which is a wrong answer.
Correct Answer is D
Explanation
Round trip means to and from, which is twice the distance from home to a medical facility.
In one day, the round trip=19+19=38 miles
So, in 22 days, the round trip=38*22=836 miles.
The patient will cover 836 miles in 22 days.
Correct Answer is D
Explanation
The given ratio of yoghurt to toppings is 4:3, meaning:
Yoghurt : toppings =4 : 3
We are given 4.5 oz of toppings and need to find the amount of yoghurt.
Step 1: Set up the proportion
=
Step 2: Solve for yoghurt
Multiply both sides by 4.5:
yoghurt=43×4.5
yoghurt=4×4.5/3=18/3=6oz
Correct Answer is B
Explanation
The median temperature can be found by organizing the temperature values from the smallest to the largest value as follows:
98.6, 98.7, 99.0, 99.0,99.2, 99.3, 99.7, 100.0
(for an even set of numbers, Median = frac{(frac{n}{2})th observation + (frac{n}{2} + 1) th observation}{2})
From the data set above, there are 8temperature values. The median is the temperature value in the middle position, which falls between the(frac{n}{2} th)and((frac{n}{2} + 1) th) position. Here N=8and median is found as:
(frac{(frac{n}{2})th + (frac{n}{2} + 1) th}{2} = )(frac{(frac{8}{2})th + (frac{8}{2} + 1) th }{2} = 4.5th position)
The element in the 4.5th position is the average of the 4th and 5th element.
(frac{99.0 + 99.2}{2} = 99.1)
Thus 99.1 is the median temperature.
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