For a school's annual budget, the total amount of money spent on supplies (s) and textbooks (t) cannot exceed $12,000. Which of the following inequalities represents this scenario?
s + t >= $12,000
s + t > $12,000
s + t < $12,000
s + t <= $12,000
Correct Answer : D
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, the required inequality is s + t <= $12,000.
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Correct Answer is B
Explanation
In the simple interest, we utilize the following formula to find the simple interest after a period of time in years.
I=P*r*t
I is the interest
P=Principal or initial deposit
r=rate
t=time in years
From the given problem, P=$600, r=6%=6/100=0.06, t=5 years. Then
I=$600*0.06*5=$180
After 5 years, Pat will earn an interest of $180.
Correct Answer is C
Explanation
When dividing fractions, the division sign is changed into multiply sign and the first fraction is multiplied by the inverse of the second fraction.
Change division to multiply sign and find invers of 5/8. The inverse of a fraction is inverting the given fraction. The denominator becomes the numerator and the numerator becomes the denominator.
Correct Answer is A
Explanation
In this problem, we take the triangle as a right-angled triangle and label it as follows:
From the Pythagoras theorem A2 + B2= C2, we can look for a combination of A and B that when the squares of A and B are summed give a square of 13. Â Mathematically,
But C=13 inches
If we take A=5 inches and B=12 inches, then
Next, we take A=2.5 inches, B=6 inches
Next, we take A=2.5 inches, B=4 inches
6.25+16=169
22.25≠169
Taking A=5 inches and B=8 inches
From the above computation, the combination of A=5 inches and B=12 inches give a triangle with a hypothenuse of 13 inches.
Correct Answer is D
Explanation
we use the US customary system of units’ equivalent to convert from yards to inches. We know that 1yard=3 ft, and 1 ft =12 inches.
First, convert 2 ¾ into an improper fraction.
Then,
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 A
Explanation
We are given that 1 teaspoon=4.93 mL, we can interpret it as:
Or
Since we are to find the amount in mL, we look for an option that will cancel teaspoon and remain with mL. The second option is the required conversion, and we proceed as follows:
Therefore, 2.5 teaspoons hold about 12.325 mL.
Correct Answer is B
Explanation
From the given scenario:
Initial charge is $40
Additional charge per circular cloth=$5c
Additional charge per rectangular cloth=$3.50r
Total cost = additional charge per circular rectangular cloths + Initial charge
Total cost, T = 5c + 3.5r + 40
Correct Answer is D
Explanation
The mean is the total divided by the number of elements in the data set. From the given data set:
Total=30+29+28+30+24+12+26+33+25+23=260
Number of items, N=10
Mean=total/N=260/10=26
The mean is 26.
Correct Answer is A
Explanation
We need to find the length of the rectangle from the given area and width of the rectangle. Let L be length if the rectangle. Then,
Area of rectangle=Length*width
Substituting area=32 in2 and w=4 inches
32=L*4
32=4L
Divide both sides by 4
32/4=4L/4
8=L
The length of the rectangle is 8 inches.
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