A child has collected 50 pennies, 40 nickels, 25 dimes, and 5 quarters. Which of the following charts accurately organizes the number of coins?
Chart 1
Chart 2
Chart 3
Chart 4
Chart 1
Chart 2
Chart 3
Chart 4
Correct Answer : B
By inspection, we find the corresponding values of the given denominations in the following manner.
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Correct Answer is C
Explanation
To find the greatest number from the given set, we first convert the decimal numbers into fractions.
12.35 becomes 1235/100
11.46 becomes 1146/10
Then, the LCM for the denominators of the given fractions of 2, 100, 3 and 10 is 300. Now we multiply each fraction with 300, which we will use to compare the give set.
25/2*300=3750
1235/100*300=3705
40/3*300=4000
1146/10*300=3438
From the calculated values, 4000 is the greatest value. Then, 40/3is the greatest value.
Correct Answer is A
Explanation
This problem asks us to compare the number of dimes to nickels.
If we let p be number of pennies in the bottle. Then,
Number of quarters in the bottle = 4p
Number of nickels in the bottle = 2p
Number of dimes in the bottle =7(2p)=14p
To find the number of dimes the child has than nickels, we use the ratio:
\(\frac{Dimes}{nickels} =\frac {14p}{2p}\ =\ 7\)
Thus, there are 7times as many dimes as nickels in the box.
Correct Answer is A
Explanation
we are asked to find the percent change in weight gain of a person.
First, we need to find the change in weight gained over the 4 months
Change in weight= 186-176=10 lb
The percent change is expressed as change in weight over original weight *100. Then
The percent change in weight is 6% to the nearest whole number.
Correct Answer is B
Explanation
we are to use the pie chart to find the number of students enrolled in dental hygiene care.
Letting x represent the number of students enrolled in dental hygiene care, we set the proportion equation with number of students as numerator and percentage as denominator. It should be noted that the whole pie chart represents 100% of the 800 students. Then,
We solve the value of x by cross-products.
Therefore, 144 students will enroll for a dental hygiene program.
Correct Answer is A
Explanation
we are tasked to find the number of cups of flour that will be used to make 90 cookies.
This is a proportion equation, and letting x be the number of cups of flour we set the equation as follows:
Solve the value of x by cross-products
Next, we convert the mixed fraction into improper fraction in order to carry out multiplication
The baker needs 15.75 cups of flour to make 120 cookies. 15.75 in mixed fraction is Â
Correct Answer is C
Explanation
We are given the equation:
6x−5=10x+15
Step 1: Move all xxx-terms to one side
Subtract 6x from both sides:
−5=10x−6x+15
Step 2: Move constants to the other side
Subtract 15 from both sides:
−5−15=4x
−20=4x
Step 3: Solve for x
Divide both sides by 4:
x=−20/4 = −5
Correct Answer is C
Explanation
We are asked to convert kg to pounds using the given relation. If we let x to represent the lb we are asked to find, we set the proportion equation with kg on numerator and lb on the denominator as follows.
The equivalent value of 55kg is 121 lb.
Correct Answer is D
Explanation
To simplify this expression, we follow the order of operations as follows:
First, we start with the numerator and solve it as follows
[2(6+3*9)]
We start with multiplication in inner brackets, 3 * 9 = 27. The expression becomes
[2(6+27)]
Then, we carry out the addition of 6+27=33. Then, the expression yields
[2(33)]=2*33=66
Now, we solve for denominator, which is 6/2=3.
Thus, the expression is reduced into
The expression reduces into 22.
Correct Answer is A
Explanation
To answer this question, we need to convert the numbers into a similar form. Converting decimal numbers into fraction is appropriate to finding the greatest number.
-0.9 becomes 9/10
-1.9 becomes 19/10
Now we find the LCM of the denominators of the four fractions. The LCM of 5, 10 and 3 is 30. Multiply each fraction with the LCM to compare the fractions.
-3/5*30=-18
-9/10*30=-27
-19/10*30=-57
-8/3*30=-24
The greatest number is -18, meaning -3/5 is the greatest number.
Correct Answer is D
Explanation
An independent variable is a variable that is manipulated or changed in the experiment. From the given equation, x is variable that is changed to obtain the desired outcome, F(x). Therefore, x is an independent variable.
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