A child has collected 50 pennies, 45 nickels, 25 dimes, and 5 quarters. Which of the following charts accurately organizes the number of coins?

A.

A
B.

B
C.

C
D.

D


Correct Answer : B

In this scenario, we use the given scale in the charts to find the number of each coin and selected the right number of coins the student collected. The second options shows that the child collected 50 pennies, 45 nickels, 25 dimes, and 5 quarters.

 


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Correct Answer is B

Explanation

We are told to find the area of the pizza given its diameter. The pizza is in circular form, and its area is found as:

However, we are not given r, which is the radius of the circle. But we can find it from the given diameter as

Substituting r=8 in the equation of the area of a circle

Thus, the area of the pizza is 64  in2.

NOTE:  (Pi) remains as a symbol because values of Pi can vary from 22/7 to 3.1415 to 3.14 and so forth.

Correct Answer is A

Explanation

To find the least common denominator (LCD) of the fractions 1/2, 2/3, and 4/5, follow these steps:

Step 1: Identify the denominators

The denominators are 2, 3, and 5.

Step 2: Find the least common multiple (LCM)

The LCM of 2, 3, and 5 is the smallest number that all three denominators divide into evenly.

  • Prime factorization:
    • 2=2
    • 3=3
    • 5=5

Since 2, 3, and 5 are all prime numbers, their LCM is:

2×3×5=30

Correct Answer is C

Explanation

we follow the order operations to solve for the unknown value of x.

2(4x+3)=7x+5

Open the bracket on the LHS by multiplying each term by 2

(2*4x)+(2*3)=7x+5

8x+6=7x+5

Subtract 6 from both sides

8x+6-6=7x+5-6

8x=7x-1

Subtract 7x on both sides

8x-7x=7x-7x-1

X=-1

Thus, the value of unknown value of x is -1.

Correct Answer is A

Explanation

The initial step is to establish the relationship between area of a circle and the radius. The area of the circle is given by the formula

Now, substituting the 49 π in2 in place of A in the equation above becomes:

We want to find r, therefore, we rearrange the equation as

Divide both sides by

Take square root both sides of the equation

The radius of the circle is 7 in, and the circumference of the circle is determined as follows

Substituting the value of r=7 becomes

Thus, the circumference of a circle whose area is 49  in2 is 14  

Correct Answer is D

Explanation

In order to solve for the value of x, we use the order of operations as follows:

The first step is to divide both sides by 4

Since 5 is subtracted, we add 5 to both sides to eliminate it from the left-hand side of the equation

Thus, the value of x is 7.

Correct Answer is D

Explanation

The length of the unknown side of the rectangle can be found by using the Pythagoras theorem. We label the triangle from the given data as shown below

Let the unknown length be x.

Applying the Pythagoras theorem, the value of x is found as:

\(a ^2 +b ^2 =c ^2\)

The unknown length of the triangle is approximately 8.9 feet.

Correct Answer is C

Explanation

To simplify the expression:

12+3×4−1+23

Step 1: Follow the order of operations (BODMAS)

Multiplication first:

3×4=12

23 = 2×2×2=8

Now the expression becomes:

12+12−1+8

Step 2: Perform addition and subtraction from left to right

  • 12+12=24
  • 24−1=23
  • 23+8=31

The correct answer is 31.

Correct Answer is C

Explanation

To solve this equation, we use a calculator and find the product as:

2.50*0.25=0.625

Correct Answer is A

Explanation

from the given estimations, we can find the actual addition of the numbers and see a trend the student utilizes to find their estimates. The exact sum is as follows

24+190=214

151+319=470

974+1022=1996

From the above evaluation, we can clearly see the students approximates the value in the ones values. So, in the problem we need to approximate 452+5017.

452+5017=5469

We can approximate 5469 based on the provided choices to 5470.

Correct Answer is B

Explanation

When dealing with percent problems, the following is utilized to find the unknown variable.

  • Is means equals
  • Of means multiply
  • What means unknown (variable)

From the problem above, we are looking for the amount of gratuity the couple can leave.

Let t be the amount of gratuity. Translating into an equation, we have

The gratuity is 15% of the total bill, which becomes

Here, of means multiply and we also convert percent into decimal before multiplying.

So, the value of t=5.76

Thus, a couple will leave a gratuity of $5.76, which is about $6.00.

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