1.### A is 40% of B. What percentage is B of A?

Answer:
250%

Explanation:

If A is 40% of B, this means A = 0.4B. To find what percentage B is of A, you rearrange this equation to solve for B in terms of A:B = A / 0.4This can be rewritten as:B = 2.5ATo convert the factor 2.5 into a percentage, you multiply it by 100:2.5 x 100 = 250%Thus, B is 250% of A, indicating that B is more than twice the size of A.

2.### X+5=10. Then x equals:

Answer:
5

Explanation:

To solve the equation x + 5 = 10 for x, you need to isolate x on one side. Subtract 5 from both sides of the equation:

x + 5 - 5 = 10 - 5

This simplifies to:

x = 5

Therefore, x equals 5.

x + 5 - 5 = 10 - 5

This simplifies to:

x = 5

Therefore, x equals 5.

3.### X2+4x+3=0; Then x equals:

Answer:
-1 or -3

Explanation:

To solve the quadratic equation x^2 + 4x + 3 = 0, you can factorize it:

(x + 3)(x + 1) = 0

Setting each factor equal to zero gives:

x + 3 = 0

Solving for x, x = -3

x + 1 = 0

Solving for x, x = -1

Thus, the solutions for x are -1 and -3. These are the values that make the original equation true when substituted back into it.

(x + 3)(x + 1) = 0

Setting each factor equal to zero gives:

x + 3 = 0

Solving for x, x = -3

x + 1 = 0

Solving for x, x = -1

Thus, the solutions for x are -1 and -3. These are the values that make the original equation true when substituted back into it.

4.### What is the next number in the sequence: 3, 7, 15, 31, ?

Answer:
63

Explanation:

The given sequence is increasing, and each number is obtained by doubling the previous number and then adding 1.

Starting with 3:

3 * 2 + 1 = 7

7 * 2 + 1 = 15

15 * 2 + 1 = 31

To find the next number, we apply the same pattern:

31 * 2 + 1 = 63

So, the next number in the sequence is 63.

Starting with 3:

3 * 2 + 1 = 7

7 * 2 + 1 = 15

15 * 2 + 1 = 31

To find the next number, we apply the same pattern:

31 * 2 + 1 = 63

So, the next number in the sequence is 63.

5.### Y2+ 4=20. Then y equals:

Answer:
4 or -4

Explanation:

To solve the equation y^2 + 4 = 20, first subtract 4 from both sides:

y^2 + 4 - 4 = 20 - 4

This simplifies to:

y^2 = 16

Next, find y by taking the square root of both sides. Remember, squaring a number results in a positive value, and the square root of a positive number has both a positive and negative solution:

y = sqrt(16)

This gives:

y = 4 and y = -4

Therefore, y equals both 4 and -4.

y^2 + 4 - 4 = 20 - 4

This simplifies to:

y^2 = 16

Next, find y by taking the square root of both sides. Remember, squaring a number results in a positive value, and the square root of a positive number has both a positive and negative solution:

y = sqrt(16)

This gives:

y = 4 and y = -4

Therefore, y equals both 4 and -4.

6.### The price of an item increases by 20% and then decreases by 20%. So the price has:

Answer:
Decreased by 4%

Explanation:

When the price of an item increases by 20% and then decreases by 20%, the final price does not return to the original because the base amounts for each percentage calculation differ.

Suppose the original price of the item is 100 dollars.

After a 20% increase, the new price becomes:

100 + 20% of 100 = 100 + 20 = 120 dollars

Then a 20% decrease on the new price (120 dollars) is calculated:

120 - 20% of 120 = 120 - 24 = 96 dollars

Comparing the final price (96 dollars) with the original price (100 dollars), there is a decrease of:

100 - 96 = 4 dollars

As a percentage of the original price, this decrease is:

(4 / 100) x 100% = 4%

So, the price has decreased by 4%.

Suppose the original price of the item is 100 dollars.

After a 20% increase, the new price becomes:

100 + 20% of 100 = 100 + 20 = 120 dollars

Then a 20% decrease on the new price (120 dollars) is calculated:

120 - 20% of 120 = 120 - 24 = 96 dollars

Comparing the final price (96 dollars) with the original price (100 dollars), there is a decrease of:

100 - 96 = 4 dollars

As a percentage of the original price, this decrease is:

(4 / 100) x 100% = 4%

So, the price has decreased by 4%.

7.### The ratio of girls: boys in a school is 5:7. If there are 525 girls, how many boys are there?

Answer:
735

Explanation:

The ratio of girls to boys in the school is 5:7. This means for every 5 girls, there are 7 boys. Given there are 525 girls, we first determine how many times the part of the ratio (5) fits into the actual number of girls (525).

Calculate the multiplier for the ratio:

525 (number of girls) / 5 (girl ratio part) = 105

Now, use this multiplier to find the number of boys:

Multiply the boy ratio part by the multiplier:

7 (boy ratio part) x 105 (multiplier) = 735

Therefore, there are 735 boys in the school.

Calculate the multiplier for the ratio:

525 (number of girls) / 5 (girl ratio part) = 105

Now, use this multiplier to find the number of boys:

Multiply the boy ratio part by the multiplier:

7 (boy ratio part) x 105 (multiplier) = 735

Therefore, there are 735 boys in the school.

8.### David and John share $455 in the ratio of 2:3, respectively. How much money does John get?

Answer:
$273

Explanation:

David and John share $455 in the ratio of 2:3. This means for every 2 units that David receives, John receives 3 units. To find out how much money each person gets, you first need to determine the total number of parts into which the money is divided:

Total parts = 2 (David) + 3 (John) = 5 parts

Now, calculate the value of one part:

Value of one part = Total money / Total parts = $455 / 5 = $91

Finally, calculate how much John receives by multiplying the value of one part by the number of parts John receives:

Money John receives = 3 parts x $91/part = $273

Therefore, John receives $273.

Total parts = 2 (David) + 3 (John) = 5 parts

Now, calculate the value of one part:

Value of one part = Total money / Total parts = $455 / 5 = $91

Finally, calculate how much John receives by multiplying the value of one part by the number of parts John receives:

Money John receives = 3 parts x $91/part = $273

Therefore, John receives $273.

9.### X-12y = 0. Then y/x equals:

Answer:
1/12

Explanation:

To find the ratio of y/x from the equation x-12y = 0, first rearrange the equation to solve for y in terms of x. By moving all terms involving y to one side and all other terms to the opposite side, we get x = 12y. Now, divide both sides of this equation by x to isolate y/x on one side. This gives us y/x = 1/12. Hence, the value of y/x equals 1/12. This is calculated by dividing the coefficient of y by the coefficient of x in the rearranged equation.

10.### Change 3/20 into a decimal:

Answer:
0.15

Explanation:

To convert the fraction 3/20 into a decimal, divide the numerator by the denominator. The calculation is performed by dividing 3 by 20. When you divide 3 by 20, you get 0.15. Therefore, the decimal equivalent of the fraction 3/20 is 0.15. This decimal value directly results from the division process, representing the proportion of 3 parts out of a total of 20 parts.

11.### Write 68/0.00001 as an ordinary number.

Answer:
6800000

Explanation:

To express the fraction 68/0.00001 as an ordinary number, you can perform the division:

68 ÷ 0.00001

Converting the decimal value into fraction, we get:

68 ÷ 1/100000 = 68 * 100000 = 6800000

So, 68/0.00001 is equal to 6,800,000 as an ordinary number.

68 ÷ 0.00001

Converting the decimal value into fraction, we get:

68 ÷ 1/100000 = 68 * 100000 = 6800000

So, 68/0.00001 is equal to 6,800,000 as an ordinary number.

12.### 4*4-2*(-3)+6= ?

Answer:
28

Explanation:

To solve the expression 4 * 4 - 2 * (-3) + 6 using the BODMAS (Brackets, Order, Division and Multiplication, Addition and Subtraction) rule:

First, evaluate the multiplication and division from left to right:

4 * 4 = 16

-2 * (-3) = 6 (The double negative becomes a positive)

Now, rewrite the expression with the results: 16 + 6 + 6

Finally, perform the addition from left to right: 16 + 6 = 22

22 + 6 = 28

So, 4 * 4 - 2 * (-3) + 6 = 28.

First, evaluate the multiplication and division from left to right:

4 * 4 = 16

-2 * (-3) = 6 (The double negative becomes a positive)

Now, rewrite the expression with the results: 16 + 6 + 6

Finally, perform the addition from left to right: 16 + 6 = 22

22 + 6 = 28

So, 4 * 4 - 2 * (-3) + 6 = 28.

13.### When you reduce $ 80 by 11%, you will get:

Answer:
$71.20

Explanation:

To find the amount remaining after reducing $80 by 11%, first calculate 11% of $80. Multiply 80 by 0.11 to get the reduction amount. This calculation gives 80 * 0.11 = $8.80. Now, subtract this amount from the original $80 to find the reduced total. The calculation is 80 - 8.80 = $71.20. Therefore, when you reduce $80 by 11%, you will get $71.20. This result is achieved by applying the percentage reduction to the original amount and subtracting the calculated value from the original total.

14.### Write 0.67543 correct to 2 significant figures.

Answer:
0.68

Explanation:

The given number, 0.67543, has 5 significant figures. Rounding it to 2 significant figures means we need to keep only the first two significant figures and round the rest. The third significant figure, 5, is less than 5, so we round down. Therefore, the correct answer is 0.68.

15.### Simplify 5ab-7ba+4ab=?

Answer:
2ab

Explanation:

The given expression involves adding and subtracting common terms. In this case, we have 5ab, -7ba, and 4ab. By rearranging the terms, we can combine the like terms. The -7ba can be rewritten as -7ab since the order of the variables does not matter. Adding 5ab and 4ab gives us 9ab. Therefore, the simplified expression is 9ab - 7ab, which simplifies further to 2ab.

16.### Solve 4(x+2)=24

Answer:
X=4

Explanation:

The equation 4(x+2)=24 can be solved by first distributing the 4 to both terms inside the parentheses, resulting in 4x + 8 = 24. Next, we can subtract 8 from both sides of the equation to isolate the variable, giving us 4x = 16. Finally, we divide both sides of the equation by 4 to solve for x, which gives us x = 4.

17.### The sum of the three consecutive even numbers is 222. Find the numbers.

Answer:
72,74,76

Explanation:

The correct answer is 72, 74, 76. The sum of three consecutive even numbers can be found by adding the first even number to the third even number and then adding the result to the second even number. In this case, 72 + 76 + 74 equals 222, which matches the given sum. Therefore, 72, 74, and 76 are the three consecutive even numbers that add up to 222. In the option, 73,74,75, all these are not even numbers. In the other option, 74, 74, 74, consecutive numbers are not present.

18.### The gradient of the line x+3y=9 is

Answer:
-1/3

Explanation:

The gradient of a line can be determined by rearranging the equation into the form y = mx + c, where m is the gradient. In this case, rearranging x + 3y = 9 gives y = (-1/3)x + 3, which means that the coefficient of x (-1/3) is the gradient of the line. Therefore, the correct answer is -1/3.

19.### If 2x-3y +4x-7y=0, then the value of y/x is:

Answer:
3/5

Explanation:

2x - 3y + 4x - 7y = 0

Combining like terms:

(2x + 4x) - (3y + 7y) = 0

6x - 10y = 0

Now, let's solve for y in terms of x:

10y = 6x

y = (6/10)x

Simplify the fraction:

y = (3/5)x

So, the value of y/x is 3/5.

Combining like terms:

(2x + 4x) - (3y + 7y) = 0

6x - 10y = 0

Now, let's solve for y in terms of x:

10y = 6x

y = (6/10)x

Simplify the fraction:

y = (3/5)x

So, the value of y/x is 3/5.

20.### If 2x+5y=18 and x=2, what is the value of 4x+5y:

Answer:
22

Explanation:

To find the value of 4x+5y, we substitute the given value of x into the equation 2x+5y=18. This gives us 2(2)+5y=18, which simplifies to 4+5y=18. By subtracting 4 from both sides of the equation, we get 5y=14. Dividing both sides by 5, we find that y=14/5. Now, we substitute the values of x and y into the expression 4x+5y, which gives us 4(2)+5(14/5)=8+14=22. Therefore, the correct answer is 22.

×

Wait!

Here's an interesting quiz for you.