Mathematics Practice Questions 2

The sum of the two given angles is 140°. The measure of the third angle is equal to the difference of 180° and 140°, which is 40°.

The amount he will need for three desserts is equal to the product of 2\(\frac{1}{2}\) and 3, which is 7\(\frac{1}{2}\).

Application of the 50% discount gives the expression \(320 – 0.50 \times 320\), which equals 160. Application of the additional 20% discount to this amount gives the expression \(160 – 0.20 \times 160\), which equals 128. Thus, the sale price of the desk was $128.

The largest percentage given is 25%, thus the beach is the most common destination.

The number of students going to the mountains is equal to the product of 0.12 and 500, which is 60.

The following proportion may be written:

\(\frac{\frac{1}{4}}{1}=\frac{6}{x}\)

Solving for \(x\) gives \(x = 24\). Thus, there are 24 milliliters in six teaspoons.

The correct graph should show one ray with a closed point on the integer -2, which points to the left, and another ray with a closed point on the integer 3, which points to the right.

The following proportion may be written as \(\frac{\frac{1}{4}}{20}=\frac{3\frac{1}{2}}{x}\), which simplifies to \(\frac{1}{4}x=70\), where \(x = 280\).

Thus, there are actually 280 miles between the two cities.

The new length may be represented by the expression \(L + 2\), while the new width may be represented by the expression \(W + 2\). Thus, the area is equal to the product of the two dimensions, or \((L + 2)(W + 2)\).

Removal of nine pairs will ensure that she has one of each color because all three colors will be represented. Removal of only seven pairs may include only pairs of black and white socks, while not including a red pair.

The fractions in Choice C may be converted to the following decimals, which are indeed in order from least to greatest:

0.25, 0.68, 0.6875, 0.75

The average may be written as \(\frac{365+7+24}{3}\), which equals 132.

Moving the decimal five places to the right gives 175,000.

The average may be written as \(\frac{0.03(2800+3200+3600)}{3}\), which equals 96.

The following proportion may be written:

\(\frac{\frac{1}{3}}{15}=\frac{3\frac{2}{3}}{x}\)

This simplifies to \(\frac{1}{3}x=\frac{165}{3}\), where \(x = 165\). Thus, there are actually 165 miles between the two cities.

Simple interest may be calculated using the formula \(I = Prt\), where \(P\) represents the principal amount, \(r\) represents the rate, and \(t\) represents the length of time.

Substituting 200 for \(I\), 4,000 for \(P\), and 0.05 for \(r\) gives \(200 = 4,000 \times 0.05 \times t\). Thus, \(t = 1\).

The following equation may be solved for \(x\):

\(650 = 0.012x\)

Dividing both sides of the equation by 0.012 gives \(x = 54,166.67\). Thus, the assessed value of her property is $54,166.67.

The problem may be modeled with the equation \(23.80 = x – 0.15x\), which simplifies to \(23.80 = 0.85x\).

Dividing both sides of the equation by 0.85 gives \(x = 28\). So, the regular price of the lamp is $28.

The expression \(750 – 0.15 \times 750\), may be used to represent the price after the first discount. This amount is $637.50.

Taking an additional 10% off of the discounted price is represented by the expression \(637.50 – 0.10 \times 637.50\), which equals 573.75. Thus, the price after both discounts is $573.75.

The problem may be modeled and solved using the equation \(0.85x = 136\). Solving for \(x\) gives \(x = 160\).

Dividing a positive number by a negative number gives a negative quotient. For example, \(4 \div -2=-2\).

The fraction \(\frac{1}{8}=0.125\), which is equivalent to 12.5%.

In order to change the mixed number to an improper fraction, the denominator should first be multiplied by the whole number. Next, the numerator should be added to this product. The resulting value should be placed over the original denominator of the fractional portion of the mixed number.

\((5 x 4) + 3 = 23\)

\(23 \div 5 = \frac{23}{5}\)

The following equation may be used to solve the problem:

\(133x + 0.15 \times 133x = 2,294.25\)

Solving for \(x\) gives \(x = 15\).

Six hours passed from 6:30 a.m. to 12:30 p.m. Thirty-five more minutes passed from 12:30 p.m. to 1:05 p.m. So, it took him 6 hours and 35 minutes to finish the race.

The circle is divided into three equal sections, whereby two of them of are shaded. Thus, the represented fraction is \(\frac{2}{3}\).

The decimals may be multiplied as integers. However, the decimal will have six place values to the right of the decimal.

The ratio may be written as \(\frac{32}{56}\), which reduces to \(\frac{4}{7}\). Thus, the ratio of games lost to games played is 4:7.

The numerator and denominator of the first fraction are both multiplied by 3.

The following proportion may be written:

\(\frac{120}{8}=\frac{x}{15}\)

Solving for \(x\) gives \(x = 225\).

7,500 tires were sold in each of the years 2016 and 2018. This number was the least amount sold in a year, as evidenced by one and a half tires shown for these years, as compared to two and two and a half for the other two years.

Using the number of tires shown, the year of 2017 may be represented by the expression \(1\frac{1}{2}+\frac{1}{3}\times 1 \frac{1}{2}\), which equals 2.

Since 2 is \(\frac{1}{3}\) more than 1\(\frac{1}{2}\), the number of tires sold in 2017 was \(\frac{1}{3}\) more than the number sold in 2016.

The average may be written as \(\frac{7,500+10,000+7,500+12,500}{4}\), which equals 9,375.

The percent increase may be represented as \(\frac{40-20}{20}\), which equals 1. Since \(1=100\), the percent increase was 100%.

The formula for area of a square is \(A=s^2\), so the area may be written as \(A=5^2\), which means \(A=25\).

The first equation may be solved for \(x\). Doing so gives \(x = 2\). Substituting 2 for \(x\) into the second equation gives \(3 \times 2 + 4\), which is 10.

Each of the base angles measures 65° since the triangle is isosceles. Thus, the same of the base angles is 130°. The measure of \(\angle B\) is equal to the difference of 180° and 130°, which is 50°.

The average may be written as \(\frac{8+12+15+21+x+11}{6}=17\), which simplifies to \(\frac{67+x}{6}=17\).

Multiplying both sides of the equation by 6 gives \(67 + x = 102\). Subtracting 67 from both sides of the equation gives the solution of \(x = 35\).

The solution may be represented by the expression \(25 – (11.23 + 8.32)\), which equals 5.45. Thus, she has $5.45 left over.

The total work in worker‑days is \(6 \times 8 = 48\). At four workers, the time required is \(48 \div 4 = 12\) days.