SAT SAT Math Practice Test 2025

Let $t$ be the number of text messages. The total bill is given by $20 + 0.05t = 32.50$. Subtract 20 from both sides: $0.05t = 12.50$. Divide both sides by $0.05$: $t = \dfrac{12.50}{0.05} = 250$. The customer sent 250 text messages.

The function $f(x) = -2x^2 + 12x - 10$ is a downward-opening parabola, so the maximum occurs at the vertex. The $x$-coordinate of the vertex is $x = -\dfrac{b}{2a} = -\dfrac{12}{2(-2)} = -\dfrac{12}{-4} = 3$. Substitute $x = 3$ into the function: $f(3) = -2(9) + 12(3) - 10 = -18 + 36 - 10 = 8$. The maximum height is 8 feet.

Let $c$ be the number of cupcakes and $k$ be the number of cookies. We have the system:

From the first equation, $k = 80 - c$. Substitute into the second equation: $3c + 2(80 - c) = 210$, which gives $3c + 160 - 2c = 210$, so $c = 50$. The bakery sold 50 cupcakes. We can verify: $k = 80 - 50 = 30$, and $3(50) + 2(30) = 150 + 60 = 210$. This checks out.

The ratio of deer to elk is $5:3$. Let $d$ be the number of deer. Then $\dfrac{d}{120} = \dfrac{5}{3}$. Cross-multiply: $3d = 5 \times 120 = 600$. Divide both sides by 3: $d = 200$. Therefore, 200 deer were observed.

After the first discount of 15%, the price becomes $1200 \times (1 - 0.15) = 1200 \times 0.85 = 1020$. After the second discount of 10% on the new price, the final price becomes $1020 \times (1 - 0.10) = 1020 \times 0.90 = 918$. The final price is \918.00$.

Draw a perpendicular from the center $O$ to the chord $AB$. This perpendicular bisects the chord, so each half has length $\dfrac{12}{2} = 6$ cm. Let $d$ be the perpendicular distance from the center to the chord. Using the Pythagorean theorem with the radius as the hypotenuse: $d^2 + 6^2 = 10^2$, so $d^2 + 36 = 100$, giving $d^2 = 64$ and $d = 8$ cm.

Original data set (already sorted): $12, 15, 18, 18, 22, 25, 30$.

• Original mean: $\dfrac{12+15+18+18+22+25+30}{7} = \dfrac{140}{7} = 20$.
• Original median (4th value of 7): $18$.

New data set (sorted): $12, 15, 18, 18, 20, 22, 25, 30$ (8 values).

• New mean: $\dfrac{140+20}{8} = \dfrac{160}{8} = 20$.
• New median (average of 4th and 5th values): $\dfrac{18+20}{2} = 19$.

The mean stays the same and the median increases from 18 to 19.

The total number of marbles is $8 + 5 + 7 = 20$. The probability that the first marble drawn is red is $\dfrac{8}{20}$. After removing one red marble, there are 7 red marbles left out of 19 total. The probability that the second marble is also red is $\dfrac{7}{19}$. Therefore, the probability that both marbles are red is:

Simplify each radical:

• $\sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}$
• $\sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3}$

So the numerator is $4\sqrt{3} + 3\sqrt{3} = 7\sqrt{3}$.

Divide by $\sqrt{3}$: $\dfrac{7\sqrt{3}}{\sqrt{3}} = 7$.

The average rate of change is calculated as:

The average rate of change in revenue is \3{,}600$per month (or$3.6$ thousand dollars per month).