Question

1. $0.49div0.7=$
2. $15enclose{longdiv}{1,230}$
3. how many faces does a triangular pyramid have?
4. what is the probability of getting a number less than 7 on a standard six - sided die?
5. a ball began to roll down a hill. it started at 1 foot per second, but the rate doubled each second after that. how fast will the ball be going in 10 seconds?

Explanation:

Step1: Solve \(0.49\div0.7\)

Multiply both numerator and denominator by 10 to get \(4.9\div7\). Then \(4.9\div7 = 0.7\).

Step2: Calculate \(1230\div15\)

\(15\times80=1200\), \(1230 - 1200=30\), \(30\div15 = 2\). So \(1230\div15=(15\times80 + 30)\div15=80 + 2=82\).

Step3: Count faces of triangular pyramid

A triangular pyramid (tetrahedron) has 4 faces.

Step4: Find probability of number less than 7 on six - sided die

A standard six - sided die has numbers \(1,2,3,4,5,6\). All 6 outcomes are less than 7. Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{6}{6}=1\).

Step5: Determine ball's speed after 10 seconds

The speed forms a geometric sequence with first term \(a_1 = 1\) and common ratio \(r = 2\). The formula for the \(n\)th term of a geometric sequence is \(a_n=a_1\times r^{n - 1}\). For \(n = 10\), \(a_{10}=1\times2^{10 - 1}=2^9=512\) feet per second.

Answer:

1. \(0.7\)
2. \(82\)
3. \(4\)
4. \(1\)
5. \(512\) feet per second