Okay. So 3/5 in decimal form is 0.6. 7/10 in decimal form is 0.7. When you put them in order from least to greatest, the order would be 0.15, 3/5, 7/10, 0.85. Converting fractions to decimals and looking at the different places and what not could help make solving questions like these much easier.
We are told that the first term is 2. The next term is 7(2) = 14; the third term is 7(14) = 98. And so on. So, the first term and the common ratio (7) are known.
The nth term of this geometric series is a_n = 2(7)^(n-1).
Check: What is the first term? We expect it is 2. 2(7)^(1-1) = 2(1) = 2. Correct.
What is the third term? We expect it is 98. 2(7)^(3-1) = 2(7)^2 = 98. Right.<span />
Answer:
see explanation
Step-by-step explanation:
x² + 3x + 7 = 5 ( subtract 5 from both sides )
x² + 3x + 2 = 0 ← in standard form
(x + 2)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x ( zero product rule )
x + 2 = 0 → x = - 2
x + 1 = 0 ⇒ x = - 1
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x² - 2 = - 2x² + 5x ( subtract - 2x² + 5x from both sides )
3x² - 5x - 2 = 0 ← in standard form
(3x + 1)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = -
x - 2 = 0 ⇒ x = 2
------------------------------------------------------------
(x + 3)² + 4x = 0 ← expand left side using FOIL and simplify
x² + 6x + 9 + 4x = 0
x² + 10x + 9 = 0 ← in standard form
(x + 9)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 9 = 0 ⇒ x = - 9
x + 1 = 0 ⇒ x = - 1
the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade is 14%.
Given, the members of the junior varsity swim team wear glasses is 55%.
And the members of junior varsity swim team who do not wear glasses and in 10th grade is 30%.
Let the total no. of members be x.
So, the members of the junior varsity swim team wear glasses (55%),will be
.
The total number of members not wearing glasses, will be
.
Now, the no. of members not wearing glasses and in 10th grade will be,
We know that the probability of an event E, P(E) will be,
So, the probability for no. of members not wearing glasses and in 10th grade will be,
Hence the nearest whole percent of probability is 14%.
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