In psychology, it has been suggested that the number of nonsense syllables that a person can repeat consecutively depends on his or her IQ score I according to the equation . Use this
relationship to estimate the IQ of a person who can repeat 7 nonsense syllables consecutively.
(Round to the nearest integer as needed.)

Ask by Schultz Gordon. in the United States

Nov 25,2024

Question

In psychology, it has been suggested that the number of nonsense syllables that a person can repeat consecutively depends on his or her IQ score I according to the equation . Use this
relationship to estimate the IQ of a person who can repeat 7 nonsense syllables consecutively.
(Round to the nearest integer as needed.)

Ask by Schultz Gordon. in the United States

Nov 25,2024

UpStudy AI · Accepted Answer

To estimate the IQ of a person who can repeat 7 nonsense syllables consecutively, we can use the given relationship between the number of nonsense syllables $$ S $$ and the IQ score $$ I $$ as follows:

Given equation: $$ S = 2 \sqrt{I} - 9 $$

We are given that $$ S = 7 $$, so we can substitute this value into the equation to solve for $$ I $$:

$$ 7 = 2 \sqrt{I} - 9 $$

Now, we can solve for $$ I $$ by isolating it on one side of the equation.
Solve the equation by following steps:
- step0: Solve for $$I$$:
  $$7=2\sqrt{I}-9$$
- step1: Find the domain:
  $$7=2\sqrt{I}-9,I\geq 0$$
- step2: Swap the sides:
  $$2\sqrt{I}-9=7$$
- step3: Move the constant to the right side:
  $$2\sqrt{I}=7-\left(-9\right)$$
- step4: Calculate:
  $$2\sqrt{I}=16$$
- step5: Divide both sides:
  $$\sqrt{I}=8$$
- step6: Raise both sides to the $$2$$-th power$$:$$
  $$\left(\sqrt{I}\right)^{2}=8^{2}$$
- step7: Evaluate the power:
  $$I=64$$
- step8: Check if the solution is in the defined range:
  $$I=64,I\geq 0$$
- step9: Find the intersection:
  $$I=64$$
- step10: Check the solution:
  $$I=64$$
The solution to the equation is $$ I = 64 $$.

Therefore, the estimated IQ of a person who can repeat 7 nonsense syllables consecutively is 64.
The estimated IQ is 64.

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