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One-step inequalities: word problems

The Leslie matrix for a female cheetah population with four age groups consisting of cubs, adolescents, young adults, and adults has largest eigenvalue c=1.255 c=1.255 and associated eigenvector [30.511.417.280.3] \left[\begin{array}{l}30.5 \\ 11.4 \\ 17.2 \\ 80.3\end{array}\right] .\newlinea) What is true about the long-term fate of this population?\newlineA. _The population dies out because the initial population is an eigenvector\newlineB. _The population dies out because the long-term growth factor c c is less than 11\newlineC. The population grows exponentially because the long-term growth factor c c is positive\newlineD. _The population grows exponentially because the long-term growth factor c c is greater than 11\newlineE. _The population stays the same because the initial population is not an eigenvector\newlineb) Determine the percentage of female cubs in the long run. Round the percentage to two decimal places.
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Pete took 33 history tests last quarter. For the first test, he studied for 6565 minutes and scored 87%87\%. For the second test, he studied for 4545 minutes and scored 73%73\%. For the third test, he studied for 8080 minutes and scored 98%98\%. Is the relationship between the amount of time Pete studied and the resulting test score a linear relationship?\newlineChoices:\newline(A)yes\newline(B)no\newlineNow, justify your answer.\newlineChoices:\newline(A)The longer Pete studied, the better his test score.\newline(B)Pete's test scores increased by 77 points for every additional 1010 minutes of study time.\newline(C)The increase in Pete's test score for every additional minute of study time is not constant.\newline(D)Pete's test score decreased from the first test to the second test and then increased from the second test to the third test.
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A factory sells backpacks for $40.00\$40.00 each. The cost to make 11 backpack is $10.00\$10.00. In addition to the costs of making backpacks, the factory has operating expenses of $12,000\$12,000 per week. The factory's goal is to make a profit of at least $980\$980 each week. Which inequality represents the number of backpacks, xx, that need to be sold each week for the factory to meet thls goal? How many backpacks must the factory sell to meet its weekly goal? Select the inequality that represents this situation and select the correct statement. \newlineThe factory must sell a minimum of 368368 backpacks to meet the weekly goal. \newline30x+12,000>=98030x + 12,000 >=980 \newlineThe factory must sell a minimum of 432432 backpacks to meet the weekly goal. \newline30x−12,000>=98030x - 12,000 >=980 \newline30x−12,000<=98030x - 12,000 <=980 \newlineThe factory must sell a minimum of 367367 backpacks to meet the weekly goal. \newline30x+12,000<=98030x + 12,000 <=980 \newline\newlineThe factory must sell a minimum of 433433 backpacks to meet the weekly goal.
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On day 11 , Jane invites 55 friends to her party. She asks each of those friends to visit and invite 44 of their friends the next day, and to have each of their friends visit and invite 44 of their friends the day after, and so on. Let P P be the number of people who are invited to Jane's party on day t t . Assume that no person is invited more than once. Which of the following best explains the relationship between t t and P P ?\newlineChoose 11 answer:\newline(A) The relationship is linear because all of the values of P P are multiples of 1010 .\newline(B) The relationship is exponential because P P increases by a factor of 44 each time t t increases by 11 .\newline(C) The relationship is exponential because P P increases by a factor of 55 each time t t increases by 11 .\newline(D) The relationship is linear because P P increases by a factor of 55 as t t changes from 11 to 22 .
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Mathias was asked whether the following equation is an identity:\newline2x2+10x+6=(x+3)(2x+1)+3(x+1) 2 x^{2}+10 x+6=(x+3)(2 x+1)+3(x+1) \newlineHe performed the following steps:\newline2x2+10x+6 2 x^{2}+10 x+6 \newline↪ Step 1=2x2+7x+3+(3x+3) \stackrel{\text { Step } 1}{\hookrightarrow}=2 x^{2}+7 x+3+(3 x+3) \newline↪ Step 2=2x2+6x+x+3+3(x+1) \stackrel{\text { Step } 2}{\hookrightarrow}=2 x^{2}+6 x+x+3+3(x+1) \newline↪ Step 3=2x(x+3)+(x+3)+3(x+1) \stackrel{\text { Step } 3}{\hookrightarrow}=2 x(x+3)+(x+3)+3(x+1) \newline↪ Step 4=(x+3)(2x+1)+3(x+1) \stackrel{\text { Step } 4}{\hookrightarrow}=(x+3)(2 x+1)+3(x+1) \newlineFor this reason, Mathias stated that the equation is a true identity.\newlineIs Mathias correct? If not, in which step did he make a mistake?\newlineChoose 11 answer:\newline(A) Mathias is correct.\newline(B) Mathias is incorrect. He made a mistake in step 11.\newline(C) Mathias is incorrect. He made a mistake in step 33.\newline(D) Mathias is incorrect. He made a mistake in step 44.
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