Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon

One-step inequalities: word problems

A solid line in the xyxy plane passes through the points (−3,1)(-3, 1), (0,2)(0, 2), and (3,3)(3, 3). The line divides the plane into two halves. The half above the line is shaded.\newline11\newline22\newline33\newline44\newline55\newline−2-2\newline−3-3\newline−4-4\newline−5-5\newline11\newline22\newline33\newline44\newline55\newline−2-2\newline−3-3\newline−4-4\newline−5-5\newlineyy\newlinexx\newlineOO\newlineThe graph of \newliney≥13x+2y \geq \frac{1}{3}x + 2 is shown. Which of the following ordered pairs (x,y)(x, y) satisfies the inequality?\newlineChoose 11 answer:\newline(Choice A) \newline(−4,1)(-4, 1)\newlineA\newline(−4,1)(-4, 1)\newline(Choice B) \newline(−2,1)(-2, 1)\newlineB\newline(−2,1)(-2, 1)\newline(Choice C) \newline(0,1)(0, 1)\newlineC\newline(0,1)(0, 1)\newline(Choice D) \newline(2,2)(2, 2)\newlineD\newline(2,2)(2, 2)
Get tutor helpright-arrow
If a group of 1212 boys with different heights: 5′5'; 5′2′′5'2''; 5′4′′5'4''; 5′6′′5'6''; 5′8′′5'8''; 5′10′′5'10''; 6′6'; 6′2′′6'2''; 6′4′′6'4''; 6′6′′6'6''; 5′2′′5'2''00; 5′2′′5'2''11, which of the following is correct?\newlineA) No boy in the group represents the median height of the group.\newlineB) There is a boy in the group who represents the arithmetic mean (average) height of the group.\newlineC) The sum of the number of boys with less than the median height and the number of boys with greater than the median height is equal to 5′2′′5'2''22.\newlineD) The arithmetic mean (average) height is greater than the median height of the group.
Get tutor helpright-arrow
Terry was asked to determine whether f(x)=x3+1x f(x)=x^{3}+\frac{1}{x} is even, odd, or neither. Here is his work:\newlineStep 11: Find expression for f(−x) f(-x) \newlinef(−x)=(−x)3+1(−x)=−x3−1x \begin{aligned} f(-x) & =(-x)^{3}+\frac{1}{(-x)} \\ & =-x^{3}-\frac{1}{x} \end{aligned} \newlineStep 22: Check if f(−x) f(-x) is equal to f(x) f(x) or −f(x) -f(x) \newline−x3−1x -x^{3}-\frac{1}{x} isn't the same as f(x)=x3+1x f(x)=x^{3}+\frac{1}{x} or\newline−f(x)=−x3+1x.  -f(x)=-x^{3}+\frac{1}{x} \text {. } \newlineStep 33: Conclusion\newlinef(−x) f(-x) isn't equivalent to either f(x) f(x) or −f(x) -f(x) , so f f is neither even nor odd.\newlineIs Terry's work correct? If not, what is the first step where Terry made a mistake?\newlineChoose 11 answer:\newline(A) Terry's work is correct.\newline(B) Terry's work is incorrect. He first made a mistake in Step 11.\newline(C) Terry's work is incorrect. He first made a mistake in Step 22.\newline(D) Terry's work is incorrect. He first made a mistake in Step 33.
Get tutor helpright-arrow
Tom was asked to determine whether f(x)=x3+x f(x)=x^{3}+x is even, odd, or neither. Here is his work:\newlineStep 11: Find expression for f(−x) f(-x) \newlinef(−x)=(−x)3+x=−x3+x \begin{aligned} f(-x) & =(-x)^{3}+x \\ & =-x^{3}+x \end{aligned} \newlineStep 22: Check if f(−x) f(-x) is equal to f(x) f(x) or −f(x) -f(x) \newline−x3+x -x^{3}+x isn't the same as f(x)=x3+x f(x)=x^{3}+x or −f(x)=−x3−x -f(x)=-x^{3}-x .\newlineStep 33: Conclusion\newlinef(−x) f(-x) isn't equivalent to either f(x) f(x) or −f(x) -f(x) , so f f is neither even nor odd.\newlineIs Tom's work correct? If not, what is the first step where Tom made a mistake?\newlineChoose 11 answer:\newline(A) Tom's work is correct.\newline(B) Tom's work is incorrect. He first made a mistake in Step 11.\newline(C) Tom's work is incorrect. He first made a mistake in Step 22.\newline(D) Tom's work is incorrect. He first made a mistake in Step 33.
Get tutor helpright-arrow
Jen was asked to determine whether f(x)=1x3 f(x)=\frac{1}{\sqrt[3]{x}} is even, odd, or neither. Here is her work:\newlineStep 11: Find expression for f(−x) f(-x) \newlinef(−x)=1(−x)3=1−13⋅x3=−1x3 \begin{aligned} f(-x) & =\frac{1}{\sqrt[3]{(-x)}} \\ & =\frac{1}{\sqrt[3]{-1} \cdot \sqrt[3]{x}} \\ & =-\frac{1}{\sqrt[3]{x}} \end{aligned} \newlineStep 22: Check if f(−x) f(-x) is equal to f(x) f(x) or −f(x) -f(x) \newline−1x3 -\frac{1}{\sqrt[3]{x}} is the same as\newline−f(x)=−1x3. -f(x)=-\frac{1}{\sqrt[3]{x}} . \newlineStep 33: Conclusion\newlinef(−x) f(-x) is equivalent to −f(x) -f(x) , so f f is even.\newlineIs Jen's work correct? If not, what is the first step where Jen made a mistake?\newlineChoose 11 answer:\newline(A) Jen's work is correct.\newline(B) Jen's work is incorrect. She first made a mistake in Step 11.\newline(C) Jen's work is incorrect. She first made a mistake in Step 22.\newline(D) Jen's work is incorrect. She first made a mistake in Step 33.
Get tutor helpright-arrow
April was asked to determine whether f(x)=x3−1 f(x)=x^{3}-1 is even, odd, or neither. Here is her work:\newlineStep 11: Find expression for f(−x) f(-x) \newlinef(−x)=(−x)3−1=−x3−1 \begin{aligned} f(-x) & =(-x)^{3}-1 \\ & =-x^{3}-1 \end{aligned} \newlineStep 22: Check if f(−x) f(-x) is equal to f(x) f(x) or −f(x) -f(x) \newline−x3−1 -x^{3}-1 is the same as\newline−f(x)=−x3−1 -f(x)=-x^{3}-1 .\newlineStep 33: Conclusion\newlinef(−x) f(-x) is equivalent to −f(x) -f(x) , so f f is odd.\newlineIs April's work correct? If not, what is the first step where April made a mistake?\newlineChoose 11 answer:\newline(A) April's work is correct.\newline(B) April's work is incorrect. She first made a mistake in Step 11.\newline(C) April's work is incorrect. She first made a mistake in Step 22.\newline(D) April's work is incorrect. She first made a mistake in Step 33.
Get tutor helpright-arrow
Kris was asked to determine whether f(x)=x3−x f(x)=x^{3}-x is even, odd, or neither. Here is his work:\newlineStep 11: Find expression for f(−x) f(-x) \newlinef(−x)=(−x)3−(−x)=(−1)3⋅x3+x=−x3+x \begin{aligned} f(-x) & =(-x)^{3}-(-x) \\ & =(-1)^{3} \cdot x^{3}+x \\ & =-x^{3}+x \end{aligned} \newlineStep 22: Check if f(−x) f(-x) is equal to f(x) f(x) or −f(x) -f(x) \newline−x3+x -x^{3}+x is the same as\newline−f(x)=−x3+x.  -f(x)=-x^{3}+x \text {. } \newlineStep 33: Conclusion\newlinef(−x) f(-x) is equivalent to −f(x) -f(x) , so f f is odd.\newlineIs Kris' work correct? If not, what is the first step where Kris made a mistake?\newlineChoose 11 answer:\newline(A) Kris' work is correct.\newline(B) Kris' work is incorrect. He first made a mistake in Step 11.\newline(C) Kris' work is incorrect. He first made a mistake in Step 22.\newline(D) Kris' work is incorrect. He first made a mistake in Step 33.
Get tutor helpright-arrow
Sydney was asked whether the following equation is an identity:\newline(2x2−18)(x+3)(x−3)=2x4−36x2+162 \left(2 x^{2}-18\right)(x+3)(x-3)=2 x^{4}-36 x^{2}+162 \newlineShe performed the following steps:\newline(2x2−18)(x+3)(x−3) \left(2 x^{2}-18\right)(x+3)(x-3) \newline↪ Step 1=2(x2−9)(x2−3x+3x−9) \stackrel{\text { Step } 1}{\hookrightarrow}=2\left(x^{2}-9\right)\left(x^{2}-3 x+3 x-9\right) \newline↪ Step 2=2(x2−9)(x2−9) \stackrel{\text { Step } 2}{\hookrightarrow}=2\left(x^{2}-9\right)\left(x^{2}-9\right) \newline↪ Step 3=2(x2−9)2 \stackrel{\text { Step } 3}{\hookrightarrow}=2\left(x^{2}-9\right)^{2} \newline↪ Step 4=2(x4−18x2+81) \stackrel{\text { Step } 4}{\hookrightarrow}=2\left(x^{4}-18 x^{2}+81\right) \newline↪ Step 5=2x4−36x2+162 \stackrel{\text { Step } 5}{\hookrightarrow}=2 x^{4}-36 x^{2}+162 \newlineFor this reason, Sydney stated that the equation is a true identity.\newlineIs Sydney correct? If not, in which step did she make a mistake?\newlineChoose 11 answer:\newline(A) Sydney is correct.\newline(B) Sydney is incorrect. She made a mistake in step 11.\newline(C) Sydney is incorrect. She made a mistake in step 33.\newline(D) Sydney is incorrect. She made a mistake in step 44.
Get tutor helpright-arrow
Socially 00ptimal Level\newlineHow does this compare to the socially optimal level of provision? The social optimum is the quantity at which the sum of the individuals' marginal rates of substitution equals the ratio of prices (which is 11 in this example). Each individual's MRS M R S is the ratio of his marginal utility of fireworks to his marginal utility of private goods, which we obtain by differentiating the previous utility function with respect to fireworks and then again with respect to private goods. So the optimal amount of fireworks is determined by:\newline(100−FB)/[2×(FB+FJ)]+(100−Fj)/[2×(FB+Fj)]=1 \left(100-F_{B}\right) /\left[2 \times\left(F_{B}+F_{J}\right)\right]+\left(100-F_{j}\right) /\left[2 \times\left(F_{B}+F_{j}\right)\right]=1 \newlineUsing the fact that total fireworks F=FB+Fβ F=F_{B}+F_{\beta} we can rewrite this equation as:\newline(200−F)/2F=1 (200-F) / 2 F=1 \newlineSolving this, we obtain F=66.6 F=66.6 . This quantity is much higher than the total provision by the private market, 4040 , due to the free rider problem. The public good is underprovided by the private market.
Get tutor helpright-arrow
A company claims that the mean monthly residential electricity consumption in a certain region is more than 860kiloWatt−hours(kWh). 860 \mathrm{kiloWatt-hours} \mathrm{(kWh).} You want to test this claim. You find that a random sample of 6565 residential customers has a mean monthly consumption of 890kWh 890 \mathrm{kWh} . Assume the population standard deviation is 128kWh 128 \mathrm{kWh} . At α=0.01 \alpha=0.01 , can you support the claim? Complete parts (a) through ( 00 ).\newline(a) Identify H0 \mathrm{H}_{0} and Ha \mathrm{H}_{\mathrm{a}} . Choose the correct answer below.\newlineA. H0:μ>860 (claim) H8:μ≤860 \begin{array}{l} H_{0}: \mu>860 \text { (claim) } \\ H_{8}: \mu \leq 860 \end{array} \newlineB. H0:μ>890 (claim) Ha:μ≤890 \begin{array}{l} H_{0}: \mu>890 \text { (claim) } \\ H_{a}: \mu \leq 890 \end{array} \newlinec. H0:μ≤890H2:μ>890 (claim)  \begin{array}{l} H_{0}: \mu \leq 890 \\ H_{2}: \mu>890 \text { (claim) } \end{array} \newlineD. H0:μ=860 (claim) Ha:μ≠860 \begin{array}{l} H_{0}: \mu=860 \text { (claim) } \\ H_{a}: \mu \neq 860 \end{array} \newlineE. H0:μ=890H8:μ≠890 (daim)  \begin{array}{l} H_{0}: \mu=890 \\ H_{8}: \mu \neq 890 \text { (daim) } \end{array} \newlineF. H0:μ≤860Ha:μ>860 (claim)  \begin{array}{l} H_{0}: \mu \leq 860 \\ H_{a}: \mu>860 \text { (claim) } \end{array}
Get tutor helpright-arrow
Ezra is making a tray of macaroni and cheese for dinner. He melts 1818 ounces of cheddar cheese in a pot. He decides to add cream cheese to make it really creamy. Ezra plans to add less cream cheese than cheddar cheese. \newlineWrite an inequality to represent the amount of cream cheese, in ounces, that Ezra might add, cc.
Get tutor helpright-arrow
A large truck, traveling 3030 miles per hour, carries a letter from the central post office to the local post office. The letter is then loaded onto a local vehicle, which travels at an average speed of 1010 miles per hour, until the letter reaches its destination. The large truck carried the letter for a a minutes and the local vehicle carried the letter for b b minutes. If the total distance that the letter travelled from the central post office to its destination was 2424 miles, which of the following equations correctly relates a a and b b ?\newlineChoose 11 answer:\newline(A) 3060a+1060b=24 \frac{30}{60} a+\frac{10}{60} b=24 \newline(B) 6030a+6010b=24 \frac{60}{30} a+\frac{60}{10} b=24 \newline(C) 30a+10b=24 30 a+10 b=24 \newline(D) 60⋅30a+60⋅10b=24 60 \cdot 30 a+60 \cdot 10 b=24
Get tutor helpright-arrow
12
Next