Answer:
$135
Step-by-step explanation:
Step 1
Conversion
Base = 2 yards
1 yard = 3 feet
2 yards = x
Cross Multiply
x = 2 × 3 feet = 6 feet
Height = 5 yards
1 yard = 3 feet
5 yards = x
Cross Multiply
x = 5 × 3 feet = 15 feet
Step 2
Find the area of the triangle
Area of a triangle = 1/2 × base × height
Base = 6 feet
Height = 15 feet
Area = 1/2 × 6 × 15
= 45 square feet
Step 3
Find the cost of the carpet
1 Square foot = $3
45 square feet = x
Cross Multiply
x = 45 × $3
x = $135
Therefore, the amount you will pay to cover a triangular section of the floor is $135
(f g)(x) means f(x) * g(x), so plug the value of each function in:
(x+2)(x-4)
And solve by distributing using FOIL:
Firsts: x * x = x²
Outers: x * -4 = -4x
Inners: 2 * x = 2x
Lasts: 2 * -4 = -8
Combine them all together:
x² - 4x + 2x - 8
Combine like terms (the -4x and 2x):
x² - 2x - 8
So the second to last one is correct.
Answer:
Step-by-step explanation:
a) Sample statistics are used to estimate population value. Since 48% is a sample proportion, therefore, it is a sample statistic.
b) For 95% confidence level, z* = 1.96.
\hat{p}\pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}= 0.61\pm 0.61\sqrt{\frac{0.61(1-0.61)}{1578}}=0.61\pm 0.024 \ or (0.586, 0.634).
We are 95% confident that the true proportion of US residents who think marijuana should be made legal lies between 58.6% and 63.4%.
c)
\\np=1578(0.61)=962.58
\\n(1-p)=1578(1-0.61)=615.42
Since both np and n(1-p), are at least 10, the normal model is a good approximation for these data.
d) As the lower limit of confidence interval is less than 0.5, less than 50% population is also a plausible value of true proportion. This means the statement "Majority of Americans think marijuana should be legalized" is not justified.
2t + 3t = 6t is false. The correct answer is 5t.
y + y + y = y(1 + 1 + 1) is true. Correct answer is 3y.
3(2 + x) = 6 + 3x is true. This is an application of the distributive rule for mult.
2a + 2b = 4ab is false. a and b are separate variables with no given relationship to each other. Correct answer would be 2(a+b).
x + 3 = 4x is false. x + 3x = 4x would be true.
