In this item, we are given with the slope, m = 2/3 and intercept of (1,1). The equation of the line that contains these properties is,
y - y₁ = m(x - x₁)
Substituting the known values,
y - 1 = (2/3)(x - 1)
Simplifying,
3y - 3 = 2x - 2
Further simplifying,
<em> 2x - 3y = -1</em>
The expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
<h3>Expression involving exponents and shaded area</h3>
The expression is:
6²- (3² + 2²)
The shaded area:
Shaded area=6²- (3² + 2²)
Shaded area=36-(9+4)
Shaded area=36-13
Shaded area=23 square inches
Therefore the expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
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Answer:
C. H0 : p = 0.8 H 1 : p ≠ 0.8
The test is:_____.
c. two-tailed
The test statistic is:______p ± z (base alpha by 2) 
The p-value is:_____. 0.09887
Based on this we:_____.
B. Reject the null hypothesis.
Step-by-step explanation:
We formulate null and alternative hypotheses as proportion of people who own cats is significantly different than 80%.
H0 : p = 0.8 H 1 : p ≠ 0.8
The alternative hypothesis H1 is that the 80% of the proportion is different and null hypothesis is , it is same.
For a two tailed test for significance level = 0.2 we have critical value ± 1.28.
We have alpha equal to 0.2 for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28
The test statistic is
p ± z (base alpha by 2) 
Where p = 0.8 , q = 1-p= 1-0.8= 0.2
n= 200
Putting the values
0.8 ± 1.28 
0.8 ± 0.03620
0.8362, 0.7638
As the calculated value of z lies within the critical region we reject the null hypothesis.
405 because 120+50+65=405
Answer:
Step-by-step explanation:The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw .