Answer:
x=9
Step-by-step explanation:
Step 1: Simplify by both sides of the equation.
80-3x=53
80+-3x=53
-3x+80=53
Step 2: Subtract 80 from both sides.
-3x+80-80=53-80
-3x=-27
Step 3: Divide by both sides by 3.
-3x/-3 = -27/-3
x=9
25 metres. Because 1/10th of a kilometre is a 100 metres. And four athletes divided by 100 metres is 25 metres.
Answer/Step-by-step explanation:
The following steps to solve equation given by join are shown below including the property of numbers applied for each reasons:
4(2a + 3) = -3(a - 1) + 31 - 11a ----› Given
Apply the distributive property to open the parentheses
4*2a + 4*3 = -3*a -3*-1 + 31 - 11a
8a + 12 = -3a + 3 + 31 - 11a ----› Distributive property
Combine like terms together
8a + 12 = 3 + 31 -3a - 11a
8a + 12 = 34 - 14a ---› Combining like terms
Add 14a to both sides
8a + 12 + 14a = 34 - 14a + 14a
22a + 12 = 34 ----› Addition property
Subtract 12 from both sides
22a + 12 - 12 = 34 - 12
22a = 22 ----› subtraction property of equality
Divide both sides by 22
22a/22 = 22/22
a = 1 ----› Division property of Equality
Answer:
a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.
b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.
About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.6619.

The standard error of the proportion is:

The critical z-value for a 90% confidence interval is z=1.6449.
The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:
The 90% confidence interval for the population proportion is (0.6290, 0.6948).
Y= -2x-5
Work:
8x+4y=-20
4y=-20-8x
y= -2x-5