In triangle ABC, m∠ABC = (4x – 12)° and m∠ACB = (2x + 26)°. Yin says that if x = 19, the triangle must be equilateral. Is he cor
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A function 
from a set A to a set B is defined as a relation that assings to each element 
in the set A exactly one element 
in the set B. The set A is called the domain of the function while the set B is the range. So we have five statements and need to find some functions. Melissa decides to reserve a patch in her vegetable garden for growing bell peppers. If each side of the tomato patch is feet, then we have a square patch as shown in the Figure below.
1.a) Write the function Wa(x) representing the width of the bell pepper patch.
We know that she wants its width to be half the width of the tomato patch. Let be the width of the tomato patch, then the function that matches this statement is:
1.b) Write the function La(x) representing the length of the bell pepper patch.
In this case Melissa wants <span>its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:
</span>
<span>
2. Ar</span>ea of the bell pepper patch in terms of x.
Given that the bell pepper patch is a rectangle, then t<span>he area of a rectangle is the product of the length and width. So:
</span>
<span>
3. C</span><span>ombined area of the tomato patch and the bell pepper patch.
This function is the sum of both the area of the tomato patch and the bell pepper patch. So:
</span>
<span>
4. W</span>rite the function Aa(x) for the remaining planting area in the garden.
The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:<span>
</span>
5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.
Given that <span>Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:
</span>
<span>
Therefore the area of the remaining space is:
</span>
1.a) Write the function Wa(x) representing the width of the bell pepper patch.
We know that she wants its width to be half the width of the tomato patch. Let
1.b) Write the function La(x) representing the length of the bell pepper patch.
In this case Melissa wants <span>its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:
</span>
<span>
2. Ar</span>ea of the bell pepper patch in terms of x.
Given that the bell pepper patch is a rectangle, then t<span>he area of a rectangle is the product of the length and width. So:
</span>
<span>
3. C</span><span>ombined area of the tomato patch and the bell pepper patch.
This function is the sum of both the area of the tomato patch and the bell pepper patch. So:
</span>
<span>
4. W</span>rite the function Aa(x) for the remaining planting area in the garden.
The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:<span>
</span>
5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.
Given that <span>Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:
</span>
<span>
Therefore the area of the remaining space is:
</span>
For this case we have the following expression:
From here, we must clear the value of a.
We then have the following steps:
Place the terms that depend on a on the same side of the equation:
Do common factor "a":
Clear the value of "a" by dividing the factor within the parenthesis:
Answer:
The clear expression for "a" is given by:
Answer:
a
The 95% confidence interval is
b
The sample proportion is
c
The critical value is
d
The standard error is
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is
The alternative hypothesis is
Generally the sample proportion is mathematically evaluated as
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
Next we obtain the critical value of from the normal distribution table, the value is
Generally the standard of error is mathematically represented as
substituting values
The margin of error is
=>
=>
The 95% confidence interval is mathematically represented as
=>
=>