W = 3x + 7y solve for y

Solution/Step-by-step breakdown:

Information provided:

m<9 = 97°

m<12 = 114°

a. m<1 = m<9 because they are corresponding angles, which are equal.

m<1 = 97° (using substitution)

b. m<2 + m<1 = 180° (since they form a linear pair)

m<2 + 97° = 180° (substitute the value)

m<2 = 180 - 97 (subtracting 97 from both sides)

m<2 = 83°

c. m<3 = m<11 (as they are corresponding angles)

m<11 + m<12 = 180° (linear pair)

m<11 + 114° = 180° (substituting the known angle)

m<11 = 180 - 114

m<11 = 66°

m<3 = m<11 = 66°

d. m<4 + m<3 = 180° (linear pair)

m<4 + 66° = 180° (substituting the known angle)

m<4 = 180 - 66

m<4 = 114°

e. m<5 = m<2 as vertical angles are equal.

m<5 = 83° (using substitution)

f. m<6 = m<1 (vertical angles are equal)

m<6 = 97° (using substitution)

g. m<7 = m<4 (as vertical angles are equal)

m<7 = 114° (using substitution)

h. m<8 = m<3 (due to vertical angles being equal)

m<8 = 66° (using substitution)

i. m<10 = m<2 (corresponding angles are equal)

m<10 = 83° (using substitution)

j. m<11 = m<3 (because they are vertical angles)

m<11 = 66° (using substitution)

k. m<13 = m<5 (corresponding angles)

m<13 = 83° (applying substitution)

l. m<14 = m<9 (as vertical angles)

m<14 = 97° (applying substitution)

m. m<15 = m<12 (as vertical angles)

m<15 = 114° (applying substitution)

n. m<16 = m<11 (because they are vertical angles)

m<16 = 66° (applying substitution)

Response:

Step-by-step explanation:

Information given:

Objective:

Calculate the maximum and minimum values

The max value is found as follows:

The min value is identified as follows:

Examining Talia's steps to derive the line equation, we identify the erroneous step as detailed below:
Step 1:
Select a point on the line, such as (2,5)
Step 2:
<span>Select another point on the line, such as (1, 3)
Step 3:
</span><span>Measure units to find the slope. The line moves 1 unit to the right and 2 units upward, resulting in a slope of
(5-3)/(2-1) = 2/1 = 2
Step 4:
</span><span>Apply these values in the point-slope form
y - y1 = m(x - x1)
y - 3 = 2(x - 1)
y = 2x + 1
Hence, the conclusion is:
</span><span>Step 4 is erroneous due to incorrect application of (1, 3) in the point-slope format.</span>

Answer:

Each coordinate pair indicates the quantity of crates and its associated cost. You can calculate the unit rate by performing division to find the y-value when the x-value equals 1.

Step-by-step explanation:

A. Mean and standard deviation.

The sampling distribution’s mean closely matches the population mean. Since the population mean is 174.5, the sampling distribution’s mean equals this value.

The standard deviation of the sampling distribution is:

            σₓ̄ = σ / √n

Plugging in values:

            σₓ̄ = 6.9 / √25 = 1.38

b. Calculate z-scores for both values:
         
      z = (value - mean) / standard deviation

For 172.5:
     z = (172.5 - 174.5) / 1.38 = -1.49
Corresponding probability ≈ 0.068

For 175.8:
   z = (175.8 - 174.5) / 1.38 = 0.94
Corresponding probability ≈ 0.83

The difference between these probabilities is 0.762.

Approximately 0.762 × 200 = 152 sample means lie between 172.5 and 175.8.

c. Z-score for 172 cm:

    z = (172 - 174.5) / 1.38 = -1.81
Probability ≈ 0.03

Hence, samples with means below 172 cm equal 0.03 × 200 = 6.