You can observe that angle 1 and angle with 47° are inside a parallelogram.
Consider that the sum of the internal angles of a parallelogram is 360°.
Moreover, consider that the angle at the top right of the parallogram is congruent with the angle of 47°, then, such an angle is if 47°.
Consider that angle down right side is congruent with angle 1, then, they have the same measure.
You can write the previous situation in the following equation:
47 + 47 + ∠1 + ∠1 = 360 simplify like terms
94 + 2∠1 = 360 subtract both sides by 94
2∠1 = 360 - 94
2∠1 = 266 divide by 2 both sides
∠1 = 266/2
∠1 = 133
Hence, the measure of angle 1 is m∠1 = 133°
Answer:
- 273 mL of 5%
- 117 mL of 15%
Step-by-step explanation:
Let q represent the quantity of 15% dressing used. Then the amount of 5% dressing is (390 -q). The amount of vinegar in the mix is ...
0.15q + 0.05(390 -q) = 0.08(390)
0.10q = 31.2 -19.5 = 11.7 . . . . . . subtract 0.05(390) and simplify
q = 117 . . . . . . . . . . . . . . . . . . multiply by 10
390-q = 273
The chef should use 273 mL of the first brand (5% vinegar) and 117 mL of the second brand (15% vinegar).
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<em>Additional comment</em>
You may have noticed that the value of q is (0.08 -0.05)/(0.10 -0.05)×390. The fraction of the mix that is the highest contributor is the ratio of the difference between the mix value and least contributor, divided by the difference between the contributors: (8-5)/(15-5) = 3/10, the fraction that is 15% vinegar. This is the generic solution to mixture problems.
Equation in slope-intercept form is y = 2x - 6
Step-by-step explanation:
- Step 1: Given slope of the line, m = 2. Form an equation y = mx + b
⇒ y = 2x + b ---- (1)
- Step 2: The line passes through the point (4,2). So it will satisfy the equation. Find b by substituting x = 4 and y = 2.
⇒ 2 = 2 × 4 + b = 8 + b
⇒ b = -6
- Step 3: Form the slope-intercept equation.
⇒ y = 2x - 6
Answer:
a) 0.3277
b) 0.0128
Step-by-step explanation:
We are given the following information in the question:
N(2750, 560).
Mean, μ = 2750
Standard Deviation, σ = 560
We are given that the distribution of distribution of birth weights is a bell shaped distribution that is a normal distribution.
Formula:
a) P (less than 2500 grams)
P(x < 2500)
Calculation the value from standard normal z table, we have,
b) P ((less than 1500 grams)
P(x < 1500)
Calculation the value from standard normal z table, we have,
