For this case we have to:
x: Let the variable representing the unknown number
We algebraically rewrite the given expression:
Twice a number plus 10, is represented as:
Three times that number less 4. is represented as:
Thus, the complete expression is:
Subtracting 3x from both sides of the inequality:
Subtracting 10 from both sides of the inequality:
Equal signs are added and the same sign is placed:
We multiply by -1 on both sides, taking into account that the sense of inequality changes:
The solution is given by all values of "x" less than 14.
Answer:
Answer:
97.10% probability that five or more of the original 2000 components fail during the useful life of the product.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either it works correctly, or it does not. The probability of a component falling is independent from other components. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
Approximate the probability that five or more of the original 2000 components fail during the useful life of the product.
We know that either less than five compoenents fail, or at least five do. The sum of the probabilities of these events is decimal 1. So
We want 
So
In which
97.10% probability that five or more of the original 2000 components fail during the useful life of the product.
Answer:
64.80
Step-by-step explanation:
The new price will equal the original price plus the markup.
The markup equal the original price * the markup percentage
markup = 54*.2
markup = 10.8
New price = original + markup
New price = 54+10.8
New price = 64.80
Answer:
m<ABC = 116°
m<CDE = 67°
Step-by-step explanation:
✔️m<ABC = 180 - m<BAD (adjacent angles of a parallelogram are supplementary)
m<ABC = 180 - 64° (Substitution)
m<ABC = 116°
✔️m<CDA = m<CDE + m<ADE (angle addition postulate)
m<CDA = m<CDE + 49°
m<CDA = m<ABC (opposite angles of a parallelogram are congruent)
m<CDE + 49° = 116° (substitution)
m<CDE = 116° - 49° (Substraction property of equality)
m<CDE = 67°
for this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle. So:
Answer:
