Timothy bought concrete mix for several projects. He used
2 answers:
Answer:
The required model is
60 pounds of concrete each bag make.
Step-by-step explanation:
Consider the provided information.
Let the number of concrete bags are used is represented by y.
Part (A)
3.5 bags of concrete mix for a new set of stairs and 2.25 bags of concrete mix for a garden wall.
This can be written as:
Timothy mixed 345 pounds of concrete in all.
Therefore,
Hence, the required model is
Part (B) Solve for y. How many pounds of concrete does each bag make?
Consider the above equation.
Solve the equation for y as shown.
Add the like terms.
Divide both the sides by 5.75
Hence, 60 pounds of concrete each bag make.
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Answer:
(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is 0.0537.
(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is 0.0023.
(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is 0.1101.
Step-by-step explanation:
We are given that according to an NRF survey conducted by BIG research, the average family spends about $237 on electronics in back-to-college spending per student.
Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54.
Let X = <u><em>back-to-college family spending on electronics</em></u>
SO, X ~ Normal()
The z score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population mean family spending = $237
= standard deviation = $54
(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is = P(X < $150)
P(X < $150) = P( <
) = P(Z < -1.61) = 1 - P(Z
1.61)
= 1 - 0.9463 = <u>0.0537</u>
The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9463.
(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is = P(X > $390)
P(X > $390) = P( >
) = P(Z > 2.83) = 1 - P(Z
2.83)
= 1 - 0.9977 = <u>0.0023</u>
The above probability is calculated by looking at the value of x = 2.83 in the z table which has an area of 0.9977.
(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is given by = P($120 < X < $175)
P($120 < X < $175) = P(X < $175) - P(X $120)
P(X < $175) = P( <
) = P(Z < -1.15) = 1 - P(Z
1.15)
= 1 - 0.8749 = 0.1251
P(X < $120) = P( <
) = P(Z < -2.17) = 1 - P(Z
2.17)
= 1 - 0.9850 = 0.015
The above probability is calculated by looking at the value of x = 1.15 and x = 2.17 in the z table which has an area of 0.8749 and 0.9850 respectively.
Therefore, P($120 < X < $175) = 0.1251 - 0.015 = <u>0.1101</u>
Notice the picture below
the directrix is above the focus point, meaning the parabola is vertical and is opening downwards
now, "p" is the distance from the vertex to the focus point or the directrix, so that means, the vertex is between those two fellows, over the axis of symmetry, x = -2, since "p" is 1 unit, that puts the vertex at -2,5
since the parabola is opening downwards, that means the "p" value is negative, so is -1
the directrix is above the focus point, meaning the parabola is vertical and is opening downwards
now, "p" is the distance from the vertex to the focus point or the directrix, so that means, the vertex is between those two fellows, over the axis of symmetry, x = -2, since "p" is 1 unit, that puts the vertex at -2,5
since the parabola is opening downwards, that means the "p" value is negative, so is -1