Answer:
3/4 of the fruits were oranges.
Step-by-step explanation:
Answer: β ≠ ±1
Step-by-step explanation: For a system of equations to have an unique solution, its determinant must be different from 0: det |A| ≠ 0. So,
det ![\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%261-%5Cbeta%5C%5C2%262%260%5C%5C2-2%5Cbeta%264%260%5Cend%7Barray%7D%5Cright%5D)
≠ 0
Determinant of a 3x3 matrix is calculated by:
det ![\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]\left[\begin{array}{ccc}1&\beta\\2&2\\2-2\beta&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%261-%5Cbeta%5C%5C2%262%260%5C%5C2-2%5Cbeta%264%260%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%5C%5C2%262%5C%5C2-2%5Cbeta%264%5Cend%7Barray%7D%5Cright%5D)
![8(1-\beta)-[2(2-2\beta)(1-\beta)]](https://tex.z-dn.net/?f=8%281-%5Cbeta%29-%5B2%282-2%5Cbeta%29%281-%5Cbeta%29%5D)
β ≠ ±1
For the system to have only one solution, β ≠ 1 or β ≠ -1.
Prime cost is the combination of a manufactured product's costs of direct materials and direct labor. In other words, prime cost refers to the direct production costs.
Prime cost=direct material cost+direct labor cost
Direct material cost of a tabletop is
380×(1÷4)=95 for each tabletop
Direct labor cost
The question says The machinist cuts and polishes five tabletops each hour
Which means 27.50 of direct labor to cut and polish 5 tabletops So direct labor cost for each tabletop is
27.50÷5=5.5
Finally the prime cost of cutting and polishing a tabletop is
Prime cost=95+5.5=100.5
The number of observations for each case in a t test for dependent samples is two is the correct answer.
In this question,
The dependent t-test also called the paired t-test or paired-samples t-test compares the means of two related groups to determine whether there is a statistically significant difference between these means. Each sample must be randomly selected from a normal population and each member of the first sample must be paired with a member of the second sample.
A dependent samples t-test uses two raw scores from each person to calculate difference scores and test for an average difference score that is equal to zero.
The groups contain either the same set of subjects or different subjects that the analysts have paired meaningfully. In dependent samples, subjects in one group do provide information about subjects in other groups.
Hence we c an conclude that the number of observations for each case in a t test for dependent samples is two is the correct answer.
Learn more about dependent t-test here
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The new area will be 320 in²
<em><u>Explanation</u></em>
Lin has a drawing with an area of 20 in² and she increases all sides by a scale factor of 4.
<u>The general rule</u> we need to use here.......
"<em>If the lengths of the sides in a shape are all increased by a scale factor of 
, then the area will be increased by a scale factor of 
"</em>
Here the sides are increased by a scale factor of 4. So, the area will be increased by a scale factor of 
Thus, the new area will be: 
