Answer: 3/10
Step-by-step explanation:
Take the derivative of 
to get 
. Set that equal to 0 to find the critical points of the function. The critical points is when the slope is either 0 or undefined.
Now do:
There are quite a few more steps to actually find the minimum, but for this example you can automatically assume its a minimum because it is the only critical point of the function. Ill show you these extra steps tho.
Plug in two numbers into the derivative. One that is less than 3/10 and one that is greater than 3/10. The numbers 0 and 1 are fine. When x = 0, the function is -6. When x = 1, the function is +14. A switch from negative to positive indicates a minimum value
Answer:
Reflection, Triangle B is a reflection of A
Step-by-step explanation:
Reflection <em>is when we flip a figure over.
</em>
Translation <em>is when we slide a figure in any direction.
</em>
Rotation <em>is when we rotate a figure a certain degree around a point.
</em>
Dilation <em>is when we enlarge or reduce a figure.</em>
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Answer:
a) Explicit Formula : aₙ = 3. (-3)ⁿ⁻¹
b) Fifth term : a₅ = 243
Step-by-step explanation:
This sequence above is the Geometric sequence. The Geometric sequence is calculated using the formula
aₙ= a1.rⁿ⁻¹
where a1 = first term
r = common ratio
n = number of terms
From the above question, we are given
a1= 3, r=-3 and asked to find the explicit formula.
The explicit formula using the geometric sequence formula =
aₙ = 3. (-3)ⁿ⁻¹
b) The fifth term in the sequence is calculated as
aₙ = 3. (-3)ⁿ⁻¹
Where n = 5
a₅ = 3.(-3)⁵⁻¹
a₅ = 3.(-3)⁴
a₅= 243
Answer:
A one-tailed hypothesis will be used to perform the test.
Step-by-step explanation:
The purpose of the marketing research consultant hired by Coca-Cola is to determine whether the the proportion of customers who prefer Coke to other brands is over 50%.
The marketing research consultant selected a random sample of <em>n</em> = 200 customers. The sample proportion of people who favored Coca-Cola over other brands was 55%.
The marketing research consultant can perform a single proportion hypothesis test to determine whether greater than 50% of customers prefer Coca-Cola to other brands.
Since we need to determine whether the population percentage is greater than a null value, the hypothesis is not two-tailed.
The hypothesis can be defined as:
<em>H₀</em>: The proportion of people who favor Coca-Cola over other brands was 55%, i.e. <em>p</em> = 0.50.
<em>Hₐ</em>: The proportion of people who favor Coca-Cola over other brands was more than 55%, i.e. <em>p</em> > 0.50.
Thus, a one-tailed hypothesis will be used to perform the test.
