well, when we use the word "the function" we're referring to the dependent part, which depends on the independent, y,x wise, we're referring to the function "y" or f(x) if you wish.
so for an exponential function
is the function ever positive only? it can be
is it negative only? it can be
can it be both? sure thing, most of the time it's both
we can say a function f(x) is always positive when the independent values of "x" yield a positive value only, mind you that when we're talking about "the function" we're really referring to the resulting values in a set, so can the values of the output no matter what "x" we use be always positive? sure, can they also be negative only? sure, how about both? sure thing.
notice the template in the picture below, we can transform any exponential function like the one above 2ˣ with some vertical shift upwards, and is always positive, or -2ˣ with a vertical shift downwards and it's always negative, or we can stretch it about and have -2ˣ shifted upwards so sometimes is positive, and sometimes is negative.
above the x-axis is always positive, below is negative, but with transformations on the parent function it can be any of the three types.
The property of real numbers that was illustrated in the above example is known as the: D. inverse property.
<h3>What is the Inverse Property of Real Numbers?</h3>
The inverse property of real numbers states that if you add the opposite of a number together with that number, the result would be zero.
For example, if "a" represents a number, the opposite of the number "a" is -a.
Applying the inverse property of real numbers, it states that: a + (-a) = a - a = 0. Both numbers will cancel each other to give zero.
In the same vein, as shown in the image given above:
6 is a number
The opposite of 6 is -6.
Applying the inverse property of real numbers, we have:
6 + (-6) = 0.
In conclusion, we can state that given the expression, 6 + (-6) = 0, the property of real numbers that was illustrated in the above example is known as the: D. inverse property.
Learn more about the inverse property on:
brainly.com/question/17407789
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Answer and explanation:
Null hypothesis(H0) says sentiment for increasing speed limit in the two populations is the same
Alternative hypothesis(Ha) says sentiment for increasing speed limit in the two populations is different
Where p1 is the first population proportion =65/297= 0.22
And p2 is the second population proportion = 78/189= 0.41
P= p1+p2/n1+n2= 65+78/297+189= 0.29
Hence H0= p1-p2=0
Ha=p1-p2≠0
Test statistic= p1-p2/√p(1-p) (1/n1+1/n2)
= 0.22-0.41/√0.29(1-0.29)(1/297+1/189)
= -4.49
Critical value at 95% significance level= 1.96( from tables)
We therefore reject null hypothesis as critical value is greater than test statistic
Therefore the sentiment for increasing speed limit in the two populations is different
b. at proportions of 0.24 and 0.40 for p1 and p2 respectively
Test statistic = 0.24-0.40/0.29(1-0.29)(1/297+1/189)
= -3.78
P value is 0.0002 at 0.05 significance level
Hence probability =0.4998
Step-by-step explanation:
The following prices for the same make and model used guitar for his work are :
$699.20,$700.30,$680.50,$700.30, and $800.25.
Mean of ungrouped data = sum of observations/total no of observations
For median, arrange the given data in ascending order.
$680.50, $699.20, $700.30, $700.30, $800.25
Median = middle value
Median = $700.30
The value that comes most often is called mode.
$700.30 comes two times. So, mode is $700.30
Hence, Mean = $716.11, median = $700.30 and mode = $700.30
Answer:
1.0754 times 10^8
Step-by-step explanation:
