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Daniel [21]
3 years ago
11

Let f(x)=4x+7 and g(x)=3x-5. find (fog)(-4) A. -9 B. -61 C. -32 D. -17

Mathematics
1 answer:
prohojiy [21]3 years ago
3 0

Answer:

B . (fog)(-4)  = - 61

Step-by-step explanation:

Here, given  f(x) = 4 x + 7, g(x) = 3 x- 5

Now, by the COMPOSITE FUNCTION:

(f o g) (x)  = f (g(x))

Now here: )f o g) ( -4)  = f (g(-4))

<u>Simplifying for g(x) =  3 x  - 5</u>

 g(-4)  = 3 (-4) -  5 = -12 - 5  = -17

or, g (-4)  = -17

Now, <u>for f(x) = 4 x + 7 </u>

f ( g(-4))  = f ( -17) = 4 (-17) + 7

= - 68 + 7 =  - 61

or, f ( g(-4))  = - 61

Hence, (fog)(-4)  = - 61

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6 0
3 years ago
The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).
natita [175]

Answer:

68% of jazz CDs play between 45 and 59 minutes.

Step-by-step explanation:

<u>The correct question is:</u> The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

According to the 68-95-99.7 rule, what percentage of jazz CDs play between 45 and 59 minutes?

Let X = <u>playing time of jazz CDs</u>

SO, X ~ Normal(\mu=52, \sigma^{2} =7)

The z-score probability distribution for the normal distribution is given by;

                                    Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

Now, according to the 68-95-99.7 rule, it is stated that;

  • 68% of the data values lie within one standard deviation points from the mean.
  • 95% of the data values lie within two standard deviation points from the mean.
  • 99.7% of the data values lie within three standard deviation points from the mean.

Here, we have to find the percentage of jazz CDs play between 45 and 59 minutes;

   For 45 minutes, z-score is =  \frac{45-52}{7}  = -1

   For 59 minutes, z-score is =  \frac{59-52}{7}  = 1

This means that our data values lie within 1 standard deviation points, so it is stated that 68% of jazz CDs play between 45 and 59 minutes.

6 0
3 years ago
Relationship between the value of the given digits 6s in 660
expeople1 [14]
We have the given number = 660
Now, explain the relationship of 6s in the given number.
=> 6 = hundreds
=> 6 = tens
=> 0 = ones
This is also another form:
=> 6 = 600
=> 6 = 60,
now, notice that the first value of 6 in the leftmost side is 10 times higher than the next number 6.
=> 60 x 10 = 600.
Thus, 600 is 10 times greater than 60 and vice versa.



5 0
3 years ago
The _______________ separates the region of rejection from the region of non rejection.
Alekssandra [29.7K]

Answer:

Critical Value

Step-by-step explanation:

The critical value separates the region of rejection from the region of non rejection.

We define critical values as:

  • Critical value helps us to give the decision rule for the rejection or acceptance of null hypothesis.
  • Critical value separates the acceptance region from the rejection region.
  • These are referred to as cut-off values that define regions where the test statistic is unlikely to lie.
  • The critical value depends on the kind of test being performed and the significance level.

6 0
3 years ago
What is the equation of this graph? <br><br>a) x=-7<br>b) y=-7<br>​
sergiy2304 [10]
Since it’s vertical it would be x=-7
4 0
3 years ago
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