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mixer [17]
1 year ago
12

The range of the function given below is the set of all positive real numbers greater than 7. F(x) = 7 + 3x A. True B. False

Mathematics
2 answers:
lianna [129]1 year ago
8 0
True. 3x is always greater than 0 so 7 +3x is always greater than 7.
lord [1]1 year ago
6 0

Answer:

Option A. True

Step-by-step explanation:

Range of the function f(x)=7+3^{x} is defined by the values of F(x) by plugging in the values of x in the function.

In other words when we graph the function as

x            1         2        3      4

F(x)       10      16       30    88

Then the x values define the domain of the given function and values of f(x) define the range.

Therefore, range of the given function will be all positive real numbers greater than 7.

Option A. is the answer.          

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Which product is negative? (Negative StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (one-four
nasty-shy [4]

Answer:

(D)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)

Step-by-step explanation:

The given options are:

(A)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(\dfrac14\right)\\(B)\left(\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)\\(C)\left(\dfrac38\right)\left(\dfrac57\right)\left(\dfrac14\right)\\(D)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)

The key to determining which product is negative is to understand the rule of sign multiplication.

Now:

  • The product of even negative terms is positive
  • The product of odd negative terms is negative.
  • The product of positive will always be positive.

In Options A and B, the number of negative signs is even, therefore our result is positive.

In option C, all the terms are positive, therefore our result will be positive.

In Option D, the number of negative signs is odd, therefore our result is negative.

4 0
1 year ago
Read 2 more answers
Kristen is 64 inches tall, and she stands 12 feet away from a streetlight. If she casts an 82-inch-long shadow, how tall is the
o-na [289]

Answer:

176.39 inches or

14.70 feet

Step-by-step explanation:

Consider the right triangle made by Kristen, ground and shadow.

This triangle has one leg as 64 inches.

Next consider the right triangle formed by street light, ground upto shadow tip.

The two triangles have common angle of elevation and also another angle as 90 degrees.

Hence the two triangles would be similar

Also if A is the angle made by hypotenuse of both triangles with the ground we have

tanx=\frac{64}{82}

This value also equals by bigger triangle as

tanx=\frac{h}{82+12(12)}=\frac{h}{226}

From these two we get

h = height of street light =\frac{226(64)}{82} =176.39

6 0
1 year ago
The rabbit population on a small island is observed to be given by the function P(t) = 130t − 0.3t^4 + 1100 where t is the time
Montano1993 [528]
The maximum occurs when the derivative of the function is equal to zero.
P(t)=-0.3t^{4}+130t+1100 \\ P'(t)=-1.2t^{3}+130 \\ 0=-1.2t^{3}+130 \\ 1.2t^{3}=130 \\ t^{3}= \frac{325}{3}  \\ t=4.76702
Then evaluate the function for that time to find the maximum population.
P(t)=-0.3t^{4}+130t \\ P(4.76702)=-0.3*4.76702^{4}+130*4.76702+1100 \\ P(4.76702)=1564.79201
Depending on the teacher, the "correct" answer will either be the exact decimal answer or the greatest integer of that value since you cannot have part of a rabbit.
7 0
2 years ago
A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not. determ
Temka [501]
The confidence interval would be (0.122, 0.278).

We first find our z-score.  We want a 95% confidence interval:

0.95/2 = 0.475

Looking this up in the z-table, (http://www.statisticshowto.com/tables/z-table/) we see the z-score is 1.96.

The formula we will use is:

p \pm z\sqrt{\frac{p(1-p)}{n}}

In this problem, p = 20/100 = 0.2, and n=100:

0.2 \pm 1.96\sqrt{\frac{(0.2)(0.8)}{100}}
\\
\\0.2\pm 0.0784
\\
\\(0.2-0.0784, 0.2+0.0784)
\\
\\(0.1216,0.2784)
8 0
2 years ago
Which is most likely the correlation coefficient for the set of data shown?
mafiozo [28]

That's a really good positive correlation pictured.  The line fits the data very well.  The slope of the line is positive, meaning as x increases so does y.  I'd choose a big positive value.

Answer: 0.872


6 0
1 year ago
Read 2 more answers
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