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3 years ago

Suppose that G(x) = F(x - 6) - 3. Which statement best compares the graph of G(x) with the graph of F(x)?

2 answers:

8 0

From the given, G(x) = F(x - 6) - 3, the graph is shifted to 6 units to the right and 3 units down. Thus, the answer is letter A. It should be noted that for horizontal shifting, negative means to the right and down for vertical shifting.

lilavasa [31]3 years ago

8 0

Answer:

Option A -The graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.

Step-by-step explanation:

Given : G(x)=F(x-6)-3

We can compare graph of G(x) with graph of F(x) by looking at a and b values in G(x)=F(x-a)-b

where, a=6 and b=3

For the value of a :

If some unit is subtract from the x value then the graph shifted to right by that unit.

mathematically we can write,

f(x)→ f(x-a) → f(x) shift right with a units.

Therefore, in G(x)=F(x-6)-3

F(x)→ F(x-6) → F(x) shift right with 6 units.

⇒Graph of G(x) is the graph of F(x) shifted 6 units right.

For the value of b:

If some units is subtract from the function then the graph shifted downward by that unit.

mathematically we can write,

f(x)→ f(x)-b → f(x) shift down with b units.

Therefore, in G(x)=F(x-6)-3

F(x)→ F(x)-3 → F(x) shift down with 3 units.

⇒Graph of G(x) is the graph of F(x) shifted 3 units down.

Therefore, option A is correct that the graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.

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if the average heart beats 60 beats per minute and there are 525600 minutes in a year multiply

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2 years ago

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Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probabili

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Answer:

(a) The mean and the standard deviation for the numbers of peas with green pods in the groups of 36 is 27 and 2.6 respectively.

(b) The significantly low values are those which are less than or equal to 21.8. And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is significantly low value.

Step-by-step explanation:

We are given that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods.

Assume that the offspring peas are randomly selected in groups of 36.

The above situation can be represented as a binomial distribution;

where, n = sample of offspring peas = 36

p = probability that a pea has green pods = 0.75

(a) The mean of the binomial distribution is given by the product of sample size (n) and the probability (p), that is;

Mean, $\mu$ = n $\times$ p

= 36 $\times$ 0.75 = 27 peas

So, the mean number of peas with green pods in the groups of 36 is 27.

Similarly, the standard deviation of the binomial distribution is given by the formula;

Standard deviation, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{36 \times 0.75 \times (1-0.75)}$

= $\sqrt{6.75}$ = 2.6 peas

So, the standard deviation for the numbers of peas with green pods in the groups of 36 is 2.6.

(b) Now, the range rule of thumb states that the usual range of values lies within the 2 standard deviations of the mean, that means;

$\mu - 2 \sigma$ = 27 - (2 $\times$ 2.6)

= 27 - 5.2 = 21.8

$\mu + 2 \sigma$ = 27 + (2 $\times$ 2.6)

= 27 + 5.2 = 32.2

This means that the significantly low values are those which are less than or equal to 21.8.

And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is a significantly low value because the value of 15 is less than 21.8 which is represented as a significantly low value.

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3 years ago

1. Identify the place value for the following: 162.891

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Answer:

Hundreds : 1

Tens : 6

Ones : 2

Tenths : 8

Hundredths : 9

Thousandths : 1

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2 years ago

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3 years ago

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A packing box has the dimensions 3 by 2 by 5 1/2 feet. What is the volume of the box?

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As already mentioned, the volume for a rectangular prism, namely a box in this case, is just the product of its dimensions, length * width * height.

$\bf \textit{volume of a rectangular prism}\\\\
V=LWH\quad 
\begin{cases}
L=length\\
W=width\\
H=height\\
------\\
L=3\\
W=2\\
H=5\frac{1}{2}
\end{cases}\implies V=3\cdot 2\cdot 5\frac{1}{2}
\\\\\\
V=3\cdot 2\cdot \cfrac{5\cdot 2+1}{2}\implies V=6\cdot\cfrac{11}{2}\implies V=3\cdot \cfrac{11}{1}
\\\\\\
V=33$

now, as far as another one... hmm is easier if you post in the channel, that way I can include any graphs if needed or tables and such.

so, what happens if you double up the dimensions?

$\bf \textit{volume of a rectangular prism}\\\\
V=LWH\quad 
\begin{cases}
L=length\\
W=width\\
H=height\\
------\\
L=6\\
W=4\\
H=10
\end{cases}\implies V=6\cdot 4\cdot 10\implies V=240\\\\
-------------------------------\\\\
\begin{cases}
L=6(2)\\
W=4(2)\\
H=10(2)
\end{cases}\implies V=6(2)8(2)10(2)\implies V=(2)(2)(2)6\cdot 8\cdot 10
\\\\\\
V=(8)6\cdot 8\cdot 10\implies V=(8)\stackrel{original~volume}{240}$

notice, how many times the new size is, is 8 times the original.

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3 years ago