Write twelve and sixteen thousand as a mixed decimal

What number should go in box A on this number line? 4. 5. A

cestrela7 [59]

Answer:

5

Step-by-step explanation:

4 0

3 years ago

In a circle of radius 30 inches, a central angle of 35 will intersect the circle forming an arc of length _____.. . A.18.33 feet

defon

The answer to the question above is letter C. To explain the answer if the given question, a circle of 30 inches radius, if the central angle is 35 degrees, intersecting the circle forms an arc of length which is 18.33 inches.

8 0

3 years ago

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What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x − 6)

olya-2409 [2.1K]

Answer:

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$ .

Step-by-step explanation:

When we Add or subtract a positive constant, let say c, to input x, it would be a horizontal shift.

For example:

Type of change Effect on y = f(x)

$y = f(x - c)$ horizontal shift: c units to right

So

Considering the function

$f(x) = x^2$

The graph is shown below. The first figure is representing $f(x) = x^2$ .

Now, considering the function

$\:f\left(x\right)=\left(x-6\right)^2$

According to the rule, as we have discussed above, as a positive constant 6 is added to the input, so there is a horizontal shift, 6 units to the right.

The graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shown below in second figure. It is clear that the graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shifted 6 units to the right as compare to the function $f(x) = x^2$ .

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$ .

5 0

3 years ago

Simplify 3(2m^3n^-2)^4

Effectus [21]

Answer:

(48 m^12)/n^8

Step-by-step explanation:

Simplify the following:

3 ((2 m^3)/(n^2))^4

Multiply each exponent in (2 m^3)/(n^2) by 4:

3×2^4 m^(4×3) n^(-2×4)

4 (-2) = -8:

3×2^4 m^(4×3) n^(-8)

4×3 = 12:

(3×2^4 m^12)/(n^8)

2^4 = (2^2)^2:

(3 (2^2)^2 m^12)/(n^8)

2^2 = 4:

(3×4^2 m^12)/(n^8)

4^2 = 16:

(3×16 m^12)/(n^8)

3×16 = 48:

Answer: (48 m^12)/n^8

5 0

3 years ago

A club consists of 21 Republicans and 25 Democrats. If four people are chosen at random to be on a committee, what is the proba

Allushta [10]

Answer:

88.58% probability that at least one person from each political party will be chosen

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Also, the order which the people are chosen is not important. So the combinations formula is used to solve this problem.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

If four people are chosen at random to be on a committee, what is the probability that at least one person from each political party will be chosen?

Either only Republicans or Democrats are chosen, or at least one member from each party is chosen. The sum of these probabilities is 100%.

The easier way to solve this is first finding the probability that members are only from one party.

Probability of having members from only one party:

Desired outcomes:

Only Democrats:

4 from a set of 25.

Only Republican:

4 from a set of 21.

So

$D = C_{25,4} + C_{21,4} = \frac{25!}{4!21!} + \frac{21!}{4!17!} = 18635$

Total outcomes:

4 from 21+25 = 46 total members

$T = C_{46,4} = \frac{46!}{4!42!} = 163185$

Probability:

$p = \frac{D}{T} = \frac{18635}{163185} = 0.1142$

11.42% probability of having people from only one party in the committee

Probability of at least one person from each party:

p + 11.42 = 100

p = 88.58

88.58% probability that at least one person from each political party will be chosen

5 0

3 years ago