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3 years ago

Explain how the number of pieces in a whole relates to the size of each piece

Mathematics

2 answers:

Stella [2.4K]3 years ago

6 0

The more pieces there are in a whole, the smaller the size of those pieces are.

katovenus [111]3 years ago

5 0

Let's take 1/3 as an example. The number of pieces in a whole are all thirds. Each piece has equal parts. 1/3+1/3+1/3=3/3 which equals 1. All the parts are equals because they all add up to 1 whole. Hope this was helpful!!

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The functions f(x) = -(x+4) +2 and g(x) =(x-2)^2 -2 have been rewritten using the completing the square method. Apply your knowl

rewona [7]

Answer:

$g(x) = (x-2)^2 -2$

If we compare this function with the vertex form we see that:

$a = 1, h =2, k =-2$

So then the vertex would be $(h,k)=(2,-2)$

And since the value for a is positive we know that the parabola open upward. We don't have a maximum defined since open upwards and the minimum point correspond to the vertex on this case (2,-2).

$f(x)= -(x+4)^2 +2$

If we compare this function with the vertex form we see that:

$a=-1, h =-4, k = 2$

And since the value for a is negative we know that the parabola open downward. We don't have a minimum defined since open downwards and the maximum point correspond to the vertex on this case (-4,2).

Step-by-step explanation:

We need to remember that the standard form for a parabola is given by the following equation:

$y = ax^2 + bx +c$

And the vertex form is given by this formula:

$y = a(x-h)^2 +k$

And we want to find the vertex and if we have a maximum or minimum for each function. Let's begin with g(x)

$g(x) = (x-2)^2 -2$

If we compare this function with the vertex form we see that:

$a = 1, h =2, k =-2$

So then the vertex would be $(h,k)=(2,-2)$

And since the value for a is positive we know that the parabola open upward. We don't have a maximum defined since open upwards and the minimum point correspond to the vertex on this case (2,-2).

For the function f(x) we assume that we have the following equation:

$f(x)= -(x+4)^2 +2$

If we compare this function with the vertex form we see that:

$a=-1, h =-4, k = 2$

And since the value for a is negative we know that the parabola open downward. We don't have a minimum defined since open downwards and the maximum point correspond to the vertex on this case (-4,2).

4 0

3 years ago

A sprinkler system is being installed in a newly renovated building on campus. The average activation time is supposed to be at

melomori [17]

Answer:

A) t = 1.73

B) p-value = 0.0558

C) Data is not statistically significant because the p-value of 0.0558 is more than the significance value of 0.05

D) The decision means that the design specifications are not met.

E) Type II error

Step-by-step explanation:

The hypotheses are:

H₀: μ = 20

H₁: μ > 20

A) Formula for the test statistic is;

t = (x' - μ)/(s/√n)

Now, we are given;

x' = 21.5

μ = 20

s = 3

n = 12

Thus;

t = (21.5 - 20)/(3/√12)

t = 1.73

B) we have our t-value as 1.73

Now, Degree of freedom(DF) = n - 1

So,DF = 12 - 1 = 11

Using significance level of α = 0.05, t-value = 1.73 and DF = 11, one tailed hypothesis, from online P-value calculator attached, we have;

p-value = 0.0558

C) Data is not statistically significant because the p-value of 0.0558 is more than the significance value of 0.05

D) We will not reject the null hypothesis. The decision means that the design specifications are not met.

E) If the true average activation time of the sprinkler system is, in fact, equal to 20 seconds, then the null hypothesis is false.

Since we did not reject the null hypothesis even though it is false, the error that was committed was therefore a type II error.

4 0

3 years ago

Answer this please screenshot 1 is to help answer screenshot 2. What doess 100 mean and 1/2 mean

GalinKa [24]

Answer:

1/2 = 0.5 / 1/2 of 100 is 50

Step-by-step explanation:

I am not sure what you are trying to say here but I will tell you what I know:

1/2 is equal to 0.5

So 50 x 1/2 = 25
And 50 x 0.5 = 25

So 100 x 0.5 = 50

4 0

2 years ago

A ship is sailing on the sea. It travels 50 miles at 60° to the horizontal. Then the ship travels 90 miles at 30° to the horizon

pav-90 [236]

Answer:

$(25\sqrt{3}+45)\ miles$