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2 years ago

The mapping diagram shows a functional relationship

Mathematics

1 answer:

Gre4nikov [31]2 years ago

8 0

Answer:

$f(4)=\frac{1}{2}$

f(x) = 4 when x is 8

Step-by-step explanation:

Domain is the set of x values that make the function defined. Allowed x values for the function (mapping).

The Range is the set of y values that make the function defined. Allowed y values for the function (mapping).

Whenever we need to find f(a), suppose, then we look for "a" in the domain and see its corresponding value mapping in the range.
Whenever we will be given a value for f(x) = a, suppose, and we have to find "x", we look at the value a in the range and find corresponding x value in the domain.

Firstly, we need f(4), so we look for "4" in domain and see which number it corresponds to in range.

That is $\frac{1}{2}$

Thus,

$f(4)=\frac{1}{2}$

Next,

We want "x" value that gives us a "y" value of 4. We look for "4" in the range and see which value it corresponds to. That is "8". So,

f(8) = 4

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A theatre has the capacity to seat people across two levels, the Circle and

andriy [413]

Answer: $76.19\%$

Step-by-step explanation:

<h3> The complete exercise is: " A theatre has the capacity to seat people across two levels, the Circle, and the stalls. The ratio of the number of seats in the circle to a number of seats in the stalls is 2:5. Last Friday, the audience occupied all the 528 seats in the circle and $\frac{2}{3}$ of the seats in the stalls. What is the percentage of occupancy of the theatre last Friday?"</h3>

Let be "s" the total number of seats in the Stalls.

The problem says that the ratio of the number of seats in the Circle to the number of seats in the Stalls is $2:5$ .

Since the number of seats that were occupied last Friday was 528 seats, we can set up the following proportion:

$\frac{2}{5}=\frac{528}{s}$

Solving for "s", we get:

$s*\frac{2}{5}=528\\\\s=528*\frac{5}{2}\\\\s=1,320$

So the sum of the number of seats in the Circle and the number of seats in the Stalls, is:

$Total=1,320\ seats+528\ seats=1,848\ seats$

We know that $\frac{2}{3}$ of the seats in the Stalls were occupied. Then, the number of seat in the Stalls that were occupied is:

$(1,320)(\frac{2}{3})=880$

Therefore, the total number of seats that were occupied las Friday is:

$Total\ occupied=880\ seats+528\ seats=1,408\ seats$

Knowing this, we can set up the following proportion, where "p" is the the percentage of occupancy of the theatre last Friday:

$\frac{100}{1,848}=\frac{p}{1,408}$

Solving for "p", we get:

$(1,408)(\frac{100}{1,848})=p\\\\p=76.19\%$

8 0

2 years 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

the diagonal length of a square window is 40 cm. find the area of the window. Btw any help is appreciated ! :)

7nadin3 [17]

Ok so area is length times width. A square has the same sides all around, which is called a quadrilateral. So you would plug in 40 for length and width. 40x40= 1,600 cm^2 <———— is your answer.

Hope this helped :)

7 0

2 years ago

The average credit card debt for a recent year was $8,776. Five years earlier the average credit card debt was $8,189. Assume sa

Anestetic [448]

Answer:

We reject H₀. We support that the new average credit card debt is bigger than the previous average

Step-by-step explanation:

Five years earlier

μ = 8189

σ = 690

Sample size n = 32

Recent year debt

x = 8776

Sample size n = 32

a) Hypothesis Test:

Null Hypothesis H₀ x = μ = 8189

Alternative Hypothesis Hₐ x > μ

b) z(c) Alternative Hypothesis establishes that the test is a one tail-test to the right.

z(c) for significance level α = 0.05 is from z-table z(c) = 1,64

c) z(s) = ( x - μ ) / σ /√n

z(s) = ( 8776 - 8189 ) / 690 /√32

z(s) = 587 *5,66/ 690

z(s) = 4,81

d) Comparing z(c) and z(s)

z(s) > z(c) Then z(c) is in the rejection region and we reject H₀

e) We have evidence that at 95 % of confidence the new value for the debt in credit card is now bigger than the average

7 0

1 year ago

Maura swims the length of a pool 8 times .The pool is 17.4 meters long .How many meters does Maura swim in all

Brums [2.3K]

Answer:

139.2

Step-by-step explanation:

8x17.4=139.2

3 0

2 years ago