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1 year ago

Which function has an inverse that is also a function? y = 3 2 - 5 3 y = 322 y= x - y = 322 – 5x + 3

Mathematics

1 answer:

olasank [31]1 year ago

4 0

Inverse function:

The only one that has an inverse that is a function is the third option because is a linear function (bijective)

y=1/3x-3/4

First, solve for x:

Add 3/4 to both sides:

y+3/4 = 1/3x-3/4+3/4

y+3/4 = 1/3x

Multiply both sides by 3

(y+3/4) 3 = 1/3x (3)

3y+ 9/4 = x

F^-1(y) = 3y+ 9/4

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An account begins the year with a

jenyasd209 [6]

$s = c(1 + in) \\ s = 4000(1 + 0.03 \times 1)$

$s = 4120.00$

<h2>Option: A</h2>

4 0

1 year ago

Standardized tests: In a particular year, the mean score on the ACT test was and the standard deviation was . The mean score on

Scorpion4ik [409]

Complete question :

Standardized tests: In a particular year, the mean score on the ACT test was 19.3 and the standard deviation was 5.3. The mean score on the SAT mathematics test was 532 and the standard deviation was 128. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places. Part: 0/4 Part 1 of 4 (a) Find the z-score for an ACT score of 26. The Z-score for an ACT score of 26 is

Answer:

1.26

Step-by-step explanation:

Given that:

For ACT:

Mean score, m = 19.3

Standard deviation, s = 5.3

Zscore for ACT score of 26;

Using the Zscore formula :

(x - mean) / standard deviation

x = 26

Zscore :

(26 - 19.3) / 5.3

= 6.7 / 5.3

= 1.2641509

= 1.26

6 0

2 years ago

Write an equation to represent the N'th term of the sequence (2,-1.-4,-7,...)

mr_godi [17]

Answer: a(n) = 5 - 3n

the sequence has:

a1 = 2

a2 = -1

a3 = -7

.........

we can see that: a2 - a1 = a3 - a2 = -3

=> the sequence is a arithmetic sequence

=> the distance between the numbers is d = -3

because this sequence is a arithmetic sequence

=> a(n) = a1 + (n - 1)d = 2 + (n - 1).(-3) = 5 - 3n

Step-by-step explanation:

7 0

3 years ago

Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.

hram777 [196]

The center of mass is mathematically given as

$\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}$

<h3>What is the center of mass.?</h3>

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

$\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end$

We calculate the total mass of the system.

$\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}$

Step 03: Calculate the moment of the system.

$\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}$

we calculate the center of mass.

$\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}$