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Finger [1]
1 year ago
12

Given that f(x) = x + 3 a) Find f(2)

Mathematics
1 answer:
Nataly_w [17]1 year ago
7 0

{ \qquad\qquad\huge\underline{{\sf Answer}}}

Here we go ~

In the above question, it is given that :

\qquad \sf  \boxed{ \sf f(x) =  \frac{x + 3}{2} }

A.) Find f(2) :

\qquad \sf  \dashrightarrow \: f(2) =  \dfrac{2 + 3}{2}

\qquad \sf  \dashrightarrow \: f(2) =  \dfrac{5}{2}

or

\qquad \sf  \dashrightarrow \: f(2) = 0.5

B.) Find { \sf {f}^{-1}(x) } :

\qquad \sf  \dashrightarrow \: let \: y = f (x)

so, we can write it as :

\qquad \sf  \dashrightarrow \: y =  \dfrac{x + 3}{2}

\qquad \sf  \dashrightarrow \: 2y = x + 3

\qquad \sf  \dashrightarrow \: x = 2y - 3

Now, put x = { \sf {f}^{-1}(x) }, and y = x and we will get our required inverse function ~

\qquad \sf  \dashrightarrow \: f {}^{ - 1}(x) = 2x- 3

C.) Find { \sf {f}^{-1}(12) } :

\qquad \sf  \dashrightarrow \: f {}^{ - 1}(12) = 2(12)- 3

\qquad \sf  \dashrightarrow \: f {}^{ - 1}(12) = 36- 3

\qquad \sf  \dashrightarrow \: f {}^{ - 1}(12) = 33

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Helen [10]

Answer:

B

Step-by-step explanation:

Given

11 - 4x = (3x - 2)² + 1 ← expand the squared factor using FOIL

11 - 4x = 9x² - 12x + 4 + 1, that is

11 - 4x = 9x² - 12x + 5 ( add 4x to both sides )

11 = 9x² - 8x + 5 ( subtract 11 from both sides )

0 = 9x² - 8x - 6 or

9x² - 8x - 6 = 0 → B

4 0
3 years ago
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A sports magazine claims that in a certain country, 45% of people like soccer A news channel asked 30 randomly selected people i
LiRa [457]

Answer:

Step-by-step explanation:

Hello!

The parameter of interest is "the population proportion of people that like soccer A news channel"= p

The hypothesis are:

H₀: p = 0.45

H₁: p ≠ 0.45

To study the population proportion you have to use the approximation of the standard normal distribution:

Z= \frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } } ≈ N(0;1)

A sample of n=30 was taken and surveyed, 18 of those answered positively, then the sample proportion is:

p'= 18/30= 0.6

The statistic under the null hypothesis is:

Z_{H_0}= \frac{0.60-0.45}{\sqrt{\frac{0.45*0.55}{30} } } = 1.6514

I hope it helps!

6 0
3 years ago
Hi! Hope You're Having A More Than Amazing Day!
SCORPION-xisa [38]

890 is the answer hope I got it

3 0
3 years ago
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Given a normal distribution with mu equals 100μ=100 and sigma equals 10 commaσ=10, complete parts​ (a) through​ (d). loading...
m_a_m_a [10]

I believe the parts are:

A. What is the probability that Upper X greater than 95X>95​?

B. What is the probability that Upper X less than 75X<75?

C.What is the probability that Upper X less than 85X<85 and Upper X greater than 125X>125?

D. 95​% of the values are between what two​ X-values (symmetrically distributed around the​ mean)?

 

<u>Solution:</u>

We use the equation for z score:

z = (X – μ) / σ

Then use the standard normal probability tables to locate for the value of P at indicated z score value.

 

A. Z = (95 – 100) / 10 = - 0.5

Using the tables, the probability at z = -0.5 using right tailed test is:

P = 0.6915

 

 

B. Z = (75 – 100) / 10 = - 2.5

Using the tables, the probability at z = -2.5 using left tailed test is:

P = 0.0062

 

 

C. Z = (85 – 100) / 10 = - 1.5

Using the tables, the probability at z = -2.5 using left tailed test is:

P = 0.0668

 

Z = (125 – 100) / 10 = 2.5

Using the tables, the probability at z = 2.5 using right tailed test is:

P = 0.0062

 

So the probability that 85<X and X>125 is:

P(total) = 0.0668 + 0.0062

P(total) = 0.073

 

 

D. P(left) = 0.025, Z = -1.96

P(right) = 0.975, Z = 1.96

 

The X’s are calculated using the formula:

X = σz + μ

 

At Z = -1.96

X = 10 (-1.96) + 100 = 80.4

 

At Z = 1.96

X = 10 (1.96) + 100 = 119.6

 

<span>So 95% of the values are between 80.4 and 119.6 (80.4< X <119.6).</span>

7 0
3 years ago
A pitcher contains 40 fluid ounces of tea Shelby pour 3 cups of tea how many pints are left
Nastasia [14]

Answer:

1 pint of tea left in the pitcher.

Step-by-step explanation:

A pitcher contains 40 fluid ounces

1 cup = 8 fluid ounces

3 cups = 3*8 = 24 fluid ounces

After pouring tea in 3 cups,

tea left in pitcher = 40 - 24 = 16 fluid ounces

1 pint = 16 ounces

Therefore, 1 pint left.

Hope this will helpful.

Thank you.

8 0
3 years ago
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