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3 years ago

If g(x)= x=2 and h(x) = 4 - X, what is the value of (gºh)(-3)?

Mathematics

1 answer:

navik [9.2K]3 years ago

8 0

The required value of (g°h)(-3) is 5.

Step-by-step explanation:

Given,

g(x)= x-2 and h(x) = 4 - x

To find (g°h)(-3)

Now,

(g°h)(x) = g(h(x))

= g(4-x)

= (4-x)-2 = 2-x

So,

(g°h)(-3) = 2-(-3) = 5 [ putting x=-3]

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Solve algebraically:

vichka [17]

<h3>Answer:</h3>

$a)\ x_1=-9,\ x_2=9\\\\b)\ x_1=1,\ x_2=5$

<h3>Step-by-step explanation:</h3>

<u>Given equations:</u>

$a)\ 2x^2 - 162 = 0\\\\b) -\dfrac{1}{2}(x-3)^2=-2$

A) 2x² - 162 = 0

Step 1: Divide both sides by 2.

<h3> $\\\implies \dfrac{2x^2 - 162}{2} = \dfrac{0}{2}\\\\\implies x^2-81=0\\\\\implies x^2=81$ </h3>

Step 2: Take the square root of both sides (using both the positive and negative roots).

$\\\implies \sqrt{x^2}=\sqrt{81}\\\\\implies x=\pm\ 9$

Step 3: Separate into two cases.

$\implies x_1 = -9,\ x_2 =-9$

----------------------------------------------------------------------------------------------------------------

B) -1/2(x - 3)² = -2

Step 1: Multiply both sides by -2.

$\\\implies -2\left(-\dfrac{1}{2}(x-3)^2\right)=-2(-2)\\\\\implies (x-3)^2=4$

Step 2: Take the square root of both sides (using both the positive and negative roots).

$\\\implies\sqrt{(x-3)^2}=\sqrt{4}\\\\\implies x-3=\pm\ 2$

Step 3: Separate into two cases and solve each one. $1)\ x-3=-2\implies x=-2+3\implies \boxed{x=1}\\\\2)\ x-3=2\implies x=2+3\implies \boxed{x=5}$

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2 years ago

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Width<br>5х<br>10x^2<br>5x<br>What is the width of Heng's area model?<br>Width =

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3 years ago

Sarah's rectangular garden has a perimeter of 327 +327 +218 +28 cm.

hodyreva [135]

Answer:

Sarah's rectangular garden has a perimeter of 900cm

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4 years ago

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Write an equation in point-slope form of the line that passes through (-1,-4) with slope -2.

andrew-mc [135]

Answer:

y+4=-2(x+1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-2(x-(-1))

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3 years ago

A public health organization reports that 40%of baby boys 6-8 months old in the United

Sveta_85 [38]

Using the binomial distribution, the probabilities are given as follows:

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters for this problem are:

n = 10, p = 0.4.

The probability that more than 4 weigh more than 20 pounds is:

$P(X > 4) = 1 - P(X \leq 4)$

In which:

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

Then:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0061$

$P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403$

$P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209$

$P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150$

$P(X = 4) = C_{10,4}.(0.4)^{4}.(0.6)^{6} = 0.2502$

Hence:

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0061 + 0.0403 + 0.1209 + 0.2150 + 0.2502 = 0.6325$

$P(X > 4) = 1 - P(X \leq 4) = 1 - 0.6325 = 0.3675$

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

The probability that fewer than 3 weigh more than 20 pounds is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0061 + 0.0403 + 0.1209 = 0.1673

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

For more than 7, the probability is:

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{10,8}.(0.4)^{8}.(0.6)^{2} = 0.0106$

$P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016$

$P(X = 10) = C_{10,10}.(0.4)^{10}.(0.6)^{0} = 0.0001$

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

More can be learned about the binomial distribution at brainly.com/question/24863377

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2 years ago