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3 years ago

Can you solve this for me

Mathematics

1 answer:

guajiro [1.7K]3 years ago

6 0

$g(h(x))=g(\sqrt{x+7})=\dfrac{2}{\sqrt{x+7}+9}\\\\f(g(h(x)))=f\left(\dfrac{2}{\sqrt{x+7}+9}\right)=7\cdot\left(\dfrac{2}{\sqrt{x+7}+9}\right)+9\\\\f(g(h(x)))=\dfrac{14+9\sqrt{x+7}+81}{\sqrt{x+7}+9}\\\\(f\circ g\circ h)(x)=\dfrac{95+9\sqrt{x+7}}{9+\sqrt{x+7}}$

With some extra effort, the radical can be removed from the denominator. That result is

$(f\circ g\circ h)(x)=\dfrac{9x+14\sqrt{x+7}-792}{x-74}$

The preferred form would be the one with the radical in the denominator, as it correctly shows the domain of the function to be x ≥ -7. The function actually is defined at x=74, which the "rationalized" form does not show.

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Evaluate 5(x + y)2 when x = 3 and y = 9

irakobra [83]

Hey there!

$Answer:\boxed{120}$

$Explanation:$

$5(x+y)2$ when x = 3 and y = 9

Let's first move to x and y.

$x=3\\y=9\\3+9=12$

Now multiply 5 by x and y(3+9).

$5*12(\text{x and y combined)}=60$

Now we have the number 2 left, so we have to multiply 60 by 2.

$60*2=120$

$\boxed{120}\text{ is your final answer.}$

Hope this helps!

$\text{-TestedHyperr}$

4 0

3 years ago

A square has a side length of 4 cm. What is the length of the diagonal of the square? What is the length from the corner to the

masya89 [10]

The length of the diagonal of the square is the square root of 32 which equals approximately 5.6569.
The length from the corner to the center of the square is half of the diagonal which is 2.8284. I hope this helps!

7 0

3 years ago

Julio solicitó un préstamo en el banco para invertir en su casa, pagó una cuota de $32,950 y otra de $25,825. Si el préstamo fue

Umnica [9.8K]

Answer:

Julio debe $ 41225 al banco por concepto del préstamo para invertir en su casa.

Step-by-step explanation:

Dada la falta de información, asumimos que el préstamo fue realizado sin tasa de interés, de modo que la deuda solo sea el monto inicial menos las cuotas pagadas por quien recibe el préstamo, la cantidad de dinero que adeuda al banco es:

$x = \$\,100000 - \$\,32950 - \$\,25825$

$x = \$ \,41225$

Julio debe $ 41225 al banco por concepto del préstamo para invertir en su casa.

7 0

3 years ago

Where is the hundred thousand place

ozzi

The 6th to the left

4 0

3 years ago

The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppos

xenn [34]

Answer:

(a) P(X > $57,000) = 0.0643

(b) P(X < $46,000) = 0.1423

(c) P(X > $40,000) = 0.0066

(d) P($45,000 < X < $54,000) = 0.6959

Step-by-step explanation:

We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.

Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.

Let X = annual salaries in the metropolitan Boston area

SO, X ~ Normal( $\mu=$50,542,\sigma^{2} = $4,246^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma }$ ~ N(0,1)

where, $\mu$ = average annual salary in the Boston area = $50,542

$\sigma$ = standard deviation = $4,246

(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)

P(X > $57,000) = P( $\frac{X-\mu}{\sigma }$ > $\frac{57,000-50,542}{4,246 }$ ) = P(Z > 1.52) = 1 - P(Z $\leq$ 1.52)

= 1 - 0.93574 = 0.0643

The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574.

(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)

P(X < $46,000) = P( $\frac{X-\mu}{\sigma }$ < $\frac{46,000-50,542}{4,246 }$ ) = P(Z < -1.07) = 1 - P(Z $\leq$ 1.07)

= 1 - 0.85769 = 0.1423

The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769.

(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)

P(X > $40,000) = P( $\frac{X-\mu}{\sigma }$ > $\frac{40,000-50,542}{4,246 }$ ) = P(Z > -2.48) = P(Z < 2.48)

= 1 - 0.99343 = 0.0066

The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343.

(d) Probability that the worker’s annual salary is between $45,000 and $54,000 is given by = P($45,000 < X < $54,000)

P($45,000 < X < $54,000) = P(X < $54,000) - P(X $\leq$ $45,000)

P(X < $54,000) = P( $\frac{X-\mu}{\sigma }$ < $\frac{54,000-50,542}{4,246 }$ ) = P(Z < 0.81) = 0.79103

P(X $\leq$ $45,000) = P( $\frac{X-\mu}{\sigma }$ $\leq$ $\frac{45,000-50,542}{4,246 }$ ) = P(Z $\leq$ -1.31) = 1 - P(Z < 1.31)

= 1 - 0.90490 = 0.0951

The above probability is calculated by looking at the value of x = 0.81 and x = 1.31 in the z table which gave an area of 0.79103 and 0.9049 respectively.

Therefore, P($45,000 < X < $54,000) = 0.79103 - 0.0951 = 0.6959

3 0

3 years ago