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4 years ago

Evaluate the function rule for the given value. y = 6 · 2^x for x = -2

Mathematics

1 answer:

strojnjashka [21]4 years ago

8 0

Answer:

Step-by-step explanation:

To evaluate, substitute x= -2 into the equation $y = 6*2^x$ .

$y = 6*2^2\\y = 6*2^(-2)\\y = 6*\frac{1}{4}\\y = \frac{3}{2}$

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A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of t

oee [108]

Answer:

The Probability = 0.20

Step-by-step explanation:

From the question stated, the first step to take is to find probability that an employee selected at random will need either eyeglasses or major dental work

Solution

Given

Now,

The exams showed tha the number of employees needed eyeglasses = 8%

Employees that needed major dental work = 15%

Employees that needed both eyeglasses and major dental work =3%

Thus,

The P(needed eyeglasses ) = 8% = 0.08

P(major dental work) = 15% = 0.15

P(eye glasses and major dental work) = 3% = 0.03

The probability that an employee selected at random will need either eyeglasses or major dental work is given as

= P(eye glasses ) + P(major dental work) - P(eyeglasses and major dental work)

= 0.08 + 0.15 - 0.03 = 0.20

Therefore the Probability = 0.20

5 0

3 years ago

The variable $x$ varies directly as the square of $y$, and $y$ varies directly as the cube of $z$. If $x$ equals $-16$ when $z$

Kisachek [45]

If $x$ varies directly as $y^2$ , then there is some constant $a$ for which

$x=ay^2$

Similarly, there is some constant $b$ such that

$y=bz^3$

Given that $x=-16$ when $z=2$ , we have

$\begin{cases}-16=ay^2\\y=8b\end{cases}\implies-16=a(8b)^2\implies ab^2=-\dfrac14$

Now when $z=\frac12$ , we get

$\begin{cases}x=ay^2\\y=\frac b8\end{cases}\implies x=a\left(\dfrac b8\right)^2=\dfrac{ab^2}{64}=\dfrac{-\frac14}{64}=\boxed{-\dfrac1{256}}$

6 0

4 years ago

How long will it take to earn $1800 in interest if $6000 is invested at a 6% annual interest rate?

Evgesh-ka [11]

Answer:

It will take 5 years.

Step-by-step explanation:

Let's find how long it will take, but first let's understand the equation.

For simple interest, we use the equation:

T=(1/R)*(((A+B)/B)-1) where,

A= interest amount

B=invested money

R=interest rate (in decimal form)

T=time

Because we want to earn $1800 in interest, then A=1800.

Because we invested $6000, then B=6000.

Because we are investing under an interest rate of 6%, then R=0.06.

'How long will it take' means that T= not given, but its value is in 'years', since an annual rate was given.

Using the equation for simple interest we write:

T=(1/0.06)*(((1800+6000)/6000)-1), the solution is then:

T=5; remember, because is an annual rate, T solution means 5 years.

6 0

3 years ago

Given the pattern rule Tn=n2-1<br><br> what are the first 3 terms of the pattern

sergeinik [125]

Answer:

0, 3 , 8

Step-by-step explanation:

substitute n = 1, 2, 3 into the pattern rule

T₁ = 1² - 1 = 1 - 1 = 0

T₂ = 2² - 1 = 4 - 1 = 3

T₃ = 3² - 1 = 9 - 1 = 8

8 0

2 years ago

Pls help!!!!!!!!!!!!!!!!!

vazorg [7]

Answer:

19 for each one

Step-by-step explanation:

Divide 57 by 3

3 0

4 years ago

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