Taylor has a $30 gift card that she can spend at the store. She has already bought

ken has 16 marbles. He wants to put them into bags that hold 5 marbles each. Can there be equal shares of marbles with no marble

LiRa [457]

There can not be equal sharings since 16/5 does not equal a whole number! Good luck :)

7 0

4 years ago

Read 2 more answers

If a line passes through the points (2.5,2.5) and (3.5,5.5), the equation of the line is y-5.5 = 3(x- blank ).

timurjin [86]

Answer:

(x- 2.5)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Use logarithmic differentiation to find dy/dx. y = (1 + x)^1/x, x > 0

vovangra [49]

Use exp/log functions to rewrite y as

$y = (1+x)^{\frac1x} \implies y = \exp\left(\ln\left(1+x)^{\frac1x}\right)\right)$

One of the properties of logarithms lets us bring down the exponent, so

$y = \exp\left(\dfrac{\ln(1+x)}x\right)$

Now take the derivative of both sides with respect to x. By the chain and quotient rules,

$\dfrac{dy}{dx} = \exp\left(\dfrac{\ln(1+x)}x\right) \times \dfrac{\frac x{1+x} - \ln(1+x)}{x^2}$

Simplify:

$\boxed{\dfrac{dy}{dx} = \frac{x - (1+x)\ln(1+x)}{x^2(1+x)} (1+x)^{\frac1x}}$

6 0

2 years ago

A restaurant manager can spend at most $400 a day for operating costs and payroll. It costs $100 each day to operate the bank an

horrorfan [7]

Answer:

The restaurant Manager can afford 6 employees for the day.

Step-by-step explanation:

Manager can spend at most of $400.

Total Money ≤ $400

Cost to operate bank = $100

Cost for each employee = $50

Let number of employees for the day be $x$

Hence the equation will become;

$50x + 100 \leq 400$

Solving this equation we get;

$50x + 100 \leq 400\\50x \leq 400-100\\50x \leq 300\\x\leq \frac{300}{50}\\\\x\leq 6$

Hence, The restaurant Manager can afford 6 employees for the day.

3 0

4 years ago

Read 2 more answers

y varies inversely with x. If y = 2.4 and k (the constant of variation) = 8.88, what is x? Round to the nearest tenth, if necess

Archy [21]

Answer:

3.7

Step-by-step explanation:

Inversely means we are taking the constant and dividing it.

So y varies inversely with x means "y=k/x".

k is a constant. We can find the constant if they give us a point on this curve.

The constant is a number that doesn't change no matter your input and output.

$y=\frac{k}{x}$

So they actually give us k=8.88 and y=2.4 so let's input this:

$2.4=\frac{8.88}{x}$

We need to solve this equation for x. You can do your favorite thing in cross-multiply. But how, Freckles? Well just slap a 1 underneath that 2.4. You can do that because 2.4/1 is still 2.4.

$\frac{2.4}{1}=\frac{8.88}{x}$

Cross-multiply:

$2.4x=8.88(1)$

$2.4x=8.88$

Divide both sides by 2.4:

$x=\frac{8.88}{2.4}$

$x=3.7$ when $y=2.4$ .

8 0

4 years ago