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9 days ago

9

Mike, a Salvation Army bell ringer, has 20% as many quarters as nickels in his cup. If Mike has $6.00 in quarters and nickels, h

ow many nickels does he have?

1 answer:

tester [12.3K]9 days ago

3 0

It amounts to 60%, which is equivalent to 3 dollars, alongside 40% in quarters
.

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An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a r

zzz [12365]

The diagram below illustrates the issue at hand.

Question 1:
The maximum area of the pool equals half the area of the circle.

To calculate the area of the circle: Area = πr², with r being half of the diameter.
Thus, Area of circle = π(60)² = 11309.73355 square feet.

Therefore, the area representing half the circle amounts to 11309.73355/2 = 5654.866... ≈ 5654.87 square feet (rounded to 2 decimal places).

Question b:

To find the pool's area, we take the circle's area and subtract the triangle's area.

The area of the circle is 11309.73 square feet.

For the triangle's area calculation: 1/2 × (60×103.92) = 3117.6 square feet.

The area of the pool thus operates as 11309.73 - 3117.6 = 7922.13 square feet.

Calculating the pool's volume: 7922.13 × 4 = 31688.52 cubic feet.

Note: Information related to the fish tank is unavailable, so the above calculation focuses solely on the entire pool's volume.

6 0

1 month ago

Jordan wants to play a basketball game at a carnival. The game costs the player $ 5 $5dollar sign, 5 to play, and the player get

babunello [11817]

Response:

absolutely yes daddy

Detailed explanation:

7 0

9 days ago

762,508 expanded form using exponents

Svet_ta [12734]

762,508 expressed in expanded form with exponents is:

$7 \times 10^5 + 6 \times 10^4 + 2 \times 10^3 + 5 \times 10^2 +0 \times 10^1 + 8 \times 10^0$

Solution:

We need to write 762,508 using expanded notation with exponents.

Expanded form indicates how to represent numbers to highlight the individual digit values.

Displaying 762508 in Expanded format

Let's determine the positional values of each digit:

The concept of place value signifies the worth assigned to each digit based on its location.

For 7, the place value is 700,000

In 762508, the digit 7 is located in the hundred-thousands position.

For 6, the place value is 60,000

In 762508, the digit 6 occupies the ten-thousands position.

For 2, the place value is 2,000

In 762508, 2 is in the thousands position.

For 5, the place value is 500

In 762508, 5 is placed in the hundreds position.

For 0, the place value is 0 x 10 = 0

In 762508, 0 is found in the tens position.

For 8, the place value is 8

In 762508, 8 is positioned in the units place.

Thus, the expanded form is:

700,000 + 60,000 + 2,000 + 500 + 0 + 8

Expressed with exponents, it can be written as:

$7 \times 10^5 + 6 \times 10^4 + 2 \times 10^3 + 5 \times 10^2 +0 \times 10^1 + 8 \times 10^0$

6 0

1 month ago

A flat circular plate has the shape of the region x2 + y2≤1. The plate, including the boundary where x2 + y2 = 1, is heated such

Leona [12618]

Setting both partial derivatives to zero results in a single critical point at $(x,y)=\left(\dfrac12,0\right)$ , located within the unit disk.

At this given point, the derivative value of the Hessian matrix is

$|H|=\begin{vmatrix}T_{xx}&T_{xy}\\T_{yx}&T_{yy}\end{vmatrix}=\begin{vmatrix}2&0\\0&4\end{vmatrix}=8>0$

and the second-order partial derivative with respect to $x$ yields

$T_{xx}\bigg|_{(x,y)=(1/2,0)}=2>0$

This suggests that the critical point represents a local minimum, marking it as the coldest area on the plate with a temperature of $T\left(\dfrac12,0\right)=-\dfrac14$ .

To find the hottest area on the plate, it must be located along the boundary. Let $x=\cos\theta$ and $y=\sin\theta$ , so that

$T(x,y)=T(\theta)=\cos^2\theta+2\sin^2\theta-\cos\theta$
$T(\theta)=\dfrac32-\cos\theta-\dfrac12\cos2\theta$

Thus, the plate's boundary (the circle $x^2+y^2=1$ ) is treated as a single variable function $\theta$ examined over $\theta\in[0,2\pi)$ . A single differentiation gives

$T'(\theta)=\sin\theta+\sin2\theta=0$
$\implies\theta=0,\theta=\dfrac{2\pi}3,\theta=\pi,\theta=\dfrac{4\pi}3$

You will discover that $T(\theta)$ achieves three extrema on the interval $(0,2\pi)$ , with relative maxima occurring at $\theta=\dfrac{2\pi}3$ and $\theta=\dfrac{4\pi}3$ , and a relative minimum at $\theta=\pi$ (and $\theta=0$ , if you wish to include that).

Our minimum has already been identified inside the plate - which you can check to have a lower temperature than at the points noted by $T(\theta)$ - and we identify two maxima at $\theta=\dfrac{2\pi}3$ and $\theta=\dfrac{4\pi}3$ , both showing a maximum temperature of $T=\dfrac94$ .

Reverting to Cartesian coordinates, these points match up with $\left(-\dfrac12,\pm\dfrac{\sqrt3}2\right)$ .

4 0

20 days ago

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. Which graph represents g(x)?

Leona [12618]

<span>The graph will shift 5 units to the right and 1 unit upwards, forming a parabola that opens up with its vertex positioned at (5, 1).

Explanation:
The subtraction of 5 from x prior to squaring indicates a horizontal movement of 5 units to the right.

The addition of 1 signifies a vertical shift of 1 unit up.

This transformation follows the vertex form of a parabola, y=a(x-h)^2 + k, where (h, k) represents the vertex. In this case, h is 5 and k is 1, placing the vertex at (5, 1).</span>

6 0

1 month ago

Read 2 more answers