All categories

1 year ago

Match each set of prices with the correct percent of increase or decrease.

1 answer:

7 0

Take the
(original price - new price)/original price
then multiply by 100
If it is a positive number, it is a decrease.
If it is a negative number, it is an increase.

original price: $63.00
new price: $56.07
11% decrease

original price: $12.25
new price: $13.23
8% increase

original price: $98.00
new price: $108.78
11% increase

original price: $37.50
new price: $34.50
8% decrease

You might be interested in

A semi-ellipse-shaped gate has a maximum height of 20 feet and a width of 15 feet, both measured along the center. Can a truck w

Free_Kalibri [48]

<h2>Answer with explanation:</h2>

We are given a semi-ellipse gate whose dimensions are as follows:

Height of 20 feet and a width of 15 feet.

Now, if a truck is loaded then:

Height of truck is: 12 feet and a width of truck is: 16 feet

The truck won't pass through the gate since the width of truck is more than that of the gate.

When the truck is not loaded then:

Height of truck is: 12 feet and a width of truck is: 10 feet

The truck would easily pass through the gate since, the dimensions of truck are less than that of the gate.

6 0

2 years ago

Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le

Dvinal [7]

Answer:

1.692 m/min

Step-by-step explanation:

Let $\theta$ be the angle between the two sides and x be the length of the third side. By cosine rule,

$x^2 = 12^2+14^2-2\times12\times14\cos\theta = 340 - 336\cos\theta$

$x= \sqrt{340 - 336\cos\theta}$

We differentiate x with respect to $\theta$ by applying chain rule.

$\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}$

Rate of change of $\theta$ is 2

$\dfrac{\theta}{dt} = 2$

Rate of change of x is

$\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}$

$\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}$

At 60°,

$\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}$

4 0

1 year ago

The first term of a finite geometric series is 6 and the last term is 4374. The sum of all the term os 6558. find the common rat

Oliga [24]

A geometric series is written as $ar^n$ , where $a$ is the first term of the series and $r$ is the common ratio.

In other words, to compute the next term in the series you have to multiply the previous one by $r$ .

Since we know that the first time is 6 (but we don't know the common ratio), the first terms are

$6, 6r, 6r^2, 6r^3, 6r^4, 6r^5, \ldots$ .

Let's use the other information, since the last term is $4374 > 6$ , we know that $r>1$ , otherwise the terms would be bigger and bigger.

The information about the sum tells us that

$\displaystyle \sum_{i=0}^n 6r^i = 6\sum_{i=0}^n r^i = 6558$

We have a formula to compute the sum of the powers of a certain variable, namely

$\displaystyle \sum_{i=0}^n r^i = \cfrac{r^{n+1}-1}{r-1}$

So, the equation becomes

$6\cfrac{r^{n+1}-1}{r-1} = 6558$

The only integer solution to this expression is $n=6, r=3$ .

If you want to check the result, we have

$6+6*3+6*3^2+6*3^3+6*3^4+6*3^5+6*3^6 = 6558$

and the last term is

$6*3^6 = 4374$

7 0

2 years ago

mark has a cabinet door in his kitchen with the dimensions shown below. he creates a scale drawing where the width of the cabine

laiz [17]

Answer:

$h^{*} = 25\,in$

Step-by-step explanation:

Let consider that door has a height of 5 feet and a width of 3 feet. The scale factor is:

$n = \frac{15\,in}{3\,ft}$

$n = 5\,\frac{in}{ft}$

The height of the cabinet is:

$h^{*} = n \cdot h_{door}$

$h_{*} = \left(5\,\frac{in}{ft} \right)\cdot (5\,ft)$

$h^{*} = 25\,in$

6 0

2 years ago

Read 2 more answers

Use a daily production cost C for x units. A manufacturer of gas grills has daily production costs of C = 400 – 5x + 0.125x2, wh

Lady bird [3.3K]

The function given is a quadratic function, so the graph will be a parabola. It'll look similar to the photo attached. The minimum cost will be at the vertex of the parabola because that is its lowest point! To find the x-value of the vertex (which is what the question is looking for), use the vertex formula: x = -b/2a. The variable b is the coefficient of the x term in the function, and the variable a is the coefficient of the x² term. In this case, a = 0.125 and b = -5.
x = -(-5)/2(0.125)
x = 5/0.25
x = 20
So, 20 gas grills should be produced each day to maintain minimum costs. Hope that helps! :)

8 0

2 years ago

Read 2 more answers