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valentinak56 [21]

3 years ago

13

A toy that was originally 35$ is now marked down to 28$ what percentage was the toy marked down?

1 answer:

son4ous [18]3 years ago

6 0

20%.
Here's the math on how I did it
The percentage we are trying to find is how 35 got to 28.
35 - 28 is 7.
Since 10% of 35 would be 3.5, I multiplied 10% by 2 and got 20%.
It was 20% marked down

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A family went to a restaurant for dinner. The subtotal for the meal including tax is $65.90. The family decided to leave a 20% t

maxonik [38]

Answer:

$79.08

Step-by-step explanation:

Find 20% of 65.90. 20% as a decimal is 0.20. Multiply 0.2 and 65.90.

65.90 x 0.20 = 13.18

Add 13.18 to the original price.

13.18 + 65.90 = 79.08

6 0

3 years ago

a. Calculate the volume of the solid of revolution created by rotating the curve y = 3 + 3 exp(-5 x) about the x-axis, for x bet

miskamm [114]

Answer:

A) The volume of solid is 18π cubic unit.

B) The volume of sphere is $\dfrac{4}{3}\pi r^3$

a = -r , b = r , $f(x)=\sqrt{r^2-x^2}$ and $V=\dfrac{4}{3}\pi r^3$

Solution A)

The given curve, $y=3+3e^{-5x}$ rotate about x-axis between 2 to 4.

Please find attachment for solid figure or rotation.

Using disk method to find the volume rotation about x-axis

$V=\int_a^b\pi R^2dx$

where, a = 2, b= 4 , $R=y=3+3e^{-5x}$ and dx is thickness of disk.

$V=\int_2^4\pi (3+3e^{-5x})^2dx$

$V=9\pi\int_2^4(1+e^{-10x}+2e^{-5x})dx$

$V=9\pi(x-\dfrac{1}{10}e^{-10x}-\dfrac{2}{5}e^{-5x})|_2^4)$

$V=9\pi(4-\dfrac{1}{10}e^{-40}-\dfrac{2}{5}e^{-20}-2+\dfrac{1}{10}e^{-20}-\dfrac{2}{5}e^{-10}))$

$V=9\pi (2-0)$

$V=18\pi$

Hence, the volume of solid is 18π cubic unit

Solution B)

The equation of circle of radius r and centered at origin (0,0).

$x^2+y^2=r^2$

$y=\sqrt{r^2-x^2}$

The solid form is sphere of radius r.

Using disk method, to find volume of solid

$V=\int_a^b\pi R^2dx$

where, a = -r, b = r , $R=y=\sqrt{r^2-x^2}$ and dx is thickness of disk.

$V=\int_{-r}^r\pi (r^2-x^2)dx$

$V=\pi(r^2x-\dfrac{x^3}{3})|_{-r}^r$

$V=\pi(2r^3-\dfrac{2r^3}{3})$

$V=\dfrac{4}{3}\pi r^3$

Hence, the volume of sphere is $\dfrac{4}{3}\pi r^3$

4 0

4 years ago

The lifetime, in years, of some electronic component is a continuous random variable with the density f(x) =   k x4 for x ≥ 1

yuradex [85]

I suppose the density is supposed to be

$f(x)=\begin{cases}\frac k{x^4}&\text{for }x\ge1\\0&\text{otherwise}\end{cases}$

(since $kx^4$ diverges as $x\to\infty$ , and 0 is conveniently left out of the domain)

For this to be a proper density function, it must be positive (it is) and its integral over the support $[1,\infty)$ must evaluate to 1. We have

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=\int_1^\infty\frac k{x^4}\,\mathrm dx=-\frac k{3x^3}\bigg|_1^\infty=\frac k3=1$

which means $k=3$ .

The distribution function is obtained by integrating the density:

$F(x)=\displaystyle\int_{-\infty}^xf(t)\,\mathrm dt=\begin{cases}0&\text{for }x$

The probability that the component exceeds 2 years in its lifetime is

$P(X>2)=1-P(X\le 2)=1-F(2)=1-\left(1-\dfrac18\right)=\dfrac18$

3 0

3 years ago

The number of chorus students increased by a factor of 1.2 from the previous year write 1.2 as a percent

IrinaVladis [17]

Answer:

1.2 as a percent is 120%.

Step-by-step explanation:

To change a decimal to a percent, multiply the decimal by 100

4 0

4 years ago

Calculate the slope of the line with points (3, 2) and (6, 4). Write your answer as a decimal rounded to 2 decimal places.

Andreas93 [3]

Answer:

0.67

Step-by-step explanation:

m is the slope

The formula is m= $\frac{y_{2}-y_1}{x_2-x_1}$

m= $\frac{4-2}{6-3}$

m= $\frac{2}{3}$

2÷3=0.66666...≈0.67

7 0

2 years ago