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3 years ago

Barry found a computer at Staples for $989. A week later, the computer went on sale for $849. What

1 answer:

8 0

Barry found a computer at Staples for $989. A week later, the computer went on sale for $849. The percentage change is 14.156 % decrease

Solution:

Given that Barry found a computer at Staples for $989

A week later, the computer went on sale for $849

To find: percent of change

Percent change is the extent to which a variable gains or loses value. The figures are arrived at by comparing the initial (or before) and final (or after) quantities according to a specific formula.

THE PERCENT CHANGE IS GIVEN AS:

$\text{ percent change } =\frac{\text { final value - initial value }}{\text { initial value }} \times 100$

If the result is positive, it is percentage increase

If the result is negative, it is percentage decrease

Here initial value = 989 and final value = 849

Substituting the values in above formula,

$\begin{aligned}&\text { percent change }=\frac{849-989}{989} \times 100\\\\&\text { percent change }=-0.14155 \times 100=-14.156 \%\end{aligned}$

Here negative sign denotes percentage decrease

Thus percentage change is 14.156 % decrease

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An ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and

mr Goodwill [35]

Answer:

The values are a = 5 , b = 3 , h = 0 , k = 3

The equation is x²/9 + (y - 3)²/25 = 1

Step-by-step explanation:

* Lets revise the standard equation of the ellipse

- The standard form of the equation of an ellipse with center (h , k)

and major axis parallel to y-axis is (x - h)²/b² + (y - k)²/a² = 1 , where

-The length of the major axis is 2a

- The coordinates of the vertices are (h , k ± a)

- The length of the minor axis is 2b

- The coordinates of the co-vertices are (h ± b , k)

- The coordinates of the foci are (h , k ± c), where c² = a² - b²

* Now lets solve the problem

∵ The vertices of the ellipse along the major axis are (0 , 8) , (0 , -2)

∴ The major axis is the y-axis

∴ The vertices are (h , k + a) and (h , k - a)

∴ h = 0

∴ k + a = 8 ⇒ (1)

∴ k - a = -2 ⇒ (2)

∵ The foci of it located at (0 , 7) , (0 , -1)

∵ The coordinates of the foci are (h , k + c) and (h , k - c)

∴ h = 0

∴ k + c = 7 ⇒ (3)

∴ k - c = -1 ⇒ (4)

- To find k and a add equations (1) and (2)

∴ (k + k) + (a + - a) = (8 + -2)

∴ 2k = 6 ⇒ divide both sides by 2

∴ k = 3

- Substitute the value of k in equation (1) or (2) to find a

∴ 3 + a = 8 ⇒ subtract 3 from both sides

∴ a = 5

- To find the value of c substitute the value of k in equation (3) or (4)

∴ 3 + c = 7 ⇒ subtract 3 from both sides

∴ c = 4

- To find b use the equation c² = a² - b²

∵ a = 5 and c = 4

∴ (4)² = (5)² - a²

∴ 16 = 25 - b² ⇒ subtract 25 from both sides

∴ -9 = -b² ⇒ multiply both sides by -1

∴ b² = 9 ⇒ take √ for both sides

∴ b = 3

* The values are a = 5 , b = 3 , h = 0 , k = 3

* The equation is x²/9 + (y - 3)²/25 = 1

7 0

3 years ago

Read 2 more answers

A shopkeeper has 438 apples. 12 of them are bad. He packs the rest equally into 6 boxes. How many apples are in each box?

WITCHER [35]

Answer:

71 apples in each box

Step-by-step explanation:

438-12=426

426 divided by 6= 71

6 0

3 years ago

Read 2 more answers

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation o

GREYUIT [131]

Answer:

And then we can conclude that the middle 75% values of her lap times are from a=126.835 to b=132.585

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Solution to the problem

Let X the random variable that represent the times of a population, and for this case we know the distribution for X is given by:

$X \sim N(129.71,2.5)$

Where $\mu=129.71$ and $\sigma=2.5$

Since we want the middle 75% values then on tha tails we need 1-0.75 =0.25 or 25% of the data and since the distribution is symmetric we need 12.5 % of the values on each tail.

For this part we want to find a value a and b, such that we satisfy this condition:

$P(X>b)=0.125$ (a)

$P(X$ (b)

We can use the z score formula in order to find the value a and b given by:

$z=\frac{x-\mu}{\sigma}$

As we can see on the figure attached the z value that satisfy the condition (b) with 0.125 of the area on the left and 0.875 of the area on the right it's z=-1.15. On this case P(Z<-1.15)=0.125 and P(z>-1.15)=0.875

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-1.15$

And if we solve for a we got

$a=129.71 -1.15*2.5=126.835$

So the value of height that separates the bottom 12.5% of data from the top 87.5% is 126.835.

As we can see on the figure attached the z value that satisfy the condition (b) with 0.875 of the area on the left and 0.125 of the area on the right it's z=1.15. On this case P(Z<1.15)=0.875 and P(Z>1.15)=0.125

If we use condition (b) from previous we have this:

$P(X>b)=P(\frac{X-\mu}{\sigma}>\frac{b-\mu}{\sigma})=0.125$