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3 days ago

The race speeds for the top eight cars in a 200-mile race are listed below. Use the range rule of thumb

2 answers:

7 0

Answer: 13.4. Step-by-step explanation: I’m unsure of the range rule of thumb, but I simply calculated the range as 189.2 - 175.8 = 13.4.

AnnZ [9.1K]3 days ago

4 0

Answer:The value of the standard deviation is approximately 3.6.

Step-by-step explanation:

Referring to the Range Rule of Thumb: The estimate for the range is roughly four times the standard deviation.

In this case, $R\approx4\sigma\Rightarrow\ \sigma\approx\dfrac{R}{4}$ (i)

The record speeds for the fastest eight cars in a 200-mile race are:

185.9 179.5 189.2 176.7 175.8 188.7. 188.3 177.9

Here, the lowest speed = 175.8 and the highest speed = 189.2

Range = highest speed - lowest speed

In other words, R = 189.2-175.8 =13.4

From (i),

$\sigma\approx\dfrac{13.4}{4}\\\\\Rightarrow\sigma\approx3.6$

Thus, the standard deviation is roughly 3.6.

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Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Leona [9281]

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

$\Rightarrow x^2+y^2 = 16900$

$\Rightarrow y^2 = 16900-x^2$

$\Rightarrow y = \sqrt{16900-x^2}$

Since the point lies on the circle, its coordinates must be,

$(x,\sqrt{16900-x^2})$

The distance "d" from the point to (30,40) can be calculated as,

$=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}$

$=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}$

$=\sqrt{9400-60x-80\sqrt{16900-x^2}}$

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when $9400-60x-80\sqrt{16900-x^2}$ is at its lowest value.

Let’s set up the equation,

$\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}$

$\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}$

$\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}$

We find the critical points,

$\Rightarrow f'(x)=0$

$\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0$

$\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60$

$\Rightarrow 80x=60\sqrt{16900-x^2}$

$\Rightarrow 80^2x^2=60^2(16900-x^2)$

$\Rightarrow 6400x^2=3600(16900-x^2)$

$\Rightarrow \dfrac{16}{9}x^2=16900-x^2$

$\Rightarrow \dfrac{25}{9}x^2=16900$

$\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78$

$\Rightarrow x=78$

Then,

$\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2$

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

$\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104$

This leads us to conclude that the closest point is (78,104)

5 0

1 month ago

For the month of June, Mae Green budgeted the following amounts: $180 for food, $475 for rent, $15 for transportation, $50 for i

tester [8859]

Question 1

Total budget sums up to 180 + 475 + 15 + 50 + 65 + 25 + 150 + 30 = $990.
Actual expenditure amounts to 182 + 475 + 12 + 65 + 68 + 12.50 + 150 + 36 = $1000.5.

Mae Green surpassed her designated budget.

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Question 2

Eleanor:
Earned = 380.48
Spent = 16.50

Peter:
Earned = 120 + 13.65 + 100 = 233.65.

Combined total income = 233.65 + 380.48 - 16.50 = 597.63.

-------------------------------------------------------------------------------------------------------------

Question 3

Aggregate expenditure = 540 + 48.55 + 34.15 + 12.80 + 18.95 + 38.60 + 2 + 6.50 = 701.55.

-------------------------------------------------------------------------------------------------------------

Question 4

Marie's updated balance = 250.65 - [21.95+48.50+75.60] + 55 = $159.50.

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Question 5

[235/825] × 100 = 28.48%

4 1

21 day ago

Read 2 more answers

On her birthday, Sonia distributed chocolates in an orphanage. She gave 5 chocolates to each child and 20 chocolates to adults.

Svet_ta [9556]

Answer with explanation:

Total number of children = x

Total chocolates shared = y

In total, the chocolates distributed to the children equals 5 times the number of children, or 5 x.

Chocolates received by adults equal 20.

Let the number of adults be z.

Expressing this situation as an equation:

y = 5 x + 20 z

$z=\frac{y-5 x}{20}$

⇒Number of adults = z

$=\frac{y-5 x}{20}$

3 0

1 month ago

If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is

Leona [9281]

Unlikely to have a significant difference.

8 0

29 days ago

David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to

Leona [9281]

Answer:

8 servings

Step-by-step explanation:

At a ratio of 15:1, for each serving that uses 75 grams of rice, it will need 75/15 = 5 grams of spice. With David having 40 grams of spice, he can prepare ...

40 g/(5 g/serving) = 8 servings

7 0

1 month ago

Read 2 more answers