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2 years ago

Caroline, Colin & Sarah share some money.

Mathematics

1 answer:

julia-pushkina [17]2 years ago

4 0

Answer:

2/9

Step-by-step explanation:

After Caroline's share,

1 - 1/9 = 8/9 is left

Sarah gets:

1/(1+3) of 8/9

1/4 × 8/9

2/9

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Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with dia

Sav [38]

Answer:

10.12 $m^{3}$

Step-by-step explanation:

Given:

0.07 cm thick = 0.007m and it is dr (the change in radius)

As we know that, the volume of a hemispherical dome with diameter 48 m is:

V = $\frac{2}{3}$ π $r^{3}$

Take the derivative of V we have:

$\frac{dV}{dr}$ = 2π $r^{2}$

<=> dV = 2π $r^{2}$ *dr

<=> dV = 2π* $48^{2}$ *0.0007 = 10.12 $m^{3}$

Hope it will find you well.

6 0

2 years ago

Read 2 more answers

In a survey of men aged 20-29 in a certain country, the mean height is 73.4 inches with a standard deviation of 2.7 inches. Find

satela [25.4K]

Answer:

The minimum height in the top 15% of heights is 76.2 inches.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 73.4, \sigma = 2.7$

Find the minimum height in the top 15% of heights.

This is the value of X when Z has a pvalue of 0.85. So it is X when Z = 1.04.

$Z = \frac{X - \mu}{\sigma}$

$1.04 = \frac{X - 73.4}{2.7}$

$X - 73.4 = 1.04*2.7$

$X = 76.2$

The minimum height in the top 15% of heights is 76.2 inches.

3 0

2 years ago

Mary Lou buys a package of 500 heels to decorate 4 different pairs of jeans. She uses the same number of jewels on each pair of

jeka57 [31]

You just want to do 500/4=125 jewels on each pair of jeans

4 0

2 years ago

The automatic car wash at a service station can wash 96 cars over a 4-hour period. What is the average number of cars that can b

Evgen [1.6K]

Answer:

Divide 96/4 to get how many cars can be washed within a single hour. Cut that in half to get 12.

Step-by-step explanation:

96÷4=24 cars/hr

24÷2=12 Cars for every 30 minutes.

7 0

2 years ago

The equation x2 16 + y2 9 = 1 defines an ellipse, which is graphed above. in this excercise we will approximate the area of this

Citrus2011 [14]

(a) 4
(b) y = sqrt(9 - (9/16)x^2)
The best guess to the formula using knowledge of the general formula for an ellipse is:
x^2/16 + y^2/9 = 1
(a). An ellipse is reflectively symmetrical across both the major and minor axis. So if you can get the area of the ellipse in a quadrant, then multiplying that area by 4 would give the total area of the ellipse. So the factor of 4 is correct.
(b). The general equation for an ellipse is not suitable for a general function since it returns 2 y values for every x value. But if we restrict ourselves to just the positive value of a square root, that problem is easy to solve. So let's do so:
x^2/16 + y^2/9 = 1
x^2/16 + y^2/9 - 1 = 0
x^2/16 - 1 = - y^2/9
-(9/16)x^2 + 9 = y^2
9 - (9/16)x^2 = y^2
sqrt(9 - (9/16)x^2) = y
y = sqrt(9 - (9/16)x^2)

4 0

2 years ago