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3 years ago

There are 600 performers in a dance recital. The ratio of men to women is 4:6. How many men performers were in the dance recital

Mathematics

1 answer:

posledela3 years ago

5 0

Answer: 240 men

Step-by-step explanation:

From the question, we are informed that there were 600 performers in a dance recital and that the ratio of men to women is 4:6.

Fraction of men at the recital = 4/10

Fraction of women at the recital = 6/10

The number of men performers that were in the dance recital will be:

= 4/10 × 600

= 240 men

There were 240 men at the recital.

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Assume that women's heights are normally distributed with a mean given by mu equals 62.3 in, and a standard deviation given by

Salsk061 [2.6K]

Answer: a) 0.6141

b) 0.9772

Step-by-step explanation:

Given : Mean : $\mu= 62.3\text{ in}$

Standard deviation : $\sigma = \text{2.4 in}$

The formula for z -score :

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

a) Sample size = 1

For x= 63 in. ,

$z=\dfrac{63-62.3}{\dfrac{2.4}{\sqrt{1}}}=0.29$

The p-value = $P(z$

$0.6140918\approx0.6141$

Thus, the probability is approximately = 0.6141

b) Sample size = 47

For x= 63 ,

$z=\dfrac{63-62.3}{\dfrac{2.4}{\sqrt{47}}}\approx2.0$

The p-value = $P(z$

$=0.9772498\approx0.9772$

Thus , the probability that they have a mean height less than 63 in =0.9772.

8 0

4 years ago

Write the ratio 3/7 to 9 as a fraction in simplest form

AleksAgata [21]

Answer:

soory i need more points

Step-by-step explanation:

7 0

3 years ago

Half-life of Po-210 is 140 days. If the initial mass of the sample is 5

Anna35 [415]

Answer:

$0.625kg$

Step-by-step explanation:

we are given half-life of PO-210 and the initial mass

we want to figure out the remaining mass after 420 days

in order to solve so we can consider the half-life formula given by

$\displaystyle f(t) = a {0.5}^{t/T}$

where:

f(t) is the remaining quantity of a substance after time t has elapsed.
a is the initial quantity of this substance.
T is the half-life

since it halves every 140 days our T is 140 and t is 420. as the initial mass of the sample is 5 our a is 5

thus substitute:

$\displaystyle f(420)=5\cdot{0.5}^{420/140}$

reduce fraction:

$\displaystyle f(420)=5\cdot{0.5}^{3}$

By using calculator we acquire:

$\displaystyle f(420)=0.625$

hence, the remaining sample after 420 days is 0.625 kg

4 0

3 years ago

A rectangular prism has a length that is 3 inches shorter than the height and a width that is 5 inches longer than the height. F

LUCKY_DIMON [66]

An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.

We are given a rectangular prism.
A rectangular prism is no different than a cuboid.
Let the height of the rectangular prism be "h".
The length of the rectangular prism is "h-3".
The width of the rectangular prism is "h+5".
The volume of the rectangular prism is the same as that of the cuboid.
The volume of the rectangular prism is the product of its length, its width, and its height.
The volume of the rectangular prism is (h - 3)*(h + 5)*h.
An equation for the volume of the prism as a function of the height is :
Volume = (h - 3)*(h + 5)*h
Volume = (h² + 2h - 15)*h
Volume = h³ + 2h² - 15h

To learn more about prism, visit :

brainly.com/question/12649592

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5 0

1 year ago

In the figure below what is the value of x?

vazorg [7]

Answer:

The value of x is 106

Step-by-step explanation:

Let us solve the question

In the given figure

∵ The triangle in the given figure has two sides equal

→ That means the triangle is an isosceles triangle

∴ The triangle is isosceles

∵ In the isosceles triangle, the base angles are equal in measures

∵ The measure of one base angle is 37°

∴ The measure of other base angle is 37°

→ The sum of the measures of the interior angles of a Δ is 180°

∵ 37° + 37° + x = 180°

→ Add the like terms

∴ 74° + x = 180°

→ Subtract 74 from both sides

∵ 74 - 74 + x = 180 - 74

∴ x = 106

∴ The value of x is 106

7 0

3 years ago