Can someone please help me with these questions? Thanks

You randomly choose one hat from 3 green hats, 4 black hats, 2 white hats, 2 red hats, and 1 blue hat. What is the probability o

kkurt [141]

Answer:

4/12= 1/3

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Y is inversely proportional to x.

Inessa [10]

Answer:

1. $xy = 63$

2. $y = 3$

Step-by-step explanation:

Given

Variation: inverse Proportion

y = 7, x = 9

Required

- Write an equation connecting y and x

- Find y when x = 21

Given that thee variation is inversely proportional;

This implies that

$y\ \alpha\ \frac{1}{x}$

Convert variation to equation

$y\ = \frac{k}{x}$ ----------- Equation 1

Where k is the constant of variation

Substitute 7 for y and 9 for x in equation 1

$7 = \frac{k}{9}$

Multiply both sides by 9

$9 * 7 = 9 * \frac{k}{9}$

$63 = k$

Substitute 63 for k in equation 1

$y = \frac{63}{x}$

Multiply both sides by x

$x * y = \frac{63}{x} * x$

$xy = 63$

Hence, the equation connecting x and y is $xy = 63$

Solving for when x = 21

Substitute 21 for x in the above equation

$21 * y = 63$

Divide both sides by 21

$\frac{21 * y}{21} = \frac{63}{21}$

$y = 3$

4 0

3 years ago

Help me pleasee (10 points)

Montano1993 [528]

Answer:

B

Step-by-step explanation:

Givens

a^2 + b^2 = c^2

a = 4x

b = x + 2

c = 3x + 4

Solution

(4x)^2 + (x + 2)^2 = (3x + 4)^3 Remove all the brackets.

16x^2 + x^2 + 4x + 4 = 9x^2 + 24x + 16 Collect like terms on the left

17x^2 + 4x + 4 = 9x^2 + 24x + 16 Subtract the terms on the right

8x^2 - 20x - 12 = 0

This factors into

(4x - 12)(2x + 1)

There are 2 answers

4x - 12 = 0

4x = 12

x = 12/4

x = 3

or

2x + 1 = 0

2x = - 1

x = - 1/2

You have to look at x = -1/2 carefully. The problem is that 4x = 4*(-1/2) = - 2 which is not possible in Euclidean Geometry.

So the only answer is x = 3

4 0

2 years ago

The width of a box is two-third of it's length and height is one-third of it's length.If the volume of the box is 384 cubic mete

Black_prince [1.1K]

Answer:

Length = 12

Width = 8

Height = 4

Step-by-step explanation:

Let length of box = l

Width = 2/3 * l

Height = 1/3 * l

Volume of the box = 384 ft³

Volume = Length * width * height

Volume of box = l * 2/3 l * 1/3 l

384 = 2l³ / 9

384 * 9 = 2l³

3456 = 2l³

l³ = 3456 / 2

l³ = 1728

Take the Cube root of 1728

l = 12

Length = 12

Width = 2/3 * 12 = 8

Height = 1/3 * 12 = 4

5 0

2 years ago

Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. assume that σ is known to be 36.8

Delvig [45]

We are given the following data:

Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22

We are to find the confidence intervals for 90%, 95% and 98% confidence level.

Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.

Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.645* \frac{36.8}{ \sqrt{22}}=110.69$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.645* \frac{36.8}{ \sqrt{22}}=136.51$

Thus the 90% confidence interval will be (110.69, 136.51)

Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.96* \frac{36.8}{ \sqrt{22}}=108.22$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.96* \frac{36.8}{ \sqrt{22}}=138.98$

Thus the 95% confidence interval will be (108.22, 138.98)

Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-2.327* \frac{36.8}{ \sqrt{22}}=105.34$
Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+2.327* \frac{36.8}{ \sqrt{22}}=141.86$

Thus the 98% confidence interval will be (105.34, 141.86)

Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)

As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.

3 0

3 years ago