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2 years ago

Claire power walks 1/9 of a mile in 1/54 of an hour compute the unit rate as the complex fraction

Mathematics

2 answers:

pav-90 [236]2 years ago

8 0

Answer:

$\frac{54}{9}\text{ miles per hour}$

Step-by-step explanation:

Unit rate is the units of first quantity in one unit of second quantity.

Given,

Number of miles walked = $\frac{1}{9}$ ,

Number of hours = $\frac{1}{54}$

Thus, the unit rate

$=\frac{\text{Number of miles walked}}{\text{Number of hours}}$

$=\frac{1/9}{1/54}$

$=\frac{54}{9}$

= 6 miles per hour

Phantasy [73]2 years ago

4 0

1/9 * 54/1 = 54/9.

So she is walking 6mph.

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How many ways can Rudy choose 4 pizza toppings from a menu of 14 toppings if each topping can only be chosen once

madam [21]

Answer:

24,024

Step-by-step explanation:

Calculation for How many ways can Rudy choose 4 pizza toppings from a menu of 14 toppings

The 4 pizza toppings from a menu of 14 toppings will be 14,13,12,11

Hence,

14*13*12*11=24,024

Therefore the numbers of way Rudy can choose 4 pizza toppings from a menu of 14 is 24,024

6 0

2 years ago

While at a carnival, Andrew comes across a game that involves rolling a die. According to the game's rules, if the number rolled

Reptile [31]

Answer:

he can expect to lose 0.5$

Step-by-step explanation:

To solve this problem we must calculate the expected value of the game.

If x is a discrete random variable that represents the gain obtained when rolling a dice, then the expected value E is:

$E =\sum xP (x)$

When throwing a dice the possible values are:

x: 1→ -$9; 2→ $4; 3→ -$9; 4→ $8; 5→ -$9; 6→ $12

The probability of obtaining any of these numbers is:

$p=\frac{1}{6}$

The gain when obtaining an even number is twice the number.

The loss to get an odd number is $ 9

So the expected gain is:

$E=-9*\frac{1}{6}-9*\frac{1}{6}-9*\frac{1}{6} + 4*\frac{1}{6} + 8*\frac{1}{6} + 12*\frac{1}{6}\\\\E =-27*\frac{1}{6} + 24*\frac{1}{6}\\\\E=-3*\frac{1}{6}\\\\E=-$0.5$

4 0

2 years ago

Last year your professor wanted to study the pattern in class grades. The following table contains a sample of grades collected

Maslowich

Answer:

mean = 78.4

median = 77.5

mode = 75

This is Right - skewed (positive skewness) distribution

Step-by-step explanation:

Mean:-

The mean (average) is found by adding all of the numbers together and dividing by the number of items and it is denoted by x⁻

mean = $\frac{64+80+75+98+75}{5}$

mean (x⁻ ) = 78.4

The mean of the given data = 78.4

Median:

The median is found by ordering the set from lowest to highest and finding the exact middle.

64 ,75, 80, 98

The middle term of the given data set = $\frac{75+80}{2} =77.5$

Mode :

The mode is the most common repeated number in a data set.

64 ,75, 75, 80, 98

in data the most common number = 75

Conclusion:-

mean = 78.4

median = 77.5

mode = 75

This is Right - skewed (positive skewness) distribution

8 0

2 years ago

It takes 6 cubic inches of colored sand to fill a plastic cone. How many cubic inches will it take to fill a plastic cylinder wi

frosja888 [35]

The volume of a cone is equal to
Volume = pi * r^2 * h / 3

The volume of a cylinder is equal to
Volume = pi * r^2 * h

The cone is filled with 6 cubic inches colored sand.
As you observed, the volume of the cone is 1 / 3 of the volume of the cylinder.

Cone = Cylinder / 3
6 = Cylinder / 3
Cylinder = 18

So the answer is A. 18.

5 0

2 years ago

Suppose T is the transformation from ℝ2 to ℝ2 that results from a reflection over the y-axis followed by a reflection over the x

LenKa [72]

Answer:

A = \begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix}

Step-by-step explanation:

Let, there be a point (x , y) in R2

After reflection on Y axis, it will be ( -x , y) and thereafter if we reflect the image over X -axis , it will be (-x , -y)

So,

we need to find out a matrix

[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex]

such that,

(x , y) [tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex] = (-x. -y)

So, we have the following set of equations.

ax + cy = -x ------------(1)

bx + dy= -y-----------(2)

We can get the solution (by inspection) as,

[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex]

= [tex]\begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix}[tex]

So, the matrix is,

A = \begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix} (answer)

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2 years ago