Fourteen runners in a marathon had these race times, in hours,

Step One

Deduct 32 from both sides.

F - 32 = \frac{9}{5}(k - 273.15)

Step Two

Multiply each side by \frac{5}{9}.

\frac{5}{9}(F - 32) = \frac{5}{9} \times \frac{9}{5}(k - 273.15)

\frac{5}{9}(F - 32) = k - 273.15

Step Three

Add 273.15 to both sides.

\frac{5}{9}(F - 32) + 273.15 = k

Problem B

F = 180

Solve for k

k = \frac{5}{9}(F - 32) + 273.15

k = \frac{5}{9}(180 - 32) + 273.15

k = \frac{5}{9} \times 148 + 273.15

k = 82.2222 + 273.15

k = 355.3722

k = 355.4  <<< Answer

<span>The flag's dimensions are 40 inches by 55 inches.

Reasoning<span>:
The perimeter equals the sum of all sides. Being rectangular, opposite sides have equal lengths. Thus, the equation is
y + 11/8 y + y + 11/8 y = 190.

Simplifying, we get
2y + 22/8 y = 190.

Expressing 22/8 as a mixed fraction results in
2y + 2 3/4 y = 190.

Combining terms: 4 3/4 y = 190.

Divide both sides by 4 3/4:
y = 190 ÷ 4 3/4.

Converting 4 3/4 to an improper fraction: y = 190 ÷ 19/4.

Dividing by a fraction means multiplying by its reciprocal:
y = 190 × 4/19 = 760/19 = 40.

Since y = 40, calculate 11/8 y = 11/8 × 40 = 440/8 = 55.</span></span>

In this scenario, we'll define the following variables:

x: total volume of potting soil in liters.

y: quantity of potting soil allocated to each pot in liters.

To determine the number of pots, we can use the expression:

Substituting in the respective values yields:

Reformatting gives us:

When rounding down to the nearest whole number, we find:

The conclusion is:

Yao Xin is capable of filling 18 pots.

Calculate the probability of each pen color by dividing the number of times each color was chosen by the total selections:

Red pens: 6 out of 30, which simplifies to 1/5

Blue pens: 10 out of 30, which simplifies to 1/3

Black pens: 14 out of 30, which simplifies to 7/15

To find the likelihood of first selecting a blue pen and then a red pen, multiply their individual probabilities:

(1/3) × (1/5) = 1/15

The resulting probability is 1/15.

Answer:

Step-by-step explanation:

It is known that the mean and standard deviation of the sampling distribution of the sample proportion() are represented as follows:-

, where p= Population proportion and n = sample size.

Let p denote the proportion of blue chips.

According to the information provided, we have

p= 0.275

n= 5

Thus, the mean and standard deviation of the sampling distribution of the sample proportion of blue chips for samples of size 5 will be:

Therefore, you will have the mean and standard deviation for the sample proportion of blue chips for samples of size 5: