Between what pair of numbers is the product of 289 and 7?

The perimeter of the norwegian flag is 190 inches. What are the dimensions of the flag?

zzz [4022]

<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>

8 0

14 days ago

Mason is tiling the floor of his bathroom, which measures 9.75 feet by 8.63 feet. He estimates the area. Will he have enough til

Leona [4166]

He will have more than sufficient, as he only has to account for an area of 84.1425 square feet.

3 0

8 days ago

Read 2 more answers

Based on daily measurements, Bob's weight has a mean of 200 pounds with a standard deviation of 16 pounds, while Mary's weight h

babunello [3635]

Answer:

(C) They have the same coefficient of variation

Step-by-step explanation:

The coefficient of variation (CV) is calculated using the formula:

$CV = \frac{\sigma}{\mu}$

Where $\sigma$ represents standard deviation and $\mu$ represents the mean.

Bob's average weight is 200 pounds with a standard deviation of 16 pounds

This indicates that $\sigma = 16, \mu = 200$ .

Thus, his coefficient of variation is

$CV = \frac{16}{200} = 0.08$

Mary's average weight is 125 pounds, with a standard deviation of 10 pounds.

This implies $\sigma = 10, \mu = 125$

Therefore, her coefficient of variation is

$CV = \frac{10}{125} = 0.08$

Since both have the same coefficient of variation, the accurate response is.

(C) They have the same coefficient of variation

6 0

2 days ago

The perimeter of a rectangle is 202. The length is 26 more than 4 times the width. Find the dimensions

Inessa [3907]

Answer:

$P = 2*(26+4y) + 4y$

Upon solving for y, we find:

$202= 52 +8y +4y$

$202= 52 +12 y$

By substitution, we have:

$150 = 12y$

Thus, we arrive at:

$y = \frac{150}{12}= 12.5$

And for x, we determine:

$x = 26 +4*12.5 = 76$

This gives us a length of 76 and a width of 12.5.

Step-by-step explanation:

We are dealing with a rectangle. The formula for the perimeter is:

$P= 2x+2y$

Here, x denotes the length and y the width. The following conditions can be established:

$x = 26 +4y$

Substituting these values yields:

$P = 2*(26+4y) + 4y$

When we solve for y, we find:

$202= 52 +8y +4y$

$202= 52 +12 y$

By substitution, we obtain:

$150 = 12y$

Thus, we conclude:

$y = \frac{150}{12}= 12.5$

The length is found to be 76, while the width measures 12.5.

6 0

4 days ago

Students have organized

tester [3916]

Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

$D=v\cdot t$

Part A.

Steve's speed: $v=3.5\ mph$

Distance: a minimum of 21 miles

Time: unknown, so

$3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6$

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: $v_M=2.4\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Mercedes's Distance walked: $D_M$ miles

Time: x hours

Mercedes is 2 miles ahead, therefore

$D_E=3.2x\\ \\D_M=2.4x+2$

Elijah will trail behind until

$D_E$

In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: $v_M=3\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Aubrey's Distance walked: $D_A$ miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

$D_E=42+3.2x\\ \\D_A=42.5+3x$

Elijah will be ahead of Aubrey when

$D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours$

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

4 0

11 days ago