The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x –

The year 1915 marks a population of 15,689. In 1940, it increased to 39,381. The required time to reach this figure is t = 137.9 years. Step-by-step explanation: To answer, we apply an exponential growth formula: A = P (1 + r) t, where P is the original number of individuals, r is the growth rate in decimal, and t is the time in years. Plugging in provided values: A = 6,250 (1 + 0.0375)^t. For the year 1915, as 1915-1890 translates to 25 years: A = 6,250 (1.0375)^25 yields 15,689. For 1940, as 1940-1890 indicates 50 years passed: A = 6,250 (1.0375)^50 results in 39,381. To find when the population hits 1,000,000, substitute A=1,000,000 and solve for t. This leads to 1,000,000/6,250 = (1.0375)^t implying log(160) = t * log(1.0375) results in t being approximately 137.9 years.

The maximum number of identical dental care bags the dentist can create with the smallest leftover is 1.

The counts of bags are 2, 4, and 3, respectively.

Clarification:

Total tubes of toothpaste = 56

Total packets of floss = 112

Total toothbrushes = 85

Therefore, the greatest number of identical dental care bags the dentist can assemble with minimal leftover for toothbrushes is found by calculating the H.C.F of 56, 112, 85 = 1 ( ∵ as they are coprime to each other )

Given that there is no common factor among 56, 112, and 85, except for the commonality between 56 and 112, which is 56, the remainder of toothbrushes will be 85-56=29.

Thus considering 28,[TAG_24]]

The numbers can be expressed as follows: 56 = 28×2, 112 = 28×4, and 84 = 28×3

Consequently, the dentist can create 28 bags containing all three supplies, with no leftover from toothpaste and floss, but with leftover from toothbrushes as we substitute 84 for 85 to maintain divisibility by 28 for common factor demonstration.

This results in 2 bags for toothpaste, 4 bags for floss, and 3 bags for toothbrushes.

Answer:

zero slope

Step-by-step explanation:

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Answer:

The formula to determine the distance Jane's trainer bikes is .

Detailed explanation:

A diagram has been included for clarity.

Known values:

Distance biked to the south = 16 miles

Distance ran west = 12 miles

We need to determine the distance covered by Jane's trainer.

Solution:

Let the biking distance be represented by 'x'.

We will assume it forms a right-angled triangle.

According to the Pythagorean theorem, it states that;

"The square of the hypotenuse is equal to the sum of the squares of the other two sides."

When set in equation form, this gives us;

Thus, the equation representing the distance biked by Jane's trainer is .

Upon solving, we find;

Consequently, Jane's trainer covers a distance of 20 miles.