MATHEMATICS COLLEGE

If 3 inches represents 90 miles on a scale drawing , how long would a line segment be that represents 240 miles?

Answers

Answer 1

Answer:

Answer:

8 inches

Step-by-step explanation:

90 miles -------------> represented by 3 inches

1 mile -------------> represented by 3/90 inches

240 miles ----------> represented by 3/90 x 240 = 8 inches

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Write an explicit equation for the arithmetic sequence
3,7,11,15,19

Answers

Answer:

Arithmetic Sequence:

d=4

Step-by-step explanation:

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 4 o the previous term in the sequence gives the next term. In other words, aₙ=a₁+d(n-1)

How many outer atoms and lone pairs are present in a molecule with a square pyramidal shape?

Answers

Answer:

5 Outer and 1 lone pair

Step-by-step explanation:

A square pyramidal shape results when one of the bonds of an octahedron structure is occupied by a lone pair.

Hence there are 5 bonded atoms and one lone pair. The hybridization about the central atom is $sp^(3) d^2$ .

One of the most common example is Xenon tetraflouride. $XeF_4$ . Looking at its structure we can see that it has 5 pairs of outer atoms and one lone pair. With its coordination number 5. The shape of the orbitals is octahedral.

Final answer:

In a molecule with a square pyramidal shape, there are two lone pairs and four outer atoms.

Explanation:

When a central atom has two lone electron pairs and four bonding regions, we have an octahedral electron-pair geometry. The two lone pairs are on opposite sides of the octahedron (180° apart), giving a square planar molecular structure that minimizes lone pair-lone pair repulsions.

Learn more about molecular structure here:

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Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2

Answers

Answer:

The area of the square is increasing at a rate of 40 square centimeters per second.

Step-by-step explanation:

The area of the square ( $A$ ), in square centimeters, is represented by the following function:

$A = l^(2)$ (1)

Where $l$ is the side length, in centimeters.

Then, we derive (1) in time to calculate the rate of change of the area of the square ( $(dA)/(dt)$ ), in square centimeters per second:

$(dA)/(dt) = 2\cdot l \cdot (dl)/(dt)$

$(dA)/(dt) = 2\cdot √(A)\cdot (dl)/(dt)$ (2)

Where $(dl)/(dt)$ is the rate of change of the side length, in centimeters per second.

If we know that $A = 25\,cm^(2)$ and $(dl)/(dt) = 4\,(cm)/(s)$ , then the rate of change of the area of the square is:

$(dA)/(dt) = 2\cdot \sqrt{25\,cm^(2)}\cdot \left(4\,(cm)/(s) \right)$

$(dA)/(dt) = 40\,(cm^(2))/(s)$

The area of the square is increasing at a rate of 40 square centimeters per second.

You sell candy at a football game for $1.50 each. You paid $50 for 300 candy bars. what is the domain and range for your profit?

Answers

Answer:

Domain is number of candy or 300

Range is profit from selling candy or $50

Step-by-step explanation:

Domain is the numbers you are allowed to use in your function. In this case, it would be the amount of candy you sold.

The range is the output from inputting the number(s) in the domain. In this case, the range is the amount of money you profit.

Profit=(amount gained)-(amount lost)

amount gained is from selling candy

amount lost is what you invested to get the candy

amount gained=(cost per candy)X(number of candy)

amount gained=(1.50)(300)

amount gained=$450

amount lost=$50

therefore

Profit=450-40=$400

a function for profit can be as follows:

P(x)=1.5x-c

where amount you sold each candy for, c is cost for those x candies, and P(x) is the profit for x candies

uppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.2 and a standard deviation of 1.49. Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67

Answers

Answer:

99.85% of American women have shoe sizes that are less than 12.67

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 8.2

Standard deviation = 1.49

Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67

12.67 = 8.2 + 3*1.49

12.67 is 3 standard deviations above the mean.

Since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above. Of those 50% above, 99.7% are between the mean and 12.67. So

0.5 + 0.997*0.5 = 0.9985

99.85% of American women have shoe sizes that are less than 12.67

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