The height of a rock thrown off a cliff can be modeled by h=-16t^2-8t+120, where h is the height in feet and t is time in seconds. How long does it take the rock to reach the ground?

This answer calculates the resistance of an aluminum wire of specific dimensions. It begins by determining the cross-sectional area of the wire, then uses a formula incorporating resistivity, length, and area to calculate resistance. The final resistance of the wire is approximately 0.037 Ohms.

To calculate the resistance of a piece of aluminum wire, we first need to figure out the cross-sectional area of the wire. As given, the diameter of the wire is 100 mils. To convert mils to cmils (circular mils), we square the diameter, thus 100^2 = 10,000 cmils is the cross-sectional area.

Next, we use the formula for resistance: R = ρL/A, where R is the resistance, ρ (Rho) is the resistivity of the material (aluminum, in this case), L is the length in feet, and A is the cross-sectional area in circular mils (cmils).

We need to convert the length from miles to feet (1 mile = 5,280 feet), so 2 miles = 10,560 feet. The resistivity of aluminum at 68°F is approximately 10.75 nanoOhms*meter, to convert this to Ohms*foot we multiply by 3.281, so ρ becomes approximately 35.28 nΩ/ft.

The resistance R can then be calculated as follows: R = ρL/A = (35.28 x 10^-9) x 10,560 / 10,000 = 0.037 Ohms, rounded to two decimal places.

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Answer:

Question 1: 1, 7, 29, 203

Question 2: 203, 29, 7, 1

Step-by-step explanation:

Total weight of six identical toys = 1.8 Kg

Therefore, the weight of one such toy = 1.8 kg/ 6 = 0.3 kg

Further, 1 kg = 1000 gms

Answer to Ques B-

Weight of one toy in grams = 0.3 * 1000 grams

= 300 grams

Answer to Ques C-

Weight of 4 toys in kilograms = 0.3 * 4 kilograms

= 1.2 kilograms

Hope this helps..!!

Thank you :)

"The correct fraction representing Japan's petroleum consumption as a percentage of the world's total is [tex]\(\frac{5.4}{100}\).[/tex]

To express the given percentage as a fraction, one must divide the percentage by 100, since percentages are parts per hundred. T

hus, 5.4% can be written as a fraction by placing 5.4 over 100, which gives us [tex]\(\frac{5.4}{100}\)[/tex].

Finally, this fraction can be reduced by dividing both the numerator and the denominator by their greatest common divisor, which is 2 in this case, yielding the simplified fraction [tex]\(\frac{27}{500}\).[/tex]

When reduced to a fraction without a decimal,  [tex]\(\frac{27}{500}\)."[/tex]

Answer:

The fifth term of [tex]a_n = 2(-1)^n[/tex] is, -2

Step-by-step explanation:

Given the sequence:

[tex]a_n = 2(-1)^n[/tex]             .....[1]

where,

n is the number of terms.

To find the fifth term of the given sequence:

Substitute n = 5 in [1]  we have;

[tex]a_5 = 2 \cdot (-1)^5[/tex]

⇒[tex]a_5 = 2 \cdot -1 = -2[/tex]

Therefore, the value of fifth term of [tex]a_n[/tex] is, -2

Answer:

1.2 acres of grass

Step-by-step explanation:

It takes 6.7 lb of seed to plant one acre of grass. The ratio of interest is 6.7 lb seed:1 acre of grass. We can find the acres of grass that can be planted with 8.04 pounds of seed using a conversion fraction.

8.04 lb × (1 acre/6.7 lb) = 1.2 acre

We can plant 1.2 acres of grass with 8.04 pounds of seed.

Answer:The measurement of angle O is greater than angle Q is the correct statement.

Explanation: Since, According to the question,  MQ = QP = PO = ON and MP is greater than NP.

Then, In first option, segment OP is longer than segment MQ is false because OP=MQ.

In second option, MN=MP can not be possible because NP is greater than MP.

In third option, The measure of angle Q equals the measure of angle O also can not be possible because MN is not parallel to QO.

But, In fourth option, Since MP is greater than NP thus NO makes larger angle than MQ.

Thus, fourth option is correct.

The minimum number of identical square tiles required to completely cover an 84 cm x 112 cm tabletop is 12 tiles, each with side lengths of 28 cm.

To determine the minimum number of identical square tiles required to completely cover a rectangular tabletop with dimensions 84 cm x 112 cm, we need to find the greatest common divisor (GCD) of the two side lengths. This is because using tiles that match the GCD will ensure that they fit perfectly across both lengths and widths without needing to cut any tiles.

The GCD of 84 and 112 is 28. Therefore, the side length of the square tile that Chen should use is 28 cm x 28 cm. To find the number of tiles needed, we then divide the area of the tabletop (which is 84 cm x 112 cm or 9408 square cm) by the area of one tile (which is 28 cm x 28 cm or 784 square cm).

The calculation is as follows: 9408 square cm / 784 square cm = 12. Therefore, Chen needs a total of 12 tiles of 28 cm x 28 cm to cover the entire tabletop.

Answer:

Kevin has 5 quarters and 8 dimes.

Step-by-step explanation:

First of all, a quarter is worth 0.25 dollars, while a dime is worth 0.10 dollars. As Kevin has 13 coins in his pocket which in sum make $2.05, and all of them are either dimes or quarters, in order to determine how many dimes and quarters does he have, we have to take into account that he's got an odd number of quarters, since the final amount of money sums $2.05, that is, it ends in 5.

Therefore, if he had 1 quarter and 12 dimes (0.25 + 12x0.10 = 1.45), he would have $1.45.

If he had 3 quarters and 10 dimes (0.25x3 + 10x0.10 = 1.75), he would have $1.75.

If he had 5 quarters ahd 8 dimes (0.25x5 + 8x0.10 = 2.05), he would have $2.05, so this is the correct option.

The probability that a spinner with 14 equal areas lands on a multiple of 5 or a multiple of 2 is 4/7, after identifying the unique numbers from 1 to 14 that fit the criteria and dividing by the total number of possible outcomes.

The student is asking about the probability of an event occurring after spinning a spinner with 14 equal areas numbered 1 through 14. Specifically, the question seeks the probability that the result is either a multiple of 5 or a multiple of 2 when the spinner is spun once.

To solve this, first identify the multiples of 5 and 2 between 1 and 14: for 5, the multiples are 5 and 10; for 2, the multiples are 2, 4, 6, 8, 10, 12, and 14. Here, the number 10 is a multiple of both 5 and 2, so it should only be counted once. In total, there are 8 unique numbers that are multiples of 2 or 5 on the spinner. Since there are 14 possible outcomes, the probability is:

Probability = Number of favorable outcomes / Total number of outcomes = 8 / 14 = 4/7.

Thus, the probability that the spinner lands on a multiple of 5 or a multiple of 2 is 4/7.

Given the equation is 7x² + 6 = 13.

Solving the quadratic equation using square roots :-

7x² + 6 = 13

Step 1 :- subtracting 6 from both sides

7x² + 6 - 6 = 13 - 6

7x² = 7

Step 2 :- Dividing by 7 on both sides

[tex] \frac{7x^{2}}{7} = \frac{7}{7} \\\\
x^{2} = 1 [/tex]

Step 3 :- Taking square root on both sides

[tex] \sqrt{x^{2}} = \sqrt{1} \\\\
x = -1 \;\;OR\;\; x=1 [/tex]

So, x = -1 or x = 1 is the final answer.