Is 81 in the sequence with the nth term 4n+1?
Explain

The product of the expressions (3p⁴)³ * (p²)⁷ is 27p²⁶

How to evaluate the product of the expressions

From the question, we have the following parameters that can be used in our computation:

(3p⁴)³ * (p²)⁷

Expanding the brackets, we have

(27p¹²) * (p¹⁴)

Remove the brackets

So, we have

27p¹² * p¹⁴

Evaluate using the law of indices

27p²⁶

Hence, the product of the expressions is 27p²⁶

Question

Find the product

(3p⁴)³ * (p²)⁷

Final answer:

To find the dimensions of the rectangle, the problem was solved by setting up and solving equations based on the given perimeter and the relationship between the length and the width. It was found that the width is 25 feet and the length is 121 feet.

Explanation:

To solve the problem, we first need to set up equations based on the information given. We are told the perimeter of a rectangle is 292 feet and that the length (L) is 4 feet less than 5 times the width (W). The formulas for the perimeter (P) of a rectangle is P = 2L + 2W. The relationship between the length and the width can be expressed as L = 5W - 4.

Substituting the second equation into the first, we get: 292 = 2(5W - 4) + 2W.

Simplifying, we find that 292 = 10W - 8 + 2W, leading to 300 = 12W. Therefore, W = 25 feet. Substituting back to find L, we find that L = 5(25) - 4 = 121 feet.

Thus, the width of the rectangle is 25 feet, and the length is 121 feet, which corresponds to option C).

Schlitterbahn becomes cheaper than Splashtown after more than 15 rides.

Let's define x as the number of rides:

Cost of Splashtown: $25 + $1 * x
Cost of Schlitterbahn: $40

We need to find the value of x for which the cost of Splashtown becomes greater than the cost of Schlitterbahn.

$25 + $1x > $40

$1x > $40 - $25

x > $15

So, after more than 15 rides, Schlitterbahn would be cheaper than Splashtown.

The inequality representing the cost of each smoothie is 4x < 16, which simplifies to x < 4, denoting that the cost of each smoothie is less than $4. Sensible values are any positive numbers less than $4.

To represent the cost of each smoothie with an inequality, let's designate the cost of one smoothie as x. Since Lina bought 4 smoothies and the total cost was less than $16, the inequality to represent this situation is:

4x < 16

To solve this inequality, we'll divide both sides by 4:

x < 16 / 4

x < 4

The cost of each smoothie is less than $4.

Values that make sense for this situation would be any positive price per smoothie that is less than $4, as Lina's total purchase for 4 smoothies must not exceed $16. So, x could be any positive real number less than 4.

The estimated value is 50, which is close to the actual value of approximately 49.74.

To estimate the value of 97.5 divided by 1.96, we can round the numbers to make the calculation simpler.

Rounding 97.5 to 100 and 1.96 to 2 gives us an easier division: 100 divided by 2, which equals 50.

This estimation tells us that the actual value will be close to 50.

If we require more accuracy and use a calculator, we would find that 97.5 divided by 1.96.

= 9.75 / 1.96

= 49.74.

Therefore, our rounded estimate of 50 is reasonably close to the actual value.

The number of friends who purchased ride passes= 6

It is given that:

A fair charges $7.25 for admission and $5.50 for a ride pass.

Now, if 10 friends visited the fair.

This means that:

Total cost of admission= 7.25×10= $ 72.5

Also, if x friends purchased the ride passes.

Then, the total cost of ride passes= 5.50x

Total cost= 72.5+5.50x

This means that:

72.5+5.50x=105.50

i.e.

5.50x=105.50-72.5

5.50x=33

x=33/5.50

x=6

     Hence, 6 friends purchased ride passes.

Each day the lizards eat about 36 crickets when we round to the nearest whole number

To calculate how many crickets the lizards eat each day, we need to divide the weekly intake by the number of days in a week. The lizards eat 250 crickets per week. There are 7 days in a week.

So, we divide 250 by 7 which equals approximately 35.71 crickets per day.

Therefore, each day the lizards eat about 36 crickets when we round to the nearest whole number, since you can't have a fraction of a cricket.

The deep-sea diver started at 82 feet below the surface and rose in five steps of 15 feet each, which resulted in a new position of -7 feet. This indicates that the diver is still 7 feet underwater, so the integer representing his position is negative.

The diver starts at 82 feet below the surface and rises in five steps of 15 feet each. To find the new position, we start with the initial position and subtract the distance risen in each step:

Initial position: -82 feet (below water is considered negative)

Total rise: 5 steps × 15 feet/step = 75 feet

New position: -82 feet + 75 feet = -7 feet

Therefore, the diver's new position is -7 feet relative to the surface, indicating he is still 7 feet underwater, thus the integer is negative.

In linear equation,  4/3  is the scale factor.

given,

The length of the ears on the shadow puppet = 3 inches

The length of the ears on the shadow = 4 inches.

so according to question we apply the formula of scale factor ,

scale factor = length of ears on the shadow/length of ears on the shadow

             scale factor = 4/3

Learn more about linear equation here:

brainly.com/question/11897796

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in order to have the smallest possible number the numbers need to be arranged from smallest to largest

 using 3, 5 & 7 the smallest number would be 357