a babysitter earns $9 for 1 h and $36 for 4 h

To simplify [tex]\(3x(-11x + 1)\)[/tex], we distribute [tex]\(3x\)[/tex] to both terms inside the parentheses, resulting in [tex]\(-33x^2 + 3x\)[/tex]. Thus, the simplified expression is [tex]\(-33x^2 + 3x\)[/tex]. Therefore, the correct answer is option A) [tex]\(-33x^2 + 3x\)[/tex].

To simplify the expression [tex]\(3x(-11x + 1)\)[/tex], we'll use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex].

1. **Apply the distributive property**:

  We distribute [tex]\(3x\)[/tex] to both terms inside the parentheses:

   [tex]\[3x \cdot (-11x) + 3x \cdot (1)\][/tex]

2. **Perform multiplication**:

   [tex]\[= -33x^2 + 3x\][/tex]

Now, let's break down each step in detail:

- **Step 1: Apply the distributive property**:

 We distribute [tex]\(3x\)[/tex] to both terms inside the parentheses: [tex]\(-11x\) and \(1\)[/tex]. This results in two separate terms.

- **Step 2: Perform multiplication**:

 Multiply each term inside the parentheses by [tex]\(3x\)[/tex]. This results in:

 [tex]\[3x \cdot (-11x) = -33x^2\][/tex]

 [tex]\[3x \cdot (1) = 3x\][/tex]

 Combining these two terms, we get [tex]\(-33x^2 + 3x\)[/tex].

Therefore, the simplified form of the expression [tex]\(3x(-11x + 1)\) is \(-33x^2 + 3x\).[/tex]

Hence, the correct answer is option A) [tex]\(-33x^2 + 3x\)[/tex].

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 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.

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

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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

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.

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 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.

The distance between the points (−5, −9) and (−5, 13) would be 22. units.

The shortest distance (length of the straight line segment connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

We have been given two points as (−5, −9) and (−5, 13)

Then the distance formula :

D = √[(x-p)² + (y-q)²]  

Now we substitute;

[tex]d = \sqrt{(-5 - (-5)^2 + (13 - (-9)^2}\\d = \sqrt (-5 + 5)^2 + (13 + 9)^2\\d = \sqrt (0^2 + 22^2)\\d = \sqrt (484)\\d = 22[/tex]

Therefore, the distance between the points (−5, −9) and (−5, 13) would be 22. units.

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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.