Harper went into a movie theater and bought 10 bags of popcorn and 6 drinks,

Answer:

   

Hence, in this case, the 98% confidence interval would be (163.626;180.374)    

Step-by-step breakdown:

Previous concepts

A confidence interval represents a range that is likely to encompass a population value within a specific confidence level, typically expressed as a percentage whereby a population mean falls between an upper and lower limit.

The margin of errorindicates the span of values surrounding the sample statistic in a confidence interval.

A normal distributionillustrates a probability distribution that is symmetrical around the mean, signifying that values near the mean occur more frequently than those farther away from it.

denote the sample mean

population mean (the variable of interest)

s=16 signifies the sample standard deviation

n=23 represents the sample size  

The solution to the query

The equation for the confidence interval of the mean is given by the following formula:

  (1)

To determine the critical value , we first need to calculate the degrees of freedom, which is expressed as:

Since the confidence level is 0.98 or 98%, we find the value of and using tools like Excel or a calculator, where the Excel command would be: "=-T.INV(0.01,22)". This yields

Having all components ready, we can substitute into formula (1):

   

Thus, for this case, the 98% confidence interval will be (163.626;180.374)    

The attached graph illustrates the region. The centroid's coordinates are (5/3, 1). The centroid's coordinates are determined by averaging the coordinates of the area; Oₓ = (Aₓ+Bₓ+Cₓ)/3 = (0+1+4)/3 = 5/3 and O(y) = (A(y) + B(y) + C(y)) = (0+3+0)/3=3/3=1.

Answer:

1458/3456 reduces to 27/64 (after simplification)

The cube root of 27/64 equals 3/4

The square of 3/4 calculates to 9/16

Multiplying 9/16 by 1024 results in 576.

THIS IS THE ACTUAL WORK AND RESULT

Please make me brainliest

The bathtub's depth measures 18 inches

It takes 2 minutes to fill 3 inches of the bathtub

Subsequently

The remaining depth needed for filling with water = (18-3) inches

                                                                        = 15 inches

The time needed to fill the remaining 15 inches of the bathtub = (15*2)/3 minutes

                                                                      = 30/3 minutes

                                                                      = 10 minutes

Therefore, John is right in believing that it will require an additional 10 minutes to fill the tub to the brim at the same rate.

Hope this clarifies things!

Response:

5.8%

Detailed reasoning:

For the business,

retail space rental = $2400

wages = $1800

utilities = $480

Total operating cost = $4680

However,

retail space rent decreased by 5%, which results in;

5% of $2400 = 0.05 x $2400 = $125

The new rental amount for retail space = $2400 - $125

                                             = $2275

wages were lowered by 6%, calculated as;

6% of $1800 = 0.06 x $1800 = $108

The revised wages = $1800 - $108

                           = $1620

Utilities experienced a 7% increase, calculated as;

7% of $480 = 0.07 x $480 = $33.6

The adjusted utilities cost = $480 + $33.6

                                               = $513.6

New total operating costs = $2275 + $1620 + $513.6

                             = $4408.6

The percentage change in monthly expenses = x 100%

                                    =

x 100%                                    = 5.8%