Tammy, John, Allison and Henry paid a total of $45 for movie tickets at the theater. Each movie ticket was the same price. How much did each person pay for a movie ticket

Answer:

Below

Step-by-step explanation:

Answer 10.1: 15

Explanation:

(-4)^2 is 16 and (-1)^3 is -1, so (-4)^2 + (-1)^3 = 16 - 1 = 15.

Answer 10.3: -23

Explanation:

(-2)^2 is 4 and -27 minus 4 is -23.

Answer 10.5: None

Explanation:

The expression is incomplete as there is no number or operation after the "^3".

Answer 10.7: 0.7

Explanation:

√0.04 is 0.2 and (0.5)^2 is 0.25, so 0.2 + 0.25 = 0.45. The square root of 0.45 is approximately 0.671.

Answer 10.9: 0.02788

Explanation:

(0.2)^3 is 0.008 and 0.027 plus 0.008 is 0.035. Raising 0.035 to the power of 1/3 gives approximately 0.315. Therefore, the final answer is approximately 0.02788.

Answer 10.2: -2018

Explanation:

Using the order of operations, we start with 62 divided by 3 which is approximately 20.67, then multiply that by -33 to get approximately -682.44.

Answer 10.4: -2

Explanation:

Empty brackets imply multiplication. Therefore, ()^2 is 0, and (-1)^3 is -1. Thus, 0 - 1 = -1.

Answer 10.6: 0.11

Explanation:

(0.1)^2 is 0.01 and (0.1)^3 is 0.001, so 0.01 + 0.001 = 0.011.

Answer 10.8: 0.38

Explanation:

0.0144 + 0.04 = 0.0544, and the square root of 0.0544 is approximately 0.2336. Subtracting (-0.2)^2 (which is 0.04) from 0.0544 gives 0.0144. Taking the square root of 0.0144 gives approximately 0.12. Finally, 0.2336 minus 0.12 is approximately 0.38.

The best measure of center for the data is: The median is the best measure of center, and it equals 3.

In statistics, the median is a measure of central tendency that represents the value separating the higher half of a dataset from the lower half.

To find the median of a dataset, the values must first be arranged in order of magnitude. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.

To determine the best measure of center for this data, we need to consider the distribution of the data. The line plot shows that the data is not symmetric, with more data points above 6 and 7 than below.

In this case, the median is the best measure of the center, because it is not affected by the extreme values in the dataset. The median is the middle value of the dataset when it is arranged in order, and in this case, the middle value is 3 which gives a median of 3.

Therefore, the best measure of the center for this data is the median, and its value is3.

Option (B) is correct.

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Answer:

Option B is correct

The numerical values of the circumference and area are equal.

Step-by-step explanation:

Circumference(C) and Area (A)of the circle is given by:              ....[1]           ......[2]where, r is the radius of the circle.As per the statement:A circle has a diameter of 4 inches. We know:Diameter = 2 (radius(r))then;4 = 2rDivide both sides by 2 we have;r = 2 inchesSubstitute these in [1] and [2] we have;Use then;Therefore, the numerical values of the circumference and area are equal i.e 12.56

Their method is not a random sample, as it did not accurately represent the nitrate levels in the entire population of mountain lakes.

The method used by the researchers to select the lakes was random, as they did not have a specific criteria for selecting the lakes. However, the method used to collect the water samples from each lake was not random, as they took only five water samples from each lake, which means that not all parts of the lake were tested. This violates the criterion of random sampling, which requires that every element in the population has an equal chance of being selected for the sample. The researchers' method of collecting nitrate levels in lake water does not result in a truly random sample. This is because they violated the criterion of equal probability of selection for each measurement. By selecting 12 mountain lakes and taking five samples from each, they created a stratified sample rather than a random one. The measurements within each lake are not independent, as they could be affected by the specific conditions of that lake. To obtain a truly random sample, the researchers should have selected 60 measurements from all mountain lakes with equal probability, ensuring that each measurement had the same chance of being included in the sample.

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The volume of the book is 595/8 cubic inches or approximately 74.375 cubic inches.

To find the volume of the book, we need to multiply the length, width, and height of the rectangular prism. The height of the book is 8 1/2 inches, the width is 7 inches, and the thickness is 2 1/2 inches.

First, we need to convert the height to a fraction: 8 1/2 inches = 17/2 inches. Then, we can use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

Volume = 7 inches x 2 1/2 inches x 17/2 inches

To simplify this calculation, we can convert 2 1/2 inches to a fraction: 2 1/2 inches = 5/2 inches.

Volume = 7 inches x 5/2 inches x 17/2 inches

Multiplying these fractions gives:

Volume = (7 x 5 x 17) / (2 x 2 x 2)

Volume = 595 / 8 cubic inches

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Let's start by defining some variables: Let x be the airspeed of the first plane in kilometers per hour.
Then the airspeed of the second plane is x+80 km/h.

Let t be the time in hours that the first plane flies before the second plane starts.
After two hours, the first plane has flown for t+2 hours, and the second plane has flown for t hours. To solve for the airspeeds, we need to use the formula: distance = rate x time.

The distance the planes fly in opposite directions is the sum of the distances each plane flies:
distance = (x)(t+2) + (x+80)(t), We are told that after two hours, the planes are 3165 kilometers apart, so we can set up an equation: 3165 = (x)(t+2) + (x+80)(t).

Simplifying this equation:
3165 = xt + 2x + xt + 80t + 80
3165 = 2xt + 82t + 2x + 80
3165 = 2t(x+40) + 2x + 80
3085 = 2t(x+40) + 2x

Now we can solve for x:
3085 = 2t(x+40) + 2x
3085 = 2tx + 80t + 2x
3085 = 4tx + 80t
38.5625 = tx + 20t
1.928125 = x + 20

So the airspeed of the first plane is x = 1.928125 - 20 = 18.071875 km/h.
The airspeed of the second plane is x+80 = 18.071875 + 80 = 98.071875 km/h. Let's denote the airspeed of the first plane as x km/h and the airspeed of the second plane as (x + 80) km/h.


Since the planes fly in opposite directions, the sum of the distances they travel is equal to the distance between them, which is 3165 km. Therefore, we can write the equation: 2x + 1.5(x + 80) = 3165

Now we can find the airspeed of the second plane: x + 80 = 870 + 80 = 950 km/h, So, the first plane's airspeed is 870 km/h and the second plane's airspeed is 950 km/h.

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False. If f''(x) > 0 for all real numbers except at x=a, this implies that the function is concave up everywhere except at x=a. A continuous function that is concave up has a positive second derivative, which means the graph is shaped like a "U." In other words, it is "curving" upwards.

Since the function is concave up everywhere except x=a, it indicates that the function is increasing on both sides of x=a. An absolute maximum would require the function to be increasing on one side and decreasing on the other side, forming a "peak." However, since the function is increasing on both sides of x=a, it cannot have an absolute maximum at x=a. Thus, the statement is false.

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To construct an 86% confidence interval with 15 data points, you would use a t-score of approximately 1.761, assuming the data follows a normal distribution.

To construct an 86% confidence interval with 15 data points, we will first need to find the appropriate t-score.

The t-score is based on the t-distribution, which is used when the sample size is small (less than 30) and the population standard deviation is unknown.

The t-score depends on the desired level of confidence and the degrees of freedom, which is equal to the sample size minus 1 (15 - 1 = 14).

To find the t-score for an 86% confidence interval, we must look at a t-distribution table or use a statistical calculator. We need to find the value corresponding to 0.930 (1 - [(1 - 0.86)/2]) in the cumulative probability column and 14 degrees of freedom in the table. The appropriate t-score is approximately 1.761.

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Answer:12cm

Step-by-step explanation: volume of a square based pyramid = base area ×height

120 = X × 10

120/10 =

12 = X

base area of square = 4× X

12= 4 × X

12/ 4 =

3= X

So , the length of its base is 3 cm

True, finding a random sample with a mean significantly higher than the population mean is indeed very unlikely. In a population with a mean of 20 fluid ounces and a standard deviation of 2 fluid ounces, most samples should have means close to the population mean.

A random sample is a subset of the population chosen without bias, ensuring that each member has an equal chance of being included. This process allows researchers to make inferences about the population based on the sample's characteristics.

The Central Limit Theorem (CLT) states that, for a sufficiently large sample size, the sampling distribution of the sample mean approaches a normal distribution with the same mean as the population and a standard deviation equal to the population's standard deviation divided by the square root of the sample size.

When a sample mean is far from the population mean, it is considered an outlier, which could be due to chance or systematic error in the sampling process. In most cases, a sample mean significantly different from the population mean indicates that the sample is not representative of the population, which may affect the validity of any conclusions drawn from the sample.

In summary, it is true that finding a random sample with a mean considerably higher than the population mean of 20 fluid ounces and a standard deviation of 2 fluid ounces is very unlikely. A genuinely random sample should produce a mean closer to the population mean.

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To find the variance, we can use the formula: variance = standard deviation squared, Using the given standard deviation of 10.4, we can calculate the variance as: variance = 10.4^2 = 108.16.

However, we are also given the sample standard deviation of 11.6. This suggests that the sample may not accurately represent the population, and we should use the sample standard deviation to estimate the population standard deviation.

To adjust for this, we can use Bessel's correction, which adjusts the sample standard deviation by dividing by (n-1) instead of n: adjusted sample standard deviation = 11.6 * sqrt(5/4) = 14.5, Then, we can use this adjusted standard deviation to estimate the variance: variance = 14.5^2 = 210.25 .

Therefore, the most nearly the variance is 210.25, a sample standard deviation of 11.6 is given, we'll use that value. Variance is the square of the standard deviation. Therefore, the variance is:

Variance = (Sample Standard Deviation)^2
Variance = (11.6)^2
Variance = 134.56, So, the variance is most nearly 134.56.

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A randomized controlled trial in which each subject is assigned to a combination of at least two independent variables is an example of a Factorial Design.

In statistics, a full factorial experiment is one in which all potential combinations of the levels across all of the factors are taken into account by the experimental units. A full factorial experiment has two or more factors with discrete possible values or "levels" in its design. A fully crossed design is another name for a full factorial design. Using such an experiment, the researcher can examine how each element affects the response variable as well as how different factors interact with one another.

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The Tragedy of the Commons is used to describe when one fisherman exceeds the legal limit for a particular type of fish by one fish, the effect on the fish population might not be harmful, but if many fishermen exceed the limit by one fish, knowing that they are depleting that particular population of fish.

The commons is a situation in which individuals who have access to a resource (also known as the commons) act in their own interests and ultimately release the resource. This economic theory was first proposed by the English writer William Forster Lloyd in 1833. The speed of the resource depends on three important factors: the number of users who want to use the resource in question, the intensity of use, and the resources involved. Fishing is a classic example of the situation of different people who occur when the property is not in full possession and the resources are open. Migration of fish often makes it difficult to establish and protect the right to fish at sea, so fishing laws apply. So giving service is an example of the situation of people who share.

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a) The original statement can be expressed as: For all x and y, if N(x) and N(y), then P(x,y)

b) The original statement can be expressed as: For all x, if R(x), then D(x)

c) For all x, if P(x), then there exist y and z such that S(x,y) and S(x,z) and y is not equal to z.

d) The original statement can be expressed as: For all x, if N(x) and R(y), then not S(x,y).

a) The product of two negative real numbers is positive:

Let P(x,y) be the statement "the product of x and y is positive", N(x) be the statement "x is a negative real number". Then the original statement can be expressed as:

For all x and y, if N(x) and N(y), then P(x,y)

b) The difference of a real number and itself is zero:

Let D(x) be the statement "the difference of x and itself is zero", R(x) be the statement "x is a real number". Then the original statement can be expressed as: For all x, if R(x), then D(x)

c) Every positive real number has exactly two square roots:

Let S(x,y) be the statement "y is a square root of x", P(x) be the statement "x is a positive real number". Then the original statement can be expressed as:

For all x, if P(x), then there exist y and z such that S(x,y) and S(x,z) and y is not equal to z.

d) A negative real number does not have a square root that is a real number:

Let R(x) be the statement "x is a real number", N(x) be the statement "x is a negative real number", S(x,y) be the statement "y is a square root of x". Then the original statement can be expressed as:

For all x, if N(x) and R(y), then not S(x,y).

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The ordered pair solutions for the system of equations are: (-1, 0) and (5, -6).

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

f(x) = x² - 5x - 6    ......equation 1.

f(x) = -x - 1 ......equation 2.

In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II and Quadrant IV, and it is given by the ordered pairs (-1, 0) and (5, -6).

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The correct answer is D. 50% long-tailed cat with long whiskers, 50% short-tailed cat with short whiskers.

This is because the long-tailed cat with long whiskers is homozygous for the recessive allele for tail length (ww) and homozygous for the dominant allele for whisker length (TT), while the short-tailed cat with short whiskers is homozygous for the dominant allele for tail length (TT) and homozygous for the recessive allele for whisker length (ww). Therefore, all the offspring will inherit one copy of the dominant allele for tail length (T) from each parent, making them all long-tailed, but half will inherit the recessive allele for whisker length (w) from each parent, making them short-whiskered.

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To calculate the probability that the sample mean would differ from the true mean by less than 0.6 dollars, we need to use the Central Limit Theorem (CLT) since the sample size is large (n = 107).

According to the CLT, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the original population distribution, when the sample size is sufficiently large.

Given that the variance of the cost of 55 gallons of ice cream is 3636 and the sample size is 107, we can calculate the standard deviation of the sampling distribution (also known as the standard error) using the formula:

Standard Error (SE) = sqrt(Variance / Sample Size)

SE = sqrt(3636 / 107)

SE ≈ 5.960

Next, we want to find the probability that the sample mean would differ from the true mean by less than 0.6 dollars. This can be interpreted as finding the probability within a certain range around the mean in a normal distribution.

To calculate this probability, we need to standardize the range by converting it into a z-score.

Z = (X - μ) / SE

where X is the value of interest (0.6 dollars in this case), μ is the true mean (3636 dollars), and SE is the standard error (5.960 dollars).

Z = (0.6 - 3636) / 5.960

Z ≈ -607.073

Since the z-score is extremely negative, the probability of the sample mean differing from the true mean by less than 0.6 dollars is almost 0.

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The term used in a confidence interval that accounts for the standard error of the estimator and the desired confidence level of the interval is called the "margin of error." Margin of error incorporates the variability of the sample estimator, usually measured by the standard error, and the desired confidence level, expressed as a percentage (e.g., 95% confidence level).

In a confidence interval, the margin of error is used to determine the range within which the true population parameter is likely to fall. It is calculated by multiplying the standard error by a critical value, which is determined based on the desired confidence level. For instance, in a 95% confidence interval, the critical value is typically 1.96, derived from the standard normal distribution.

By including the margin of error in the calculation, the confidence interval provides an estimate of the population parameter that accounts for the uncertainty inherent in using a sample to make inferences about a larger population. The larger the margin of error, the wider the confidence interval, indicating greater uncertainty in the estimate. Conversely, a smaller margin of error suggests a more precise estimate.

In summary, the margin of error is a crucial component of confidence intervals, as it combines the standard error of the estimator and the desired confidence level to quantify the uncertainty in the estimate and provide a range within which the true population parameter is likely to lie.

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To minimize problems in repeated-measures designs that can result from systematic differences between successive measurements, a researcher should use a method called counterbalancing.

Counterbalancing is a technique used in research experiments to control for the effects of order and practice on the results of the study. It involves systematically changing the order in which participants experience different conditions of the experiment to ensure that any observed effects are not simply due to the order of presentation.

For example, if a study involves testing the effects of two different drugs on a group of participants, counterbalancing would involve dividing the participants into two groups, with one group receiving drug A first followed by drug B, while the other group receives drug B first followed by drug A. This ensures that any observed effects are not simply due to the order in which the drugs were administered.

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The range of values where the true proportion is likely to be found and determine whether a sample proportion is significantly different from a hypothesized proportion.

To estimate the standard deviation of the sampling distribution of sample proportions, we need to use the formula:
σp = sqrt(p*(1-p)/n)
where σp is the standard deviation of the sampling distribution of sample proportions, p is the proportion of successes in the population, and n is the sample size.
If we don't know the proportion of successes in the population, we can use the sample proportion as an estimate. However, if the sample size is small, we need to use a correction factor called the finite population correction:
σp = sqrt(p*(1-p)/(n-1)) * sqrt((N-n)/(N-1))
where N is the population size.
In general, the standard deviation of the sampling distribution of sample proportions decreases as the sample size increases. This is because larger samples are more representative of the population and have less sampling error.
The standard deviation of the sampling distribution of sample proportions is an important concept in statistics, as it allows us to calculate confidence intervals and perform hypothesis tests on proportions.

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Thus, we need a sample size of at least 22 to obtain a 90 percent confidence interval for the mean protein content of meat with an estimate within 2 pounds of the true mean value.

To obtain a 90 percent confidence interval for the mean protein content of meat with an estimate within 2 pounds of the true mean value, we need to calculate the required sample size. The formula for the required sample size is:

n = (Zα/2 * σ / E)^2

where n is the required sample size, Zα/2 is the z-score for the desired confidence level (in this case 90%), σ is the standard deviation of the population (in this case 7 pounds, the square root of the variance), and E is the margin of error (in this case 2 pounds).

Plugging in the values, we get:

n = (1.645 * 7 / 2)^2
n = 21.16

Therefore, we need a sample size of at least 22 to obtain a 90 percent confidence interval for the mean protein content of meat with an estimate within 2 pounds of the true mean value. It is important to note that this assumes that the sample is drawn randomly and is representative of the population.

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The infant's weight is 7 pounds and 10 ounces using weight conversion.

To convert the weight of the newborn from grams to pounds, we need to divide the weight by the number of grams in one pound, which is 453.59. So, 3,459 grams divided by 453.59 grams per pound is equal to 7.628 pounds.

To find the weight in ounces, we need to multiply the decimal part of the pounds by 16 (since there are 16 ounces in one pound). So, 0.628 x 16 = 10.048 ounces.

Therefore, the infant's weight is 7 pounds and 10 ounces.

It is important to note that weight conversion is often used in the medical field to monitor the health and growth of newborns. By tracking their weight in pounds and ounces, doctors can ensure that they are gaining weight at a healthy rate and are meeting their developmental milestones.

This information can also be used to make adjustments to their feeding or treatment plans if necessary. It is crucial for healthcare professionals to accurately convert weight measurements to ensure the best possible care for their patients.

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The perimeter of ABCD in inches is 30 in.

Perimeter is the measurement of the total distance around an object.

To calculate the perimeter of ABCD, we use the formula below

Formula:

Where:

To find /BC/ we use Pythagoras theorem

Substitute these values into equation 1

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Answer:

The best buy item is the Frito-Lay mi Variety Pack. Going for only 0.35 per item.

Step-by-step explanation:

Frito-Lay:

9.88/28 = 0.35

Unit rate is 35 cents

Pringles:

6.48/18 = 0.36

Unit rate is 36 cents

Pack of 18:

11.21/18 = 0.6

Unit rate is 60 cents

Pack of 24:

15.85/24 = 0.66

Unit rate is 66 cents

GC:

14.75/30 = 0.49

Unit rate is 49 cents

Sweet Treats:

10.75/25 = 0.43

Unit rate is 43 cents

Comparing all of this data, it can easily be seen that the Frito-Lay mi Variety Pack is the best deal you can find out of these 6 deals.

Answer:

a. area = 78.5

circumference = 31.4

b. area = 113.04

circumference = 37.68

Step-by-step explanation:

To find the area use:

Area = pi • r^2

They said to use 3.14 for pi.

Area = 3.14r^2

For part a, the diameter is given, 10. Radius is half of diameter. Radius is 5.

Area = 3.14•5^2

= 3.14•25

= 78.5

Same formula for area for part b. But the radius is given, 6.

area = 3.14•6^2

= 3.14 • 36

= 113.04

Circumference is

C = pi•d

part a the diameter is 10.

C = pi • 10

= 3.14 • 10

= 31.4

for part b, double the radius to find the diameter. Radius is 6, so diameter is 12.

C = pi • d

= 3.14 • 12

= 37.68

The solution is: Garret placed the treasure at the right place.

Here, we have,

The Cartesian plane can be used to locate the position of any given point with a coordinate. It consists of two numbered lines perpendicular to each other and intersecting at point zero of the lines.

From the statements given, 5 units from x-axis is not the same as 5 units on x-axis. Also, 3 units from y-axis is not the same as 3 units on y-axis.

So, distance 5 units from x-axis implies that a point 5 units after the x-axis. And also, distance 3 units from y-axis means 3 units after the y-axis.

With these conditions of the coordinate of the treasure, Garrett placed the treasure at the right place.

Hence, The solution is: Garret placed the treasure at the right place.

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complete question:

Garrett and Jeffrey are planning a treasure hunt. They decide to place a treasure at a point that is a

distance of 5 units from the x-axis and 3 units from the y-axis. Jeffrey places a treasure at point J, and

Garrett places one at point G. Who put the treasure in the right place? Explain how you know.

This NPDA works by pushing all the a's onto the stack and then popping them off as b's are read. If there are ever more b's than a's on the stack, the NPDA enters a non-accepting state. If the input string is read completely and the stack is empty, the NPDA enters an accepting state.

To define a NPDA for the language L = {anbm | m,n ∈ N, n ≥ 3, m > n}, we can use the following construction:

1. The NPDA has a single initial state, q0, with an empty stack.
2. For each symbol a in the input alphabet, the NPDA has a transition from q0 to q0 that reads a and pushes it onto the stack.
3. For each symbol b in the input alphabet, the NPDA has a transition from q0 to q1 that reads b and pops a single symbol from the stack.
4. The NPDA has a series of transitions from q1 back to q1 that read b and pop a single symbol from the stack for each b in the input string, until the stack is empty.
5. The NPDA has a final state, q2, that is reached only when the input string has been completely read and the stack is empty.

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The diameter of the circle is 40/3 units.

We have,

Let's first recall the formulas for the area of a sector and the length of an arc of a circle:

Area of a sector with central angle θ and radius r: A = (θ/360)πr²

Length of an arc with central angle θ and radius r: L = (θ/360)2πr

We are given that the area of the sector is 5π and the arc measure is 50 degrees.

Let's denote the radius of the circle by r and the central angle of the sector by θ.

We can set up a system of equations using the formulas above:

(θ/360)πr² = 5π (since the area of the sector is 5π)

(θ/360)2πr = L (since the length of the arc is given as 50 degrees)

Simplifying these equations.

(θ/360)r² = 5 (canceling out π on both sides)

(θ/180)r = L/π

Solving for θ in the second equation.

θ = (180/π)(L/r)

Substituting this into the first equation and solving for r.

((180/π)(L/r))/360 r² = 5

(L/r) r = (5π/9)

r = (5π/9) / (L/r)

r = (5πr)/(9L)

Now we can substitute the given values for L and θ into the above expression for r:

L = (50/360)(2πr) = (5/36)πr

θ = 50 degrees = (50/180)π radians

Substituting these into the expression for r.

r = (5πr)/(9L) = (5πr)/(9*(5/36)πr) = (20/3)

Now,

The diameter of the circle is twice the radius.

2r = 2*(20/3) = 40/3

Thus,

The diameter of the circle is 40/3 units.

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To find the probability that the student will be from Kenilworth, we need to divide the number of students from Kenilworth by the total number of students in the class.

The number of students from Kenilworth is 4 girls + 5 boys = 9 students. The total number of students in the class is 11 boys from Wilmette + 4 girls from Kenilworth + 10 girls from Wilmette + 4 boys from Glencoe + 5 boys from Kenilworth + 8 girls from Glencoe = 42 students.

Therefore, the probability that the student called upon will be from Kenilworth is 9/42 or approximately 0.214 or 21.4%.
In this class, there are 4 girls from Kenilworth and 5 boys from Kenilworth, totaling 9 students from Kenilworth.

The total number of students in the class is 11 boys from Wilmette + 4 girls from Kenilworth + 10 girls from Wilmette + 4 boys from Glencoe + 5 boys from Kenilworth + 8 girls from Glencoe = 42 students.

The probability that the teacher calls upon a student from Kenilworth is the number of Kenilworth students divided by the total number of students, which is 9/42. Simplified, this probability is 3/14, or approximately 0.214.

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The molds filled by the machine will hold weights between 1032.69 and 1123.31 pounds.

To find the interval of weights for 90% of the molds filled by the machine, we need to use the properties of the normal distribution.

Since we know the mean and standard deviation of the weights, we can standardize the distribution using the z-score formula:
z = (x - μ) / σ
Where x is the weight of the concrete poured into the mold, μ is the mean weight, and σ is the standard deviation.
To find the interval of weights that covers 90% of the molds, we need to find the z-scores that correspond to the 5th and 95th percentiles of the standard normal distribution.

These percentiles are represented by the values -1.645 and 1.645, respectively.
So, we can solve for the corresponding weights using the z-score formula:
normal distribution, 90% of the data falls within the range of the mean ± 1.645 standard deviations (this value corresponds to a 90% confidence interval).

Using this information, we can calculate the interval as follows:

Lower bound: µ - 1.645 * σ = 1078 - 1.645 * 23 ≈ 1044.515

Upper bound: µ + 1.645 * σ = 1078 + 1.645 * 23 ≈ 1111.485
-1.645 = (x - 1078) / 23
x = 1032.69
And
1.645 = (x - 1078) / 23
x = 1123.31
Therefore, approximately 90% of the molds filled by the machine will hold weights between 1032.69 and 1123.31 pounds.

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