The lead bank clerk of a bank would like a quick estimate of the mean checking account
balance of all checking account customers. A random sample of 18 checking account balances
results in a sample mean of $1069 and a standard deviation of $55. Calculate a 95%
confidence interval for the mean checking account.

Answer:

$244.81

Step-by-step explanation:

A (total amount) = P(principal) · (1 + r/n)^nt

r = interest rate

n = # times per year interest is compounded

t = term of investment

2500 = P[1 + (.021/10)]^10·1

2500 = 1.021199565 · P

P = 244.81

The pair of hypotheses used to test if the mean of the first population is smaller than the mean of the second population, using independent random sampling, is H0: µ1-µ2 ≥ 0 and HA: µ1-µ2 < 0.

The given pair of hypotheses represents a one-tailed test where we are interested in determining if the mean of the first population (µ1) is smaller than the mean of the second population (µ2).

The null hypothesis (H0) states that the difference between the means, represented by (µ1-µ2), is greater than or equal to zero. This means that there is no significant difference between the means or that the mean of the first population is equal to or greater than the mean of the second population.

The alternative hypothesis (HA) states that the difference between the means, represented by (µ1-µ2), is less than zero. This suggests that there is a significant difference between the means and specifically indicates that the mean of the first population is smaller than the mean of the second population.

By conducting a statistical test, such as a t-test or z-test, and analyzing the results, we can evaluate the evidence and make an inference regarding the relationship between the means of the two populations based on the given pair of hypotheses.

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Answer:

m = 1.2

Step-by-step explanation:

12m = 14.4

Divide each side by 12

12m/12 = 14.4/12

m = 1.2

m = 1.2  is the answer

because..

12m = 14.4

Divide each side by 12

12m/12 = 14.4/12

m = 1.2

hope this helped ヾ(•ω•`)oヾ(•ω•`)o

Answer:

your not showing the whole thing

Step-by-step explanation:

The region's sector AHB is a circle's sector. This is due to the fact that it diameter is shaped like a slice of pizza and is bounded by two radii and an arc of the circle.

In geometry, the diameter of a circle is any linear fashion segment that has an endpoint mostly on circle and travels through its centre. Another way to put it is the tallest chord of a circle

The diameter of the circle is represented by the line segment AB. This is due to the fact that it runs through the centre H and connects two points on the circle.

The radius of the circle is represented by the line segment AH. This is because it connects the circle's centre H to a point A.

The chord is the line segment. The chord CD is a circle chord. This is due to the fact that it connects two points on a circle but does not pass through the centre.

Tangent to the circle: The line segment EF is tangent to the circle. This is due to the fact that it only intersects the circle at one point, G, and is perpendicular to the radius GH at that point.

ABG's curve is an arc of the circle. This is because it is part of the circle's circumference, connecting two points A and B.

The region's sector AHB is a circle's sector. This is due to the fact that it is shaped like a slice of pizza and is bounded by two radii and an arc of the circle.

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Answer:

644.89

Step-by-step explanation:

Answer:

644.89 m

Step-by-step explanation:

68 / 100 * 948.37 = 0.68 * 948.37 = 644.89 m (2 d.p.)

The amount of money in the savings account depends on how much time has passed since the account was opened. Then, the amount of money is the depenent variable, and the amount of time is the independent variable.

Then, money is a function of time.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.

Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.

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Answer:

\( \frac{73}{48} \)

Step-by-step explanation:

.......

The rule each sister wrote should be matched with the diagram that represent the rule as follows;

Ella  ⇒ p = 2t + 2.

Della ⇒ p = 2(t + 1)

Stella ⇒ p = 2(t - 1) + 4

In Mathematics and Geometry, a linear function refers to a type of function whose equation is graphically represented by a straight line on the cartesian coordinate (graph).

Assuming the variable t represent the number of smaller tables pushed together and the variable p represent the number of people that can be seated, a linear function (rule) that models the thinking of each sister can be written as follows;

Ella  ⇒ p = 2t + 2.

When t = 1, the value of p is given by;

p = 2(1) + 2 = 4.

When t = 2, the value of p is given by;

p = 2(2) + 2 = 6.

When t = 3, the value of p is given by;

p = 2(3) + 2 = 8.

For Della, we have:

p = 2(t + 1)

When t = 1, the value of p is given by;

p = 2(1 + 1) = 4.

When t = 2, the value of p is given by;

p = 2(2 + 1) = 6.

When t = 3, the value of p is given by;

p = 2(3 + 1) = 8.

For Stella, we have:

p = 2(t - 1) + 4

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Answer:

she can buy 13.333 repeating ounces (13 as a full number) of chocolate drops or 20 ounces of gummy bears.

Step-by-step explanation:

take the amount of money you have, $10 and divide that by the price per ounce $10÷.5=20

Answer:

8 ounces

Step-by-step explanation:

Imagine X is the number of ounces she can buy for each type

.5 (x) the gummy and  .75 (x) the chocolage = 10

combine like terms.

1.25 (X) = 10

X = 8

.5 (8) + .75(8) = 10

4+ 6 = 10

The most effective chunking of the digit sequence 14929111776 would depend on the purpose of chunking.

However, a possible effective chunking could be 14-92-91-11-77-6, which groups the digits into pairs or triplets based on their similarity or pattern. Another possible chunking could be 1492-911-1776, which separates the digits based on significant historical events. Ultimately, the effectiveness of chunking would depend on the context and intended use of the sequence. The most effective chunking of the digit sequence 14929111776 would be to group the numbers into smaller, manageable chunks. One possible way to chunk the sequence is: 149-29-11-17-76. This breaks the sequence into five groups, making it easier to remember and process.

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Answer:

The daughter got 31 cows

Step-by-step explanation:

1/2 of 124 is 62

1/4 of 124 is 31

124 - (62 + 31)

124 - 93 = 31

helping in the name of Jesus.

Answer:

answer below  

Step-by-step explanation

128-B

The roots of the polynomial functions are

(a) x = -1 or x = -1.2 and x = -0.16

(b) x = -1/7 or x = 2

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

a) y = (x + 1)(5x² + 7x + 1)

b). y = (7x + 1) (2x - 4)

The roots of the polynomial functions are calculated by setting the functions to 0

So, we have

(x + 1)(5x² + 7x + 1) = 0

(7x + 1) (2x - 4) = 0

Using the zero product property, we have

x + 1 = 0 or 5x² + 7x + 1 = 0 and

7x + 1 = 0 or 2x - 4 = 0

When evaluated, we have

x = -1 or x = -1.2 and x = -0.16

x = -1/7 or x = 2

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Complete question

For each polynomial function below, determine all of the roots.

a) y = (x + 1)(5x² + 7x + 1)

b). y = (7x + 1) (2x - 4)

Answer:

52 hours

Step-by-step explanation:

figure it out genius

An online store ships 15 orders every 5 hours. It will take approximately 52 hours to ship 156 orders at this rate.

Use the concept of ratio defined as:

A ratio indicates how many times one number contains another number. The ratio of two numbers is written as x : y, which is equivalent to x/y.

Where x and y are individual amounts of two quantities.

And, the Total quantity is given after combining as x + y.

Given that,

Online store ships packages at a rate of 15 orders every 5 hours.

We need to determine how many hours it will take to ship 156 orders.

The rate can be expressed as 15 orders per 5 hours or 15/5.

To figure this out,

Set up a proportion.

If the online store ships 15 orders every 5 hours,

Then the rate is 15 orders per 5 hours, or 15/5.

Now, let's set up the proportion:

15/5 = 156/x

To solve for x, cross multiply:

15x = 5(156)

Now, divide both sides of the equation by 15 to isolate x:

x =780/15

Calculating that out, x is equal to 52.

Hence, it will take approximately 52 hours to ship 156 orders at the given rate.

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Answer:

2+2.35<47

Step-by-step explanation:

because the taxi charge $2 + $2.35 per mile and < means you spend less than $47.

Answer:

63 degrees

Step-by-step explanation:

m<FGH is asking for the measure of angle fgh.

when there are 3 letters, the middle one represents the point of the angle

m<FGH=63

I'm not sure about the second part because it's a drop down menu, but hope my explanation helps.

The given scenario can be modeled using a Poisson distribution.  

A Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space, given the average rate at which those events occur. It is often used to describe rare or random events, such as the arrival of customers at a bank's automatic teller machine.

In this context, the Poisson distribution helps us understand the likelihood of a certain number of customers arriving during a specific time frame. The fact that customers arrive at a rate of one every other minute means that the average rate λ (lambda) is 0.5 customers per minute.

To calculate the probability of a specific number of customers arriving during a given time frame, we can use the Poisson probability formula:

P(x;λ) = (e^(-λ) * λ^x) / x!

Where:
- P(x;λ) represents the probability of x customers arriving during the specified time frame,
- e is the base of the natural logarithm (approximately 2.71828),
- λ is the average rate of arrival (0.5 customers per minute in this case),
- x is the number of customers we want to calculate the probability for, and
- x! denotes the factorial of x.

Furthermore, we are given that each customer spends an average of 92 seconds (or 1.53 minutes) completing their transactions. This transaction time can be modeled using an exponential distribution.

The exponential distribution is commonly used to model the time between events in a Poisson process. In this case, it helps us understand the time it takes for a customer to complete their transaction. The average transaction time is 1.53 minutes.

The exponential distribution has a probability density function (pdf) given by:

f(x;λ) = λ * e^(-λx)

Where:
- f(x;λ) represents the probability density function,
- e is the base of the natural logarithm (approximately 2.71828),
- λ is the rate parameter (the reciprocal of the average transaction time), and
- x is the time we want to calculate the probability density for.

By understanding and applying the concepts of the Poisson distribution and the exponential distribution, we can model and analyze the arrival rate of customers at the bank's automatic teller machine and the time it takes for them to complete their transactions.

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Answer:

hi this is my old account

Step-by-step explanation:

To show that sin 2x = 2 sin x cos x, we can use the formula sin(A + B) = sin A cos B + cos A sin B. Taking A = B = x, we have:

sin(2x) = sin(x + x)

Using the formula, we have:

sin(2x) = sin(x) cos(x) + cos(x) sin(x)

Since sin(x) cos(x) is commutative, we can write:

sin(2x) = 2 sin(x) cos(x)

Therefore, sin 2x = 2 sin x cos x.

To show that cos 2x = 1 - 2 sin²x, we can use the formula cos(A + B) = cos A cos B - sin A sin B. Taking A = B = x, we have:

cos(2x) = cos(x + x)

Using the formula, we have:

cos(2x) = cos(x) cos(x) - sin(x) sin(x)

Since cos(x) cos(x) is equal to sin²x, we can write:

cos(2x) = sin²x - sin²x

Simplifying further, we get:

cos(2x) = 1 - 2 sin²x

Therefore, cos 2x = 1 - 2 sin²x.

Using the results from parts (b) and (c), we can now show that sin 3x = 3 sin x - 4 sin³x.

Let's start with sin 3x. We can express it as sin (2x + x):

sin 3x = sin (2x + x)

Using the formula sin(A + B) = sin A cos B + cos A sin B, we have:

sin 3x = sin 2x cos x + cos 2x sin x

Substituting the values from part (b) and (c), we get:

sin 3x = (2 sin x cos x) cos x + (1 - 2 sin²x) sin x

Expanding and simplifying further:

sin 3x = 2 sin x cos²x + sin x - 2 sin³x

sin 3x = sin x + 2 sin x cos²x - 2 sin³x

Rearranging the terms:

sin 3x = sin x - 2 sin³x + 2 sin x cos²x

Finally, factoring out sin x:

sin 3x = sin x (1 - 2 sin²x) + 2 sin x cos²x

Using the identity cos²x = 1 - sin²x:

sin 3x = sin x (1 - 2 sin²x) + 2 sin x (1 - sin²x)

sin 3x = sin x - 2 sin³x + 2 sin x - 2 sin³x

sin 3x = 3 sin x - 4 sin³x

Therefore, sin 3x = 3 sin x - 4 sin³x.

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The expression "five to the three-fourths power raised to the two-thirds power" can be rewritten as a radical expression.

First, let's calculate the exponentiation inside the parentheses:

(5^(3/4))^2/3

To simplify this, we can use the property of exponentiation that states raising a power to another power involves multiplying the exponents:

5^((3/4) * (2/3))

When multiplying fractions, we multiply the numerators and denominators separately:

5^((3 * 2)/(4 * 3))

Simplifying further:

5^(6/12)

The numerator and denominator of the exponent can be divided by 6, which results in:

5^(1/2)

Now, let's express this in radical form. Since the exponent 1/2 represents the square root, we can write it as:

√5

Therefore, the expression "five to the three-fourths power raised to the two-thirds power" simplifies to the radical expression √5.

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Answer:

C. Wright Mills

Step-by-step explanation:

was the American sociologist who strongly criticized the structural functionalist approach to sociology.

Answer: x=8

Step-by-step explanation:

Therefore, the 90% confidence interval for the mean repair cost for the VCRs is ($82.40,$90.12).

Subject to the exclusions outlined in this clause, the repair cost is defined as the cost of the parts and labor required to fix or replace any covered component as a result of a covered mechanical breakdown. We reserve the right to substitute components of comparable sort and quality, whether they are new, OEM, swapped, rebuilt, remanufactured, or used. The suggested retail price of a part of a like type and quality, or the manufacturer's indicated retail price for Your Vehicle, whichever is higher, may not be exceeded when pricing out parts. A current, widely used flat-rate labor guide will be used to calculate labor costs. According to state-specific rules, the Repair Cost includes the necessary taxes related to the covered Mechanical Breakdown.

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A scale model of a regulation-sized gymnasium that is 12 inches long would be 10 inches wide.

To determine the width of a scale model of a regulation-sized gymnasium, you need to determine the scale factor used to create the model. The scale factor is the ratio of the size of the model to the size of the actual object.

In this case, the length of the model is 12 inches, while the length of the actual gymnasium is 100 feet, or 1200 inches. So, the scale factor is: 12/1200 = 1/100.

To find the width of the model, you would multiply the width of the actual gymnasium, 80 feet, by the scale factor, 1/100. This gives you a width of:

80 × 1/100 = 0.8 feet = 10 inches.

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Angle 1 is 112

Angle 2 is 68

Angle 3 is 90

Angle 4 is 90

Angle 5 is 22

Angle 6 is 158

If a tailor bought 5 yards of cloth he used  \(2\frac{3}{8}\) yards of cloth to make 1 pair of pants and he made 2 pairs, the length of the cloth that left is 1/4 yards

The total length of the cloth that he bought = 5 yards

The length of cloth that he used to make 1 pair of pants = \(2\frac{3}{8}\) yards

Convert the mixed fraction to the simple fraction

\(2\frac{3}{8}\) yards = 19/8 yards

The length of cloth required to make 2 pants = 2 × The length of cloth that he used to make 1 pair of pants

Substitute the values in the equation

= 2 × (19/8)

= 19/4 yards

The remaining cloth = The total length of the cloth that he bought - The length of cloth required to make 2 pants

= 5 - (19/4)

= 1/4  yards

Hence, the length of the cloth left is 1/4 yards

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