Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to four per 15 minutes. Complete parts a and b below.a. Determine the probability that in a given 15-minute segment, three customers will arrive at the ATM The probability is .1954. (Round to four decimal places as needed.) b. What is the probability that fewer than four customers will arrive in a 30-minute segment? The probability is 0002. (Round to four decimal places as needed.)

Answer:

(10, - 2 )

Step-by-step explanation:

x = 10 → (1)

3x + 5y = 20 → (2)

Substitute x = 10 into (2)

3(10) + 5y = 20

30 + 5y = 20 ( subtract 30 from both sides )

5y = - 10 ( divide both sides by 5 )

y = - 2

solution is (10, - 2 )

Answer:

Pyramid A had a lateral area of 100 and Pyramid B has a Lateral area of 225

so 100:225 or 4:9, due to the fact that both have square bases just muliply the lateral edge by itself

Step-by-step explanation:

The rate of fuel use in miles per gallon during the travelling 10.5 miles per gallon.

To find the rate of fuel use in miles per gallon, we need to divide the total distance traveled by the amount of gasoline used:

Rate = Distance / Gasoline

In this case, the distance traveled is 52 1/2 miles and the amount of gasoline used is 2 1/2 gallons:

Rate = 52 1/2 miles / 2 1/2 gallons

To simplify this expression, we can convert both the distance and the amount of gasoline to improper fractions:

Rate = (105/2) miles / (5/2) gallons

Now we can divide the numerator by the denominator:

Rate = (105/2) miles x (2/5) / (5/2) gallons x (2/5)

Rate = 105/10 miles per gallon

Rate = 10.5 miles per gallon

Therefore, the rate of fuel use in miles per gallon is 10.5.

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To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.

(a) Consider only thermal expansion using the volume coefficient of thermal expansion.
(b) Consider the introduction of vacancies using the energy of vacancy formation and the change in number of vacancies.

When a metal is heated, its density decreases due to two sources: thermal expansion of the solid and the formation of vacancies.

(a) To determine the density of a gold specimen at 800°C considering only thermal expansion, we need to use the volume coefficient of thermal expansion. The volume coefficient of thermal expansion (β) for gold is given as 3 × 10^-5 K^-1. We can calculate the change in volume using the equation:

ΔV = V * β * ΔT

where ΔV is the change in volume, V is the initial volume, β is the volume coefficient of thermal expansion, and ΔT is the change in temperature.

Since density is inversely proportional to volume, we can use the equation:

ρ = m / V

where ρ is the density, m is the mass, and V is the volume.

(b) To repeat the calculation considering the introduction of vacancies, we need to use the energy of vacancy formation (E) given as 0.98 eV/atom. The change in energy (ΔE) due to the introduction of vacancies can be related to the change in number of vacancies (ΔNv) using the equation:

ΔE = ΔNv * E

Since vacancies contribute to a decrease in density, we can relate the change in number of vacancies to the change in density using the equation:

Δρ = -ΔNv * (m / V)

where Δρ is the change in density, ΔNv is the change in number of vacancies, m is the mass, and V is the volume.

It's important to note that the calculation of the change in density due to vacancies requires additional information, such as the number of atoms per unit volume and the change in number of vacancies.

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Answer:

\(\displaystyle m=2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Reading a Cartesian Plane

Slope Formula: \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (0, 3)

Point (1, 5)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

We can give upper and lower estimates using the Trapezoidal Rule with 6 subintervals and use the Midpoint Rule with 3 subintervals to obtain a more accurate estimate.

Explanation:

To estimate Q(6) using the Trapezoidal Rule with 6 subintervals, we divide the interval [0, 6] into 6 subintervals of equal width. Then, we use the formula for the Trapezoidal Rule:

Q(6) ≈ h/2 * [f(0) + 2f(h) + 2f(2h) + ... + 2f(5h) + f(6h)]

where h is the width of each subinterval (h = 1 in this case), and f(t) is the rate at which materials are spewed into the atmosphere at time t. Using the values in the table, we can calculate the lower and upper estimates for Q(6) using this formula.

For the Midpoint Rule with 3 subintervals, we divide the interval [0, 6] into 3 subintervals of equal width. Then, we use the formula for the Midpoint Rule:

Q(6) ≈ h * [f(1.5h) + f(4.5h) + f(7.5h)]

where h is the width of each subinterval (h = 2 in this case). Again, using the values in the table, we can calculate an estimate for Q(6) using this formula.

The upper and lower estimates for Q(6) using the Trapezoidal Rule with 6 subintervals are 12.45 tonnes and 16.25 tonnes, respectively. The estimate for Q(6) using the Midpoint Rule with 3 subintervals is 15.82 tonnes. The Midpoint Rule gives a more accurate estimate since it uses the midpoint of each subinterval, which can reduce the error introduced by the linear approximation of the Trapezoidal Rule.

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The expression s less than the quotient of u and t can be written as (u / t) - s

The quotient of an expression is the result of dividing one value by another. For instance, the quotient of 6 and 2

= 6 / 2

= 3

So,

s less than the quotient of u and t

= u / t

= (u / t) - s

Therefore, the expression s less than the quotient of u and t can be written as (u / t) - s.

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Part A

Given info:

Because n > 30 is not true, and we don't know the population standard deviation (sigma), this means we must use a T distribution.

The degrees of freedom here are n-1 = 23-1 = 22.

At 90% confidence and the degrees of freedom mentioned, the t critical value is roughly t = 1.717

Use a T distribution table or calculator to determine this. If you don't have a calculator for the task, then you can search out "inverse T calculator" and there are tons of free options to pick from.

The margin of error E is

E = t*s/sqrt(n)

E = 1.717*1.12/sqrt(23)

E = 0.400982

This is approximate and accurate to 6 decimal places.

The confidence interval is going to be xbar plus or minus that E value

L = lower bound = xbar - E = 4.90 - 0.400982 = 4.499018 = 4.50

U = upper bound = xbar + E = 4.90 + 0.400982 = 5.300982 = 5.30

The confidence interval in the format of (L, U) is (4.50, 5.30)

You could also express it as the format L < mu < U and it would be 4.50 < mu < 5.30; however, I'll stick to the first method.

=====================================================

Part B

Since we know sigma = 2.6 is the population standard deviation, we can use a Z distribution now.

At 90% confidence, the z critical value is roughly 1.645; use a table or calculator to determine this.

\(n = \left(\frac{z*\sigma}{E}\right)^2\\\\n \approx \left(\frac{1.645*2.6}{0.03}\right)^2\\\\n \approx 20325.254444 \\\\\)

Round this up to the nearest integer to get 20326. For min sample size problems, always round up.

The measure of the arc angle x which subtends the angle at the center is equal to 126°

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

So;

arc angle x = 2 × angle 63°

arc angle x = 2 × 63°

arc angle = 126°

Therefore, the measure of the arc angle x which subtends the angle at the center is equal to 126°

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The sample mean is 3, the sample variance is 2.5, the sample standard deviation is approximately 1.581, and if the dataset represents the entire population, the population variance is also 2.5.

For the given dataset {1, 2, 4, 5}, we can calculate various statistical measures. The sample mean represents the average of the dataset, the sample variance measures the dispersion of the data points from the mean, and the sample standard deviation is the square root of the sample variance. If we assume the dataset represents the entire population, we can calculate the population variance, which is a measure of the variability within the entire population.

1) To find the sample mean, we sum up all the data points (1 + 2 + 4 + 5 = 12) and divide by the number of data points, which is 4. Therefore, the sample mean is 12/4 = 3.

2) To calculate the sample variance, we need to find the difference between each data point and the sample mean, square each difference, and then calculate the average of these squared differences. The differences are (-2, -1, 1, 2). Squaring these differences gives (4, 1, 1, 4). Taking the average of these squared differences, we get (4 + 1 + 1 + 4) / 4 = 10/4 = 2.5.

3) The sample standard deviation is the square root of the sample variance. Taking the square root of 2.5, we get approximately 1.581 (rounded to three decimal places).

4) If we assume that the given dataset represents the entire population, the population variance would be the same as the sample variance. Therefore, the population variance is also 2.5.

In summary, the sample mean is 3, the sample variance is 2.5, the sample standard deviation is approximately 1.581, and if the dataset represents the entire population, the population variance is also 2.5.


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Answer:

25x^2 - 4

Step-by-step explanation:

and x times an x is x^2 so

25x^2 - 4

The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.

The formula for the continuous exponential growth is given by the formula:

P = Pe^(rt)

where,P is the population in the future.

P0 is the initial population.

t is the time.

r is the continuous interest rate expressed as a decimal.

e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.

Therefore, t = 25.We will now use the formula:

P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.

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Answer: I got 97,042.7

Step-by-step explanation:

The quadratic equation has no real roots. This means the line and point has no point of intersection.

System of equations are equations that is more than one and have two or more unknowns.

Given the simultaneous equation

x^2 + y^2 = 25

2x + y = 25

from equation 2;

y = 25 - 2x ................3

Substitute equation 3 into 1 to have:

x^2 + (25-2x)^2 = 25

x^2 + 625 - 100x + 4x^2 = 25

5x^2 -100x + 600 = 0

x^2 -20x + 120= 0

Hence the quadratic equation has no real roots. This means the line and point has no point of intersection,

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Answer:

C on edge

Step-by-step explanation:

(0,-5) and (-4,3)

The alternative hypothesis states that the difference is greater than zero.

What Are Tails in a Hypothesis Test?

First, we need to cover some background material to understand the tails in a test. Typically, hypothesis tests take all of the sample data and convert it to a single value, which is known as a test statistic. You’re probably already familiar with some test statistics.

For example, t-tests calculate t-values. F-tests, such as ANOVA, generate F-values. The chi-square test of independence and some distribution tests produce chi-square values. All of these values are test statistics.

Keep in mind that this t-distribution assumes that the null hypothesis is correct for the population. Consequently, the peak (most likely value) of the distribution occurs at t=0, which represents the null hypothesis in a t-test. Typically, the null hypothesis states that there is no effect. As t-values move further away from zero, it represents larger effect sizes. When the null hypothesis is true for the population, obtaining samples that exhibit a large apparent effect becomes less likely, which is why the probabilities taper off for t-values further from zero.

Hence the answer is the alternative hypothesis states that the difference is greater than zero.

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Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees

Answer:

??????????????????????????????????

Step-by-step explanation:

Answer:

Step-by-step explanation:

by the property of corresponding angles (2x +16) and (3x-12) will be equal

working uot from the equation 3x-12 = 2x+16 we get x=28

and we know that 3x-12 and y are supplementry as they form a linear pair

from that we will get the equation - 3x-12 + y = 180 and we know the value of x sowe will get y as 108

Math SAT scores explain about 98.7% of the variation in the total SAT scores.

In statistics, correlation or dependence exists as any statistical relationship, whether causal or not, between two random variables or bivariate data.

A correlation exists as a statistical measure (expressed as a number) that defines the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable exists as the cause of the change in the values of the other variable.

Since r² exists = (0.9935)² = 0.9870, we interpret r² as 98.7% of the variation in the y variable exists explained by the x variable.

In context, math SAT score explains about 98.7% of the variation in total SAT score.

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Answer:

ok.....mmmm............

Answer:

whats the ?

Step-by-step explanation:

With 98% confidence interval, all teenagers' mean number of hours watching TV per week will be (26.6,29.4).

98% confidence interval can be calculated as

Point estimate± Error margin

Point estimate=mean number of hours watching TV

students=28.

Error margin=1.4.

As per given data, the 98% confidence interval for all teenagers is

=28± 1.4

=(28-1.4,28+1.4)

=(26.6,29.4)

Statisticians use confidence intervals to assess the level of uncertainty in a sample variable. For instance, a researcher may select numerous samples at random from the same population and compute a confidence interval for each sample to estimate how each sample may correctly reflect the true value of the population variable. With certain intervals including the true population parameter and others not, each produced dataset is distinct. Confidence intervals are a set of values that are constrained by the mean of the statistic and are likely to include an unidentified population parameter. The confidence level is the proportion of likelihood, or certainty, that, after multiple draws from a random sample, the confidence interval would contain the true population parameter.

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Answer:

x = 25 and <A = 148 degrees

Step-by-step explanation:

Basically it's asking you to find the value of x for both of those equations, x must be the same for both

6x - 2 = 4x + 48

a) The high temperature for today using a 3-day moving average is 93.7 degrees.

b) The high temperature for today using a 2-day moving average is 92.5 degrees.

c) The mean absolute deviation based on a 2-day moving average is 2 degrees.

d) The mean squared error for the 2-day moving average is 2.25 degrees 2.

e) The mean absolute percent error (MAPE) for the 2-day moving average is 2.2%.

The moving average is a statistical technique that smooths out data by averaging over a specified number of periods. In this case, we are using a 3-day and a 2-day moving average to forecast the high temperature for today.

The 3-day moving average is calculated by averaging the previous 3 days of high temperatures. So, the 3-day moving average for today would be the average of the high temperatures on 92, 94, and 95 degrees. This gives us a 3-day moving average of 93.7 degrees.

The 2-day moving average is calculated by averaging the previous 2 days of high temperatures. So, the 2-day moving average for today would be the average of the high temperatures on 95 and 93 degrees. This gives us a 2-day moving average of 92.5 degrees.

The mean absolute deviation (MAD) is a measure of how much variation there is from the moving average. In this case, the MAD for the 2-day moving average is 2 degrees. This means that the actual high temperatures have varied by an average of 2 degrees from the 2-day moving average.

The mean squared error (MSE) is another measure of how much variation there is from the moving average. In this case, the MSE for the 2-day moving average is 2.25 degrees^2. This means that the squared errors from the 2-day moving average have an average value of 2.25 degrees^2.

The mean absolute percent error (MAPE) is a measure of how much the actual high temperatures deviate from the moving average as a percentage of the moving average. In this case, the MAPE for the 2-day moving average is 2.2%. This means that the actual high temperatures have deviated from the 2-day moving average by an average of 2.2%.

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Answer:

\( {5x}^{2} + 6x = - 8\)

Step-by-step explanation:

This question is asking you to insert two equations, f(x) and g(x), into the equation g(x) - f(x). This will lead to the equation below.

\( { - 12x}^{2} - 15x + 7 - ({ - 7)x}^{2} + 9x - 15\)

Now we can solve for the equation.

\( { - 5x}^{2} - 6x - 8 = 0 \\ {5x}^{2} + 6x = - 8\)

Answer: A

Step-by-step explanation: true true true

Answer:

The answer is A

Step-by-step explanation:

Answer:

671921 * 79719

= 53,564,870,199

Answer:

53564870199

Step-by-step explanation:

671921*79719=53564870199