You start driving north for 6 miles turn right and drive east for another 19 miles

Answer:

a) 4/11

b) 11/30

c) 9/25

Step-by-step explanation:

As it says we can't use a calculator we can just type them into a calculator and simplify the fraction. If you need to know how to do it without a calculator then post a comment.

Since the limit of a_n is not zero, the Alternating Series Test is inconclusive. However, it's clear that the series does not converge to a single value due to the oscillating behavior of the (-1)^n term.

Thus, the given series diverges.

To test the convergence or divergence of the given series, we can use the Alternating Series Test. The series is in the form (-1)^n * a_n, where a_n = (7n - 3) / (4n + 3).

First, we need to check if a_n is positive and decreasing. For all n >= 1, a_n is positive as the denominator (4n + 3) is always larger than the numerator (7n - 3). Now let's check if a_n is decreasing:

a_(n+1) = (7(n+1) - 3) / (4(n+1) + 3)
a_(n+1) = (7n + 4) / (4n + 7)

Since both the numerator and the denominator increase with n, a_(n+1) < a_n for all n >= 1. Therefore, a_n is decreasing.

Now, we need to find the limit of a_n as n approaches infinity:

lim (n → infinity) (7n - 3) / (4n + 3)

To find this limit, we can divide the numerator and the denominator by n:

lim (n → infinity) [(7 - 3/n) / (4 + 3/n)]

As n approaches infinity, the terms with 1/n approach zero:

lim (n → infinity) [7 / 4] = 7/4

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The probability that it takes at most 1 hour of machining time to produce a randomly selected component is approximately 0.00003 or 0.003%.

To solve this problem, we need to first calculate the total mean and standard deviation for the machining time of a single component.

The total mean machining time can be found by adding the means for each component:

30 + 20 + 15 = 65 minutes

The total standard deviation can be found using the formula:

[tex]\sqrt{((1^2 + 2^2 + 1.2^2)/3)} = 1.247 minutes[/tex]

Now we need to find the probability that it takes at most 1 hour (60 minutes) to produce a randomly selected component. We can use the standard normal distribution to calculate this probability.

z-score = (60 - 65) / 1.247 = -4.01

Using a standard normal distribution table, we can find that the probability of a z-score being less than or equal to -4.01 is approximately 0.00003.

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If you hear a 1000 Hz tone from a radio that is 20 feet away from you and listen for 5 seconds, approximately 5000 pressure maxima will pass by your ear.

The speed of sound in air at room temperature is approximately 343 meters per second or 1125 feet per second.

The wavelength of a 1000 Hz tone in air can be calculated using the formula:

wavelength = speed of sound / frequency

wavelength = 1125 ft/s / 1000 Hz = 1.125 ft = 13.5 inches

This means that one complete cycle of the wave has a length of 13.5 inches.

If the radio is 20 feet away, then the sound wave will travel a distance of 20 feet from the radio to your ear.

During the 5 seconds you listen to the tone, the wavefronts will be reaching your ear continuously. The number of pressure maxima that pass by your ear will depend on the frequency of the tone and the distance traveled by the wavefront during those 5 seconds.

The distance traveled by the wavefront can be calculated using the formula:

distance = speed of sound x time

distance = 1125 ft/s x 5 s = 5625 ft

The number of pressure maxima that pass by your ear can be calculated by dividing the distance traveled by the wavelength:

number of maxima = distance / wavelength

number of maxima = 5625 ft / 1.125 ft = 5000

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a. Therefore, the distribution of X is: P(X=3) = 1/9
b. E(X) = 1(1/9) + 2(2/3) + 3(1/9) = 2
Therefore, the expected value of X is 2.

a. Find the distribution of X:

Since there are 3 possible outcomes on each spinner (1, 2, or 3), there are a total of 3 x 3 = 9 possible pairs of outcomes. We can list them as follows:

(1,1), (1,2), (1,3)
(2,1), (2,2), (2,3)
(3,1), (3,2), (3,3)

Now, we need to find the probability distribution of the maximum value (X) of the two spinners:

1. X = 1: This occurs only when both spinners show a 1, which is 1 out of the 9 total outcomes. Thus, P(X=1) = 1/9.

2. X = 2: This occurs when either both spinners show a 2 or one of them shows a 1 and the other shows a 2. There are 3 such pairs: (1,2), (2,1), and (2,2). So, P(X=2) = 3/9 = 1/3.

3. X = 3: This occurs when at least one spinner shows a 3. There are 5 such pairs: (1,3), (2,3), (3,1), (3,2), and (3,3). Thus, P(X=3) = 5/9.

b. Calculate E(X):

E(X) represents the expected value of the maximum of the two spinners. We calculate it as follows:

E(X) = (1 * P(X=1)) + (2 * P(X=2)) + (3 * P(X=3))
E(X) = (1 * 1/9) + (2 * 1/3) + (3 * 5/9)
E(X) = (1/9) + (2/3) + (15/9)
E(X) = (1 + 6 + 15) / 9
E(X) = 22/9

So, the expected value E(X) is 22/9.

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Confidence intervals are used to estimate the range of values in which a true population parameter is likely to lie.

One example where confidence interval must be used for statistical inference is when we want to estimate the mean or proportion of a population based on a sample.

For instance, if we want to estimate the average weight of adult females in a city, we can take a random sample of 100 women and calculate the sample mean and standard deviation.

We can then construct a 95% confidence interval for the population mean weight using the sample data and statistical formulas.

This interval provides us with a range of plausible values for the population mean weight with a 95% level of confidence. Hypothesis testing is used to determine whether a given hypothesis about a population parameter is supported by the sample data or not.

One example where hypothesis testing must be used for statistical inference is when we want to compare two population means or proportions based on their sample estimates.

For instance, if we want to test whether there is a significant difference in the mean salary between male and female employees in a company, we can take a random sample of 50 male and 50 female employees and calculate their sample means and standard deviations.

We can then use a t-test or z-test to test the null hypothesis that the population means are equal versus the alternative hypothesis that they are not equal.

If the p-value of the test statistic is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference between the two population means at that level of significance.

P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true.

It measures the strength of evidence against the null hypothesis and is used to make a decision about whether to reject or fail to reject the null hypothesis.

A smaller p-value indicates stronger evidence against the null hypothesis and supports the alternative hypothesis.

Typically, a significance level of 0.05 or less is used to determine whether the p-value is statistically significant or not.

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The approximate chi-square value for this study is 10.84.

In a brand awareness study involving 35 males and 35 females, 25 males and 15 females identified the brand correctly.

To find the chi-square value, we need to create a contingency table and apply the chi-square formula. Here's a quick breakdown of the process:

1. Create a contingency table:
       Males    Females
Correct    25          15
Incorrect  10          20

2. Calculate row and column totals:
       Males    Females    Total
Correct    25          15          40
Incorrect  10          20          30
Total         35          35          70

3. Find the expected frequencies for each cell by multiplying row and column totals and dividing by the overall total (for example, for the 'Correct Males' cell, multiply 40*35 and divide by 70):
       Males    Females
Correct    20          20
Incorrect  15          15

4. Apply the chi-square formula: Χ² = Σ[(Observed-Expected)²/Expected]
Χ² = [(25-20)²/20] + [(15-20)²/20] + [(10-15)²/15] + [(20-15)²/15]
Χ² ≈ 5 + 2.5 + 1.67 + 1.67
Χ² ≈ 10.84

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The equation x^2 + y^2 + 12x + 4y + 15 = 0 represents a circle with center (-6, -2) and radius 5.

To find the center and radius of the circle represented by the equation x^2 + y^2 + 12x + 4y + 15 = 0, we need to complete the square for both x and y terms. First, we will focus on the x terms:

x^2 + 12x = (x + 6)^2 - 36

Next, we will focus on the y terms:

y^2 + 4y = (y + 2)^2 - 4

Substituting these into the original equation, we get:

(x + 6)^2 - 36 + (y + 2)^2 - 4 + 15 = 0

Simplifying, we get:

(x + 6)^2 + (y + 2)^2 = 25

Comparing this to the standard form of the equation of a circle, (x - h)^2 + (y - k)^2 = r^2, we can see that the center of the circle is (-6, -2) and the radius is √25 = 5..

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The curve starts at the origin, moves upwards and to the right, reaches a peak at (1,1), and then moves downwards and to the left before returning to the origin.

The parametric equations given are x = sin(t) and y = 1 - cos(t), where t represents the parameter.

To plot points on this curve, we can start by choosing different values of t and substituting them into the equations to find the corresponding (x,y) pairs. For example, if we set t = 0, we get x = sin(0) = 0 and y = 1 - cos(0) = 0. So the first point on the curve is (0,0).

Similarly, if we set t = pi/2, we get x = sin(pi/2) = 1 and y = 1 - cos(pi/2) = 1. So the second point on the curve is (1,1).

Finally, if we set t = pi, we get x = sin(pi) = 0 and y = 1 - cos(pi) = 2. So the third point on the curve is (0,2).

To indicate the direction in which the curve is traced as t increases, we can look at the values of x and y for increasing values of t. As t increases from 0 to pi/2, x increases from 0 to 1 and y increases from 0 to 1. This means that the curve is traced in the direction of the positive x-axis and the positive y-axis.

As t increases from pi/2 to pi, x decreases from 1 to 0 and y increases from 1 to 2. This means that the curve is traced in the direction of the negative x-axis and the positive y-axis.

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a) The equation that models the pieces of chicken Walter ordered is 1.75x + 5 = $15.5.

b) Solving the equation, Walter order 6 pieces of chicken and drinks that cost him $15.50.

An equation is a mathematical statement showing the equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine variables with constants, numbers, and values without the equal symbol (+), unlike equations.

The selling price of chicken per unit = $1.75

The cost of unlimited drinks = $5.00

The total cost of Walter's order = $15.50

Let the number of chickens ordered = x

1.75x + 5 = $15.5

1.75x = 10.5

x = 6

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The volume of the  is right triangular prism is   600 cubic feet.

In a right triangular prism, the area of the triangular base is 50 square feet, and the height of the prism is 12 feet. To find the volume of the prism, we can use the formula:

Volume = Base Area × Height

Step 1: Identify the base area, which is given as 50 square feet.
Step 2: Identify the height of the prism, which is given as 12 feet.
Step 3: Multiply the base area by the height to find the volume.

Volume = 50 square feet × 12 feet = 600 cubic feet

So, the volume of the right triangular prism is 600 cubic feet.

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Thus, the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years is approximately 7,525.14.

To find the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years, we need to add up the total number of degrees awarded over those years and then divide that total by seven (the number of years being considered).

So, adding up the numbers given in the question, we get:

4,820 + 13,188 + 4,614 + 5,920 + 12,372 + 5,885 + 5,877 = 52,676

Now, to find the mean, we divide this total by seven:

52,676 ÷ 7 = 7,525.14

So, the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years is approximately 7,525.14.

If we wanted to understand more about how the number of degrees awarded in computer science has changed over time, we would need to look at additional data and analyze it in more detail.

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The data collected from customers in restaurants about the quality of food is an example of a customer feedback data.

It is important for restaurants to collect and analyze this data to improve their food quality and overall customer experience.

However, the quality of the data collected is also crucial as inaccurate or biased data can lead to ineffective decision-making.

Therefore, it is important for restaurants to ensure the quality of the data collected by using reliable methods for collecting and analyzing data, and by verifying the accuracy and consistency of the data before using it for decision-making.

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The angle that a side of 15 inches makes with the 6-inch side is approximately 78.46 degrees.

c²= a² + b² - 2ab cos(C)

In this case, we know that the lengths of the two congruent sides are both 15 inches, and the length of the remaining side is 6 inches. So we have:

15² = 6² + 15² - 2(6)(15)cos(x)

225 = 261 - 180cos(x)

180cos(x) = 36

cos(x) =[tex]\frac{36}{180}[/tex]

cos(x) = 0.2

Now we can use the inverse cosine function ([tex]cos^{-1}[/tex]) to find the value of "x" in degrees:

x = [tex]cos^{-1}[/tex](0.2)

x ≈ 78.46 degrees

An angle is a geometric figure formed by two rays with a common endpoint, called the vertex. The rays are known as the sides of the angle. The measure of an angle is usually expressed in degrees, and it represents the amount of rotation needed to rotate one of the sides of the angle onto the other. A full rotation around a point is 360 degrees, so an angle measuring 180 degrees is called a straight angle.

Angles can be classified according to their measure. An acute angle is an angle measuring less than 90 degrees. A right angle is an angle measuring exactly 90 degrees. An obtuse angle measures more than 90 degrees but less than 180 degrees. A reflex angle measures more than 180 degrees but less than 360 degrees.

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The solution to this system is a1 = 2, a2 = -1, and a3 = 0. Therefore, the coordinate vector of p(x) relative to the basis B is [2, -1, 0].

(a) To show that B is a basis for P2, we need to show that B is linearly independent and spans P2.

Linear Independence:
Suppose that a1(1 + x + x2) + a2(1 + 2x − x2) + a3(1 − 2x − x2) = 0 for some scalars a1, a2, and a3. Then we have:

a1 + a2 + a3 = 0    (coefficients of x^0)
a1 + 2a2 - 2a3 = 0  (coefficients of x^1)
a1 - a2 - a3 = 0    (coefficients of x^2)

We can solve this system of equations to get a1 = 1, a2 = 1, and a3 = -1. Since the only solution is the trivial one, B is linearly independent.

Spanning:
Let p(x) be an arbitrary polynomial of degree at most 2. We need to show that we can write p(x) as a linear combination of the polynomials in B. We can do this by solving the system of equations:

a1 + a2 + a3 = p(0)      (coefficients of x^0)
a1 + 2a2 - 2a3 = p(1)    (coefficients of x^1)
a1 - a2 - a3 = p(-1)     (coefficients of x^2)

This is a system of linear equations with unknowns a1, a2, and a3. It can be solved using standard techniques, and the solution will always exist since the system is consistent. Therefore, B spans P2.

Since B is linearly independent and spans P2, it is a basis for P2.

(b) To find the coordinate vector of p(x) = 1 + 2x + 3x^2 relative to the basis B, we need to find scalars a1, a2, and a3 such that:

1 + 2x + 3x^2 = a1(1 + x + x^2) + a2(1 + 2x - x^2) + a3(1 - 2x - x^2)

This is equivalent to solving the system of equations:

a1 + a2 + a3 = 1
a1 + 2a2 - 2a3 = 2
a1 - a2 - a3 = 3

The solution to this system is a1 = 2, a2 = -1, and a3 = 0. Therefore, the coordinate vector of p(x) relative to the basis B is [2, -1, 0].

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Probability that Jeff's sum is an odd number is 1/4.

To find the probability that Jeff's sum is an odd number, we need to consider the possible outcomes of his spinners. Each spinner has an equal probability of landing on any number from 1 to 6, and there are 3 spinners in total.
To get an odd number sum, Jeff must have an odd number from at least one of his spinners. There are two ways this can happen:
1. Jeff gets an odd number from just one spinner. There are 3 spinners to choose from, and each spinner has 3 odd numbers and 3 even numbers. So the probability of Jeff getting an odd number from just one spinner is:
(3/6) x (3/6) x (3/6) = 27/216
2. Jeff gets odd numbers from two spinners. There are 3 ways this can happen:
- Spinner P and Q are odd, and Spinner R is even
- Spinner P and R are odd, and Spinner Q is even
- Spinner Q and R are odd, and Spinner P is even
For each of these scenarios, the probability is:
(3/6) x (3/6) x (3/6) = 27/216
So the total probability of Jeff getting an odd number sum is the sum of the probabilities from both scenarios:
27/216 + 27/216 = 54/216 = 1/4
Therefore, the probability that Jeff's sum is an odd number is 1/4.

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The type of bias that is most likely to affect the survey results in this scenario is selection bias. This is because the council representatives plan to conduct the survey outside of a large concert in the summer and ask selected adults if they would support an increase in the ticket tax to pay for the new concert hall. This means that the sample of people who will be surveyed will not be representative of the entire population of the city.

For example, the people who attend concerts may not be representative of the entire population of the city, as they may be more likely to be interested in music and cultural events, and therefore more likely to support the proposal for a new concert hall. Additionally, the people who choose to participate in the survey may not be representative of the people who attend concerts, as they may have stronger opinions on the issue or may have a personal interest in the outcome.

Therefore, the results of the survey may be skewed and not truly reflect the opinions of the entire population of the city. To ensure more accurate results, the survey should be conducted in a way that ensures a random and representative sample of the population is surveyed.

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Larger sample sizes provide more accurate estimates of the population mean, even if the population is not normally distributed.

For a population that is not normally distributed, the distribution of the sample means will approach a normal distribution as the size of the sample increases.

This is known as the Central Limit Theorem, which states that as the sample size increases, the distribution of sample means becomes more normal regardless of the shape of the population distribution.

Therefore, larger sample sizes provide more accurate estimates of the population mean, even if the population is not normally distributed.

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Samantha is baking cookies and the recipe calls for 7/8 cups of sugar to make 1 cookie, How much sugar is needed to make three cookies? and value of 3 x 7/8 is 21/8.

Samantha is baking cookies and the recipe calls for 7/8 cups of sugar to make 1 cookie, How much sugar is needed to make three cookies

This we get by multiplying 7/8 with 3

3×7/8

21/8

So 21/8 cups of sugar is needed to make three cookies

Hence, the value of multiplication 3×7/8 is 21/8.

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All of the statements are valid in terms of syntax, but their logic may or may not be correct depending on the context in which they are used.

Let's break down each statement:

double v; v = 1.0f; - This declares a variable v of type double and assigns it the value of 1.0f, which is a single-precision floating-point literal. Since v is a double, this literal is implicitly converted to a double.

float y; y = 54.9; - This declares a variable y of type float and assigns it the value of 54.9, which is a double-precision floating-point literal. Since y is a float, this literal is implicitly converted to a float.

float y; double z; z = 934.21; y = z; - This declares two variables, y of type float and z of type double. It assigns z the value of 934.21, which is a double-precision floating-point literal. It then assigns y the value of z, which is allowed because a double can be safely cast to a float.

float w; w = 1.0f; - This declares a variable w of type float and assigns it the value of 1.0f, which is a single-precision floating-point literal.

So, all the statements are valid in terms of syntax, but their logical correctness depends on the context in which they are used.

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To find next year's population in one step, we need to multiply the current population by the decay factor of 0.974.

To find next year's population in one step, we need to multiply the current population by the growth factor. However, in this case, the population is decreasing by 2.6% per year, which means that we need to use a decay factor instead of a growth factor.

To calculate the decay factor, we first need to convert the percentage into a decimal. We can do this by dividing the percentage by 100, which gives us 0.026. This represents the rate of decrease per year.

Next, we can calculate the decay factor by subtracting the rate of decrease from 1. For example, if the rate of decrease was 10%, the decay factor would be 1 - 0.1 = 0.9. In this case, since the rate of decrease is 2.6%, the decay factor is 1 - 0.026 = 0.974.

Therefore, to find next year's population in one step, we need to multiply the current population by the decay factor of 0.974. For example, if the current population is 100,000, we would calculate next year's population as follows:

Next year's population = current population x decay factor
Next year's population = 100,000 x 0.974
Next year's population = 97,400

So, next year's population would be 97,400 if the current population is 100,000 and the population is decreasing by 2.6% per year.

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The probability that a person who tested positive has the disease is about 0.394 or 39.4%.

To solve this problem, we can use Bayes' theorem, which relates conditional probabilities. Let's define:

A: the event that a person has the disease

B: the event that a person tests positive

We want to calculate the conditional probability P(A|B), which is the probability that a person has the disease, given that they tested positive. Bayes' theorem says:

[tex]$P(A|B) = \frac{P(B|A) \times P(A)}{P(B)}$[/tex]

We know that P(A) = 0.01 since 1% of people have the disease. We also know that the test does not give a negative result if the person has the disease, so P(B|A) = 1. Finally, we need to calculate P(B), the probability that a person tests positive, regardless of whether they have the disease or not.

To calculate P(B), we can use the law of total probability, which says that:

[tex]$P(B) = P(B|A) \times P(A) + P(B|\neg A) \times P(\neg A)$[/tex]

We know that P(B|not A) = 0.015, since 1.5% of people who do not have the disease test positive. We also know that P(not A) = 0.99, since the complement of having the disease is not having the disease. Therefore:

[tex]$P(B) = 1 \times 0.01 + 0.015 \times 0.99 = 0.02535$[/tex]

Now we can substitute these values into Bayes' theorem:

[tex]$P(A|B) = \frac{1 \times 0.01}{0.02535} = 0.394$[/tex]

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The value of θ for the given trigonometric equation are 37° and -63°.

Given trigonometric equation is,

4tan²θ + 5tanθ = 6

We have to find the value of θ.

The value of θ is in the range [0, 360).

This is in the form of a quadratic equation.

4tan²θ + 5tanθ - 6 = 0

Discriminant = 25 - (4 × 4 × -6) = 121

tan θ = (-5 ± √121) / 8

tan θ = (-5 ± 11) / 8

tan θ = 6/8 = 3/4 and tan θ = -16/8 = -2

The value of θ are tan⁻¹ (3/4) and tan⁻¹(-2).

The value of θ are approximately 37° and -63°.

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The answer is that the form of fiber art that involves placing two sets of parallel fibers at right angles and interlacing one set with the other is called weaving.

Weaving is the process of creating fabric by interlacing two sets of threads, known as the warp and weft, at right angles. The warp threads are stretched vertically on a loom, while the weft threads are woven horizontally across the warp. This results in a stable and durable fabric that can be used for a variety of purposes. Weaving has been used for centuries in cultures around the world to create clothing, textiles, and other functional and decorative items.

In weaving, the two sets of fibers are called the warp and the weft. The warp fibers run vertically and are held in tension on a loom. The weft fibers run horizontally and are woven over and under the warp fibers. This process of interlacing the warp and weft fibers creates a strong and flexible fabric, and it allows for the creation of various patterns and designs. Weaving is used in many different cultures and can be seen in a variety of fiber art forms, such as tapestries, rugs, and clothing.

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The ΔADE ≅ ΔCDF using the SAS congruence theorem.

To Show that two sides and one included angle in one triangle correspond to two sides and one included angle in the second triangle to demonstrate the SAS congruence theorem's conclusion that two triangles are congruent.

We have, the image showing the two triangles

Statement                                  Reason                                                

1. DE ≅ DF; AD ≅ DC                1. Given

2. ∠ADE ≅ ∠CDF                      2. Vertical angles theorem  

2. ΔADE ≅ ΔCDF                      3. SAS congruence theorem

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Sarah left work at 5:20 p.m. on Friday. She work d) 5 1/3 hrs after noon.

To calculate the hours, we know that noon is 12:00 PM, so we have to find the difference between 12 PM and 5:20 PM. We know that clock resets at 12, so she works 5 hours 20 mins after noon.

We can write 5 hours 20 mins as

5 20/60

= 5 1/3 because in 1 hour there are 60 minutes.

Hence, the answer is 5 1/3.

Equal hours, also known as equinoctial hours, were defined as 124 of a day measured from noon to noon; small seasonal changes in this unit were subsequently smoothed out by making it 124 of a solar day.

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The one-way ANOVA test would be the best choice to compare the average number of adjustments made by service representatives at five different locations in Texas.

To compare the average number of adjustments made by service representatives at five different locations in Texas, the best choice of statistical test would be the one-way ANOVA (Analysis of Variance) test.

The one-way ANOVA test is used to compare the means of three or more independent groups to determine whether there is a statistically significant difference between them.

Five different groups (locations) that we want to compare.

The one-way ANOVA test allows us to test the null hypothesis that all the groups have the same population mean, against the alternative hypothesis that at least one group has a different population mean than the others.

If the p-value is less than the significance level (usually set at 0.05), we can reject the null hypothesis and conclude that there is a statistically significant difference between the means of the groups.

The one-way ANOVA test, we can determine whether there is a significant difference in the average number of adjustments made by service representatives across the five different locations in Texas.

If a significant difference is found, we can then conduct post-hoc tests to determine which specific locations have different means.

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Maricella has 4 quarters and 31 nickels in her bag.

Let's use the given terms and set up a system of equations to solve this problem:
Let n = number of nickels
Let q = number of quarters
We know two things:
There are 35 coins in total, so n + q = 35.
The total value is less than $2.75, so 0.05n + 0.25q < 2.75
Now let's solve the system of equations:
Solve the first equation for n:
n = 35 - q.

Substitute this expression for n into the second equation:
0.05(35 - q) + 0.25q < 2.75
Distribute the 0.05 to the terms inside the parentheses:
1.75 - 0.05q + 0.25q < 2.75
Combine like terms:
0.20q < 1
Divide by 0.20:
q < 5
Since q must be a whole number (as it represents the number of quarters), the highest possible value for q is 4.

Now we need to find the number of nickels.
Step 6: Substitute q = 4 back into the equation for n:
n = 35 - q
n = 35 - 4
n = 31.

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The axis of symmetry of the quadratic function for this problem is given as follows:

x = -1.

Considering a quadratic function with equation y = ax² + bc + c, the line of symmetry is defined as follows:

L: x = -b/2a.

The line of symmetry is the x-coordinate of the vertex of the function (turning point on the graph).

The coordinates of the vertex are given as follows:

(-1, -1).

Hence the line of symmetry is given as follows:

x = -1.

The problem asks for the axis of symmetry of the quadratic function.

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