FInd the surface area.

FInd The Surface Area.

Answers

Answer 1

Answer:

77 cm^2

Step-by-step explanation:

rectangular prism or cuboid

Right rectangular prism Solve for surface area▾

A = 77

L = 2

w = 3

h = 6.5

A=2(wl+hl+hw) = 2.(3.2+6.5.2+6.5.3)=77

chegg


Related Questions

Casey went to her favorite pizza place where she always bought lunch for $5.50. When she got to the restaurant, she was surprised to see the pizza now cost $6. What percentage was the pizza marked up?

A. between 8% and 9%
B. between 9% and 10%
C. between 10% and 11%
D. between 11% and 12%

Answers

Answer:

option B.

Step-by-step explanation:

The original price of Casey's favorite pizza was $5.50, but now it costs $6. To find the percentage markup, we can use the formula:

(markup / original price) * 100%

The markup is the difference between the new price and the original price:

$6.00 - $5.50 = $0.50

So the markup is $0.50.

Using the formula above:

(markup / original price) * 100% = ($0.50 / $5.50) * 100% = 9.09%

Therefore, the pizza was marked up by about 9%, which is option B.

What is the median of the data set?

A. 49

B. 86

C. 87

D. 85

Answers

The value of the median of the data set is,

⇒ 86

We have to given that;

Math test score are shown in figure.

Here Number of values are 21

Hence, The value of the median of the data set is,

⇒ (21 + 1)/2

⇒ 22/2

⇒ 11th term

⇒ 8 | 6

⇒ 86

Hence, The value of the median of the data set is,

⇒ 86

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Find the area of the composite figure. In neccesary, round your answer to the nearest hundredth.

Answers

Answer:

(1/2)(3)(4) + (1/2)π(2^2)

= 6 + 2π square kilometers

= 12.28 square kilometers

Suppose that we have two events, A and B, with P(A) = .50, P(B) = .50, and P(A ∩ B) = .20.
a. Find P(A | B) (to 4 decimals).
b. Find P(B | A) (to 4 decimals).
c. Are A and B independent? Why or why not?

Answers

To find P(A | B),  first we use the formula P(A | B) = P(A ∩ B) / P(B).To find P(B | A), we use the formula P(B | A) = P(A ∩ B) / P(A).  To determine if A and B are independent, we need to compare P(A ∩ B) with P(A)P(B). If P(A ∩ B) = P(A)P(B), then A and B are independent. If P(A ∩ B) ≠ P(A)P(B), then A and B are dependent.

a. Plugging in the given values, we have:
P(A | B) = 0.20 / 0.50 = 0.40
So, P(A | B) = 0.4000 (to 4 decimals).

b. Plugging in the given values, we have:
P(B | A) = 0.20 / 0.50 = 0.40
So, P(B | A) = 0.4000 (to 4 decimals).

c. Given values are:
P(A) = 0.50
P(B) = 0.50
P(A ∩ B) = 0.20
Calculating P(A) * P(B):
0.50 * 0.50 = 0.25

Since P(A ∩ B) ≠ P(A) * P(B), events A and B are not independent. The occurrence of one event affects the probability of the other event occurring.

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Q1 ***Open Data1 Population average for social conservatism is M=5.40 Effect size for the variable of social conservatism is d = 0.4 2) Is your data normally distributed? Report. 4p

Answers

We need additional information, such as a dataset or summary statistics to perform a normality test.

To determine if the data is normally distributed, we need to look at the distribution of the variable of interest. In this case, we are interested in the distribution of social conservatism scores.

If we have access to the data, we can use statistical tests such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test to determine if the data is normally distributed. However, since we only have information about the population average and effect size, we cannot directly test for normality.

However, based on the central limit theorem, we can assume that if the sample size is large enough (typically >30), the distribution of the variable of interest will be approximately normal. In this case, since we do not have information about the sample size, we cannot definitively say if the data is normally distributed.

In summary, without more information about the sample size or access to the data, we cannot determine if the data is normally distributed.

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Write the coordinates of the vertices after a reflection over the y-axis.

Answers

To reflect a figure over the y-axis, we simply change the sign of its x-coordinates while keeping the y-coordinates the same. So, the coordinates of the vertices after a reflection over the y-axis would be:

A'(-2, 1), B'(-1, 3), C'(1, 2), D'(2, 0)

When we reflect a figure over the y-axis, we are essentially flipping the figure horizontally along a vertical line passing through the origin.

This means that every point on the original figure is reflected across this vertical line, resulting in a new figure that is a mirror image of the original.

Thus, the coordinates of the vertices after a reflection over the y-axis are A'(-2, 1), B'(-1, 3), C'(1, 2), and D'(2, 0).

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Addition of which of the following would increase the rate of actin depolymerization on the minus end of the filament?
A) ATP-G-actin
B) Cap Z
C) cofilin
D) profilin
E) thymosin β4

Answers

Of the options given, cofilin would be expected to increase the rate of actin depolymerization on the minus end of the filament.

The depolymerization of actin filaments is a dynamic process that is regulated by a variety of proteins. Actin filaments grow by the addition of ATP-G-actin subunits to the plus end of the filament and can depolymerize from the minus end. Several proteins regulate actin depolymerization by binding to actin filaments and promoting filament disassembly. Of the options given, cofilin would be expected to increase the rate of actin depolymerization on the minus end of the filament.

Cofilin is a small actin-binding protein that binds to ADP-actin subunits within the filament, inducing a conformational change that destabilizes the filament and promotes depolymerization. Cofilin binds preferentially to the ADP-bound subunits, which are found primarily at the minus end of the filament. By binding to these subunits, cofilin promotes the disassembly of the filament from the minus end, increasing the rate of depolymerization.

In contrast, ATP-G-actin is the monomeric form of actin that is added to the plus end of the filament and promotes filament growth. Cap Z is a capping protein that binds to the plus end of the filament, stabilizing it and preventing depolymerization. Profilin is an actin-binding protein that binds to ATP-G-actin, promoting its polymerization into filaments. Thymosin β4 is a protein that binds to actin monomers, preventing their polymerization into filaments and sequestering them in the cytoplasm.

Therefore, of the options given, cofilin would be expected to increase the rate of actin depolymerization on the minus end of the filament.

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3. What is the radius of the circle?

Answers

The value of radius of the circle is,

⇒ r = 7 units

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

A circle is shown in figure.

Now, We ca formulate the value of radius of the circle is,

⇒ r = 8 - 1

⇒ r = 7 units

Thus, The value of radius of the circle is,

⇒ r = 7 units

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Donna owes $3,000 on her credit cards. She decided to pay $104.00 per month without charging any
new money to the card. How many months did it take for Donna to pay off her credit card if she paid
$126.00 in interest? Round to the nearest whole.

Answers

It took Donna 30 months to pay off her credit card.

Total amount paid = Monthly payment x Number of months

Total amount paid = $104 x Number of months

Amount paid towards principal = Total amount paid - Total interest paid - Original amount owed

We know that she paid $126 in interest and originally owed $3,000, so we can substitute those values:

Amount paid towards principal = Total amount paid - $126 - $3,000

= $104 x Number of months - $126 - $3,000

We want to know how many months it takes for her to pay off the entire debt, so we can set the amount paid towards principal equal to zero:

$104 x Number of months - $126 - $3,000 = 0

$104 x Number of months = $3,126

Number of months = $3,126 / $104

Number of months = 30.1

So it took Donna 30 months to pay off her credit card.

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What number should go in the space? Multiplying by 1. 36 is the same as increasing by _____%

Answers

The number 36 should be placed in the blank space. So, Multiplying by 1. 36 is the same as increasing by 36 percent from a decimal number.

The decimal system has a base of ten . These numbers are generally represented by the dot "." between the digits called "decimal point". We can express an integer as a decimal by putting a decimal point after the digit in one's place and writing 0 onwards. The term "percent" is a number or ratio that represents a fraction of 100. Steps to convert decimal to Percent :

First multiply the number by 100 on shifting the decimal point to the right by 2 places. Put the percent symbol (%). For example: 0.23 = 0.23 x 100% = 23%.

We have to fill up a blank space with a number. We have a decimal number 1.36. From above discussion, we need to convert this decimal value into a percent : 0.36 × 100 = 36% So, multiplying by 1.36 is the same as increasing by 36%. Hence, required value is 36.

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A study of the number of highway deaths due to failure to wear seat belts in a year versus percentage seat belt usage in that year in 300 national regions shows a strong negative linear association. The least squares regression equation is:
Predicted number of deaths -11,100 - 305.1 Belt usage What does "negative" mean in this context?
(A) If no one wore seat belts in a given region, it is predicted that there will be 11,100 highway deaths due to failure to wear seat belts.
(B) The correlation, between the number of highway deaths due to failure to wear seat belts and the
percentage of seat belt usage is negative.
(C) If a given region has a lower percentage of seat belt usage than a second region, the given region will have a higher number of highway deaths due to failure to wear seat belts than the second region.
(D) Regions with a higher percentage of seat belt usage tend to have lower numbers of highway deaths due to failure to wear seat belts.
(E) If a region has a one percent gain in seat belt usage, then it will have a reduction of 305 highway deaths due to failure to wear seat belts, on average.

Answers

Your answer: (D) Regions with a higher percentage of seat belt usage tend to have lower numbers of highway deaths due to failure to wear seat belts.

In this context, "negative" means that there is an inverse relationship between the number of highway deaths due to failure to wear seat belts and the percentage of seat belt usage. Option (B) correctly states that the correlation is negative. Option (C) is incorrect because it suggests a comparison between two regions.

whereas the regression equation predicts the number of deaths based on seat belt usage within a given region. Option (D) is correct and states that regions with higher seat belt usage tend to have lower numbers of deaths. Option (A) and (E) are incorrect because they do not accurately describe the negative association between the variables.

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an online computer game company has 10,000 subscribers paying $8 per month. their research shows that for every 25-cent reduction in their fee, they will attract another 500 users. the table below models the revenue for several fee rates.what fee should the company charge to maximize their revenue? how do you know?

Answers

The fee should the companyfee should the company charge to maximize their revenue charge to maximize their revenue is $7.50.

To determine the fee that the online computer game company should charge to maximize their revenue, we need to calculate the revenue for each fee rate listed in the table below:

| Fee Rate | Number of Subscribers | Revenue |
|----------|----------------------|---------|
| $8.00    | 10,000               | $80,000 |
| $7.75    | 10,500               | $81,375 |
| $7.50    | 11,000               | $82,500 |
| $7.25    | 11,500               | $83,375 |
| $7.00    | 12,000               | $84,000 |
| $6.75    | 12,500               | $84,375 |
| $6.50    | 13,000               | $84,500 |
| $6.25    | 13,500               | $84,375 |
| $6.00    | 14,000               | $84,000 |

From the table, we can see that the revenue initially increases as the fee rate decreases, but then starts to decrease after $7.50. This is because although the number of subscribers increases with a lower fee rate, the decrease in revenue from each individual subscriber outweighs the increase in subscribers.

Therefore, the fee rate that would maximize revenue for the online computer game company is $7.50. This is the fee rate where the revenue is the highest, at $82,500. We know this is the optimal fee rate because any higher fee rate will result in fewer subscribers, and any lower fee rate will result in a decrease in revenue per subscriber.

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X
5. In a swimming pool, two lanes are represented by lines / and m. If a string of flags strung across the lanes is
represented by transversal r, and x = 10, show that the lanes are parallel. Choose the best answer below.
(3x+4)⁰1
J.
(4x-62
m
work?
a. 3x+43(10) + 4 = 34°;
4x-6-4(10)-6-34°
The angles are alternate interior angles and they are congruent, so the lanes are parallel by
the Alternate Interior Angles Theorem.
b. 3x+43(10) + 4 = 34°;
4x-6-4(10)-6-34°
The angles are alternate interior angles, and they are congruent, so the lanes are parallel by
the Converse of the Alternate Interior Angles Theorem.
c. 3x+4=3(10) + 4 = 34°;

Answers

Both angles have the same measure of 34 degrees, therefore, both lanes are parallel based on the converse of alternate interior angles theorem. The correct option is: D.

What are Alternate Interior Angles?

Two interior angles that alternate each other along a transversal that crosses two parallel lines are said to be alternate interior angles, and they are congruent to each other.

Plugging the value of x, both angles indicated in the image are congruent to each other:

3x + 4 = 3(10) + 4 = 34°;

4x - 6 = 4(10) - 6 = 34°

Therefore, since they are congruent to each other, the lanes are parallel based on the converse of alternate interior angles theorem.

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evaluate m-p-n for m= -12,n=23 and p=4.5

Answers

The value of expression is, - 39.5

Given that;

All the Values are,

m = - 12

n = 23

p = 4.5

Now, We can formulate;

⇒ m - p - n

Substitute all the values, we get;

⇒ - 12 - 4.5 - 23

⇒ - 39.5

Thus, The value of expression is, - 39.5

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Suppose follows the standard normal distribution. Use the calculator provided, or that, to determine the value of c so that the following true P(2>c) 0.2643 Round your answer to two decimal places 0 X

Answers

The z-score for 0.7129 is approximately 0.55. The value of c is 0.55, rounded to two decimal places.

1. We're given P(2 > c) = 0.2643, which means the area under the standard normal distribution curve between 2 and c is 0.2643.

2. We'll use the z-table or a calculator with a standard normal distribution function to find the corresponding z-score for c.

3. To find the area to the left of c, we need to first find the area to the left of 2. The z-score for 2 is 0.9772 (from the z-table or using a calculator).

4. Now, subtract the given area (0.2643) from the area to the left of 2: 0.9772 - 0.2643 = 0.7129.

5. Look up the z-score corresponding to the area 0.7129 in the z-table, or use a calculator with the inverse standard normal distribution function. The z-score for 0.7129 is approximately 0.55.

6. Therefore, the value of c is 0.55, rounded to two decimal places.

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The following notice appeared in the golf shop at a Myrtle Beach, South Carolina, golf course. Take into account the price of the ticket. Blackmoor Golf Club Members
The golf shop is holding a raffie to win a Taylormade R9 10.5 regular flex driver ($300 value)
Tickets are $5.00 each
Only 80 tickets will be sold
Please see the golf shop to get your tickets!
John Underpar buys a ticket. a. What are Mr. Underpar's possible monetary outcomes? - Either wins the driver (worth $295) or has a worthless ticket (worth -$5) - Either wins the driver (worth $300) or has a worthless ticket (worth $0) c. Summarize Mr. Underpar's "experiment" as a probability distribution. Probability
Getting nithing ______
Winning the driver ______
d. What is the mean or expected value of the probability distribution? expected value ___________
e. If all 80 tickets are sold, what is the expected return to the club?
expected return ________

Answers

a. John Underpar's possible monetary outcomes are either winning, which is worth -$5 (the cost of the ticket).

b. the driver (worth $300) or having a worthless ticket (worth $0).

c) Probability of getting nothing = 79/80 = 0.9875
Probability of winning the driver = 1/80 = 0.0125
d. the expected value of buying a ticket is -$1.19, which means on average, a person can expect to lose $1.19 by buying a ticket.
e.the expected return to the club is $100 if all 80 tickets are sold.

a. John Underpar's possible monetary outcomes are either winning the Taylormade R9 10.5 regular flex driver, which is worth $300, or having a worthless ticket, which is worth -$5 (the cost of the ticket).

b. Actually, winning the driver is worth $300, not $295. So, Mr. Underpar's possible monetary outcomes are either winning the driver (worth $300) or having a worthless ticket (worth $0).

c. Mr. Underpar's "experiment" can be summarized as a probability distribution with the following probabilities:

Probability of getting nothing = 79/80 = 0.9875
Probability of winning the driver = 1/80 = 0.0125

d. The mean or expected value of the probability distribution can be calculated as:

Expected value = (Probability of winning the driver x Value of winning) + (Probability of getting nothing x Value of nothing)
Expected value = (0.0125 x $300) + (0.9875 x -$5)
Expected value = $3.75 - $4.94
Expected value = -$1.19

Therefore, the expected value of buying a ticket is -$1.19, which means on average, a person can expect to lose $1.19 by buying a ticket.

e. If all 80 tickets are sold, the expected return to the club can be calculated as:

Expected return = (Number of tickets sold x Price of a ticket) - Value of the prize
Expected return = (80 x $5) - $300
Expected return = $400 - $300
Expected return = $100

Therefore, the expected return to the club is $100 if all 80 tickets are sold.

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Use the equation x 2 −7x+6 = 0 to answer all of the following questions.

Answers

Answer:

Part A: -6 and -1

Part B: (x - 6)(x - 1) = 0

Part C: x = 6 and x = 1

Step-by-step explanation:

    We need to find two numbers that add up -7 and multiply to 6.

    We know that 6 * 1 = 6, but 6 + 1 is not -7. However, -6 * -1 = 6 and -6 + -1 = -7. Our factors are -6 and -1.

    Next, we will rewrite this in factored form. Using the factors above, the form is as follows.

(x - 6)(x - 1) = 0

    Lastly, we will use the zero product property to solve. This states that if xy = 0, then x = 0 and y = 0 because anything times zero is equal to zero.

x - 6 = 0       x - 1 = 0

x = 6             x = 1

the natural rate of unemployment is the rate of unemployment that occurs when both the goods and financial markets are in equilibrium

Answers

The natural rate of unemployment refers to the level of unemployment that exists when the economy is in equilibrium, meaning both the goods and financial markets are balanced. This rate is typically considered as the baseline level of unemployment, which can be observed in a healthy and stable economy. It consists of two primary components: frictional and structural unemployment.


Frictional unemployment arises due to job transitions, such as workers changing careers or locations, and is often temporary. Structural unemployment, on the other hand, occurs when there is a mismatch between the skills possessed by job seekers and those demanded by employers. This type of unemployment is more long-lasting and requires targeted efforts to address it, such as worker retraining or education initiatives.

When the economy is in equilibrium, the natural rate of unemployment indicates that the labor market is functioning efficiently. The supply and demand for labor are balanced, and there are no external shocks affecting the market. In this state, the overall rate of unemployment remains relatively stable, with changes occurring mainly due to the natural fluctuations in frictional and structural unemployment.

In summary, the natural rate of unemployment represents the level of unemployment that occurs when the goods and financial markets are in equilibrium. It consists of frictional and structural unemployment, and serves as a benchmark for policymakers to evaluate the health and efficiency of the labor market in an economy.

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Complete the statement blank is a function of blank

Answers

Fill in each blank so that the resulting statement is true: A function f has an inverse that is a function if there is no vertical line that intersects the graph of f at more than one point. Such a function is called a/an injective function or a one-to-one function.

A function is injective if every distinct input produces a distinct output. Geometrically, this means that the function does not repeat any output values . If there is a vertical line that intersects the graph of f at more than one point, then the function fails to be injective, since two distinct input values will produce the same output value. In this case, the function does not have an inverse that is a function.

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Full Question ;

Fill in each blank so that the resulting statement is true. A function f has an inverse that is a function if there is no ____ line that intersects the graph of f at more than one point. Such a function is called a/an ____ function.

Multiply: 7/11 x 1 1/6

Answers

Answer:

1(1/2)

Step-by-step explanation:

how you use this is do 7 divided by 11 and 11 divided by 6 which is 1 and 1/2

Answer:

77/66 (simplified would equal 7/6)

Step-by-step explanation:

When multiplying fractions you simply just multiply the numerators together, making the new numerator, then multiply the denominators together, making the new denominator, and  you have your answer.

EXTRA: To simplify the fraction to its simplest you find a number that both the numerator and the denominator can be divided into equally, in this case it would be 11, then divide the numerator and denominator by this number and that would be your answer. Example; 77/66, divide 77 and 66 by 11 and you get 7/6.

Hope this helps (:

What is the value of the expression −3 1/3÷(−2.4) ?

Answers

Answer:

First, we need to convert the mixed number −3 1/3 to a fraction. −3 1/3 = −(3 + 1/3) = −(10/3).

Now, we can divide the fraction by the decimal. −(10/3) ÷ (-2.4) = −(10/3) ÷ (-24/10) = −(10/3) x (10/-24) = 10/-7.2 = -1.388888889.

Therefore, the value of the expression is −1.388888889.

Step-by-step explanation:

1. Convert the mixed number to a fraction.

```

-3 1/3 = -(3 + 1/3) = -(10/3)

```

2. Multiply the numerator and denominator of the fraction by -1.

```

-(10/3) = (-1)(10/3) = -10/3

```

3. Divide the numerator and denominator of the fraction by -24.

```

-10/3 = (-10/3) ÷ (-24/10) = 10/-7.2 = -1.388888889

```

Therefore, the value of the expression is −1.388888889.

Here is a visual representation of the steps:

```

-3 1/3 ÷ (-2.4)

= -(10/3) ÷ (-24/10)

= -(10/3) x (10/-24)

= 10/-7.2

= -1.388888889

```

For number 1-3, identify wether or not the relation shown is a function?

Answers

Answer:

1. Yes

2. No

3. Yes

Step-by-step explanation:

A function is a relationship with unique x-values.

Defining a Function

For a relationship to be a function, the x-values cannot repeat. This means that inputs, aka x-values, can only have one possible output value, also called y-values. For example, if inputting x = 5 resulted in both y = 3 and y = 7, then the relationship would not be a function.

However, y-values do not have to be unique. Functions can repeat y-values and still be functions.

Answers

Now, let's apply this definition to the problems above.

1. The first question gives us a table of x and y-values. From the x-values in the left column, we can see that x-values do not repeat. This means the relationship is a function.

2. The second question gives the inputs and outputs of a function. From looking at the outputs for 0, we can tell that x = 0 produces multiple outputs. This means that not all x-values are unique. Thus, the relationship is not a function.

3. The third image is a graph. At no point on the graph do x-values repeat. Each x-value has one y-value. So, the relationship is a function. Specifically, this graph represents a quadratic function.

580 sat scores: the college board reports that in , the mean score on the math sat was and the population standard deviation was . a random sample of students who took the test in had a mean score of . following is a dotplot of the scores. (a) are the assumptions for a hypothesis test satisfied? explain. (b) if appropriate, perform a hypothesis test to investigate whether the mean score in differs from the mean score in . assume the population standard deviation is . what can you conclude? use the level of significance and the

Answers

We fail to reject the null hypothesis since the calculated t-statistic (0) is not greater than the critical values (-2.093 and 2.093). There is not enough evidence to suggest that the mean score in 2018 differs significantly from the mean score in 2017.

Based on the information given, the mean score on the math SAT in 2017 was not provided. However, assuming that the question is asking about the mean score in 2018, we can use the given values to answer the question.

(a) In order to determine if the assumptions for a hypothesis test are satisfied, we need to check if the sample is random and if the data is normally distributed. As long as the sample was selected randomly and independently of each other and the population is normally distributed, the assumptions for a hypothesis test are satisfied.

(b) We can perform a hypothesis test to investigate if the mean score in 2018 differs from the mean score in 2017 using the following steps:

Null Hypothesis (H0): The mean score in 2018 is equal to the mean score in 2017.
Alternative Hypothesis (Ha): The mean score in 2018 is not equal to the mean score in 2017.

We can use a two-tailed t-test to test the hypothesis since the population standard deviation is not known. Assuming a level of significance of 0.05, and using a t-distribution table with a degree of freedom of n-1=19, the critical values are -2.093 and 2.093.

The sample mean score in 2018 is given as 580. The mean score in 2017 is not provided in the question. Assuming that the mean score in 2017 is also 580, we can calculate the t-statistic as follows:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
t = (580 - 580) / (15 / sqrt(20))
t = 0

Since the calculated t-statistic (0) is not greater than the critical values (-2.093 and 2.093), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the mean score in 2018 differs significantly from the mean score in 2017.

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find the orthogonal trajectories of the family of curves. (use c for any needed constant.) x2 2y2

Answers

To find the orthogonal trajectories of the given family of curves, we first need to understand what the term "orthogonal" means. In simple terms, two lines or curves are said to be orthogonal if they intersect at a right angle. Now, coming back to the problem, the given family of curves can be written as x^2 - 2y^2 = c, where c is a constant.

To find the orthogonal trajectories, we need to differentiate this equation with respect to y, treating x as a constant. This gives us:
-4xy = dy/dx

Now, we need to find the equation of the curves that intersect the given family of curves at a right angle, i.e., the slopes of the curves must be negative reciprocals of each other. Therefore, we can write:
dy/dx = 4xy/k

where k is a constant. To solve this differential equation, we can separate the variables and integrate:

∫dy/4xy = ∫dx/k

ln|y| - ln|x^2| = ln|c| + ln|k|

ln|y/x^2| = ln|ck|

y/x^2 = ±ck

Therefore, the orthogonal trajectories of the given family of curves are given by y = ±kx^2/c, where k is a constant. These curves intersect the original family of curves at right angles.

1. Identify the family of curves: The given equation is x^2 + 2y^2 = c, where c is a constant. This represents a family of ellipses with different sizes depending on the value of c.

2. Calculate the derivative: To find the orthogonal trajectories, we first need to find the derivative of the given equation with respect to x. Differentiate both sides with respect to x:

d/dx(x^2) + d/dx(2y^2) = d/dx(c)
2x + 4yy' = 0

3. Find the orthogonal slope: The slope of the orthogonal trajectory is the negative reciprocal of the original slope. Since the original slope is y', the orthogonal slope is -1/y':

Orthogonal slope = -1/y'

4. Replace the original slope with the orthogonal slope:

2x + 4y(-1/y') = 0

5. Solve for y':

y' = -2x/(4y)

6. Solve the differential equation: Now we have a first-order differential equation to find the equation of the orthogonal trajectories:

dy/dx = -2x/(4y)

Separate variables and integrate both sides:

∫(1/y) dy = ∫(-2x/4) dx

ln|y| = -x^2/4 + k

7. Solve for y:

y = e^(-x^2/4 + k) = C * e^(-x^2/4), where C is a new constant.

The orthogonal trajectories of the given family of curves are represented by the equation y = C * e^(-x^2/4).

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Is there a rigid transformation that would map ΔABC to ΔDEC?

Answers

Yes, there is a rigid transformation that would map ΔABC to ΔDEC

Checking if there is a rigid transformation

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

The triangles ABC and DEC

From the figure of the the triangles, we can see that

The triangles can be rotated to map one over the other

This is because the triangles have two congruent angle and two congruent sides i.e. they are similar by SAS

Hence. there is a rigid transformation that would map ΔABC to ΔDEC

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When would you need to transfer measurements from the metricsystem to the US system and from the US system to the metricsystem.

Answers

You might need to transfer measurements from the metric system to the US system and vice versa in various situations.

Some examples include:

1. International trade: If you are exporting or importing goods, it's essential to convert measurements to the recipient's preferred system, ensuring proper understanding of product specifications.

2. Travel: When traveling to a different country, you may need to convert distances, speed limits, or temperatures to better understand local road signs or weather conditions.

3. Cooking and recipes: When following a recipe from a different country, converting ingredient measurements can be crucial for accurate results.

4. Construction and engineering: Working on projects with international collaboration may require converting measurements to ensure all parties understand the specifications.

5. Science and education: As the metric system is the standard for scientific research, it may be necessary to convert US measurements to metric for consistency in data reporting and understanding.

Remember to use appropriate conversion factors when transferring measurements between the metric system and the US system to ensure accurate results.

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You are given two numbers, stored in a variable with the names, a, b You have to find the sum of X, Y and z 1. X = (a*3) + (b*5) 2. Y = (a*7) + (b*4) 3. Z = a*b Find the value of sum, such that sum = x + y + Z

Answers

The value of sum is X+Y+Z.

To find the sum of X, Y, and Z using the given variables a and b, you'll need to calculate the values of X, Y, and Z first, then add them together.

Here's a step-by-step explanation:

1. Calculate X: X = (a * 3) + (b * 5)
2. Calculate Y: Y = (a * 7) + (b * 4)
3. Calculate Z: Z = a * b
4. Find the sum: sum = X + Y + Z

By following these steps with the given values of a and b, you will find the value of sum, such that sum = X + Y + Z.

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sara mcmahon purchased a new car 3 years ago for $24,500.00. the current estimated value is $17,900.00. annual variable costs this year were $895.60. insurance was $1,350.00, registration was $132.50, and loan interest totaled $1,080.00. she drove 12,540 miles this year. compute the cost per mile in dollars. round to the nearest hundredth.

Answers

The cost per mile to the nearest hundredth: $0.28 per mile.

Sara McMahon purchased a new car 3 years ago for $24,500.00, and the current estimated value is $17,900.00. The annual variable costs this year were $895.60, insurance was $1,350.00, registration was $132.50, and loan interest totaled $1,080.00. She drove 12,540 miles this year.

To compute the cost per mile, first, find the total cost for this year by adding the variable costs, insurance, registration, and loan interest: $895.60 + $1,350.00 + $132.50 + $1,080.00 = $3,458.10.

Next, divide the total cost by the number of miles driven: $3,458.10 ÷ 12,540 miles = $0.2757 per mile.

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Kaitlyn purchased a 91-day T-Bill that has a face value of $1260
and an interest rate of 5.07% p.a. Calculate the purchase price of
the T-Bill. Round to the nearest cent

Answers

The purchase price of the T-Bill is $1,239.17.

To calculate the purchase price of the T-Bill, we need to use the formula:

Purchase Price = Face Value / (1 + (interest rate x days to maturity / 365))

In this case, the face value is $1260, the interest rate is 5.07% p.a., and the days to maturity is 91. Plugging in the values, we get:

Purchase Price = $1260 / (1 + (0.0507 x 91 / 365))
Purchase Price = $1260 / 1.0123
Purchase Price = $1,239.17 (rounded to the nearest cent)

The purchase price of the T-Bill is $1,239.17.

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Find the value of c using the given chord and secant lengths in the diagram shown to the right.

Answers

The value of each variable in the circle is:

b = 90°

c = 47°

a = 43°

How to find the value of each variable in the circle?

A circle is a round-shaped figure that has no corners or edges. It can be defined as a closed shape, two-dimensional shape, curved shape.

An angle inscribed in a semicircle is a right angle. Thus,

b = 90°

c = 360 - 133 - 180 (sum of angle in a circle)

c = 47°

a = 180 - 90 - 47  (sum of angle in a triangle)

a = 43°

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