Mr. Wade took his family on an 8-hour boat trip. During the trip, the boat used 48 gallons of gasoline. The boat used the same number of gallons each hour. At what rate did the boat use gasoline?​

y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given,

y-intercept 4 and slope -1/5

Now y=-1/5x+4

Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

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Answer:

AB

Step-by-step explanation:

The segments that are parallel need to be in the same direction ( up and down)

The segments that are parallel are FH, AB, GC

Answer:

AB

Step-by-step explanation:

since is a cube all of the angles are 90 degees and this only possibel whn the line That a vertical a parrelllt to each other

The estimate of the probability that he will hit at least 6 times in his next 10 attempts is given as follows:

80%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

An amateur golfer hits the ball 48% of the time he attempts, hence we round the probability to 50%, and have that the numbers are given as follows:

From the table, we have 20 sets of 10 attempts, and in 16 of them he hit at least 6 attempts, hence the probability is given as follows:

16/20 = 0.8 = 80%.

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Answer:

Step-by-step explanation:

Dimensions of the picture:

Area of the picture:

Scale factor = 2.5

Enlarged picture's area:

Option B is correct

The area of the picture after it is enlarged is 250 inches².

Given that,

The length of the rectangle is labeled 5 inches. The width of the rectangle is labeled 8 inches.

A photographer wants to use a scale factor of 2.5 to enlarge a picture.

Based on the above information, the calculation is as follows:

Here, the dimensions of the picture are 5 in and 8 in

Hence, the area of the picture is,

5 × 8 = 40 in²

Since, Scale factor = 2.5

So, the enlarged picture's area would be,

40 × 2.5 ×2.5

= 250 in²

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The equivalent ratio is 12: 18

The ratio is 12:_ = 16: 24

12/x = 16/ 24

x≠0, because the denominator can never be 0.

Solve the equation

12/x = 16/24

12/x = 2/3

x = 18

Therefore the equivalent ratio is 12:18.

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There are six possible interactions in a 2 × 3 factorial ANOVA. The correct option is (d) 6.

In a 2 × 3 factorial ANOVA, there are two factors, each with two levels and three levels, respectively. The number of interactions that can be observed in a factorial ANOVA is determined by the product of the number of levels of each factor.

In this case, the first factor has two levels, and the second factor has three levels.

Therefore, the number of possible interactions is given by multiplying the number of levels of the first factor by the number of levels of the second factor: 2 × 3 = 6.

Each interaction represents a unique combination of the levels of the two factors.

For example, one interaction might represent the effect of the first factor at the first level interacting with the second factor at the first level, while another interaction might represent the effect of the first factor at the second level interacting with the second factor at the third level, and so on.

Therefore, the correct answer is d. 6, as there are six possible interactions in a 2 × 3 factorial ANOVA.

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Answer:

Mean: 7

Median: 8

Range: 9

Mode: 3

Step-by-step explanation:

First, to find the mean of a set of numbers you need to add up all of the numbers and divide that by the total amount of numbers. In this case that makes this equation, \(\frac{3+3+4+8+9+10+12}{7}\), which is \(\frac{49}{7}\), which is 7.

To find a median you need to find the middle number. A handy trick I use for this is to place my fingers on the first and last number, and then move them towards the middle, at the same time by one number until there is just one number left in the middle. If there are no numbers left after doing this, meaning there are an even amount of numbers given, the median is the mean of the last two numbers that were covered. In this case, this is not necessary, so the median is 8.

The range is the difference between the maximum and minimum of a data set. In this case that would give you the equation Range=12-3, which means the range is 9.

Finally, the mode is the number that occurs the most in a given data set. In this case the number that occurs the most is 3, which occurs twice compared to every other number which only occurs once.

Hey there!

‘‘Find the mean median range and mode for 3, 3, 4, 8, 9, 10, and 12’’

• Mean is known as your AVERAGE number. You have to ADD all of your NUMBERS the DIVIDE it by the TOTAL numbers in your given set

• We have the total of SEVEN numbers in your set

“3 + 3 + 4 + 8 + 9 + 10 + 12 / 7”

6 + 4 + 8 + 9 + 10 + 12/7

10 + 8 + 9 + 10 + 12/7

18 + 9 + 10 + 12/7

27 + 10 + 12/

37 + 12/7

49/7 = 7

Answer: Mean = 7 ✔️

• Median is the number you see in the center (the middle) of the problem. You can solve for this by putting your numbers from least to greatest

• If you have an ODD number in your given set then your middle number will be the single number)

• If you have an EVEN number then you have to average your TWO middle number

“ 3, 3, 4, 8, 9, 10, 12”

• you still have 3 on both sides of your 8 (3 is an ODD number, so we have to let it be be a single number)

Answer: mean = 8 ✔️

• Mode is your number than you see repeated OR more than once

• We “3” repeated so it is your Mode

Answer: Mode = 3 ✔️

Answers ⬇️

• Mean: 7 ☑️

• Median: 8 ☑️

• Mode: 3 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

We will have the following:

So, its zeros are x = -3, x = 0 & x = 3.

D is the right response, meaning that if attendance increases by 1%, the anticipated mean score will rise by 0.341 percentage points.

What is Statistics?

The study of gathering, analysing, interpreting, presenting, and arranging data in a certain way is the focus of the mathematic branch known as statistics. The act of gathering data, classifying it, presenting it in a way that makes it understandable, and then conducting additional analyses of the data is known as statistics. Statistics is also the process of drawing inferences from samples of data gathered through experiments or surveys. Statistics are also used to operate in a variety of fields, including psychology, sociology, geology, probability, and more.

Results of an EXA are a dependent variable.

Percentage Attendance is a standalone factor.

As a result, the regession equation is Scores received = 39.390 + 0.341*X.

In other words, if we increase attendance by 1%, the estimated mean score received will increase by 0.341 percentage, according to the slope of the regression line.

Therefore, D is the right response, meaning that if attendance increases by 1%, the anticipated mean score will rise by 0.341 percentage points.

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To use Stokes' theorem to evaluate the given vector field, we need to find the curl of the vector field and calculate the surface integral over the cone.

First, let's find the curl of the vector field f(x, y, z) = arctan(x^2yz^2)i + x^2yj + x^2z^2k.

The curl of a vector field F = P i + Q j + R k is given by the following formula:
curl F = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, P = arctan(x^2yz^2), Q = x^2y, and R = x^2z^2.

Taking the partial derivatives, we get:
∂P/∂x = 0, ∂P/∂y = 2x^2z^2, ∂P/∂z = 2x^2yz^2
∂Q/∂x = 2xy, ∂Q/∂y = x^2, ∂Q/∂z = 0
∂R/∂x = 2xz^2, ∂R/∂y = 0, ∂R/∂z = 2x^2z

Now, substituting these values into the formula for the curl, we have:
curl f = (2x^2z^2 - 0)i + (0 - 2xz^2)j + (2xy - 2x^2yz^2)k
      = 2x^2z^2i - 2xz^2j + 2xyk

Next, we need to calculate the surface integral over the cone.

The surface integral can be evaluated using the formula:
∫∫S (curl f) · dS = ∫∫D (curl f) · (r_u × r_v) dA

Here, (r_u × r_v) is the cross product of the partial derivatives of the position vector r(u, v) with respect to the parameters u and v, and dA is the differential area element.

In this case, the cone is given by x = sqrt(y^2 + z^2), 0 <= x <= 2, and we can parameterize the surface as r(u, v) = u sqrt(1 + v^2) i + u v j + u sqrt(1 + v^2) k, where 0 <= u <= 2, -1 <= v <= 1.

Taking the partial derivatives of r with respect to u and v, we have:
r_u = sqrt(1 + v^2) i + v j + sqrt(1 + v^2) k
r_v = u v i + j + u v k

Now, calculating the cross product r_u × r_v, we get:
r_u × r_v = (v sqrt(1 + v^2) - u v sqrt(1 + v^2)) i - (sqrt(1 + v^2) - u v) j + (u v - v sqrt(1 + v^2)) k

Finally, substituting the values into the surface integral formula, we have:
∫∫S (curl f) · dS = ∫∫D (2x^2z^2i - 2xz^2j + 2xyk) · ((v sqrt(1 + v^2) - u v sqrt(1 + v^2)) i - (sqrt(1 + v^2) - u v) j + (u v - v sqrt(1 + v^2)) k) dA

Now, you can evaluate this surface integral to find the answer.

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Answer:

Step-by-step explanation:25

Parallelogram II and IV have the same area.

A parallelogram with the same base and height has the same area, regardless of shape. The product of base and height is equal. 

The following is a list of the characteristics of a parallelogram:

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Step-by-step explanation:

In a equation of a line

y=mx+c

Let's take two points from the graph (0,1) and (4,3)

Slope=m= (3-1/4-0)= 2/4=1/2

C= 1

y=½x+1

Answer:

y = ½x + 1

Step-by-step explanation:

the line pass through (x1,y1) as (-2,0) and (x2,y2) as (0,1) so the line equation can be determine by

\( \frac{y - y1}{y2 - y1} = \frac{x - x1}{x2 - x1} \)

(y-0)/(1-0) = (x-(-2))/(0-(-2))

y = (x+2)/2

y = ½x + 1

Answer:

171/400 or 0.4275

Step-by-step explanation:

multiply the expressions and simplify

Answer:

m = 2k/v²

Step-by-step explanation:

I think you mean solve for m, not k

Multiply both sides of the equation by 2

2 * 1/2 *(mv²) = 2 * k

Rewrite the expression.

1*(mv²) = 2*k

Multiply mv² by 1

mv² = 2*k

Divide each term by v² and simplify

mv²/v² = 2k/v²

mv²/v² cancel out and you get

m = 2k/v²

The probability of having no more than two errors in five pages, with an average error rate of one in every 500 words typeset and each page containing 300 words, can be calculated using the binomial distribution. The probability is approximately 0.9947, or 99.47%.

Let's calculate the probability step by step. The average error rate is given as one error in every 500 words typeset. Therefore, the probability of making an error on a single word is 1/500, and the probability of not making an error on a single word is 499/500.

Since each page contains 300 words, the probability of not making an error on a single page is \((499/500)^{({300)\), as the events are independent. The probability of making at least one error on a page is the complement of not making any errors, which is 1 -  \((499/500)^{({300)\).

Now, we need to calculate the probability of having no more than two errors in five pages. We can use the binomial distribution to find this probability. The formula for the binomial distribution is

P(X ≤ k) = ∑(i=0 to k) (n choose i) * p^i * (1-p)^(n-i), where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose i) is the binomial coefficient.

In this case, n = 5 (number of pages), k = 2 (maximum number of errors), and p = 1 -  \((499/500)^{({300)\). By calculating the sum using the binomial distribution formula, we find that the probability of having no more than two errors in five pages is approximately 0.9947, or 99.47%.

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a. The probability that a randomly selected pipe is made of PVC is approximately 0.242 or 24.2%.

b. The probability that randomly selected pipe is a trunk is 0.104

c. The probability that randomly selected pipe is a main made of galvanized iron (gi) is 0

d. The probability that randomly selected pipe is  a submain made of asbestos cement is 0.168

What is probability?

The chance of an event can be calculated using the probability formula by simply dividing the favorable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favorable number of outcomes can never exceed the total number of outcomes.

a. The total number of pipes is 8646, and the number of pipes made of PVC is 2092. The probability of a randomly selected pipe being made of PVC is:

P(PVC) = 2092/8646 ≈ 0.242

b. The total number of pipes is 8646, and the number of trunk pipes is 903. The probability of a randomly selected pipe being a trunk is:

P(trunk) = 903/8646 ≈ 0.104

c. The total number of main pipes is 5299, and the number of main pipes made of galvanized iron (GI) is 0 (according to the table). Therefore, the probability of a randomly selected main pipe being made of GI is:

P(GI|main) = 0/5299 = 0

Note that the vertical bar "|" means "given" or "conditioned on".

d. The total number of submain pipes is 2444, and the number of submain pipes made of asbestos cement (AC) is 411. Therefore, the probability of a randomly selected submain pipe being made of AC is:

P(AC|submain) = 411/2444 ≈ 0.168

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Evaluating the limit given by \({ lim_{(x- > 9)} } (7x-63)/(x^2-2x-63)\), we will obtain as a result \(7/16\)

To evaluate the limit, we need to simplify the expression first. We can do this by factoring the numerator and denominator of the fraction:

\(lim_{(x->9)} (7x-63)/(x^2-2x-63) = lim_{(x->9)} (7(x-9))/((x-9)(x+7))\)

Next, we can cancel out the \((x-9)\) terms in the numerator and denominator:

\(lim_{(x->9)} (7)/(x+7)\)

Now, we can plug in the value of x that the limit is approaching (9) into the expression:

\(lim_{(x->9)} (7)/(x+7) = (7)/(9+7) = (7)/(16)\)

Therefore, the limit of the expression as x approaches 9 is 7/16.

Answer: \({ lim_{(x->9)} } (7x-63)/(x^2-2x-63) = 7/16\)

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what values of a are the following expressions true?

|a-5| =5-a

Try putting values of ( a )

picking random number :-

Putting a = 6 :-

\( |a-5| =5-a \\ |6-5| =5-6 \\ | 1| = -1 \\ 1 \cancel = ( - 1) \)

so a is not equal to 6

Putting a = 8

\(|a-5| =5-a \\ |8 - 5| =5-8 \\ |3| = - 3 \\ 3 \cancel = - 3\)

a is also not equal to 8

so above values we can find a common result that a not equal to value bigger than 5

picking random number

Putting a equal to 1

\(|a-5| =5-a \\|1-5| =5-1 \\ | - 4| =4 \\ 4 = 4\)

a can be equal to 1

Putting a equal to -3

\(|a-5| =5-a \\| - 3-5| =5-( - 3) \\ | - 8| = 8\\ 8 = 8\)

a can be equal to -3

So we can have a common result that a can be equal to values less than 5

putting a equal to 5

\(|a-5| =5-a \\ |5 - 5| =5-5 \\ |0| =0 \\ 0 = 0\)

So we can say a can be equal to 5

Answer:

The population after x years will be P = 29000 + 700x

Let the population after the years be represented by P

Population of the town in 2003 = 29000

Annual increase in growth = 700

Then, the population after x years will be:

P = 29000 + 700(x)

P = 29000 + 700x

Therefore, the population will be P = 29000 + 700x.

(a) Create a vector A from 40 to 80 with step increase of 6.The linspace function of MATLAB can be used to create vectors that have the specified number of values between two endpoints. Here is how it can be used to create the vector A.  A = linspace(40,80,7)The above line will create a vector A starting from 40 and ending at 80, with 7 values in between. This will create a step increase of 6.

(b) Create a vector B containing 20 evenly spaced values from 20 to 40. linspace can also be used to create this vector. Here's the code to do it.  B = linspace(20,40,20)This will create a vector B starting from 20 and ending at 40 with 20 values evenly spaced between them.

MATLAB, linspace is used to create a vector of equally spaced values between two specified endpoints. linspace can also create vectors of a specific length with equally spaced values.To create a vector A from 40 to 80 with a step increase of 6, we can use linspace with the specified start and end points and the number of values in between. The vector A can be created as follows:A = linspace(40, 80, 7)The linspace function creates a vector with 7 equally spaced values between 40 and 80, resulting in a step increase of 6.

To create a vector B containing 20 evenly spaced values from 20 to 40, we use the linspace function again. The vector B can be created as follows:B = linspace(20, 40, 20)The linspace function creates a vector with 20 equally spaced values between 20 and 40, resulting in the required vector.

we have learned that the linspace function can be used in MATLAB to create vectors with equally spaced values between two specified endpoints or vectors of a specific length. We also used the linspace function to create vector A starting from 40 to 80 with a step increase of 6 and vector B containing 20 evenly spaced values from 20 to 40.

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Answer:

27 and 63 degrees

Step-by-step explanation:

Encino Ltd. received an invoice dated February 16 for $520.00 less 25%, 8.75%, terms 3/15 E.O.M. A cheque for $159.20 was mailed by Encino on March 15 as payment of the invoice. Encino still owes $302.49.

To calculate the amount Encino still owes, let's break down the given information step by step:

Invoice Amount: $520.00

The original invoice amount is $520.00.

Discount of 25% and 8.75%:

The invoice states a discount of 25% and an additional 8.75%. Let's calculate the total t:

Discount 1: 25% of $520.00

= 0.25 * $520.00

= $130.00

Discount 2: 8.75% of ($520.00 - $130.00)

                  = 0.0875 * $390.00

                  = $34.13

Total Discount: $130.00 + $34.13

                       = $164.13

After applying the discounts, the amount remaining to be paid is $520.00 - $164.13 = $355.87.

Terms 3/15 E.O.M.:

The terms "3/15 E.O.M." mean that if the payment is made within three days (by March 15 in this case), a discount of 15% can be applied.

Payment made on March 15: $159.20

Since Encino mailed a check for $159.20 on March 15, we can calculate the remaining balance after applying the discount:

Remaining balance after discount: $355.87 - (15% of $355.87)

= $355.87 - (0.15 * $355.87)

= $355.87 - $53.38

= $302.49

Therefore, Encino still owes $302.49.

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Complete Question:

Encino Ltd. received an invoice dated February 16 for $520.00 less 25%, 8.75%, terms 3/15 E.O.M. A cheque for $159.20 was mailed by Encino on March 15 as payment of the invoice. How much does Encino still owe?

Organizations that build strategic information systems create systems that are paramount to business success. The correct option is(D).

Strategic information systems are those that support the long-term goals and objectives of an organization, aligning the use of technology with the strategic direction of the business. These systems provide a competitive advantage by enabling the organization to achieve its strategic goals and objectives more efficiently and effectively.

They typically involve the integration of different types of information systems, such as transaction processing systems, decision support systems, and executive information systems, to support the decision-making process at all levels of the organization.

By building strategic information systems, organizations can improve their overall performance, enhance their operational efficiency, and gain a competitive advantage in the marketplace.

Such systems can help organizations to better understand their customers, identify new market opportunities, improve supply chain management, and optimize business processes.

In today's rapidly changing business environment, strategic information systems are essential for organizations to remain competitive and achieve long-term success.

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From the given information, the relative frequency of choosing a person who prefers a dog is 60%.

The relative frequency of choosing a person who prefers a dog is the number of people who prefer dogs divided by the total number of people in the sample:

Relative frequency of dog preference = Number of people who prefer dogs / Total number of people

Relative frequency of dog preference = 24 / (24 + 12 + 4)

Relative frequency of dog preference = 24 / 40

Relative frequency of dog preference = 0.6

To express this as a percent, we can multiply by 100:

Relative frequency of dog preference = 0.6 × 100

Relative frequency of dog preference = 60%

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The value of the test statistic used to test the claim is -2.00.

And, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

Now, If a two-sided test of hypothesis is conducted at a 0.05 level of significance and the test statistic resulting from the analysis was 1.23, the potential type of statistical error is Type II error.

A Type II error occurs when we fail to reject a false null hypothesis, meaning that we conclude there is no significant difference or effect when there actually is one.

To answer the second question, we can perform a one-sample t-test to test the claim that the mean GPA for Psychology students at a certain college is less than 3.2.

The hypotheses are:

H₀: μ = 3.2

Ha: μ < 3.2

where μ is the population mean GPA.

We can use the t-statistic formula to calculate the test statistic:

t = (x - μ) / (s / √n)

where, x is the sample mean GPA, s is the sample standard deviation, n is the sample size, and μ is the hypothesized population mean.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

Therefore, the value of the test statistic used to test the claim is -2.00.

Since this is a one-tailed test with a significance level of 0.05, we compare the t-statistic to the critical t-value from a t-table with 48 degrees of freedom.

At a significance level of 0.05 and 48 degrees of freedom, the critical t-value is -1.677.

Since the calculated t-statistic (-2.00) is less than the critical t-value (-1.677), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean GPA for Psychology students at the college is less than 3.2.

To calculate the p-value of the test, we can perform a one-sample t-test using the formula:

t = (x - μ) / (s / √n)

where x is the sample mean GPA, μ is the hypothesized population mean GPA, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

The degrees of freedom for this test is 49 - 1 = 48.

Using a t-distribution table or calculator, we can find the probability of getting a t-value as extreme as -2.00 or more extreme under the null hypothesis.

Since this is a two-sided test, we need to find the area in both tails beyond |t| = 2.00. The p-value is the sum of these two areas.

Looking up the t-distribution table with 48 degrees of freedom, we find that the area beyond -2.00 is 0.0257, and the area beyond 2.00 is also 0.0257. So the p-value is:

p-value = 0.0257 + 0.0257

p-value = 0.0514

Rounding to three decimal places, the p-value of the test is 0.051.

Therefore, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

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The possible values of x be  4.8, 5.6 and 6.4.

The statement of equality between two expressions consisting of variables and/or numbers.

Given:

5x -4y = 24

when y=0

5x = 24

x = 4.8

when y=1,

5x= 28

x= 5.6

when y=2,

5x= 32

x= 6.4

Hence, the possible values of x is 4.8, 5.6 and 6.4.

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Answer:

height = 25.12 cm

Step-by-step explanation:

SA = 2πr (r+h)

1243 = 2*3.14* 6.3 (6.3+h) = 39.56*(6.3+h) = 249.25 + 39.56h

39.56h = 1243 - 249.25 = 993.75

h = 25.12