Function g can be thought of as a translated (shifted)
version of f(x) = |x|.

Answer:

15.3 miles.

Step-by-step explanation:

Area of trapezoid is given by = 1/2*( sum of parallel side) height

Given area of trapezoid = 221.85 sq. miles

Length of parallel sides = 19 miles and 10 miles.

Sum of parallel sides = 19 miles + 10 miles = 29 miles.

Plugging the above values in formula for area of trapezoid we have

Area of trapezoid is given by = 1/2*( sum of parallel sides) height

221.85 = 1/2 (29) height

=> 221.85* 2 = 29* height

=> 443.7 = 29* height

=> 443.7/29 =  height

=> height = 15.3

Thus, height is 15.3 miles.

Using a chi-square distribution table with 3 degrees of freedom and a significance level of 0.05, the critical value is 7.815.

To test if the model the designer described is a good fit, we can use the chi-square goodness-of-fit test. We first state the null hypothesis as: The model is a good fit and the observed frequencies are close to the expected frequencies.

We then compute the expected frequencies for each category using the proportions given by the designer. The chi-square test statistic is then calculated using the formula: chi-square = ∑(observed frequency - expected frequency)²/expected frequency.

Using the given data, we obtain expected frequencies of 20, 100, 200, and 1680 for the grand prize, second prize, third prize, and no prize categories, respectively. We then calculate the chi-square test statistic to be 16.53.

Using a chi-square distribution table with 3 degrees of freedom and a significance level of 0.05, the critical value is 7.815. Since the calculated chi-square value is greater than the critical value,

we reject the null hypothesis and conclude that the model is not a good fit and the observed frequencies are significantly different from the expected frequencies.

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The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.

The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.

In this case, applying the EDD rule, the sequence of jobs would be as follows:

D (Due on Friday 10th June)

F (Due on Tuesday 14th June)

E (Due on Wednesday 15th June)

C (Due on Friday 17th June)

G (Due on Thursday 16th June)

H (Due on Saturday 18th June)

A (Due on Monday 13th June)

B (Due on Monday 20th June)

By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.

Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.

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Answer:

1, -3, 9, -27, (81),-243,729,-2187

Step-by-step explanation:

81 is the answer

Answer:

81, - 243, 729

Step-by-step explanation:

There is a common ratio between consecutive terms in the sequence, that is

r = - 3 ÷ 1 = 9 ÷ - 3 = - 27 ÷ 9 = - 3

Thus to obtain a term in the sequence multiply the previous term by - 3

- 27 × - 3 = 81

81 × - 3 = - 243

- 243 × - 3 = 729

Number of cards made from the sheet of paper is 243.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

On the entire sheet of paper, 243 cards were created.

The sheet is described as being 324 cm 144 cm in size.

Measures 324 centimeters in length.

The sheet has a 144-cm width.

We need to determine how many cards with a 16 cm by 12 cm size can be produced from a single sheet of paper.

The paper's size is 324 144.

46656 sq. cm is the size of the paper's surface.

Now, one card is equal to 16 divided by 12.

Currently, the area of a single card is 192 square centimetres.

Hence, Number of cards made from the sheet of paper is 243.

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Answer:

The y and m2 and the m (0, 2) when x=3

Step-by-step explanation:

Answer:

\(\frac{2x^3-13x^2+26x-24}{x-4}=2x^2-5x+6\)

Step-by-step explanation:

Use synthetic division:

4 | 2 -13   26 -24

  ___ 8  -20  24__

    2  -5     6 |  0

Use long division:

x-4 | 2x^3 - 13x^2 + 26x - 24

    -  2x^3 -  8x^2                   <-- 2x^2

                  -5x^2 + 26x - 24

               - -5x^2 - 20x          <-- -5x

                                 6x - 24

       ____________6x - 24  <--  6

                                           0 | 2x^2 - 5x + 6

Therefore, \(\frac{2x^3-13x^2+26x-24}{x-4}=2x^2-5x+6\)

Let the original price be p.

Then

p + (10% of p) = 548.90

1.1p = 548.90

p = 548.9 / 1.1 = $499.00

Hence the refrigerator was $499.00 originally

Answer:

8y+9

Step-by-step explanation:

Answer:

6y + 44

Step-by-step explanation:

y + 4 + 5(y + 8)

y + 4 + 5y + 40

6y + 44

Arithmetic overflow error converting numeric to data type numeric can be solved by increasing the precision and the scale, storing number in different data type or use user-defined datatype.

An "arithmetic overflow error converting numeric to data type numeric" error occurs when you try to store a number in a numeric column that is too large to be represented by the specified precision and scale. To resolve this error, you have a few options:

Increase the precision and scale of the numeric column, you can increase the precision and scale of the numeric column so that it can store larger numbers.

If you don't need the precision and scale of a numeric column, you can store the number in a different data type, such as float or big int.

 If the number is too large to be represented in the numeric column, you can round it to a smaller value before inserting it into the database.

 If the number is still too large to be represented in a numeric column or a different data type, you can create a custom data type in SQL Server to store the number.

It's important to choose the right solution based on your requirements and the specific use case. You may also need to consider the performance implications of each solution, especially if the data being stored is very large or complex.

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Answer: 7/25

Step-by-step explanation: you have 7 yellow marbles and then to get your denominator you have to add up all the marbles from container a and container b and you will get 25.

7= yellow marbles

25= all the marbles in container a and b

hope this helps.

Answer:

Container B has a greater probability of picking a yellow marble.

Step-by-step explanation:

You may think that the answer is container A, but it's not. Container A has 15 total marbles. Container B has 10 marbles, and 70% of those 10 marbles, are yellow.

The reasonable solutions for this situation is (1, 3.5) and (2, 2)

A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.

Audrey has x pounds of red grapes and y pounds of green grapes.

She has less than 5 pounds of grapes in all, hence:

x + y < 5

Also, x ≥ 0, y ≥ 0

a) The option (–1, 2) is wrong because x = -1 < 0

b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5

c) The option (2, 2) is correct because 2 + 2 = 4 < 5

d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.

e) The option (5, 0) is wrong because 5 + 0 is not less than 5

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Answer:

17.2ft

Step-by-step explanation:

just add

11.4+5.8=17.2

To find the area of triangle ABC, we need to first find the length of its sides. Since triangle ABC is an equilateral triangle, all sides are equal. Let's denote the length of one side as 's'.

The radius of the inscribed circle is the distance from the center of the circle (O) to any of the sides of the triangle. It is also equal to the height of the equilateral triangle. Let's denote this radius as 'r'. The area of the circle is given as 4π square cm. We know that the area of a circle with radius r is given by πr^2. Therefore, we have:

\(πr^2 = 4π\\r^2 = 4\\r = 2\)

Now, in an equilateral triangle, the height can be found using the formula:\(h = (s√3)/2.\) We know that the radius (r) is equal to the height (h). Therefore, we have:

\(2 = (s√3)/2\\4 = s√3\\s = 4/√3\)

To find the area of the triangle, we can use the formula: \(area = (s^2√3)/4.\)Plugging in the value of 's', we get:

\(area = ((4/√3)^2√3)/4\\area = (16/3)√3\)

So, the area of triangle ABC is \((16/3)√3\) square cm.

In conclusion, the area of triangle ABC is \((16/3)√3\) square cm. This answer is expressed in simplest radical form.

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Answer:

1 / 663

Step-by-step explanation:

First, let's find the total number of ways you can pick 2 cards from the deck. This is 52 * 51 = 2652 because there are 52 cards available for your first pick, and after you pick one, you'll have 51 left for your second pick.

There are 4 5's  (one for every suite) and only 1 Queen of Hearts in a deck of cards. Therefore, the total number of successful outcomes will be 4 * 1 = 4.

The probability of picking a 5 and then a Queen of Hearts is 4 / 2652 =

1 / 663. Hope this helps!

The area of the part of the sphere x² + y² + z² = a² that lies within the cylinder x² + y² = ax and above the xy-plane.

Step 1: Determine the intersection curve

To find the region on the sphere that lies within the cylinder, we need to determine the points where the sphere and the cylinder intersect. By substituting the equation of the cylinder into the equation of the sphere, we can find the points of intersection.

Substituting x² + y² = ax into x² + y² + z² = a², we have:

(ax) + z² = a²,

z² = a² - ax,

z = ±√(a² - ax).

Step 2: Set up the integral

To find the area of the surface, we'll use a double integral over the region of interest. Since we're dealing with surfaces, it's convenient to express the area element in terms of the cylindrical coordinates (r, θ, z).

The area element in cylindrical coordinates is given by dA = r dz dθ.

Step 3: Define the limits of integration

To set up the limits of integration, we need to consider the region of interest.

Therefore, the limits of integration are:

For θ: 0 ≤ θ ≤ 2π (since we want to integrate over the entire circle)

For r: 0 ≤ r ≤ a (to stay within the sphere)

For z: 0 ≤ z ≤ √(a² - ax) (to stay above the xy-plane and below the sphere)

Step 4: Evaluate the integral

Now, we can set up and evaluate the double integral using the defined limits of integration:

Area = ∫∫r dz dθ.

Integrating with respect to z:

Area = ∫[0 to 2π] ∫[0 to a] r √(a² - ax) dr dθ.

Evaluating this integral will give us the desired area.

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(A) A 95% confidence interval estimate for the percentage of all voters who believe competence is more important than character is (0.538, 0.602).

(B) This is due to the interval's lower bound's value of 0.538, which is higher than 0.5.

(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample

(A) Using the method below, we can calculate an estimate with a 95% confidence interval for the proportion of voters who think competence is more significant than character:

CI equals p z*(sqrt(p*(1-p)/n)/p)).

where: p = the percentage of voters who say character is more essential than competence = 0.57; n = the sample size; 1000; and z = the z-score for a 95% confidence level; 1.96.

By entering the numbers, we obtain:

CI = 0.57 1.96*(sqrt(0.57*(1-0.57)/1000)), which equals 0.57 0.032. (0.538, 0.602)

the 95% confidence interval estimate for the proportion of respondents overall who think competence is more significant than character is (0.538, 0.602).

(B) Based on the range discovered in part, it is reasonable to infer that the majority of voters value competence over character (a). This is due to the interval's lower bound's value of 0.538, which is higher than 0.5. Therefore, we can state with 95% certainty that the actual proportion of voters who think competence is more crucial than character is at least 53.8%, which is a majority.

(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample, then roughly 95% of those intervals would contain the actual proportion of voters who believe competence is more significant than character. That is to say, we have a 95% confidence interval (0.538, 0.602) that contains the actual proportion of voters who think competence is more significant than character.

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The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

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Answer:

\(\sqrt{x} +3 =13\)

Step-by-step explanation:

A radical equation is any equation in which a variable is under a root. This is the only equation in which x is under the square root, so this is the radical equation.

Step-by-step explanation:

so, we need to find the x values (A) that create the defined result values (f(x)) of B.

so, when taking the lower interval limit of B as the first f(x), we get

-1 = (x-2)/3

-3 = x - 2

-1 = x

so, the lower interval limit for A is also -1.

-1 as input value for the function delivers also -1 as functional result.

now for the upper limit :

2 = (x-2)/3

6 = x - 2

8 = x

so, the upper interval limit for A is 8.

and since the limit is excluded for B, it is also excluded for A.

so, C) is the correct answer.

Answer:

Step-by-step explanation:

a:b = 3:2    ⇒   a = 3x  and  b = 2x

a - b = 5

3x - 2x = 5

x = 5

a = 3•5 = 15

b = 2•5 = 10

K, x<18 is the inequality.

Step-by-step explanation:

Calculate the term

Answer:

x = 25

y = 6

Step-by-step explanation:

In a parallelogram, opposite angles are equal.

2x and 50 are opposite angles,

2x = 50

Divide 2 on both sides,

x = 50 / 2

x = 25

In a parallelogram opposite sides are equal.

y + 5 and 11 are opposite sides,

y + 5 = 11

y = 11 - 5

y = 6

Answer:

x=25

y=6

Step-by-step explanation:

from the diagram,

2x= 50(opposite angles of a parallelogram)

2x= 50

dividing bothsides by 2

2x/2=50/2

x= 25

then,

y+5=11(opposite sides of a parallelogram)

y= 11-5

y= 6

Answer:

(x,y) = (—2,—5)

Step-by-step explanation:

I attached a picture

Answer: The common ratio, r, is found by dividing any term after the first term by the term that directly precedes it. In the following examples, the common ratio is found by dividing the second term by the first term, a2 / a1 . When the common ratio of a geometric sequence is negative, the signs of the terms alternate.

Step-by-step explanation:

Answer:

\(r =0.8\)

Step-by-step explanation:

\(\text{By Comparing}~ 1.3(0.8)^{n-1}~ \text{with the nth term}~ ar^{n-1},\\\\\text{First term,}~a= 1.3\\\\\text{Common ratio,}~ r = 0.8\)

Answer:

D

Step-by-step explanation:

Because its not randomly selecting

Answer:

AC + CB < AB

Answer:

AC + CB < AB

Step-by-step explanation:

The amount remaining out the money earned is $37.5

Given the following parameters

Amount earned by kevin = $80

If he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi, the total money spent is given as;

Total money spent = 51/2 + 68/5 + 22/5

Total money spent = 51/2 + 90/5

Total money spent = 25.5 + 18

Total money spent = 43.5

Amount remaining = 80. - 43.5

Amount remaining = 37.5

Hence the amount remaining out the money earned is $37.5

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Answer:

The correct answer should be 4

The height and radius of the cup are 4.41 cm and 2.07 cm respectively

To minimize the amount of paper used, we need to minimize the surface area of the cup. Let h be the height and r be the radius of the cone. Then we have:
\(Volume of cone = \frac{1}{3}  πr^{2} h = 36 cm^{3}\)

Solving for h, we get:
\(h = \frac{108}{(πr^2)}\)

Now we can express the surface area of the cone as:
\(Surface area = πr^2+ πr\sqrt{r^{2}+h^{2}  }\)

Substituting the expression for h, we get:

\(Surface area = πr^2+πr \sqrt{(r^{2} +(\frac{108}{(πr^2)^{2}) } )}\)

To minimize this function, we take its derivative with respect to r and set it equal to zero:
\(\frac{d}{dx} (Surface area) =  \frac{2πr - 108r }{[(r^2+(\frac{108}{πr^2}))^{0.5}  }] - \frac{108π}{r^2 }  = 0\)

Simplifying, we get:
\(2r^3 - \frac{108^2}{π} = 0\)

Solving for r, we get:
\(r = (\frac{54}{π})^{\frac{1}{3} }\)

Substituting this value into the expression for h, we get:
\(h = \frac{108}{\frac{54}{π} ^{(\frac{2}{3}π )} }\)

Thus, the height and radius of the cup that will use the smallest amount of paper are:
height = 4.41 cm
radius = 2.07 cm (rounded to two decimal places)

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