If R = {(x, y) : x and y are integers and x^2 + y^2 = 64} is a relation, then find R.

Answer:

The smallest number is 40.

Step-by-step explanation:

Let the number be x. Then the next 4 number will be x+2, x+4, x+6, x+8

.°. x+x+2+x+4+x+6+x+8 = 220

5x + 20 = 220

5x = 200

x = 40

Therefore the smallest of the five consecutive numbers is 40

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Answer:

Step-by-step explanation:

Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.

The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:

P = 2(3x + 2x)

40 = 2(5x)

Now, let's solve for x:

40 = 10x

x = 40/10

x = 4

Now that we have the value of x, we can find the length of the rectangle:

Length = 3x = 3(4) = 12

Therefore, the length of the rectangle is 12.

The boundaries of the 99% confidence interval are

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

Selected, x = 28021

Sample, n = 38433

This means that the proportion, p is

p = 28021/38433

p = 0.729

The 99% confidence interval is then calculated as

CI = p ± z * √(p * (1 - p)/n)

Where

z = 2.576 i.e. the z-score at 99% confidence interval

So, we have

CI = 0.729 ± 2.576  * √(0.729 * (1 - 0.729)/38433)

Evaluate

CI = 0.729 ± 0.0058

Evaluate

CI = (0.7232, 0.7348)

Hence, the confidence interval is (0.7232, 0.7348)

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The area of the region bounded by the graphs of [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex] is 69 1/3 square units.

To find the area of the region bounded by the graphs of the functions [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex], we need to determine the points of intersection and evaluate the definite integral.

First, let's find the points of intersection by setting f(x) equal to g(x):

[tex]x^3 + x^2 - 6x = 2x - x^2[/tex]

Rearranging the equation, we get:

[tex]x^3 + 2x^2 - 8x = 0[/tex]

Factoring out an x, we have:

[tex]x(x^2 + 2x - 8) = 0[/tex]

Using the quadratic formula, we find the solutions for [tex]x^2 + 2x - 8 = 0[/tex] to be x = -4 and x = 2. Therefore, the points of intersection are (-4, -16) and (2, 4).

To calculate the area, we integrate the difference of the two functions within the bounds of -4 to 2:

Area = ∫[from -4 to 2] (f(x) - g(x)) dx

Evaluating the definite integral, we have:

Area = ∫[-4 to 2] [(x^3 + x^2 - 6x) - (2x - x^2)] dx

= ∫[-4 to 2] (x^3 + 2x^2 - 8x) dx

Integrating each term and evaluating the integral, we find:

Area = [1/4x^4 + 2/3x^3 - 4x^2] from -4 to 2

= [(1/4)(2)^4 + (2/3)(2)^3 - 4(2)^2] - [(1/4)(-4)^4 + (2/3)(-4)^3 - 4(-4)^2]

= [4/4 + 16/3 - 16] - [16/4 + (-128/3) - 64]

= 1/3 + 128/3 - 16 + 4 - 128/3 + 64

= 1/3 + 4 + 64

= 69 1/3

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Answer:424000

Step-by-step explanation:

First, you need to find out what is 8 percent of 200,000 which is 16000

So now we know that every year Tacoma's population grows by 16000

Now we calculate 16000 for 14 years which is 224000

Finally, we had the original population which was 200,000, and the people who moved to Tocoma in those 14 years which is 224000

Add it together and you get 424,000

The third option best describes a stratified sample of customers. The Option C.

To form a stratified sample, the analyst divides the customers into six groups based on their mortgage amounts. This ensures that customers from different mortgage amount ranges are represented in the sample.

Then, the analyst randomly selects 13 customers from each group. By stratifying the sample based on mortgage amounts and selecting customers at random within each group, the analyst ensures that the sample is representative of the overall population of mortgage customers.

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Answer:

$ 6.20 Cents

Step-by-step explanation:

17 - 5.50= 11.5

11.50 - 5.30= 6.2

Add A Zero at the end

You Get 6.20

Answer: 2 1/2 pounds of more clay

Step-by-step explanation:

To calculate how much more clay Ms. Garcia needs, we need to add up the clay requirements for each grade level and then subtract the amount she already has.

For the sixth graders:

Number of students: 25

Clay required per student: 3/4 pound

Total clay required for sixth graders: 25 * (3/4) = 75/4 = 18 3/4 pounds

For the seventh graders:

Clay required for sculptures: 20 pounds

Total clay required for both grade levels: 18 3/4 + 20 = 38 3/4 pounds

Clay leftover from last year: 5 2/5 pounds

To find out how much more clay Ms. Garcia needs, we subtract the clay she already has from the total required:

38 3/4 - 5 2/5 = 38 3/4 - 27/5 = 38 3/4 - 27/5 = (155 - 108 + 3)/20 = 50/20 = 5/2 = 2 1/2 pounds

Therefore, Ms. Garcia needs an additional 2 1/2 pounds of clay.

The difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.

To calculate the difference in size between two people, one measuring in inches and the other measuring in centimeters, we must first convert all measurements to a common unit.

Guy measures 3 inches + 1/4 inch. We can convert 1/4 inch to a decimal fraction by dividing 1 by 4, which gives us 0.25 inches. So your measurement in inches would be 3 + 0.25 = 3.25 inches.

The other guy measures 9.045 cm. To convert centimeters to inches, we use the following relationship: 1 cm = 0.3937 inches. Multiplying the measurement in centimeters by 0.3937, we get the measurement in inches: 9.045 cm * 0.3937 = 3.5608 inches (approximately).

Now we can calculate the size difference between them. We subtract the measurement of the second chavo (3.5608 inches) from the measurement of the first chavo (3.25 inches):

3.25 inches - 3.5608 inches = -0.3108 inches.

The resulting difference is -0.3108 inches. This means that the second chavo is smaller in size than the first. Since the difference is negative, it indicates that the first chavo is bigger than the second.

In summary, the difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.

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Answer:

12

Step-by-step explanation:

[tex]\frac{3}{4}[/tex](x - 3) - [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]

We are looking at the denominators of 4, 2 and 3.  We are looking for the least common multiple.  If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.

4,8,12

2,4,6,8,10,12

3,6,9,12

the lowest number that we see on all three lists is 12.

The difference table for the sequence (-1, 6, 24, 56, 105, 174, 266) reveals a cubic pattern, where the third differences are constant at 3. Based on this pattern, the next term in the sequence is predicted to be 289.

The difference table for the given sequence (-1, 6, 24, 56, 105, 174, 266):

Term     |   First Difference   |   Second Difference   |   Third Difference

----------------------------------------------------------------------------------------------------------

-1

6                         7

24                    18                                  11

56                   32                                 14                                   3

105                  49                                17                                   3

174                 69                                 20                                  3

266                92

To construct the difference table, we start by writing down the given sequence. Then, in the first column, we calculate the differences between consecutive terms. In the second column, we calculate the differences between the values in the first difference column. Similarly, in the third column, we calculate the differences between the values in the second difference column.

Analyzing the difference table, we observe that the third differences are constant at 3. This indicates a cubic pattern in the sequence, where the difference between consecutive terms is increasing by a constant amount each time.

To predict the next term, we take the last term of the sequence (266) and add the next difference (23) to it:

Next term = 266 + 23 = 289

Therefore, based on the pattern observed in the difference table, the next term in the sequence is predicted to be 289.

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The total volume of the dill spears is approximately 1013 cm³.

To find the total volume of the dill spears, we can use the formula for the volume of a cylinder, which is given by V = πr²h,

where V is the volume, r is the radius of the base, and h is the height of the cylinder.

First, let's find the radius of the base.

Since the area of the base is given as 45 cm², we can use the formula for the area of a circle,

A = πr², to solve for the radius.

Rearranging the formula, we have r = √(A/π).

Given that the area of the base is 45 cm², we can substitute this value into the formula to find the radius:

r = √(45/π) ≈ 3 cm (rounded to the nearest centimeter)

Now that we have the radius and the height of the jar, we can calculate the volume of the jar using the formula V = πr²h:

V = π(3²)(13) ≈ 1173 cm³ (rounded to the nearest cubic centimeter)

However, we need to subtract the volume of the pickle juice that was drained from the jar.

We are given that the amount of pickle juice is 160 cm³, so the total volume of the dill spears is:

Total volume = Volume of jar - Volume of pickle juice = 1173 cm³ - 160 cm³ = 1013 cm³

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Answer:

Hope this helps and have a nice day

Step-by-step explanation:

To find the probability that a student is accepted at FSU or accepted at UF, we can use the concept of conditional probability and the law of total probability.

Let's denote the events as follows:

A: Accepted at FSU

B: Accepted at UF

We need to find P(A or B), which can be calculated as the sum of the probabilities of each event minus the probability of their intersection:

P(A or B) = P(A) + P(B) - P(A and B)

Given the information provided, we can calculate the probabilities:

P(A) = 0.4 (40% chance of being accepted at FSU)

P(B|A) = 0.6 (60% chance of being accepted at UF if accepted at FSU)

P(B|A') = 0.9 (90% chance of non-acceptance at UF if not accepted at FSU)

P(A and B) = P(A) * P(B|A) = 0.4 * 0.6 = 0.24 (probability of being accepted at both FSU and UF)

Now we can substitute these values into the formula:

P(A or B) = P(A) + P(B) - P(A and B)

= 0.4 + (1 - 0.4) * P(B|A') - P(A and B)

= 0.4 + 0.6 * 0.9 - 0.24

= 0.4 + 0.54 - 0.24

= 0.7

Therefore, the probability that a student is accepted at FSU or accepted at UF is 0.7, or 70%.

Answer:

Step-by-step explanation:

To determine the percentage of adults who had 2 children, we need to first find the total number of adults questioned.

Looking at the bar graph, we can see that the bar representing 2 children has a height of 2.5. This means that 2.5 adults indicated having 2 children.

Let's assume the total number of adults questioned is "m". According to the bar graph, the sum of the heights of all the bars represents the total number of adults questioned.

From the bar graph, we can see the following:

The bar representing 4+ children has a height of 4.

The bar representing 3- children has a height of 3.5.

The bar representing 2- children has a height of 2.5.

The bar representing 1- children has a height of 1.5.

The bar representing 1 child has a height of 1.

The bar representing 0.5- children has a height of 0.5.

The bar representing 0 children has a height of 0.

To find the total number of adults questioned (m), we sum up the heights of all the bars:

m = 4 + 3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5 + 0

m = 18

Therefore, the total number of adults questioned is 18.

To find the percentage of adults who had 2 children, we divide the number of adults with 2 children (2.5) by the total number of adults questioned (18) and multiply by 100:

Percentage = (2.5 / 18) * 100

Percentage ≈ 13.9 (rounded to 1 decimal place)

Therefore, approximately 13.9% of the adults questioned had 2 children.

Answer:

Step-by-step explanation:

Let's calculate the expression step by step:

93 - (15 × 10) + (160 ÷ 16)

First, we perform the multiplication:

93 - 150 + (160 ÷ 16)

Next, we perform the division:

93 - 150 + 10

Finally, we perform the subtraction and addition:

-57 + 10

The result is:

-47

Therefore, 93 - (15 × 10) + (160 ÷ 16) equals -47.

The composite functions for this problem are given as follows:

a) (f ∘ g)(x) = 4x² + 24x + 32.

b) (g ∘ f)(x) = 2x² - 8x

The composite function of f(x) and g(x) is defined by the function presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the function for item a is given as follows:

(f ∘ g)(x) = f(2x + 8)

(f ∘ g)(x) = (2x + 8)² - 4(2x + 8)

(f ∘ g)(x) = 4x² + 32x + 64 - 8x - 32

(f ∘ g)(x) = 4x² + 24x + 32.

For item b, the function is given as follows:

(g ∘ f)(x) = g(x² - 4x)

(g ∘ f)(x) = 2(x² - 4x)

(g ∘ f)(x) = 2x² - 8x

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Answer:On a coordinate plane, a straight line with positive slope goes through points (3, 3) and (4, 4).

Step-by-step explanation:

a. The interval of time between eruptions if the previous eruption lasted 4 minutes is 86.51 minutes.

b. The residual for this cycle is 2.07 minutes.

c. The interval of time between eruptions lasted for 2.07 minutes than the regression line equation predicted.

d. The slope of the regression line means that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

e. No, the value of the y-intercept doesn't have meaning in the context of the problem.

Based on the information provided above, the relationship between the duration of the previous eruption (x in minutes) and the interval of time between eruptions (y in minutes) is modeled by this regression line equation:

ÿ = 33.35 + 13.29x

Part a.

When x = 4 minutes, the value of is given by:

ÿ = 33.35 + 13.29(4)

ÿ = 86.51 minutes.

Part b.

The residual for the given cycle can be calculated as follows;

Residual = y - ÿ

Residual = 62 - (33.35 + 13.29(2))

Residual = 62 - 59.93

Residual = 2.07 minutes.

Part c.

Based on the calculation above, we can logically deduce that the interval of time between eruptions lasted for 2.07 minutes than the equation of regression line predicted.

Part d.

The slope of the regression line is equal to 13.29 and it implies that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

Part e.

In the context of the problem, we can logically deduce that the value of the y-intercept doesn't have any meaning because the duration of the previous eruption cannot be equal to 0 minutes.

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Answer:

Step-by-step explanation:

To recover your investment in 5 years or less, you would need to earn enough to cover the cost of going to school ($30,000) as well as make up for the lost salary over the 2 years of schooling ($45,000/year * 2 years = $90,000).

Therefore, the minimum salary you would need to earn upon earning your degree is the sum of the cost of going to school and the lost salary:

Minimum salary = $30,000 + $90,000 = $120,000.

In order to recover your investment in 5 years or less, you would need to earn a minimum salary of $120,000 per year.

To recuperate the total cost of $120,000 ($30,000 tuition + $90,000 forgone salary) over 5 years, you would need to earn $24,000 more per year on top of your original $45,000 salary. This implies that the minimum salary you need to earn after graduating is $69,000 per annum.

To determine the minimum salary, we first need to calculate your total forfeiture over the 2 years of school, which equates to real costs and opportunity costs. Firstly, the real cost is the tuition of $30,000. Secondly, the opportunity costs are the 2 years of salary you're forgoing, best understood as the wages you would've made if you hadn't gone to school. Assuming the salary of $45,000 per year, the total opportunity cost for the 2 years would be $90,000.

Therefore, the total investment is calculated as the sum costs of tuition and forgone salary i.e. $30,000 (tuition) + $90,000 (forgone salary) = $120,000. So to recover this investment in 5 years, you would need to earn an addition of $120,000 above your original salary. Meaning, you will have to recover $120,000 / 5 years = $24,000 per year on top of your initial salary to recover your total costs in the stated timeframe.

Therefore, the minimum salary you need to earn after earning your degree is equal to your original salary plus recovered investment per year: $45,000 (original salary) + $24,000 (increase) = $69,000. Hence, upon completion of your degree, you will have to earn at least $69,000 per year to recover your total investment within 5 years.

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Answer:

Sure, here is the inequality that represents the number of gigabytes of data (G) you can use to stay under your budget of $130:

```

cost_per_gb * G <= budget

```

where:

* cost_per_gb is the cost of data per gigabyte, which is $10 in this case

* G is the number of gigabytes of data

* budget is your budget, which is $130 in this case

To solve this inequality, we can first subtract cost_per_gb from both sides of the inequality. This gives us:

```

G <= budget / cost_per_gb

```

We can then plug in the values for cost_per_gb and budget to get:

```

G <= 130 / 10

```

```

G <= 13

```

This means that you can use up to 13 gigabytes of data and still stay under your budget. If you use more than 13 gigabytes of data, you will exceed your budget.

Here is a table that shows the cost of data for different amounts of data:

```

| Amount of data (G) | Cost (\$) |

|---|---|

| 1 | 10 |

| 2 | 20 |

| 3 | 30 |

| ... | ... |

| 13 | 130 |

| 14 | 140 |

| ... | ... |

```

Step-by-step explanation:

Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]

Answer: 0.3464 (correct upto 4 decimal places )

Step-by-step explanation:

[tex]\sqrt{3/25}[/tex]= [tex]\sqrt{3} /\sqrt{25\\}[/tex]     (as the square root of 25 is 5)

=1.73205/5

=0.3464

The loan principal is $12,483.33, and the loan's maturity value is $15,479.33.

To calculate the loan principal, we can use the formula for simple interest:

Interest = Principal x Rate x Time

Given that Rebecca earned $2,996 as interest, the rate is 2.00% per month (or 0.02), and the time is 12 months, we can plug in these values into the formula and solve for the principal:

$2,996 = Principal x 0.02 x 12

$2,996 = Principal x 0.24

Dividing both sides of the equation by 0.24, we get:

Principal = $2,996 / 0.24

Principal = $12,483.33

So, the loan principal is $12,483.33.

To calculate the loan's maturity value, we need to add the principal and the interest earned. Since the interest earned is $2,996 and the principal is $12,483.33, the maturity value can be calculated as:

Maturity Value = Principal + Interest

Maturity Value = $12,483.33 + $2,996

Maturity Value = $15,479.33

Therefore, the loan's maturity value is $15,479.33.

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First, we need to convert the length of the ribbon to centimeters to match the length of the ribbon pieces we plan to cut:

4m 20cm = (4 x 100)cm + 20cm = 420cm

Next, we can divide the total length of the ribbon by the length of each piece to find how many pieces we can cut:

420cm ÷ 70cm = 6

Therefore, we can cut 6 smaller ribbons, each 70cm long, from the 4m 20cm length of ribbon we have.

The man is in the south direction from the starting point.

Let's visualize the movements of the man step by step:

The man starts by going 10 meters north.

He then turns left (which means he is now facing west) and covers 6 meters in that direction.

Next, he turns left again (which means he is now facing south) and walks 5 meters.

To determine the final direction of the man from the starting point, we can consider the net effect of his movements.

Starting from the north, he moved 10 meters in that direction. Then, he turned left twice, which corresponds to a 180-degree turn, effectively changing his direction by 180 degrees.

Since he initially faced north and then made a 180-degree turn, he is now facing south. Therefore, the direction he is in from the starting point is "south."

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