quadratic equation y=(x+4)²+3

the equation of the circle with center (0,-3) containing the point (√32,-2) is x² + (y + 3)² = 33.

How to solve an equation?

To determine the equation of a circle, we need to know the coordinates of its center and the radius. The formula for the equation of a circle is (x - a)² + (y - b)² = r², where (a, b) represents the center of the circle and r represents its radius.

In this case, the center of the circle is given as (0,-3), so we can substitute these values into the formula: (x - 0)² + (y - (-3))² = r²

To find the value of r, we need to use the fact that the circle contains the point (√32,-2). We know that any point on the circle will be a distance r away from the center, so we can use the distance formula to find r.

The distance between the center (0,-3) and the point (√32,-2) is:

sqrt[(√32 - 0)² + (-2 - (-3))²] = sqrt[32 + 1] = sqrt(33)

Therefore, the radius r is sqrt(33).

Substituting this value into the equation of the circle, we get:

(x - 0)² + (y - (-3))² = (sqrt(33))²

Simplifying this equation, we get:

x² + (y + 3)² = 33

So the equation of the circle with center (0,-3) containing the point (√32,-2) is x² + (y + 3)² = 33.

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Using the recursive rule we know that the explicit formula for f(11) would be a₁₁ = a₁₀ + 11.

A formula that explains how to move from one word in a sequence to the next is known as a recursive rule for a sequence.

The variable is typically used to represent the term "number." In other words, takes on the values 1, 2, 3, etc.

For the first, second, third, etc. terms.

So, the recursive rule formula is:

aₙ = aₙ₋₁ + d

d = 72 - 61 = 11

Then, insert values and calculate as follows:

aₙ = aₙ₋₁ + d

a₁₁ = a₁₁₋₁ + d

a₁₁ = a₁₀ + d

a₁₁ = a₁₀ + 11

Therefore, using the recursive rule we know that the explicit formula for f(11) would be a₁₁ = a₁₀ + 11.

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The length of the altitude is

The similarity statement about the triangles is

The value of x in the pentagon is 21

The value of x is solved by applying the the proportions of the pentagon

20 / 15 = 18 / 13.5 = 4/3

therefore, 12 * 4/3 = x - 5

16 = x - 5

16 + 5 = x

x = 21

The altitude of the right triangle

h / 14 = 4 / h

h^2 = 14 * 4

h^2 = 56

h = sqrt (56)

h = 7.5

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Answer:

Asymptotes can be defined as lines that the curve approaches but never touches or crosses.

The probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board is 0.031.

Mean = 196 × 43

Mean = 8428

Std. Dev. = 63 × √(43)

Std. Dev. = 63 × 6.56

Std. Dev. = 413.28

Here, μ = 8428, σ = 413.1186 and x = 9200. We must calculate P(X ≥ 9200).

he central limit theorem states that, for a sufficiently large sample size, the sample mean of all observations will be approximately normally distributed, regardless of the distribution of the population from which it was sampled.

The Central Limit Theorem is used to get the associated z-value.

z = (x - μ)/σ

z = (9200 - 8428)/413.28

z = 772/413.28

z = 1.87

Therefore,

P(X ≥ 9200) = P(z ≤ (9200 - 8428)/413.1186)

P(X ≥ 9200) = P(z ≤ 772/413.1186)

P(X ≥ 9200) = P(z ≥ 1.87)

P(X ≥ 9200) = 1 - 0.9693

P(X ≥ 9200) = 0.031

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The complete question is:

A small jet can carry up to 40 passengers and 3 crew members. There is a weight restriction of 9200 pounds on board. The combined weight of each passenger (or crew member) and his luggage has a mean of 196 pounds, with a standard deviation of 63 pounds. What is the probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

The sum οf the angle measures οf 7 οf the sectiοns is 315 degrees.

An angle is a geοmetric figure fοrmed by twο rays that share a cοmmοn endpοint, called the vertex. It is usually measured in degrees οr radians and describes the amοunt οf rοtatiοn between the twο rays.

If we arrange eight chairs arοund a circle that has eight sectiοns, each sectiοn will have a central angle οf 360 degrees / 8 = 45 degrees.

Tο find the sum οf the angle measures οf 7 οf the sectiοns, we can add the central angles οf thοse 7 sectiοns:

7 x 45 degrees = 315 degrees.

Therefοre, the sum οf the angle measures οf 7 οf the sectiοns is 315 degrees.

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[tex] \bf Question[/tex]

Write 8,360,000 in scientific notation

8,360,000

After one digit you should mark decimal then count after decimal how many digits are remaining after you get Ans then put your Ans always on 10.

Like this,

8.36× 100,000 = as 8.36 × 10⁶

Am mark decimal after one digit and count how many digits are remaining then am put my ans on 10

So, 8,360,000 written as 8.36 × 10⁶ in scientific notation

See this, there are two pairs one is 8.36 and one is 100,000 in first one we can't write zeros. We write numbers like 1,2,3,4,5,6,7,8,9 but not 0. Like this question is 8,360,000 , our first work is to mark decimal after one digit 8. then we have to notice that after decimal how many number are remaining like 360,000 As, we know we can't write zeros in first pair so we can write only 8.36× now our first pair is done , Second pair is so easy only you have to count digits after decimal 8360,000 So digits are 6 so our final answer is 8.36×10⁶

Always remember in second pair we write remaining no. of digits only on 10 like this 10⁶

8.36 × 10⁶

The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

Now, can you express 40,000,000,000 in the similar way ?

Count the number of zeros in it. It is 10.

So, 40,000,000,000 = 4.0×10¹⁰

Do you agree with the fact, that the number when written in scientific notation is much easier to read and understand.

The scientific notation of the given number is 8.36×10⁶.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

The given number is 8,360,000.

In scientific notation

8,360,000 = 8.36×10⁶

Therefore, the scientific notation of the given number is 8.36×10⁶.

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Answer:

one solution, x = - [tex]\frac{24}{7}[/tex]

Step-by-step explanation:

- 5x + 12 = - 12x - 12 ( add 12x to both sides )

7x + 12 = - 12 ( subtract 12 from both sides )

7x = - 24 ( divide both sides by 7 )

x = - [tex]\frac{24}{7}[/tex]

Answer:

Step-by-step explanation:

200 Items were sold

For A total of $130

The Items sold were 0.50

and 0.75.

130 Cans of soda were sold

86 Bags Of popcorn were sold.

Answer:

A) $85.00

Step-by-step explanation:

To find Jerome's monthly premium, we need to divide his six-month premium by 6:

P = DB/6

P = (1.02)(500)/6

P = 85

Therefore, Jerome's monthly premium will be $85. Answer choice A is correct.

Alice receives 2 more paychecks in a year compared to Ralph.

Since Ralph is paid semimonthly, he receives 24 paychecks in a year (twice a month). Alice, on the other hand, is paid biweekly, which means she receives 26 paychecks in a year (once every two weeks).

To calculate the difference in the number of paychecks, we can subtract the number of paychecks Ralph receives from the number Alice receives:

Number of paychecks for Alice - Number of paychecks for Ralph = 26 - 24 = 2

Therefore, Alice receives 2 more paychecks in a year compared to Ralph.

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False. If one assumes two or more groups are from separate populations, the different groups are considered unrelated or independent samples for conducting statistical tests.

In statistical analysis, there are two types of samples: related (also known as dependent or paired) and unrelated (also known as independent or unpaired). Related samples are taken from the same population, often involving before-and-after measurements, repeated measures, or matched pairs.

Unrelated samples are taken from separate populations, with no inherent connection between the samples.
When you want to compare two or more groups, the choice of related or unrelated samples will determine the type of statistical test you should use.

For related samples, you can use tests like the paired t-test, Wilcoxon signed-rank test, or repeated measures ANOVA. For unrelated samples, you can use tests like the independent t-test, Mann-Whitney U test, or one-way ANOVA.
In summary, assuming that two or more groups are from separate populations means they are considered unrelated or independent samples, not related samples, for conducting statistical tests.

The choice of related or unrelated samples will guide you in selecting the appropriate statistical test for your analysis.

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The required confidence interval for the given sample size and sample mean is,

95% confident interval which is true average porosity of the seam lies between 4.49 and 5.20 percent.

98% confident interval which is true average porosity of the other seam lies between 4.10 and 5.02 percent.

Sample size with 95% confidence interval with a width of 0.37 is 16 .

Sample size with 99% confidence interval with a width of 0.21 is 11 .

Sample size 'n' = 19

Confidence interval = 95%

Sample mean = 4.85

True average porosity of a certain seam is , we use the formula,

CI = sample mean ± t(α/2, n-1) ×(standard deviation / √(n))

where t(α/2, n-1) is the critical t-value.

α level (0.05 for a 95% confidence interval)

Degrees of freedom (n-1 = 18).

Plugging in the values, we get,

CI

= 4.85 ± t(0.025, 18) × (0.74 / √(19))

Using a t-table ,

t(0.025, 18) = 2.101.

So the confidence interval is,

CI

= 4.85 ± 2.101 × (0.74 / √(19))

= (4.49, 5.20)

95% confident that the true average porosity of the seam lies between 4.49 and 5.20 percent.

Compute a 98% confidence interval for the true average porosity of another seam .

Sample size = 18

Sample mean = 4.56,

Use the same formula as above but with a different t-value,

CI = 4.56 ± t(0.01, 17) ×(0.74 / √(18))

Using a t-table

t(0.01, 17) = 2.898.

So the confidence interval is,

CI

= 4.56 ± 2.898 × (0.74 / sqrt(18))

= (4.10, 5.02)

98% confident that the true average porosity of the other seam lies between 4.10 and 5.02 percent.

Sample size to obtain a 95% confidence interval with a width of 0.37,

Use the formula,

n = (t(α/2, n-1) × standard deviation / (width / 2))^2

Solving for n, we get,

n = [(t(α/2, n-1) × standard deviation) / (width / 2)]^2

Substituting the given values, we get,

n = [(t(0.025, n-1) × 0.74) / 0.37]^2

Using trial and error or a t-table,

t(0.025, n-1) is approximately 2 for large sample sizes.

So we have,

n = [(2 × 0.74) / 0.37]^2

  = 16

A sample size of at least 16 specimens is necessary to obtain a 95% confidence interval with a width of 0.37.

Sample size to estimate the true average porosity to within 0.21 with 99% confidence,

Use the same formula as above but solve for n with the given width and confidence level,

n = [(t(α/2, n-1) ×standard deviation) / (width / 2)]^2

Substituting the given values, we get,

n = [(t(0.005, n-1) × 0.74) / 0.21]^2

Using trial and error or a t-table,

t(0.005, n-1) is approximately 3 for large sample sizes.

So we have

n = [3 × 0.74) / 0.21]^2

  = 11.17

  ≈ 11

Sample size to estimate the true average porosity to within 0.21 with 99% confidence is 11.

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The price of Groupon for revenue of $300 is $4 if the expected revenue is at least $390 per day.

Probability is assigned as

x =30, 60, 120, 180

P(x) = 0.10,0.40, 0.40, 0.10

Expected sales volume:

Number of tubes x =30, 60, 120, 180

Probability P(x)= 0.10,0.40, 0.40, 0.10

Expected values are 3, 24,48,18

Total = 93 tubes

Groupon price = $390/$93 = $4.19

Jane's price for each Groupon is the daily rental income divided by the expected number of tubes rented per day. The expected number of tubes is derived by multiplying the expected number of each tube by its probability and then summing the results. 

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Exponential growth function that relates the number n of plants found to the number x of volunteers Seth has,  

[tex]n = p\left(1+\frac{r}{100}\right)^x[/tex]

How to find an exponential function?

Exponential function is the function of growth or decay with the power of the independent variable.

As, n is the number of plants increased.

r is the percent increase

p is the initial plants

and x is the volunteers

Compound Interest/ Exponential equation is,

[tex]n = p\left(1+\frac{r}{100}\right)^x[/tex]

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The exponential growth function  [tex]n = p(1 + r)^X[/tex]

The exponential growth function that relates the number n of plants found to the number X of volunteers Seth has can be expressed as:

[tex]n = p(1 + r)^X[/tex]

where:

n is the number of plants found

p is the initial number of plants found before adding any volunteers

X is the number of volunteers added to the search

r is the percentage increase in the number of plants found per volunteer

he growth factor is represented by the term (1 + r), which is multiplied by the initial number of plants discovered to determine the new number of plants discovered when each volunteer is added. The value of (1 + r)X increases exponentially as X increases, resulting in an exponential increase in the number of plants found.

It is essential to keep in mind that the growth rate r in the formula must be expressed as a decimal rather than a percentage. For instance, r = 0.05 if the number of plants discovered increases by 5% for each volunteer added.

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The conclusion that can be drawn from the excerpt is: "If they are well planned, they can protect the shore from erosion while minimizing damage to important habitats for plants and animals." Therefore, the option "If they are well planned, they can replace sand that has been washed away" is not accurate, and the options "If they are well planned, they will most likely be too expensive," and "If they are not well planned, they can damage other structures" are not supported by the information provided in the excerpt. The correct answer is: "If they are not well planned, they can damage places with sea life."

The data support the researcher's claim that the current ozone level is not at a normal level, at the 0.05 level of significance, concluded with the help of a one-sample t-test.

To test whether the current ozone level is significantly different from the normal level of 5.5 ppm, we can use a one-sample t-test.

The null hypothesis is that the mean ozone level is equal to 5.5 ppm:

H0: mu = 5.5

The alternative theory is that the average ozone level exceeds 5.5 ppm:

Ha: mu > 5.5

The significance threshold will be set at 0.05.

t = (x - mu) / (s / sqrt(n)) is the test statistic for a one-sample t-test.

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

When we substitute the provided values, we get:

t = (6.0 - 5.5) / (0.9 / sqrt(13)) = 1.936

Using a t-table with 12 degrees of freedom (n-1=13-1=12) and a significance level of 0.05, the critical value is 1.782. Since our calculated t-value (1.936) is greater than the critical value (1.782), we reject the null hypothesis.

Therefore, we can conclude that the data support the researcher's claim that the current ozone level is not at a normal level, at the 0.05 level of significance.

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The measures of the angles x and y are:

m∠y =  = 148°

m∠x  = 153°

Remember that:

The sum of two adjacent angles is always 180°

The sym of the interior angles of a triangle is always 180°

With the first rule, we know that:

m∠a + m∠y = 180°

And we know that m∠a = 32°, then:

32° +  m∠y = 180°

m∠y = 180° - 32° = 148°

Now, the angle at b is 59°, then the top angle of the triangle is:

180° - 59° = 121°

And the left angle in the triangle is A, such that:

A + 121° + 32° = 180°

A = 180° - 32° - 121° = 27°

And that angle plus the measure of x must be 180°, then:

m∠x + 27° = 180°

m∠x = 180° - 27° = 153°

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Answer:

7/10 because 3/5 is equal to 6/10.

The median between 6/10 and 8/10 is 7/10

Therefore that is the answer.

"The beautiful thing about learning is that no one can take it away from you." :)

The relation between the area (a) and the side length (s) in the table is:

A. a = s²

What is an area?

To see this relationship, we can observe that the areas of the poster boards are the square of their respective side lengths. For example, when the side length is 2 feet, the area is 4 square feet (2²).

Similarly, when the side length is 4 feet, the area is 16 square feet (4²). This pattern holds true for all the side lengths listed in the table. Therefore, we can conclude that the area of each poster board is equal to the square of its side length.

Calculation:

Side Length (s)    |       Area (a)

  1                         |        1

  2                        |        4

  3                        |        9

  4                        |        16

As we can see, the area of each poster board is equal to the square of its side length. Thus, the relation between the area (a) and the side length (s) in the table is a = s².

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Answer:

A

Step-by-step explanation:

[tex]a = s {}^{2} \\ 1. \: + - \sqrt{a = s} \\ 2. \: s = + - \sqrt{a} [/tex]

A state with a sales tax is a better option for both individuals and state governments.

WHAT IS SLES TAX?

A state without a sales tax may seem preferable since they do not have to pay additional taxes on purchases. However, in such states, the government often imposes higher income taxes or property taxes to compensate for the lack of sales tax revenue. Therefore, it ultimately depends on the individual's financial situation and spending habits.

From the state government's perspective, having a sales tax is generally more beneficial as it provides a consistent and reliable revenue stream. Sales tax revenue is collected on a regular basis and is not subject to fluctuations in the economy or changes in demographics. Additionally, sales tax revenue is not as heavily reliant on the state's residents and can be partially collected from tourists and visitors who make purchases within the state.

In my opinion, a state with a sales tax is a better option for both individuals and state governments. While paying additional taxes may not seem appealing, it allows the state to fund essential services such as education, healthcare, and infrastructure. Additionally, sales tax revenue is spread across a wider population, making it more equitable and less burdensome on individual taxpayers. Overall, having a sales tax system in place helps to ensure that the state government can continue to provide essential services and maintain a stable economy.

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Answer:A

Step-by-step explanation:

To simplify the rational expression (x²+6x)/(x+5) + (4x+15)/(x+5), we first factor the numerator of the first fraction as x(x+6). Then, we factor the numerator of the second fraction as 4(x+3). Now, we can combine the fractions by finding a common denominator of (x+5) and adding the numerators:

(x²+6x)/(x+5) + (4x+15)/(x+5) = (x(x+6) + 4(x+3))/(x+5)

Simplifying the numerator further, we get:

(x²+6x + 4x + 12)/(x+5) = (x²+10x+12)/(x+5)

Now we can factor the numerator by finding two numbers that multiply to 12 and add to 10. Those numbers are 2 and 6. So we can write:

(x²+10x+12)/(x+5) = (x+2)(x+6)/(x+5)

Therefore, the completely factored and simplified form of the given rational expression is (x+2)(x+6)/(x+5). So the answer is A.

The probability that the student will get exactly four correct answers is approximately 0.1706

To solve this problem, we can use the binomial distribution, which gives the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, each question has three possible answers, only one of which is correct. So the probability of getting a correct answer by guessing is 1/3.

Let X be the number of correct answers out of 8. Then X follows a binomial distribution with n=8 and p=1/3.

To get exactly four correct answers, we need to get four successes and four failures in any order. The number of ways to choose four questions to answer correctly is 8 choose 4 (written as 8C4), which is equal to 70. The probability of getting four successes and four failures is therefore

P(X=4) = (8C4) × (1/3)^4 × (2/3)^4

= 70 × 1/81 × 16/81

= 1120/6561

≈ 0.1706

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Answer:

let the height of second container be x

Then volume=6912

we know that volume of cuboid= lbh

so ，

24.x.16=6912

384.x=6912

x =6912divide 384

therefore x =18 that is the height of the container

The values of a, b, c ,d are 54,31,28,67 respectively

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

There are different theorems that can be used to determine various missing angles In a circle.

angle c = 28°( angle in the same segment are equal)

angle b = 31( angle in the same segment)

angle d = 180-( 82+31) ( sum of angle in a triangle)

d = 180 - 113

d = 67°

angle a = 180-( 98+28) ( sum of angle Ina triangle)

a = 180- 126

a = 54°

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Kayden has 5 dimes and 15 quarters because he has three times as many quarters as dimes, and their total value of coins is 425 cents.

Let's use algebra to solve the problem.

Let x be the number of dimes that Kayden has.

Then the number of quarters he has is 3x (since he has 3 times as many quarters as dimes).

The value of x dimes is 10x cents, and the value of 3x quarters is 75x cents (since a quarter is worth 25 cents).

According to the problem, the total value of the coins is 425 cents. So we can write the equation:

10x + 75x = 425

Simplifying and solving for x, we get:

85x = 425

x = 5

Therefore, Kayden has 5 dimes and 3x = 15 quarters.

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The length of the side is 67.8 which gives us the perimeter as 67.8 x 10 = 678units

We are given a decagon, which is a 10-sided polygon with center O, and a radius of 11 units.

We are required to find the perimeter of the decagon and round the answer to the nearest tenth.

We begin by calculating the interior angle of e decagon.

We use the formula;

S = (n-2) 180, where,

S = sum of interior angles,

n = number of sides

therefore, S = (10 - 2) 180

S = 8 x 180

S = 1440

For a 10-sided polygon, each interior angle will now measure;

Interior angle = 1440/10 = 144

take note that the radius of the polygon divides the angle at the vertex (that is, the interior angle) into two equal halves.

With that in mind we can now construct the following triangle:

Take note that the line from the center to the side is the apothem, while the side labeled 11 is the radius (which was given). We can now extract one of the right angled triangles and use that calculate the apothem as follows:

The side labeled a; the apothem can be calculated using the angle 72 degrees as the reference angle:

reference angle = 72

opposite = a

hypotenuse = 11

therefore when we use the formula of sin, we get a = 10.46

Also, for the side labeled s (half the length of one side of the decagon); s = 3.39

For the length of one side of the decagon, we have the side s times 2. Hence, the length of the side is 67.8

67.8 x 10 = 678units

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Answer:

Ok

Step-by-step explanation:

Y = mx + c

Slope is for the gradient =m therefore we have +3 as our gradient

Now we are going to substitute pont - 8mac- 8 on the above equation

Y = mx +c

-8=3(-8) +c

-8=-24 +c

-8+24 =c

16=c

This means that the y intecept of this straight line is 0 mac 16

Meaning that when the line touches the y axis at 16 x will be equal to zero

Therefore our equation is

Y =3x +16